Finite Group Databasebeta

← #11233501

Subgroups — #11233501

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×#2519C211yesmaximal, characteristic
2#83085C211yesmaximal, characteristic
3#83083C211yesmaximal, characteristic
4#83050C211yesmaximal, characteristic, complemented
5#83034C211yesmaximal, characteristic, complemented
6#78033C211yesmaximal, characteristic
7#78018C211yesmaximal, characteristic
8#77806C211yesmaximal, characteristic, complemented
9#77787C211yesmaximal, characteristic, complemented
10#77774C211yesmaximal, characteristic, complemented
11#77769C211yesmaximal, characteristic, complemented
12#77384C211yesmaximal, characteristic
13#77305C211yesmaximal, characteristic
14#76142C211yesmaximal, characteristic, complemented
15#76077C211yesmaximal, characteristic, complemented
16#75757C211yesmaximal, characteristic
17#75737C211yesmaximal, characteristic
18#75736C211yesmaximal, characteristic
19#75564C211yesmaximal, characteristic
20#75498C211yesmaximal, characteristic
21#75497C211yesmaximal, characteristic
22#75460C211yesmaximal, characteristic
23#75456C211yesmaximal, characteristic
24#75207C211yesmaximal, characteristic, complemented
25#74963C211yesmaximal, characteristic, complemented
26#74199C211yesmaximal, characteristic, complemented
27#74158C211yesmaximal, characteristic, complemented
28#73733C211yesmaximal, characteristic, complemented
29#73700C211yesmaximal, characteristic, complemented
30#73642C211yesmaximal, characteristic, complemented
31#73637C211yesmaximal, characteristic, complemented
32#45346—31nomaximal, Sylow
33C2×C3×#126C2211yescharacteristic
34C2×C3×#125C2211yescharacteristic
35C2×#889C2211yescharacteristic
36C2×#889C2211yescharacteristic
37C2×#889C2211yescharacteristic
38C2×#887C2211yescharacteristic
39C2×#879C2211yescharacteristic
40C2×#878C2211yescharacteristic
41C2×#877C2211yescharacteristic
42C2×C4×Dic6C2211yescharacteristic
43C2×C4×Dic6C2211yescharacteristic
44C2×C4×Dic6C2211yescharacteristic
45C3×#399C2211yescharacteristic
46C3×#398C2211yescharacteristic
47C3×#398C2211yescharacteristic
48C3×#396C2211yescharacteristic
49C3×#389C2211yescharacteristic
50C3×#388C2211yescharacteristic
51C3×#388C2211yescharacteristic
52C3×#388C2211yescharacteristic
53C3×#388C2211yescharacteristic
54C3×#387C2211yescharacteristic
55C3×#382C2211yescharacteristic
56C3×C4×C4⋊C4C2211yescharacteristic
57C3×C4×C4⋊C4C2211yescharacteristic
58#4986C2211yescharacteristic
59#4986C2211yescharacteristic
60#4985C2211yescharacteristic
61#4985C2211yescharacteristic
62#4985C2211yescharacteristic
63#4985C2211yescharacteristic
64#4985C2211yescharacteristic
65#4983C2211yescharacteristic
66#4983C2211yescharacteristic
67#4983C2211yescharacteristic
68#4983C2211yescharacteristic
69#4983C2211yescharacteristic
70#4982C2211yescharacteristic
71#4982C2211yescharacteristic
72#4982C2211yescharacteristic
73#4982C2211yescharacteristic
74#4980C2211yescharacteristic
75#4980C2211yescharacteristic
76#4980C2211yescharacteristic
77#4980C2211yescharacteristic
78#4978C2211yescharacteristic
79#4978C2211yescharacteristic
80#4978C2211yescharacteristic
81#4978C2211yescharacteristic
82#4978C2211yescharacteristic
83#4977C2211yescharacteristic
84#4977C2211yescharacteristic
85#4977C2211yescharacteristic
86#4976C2211yescharacteristic
87#4976C2211yescharacteristic
88#4976C2211yescharacteristic
89#4976C2211yescharacteristic
90#4976C2211yescharacteristic
91#4976C2211yescharacteristic
92#4976C2211yescharacteristic
93#4976C2211yescharacteristic
94#4976C2211yescharacteristic
95#4975C2211yescharacteristic
96#4975C2211yescharacteristic
97#4975C2211yescharacteristic
98#4975C2211yescharacteristic
99Dic3×C4⋊C4C2211yescharacteristic
100Dic3×C4⋊C4C2211yescharacteristic
101Dic3×C4⋊C4C2211yescharacteristic
102Dic3×C4⋊C4C2211yescharacteristic
103#4973C2211yescharacteristic
104#4972C2211yescharacteristic
105#4972C2211yescharacteristic
106#4953C2211yescharacteristic
107#4952C2211yescharacteristic
108#4952C2211yescharacteristic
109#4952C2211yescharacteristic
110#4951C2211yescharacteristic
111#4951C2211yescharacteristic
