Finite Group Databasebeta

← #33256156

Subgroups — #33256156

Order 18688.

2804 conjugacy classes of subgroups.

The subgroup lattice has 1708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989117C211yesmaximal, characteristic, complemented
2#22615071C211yesmaximal, characteristic, complemented
3#22615056C211yesmaximal, characteristic, complemented
4#22615041C211yesmaximal, characteristic, complemented
5#22615026C211yesmaximal, characteristic, complemented
6#22615013C211yesmaximal, characteristic, complemented
7#22615004C211yesmaximal, characteristic, complemented
8#22614987C211yesmaximal, characteristic, complemented
9#22614972C211yesmaximal, characteristic, complemented
10#22614939C211yesmaximal, characteristic, complemented
11#22614889C211yesmaximal, characteristic, complemented
12#22614859C211yesmaximal, characteristic, complemented
13#22614818C211yesmaximal, characteristic, complemented
14#22614263C211yesmaximal, characteristic, complemented
15#22614056C211yesmaximal, characteristic, complemented
16#22613488C211yesmaximal, characteristic, complemented
17#22613471C211yesmaximal, characteristic, complemented
18#22613199C211yesmaximal, characteristic, complemented
19#22613190C211yesmaximal, characteristic, complemented
20#22613169C211yesmaximal, characteristic, complemented
21#22613144C211yesmaximal, characteristic, complemented
22C4×#14556578C211yesmaximal, characteristic, complemented
23C4×#14556572C211yesmaximal, characteristic, complemented
24C4×#14556563C211yesmaximal, characteristic, complemented
25C4×#14556563C211yesmaximal, characteristic, complemented
26C4×#14556560C211yesmaximal, characteristic, complemented
27#22612422C211yesmaximal, characteristic, complemented
28#22612390C211yesmaximal, characteristic, complemented
29C4×D4×Dic73C211yesmaximal, characteristic, complemented
30C2×C4×C22⋊Dic73C211yesmaximal, characteristic, complemented
31C2×#525×C73C211yesmaximal, characteristic, complemented
32#17989117—28no—
33C2×#14556586C2211yescharacteristic, complemented
34C2×#14556584C2211yescharacteristic, complemented
35C2×#14556581C2211yescharacteristic, complemented
36C2×#14556578C2211yescharacteristic
37C2×#14556577C2211yescharacteristic, complemented
38C2×#14556575C2211yescharacteristic
39C2×#14556572C2211yescharacteristic
40C2×#14556572C2211yescharacteristic
41C2×#14556568C2211yescharacteristic
42C2×#14556563C2211yescharacteristic
43C2×#14556563C2211yescharacteristic
44C2×#14556563C2211yescharacteristic
45C2×#14556560C2211yescharacteristic
46C2×C4×Dic146C2211yescharacteristic, complemented
47C2×D4×Dic73C2211yescharacteristic
48C2×D4×Dic73C2211yescharacteristic
49C2×C4×C22⋊D73C2211yescharacteristic
50C2×C4×C22⋊D73C2211yescharacteristic
51C2×C4×C22⋊D73C2211yescharacteristic
52C2×C4×C22⋊D73C2211yescharacteristic, complemented
53C2×C4×C22⋊D73C2211yescharacteristic, complemented
54C2×#14556550C2211yescharacteristic, complemented
55C2×#14556548C2211yescharacteristic, complemented
56C22×C22⋊Dic73C2211yescharacteristic
57C22×C22⋊Dic73C2211yescharacteristic
58C22×C4×Dic73C2211yescharacteristic
59C22×C4×Dic73C2211yescharacteristic
60C22×C4×Dic73C2211yescharacteristic, complemented
61#17988526C2211yescharacteristic, complemented
62#17988526C2211yescharacteristic, complemented
63#17988523C2211yescharacteristic
64#17988523C2211yescharacteristic
65#17988520C2211yescharacteristic, complemented
66#17988520C2211yescharacteristic, complemented
67#17988518C2211yescharacteristic, complemented
68#17988517C2211yescharacteristic, complemented
69#17988515C2211yescharacteristic, complemented
70#17988515C2211yescharacteristic, complemented
71#17988513C2211yescharacteristic, complemented
72#17988512C2211yescharacteristic
73#17988510C2211yescharacteristic
74#17988510C2211yescharacteristic
75#17988510C2211yescharacteristic
76#17988510C2211yescharacteristic, complemented
77#17988507C2211yescharacteristic, complemented
78#17988506C2211yescharacteristic, complemented
79#17988503C2211yescharacteristic
80#17988503C2211yescharacteristic, complemented
81#17988501C2211yescharacteristic
82#17988501C2211yescharacteristic
83#17988501C2211yescharacteristic
84#17988501C2211yescharacteristic
85#17988501C2211yescharacteristic
86#17988501C2211yescharacteristic, complemented
87#17988499C2211yescharacteristic
88#17988498C2211yescharacteristic, complemented
89#17988495C2211yescharacteristic
90#17988495C2211yescharacteristic
91#17988495C2211yescharacteristic
