Finite Group Databasebeta

← #33253753

Subgroups — #33253753

Order 18688.

3014 conjugacy classes of subgroups.

The subgroup lattice has 1724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989117C211yesmaximal, characteristic, complemented
2#22614186C211yesmaximal, characteristic, complemented
3#22614171C211yesmaximal, characteristic, complemented
4#22614066C211yesmaximal, characteristic, complemented
5#22614051C211yesmaximal, characteristic, complemented
6#22613976C211yesmaximal, characteristic, complemented
7#22613961C211yesmaximal, characteristic, complemented
8#22613877C211yesmaximal, characteristic, complemented
9#22613862C211yesmaximal, characteristic, complemented
10#22613749C211yesmaximal, characteristic, complemented
11#22613675C211yesmaximal, characteristic, complemented
12#22613592C211yesmaximal, characteristic, complemented
13#22613476C211yesmaximal, characteristic, complemented
14#22613402C211yesmaximal, characteristic, complemented
15#22613321C211yesmaximal, characteristic, complemented
16#22613305C211yesmaximal, characteristic
17#22613254C211yesmaximal, characteristic, complemented
18#22613215C211yesmaximal, characteristic, complemented
19#22613190C211yesmaximal, characteristic, complemented
20#22613173C211yesmaximal, characteristic, complemented
21#22613169C211yesmaximal, characteristic, complemented
22C4×#14556570C211yesmaximal, characteristic, complemented
23C4×#14556572C211yesmaximal, characteristic, complemented
24C4×#14556563C211yesmaximal, characteristic, complemented
25C4×#14556560C211yesmaximal, characteristic, complemented
26C4×#14556560C211yesmaximal, characteristic, complemented
27#22612376C211yesmaximal, characteristic, complemented
28#22612374C211yesmaximal, characteristic, complemented
29#22612314C211yesmaximal, characteristic, complemented
30C2×C4×C22⋊Dic73C211yesmaximal, characteristic, complemented
31C22×C4×D4×C73C211yesmaximal, characteristic, complemented
32#17989117—28no—
33C2×#14556586C2211yescharacteristic, complemented
34C2×#14556584C2211yescharacteristic, complemented
35C2×#14556581C2211yescharacteristic, complemented
36C2×#14556577C2211yescharacteristic, complemented
37C2×#14556575C2211yescharacteristic, complemented
38C2×#14556572C2211yescharacteristic
39C2×#14556572C2211yescharacteristic
40C2×#14556570C2211yescharacteristic
41C2×#14556568C2211yescharacteristic, complemented
42C2×#14556563C2211yescharacteristic
43C2×#14556563C2211yescharacteristic
44C2×#14556560C2211yescharacteristic
45C2×#14556560C2211yescharacteristic
46C2×C4×Dic146C2211yescharacteristic, complemented
47C2×C4×C22⋊D73C2211yescharacteristic
48C2×C4×C22⋊D73C2211yescharacteristic, complemented
49C2×C4×C22⋊D73C2211yescharacteristic, complemented
50C2×C4×C22⋊D73C2211yescharacteristic, complemented
51C2×C4×C22⋊D73C2211yescharacteristic, complemented
52C2×#14556550C2211yescharacteristic, complemented
53C2×#14556550C2211yescharacteristic, complemented
54C2×#14556548C2211yescharacteristic, complemented
55C22×C22⋊Dic73C2211yescharacteristic
56C22×C22⋊Dic73C2211yescharacteristic
57C22×C4×Dic73C2211yescharacteristic, complemented
58C22×C4×Dic73C2211yescharacteristic, complemented
59#17988526C2211yescharacteristic, complemented
60#17988525C2211yescharacteristic, complemented
61#17988525C2211yescharacteristic, complemented
62#17988523C2211yescharacteristic, complemented
63#17988520C2211yescharacteristic, complemented
64#17988518C2211yescharacteristic, complemented
65#17988517C2211yescharacteristic, complemented
66#17988515C2211yescharacteristic, complemented
67#17988515C2211yescharacteristic, complemented
68#17988515C2211yescharacteristic, complemented
69#17988513C2211yescharacteristic, complemented
70#17988512C2211yescharacteristic, complemented
71#17988512C2211yescharacteristic, complemented
72#17988512C2211yescharacteristic, complemented
73#17988510C2211yescharacteristic, complemented
74#17988510C2211yescharacteristic, complemented
75#17988510C2211yescharacteristic, complemented
76#17988509C2211yescharacteristic, complemented
77#17988503C2211yescharacteristic, complemented
78#17988503C2211yescharacteristic, complemented
79#17988503C2211yescharacteristic, complemented
80#17988502C2211yescharacteristic, complemented
81#17988501C2211yescharacteristic
82#17988501C2211yescharacteristic
83#17988501C2211yescharacteristic
84#17988501C2211yescharacteristic
85#17988501C2211yescharacteristic
86#17988501C2211yescharacteristic
87#17988499C2211yescharacteristic, complemented
88#17988499C2211yescharacteristic, complemented
89#17988495C2211yescharacteristic
90#17988495C2211yescharacteristic
91#17988493C2211yescharacteristic, complemented
92#17988487C2211yescharacteristic, complemented
93#17988485C2211yescharacteristic, complemented
94#17988482C2211yescharacteristic, complemented
95#17988481C2211yescharacteristic, complemented
96#17988480C2211yescharacteristic, complemented
97#17988480C2211yescharacteristic, complemented
98#17988478C2211yescharacteristic, complemented
99#17988478C2211yescharacteristic, complemented
100#17988477C2211yescharacteristic, complemented
101#17988475C2211yescharacteristic, complemented
102#17988475C2211yescharacteristic, complemented
103#17988473C2211yescharacteristic, complemented
104#17988473C2211yescharacteristic, complemented
105#17988471C2211yescharacteristic, complemented
106#17988471C2211yescharacteristic, complemented
107#17988471C2211yescharacteristic, complemented
108#17988471C2211yescharacteristic, complemented
109#17988468C2211yescharacteristic, complemented
110#17988468C2211yescharacteristic, complemented
111#17988467C2211yescharacteristic
112#17988467C2211yescharacteristic
113#17988467C2211yescharacteristic
114#17988467C2211yescharacteristic
115#17988466C2211yescharacteristic
116#17988466C2211yescharacteristic
