Finite Group Databasebeta

← #11233511

Subgroups — #11233511

Order 768.

1526 conjugacy classes of subgroups.

The subgroup lattice has 1280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2520C211yesmaximal, characteristic, complemented
2#78246C211yesmaximal, characteristic, complemented
3#78150C211yesmaximal, characteristic
4#77787C211yesmaximal, characteristic, complemented
5#77772C211yesmaximal, characteristic
6#77771C211yesmaximal, characteristic
7#77766C211yesmaximal, characteristic, complemented
8#77183C211yesmaximal, characteristic, complemented
9#77170C211yesmaximal, characteristic
10#76576C211yesmaximal, characteristic
11#76575C211yesmaximal, characteristic
12#76548C211yesmaximal, characteristic, complemented
13#76489C211yesmaximal, characteristic, complemented
14#75218C211yesmaximal, characteristic
15#75208C211yesmaximal, characteristic, complemented
16#75206C211yesmaximal, characteristic, complemented
17#75166C211yesmaximal, characteristic, complemented
18#75113C211yesmaximal, characteristic, complemented
19#75109C211yesmaximal, characteristic, complemented
20#75028C211yesmaximal, characteristic, complemented
21#75024C211yesmaximal, characteristic
22#74982C211yesmaximal, characteristic
23#74981C211yesmaximal, characteristic
24#74947C211yesmaximal, characteristic
25#74944C211yesmaximal, characteristic
26#74210C211yesmaximal, characteristic
27#74158C211yesmaximal, characteristic, complemented
28#73698C211yesmaximal, characteristic
29#73698C211yesmaximal, characteristic
30#73642C211yesmaximal, characteristic, complemented
31#73637C211yesmaximal, characteristic, complemented
32#45346—31nomaximal, Sylow
33C2×Q8×Dic3C2211yescharacteristic
34C2×#898C2211yescharacteristic
35C2×#898C2211yescharacteristic
36C2×#896C2211yescharacteristic
37C2×#892C2211yescharacteristic
38C2×#890C2211yescharacteristic
39C2×#889C2211yescharacteristic
40C2×#889C2211yescharacteristic
41C2×#889C2211yescharacteristic
42C2×C4×Dic6C2211yescharacteristic
43C2×C4×Dic6C2211yescharacteristic
44C2×C4×Dic6C2211yescharacteristic
45C3×#400C2211yescharacteristic
46C3×#398C2211yescharacteristic
47C3×#398C2211yescharacteristic
48C3×#395C2211yescharacteristic
49C3×#391C2211yescharacteristic
50C3×#391C2211yescharacteristic
51C3×#387C2211yescharacteristic
52C3×#387C2211yescharacteristic
53C3×#387C2211yescharacteristic
54C3×#387C2211yescharacteristic
55C3×#387C2211yescharacteristic
56C3×#387C2211yescharacteristic
57C3×#382C2211yescharacteristic
58C3×C4×C4⋊C4C2211yescharacteristic
59C3×C4×C4⋊C4C2211yescharacteristic
60#5231C2211yescharacteristic
61#5229C2211yescharacteristic
62#5229C2211yescharacteristic
63#4994C2211yescharacteristic
64#4994C2211yescharacteristic
65#4994C2211yescharacteristic
66#4994C2211yescharacteristic
67#4993C2211yescharacteristic
68#4990C2211yescharacteristic
69#4990C2211yescharacteristic
70#4986C2211yescharacteristic
71#4986C2211yescharacteristic
72#4984C2211yescharacteristic
73#4984C2211yescharacteristic
74#4982C2211yescharacteristic
75#4981C2211yescharacteristic
76#4981C2211yescharacteristic
77#4981C2211yescharacteristic
78#4980C2211yescharacteristic
79#4980C2211yescharacteristic
80#4978C2211yescharacteristic
81#4978C2211yescharacteristic
82#4977C2211yescharacteristic
83#4977C2211yescharacteristic
84#4976C2211yescharacteristic
