Finite Group Databasebeta

← #10965987

Subgroups — #10965987

Order 768.

1782 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2596C211yesmaximal, characteristic, complemented
2#78176C211yesmaximal, characteristic, complemented
3#78142C211yesmaximal, characteristic, complemented
4#78133C211yesmaximal, characteristic, complemented
5#78130C211yesmaximal, characteristic, complemented
6#78027C211yesmaximal, characteristic
7#78018C211yesmaximal, characteristic, complemented
8#77507C211yesmaximal, characteristic, complemented
9#77458C211yesmaximal, characteristic
10#76017C211yesmaximal, characteristic, complemented
11#75963C211yesmaximal, characteristic, complemented
12#75885C211yesmaximal, characteristic
13#75854C211yesmaximal, characteristic
14#75649C211yesmaximal, characteristic, complemented
15#75644C211yesmaximal, characteristic
16#75564C211yesmaximal, characteristic, complemented
17#75455C211yesmaximal, characteristic, complemented
18#75455C211yesmaximal, characteristic, complemented
19#75453C211yesmaximal, characteristic
20#75451C211yesmaximal, characteristic, complemented
21#75450C211yesmaximal, characteristic
22#75344C211yesmaximal, characteristic, complemented
23#75130C211yesmaximal, characteristic, complemented
24#75125C211yesmaximal, characteristic, complemented
25#74943C211yesmaximal, characteristic, complemented
26#74943C211yesmaximal, characteristic, complemented
27#74939C211yesmaximal, characteristic, complemented
28#73809C211yesmaximal, characteristic, complemented
29#73733C211yesmaximal, characteristic, complemented
30C4×#887C211yesmaximal, characteristic, complemented
31C4×#892C211yesmaximal, characteristic, complemented
32#34866—31nomaximal, Sylow
33C2×#892C2211yescharacteristic
34C2×#892C2211yescharacteristic
35C2×#892C2211yescharacteristic
36C2×#892C2211yescharacteristic
37C2×#889C2211yescharacteristic
38C2×#889C2211yescharacteristic
39C2×#887C2211yescharacteristic
40C2×#887C2211yescharacteristic
41C2×#883C2211yescharacteristic
42C2×#67⋊C4C2211yescharacteristic
43C2×#879C2211yescharacteristic
44C2×#879C2211yescharacteristic
45C2×#877C2211yescharacteristic
46C2×C42×D3C2211yescharacteristic
47C2×C4×Dic6C2211yescharacteristic
48C3×#400C2211yescharacteristic
49C3×#400C2211yescharacteristic
50C3×#399C2211yescharacteristic
51C3×#397C2211yescharacteristic
52C3×#389C2211yescharacteristic
53C3×#388C2211yescharacteristic
54C3×#388C2211yescharacteristic
55C3×#388C2211yescharacteristic
56C3×#388C2211yescharacteristic
57C3×#388C2211yescharacteristic
58C3×#387C2211yescharacteristic
59C3×#387C2211yescharacteristic
60C3×#387C2211yescharacteristic
61C3×C4×C4⋊C4C2211yescharacteristic
62C3×C4×C4⋊C4C2211yescharacteristic
63#4993C2211yescharacteristic
64#4990C2211yescharacteristic
65#4989C2211yescharacteristic
66#4989C2211yescharacteristic
67#4989C2211yescharacteristic
68#4985C2211yescharacteristic
69#4984C2211yescharacteristic
