Finite Group Databasebeta

← #11041763

Subgroups — #11041763

Order 768.

1474 conjugacy classes of subgroups.

The subgroup lattice has 1298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2531C211yesmaximal, characteristic
2#77876C211yesmaximal, characteristic, complemented
3#77836C211yesmaximal, characteristic, complemented
4#77623C211yesmaximal, characteristic, complemented
5#77590C211yesmaximal, characteristic, complemented
6#77530C211yesmaximal, characteristic, complemented
7#77496C211yesmaximal, characteristic, complemented
8#77078C211yesmaximal, characteristic
9#76988C211yesmaximal, characteristic
10#76366C211yesmaximal, characteristic
11#76343C211yesmaximal, characteristic
12#75822C211yesmaximal, characteristic, complemented
13#75797C211yesmaximal, characteristic, complemented
14#75633C211yesmaximal, characteristic, complemented
15#75591C211yesmaximal, characteristic, complemented
16#75582C211yesmaximal, characteristic, complemented
17#75514C211yesmaximal, characteristic, complemented
18#75464C211yesmaximal, characteristic, complemented
19#75455C211yesmaximal, characteristic, complemented
20#75191C211yesmaximal, characteristic, complemented
21#75095C211yesmaximal, characteristic, complemented
22#75030C211yesmaximal, characteristic, complemented
23#74968C211yesmaximal, characteristic, complemented
24#74812C211yesmaximal, characteristic
25#74733C211yesmaximal, characteristic
26#73960C211yesmaximal, characteristic, complemented
27#73868C211yesmaximal, characteristic, complemented
28#73528C211yesmaximal, characteristic, complemented
29#73468C211yesmaximal, characteristic, complemented
30#73399C211yesmaximal, characteristic, complemented
31#73384C211yesmaximal, characteristic, complemented
32#38337—31nomaximal, Sylow
33C2×#926C2211yescharacteristic
34C2×#924C2211yescharacteristic
35C2×#889C2211yescharacteristic
36C2×#879C2211yescharacteristic
37C2×#878C2211yescharacteristic
38C2×C4×Dic6C2211yescharacteristic
39C3×#398C2211yescharacteristic
40C3×#397C2211yescharacteristic
41C3×#397C2211yescharacteristic
42C3×#394C2211yescharacteristic
43C3×#390C2211yescharacteristic
44C3×#388C2211yescharacteristic
45C3×#388C2211yescharacteristic
46C3×#388C2211yescharacteristic
47C3×#388C2211yescharacteristic
48C3×#387C2211yescharacteristic
49C3×#387C2211yescharacteristic
50C3×#386C2211yescharacteristic
51C3×#380C2211yescharacteristic
52C3×C4×C22⋊C4C2211yescharacteristic
53C3×#376C2211yescharacteristic
54#5222C2211yescharacteristic
55#5222C2211yescharacteristic
56#5222C2211yescharacteristic
57#5220C2211yescharacteristic
58#5212C2211yescharacteristic
59#5210C2211yescharacteristic
60#4986C2211yescharacteristic
61#4986C2211yescharacteristic
62#4986C2211yescharacteristic
63#4985C2211yescharacteristic
64#4985C2211yescharacteristic
65#4985C2211yescharacteristic
66#4981C2211yescharacteristic
67#4981C2211yescharacteristic
68#4980C2211yescharacteristic
69#4980C2211yescharacteristic
70#4980C2211yescharacteristic
71#4979C2211yescharacteristic
72#4978C2211yescharacteristic
73#4978C2211yescharacteristic
74#4977C2211yescharacteristic
75#4976C2211yescharacteristic
76#4976C2211yescharacteristic
77#4975C2211yescharacteristic
78Dic3×C4⋊C4C2211yescharacteristic
79Dic3×C4⋊C4C2211yescharacteristic
80#4973C2211yescharacteristic
81#4972C2211yescharacteristic
82#4972C2211yescharacteristic
83#4953C2211yescharacteristic
84#4952C2211yescharacteristic
85#4952C2211yescharacteristic
86#4952C2211yescharacteristic
87#4951C2211yescharacteristic
88#4951C2211yescharacteristic
89#4951C2211yescharacteristic
90#4951C2211yescharacteristic
91#4951C2211yescharacteristic
92#4951C2211yescharacteristic
93#4951C2211yescharacteristic
94#4951C2211yescharacteristic
95#4949C2211yescharacteristic
