Finite Group Databasebeta

← #11044241

Subgroups — #11044241

Order 768.

1496 conjugacy classes of subgroups.

The subgroup lattice has 1300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2290C211yesmaximal, characteristic
2#82371C211yesmaximal, characteristic
3#82369C211yesmaximal, characteristic
4#82261C211yesmaximal, characteristic, complemented
5#82239C211yesmaximal, characteristic, complemented
6#82074C211yesmaximal, characteristic, complemented
7#82060C211yesmaximal, characteristic, complemented
8#75766C211yesmaximal, characteristic, complemented
9#75763C211yesmaximal, characteristic, complemented
10#75637C211yesmaximal, characteristic, complemented
11#75628C211yesmaximal, characteristic, complemented
12#75229C211yesmaximal, characteristic, complemented
13#75203C211yesmaximal, characteristic, complemented
14#75113C211yesmaximal, characteristic, complemented
15#75105C211yesmaximal, characteristic, complemented
16#74833C211yesmaximal, characteristic
17#74833C211yesmaximal, characteristic
18#74789C211yesmaximal, characteristic
19#74788C211yesmaximal, characteristic
20#74544C211yesmaximal, characteristic, complemented
21#74536C211yesmaximal, characteristic, complemented
22#74389C211yesmaximal, characteristic, complemented
23#74388C211yesmaximal, characteristic, complemented
24#73706C211yesmaximal, characteristic, complemented
25#73687C211yesmaximal, characteristic, complemented
26#73543C211yesmaximal, characteristic, complemented
27#73542C211yesmaximal, characteristic, complemented
28#73531C211yesmaximal, characteristic, complemented
29#73524C211yesmaximal, characteristic, complemented
30#73406C211yesmaximal, characteristic, complemented
31#73394C211yesmaximal, characteristic, complemented
32#38417—31nomaximal, Sylow
33C2×C3×C4×D4C2211yescharacteristic
34C2×C3×#117C2211yescharacteristic
35C22×C3×C42C2211yescharacteristic
36C2×#879C2211yescharacteristic
37C2×#879C2211yescharacteristic
38C2×#870C2211yescharacteristic
39C3×#388C2211yescharacteristic
40C3×#388C2211yescharacteristic
41C3×#387C2211yescharacteristic
42C3×#387C2211yescharacteristic
43C3×#386C2211yescharacteristic
44C3×#386C2211yescharacteristic
45C3×#385C2211yescharacteristic
46C3×#385C2211yescharacteristic
47C3×C4×C4⋊C4C2211yescharacteristic
48C3×C4×C22⋊C4C2211yescharacteristic
49C3×C4×C22⋊C4C2211yescharacteristic
50C3×#376C2211yescharacteristic
51#5222C2211yescharacteristic
52#5222C2211yescharacteristic
53#5222C2211yescharacteristic
54#5222C2211yescharacteristic
55#5212C2211yescharacteristic
56#5212C2211yescharacteristic
57#5212C2211yescharacteristic
58#5212C2211yescharacteristic
59#5212C2211yescharacteristic
60#5211C2211yescharacteristic
61#5211C2211yescharacteristic
62#5210C2211yescharacteristic
63#5210C2211yescharacteristic
64#5210C2211yescharacteristic
65#5210C2211yescharacteristic
66#5210C2211yescharacteristic
67#5210C2211yescharacteristic
68C4×#217C2211yescharacteristic
69C4×#217C2211yescharacteristic
70C4×#217C2211yescharacteristic
71#4986C2211yescharacteristic
72#4986C2211yescharacteristic
73#4984C2211yescharacteristic
74#4984C2211yescharacteristic
75#4984C2211yescharacteristic
76#4984C2211yescharacteristic
77#4982C2211yescharacteristic
78#4981C2211yescharacteristic
79#4981C2211yescharacteristic
80#4981C2211yescharacteristic
81#4978C2211yescharacteristic
82#4978C2211yescharacteristic
83#4977C2211yescharacteristic
84#4976C2211yescharacteristic
85#4976C2211yescharacteristic
