Finite Group Databasebeta

← #11044291

Subgroups — #11044291

Order 768.

1510 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2758C211yesmaximal, characteristic, complemented
2#78352C211yesmaximal, characteristic, complemented
3#78341C211yesmaximal, characteristic
4#78251C211yesmaximal, characteristic, complemented
5#78225C211yesmaximal, characteristic, complemented
6#78224C211yesmaximal, characteristic, complemented
7#78206C211yesmaximal, characteristic, complemented
8#78197C211yesmaximal, characteristic, complemented
9#78188C211yesmaximal, characteristic, complemented
10#78187C211yesmaximal, characteristic, complemented
11#78185C211yesmaximal, characteristic, complemented
12#77268C211yesmaximal, characteristic
13#77200C211yesmaximal, characteristic, complemented
14#76551C211yesmaximal, characteristic, complemented
15#76528C211yesmaximal, characteristic, complemented
16#76506C211yesmaximal, characteristic
17#76488C211yesmaximal, characteristic
18#76285C211yesmaximal, characteristic, complemented
19#76272C211yesmaximal, characteristic, complemented
20#75422C211yesmaximal, characteristic
21#75421C211yesmaximal, characteristic, complemented
22#75304C211yesmaximal, characteristic, complemented
23#75213C211yesmaximal, characteristic, complemented
24#75049C211yesmaximal, characteristic, complemented
25#74971C211yesmaximal, characteristic, complemented
26#74956C211yesmaximal, characteristic
27#74937C211yesmaximal, characteristic
28#74305C211yesmaximal, characteristic, complemented
29#74287C211yesmaximal, characteristic, complemented
30#74268C211yesmaximal, characteristic, complemented
31#74258C211yesmaximal, characteristic, complemented
32#38418—31nomaximal, Sylow
33C2×#947C2211yescharacteristic
34C2×#894C2211yescharacteristic
35C2×#893C2211yescharacteristic
36C2×#892C2211yescharacteristic
37C2×#890C2211yescharacteristic
38C2×C42×D3C2211yescharacteristic
39C3×#400C2211yescharacteristic
40C3×#400C2211yescharacteristic
41C3×#400C2211yescharacteristic
42C3×#400C2211yescharacteristic
43C3×#400C2211yescharacteristic
44C3×#395C2211yescharacteristic
45C3×#391C2211yescharacteristic
46C3×#391C2211yescharacteristic
47C3×#389C2211yescharacteristic
48C3×#387C2211yescharacteristic
49C3×#387C2211yescharacteristic
50C3×#387C2211yescharacteristic
51C3×#387C2211yescharacteristic
52C3×#383C2211yescharacteristic
53C3×#383C2211yescharacteristic
54#5230C2211yescharacteristic
55#5229C2211yescharacteristic
56#5229C2211yescharacteristic
57#4994C2211yescharacteristic
58#4993C2211yescharacteristic
59#4993C2211yescharacteristic
60#4992C2211yescharacteristic
61#4990C2211yescharacteristic
62#4989C2211yescharacteristic
63#4989C2211yescharacteristic
64#4989C2211yescharacteristic
65#4989C2211yescharacteristic
66#4989C2211yescharacteristic
67#4987C2211yescharacteristic
68#4987C2211yescharacteristic
69#4987C2211yescharacteristic
70#4986C2211yescharacteristic
71#4984C2211yescharacteristic
72#4984C2211yescharacteristic
73#4983C2211yescharacteristic
74#4983C2211yescharacteristic
75#4982C2211yescharacteristic
76#4981C2211yescharacteristic