96#4949C2211yescharacteristic
97#4949C2211yescharacteristic
98#4948C2211yescharacteristic
99#4948C2211yescharacteristic
100#4948C2211yescharacteristic
101#4947C2211yescharacteristic
102#4947C2211yescharacteristic
103#4946C2211yescharacteristic
104#4945C2211yescharacteristic
105#4945C2211yescharacteristic
106#4945C2211yescharacteristic
107#4945C2211yescharacteristic
108#4945C2211yescharacteristic
109#4945C2211yescharacteristic
110#4945C2211yescharacteristic
111#4945C2211yescharacteristic
112#4945C2211yescharacteristic
113#4945C2211yescharacteristic
114#4944C2211yescharacteristic
115#4944C2211yescharacteristic
116#4944C2211yescharacteristic
117#4944C2211yescharacteristic
118#4944C2211yescharacteristic
119#4944C2211yescharacteristic
120#4944C2211yescharacteristic
121#4943C2211yescharacteristic
122Dic3×C22⋊C4C2211yescharacteristic
123Dic3×C22⋊C4C2211yescharacteristic
124Dic3×C22⋊C4C2211yescharacteristic
125C4×C4⋊Dic3C2211yescharacteristic
126C4×C4⋊Dic3C2211yescharacteristic
127#4933C2211yescharacteristic
128#4933C2211yescharacteristic
129#4933C2211yescharacteristic
130#4933C2211yescharacteristic
131#4933C2211yescharacteristic
132#4932C2211yescharacteristic
133C4×Dic3⋊C4C2211yescharacteristic
134C4×Dic3⋊C4C2211yescharacteristic
135C4×Dic3⋊C4C2211yescharacteristic
136C42×Dic3C2211yescharacteristic
137#4929C2211yescharacteristic
138#4928C2211yescharacteristic
139#4928C2211yescharacteristic
140C3⋊#401C2211yescharacteristic
141#4661C2211yescharacteristic
142#4661C2211yescharacteristic
143#4660C2211yescharacteristic
144#4660C2211yescharacteristic
145#4659C2211yescharacteristic
146#4659C2211yescharacteristic
147#4658C2211yescharacteristic
148#4658C2211yescharacteristic
149#4657C2211yescharacteristic
150#4657C2211yescharacteristic
151#4656C2211yescharacteristic
152#4655C2211yescharacteristic
153#4655C2211yescharacteristic
154#4655C2211yescharacteristic
155#4655C2211yescharacteristic
156#4654C2211yescharacteristic
157#4654C2211yescharacteristic
158#4654C2211yescharacteristic
159#4654C2211yescharacteristic
160#4654C2211yescharacteristic
161#4653C2211yescharacteristic
162#4653C2211yescharacteristic
163#4653C2211yescharacteristic
164#4652C2211yescharacteristic
165#4652C2211yescharacteristic
166#4652C2211yescharacteristic
167#4652C2211yescharacteristic
168#4652C2211yescharacteristic
169#4652C2211yescharacteristic
170#4652C2211yescharacteristic
171#4651C2211yescharacteristic
172#4651C2211yescharacteristic
173#4650C2211yescharacteristic
174#4649C2211yescharacteristic
175#4649C2211yescharacteristic
176#4649C2211yescharacteristic
177#4649C2211yescharacteristic
178#4649C2211yescharacteristic
179#4647C2211yescharacteristic
180#4647C2211yescharacteristic
181#4647C2211yescharacteristic
182#4647C2211yescharacteristic
183#4646C2211yescharacteristic
184#4646C2211yescharacteristic
185#4646C2211yescharacteristic
186#4646C2211yescharacteristic
187#4646C2211yescharacteristic
188#2865—31no—
189#2801—31no—
190#2798—31no—
191#2775—31no—
192#2758—31no—
193#2755—31no—
194#2721—31no—
195#2702—31no—
196#2690—31no—
197#2655—31no—
198#2649—31no—
199#2596—31no—
200#2596—31no—
201#2593—31no—
202#2585—31no—
203#2532—31no—
204#2531D311yescharacteristic
205#2529—31no—
206#2528—31no—
207#2522—31no—
208#2516—31no—
209#2515—31no—
210#2511—31no—
211#2477—31no—
212#2465—31no—
213#2370—31no—
214#2362—31no—
215#2332—31no—
216#2314—31no—
217C4×#126—31no—
218#2295—31no—
219C22×C3×D4C2311yescharacteristic
220C23×C3×C4C2311yescharacteristic
221C23×Dic3C2311yescharacteristic
222C22×Dic6C2311yescharacteristic
223C22×Dic6C2311yescharacteristic
224C2×C3×C4⋊C4C2311yescharacteristic
225C2×C3×C4⋊C4C2311yescharacteristic
226C2×C3×C4⋊C4C2311yescharacteristic
227C2×C3×C4⋊C4C2311yescharacteristic
228C2×C3×C4⋊C4C2311yescharacteristic