70#4983C2211yescharacteristic
71#4983C2211yescharacteristic
72#4983C2211yescharacteristic
73#4983C2211yescharacteristic
74#4982C2211yescharacteristic
75#4980C2211yescharacteristic
76#4979C2211yescharacteristic
77#4978C2211yescharacteristic
78#4978C2211yescharacteristic
79#4978C2211yescharacteristic
80#4976C2211yescharacteristic
81#4976C2211yescharacteristic
82#4976C2211yescharacteristic
83Dic3×C4⋊C4C2211yescharacteristic
84Dic3×C4⋊C4C2211yescharacteristic
85Dic3×C4⋊C4C2211yescharacteristic
86Dic3×C4⋊C4C2211yescharacteristic
87Dic3×C4⋊C4C2211yescharacteristic
88Dic3×C4⋊C4C2211yescharacteristic
89Dic3×C4⋊C4C2211yescharacteristic
90#4972C2211yescharacteristic
91#4959C2211yescharacteristic
92#4959C2211yescharacteristic
93#4957C2211yescharacteristic
94#4957C2211yescharacteristic
95#4956C2211yescharacteristic
96#4951C2211yescharacteristic
97#4951C2211yescharacteristic
98#4949C2211yescharacteristic
99#4948C2211yescharacteristic
100#4948C2211yescharacteristic
101#4947C2211yescharacteristic
102#4945C2211yescharacteristic
103#4945C2211yescharacteristic
104#4945C2211yescharacteristic
105#4944C2211yescharacteristic
106#4944C2211yescharacteristic
107#4944C2211yescharacteristic
108#4944C2211yescharacteristic
109Dic3×C22⋊C4C2211yescharacteristic
110Dic3×C22⋊C4C2211yescharacteristic
111Dic3×C22⋊C4C2211yescharacteristic
112Dic3×C22⋊C4C2211yescharacteristic
113Dic3×C22⋊C4C2211yescharacteristic
114#4940C2211yescharacteristic
115#4940C2211yescharacteristic
116C4×(C2×D3)⋊C4C2211yescharacteristic
117C4×(C2×D3)⋊C4C2211yescharacteristic
118C4×C4⋊Dic3C2211yescharacteristic
119#4933C2211yescharacteristic
120#4933C2211yescharacteristic
121#4933C2211yescharacteristic
122#4933C2211yescharacteristic
123#4933C2211yescharacteristic
124#4933C2211yescharacteristic
125C4×Dic3⋊C4C2211yescharacteristic
126C4×Dic3⋊C4C2211yescharacteristic
127C42×Dic3C2211yescharacteristic
128C42×Dic3C2211yescharacteristic
129C42×Dic3C2211yescharacteristic
130C42×Dic3C2211yescharacteristic
131#4928C2211yescharacteristic
132#4676C2211yescharacteristic
133#4676C2211yescharacteristic
134#4675C2211yescharacteristic
135#4675C2211yescharacteristic
136#4673C2211yescharacteristic
137#4670C2211yescharacteristic
138#4669C2211yescharacteristic
139#4669C2211yescharacteristic
140#4668C2211yescharacteristic
141#4668C2211yescharacteristic
142#4666C2211yescharacteristic
143#4666C2211yescharacteristic
144#4666C2211yescharacteristic
145#4664C2211yescharacteristic
146#4660C2211yescharacteristic
147#4659C2211yescharacteristic
148#4658C2211yescharacteristic
149#4658C2211yescharacteristic
150#4657C2211yescharacteristic
151#4657C2211yescharacteristic
152#4657C2211yescharacteristic
153#4657C2211yescharacteristic
154#4656C2211yescharacteristic
155#4655C2211yescharacteristic
156#4655C2211yescharacteristic
157#4655C2211yescharacteristic
158#4654C2211yescharacteristic
159#4654C2211yescharacteristic
160#4654C2211yescharacteristic