77#4980C2211yescharacteristic
78#4980C2211yescharacteristic
79#4980C2211yescharacteristic
80#4980C2211yescharacteristic
81#4980C2211yescharacteristic
82#4978C2211yescharacteristic
83#4978C2211yescharacteristic
84#4978C2211yescharacteristic
85#4978C2211yescharacteristic
86#4977C2211yescharacteristic
87Dic3×C4⋊C4C2211yescharacteristic
88#4972C2211yescharacteristic
89#4940C2211yescharacteristic
90#4940C2211yescharacteristic
91#4939C2211yescharacteristic
92C4×(C2×D3)⋊C4C2211yescharacteristic
93#4937C2211yescharacteristic
94C4×C4⋊Dic3C2211yescharacteristic
95#4933C2211yescharacteristic
96#4933C2211yescharacteristic
97C4×Dic3⋊C4C2211yescharacteristic
98C4×Dic3⋊C4C2211yescharacteristic
99#4928C2211yescharacteristic
100#4676C2211yescharacteristic
101#4675C2211yescharacteristic
102#4675C2211yescharacteristic
103#4675C2211yescharacteristic
104#4675C2211yescharacteristic
105#4675C2211yescharacteristic
106#4675C2211yescharacteristic
107#4674C2211yescharacteristic
108#4674C2211yescharacteristic
109#4674C2211yescharacteristic
110#4670C2211yescharacteristic
111#4670C2211yescharacteristic
112#4670C2211yescharacteristic
113#4670C2211yescharacteristic
114#4669C2211yescharacteristic
115#4669C2211yescharacteristic
116#4669C2211yescharacteristic
117#4668C2211yescharacteristic
118#4668C2211yescharacteristic
119#4668C2211yescharacteristic
120#4668C2211yescharacteristic
121#4668C2211yescharacteristic
122#4668C2211yescharacteristic
123#4668C2211yescharacteristic
124#4668C2211yescharacteristic
125#4667C2211yescharacteristic
126#4667C2211yescharacteristic
127#4667C2211yescharacteristic
128#4666C2211yescharacteristic
129#4666C2211yescharacteristic
130#4666C2211yescharacteristic
131#4666C2211yescharacteristic
132#4666C2211yescharacteristic
133#4665C2211yescharacteristic
134#4665C2211yescharacteristic
135#4665C2211yescharacteristic
136#4664C2211yescharacteristic
137#4664C2211yescharacteristic
138#4664C2211yescharacteristic
139#4664C2211yescharacteristic
140D3×#95C2211yescharacteristic
141#4661C2211yescharacteristic
142#4661C2211yescharacteristic
143#4660C2211yescharacteristic
144#4660C2211yescharacteristic
145#4659C2211yescharacteristic
146#4658C2211yescharacteristic
147#4658C2211yescharacteristic
148#4658C2211yescharacteristic
149#4658C2211yescharacteristic
150#4658C2211yescharacteristic
151#4657C2211yescharacteristic
152#4657C2211yescharacteristic
153#4657C2211yescharacteristic
154#4657C2211yescharacteristic
155#4655C2211yescharacteristic
156#4655C2211yescharacteristic
157#4655C2211yescharacteristic
158#4655C2211yescharacteristic
159#4655C2211yescharacteristic
160#4654C2211yescharacteristic
161#4654C2211yescharacteristic
162#4654C2211yescharacteristic
163#4654C2211yescharacteristic
164#4653C2211yescharacteristic
165#4653C2211yescharacteristic
166#4653C2211yescharacteristic
167#4653C2211yescharacteristic
168#4653C2211yescharacteristic
169#4653C2211yescharacteristic
170#4652C2211yescharacteristic
171#4652C2211yescharacteristic
172#4652C2211yescharacteristic
173#4652C2211yescharacteristic
174#4651C2211yescharacteristic
175#4651C2211yescharacteristic
