Finite Group Databasebeta

← #33246616

Subgroups — #33246616

Order 18688.

2726 conjugacy classes of subgroups.

The subgroup lattice has 1618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989093C211yesmaximal, characteristic
2#22613012C211yesmaximal, characteristic, complemented
3#22613009C211yesmaximal, characteristic, complemented
4#22612979C211yesmaximal, characteristic, complemented
5#22612976C211yesmaximal, characteristic, complemented
6#22612915C211yesmaximal, characteristic, complemented
7#22612910C211yesmaximal, characteristic, complemented
8#22612910C211yesmaximal, characteristic, complemented
9#22612903C211yesmaximal, characteristic, complemented
10#22612901C211yesmaximal, characteristic, complemented
11#22612869C211yesmaximal, characteristic, complemented
12#22612866C211yesmaximal, characteristic, complemented
13#22612789C211yesmaximal, characteristic, complemented
14#22612785C211yesmaximal, characteristic, complemented
15#22612757C211yesmaximal, characteristic, complemented
16#22612756C211yesmaximal, characteristic, complemented
17#22612697C211yesmaximal, characteristic, complemented
18#22612690C211yesmaximal, characteristic, complemented
19#22612688C211yesmaximal, characteristic, complemented
20#22612681C211yesmaximal, characteristic, complemented
21#22612559C211yesmaximal, characteristic, complemented
22#22612557C211yesmaximal, characteristic, complemented
23#22612456C211yesmaximal, characteristic, complemented
24C4×#14556575C211yesmaximal, characteristic, complemented
25#22612450C211yesmaximal, characteristic, complemented
26C4×#14556572C211yesmaximal, characteristic, complemented
27C2×#17988448C211yesmaximal, characteristic, complemented
28#22612292C211yesmaximal, characteristic, complemented
29#22612290C211yesmaximal, characteristic, complemented
30C2×C22⋊C4×Dic73C211yesmaximal, characteristic, complemented
31C73×#2358C211yesmaximal, characteristic, complemented
32C22×#11924027C2211yescharacteristic
33C24×Dic73C2211yescharacteristic
34#17989093C4116yescomplemented
35C2×#14556575C2211yescharacteristic
36C2×#14556572C2211yescharacteristic
37C2×#14556568C2211yescharacteristic
38C2×#14556568C2211yescharacteristic
39C2×#14556563C2211yescharacteristic
40C2×#14556563C2211yescharacteristic
41C2×#14556560C2211yescharacteristic
42C2×D4×Dic73C2211yescharacteristic
43C2×D4×Dic73C2211yescharacteristic
44C2×D4×Dic73C2211yescharacteristic
45C2×D4×Dic73C2211yescharacteristic
46C2×C4×C22⋊D73C2211yescharacteristic
47C2×C4×C22⋊D73C2211yescharacteristic
48C2×#14556551C2211yescharacteristic
49C2×#14556551C2211yescharacteristic
50C2×#14556551C2211yescharacteristic
51C2×#14556551C2211yescharacteristic
52C2×#14556547C2211yescharacteristic
53C22×C22⋊Dic73C2211yescharacteristic
54C22×C22⋊Dic73C2211yescharacteristic
55C22×C4×Dic73C2211yescharacteristic
56C22×C4×Dic73C2211yescharacteristic
57#17988493C2211yescharacteristic, complemented
58#17988492C2211yescharacteristic, complemented
59#17988491C2211yescharacteristic, complemented
60#17988491C2211yescharacteristic, complemented
61#17988490C2211yescharacteristic
62#17988487C2211yescharacteristic
63#17988487C2211yescharacteristic
64#17988481C2211yescharacteristic
65#17988481C2211yescharacteristic
66#17988481C2211yescharacteristic, complemented
67#17988481C2211yescharacteristic, complemented
68#17988480C2211yescharacteristic
69#17988480C2211yescharacteristic
70#17988479C2211yescharacteristic, complemented
71#17988479C2211yescharacteristic, complemented
72#17988477C2211yescharacteristic, complemented
73#17988477C2211yescharacteristic, complemented
74#17988475C2211yescharacteristic
75#17988475C2211yescharacteristic
76#17988475C2211yescharacteristic, complemented
77#17988475C2211yescharacteristic, complemented
78#17988474C2211yescharacteristic, complemented
79#17988474C2211yescharacteristic, complemented
80#17988474C2211yescharacteristic, complemented
81#17988474C2211yescharacteristic, complemented
82#17988472C2211yescharacteristic, complemented
83#17988472C2211yescharacteristic, complemented
84#17988471C2211yescharacteristic, complemented
85#17988471C2211yescharacteristic, complemented
86#17988470C2211yescharacteristic, complemented
87#17988470C2211yescharacteristic, complemented
88#17988469C2211yescharacteristic, complemented
89#17988469C2211yescharacteristic, complemented
90#17988468C2211yescharacteristic, complemented
91#17988468C2211yescharacteristic, complemented
92#17988468C2211yescharacteristic, complemented
93#17988468C2211yescharacteristic, complemented
94#17988467C2211yescharacteristic
95#17988467C2211yescharacteristic
96#17988467C2211yescharacteristic
97#17988466C2211yescharacteristic
98#17988466C2211yescharacteristic
99#17988466C2211yescharacteristic, complemented
100#17988464C2211yescharacteristic
101#17988464C2211yescharacteristic
102#17988464C2211yescharacteristic, complemented
103#17988463C2211yescharacteristic
104#17988463C2211yescharacteristic
105#17988463C2211yescharacteristic, complemented
106#17988463C2211yescharacteristic, complemented
107#17988462C2211yescharacteristic
108#17988462C2211yescharacteristic
