Finite Group Databasebeta

← #11044235

Subgroups — #11044235

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×#2468C211yesmaximal, characteristic
2#83099C211yesmaximal, characteristic, complemented
3#83074C211yesmaximal, characteristic, complemented
4#82369C211yesmaximal, characteristic
5#82318C211yesmaximal, characteristic
6#77899C211yesmaximal, characteristic, complemented
7#77882C211yesmaximal, characteristic, complemented
8#77806C211yesmaximal, characteristic, complemented
9#77803C211yesmaximal, characteristic, complemented
10#77051C211yesmaximal, characteristic
11#77051C211yesmaximal, characteristic
12#76993C211yesmaximal, characteristic
13#76989C211yesmaximal, characteristic
14#75768C211yesmaximal, characteristic, complemented
15#75765C211yesmaximal, characteristic, complemented
16#75722C211yesmaximal, characteristic, complemented
17#75633C211yesmaximal, characteristic, complemented
18#75626C211yesmaximal, characteristic, complemented
19#75466C211yesmaximal, characteristic, complemented
20#75134C211yesmaximal, characteristic, complemented
21#75060C211yesmaximal, characteristic, complemented
22#74586C211yesmaximal, characteristic, complemented
23#74501C211yesmaximal, characteristic, complemented
24#74470C211yesmaximal, characteristic, complemented
25#74467C211yesmaximal, characteristic, complemented
26#74086C211yesmaximal, characteristic, complemented
27#74051C211yesmaximal, characteristic, complemented
28#73946C211yesmaximal, characteristic, complemented
29#73881C211yesmaximal, characteristic, complemented
30#73686C211yesmaximal, characteristic, complemented
31#73663C211yesmaximal, characteristic, complemented
32#38417—31nomaximal, Sylow
33C2×C3×#126C2211yescharacteristic
34C2×C3×C4×D4C2211yescharacteristic
35C2×#926C2211yescharacteristic
36C22×C4×Dic3C2211yescharacteristic
37C2×#889C2211yescharacteristic
38C2×#879C2211yescharacteristic
39C3×#398C2211yescharacteristic
40C3×#398C2211yescharacteristic
41C3×#394C2211yescharacteristic
42C3×#394C2211yescharacteristic
43C3×#388C2211yescharacteristic
44C3×#388C2211yescharacteristic
45C3×#388C2211yescharacteristic
46C3×#387C2211yescharacteristic
47C3×#385C2211yescharacteristic
48C3×#385C2211yescharacteristic
49C3×#381C2211yescharacteristic
50C3×#380C2211yescharacteristic
51C3×C4×C4⋊C4C2211yescharacteristic
52#5222C2211yescharacteristic
53#5222C2211yescharacteristic
54#5220C2211yescharacteristic
55#5220C2211yescharacteristic
56#5211C2211yescharacteristic
57#5210C2211yescharacteristic
58#5210C2211yescharacteristic
59C4×#217C2211yescharacteristic
60C4×#217C2211yescharacteristic
61C4×#217C2211yescharacteristic
62#4986C2211yescharacteristic
63#4986C2211yescharacteristic
64#4984C2211yescharacteristic
65#4984C2211yescharacteristic
66#4983C2211yescharacteristic
67#4983C2211yescharacteristic
68#4983C2211yescharacteristic
69#4983C2211yescharacteristic
70#4982C2211yescharacteristic
71#4982C2211yescharacteristic
72#4981C2211yescharacteristic
73#4980C2211yescharacteristic
74#4980C2211yescharacteristic
75#4980C2211yescharacteristic
76#4980C2211yescharacteristic
77#4980C2211yescharacteristic
78#4980C2211yescharacteristic
79#4980C2211yescharacteristic
80#4979C2211yescharacteristic
81#4978C2211yescharacteristic
82#4978C2211yescharacteristic
83#4978C2211yescharacteristic
84#4978C2211yescharacteristic
85#4978C2211yescharacteristic
86#4978C2211yescharacteristic
87#4978C2211yescharacteristic
88#4978C2211yescharacteristic
89#4976C2211yescharacteristic
90#4976C2211yescharacteristic
91Dic3×C4⋊C4C2211yescharacteristic