176#4650C2211yescharacteristic
177#4650C2211yescharacteristic
178#4650C2211yescharacteristic
179#4649C2211yescharacteristic
180#4649C2211yescharacteristic
181#4649C2211yescharacteristic
182#4649C2211yescharacteristic
183#4648C2211yescharacteristic
184#4648C2211yescharacteristic
185#4648C2211yescharacteristic
186#4647C2211yescharacteristic
187#4647C2211yescharacteristic
188#2851—31no—
189#2770—31no—
190#2769—31no—
191#2758D311yescharacteristic, complemented
192#2748—31no—
193#2747—31no—
194#2747—31no—
195#2738—31no—
196#2717—31no—
197#2652—31no—
198#2652—31no—
199#2612—31no—
200#2611—31no—
201#2590—31no—
202#2588—31no—
203#2577—31no—
204#2575—31no—
205#2575—31no—
206#2573—31no—
207#2524—31no—
208#2520—31no—
209#2515—31no—
210#2505—31no—
211#2447—31no—
212#2419—31no—
213#2371—31no—
214#2343—31no—
215#2337—31no—
216#2335—31no—
217#2290—31no—
218#2283—31no—
219C22×C3×Q8C2311yescharacteristic
220C22×D12C2311yescharacteristic
221C22×C4×D3C2311yescharacteristic
222C22×C4×D3C2311yescharacteristic
223C22×C4×D3C2311yescharacteristic
224C22×C4×D3C2311yescharacteristic
225C22×C4×D3C2311yescharacteristic
226C22×C4×D3C2311yescharacteristic
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×C42C2311yescharacteristic
237C2×C3×C42C2311yescharacteristic
238C2×C3×C42C2311yescharacteristic
239#947—24no—
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×(C2×D3)⋊C4C2311yescharacteristic
254C2×(C2×D3)⋊C4C2311yescharacteristic
255C2×(C2×D3)⋊C4C2311yescharacteristic
256C2×(C2×D3)⋊C4C2311yescharacteristic
257C2×(C2×D3)⋊C4C2311yescharacteristic
258C2×(C2×D3)⋊C4C2311yescharacteristic
259C2×(C2×D3)⋊C4C2311yescharacteristic
260C2×(C2×D3)⋊C4C2311yescharacteristic
261C2×(C2×D3)⋊C4C2311yescharacteristic
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×C4⋊Dic3C2311yescharacteristic
271C2×C4⋊Dic3C2311yescharacteristic
272C2×C4⋊Dic3C2311yescharacteristic
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×C4×Dic3C2311yescharacteristic
294C2×C4×Dic3C2311yescharacteristic
295C2×C4×Dic3C2311yescharacteristic
296C2×C4×Dic3C2311yescharacteristic
297C2×C4×Dic3C2311yescharacteristic
298C2×C4×Dic3C2311yescharacteristic
299C2×C4×Dic3C2311yescharacteristic
300C2×C4×Dic3C2311yescharacteristic
301C2×C4×Dic3C2311yescharacteristic
302C2×C4×Dic3C2311yescharacteristic
303C2×C4×Dic3C2311yescharacteristic
304C2×C4×Dic3C2311yescharacteristic
305C2×C4×Dic3C2311yescharacteristic
306C2×C4×Dic3C2311yescharacteristic
307#894—24no—
308#893—24no—
309#892—24no—
310#890—24no—
311C42×D3—24no—
312C3×#95C2311yescharacteristic
313C3×#95C2311yescharacteristic
314C3×#95C2311yescharacteristic
315C3×#95C2311yescharacteristic
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×#125—31no—
381C2×#124—31no—
382C2×#123—31no—
383C2×C4×D4—31no—
384C2×#117—31no—
385C22×C42—31no—
386#400—31no—
387#400—31no—
388#400—31no—
389#400—31no—
390#400—31no—
391#400—31no—
392#400—31no—
393#400—31no—
394#400—31no—
395#400C2×D311yescharacteristic
396#400C2×D311yescharacteristic
397#400C2×D311yescharacteristic
398#400C2×D311yescharacteristic
399#400C2×D311yescharacteristic
400#399—31no—
