Finite Group Databasebeta

← #11223023

Subgroups — #11223023

Order 768.

1542 conjugacy classes of subgroups.

The subgroup lattice has 1286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2529C211yesmaximal, characteristic
2#78284C211yesmaximal, characteristic, complemented
3#78191C211yesmaximal, characteristic, complemented
4#77748C211yesmaximal, characteristic, complemented
5#77740C211yesmaximal, characteristic, complemented
6#77504C211yesmaximal, characteristic
7#77478C211yesmaximal, characteristic
8#77298C211yesmaximal, characteristic
9#77296C211yesmaximal, characteristic
10#76139C211yesmaximal, characteristic, complemented
11#75986C211yesmaximal, characteristic, complemented
12#75745C211yesmaximal, characteristic
13#75736C211yesmaximal, characteristic
14#75672C211yesmaximal, characteristic
15#75667C211yesmaximal, characteristic
16#75648C211yesmaximal, characteristic
17#75608C211yesmaximal, characteristic
18#75587C211yesmaximal, characteristic
19#75581C211yesmaximal, characteristic
20#75478C211yesmaximal, characteristic
21#75459C211yesmaximal, characteristic
22#75187C211yesmaximal, characteristic, complemented
23#75098C211yesmaximal, characteristic, complemented
24#75057C211yesmaximal, characteristic, complemented
25#75041C211yesmaximal, characteristic, complemented
26#74212C211yesmaximal, characteristic, complemented
27#74152C211yesmaximal, characteristic, complemented
28#73713C211yesmaximal, characteristic, complemented
29#73644C211yesmaximal, characteristic, complemented
30#73405C211yesmaximal, characteristic, complemented
31#73394C211yesmaximal, characteristic, complemented
32#44866—31nomaximal, Sylow
33C2×#888C2211yescharacteristic
34C2×#887C2211yescharacteristic
35C2×#887C2211yescharacteristic
36C2×#887C2211yescharacteristic
37C2×#887C2211yescharacteristic
38C2×#887C2211yescharacteristic
39C2×#879C2211yescharacteristic
40C2×#878C2211yescharacteristic
41C2×#878C2211yescharacteristic
42C2×#877C2211yescharacteristic
43C2×#870C2211yescharacteristic
44C2×#869C2211yescharacteristic
45C3×#400C2211yescharacteristic
46C3×#398C2211yescharacteristic
47C3×#397C2211yescharacteristic
48C3×#396C2211yescharacteristic
49C3×#389C2211yescharacteristic
50C3×#388C2211yescharacteristic
51C3×#388C2211yescharacteristic
52C3×#388C2211yescharacteristic
53C3×#388C2211yescharacteristic
54C3×#388C2211yescharacteristic
55C3×#387C2211yescharacteristic
56C3×#387C2211yescharacteristic
57C3×#382C2211yescharacteristic
58C3×C4×C4⋊C4C2211yescharacteristic
59C3×#376C2211yescharacteristic
60#4986C2211yescharacteristic
61#4985C2211yescharacteristic
62#4985C2211yescharacteristic
63#4984C2211yescharacteristic
64#4983C2211yescharacteristic
65#4982C2211yescharacteristic
66#4982C2211yescharacteristic
67#4980C2211yescharacteristic