161#4654C2211yescharacteristic
162#4654C2211yescharacteristic
163#4653C2211yescharacteristic
164#4653C2211yescharacteristic
165#4652C2211yescharacteristic
166#4651C2211yescharacteristic
167#4651C2211yescharacteristic
168#4650C2211yescharacteristic
169#4650C2211yescharacteristic
170#4649C2211yescharacteristic
171#4649C2211yescharacteristic
172#4649C2211yescharacteristic
173#4649C2211yescharacteristic
174#4649C2211yescharacteristic
175#4649C2211yescharacteristic
176#4649C2211yescharacteristic
177#4649C2211yescharacteristic
178#4649C2211yescharacteristic
179#4649C2211yescharacteristic
180#4649C2211yescharacteristic
181#4649C2211yescharacteristic
182#4648C2211yescharacteristic
183#4648C2211yescharacteristic
184#4648C2211yescharacteristic
185#4647C2211yescharacteristic
186#4647C2211yescharacteristic
187#4647C2211yescharacteristic
188#2606—31no—
189#2604—31no—
190#2601—31no—
191#2599—31no—
192#2596D311yescharacteristic, complemented
193#2590—31no—
194#2575—31no—
195#2558—31no—
196#2533—31no—
197#2529—31no—
198#2519—31no—
199#2515—31no—
200#2479—31no—
201#2475—31no—
202#2462—31no—
203#2458—31no—
204#2402—31no—
205#2396—31no—
206#2396—31no—
207#2395—31no—
208C4×#125—31no—
209C4×#125—31no—
210C4×#126—31no—
211C4×#126—31no—
212C4×#123—31no—
213#2298—31no—
214#2298—31no—
215#2296—31no—
216#2293—31no—
217C42×Q8—31no—
218C4×#117—31no—
219C22×#67C2311yescharacteristic
220C23×Dic3C2311yescharacteristic
221C22×C4×D3C2311yescharacteristic
222C22×C4×D3C2311yescharacteristic
223C22×C4×D3C2311yescharacteristic
224C22×Dic6C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
234C2×C3×C22⋊C4C2311yescharacteristic
235C2×C3×C22⋊C4C2311yescharacteristic
236C2×C3×C22⋊C4C2311yescharacteristic
237C2×C3×C22⋊C4C2311yescharacteristic
238C2×C3×C22⋊C4C2311yescharacteristic
239C2×C3×C22⋊C4C2311yescharacteristic
240C2×C3×C22⋊C4C2311yescharacteristic
241C2×C3×C42C2311yescharacteristic
242C2×C3×C42C2311yescharacteristic
243C2×C3×C42C2311yescharacteristic
244C2×C3×C42C2311yescharacteristic
245C2×C3×C42C2311yescharacteristic
246C2×#217C2311yescharacteristic
247C2×#217C2311yescharacteristic
248C2×#217C2311yescharacteristic
249C2×#217C2311yescharacteristic
250C2×#217C2311yescharacteristic
251C2×#217C2311yescharacteristic
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×(C2×D3)⋊C4C2311yescharacteristic
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×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×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
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
316C2×C4×Dic3C2311yescharacteristic
317C2×C4×Dic3C2311yescharacteristic
318C2×C4×Dic3C2311yescharacteristic
319C2×C4×Dic3C2311yescharacteristic
320C2×C4×Dic3C2311yescharacteristic
321C2×C4×Dic3C2311yescharacteristic
322#892—24no—
323#892—24no—
324#892—24no—
325#892—24no—
326#889—24no—
327#889—24no—
328#887—24no—
329#887—24no—
330#883—24no—
331#67⋊C4—24no—
332#879—24no—
333#879—24no—