401#399—31no—
402#398—31no—
403#398—31no—
404#398—31no—
405#398—31no—
406#398—31no—
407#398—31no—
408#398—31no—
409#398—31no—
410#398—31no—
411#398—31no—
412#397—31no—
413#397—31no—
414#397—31no—
415#397—31no—
416#397—31no—
417#397—31no—
418#397—31no—
419#397—31no—
420#397—31no—
421#397—31no—
422#396—31no—
423#396—31no—
424#395—31no—
425#395C2×D311yescharacteristic
426#391—31no—
427#391—31no—
428#391C2×D311yescharacteristic
429#391C2×D311yescharacteristic
430#390—31no—
431#389—31no—
432#389—31no—
433#389—31no—
434#389—31no—
435#389—31no—
436#389—31no—
437#389C2×D311yescharacteristic
438#388—31no—
439#388—31no—
440#388—31no—
441#388—31no—
442#388—31no—
443#388—31no—
444#388—31no—
445#388—31no—
446#388—31no—
447#388—31no—
448#387—31no—
449#387—31no—
450#387—31no—
451#387—31no—
452#387—31no—
453#387—31no—
454#387—31no—
455#387—31no—
456#387—31no—
457#387—31no—
458#387—31no—
459#387—31no—
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#387C2×D311yescharacteristic
479#387C2×D311yescharacteristic
480#387C2×D311yescharacteristic
481#387C2×D311yescharacteristic
482#386—31no—
483#386—31no—
484#386—31no—
485#385—31no—
486#385—31no—
487#385—31no—
488#385—31no—
489#385—31no—
490#385—31no—
491#385—31no—
492#385—31no—
493#385—31no—
494#385—31no—
495#385—31no—
496#385—31no—
497#385—31no—
498#383—31no—
499#383—31no—
500#383—31no—
501#383C2×D311yescharacteristic
502#383C2×D311yescharacteristic
503#382—31no—
504#382—31no—
505#382—31no—
506#382—31no—
507#381—31no—
508#381—31no—
509#381—31no—
510#381—31no—
511#380—31no—
512#380—31no—
513#380—31no—
514#380—31no—
515#380—31no—
516#380—31no—
517C4×C4⋊C4—31no—
518C4×C4⋊C4—31no—
519C4×C4⋊C4—31no—
520C4×C4⋊C4—31no—
521C4×C4⋊C4—31no—
522C4×C4⋊C4—31no—
523C4×C4⋊C4—31no—
524C4×C4⋊C4—31no—
525C4×C22⋊C4—31no—
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—
534C2×#95—31no—
535C23×D3C2411yescharacteristic
536C23×D3C2411yescharacteristic
537C2×C3×Q8—22no—
538C2×C3×Q8—41no—
539C2×C3×Q8—41no—
540C22×C3×C4C2411yescharacteristic
541C22×C3×C4C2411yescharacteristic
542C22×C3×C4C2411yescharacteristic
543C22×C3×C4C2411yescharacteristic
544C22×C3×C4C2411yescharacteristic
545C22×C3×C4C2411yescharacteristic
546C22×C3×C4C2411yescharacteristic
547C22×C3×C4C2411yescharacteristic
548C22×C3×C4C2411yescharacteristic
549C22×C3×C4C2411yescharacteristic
550C22×C3×C4C2411yescharacteristic
551C22×C3×C4C2411yescharacteristic
552C22×C3×C4C2411yescharacteristic
553C22×C3×C4C2411yescharacteristic
554C22×C3×C4C2411yescharacteristic
555C22×Dic3C2411yescharacteristic
556C22×Dic3C2411yescharacteristic
557C22×Dic3C2411yescharacteristic
558C22×Dic3C2411yescharacteristic
559C22×Dic3C2411yescharacteristic
560C22×Dic3C2411yescharacteristic
561C22×Dic3C2411yescharacteristic
562C22×Dic3C2411yescharacteristic
563C22×Dic3C2411yescharacteristic
564C22×Dic3C2411yescharacteristic
565C22×Dic3C2411yescharacteristic
566C22×Dic3C2411yescharacteristic
567C22×Dic3C2411yescharacteristic
568C22×Dic3C2411yescharacteristic
569C2×D12—41no—
570C2×D12—41no—
571C2×D12#4114yes—
572C2×C4×D3—22no—
573C2×C4×D3—22no—
574C2×C4×D3—22no—