85#4976C2211yescharacteristic
86#4976C2211yescharacteristic
87#4976C2211yescharacteristic
88#4976C2211yescharacteristic
89#4976C2211yescharacteristic
90#4975C2211yescharacteristic
91#4975C2211yescharacteristic
92#4975C2211yescharacteristic
93#4975C2211yescharacteristic
94Dic3×C4⋊C4C2211yescharacteristic
95Dic3×C4⋊C4C2211yescharacteristic
96Dic3×C4⋊C4C2211yescharacteristic
97Dic3×C4⋊C4C2211yescharacteristic
98Dic3×C4⋊C4C2211yescharacteristic
99#4940C2211yescharacteristic
100#4940C2211yescharacteristic
101#4940C2211yescharacteristic
102#4940C2211yescharacteristic
103#4940C2211yescharacteristic
104#4936C2211yescharacteristic
105#4936C2211yescharacteristic
106#4936C2211yescharacteristic
107C4×C4⋊Dic3C2211yescharacteristic
108C4×C4⋊Dic3C2211yescharacteristic
109#4933C2211yescharacteristic
110#4933C2211yescharacteristic
111C4×Dic3⋊C4C2211yescharacteristic
112C4×Dic3⋊C4C2211yescharacteristic
113#4928C2211yescharacteristic
114#4928C2211yescharacteristic
115#4928C2211yescharacteristic
116#4677C2211yescharacteristic
117#4677C2211yescharacteristic
118#4675C2211yescharacteristic
119#4675C2211yescharacteristic
120#4675C2211yescharacteristic
121#4674C2211yescharacteristic
122#4670C2211yescharacteristic
123#4670C2211yescharacteristic
124#4670C2211yescharacteristic
125#4669C2211yescharacteristic
126#4669C2211yescharacteristic
127#4669C2211yescharacteristic
128#4669C2211yescharacteristic
129#4667C2211yescharacteristic
130#4667C2211yescharacteristic
131#4667C2211yescharacteristic
132#4666C2211yescharacteristic
133#4666C2211yescharacteristic
134#4661C2211yescharacteristic
135#4661C2211yescharacteristic
136#4661C2211yescharacteristic
137#4661C2211yescharacteristic
138#4661C2211yescharacteristic
139#4661C2211yescharacteristic
140#4660C2211yescharacteristic
141#4660C2211yescharacteristic
142#4659C2211yescharacteristic
143#4659C2211yescharacteristic
144#4659C2211yescharacteristic
145#4658C2211yescharacteristic
146#4658C2211yescharacteristic
147#4658C2211yescharacteristic
148#4657C2211yescharacteristic
149#4657C2211yescharacteristic
150#4657C2211yescharacteristic
151#4657C2211yescharacteristic
152#4655C2211yescharacteristic
153#4655C2211yescharacteristic
154#4654C2211yescharacteristic
155#4654C2211yescharacteristic
156#4654C2211yescharacteristic
157#4654C2211yescharacteristic
158#4654C2211yescharacteristic
159#4654C2211yescharacteristic
160#4654C2211yescharacteristic
161#4653C2211yescharacteristic
162#4653C2211yescharacteristic
163#4653C2211yescharacteristic
164#4653C2211yescharacteristic
165#4653C2211yescharacteristic
166#4652C2211yescharacteristic
167#4652C2211yescharacteristic
168#4652C2211yescharacteristic
169#4652C2211yescharacteristic
170#4650C2211yescharacteristic
171#4650C2211yescharacteristic
172#4650C2211yescharacteristic
173#4650C2211yescharacteristic
174#4649C2211yescharacteristic
175#4649C2211yescharacteristic
176#4649C2211yescharacteristic
177#4649C2211yescharacteristic
178#4649C2211yescharacteristic
179#4647C2211yescharacteristic
180#4647C2211yescharacteristic
181#4647C2211yescharacteristic
182#4647C2211yescharacteristic
183#4647C2211yescharacteristic
184#4647C2211yescharacteristic
185#4646C2211yescharacteristic
186#4646C2211yescharacteristic
187#4646C2211yescharacteristic
188#2772—31no—
189#2772—31no—
190#2767—31no—