334#877—24no—
335C42×D3—24no—
336C4×Dic6—24no—
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
386C3⋊#95C2311yescharacteristic
387C3⋊#95C2311yescharacteristic
388C3⋊#95C2311yescharacteristic
389C2×#126—31no—
390C2×#126—31no—
391C2×#125—31no—
392C2×#125—31no—
393C2×#123—31no—
394C2×C4×Q8—31no—
395C2×C4×Q8—31no—
396C2×C4×Q8—31no—
397C2×C4×D4—31no—
398C2×#117—31no—
399C2×#117—31no—
400C2×#117—31no—
401C2×#117—31no—
402C2×#117—31no—
403C22×C42—31no—
404#400—31no—
405#400—31no—
406#400—31no—
407#400—31no—
408#400—31no—
409#400C2×D311yescharacteristic
410#400C2×D311yescharacteristic
411#399—31no—
412#399—31no—
413#399C2×D311yescharacteristic
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#397—31no—
424#397—31no—
425#397C2×D311yescharacteristic
426#396—31no—
427#396—31no—
428#396—31no—
429#396—31no—
430#395—31no—
431#395—31no—
432#394—31no—
433#394—31no—
434#393—31no—
435#393—31no—
436#390—31no—
437#390—31no—
438#389—31no—
439#389—31no—
440#389—31no—
441#389—31no—
442#389—31no—
443#389—31no—
444#389—31no—
445#389—31no—
446#389—31no—
447#389C2×D311yescharacteristic
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#388C2×D311yescharacteristic
464#388C2×D311yescharacteristic
465#388C2×D311yescharacteristic
466#388C2×D311yescharacteristic
467#388C2×D311yescharacteristic
468#387—31no—
469#387—31no—
470#387—31no—
471#387—31no—
472#387—31no—
473#387—31no—
474#387—31no—
475#387—31no—
476#387—31no—
477#387—31no—
478#387—31no—
479#387—31no—
480#387—31no—
481#387—31no—
482#387—31no—
483#387—31no—
484#387—31no—
485#387—31no—
486#387—31no—
487#387—31no—
488#387—31no—
489#387C2×D311yescharacteristic
490#387C2×D311yescharacteristic
491#387C2×D311yescharacteristic
492#386—31no—
493#385—31no—
494#385—31no—
495#385—31no—
496#385—31no—
497#385—31no—
498#383—31no—
499#383—31no—
500#382—31no—
501#382—31no—
502#381—31no—
503C4×C4⋊C4—31no—
504C4×C4⋊C4—31no—
505C4×C4⋊C4—31no—
506C4×C4⋊C4—31no—
507C4×C4⋊C4—31no—
508C4×C4⋊C4—31no—
509C4×C4⋊C4—31no—
510C4×C4⋊C4—31no—
511C4×C4⋊C4—31no—
512C4×C4⋊C4—31no—
513C4×C4⋊C4—31no—
514C4×C4⋊C4—31no—
515C4×C4⋊C4—31no—
516C4×C4⋊C4—31no—
517C4×C4⋊C4—31no—
518C4×C4⋊C4—31no—
519C4×C4⋊C4—31no—
520C4×C4⋊C4—31no—
521C4×C4⋊C4—31no—
522C4×C4⋊C4—31no—
523C4×C4⋊C4—31no—
524C4×C4⋊C4—31no—
525C4×C4⋊C4C2×D311yescharacteristic
526C4×C4⋊C4C2×D311yescharacteristic
527C4×C22⋊C4—31no—
528C4×C22⋊C4—31no—
529C4×C22⋊C4—31no—
530C4×C22⋊C4—31no—
531C4×C22⋊C4—31no—
532C4×C22⋊C4—31no—
533C4×C22⋊C4—31no—
534C4×C22⋊C4—31no—
535C4×C22⋊C4—31no—
536C4×C22⋊C4—31no—
537#376—31no—
538#376—31no—
539#376—31no—
540C43—31no—
541C43—31no—
542C43—31no—
543C43—31no—
544C24×C3C2411yescharacteristic
545C23×D3C2411yescharacteristic
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
560C2×#67—22no—
561C2×#67—22no—
562C2×#67—41no—
563C22×Dic3—22no—
564C22×Dic3—22no—
565C22×Dic3—22no—
566C22×Dic3C2411yescharacteristic
567C22×Dic3C2411yescharacteristic
