Finite Group Databasebeta

← #11043923

Subgroups — #11043923

Order 768.

1638 conjugacy classes of subgroups.

The subgroup lattice has 1382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2793C211yesmaximal, characteristic, complemented
2#78392C211yesmaximal, characteristic, complemented
3#78205C211yesmaximal, characteristic, complemented
4#77953C211yesmaximal, characteristic, complemented
5#77834C211yesmaximal, characteristic, complemented
6#77678C211yesmaximal, characteristic, complemented
7#77486C211yesmaximal, characteristic, complemented
8#77477C211yesmaximal, characteristic, complemented
9#77473C211yesmaximal, characteristic
10#77446C211yesmaximal, characteristic, complemented
11#77340C211yesmaximal, characteristic, complemented
12#77328C211yesmaximal, characteristic, complemented
13#77293C211yesmaximal, characteristic
14#75958C211yesmaximal, characteristic, complemented
15#75949C211yesmaximal, characteristic
16#75668C211yesmaximal, characteristic, complemented
17#75586C211yesmaximal, characteristic, complemented
18#75486C211yesmaximal, characteristic, complemented
19#75468C211yesmaximal, characteristic, complemented
20#75437C211yesmaximal, characteristic, complemented
21#75334C211yesmaximal, characteristic, complemented
22#75303C211yesmaximal, characteristic, complemented
23#75262C211yesmaximal, characteristic, complemented
24#75085C211yesmaximal, characteristic, complemented
25#75082C211yesmaximal, characteristic, complemented
26#75063C211yesmaximal, characteristic, complemented
27#75012C211yesmaximal, characteristic, complemented
28#74951C211yesmaximal, characteristic, complemented
29#74937C211yesmaximal, characteristic, complemented
30#74347C211yesmaximal, characteristic, complemented
31#74318C211yesmaximal, characteristic, complemented
32#38406—31nomaximal, Sylow
33C2×#897C2211yescharacteristic
34C2×#896C2211yescharacteristic
35C2×#893C2211yescharacteristic
36C2×#892C2211yescharacteristic
37C2×#892C2211yescharacteristic
38C2×#892C2211yescharacteristic
39C2×#889C2211yescharacteristic
40C2×#886C2211yescharacteristic
41C2×#883C2211yescharacteristic
42C2×#879C2211yescharacteristic
43C2×#878C2211yescharacteristic
44C2×C42×D3C2211yescharacteristic
45C3×#400C2211yescharacteristic
46C3×#398C2211yescharacteristic
47C3×#397C2211yescharacteristic
48C3×#397C2211yescharacteristic
49C3×#396C2211yescharacteristic
50C3×#396C2211yescharacteristic
51C3×#388C2211yescharacteristic
52C3×#388C2211yescharacteristic
53C3×#388C2211yescharacteristic
54C3×#387C2211yescharacteristic
55C3×#387C2211yescharacteristic
56C3×#387C2211yescharacteristic
57C3×#387C2211yescharacteristic
58C3×#387C2211yescharacteristic
59C3×#384C2211yescharacteristic
60#4994C2211yescharacteristic
61#4994C2211yescharacteristic
62#4993C2211yescharacteristic
63#4991C2211yescharacteristic
64#4990C2211yescharacteristic
65#4989C2211yescharacteristic
66#4989C2211yescharacteristic
67#4989C2211yescharacteristic
68#4989C2211yescharacteristic
69#4989C2211yescharacteristic
70#4987C2211yescharacteristic
71#4987C2211yescharacteristic
72#4987C2211yescharacteristic
73#4987C2211yescharacteristic
74#4986C2211yescharacteristic
75#4986C2211yescharacteristic
76#4986C2211yescharacteristic
77#4985C2211yescharacteristic
78#4985C2211yescharacteristic
79#4984C2211yescharacteristic
80#4982C2211yescharacteristic
81#4982C2211yescharacteristic
82#4981C2211yescharacteristic
83#4980C2211yescharacteristic