68#4980C2211yescharacteristic
69#4979C2211yescharacteristic
70#4979C2211yescharacteristic
71#4979C2211yescharacteristic
72#4979C2211yescharacteristic
73#4979C2211yescharacteristic
74#4979C2211yescharacteristic
75#4978C2211yescharacteristic
76#4978C2211yescharacteristic
77#4978C2211yescharacteristic
78#4978C2211yescharacteristic
79#4978C2211yescharacteristic
80#4977C2211yescharacteristic
81#4976C2211yescharacteristic
82#4976C2211yescharacteristic
83Dic3×C4⋊C4C2211yescharacteristic
84Dic3×C4⋊C4C2211yescharacteristic
85Dic3×C4⋊C4C2211yescharacteristic
86#4973C2211yescharacteristic
87#4973C2211yescharacteristic
88#4973C2211yescharacteristic
89#4972C2211yescharacteristic
90#4953C2211yescharacteristic
91#4952C2211yescharacteristic
92#4952C2211yescharacteristic
93#4951C2211yescharacteristic
94#4951C2211yescharacteristic
95#4951C2211yescharacteristic
96#4951C2211yescharacteristic
97#4950C2211yescharacteristic
98#4949C2211yescharacteristic
99#4948C2211yescharacteristic
100#4947C2211yescharacteristic
101#4947C2211yescharacteristic
102#4947C2211yescharacteristic
103#4946C2211yescharacteristic
104#4945C2211yescharacteristic
105#4945C2211yescharacteristic
106#4945C2211yescharacteristic
107#4944C2211yescharacteristic
108#4944C2211yescharacteristic
109#4944C2211yescharacteristic
110#4944C2211yescharacteristic
111#4944C2211yescharacteristic
112#4942C2211yescharacteristic
113Dic3×C22⋊C4C2211yescharacteristic
114#4937C2211yescharacteristic
115#4936C2211yescharacteristic
116C4×C4⋊Dic3C2211yescharacteristic
117C4×C4⋊Dic3C2211yescharacteristic
118#4933C2211yescharacteristic
119#4933C2211yescharacteristic
120#4933C2211yescharacteristic
121#4933C2211yescharacteristic
122#4933C2211yescharacteristic
123#4932C2211yescharacteristic
124#4932C2211yescharacteristic
125C4×Dic3⋊C4C2211yescharacteristic
126C4×Dic3⋊C4C2211yescharacteristic
127C4×Dic3⋊C4C2211yescharacteristic
128#4929C2211yescharacteristic
129#4928C2211yescharacteristic
130#4928C2211yescharacteristic
131#4928C2211yescharacteristic
132C3⋊#401C2211yescharacteristic
133#4661C2211yescharacteristic
134#4661C2211yescharacteristic
135#4660C2211yescharacteristic
136#4660C2211yescharacteristic
137#4659C2211yescharacteristic
138#4658C2211yescharacteristic
139#4658C2211yescharacteristic
140#4657C2211yescharacteristic
141#4657C2211yescharacteristic
142#4657C2211yescharacteristic
143#4657C2211yescharacteristic
144#4657C2211yescharacteristic
145#4656C2211yescharacteristic
146#4656C2211yescharacteristic
147#4656C2211yescharacteristic
148#4655C2211yescharacteristic
149#4654C2211yescharacteristic
150#4654C2211yescharacteristic
151#4654C2211yescharacteristic
152#4654C2211yescharacteristic
153#4654C2211yescharacteristic
154#4654C2211yescharacteristic