568C22×Dic3C2411yescharacteristic
569C22×Dic3C2411yescharacteristic
570C22×Dic3C2411yescharacteristic
571C22×Dic3C2411yescharacteristic
572C22×Dic3C2411yescharacteristic
573C22×Dic3C2411yescharacteristic
574C22×Dic3C2411yescharacteristic
575C22×Dic3C2411yescharacteristic
576C22×Dic3C2411yescharacteristic
577C22×Dic3C2411yescharacteristic
578C22×Dic3C2411yescharacteristic
579C22×Dic3C2411yescharacteristic
580C22×Dic3C2411yescharacteristic
581C2×C4×D3—22no—
582C2×C4×D3—22no—
583C2×C4×D3—22no—
584C2×C4×D3—22no—
585C2×C4×D3—22no—
586C2×C4×D3—22no—
587C2×C4×D3—22no—
588C2×C4×D3—41no—
589C2×C4×D3#4114yes—
590C2×Dic6—22no—
591C2×Dic6—22no—
592C2×Dic6—22no—
593C3×C4⋊C4—22no—
594C3×C4⋊C4—22no—
595C3×C4⋊C4—22no—
596C3×C4⋊C4—22no—
597C3×C4⋊C4—22no—
598C3×C4⋊C4—22no—
599C3×C4⋊C4—22no—
600C3×C4⋊C4—22no—
601C3×C4⋊C4—41no—
602C3×C22⋊C4—22no—
603C3×C22⋊C4—22no—
604C3×C22⋊C4—22no—
605C3×C22⋊C4—22no—
606C3×C22⋊C4—22no—
607C3×C22⋊C4—41no—
608C3×C22⋊C4—41no—
609C3×C42—22no—
610C3×C42—22no—
611C3×C42—41no—
612C3×C42—41no—
613C3×C42—41no—
614#217—22no—
615#217—22no—
616#217—22no—
617#217—22no—
618#217—22no—
619#217—22no—
620(C2×D3)⋊C4—22no—
621(C2×D3)⋊C4—22no—
622(C2×D3)⋊C4—22no—
623(C2×D3)⋊C4—22no—
624(C2×D3)⋊C4—22no—
625(C2×D3)⋊C4—22no—
626(C2×D3)⋊C4—22no—
627(C2×D3)⋊C4—22no—
628(C2×D3)⋊C4—22no—
629(C2×D3)⋊C4—22no—
630(C2×D3)⋊C4—41no—
631C4⋊Dic3—22no—
632C4⋊Dic3—22no—
633C4⋊Dic3—22no—
634C4⋊Dic3—22no—
635C4⋊Dic3—22no—
636C4⋊Dic3—22no—
637C4⋊Dic3—22no—
638C4⋊Dic3#4114yes—
639Dic3⋊C4—22no—
640Dic3⋊C4—22no—
641Dic3⋊C4—22no—
642Dic3⋊C4—22no—
643Dic3⋊C4—22no—
644Dic3⋊C4—22no—
645Dic3⋊C4—22no—
646Dic3⋊C4—22no—
647Dic3⋊C4—22no—
648Dic3⋊C4—22no—
649Dic3⋊C4—22no—
650Dic3⋊C4—22no—
651Dic3⋊C4—22no—
652Dic3⋊C4—22no—
653Dic3⋊C4—22no—
654Dic3⋊C4—22no—
655Dic3⋊C4—22no—
656Dic3⋊C4—22no—
657Dic3⋊C4—22no—
658Dic3⋊C4—41no—
659Dic3⋊C4—41no—
660Dic3⋊C4—41no—
661Dic3⋊C4—41no—
662Dic3⋊C4—41no—
663Dic3⋊C4#4114yes—
664C4×Dic3—22no—
665C4×Dic3—22no—
666C4×Dic3—22no—
667C4×Dic3—22no—
668C4×Dic3—22no—
669C4×Dic3—22no—
670C4×Dic3—22no—
671C4×Dic3—22no—
672C4×Dic3—22no—
673C4×Dic3—22no—
674C4×Dic3—22no—
675C4×Dic3—22no—
676C4×Dic3—22no—
677C4×Dic3—22no—
678C4×Dic3—22no—
679C4×Dic3—22no—
680C4×Dic3—22no—
681C4×Dic3—22no—
682C4×Dic3—22no—
683C4×Dic3—22no—
684C4×Dic3—22no—
685C4×Dic3—22no—
686C4×Dic3—22no—
687C4×Dic3—41no—
688C4×Dic3#4114yes—
689C4×Dic3#4114yes—
690C22×Q8—31no—
691C22×D4—31no—
692C23×C4—31no—
693C23×C4—31no—
694C23×C4—31no—
695C23×C4—31no—
696#126—64no—
697#126—64no—
698#125—64no—
699#125—64no—
700#123—64no—
701C4×Q8—64no—
702C4×Q8—64no—
703C4×Q8—64no—
704C4×D4—64no—
705#117—64no—
706#117—64no—
707#117—64no—
708#117—64no—
709#117—64no—
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⋊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⋊C4—31no—
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×C22⋊C4—31no—
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⋊C4C22×D311yescharacteristic