86#4976C2211yescharacteristic
87#4976C2211yescharacteristic
88Dic3×C4⋊C4C2211yescharacteristic
89Dic3×C4⋊C4C2211yescharacteristic
90#4972C2211yescharacteristic
91#4953C2211yescharacteristic
92#4953C2211yescharacteristic
93#4953C2211yescharacteristic
94#4953C2211yescharacteristic
95#4953C2211yescharacteristic
96#4952C2211yescharacteristic
97#4952C2211yescharacteristic
98#4951C2211yescharacteristic
99#4951C2211yescharacteristic
100#4951C2211yescharacteristic
101#4951C2211yescharacteristic
102#4951C2211yescharacteristic
103#4951C2211yescharacteristic
104#4951C2211yescharacteristic
105#4951C2211yescharacteristic
106#4949C2211yescharacteristic
107#4949C2211yescharacteristic
108#4949C2211yescharacteristic
109#4948C2211yescharacteristic
110#4948C2211yescharacteristic
111#4947C2211yescharacteristic
112#4947C2211yescharacteristic
113#4945C2211yescharacteristic
114#4945C2211yescharacteristic
115#4945C2211yescharacteristic
116#4945C2211yescharacteristic
117#4945C2211yescharacteristic
118#4944C2211yescharacteristic
119#4944C2211yescharacteristic
120#4944C2211yescharacteristic
121#4937C2211yescharacteristic
122#4937C2211yescharacteristic
123#4936C2211yescharacteristic
124#4936C2211yescharacteristic
125#4936C2211yescharacteristic
126#4936C2211yescharacteristic
127C4×C4⋊Dic3C2211yescharacteristic
128C4×C4⋊Dic3C2211yescharacteristic
129#4933C2211yescharacteristic
130#4933C2211yescharacteristic
131#4933C2211yescharacteristic
132#4933C2211yescharacteristic
133#4933C2211yescharacteristic
134#4933C2211yescharacteristic
135#4933C2211yescharacteristic
136#4933C2211yescharacteristic
137#4933C2211yescharacteristic
138#4933C2211yescharacteristic
139#4932C2211yescharacteristic
140#4932C2211yescharacteristic
141#4932C2211yescharacteristic
142C4×Dic3⋊C4C2211yescharacteristic
143C4×Dic3⋊C4C2211yescharacteristic
144#4929C2211yescharacteristic
145#4928C2211yescharacteristic
146#4928C2211yescharacteristic
147#4928C2211yescharacteristic
148C3⋊#401C2211yescharacteristic
149C3⋊#401C2211yescharacteristic
150#4661C2211yescharacteristic
151#4661C2211yescharacteristic
152#4660C2211yescharacteristic
153#4660C2211yescharacteristic
154#4660C2211yescharacteristic
155#4658C2211yescharacteristic
156#4658C2211yescharacteristic
157#4658C2211yescharacteristic
158#4658C2211yescharacteristic
159#4657C2211yescharacteristic
160#4657C2211yescharacteristic
161#4657C2211yescharacteristic
162#4656C2211yescharacteristic
163#4656C2211yescharacteristic
164#4655C2211yescharacteristic
165#4655C2211yescharacteristic
166#4654C2211yescharacteristic
167#4654C2211yescharacteristic
168#4654C2211yescharacteristic
169#4654C2211yescharacteristic
170#4654C2211yescharacteristic
171#4654C2211yescharacteristic
172#4654C2211yescharacteristic
173#4653C2211yescharacteristic
174#4653C2211yescharacteristic
175#4653C2211yescharacteristic
176#4653C2211yescharacteristic
177#4653C2211yescharacteristic
178#4653C2211yescharacteristic
179#4652C2211yescharacteristic
180#4652C2211yescharacteristic
181#4652C2211yescharacteristic
182#4650C2211yescharacteristic
183#4649C2211yescharacteristic
184#4649C2211yescharacteristic
185#4647C2211yescharacteristic
186#4646C2211yescharacteristic
187#4646C2211yescharacteristic
188#2851—31no—
189#2777—31no—
190#2776—31no—
191#2775—31no—
192#2766—31no—
193#2742—31no—
194#2741—31no—
195#2741—31no—
196#2722—31no—
197#2653—31no—
198#2649—31no—
199#2612—31no—
200#2611—31no—
201#2596—31no—
202#2594—31no—