155#4654C2211yescharacteristic
156#4654C2211yescharacteristic
157#4654C2211yescharacteristic
158#4654C2211yescharacteristic
159#4654C2211yescharacteristic
160#4653C2211yescharacteristic
161#4653C2211yescharacteristic
162#4652C2211yescharacteristic
163#4652C2211yescharacteristic
164#4652C2211yescharacteristic
165#4652C2211yescharacteristic
166#4652C2211yescharacteristic
167#4652C2211yescharacteristic
168#4651C2211yescharacteristic
169#4651C2211yescharacteristic
170#4650C2211yescharacteristic
171#4649C2211yescharacteristic
172#4649C2211yescharacteristic
173#4649C2211yescharacteristic
174#4648C2211yescharacteristic
175#4647C2211yescharacteristic
176#4647C2211yescharacteristic
177#4647C2211yescharacteristic
178#4647C2211yescharacteristic
179#4647C2211yescharacteristic
180#4646C2211yescharacteristic
181#4646C2211yescharacteristic
182#4646C2211yescharacteristic
183#4646C2211yescharacteristic
184#4646C2211yescharacteristic
185#4646C2211yescharacteristic
186#4646C2211yescharacteristic
187#4646C2211yescharacteristic
188#2776—31no—
189#2774—31no—
190#2759—31no—
191#2758—31no—
192#2755—31no—
193#2754—31no—
194#2690—31no—
195#2677—31no—
196#2606—31no—
197#2604—31no—
198#2586—31no—
199#2581—31no—
200#2574—31no—
201#2550—31no—
202#2532—31no—
203#2529—31no—
204#2529D311yescharacteristic
205#2528—31no—
206#2525—31no—
207#2520—31no—
208#2478—31no—
209#2469—31no—
210#2465—31no—
211#2451—31no—
212#2399—31no—
213#2371—31no—
214#2365—31no—
215#2362—31no—
216#2356—31no—
217#2327—31no—
218#2323—31no—
219C23×Dic3C2311yescharacteristic
220C22×Dic6C2311yescharacteristic
221C22×Dic6C2311yescharacteristic
222C22×Dic6C2311yescharacteristic
223C22×Dic6C2311yescharacteristic
224C22×Dic6C2311yescharacteristic
225C2×C3×C4⋊C4C2311yescharacteristic
226C2×C3×C4⋊C4C2311yescharacteristic
227C2×C3×C4⋊C4C2311yescharacteristic
228C2×C3×C4⋊C4C2311yescharacteristic
229C2×C3×C4⋊C4C2311yescharacteristic
230C2×C3×C4⋊C4C2311yescharacteristic
231C2×C3×C4⋊C4C2311yescharacteristic
232C2×C3×C4⋊C4C2311yescharacteristic
233C2×C3×C4⋊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×C3×C42C2311yescharacteristic
246C2×#217C2311yescharacteristic
247C2×#217C2311yescharacteristic
248C2×#217C2311yescharacteristic
249C2×#217C2311yescharacteristic
250C2×#217C2311yescharacteristic
251C2×#217C2311yescharacteristic
252C2×#217C2311yescharacteristic
253C2×C4⋊Dic3C2311yescharacteristic
254C2×C4⋊Dic3C2311yescharacteristic
255C2×C4⋊Dic3C2311yescharacteristic
256C2×C4⋊Dic3C2311yescharacteristic
257C2×C4⋊Dic3C2311yescharacteristic
258C2×C4⋊Dic3C2311yescharacteristic
259C2×C4⋊Dic3C2311yescharacteristic
260C2×C4⋊Dic3C2311yescharacteristic
261C2×C4⋊Dic3C2311yescharacteristic
262C2×C4⋊Dic3C2311yescharacteristic
263C2×C4⋊Dic3C2311yescharacteristic
264C2×C4⋊Dic3C2311yescharacteristic