92#17988495C2211yescharacteristic, complemented
93#17988494C2211yescharacteristic, complemented
94#17988494C2211yescharacteristic, complemented
95#17988492C2211yescharacteristic, complemented
96#17988490C2211yescharacteristic
97#17988490C2211yescharacteristic
98#17988490C2211yescharacteristic
99#17988487C2211yescharacteristic
100#17988487C2211yescharacteristic
101#17988487C2211yescharacteristic
102#17988487C2211yescharacteristic, complemented
103#17988482C2211yescharacteristic, complemented
104#17988482C2211yescharacteristic, complemented
105#17988482C2211yescharacteristic, complemented
106#17988482C2211yescharacteristic, complemented
107#17988481C2211yescharacteristic
108#17988481C2211yescharacteristic
109#17988481C2211yescharacteristic
110#17988481C2211yescharacteristic
111#17988481C2211yescharacteristic
112#17988481C2211yescharacteristic, complemented
113#17988481C2211yescharacteristic, complemented
114#17988481C2211yescharacteristic, complemented
115#17988477C2211yescharacteristic, complemented
116#17988477C2211yescharacteristic, complemented
117#17988477C2211yescharacteristic, complemented
118#17988477C2211yescharacteristic, complemented
119#17988475C2211yescharacteristic, complemented
120#17988475C2211yescharacteristic, complemented
121#17988468C2211yescharacteristic, complemented
122#17988468C2211yescharacteristic, complemented
123#17988467C2211yescharacteristic
124#17988467C2211yescharacteristic
125#17988467C2211yescharacteristic
126#17988467C2211yescharacteristic
127#17988467C2211yescharacteristic
128#17988467C2211yescharacteristic, complemented
129#17988467C2211yescharacteristic, complemented
130#17988466C2211yescharacteristic
131#17988466C2211yescharacteristic
132#17988466C2211yescharacteristic
133#17988464C2211yescharacteristic
134#17988464C2211yescharacteristic, complemented
135#17988460C2211yescharacteristic
136#17988460C2211yescharacteristic
137#17988460C2211yescharacteristic
138#17988459C2211yescharacteristic
139#17988452C2211yescharacteristic, complemented
140#17988448C2211yescharacteristic
141#17988445C2211yescharacteristic
142#17988445C2211yescharacteristic, complemented
143#17988443C2211yescharacteristic
144C4⋊C4×Dic73C2211yescharacteristic, complemented
145C4⋊C4×Dic73C2211yescharacteristic, complemented
146C4×#11924007C2211yescharacteristic, complemented
147C4×#11924007C2211yescharacteristic, complemented
148C4×#11924007C2211yescharacteristic, complemented
149C4×C4⋊Dic73C2211yescharacteristic, complemented
150C22⋊C4×Dic73C2211yescharacteristic
151C22⋊C4×Dic73C2211yescharacteristic
152C22⋊C4×Dic73C2211yescharacteristic, complemented
153C22⋊C4×Dic73C2211yescharacteristic, complemented
154C4×#11924005C2211yescharacteristic, complemented
155C4×C22⋊Dic73C2211yescharacteristic
156C4×C22⋊Dic73C2211yescharacteristic
157C4×C22⋊Dic73C2211yescharacteristic
158C4×C22⋊Dic73C2211yescharacteristic
159C4×C22⋊Dic73C2211yescharacteristic
160C4×C22⋊Dic73C2211yescharacteristic
161C4×C22⋊Dic73C2211yescharacteristic
162C4×C22⋊Dic73C2211yescharacteristic
163C4×C22⋊Dic73C2211yescharacteristic
164C4×C22⋊Dic73C2211yescharacteristic
165C4×C22⋊Dic73C2211yescharacteristic
166C4×C22⋊Dic73C2211yescharacteristic, complemented
167C4×C22⋊Dic73C2211yescharacteristic, complemented
168C4×C22⋊Dic73C2211yescharacteristic, complemented
169C4×C22⋊Dic73C2211yescharacteristic, complemented
170C2×#14556498C2211yescharacteristic
171C2×#14556498C2211yescharacteristic
172C42×Dic73C2211yescharacteristic, complemented
173C22×#41×C73C2211yescharacteristic
174C24×C4×C73C2211yescharacteristic
175#525×C73—28no—
176C2×#123×C73C2211yescharacteristic
177C2×#123×C73C2211yescharacteristic
178C2×C22⋊Q8×C73C2211yescharacteristic
179C2×C22⋊Q8×C73C2211yescharacteristic
180C2×#121×C73C2211yescharacteristic
181C2×#121×C73C2211yescharacteristic
182C2×#120×C73C2211yescharacteristic
183C2×#120×C73C2211yescharacteristic
184C2×C4×D4×C73C2211yescharacteristic
185C2×C4×D4×C73C2211yescharacteristic
186C2×C4×D4×C73C2211yescharacteristic
187C2×C4×D4×C73C2211yescharacteristic
188C2×#117×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
199C23×Dic73C2311yescharacteristic
200C23×Dic73C2311yescharacteristic
201C22×C4×D73C2311yescharacteristic
202#14556586—24no—
203#14556584—24no—
204#14556581—24no—
205#14556578—24no—
206#14556577—24no—
207#14556575—24no—
208#14556572—24no—
209#14556572—24no—
210#14556568—24no—
211#14556563—24no—
212#14556563—24no—
213#14556563—24no—
214#14556560—24no—
215C4×Dic146—24no—
216D4×Dic73—24no—