109#17988460C2211yescharacteristic
110#17988460C2211yescharacteristic
111#17988459C2211yescharacteristic
112#17988459C2211yescharacteristic
113#17988454C2211yescharacteristic, complemented
114#17988454C2211yescharacteristic, complemented
115#17988452C2211yescharacteristic, complemented
116#17988451C2211yescharacteristic, complemented
117#17988449C2211yescharacteristic, complemented
118#17988448C2211yescharacteristic
119#17988448C2211yescharacteristic
120#17988448C2211yescharacteristic
121#17988448C2211yescharacteristic
122#17988448C2211yescharacteristic
123#17988448C2211yescharacteristic
124#17988448C2211yescharacteristic
125#17988448C2211yescharacteristic
126#17988448C2211yescharacteristic, complemented
127#17988445C2211yescharacteristic, complemented
128#17988444C2211yescharacteristic, complemented
129C4⋊C4×Dic73C2211yescharacteristic, complemented
130C4⋊C4×Dic73C2211yescharacteristic, complemented
131C4⋊C4×Dic73C2211yescharacteristic, complemented
132C4×#11924007C2211yescharacteristic, complemented
133C4×#11924007C2211yescharacteristic, complemented
134C4×#11924007C2211yescharacteristic, complemented
135C4×C4⋊Dic73C2211yescharacteristic, complemented
136C4×C4⋊Dic73C2211yescharacteristic, complemented
137#17988438C2211yescharacteristic, complemented
138#17988438C2211yescharacteristic, complemented
139C22⋊C4×Dic73C2211yescharacteristic
140C22⋊C4×Dic73C2211yescharacteristic
141C22⋊C4×Dic73C2211yescharacteristic
142C22⋊C4×Dic73C2211yescharacteristic
143C22⋊C4×Dic73C2211yescharacteristic
144C22⋊C4×Dic73C2211yescharacteristic
145C22⋊C4×Dic73C2211yescharacteristic
146C22⋊C4×Dic73C2211yescharacteristic
147C22⋊C4×Dic73C2211yescharacteristic
148C22⋊C4×Dic73C2211yescharacteristic
149C22⋊C4×Dic73C2211yescharacteristic
150C22⋊C4×Dic73C2211yescharacteristic
151C22⋊C4×Dic73C2211yescharacteristic, complemented
152C22⋊C4×Dic73C2211yescharacteristic, complemented
153C22⋊C4×Dic73C2211yescharacteristic, complemented
154C4×#11924005C2211yescharacteristic, complemented
155C4×#11924005C2211yescharacteristic, complemented
156C4×#11924005C2211yescharacteristic, complemented
157C4×C22⋊Dic73C2211yescharacteristic
158C4×C22⋊Dic73C2211yescharacteristic
159C4×C22⋊Dic73C2211yescharacteristic, complemented
160C4×C22⋊Dic73C2211yescharacteristic, complemented
161#17988434C2211yescharacteristic, complemented
162#17988434C2211yescharacteristic, complemented
163#17988433C2211yescharacteristic, complemented
164#17988432C2211yescharacteristic, complemented
165C2×#14556498C2211yescharacteristic
166C2×#14556498C2211yescharacteristic
167C2×#14556498C2211yescharacteristic
168C2×#14556498C2211yescharacteristic
169C2×#14556498C2211yescharacteristic
170C2×#14556498C2211yescharacteristic
171C2×#14556498C2211yescharacteristic, complemented
172#95×D73C2211yescharacteristic, complemented
173C2×#120×C73C2211yescharacteristic
174C2×C4×D4×C73C2211yescharacteristic
175C2×C4×D4×C73C2211yescharacteristic
176C22×C22⋊C4×C73C2211yescharacteristic
177C22×C22⋊C4×C73C2211yescharacteristic
178#390×C73C2211yescharacteristic
179#388×C73C2211yescharacteristic
180#388×C73C2211yescharacteristic
181#386×C73C2211yescharacteristic
182#386×C73C2211yescharacteristic
183#386×C73C2211yescharacteristic
184#385×C73C2211yescharacteristic
185#385×C73C2211yescharacteristic
186C4×C22⋊C4×C73C2211yescharacteristic
187C4×C22⋊C4×C73C2211yescharacteristic
188C2×#11924027—42no—
189C2×#11924027—42no—
190C2×#11924027C2×C418yescomplemented
191C22×Dic146C2311yescharacteristic
192C22×C22⋊D73C2311yescharacteristic
193C22×C22⋊D73C2311yescharacteristic
194C22×C22⋊D73C2311yescharacteristic
195C22×C22⋊D73C2311yescharacteristic
196C23×Dic73—42no—
197C23×Dic73—42no—
198C23×Dic73C2×C418yescomplemented
199C23×Dic73C2311yescharacteristic
200C23×Dic73C2311yescharacteristic
201C23×Dic73C2311yescharacteristic
202C23×Dic73C2311yescharacteristic
203C23×Dic73C2311yescharacteristic
204C23×Dic73C2311yescharacteristic
205C23×Dic73C2311yescharacteristic
206C23×Dic73C2311yescharacteristic
207C23×Dic73C2311yescharacteristic
208C23×Dic73C2311yescharacteristic
209C23×Dic73C2311yescharacteristic
210C23×Dic73C2311yescharacteristic
211C22×C4×D73C2311yescharacteristic
212C22×C4×D73C2311yescharacteristic
213C22×C4×D73C2311yescharacteristic
214#14556575C2×C418yescomplemented
215#14556572C2×C418yescomplemented
216#14556568C2×C418yescomplemented
217#14556568C2×C418yescomplemented
218#14556563C2×C418yescomplemented
219#14556563C2×C418yescomplemented
220#14556560C2×C418yescomplemented
221D4×Dic73—24no—
222D4×Dic73—42no—
223D4×Dic73C2×C418yescomplemented
224D4×Dic73C2×C418yescomplemented
225C4×C22⋊D73—24no—
226C4×C22⋊D73—42no—
227#14556551—24no—
228#14556551—42no—
229#14556551C2×C418yescomplemented
230#14556551C2×C418yescomplemented
231#14556547C2×C418yescomplemented
232C2×C4⋊Dic73C2311yescharacteristic
233C2×C4⋊Dic73C2311yescharacteristic
234C2×C4⋊Dic73C2311yescharacteristic
235C2×C4⋊Dic73C2311yescharacteristic
236C2×C4⋊Dic73C2311yescharacteristic
237C2×#11924007C2311yescharacteristic
238C2×#11924007C2311yescharacteristic
239C2×#11924007C2311yescharacteristic
240C2×#11924007C2311yescharacteristic
241C2×#11924007C2311yescharacteristic