770C2×C22⋊C4C22×D311yescharacteristic
771C2×C22⋊C4C22×D311yescharacteristic
772C2×C22⋊C4C22×D311yescharacteristic
773C2×C22⋊C4C22×D311yescharacteristic
774C2×C22⋊C4C22×D311yescharacteristic
775C2×C22⋊C4C22×D311yescharacteristic
776C2×C42—31no—
777C2×C42—31no—
778C2×C42—31no—
779C2×C42—31no—
780C2×C42—31no—
781C2×C42—31no—
782C2×C42—31no—
783C2×C42—31no—
784C2×C42—31no—
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—31no—
799C2×C42—31no—
800C2×C42—31no—
801C2×C42—31no—
802C2×C42—64no—
803C2×C42C22×D311yescharacteristic
804C2×C42C22×D311yescharacteristic
805C2×C42C22×D311yescharacteristic
806C2×C42C22×D311yescharacteristic
807C2×C42C22×D311yescharacteristic
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×D3C2×#4112yes—
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×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×C4C2×#4112yes—
913C2×C3×C4C2×#4112yes—
914C2×C3×C4C2×#4112yes—
915C2×C3×C4C2×#4112yes—
916C2×C3×C4C2×#4112yes—
917#67—44no—
918C2×Dic3—21no—
919C2×Dic3—21no—
920C2×Dic3—21no—
921C2×Dic3—21no—
922C2×Dic3—21no—
923C2×Dic3—21no—
924C2×Dic3—21no—
925C2×Dic3—21no—
926C2×Dic3—21no—
927C2×Dic3—21no—
928C2×Dic3—21no—
929C2×Dic3—21no—
930C2×Dic3—21no—
931C2×Dic3—21no—
932C2×Dic3—21no—
933C2×Dic3—21no—
934C2×Dic3—21no—
935C2×Dic3—21no—
936C2×Dic3—21no—
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—44no—
954C2×Dic3C2×#4112yes—
955C2×Dic3C2×#4112yes—
956C2×Dic3C2×#4112yes—
957C2×Dic3C2×#4112yes—
958C2×Dic3C2×#4112yes—
959C2×Dic3C2×#4112yes—
960C2×Dic3C2×#4112yes—
961C2×Dic3C2×#4112yes—
962C2×Dic3C2×#4112yes—
963C2×Dic32−1+412yes—
964C4×D3—28no—
965C4×D3—28no—
966C4×D3—44no—
967Dic6—28no—
968C24—31no—
969C24C23×D311yescharacteristic
970C2×Q8—62no—
971C2×Q8—62no—
972C2×Q8—62no—
973C2×D4—62no—
974C2×D4—62no—
975C2×D4—121no—
976C22×C4—31no—
977C22×C4—31no—
978C22×C4—31no—
979C22×C4—31no—
980C22×C4—31no—
981C22×C4—31no—
982C22×C4—31no—
983C22×C4—31no—
984C22×C4—34no—
985C22×C4—31no—
986C22×C4—31no—
987C22×C4—31no—
988C22×C4—31no—
989C22×C4—31no—
990C22×C4—31no—
991C22×C4—31no—
992C22×C4—62no—
993C22×C4—62no—
994C22×C4—62no—
995C22×C4—62no—
996C22×C4—62no—
997C22×C4—62no—
998C22×C4—62no—
999C22×C4—62no—
1000C22×C4—62no—
1001C22×C4—62no—
1002C22×C4—121no—
1003C22×C4C23×D311yescharacteristic
1004C22×C4C23×D311yescharacteristic
1005C22×C4C23×D311yescharacteristic
1006C22×C4C23×D311yescharacteristic
1007C22×C4C23×D311yescharacteristic
1008C22×C4C23×D311yescharacteristic
1009C22×C4C23×D311yescharacteristic
1010C22×C4C23×D311yescharacteristic
1011C22×C4C23×D311yescharacteristic
1012C22×C4C23×D311yescharacteristic
1013C22×C4C23×D311yescharacteristic
1014C22×C4C23×D311yescharacteristic
1015C22×C4C23×D311yescharacteristic
1016C22×C4C23×D311yescharacteristic
1017C4⋊C4—22no—
1018C4⋊C4—22no—
1019C4⋊C4—22no—
1020C4⋊C4—22no—
1021C4⋊C4—22no—
1022C4⋊C4—22no—
1023C4⋊C4—22no—
1024C4⋊C4—22no—
1025C4⋊C4—34no—
1026C4⋊C4—34no—