191#2767—31no—
192#2754—31no—
193#2754—31no—
194#2719—31no—
195#2719—31no—
196#2590—31no—
197#2590—31no—
198#2582—31no—
199#2552—31no—
200#2520—31no—
201#2520D311yescharacteristic, complemented
202#2519—31no—
203#2519—31no—
204#2519—31no—
205#2519—31no—
206#2508—31no—
207#2506—31no—
208#2497—31no—
209#2496—31no—
210#2423—31no—
211#2421—31no—
212#2396—31no—
213#2355—31no—
214#2355—31no—
215#2355—31no—
216#2351—31no—
217#2323—31no—
218#2314—31no—
219C22×C3×Q8C2311yescharacteristic
220C22×C4×D3C2311yescharacteristic
221C22×Dic6C2311yescharacteristic
222C2×C3×C4⋊C4C2311yescharacteristic
223C2×C3×C4⋊C4C2311yescharacteristic
224C2×C3×C4⋊C4C2311yescharacteristic
225C2×C3×C4⋊C4C2311yescharacteristic
226C2×C3×C4⋊C4C2311yescharacteristic
227C2×C3×C4⋊C4C2311yescharacteristic
228C2×C3×C4⋊C4C2311yescharacteristic
229C2×C3×C4⋊C4C2311yescharacteristic
230C2×C3×C4⋊C4C2311yescharacteristic
231C2×C3×C4⋊C4C2311yescharacteristic
232C2×C3×C4⋊C4C2311yescharacteristic
233C2×C3×C42C2311yescharacteristic
234C2×C3×C42C2311yescharacteristic
235C2×C3×C42C2311yescharacteristic
236C2×C3×C42C2311yescharacteristic
237C2×C3×C42C2311yescharacteristic
238Q8×Dic3—24no—
239C2×(C2×D3)⋊C4C2311yescharacteristic
240C2×(C2×D3)⋊C4C2311yescharacteristic
241C2×(C2×D3)⋊C4C2311yescharacteristic
242C2×(C2×D3)⋊C4C2311yescharacteristic
243C2×(C2×D3)⋊C4C2311yescharacteristic
244C2×(C2×D3)⋊C4C2311yescharacteristic
245C2×(C2×D3)⋊C4C2311yescharacteristic
246C2×(C2×D3)⋊C4C2311yescharacteristic
247C2×(C2×D3)⋊C4C2311yescharacteristic
248C2×(C2×D3)⋊C4C2311yescharacteristic
249C2×(C2×D3)⋊C4C2311yescharacteristic
250C2×(C2×D3)⋊C4C2311yescharacteristic
251C2×(C2×D3)⋊C4C2311yescharacteristic
252C2×(C2×D3)⋊C4C2311yescharacteristic
253C2×C4⋊Dic3C2311yescharacteristic
254C2×C4⋊Dic3C2311yescharacteristic
255C2×C4⋊Dic3C2311yescharacteristic
256C2×C4⋊Dic3C2311yescharacteristic
257C2×C4⋊Dic3C2311yescharacteristic
258C2×C4⋊Dic3C2311yescharacteristic
259C2×C4⋊Dic3C2311yescharacteristic
260C2×C4⋊Dic3C2311yescharacteristic
261C2×C4⋊Dic3C2311yescharacteristic
262C2×C4⋊Dic3C2311yescharacteristic
263C2×C4⋊Dic3C2311yescharacteristic
264C2×C4⋊Dic3C2311yescharacteristic
265C2×C4⋊Dic3C2311yescharacteristic
266C2×C4⋊Dic3C2311yescharacteristic
267C2×C4⋊Dic3C2311yescharacteristic
268C2×C4⋊Dic3C2311yescharacteristic
269C2×C4⋊Dic3C2311yescharacteristic
270C2×Dic3⋊C4C2311yescharacteristic
271C2×Dic3⋊C4C2311yescharacteristic
272C2×Dic3⋊C4C2311yescharacteristic
273C2×Dic3⋊C4C2311yescharacteristic
274C2×Dic3⋊C4C2311yescharacteristic
275C2×Dic3⋊C4C2311yescharacteristic
276C2×Dic3⋊C4C2311yescharacteristic
277C2×Dic3⋊C4C2311yescharacteristic
278C2×Dic3⋊C4C2311yescharacteristic
279C2×Dic3⋊C4C2311yescharacteristic
280C2×Dic3⋊C4C2311yescharacteristic
281C2×Dic3⋊C4C2311yescharacteristic
282C2×Dic3⋊C4C2311yescharacteristic
283C2×Dic3⋊C4C2311yescharacteristic
284C2×Dic3⋊C4C2311yescharacteristic
285C2×Dic3⋊C4C2311yescharacteristic
286C2×Dic3⋊C4C2311yescharacteristic
287C2×Dic3⋊C4C2311yescharacteristic
288C2×Dic3⋊C4C2311yescharacteristic
289C2×Dic3⋊C4C2311yescharacteristic
290C2×Dic3⋊C4C2311yescharacteristic
291C2×Dic3⋊C4C2311yescharacteristic
292C2×Dic3⋊C4C2311yescharacteristic
293C2×Dic3⋊C4C2311yescharacteristic
294C2×Dic3⋊C4C2311yescharacteristic
295C2×Dic3⋊C4C2311yescharacteristic
296C2×Dic3⋊C4C2311yescharacteristic