84#4980C2211yescharacteristic
85#4980C2211yescharacteristic
86#4980C2211yescharacteristic
87#4979C2211yescharacteristic
88#4979C2211yescharacteristic
89#4977C2211yescharacteristic
90#4977C2211yescharacteristic
91#4976C2211yescharacteristic
92Dic3×C4⋊C4C2211yescharacteristic
93Dic3×C4⋊C4C2211yescharacteristic
94Dic3×C4⋊C4C2211yescharacteristic
95Dic3×C4⋊C4C2211yescharacteristic
96#4973C2211yescharacteristic
97#4961C2211yescharacteristic
98#4960C2211yescharacteristic
99#4959C2211yescharacteristic
100#4958C2211yescharacteristic
101#4957C2211yescharacteristic
102#4957C2211yescharacteristic
103#4956C2211yescharacteristic
104#4956C2211yescharacteristic
105#4956C2211yescharacteristic
106#4956C2211yescharacteristic
107#4956C2211yescharacteristic
108#4953C2211yescharacteristic
109#4952C2211yescharacteristic
110#4951C2211yescharacteristic
111#4951C2211yescharacteristic
112#4951C2211yescharacteristic
113#4950C2211yescharacteristic
114#4947C2211yescharacteristic
115#4945C2211yescharacteristic
116#4945C2211yescharacteristic
117#4944C2211yescharacteristic
118#4942C2211yescharacteristic
119Dic3×C22⋊C4C2211yescharacteristic
120Dic3×C22⋊C4C2211yescharacteristic
121#4940C2211yescharacteristic
122#4940C2211yescharacteristic
123#4940C2211yescharacteristic
124#4940C2211yescharacteristic
125C4×(C2×D3)⋊C4C2211yescharacteristic
126#4935C2211yescharacteristic
127C4×C4⋊Dic3C2211yescharacteristic
128#4933C2211yescharacteristic
129#4932C2211yescharacteristic
130C4×Dic3⋊C4C2211yescharacteristic
131#4928C2211yescharacteristic
132#4676C2211yescharacteristic
133#4674C2211yescharacteristic
134#4674C2211yescharacteristic
135#4673C2211yescharacteristic
136#4673C2211yescharacteristic
137#4670C2211yescharacteristic
138#4670C2211yescharacteristic
139#4670C2211yescharacteristic
140#4669C2211yescharacteristic
141#4669C2211yescharacteristic
142#4668C2211yescharacteristic
143#4668C2211yescharacteristic
144#4668C2211yescharacteristic
145#4668C2211yescharacteristic
146#4666C2211yescharacteristic
147#4666C2211yescharacteristic
148#4666C2211yescharacteristic
149#4665C2211yescharacteristic
150#4665C2211yescharacteristic
151#4665C2211yescharacteristic
152#4665C2211yescharacteristic
153#4664C2211yescharacteristic
154#4664C2211yescharacteristic
155D3×#95C2211yescharacteristic
156C3⋊#401C2211yescharacteristic
157#4661C2211yescharacteristic
158#4660C2211yescharacteristic
159#4660C2211yescharacteristic
160#4660C2211yescharacteristic
161#4659C2211yescharacteristic
162#4659C2211yescharacteristic
163#4658C2211yescharacteristic
164#4656C2211yescharacteristic
165#4655C2211yescharacteristic
166#4655C2211yescharacteristic
167#4654C2211yescharacteristic
168#4654C2211yescharacteristic
169#4654C2211yescharacteristic
170#4654C2211yescharacteristic
171#4653C2211yescharacteristic
172#4653C2211yescharacteristic
173#4653C2211yescharacteristic
174#4653C2211yescharacteristic
175#4653C2211yescharacteristic
176#4653C2211yescharacteristic
177#4652C2211yescharacteristic
178#4652C2211yescharacteristic
179#4652C2211yescharacteristic
180#4651C2211yescharacteristic
181#4650C2211yescharacteristic
182#4649C2211yescharacteristic
183#4648C2211yescharacteristic
184#4646C2211yescharacteristic
185#4646C2211yescharacteristic
186#4646C2211yescharacteristic
187#4646C2211yescharacteristic
188#2852—31no—
189#2794—31no—
190#2793D311yescharacteristic, complemented
191#2788—31no—
192#2784—31no—
193#2778—31no—
194#2750—31no—
195#2720—31no—