229C2×C3×C4⋊C4C2311yescharacteristic
230C2×C3×C22⋊C4C2311yescharacteristic
231C2×C3×C22⋊C4C2311yescharacteristic
232C2×C3×C22⋊C4C2311yescharacteristic
233C2×C3×C22⋊C4C2311yescharacteristic
234C2×C3×C22⋊C4C2311yescharacteristic
235C2×C3×C22⋊C4C2311yescharacteristic
236C2×C3×C22⋊C4C2311yescharacteristic
237C2×C3×C22⋊C4C2311yescharacteristic
238C2×C3×C22⋊C4C2311yescharacteristic
239C2×C3×C22⋊C4C2311yescharacteristic
240C2×C3×C22⋊C4C2311yescharacteristic
241C2×C3×C42C2311yescharacteristic
242C2×C3×C42C2311yescharacteristic
243C2×C3×C42C2311yescharacteristic
244C2×C3×C42C2311yescharacteristic
245C2×#217C2311yescharacteristic
246C2×#217C2311yescharacteristic
247C2×#217C2311yescharacteristic
248C2×#217C2311yescharacteristic
249C2×#217C2311yescharacteristic
250C2×#217C2311yescharacteristic
251C2×#217C2311yescharacteristic
252C2×#217C2311yescharacteristic
253C2×#217C2311yescharacteristic
254C2×#217C2311yescharacteristic
255C2×#217C2311yescharacteristic
256C2×#217C2311yescharacteristic
257C2×#217C2311yescharacteristic
258C2×#217C2311yescharacteristic
259C2×#217C2311yescharacteristic
260#926—24no—
261C2×C4⋊Dic3C2311yescharacteristic
262C2×C4⋊Dic3C2311yescharacteristic
263C2×C4⋊Dic3C2311yescharacteristic
264C2×C4⋊Dic3C2311yescharacteristic
265C2×C4⋊Dic3C2311yescharacteristic
266C2×C4⋊Dic3C2311yescharacteristic
267C2×C4⋊Dic3C2311yescharacteristic
268C2×C4⋊Dic3C2311yescharacteristic
269C2×C4⋊Dic3C2311yescharacteristic
270C2×C4⋊Dic3C2311yescharacteristic
271C2×C4⋊Dic3C2311yescharacteristic
272#924—24no—
273C2×Dic3⋊C4C2311yescharacteristic
274C2×Dic3⋊C4C2311yescharacteristic
275C2×Dic3⋊C4C2311yescharacteristic
276C2×Dic3⋊C4C2311yescharacteristic
277C2×Dic3⋊C4C2311yescharacteristic
278C2×Dic3⋊C4C2311yescharacteristic
279C2×Dic3⋊C4C2311yescharacteristic
280C2×Dic3⋊C4C2311yescharacteristic
281C2×Dic3⋊C4C2311yescharacteristic
282C2×Dic3⋊C4C2311yescharacteristic
283C2×Dic3⋊C4C2311yescharacteristic
284C2×Dic3⋊C4C2311yescharacteristic
285C2×Dic3⋊C4C2311yescharacteristic
286C2×Dic3⋊C4C2311yescharacteristic
287C2×Dic3⋊C4C2311yescharacteristic
288C2×Dic3⋊C4C2311yescharacteristic
289C2×Dic3⋊C4C2311yescharacteristic
290C2×Dic3⋊C4C2311yescharacteristic
291C2×Dic3⋊C4C2311yescharacteristic
292C2×Dic3⋊C4C2311yescharacteristic
293C2×Dic3⋊C4C2311yescharacteristic
294C2×Dic3⋊C4C2311yescharacteristic
295C2×Dic3⋊C4C2311yescharacteristic
296C2×Dic3⋊C4C2311yescharacteristic
297C2×C4×Dic3C2311yescharacteristic
298C2×C4×Dic3C2311yescharacteristic
299C2×C4×Dic3C2311yescharacteristic
300C2×C4×Dic3C2311yescharacteristic
301C2×C4×Dic3C2311yescharacteristic
302C2×C4×Dic3C2311yescharacteristic
303C2×C4×Dic3C2311yescharacteristic
304C2×C4×Dic3C2311yescharacteristic
305C2×C4×Dic3C2311yescharacteristic
306C2×C4×Dic3C2311yescharacteristic
307C2×C4×Dic3C2311yescharacteristic
308C2×C4×Dic3C2311yescharacteristic
309C2×C4×Dic3C2311yescharacteristic
310C2×C4×Dic3C2311yescharacteristic
311C2×C4×Dic3C2311yescharacteristic
312C2×C4×Dic3C2311yescharacteristic
313C2×C4×Dic3C2311yescharacteristic
314#889—24no—
315#879—24no—
316#878—24no—
317C4×Dic6—24no—
318C3×#95C2311yescharacteristic
319C3×#95C2311yescharacteristic
320C3×#95C2311yescharacteristic
321C3×#95C2311yescharacteristic
322C3×#95C2311yescharacteristic
323C3×#95C2311yescharacteristic
324C3×#95C2311yescharacteristic
325C3×#95C2311yescharacteristic
326C3×#95C2311yescharacteristic
327C3×#95C2311yescharacteristic
328C3×#95C2311yescharacteristic
329C3×#95C2311yescharacteristic
330C3⋊#95C2311yescharacteristic
331C3⋊#95C2311yescharacteristic
332C3⋊#95C2311yescharacteristic
333C3⋊#95C2311yescharacteristic
334C3⋊#95C2311yescharacteristic
335C3⋊#95C2311yescharacteristic
336C3⋊#95C2311yescharacteristic
337C3⋊#95C2311yescharacteristic