92Dic3×C4⋊C4C2211yescharacteristic
93#4973C2211yescharacteristic
94#4972C2211yescharacteristic
95#4972C2211yescharacteristic
96#4972C2211yescharacteristic
97#4953C2211yescharacteristic
98#4953C2211yescharacteristic
99#4952C2211yescharacteristic
100#4952C2211yescharacteristic
101#4952C2211yescharacteristic
102#4952C2211yescharacteristic
103#4952C2211yescharacteristic
104#4951C2211yescharacteristic
105#4951C2211yescharacteristic
106#4951C2211yescharacteristic
107#4951C2211yescharacteristic
108#4951C2211yescharacteristic
109#4951C2211yescharacteristic
110#4950C2211yescharacteristic
111#4950C2211yescharacteristic
112#4950C2211yescharacteristic
113#4949C2211yescharacteristic
114#4949C2211yescharacteristic
115#4949C2211yescharacteristic
116#4948C2211yescharacteristic
117#4948C2211yescharacteristic
118#4947C2211yescharacteristic
119#4947C2211yescharacteristic
120#4946C2211yescharacteristic
121#4945C2211yescharacteristic
122#4945C2211yescharacteristic
123#4945C2211yescharacteristic
124#4945C2211yescharacteristic
125#4945C2211yescharacteristic
126#4945C2211yescharacteristic
127#4944C2211yescharacteristic
128#4944C2211yescharacteristic
129#4944C2211yescharacteristic
130#4942C2211yescharacteristic
131#4942C2211yescharacteristic
132#4942C2211yescharacteristic
133#4942C2211yescharacteristic
134Dic3×C22⋊C4C2211yescharacteristic
135Dic3×C22⋊C4C2211yescharacteristic
136#4936C2211yescharacteristic
137C4×C4⋊Dic3C2211yescharacteristic
138C4×C4⋊Dic3C2211yescharacteristic
139#4933C2211yescharacteristic
140#4933C2211yescharacteristic
141#4933C2211yescharacteristic
142#4932C2211yescharacteristic
143C4×Dic3⋊C4C2211yescharacteristic
144#4928C2211yescharacteristic
145#4928C2211yescharacteristic
146#4928C2211yescharacteristic
147#4928C2211yescharacteristic
148C3⋊#401C2211yescharacteristic
149C3⋊#401C2211yescharacteristic
150#4660C2211yescharacteristic
151#4660C2211yescharacteristic
152#4660C2211yescharacteristic
153#4660C2211yescharacteristic
154#4658C2211yescharacteristic
155#4658C2211yescharacteristic
156#4658C2211yescharacteristic
157#4656C2211yescharacteristic
158#4655C2211yescharacteristic
159#4655C2211yescharacteristic
160#4655C2211yescharacteristic
161#4655C2211yescharacteristic
162#4655C2211yescharacteristic
163#4653C2211yescharacteristic
164#4653C2211yescharacteristic
165#4653C2211yescharacteristic
166#4653C2211yescharacteristic
167#4652C2211yescharacteristic
168#4652C2211yescharacteristic
169#4652C2211yescharacteristic
170#4652C2211yescharacteristic
171#4651C2211yescharacteristic
172#4651C2211yescharacteristic
173#4650C2211yescharacteristic
174#4650C2211yescharacteristic
175#4650C2211yescharacteristic
176#4650C2211yescharacteristic
177#4650C2211yescharacteristic
178#4649C2211yescharacteristic
179#4649C2211yescharacteristic
180#4649C2211yescharacteristic
181#4648C2211yescharacteristic
182#4648C2211yescharacteristic
183#4648C2211yescharacteristic
184#4647C2211yescharacteristic
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#2468D311yescharacteristic
212#2466—31no—
213#2371—31no—
214#2346—31no—
215#2334—31no—
216#2334—31no—
217#2290—31no—
218#2283—31no—
219C22×C3×D4C2311yescharacteristic
220C23×C3×C4C2311yescharacteristic
221C23×C3×C4C2311yescharacteristic
222C23×Dic3C2311yescharacteristic
223C23×Dic3C2311yescharacteristic
224C22×Dic6C2311yescharacteristic
225C3×#126—24no—
226C3×C4×D4—24no—
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×C4⋊C4C2311yescharacteristic
235C2×C3×C4⋊C4C2311yescharacteristic
236C2×C3×C22⋊C4C2311yescharacteristic