1027C4⋊C4—41no—
1028C4⋊C4—62no—
1029C4⋊C4—62no—
1030C4⋊C4—62no—
1031C4⋊C4—62no—
1032C4⋊C4—62no—
1033C4⋊C4—62no—
1034C4⋊C4—62no—
1035C4⋊C4—62no—
1036C4⋊C4—62no—
1037C4⋊C4—62no—
1038C4⋊C4—62no—
1039C4⋊C4—62no—
1040C4⋊C4—62no—
1041C4⋊C4—62no—
1042C4⋊C4—62no—
1043C4⋊C4—62no—
1044C4⋊C4—62no—
1045C4⋊C4—62no—
1046C4⋊C4—62no—
1047C4⋊C4—62no—
1048C4⋊C4—62no—
1049C4⋊C4—62no—
1050C4⋊C4—62no—
1051C4⋊C4—62no—
1052C4⋊C4—62no—
1053C4⋊C4—62no—
1054C4⋊C4—121no—
1055C4⋊C4—121no—
1056C4⋊C4—121no—
1057C4⋊C4—121no—
1058C4⋊C4—121no—
1059C22⋊C4—22no—
1060C22⋊C4—22no—
1061C22⋊C4—22no—
1062C22⋊C4—22no—
1063C22⋊C4—22no—
1064C22⋊C4—41no—
1065C22⋊C4—41no—
1066C22⋊C4—62no—
1067C22⋊C4—62no—
1068C22⋊C4—62no—
1069C22⋊C4—62no—
1070C22⋊C4—62no—
1071C22⋊C4—62no—
1072C22⋊C4—62no—
1073C22⋊C4—62no—
1074C22⋊C4—62no—
1075C22⋊C4—62no—
1076C22⋊C4—62no—
1077C22⋊C4—62no—
1078C22⋊C4—62no—
1079C22⋊C4—62no—
1080C22⋊C4—62no—
1081C22⋊C4—62no—
1082C22⋊C4—121no—
1083C42—22no—
1084C42—22no—
1085C42—34no—
1086C42—34no—
1087C42—41no—
1088C42—41no—
1089C42—41no—
1090C42—62no—
1091C42—62no—
1092C42—62no—
1093C42—62no—
1094C42—62no—
1095C42—62no—
1096C42—62no—
1097C42—62no—
1098C42—62no—
1099C42—62no—
1100C42—62no—
1101C42—62no—
1102C42—62no—
1103C42—62no—
1104C42—62no—
1105C42—62no—
1106C42—62no—
1107C42—62no—
1108C42—62no—
1109C42—62no—
1110C42—62no—
1111C42—62no—
1112C42—62no—
1113C42—121no—
1114C22×C3—41no—
1115C22×C3—41no—
1116C22×C3—41no—
1117C22×C3—41no—
1118C22×C3—41no—
1119C22×C3—41no—
1120C22×C3—41no—
1121C22×C3C22×#4111yescharacteristic
1122C22×C3C22×#4111yescharacteristic
1123C22×C3C22×#4111yescharacteristic
1124C22×C3C22×#4111yescharacteristic
1125C22×C3C22×#4111yescharacteristic
1126C22×C3C2×2−1+411yescharacteristic
1127C22×C3#58511yescharacteristic
1128C2×D3—22no—
1129C2×D3—22no—
1130C2×D3—22no—
1131C2×D3—41no—
1132C2×D3—41no—
1133C2×D3—41no—
1134C2×D3—41no—
1135C3×C4—22no—
1136C3×C4—22no—
1137C3×C4—22no—
1138C3×C4—22no—
1139C3×C4—22no—
1140C3×C4—41no—
1141C3×C4—41no—
1142C3×C4—41no—
1143C3×C4—41no—
1144C3×C4—41no—
1145C3×C4—41no—
1146C3×C4—41no—
1147C3×C4—41no—
1148C3×C4—41no—
1149Dic3—22no—
1150Dic3—22no—
1151Dic3—22no—
1152Dic3—22no—
1153Dic3—22no—
1154Dic3—22no—
1155Dic3—22no—
1156Dic3—41no—
1157Dic3—41no—
1158Dic3—41no—
1159Dic3—41no—
1160Dic3—41no—
1161Dic3—41no—
1162Dic3—41no—
1163Dic3#55214yes—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—32no—
1172C23—61no—
1173C23—61no—
1174C23—61no—
1175C23—61no—
1176C23—61no—
1177C23—61no—
1178C23C24×D311yescharacteristic
1179Q8—68no—
1180D4—124no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—32no—
1219C2×C4—32no—
1220C2×C4—32no—
1221C2×C4—32no—
1222C2×C4—32no—
1223C2×C4—32no—
1224C2×C4—32no—
1225C2×C4—32no—
1226C2×C4—32no—
1227C2×C4—32no—
1228C2×C4—68no—
1229C2×C4—68no—
1230C2×C4—61no—
1231C2×C4—61no—
1232C2×C4—61no—
1233C2×C4—61no—
1234C2×C4—61no—
1235C2×C4—61no—
1236C2×C4—61no—
1237C2×C4—61no—
1238C2×C4—61no—
1239C2×C4—61no—