338C3⋊#95C2311yescharacteristic
339C3⋊#95C2311yescharacteristic
340C3⋊#95C2311yescharacteristic
341C3⋊#95C2311yescharacteristic
342C3⋊#95C2311yescharacteristic
343C3⋊#95C2311yescharacteristic
344C3⋊#95C2311yescharacteristic
345C3⋊#95C2311yescharacteristic
346C3⋊#95C2311yescharacteristic
347C3⋊#95C2311yescharacteristic
348C3⋊#95C2311yescharacteristic
349C3⋊#95C2311yescharacteristic
350C3⋊#95C2311yescharacteristic
351C3⋊#95C2311yescharacteristic
352C3⋊#95C2311yescharacteristic
353C3⋊#95C2311yescharacteristic
354C3⋊#95C2311yescharacteristic
355C3⋊#95C2311yescharacteristic
356C3⋊#95C2311yescharacteristic
357C3⋊#95C2311yescharacteristic
358C3⋊#95C2311yescharacteristic
359C3⋊#95C2311yescharacteristic
360C3⋊#95C2311yescharacteristic
361C3⋊#95C2311yescharacteristic
362C3⋊#95C2311yescharacteristic
363C3⋊#95C2311yescharacteristic
364C3⋊#95C2311yescharacteristic
365C3⋊#95C2311yescharacteristic
366C3⋊#95C2311yescharacteristic
367C3⋊#95C2311yescharacteristic
368C3⋊#95C2311yescharacteristic
369C3⋊#95C2311yescharacteristic
370C3⋊#95C2311yescharacteristic
371C3⋊#95C2311yescharacteristic
372C3⋊#95C2311yescharacteristic
373C3⋊#95C2311yescharacteristic
374C3⋊#95C2311yescharacteristic
375C3⋊#95C2311yescharacteristic
376C3⋊#95C2311yescharacteristic
377C3⋊#95C2311yescharacteristic
378C3⋊#95C2311yescharacteristic
379C3⋊#95C2311yescharacteristic
380C2×#126—31no—
381C2×#125—31no—
382C2×C22⋊Q8—31no—
383C2×C22⋊Q8—31no—
384C2×C4×Q8—31no—
385C2×#117—31no—
386#401—31no—
387#400—31no—
388#400—31no—
389#400—31no—
390#400—31no—
391#400—31no—
392#400—31no—
393#400—31no—
394#400—31no—
395#400—31no—
396#400—31no—
397#400—31no—
398#400—31no—
399#399—31no—
400#399—31no—
401#399—31no—
402#398—31no—
403#398—31no—
404#398—31no—
405#398—31no—
406#398—31no—
407#398—31no—
408#398C2×D311yescharacteristic
409#397—31no—
410#397—31no—
411#397—31no—
412#397—31no—
413#397C2×D311yescharacteristic
414#397C2×D311yescharacteristic
415#396—31no—
416#396—31no—
417#396—31no—
418#395—31no—
419#395—31no—
420#394—31no—
421#394—31no—
422#394—31no—
423#394C2×D311yescharacteristic
424#393—31no—
425#393—31no—
426#391—31no—
427#391—31no—
428#391—31no—
429#391—31no—
430#391—31no—
431#391—31no—
432#391—31no—
433#390C2×D311yescharacteristic
434#389—31no—
435#389—31no—
436#389—31no—
437#389—31no—
438#389—31no—
439#389—31no—
440#389—31no—
441#389—31no—
442#389—31no—
443#389—31no—
444#388—31no—
445#388—31no—
446#388—31no—
447#388—31no—
448#388—31no—
449#388—31no—
450#388—31no—
451#388—31no—
452#388—31no—
453#388—31no—
454#388—31no—
455#388—31no—
456#388—31no—
457#388—31no—
458#388—31no—
459#388—31no—
460#388—31no—
461#388—31no—
462#388—31no—
463#388—31no—
464#388—31no—
465#388—31no—
466#388—31no—
467#388—31no—
468#388—31no—
469#388C2×D311yescharacteristic
470#388C2×D311yescharacteristic
471#388C2×D311yescharacteristic
472#388C2×D311yescharacteristic
473#387—31no—
474#387—31no—
475#387—31no—
476#387—31no—
477#387—31no—
478#387—31no—
479#387—31no—
480#387—31no—
481#387—31no—
482#387—31no—
483#387—31no—
484#387—31no—
485#387—31no—
486#387—31no—
487#387—31no—
488#387—31no—
489#387—31no—
490#387—31no—
491#387—31no—
492#387—31no—
493#387—31no—
494#387—31no—
495#387—31no—
496#387—31no—
497#387—31no—
498#387—31no—
499#387—31no—
500#387—31no—
501#387—31no—
502#387C2×D311yescharacteristic
503#387C2×D311yescharacteristic
504#386—31no—
505#386C2×D311yescharacteristic
506#385—31no—
507#385—31no—
508#384—31no—
509#383—31no—
510#383—31no—
511#382—31no—
512#382—31no—
513#381—31no—
514#380—31no—
515#380C2×D311yescharacteristic
516C4×C4⋊C4—31no—
517C4×C4⋊C4—31no—
518C4×C4⋊C4—31no—
519C4×C4⋊C4—31no—
520C4×C4⋊C4—31no—
521C4×C4⋊C4—31no—
522C4×C4⋊C4—31no—
523C4×C4⋊C4—31no—
524C4×C4⋊C4—31no—
525C4×C4⋊C4—31no—
526C4×C4⋊C4—31no—
527C4×C4⋊C4—31no—