265C2×Dic3⋊C4C2311yescharacteristic
266C2×Dic3⋊C4C2311yescharacteristic
267C2×Dic3⋊C4C2311yescharacteristic
268C2×Dic3⋊C4C2311yescharacteristic
269C2×Dic3⋊C4C2311yescharacteristic
270C2×Dic3⋊C4C2311yescharacteristic
271C2×Dic3⋊C4C2311yescharacteristic
272C2×Dic3⋊C4C2311yescharacteristic
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×C4×Dic3C2311yescharacteristic
292C2×C4×Dic3C2311yescharacteristic
293C2×C4×Dic3C2311yescharacteristic
294C2×C4×Dic3C2311yescharacteristic
295C2×C4×Dic3C2311yescharacteristic
296C2×C4×Dic3C2311yescharacteristic
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
308#888—24no—
309#887—24no—
310#887—42no—
311#887—42no—
312#887—42no—
313#887—42no—
314#879—42no—
315#878—24no—
316#878—24no—
317#877—42no—
318#870—24no—
319#869—24no—
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
380C3⋊#95C2311yescharacteristic
381C3⋊#95C2311yescharacteristic
382C3⋊#95C2311yescharacteristic
383C3⋊#95C2311yescharacteristic
384C3⋊#95C2311yescharacteristic
385C3⋊#95C2311yescharacteristic
386C2×C4⋊Q8—31no—
387C2×C4⋊Q8—31no—
388C2×#126—31no—
389C2×#125—31no—
390C2×C22⋊Q8—31no—
391C2×C22⋊Q8—31no—
392C2×C4×Q8—31no—
393C2×C4×Q8—31no—
394C2×C4×Q8—31no—
395C2×C4×Q8—31no—
396C2×C4×Q8—31no—
397C2×#117—31no—
398#401—31no—
399#400—31no—
400#400—31no—
401#400—31no—
402#400—31no—
403#400—31no—
404#400—31no—
405#400—31no—
406#400—31no—
407#400C2×D311yescharacteristic
408#399—31no—
409#398—31no—
410#398—31no—
411#398—31no—
412#398—31no—
413#398—31no—
414#398—31no—
415#398—31no—
416#398—31no—
417#398—31no—
418#398—31no—
419#398C2×D311yescharacteristic
420#397—31no—
421#397—31no—
422#397—31no—
423#397C2×D311yescharacteristic
424#396—31no—
425#396C2×D311yescharacteristic
426#395—31no—
427#395—31no—
428#395—31no—
429#395—31no—
430#395—31no—
431#395—31no—
432#395—31no—
433#395—31no—
434#395—31no—
435#393—31no—
436#393—31no—
437#393—31no—
438#391—31no—
439#391—31no—
440#391—31no—
441#391—31no—
442#391—31no—
443#391—31no—
444#391—31no—
445#391—31no—
446#391—31no—
447#391—31no—
448#391—31no—
449#391—31no—
450#389—31no—
451#389—31no—
452#389—31no—
453#389—31no—
454#389—31no—
455#389—31no—
456#389—31no—
457#389—31no—
458#389—31no—
459#389—31no—
460#389—31no—
461#389—31no—
462#389C2×D311yescharacteristic
463#388—31no—
464#388—31no—
465#388—31no—
466#388—31no—
467#388—31no—
468#388—31no—
469#388—31no—
470#388—31no—
471#388—31no—
472#388—31no—
473#388—31no—
474#388—31no—
475#388C2×D311yescharacteristic
476#388C2×D311yescharacteristic
477#388C2×D311yescharacteristic
478#388C2×D311yescharacteristic
479#388C2×D311yescharacteristic
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#387—31no—
503#387—31no—
504#387—31no—
505#387—31no—
506#387—31no—
507#387—31no—
508#387—31no—
509#387—31no—