196#2680—31no—
197#2655—31no—
198#2650—31no—
199#2605—31no—
200#2601—31no—
201#2575—31no—
202#2574—31no—
203#2531—31no—
204#2528—31no—
205#2489—31no—
206#2488—31no—
207#2477—31no—
208#2477—31no—
209#2475—31no—
210#2471—31no—
211#2457—31no—
212#2450—31no—
213#2373—31no—
214#2343—31no—
215#2335—31no—
216#2332—31no—
217#2290—31no—
218#2285—31no—
219C22×#67C2311yescharacteristic
220C22×#67C2311yescharacteristic
221C23×Dic3C2311yescharacteristic
222C22×D12C2311yescharacteristic
223C22×C4×D3C2311yescharacteristic
224C22×C4×D3C2311yescharacteristic
225C22×C4×D3C2311yescharacteristic
226C22×C4×D3C2311yescharacteristic
227C22×C4×D3C2311yescharacteristic
228C22×C4×D3C2311yescharacteristic
229C22×Dic6C2311yescharacteristic
230C22×Dic6C2311yescharacteristic
231C2×C3×C4⋊C4C2311yescharacteristic
232C2×C3×C4⋊C4C2311yescharacteristic
233C2×C3×C4⋊C4C2311yescharacteristic
234C2×C3×C4⋊C4C2311yescharacteristic
235C2×C3×C4⋊C4C2311yescharacteristic
236C2×C3×C4⋊C4C2311yescharacteristic
237C2×C3×C4⋊C4C2311yescharacteristic
238C2×C3×C4⋊C4C2311yescharacteristic
239C2×C3×C4⋊C4C2311yescharacteristic
240C2×C3×C4⋊C4C2311yescharacteristic
241C2×C3×C4⋊C4C2311yescharacteristic
242C2×C3×C22⋊C4C2311yescharacteristic
243C2×C3×C22⋊C4C2311yescharacteristic
244C2×C3×C22⋊C4C2311yescharacteristic
245C2×C3×C22⋊C4C2311yescharacteristic
246C2×C3×C22⋊C4C2311yescharacteristic
247C2×C3×C22⋊C4C2311yescharacteristic
248C2×C3×C22⋊C4C2311yescharacteristic
249C2×C3×C42C2311yescharacteristic
250C2×C3×C42C2311yescharacteristic
251C2×C3×C42C2311yescharacteristic
252C2×#217C2311yescharacteristic
253C2×#217C2311yescharacteristic
254C2×#217C2311yescharacteristic
255C2×#217C2311yescharacteristic
256C2×#217C2311yescharacteristic
257C2×(C2×D3)⋊C4C2311yescharacteristic
258C2×(C2×D3)⋊C4C2311yescharacteristic
259C2×(C2×D3)⋊C4C2311yescharacteristic
260C2×(C2×D3)⋊C4C2311yescharacteristic
261C2×(C2×D3)⋊C4C2311yescharacteristic
262C2×(C2×D3)⋊C4C2311yescharacteristic
263C2×(C2×D3)⋊C4C2311yescharacteristic
264C2×(C2×D3)⋊C4C2311yescharacteristic
265C2×(C2×D3)⋊C4C2311yescharacteristic
266C2×(C2×D3)⋊C4C2311yescharacteristic
267C2×(C2×D3)⋊C4C2311yescharacteristic
268C2×(C2×D3)⋊C4C2311yescharacteristic
269C2×(C2×D3)⋊C4C2311yescharacteristic
270C2×(C2×D3)⋊C4C2311yescharacteristic
271C2×(C2×D3)⋊C4C2311yescharacteristic
272C2×(C2×D3)⋊C4C2311yescharacteristic
273C2×(C2×D3)⋊C4C2311yescharacteristic
274C2×(C2×D3)⋊C4C2311yescharacteristic
275C2×(C2×D3)⋊C4C2311yescharacteristic
276C2×(C2×D3)⋊C4C2311yescharacteristic
277C2×C4⋊Dic3C2311yescharacteristic
278C2×C4⋊Dic3C2311yescharacteristic
279C2×C4⋊Dic3C2311yescharacteristic
280C2×C4⋊Dic3C2311yescharacteristic
281C2×C4⋊Dic3C2311yescharacteristic
282C2×C4⋊Dic3C2311yescharacteristic
283C2×C4⋊Dic3C2311yescharacteristic
284C2×C4⋊Dic3C2311yescharacteristic
285C2×C4⋊Dic3C2311yescharacteristic
286C2×C4⋊Dic3C2311yescharacteristic
287C2×C4⋊Dic3C2311yescharacteristic
288C2×C4⋊Dic3C2311yescharacteristic
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×Dic3⋊C4C2311yescharacteristic
302C2×Dic3⋊C4C2311yescharacteristic
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
314C2×C4×Dic3C2311yescharacteristic
315C2×C4×Dic3C2311yescharacteristic
316#897—24no—
317#896—42no—
318#893—24no—
319#892—24no—
320#892—42no—
321#892—42no—
322#889—42no—
323#886—24no—
324#883—42no—
325#879—24no—
326#878—42no—
327C42×D3—24no—
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×#126—31no—
387C2×#125—31no—