528C4×C22⋊C4—31no—
529C4×C22⋊C4—31no—
530C4×C22⋊C4—31no—
531C4×C22⋊C4C2×D311yescharacteristic
532#376—31no—
533#376C2×D311yescharacteristic
534C43—31no—
535C24×C3C2411yescharacteristic
536C24×C3C2411yescharacteristic
537C2×C3×D4—41no—
538C2×C3×D4—41no—
539C2×C3×D4—41no—
540C22×C3×C4—22no—
541C22×C3×C4—22no—
542C22×C3×C4—41no—
543C22×C3×C4C2411yescharacteristic
544C22×C3×C4C2411yescharacteristic
545C22×C3×C4C2411yescharacteristic
546C22×C3×C4C2411yescharacteristic
547C22×C3×C4C2411yescharacteristic
548C22×C3×C4C2411yescharacteristic
549C22×C3×C4C2411yescharacteristic
550C22×C3×C4C2411yescharacteristic
551C22×C3×C4C2411yescharacteristic
552C22×C3×C4C2411yescharacteristic
553C22×C3×C4C2411yescharacteristic
554C22×C3×C4C2411yescharacteristic
555C22×C3×C4C2411yescharacteristic
556C22×Dic3—22no—
557C22×Dic3—41no—
558C22×Dic3—41no—
559C22×Dic3C2411yescharacteristic
560C22×Dic3C2411yescharacteristic
561C22×Dic3C2411yescharacteristic
562C22×Dic3C2411yescharacteristic
563C22×Dic3C2411yescharacteristic
564C22×Dic3C2411yescharacteristic
565C22×Dic3C2411yescharacteristic
566C22×Dic3C2411yescharacteristic
567C22×Dic3C2411yescharacteristic
568C22×Dic3C2411yescharacteristic
569C22×Dic3C2411yescharacteristic
570C22×Dic3C2411yescharacteristic
571C22×Dic3C2411yescharacteristic
572C22×Dic3C2411yescharacteristic
573C22×Dic3C2411yescharacteristic
574C22×Dic3C2411yescharacteristic
575C2×Dic6—22no—
576C2×Dic6—22no—
577C2×Dic6—22no—
578C2×Dic6—41no—
579C2×Dic6—41no—
580C2×Dic6—41no—
581C3×C4⋊C4—22no—
582C3×C4⋊C4—41no—
583C3×C4⋊C4—41no—
584C3×C4⋊C4—41no—
585C3×C4⋊C4—41no—
586C3×C4⋊C4—41no—
587C3×C22⋊C4—22no—
588C3×C22⋊C4—22no—
589C3×C22⋊C4—22no—
590C3×C22⋊C4—22no—
591C3×C22⋊C4—41no—
592C3×C22⋊C4—41no—
593C3×C22⋊C4—41no—
594C3×C22⋊C4—41no—
595C3×C22⋊C4—41no—
596C3×C22⋊C4—41no—
597C3×C22⋊C4—41no—
598C3×C42—22no—
599C3×C42—22no—
600C3×C42—41no—
601C3×C42—41no—
602#217—22no—
603#217—22no—
604#217—22no—
605#217—22no—
606#217—22no—
607#217—22no—
608#217—22no—
609#217—41no—
610#217—41no—
611#217—41no—
612#217—41no—
613#217—41no—
614#217—41no—
615#217—41no—
616#217—41no—
617C4⋊Dic3—22no—
618C4⋊Dic3—22no—
619C4⋊Dic3—22no—
620C4⋊Dic3—22no—
621C4⋊Dic3—41no—
622C4⋊Dic3—41no—
623C4⋊Dic3—41no—
624C4⋊Dic3—41no—
625C4⋊Dic3—41no—
626C4⋊Dic3—41no—
627C4⋊Dic3#4114yes—
628Dic3⋊C4—22no—
629Dic3⋊C4—22no—
630Dic3⋊C4—22no—
631Dic3⋊C4—22no—
632Dic3⋊C4—22no—
633Dic3⋊C4—22no—
634Dic3⋊C4—22no—
635Dic3⋊C4—22no—
636Dic3⋊C4—22no—
637Dic3⋊C4—22no—
638Dic3⋊C4—22no—
639Dic3⋊C4—41no—
640Dic3⋊C4—41no—
641Dic3⋊C4—41no—
642Dic3⋊C4—41no—
643Dic3⋊C4—41no—
644Dic3⋊C4—41no—
645Dic3⋊C4—41no—
646Dic3⋊C4—41no—
647Dic3⋊C4—41no—
648Dic3⋊C4—41no—
649Dic3⋊C4—41no—
650Dic3⋊C4—41no—
651Dic3⋊C4#4114yes—
652C4×Dic3—22no—
653C4×Dic3—22no—
654C4×Dic3—22no—
655C4×Dic3—22no—
656C4×Dic3—22no—
657C4×Dic3—22no—
658C4×Dic3—41no—
659C4×Dic3—41no—
660C4×Dic3—41no—
661C4×Dic3—41no—
662C4×Dic3—41no—
663C4×Dic3—41no—
664C4×Dic3—41no—
665C4×Dic3—41no—
666C4×Dic3—41no—
667C4×Dic3—41no—
668C4×Dic3—41no—
669C22×Q8—31no—
670C22×Q8—31no—
671C22×D4C22×D311yescharacteristic
672C23×C4—31no—
673C23×C4C22×D311yescharacteristic
674#126—64no—
675#125—64no—
676C22⋊Q8—64no—
677C22⋊Q8—64no—
678C4×Q8—64no—
679#117—64no—
680C2×C4⋊C4—31no—
681C2×C4⋊C4—31no—
682C2×C4⋊C4—31no—
683C2×C4⋊C4—31no—
684C2×C4⋊C4—31no—
685C2×C4⋊C4—31no—
686C2×C4⋊C4—31no—
687C2×C4⋊C4—31no—
688C2×C4⋊C4—31no—
689C2×C4⋊C4—31no—
690C2×C4⋊C4—31no—
691C2×C4⋊C4—31no—
692C2×C4⋊C4—31no—
693C2×C4⋊C4—31no—
694C2×C4⋊C4—31no—
695C2×C4⋊C4—31no—
696C2×C4⋊C4—31no—
697C2×C4⋊C4—31no—
698C2×C4⋊C4—31no—
699C2×C4⋊C4—31no—
700C2×C4⋊C4—31no—
701C2×C4⋊C4—31no—
702C2×C4⋊C4—31no—
703C2×C4⋊C4—31no—
704C2×C4⋊C4—31no—
705C2×C4⋊C4—31no—
706C2×C4⋊C4—31no—
707C2×C4⋊C4—31no—
708C2×C4⋊C4—31no—
709C2×C4⋊C4—31no—