242C2×#11924007C2311yescharacteristic
243C2×#11924007C2311yescharacteristic
244C2×#11924007C2311yescharacteristic
245C2×#11924007C2311yescharacteristic
246C2×#11924007C2311yescharacteristic
247C2×C22⋊Dic73—24no—
248C2×C22⋊Dic73—42no—
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×#11924005C2311yescharacteristic
266C2×#11924005C2311yescharacteristic
267C2×#11924005C2311yescharacteristic
268C2×#11924005C2311yescharacteristic
269C2×#11924005C2311yescharacteristic
270C2×#11924005C2311yescharacteristic
271C2×#11924005C2311yescharacteristic
272C2×#11924005C2311yescharacteristic
273C2×C4×Dic73—42no—
274C2×C4×Dic73—42no—
275C2×C4×Dic73C2311yescharacteristic
276C2×C4×Dic73C2311yescharacteristic
277C2×C4×Dic73C2311yescharacteristic
278C2×C4×Dic73C2311yescharacteristic
279C2×C4×Dic73C2311yescharacteristic
280C2×C4×Dic73C2311yescharacteristic
281C2×C4×Dic73C2311yescharacteristic
282C2×C4×Dic73C2311yescharacteristic
283C2×C4×Dic73C2311yescharacteristic
284C2×C4×Dic73C2311yescharacteristic
285C2×C4×Dic73C2311yescharacteristic
286C2×C4×Dic73C2311yescharacteristic
287C2×C4×Dic73C2311yescharacteristic
288C2×C4×Dic73C2311yescharacteristic
289C2×C4×Dic73C2311yescharacteristic
290C2×C4×Dic73C2311yescharacteristic
291C2×C4×Dic73C2311yescharacteristic
292C2×C4×Dic73C2311yescharacteristic
293C2×C4×Dic73C2311yescharacteristic
294#14556498C2311yescharacteristic
295#14556498C2311yescharacteristic
296#14556498C2311yescharacteristic
297#14556498C2311yescharacteristic
298#14556498C2311yescharacteristic
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
335#14556498C2311yescharacteristic
336C25×C73C2311yescharacteristic
337C22×D4×C73C2311yescharacteristic
338C22×D4×C73C2311yescharacteristic
339C22×D4×C73C2311yescharacteristic
340C23×C4×C73C2311yescharacteristic
341C23×C4×C73C2311yescharacteristic
342C23×C4×C73C2311yescharacteristic
343C23×C4×C73C2311yescharacteristic
344C23×C4×C73C2311yescharacteristic
345#120×C73C2×C418yescomplemented
346C4×D4×C73—24no—
347C4×D4×C73—42no—
348C2×C4⋊C4×C73C2311yescharacteristic
349C2×C4⋊C4×C73C2311yescharacteristic
350C2×C4⋊C4×C73C2311yescharacteristic
351C2×C22⋊C4×C73—24no—
352C2×C22⋊C4×C73—42no—
353C2×C22⋊C4×C73C2311yescharacteristic
354C2×C22⋊C4×C73C2311yescharacteristic
355C2×C22⋊C4×C73C2311yescharacteristic
356C2×C22⋊C4×C73C2311yescharacteristic
357C2×C22⋊C4×C73C2311yescharacteristic
358C2×C22⋊C4×C73C2311yescharacteristic
359C2×C22⋊C4×C73C2311yescharacteristic
360C2×C22⋊C4×C73C2311yescharacteristic
361C2×C22⋊C4×C73C2311yescharacteristic
362C2×C22⋊C4×C73C2311yescharacteristic
363C2×C22⋊C4×C73C2311yescharacteristic
364C2×C22⋊C4×C73C2311yescharacteristic
365C2×C22⋊C4×C73C2311yescharacteristic
366C2×C22⋊C4×C73C2311yescharacteristic
367C2×C42×C73C2311yescharacteristic
368C2×C42×C73C2311yescharacteristic
369C2×C42×C73C2311yescharacteristic
370#95×C73C2311yescharacteristic
371#95×C73C2311yescharacteristic
372#95×C73C2311yescharacteristic
373#95×C73C2311yescharacteristic
374#95×C73C2311yescharacteristic
375#95×C73C2311yescharacteristic
376C23×D73C2411yescharacteristic
377#11924027—416no—
378C2×Dic146—41no—
379C2×Dic146—41no—
380C2×Dic146C22×C414yes—
381C2×C22⋊D73—22no—
382C2×C22⋊D73—22no—
383C2×C22⋊D73—22no—
384C2×C22⋊D73—22no—
385C2×C22⋊D73—41no—
386C2×C22⋊D73—41no—
387C2×C22⋊D73—41no—
388C2×C22⋊D73—41no—
389C2×C22⋊D73C22×C414yes—
390C2×C22⋊D73C22×C414yes—
391C2×C22⋊D73C22×C414yes—
392C2×C22⋊D73C22×C414yes—
393C22×Dic73—22no—
394C22×Dic73—22no—
395C22×Dic73—22no—
396C22×Dic73—22no—
397C22×Dic73—22no—
398C22×Dic73—22no—
399C22×Dic73—22no—
400C22×Dic73—22no—
401C22×Dic73—22no—
402C22×Dic73—22no—
403C22×Dic73—22no—
404C22×Dic73—416no—
405C22×Dic73—41no—
406C22×Dic73—41no—
407C22×Dic73—41no—
408C22×Dic73—41no—
409C22×Dic73—41no—
410C22×Dic73—41no—
411C22×Dic73—41no—
412C22×Dic73—41no—
413C22×Dic73—41no—
414C22×Dic73—41no—
415C22×Dic73—41no—
416C22×Dic73—41no—
417C22×Dic73—41no—
418C22×Dic73—41no—
419C22×Dic73—41no—
420C22×Dic73—41no—
421C22×Dic73—41no—
422C22×Dic73—41no—
423C22×Dic73C22×C414yes—
424C22×Dic73C22×C414yes—
425C22×Dic73C22×C414yes—
426C22×Dic73C22×C414yes—
427C22×Dic73C22×C414yes—
428C22×Dic73C22×C414yes—
429C22×Dic73C22×C414yes—
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
443C22×Dic73C2411yescharacteristic
444C22×Dic73C2411yescharacteristic
445C2×C4×D73—22no—
446C2×C4×D73—22no—
447C2×C4×D73—41no—
448C2×C4×D73—41no—
449C2×C4×D73—41no—
450C2×C4×D73—41no—
451C2×C4×D73—41no—
452C2×C4×D73—41no—
453C2×C4×D73C22×C414yes—
454C4⋊Dic73—22no—
455C4⋊Dic73—41no—
456C4⋊Dic73—41no—
457C4⋊Dic73C22×C414yes—
458C4⋊Dic73C22×C414yes—
459#11924007—22no—
460#11924007—22no—
461#11924007—41no—
462#11924007—41no—
463#11924007—41no—
464#11924007—41no—
465#11924007C22×C414yes—
466#11924007C22×C414yes—
467#11924007C22×C414yes—
468#11924007C22×C414yes—
469C22⋊Dic73—22no—
470C22⋊Dic73—22no—
471C22⋊Dic73—22no—
472C22⋊Dic73—22no—
473C22⋊Dic73—22no—
474C22⋊Dic73—22no—
475C22⋊Dic73—41no—
476C22⋊Dic73—41no—
477C22⋊Dic73—41no—
478C22⋊Dic73—41no—
479C22⋊Dic73C22×C414yes—
480C22⋊Dic73C22×C414yes—
481C22⋊Dic73C22×C414yes—
482C22⋊Dic73C22×C414yes—
483C22⋊Dic73C22×C414yes—