217D4×Dic73—24no—
218C4×C22⋊D73—24no—
219C4×C22⋊D73—24no—
220C4×C22⋊D73—24no—
221C4×C22⋊D73—42no—
222C4×C22⋊D73—42no—
223#14556550—24no—
224#14556548—24no—
225C2×C4⋊Dic73C2311yescharacteristic
226C2×C4⋊Dic73C2311yescharacteristic
227C2×C4⋊Dic73C2311yescharacteristic
228C2×C4⋊Dic73C2311yescharacteristic
229C2×C4⋊Dic73C2311yescharacteristic
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×#11924007C2311yescharacteristic
245C2×C22⋊Dic73—24no—
246C2×C22⋊Dic73—24no—
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×#11924005C2311yescharacteristic
277C2×#11924005C2311yescharacteristic
278C2×#11924005C2311yescharacteristic
279C2×#11924005C2311yescharacteristic
280C2×#11924005C2311yescharacteristic
281C2×#11924005C2311yescharacteristic
282C2×#11924005C2311yescharacteristic
283C2×#11924005C2311yescharacteristic
284C2×#11924005C2311yescharacteristic
285C2×C4×Dic73—24no—
286C2×C4×Dic73—42no—
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
299C2×C4×Dic73C2311yescharacteristic
300C2×C4×Dic73C2311yescharacteristic
301C2×C4×Dic73C2311yescharacteristic
302C2×C4×Dic73C2311yescharacteristic
303C2×C4×Dic73C2311yescharacteristic
304C2×C4×Dic73C2311yescharacteristic
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
335#14556498C2311yescharacteristic
336#14556498C2311yescharacteristic
337C25×C73C2311yescharacteristic
338C2×#41×C73—24no—
339C2×#41×C73—24no—
340C2×#41×C73—42no—
341C22×Q8×C73C2311yescharacteristic
342C22×D4×C73C2311yescharacteristic
343C22×D4×C73C2311yescharacteristic
344C22×D4×C73C2311yescharacteristic
345C22×D4×C73C2311yescharacteristic
346C22×D4×C73C2311yescharacteristic
347C22×D4×C73C2311yescharacteristic
348C22×D4×C73C2311yescharacteristic
349C23×C4×C73—24no—
350C23×C4×C73—24no—
351C23×C4×C73—42no—
352C23×C4×C73C2311yescharacteristic
353C23×C4×C73C2311yescharacteristic
354C23×C4×C73C2311yescharacteristic
355C23×C4×C73C2311yescharacteristic
356C23×C4×C73C2311yescharacteristic
357C23×C4×C73C2311yescharacteristic
358C23×C4×C73C2311yescharacteristic
359C23×C4×C73C2311yescharacteristic
360#123×C73—24no—
361#123×C73—24no—
362C22⋊Q8×C73—24no—
363C22⋊Q8×C73—24no—
364#121×C73—24no—
365#121×C73—24no—
366#120×C73—24no—
367#120×C73—24no—
368C4×D4×C73—24no—
369C4×D4×C73—24no—
370C4×D4×C73—24no—
371C4×D4×C73D418yescomplemented
372#117×C73—24no—
373C2×C4⋊C4×C73C2311yescharacteristic
374C2×C4⋊C4×C73C2311yescharacteristic
375C2×C4⋊C4×C73C2311yescharacteristic
376C2×C4⋊C4×C73C2311yescharacteristic
377C2×C4⋊C4×C73C2311yescharacteristic
378C2×C4⋊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×C22⋊C4×C73C2311yescharacteristic
387C2×C22⋊C4×C73C2311yescharacteristic
388C2×C22⋊C4×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—41no—
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—22no—
419C22×Dic73—22no—
420C22×Dic73—41no—
421C22×Dic73—41no—
422C22×Dic73—41no—
423C22×Dic73—41no—
424C22×Dic73—41no—
425C22×Dic73—41no—
426C22×Dic73—41no—
427C22×Dic73#4114yescomplemented
428C22×Dic73C2411yescharacteristic
429C22×Dic73C2411yescharacteristic
430C22×Dic73C2411yescharacteristic
431C22×Dic73C2411yescharacteristic
432C22×Dic73C2411yescharacteristic
433C22×Dic73C2411yescharacteristic
434C22×Dic73C2411yescharacteristic
435C22×Dic73C2411yescharacteristic
436C22×Dic73C2411yescharacteristic
437C22×Dic73C2411yescharacteristic
438C22×Dic73C2411yescharacteristic
439C22×Dic73C2411yescharacteristic
440C22×Dic73C2411yescharacteristic
441C22×Dic73C2411yescharacteristic
442C22×Dic73C2411yescharacteristic
443C2×C4×D73—22no—
444C2×C4×D73—22no—
445C2×C4×D73—22no—
446C4⋊Dic73—22no—
447C4⋊Dic73—22no—
448C4⋊Dic73—22no—
449C4⋊Dic73—22no—
450C4⋊Dic73—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—22no—
460#11924007—22no—
461#11924007—22no—
462#11924007—41no—
463#11924007—41no—
464#11924007—41no—
465#11924007—41no—
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—22no—
485C22⋊Dic73—22no—
486C22⋊Dic73—22no—
487C22⋊Dic73—22no—
488C22⋊Dic73—22no—
489C22⋊Dic73—41no—
490C22⋊Dic73—41no—
491C22⋊Dic73—41no—
492C22⋊Dic73—41no—
493C22⋊Dic73#4114yescomplemented
494C22⋊Dic73#4114yescomplemented
495#11924005—22no—
496#11924005—22no—
497#11924005—22no—
498#11924005—22no—
499#11924005—22no—
500#11924005—22no—
501#11924005—22no—
502#11924005—41no—
503#11924005—41no—
504C4×Dic73—22no—
505C4×Dic73—22no—
506C4×Dic73—22no—
507C4×Dic73—22no—
508C4×Dic73—22no—
509C4×Dic73—22no—
510C4×Dic73—22no—
511C4×Dic73—22no—
512C4×Dic73—22no—
513C4×Dic73—22no—
514C4×Dic73—22no—
515C4×Dic73—22no—