297C2×Dic3⋊C4C2311yescharacteristic
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
314C2×C4×Dic3C2311yescharacteristic
315#898—42no—
316#898—42no—
317#896—24no—
318#892—24no—
319#890—42no—
320#889—42no—
321#889—42no—
322#889—42no—
323C4×Dic6—24no—
324C4×Dic6—24no—
325C4×Dic6—24no—
326C3×#95C2311yescharacteristic
327C3×#95C2311yescharacteristic
328C3×#95C2311yescharacteristic
329C3×#95C2311yescharacteristic
330C3×#95C2311yescharacteristic
331C3×#95C2311yescharacteristic
332C3×#95C2311yescharacteristic
333C3×#95C2311yescharacteristic
334C3×#95C2311yescharacteristic
335C3×#95C2311yescharacteristic
336C3×#95C2311yescharacteristic
337C3×#95C2311yescharacteristic
338C3×#95C2311yescharacteristic
339C3×#95C2311yescharacteristic
340C3×#95C2311yescharacteristic
341C3×#95C2311yescharacteristic
342C3×#95C2311yescharacteristic
343C3×#95C2311yescharacteristic
344C3⋊#95C2311yescharacteristic
345C3⋊#95C2311yescharacteristic
346C3⋊#95C2311yescharacteristic
347C3⋊#95C2311yescharacteristic
348C3⋊#95C2311yescharacteristic
349C3⋊#95C2311yescharacteristic
350C3⋊#95C2311yescharacteristic
351C3⋊#95C2311yescharacteristic
352C3⋊#95C2311yescharacteristic
353C3⋊#95C2311yescharacteristic
354C3⋊#95C2311yescharacteristic
355C3⋊#95C2311yescharacteristic
356C3⋊#95C2311yescharacteristic
357C3⋊#95C2311yescharacteristic
358C3⋊#95C2311yescharacteristic
359C3⋊#95C2311yescharacteristic
360C3⋊#95C2311yescharacteristic
361C3⋊#95C2311yescharacteristic
362C3⋊#95C2311yescharacteristic
363C3⋊#95C2311yescharacteristic
364C3⋊#95C2311yescharacteristic
365C3⋊#95C2311yescharacteristic
366C3⋊#95C2311yescharacteristic
367C3⋊#95C2311yescharacteristic
368C3⋊#95C2311yescharacteristic
369C3⋊#95C2311yescharacteristic
370C3⋊#95C2311yescharacteristic
371C3⋊#95C2311yescharacteristic
372C3⋊#95C2311yescharacteristic
373C3⋊#95C2311yescharacteristic
374C3⋊#95C2311yescharacteristic
375C3⋊#95C2311yescharacteristic
376C3⋊#95C2311yescharacteristic
377C3⋊#95C2311yescharacteristic
378C3⋊#95C2311yescharacteristic
379C3⋊#95C2311yescharacteristic
380C3⋊#95C2311yescharacteristic
381C3⋊#95C2311yescharacteristic
382C3⋊#95C2311yescharacteristic
383C3⋊#95C2311yescharacteristic
384C3⋊#95C2311yescharacteristic
385C3⋊#95C2311yescharacteristic
386C2×#126—31no—
387C2×#126—31no—
388C2×#125—31no—
389C2×#125—31no—
390C2×#125—31no—
391C2×#125—31no—
392C2×C22⋊Q8—31no—
393C2×C4×Q8—31no—
394C2×C4×Q8—31no—
395C2×C4×Q8—31no—
396C2×C4×Q8—31no—
397C2×#117—31no—
398#400—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#400C2×D311yescharacteristic
409#399—31no—
410#399—31no—
411#399—31no—
412#398—31no—
413#398—31no—
414#398—31no—
415#398—31no—
416#398—31no—
417#398—31no—
418#398—31no—
419#398—31no—
420#398—31no—
421#398—31no—
422#398—31no—
423#398—31no—
424#398—31no—
425#398—31no—
426#398C2×D311yescharacteristic
427#398C2×D311yescharacteristic
428#397—31no—
429#397—31no—
430#397—31no—
431#397—31no—
432#396—31no—
433#396—31no—
434#396—31no—
435#396—31no—
436#395C2×D311yescharacteristic
437#393—31no—
438#391—31no—
439#391—31no—
440#391—31no—
441#391—31no—
442#391—31no—
443#391C2×D311yescharacteristic
444#391C2×D311yescharacteristic
445#389—31no—
446#389—31no—
447#389—31no—
448#389—31no—
449#389—31no—
450#389—31no—
451#389—31no—
452#389—31no—
453#389—31no—
454#389—31no—
455#389—31no—