484C22⋊Dic73#4114yescomplemented
485#11924005—22no—
486#11924005—22no—
487#11924005—41no—
488#11924005—41no—
489#11924005—41no—
490#11924005—41no—
491#11924005C22×C414yes—
492#11924005C22×C414yes—
493C4×Dic73—22no—
494C4×Dic73—22no—
495C4×Dic73—22no—
496C4×Dic73—41no—
497C4×Dic73—41no—
498C4×Dic73—41no—
499C4×Dic73—41no—
500C4×Dic73—41no—
501C4×Dic73—41no—
502C4×Dic73—41no—
503C4×Dic73—41no—
504C4×Dic73—41no—
505C4×Dic73—41no—
506C4×Dic73—41no—
507C4×Dic73—41no—
508C4×Dic73—41no—
509C4×Dic73—41no—
510C4×Dic73C22×C414yes—
511C4×Dic73C22×C414yes—
512C24×C73—22no—
513C24×C73—22no—
514C24×C73—22no—
515C24×C73—22no—
516C24×C73—41no—
517C24×C73—41no—
518C24×C73C22×C414yes—
519C24×C73C2411yescharacteristic
520C24×C73C2411yescharacteristic
521C24×C73C2411yescharacteristic
522C24×C73C2411yescharacteristic
523C2×D4×C73—22no—
524C2×D4×C73—22no—
525C2×D4×C73—22no—
526C2×D4×C73—22no—
527C2×D4×C73—41no—
528C2×D4×C73—41no—
529C2×D4×C73C22×C414yes—
530C2×D4×C73C22×C414yes—
531C2×D4×C73C22×C414yes—
532C22×C4×C73—22no—
533C22×C4×C73—22no—
534C22×C4×C73—22no—
535C22×C4×C73—22no—
536C22×C4×C73—22no—
537C22×C4×C73—22no—
538C22×C4×C73—22no—
539C22×C4×C73—41no—
540C22×C4×C73—41no—
541C22×C4×C73—41no—
542C22×C4×C73—41no—
543C22×C4×C73—41no—
544C22×C4×C73—41no—
545C22×C4×C73—41no—
546C22×C4×C73—41no—
547C22×C4×C73C2411yescharacteristic
548C22×C4×C73C2411yescharacteristic
549C22×C4×C73C2411yescharacteristic
550C22×C4×C73C2411yescharacteristic
551C22×C4×C73C2411yescharacteristic
552C22×C4×C73C2411yescharacteristic
553C22×C4×C73C2411yescharacteristic
554C22×C4×C73C2411yescharacteristic
555C22×C4×C73C2411yescharacteristic
556C22×C4×C73C2411yescharacteristic
557C22×C4×C73C2411yescharacteristic
558C4⋊C4×C73—22no—
559C4⋊C4×C73—41no—
560C4⋊C4×C73—41no—
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—41no—
568C22⋊C4×C73—41no—
569C22⋊C4×C73—41no—
570C22⋊C4×C73—41no—
571C22⋊C4×C73C22×C414yes—
572C22⋊C4×C73C22×C414yes—
573C22⋊C4×C73C22×C414yes—
574C22⋊C4×C73#4114yescomplemented
575C42×C73—22no—
576C42×C73—41no—
577C42×C73—41no—
578C23×C73—21no—
579C23×C73—21no—
580C23×C73—21no—
581C23×C73—21no—
582C23×C73—21no—
583C23×C73—21no—
584C23×C73—21no—
585C23×C73—21no—
586C23×C73—28no—
587C23×C73—28no—
588C23×C73—21no—
589C23×C73—21no—
590C23×C73—21no—
591C23×C73—21no—
592C23×C73—21no—
593C23×C73—21no—
594C23×C73—21no—
595C23×C73—21no—
596C23×C73—21no—
597C23×C73—21no—
598C23×C73—21no—
599C23×C73—21no—
600C23×C73—44no—
601C23×C73—44no—
602C23×C73—44no—
603C23×C73—44no—
604C23×C73—44no—
605C23×C73C23×C412yes—
606C23×C73C23×C412yes—
607C23×C73C23×C412yes—
608C23×C73C23×C412yes—
609C23×C73C2×#4112yes—
610C23×C73C2×#4112yes—
611C23×C73H(5,𝔽2)12yes—
612C23×C73H(5,𝔽2)12yes—
613C23×C73C2511yescharacteristic
614C22×D73—21no—
615C22×D73—21no—
616C22×D73—21no—
617C22×D73—21no—
618C22×D73—21no—
619C22×D73—21no—
620C22×D73C23×C412yes—
621D4×C73—28no—
622D4×C73—28no—
623D4×C73—44no—
624C2×C4×C73—21no—
625C2×C4×C73—21no—
626C2×C4×C73—21no—
627C2×C4×C73—21no—
628C2×C4×C73—21no—
629C2×C4×C73—21no—
630C2×C4×C73—21no—
631C2×C4×C73—21no—
632C2×C4×C73—21no—
633C2×C4×C73—21no—
634C2×C4×C73—21no—
635C2×C4×C73—21no—
636C2×C4×C73—21no—
637C2×C4×C73—21no—
638C2×C4×C73—21no—
639C2×C4×C73—21no—
640C2×C4×C73—21no—
641C2×C4×C73—21no—
642C2×C4×C73—21no—
643C2×C4×C73—21no—
644C2×C4×C73—21no—
645C2×C4×C73—21no—
646C2×C4×C73—21no—
647C2×C4×C73—21no—
648C2×C4×C73—21no—
649C2×C4×C73—21no—
650C2×C4×C73—21no—
651C2×C4×C73—21no—
652C2×C4×C73—44no—
653C2×C4×C73—44no—
654C2×C4×C73—82no—
655C2×C4×C73—82no—
656C2×C4×C73—82no—
657C2×C4×C73C23×C412yes—
658C2×C4×C73C23×C412yes—
659C2×C4×C73C23×C412yes—
660C2×C4×C73C2×#4112yes—
661C2×C4×C73C2×#4112yes—
662C22⋊D73—28no—
663C22⋊D73—28no—
664C22⋊D73—44no—
665C22⋊D73—44no—
666C2×Dic73—28no—
667C2×Dic73—28no—
668C2×Dic73—21no—
669C2×Dic73—21no—
670C2×Dic73—21no—
671C2×Dic73—21no—
672C2×Dic73—21no—
673C2×Dic73—21no—
674C2×Dic73—21no—
675C2×Dic73—21no—
676C2×Dic73—21no—
677C2×Dic73—21no—
678C2×Dic73—21no—
679C2×Dic73—21no—
680C2×Dic73—21no—
681C2×Dic73—21no—
682C2×Dic73—21no—
683C2×Dic73—21no—
684C2×Dic73—21no—
685C2×Dic73—21no—
686C2×Dic73—21no—
687C2×Dic73—21no—
688C2×Dic73—21no—
689C2×Dic73—21no—
690C2×Dic73—21no—
691C2×Dic73—21no—
692C2×Dic73—21no—
693C2×Dic73—21no—
694C2×Dic73—21no—
695C2×Dic73—21no—
696C2×Dic73—21no—
697C2×Dic73—21no—
698C2×Dic73—21no—
699C2×Dic73—21no—
700C2×Dic73—21no—
701C2×Dic73—21no—
702C2×Dic73—21no—
703C2×Dic73—21no—
704C2×Dic73—44no—
705C2×Dic73—44no—
706C2×Dic73—44no—
707C2×Dic73—44no—
708C2×Dic73—44no—
709C2×Dic73—44no—
710C2×Dic73—44no—
711C2×Dic73—82no—
712C2×Dic73—82no—
713C2×Dic73—82no—
714C2×Dic73C23×C412yes—
715C2×Dic73C23×C412yes—
716C2×Dic73C23×C412yes—
717C2×Dic73C23×C412yes—
718C2×Dic73C23×C412yes—
719C2×Dic73C23×C412yes—
720C2×Dic73C23×C412yes—
721C2×Dic73C2×#4112yes—
722C2×Dic73C2×#4112yes—
723C4×D73—44no—
724C4×D73—82no—
725C4×D73—82no—
726Dic146—44no—
727C22×C73—22no—
728C22×C73—22no—
729C22×C73—22no—
730C22×C73—22no—
731C22×C73—22no—
732C22×C73—22no—
733C22×C73—22no—
734C22×C73—22no—
735C22×C73—22no—
736C22×C73—22no—
737C22×C73—22no—
738C22×C73—22no—
739C22×C73—22no—
740C22×C73—22no—