1240C2×C4—61no—
1241C2×C4—61no—
1242C2×C4—61no—
1243C2×C4—61no—
1244C2×C4—61no—
1245C2×C4—61no—
1246C2×C4—61no—
1247C2×C4—61no—
1248C2×C4—61no—
1249C2×C4—61no—
1250C2×C4—61no—
1251C2×C4—61no—
1252C2×C4—61no—
1253C2×C4—61no—
1254C2×C4—61no—
1255C2×C4—61no—
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—124no—
1266C2×C4—124no—
1267C2×C4D3×#4112yes—
1268C2×C4D3×#4112yes—
1269C2×C4D3×#4112yes—
1270C2×C4D3×#4112yes—
1271C2×C4D3×#4112yes—
1272C2×C3—81no—
1273C2×C3#344411yescharacteristic
1274C2×C3#344411yescharacteristic
1275C2×C3#346111yescharacteristic
1276C2×C3C2×#55211yescharacteristic
1277C2×C3#347511yescharacteristic
1278C2×C3#348011yescharacteristic
1279C2×C3#348211yescharacteristic
1280D3—42no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—62no—
1289C22—62no—
1290C22—62no—
1291C22—121no—
1292C22—121no—
1293C22—121no—
1294C22—121no—
1295C22C2×D3×#4111yescharacteristic
1296C22C2×D3×#4111yescharacteristic
1297C22C2×D3×#4111yescharacteristic
1298C22C2×D3×#4111yescharacteristic
1299C22C2×D3×#4111yescharacteristic
1300C22#596611yescharacteristic
1301C22D3×2−1+411yescharacteristic
1302C4—22no—
1303C4—22no—
1304C4—22no—
1305C4—22no—
1306C4—22no—
1307C4—34no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—62no—
1318C4—62no—
1319C4—62no—
1320C4—62no—
1321C4—62no—
1322C4—62no—
1323C4—62no—
1324C4—121no—
1325C4—121no—
1326C4—121no—
1327C4—121no—
1328C4—121no—
1329C4—121no—
1330C4—121no—
1331C3#3486611yescharacteristic, complemented, Sylow
1332C2—81no—
1333C2—122no—
1334C2#8611911yescharacteristic
1335C2#8611911yescharacteristic
1336C2#8642911yescharacteristic
1337C2D3×#55211yescharacteristic
1338C2#8687411yescharacteristic
1339C2#8698111yescharacteristic
1340C2#8704911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2596C2
prime radicalC22×#67C23
hypercenter#2596D3
hypocenterC3#34866
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2596

Complements

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

NH ≅ G/Ntype
1. C3×#2596C2semidirect
2. #78176C2semidirect
3. #78142C2semidirect
4. #78133C2semidirect
5. #78130C2semidirect
7. #78018C2semidirect
8. #77507C2semidirect
10. #76017C2semidirect
11. #75963C2semidirect
14. #75649C2semidirect
16. #75564C2semidirect
17. #75455C2semidirect
18. #75455C2semidirect
20. #75451C2semidirect
22. #75344C2semidirect
23. #75130C2semidirect
24. #75125C2semidirect
25. #74943C2semidirect
26. #74943C2semidirect
27. #74939C2semidirect
28. #73809C2semidirect
29. #73733C2semidirect
30. C4×#887C2semidirect
31. C4×#892C2semidirect
192. #2596D3semidirect
1331. C3#34866semidirect

Maximal subgroups

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

subgroupindex
C3×#25962
#781762
#781422
#781332
#781302
#780272
#780182
#775072
#774582
#760172
#759632
#758852
#758542
#756492
#756442
#755642
#754552
#754532
#754512
#754502
#753442
#751302
#751252
#749432
#749392
#738092
#737332
C4×#8872
C4×#8922
#348663