516C4×Dic73—41no—
517C4×Dic73—41no—
518C4×Dic73—41no—
519C4×Dic73—41no—
520C4×Dic73—41no—
521C24×C73—22no—
522C24×C73—22no—
523C24×C73—22no—
524C24×C73—22no—
525C24×C73—22no—
526C24×C73—41no—
527C24×C73—41no—
528C24×C73C2411yescharacteristic
529C24×C73C2411yescharacteristic
530C24×C73C2411yescharacteristic
531C24×C73C2411yescharacteristic
532C24×C73C2411yescharacteristic
533#41×C73—416no—
534C2×Q8×C73—22no—
535C2×Q8×C73—22no—
536C2×Q8×C73—41no—
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×C73—22no—
544C2×D4×C73—22no—
545C2×D4×C73—22no—
546C2×D4×C73—22no—
547C2×D4×C73—22no—
548C2×D4×C73—22no—
549C2×D4×C73—22no—
550C2×D4×C73—22no—
551C2×D4×C73—22no—
552C2×D4×C73—41no—
553C2×D4×C73—41no—
554C2×D4×C73—41no—
555C2×D4×C73—41no—
556C2×D4×C73—41no—
557C2×D4×C73C2×D414yes—
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—22no—
575C22×C4×C73—22no—
576C22×C4×C73—41no—
577C22×C4×C73—41no—
578C22×C4×C73—41no—
579C22×C4×C73—416no—
580C22×C4×C73C2×D414yes—
581C22×C4×C73C2×D414yes—
582C22×C4×C73#4114yes—
583C22×C4×C73C2411yescharacteristic
584C22×C4×C73C2411yescharacteristic
585C22×C4×C73C2411yescharacteristic
586C22×C4×C73C2411yescharacteristic
587C22×C4×C73C2411yescharacteristic
588C22×C4×C73C2411yescharacteristic
589C22×C4×C73C2411yescharacteristic
590C22×C4×C73C2411yescharacteristic
591C22×C4×C73C2411yescharacteristic
592C22×C4×C73C2411yescharacteristic
593C4⋊C4×C73—22no—
594C4⋊C4×C73—22no—
595C4⋊C4×C73—22no—
596C4⋊C4×C73—22no—
597C4⋊C4×C73—22no—
598C4⋊C4×C73C2×D414yes—
599C22⋊C4×C73—22no—
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×C73—22no—
607C22⋊C4×C73C2×D414yes—
608C22⋊C4×C73C2×D414yes—
609C42×C73—22no—
610C42×C73C2×D414yes—
611C23×C73—21no—
612C23×C73—21no—
613C23×C73—21no—
614C23×C73—21no—
615C23×C73—28no—
616C23×C73—21no—
617C23×C73—21no—
618C23×C73—21no—
619C23×C73—21no—
620C23×C73—21no—
621C23×C73—21no—
622C23×C73—21no—
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×C73C22×D412yes—
648C23×C73C22×D412yes—
649C23×C73C2×#4112yes—
650C23×C73C2×#4112yes—
651C23×C73C2×#4112yes—
652C23×C73C2×#4112yes—
653C23×C73C2511yescharacteristic
654C22×D73—21no—
655C22×D73—21no—
656C22×D73—21no—
657C22×D73—21no—
658C22×D73—21no—
659C22×D73—21no—
660C22×D73—21no—
661Q8×C73—44no—
662D4×C73—28no—
663D4×C73—44no—
664D4×C73—44no—
665D4×C73—44no—
666D4×C73—44no—
667D4×C73—44no—
668D4×C73—44no—
669C2×C4×C73—21no—
670C2×C4×C73—21no—
671C2×C4×C73—21no—
672C2×C4×C73—21no—
673C2×C4×C73—21no—
674C2×C4×C73—21no—
675C2×C4×C73—21no—
676C2×C4×C73—21no—
677C2×C4×C73—21no—
678C2×C4×C73—21no—
679C2×C4×C73—28no—
680C2×C4×C73—28no—
681C2×C4×C73—28no—
682C2×C4×C73—21no—
683C2×C4×C73—21no—
684C2×C4×C73—21no—
685C2×C4×C73—21no—
686C2×C4×C73—21no—
687C2×C4×C73—21no—
688C2×C4×C73—21no—
689C2×C4×C73—21no—
690C2×C4×C73—21no—
691C2×C4×C73—21no—
692C2×C4×C73—21no—
693C2×C4×C73—21no—
694C2×C4×C73—44no—
695C2×C4×C73—44no—
696C2×C4×C73—44no—
697C2×C4×C73—44no—
698C2×C4×C73—44no—
699C2×C4×C73C22×D412yes—
700C2×C4×C73C22×D412yes—
701C2×C4×C73C22×D412yes—
702C2×C4×C73C22×D412yes—
703C2×C4×C73C22×D412yes—
704C2×C4×C73C2×#4112yes—
705C2×C4×C73C2×#4112yes—
706C2×C4×C73H(5,𝔽2)12yes—
707C22⋊D73—44no—
708C22⋊D73—44no—
709C22⋊D73—44no—
710C22⋊D73—44no—
711C22⋊D73—44no—
712C2×Dic73—21no—
713C2×Dic73—21no—
714C2×Dic73—21no—
715C2×Dic73—21no—
716C2×Dic73—21no—
717C2×Dic73—21no—
718C2×Dic73—21no—
719C2×Dic73—21no—
720C2×Dic73—21no—
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—44no—
752C2×Dic73—44no—
753C2×Dic73—44no—
754C2×Dic73—44no—
755C2×Dic73—44no—
756C2×Dic73—44no—
757C2×Dic73C2×#4112yes—
758C2×Dic73C2×#4112yes—
759C2×Dic73C2×#4112yes—
760C2×Dic73C2×#4112yes—
761C2×Dic73C2×#4112yes—
762C2×Dic73C2×#4112yes—
763C4×D73—44no—
764Dic146—44no—
765C22×C73—22no—
766C22×C73—22no—
767C22×C73—22no—
768C22×C73—22no—
769C22×C73—22no—
770C22×C73—22no—
771C22×C73—22no—
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—416no—
781C22×C73—41no—
782C22×C73—41no—
783C22×C73—41no—
784C22×C73—41no—
785C22×C73—41no—
786C22×C73—41no—
787C22×C73—41no—
788C22×C73—41no—
789C22×C73—41no—
790C22×C73—41no—
791C22×C73—41no—
792C22×C73—41no—
793C22×C73—41no—
794C22×C73—41no—
795C22×C73—41no—
796C22×C73—41no—
797C22×C73—41no—
798C22×C73—41no—
799C22×C73—41no—
800C22×C73#53214yes—
801C22×C73C23×D411yescharacteristic
802C22×C73C22×#4111yescharacteristic
803C22×C73C22×#4111yescharacteristic
804C22×C73C22×#4111yescharacteristic
805C22×C73C22×#4111yescharacteristic
806C22×C73C2×H(5,𝔽2)11yescharacteristic