741C22×C73—22no—
742C22×C73—22no—
743C22×C73—22no—
744C22×C73—22no—
745C22×C73—416no—
746C22×C73—41no—
747C22×C73—41no—
748C22×C73—41no—
749C22×C73—41no—
750C22×C73—41no—
751C22×C73—41no—
752C22×C73—41no—
753C22×C73—41no—
754C22×C73C4×#4114yes—
755C22×C73#51814yes—
756C22×C73C24×C411yescharacteristic
757C22×C73C22×#4111yescharacteristic
758C22×C73C22×#4111yescharacteristic
759C22×C73C2×H(5,𝔽2)11yescharacteristic
760C22×C73C2×H(5,𝔽2)11yescharacteristic
761C22×C73#58511yescharacteristic
762C22×C73#58511yescharacteristic
763C2×D73—22no—
764C2×D73—22no—
765C2×D73—22no—
766C2×D73—41no—
767C2×D73—41no—
768C2×D73—41no—
769C2×D73—41no—
770C4×C73—22no—
771C4×C73—22no—
772C4×C73—22no—
773C4×C73—22no—
774C4×C73—22no—
775C4×C73—41no—
776C4×C73—41no—
777C4×C73—41no—
778C4×C73—41no—
779C4×C73—41no—
780C4×C73—41no—
781Dic73—22no—
782Dic73—22no—
783Dic73—22no—
784Dic73—22no—
785Dic73—22no—
786Dic73—22no—
787Dic73—22no—
788Dic73—22no—
789Dic73—22no—
790Dic73—41no—
791Dic73—41no—
792Dic73—41no—
793Dic73—41no—
794Dic73—41no—
795Dic73—41no—
796#34228—731nomaximal, Sylow
797C2×C73—24no—
798C2×C73—24no—
799C2×C73—42no—
800C2×C73—42no—
801C2×C73C2×C4×#4111yescharacteristic
802C2×C73C2×#51811yescharacteristic
803C2×C73#342811yescharacteristic
804C2×C73#351311yescharacteristic
805C2×C73#351311yescharacteristic
806C2×C73#351311yescharacteristic
807C2×C73#351311yescharacteristic
808D73—42no—
809C2×#525—731no—
810#2368—731no—
811#2368—731no—
812#2364—731no—
813#2364—731no—
814#2358—731no—
815#2358—731no—
816#2358—731no—
817#2358D7311yescharacteristic, complemented
818#2357—731no—
819#2357—731no—
820#2353—731no—
821#2353—731no—
822#2343—731no—
823#2343—731no—
824#2339—731no—
825#2339—731no—
826#2333—731no—
827#2333—731no—
828#2332—731no—
829#2332—731no—
830#2318—731no—
831#2318—731no—
832C4×#123—731no—
833C4×#123—731no—
834C4×#123—731no—
835C4×#123—731no—
836C2×#381—731no—
837#2275—731no—
838#2275—731no—
839C2×C4×C22⋊C4—731no—
840C73#3422811yescharacteristic, complemented, Sylow
841C22×#41—731no—
842C24×C4—731no—
843#525—7316no—
844C2×#123—731no—
845C2×#123—731no—
846C2×C22⋊Q8—731no—
847C2×C22⋊Q8—731no—
848C2×#121—731no—
849C2×#121—731no—
850C2×#120—731no—
851C2×#120C2×D7311yescharacteristic
852C2×C4×D4—731no—
853C2×C4×D4—731no—
854C2×C4×D4—731no—
855C2×C4×D4—731no—
856C2×C4×D4—731no—
857C2×C4×D4—731no—
858C2×C4×D4—731no—
859C2×C4×D4—731no—
860C2×C4×D4—731no—
861C2×C4×D4—731no—
862C2×C4×D4C2×D7311yescharacteristic
863C2×C4×D4C2×D7311yescharacteristic
864C2×#117—731no—
865C22×C22⋊C4—731no—
866C22×C22⋊C4—731no—
867C22×C22⋊C4C2×D7311yescharacteristic
868C22×C22⋊C4C2×D7311yescharacteristic
869C22×C42—731no—
870C22×C42—731no—
871#391—731no—
872#391—731no—
873#391—731no—
874#391—731no—
875#390—731no—
876#390—731no—
877#390—731no—
878#390C2×D7311yescharacteristic
879#388—731no—
880#388—731no—
881#388—731no—
882#388—731no—
883#388—731no—
884#388—731no—
885#388—731no—
886#388—731no—
887#388—731no—
888#388—731no—
889#388—731no—
890#388—731no—
891#388—731no—
892#388—731no—
893#388C2×D7311yescharacteristic
894#388C2×D7311yescharacteristic
895#387—731no—
896#387—731no—
897#387—731no—
898#387—731no—
899#387—731no—
900#387—731no—
901#387—731no—
902#387—731no—
903#387—731no—
904#387—731no—
905#387—731no—
906#387—731no—
907#387—731no—
908#387—731no—
909#387—731no—
910#387—731no—
911#386—731no—
912#386—731no—
913#386—731no—
914#386—731no—
915#386—731no—
916#386—731no—
917#386—731no—
918#386—731no—
919#386—731no—
920#386—731no—
921#386—731no—
922#386—731no—
923#386—731no—
924#386C2×D7311yescharacteristic
925#386C2×D7311yescharacteristic
926#386C2×D7311yescharacteristic
927#385—731no—
928#385—731no—
929#385—731no—
930#385—731no—
931#385—731no—
932#385—731no—
933#385C2×D7311yescharacteristic
934#385C2×D7311yescharacteristic
935#383—731no—
936#383—731no—
937#382—731no—
938#382—731no—
939#381—731no—
940#381—731no—
941#381—731no—
942#381—731no—
943#381—731no—
944#381—731no—
945#381—731no—
946#381—731no—
947#381—731no—
948#381—731no—
949#380—731no—
950#380—731no—
951C4×C4⋊C4—731no—
952C4×C4⋊C4—731no—
953C4×C4⋊C4—731no—
954C4×C4⋊C4—731no—
955C4×C4⋊C4—731no—
956C4×C4⋊C4—731no—
957C4×C4⋊C4—731no—
958C4×C4⋊C4—731no—
959C4×C4⋊C4—731no—
960C4×C4⋊C4—731no—
961C4×C22⋊C4—731no—
962C4×C22⋊C4—731no—
963C4×C22⋊C4—731no—
964C4×C22⋊C4—731no—
965C4×C22⋊C4—731no—
966C4×C22⋊C4—731no—
967C4×C22⋊C4—731no—
968C4×C22⋊C4—731no—
969C4×C22⋊C4—731no—
970C4×C22⋊C4—731no—
971C4×C22⋊C4—731no—
972C4×C22⋊C4—731no—
973C4×C22⋊C4—731no—
974C4×C22⋊C4—731no—
975C4×C22⋊C4—731no—
976C4×C22⋊C4—731no—
977C4×C22⋊C4—731no—
978C4×C22⋊C4—731no—
979C4×C22⋊C4—731no—
980C4×C22⋊C4—731no—
981C4×C22⋊C4—731no—
982C4×C22⋊C4—731no—
983C4×C22⋊C4—731no—
984C4×C22⋊C4—731no—
985C4×C22⋊C4C2×D7311yescharacteristic
986C4×C22⋊C4C2×D7311yescharacteristic
987#376—731no—
988#376—731no—
989C2×#95—731no—
990C2×#95—731no—
991C2×#95—731no—
992C2×#95—731no—
993C2×#95—731no—
994C2×#95—731no—
995C2×#95—731no—
996C2×#95—731no—
997C25C22×D7311yescharacteristic
998C2×#41—2922no—
999C2×#41—2922no—
1000C2×#41—738no—
1001C22×Q8—731no—
1002C22×D4—731no—
1003C22×D4—731no—
1004C22×D4—731no—
1005C22×D4—731no—