117#17988466C2211yescharacteristic
118#17988466C2211yescharacteristic
119#17988466C2211yescharacteristic, complemented
120#17988466C2211yescharacteristic, complemented
121#17988466C2211yescharacteristic, complemented
122#17988466C2211yescharacteristic, complemented
123#17988464C2211yescharacteristic, complemented
124#17988462C2211yescharacteristic, complemented
125#17988462C2211yescharacteristic, complemented
126#17988460C2211yescharacteristic
127#17988460C2211yescharacteristic
128#17988460C2211yescharacteristic
129#17988460C2211yescharacteristic
130#17988460C2211yescharacteristic
131#17988460C2211yescharacteristic
132#17988460C2211yescharacteristic, complemented
133#17988460C2211yescharacteristic, complemented
134#17988460C2211yescharacteristic, complemented
135#17988460C2211yescharacteristic, complemented
136#17988459C2211yescharacteristic, complemented
137#17988450C2211yescharacteristic, complemented
138#17988450C2211yescharacteristic, complemented
139#17988448C2211yescharacteristic, complemented
140#17988447C2211yescharacteristic
141#17988447C2211yescharacteristic
142#17988447C2211yescharacteristic
143#17988447C2211yescharacteristic, complemented
144#17988447C2211yescharacteristic, complemented
145#17988445C2211yescharacteristic, complemented
146#17988443C2211yescharacteristic
147#17988443C2211yescharacteristic
148#17988443C2211yescharacteristic
149#17988443C2211yescharacteristic
150C4×#11924007C2211yescharacteristic, complemented
151C4×#11924007C2211yescharacteristic, complemented
152C4×#11924007C2211yescharacteristic, complemented
153C4×C4⋊Dic73C2211yescharacteristic, complemented
154C4×#11924005C2211yescharacteristic, complemented
155C4×C22⋊Dic73C2211yescharacteristic
156C4×C22⋊Dic73C2211yescharacteristic
157C4×C22⋊Dic73C2211yescharacteristic
158C4×C22⋊Dic73C2211yescharacteristic
159C4×C22⋊Dic73C2211yescharacteristic
160C4×C22⋊Dic73C2211yescharacteristic, complemented
161C4×C22⋊Dic73C2211yescharacteristic, complemented
162C4×C22⋊Dic73C2211yescharacteristic, complemented
163C4×C22⋊Dic73C2211yescharacteristic, complemented
164C4×C22⋊Dic73C2211yescharacteristic, complemented
165C4×C22⋊Dic73C2211yescharacteristic, complemented
166C4×C22⋊Dic73C2211yescharacteristic, complemented
167C4×C22⋊Dic73C2211yescharacteristic, complemented
168C4×C22⋊Dic73C2211yescharacteristic, complemented
169C4×C22⋊Dic73C2211yescharacteristic, complemented
170#17988433C2211yescharacteristic, complemented
171C2×#14556498C2211yescharacteristic, complemented
172C2×#14556498C2211yescharacteristic, complemented
173C23×D4×C73C2211yescharacteristic
174C24×C4×C73C2211yescharacteristic
175C24×C4×C73C2211yescharacteristic
176C2×C4×D4×C73—28no—
177C2×C4×D4×C73C2211yescharacteristic
178C2×C4×D4×C73C2211yescharacteristic
179C2×C4×D4×C73C2211yescharacteristic
180C2×C4×D4×C73C2211yescharacteristic
181C2×C4×D4×C73C2211yescharacteristic
182C2×C4×D4×C73C2211yescharacteristic
183C2×C4×D4×C73C2211yescharacteristic
184C2×C4×D4×C73C2211yescharacteristic
185C22×C4⋊C4×C73C2211yescharacteristic
186C22×C22⋊C4×C73C2211yescharacteristic
187C22×C22⋊C4×C73C2211yescharacteristic
188C22×C42×C73C2211yescharacteristic
189C22×Dic146C2311yescharacteristic
190C22×C22⋊D73C2311yescharacteristic
191C22×C22⋊D73C2311yescharacteristic
192C22×C22⋊D73C2311yescharacteristic
193C22×C22⋊D73C2311yescharacteristic
194C22×C22⋊D73C2311yescharacteristic
195C23×Dic73C2311yescharacteristic
196C23×Dic73C2311yescharacteristic
197C23×Dic73C2311yescharacteristic
198C23×Dic73C2311yescharacteristic
199C22×C4×D73C2311yescharacteristic
200#14556586—24no—
201#14556584—24no—
202#14556581—24no—
203#14556577—24no—
204#14556575—24no—
205#14556572—24no—
206#14556572—24no—
207#14556570—24no—
208#14556568—24no—
209#14556563—24no—
210#14556563—24no—
211#14556560—24no—
212#14556560—24no—
213C4×Dic146—24no—
214C4×C22⋊D73—24no—
215C4×C22⋊D73—24no—
216C4×C22⋊D73—24no—
217C4×C22⋊D73—42no—
218C4×C22⋊D73—42no—
219#14556550—24no—
220#14556550—42no—
221#14556548—24no—
222C2×C4⋊Dic73C2311yescharacteristic
223C2×C4⋊Dic73C2311yescharacteristic
224C2×C4⋊Dic73C2311yescharacteristic
225C2×C4⋊Dic73C2311yescharacteristic
226C2×C4⋊Dic73C2311yescharacteristic
227C2×C4⋊Dic73C2311yescharacteristic
228C2×C4⋊Dic73C2311yescharacteristic
229C2×#11924007C2311yescharacteristic
230C2×#11924007C2311yescharacteristic
231C2×#11924007C2311yescharacteristic
232C2×#11924007C2311yescharacteristic
233C2×#11924007C2311yescharacteristic
234C2×#11924007C2311yescharacteristic
235C2×#11924007C2311yescharacteristic
236C2×#11924007C2311yescharacteristic
237C2×#11924007C2311yescharacteristic
238C2×#11924007C2311yescharacteristic
239C2×#11924007C2311yescharacteristic
240C2×#11924007C2311yescharacteristic
241C2×#11924007C2311yescharacteristic
242C2×#11924007C2311yescharacteristic
243C2×#11924007C2311yescharacteristic
244C2×C22⋊Dic73—24no—
245C2×C22⋊Dic73—24no—
246C2×C22⋊Dic73C2311yescharacteristic
247C2×C22⋊Dic73C2311yescharacteristic
248C2×C22⋊Dic73C2311yescharacteristic
249C2×C22⋊Dic73C2311yescharacteristic
250C2×C22⋊Dic73C2311yescharacteristic
251C2×C22⋊Dic73C2311yescharacteristic
252C2×C22⋊Dic73C2311yescharacteristic
253C2×C22⋊Dic73C2311yescharacteristic
254C2×C22⋊Dic73C2311yescharacteristic
255C2×C22⋊Dic73C2311yescharacteristic
256C2×C22⋊Dic73C2311yescharacteristic
257C2×C22⋊Dic73C2311yescharacteristic
258C2×C22⋊Dic73C2311yescharacteristic
259C2×C22⋊Dic73C2311yescharacteristic
260C2×C22⋊Dic73C2311yescharacteristic
261C2×C22⋊Dic73C2311yescharacteristic
262C2×C22⋊Dic73C2311yescharacteristic
263C2×C22⋊Dic73C2311yescharacteristic
264C2×C22⋊Dic73C2311yescharacteristic
265C2×C22⋊Dic73C2311yescharacteristic
266C2×C22⋊Dic73C2311yescharacteristic
267C2×C22⋊Dic73C2311yescharacteristic
268C2×C22⋊Dic73C2311yescharacteristic
269C2×C22⋊Dic73C2311yescharacteristic