456#389—31no—
457#389—31no—
458#389—31no—
459#389—31no—
460#389—31no—
461#389—31no—
462#388—31no—
463#388—31no—
464#388—31no—
465#388—31no—
466#388—31no—
467#388—31no—
468#388—31no—
469#388—31no—
470#388—31no—
471#388—31no—
472#388—31no—
473#388—31no—
474#388—31no—
475#388—31no—
476#387—31no—
477#387—31no—
478#387—31no—
479#387—31no—
480#387—31no—
481#387—31no—
482#387—31no—
483#387—31no—
484#387—31no—
485#387—31no—
486#387—31no—
487#387—31no—
488#387—31no—
489#387—31no—
490#387—31no—
491#387—31no—
492#387—31no—
493#387—31no—
494#387—31no—
495#387—31no—
496#387—31no—
497#387—31no—
498#387—31no—
499#387—31no—
500#387C2×D311yescharacteristic
501#387C2×D311yescharacteristic
502#387C2×D311yescharacteristic
503#387C2×D311yescharacteristic
504#387C2×D311yescharacteristic
505#387C2×D311yescharacteristic
506#384—31no—
507#384—31no—
508#384—31no—
509#384—31no—
510#382—31no—
511#382—31no—
512#382—31no—
513#382—31no—
514#382—31no—
515#382—31no—
516#382—31no—
517#382—31no—
518#382—31no—
519#382C2×D311yescharacteristic
520#380—31no—
521#380—31no—
522#380—31no—
523C4×C4⋊C4—31no—
524C4×C4⋊C4—31no—
525C4×C4⋊C4—31no—
526C4×C4⋊C4—31no—
527C4×C4⋊C4—31no—
528C4×C4⋊C4—31no—
529C4×C4⋊C4—31no—
530C4×C4⋊C4—31no—
531C4×C4⋊C4—31no—
532C4×C4⋊C4—31no—
533C4×C4⋊C4—31no—
534C4×C4⋊C4—31no—
535C4×C4⋊C4—31no—
536C4×C4⋊C4—31no—
537C4×C4⋊C4C2×D311yescharacteristic
538C4×C4⋊C4C2×D311yescharacteristic
539C4×C22⋊C4—31no—
540C4×C22⋊C4—31no—
541C23×D3C2411yescharacteristic
542C2×C3×Q8—22no—
543C2×C3×Q8—22no—
544C2×C3×Q8—41no—
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
558C22×C3×C4C2411yescharacteristic
559C22×C3×C4C2411yescharacteristic
560C22×Dic3C2411yescharacteristic
561C22×Dic3C2411yescharacteristic
562C22×Dic3C2411yescharacteristic
563C22×Dic3C2411yescharacteristic
564C22×Dic3C2411yescharacteristic
565C22×Dic3C2411yescharacteristic
566C22×Dic3C2411yescharacteristic
567C22×Dic3C2411yescharacteristic
568C22×Dic3C2411yescharacteristic
569C22×Dic3C2411yescharacteristic
570C22×Dic3C2411yescharacteristic
571C22×Dic3C2411yescharacteristic
572C22×Dic3C2411yescharacteristic
573C22×Dic3C2411yescharacteristic
574C22×Dic3C2411yescharacteristic
575C2×C4×D3—22no—
576C2×C4×D3—22no—
577C2×C4×D3—22no—
578C2×Dic6—22no—
579C2×Dic6—22no—
580C2×Dic6#4114yes—
581C3×C4⋊C4—22no—
582C3×C4⋊C4—22no—
583C3×C4⋊C4—22no—
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×C42—22no—
593C3×C42—22no—
594C3×C42—22no—
595C3×C42—41no—
596C3×C42—41no—
597(C2×D3)⋊C4—22no—
598(C2×D3)⋊C4—22no—
599(C2×D3)⋊C4—22no—
600(C2×D3)⋊C4—22no—
601(C2×D3)⋊C4—22no—
602(C2×D3)⋊C4—22no—
603(C2×D3)⋊C4—22no—
604(C2×D3)⋊C4—41no—
605(C2×D3)⋊C4—41no—
606(C2×D3)⋊C4—41no—
607(C2×D3)⋊C4—41no—
608(C2×D3)⋊C4—41no—
609(C2×D3)⋊C4—41no—
610(C2×D3)⋊C4—41no—
611C4⋊Dic3—22no—
612C4⋊Dic3—22no—
613C4⋊Dic3—22no—
614C4⋊Dic3—22no—
615C4⋊Dic3—22no—
616C4⋊Dic3—22no—
617C4⋊Dic3—22no—
618C4⋊Dic3—22no—
619C4⋊Dic3—22no—
620C4⋊Dic3—22no—
621C4⋊Dic3—22no—
622C4⋊Dic3—41no—
623C4⋊Dic3—41no—
624C4⋊Dic3—41no—
625C4⋊Dic3—41no—
626C4⋊Dic3—41no—
627C4⋊Dic3—41no—
628Dic3⋊C4—22no—
629Dic3⋊C4—22no—
630Dic3⋊C4—22no—
631Dic3⋊C4—22no—
632Dic3⋊C4—22no—
633Dic3⋊C4—22no—
634Dic3⋊C4—22no—
635Dic3⋊C4—22no—
636Dic3⋊C4—22no—
637Dic3⋊C4—22no—
638Dic3⋊C4—22no—
639Dic3⋊C4—22no—
640Dic3⋊C4—22no—
641Dic3⋊C4—22no—
642Dic3⋊C4—22no—