575C2×C4×D3—22no—
576C2×C4×D3—22no—
577C2×C4×D3—22no—
578C2×C4×D3—22no—
579C2×C4×D3—22no—
580C2×C4×D3—41no—
581C2×C4×D3—41no—
582C2×C4×D3—41no—
583C2×C4×D3—41no—
584C2×C4×D3—41no—
585C2×C4×D3—41no—
586C2×C4×D3—41no—
587C2×C4×D3—41no—
588C2×C4×D3—41no—
589C2×C4×D3—41no—
590C3×C4⋊C4—22no—
591C3×C4⋊C4—22no—
592C3×C4⋊C4—22no—
593C3×C4⋊C4—22no—
594C3×C4⋊C4—41no—
595C3×C4⋊C4—41no—
596C3×C4⋊C4—41no—
597C3×C4⋊C4—41no—
598C3×C4⋊C4—41no—
599C3×C42—22no—
600C3×C42—41no—
601C3×C42—41no—
602(C2×D3)⋊C4—22no—
603(C2×D3)⋊C4—22no—
604(C2×D3)⋊C4—22no—
605(C2×D3)⋊C4—22no—
606(C2×D3)⋊C4—22no—
607(C2×D3)⋊C4—22no—
608(C2×D3)⋊C4—22no—
609(C2×D3)⋊C4—22no—
610(C2×D3)⋊C4—22no—
611(C2×D3)⋊C4—22no—
612(C2×D3)⋊C4—22no—
613(C2×D3)⋊C4—22no—
614(C2×D3)⋊C4—41no—
615(C2×D3)⋊C4—41no—
616(C2×D3)⋊C4—41no—
617(C2×D3)⋊C4—41no—
618(C2×D3)⋊C4—41no—
619(C2×D3)⋊C4—41no—
620(C2×D3)⋊C4—41no—
621(C2×D3)⋊C4—41no—
622(C2×D3)⋊C4—41no—
623(C2×D3)⋊C4—41no—
624C4⋊Dic3—22no—
625C4⋊Dic3—22no—
626C4⋊Dic3—22no—
627C4⋊Dic3—22no—
628C4⋊Dic3—41no—
629C4⋊Dic3—41no—
630C4⋊Dic3—41no—
631C4⋊Dic3—41no—
632C4⋊Dic3—41no—
633C4⋊Dic3—41no—
634C4⋊Dic3—41no—
635Dic3⋊C4—22no—
636Dic3⋊C4—22no—
637Dic3⋊C4—22no—
638Dic3⋊C4—22no—
639Dic3⋊C4—22no—
640Dic3⋊C4—22no—
641Dic3⋊C4—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—
653Dic3⋊C4—41no—
654Dic3⋊C4—41no—
655C4×Dic3—22no—
656C4×Dic3—22no—
657C4×Dic3—22no—
658C4×Dic3—22no—
659C4×Dic3—22no—
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×Q8C22×D311yescharacteristic
670C22×D4—31no—
671C23×C4—31no—
672C23×C4—31no—
673C23×C4—31no—
674C23×C4—31no—
675C23×C4—31no—
676C23×C4—31no—
677#125—64no—
678#124—64no—
679#123—64no—
680C4×D4—64no—
681#117—64no—
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⋊C4—31no—
737C2×C22⋊C4—31no—
738C2×C22⋊C4—31no—
739C2×C22⋊C4—31no—
740C2×C22⋊C4—31no—
741C2×C22⋊C4—31no—
742C2×C22⋊C4—31no—
743C2×C22⋊C4—31no—
744C2×C42—31no—
745C2×C42—31no—
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—64no—
759C2×C42C22×D311yescharacteristic
760C2×C42C22×D311yescharacteristic
761C2×C42C22×D311yescharacteristic
762#95—31no—
763#95—31no—
764#95—31no—
765#95—31no—
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#95C22×D311yescharacteristic
809#95C22×D311yescharacteristic
810#95C22×D311yescharacteristic
811#95C22×D311yescharacteristic
812#95C22×D311yescharacteristic
813#95C22×D311yescharacteristic
814#95C22×D311yescharacteristic
815#95C22×D311yescharacteristic
816#95C22×D311yescharacteristic
817#95C22×D311yescharacteristic
818#95C22×D311yescharacteristic
819#95C22×D311yescharacteristic
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×C3C2511yescharacteristic
831C22×D3—21no—
832C22×D3—21no—
833C22×D3—21no—
834C22×D3—21no—
835C22×D3—21no—
836C22×D3—21no—
837C22×D3—21no—
838C22×D3—21no—
839C22×D3—21no—
840C22×D3—21no—
841C22×D3—21no—
842C22×D3—21no—
843C22×D3C2×#4112yes—
844C22×D3C2×#4112yes—
845C3×Q8—82no—
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—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×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×Dic3C2×#4112yes—
931C2×Dic3C2×#4112yes—