270C2×C22⋊Dic73C2311yescharacteristic
271C2×C22⋊Dic73C2311yescharacteristic
272C2×C22⋊Dic73C2311yescharacteristic
273C2×C22⋊Dic73C2311yescharacteristic
274C2×C22⋊Dic73C2311yescharacteristic
275C2×C22⋊Dic73C2311yescharacteristic
276C2×C22⋊Dic73C2311yescharacteristic
277C2×#11924005C2311yescharacteristic
278C2×#11924005C2311yescharacteristic
279C2×#11924005C2311yescharacteristic
280C2×#11924005C2311yescharacteristic
281C2×#11924005C2311yescharacteristic
282C2×#11924005C2311yescharacteristic
283C2×#11924005C2311yescharacteristic
284C2×#11924005C2311yescharacteristic
285C2×#11924005C2311yescharacteristic
286C2×C4×Dic73—24no—
287C2×C4×Dic73—42no—
288C2×C4×Dic73C2311yescharacteristic
289C2×C4×Dic73C2311yescharacteristic
290C2×C4×Dic73C2311yescharacteristic
291C2×C4×Dic73C2311yescharacteristic
292C2×C4×Dic73C2311yescharacteristic
293C2×C4×Dic73C2311yescharacteristic
294C2×C4×Dic73C2311yescharacteristic
295C2×C4×Dic73C2311yescharacteristic
296C2×C4×Dic73C2311yescharacteristic
297C2×C4×Dic73C2311yescharacteristic
298C2×C4×Dic73C2311yescharacteristic
299#14556498C2311yescharacteristic
300#14556498C2311yescharacteristic
301#14556498C2311yescharacteristic
302#14556498C2311yescharacteristic
303#14556498C2311yescharacteristic
304#14556498C2311yescharacteristic
305#14556498C2311yescharacteristic
306#14556498C2311yescharacteristic
307#14556498C2311yescharacteristic
308#14556498C2311yescharacteristic
309#14556498C2311yescharacteristic
310#14556498C2311yescharacteristic
311#14556498C2311yescharacteristic
312#14556498C2311yescharacteristic
313#14556498C2311yescharacteristic
314#14556498C2311yescharacteristic
315#14556498C2311yescharacteristic
316#14556498C2311yescharacteristic
317#14556498C2311yescharacteristic
318#14556498C2311yescharacteristic
319#14556498C2311yescharacteristic
320#14556498C2311yescharacteristic
321#14556498C2311yescharacteristic
322#14556498C2311yescharacteristic
323#14556498C2311yescharacteristic
324#14556498C2311yescharacteristic
325#14556498C2311yescharacteristic
326#14556498C2311yescharacteristic
327#14556498C2311yescharacteristic
328#14556498C2311yescharacteristic
329#14556498C2311yescharacteristic
330#14556498C2311yescharacteristic
331#14556498C2311yescharacteristic
332#14556498C2311yescharacteristic
333#14556498C2311yescharacteristic
334#14556498C2311yescharacteristic
335C25×C73C2311yescharacteristic
336C25×C73C2311yescharacteristic
337C22×D4×C73—24no—
338C22×D4×C73—24no—
339C22×D4×C73—24no—
340C22×D4×C73C2311yescharacteristic
341C22×D4×C73C2311yescharacteristic
342C22×D4×C73C2311yescharacteristic
343C22×D4×C73C2311yescharacteristic
344C23×C4×C73—24no—
345C23×C4×C73—24no—
346C23×C4×C73—24no—
347C23×C4×C73—24no—
348C23×C4×C73—42no—
349C23×C4×C73—42no—
350C23×C4×C73C2311yescharacteristic
351C23×C4×C73C2311yescharacteristic
352C23×C4×C73C2311yescharacteristic
353C23×C4×C73C2311yescharacteristic
354C23×C4×C73C2311yescharacteristic
355C23×C4×C73C2311yescharacteristic
356C23×C4×C73C2311yescharacteristic
357C23×C4×C73C2311yescharacteristic
358C23×C4×C73C2311yescharacteristic
359C23×C4×C73C2311yescharacteristic
360C23×C4×C73C2311yescharacteristic
361C23×C4×C73C2311yescharacteristic
362C23×C4×C73C2311yescharacteristic
363C4×D4×C73—24no—
364C4×D4×C73—24no—
365C4×D4×C73—24no—
366C4×D4×C73—24no—
367C4×D4×C73—24no—
368C4×D4×C73—24no—
369C4×D4×C73—24no—
370C4×D4×C73D418yescomplemented
371C2×C4⋊C4×C73—24no—
372C2×C4⋊C4×C73C2311yescharacteristic
373C2×C4⋊C4×C73C2311yescharacteristic
374C2×C4⋊C4×C73C2311yescharacteristic
375C2×C4⋊C4×C73C2311yescharacteristic
376C2×C22⋊C4×C73—24no—
377C2×C22⋊C4×C73—24no—
378C2×C22⋊C4×C73C2311yescharacteristic
379C2×C22⋊C4×C73C2311yescharacteristic
380C2×C22⋊C4×C73C2311yescharacteristic
381C2×C22⋊C4×C73C2311yescharacteristic
382C2×C22⋊C4×C73C2311yescharacteristic
383C2×C22⋊C4×C73C2311yescharacteristic
384C2×C22⋊C4×C73C2311yescharacteristic
385C2×C22⋊C4×C73C2311yescharacteristic
386C2×C42×C73—24no—
387C2×C42×C73C2311yescharacteristic
388C2×C42×C73C2311yescharacteristic
389C2×C42×C73C2311yescharacteristic
390C2×C42×C73C2311yescharacteristic
391C23×D73C2411yescharacteristic
392C2×Dic146—22no—
393C2×Dic146—22no—
394C2×Dic146—41no—
395C2×C22⋊D73—22no—
396C2×C22⋊D73—22no—
397C2×C22⋊D73—22no—
398C2×C22⋊D73—22no—
399C2×C22⋊D73—22no—
400C2×C22⋊D73—22no—
401C2×C22⋊D73—22no—
402C2×C22⋊D73—22no—
403C2×C22⋊D73—22no—
404C2×C22⋊D73—22no—
405C2×C22⋊D73—22no—
406C2×C22⋊D73—41no—
407C2×C22⋊D73—41no—
408C2×C22⋊D73—41no—
409C2×C22⋊D73—41no—
410C22×Dic73—22no—
411C22×Dic73—22no—
412C22×Dic73—22no—
413C22×Dic73—22no—
414C22×Dic73—22no—
415C22×Dic73—22no—
416C22×Dic73—22no—
417C22×Dic73—22no—
418C22×Dic73—41no—
419C22×Dic73—41no—
420C22×Dic73—41no—
421C22×Dic73—41no—
422C22×Dic73C2411yescharacteristic
423C22×Dic73C2411yescharacteristic
424C22×Dic73C2411yescharacteristic
425C22×Dic73C2411yescharacteristic
426C22×Dic73C2411yescharacteristic
427C22×Dic73C2411yescharacteristic
428C22×Dic73C2411yescharacteristic
429C22×Dic73C2411yescharacteristic
430C22×Dic73C2411yescharacteristic
431C22×Dic73C2411yescharacteristic
432C22×Dic73C2411yescharacteristic
433C22×Dic73C2411yescharacteristic
434C22×Dic73C2411yescharacteristic
435C22×Dic73C2411yescharacteristic
436C22×Dic73C2411yescharacteristic
437C2×C4×D73—22no—
438C2×C4×D73—22no—
439C2×C4×D73—22no—
440C4⋊Dic73—22no—
441C4⋊Dic73—22no—
442C4⋊Dic73—22no—
443C4⋊Dic73—22no—
444C4⋊Dic73—41no—
445C4⋊Dic73—41no—
446C4⋊Dic73—41no—
447#11924007—22no—
448#11924007—22no—
449#11924007—22no—
450#11924007—22no—
451#11924007—22no—
452#11924007—22no—
453#11924007—22no—
454#11924007—22no—
455#11924007—22no—
456#11924007—22no—
457#11924007—22no—
458#11924007—22no—
459#11924007—41no—
460#11924007—41no—
461#11924007—41no—
462C22⋊Dic73—22no—
463C22⋊Dic73—22no—
464C22⋊Dic73—22no—
465C22⋊Dic73—22no—