388C2×#123—31no—
389C2×#123—31no—
390C2×C22⋊Q8—31no—
391C2×C22⋊Q8—31no—
392C2×C22⋊Q8—31no—
393C2×C4×D4—31no—
394C2×#117—31no—
395C2×#117—31no—
396C2×#117—31no—
397C22×C42—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#400—31no—
408#400—31no—
409#400—31no—
410#400C2×D311yescharacteristic
411#399—31no—
412#398—31no—
413#398—31no—
414#398—31no—
415#398—31no—
416#398C2×D311yescharacteristic
417#397—31no—
418#397—31no—
419#397—31no—
420#397—31no—
421#397C2×D311yescharacteristic
422#397C2×D311yescharacteristic
423#396—31no—
424#396—31no—
425#396—31no—
426#396C2×D311yescharacteristic
427#396C2×D311yescharacteristic
428#395—31no—
429#395—31no—
430#395—31no—
431#394—31no—
432#394—31no—
433#394—31no—
434#393—31no—
435#393—31no—
436#393—31no—
437#392—31no—
438#391—31no—
439#391—31no—
440#391—31no—
441#391—31no—
442#391—31no—
443#390—31no—
444#390—31no—
445#389—31no—
446#389—31no—
447#389—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#388C2×D311yescharacteristic
465#388C2×D311yescharacteristic
466#388C2×D311yescharacteristic
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#387C2×D311yescharacteristic
488#387C2×D311yescharacteristic
489#387C2×D311yescharacteristic
490#387C2×D311yescharacteristic
491#387C2×D311yescharacteristic
492#386—31no—
493#386—31no—
494#386—31no—
495#386—31no—
496#386—31no—
497#386—31no—
498#386—31no—
499#386—31no—
500#386—31no—
501#386—31no—
502#385—31no—
503#385—31no—
504#385—31no—
505#385—31no—
506#385—31no—
507#385—31no—
508#385—31no—
509#385—31no—
510#385—31no—
511#385—31no—
512#384—31no—
513#384C2×D311yescharacteristic
514#383—31no—
515#382—31no—
516#382—31no—
517#382—31no—
518#381—31no—
519#381—31no—
520#380—31no—
521#380—31no—
522#380—31no—
523#380—31no—
524#380—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×C22⋊C4—31no—
533C4×C22⋊C4—31no—
534C4×C22⋊C4—31no—
535C4×C22⋊C4—31no—
536C4×C22⋊C4—31no—
537C4×C22⋊C4—31no—
538#376—31no—
539#376—31no—
540C2×#95—31no—
541C24×C3C2411yescharacteristic
542C23×D3C2411yescharacteristic
543C23×D3C2411yescharacteristic
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×C3×C4C2411yescharacteristic
557C22×C3×C4C2411yescharacteristic
558C2×#67—22no—
559C2×#67—22no—
560C2×#67—41no—
561C2×#67—41no—
562C2×#67—41no—
563C2×#67—41no—
564C22×Dic3—22no—
565C22×Dic3—41no—
566C22×Dic3—41no—
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×D12—22no—
582C2×D12—22no—
583C2×D12—41no—
584C2×C4×D3—22no—
585C2×C4×D3—22no—
586C2×C4×D3—22no—
587C2×C4×D3—22no—
588C2×C4×D3—22no—
589C2×C4×D3—22no—
590C2×C4×D3—22no—
591C2×C4×D3—22no—
592C2×C4×D3—22no—
593C2×C4×D3—41no—
594C2×C4×D3—41no—
595C2×C4×D3—41no—
596C2×C4×D3—41no—
597C2×C4×D3—41no—
598C2×C4×D3—41no—
599C2×C4×D3—41no—
600C2×C4×D3—41no—
601C2×C4×D3—41no—
602C2×Dic6—22no—
603C2×Dic6—41no—
604C2×Dic6—41no—
605C2×Dic6—41no—
606C2×Dic6—41no—
607C2×Dic6—41no—
608C3×C4⋊C4—22no—
609C3×C4⋊C4—22no—
610C3×C4⋊C4—22no—
611C3×C4⋊C4—22no—
612C3×C4⋊C4—22no—
613C3×C4⋊C4—41no—
614C3×C4⋊C4—41no—
615C3×C4⋊C4—41no—
616C3×C4⋊C4—41no—
617C3×C4⋊C4—41no—
618C3×C4⋊C4—41no—
619C3×C22⋊C4—22no—
620C3×C22⋊C4—22no—
621C3×C22⋊C4—22no—
622C3×C22⋊C4—41no—
623C3×C22⋊C4—41no—
624C3×C22⋊C4—41no—
625C3×C22⋊C4—41no—
626C3×C42—22no—
627C3×C42—41no—
628C3×C42—41no—
629#217—22no—
630#217—22no—
631#217—41no—
632#217—41no—
633#217—41no—
634(C2×D3)⋊C4—22no—
635(C2×D3)⋊C4—22no—
636(C2×D3)⋊C4—22no—
637(C2×D3)⋊C4—22no—
638(C2×D3)⋊C4—22no—
639(C2×D3)⋊C4—22no—