510#387—31no—
511#387—31no—
512#387C2×D311yescharacteristic
513#387C2×D311yescharacteristic
514#385—31no—
515#385—31no—
516#383—31no—
517#383—31no—
518#383—31no—
519#382—31no—
520#382—31no—
521#382—31no—
522#382C2×D311yescharacteristic
523#380—31no—
524C4×C4⋊C4—31no—
525C4×C4⋊C4—31no—
526C4×C4⋊C4—31no—
527C4×C4⋊C4—31no—
528C4×C4⋊C4—31no—
529C4×C4⋊C4—31no—
530C4×C4⋊C4—31no—
531C4×C4⋊C4—31no—
532C4×C4⋊C4—31no—
533C4×C4⋊C4—31no—
534C4×C4⋊C4—31no—
535C4×C4⋊C4C2×D311yescharacteristic
536C4×C22⋊C4—31no—
537#376—31no—
538#376—31no—
539#376—31no—
540#376C2×D311yescharacteristic
541C24×C3C2411yescharacteristic
542C22×C3×C4C2411yescharacteristic
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—22no—
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—22no—
579C2×Dic6—22no—
580C2×Dic6—22no—
581C2×Dic6—22no—
582C2×Dic6—22no—
583C2×Dic6—22no—
584C2×Dic6—41no—
585C2×Dic6—41no—
586C2×Dic6—41no—
587C2×Dic6—41no—
588C2×Dic6—41no—
589C2×Dic6—41no—
590C3×C4⋊C4—22no—
591C3×C4⋊C4—22no—
592C3×C4⋊C4—22no—
593C3×C4⋊C4—22no—
594C3×C4⋊C4—41no—
595C3×C4⋊C4—41no—
596C3×C4⋊C4—41no—
597C3×C4⋊C4—41no—
598C3×C4⋊C4—41no—
599C3×C22⋊C4—22no—
600C3×C22⋊C4—22no—
601C3×C22⋊C4—22no—
602C3×C22⋊C4—22no—
603C3×C22⋊C4—41no—
604C3×C22⋊C4—41no—
605C3×C22⋊C4—41no—
606C3×C42—22no—
607C3×C42—22no—
608C3×C42—22no—
609C3×C42—22no—
610C3×C42—41no—
611#217—22no—
612#217—22no—
613#217—22no—
614#217—22no—
615#217—41no—
616#217—41no—
617#217—41no—
618C4⋊Dic3—22no—
619C4⋊Dic3—22no—
620C4⋊Dic3—22no—
621C4⋊Dic3—22no—
622C4⋊Dic3—22no—
623C4⋊Dic3—22no—
624C4⋊Dic3—22no—
625C4⋊Dic3—22no—
626C4⋊Dic3—41no—
627C4⋊Dic3—41no—
628C4⋊Dic3—41no—
629C4⋊Dic3#4114yes—
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—22no—
640Dic3⋊C4—22no—
641Dic3⋊C4—22no—
642Dic3⋊C4—22no—
643Dic3⋊C4—22no—
644Dic3⋊C4—41no—
645Dic3⋊C4—41no—
646Dic3⋊C4—41no—
647Dic3⋊C4—41no—
648Dic3⋊C4—41no—
649Dic3⋊C4—41no—
650Dic3⋊C4—41no—
651Dic3⋊C4—41no—
652Dic3⋊C4—41no—
653Dic3⋊C4—41no—
654Dic3⋊C4—41no—
655Dic3⋊C4#4114yes—
656C4×Dic3—22no—
657C4×Dic3—22no—
658C4×Dic3—22no—
659C4×Dic3—22no—
660C4×Dic3—22no—
661C4×Dic3—22no—
662C4×Dic3—22no—
663C4×Dic3—22no—
664C4×Dic3—22no—
665C4×Dic3—22no—
666C4×Dic3—22no—
667C4×Dic3—41no—
668C4×Dic3—41no—
669C4×Dic3—41no—
670C4×Dic3—41no—
671C4×Dic3—41no—
672C4×Dic3—41no—
673C22×Q8—31no—
674C22×Q8—31no—
675C22×Q8—31no—
676C22×Q8—31no—
677C22×Q8—31no—
678C23×C4—31no—
679C4⋊Q8—64no—
680C4⋊Q8—64no—
681#126—122no—
682#125—64no—
683C22⋊Q8—64no—
684C22⋊Q8—64no—
685C4×Q8—64no—
686C4×Q8—122no—
687C4×Q8—122no—
688C4×Q8—122no—
689C4×Q8—122no—
690#117—122no—
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⋊C4—31no—
716C2×C4⋊C4—31no—
717C2×C4⋊C4—31no—
718C2×C4⋊C4—31no—
719C2×C4⋊C4—31no—
720C2×C4⋊C4—31no—
721C2×C4⋊C4—31no—
722C2×C4⋊C4—31no—
723C2×C4⋊C4—31no—