203#2590—31no—
204#2588—31no—
205#2575—31no—
206#2574—31no—
207#2528—31no—
208#2527—31no—
209#2517—31no—
210#2508—31no—
211#2468—31no—
212#2466—31no—
213#2371—31no—
214#2346—31no—
215#2334—31no—
216#2334—31no—
217#2290D311yescharacteristic
218#2283—31no—
219C22×C3×D4C2311yescharacteristic
220C23×C3×C4C2311yescharacteristic
221C23×C3×C4C2311yescharacteristic
222C23×C3×C4C2311yescharacteristic
223C23×C3×C4C2311yescharacteristic
224C22×Dic6C2311yescharacteristic
225C3×C4×D4—24no—
226C3×#117—24no—
227C2×C3×C4⋊C4C2311yescharacteristic
228C2×C3×C4⋊C4C2311yescharacteristic
229C2×C3×C4⋊C4C2311yescharacteristic
230C2×C3×C4⋊C4C2311yescharacteristic
231C2×C3×C4⋊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×C42—24no—
241C2×C3×C42C2311yescharacteristic
242C2×C3×C42C2311yescharacteristic
243C2×C3×C42C2311yescharacteristic
244C2×C3×C42C2311yescharacteristic
245C2×C3×C42C2311yescharacteristic
246C2×C3×C42C2311yescharacteristic
247C2×C3×C42C2311yescharacteristic
248C2×#217C2311yescharacteristic
249C2×#217C2311yescharacteristic
250C2×#217C2311yescharacteristic
251C2×#217C2311yescharacteristic
252C2×#217C2311yescharacteristic
253C2×#217C2311yescharacteristic
254C2×#217C2311yescharacteristic
255C2×#217C2311yescharacteristic
256C2×#217C2311yescharacteristic
257C2×#217C2311yescharacteristic
258C2×#217C2311yescharacteristic
259C2×#217C2311yescharacteristic
260C2×#217C2311yescharacteristic
261C2×#217C2311yescharacteristic
262C2×#217C2311yescharacteristic
263C2×#217C2311yescharacteristic
264C2×C4⋊Dic3C2311yescharacteristic
265C2×C4⋊Dic3C2311yescharacteristic
266C2×C4⋊Dic3C2311yescharacteristic
267C2×C4⋊Dic3C2311yescharacteristic
268C2×C4⋊Dic3C2311yescharacteristic
269C2×C4⋊Dic3C2311yescharacteristic
270C2×C4⋊Dic3C2311yescharacteristic
271C2×C4⋊Dic3C2311yescharacteristic
272C2×C4⋊Dic3C2311yescharacteristic
273C2×C4⋊Dic3C2311yescharacteristic
274C2×C4⋊Dic3C2311yescharacteristic
275C2×C4⋊Dic3C2311yescharacteristic
276C2×C4⋊Dic3C2311yescharacteristic
277C2×C4⋊Dic3C2311yescharacteristic
278C2×C4⋊Dic3C2311yescharacteristic
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×Dic3⋊C4C2311yescharacteristic
298C2×Dic3⋊C4C2311yescharacteristic
299C2×Dic3⋊C4C2311yescharacteristic
300C2×Dic3⋊C4C2311yescharacteristic
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
313#879—24no—
314#879—24no—
315#870—24no—
316C3×#95C2311yescharacteristic
317C3×#95C2311yescharacteristic
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×#126—31no—
382C2×#125—31no—
383C2×C4×D4C2×D311yescharacteristic
384C2×#117C2×D311yescharacteristic
385C22×C42C2×D311yescharacteristic
386#401—31no—
387#401—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#399—31no—
398#399—31no—
399#399—31no—
400#398—31no—
401#398—31no—
402#398—31no—
403#398—31no—
404#398—31no—
405#398—31no—
406#398—31no—
407#398—31no—
408#398—31no—
409#397—31no—
410#397—31no—
411#397—31no—
412#397—31no—
413#397—31no—
414#397—31no—
415#397—31no—
416#396—31no—
417#396—31no—
418#395—31no—
419#395—31no—
420#394—31no—
421#394—31no—
422#394—31no—
423#394—31no—
424#393—31no—
425#393—31no—
426#391—31no—
427#391—31no—
428#391—31no—
429#389—31no—
430#389—31no—
431#389—31no—
432#389—31no—
433#389—31no—
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#388—31no—
443#388—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#388C2×D311yescharacteristic
459#388C2×D311yescharacteristic
460#387—31no—
461#387—31no—
462#387—31no—
463#387—31no—