643Dic3⋊C4—22no—
644Dic3⋊C4—41no—
645Dic3⋊C4—41no—
646Dic3⋊C4—41no—
647Dic3⋊C4—41no—
648Dic3⋊C4—41no—
649Dic3⋊C4—41no—
650Dic3⋊C4—41no—
651Dic3⋊C4—41no—
652Dic3⋊C4—41no—
653Dic3⋊C4—41no—
654Dic3⋊C4—41no—
655Dic3⋊C4—41no—
656C4×Dic3—22no—
657C4×Dic3—22no—
658C4×Dic3—22no—
659C4×Dic3—22no—
660C4×Dic3—22no—
661C4×Dic3—22no—
662C4×Dic3—22no—
663C4×Dic3—22no—
664C4×Dic3—41no—
665C4×Dic3—41no—
666C4×Dic3—41no—
667C4×Dic3—41no—
668C4×Dic3—41no—
669C4×Dic3—41no—
670C4×Dic3—41no—
671C4×Dic3—41no—
672C4×Dic3#4114yes—
673C22×Q8—31no—
674C22×Q8C22×D311yescharacteristic
675C23×C4—31no—
676#126—122no—
677#126—122no—
678#125—122no—
679#125—122no—
680#125—122no—
681#125—122no—
682C22⋊Q8—64no—
683C4×Q8—64no—
684C4×Q8—64no—
685C4×Q8—64no—
686C4×Q8—64no—
687#117—64no—
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⋊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⋊C4C22×D311yescharacteristic
734C2×C4⋊C4C22×D311yescharacteristic
735C2×C4⋊C4C22×D311yescharacteristic
736C2×C4⋊C4C22×D311yescharacteristic
737C2×C4⋊C4C22×D311yescharacteristic
738C2×C4⋊C4C22×D311yescharacteristic
739C2×C4⋊C4C22×D311yescharacteristic
740C2×C4⋊C4C22×D311yescharacteristic
741C2×C4⋊C4C22×D311yescharacteristic
742C2×C4⋊C4C22×D311yescharacteristic
743C2×C4⋊C4C22×D311yescharacteristic
744C2×C22⋊C4—31no—
745C2×C22⋊C4—31no—
746C2×C22⋊C4—31no—
747C2×C22⋊C4—31no—
748C2×C22⋊C4—31no—
749C2×C22⋊C4—31no—
750C2×C22⋊C4—31no—
751C2×C22⋊C4—31no—
752C2×C22⋊C4—31no—
753C2×C22⋊C4—31no—
754C2×C22⋊C4—31no—
755C2×C22⋊C4—31no—
756C2×C22⋊C4—31no—
757C2×C22⋊C4—31no—
758C2×C42—31no—
759C2×C42—31no—
760C2×C42—31no—
761C2×C42—31no—
762C2×C42—31no—
763C2×C42—31no—
764C2×C42—31no—
765C2×C42—31no—
766C2×C42—31no—
767C2×C42—31no—
768C2×C42—31no—
769C2×C42—31no—
770C2×C42—31no—
771C2×C42—31no—
772C2×C42—31no—
773C2×C42—31no—
774C2×C42—31no—
775C2×C42C22×D311yescharacteristic
776C2×C42C22×D311yescharacteristic
777C2×C42C22×D311yescharacteristic
778C2×C42C22×D311yescharacteristic
779C2×C42C22×D311yescharacteristic
780#95—31no—
781#95—31no—
782#95—31no—
783#95—31no—
784#95—31no—
785#95—31no—
786#95—31no—
787#95—31no—
788#95—31no—
789#95—31no—
790#95—31no—
791#95—31no—
792#95—31no—
793#95—31no—
794#95—31no—
795#95—31no—
796#95—31no—
797#95—31no—
798#95—31no—
799#95—31no—
800#95—31no—
801#95—31no—
802#95—31no—
803#95—31no—
804#95—31no—
805#95—31no—
806#95—31no—
807#95—31no—
808#95—31no—
809#95—31no—
810#95—31no—
811#95—31no—
812#95—31no—
813#95—31no—
814#95—31no—
815#95—31no—
816#95—31no—
817#95—31no—
818#95—31no—
819#95—31no—
820#95—31no—
821#95—31no—
822#95C22×D311yescharacteristic
823#95C22×D311yescharacteristic
824#95C22×D311yescharacteristic
825#95C22×D311yescharacteristic
826#95C22×D311yescharacteristic
827#95C22×D311yescharacteristic
828#95C22×D311yescharacteristic
829#95C22×D311yescharacteristic
830#95C22×D311yescharacteristic
831#95C22×D311yescharacteristic
832#95C22×D311yescharacteristic
833#95C22×D311yescharacteristic
834#95C22×D311yescharacteristic
835#95C22×D311yescharacteristic
836#95C22×D311yescharacteristic
837#95C22×D311yescharacteristic
838#95C22×D311yescharacteristic
839#95C22×D311yescharacteristic
840C23×C3C2511yescharacteristic
841C22×D3—21no—
842C22×D3—21no—
843C22×D3—21no—
844C22×D3—21no—
845C22×D3—21no—
846C22×D3—21no—
847C22×D3—21no—
848C3×Q8—44no—
849C2×C3×C4—21no—