640(C2×D3)⋊C4—22no—
641(C2×D3)⋊C4—22no—
642(C2×D3)⋊C4—41no—
643(C2×D3)⋊C4—41no—
644(C2×D3)⋊C4—41no—
645(C2×D3)⋊C4—41no—
646(C2×D3)⋊C4—41no—
647(C2×D3)⋊C4—41no—
648(C2×D3)⋊C4—41no—
649(C2×D3)⋊C4—41no—
650(C2×D3)⋊C4—41no—
651(C2×D3)⋊C4—41no—
652(C2×D3)⋊C4—41no—
653(C2×D3)⋊C4#4114yes—
654C4⋊Dic3—22no—
655C4⋊Dic3—22no—
656C4⋊Dic3—22no—
657C4⋊Dic3—22no—
658C4⋊Dic3—22no—
659C4⋊Dic3—22no—
660C4⋊Dic3—22no—
661C4⋊Dic3—22no—
662C4⋊Dic3—41no—
663C4⋊Dic3—41no—
664C4⋊Dic3—41no—
665C4⋊Dic3—41no—
666Dic3⋊C4—22no—
667Dic3⋊C4—22no—
668Dic3⋊C4—22no—
669Dic3⋊C4—22no—
670Dic3⋊C4—41no—
671Dic3⋊C4—41no—
672Dic3⋊C4—41no—
673Dic3⋊C4—41no—
674Dic3⋊C4—41no—
675Dic3⋊C4—41no—
676Dic3⋊C4—41no—
677Dic3⋊C4—41no—
678Dic3⋊C4—41no—
679Dic3⋊C4—41no—
680C4×Dic3—22no—
681C4×Dic3—22no—
682C4×Dic3—22no—
683C4×Dic3—22no—
684C4×Dic3—41no—
685C4×Dic3—41no—
686C4×Dic3—41no—
687C4×Dic3—41no—
688C4×Dic3—41no—
689C4×Dic3—41no—
690C4×Dic3—41no—
691C4×Dic3—41no—
692C4×Dic3#4114yes—
693C22×Q8—31no—
694C22×Q8—31no—
695C22×D4—31no—
696C22×D4—31no—
697C22×D4—31no—
698C23×C4—31no—
699C23×C4—31no—
700C23×C4—31no—
701C23×C4—31no—
702C23×C4—31no—
703C23×C4—31no—
704C23×C4—31no—
705#126—64no—
706#125—122no—
707#123—64no—
708#123—122no—
709C22⋊Q8—64no—
710C22⋊Q8—122no—
711C22⋊Q8—122no—
712C4×D4—64no—
713#117—64no—
714#117—122no—
715#117—122no—
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⋊C4—31no—
730C2×C4⋊C4—31no—
731C2×C4⋊C4—31no—
732C2×C4⋊C4—31no—
733C2×C4⋊C4—31no—
734C2×C4⋊C4—31no—
735C2×C4⋊C4—31no—
736C2×C4⋊C4—31no—
737C2×C4⋊C4—31no—
738C2×C4⋊C4—31no—
739C2×C4⋊C4—31no—
740C2×C4⋊C4—31no—
741C2×C4⋊C4—31no—
742C2×C4⋊C4C22×D311yescharacteristic
743C2×C4⋊C4C22×D311yescharacteristic
744C2×C4⋊C4C22×D311yescharacteristic
745C2×C4⋊C4C22×D311yescharacteristic
746C2×C4⋊C4C22×D311yescharacteristic
747C2×C4⋊C4C22×D311yescharacteristic
748C2×C4⋊C4C22×D311yescharacteristic
749C2×C4⋊C4C22×D311yescharacteristic
750C2×C4⋊C4C22×D311yescharacteristic
751C2×C4⋊C4C22×D311yescharacteristic
752C2×C4⋊C4C22×D311yescharacteristic
753C2×C22⋊C4—31no—
754C2×C22⋊C4—31no—
755C2×C22⋊C4—31no—
756C2×C22⋊C4—31no—
757C2×C22⋊C4—31no—
758C2×C22⋊C4—31no—
759C2×C22⋊C4—31no—
760C2×C22⋊C4—31no—
761C2×C22⋊C4—31no—
762C2×C22⋊C4—31no—
763C2×C22⋊C4—31no—
764C2×C22⋊C4—31no—
765C2×C22⋊C4—31no—
766C2×C22⋊C4—31no—
767C2×C22⋊C4—31no—
768C2×C22⋊C4—31no—
769C2×C22⋊C4—31no—
770C2×C22⋊C4—31no—
771C2×C22⋊C4—31no—
772C2×C22⋊C4—31no—
773C2×C22⋊C4—31no—
774C2×C22⋊C4—31no—
775C2×C22⋊C4—31no—
776C2×C22⋊C4—31no—
777C2×C22⋊C4—31no—
778C2×C22⋊C4C22×D311yescharacteristic
779C2×C22⋊C4C22×D311yescharacteristic
780C2×C22⋊C4C22×D311yescharacteristic
781C2×C22⋊C4C22×D311yescharacteristic
782C2×C22⋊C4C22×D311yescharacteristic
783C2×C22⋊C4C22×D311yescharacteristic
784C2×C22⋊C4C22×D311yescharacteristic
785C2×C42—31no—
786C2×C42—31no—
787C2×C42—31no—
788C2×C42—31no—
789C2×C42—31no—
790C2×C42—31no—
791C2×C42—31no—
792C2×C42—31no—
793C2×C42—31no—
794C2×C42—31no—
795C2×C42—31no—
796C2×C42—31no—
797C2×C42—31no—
798C2×C42—64no—
799C2×C42C22×D311yescharacteristic
800C2×C42C22×D311yescharacteristic
801C2×C42C22×D311yescharacteristic
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#95—31no—
827#95—31no—
828#95—31no—
829#95—31no—
830#95—31no—
831#95—31no—
832#95—31no—
833#95—31no—
834#95—31no—
835#95—31no—
836#95—31no—
837#95—31no—
838#95—31no—
839#95—31no—
840#95—31no—
841#95—31no—
842#95—31no—
843#95—31no—
844#95—31no—
845#95—31no—
846#95C22×D311yescharacteristic