464#387—31no—
465#387—31no—
466#387—31no—
467#387—31no—
468#387—31no—
469#387—31no—
470#387—31no—
471#387—31no—
472#387—31no—
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#387C2×D311yescharacteristic
491#387C2×D311yescharacteristic
492#386C2×D311yescharacteristic
493#386C2×D311yescharacteristic
494#385—31no—
495#385—31no—
496#385—31no—
497#385—31no—
498#385—31no—
499#385—31no—
500#385C2×D311yescharacteristic
501#385C2×D311yescharacteristic
502#383—31no—
503#383—31no—
504#382—31no—
505#382—31no—
506#382—31no—
507#382—31no—
508#382—31no—
509#382—31no—
510#381—31no—
511#381—31no—
512#380—31no—
513#380—31no—
514#380—31no—
515#380—31no—
516#380—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⋊C4C2×D311yescharacteristic
526C4×C22⋊C4—31no—
527C4×C22⋊C4—31no—
528C4×C22⋊C4—31no—
529C4×C22⋊C4C2×D311yescharacteristic
530C4×C22⋊C4C2×D311yescharacteristic
531#376—31no—
532#376—31no—
533#376—31no—
534#376C2×D311yescharacteristic
535C24×C3C2411yescharacteristic
536C24×C3C2411yescharacteristic
537C2×C3×D4—22no—
538C2×C3×D4—41no—
539C2×C3×D4—41no—
540C22×C3×C4—22no—
541C22×C3×C4—22no—
542C22×C3×C4—22no—
543C22×C3×C4—22no—
544C22×C3×C4—22no—
545C22×C3×C4—22no—
546C22×C3×C4—22no—
547C22×C3×C4—41no—
548C22×C3×C4—41no—
549C22×C3×C4—41no—
550C22×C3×C4—41no—
551C22×C3×C4—41no—
552C22×C3×C4C2411yescharacteristic
553C22×C3×C4C2411yescharacteristic
554C22×C3×C4C2411yescharacteristic
555C22×C3×C4C2411yescharacteristic
556C22×C3×C4C2411yescharacteristic
557C22×C3×C4C2411yescharacteristic
558C22×C3×C4C2411yescharacteristic
559C22×C3×C4C2411yescharacteristic
560C22×C3×C4C2411yescharacteristic
561C22×C3×C4C2411yescharacteristic
562C22×C3×C4C2411yescharacteristic
563C22×C3×C4C2411yescharacteristic
564C22×C3×C4C2411yescharacteristic
565C22×Dic3C2411yescharacteristic
566C22×Dic3C2411yescharacteristic
567C22×Dic3C2411yescharacteristic
568C22×Dic3C2411yescharacteristic
569C22×Dic3C2411yescharacteristic
570C22×Dic3C2411yescharacteristic
571C22×Dic3C2411yescharacteristic
572C22×Dic3C2411yescharacteristic
573C22×Dic3C2411yescharacteristic
574C22×Dic3C2411yescharacteristic
575C22×Dic3C2411yescharacteristic
576C22×Dic3C2411yescharacteristic
577C22×Dic3C2411yescharacteristic
578C22×Dic3C2411yescharacteristic
579C22×Dic3C2411yescharacteristic
580C22×Dic3C2411yescharacteristic
581C2×Dic6—41no—
582C2×Dic6—41no—
583C2×Dic6—41no—
584C3×C4⋊C4—22no—
585C3×C4⋊C4—22no—
586C3×C4⋊C4—22no—
587C3×C4⋊C4—22no—
588C3×C4⋊C4—41no—
589C3×C22⋊C4—22no—
590C3×C22⋊C4—22no—
591C3×C22⋊C4—22no—
592C3×C22⋊C4—22no—
593C3×C22⋊C4—41no—
594C3×C22⋊C4—41no—
595C3×C22⋊C4—41no—
596C3×C22⋊C4#4114yes—
597C3×C42—22no—
598C3×C42—22no—
599C3×C42—22no—
600C3×C42—22no—
601C3×C42—22no—
602C3×C42—41no—
603C3×C42#4114yes—
604#217—22no—
605#217—22no—
606#217—22no—
607#217—22no—
608#217—41no—
609#217—41no—
610#217—41no—
611#217—41no—
612#217—41no—
613#217—41no—
614#217—41no—
615#217—41no—
616#217—41no—
617#217—41no—
618#217—41no—
619#217—41no—
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—41no—
630C4⋊Dic3—41no—
631C4⋊Dic3—41no—
632C4⋊Dic3—41no—
633C4⋊Dic3—41no—
634C4⋊Dic3—41no—
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—41no—
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—41no—
656Dic3⋊C4—41no—
657C4×Dic3—22no—
658C4×Dic3—22no—
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×D4C22×D311yescharacteristic
671C23×C4C22×D311yescharacteristic
672C23×C4C22×D311yescharacteristic
673C23×C4C22×D311yescharacteristic