237C2×C3×C22⋊C4C2311yescharacteristic
238C2×C3×C22⋊C4C2311yescharacteristic
239C2×C3×C22⋊C4C2311yescharacteristic
240C2×C3×C22⋊C4C2311yescharacteristic
241C2×C3×C22⋊C4C2311yescharacteristic
242C2×C3×C22⋊C4C2311yescharacteristic
243C2×C3×C22⋊C4C2311yescharacteristic
244C2×C3×C22⋊C4C2311yescharacteristic
245C2×C3×C22⋊C4C2311yescharacteristic
246C2×C3×C42C2311yescharacteristic
247C2×C3×C42C2311yescharacteristic
248C2×C3×C42C2311yescharacteristic
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
263#926—24no—
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×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×Dic3—24no—
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—
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×#126C2×D311yescharacteristic
382C2×#125—31no—
383C2×C4×D4C2×D311yescharacteristic
384C2×#117—31no—
385C22×C42—31no—
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#398C2×D311yescharacteristic
408#398C2×D311yescharacteristic
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#394C2×D311yescharacteristic
423#394C2×D311yescharacteristic
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#388C2×D311yescharacteristic
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#387—31no—
491#387C2×D311yescharacteristic
492#386—31no—
493#386—31no—
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#381C2×D311yescharacteristic
512#380—31no—
513#380—31no—
514#380—31no—
515#380—31no—
516#380C2×D311yescharacteristic
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⋊C4—31no—
530C4×C22⋊C4—31no—
531#376—31no—
532#376—31no—
533#376—31no—
534#376—31no—
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—41no—
545C22×C3×C4—41no—
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×C3×C4C2411yescharacteristic
557C22×C3×C4C2411yescharacteristic
558C22×C3×C4C2411yescharacteristic
559C22×Dic3—22no—
560C22×Dic3—22no—
561C22×Dic3—22no—
562C22×Dic3—41no—
563C22×Dic3—41no—
564C22×Dic3—41no—
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—22no—
589C3×C4⋊C4—41no—
590C3×C4⋊C4—41no—
591C3×C4⋊C4—41no—
592C3×C4⋊C4—41no—
593C3×C22⋊C4—22no—
594C3×C22⋊C4—22no—
595C3×C22⋊C4—22no—
596C3×C22⋊C4—41no—
597C3×C22⋊C4—41no—
598C3×C22⋊C4—41no—
599C3×C22⋊C4—41no—
600C3×C22⋊C4—41no—
601C3×C22⋊C4—41no—
602C3×C22⋊C4#4114yes—
603C3×C42—22no—
604C3×C42—22no—
605C3×C42—41no—
606#217—22no—
607#217—22no—
608#217—22no—
609#217—22no—
610#217—22no—
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—41no—
626C4⋊Dic3—41no—
627C4⋊Dic3—41no—
628C4⋊Dic3—41no—
629C4⋊Dic3—41no—
630C4⋊Dic3—41no—
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—41no—
652Dic3⋊C4—41no—
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#4114yes—
669C22×Q8—31no—
670C22×D4C22×D311yescharacteristic
671C23×C4—31no—
672C23×C4—31no—
673C23×C4C22×D311yescharacteristic
674C23×C4C22×D311yescharacteristic
675#126—24no—
676#126—64no—
677#125—64no—
678C4×D4—24no—
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⋊C4C22×D311yescharacteristic
714C2×C4⋊C4C22×D311yescharacteristic
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×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⋊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×C42—31no—
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—64no—
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—21no—
880C2×C3×C4—21no—
881C2×C3×C4—21no—
882C2×C3×C4—44no—
883C2×C3×C4—44no—
884C2×C3×C4C2×#4112yes—
885C2×C3×C4C2×#4112yes—
886C2×C3×C4C2×#4112yes—
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—21no—
931C2×Dic3—21no—