847#95C22×D311yescharacteristic
848#95C22×D311yescharacteristic
849#95C22×D311yescharacteristic
850#95C22×D311yescharacteristic
851#95C22×D311yescharacteristic
852#95C22×D311yescharacteristic
853#95C22×D311yescharacteristic
854#95C22×D311yescharacteristic
855#95C22×D311yescharacteristic
856#95C22×D311yescharacteristic
857#95C22×D311yescharacteristic
858#95C22×D311yescharacteristic
859#95C22×D311yescharacteristic
860C23×C3—21no—
861C23×C3—21no—
862C23×C3—21no—
863C23×C3—21no—
864C23×C3—21no—
865C23×C3—21no—
866C23×C3—21no—
867C23×C3C2511yescharacteristic
868C22×D3—21no—
869C22×D3—21no—
870C22×D3—21no—
871C22×D3—21no—
872C22×D3—21no—
873C22×D3—21no—
874C22×D3—21no—
875C22×D3—21no—
876C22×D3—21no—
877C22×D3—21no—
878C22×D3—21no—
879C22×D3—21no—
880C22×D3C2×#4112yes—
881C22×D32−1+412yes—
882C2×C3×C4—21no—
883C2×C3×C4—21no—
884C2×C3×C4—21no—
885C2×C3×C4—21no—
886C2×C3×C4—21no—
887C2×C3×C4—21no—
888C2×C3×C4—21no—
889C2×C3×C4—21no—
890C2×C3×C4—21no—
891C2×C3×C4—21no—
892C2×C3×C4—21no—
893C2×C3×C4—21no—
894C2×C3×C4—21no—
895C2×C3×C4—21no—
896C2×C3×C4—21no—
897C2×C3×C4—21no—
898C2×C3×C4—21no—
899C2×C3×C4—21no—
900C2×C3×C4—21no—
901C2×C3×C4—21no—
902C2×C3×C4—21no—
903C2×C3×C4—21no—
904C2×C3×C4—21no—
905C2×C3×C4—21no—
906C2×C3×C4—21no—
907C2×C3×C4—21no—
908C2×C3×C4—21no—
909C2×C3×C4—21no—
910C2×C3×C4—21no—
911C2×C3×C4—21no—
912C2×C3×C4—21no—
913C2×C3×C4—21no—
914C2×C3×C4—21no—
915C2×C3×C4—21no—
916C2×C3×C4—21no—
917C2×C3×C4—21no—
918C2×C3×C4—21no—
919C2×C3×C4—21no—
920C2×C3×C4—21no—
921C2×C3×C4C2×#4112yes—
922C2×C3×C4C2×#4112yes—
923C2×C3×C4H(5,𝔽2)12yes—
924#67—82no—
925#67—82no—
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—
937C2×Dic3—21no—
938C2×Dic3—21no—
939C2×Dic3—21no—
940C2×Dic3—21no—
941C2×Dic3—21no—
942C2×Dic3—21no—
943C2×Dic3—21no—
944C2×Dic3—21no—
945C2×Dic3—21no—
946C2×Dic3—21no—
947C2×Dic3—21no—
948C2×Dic3—21no—
949C2×Dic3—21no—
950C2×Dic3—21no—
951C2×Dic3—21no—
952C2×Dic3—21no—
953C2×Dic3—21no—
954C2×Dic3—21no—
955C2×Dic3—21no—
956C2×Dic3—21no—
957C2×Dic3—21no—
958C2×Dic3—21no—
959C2×Dic3—21no—
960C2×Dic3—21no—
961C2×Dic3—21no—
962C2×Dic3—21no—
963C2×Dic3—21no—
964C2×Dic3—21no—
965C2×Dic3—82no—
966C2×Dic3C2×#4112yes—
967C2×Dic3C2×#4112yes—
968C2×Dic3C2×#4112yes—
969D12—44no—
970C4×D3—28no—
971C4×D3—44no—
972C4×D3—44no—
973C4×D3—44no—
974C4×D3—82no—
975C4×D3—82no—
976Dic6—82no—
977Dic6—82no—
978C24—31no—
979C24—31no—
980C24C23×D311yescharacteristic
981C2×Q8—62no—
982C2×Q8—121no—
983C2×Q8—121no—
984C2×Q8—121no—
985C2×Q8—121no—
986C2×Q8—121no—
987C2×D4—62no—
988C2×D4—62no—
989C2×D4—62no—
990C2×D4—62no—
991C2×D4—121no—
992C2×D4—121no—
993C2×D4—121no—
994C2×D4—121no—
995C2×D4—121no—
996C22×C4—31no—
997C22×C4—31no—
998C22×C4—31no—
999C22×C4—31no—
1000C22×C4—31no—
1001C22×C4—31no—
1002C22×C4—31no—
1003C22×C4—31no—
1004C22×C4—31no—
1005C22×C4—31no—
1006C22×C4—31no—
1007C22×C4—31no—
1008C22×C4—31no—
1009C22×C4—31no—
1010C22×C4—62no—
1011C22×C4—62no—
1012C22×C4—62no—
1013C22×C4—62no—
1014C22×C4—62no—
1015C22×C4—62no—
1016C22×C4—62no—
1017C22×C4—62no—
1018C22×C4—62no—
1019C22×C4—62no—
1020C22×C4—121no—
1021C22×C4—121no—
1022C22×C4—121no—
1023C22×C4—121no—
1024C22×C4—121no—
1025C22×C4—121no—
1026C22×C4—121no—
1027C22×C4—121no—
1028C22×C4—121no—
1029C22×C4—121no—
1030C22×C4—121no—
1031C22×C4C23×D311yescharacteristic
1032C22×C4C23×D311yescharacteristic
1033C22×C4C23×D311yescharacteristic
1034C22×C4C23×D311yescharacteristic
1035C22×C4C23×D311yescharacteristic