466C22⋊Dic73—22no—
467C22⋊Dic73—22no—
468C22⋊Dic73—22no—
469C22⋊Dic73—22no—
470C22⋊Dic73—22no—
471C22⋊Dic73—22no—
472C22⋊Dic73—22no—
473C22⋊Dic73—22no—
474C22⋊Dic73—22no—
475C22⋊Dic73—22no—
476C22⋊Dic73—22no—
477C22⋊Dic73—22no—
478C22⋊Dic73—22no—
479C22⋊Dic73—22no—
480C22⋊Dic73—22no—
481C22⋊Dic73—22no—
482C22⋊Dic73—22no—
483C22⋊Dic73—22no—
484C22⋊Dic73—41no—
485C22⋊Dic73—41no—
486C22⋊Dic73—41no—
487C22⋊Dic73—41no—
488C22⋊Dic73—41no—
489C22⋊Dic73—41no—
490C22⋊Dic73—41no—
491C22⋊Dic73—41no—
492C22⋊Dic73#4114yes—
493#11924005—22no—
494#11924005—22no—
495#11924005—22no—
496#11924005—22no—
497#11924005—22no—
498#11924005—22no—
499#11924005—41no—
500#11924005—41no—
501#11924005—41no—
502C4×Dic73—22no—
503C4×Dic73—22no—
504C4×Dic73—22no—
505C4×Dic73—22no—
506C4×Dic73—22no—
507C4×Dic73—22no—
508C4×Dic73—22no—
509C4×Dic73—22no—
510C4×Dic73—22no—
511C4×Dic73—41no—
512C4×Dic73—41no—
513C24×C73—22no—
514C24×C73—22no—
515C24×C73—22no—
516C24×C73—22no—
517C24×C73—22no—
518C24×C73—22no—
519C24×C73—22no—
520C24×C73—22no—
521C24×C73—22no—
522C24×C73—41no—
523C24×C73—41no—
524C24×C73—41no—
525C24×C73—41no—
526C24×C73#4114yes—
527C24×C73C2411yescharacteristic
528C24×C73C2411yescharacteristic
529C24×C73C2411yescharacteristic
530C24×C73C2411yescharacteristic
531C24×C73C2411yescharacteristic
532C2×D4×C73—232no—
533C2×D4×C73—22no—
534C2×D4×C73—22no—
535C2×D4×C73—22no—
536C2×D4×C73—22no—
537C2×D4×C73—22no—
538C2×D4×C73—22no—
539C2×D4×C73—22no—
540C2×D4×C73—22no—
541C2×D4×C73—22no—
542C2×D4×C73—22no—
543C2×D4×C73C2×D414yes—
544C2×D4×C73#4114yes—
545C22×C4×C73—22no—
546C22×C4×C73—22no—
547C22×C4×C73—22no—
548C22×C4×C73—22no—
549C22×C4×C73—22no—
550C22×C4×C73—22no—
551C22×C4×C73—22no—
552C22×C4×C73—22no—
553C22×C4×C73—22no—
554C22×C4×C73—22no—
555C22×C4×C73—22no—
556C22×C4×C73—22no—
557C22×C4×C73—22no—
558C22×C4×C73—22no—
559C22×C4×C73—22no—
560C22×C4×C73—22no—
561C22×C4×C73—22no—
562C22×C4×C73—22no—
563C22×C4×C73—22no—
564C22×C4×C73—22no—
565C22×C4×C73—22no—
566C22×C4×C73—22no—
567C22×C4×C73—22no—
568C22×C4×C73—22no—
569C22×C4×C73—22no—
570C22×C4×C73—22no—
571C22×C4×C73—22no—
572C22×C4×C73—22no—
573C22×C4×C73—22no—
574C22×C4×C73—41no—
575C22×C4×C73—41no—
576C22×C4×C73—41no—
577C22×C4×C73—41no—
578C22×C4×C73—41no—
579C22×C4×C73—41no—
580C22×C4×C73—41no—
581C22×C4×C73—416no—
582C22×C4×C73—416no—
583C22×C4×C73C2×D414yes—
584C22×C4×C73C2×D414yes—
585C22×C4×C73#4114yes—
586C22×C4×C73C2411yescharacteristic
587C22×C4×C73C2411yescharacteristic
588C22×C4×C73C2411yescharacteristic
589C22×C4×C73C2411yescharacteristic
590C22×C4×C73C2411yescharacteristic
591C22×C4×C73C2411yescharacteristic
592C22×C4×C73C2411yescharacteristic
593C22×C4×C73C2411yescharacteristic
594C22×C4×C73C2411yescharacteristic
595C22×C4×C73C2411yescharacteristic
596C4⋊C4×C73—22no—
597C4⋊C4×C73—22no—
598C4⋊C4×C73—22no—
599C4⋊C4×C73C2×D414yes—
600C22⋊C4×C73—22no—
601C22⋊C4×C73—22no—
602C22⋊C4×C73—22no—
603C22⋊C4×C73—22no—
604C22⋊C4×C73—22no—
605C22⋊C4×C73—22no—
606C22⋊C4×C73C2×D414yes—
607C22⋊C4×C73C2×D414yes—
608C42×C73—22no—
609C42×C73—22no—
610C42×C73—22no—
611C42×C73C2×D414yes—
612C23×C73—21no—
613C23×C73—21no—
614C23×C73—21no—
615C23×C73—21no—
616C23×C73—21no—
617C23×C73—21no—
618C23×C73—21no—
619C23×C73—21no—
620C23×C73—28no—
621C23×C73—28no—
622C23×C73—28no—
623C23×C73—21no—
624C23×C73—21no—
625C23×C73—21no—
626C23×C73—21no—
627C23×C73—21no—
628C23×C73—21no—
629C23×C73—21no—
630C23×C73—21no—
631C23×C73—21no—
632C23×C73—21no—
633C23×C73—21no—
634C23×C73—21no—
635C23×C73—21no—
636C23×C73—21no—
637C23×C73—21no—
638C23×C73—21no—
639C23×C73—21no—
640C23×C73—21no—
641C23×C73—44no—
642C23×C73—44no—
643C23×C73—44no—
644C23×C73—44no—
645C23×C73—44no—
646C23×C73—44no—
647C23×C73—44no—
648C23×C73—44no—
649C23×C73—44no—
650C23×C73—44no—
651C23×C73—44no—
652C23×C73C22×D412yes—
653C23×C73C22×D412yes—
654C23×C73C2×#4112yes—
655C23×C73C2×#4112yes—
656C23×C73C2×#4112yes—
657C23×C73C2×#4112yes—
658C23×C73C2×#4112yes—
659C23×C73C2×#4112yes—
660C23×C73C2×#4112yes—
661C23×C73C2511yescharacteristic
662C22×D73—21no—
663C22×D73—21no—
664C22×D73—21no—
665C22×D73—21no—
666C22×D73—21no—
667C22×D73—21no—
668C22×D73—21no—
669D4×C73—28no—
670D4×C73—28no—
671D4×C73—28no—
672D4×C73—28no—
673C2×C4×C73—28no—
674C2×C4×C73—21no—
675C2×C4×C73—21no—
676C2×C4×C73—21no—
677C2×C4×C73—21no—
678C2×C4×C73—21no—
679C2×C4×C73—21no—
680C2×C4×C73—21no—
681C2×C4×C73—21no—
682C2×C4×C73—21no—
683C2×C4×C73—21no—
684C2×C4×C73—21no—
685C2×C4×C73—21no—
686C2×C4×C73—28no—
687C2×C4×C73—28no—
688C2×C4×C73—28no—
689C2×C4×C73—21no—
690C2×C4×C73—21no—
691C2×C4×C73—21no—
692C2×C4×C73—21no—
693C2×C4×C73—21no—
694C2×C4×C73—21no—
695C2×C4×C73—21no—
696C2×C4×C73—21no—
697C2×C4×C73—21no—
698C2×C4×C73—44no—
699C2×C4×C73—44no—
700C2×C4×C73—44no—
701C2×C4×C73—44no—
702C2×C4×C73—44no—
703C2×C4×C73—44no—
704C2×C4×C73—44no—
705C2×C4×C73—44no—
706C2×C4×C73—44no—
707C2×C4×C73C22×D412yes—
708C2×C4×C73C22×D412yes—
709C2×C4×C73C22×D412yes—
710C2×C4×C73C22×D412yes—
711C2×C4×C73C22×D412yes—
712C2×C4×C73C2×#4112yes—
713C2×C4×C73C2×#4112yes—
714C2×C4×C73C2×#4112yes—
715C2×C4×C73H(5,𝔽2)12yes—
716C22⋊D73—44no—
717C22⋊D73—44no—
718C22⋊D73—44no—
719C22⋊D73—44no—
720C22⋊D73—44no—
721C2×Dic73—21no—
722C2×Dic73—21no—
723C2×Dic73—21no—
724C2×Dic73—21no—
725C2×Dic73—21no—
726C2×Dic73—21no—
727C2×Dic73—21no—
728C2×Dic73—21no—
729C2×Dic73—21no—
730C2×Dic73—21no—
731C2×Dic73—21no—
732C2×Dic73—21no—
733C2×Dic73—21no—
734C2×Dic73—21no—
735C2×Dic73—21no—
736C2×Dic73—21no—
737C2×Dic73—21no—
738C2×Dic73—21no—
739C2×Dic73—21no—
740C2×Dic73—21no—
741C2×Dic73—21no—
742C2×Dic73—21no—
743C2×Dic73—21no—
744C2×Dic73—21no—
745C2×Dic73—21no—
746C2×Dic73—21no—
747C2×Dic73—21no—
748C2×Dic73—21no—
749C2×Dic73—21no—
750C2×Dic73—21no—
751C2×Dic73—21no—
752C2×Dic73—21no—
753C2×Dic73—21no—
754C2×Dic73—21no—