724C2×C4⋊C4—31no—
725C2×C4⋊C4—31no—
726C2×C4⋊C4—31no—
727C2×C4⋊C4—31no—
728C2×C4⋊C4—31no—
729C2×C4⋊C4C22×D311yescharacteristic
730C2×C4⋊C4C22×D311yescharacteristic
731C2×C4⋊C4C22×D311yescharacteristic
732C2×C4⋊C4C22×D311yescharacteristic
733C2×C4⋊C4C22×D311yescharacteristic
734C2×C4⋊C4C22×D311yescharacteristic
735C2×C4⋊C4C22×D311yescharacteristic
736C2×C4⋊C4C22×D311yescharacteristic
737C2×C4⋊C4C22×D311yescharacteristic
738C2×C22⋊C4—31no—
739C2×C22⋊C4—31no—
740C2×C22⋊C4—31no—
741C2×C22⋊C4—31no—
742C2×C22⋊C4—31no—
743C2×C22⋊C4—31no—
744C2×C22⋊C4—31no—
745C2×C22⋊C4C22×D311yescharacteristic
746C2×C22⋊C4C22×D311yescharacteristic
747C2×C22⋊C4C22×D311yescharacteristic
748C2×C22⋊C4C22×D311yescharacteristic
749C2×C22⋊C4C22×D311yescharacteristic
750C2×C22⋊C4C22×D311yescharacteristic
751C2×C22⋊C4C22×D311yescharacteristic
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×C42—31no—
765C2×C42—31no—
766C2×C42—31no—
767C2×C42—31no—
768C2×C42—31no—
769C2×C42C22×D311yescharacteristic
770C2×C42C22×D311yescharacteristic
771C2×C42C22×D311yescharacteristic
772C2×C42C22×D311yescharacteristic
773C2×C42C22×D311yescharacteristic
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#95—31no—
819#95—31no—
820#95—31no—
821#95—31no—
822#95—31no—
823#95—31no—
824#95—31no—
825#95—31no—
826#95C22×D311yescharacteristic
827#95C22×D311yescharacteristic
828#95C22×D311yescharacteristic
829#95C22×D311yescharacteristic
830#95C22×D311yescharacteristic
831#95C22×D311yescharacteristic
832#95C22×D311yescharacteristic
833#95C22×D311yescharacteristic
834#95C22×D311yescharacteristic
835#95C22×D311yescharacteristic
836#95C22×D311yescharacteristic
837#95C22×D311yescharacteristic
838#95C22×D311yescharacteristic
839#95C22×D311yescharacteristic
840C23×C3—21no—
841C23×C3—21no—
842C23×C3—21no—
843C23×C3—21no—
844C23×C3—21no—
845C23×C3—21no—
846C23×C3—21no—
847C23×C3C2511yescharacteristic
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—21no—
883C2×C3×C4—21no—
884C2×C3×C4—21no—
885C2×C3×C4—21no—
886C2×C3×C4C2×#4112yes—
887C2×C3×C4C2×#4112yes—
888C2×C3×C42−1+412yes—
889C2×C3×C42−1+412yes—
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—21no—
931C2×Dic3—21no—
932C2×Dic3—44no—
933C2×Dic3C2×#4112yes—
934C2×Dic3C2×#4112yes—
935C2×Dic3C2×#4112yes—
936C2×Dic3C2×#4112yes—
937C2×Dic3H(5,𝔽2)12yes—
938C2×Dic32−1+412yes—
939Dic6—44no—
940Dic6—44no—
941Dic6—44no—
942Dic6—44no—
943Dic6—44no—
944C24C23×D311yescharacteristic
945C2×Q8—62no—
946C2×Q8—62no—
947C2×Q8—62no—
948C2×Q8—62no—
949C2×Q8—62no—
950C2×Q8—62no—
951C2×Q8—62no—
952C2×Q8—62no—
953C2×Q8—62no—
954C2×Q8—121no—
955C2×Q8—121no—
956C2×Q8—121no—
957C2×Q8—121no—
958C2×Q8—121no—
959C2×Q8—121no—
960C22×C4—31no—
961C22×C4—31no—
962C22×C4—31no—
963C22×C4—31no—
964C22×C4—31no—
965C22×C4—31no—