1036C22×C4C23×D311yescharacteristic
1037C22×C4C23×D311yescharacteristic
1038C22×C4C23×D311yescharacteristic
1039C22×C4C23×D311yescharacteristic
1040C22×C4C23×D311yescharacteristic
1041C22×C4C23×D311yescharacteristic
1042C22×C4C23×D311yescharacteristic
1043C22×C4C23×D311yescharacteristic
1044C22×C4C23×D311yescharacteristic
1045C4⋊C4—22no—
1046C4⋊C4—22no—
1047C4⋊C4—22no—
1048C4⋊C4—22no—
1049C4⋊C4—22no—
1050C4⋊C4—41no—
1051C4⋊C4—41no—
1052C4⋊C4—41no—
1053C4⋊C4—41no—
1054C4⋊C4—41no—
1055C4⋊C4—41no—
1056C4⋊C4—62no—
1057C4⋊C4—62no—
1058C4⋊C4—62no—
1059C4⋊C4—62no—
1060C4⋊C4—62no—
1061C4⋊C4—62no—
1062C4⋊C4—62no—
1063C4⋊C4—62no—
1064C4⋊C4—62no—
1065C4⋊C4—62no—
1066C4⋊C4—62no—
1067C4⋊C4—62no—
1068C4⋊C4—121no—
1069C4⋊C4—121no—
1070C4⋊C4—121no—
1071C4⋊C4—121no—
1072C4⋊C4—121no—
1073C4⋊C4—121no—
1074C4⋊C4—121no—
1075C4⋊C4—121no—
1076C4⋊C4—121no—
1077C4⋊C4—121no—
1078C4⋊C4—121no—
1079C4⋊C4—121no—
1080C4⋊C4—121no—
1081C4⋊C4—121no—
1082C22⋊C4—22no—
1083C22⋊C4—22no—
1084C22⋊C4—22no—
1085C22⋊C4—34no—
1086C22⋊C4—41no—
1087C22⋊C4—41no—
1088C22⋊C4—41no—
1089C22⋊C4—41no—
1090C22⋊C4—62no—
1091C22⋊C4—62no—
1092C22⋊C4—62no—
1093C22⋊C4—62no—
1094C22⋊C4—62no—
1095C22⋊C4—62no—
1096C22⋊C4—62no—
1097C22⋊C4—62no—
1098C22⋊C4—62no—
1099C22⋊C4—62no—
1100C22⋊C4—121no—
1101C22⋊C4—121no—
1102C22⋊C4—121no—
1103C22⋊C4—121no—
1104C22⋊C4—121no—
1105C22⋊C4—121no—
1106C22⋊C4—121no—
1107C22⋊C4—121no—
1108C22⋊C4—121no—
1109C22⋊C4—121no—
1110C22⋊C4—121no—
1111C22⋊C4—121no—
1112C22⋊C4—121no—
1113C22⋊C4—121no—
1114C42—22no—
1115C42—34no—
1116C42—41no—
1117C42—41no—
1118C42—62no—
1119C42—62no—
1120C42—62no—
1121C42—62no—
1122C42—121no—
1123C42—121no—
1124C42—121no—
1125C42—121no—
1126C42—121no—
1127C42—121no—
1128C42—121no—
1129C42—121no—
1130C22×C3—41no—
1131C22×C3—41no—
1132C22×C3—41no—
1133C22×C3—41no—
1134C22×C3—41no—
1135C22×C3—41no—
1136C22×C3—41no—
1137C22×C3C22×#4111yescharacteristic
1138C22×C3C22×#4111yescharacteristic
1139C22×C3C2×H(5,𝔽2)11yescharacteristic
1140C22×C3C2×2−1+411yescharacteristic
1141C22×C3#58511yescharacteristic
1142C22×C3#58511yescharacteristic
1143C22×C3#58511yescharacteristic
1144C2×D3—22no—
1145C2×D3—22no—
1146C2×D3—22no—
1147C2×D3—22no—
1148C2×D3—22no—
1149C2×D3—22no—
1150C2×D3—41no—
1151C2×D3—41no—
1152C2×D3—41no—
1153C2×D3—41no—
1154C2×D3—41no—
1155C2×D3—41no—
1156C2×D3—41no—
1157C2×D3—41no—
1158C3×C4—22no—
1159C3×C4—22no—
1160C3×C4—22no—
1161C3×C4—41no—
1162C3×C4—41no—
1163C3×C4—41no—
1164C3×C4—41no—
1165C3×C4—41no—
1166C3×C4—41no—
1167C3×C4—41no—
1168C3×C4—41no—
1169C3×C4—41no—
1170C3×C4—41no—
1171C3×C4—41no—
1172Dic3—22no—
1173Dic3—22no—
1174Dic3—22no—
1175Dic3—41no—
1176Dic3—41no—
1177Dic3—41no—
1178Dic3—41no—
1179Dic3—41no—
1180Dic3—41no—
1181Dic3—41no—
1182Dic3—41no—
1183Dic3—41no—
1184Dic3—41no—
1185Dic3—41no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—21no—
1190C23—21no—
1191C23—21no—
1192C23—21no—
1193C23—32no—
1194C23—32no—
1195C23—61no—
1196C23—61no—
1197C23—61no—
1198C23—61no—
1199C23—61no—
1200C23—61no—
1201C23—61no—
1202C23—61no—
1203C23—61no—
1204C23—61no—
1205C23—61no—
1206C23—61no—
1207C23C24×D311yescharacteristic
1208Q8—242no—
1209Q8—242no—
1210D4—124no—
1211D4—242no—
1212D4—242no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—32no—
1253C2×C4—32no—
1254C2×C4—32no—
1255C2×C4—68no—
1256C2×C4—61no—
1257C2×C4—61no—
1258C2×C4—61no—
1259C2×C4—61no—
1260C2×C4—61no—
1261C2×C4—61no—
1262C2×C4—61no—
1263C2×C4—61no—