755C2×Dic73—21no—
756C2×Dic73—21no—
757C2×Dic73—21no—
758C2×Dic73—21no—
759C2×Dic73—21no—
760C2×Dic73—21no—
761C2×Dic73—21no—
762C2×Dic73—21no—
763C2×Dic73—21no—
764C2×Dic73—44no—
765C2×Dic73—44no—
766C2×Dic73—44no—
767C2×Dic73—44no—
768C2×Dic73C2×#4112yes—
769C2×Dic73C2×#4112yes—
770C4×D73—44no—
771Dic146—44no—
772C22×C73—22no—
773C22×C73—22no—
774C22×C73—22no—
775C22×C73—22no—
776C22×C73—22no—
777C22×C73—22no—
778C22×C73—22no—
779C22×C73—22no—
780C22×C73—22no—
781C22×C73—22no—
782C22×C73—22no—
783C22×C73—22no—
784C22×C73—22no—
785C22×C73—22no—
786C22×C73—22no—
787C22×C73—22no—
788C22×C73—22no—
789C22×C73—22no—
790C22×C73—22no—
791C22×C73—22no—
792C22×C73—22no—
793C22×C73—416no—
794C22×C73—416no—
795C22×C73—41no—
796C22×C73—41no—
797C22×C73—41no—
798C22×C73—41no—
799C22×C73—41no—
800C22×C73—41no—
801C22×C73—41no—
802C22×C73—41no—
803C22×C73—41no—
804C22×C73—41no—
805C22×C73—41no—
806C22×C73—41no—
807C22×C73#52514yes—
808C22×C73#52914yescomplemented
809C22×C73C23×D411yescharacteristic
810C22×C73C22×#4111yescharacteristic
811C22×C73C22×#4111yescharacteristic
812C22×C73C22×#4111yescharacteristic
813C22×C73C22×#4111yescharacteristic
814C22×C73C2×H(5,𝔽2)11yescharacteristic
815C22×C73#58511yescharacteristic
816C2×D73—41no—
817C2×D73—41no—
818C2×D73—41no—
819C2×D73—41no—
820C2×D73—41no—
821C2×D73—41no—
822C2×D73—41no—
823C4×C73—22no—
824C4×C73—22no—
825C4×C73—22no—
826C4×C73—22no—
827C4×C73—22no—
828C4×C73—22no—
829C4×C73—41no—
830C4×C73—41no—
831C4×C73—41no—
832C4×C73#54614yes—
833Dic73—22no—
834Dic73—22no—
835Dic73—41no—
836Dic73—41no—
837Dic73—41no—
838Dic73—41no—
839Dic73—41no—
840Dic73—41no—
841Dic73—41no—
842Dic73—41no—
843Dic73—41no—
844Dic73—41no—
845Dic73—41no—
846Dic73—41no—
847Dic73—41no—
848#34670—731nomaximal, Sylow
849C2×C73—24no—
850C2×C73—24no—
851C2×C73—42no—
852C2×C73—42no—
853C2×C73—42no—
854C2×C73C2×#52511yescharacteristic
855C2×C73C2×#52911yescharacteristic
856C2×C73#345911yescharacteristic
857C2×C73C2×#54611yescharacteristic
858C2×C73D4×#4111yescharacteristic
859C2×C73#347511yescharacteristic
860C2×C73#348111yescharacteristic
861D73—81no—
862C2×#529—731no—
863C22×C4×D4D7311yescharacteristic, complemented
864#2481—731no—
865#2480—731no—
866#2473—731no—
867#2472—731no—
868#2467—731no—
869#2466—731no—
870#2460—731no—
871#2459—731no—
872#2450—731no—
873#2444—731no—
874#2437—731no—
875#2425—731no—
876#2419—731no—
877#2412—731no—
878#2410—731no—
879#2405—731no—
880#2398—731no—
881#2395—731no—
882#2392—731no—
883#2392—731no—
884C4×C22⋊Q8—731no—
885C4×#123—731no—
886C4×#121—731no—
887C4×#120—731no—
888C4×#120—731no—
889#2290—731no—
890#2290—731no—
891#2280—731no—
892C2×C4×C22⋊C4—731no—
893C73#3467011yescharacteristic, complemented, Sylow
894C23×D4C2×D7311yescharacteristic
895C24×C4C2×D7311yescharacteristic
896C24×C4C2×D7311yescharacteristic
897#529—1468no—
898C2×#126—731no—
899C2×#126—731no—
900C2×#125—731no—
901C2×#124—731no—
902C2×#123—731no—
903C2×#123—731no—
904C2×#123—731no—
905C2×C22⋊Q8—731no—
906C2×C22⋊Q8—731no—
907C2×#121—731no—
908C2×#121—731no—
909C2×#120—731no—
910C2×#120—731no—
911C2×C4×Q8—731no—
912C2×C4×D4—28no—
913C2×C4×D4—731no—
914C2×C4×D4—731no—
915C2×C4×D4—731no—
916C2×C4×D4—731no—
917C2×C4×D4—731no—
918C2×C4×D4C2×D7311yescharacteristic
919C2×C4×D4C2×D7311yescharacteristic
920C2×C4×D4C2×D7311yescharacteristic
921C2×C4×D4C2×D7311yescharacteristic
922C2×C4×D4C2×D7311yescharacteristic
923C2×C4×D4C2×D7311yescharacteristic
924C2×C4×D4C2×D7311yescharacteristic
925C2×C4×D4C2×D7311yescharacteristic
926C2×#117—731no—
927C2×#117—731no—
928C2×#117—731no—
929C22×C4⋊C4C2×D7311yescharacteristic
930C22×C22⋊C4—731no—
931C22×C22⋊C4—731no—
932C22×C22⋊C4C2×D7311yescharacteristic
933C22×C22⋊C4C2×D7311yescharacteristic
934C22×C42—731no—
935C22×C42—731no—
936C22×C42C2×D7311yescharacteristic
937#400—731no—
938#400—731no—
939#400—731no—
940#399—731no—
941#398—731no—
942#398—731no—
943#398—731no—
944#397—731no—
945#397—731no—
946#397—731no—
947#397—731no—
948#397—731no—
949#397—731no—
950#397—731no—
951#396—731no—
952#396—731no—
953#396—731no—
954#396—731no—
955#394—731no—
956#394—731no—
957#394—731no—
958#394—731no—
959#394—731no—
960#394—731no—
961#394—731no—
962#394—731no—
963#394—731no—
964#394—731no—
965#393—731no—
966#393—731no—
967#392—731no—
968#392—731no—
969#391—731no—
970#390—731no—
971#389—731no—
972#389—731no—
973#388—731no—
974#388—731no—
975#388—731no—
976#388—731no—
977#388—731no—
978#388—731no—
979#388—731no—
980#388—731no—
981#387—731no—
982#387—731no—
983#387—731no—
984#387—731no—
985#387—731no—
986#387—731no—
987#387—731no—
988#387—731no—
989#386—731no—
990#386—731no—
991#386—731no—
992#386—731no—
993#386—731no—
994#386—731no—
995#386—731no—
996#386—731no—
997#386—731no—
998#386—731no—
999#386—731no—
1000#386—731no—
1001#386—731no—
1002#385—731no—
1003#385—731no—
1004#385—731no—
1005#385—731no—
1006#385—731no—
1007#385—731no—
1008#385—731no—
1009#385—731no—
1010#385—731no—
1011#385—731no—
1012#385—731no—
1013#385—731no—
1014#385—731no—
1015#381—731no—
1016#381—731no—
1017#381—731no—
1018#380—731no—
1019#380—731no—
1020#380—731no—
1021#380—731no—
1022#380—731no—
1023#380—731no—
1024#379—731no—
1025#379—731no—
1026#379—731no—
1027#379—731no—
1028C4×C4⋊C4—731no—
1029C4×C4⋊C4—731no—
1030C4×C4⋊C4—731no—
1031C4×C4⋊C4—731no—
1032C4×C22⋊C4—731no—
1033C4×C22⋊C4—731no—
1034C4×C22⋊C4—731no—
1035C4×C22⋊C4—731no—
1036C4×C22⋊C4—731no—
1037C4×C22⋊C4—731no—
1038C4×C22⋊C4—731no—
1039C4×C22⋊C4—731no—
1040C4×C22⋊C4—731no—
1041C4×C22⋊C4—731no—
1042C4×C22⋊C4—731no—
1043C4×C22⋊C4—731no—
1044C4×C22⋊C4—731no—
1045C4×C22⋊C4—731no—
1046C4×C22⋊C4—731no—
1047C4×C22⋊C4—731no—
1048#376—731no—
1049C2×#95—731no—
1050C2×#95—731no—
1051C25C22×D7311yescharacteristic
1052C25C22×D7311yescharacteristic
1053C22×Q8—731no—
1054C22×D4—24no—