710C2×C4⋊C4—31no—
711C2×C4⋊C4—31no—
712C2×C4⋊C4—31no—
713C2×C4⋊C4—31no—
714C2×C4⋊C4—31no—
715C2×C4⋊C4C22×D311yescharacteristic
716C2×C4⋊C4C22×D311yescharacteristic
717C2×C4⋊C4C22×D311yescharacteristic
718C2×C4⋊C4C22×D311yescharacteristic
719C2×C4⋊C4C22×D311yescharacteristic
720C2×C4⋊C4C22×D311yescharacteristic
721C2×C22⋊C4—31no—
722C2×C22⋊C4—31no—
723C2×C22⋊C4—31no—
724C2×C22⋊C4—31no—
725C2×C22⋊C4—31no—
726C2×C22⋊C4—31no—
727C2×C22⋊C4—31no—
728C2×C22⋊C4—31no—
729C2×C22⋊C4—31no—
730C2×C22⋊C4—31no—
731C2×C22⋊C4—31no—
732C2×C22⋊C4—31no—
733C2×C22⋊C4—31no—
734C2×C22⋊C4—31no—
735C2×C22⋊C4—31no—
736C2×C22⋊C4C22×D311yescharacteristic
737C2×C22⋊C4C22×D311yescharacteristic
738C2×C22⋊C4C22×D311yescharacteristic
739C2×C22⋊C4C22×D311yescharacteristic
740C2×C22⋊C4C22×D311yescharacteristic
741C2×C22⋊C4C22×D311yescharacteristic
742C2×C22⋊C4C22×D311yescharacteristic
743C2×C22⋊C4C22×D311yescharacteristic
744C2×C22⋊C4C22×D311yescharacteristic
745C2×C22⋊C4C22×D311yescharacteristic
746C2×C22⋊C4C22×D311yescharacteristic
747C2×C42—31no—
748C2×C42—31no—
749C2×C42—31no—
750C2×C42—31no—
751C2×C42—31no—
752C2×C42—31no—
753C2×C42—31no—
754C2×C42—31no—
755C2×C42—31no—
756C2×C42—31no—
757C2×C42—31no—
758C2×C42—31no—
759C2×C42—31no—
760C2×C42—31no—
761C2×C42—31no—
762C2×C42—31no—
763C2×C42—31no—
764C2×C42C22×D311yescharacteristic
765C2×C42C22×D311yescharacteristic
766C2×C42C22×D311yescharacteristic
767C2×C42C22×D311yescharacteristic
768#95—31no—
769#95—31no—
770#95—31no—
771#95—31no—
772#95—31no—
773#95—31no—
774#95—31no—
775#95—31no—
776#95—31no—
777#95—31no—
778#95—31no—
779#95—31no—
780#95—31no—
781#95—31no—
782#95—31no—
783#95—31no—
784#95—31no—
785#95—31no—
786#95—31no—
787#95—31no—
788#95—31no—
789#95—31no—
790#95—31no—
791#95—31no—
792#95—31no—
793#95—31no—
794#95—31no—
795#95—31no—
796#95—31no—
797#95—31no—
798#95—31no—
799#95—31no—
800#95—31no—
801#95—31no—
802#95—31no—
803#95—31no—
804#95—31no—
805#95—31no—
806#95—31no—
807#95—31no—
808#95—31no—
809#95—31no—
810#95—31no—
811#95—31no—
812#95—31no—
813#95—31no—
814#95—31no—
815#95—31no—
816#95—31no—
817#95—31no—
818#95C22×D311yescharacteristic
819#95C22×D311yescharacteristic
820#95C22×D311yescharacteristic
821#95C22×D311yescharacteristic
822#95C22×D311yescharacteristic
823#95C22×D311yescharacteristic
824#95C22×D311yescharacteristic
825#95C22×D311yescharacteristic
826#95C22×D311yescharacteristic
827#95C22×D311yescharacteristic
828#95C22×D311yescharacteristic
829#95C22×D311yescharacteristic
830C23×C3—21no—
831C23×C3—21no—
832C23×C3—21no—
833C23×C3—21no—
834C23×C3—21no—
835C23×C3—21no—
836C23×C3—21no—
837C23×C3—21no—
838C23×C3—21no—
839C23×C3—21no—
840C23×C3—21no—
841C23×C3—21no—
842C23×C3—21no—
843C23×C3—21no—
844C23×C3C2511yescharacteristic
845C3×D4—82no—
846C2×C3×C4—21no—
847C2×C3×C4—21no—
848C2×C3×C4—21no—
849C2×C3×C4—21no—
850C2×C3×C4—21no—
851C2×C3×C4—21no—
852C2×C3×C4—21no—
853C2×C3×C4—21no—
854C2×C3×C4—21no—
855C2×C3×C4—21no—
856C2×C3×C4—21no—
857C2×C3×C4—21no—
858C2×C3×C4—21no—
859C2×C3×C4—21no—
860C2×C3×C4—21no—
861C2×C3×C4—21no—
862C2×C3×C4—21no—
863C2×C3×C4—21no—
864C2×C3×C4—21no—
865C2×C3×C4—21no—
866C2×C3×C4—21no—
867C2×C3×C4—21no—
868C2×C3×C4—21no—
869C2×C3×C4—21no—
870C2×C3×C4—21no—
871C2×C3×C4—21no—
872C2×C3×C4—21no—
873C2×C3×C4—21no—
874C2×C3×C4—21no—
875C2×C3×C4—21no—
876C2×C3×C4—21no—
877C2×C3×C4—21no—
878C2×C3×C4—21no—
879C2×C3×C4—21no—
880C2×C3×C4—21no—
881C2×C3×C4—21no—
882C2×C3×C4—44no—
883C2×C3×C4C2×#4112yes—
884C2×C3×C4C2×#4112yes—
885C2×C3×C42−1+412yes—
886C2×Dic3—21no—
887C2×Dic3—21no—
888C2×Dic3—21no—
889C2×Dic3—21no—
890C2×Dic3—21no—
891C2×Dic3—21no—
892C2×Dic3—21no—
893C2×Dic3—21no—
894C2×Dic3—21no—
895C2×Dic3—21no—
896C2×Dic3—21no—
897C2×Dic3—21no—
898C2×Dic3—21no—
899C2×Dic3—21no—