1006C22×D4C22×D7311yescharacteristic
1007C22×D4C22×D7311yescharacteristic
1008C22×D4C22×D7311yescharacteristic
1009C23×C4—2922no—
1010C23×C4—2922no—
1011C23×C4—738no—
1012C23×C4—731no—
1013C23×C4—731no—
1014C23×C4—731no—
1015C23×C4—731no—
1016C23×C4—731no—
1017C23×C4—731no—
1018C23×C4—731no—
1019C23×C4—731no—
1020C23×C4—731no—
1021C23×C4—731no—
1022C23×C4—731no—
1023C23×C4—731no—
1024C23×C4—731no—
1025C23×C4—731no—
1026C23×C4—731no—
1027C23×C4C22×D7311yescharacteristic
1028C23×C4C22×D7311yescharacteristic
1029C23×C4C22×D7311yescharacteristic
1030C23×C4C22×D7311yescharacteristic
1031C23×C4C22×D7311yescharacteristic
1032#123—738no—
1033#123—738no—
1034C22⋊Q8—738no—
1035C22⋊Q8—738no—
1036#121—738no—
1037#121—738no—
1038#120—738no—
1039#120C4×D7318yescomplemented
1040C4×D4—24no—
1041C4×D4—42no—
1042C4×D4—2922no—
1043C4×D4—2922no—
1044C4×D4—2922no—
1045C4×D4—738no—
1046C4×D4—738no—
1047C4×D4—738no—
1048C4×D4—738no—
1049C4×D4—1464no—
1050C4×D4—1464no—
1051C4×D4—1464no—
1052#117—738no—
1053C2×C4⋊C4—731no—
1054C2×C4⋊C4—731no—
1055C2×C4⋊C4—731no—
1056C2×C4⋊C4—731no—
1057C2×C4⋊C4—731no—
1058C2×C4⋊C4—731no—
1059C2×C4⋊C4—731no—
1060C2×C4⋊C4—731no—
1061C2×C4⋊C4—731no—
1062C2×C4⋊C4—731no—
1063C2×C4⋊C4—731no—
1064C2×C4⋊C4—731no—
1065C2×C4⋊C4—731no—
1066C2×C4⋊C4—731no—
1067C2×C4⋊C4—731no—
1068C2×C4⋊C4C22×D7311yescharacteristic
1069C2×C4⋊C4C22×D7311yescharacteristic
1070C2×C4⋊C4C22×D7311yescharacteristic
1071C2×C22⋊C4—24no—
1072C2×C22⋊C4—42no—
1073C2×C22⋊C4—2922no—
1074C2×C22⋊C4—731no—
1075C2×C22⋊C4—731no—
1076C2×C22⋊C4—731no—
1077C2×C22⋊C4—731no—
1078C2×C22⋊C4—731no—
1079C2×C22⋊C4—731no—
1080C2×C22⋊C4—731no—
1081C2×C22⋊C4—731no—
1082C2×C22⋊C4—731no—
1083C2×C22⋊C4—731no—
1084C2×C22⋊C4—731no—
1085C2×C22⋊C4—731no—
1086C2×C22⋊C4—731no—
1087C2×C22⋊C4—731no—
1088C2×C22⋊C4—731no—
1089C2×C22⋊C4—731no—
1090C2×C22⋊C4—731no—
1091C2×C22⋊C4—731no—
1092C2×C22⋊C4—731no—
1093C2×C22⋊C4—731no—
1094C2×C22⋊C4—731no—
1095C2×C22⋊C4—731no—
1096C2×C22⋊C4—731no—
1097C2×C22⋊C4—731no—
1098C2×C22⋊C4—1464no—
1099C2×C22⋊C4C22×D7311yescharacteristic
1100C2×C22⋊C4C22×D7311yescharacteristic
1101C2×C22⋊C4C22×D7311yescharacteristic
1102C2×C22⋊C4C22×D7311yescharacteristic
1103C2×C22⋊C4C22×D7311yescharacteristic
1104C2×C22⋊C4C22×D7311yescharacteristic
1105C2×C22⋊C4C22×D7311yescharacteristic
1106C2×C22⋊C4C22×D7311yescharacteristic
1107C2×C22⋊C4C22×D7311yescharacteristic
1108C2×C22⋊C4C22×D7311yescharacteristic
1109C2×C22⋊C4C22×D7311yescharacteristic
1110C2×C22⋊C4C22×D7311yescharacteristic
1111C2×C22⋊C4C22×D7311yescharacteristic
1112C2×C22⋊C4C22×D7311yescharacteristic
1113C2×C42—2922no—
1114C2×C42—2922no—
1115C2×C42—731no—
1116C2×C42—731no—
1117C2×C42—731no—
1118C2×C42—731no—
1119C2×C42—731no—
1120C2×C42—731no—
1121C2×C42—731no—
1122C2×C42—731no—
1123C2×C42—731no—
1124C2×C42—731no—
1125C2×C42—731no—
1126C2×C42—731no—
1127C2×C42—731no—
1128C2×C42—731no—
1129C2×C42—731no—
1130C2×C42—731no—
1131C2×C42—731no—
1132C2×C42—731no—
1133C2×C42—731no—
1134C2×C42C22×D7311yescharacteristic
1135C2×C42C22×D7311yescharacteristic
1136C2×C42C22×D7311yescharacteristic
1137#95—731no—
1138#95—731no—
1139#95—731no—
1140#95—731no—
1141#95—731no—
1142#95—731no—
1143#95—731no—
1144#95—731no—
1145#95—731no—
1146#95—731no—
1147#95—731no—
1148#95—731no—
1149#95—731no—
1150#95—731no—
1151#95—731no—
1152#95—731no—
1153#95—731no—
1154#95—731no—
1155#95—731no—
1156#95—731no—
1157#95—731no—
1158#95—731no—
1159#95—731no—
1160#95—731no—
1161#95—731no—
1162#95—731no—
1163#95—731no—
1164#95—731no—
1165#95—731no—
1166#95—731no—
1167#95—731no—
1168#95—731no—
1169#95—731no—
1170#95—731no—
1171#95—731no—
1172#95—731no—
1173#95—731no—
1174#95—731no—
1175#95—731no—
1176#95—731no—
1177#95—731no—
1178#95—731no—
1179#95C22×D7311yescharacteristic
1180#95C22×D7311yescharacteristic
1181#95C22×D7311yescharacteristic
1182#95C22×D7311yescharacteristic
1183#95C22×D7311yescharacteristic
1184#95C22×D7311yescharacteristic
1185C24—22no—
1186C24—22no—
1187C24—22no—
1188C24—22no—
1189C24—41no—
1190C24—41no—
1191C24—731no—
1192C24C2×C4×D7314yes—
1193C24C23×D7311yescharacteristic
1194C24C23×D7311yescharacteristic
1195C24C23×D7311yescharacteristic
1196C24C23×D7311yescharacteristic
1197#41—29216no—
1198C2×Q8—2921no—
1199C2×Q8—2921no—
1200C2×Q8—734no—
1201C2×D4—22no—
1202C2×D4—22no—
1203C2×D4—22no—
1204C2×D4—22no—
1205C2×D4—41no—
1206C2×D4—41no—
1207C2×D4—2921no—
1208C2×D4—2921no—
1209C2×D4—2921no—
1210C2×D4—2921no—
1211C2×D4—734no—
1212C2×D4—734no—
1213C2×D4—734no—
1214C2×D4—734no—
1215C2×D4—1462no—
1216C2×D4—1462no—
1217C2×D4—1462no—
1218C2×D4—1462no—
1219C2×D4C2×C4×D7314yes—
1220C2×D4C2×C4×D7314yes—
1221C2×D4C2×C4×D7314yes—
1222C22×C4—22no—
1223C22×C4—22no—
1224C22×C4—22no—
1225C22×C4—22no—
1226C22×C4—22no—
1227C22×C4—22no—
1228C22×C4—22no—
1229C22×C4—41no—
1230C22×C4—41no—
1231C22×C4—41no—
1232C22×C4—41no—
1233C22×C4—41no—
1234C22×C4—41no—
1235C22×C4—41no—
1236C22×C4—41no—
1237C22×C4—2921no—
1238C22×C4—2921no—
1239C22×C4—2921no—
1240C22×C4—2921no—
1241C22×C4—2921no—
1242C22×C4—2921no—
1243C22×C4—2921no—
1244C22×C4—2921no—
1245C22×C4—2921no—
1246C22×C4—2921no—
1247C22×C4—2921no—
1248C22×C4—2921no—
1249C22×C4—2921no—