1055C22×D4—24no—
1056C22×D4—24no—
1057C22×D4—731no—
1058C22×D4—731no—
1059C22×D4—731no—
1060C22×D4—731no—
1061C22×D4—731no—
1062C22×D4C22×D7311yescharacteristic
1063C22×D4C22×D7311yescharacteristic
1064C22×D4C22×D7311yescharacteristic
1065C22×D4C22×D7311yescharacteristic
1066C23×C4—24no—
1067C23×C4—24no—
1068C23×C4—24no—
1069C23×C4—24no—
1070C23×C4—42no—
1071C23×C4—42no—
1072C23×C4—731no—
1073C23×C4—731no—
1074C23×C4—731no—
1075C23×C4—731no—
1076C23×C4—731no—
1077C23×C4C22×D7311yescharacteristic
1078C23×C4C22×D7311yescharacteristic
1079C23×C4C22×D7311yescharacteristic
1080C23×C4C22×D7311yescharacteristic
1081C23×C4C22×D7311yescharacteristic
1082C23×C4C22×D7311yescharacteristic
1083C23×C4C22×D7311yescharacteristic
1084C23×C4C22×D7311yescharacteristic
1085C23×C4C22×D7311yescharacteristic
1086C23×C4C22×D7311yescharacteristic
1087C23×C4C22×D7311yescharacteristic
1088C23×C4C22×D7311yescharacteristic
1089C23×C4C22×D7311yescharacteristic
1090#126—1464no—
1091#126—1464no—
1092#125—1464no—
1093#124—1464no—
1094#123—1464no—
1095#123—1464no—
1096#123—1464no—
1097C22⋊Q8—1464no—
1098C22⋊Q8—1464no—
1099#121—1464no—
1100#121—1464no—
1101#120—1464no—
1102#120—1464no—
1103C4×Q8—1464no—
1104C4×D4—24no—
1105C4×D4—24no—
1106C4×D4—24no—
1107C4×D4—24no—
1108C4×D4—24no—
1109C4×D4—24no—
1110C4×D4—24no—
1111C4×D4—2922no—
1112C4×D4—2922no—
1113C4×D4—1464no—
1114C4×D4—1464no—
1115C4×D4—1464no—
1116C4×D4C22⋊D7318yescomplemented
1117#117—2922no—
1118#117—1464no—
1119#117—1464no—
1120C2×C4⋊C4—24no—
1121C2×C4⋊C4—731no—
1122C2×C4⋊C4—731no—
1123C2×C4⋊C4—731no—
1124C2×C4⋊C4—731no—
1125C2×C4⋊C4—731no—
1126C2×C4⋊C4—731no—
1127C2×C4⋊C4—731no—
1128C2×C4⋊C4—731no—
1129C2×C4⋊C4—731no—
1130C2×C4⋊C4—731no—
1131C2×C4⋊C4—731no—
1132C2×C4⋊C4—731no—
1133C2×C4⋊C4—731no—
1134C2×C4⋊C4—731no—
1135C2×C4⋊C4—731no—
1136C2×C4⋊C4—731no—
1137C2×C4⋊C4—731no—
1138C2×C4⋊C4—731no—
1139C2×C4⋊C4—731no—
1140C2×C4⋊C4—731no—
1141C2×C4⋊C4—731no—
1142C2×C4⋊C4—731no—
1143C2×C4⋊C4C22×D7311yescharacteristic
1144C2×C4⋊C4C22×D7311yescharacteristic
1145C2×C4⋊C4C22×D7311yescharacteristic
1146C2×C4⋊C4C22×D7311yescharacteristic
1147C2×C22⋊C4—24no—
1148C2×C22⋊C4—24no—
1149C2×C22⋊C4—731no—
1150C2×C22⋊C4—731no—
1151C2×C22⋊C4—731no—
1152C2×C22⋊C4—731no—
1153C2×C22⋊C4—731no—
1154C2×C22⋊C4—731no—
1155C2×C22⋊C4—731no—
1156C2×C22⋊C4—731no—
1157C2×C22⋊C4—731no—
1158C2×C22⋊C4—731no—
1159C2×C22⋊C4—731no—
1160C2×C22⋊C4—731no—
1161C2×C22⋊C4—731no—
1162C2×C22⋊C4—731no—
1163C2×C22⋊C4—731no—
1164C2×C22⋊C4—731no—
1165C2×C22⋊C4—731no—
1166C2×C22⋊C4—731no—
1167C2×C22⋊C4—731no—
1168C2×C22⋊C4—731no—
1169C2×C22⋊C4—731no—
1170C2×C22⋊C4—731no—
1171C2×C22⋊C4—731no—
1172C2×C22⋊C4—731no—
1173C2×C22⋊C4—731no—
1174C2×C22⋊C4—731no—
1175C2×C22⋊C4—731no—
1176C2×C22⋊C4—731no—
1177C2×C22⋊C4—731no—
1178C2×C22⋊C4—731no—
1179C2×C22⋊C4—731no—
1180C2×C22⋊C4—731no—
1181C2×C22⋊C4—731no—
1182C2×C22⋊C4—731no—
1183C2×C22⋊C4—731no—
1184C2×C22⋊C4—731no—
1185C2×C22⋊C4—731no—
1186C2×C22⋊C4—731no—
1187C2×C22⋊C4—731no—
1188C2×C22⋊C4—731no—
1189C2×C22⋊C4—1464no—
1190C2×C22⋊C4—1464no—
1191C2×C22⋊C4C22×D7311yescharacteristic
1192C2×C22⋊C4C22×D7311yescharacteristic
1193C2×C22⋊C4C22×D7311yescharacteristic
1194C2×C22⋊C4C22×D7311yescharacteristic
1195C2×C22⋊C4C22×D7311yescharacteristic
1196C2×C22⋊C4C22×D7311yescharacteristic
1197C2×C22⋊C4C22×D7311yescharacteristic
1198C2×C22⋊C4C22×D7311yescharacteristic
1199C2×C42—24no—
1200C2×C42—2922no—
1201C2×C42—731no—
1202C2×C42—731no—
1203C2×C42—731no—
1204C2×C42—731no—
1205C2×C42—731no—
1206C2×C42—731no—
1207C2×C42—731no—
1208C2×C42—731no—
1209C2×C42—731no—
1210C2×C42—731no—
1211C2×C42—731no—
1212C2×C42—1464no—
1213C2×C42C22×D7311yescharacteristic
1214C2×C42C22×D7311yescharacteristic
1215C2×C42C22×D7311yescharacteristic
1216C2×C42C22×D7311yescharacteristic
1217#95—731no—
1218#95—731no—
1219#95—731no—
1220#95—731no—
1221#95—731no—
1222#95—731no—
1223#95—731no—
1224#95—731no—
1225#95—731no—
1226#95—731no—
1227#95—731no—
1228#95—731no—
1229#95—731no—
1230#95—731no—
1231#95—731no—
1232#95—731no—
1233#95—731no—
1234#95—731no—
1235#95—731no—
1236#95—731no—
1237#95—731no—
1238#95—731no—
1239#95—731no—
1240#95—731no—
1241#95—731no—
1242#95—731no—
1243#95—731no—
1244#95—731no—
1245#95—731no—
1246#95—731no—
1247#95—731no—
1248#95—731no—
1249#95—731no—
1250#95—731no—
1251#95—731no—
1252#95—731no—
1253C24—22no—
1254C24—22no—
1255C24—22no—
1256C24—22no—
1257C24—22no—
1258C24—22no—
1259C24—22no—
1260C24—22no—
1261C24—22no—
1262C24—41no—
1263C24—41no—
1264C24—41no—
1265C24—41no—
1266C24—731no—
1267C24#1192402814yes—
1268C24C23×D7311yescharacteristic
1269C24C23×D7311yescharacteristic
1270C24C23×D7311yescharacteristic
1271C24C23×D7311yescharacteristic
1272C24C23×D7311yescharacteristic
1273C2×Q8—2921no—
1274C2×Q8—1462no—
1275C2×Q8—1462no—
1276C2×D4—232no—
1277C2×D4—22no—
1278C2×D4—22no—
1279C2×D4—22no—
1280C2×D4—22no—
1281C2×D4—22no—
1282C2×D4—22no—
1283C2×D4—22no—
1284C2×D4—22no—
1285C2×D4—22no—
1286C2×D4—22no—
1287C2×D4—2921no—
1288C2×D4—2921no—
1289C2×D4—2921no—
1290C2×D4—2921no—
1291C2×D4—1462no—
1292C2×D4—1462no—
1293C2×D4—1462no—
1294C2×D4—1462no—
1295C2×D4—1462no—
1296C2×D4—1462no—
1297C2×D4—1462no—
1298C2×D4—1462no—
1299C2×D4—1462no—
1300C2×D4—1462no—
1301C2×D4—1462no—
1302C2×D4C2×C22⋊D7314yes—
1303C2×D4#1192402814yes—
1304C22×C4—22no—
1305C22×C4—22no—
1306C22×C4—22no—
1307C22×C4—22no—
1308C22×C4—22no—
1309C22×C4—22no—
1310C22×C4—22no—
1311C22×C4—22no—
1312C22×C4—22no—
1313C22×C4—22no—
1314C22×C4—22no—
1315C22×C4—22no—
1316C22×C4—22no—
1317C22×C4—22no—
1318C22×C4—22no—
1319C22×C4—22no—
1320C22×C4—22no—
1321C22×C4—22no—
1322C22×C4—22no—
1323C22×C4—22no—
1324C22×C4—22no—
1325C22×C4—22no—
1326C22×C4—22no—
1327C22×C4—22no—
1328C22×C4—22no—
1329C22×C4—22no—
1330C22×C4—22no—
1331C22×C4—22no—
1332C22×C4—22no—
1333C22×C4—41no—
1334C22×C4—41no—