1264C2×C4—61no—
1265C2×C4—61no—
1266C2×C4—61no—
1267C2×C4—61no—
1268C2×C4—61no—
1269C2×C4—61no—
1270C2×C4—61no—
1271C2×C4—61no—
1272C2×C4—61no—
1273C2×C4—61no—
1274C2×C4—61no—
1275C2×C4—61no—
1276C2×C4—61no—
1277C2×C4—61no—
1278C2×C4—61no—
1279C2×C4—61no—
1280C2×C4—61no—
1281C2×C4—61no—
1282C2×C4—61no—
1283C2×C4—61no—
1284C2×C4—61no—
1285C2×C4—61no—
1286C2×C4—61no—
1287C2×C4—61no—
1288C2×C4—61no—
1289C2×C4—61no—
1290C2×C4—61no—
1291C2×C4—61no—
1292C2×C4—61no—
1293C2×C4—61no—
1294C2×C4—61no—
1295C2×C4—124no—
1296C2×C4—124no—
1297C2×C4—124no—
1298C2×C4—242no—
1299C2×C4—242no—
1300C2×C4—242no—
1301C2×C4D3×#4112yes—
1302C2×C4D3×#4112yes—
1303C2×C4#100912yes—
1304C2×C3—81no—
1305C2×C3#345511yescharacteristic
1306C2×C3#347511yescharacteristic
1307C2×C3#349211yescharacteristic
1308C2×C3#349511yescharacteristic
1309C2×C3#351411yescharacteristic
1310C2×C3#356211yescharacteristic
1311C2×C3#356411yescharacteristic
1312D3—42no—
1313D3—42no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—41no—
1321C22—62no—
1322C22—62no—
1323C22—62no—
1324C22—62no—
1325C22—62no—
1326C22—62no—
1327C22—121no—
1328C22—121no—
1329C22—121no—
1330C22—121no—
1331C22—121no—
1332C22—121no—
1333C22—121no—
1334C22—121no—
1335C22C2×D3×#4111yescharacteristic
1336C22C2×D3×#4111yescharacteristic
1337C22C2×#100911yescharacteristic
1338C22#596611yescharacteristic
1339C22#596611yescharacteristic
1340C22D3×2−1+411yescharacteristic
1341C22#596811yescharacteristic
1342C4—22no—
1343C4—22no—
1344C4—22no—
1345C4—41no—
1346C4—41no—
1347C4—41no—
1348C4—41no—
1349C4—41no—
1350C4—41no—
1351C4—41no—
1352C4—41no—
1353C4—41no—
1354C4—41no—
1355C4—41no—
1356C4—62no—
1357C4—62no—
1358C4—62no—
1359C4—121no—
1360C4—121no—
1361C4—121no—
1362C4—121no—
1363C4—121no—
1364C4—121no—
1365C4—121no—
1366C4—121no—
1367C4—121no—
1368C4—121no—
1369C4—121no—
1370C3#3840611yescharacteristic, complemented, Sylow
1371C2—81no—
1372C2—122no—
1373C2—122no—
1374C2#8642711yescharacteristic
1375C2#8648011yescharacteristic
1376C2#8655111yescharacteristic
1377C2#8686011yescharacteristic
1378C2#8687411yescharacteristic
1379C2#8698611yescharacteristic
1380C2#8713811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2793C2
prime radical#4960C22
hypercenter#2793D3
hypocenterC3#38406
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2793

Complements

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

NH ≅ G/Ntype
1. C3×#2793C2semidirect
2. #78392C2semidirect
3. #78205C2semidirect
4. #77953C2semidirect
5. #77834C2semidirect
6. #77678C2semidirect
7. #77486C2semidirect
8. #77477C2semidirect
10. #77446C2semidirect
11. #77340C2semidirect
12. #77328C2semidirect
14. #75958C2semidirect
16. #75668C2semidirect
17. #75586C2semidirect
18. #75486C2semidirect
19. #75468C2semidirect
20. #75437C2semidirect
21. #75334C2semidirect
22. #75303C2semidirect
23. #75262C2semidirect
24. #75085C2semidirect
25. #75082C2semidirect
26. #75063C2semidirect
27. #75012C2semidirect
28. #74951C2semidirect
29. #74937C2semidirect
30. #74347C2semidirect
31. #74318C2semidirect
190. #2793D3semidirect
1370. C3#38406semidirect

Maximal subgroups

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

subgroupindex
C3×#27932
#783922
#782052
#779532
#778342
#776782
#774862
#774772
#774732
#774462
#773402
#773282
#772932
#759582
#759492
#756682
#755862
#754862
#754682
#754372
#753342
#753032
#752622
#750852
#750822
#750632
#750122
#749512
#749372
#743472
#743182
#384063