1250C22×C4—2921no—
1251C22×C4—29216no—
1252C22×C4—2921no—
1253C22×C4—2921no—
1254C22×C4—2921no—
1255C22×C4—2921no—
1256C22×C4—2921no—
1257C22×C4—2921no—
1258C22×C4—2921no—
1259C22×C4—2921no—
1260C22×C4—2921no—
1261C22×C4—2921no—
1262C22×C4—734no—
1263C22×C4—734no—
1264C22×C4—734no—
1265C22×C4—734no—
1266C22×C4—734no—
1267C22×C4—734no—
1268C22×C4—734no—
1269C22×C4—734no—
1270C22×C4—731no—
1271C22×C4—731no—
1272C22×C4—731no—
1273C22×C4—731no—
1274C22×C4—731no—
1275C22×C4—731no—
1276C22×C4—731no—
1277C22×C4—731no—
1278C22×C4—731no—
1279C22×C4—731no—
1280C22×C4—731no—
1281C22×C4—731no—
1282C22×C4—731no—
1283C22×C4—731no—
1284C22×C4—731no—
1285C22×C4—1462no—
1286C22×C4—1462no—
1287C22×C4—1462no—
1288C22×C4—1462no—
1289C22×C4—1462no—
1290C22×C4—1462no—
1291C22×C4—1462no—
1292C22×C4—1462no—
1293C22×C4—1462no—
1294C22×C4—1462no—
1295C22×C4—1462no—
1296C22×C4—1462no—
1297C22×C4—1462no—
1298C22×C4C23×D7311yescharacteristic
1299C22×C4C23×D7311yescharacteristic
1300C22×C4C23×D7311yescharacteristic
1301C22×C4C23×D7311yescharacteristic
1302C22×C4C23×D7311yescharacteristic
1303C22×C4C23×D7311yescharacteristic
1304C22×C4C23×D7311yescharacteristic
1305C22×C4C23×D7311yescharacteristic
1306C22×C4C23×D7311yescharacteristic
1307C22×C4C23×D7311yescharacteristic
1308C22×C4C23×D7311yescharacteristic
1309C4⋊C4—22no—
1310C4⋊C4—41no—
1311C4⋊C4—41no—
1312C4⋊C4—2921no—
1313C4⋊C4—2921no—
1314C4⋊C4—2921no—
1315C4⋊C4—2921no—
1316C4⋊C4—2921no—
1317C4⋊C4—2921no—
1318C4⋊C4—734no—
1319C4⋊C4—734no—
1320C4⋊C4—734no—
1321C4⋊C4—734no—
1322C4⋊C4—734no—
1323C4⋊C4—734no—
1324C4⋊C4—1462no—
1325C4⋊C4—1462no—
1326C4⋊C4—1462no—
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—2921no—
1338C22⋊C4—2921no—
1339C22⋊C4—2921no—
1340C22⋊C4—2921no—
1341C22⋊C4—2921no—
1342C22⋊C4—2921no—
1343C22⋊C4—2921no—
1344C22⋊C4—2921no—
1345C22⋊C4—734no—
1346C22⋊C4—734no—
1347C22⋊C4—734no—
1348C22⋊C4—734no—
1349C22⋊C4—734no—
1350C22⋊C4—734no—
1351C22⋊C4—734no—
1352C22⋊C4—734no—
1353C22⋊C4—1462no—
1354C22⋊C4—1462no—
1355C22⋊C4—1462no—
1356C22⋊C4—1462no—
1357C22⋊C4—1462no—
1358C22⋊C4—1462no—
1359C22⋊C4—1462no—
1360C22⋊C4—1462no—
1361C22⋊C4C2×C4×D7314yes—
1362C22⋊C4C2×C4×D7314yes—
1363C22⋊C4C2×C4×D7314yes—
1364C22⋊C4#1192402714yescomplemented
1365C42—22no—
1366C42—41no—
1367C42—41no—
1368C42—2921no—
1369C42—2921no—
1370C42—2921no—
1371C42—2921no—
1372C42—2921no—
1373C42—2921no—
1374C42—2921no—
1375C42—2921no—
1376C42—2921no—
1377C42—2921no—
1378C42—2921no—
1379C42—2921no—
1380C42—2921no—
1381C42—2921no—
1382C42—734no—
1383C42—734no—
1384C42—1462no—
1385C42—1462no—
1386C42—1462no—
1387C23—21no—
1388C23—21no—
1389C23—21no—
1390C23—21no—
1391C23—21no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—21no—
1397C23—21no—
1398C23—21no—
1399C23—21no—
1400C23—21no—
1401C23—21no—
1402C23—21no—
1403C23—21no—
1404C23—21no—
1405C23—21no—
1406C23—21no—
1407C23—28no—
1408C23—28no—
1409C23—44no—
1410C23—44no—
1411C23—44no—
1412C23—44no—
1413C23—44no—
1414C23—732no—
1415C23—1461no—
1416C23—1461no—
1417C23—1461no—
1418C23—1461no—
1419C23—1461no—
1420C23—1461no—
1421C23C22×C4×D7312yes—
1422C23C22×C4×D7312yes—
1423C23C22×C4×D7312yes—
1424C23C22×C4×D7312yes—
1425C23#41×D7312yes—
1426C23C2×#1192402712yes—
1427C23#1455663612yes—
1428C23#1455663712yes—
1429C23C24×D7311yescharacteristic
1430Q8—2924no—
1431D4—28no—
1432D4—28no—
1433D4—44no—
1434D4—2924no—
1435D4—2924no—
1436D4—1468no—
1437D4—1468no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—44no—
1467C2×C4—44no—
1468C2×C4—82no—
1469C2×C4—82no—
1470C2×C4—82no—
1471C2×C4—2924no—
1472C2×C4—2924no—
1473C2×C4—2924no—
1474C2×C4—2924no—
1475C2×C4—2924no—
1476C2×C4—2924no—
1477C2×C4—2924no—
1478C2×C4—2924no—
1479C2×C4—5842no—
1480C2×C4—5842no—
1481C2×C4—5842no—
1482C2×C4—5842no—
1483C2×C4—5842no—
1484C2×C4—732no—
1485C2×C4—732no—
1486C2×C4—732no—
1487C2×C4—732no—
1488C2×C4—732no—
1489C2×C4—732no—
1490C2×C4—732no—
1491C2×C4—732no—
1492C2×C4—732no—
1493C2×C4—1461no—
1494C2×C4—1461no—
1495C2×C4—1461no—
1496C2×C4—1461no—
1497C2×C4—1461no—
1498C2×C4—1461no—
1499C2×C4—1461no—
1500C2×C4—1461no—
1501C2×C4—1461no—
1502C2×C4—1461no—
1503C2×C4—1461no—
1504C2×C4—1461no—
1505C2×C4—1461no—
1506C2×C4—1461no—
1507C2×C4—1461no—
1508C2×C4—1461no—
1509C2×C4—1461no—
1510C2×C4—1461no—
1511C2×C4—1461no—
1512C2×C4—1461no—
1513C2×C4—1461no—
1514C2×C4—1461no—
1515C2×C4—1461no—
1516C2×C4—1461no—
1517C2×C4—1461no—
1518C2×C4—1461no—
1519C2×C4—1461no—
1520C2×C4—1461no—
1521C2×C4—1461no—
1522C2×C4—1461no—
1523C2×C4—1461no—
1524C2×C4—1461no—
1525C2×C4—1461no—
1526C2×C4—1461no—
1527C2×C4—1461no—
1528C2×C4—1461no—
1529C2×C4—1468no—
1530C2×C4—1468no—
1531C2×C4C22×C4×D7312yes—
1532C2×C4C22×C4×D7312yes—
1533C2×C4C22×C4×D7312yes—
1534C2×C4C2×#1192402712yes—
1535C2×C4C2×#1192402712yes—
1536C22—22no—
1537C22—22no—
1538C22—22no—
1539C22—22no—
1540C22—22no—
1541C22—22no—
1542C22—22no—
1543C22—22no—
1544C22—22no—
1545C22—22no—
1546C22—22no—
1547C22—22no—
1548C22—22no—
1549C22—22no—
1550C22—22no—
1551C22—22no—
1552C22—22no—
1553C22—22no—
1554C22—416no—
1555C22—41no—
1556C22—41no—
1557C22—41no—
1558C22—41no—
1559C22—41no—
1560C22—41no—
1561C22—41no—
1562C22—41no—