1335C22×C4—41no—
1336C22×C4—41no—
1337C22×C4—41no—
1338C22×C4—41no—
1339C22×C4—41no—
1340C22×C4—416no—
1341C22×C4—416no—
1342C22×C4—2921no—
1343C22×C4—2921no—
1344C22×C4—2921no—
1345C22×C4—2921no—
1346C22×C4—731no—
1347C22×C4—731no—
1348C22×C4—731no—
1349C22×C4—731no—
1350C22×C4—731no—
1351C22×C4—731no—
1352C22×C4—731no—
1353C22×C4—731no—
1354C22×C4—731no—
1355C22×C4—731no—
1356C22×C4—731no—
1357C22×C4—731no—
1358C22×C4—731no—
1359C22×C4—731no—
1360C22×C4—731no—
1361C22×C4—1462no—
1362C22×C4—1462no—
1363C22×C4—1462no—
1364C22×C4—1462no—
1365C22×C4—1462no—
1366C22×C4—1462no—
1367C22×C4—1462no—
1368C22×C4—1462no—
1369C22×C4—1462no—
1370C22×C4—1462no—
1371C22×C4—1462no—
1372C22×C4C2×C22⋊D7314yes—
1373C22×C4C2×C22⋊D7314yes—
1374C22×C4#1192402714yes—
1375C22×C4C23×D7311yescharacteristic
1376C22×C4C23×D7311yescharacteristic
1377C22×C4C23×D7311yescharacteristic
1378C22×C4C23×D7311yescharacteristic
1379C22×C4C23×D7311yescharacteristic
1380C22×C4C23×D7311yescharacteristic
1381C22×C4C23×D7311yescharacteristic
1382C22×C4C23×D7311yescharacteristic
1383C22×C4C23×D7311yescharacteristic
1384C22×C4C23×D7311yescharacteristic
1385C4⋊C4—22no—
1386C4⋊C4—22no—
1387C4⋊C4—22no—
1388C4⋊C4—2921no—
1389C4⋊C4—2921no—
1390C4⋊C4—2921no—
1391C4⋊C4—2921no—
1392C4⋊C4—2921no—
1393C4⋊C4—2921no—
1394C4⋊C4—1462no—
1395C4⋊C4—1462no—
1396C4⋊C4—1462no—
1397C4⋊C4—1462no—
1398C4⋊C4—1462no—
1399C4⋊C4—1462no—
1400C4⋊C4—1462no—
1401C4⋊C4—1462no—
1402C4⋊C4—1462no—
1403C4⋊C4—1462no—
1404C4⋊C4—1462no—
1405C4⋊C4—1462no—
1406C4⋊C4—1462no—
1407C4⋊C4—1462no—
1408C4⋊C4—1462no—
1409C4⋊C4—1462no—
1410C4⋊C4C2×C22⋊D7314yes—
1411C22⋊C4—22no—
1412C22⋊C4—22no—
1413C22⋊C4—22no—
1414C22⋊C4—22no—
1415C22⋊C4—22no—
1416C22⋊C4—22no—
1417C22⋊C4—2921no—
1418C22⋊C4—2921no—
1419C22⋊C4—2921no—
1420C22⋊C4—2921no—
1421C22⋊C4—2921no—
1422C22⋊C4—2921no—
1423C22⋊C4—2921no—
1424C22⋊C4—2921no—
1425C22⋊C4—2921no—
1426C22⋊C4—2921no—
1427C22⋊C4—2921no—
1428C22⋊C4—734no—
1429C22⋊C4—1462no—
1430C22⋊C4—1462no—
1431C22⋊C4—1462no—
1432C22⋊C4—1462no—
1433C22⋊C4—1462no—
1434C22⋊C4—1462no—
1435C22⋊C4—1462no—
1436C22⋊C4—1462no—
1437C22⋊C4—1462no—
1438C22⋊C4—1462no—
1439C22⋊C4—1462no—
1440C22⋊C4—1462no—
1441C22⋊C4—1462no—
1442C22⋊C4—1462no—
1443C22⋊C4—1462no—
1444C22⋊C4—1462no—
1445C22⋊C4—1462no—
1446C22⋊C4—1462no—
1447C22⋊C4—1462no—
1448C22⋊C4—1462no—
1449C22⋊C4—1462no—
1450C22⋊C4—1462no—
1451C22⋊C4—1462no—
1452C22⋊C4—1462no—
1453C22⋊C4—1462no—
1454C22⋊C4—1462no—
1455C22⋊C4—1462no—
1456C22⋊C4—1462no—
1457C22⋊C4C2×C22⋊D7314yes—
1458C22⋊C4C2×C22⋊D7314yes—
1459C42—22no—
1460C42—22no—
1461C42—22no—
1462C42—2921no—
1463C42—2921no—
1464C42—1462no—
1465C42—1462no—
1466C42—1462no—
1467C42—1462no—
1468C42—1462no—
1469C42—1462no—
1470C42—1462no—
1471C42—1462no—
1472C42—1462no—
1473C42C2×C22⋊D7314yes—
1474C23—21no—
1475C23—21no—
1476C23—21no—
1477C23—21no—
1478C23—21no—
1479C23—21no—
1480C23—21no—
1481C23—21no—
1482C23—28no—
1483C23—21no—
1484C23—21no—
1485C23—21no—
1486C23—21no—
1487C23—21no—
1488C23—21no—
1489C23—21no—
1490C23—21no—
1491C23—21no—
1492C23—21no—
1493C23—21no—
1494C23—21no—
1495C23—21no—
1496C23—21no—
1497C23—21no—
1498C23—21no—
1499C23—21no—
1500C23—21no—
1501C23—28no—
1502C23—28no—
1503C23—44no—
1504C23—44no—
1505C23—44no—
1506C23—44no—
1507C23—44no—
1508C23—44no—
1509C23—44no—
1510C23—44no—
1511C23—44no—
1512C23—44no—
1513C23—44no—
1514C23—1461no—
1515C23—1461no—
1516C23—1461no—
1517C23—1461no—
1518C23—1461no—
1519C23—1461no—
1520C23—1461no—
1521C23C22×C22⋊D7312yes—
1522C23C22×C22⋊D7312yes—
1523C23#41×D7312yes—
1524C23C2×#1192402712yes—
1525C23C2×#1192402812yes—
1526C23C2×#1192402812yes—
1527C23C2×#1192402812yes—
1528C23C2×#1192402812yes—
1529C23C2×#1192402812yes—
1530C23C24×D7311yescharacteristic
1531Q8—2924no—
1532D4—28no—
1533D4—28no—
1534D4—28no—
1535D4—28no—
1536D4—2924no—
1537D4—2924no—
1538D4—2924no—
1539D4—2924no—
1540D4—2924no—
1541C2×C4—28no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—21no—
1551C2×C4—21no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—28no—
1555C2×C4—28no—
1556C2×C4—28no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—21no—
1561C2×C4—21no—
1562C2×C4—21no—
1563C2×C4—21no—
1564C2×C4—21no—
1565C2×C4—21no—
1566C2×C4—44no—
1567C2×C4—44no—
1568C2×C4—44no—
1569C2×C4—44no—
1570C2×C4—44no—
1571C2×C4—44no—
1572C2×C4—44no—
1573C2×C4—44no—
1574C2×C4—44no—
1575C2×C4—2924no—
1576C2×C4—2924no—
1577C2×C4—2924no—
1578C2×C4—2924no—
1579C2×C4—2924no—
1580C2×C4—732no—
1581C2×C4—732no—
1582C2×C4—1461no—
1583C2×C4—1461no—
1584C2×C4—1461no—
1585C2×C4—1461no—
1586C2×C4—1461no—
1587C2×C4—1461no—
1588C2×C4—1461no—
1589C2×C4—1461no—
1590C2×C4—1461no—
1591C2×C4—1461no—
1592C2×C4—1461no—
1593C2×C4—1461no—
1594C2×C4—1461no—
1595C2×C4—1461no—
1596C2×C4—1461no—
1597C2×C4—1461no—
1598C2×C4—1461no—
1599C2×C4—1461no—
1600C2×C4—1461no—
1601C2×C4—1461no—
1602C2×C4—1461no—
1603C2×C4—1461no—
1604C2×C4—1461no—
1605C2×C4—1461no—
1606C2×C4—1461no—
1607C2×C4—1461no—
1608C2×C4—1461no—
1609C2×C4—1461no—
1610C2×C4—1461no—
1611C2×C4—1461no—
1612C2×C4—1461no—
1613C2×C4—1461no—
1614C2×C4—1461no—
1615C2×C4—1461no—
1616C2×C4—1461no—
1617C2×C4—1461no—
1618C2×C4—1461no—
1619C2×C4—1461no—
1620C2×C4—1461no—
1621C2×C4—1461no—
1622C2×C4—1461no—
1623C2×C4—1461no—
1624C2×C4—1461no—
1625C2×C4C22×C22⋊D7312yes—
1626C2×C4C22×C22⋊D7312yes—
1627C2×C4C22×C22⋊D7312yes—
1628C2×C4C22×C22⋊D7312yes—
1629C2×C4C22×C22⋊D7312yes—
1630C2×C4C2×#1192402712yes—
1631C2×C4C2×#1192402712yes—
1632C2×C4C2×#1192402812yes—
1633C2×C4#1455663612yes—
1634C22—22no—
1635C22—22no—
1636C22—22no—
1637C22—22no—
1638C22—22no—
1639C22—22no—
1640C22—22no—
1641C22—22no—
1642C22—22no—
1643C22—22no—
1644C22—22no—
1645C22—22no—
1646C22—22no—
1647C22—22no—
1648C22—22no—
1649C22—22no—
1650C22—22no—
1651C22—22no—
1652C22—22no—
1653C22—22no—
1654C22—22no—