900C2×Dic3—21no—
901C2×Dic3—21no—
902C2×Dic3—21no—
903C2×Dic3—21no—
904C2×Dic3—21no—
905C2×Dic3—21no—
906C2×Dic3—21no—
907C2×Dic3—21no—
908C2×Dic3—21no—
909C2×Dic3—21no—
910C2×Dic3—21no—
911C2×Dic3—21no—
912C2×Dic3—21no—
913C2×Dic3—21no—
914C2×Dic3—21no—
915C2×Dic3—21no—
916C2×Dic3—21no—
917C2×Dic3—21no—
918C2×Dic3—21no—
919C2×Dic3—21no—
920C2×Dic3—21no—
921C2×Dic3—21no—
922C2×Dic3—21no—
923C2×Dic3—21no—
924C2×Dic3—21no—
925C2×Dic3—21no—
926C2×Dic3—21no—
927C2×Dic3—21no—
928C2×Dic3—21no—
929C2×Dic3—21no—
930C2×Dic3—82no—
931C2×Dic3C2×#4112yes—
932C2×Dic3C2×#4112yes—
933C2×Dic3C2×#4112yes—
934C2×Dic3C2×#4112yes—
935Dic6—44no—
936Dic6—82no—
937C24C23×D311yescharacteristic
938C24C23×D311yescharacteristic
939C2×Q8—62no—
940C2×Q8—62no—
941C2×Q8—62no—
942C2×Q8—121no—
943C2×Q8—121no—
944C2×Q8—121no—
945C2×D4—41no—
946C2×D4—41no—
947C2×D4—41no—
948C22×C4—22no—
949C22×C4—22no—
950C22×C4—31no—
951C22×C4—31no—
952C22×C4—31no—
953C22×C4—31no—
954C22×C4—31no—
955C22×C4—31no—
956C22×C4—31no—
957C22×C4—31no—
958C22×C4—31no—
959C22×C4—31no—
960C22×C4—31no—
961C22×C4—31no—
962C22×C4—31no—
963C22×C4—31no—
964C22×C4—31no—
965C22×C4—31no—
966C22×C4—41no—
967C22×C4—62no—
968C22×C4—121no—
969C22×C4—121no—
970C22×C4C23×D311yescharacteristic
971C22×C4C23×D311yescharacteristic
972C22×C4C23×D311yescharacteristic
973C22×C4C23×D311yescharacteristic
974C22×C4C23×D311yescharacteristic
975C22×C4C23×D311yescharacteristic
976C22×C4C23×D311yescharacteristic
977C22×C4C23×D311yescharacteristic
978C22×C4C23×D311yescharacteristic
979C22×C4C23×D311yescharacteristic
980C22×C4C23×D311yescharacteristic
981C22×C4C23×D311yescharacteristic
982C22×C4C23×D311yescharacteristic
983C4⋊C4—22no—
984C4⋊C4—34no—
985C4⋊C4—34no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—62no—
992C4⋊C4—62no—
993C4⋊C4—62no—
994C4⋊C4—62no—
995C4⋊C4—62no—
996C4⋊C4—62no—
997C4⋊C4—62no—
998C4⋊C4—62no—
999C4⋊C4—62no—
1000C4⋊C4—62no—
1001C4⋊C4—62no—
1002C4⋊C4—62no—
1003C4⋊C4—62no—
1004C4⋊C4—62no—
1005C4⋊C4—62no—
1006C4⋊C4—121no—
1007C4⋊C4—121no—
1008C4⋊C4—121no—
1009C4⋊C4—121no—
1010C4⋊C4—121no—
1011C4⋊C4—121no—
1012C4⋊C4—121no—
1013C4⋊C4—121no—
1014C4⋊C4—121no—
1015C4⋊C4—121no—
1016C4⋊C4—121no—
1017C4⋊C4—121no—
1018C4⋊C4—121no—
1019C4⋊C4—121no—
1020C4⋊C4—121no—
1021C4⋊C4—121no—
1022C4⋊C4—121no—
1023C4⋊C4—121no—
1024C22⋊C4—22no—
1025C22⋊C4—22no—
1026C22⋊C4—22no—
1027C22⋊C4—22no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
1034C22⋊C4—41no—
1035C22⋊C4—62no—
1036C22⋊C4—62no—
1037C22⋊C4—62no—
1038C22⋊C4—62no—
1039C22⋊C4—62no—
1040C22⋊C4—62no—
1041C22⋊C4—62no—
1042C22⋊C4—121no—
1043C22⋊C4—121no—
1044C22⋊C4—121no—
1045C22⋊C4—121no—
1046C22⋊C4—121no—
1047C22⋊C4—121no—
1048C22⋊C4—121no—
1049C22⋊C4—121no—
1050C42—22no—
1051C42—22no—
1052C42—41no—
1053C42—41no—
1054C42—62no—
1055C42—62no—
1056C42—62no—
1057C42—62no—
1058C42—62no—
1059C42—62no—
1060C42—121no—
1061C42—121no—
1062C42—121no—
1063C42—121no—
1064C42—121no—
1065C42—121no—
1066C42—121no—
1067C42—121no—
1068C42—121no—
1069C42—121no—
1070C42—121no—
1071C22×C3—41no—
1072C22×C3—41no—
1073C22×C3—41no—
1074C22×C3—41no—
1075C22×C3—41no—
1076C22×C3—41no—
1077C22×C3—41no—
1078C22×C3—41no—
1079C22×C3—41no—
1080C22×C3—41no—
1081C22×C3—41no—
1082C22×C3—41no—
1083C22×C3—41no—
1084C22×C3—41no—
1085C22×C3C22×#4111yescharacteristic
1086C22×C3C22×#4111yescharacteristic
1087C22×C3C2×2−1+411yescharacteristic
1088C22×C3#58511yescharacteristic
1089C22×C3#58511yescharacteristic
1090C22×C3#58511yescharacteristic
1091C22×C3#58511yescharacteristic
1092C3×C4—22no—
1093C3×C4—22no—
1094C3×C4—22no—
1095C3×C4—41no—
1096C3×C4—41no—
1097C3×C4—41no—
1098C3×C4—41no—
1099C3×C4—41no—
1100C3×C4—41no—
1101C3×C4—41no—
1102C3×C4—41no—
1103C3×C4—41no—
1104C3×C4—41no—
1105Dic3—22no—
1106Dic3—22no—