932C2×Dic32−1+412yes—
933D12—44no—
934C4×D3—44no—
935C4×D3—44no—
936C4×D3—44no—
937C4×D3—44no—
938C4×D3—82no—
939C4×D3—82no—
940C24—31no—
941C24—31no—
942C2×Q8—22no—
943C2×Q8—41no—
944C2×Q8—41no—
945C2×D4—34no—
946C2×D4—121no—
947C2×D4—121no—
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—62no—
963C22×C4—62no—
964C22×C4—62no—
965C22×C4—62no—
966C22×C4—62no—
967C22×C4—62no—
968C22×C4—62no—
969C22×C4—62no—
970C22×C4—121no—
971C22×C4—121no—
972C22×C4—121no—
973C22×C4—121no—
974C22×C4—121no—
975C22×C4—121no—
976C22×C4—121no—
977C22×C4—121no—
978C22×C4—121no—
979C22×C4—121no—
980C22×C4C23×D311yescharacteristic
981C22×C4C23×D311yescharacteristic
982C22×C4C23×D311yescharacteristic
983C22×C4C23×D311yescharacteristic
984C22×C4C23×D311yescharacteristic
985C22×C4C23×D311yescharacteristic
986C22×C4C23×D311yescharacteristic
987C22×C4C23×D311yescharacteristic
988C22×C4C23×D311yescharacteristic
989C22×C4C23×D311yescharacteristic
990C22×C4C23×D311yescharacteristic
991C22×C4C23×D311yescharacteristic
992C22×C4C23×D311yescharacteristic
993C22×C4C23×D311yescharacteristic
994C22×C4C23×D311yescharacteristic
995C4⋊C4—22no—
996C4⋊C4—22no—
997C4⋊C4—22no—
998C4⋊C4—22no—
999C4⋊C4—41no—
1000C4⋊C4—41no—
1001C4⋊C4—41no—
1002C4⋊C4—41no—
1003C4⋊C4—41no—
1004C4⋊C4—62no—
1005C4⋊C4—62no—
1006C4⋊C4—62no—
1007C4⋊C4—62no—
1008C4⋊C4—62no—
1009C4⋊C4—62no—
1010C4⋊C4—62no—
1011C4⋊C4—62no—
1012C4⋊C4—62no—
1013C4⋊C4—62no—
1014C4⋊C4—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—
1029C4⋊C4—121no—
1030C4⋊C4—121no—
1031C4⋊C4—121no—
1032C4⋊C4—121no—
1033C4⋊C4—121no—
1034C4⋊C4—121no—
1035C22⋊C4—62no—
1036C22⋊C4—62no—
1037C22⋊C4—62no—
1038C22⋊C4—62no—
1039C22⋊C4—62no—
1040C22⋊C4—62no—
1041C22⋊C4—62no—
1042C22⋊C4—62no—
1043C22⋊C4—62no—
1044C22⋊C4—62no—
1045C22⋊C4—62no—
1046C22⋊C4—62no—
1047C22⋊C4—121no—
1048C22⋊C4—121no—
1049C22⋊C4—121no—
1050C22⋊C4—121no—
1051C22⋊C4—121no—
1052C22⋊C4—121no—
1053C22⋊C4—121no—
1054C22⋊C4—121no—
1055C22⋊C4—121no—
1056C22⋊C4—121no—
1057C42—22no—
1058C42—34no—
1059C42—41no—
1060C42—41no—
1061C42—62no—
1062C42—62no—
1063C42—62no—
1064C42—62no—
1065C42—62no—
1066C42—121no—
1067C42—121no—
1068C42—121no—
1069C42—121no—
1070C42—121no—
1071C42—121no—
1072C42—121no—
1073C42—121no—
1074C22×C3C22×#4111yescharacteristic
1075C22×C3C22×#4111yescharacteristic
1076C22×C3C2×2−1+411yescharacteristic
1077C22×C3#58511yescharacteristic
1078C22×C3#58511yescharacteristic
1079C22×C3#58511yescharacteristic
1080C22×C3#58511yescharacteristic
1081C2×D3—22no—
1082C2×D3—22no—
1083C2×D3—22no—
1084C2×D3—22no—
1085C2×D3—22no—
1086C2×D3—22no—
1087C2×D3—41no—
1088C2×D3—41no—
1089C2×D3—41no—
1090C2×D3—41no—
1091C2×D3—41no—
1092C2×D3—41no—
1093C2×D3—41no—
1094C2×D3—41no—
1095C3×C4—22no—
1096C3×C4—22no—
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—
1106C3×C4—41no—
1107C3×C4—41no—
1108C3×C4—41no—
1109C3×C4—41no—
1110Dic3—22no—
1111Dic3—22no—
1112Dic3—22no—
1113Dic3—41no—
1114Dic3—41no—
1115Dic3—41no—
1116Dic3—41no—
1117Dic3—41no—
1118Dic3—41no—
1119Dic3—41no—
1120Dic3—41no—
1121Dic3—41no—
1122Dic3—41no—
1123Dic3—41no—
1124C23—32no—
1125C23—32no—