850C2×C3×C4—21no—
851C2×C3×C4—21no—
852C2×C3×C4—21no—
853C2×C3×C4—21no—
854C2×C3×C4—21no—
855C2×C3×C4—21no—
856C2×C3×C4—21no—
857C2×C3×C4—21no—
858C2×C3×C4—21no—
859C2×C3×C4—21no—
860C2×C3×C4—21no—
861C2×C3×C4—21no—
862C2×C3×C4—21no—
863C2×C3×C4—21no—
864C2×C3×C4—21no—
865C2×C3×C4—21no—
866C2×C3×C4—21no—
867C2×C3×C4—21no—
868C2×C3×C4—21no—
869C2×C3×C4—21no—
870C2×C3×C4—21no—
871C2×C3×C4—21no—
872C2×C3×C4—21no—
873C2×C3×C4—21no—
874C2×C3×C4—21no—
875C2×C3×C4—21no—
876C2×C3×C4—21no—
877C2×C3×C4—21no—
878C2×C3×C4—21no—
879C2×C3×C4—21no—
880C2×C3×C4—21no—
881C2×C3×C4—21no—
882C2×C3×C4—21no—
883C2×C3×C4—21no—
884C2×C3×C4—21no—
885C2×C3×C4—21no—
886C2×C3×C4—21no—
887C2×C3×C4—21no—
888C2×C3×C4—21no—
889C2×C3×C4C2×#4112yes—
890C2×C3×C4C2×#4112yes—
891C2×C3×C4H(5,𝔽2)12yes—
892C2×C3×C42−1+412yes—
893C2×C3×C42−1+412yes—
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×Dic3C2×#4112yes—
935C2×Dic3C2×#4112yes—
936C2×Dic3C2×#4112yes—
937C2×Dic3C2×#4112yes—
938C2×Dic32−1+412yes—
939C4×D3—44no—
940Dic6—28no—
941C24—31no—
942C2×Q8—22no—
943C2×Q8—22no—
944C2×Q8—34no—
945C2×Q8—41no—
946C2×Q8—62no—
947C2×Q8—62no—
948C22×C4—31no—
949C22×C4—31no—
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—62no—
964C22×C4—62no—
965C22×C4—62no—
966C22×C4C23×D311yescharacteristic
967C22×C4C23×D311yescharacteristic
968C22×C4C23×D311yescharacteristic
969C22×C4C23×D311yescharacteristic
970C22×C4C23×D311yescharacteristic
971C22×C4C23×D311yescharacteristic
972C22×C4C23×D311yescharacteristic
973C22×C4C23×D311yescharacteristic
974C22×C4C23×D311yescharacteristic
975C22×C4C23×D311yescharacteristic
976C22×C4C23×D311yescharacteristic
977C22×C4C23×D311yescharacteristic
978C22×C4C23×D311yescharacteristic
979C22×C4C23×D311yescharacteristic
980C22×C4C23×D311yescharacteristic
981C4⋊C4—22no—
982C4⋊C4—22no—
983C4⋊C4—22no—
984C4⋊C4—22no—
985C4⋊C4—22no—
986C4⋊C4—22no—
987C4⋊C4—22no—
988C4⋊C4—22no—
989C4⋊C4—41no—
990C4⋊C4—41no—
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—62no—
1007C4⋊C4—62no—
1008C4⋊C4—62no—
1009C4⋊C4—62no—
1010C4⋊C4—62no—
1011C4⋊C4—62no—
1012C4⋊C4—62no—
1013C4⋊C4—62no—
1014C4⋊C4—62no—
1015C4⋊C4—62no—
1016C4⋊C4—62no—
1017C4⋊C4—62no—
1018C4⋊C4—62no—
1019C4⋊C4—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—
1029C4⋊C4—121no—
1030C4⋊C4—121no—
1031C4⋊C4—121no—
1032C4⋊C4—121no—
1033C4⋊C4—121no—
1034C4⋊C4—121no—
1035C4⋊C4—121no—
1036C4⋊C4—121no—
1037C22⋊C4—62no—
1038C22⋊C4—62no—
1039C22⋊C4—62no—
1040C22⋊C4—62no—
1041C22⋊C4—62no—
1042C22⋊C4—62no—
1043C22⋊C4—62no—
1044C22⋊C4—121no—
1045C22⋊C4—121no—
1046C22⋊C4—121no—
1047C22⋊C4—121no—
1048C22⋊C4—121no—
1049C22⋊C4—121no—
1050C22⋊C4—121no—
1051C42—22no—
1052C42—22no—
1053C42—22no—
1054C42—34no—
1055C42—41no—
1056C42—41no—
1057C42—62no—
1058C42—62no—
1059C42—62no—
1060C42—62no—
1061C42—62no—
1062C42—62no—
1063C42—62no—
1064C42—62no—
1065C42—121no—
1066C42—121no—
1067C42—121no—
1068C42—121no—
1069C42—121no—
1070C42—121no—
1071C42—121no—
1072C42—121no—
1073C22×C3C22×#4111yescharacteristic
1074C22×C3C22×#4111yescharacteristic
1075C22×C3C2×H(5,𝔽2)11yescharacteristic
1076C22×C3C2×2−1+411yescharacteristic
1077C22×C3C2×2−1+411yescharacteristic
1078C22×C3C2×2−1+411yescharacteristic
1079C22×C3#58511yescharacteristic
1080C2×D3—41no—
1081C2×D3—41no—
1082C2×D3—41no—
1083C2×D3—41no—
1084C2×D3—41no—