1107Dic3—22no—
1108Dic3—22no—
1109Dic3—41no—
1110Dic3—41no—
1111Dic3—41no—
1112Dic3—41no—
1113Dic3—41no—
1114Dic3—41no—
1115Dic3—41no—
1116Dic3—41no—
1117Dic3—41no—
1118Dic3—41no—
1119Dic3—41no—
1120Dic3—41no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23C24×D311yescharacteristic
1136Q8—124no—
1137Q8—242no—
1138D4—82no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—32no—
1176C2×C4—32no—
1177C2×C4—32no—
1178C2×C4—32no—
1179C2×C4—44no—
1180C2×C4—61no—
1181C2×C4—61no—
1182C2×C4—61no—
1183C2×C4—61no—
1184C2×C4—61no—
1185C2×C4—61no—
1186C2×C4—61no—
1187C2×C4—61no—
1188C2×C4—61no—
1189C2×C4—61no—
1190C2×C4—61no—
1191C2×C4—61no—
1192C2×C4—61no—
1193C2×C4—61no—
1194C2×C4—61no—
1195C2×C4—61no—
1196C2×C4—61no—
1197C2×C4—61no—
1198C2×C4—61no—
1199C2×C4—61no—
1200C2×C4—61no—
1201C2×C4—61no—
1202C2×C4—61no—
1203C2×C4—61no—
1204C2×C4—61no—
1205C2×C4—61no—
1206C2×C4—61no—
1207C2×C4—61no—
1208C2×C4—61no—
1209C2×C4—61no—
1210C2×C4—61no—
1211C2×C4—61no—
1212C2×C4—61no—
1213C2×C4—61no—
1214C2×C4—61no—
1215C2×C4—61no—
1216C2×C4—61no—
1217C2×C4—61no—
1218C2×C4—61no—
1219C2×C4—61no—
1220C2×C4—61no—
1221C2×C4—61no—
1222C2×C4—61no—
1223C2×C4—61no—
1224C2×C4—242no—
1225C2×C4D3×#4112yes—
1226C2×C4D3×#4112yes—
1227C2×C4#101012yes—
1228C2×C3—81no—
1229C2×C3—81no—
1230C2×C3#346111yescharacteristic
1231C2×C3#347511yescharacteristic
1232C2×C3#351611yescharacteristic
1233C2×C3#352111yescharacteristic
1234C2×C3#352411yescharacteristic
1235C2×C3#355711yescharacteristic
1236C2×C3#356611yescharacteristic
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—41no—
1241C22—41no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22—41no—
1249C22—41no—
1250C22—41no—
1251C22C2×D3×#4111yescharacteristic
1252C22C2×D3×#4111yescharacteristic
1253C22C2×#101011yescharacteristic
1254C22#596411yescharacteristic
1255C22#596411yescharacteristic
1256C22#596611yescharacteristic
1257C22#596611yescharacteristic
1258C4—22no—
1259C4—22no—
1260C4—22no—
1261C4—41no—
1262C4—41no—
1263C4—41no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—62no—
1272C4—62no—
1273C4—62no—
1274C4—62no—
1275C4—121no—
1276C4—121no—
1277C4—121no—
1278C4—121no—
1279C4—121no—
1280C4—121no—
1281C4—121no—
1282C4—121no—
1283C4—121no—
1284C4—121no—
1285C4—121no—
1286C4—121no—
1287C3#3833711yescharacteristic, complemented, Sylow
1288C2—81no—
1289C2—81no—
1290C2#8612411yescharacteristic
1291C2#8614911yescharacteristic
1292C2#8647911yescharacteristic
1293C2#8679011yescharacteristic
1294C2#8682411yescharacteristic
1295C2#8689011yescharacteristic
1296C2#8696511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2531C2
prime radicalC22×C3×D4C23
hypercenter#2531D3
hypocenterC3#38337
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2531

Complements

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

NH ≅ G/Ntype
2. #77876C2semidirect
3. #77836C2semidirect
4. #77623C2semidirect
5. #77590C2semidirect
6. #77530C2semidirect
7. #77496C2semidirect
12. #75822C2semidirect
13. #75797C2semidirect
14. #75633C2semidirect
15. #75591C2semidirect
16. #75582C2semidirect
17. #75514C2semidirect
18. #75464C2semidirect
19. #75455C2semidirect
20. #75191C2semidirect
21. #75095C2semidirect
22. #75030C2semidirect
23. #74968C2semidirect
26. #73960C2semidirect
27. #73868C2semidirect
28. #73528C2semidirect
29. #73468C2semidirect
30. #73399C2semidirect
31. #73384C2semidirect
1287. C3#38337semidirect

Maximal subgroups

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

subgroupindex
C3×#25312
#778762
#778362
#776232
#775902
#775302
#774962
#770782
#769882
#763662
#763432
#758222
#757972
#756332
#755912
#755822
#755142
#754642
#754552
#751912
#750952
#750302
#749682
#748122
#747332
#739602
#738682
#735282
#734682
#733992
#733842
#383373