932C2×Dic3—44no—
933C2×Dic3—44no—
934C2×Dic3C2×#4112yes—
935C2×Dic3C2×#4112yes—
936C2×Dic32−1+412yes—
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—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—41no—
968C22×C4—62no—
969C22×C4—62no—
970C22×C4—62no—
971C22×C4—121no—
972C22×C4—121no—
973C22×C4—121no—
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—22no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—41no—
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—62no—
1007C4⋊C4—62no—
1008C4⋊C4—62no—
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—41no—
1033C22⋊C4—41no—
1034C22⋊C4—41no—
1035C22⋊C4—41no—
1036C22⋊C4—41no—
1037C22⋊C4—41no—
1038C22⋊C4—62no—
1039C22⋊C4—62no—
1040C22⋊C4—62no—
1041C22⋊C4—62no—
1042C22⋊C4—62no—
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#23714yes—
1053C42—22no—
1054C42—22no—
1055C42—34no—
1056C42—41no—
1057C42—62no—
1058C42—62no—
1059C42—62no—
1060C42—62no—
1061C42—62no—
1062C42—121no—
1063C42—121no—
1064C42—121no—
1065C42—121no—
1066C42—121no—
1067C42—121no—
1068C42—121no—
1069C42—121no—
1070C42—121no—
1071C42—121no—
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—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—
1105C3×C4—41no—
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—
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×#23712yes—
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—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—32no—
1176C2×C4—32no—
1177C2×C4—32no—
1178C2×C4—44no—
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—61no—
1225C2×C4—124no—
1226C2×C4—124no—
1227C2×C4C2×#23712yes—
1228C2×C4C2×#23712yes—
1229C2×C4D3×#4112yes—
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×#23711yescharacteristic
1254C22C2×D3×#4111yescharacteristic
1255C22#596411yescharacteristic
1256C22#596411yescharacteristic
1257C22#596411yescharacteristic
1258C22#596611yescharacteristic
1259C22D3×2−1+411yescharacteristic
1260C4—22no—
1261C4—22no—
1262C4—22no—
1263C4—41no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—62no—
1274C4—62no—
1275C4—62no—
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#8602611yescharacteristic
1293C2#8614611yescharacteristic
1294C2#8653911yescharacteristic
1295C2#8662711yescharacteristic
1296C2#8668211yescharacteristic
1297C2#8683111yescharacteristic
1298C2#8690511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2468C2
prime radicalC22×C3×D4C23
hypercenter#2468D3
hypocenterC3#38417
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2468

Complements

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

NH ≅ G/Ntype
2. #83099C2semidirect
3. #83074C2semidirect
6. #77899C2semidirect
7. #77882C2semidirect
8. #77806C2semidirect
9. #77803C2semidirect
14. #75768C2semidirect
15. #75765C2semidirect
16. #75722C2semidirect
17. #75633C2semidirect
18. #75626C2semidirect
19. #75466C2semidirect
20. #75134C2semidirect
21. #75060C2semidirect
22. #74586C2semidirect
23. #74501C2semidirect
24. #74470C2semidirect
25. #74467C2semidirect
26. #74086C2semidirect
27. #74051C2semidirect
28. #73946C2semidirect
29. #73881C2semidirect
30. #73686C2semidirect
31. #73663C2semidirect
1289. C3#38417semidirect

Maximal subgroups

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

subgroupindex
C3×#24682
#830992
#830742
#823692
#823182
#778992
#778822
#778062
#778032
#770512
#769932
#769892
#757682
#757652
#757222
#756332
#756262
#754662
#751342
#750602
#745862
#745012
#744702
#744672
#740862
#740512
#739462
#738812
#736862
#736632
#384173