674C23×C4C22×D311yescharacteristic
675#126—64no—
676#126—64no—
677#125—64no—
678C4×D4—24no—
679#117—24no—
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⋊C4—31no—
716C2×C4⋊C4—31no—
717C2×C4⋊C4C22×D311yescharacteristic
718C2×C4⋊C4C22×D311yescharacteristic
719C2×C4⋊C4C22×D311yescharacteristic
720C2×C4⋊C4C22×D311yescharacteristic
721C2×C4⋊C4C22×D311yescharacteristic
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⋊C4—31no—
737C2×C22⋊C4—31no—
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×C42—24no—
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×C42C22×D311yescharacteristic
760C2×C42C22×D311yescharacteristic
761C2×C42C22×D311yescharacteristic
762C2×C42C22×D311yescharacteristic
763C2×C42C22×D311yescharacteristic
764C2×C42C22×D311yescharacteristic
765C2×C42C22×D311yescharacteristic
766#95—31no—
767#95—31no—
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#95—31no—
819#95—31no—
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×C3C2×#4112yes—
844C23×C3C2511yescharacteristic
845C3×D4—44no—
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—44no—
880C2×C3×C4—44no—
881C2×C3×C4—44no—
882C2×C3×C4—44no—
883C2×C3×C4C2×#4112yes—
884C2×C3×C4C2×#4112yes—
885C2×C3×C4C2×#4112yes—
886C2×C3×C4C2×#4112yes—
887C2×C3×C4C2×#4112yes—
888C2×C3×C42−1+412yes—
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—21no—
931C2×Dic3—21no—
932C2×Dic3—21no—
933C2×Dic3—21no—
934C2×Dic3—21no—
935C2×Dic3—21no—
936C2×Dic3—21no—
937Dic6—82no—
938C24C23×D311yescharacteristic
939C24C23×D311yescharacteristic
940C2×Q8—121no—
941C2×Q8—121no—
942C2×Q8—121no—
943C2×D4—22no—
944C2×D4—41no—
945C2×D4—41no—
946C22×C4—22no—
947C22×C4—22no—
948C22×C4—22no—
949C22×C4—22no—
950C22×C4—22no—
951C22×C4—22no—
952C22×C4—22no—
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—31no—
967C22×C4—31no—
968C22×C4—31no—
969C22×C4—41no—
970C22×C4—41no—
971C22×C4—41no—
972C22×C4—41no—
973C22×C4—41no—
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
983C22×C4C23×D311yescharacteristic
984C22×C4C23×D311yescharacteristic
985C22×C4C23×D311yescharacteristic
986C22×C4C23×D311yescharacteristic
987C4⋊C4—22no—
988C4⋊C4—22no—
989C4⋊C4—22no—
990C4⋊C4—22no—
991C4⋊C4—41no—
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—
1024C4⋊C4—121no—
1025C4⋊C4—121no—
1026C4⋊C4—121no—
1027C4⋊C4—121no—
1028C4⋊C4—121no—
1029C22⋊C4—22no—
1030C22⋊C4—22no—
1031C22⋊C4—22no—
1032C22⋊C4—22no—
1033C22⋊C4—41no—
1034C22⋊C4—41no—
1035C22⋊C4—41no—
1036C22⋊C4—62no—
1037C22⋊C4—62no—
1038C22⋊C4—62no—
1039C22⋊C4—62no—
1040C22⋊C4—121no—
1041C22⋊C4—121no—
1042C22⋊C4—121no—
1043C22⋊C4—121no—
1044C22⋊C4—121no—
1045C22⋊C4—121no—
1046C22⋊C4—121no—
1047C22⋊C4—121no—
1048C22⋊C4—121no—
1049C22⋊C4—121no—
1050C22⋊C4—121no—
1051C22⋊C4—121no—
1052C22⋊C4#23514yes—
1053C42—22no—
1054C42—22no—
1055C42—22no—
1056C42—22no—
1057C42—22no—
1058C42—41no—
1059C42—62no—
1060C42—62no—
1061C42—121no—
1062C42—121no—
1063C42—121no—
1064C42—121no—
1065C42—121no—
1066C42—121no—
1067C42—121no—
1068C42—121no—
1069C42—121no—
1070C42—121no—
1071C42#23714yes—
1072C22×C3—22no—
1073C22×C3—22no—
1074C22×C3—22no—
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×C3—41no—
1086C22×C3C22×#4111yescharacteristic
1087C22×C3C22×#4111yescharacteristic
1088C22×C3C2×2−1+411yescharacteristic
1089C22×C3#58511yescharacteristic
1090C22×C3#58511yescharacteristic
1091C22×C3#58511yescharacteristic
1092C22×C3#58511yescharacteristic
1093C3×C4—22no—