807C22×C73#58511yescharacteristic
808C2×D73—41no—
809C2×D73—41no—
810C2×D73—41no—
811C2×D73—41no—
812C2×D73—41no—
813C2×D73—41no—
814C2×D73—41no—
815C4×C73—22no—
816C4×C73—22no—
817C4×C73—22no—
818C4×C73—22no—
819C4×C73—22no—
820C4×C73—41no—
821C4×C73—41no—
822C4×C73—41no—
823C4×C73—41no—
824C4×C73#54614yes—
825Dic73—22no—
826Dic73—22no—
827Dic73—22no—
828Dic73—22no—
829Dic73—22no—
830Dic73—22no—
831Dic73—41no—
832Dic73—41no—
833Dic73—41no—
834Dic73—41no—
835Dic73—41no—
836Dic73—41no—
837Dic73—41no—
838Dic73—41no—
839Dic73—41no—
840#34829—731nomaximal, Sylow
841C2×C73—24no—
842C2×C73—42no—
843C2×C73—42no—
844C2×C73—42no—
845C2×C73—81no—
846C2×C73C2×#53211yescharacteristic
847C2×C73#344411yescharacteristic
848C2×C73#345911yescharacteristic
849C2×C73C2×#54611yescharacteristic
850C2×C73D4×#4111yescharacteristic
851C2×C73#347511yescharacteristic
852C2×C73#348111yescharacteristic
853D73—81no—
854C2×#529—731no—
855C2×#525D7311yescharacteristic, complemented
856#2560—731no—
857#2559—731no—
858#2558—731no—
859#2557—731no—
860#2556—731no—
861#2555—731no—
862#2554—731no—
863#2553—731no—
864#2549—731no—
865#2543—731no—
866#2539—731no—
867#2534—731no—
868#2488—731no—
869#2472—731no—
870#2425—731no—
871#2424—731no—
872#2396—731no—
873#2395—731no—
874#2392—731no—
875#2388—731no—
876C4×#124—731no—
877C4×#123—731no—
878C4×#121—731no—
879C4×#121—731no—
880C4×#120—731no—
881#2297—731no—
882#2293—731no—
883C42×D4—731no—
884C2×C4×C22⋊C4—731no—
885C73#3482911yescharacteristic, complemented, Sylow
886C22×#41C2×D7311yescharacteristic
887C24×C4C2×D7311yescharacteristic
888#529—1468no—
889C2×#126—731no—
890C2×#126—731no—
891C2×#125—731no—
892C2×#124—731no—
893C2×#124—731no—
894#525—28no—
895C2×#123—731no—
896C2×#123—731no—
897C2×#123—731no—
898C2×#123C2×D7311yescharacteristic
899C2×#123C2×D7311yescharacteristic
900C2×C22⋊Q8—731no—
901C2×C22⋊Q8C2×D7311yescharacteristic
902C2×C22⋊Q8C2×D7311yescharacteristic
903C2×#121—731no—
904C2×#121—731no—
905C2×#121—731no—
906C2×#121C2×D7311yescharacteristic
907C2×#121C2×D7311yescharacteristic
908C2×#120—731no—
909C2×#120C2×D7311yescharacteristic
910C2×#120C2×D7311yescharacteristic
911C2×C4×Q8—731no—
912C2×C4×D4—731no—
913C2×C4×D4—731no—
914C2×C4×D4—731no—
915C2×C4×D4—731no—
916C2×C4×D4—731no—
917C2×C4×D4—731no—
918C2×C4×D4—731no—
919C2×C4×D4C2×D7311yescharacteristic
920C2×C4×D4C2×D7311yescharacteristic
921C2×C4×D4C2×D7311yescharacteristic
922C2×C4×D4C2×D7311yescharacteristic
923C2×#117—731no—
924C2×#117—731no—
925C2×#117C2×D7311yescharacteristic
926C22×C22⋊C4—731no—
927C22×C22⋊C4—731no—
928C22×C42—731no—
929C22×C42—731no—
930C22×C42—731no—
931#400—731no—
932#400—731no—
933#399—731no—
934#399—731no—
935#398—731no—
936#398—731no—
937#398—731no—
938#398—731no—
939#397—731no—
940#397—731no—
941#397—731no—
942#397—731no—
943#396—731no—
944#396—731no—
945#396—731no—
946#396—731no—
947#395—731no—
948#395—731no—
949#394—731no—
950#394—731no—
951#394—731no—
952#394—731no—
953#394—731no—
954#394—731no—
955#394—731no—
956#394—731no—
957#393—731no—
958#393—731no—
959#392—731no—
960#392—731no—
961#392—731no—
962#392—731no—
963#391—731no—
964#391—731no—
965#391—731no—
966#390—731no—
967#390—731no—
968#390—731no—
969#390—731no—
970#390—731no—
971#390—731no—
972#390—731no—
973#389—731no—
974#389—731no—
975#389—731no—
976#389—731no—
977#388—731no—
978#388—731no—
979#388—731no—
980#388—731no—
981#388—731no—
982#388—731no—
983#388—731no—
984#388—731no—
985#388—731no—
986#388—731no—
987#388—731no—
988#388—731no—
989#388—731no—
990#388—731no—
991#387—731no—
992#387—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#386—731no—
1003#386—731no—
1004#386—731no—
1005#385—731no—
1006#385—731no—
1007#385—731no—
1008#385—731no—
1009#382—731no—
1010#381—731no—
1011#380—731no—
1012#380—731no—
1013#379—731no—
1014C4×C4⋊C4—731no—
1015C4×C4⋊C4—731no—
1016C4×C4⋊C4—731no—
1017C4×C4⋊C4—731no—
1018C4×C4⋊C4—731no—
1019C4×C4⋊C4—731no—
1020C4×C22⋊C4—731no—
1021C4×C22⋊C4—731no—
1022C4×C22⋊C4—731no—
1023C4×C22⋊C4—731no—
1024C4×C22⋊C4—731no—
1025C4×C22⋊C4—731no—
1026C4×C22⋊C4—731no—
1027C4×C22⋊C4—731no—
1028C4×C22⋊C4—731no—
1029C4×C22⋊C4—731no—
1030C4×C22⋊C4—731no—
1031C4×C22⋊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—
1040C2×#95—731no—
1041C2×#95—731no—
1042C43—731no—
1043C25C22×D7311yescharacteristic
1044C2×#41—24no—
1045C2×#41—24no—
1046C2×#41—42no—
1047C22×Q8—731no—
1048C22×Q8C22×D7311yescharacteristic
1049C22×D4—731no—
1050C22×D4—731no—
1051C22×D4—731no—