1126C23—61no—
1127C23—61no—
1128C23—61no—
1129C23—61no—
1130C23—61no—
1131C23—61no—
1132C23—61no—
1133C23—61no—
1134C23—61no—
1135C23—61no—
1136C23—61no—
1137C23—61no—
1138C23C24×D311yescharacteristic
1139Q8—82no—
1140D4—124no—
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—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—32no—
1185C2×C4—32no—
1186C2×C4—32no—
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—61no—
1226C2×C4—124no—
1227C2×C4—124no—
1228C2×C4—124no—
1229C2×C4—124no—
1230C2×C4—242no—
1231C2×C4—242no—
1232C2×C4D3×#4112yes—
1233C2×C4D3×#4112yes—
1234C2×C3#345511yescharacteristic
1235C2×C3#347511yescharacteristic
1236C2×C3#349111yescharacteristic
1237C2×C3#349511yescharacteristic
1238C2×C3#351511yescharacteristic
1239C2×C3#355711yescharacteristic
1240C2×C3#356611yescharacteristic
1241D3—42no—
1242D3—42no—
1243C22—62no—
1244C22—62no—
1245C22—62no—
1246C22—62no—
1247C22—62no—
1248C22—62no—
1249C22—121no—
1250C22—121no—
1251C22—121no—
1252C22—121no—
1253C22—121no—
1254C22—121no—
1255C22—121no—
1256C22—121no—
1257C22C2×D3×#4111yescharacteristic
1258C22C2×D3×#4111yescharacteristic
1259C22#596411yescharacteristic
1260C22#596611yescharacteristic
1261C22D3×2−1+411yescharacteristic
1262C22#596811yescharacteristic
1263C22#596811yescharacteristic
1264C4—22no—
1265C4—22no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—41no—
1278C4—41no—
1279C4—62no—
1280C4—62no—
1281C4—62no—
1282C4—121no—
1283C4—121no—
1284C4—121no—
1285C4—121no—
1286C4—121no—
1287C4—121no—
1288C4—121no—
1289C4—121no—
1290C4—121no—
1291C4—121no—
1292C4—121no—
1293C3#3841811yescharacteristic, complemented, Sylow
1294C2—122no—
1295C2—122no—
1296C2#8650711yescharacteristic
1297C2#8651111yescharacteristic
1298C2#8652311yescharacteristic
1299C2#8681611yescharacteristic
1300C2#8682911yescharacteristic
1301C2#8697911yescharacteristic
1302C2#8712211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2758C2
prime radicalC22×D12C23
hypercenter#2758D3
hypocenterC3#38418
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2758

Complements

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

NH ≅ G/Ntype
1. C3×#2758C2semidirect
2. #78352C2semidirect
4. #78251C2semidirect
5. #78225C2semidirect
6. #78224C2semidirect
7. #78206C2semidirect
8. #78197C2semidirect
9. #78188C2semidirect
10. #78187C2semidirect
11. #78185C2semidirect
13. #77200C2semidirect
14. #76551C2semidirect
15. #76528C2semidirect
18. #76285C2semidirect
19. #76272C2semidirect
21. #75421C2semidirect
22. #75304C2semidirect
23. #75213C2semidirect
24. #75049C2semidirect
25. #74971C2semidirect
28. #74305C2semidirect
29. #74287C2semidirect
30. #74268C2semidirect
31. #74258C2semidirect
191. #2758D3semidirect
1293. C3#38418semidirect

Maximal subgroups

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

subgroupindex
C3×#27582
#783522
#783412
#782512
#782252
#782242
#782062
#781972
#781882
#781872
#781852
#772682
#772002
#765512
#765282
#765062
#764882
#762852
#762722
#754222
#754212
#753042
#752132
#750492
#749712
#749562
#749372
#743052
#742872
#742682
#742582
#384183