1094C3×C4—22no—
1095C3×C4—22no—
1096C3×C4—22no—
1097C3×C4—22no—
1098C3×C4—22no—
1099C3×C4—41no—
1100C3×C4—41no—
1101C3×C4—41no—
1102C3×C4—41no—
1103C3×C4—41no—
1104C3×C4—41no—
1105C3×C4—41no—
1106Dic3—41no—
1107Dic3—41no—
1108Dic3—41no—
1109Dic3—41no—
1110Dic3—41no—
1111Dic3—41no—
1112Dic3—41no—
1113Dic3—41no—
1114Dic3—41no—
1115Dic3—41no—
1116Dic3—41no—
1117Dic3—41no—
1118Dic3—41no—
1119Dic3—41no—
1120Dic3—41no—
1121Dic3—41no—
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—
1135C23C2×#23512yes—
1136C23C24×D311yescharacteristic
1137Q8—242no—
1138D4—44no—
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—44no—
1173C2×C4—44no—
1174C2×C4—44no—
1175C2×C4—44no—
1176C2×C4—61no—
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—61no—
1220C2×C4—61no—
1221C2×C4—61no—
1222C2×C4—61no—
1223C2×C4—61no—
1224C2×C4C2×#23512yes—
1225C2×C4C2×#23512yes—
1226C2×C4C2×#23712yes—
1227C2×C4C2×#23712yes—
1228C2×C4C2×#23712yes—
1229C2×C4#101012yes—
1230C2×C3—42no—
1231C2×C3—81no—
1232C2×C3#345511yescharacteristic
1233C2×C3#347511yescharacteristic
1234C2×C3#349311yescharacteristic
1235C2×C3#349511yescharacteristic
1236C2×C3#351511yescharacteristic
1237C2×C3#355711yescharacteristic
1238C2×C3#356611yescharacteristic
1239C22—22no—
1240C22—22no—
1241C22—22no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22—41no—
1249C22—41no—
1250C22—41no—
1251C22—41no—
1252C22—41no—
1253C22C22×#23511yescharacteristic
1254C22C22×#23711yescharacteristic
1255C22C2×#101011yescharacteristic
1256C22#596411yescharacteristic
1257C22#596411yescharacteristic
1258C22#596411yescharacteristic
1259C22#596411yescharacteristic
1260C4—22no—
1261C4—22no—
1262C4—22no—
1263C4—22no—
1264C4—22no—
1265C4—22no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—121no—
1274C4—121no—
1275C4—121no—
1276C4—121no—
1277C4—121no—
1278C4—121no—
1279C4—121no—
1280C4—121no—
1281C4—121no—
1282C4—121no—
1283C4—121no—
1284C4—121no—
1285C4—121no—
1286C4—121no—
1287C4—121no—
1288C4—121no—
1289C3#3841711yescharacteristic, complemented, Sylow
1290C2—42no—
1291C2—81no—
1292C2#8574611yescharacteristic
1293C2#8576411yescharacteristic
1294C2#8583111yescharacteristic
1295C2#8601911yescharacteristic
1296C2#8602811yescharacteristic
1297C2#8613911yescharacteristic
1298C2#8618511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2290C2
prime radicalC22×C3×D4C23
hypercenter#2290D3
hypocenterC3#38417
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2290

Complements

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

NH ≅ G/Ntype
4. #82261C2semidirect
5. #82239C2semidirect
6. #82074C2semidirect
7. #82060C2semidirect
8. #75766C2semidirect
9. #75763C2semidirect
10. #75637C2semidirect
11. #75628C2semidirect
12. #75229C2semidirect
13. #75203C2semidirect
14. #75113C2semidirect
15. #75105C2semidirect
20. #74544C2semidirect
21. #74536C2semidirect
22. #74389C2semidirect
23. #74388C2semidirect
24. #73706C2semidirect
25. #73687C2semidirect
26. #73543C2semidirect
27. #73542C2semidirect
28. #73531C2semidirect
29. #73524C2semidirect
30. #73406C2semidirect
31. #73394C2semidirect
1289. C3#38417semidirect

Maximal subgroups

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

subgroupindex
C3×#22902
#823712
#823692
#822612
#822392
#820742
#820602
#757662
#757632
#756372
#756282
#752292
#752032
#751132
#751052
#748332
#747892
#747882
#745442
#745362
#743892
#743882
#737062
#736872
#735432
#735422
#735312
#735242
#734062
#733942
#384173