1052C22×D4—731no—
1053C22×D4—731no—
1054C22×D4C22×D7311yescharacteristic
1055C22×D4C22×D7311yescharacteristic
1056C22×D4C22×D7311yescharacteristic
1057C22×D4C22×D7311yescharacteristic
1058C22×D4C22×D7311yescharacteristic
1059C22×D4C22×D7311yescharacteristic
1060C22×D4C22×D7311yescharacteristic
1061C23×C4—24no—
1062C23×C4—24no—
1063C23×C4—42no—
1064C23×C4—731no—
1065C23×C4—731no—
1066C23×C4—731no—
1067C23×C4—731no—
1068C23×C4—731no—
1069C23×C4—731no—
1070C23×C4—731no—
1071C23×C4C22×D7311yescharacteristic
1072C23×C4C22×D7311yescharacteristic
1073C23×C4C22×D7311yescharacteristic
1074C23×C4C22×D7311yescharacteristic
1075C23×C4C22×D7311yescharacteristic
1076C23×C4C22×D7311yescharacteristic
1077C23×C4C22×D7311yescharacteristic
1078C23×C4C22×D7311yescharacteristic
1079#126—1464no—
1080#126—1464no—
1081#125—1464no—
1082#124—1464no—
1083#124—1464no—
1084#123—24no—
1085#123—24no—
1086#123—1464no—
1087#123—1464no—
1088#123—1464no—
1089C22⋊Q8—24no—
1090C22⋊Q8—24no—
1091C22⋊Q8—1464no—
1092#121—24no—
1093#121—24no—
1094#121—1464no—
1095#121—1464no—
1096#121—1464no—
1097#120—24no—
1098#120—24no—
1099#120—1464no—
1100C4×Q8—1464no—
1101C4×D4—24no—
1102C4×D4—24no—
1103C4×D4—24no—
1104C4×D4—2922no—
1105C4×D4—2922no—
1106C4×D4—1464no—
1107C4×D4—1464no—
1108C4×D4—1464no—
1109C4×D4—1464no—
1110C4×D4—1464no—
1111C4×D4C22⋊D7318yescomplemented
1112#117—24no—
1113#117—1464no—
1114#117—1464no—
1115C2×C4⋊C4—731no—
1116C2×C4⋊C4—731no—
1117C2×C4⋊C4—731no—
1118C2×C4⋊C4—731no—
1119C2×C4⋊C4—731no—
1120C2×C4⋊C4—731no—
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⋊C4C22×D7311yescharacteristic
1136C2×C4⋊C4C22×D7311yescharacteristic
1137C2×C4⋊C4C22×D7311yescharacteristic
1138C2×C4⋊C4C22×D7311yescharacteristic
1139C2×C4⋊C4C22×D7311yescharacteristic
1140C2×C4⋊C4C22×D7311yescharacteristic
1141C2×C22⋊C4—731no—
1142C2×C22⋊C4—731no—
1143C2×C22⋊C4—731no—
1144C2×C22⋊C4—731no—
1145C2×C22⋊C4—731no—
1146C2×C22⋊C4—731no—
1147C2×C22⋊C4—731no—
1148C2×C22⋊C4—731no—
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—1464no—
1180C2×C22⋊C4—1464no—
1181C2×C22⋊C4C22×D7311yescharacteristic
1182C2×C22⋊C4C22×D7311yescharacteristic
1183C2×C22⋊C4C22×D7311yescharacteristic
1184C2×C22⋊C4C22×D7311yescharacteristic
1185C2×C22⋊C4C22×D7311yescharacteristic
1186C2×C22⋊C4C22×D7311yescharacteristic
1187C2×C22⋊C4C22×D7311yescharacteristic
1188C2×C22⋊C4C22×D7311yescharacteristic
1189C2×C22⋊C4C22×D7311yescharacteristic
1190C2×C22⋊C4C22×D7311yescharacteristic
1191C2×C42—2922no—
1192C2×C42—2922no—
1193C2×C42—731no—
1194C2×C42—731no—
1195C2×C42—731no—
1196C2×C42—731no—
1197C2×C42—731no—
1198C2×C42—731no—
1199C2×C42—731no—
1200C2×C42—731no—
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—1464no—
1211C2×C42C22×D7311yescharacteristic
1212C2×C42C22×D7311yescharacteristic
1213#95—731no—
1214#95—731no—
1215#95—731no—
1216#95—731no—
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—
1245C24—22no—
1246C24—22no—
1247C24—22no—
1248C24—22no—
1249C24—22no—
1250C24—41no—
1251C24—41no—
1252C24—731no—
1253C24C23×D7311yescharacteristic
1254C24C23×D7311yescharacteristic
1255C24C23×D7311yescharacteristic
1256C24C23×D7311yescharacteristic
1257C24C23×D7311yescharacteristic
1258#41—416no—
1259C2×Q8—22no—
1260C2×Q8—22no—
1261C2×Q8—41no—
1262C2×Q8—2921no—
1263C2×Q8—1462no—
1264C2×Q8—1462no—
1265C2×D4—22no—
1266C2×D4—22no—
1267C2×D4—22no—
1268C2×D4—22no—
1269C2×D4—22no—
1270C2×D4—22no—
1271C2×D4—22no—
1272C2×D4—22no—
1273C2×D4—22no—
1274C2×D4—22no—
1275C2×D4—22no—
1276C2×D4—22no—
1277C2×D4—22no—
1278C2×D4—22no—
1279C2×D4—22no—
1280C2×D4—41no—
1281C2×D4—41no—
1282C2×D4—41no—
1283C2×D4—41no—
1284C2×D4—41no—
1285C2×D4—2921no—
1286C2×D4—2921no—
1287C2×D4—2921no—
1288C2×D4—2921no—
1289C2×D4—2921no—
1290C2×D4—1462no—
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×D4C2×C22⋊D7314yes—
1301C22×C4—22no—
1302C22×C4—22no—
1303C22×C4—22no—
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—41no—
1320C22×C4—41no—
1321C22×C4—41no—
1322C22×C4—416no—
1323C22×C4—2921no—
1324C22×C4—2921no—
1325C22×C4—2921no—
1326C22×C4—2921no—
1327C22×C4—2921no—
1328C22×C4—2921no—
1329C22×C4—2921no—
1330C22×C4—734no—
1331C22×C4—731no—
1332C22×C4—731no—
1333C22×C4—731no—
1334C22×C4—731no—
1335C22×C4—731no—
1336C22×C4—731no—
1337C22×C4—731no—
1338C22×C4—731no—
1339C22×C4—731no—
1340C22×C4—731no—
1341C22×C4—731no—
1342C22×C4—731no—
1343C22×C4—731no—
1344C22×C4—731no—
1345C22×C4—731no—
1346C22×C4—1462no—
1347C22×C4—1462no—
1348C22×C4—1462no—
1349C22×C4—1462no—