1563C22—2921no—
1564C22—2921no—
1565C22—2921no—
1566C22—2921no—
1567C22—1462no—
1568C22—1462no—
1569C22—1462no—
1570C22C4×#1192402714yes—
1571C22#1798905914yes—
1572C22C23×C4×D7311yescharacteristic
1573C22C2×#41×D7311yescharacteristic
1574C22C22×#1192402711yescharacteristic
1575C22C2×#1455663611yescharacteristic
1576C22C2×#1455663711yescharacteristic
1577C22#1798942211yescharacteristic
1578C22#1798942211yescharacteristic
1579C4—22no—
1580C4—22no—
1581C4—22no—
1582C4—22no—
1583C4—22no—
1584C4—41no—
1585C4—41no—
1586C4—41no—
1587C4—41no—
1588C4—41no—
1589C4—41no—
1590C4—2921no—
1591C4—2921no—
1592C4—2921no—
1593C4—2921no—
1594C4—2921no—
1595C4—2921no—
1596C4—1462no—
1597C4—1462no—
1598C4—1462no—
1599C4—1462no—
1600C4—1462no—
1601C4—1462no—
1602C4—1462no—
1603C4—1462no—
1604C4—1462no—
1605C2—24no—
1606C2—24no—
1607C2—42no—
1608C2—42no—
1609C2—2922no—
1610C2C2×C4×#1192402711yescharacteristic
1611C2C2×#1798905911yescharacteristic
1612C2#2262312911yescharacteristic
1613C2#2262385611yescharacteristic
1614C2#2262385811yescharacteristic
1615C2#2262386411yescharacteristic
1616C2#2262387211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
FittingC73×#2358C2
socle, cosocleC23×C73C25
prime radicalC2×#17989093C2
hypercenter#2358D73
hypocenterC73#34228
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2358

Complements

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

NH ≅ G/Ntype
2. #22613012C2semidirect
3. #22613009C2semidirect
4. #22612979C2semidirect
5. #22612976C2semidirect
6. #22612915C2semidirect
7. #22612910C2semidirect
8. #22612910C2semidirect
9. #22612903C2semidirect
10. #22612901C2semidirect
11. #22612869C2semidirect
12. #22612866C2semidirect
13. #22612789C2semidirect
14. #22612785C2semidirect
15. #22612757C2semidirect
16. #22612756C2semidirect
17. #22612697C2semidirect
18. #22612690C2semidirect
19. #22612688C2semidirect
20. #22612681C2semidirect
21. #22612559C2semidirect
22. #22612557C2semidirect
23. #22612456C2semidirect
24. C4×#14556575C2semidirect
25. #22612450C2semidirect
26. C4×#14556572C2semidirect
27. C2×#17988448C2semidirect
28. #22612292C2semidirect
29. #22612290C2semidirect
30. C2×C22⋊C4×Dic73C2semidirect
31. C73×#2358C2semidirect
34. #17989093C4semidirect
57. #17988493C22semidirect
58. #17988492C22semidirect
59. #17988491C22semidirect
60. #17988491C22semidirect
66. #17988481C22semidirect
67. #17988481C22semidirect
70. #17988479C22semidirect
71. #17988479C22semidirect
72. #17988477C22semidirect
73. #17988477C22semidirect
76. #17988475C22semidirect
77. #17988475C22semidirect
78. #17988474C22semidirect
79. #17988474C22semidirect
80. #17988474C22semidirect
81. #17988474C22semidirect
82. #17988472C22semidirect
83. #17988472C22semidirect
84. #17988471C22semidirect
85. #17988471C22semidirect
86. #17988470C22semidirect
87. #17988470C22semidirect
88. #17988469C22semidirect
89. #17988469C22semidirect
90. #17988468C22semidirect
91. #17988468C22semidirect
92. #17988468C22semidirect
93. #17988468C22semidirect
99. #17988466C22semidirect
102. #17988464C22semidirect
105. #17988463C22semidirect
106. #17988463C22semidirect
113. #17988454C22semidirect
114. #17988454C22semidirect
115. #17988452C22semidirect
116. #17988451C22semidirect
117. #17988449C22semidirect
126. #17988448C22semidirect
127. #17988445C22semidirect
128. #17988444C22semidirect
129. C4⋊C4×Dic73C22semidirect
130. C4⋊C4×Dic73C22semidirect
131. C4⋊C4×Dic73C22semidirect
132. C4×#11924007C22semidirect
133. C4×#11924007C22semidirect
134. C4×#11924007C22semidirect
135. C4×C4⋊Dic73C22semidirect
136. C4×C4⋊Dic73C22semidirect
137. #17988438C22semidirect
138. #17988438C22semidirect
151. C22⋊C4×Dic73C22semidirect
152. C22⋊C4×Dic73C22semidirect
153. C22⋊C4×Dic73C22semidirect
154. C4×#11924005C22semidirect
155. C4×#11924005C22semidirect
156. C4×#11924005C22semidirect
159. C4×C22⋊Dic73C22semidirect
160. C4×C22⋊Dic73C22semidirect
161. #17988434C22semidirect
162. #17988434C22semidirect
163. #17988433C22semidirect
164. #17988432C22semidirect
171. C2×#14556498C22semidirect
172. #95×D73C22semidirect
190. C2×#11924027C2×C4semidirect
198. C23×Dic73C2×C4semidirect
214. #14556575C2×C4semidirect
215. #14556572C2×C4semidirect
216. #14556568C2×C4semidirect
217. #14556568C2×C4semidirect
218. #14556563C2×C4semidirect
219. #14556563C2×C4semidirect
220. #14556560C2×C4semidirect
223. D4×Dic73C2×C4semidirect
224. D4×Dic73C2×C4semidirect
229. #14556551C2×C4semidirect
230. #14556551C2×C4semidirect
231. #14556547C2×C4semidirect
345. #120×C73C2×C4semidirect
484. C22⋊Dic73#41semidirect
574. C22⋊C4×C73#41semidirect
817. #2358D73semidirect
840. C73#34228semidirect
1039. #120C4×D73semidirect
1364. C22⋊C4#11924027semidirect

Maximal subgroups

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

subgroupindex
C2×#179890932
#226130122
#226130092
#226129792
#226129762
#226129152
#226129102
#226129032
#226129012
#226128692
#226128662
#226127892
#226127852
#226127572
#226127562
#226126972
#226126902
#226126882
#226126812
#226125592
#226125572
#226124562
C4×#145565752
#226124502
C4×#145565722
C2×#179884482
#226122922
#226122902
C2×C22⋊C4×Dic732
C73×#23582
#3422873