1655C22—416no—
1656C22—416no—
1657C22—41no—
1658C22—41no—
1659C22—41no—
1660C22—41no—
1661C22—41no—
1662C22—41no—
1663C22—41no—
1664C22—41no—
1665C22—41no—
1666C22—41no—
1667C22—41no—
1668C22—41no—
1669C22—2921no—
1670C22—2921no—
1671C22—2921no—
1672C22—2921no—
1673C22—2921no—
1674C22—2921no—
1675C22—2921no—
1676C22#1798909814yes—
1677C22#1798911714yescomplemented
1678C22C23×C22⋊D7311yescharacteristic
1679C22C2×#41×D7311yescharacteristic
1680C22C22×#1192402711yescharacteristic
1681C22C22×#1192402811yescharacteristic
1682C22C22×#1192402811yescharacteristic
1683C22C2×#1455663611yescharacteristic
1684C22#1798942311yescharacteristic
1685C4—22no—
1686C4—22no—
1687C4—22no—
1688C4—22no—
1689C4—22no—
1690C4—22no—
1691C4—41no—
1692C4—41no—
1693C4—41no—
1694C4—2921no—
1695C4—2921no—
1696C4—2921no—
1697C4—2921no—
1698C4—2921no—
1699C4—2921no—
1700C4—2921no—
1701C4—2921no—
1702C4—2921no—
1703C4—2921no—
1704C4—2921no—
1705C4—2921no—
1706C4—2921no—
1707C4—1462no—
1708C4—1462no—
1709C4#1798923114yes—
1710C2—24no—
1711C2—24no—
1712C2—42no—
1713C2—42no—
1714C2—42no—
1715C2—5841no—
1716C2C2×#1798909811yescharacteristic
1717C2C2×#1798911711yescharacteristic
1718C2#2262334011yescharacteristic
1719C2C2×#1798923111yescharacteristic
1720C2#41×C22⋊D7311yescharacteristic
1721C2#2262348911yescharacteristic
1722C2#2262353511yescharacteristic
subgroupG/H
centerC22×C4C23×D73
commutator, socle, cosocleC23×C73C25
FrattiniC23C24×D73
FittingC22×C4×D4×C73C2
prime radical#22613305C2
hypercenterC22×C4×D4D73
hypocenterC73#34670
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C22×C4×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#17989117C2semidirect
2. #22614186C2semidirect
3. #22614171C2semidirect
4. #22614066C2semidirect
5. #22614051C2semidirect
6. #22613976C2semidirect
7. #22613961C2semidirect
8. #22613877C2semidirect
9. #22613862C2semidirect
10. #22613749C2semidirect
11. #22613675C2semidirect
12. #22613592C2semidirect
13. #22613476C2semidirect
14. #22613402C2semidirect
15. #22613321C2semidirect
17. #22613254C2semidirect
18. #22613215C2semidirect
19. #22613190C2semidirect
20. #22613173C2semidirect
21. #22613169C2semidirect
22. C4×#14556570C2semidirect
23. C4×#14556572C2semidirect
24. C4×#14556563C2semidirect
25. C4×#14556560C2semidirect
26. C4×#14556560C2semidirect
27. #22612376C2semidirect
28. #22612374C2semidirect
29. #22612314C2semidirect
30. C2×C4×C22⋊Dic73C2semidirect
31. C22×C4×D4×C73C2semidirect
33. C2×#14556586C22semidirect
34. C2×#14556584C22semidirect
35. C2×#14556581C22semidirect
36. C2×#14556577C22semidirect
37. C2×#14556575C22semidirect
41. C2×#14556568C22semidirect
46. C2×C4×Dic146C22semidirect
48. C2×C4×C22⋊D73C22semidirect
49. C2×C4×C22⋊D73C22semidirect
50. C2×C4×C22⋊D73C22semidirect
51. C2×C4×C22⋊D73C22semidirect
52. C2×#14556550C22semidirect
53. C2×#14556550C22semidirect
54. C2×#14556548C22semidirect
57. C22×C4×Dic73C22semidirect
58. C22×C4×Dic73C22semidirect
59. #17988526C22semidirect
60. #17988525C22semidirect
61. #17988525C22semidirect
62. #17988523C22semidirect
63. #17988520C22semidirect
64. #17988518C22semidirect
65. #17988517C22semidirect
66. #17988515C22semidirect
67. #17988515C22semidirect
68. #17988515C22semidirect
69. #17988513C22semidirect
70. #17988512C22semidirect
71. #17988512C22semidirect
72. #17988512C22semidirect
73. #17988510C22semidirect
74. #17988510C22semidirect
75. #17988510C22semidirect
76. #17988509C22semidirect
77. #17988503C22semidirect
78. #17988503C22semidirect
79. #17988503C22semidirect
80. #17988502C22semidirect
87. #17988499C22semidirect
88. #17988499C22semidirect
91. #17988493C22semidirect
92. #17988487C22semidirect
93. #17988485C22semidirect
94. #17988482C22semidirect
95. #17988481C22semidirect
96. #17988480C22semidirect
97. #17988480C22semidirect
98. #17988478C22semidirect
99. #17988478C22semidirect
100. #17988477C22semidirect
101. #17988475C22semidirect
102. #17988475C22semidirect
103. #17988473C22semidirect
104. #17988473C22semidirect
105. #17988471C22semidirect
106. #17988471C22semidirect
107. #17988471C22semidirect
108. #17988471C22semidirect
109. #17988468C22semidirect
110. #17988468C22semidirect
119. #17988466C22semidirect
120. #17988466C22semidirect
121. #17988466C22semidirect
122. #17988466C22semidirect
123. #17988464C22semidirect
124. #17988462C22semidirect
125. #17988462C22semidirect
132. #17988460C22semidirect
133. #17988460C22semidirect
134. #17988460C22semidirect
135. #17988460C22semidirect
136. #17988459C22semidirect
137. #17988450C22semidirect
138. #17988450C22semidirect
139. #17988448C22semidirect
143. #17988447C22semidirect
144. #17988447C22semidirect
145. #17988445C22semidirect
150. C4×#11924007C22semidirect
151. C4×#11924007C22semidirect
152. C4×#11924007C22semidirect
153. C4×C4⋊Dic73C22semidirect
154. C4×#11924005C22semidirect
160. C4×C22⋊Dic73C22semidirect
161. C4×C22⋊Dic73C22semidirect
162. C4×C22⋊Dic73C22semidirect
163. C4×C22⋊Dic73C22semidirect
164. C4×C22⋊Dic73C22semidirect
165. C4×C22⋊Dic73C22semidirect
166. C4×C22⋊Dic73C22semidirect
167. C4×C22⋊Dic73C22semidirect
168. C4×C22⋊Dic73C22semidirect
169. C4×C22⋊Dic73C22semidirect
170. #17988433C22semidirect
171. C2×#14556498C22semidirect
172. C2×#14556498C22semidirect
370. C4×D4×C73D4semidirect
808. C22×C73#529semidirect
863. C22×C4×D4D73semidirect
893. C73#34670semidirect
1116. C4×D4C22⋊D73semidirect
1677. C22#17989117semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#179891172
#226141862
#226141712
#226140662
#226140512
#226139762
#226139612
#226138772
#226138622
#226137492
#226136752
#226135922
#226134762
#226134022
#226133212
#226133052
#226132542
#226132152
#226131902
#226131732
#226131692
C4×#145565702
C4×#145565722
C4×#145565632
C4×#145565602
#226123762
#226123742
#226123142
C2×C4×C22⋊Dic732
C22×C4×D4×C732
#3467073