1085C2×D3—41no—
1086C2×D3—41no—
1087C3×C4—22no—
1088C3×C4—22no—
1089C3×C4—22no—
1090C3×C4—22no—
1091C3×C4—22no—
1092C3×C4—41no—
1093C3×C4—41no—
1094C3×C4—41no—
1095C3×C4—41no—
1096C3×C4—41no—
1097C3×C4—41no—
1098C3×C4—41no—
1099C3×C4—41no—
1100C3×C4—41no—
1101C3×C4—41no—
1102Dic3—22no—
1103Dic3—22no—
1104Dic3—41no—
1105Dic3—41no—
1106Dic3—41no—
1107Dic3—41no—
1108Dic3—41no—
1109Dic3—41no—
1110Dic3—41no—
1111Dic3—41no—
1112Dic3—41no—
1113Dic3—41no—
1114Dic3—41no—
1115Dic3—41no—
1116Dic3#55214yes—
1117C23—61no—
1118C23—61no—
1119C23—61no—
1120C23—61no—
1121C23—61no—
1122C23—61no—
1123C23—61no—
1124C23C24×D311yescharacteristic
1125Q8—44no—
1126Q8—68no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—32no—
1168C2×C4—32no—
1169C2×C4—32no—
1170C2×C4—32no—
1171C2×C4—32no—
1172C2×C4—61no—
1173C2×C4—61no—
1174C2×C4—61no—
1175C2×C4—61no—
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—124no—
1213C2×C4#100712yes—
1214C2×C4D3×#4112yes—
1215C2×C4D3×#4112yes—
1216C2×C4#100912yes—
1217C2×C4#101012yes—
1218C2×C3C2×#55211yescharacteristic
1219C2×C3#349511yescharacteristic
1220C2×C3#351111yescharacteristic
1221C2×C3#351611yescharacteristic
1222C2×C3#352211yescharacteristic
1223C2×C3#355411yescharacteristic
1224C2×C3#355611yescharacteristic
1225D3—81no—
1226C22—121no—
1227C22—121no—
1228C22—121no—
1229C22—121no—
1230C22—121no—
1231C22—121no—
1232C22—121no—
1233C22C2×#100711yescharacteristic
1234C22C2×D3×#4111yescharacteristic
1235C22C2×D3×#4111yescharacteristic
1236C22C2×#100911yescharacteristic
1237C22C2×#101011yescharacteristic
1238C22#596611yescharacteristic
1239C22D3×2−1+411yescharacteristic
1240C4—22no—
1241C4—22no—
1242C4—22no—
1243C4—22no—
1244C4—22no—
1245C4—34no—
1246C4—41no—
1247C4—41no—
1248C4—41no—
1249C4—41no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—62no—
1257C4—62no—
1258C4—121no—
1259C4—121no—
1260C4—121no—
1261C4—121no—
1262C4—121no—
1263C4—121no—
1264C4—121no—
1265C4—121no—
1266C4—121no—
1267C4—121no—
1268C4—121no—
1269C4—121no—
1270C3#4534611yescharacteristic, complemented, Sylow
1271C2—241no—
1272C2#8612811yescharacteristic
1273C2#8626411yescharacteristic
1274C2#8653611yescharacteristic
1275C2#8679311yescharacteristic
1276C2D3×#55211yescharacteristic
1277C2#8693211yescharacteristic
1278C2#8702711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2520C2
prime radicalC23×D3C24
hypercenter#2520D3
hypocenterC3#45346
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2520

Complements

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

NH ≅ G/Ntype
1. C3×#2520C2semidirect
2. #78246C2semidirect
4. #77787C2semidirect
7. #77766C2semidirect
8. #77183C2semidirect
12. #76548C2semidirect
13. #76489C2semidirect
15. #75208C2semidirect
16. #75206C2semidirect
17. #75166C2semidirect
18. #75113C2semidirect
19. #75109C2semidirect
20. #75028C2semidirect
27. #74158C2semidirect
30. #73642C2semidirect
31. #73637C2semidirect
201. #2520D3semidirect
1270. C3#45346semidirect

Maximal subgroups

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

subgroupindex
C3×#25202
#782462
#781502
#777872
#777722
#777712
#777662
#771832
#771702
#765762
#765752
#765482
#764892
#752182
#752082
#752062
#751662
#751132
#751092
#750282
#750242
#749822
#749812
#749472
#749442
#742102
#741582
#736982
#736422
#736372
#453463