1350C22×C4—1462no—
1351C22×C4—1462no—
1352C22×C4—1462no—
1353C22×C4—1462no—
1354C22×C4—1462no—
1355C22×C4—1462no—
1356C22×C4—1462no—
1357C22×C4—1462no—
1358C22×C4—1462no—
1359C22×C4C2×C22⋊D7314yes—
1360C22×C4C2×C22⋊D7314yes—
1361C22×C4#1192402714yes—
1362C22×C4C23×D7311yescharacteristic
1363C22×C4C23×D7311yescharacteristic
1364C22×C4C23×D7311yescharacteristic
1365C22×C4C23×D7311yescharacteristic
1366C22×C4C23×D7311yescharacteristic
1367C22×C4C23×D7311yescharacteristic
1368C22×C4C23×D7311yescharacteristic
1369C22×C4C23×D7311yescharacteristic
1370C22×C4C23×D7311yescharacteristic
1371C22×C4C23×D7311yescharacteristic
1372C4⋊C4—22no—
1373C4⋊C4—22no—
1374C4⋊C4—22no—
1375C4⋊C4—22no—
1376C4⋊C4—22no—
1377C4⋊C4—2921no—
1378C4⋊C4—2921no—
1379C4⋊C4—2921no—
1380C4⋊C4—2921no—
1381C4⋊C4—1462no—
1382C4⋊C4—1462no—
1383C4⋊C4—1462no—
1384C4⋊C4—1462no—
1385C4⋊C4—1462no—
1386C4⋊C4—1462no—
1387C4⋊C4—1462no—
1388C4⋊C4—1462no—
1389C4⋊C4—1462no—
1390C4⋊C4—1462no—
1391C4⋊C4—1462no—
1392C4⋊C4—1462no—
1393C4⋊C4—1462no—
1394C4⋊C4—1462no—
1395C4⋊C4—1462no—
1396C4⋊C4—1462no—
1397C4⋊C4C2×C22⋊D7314yes—
1398C22⋊C4—22no—
1399C22⋊C4—22no—
1400C22⋊C4—22no—
1401C22⋊C4—22no—
1402C22⋊C4—22no—
1403C22⋊C4—22no—
1404C22⋊C4—22no—
1405C22⋊C4—22no—
1406C22⋊C4—2921no—
1407C22⋊C4—2921no—
1408C22⋊C4—2921no—
1409C22⋊C4—2921no—
1410C22⋊C4—2921no—
1411C22⋊C4—2921no—
1412C22⋊C4—734no—
1413C22⋊C4—734no—
1414C22⋊C4—1462no—
1415C22⋊C4—1462no—
1416C22⋊C4—1462no—
1417C22⋊C4—1462no—
1418C22⋊C4—1462no—
1419C22⋊C4—1462no—
1420C22⋊C4—1462no—
1421C22⋊C4—1462no—
1422C22⋊C4—1462no—
1423C22⋊C4—1462no—
1424C22⋊C4—1462no—
1425C22⋊C4—1462no—
1426C22⋊C4—1462no—
1427C22⋊C4—1462no—
1428C22⋊C4—1462no—
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⋊C4C2×C22⋊D7314yes—
1445C22⋊C4C2×C22⋊D7314yes—
1446C42—22no—
1447C42—2921no—
1448C42—2921no—
1449C42—2921no—
1450C42—2921no—
1451C42—2921no—
1452C42—1462no—
1453C42—1462no—
1454C42—1462no—
1455C42—1462no—
1456C42—1462no—
1457C42—1462no—
1458C42—1462no—
1459C42—1462no—
1460C42—1462no—
1461C42—1462no—
1462C42—1462no—
1463C42—1462no—
1464C42C2×C22⋊D7314yes—
1465C23—21no—
1466C23—21no—
1467C23—21no—
1468C23—21no—
1469C23—28no—
1470C23—21no—
1471C23—21no—
1472C23—21no—
1473C23—21no—
1474C23—21no—
1475C23—21no—
1476C23—21no—
1477C23—21no—
1478C23—21no—
1479C23—21no—
1480C23—21no—
1481C23—21no—
1482C23—21no—
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—44no—
1496C23—44no—
1497C23—44no—
1498C23—44no—
1499C23—44no—
1500C23—44no—
1501C23—1461no—
1502C23—1461no—
1503C23—1461no—
1504C23—1461no—
1505C23—1461no—
1506C23—1461no—
1507C23—1461no—
1508C23C22×C22⋊D7312yes—
1509C23C22×C22⋊D7312yes—
1510C23#41×D7312yes—
1511C23#41×D7312yes—
1512C23#41×D7312yes—
1513C23C2×#1192402712yes—
1514C23C24×D7311yescharacteristic
1515Q8—44no—
1516Q8—2924no—
1517D4—28no—
1518D4—44no—
1519D4—44no—
1520D4—44no—
1521D4—44no—
1522D4—44no—
1523D4—44no—
1524D4—2924no—
1525D4—2924no—
1526D4—2924no—
1527D4—2924no—
1528D4—2924no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—21no—
1538C2×C4—21no—
1539C2×C4—28no—
1540C2×C4—28no—
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—44no—
1555C2×C4—44no—
1556C2×C4—44no—
1557C2×C4—44no—
1558C2×C4—44no—
1559C2×C4—2924no—
1560C2×C4—2924no—
1561C2×C4—2924no—
1562C2×C4—2924no—
1563C2×C4—2924no—
1564C2×C4—2924no—
1565C2×C4—2924no—
1566C2×C4—732no—
1567C2×C4—732no—
1568C2×C4—732no—
1569C2×C4—732no—
1570C2×C4—732no—
1571C2×C4—732no—
1572C2×C4—1461no—
1573C2×C4—1461no—
1574C2×C4—1461no—
1575C2×C4—1461no—
1576C2×C4—1461no—
1577C2×C4—1461no—
1578C2×C4—1461no—
1579C2×C4—1461no—
1580C2×C4—1461no—
1581C2×C4—1461no—
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×C4C22×C22⋊D7312yes—
1612C2×C4C22×C22⋊D7312yes—
1613C2×C4C22×C22⋊D7312yes—
1614C2×C4C22×C22⋊D7312yes—
1615C2×C4C22×C22⋊D7312yes—
1616C2×C4C2×#1192402712yes—
1617C2×C4C2×#1192402712yes—
1618C2×C4#1455663612yes—
1619C22—22no—
1620C22—22no—
1621C22—22no—
1622C22—22no—
1623C22—22no—
1624C22—22no—
1625C22—22no—
1626C22—22no—
1627C22—22no—
1628C22—22no—
1629C22—22no—
1630C22—22no—
1631C22—22no—
1632C22—22no—
1633C22—22no—
1634C22—416no—
1635C22—41no—
1636C22—41no—
1637C22—41no—
1638C22—41no—
1639C22—41no—
1640C22—41no—
1641C22—41no—
1642C22—41no—
1643C22—41no—
1644C22—41no—
1645C22—41no—
1646C22—41no—
1647C22—41no—
1648C22—41no—
1649C22—41no—
1650C22—41no—
1651C22—41no—
1652C22—41no—
1653C22—41no—
1654C22—2921no—
1655C22—2921no—
1656C22—2921no—
1657C22—2921no—
1658C22—2921no—
1659C22—2921no—
1660C22—2921no—