966C22×C4—31no—
967C22×C4—31no—
968C22×C4—31no—
969C22×C4—31no—
970C22×C4—31no—
971C22×C4—31no—
972C22×C4—31no—
973C22×C4—31no—
974C22×C4—31no—
975C22×C4—31no—
976C22×C4—62no—
977C22×C4—62no—
978C22×C4—121no—
979C22×C4C23×D311yescharacteristic
980C22×C4C23×D311yescharacteristic
981C22×C4C23×D311yescharacteristic
982C22×C4C23×D311yescharacteristic
983C22×C4C23×D311yescharacteristic
984C22×C4C23×D311yescharacteristic
985C22×C4C23×D311yescharacteristic
986C22×C4C23×D311yescharacteristic
987C22×C4C23×D311yescharacteristic
988C22×C4C23×D311yescharacteristic
989C22×C4C23×D311yescharacteristic
990C22×C4C23×D311yescharacteristic
991C22×C4C23×D311yescharacteristic
992C22×C4C23×D311yescharacteristic
993C4⋊C4—22no—
994C4⋊C4—22no—
995C4⋊C4—22no—
996C4⋊C4—22no—
997C4⋊C4—34no—
998C4⋊C4—34no—
999C4⋊C4—41no—
1000C4⋊C4—41no—
1001C4⋊C4—41no—
1002C4⋊C4—41no—
1003C4⋊C4—41no—
1004C4⋊C4—62no—
1005C4⋊C4—62no—
1006C4⋊C4—62no—
1007C4⋊C4—62no—
1008C4⋊C4—62no—
1009C4⋊C4—62no—
1010C4⋊C4—62no—
1011C4⋊C4—62no—
1012C4⋊C4—62no—
1013C4⋊C4—62no—
1014C4⋊C4—62no—
1015C4⋊C4—62no—
1016C4⋊C4—62no—
1017C4⋊C4—62no—
1018C4⋊C4—62no—
1019C4⋊C4—62no—
1020C4⋊C4—62no—
1021C4⋊C4—62no—
1022C4⋊C4—62no—
1023C4⋊C4—62no—
1024C4⋊C4—62no—
1025C4⋊C4—62no—
1026C4⋊C4—121no—
1027C4⋊C4—121no—
1028C4⋊C4—121no—
1029C4⋊C4—121no—
1030C4⋊C4—121no—
1031C4⋊C4—121no—
1032C4⋊C4—121no—
1033C4⋊C4—121no—
1034C4⋊C4—121no—
1035C4⋊C4—121no—
1036C4⋊C4—121no—
1037C4⋊C4—121no—
1038C4⋊C4—121no—
1039C4⋊C4—121no—
1040C22⋊C4—22no—
1041C22⋊C4—22no—
1042C22⋊C4—22no—
1043C22⋊C4—22no—
1044C22⋊C4—41no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—62no—
1048C22⋊C4—62no—
1049C22⋊C4—62no—
1050C22⋊C4—62no—
1051C22⋊C4—121no—
1052C22⋊C4—121no—
1053C22⋊C4—121no—
1054C42—22no—
1055C42—22no—
1056C42—22no—
1057C42—22no—
1058C42—41no—
1059C42—62no—
1060C42—62no—
1061C42—62no—
1062C42—62no—
1063C42—62no—
1064C42—62no—
1065C42—62no—
1066C42—62no—
1067C42—62no—
1068C42—62no—
1069C42—62no—
1070C42—121no—
1071C42—121no—
1072C42—121no—
1073C42—121no—
1074C42—121no—
1075C42—121no—
1076C22×C3—41no—
1077C22×C3—41no—
1078C22×C3—41no—
1079C22×C3—41no—
1080C22×C3—41no—
1081C22×C3—41no—
1082C22×C3—41no—
1083C22×C3C22×#4111yescharacteristic
1084C22×C3C22×#4111yescharacteristic
1085C22×C3C2×H(5,𝔽2)11yescharacteristic
1086C22×C3C2×2−1+411yescharacteristic
1087C22×C3C2×2−1+411yescharacteristic
1088C22×C3C2×2−1+411yescharacteristic
1089C22×C3#58511yescharacteristic
1090C3×C4—22no—
1091C3×C4—22no—
1092C3×C4—22no—
1093C3×C4—22no—
1094C3×C4—41no—
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—
1104Dic3—22no—
1105Dic3—22no—
1106Dic3—22no—
1107Dic3—22no—
1108Dic3—22no—
1109Dic3—22no—
1110Dic3—41no—
1111Dic3—41no—
1112Dic3—41no—
1113Dic3—41no—
1114Dic3—41no—
1115Dic3—41no—
1116Dic3—41no—
1117Dic3—41no—
1118Dic3—41no—
1119Dic3—41no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23C24×D311yescharacteristic
1128Q8—124no—
1129Q8—124no—
1130Q8—124no—
1131Q8—124no—
1132Q8—124no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
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—32no—
1172C2×C4—32no—
1173C2×C4—32no—
1174C2×C4—32no—
1175C2×C4—32no—
1176C2×C4—32no—
1177C2×C4—61no—
1178C2×C4—61no—
1179C2×C4—61no—
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—124no—
1220C2×C4D3×#4112yes—
1221C2×C4D3×#4112yes—
1222C2×C4#101012yes—
1223C2×C4#101012yes—
1224C2×C3—81no—
1225C2×C3#348111yescharacteristic
1226C2×C3#349511yescharacteristic
1227C2×C3#350911yescharacteristic
1228C2×C3#351811yescharacteristic
1229C2×C3#352311yescharacteristic
1230C2×C3#354111yescharacteristic
1231C2×C3#354411yescharacteristic
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22C2×D3×#4111yescharacteristic
1240C22C2×D3×#4111yescharacteristic
1241C22C2×#101011yescharacteristic
1242C22C2×#101011yescharacteristic
1243C22#596411yescharacteristic
1244C22D3×H(5,𝔽2)11yescharacteristic
1245C22D3×2−1+411yescharacteristic
1246C4—22no—
1247C4—22no—
1248C4—22no—
1249C4—22no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—41no—
1259C4—41no—
1260C4—62no—
1261C4—62no—
1262C4—62no—
1263C4—62no—
1264C4—62no—
1265C4—62no—
1266C4—121no—
1267C4—121no—
1268C4—121no—
1269C4—121no—
1270C4—121no—
1271C4—121no—
1272C4—121no—
1273C4—121no—
1274C4—121no—
1275C4—121no—
1276C3#4486611yescharacteristic, complemented, Sylow
1277C2—81no—
1278C2#8612711yescharacteristic
1279C2#8615711yescharacteristic
1280C2#8653111yescharacteristic
1281C2#8683211yescharacteristic
1282C2#8684211yescharacteristic
1283C2#8687611yescharacteristic
1284C2#8697511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2529C2
prime radicalC24×C3C24
hypercenter#2529D3
hypocenterC3#44866
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2529

Complements

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

NH ≅ G/Ntype
2. #78284C2semidirect
3. #78191C2semidirect
4. #77748C2semidirect
5. #77740C2semidirect
10. #76139C2semidirect
11. #75986C2semidirect
22. #75187C2semidirect
23. #75098C2semidirect
24. #75057C2semidirect
25. #75041C2semidirect
26. #74212C2semidirect
27. #74152C2semidirect
28. #73713C2semidirect
29. #73644C2semidirect
30. #73405C2semidirect
31. #73394C2semidirect
1276. C3#44866semidirect

Maximal subgroups

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

subgroupindex
C3×#25292
#782842
#781912
#777482
#777402
#775042
#774782
#772982
#772962
#761392
#759862
#757452
#757362
#756722
#756672
#756482
#756082
#755872
#755812
#754782
#754592
#751872
#750982
#750572
#750412
#742122
#741522
#737132
#736442
#734052
#733942
#448663