1661C22#1798913314yes—
1662C22C23×C22⋊D7311yescharacteristic
1663C22C2×#41×D7311yescharacteristic
1664C22C2×#41×D7311yescharacteristic
1665C22C2×#41×D7311yescharacteristic
1666C22C22×#1192402711yescharacteristic
1667C22C2×#1455663611yescharacteristic
1668C22#1798942311yescharacteristic
1669C4—22no—
1670C4—22no—
1671C4—22no—
1672C4—22no—
1673C4—22no—
1674C4—41no—
1675C4—41no—
1676C4—41no—
1677C4—41no—
1678C4—2921no—
1679C4—2921no—
1680C4—2921no—
1681C4—2921no—
1682C4—2921no—
1683C4—2921no—
1684C4—2921no—
1685C4—2921no—
1686C4—2921no—
1687C4—1462no—
1688C4—1462no—
1689C4—1462no—
1690C4—1462no—
1691C4—1462no—
1692C4—1462no—
1693C4#1798923114yes—
1694C2—24no—
1695C2—42no—
1696C2—42no—
1697C2—42no—
1698C2—81no—
1699C2—5841no—
1700C2C2×#1798913311yescharacteristic
1701C2#2262322311yescharacteristic
1702C2#2262333811yescharacteristic
1703C2C2×#1798923111yescharacteristic
1704C2#41×C22⋊D7311yescharacteristic
1705C2#2262349111yescharacteristic
1706C2#2262353311yescharacteristic
subgroupG/H
centerC22×C4C23×D73
commutator, socle, cosocleC23×C73C25
FrattiniC23C24×D73
FittingC2×#525×C73C2
hypercenterC2×#525D73
hypocenterC73#34829
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#17989117C2semidirect
2. #22615071C2semidirect
3. #22615056C2semidirect
4. #22615041C2semidirect
5. #22615026C2semidirect
6. #22615013C2semidirect
7. #22615004C2semidirect
8. #22614987C2semidirect
9. #22614972C2semidirect
10. #22614939C2semidirect
11. #22614889C2semidirect
12. #22614859C2semidirect
13. #22614818C2semidirect
14. #22614263C2semidirect
15. #22614056C2semidirect
16. #22613488C2semidirect
17. #22613471C2semidirect
18. #22613199C2semidirect
19. #22613190C2semidirect
20. #22613169C2semidirect
21. #22613144C2semidirect
22. C4×#14556578C2semidirect
23. C4×#14556572C2semidirect
24. C4×#14556563C2semidirect
25. C4×#14556563C2semidirect
26. C4×#14556560C2semidirect
27. #22612422C2semidirect
28. #22612390C2semidirect
29. C4×D4×Dic73C2semidirect
30. C2×C4×C22⋊Dic73C2semidirect
31. C2×#525×C73C2semidirect
33. C2×#14556586C22semidirect
34. C2×#14556584C22semidirect
35. C2×#14556581C22semidirect
37. C2×#14556577C22semidirect
46. C2×C4×Dic146C22semidirect
52. C2×C4×C22⋊D73C22semidirect
53. C2×C4×C22⋊D73C22semidirect
54. C2×#14556550C22semidirect
55. C2×#14556548C22semidirect
60. C22×C4×Dic73C22semidirect
61. #17988526C22semidirect
62. #17988526C22semidirect
65. #17988520C22semidirect
66. #17988520C22semidirect
67. #17988518C22semidirect
68. #17988517C22semidirect
69. #17988515C22semidirect
70. #17988515C22semidirect
71. #17988513C22semidirect
76. #17988510C22semidirect
77. #17988507C22semidirect
78. #17988506C22semidirect
80. #17988503C22semidirect
86. #17988501C22semidirect
88. #17988498C22semidirect
92. #17988495C22semidirect
93. #17988494C22semidirect
94. #17988494C22semidirect
95. #17988492C22semidirect
102. #17988487C22semidirect
103. #17988482C22semidirect
104. #17988482C22semidirect
105. #17988482C22semidirect
106. #17988482C22semidirect
112. #17988481C22semidirect
113. #17988481C22semidirect
114. #17988481C22semidirect
115. #17988477C22semidirect
116. #17988477C22semidirect
117. #17988477C22semidirect
118. #17988477C22semidirect
119. #17988475C22semidirect
120. #17988475C22semidirect
121. #17988468C22semidirect
122. #17988468C22semidirect
128. #17988467C22semidirect
129. #17988467C22semidirect
134. #17988464C22semidirect
139. #17988452C22semidirect
142. #17988445C22semidirect
144. C4⋊C4×Dic73C22semidirect
145. C4⋊C4×Dic73C22semidirect
146. C4×#11924007C22semidirect
147. C4×#11924007C22semidirect
148. C4×#11924007C22semidirect
149. C4×C4⋊Dic73C22semidirect
152. C22⋊C4×Dic73C22semidirect
153. C22⋊C4×Dic73C22semidirect
154. C4×#11924005C22semidirect
166. C4×C22⋊Dic73C22semidirect
167. C4×C22⋊Dic73C22semidirect
168. C4×C22⋊Dic73C22semidirect
169. C4×C22⋊Dic73C22semidirect
172. C42×Dic73C22semidirect
371. C4×D4×C73D4semidirect
427. C22×Dic73#41semidirect
493. C22⋊Dic73#41semidirect
494. C22⋊Dic73#41semidirect
855. C2×#525D73semidirect
885. C73#34829semidirect
1111. C4×D4C22⋊D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179891172
#226150712
#226150562
#226150412
#226150262
#226150132
#226150042
#226149872
#226149722
#226149392
#226148892
#226148592
#226148182
#226142632
#226140562
#226134882
#226134712
#226131992
#226131902
#226131692
#226131442
C4×#145565782
C4×#145565722
C4×#145565632
C4×#145565602
#226124222
#226123902
C4×D4×Dic732
C2×C4×C22⋊Dic732
C2×#525×C732
#3482973