112#4951C2211yescharacteristic
113#4949C2211yescharacteristic
114#4949C2211yescharacteristic
115#4948C2211yescharacteristic
116#4948C2211yescharacteristic
117#4948C2211yescharacteristic
118#4947C2211yescharacteristic
119#4945C2211yescharacteristic
120#4945C2211yescharacteristic
121#4945C2211yescharacteristic
122#4944C2211yescharacteristic
123#4944C2211yescharacteristic
124#4944C2211yescharacteristic
125#4944C2211yescharacteristic
126#4942C2211yescharacteristic
127#4942C2211yescharacteristic
128#4942C2211yescharacteristic
129Dic3×C22⋊C4C2211yescharacteristic
130Dic3×C22⋊C4C2211yescharacteristic
131#4936C2211yescharacteristic
132#4936C2211yescharacteristic
133C4×C4⋊Dic3C2211yescharacteristic
134#4933C2211yescharacteristic
135#4933C2211yescharacteristic
136#4933C2211yescharacteristic
137#4933C2211yescharacteristic
138#4933C2211yescharacteristic
139#4933C2211yescharacteristic
140#4933C2211yescharacteristic
141#4933C2211yescharacteristic
142C4×Dic3⋊C4C2211yescharacteristic
143C4×Dic3⋊C4C2211yescharacteristic
144C4×Dic3⋊C4C2211yescharacteristic
145#4929C2211yescharacteristic
146#4928C2211yescharacteristic
147#4928C2211yescharacteristic
148#4661C2211yescharacteristic
149#4661C2211yescharacteristic
150#4660C2211yescharacteristic
151#4660C2211yescharacteristic
152#4659C2211yescharacteristic
153#4658C2211yescharacteristic
154#4657C2211yescharacteristic
155#4657C2211yescharacteristic
156#4657C2211yescharacteristic
157#4656C2211yescharacteristic
158#4655C2211yescharacteristic
159#4655C2211yescharacteristic
160#4655C2211yescharacteristic
161#4655C2211yescharacteristic
162#4654C2211yescharacteristic
163#4654C2211yescharacteristic
164#4653C2211yescharacteristic
165#4653C2211yescharacteristic
166#4653C2211yescharacteristic
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#4649C2211yescharacteristic
180#4647C2211yescharacteristic
181#4647C2211yescharacteristic
182#4647C2211yescharacteristic
183#4646C2211yescharacteristic
184#4646C2211yescharacteristic
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#2520—31no—
202#2519—31no—
203#2519—31no—
204#2519—31no—
205#2519D311yescharacteristic
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—
219C23×Dic3C2311yescharacteristic
220C22×Dic6C2311yescharacteristic
221C22×Dic6C2311yescharacteristic
222C3×#126—42no—
223C3×#125—42no—
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×C4⋊C4C2311yescharacteristic
234C2×C3×C4⋊C4C2311yescharacteristic
235C2×C3×C4⋊C4C2311yescharacteristic
236C2×C3×C4⋊C4C2311yescharacteristic
237C2×C3×C22⋊C4C2311yescharacteristic
238C2×C3×C22⋊C4C2311yescharacteristic
239C2×C3×C22⋊C4C2311yescharacteristic
240C2×C3×C22⋊C4C2311yescharacteristic
241C2×C3×C22⋊C4C2311yescharacteristic
242C2×C3×C22⋊C4C2311yescharacteristic
243C2×C3×C22⋊C4C2311yescharacteristic
244C2×C3×C42C2311yescharacteristic
245C2×C3×C42C2311yescharacteristic
246C2×C3×C42C2311yescharacteristic
247C2×C3×C42C2311yescharacteristic
248C2×C3×C42C2311yescharacteristic
249C2×#217C2311yescharacteristic
250C2×#217C2311yescharacteristic
251C2×#217C2311yescharacteristic
252C2×#217C2311yescharacteristic
253C2×#217C2311yescharacteristic
254C2×#217C2311yescharacteristic
255C2×#217C2311yescharacteristic
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×Dic3⋊C4C2311yescharacteristic
268C2×Dic3⋊C4C2311yescharacteristic
269C2×Dic3⋊C4C2311yescharacteristic
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×Dic3⋊C4C2311yescharacteristic
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
316#889—42no—
317#889—42no—
318#889—42no—
319#887—24no—
320#879—42no—
321#878—24no—
322#877—24no—
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×#126C2×D311yescharacteristic
388C2×#125—31no—
389C2×#125—31no—
390C2×#125—31no—
391C2×#125C2×D311yescharacteristic
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#400—31no—
409#399—31no—
410#399—31no—
411#399C2×D311yescharacteristic
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#396C2×D311yescharacteristic
436#395—31no—
437#393—31no—
438#391—31no—
439#391—31no—
440#391—31no—
441#391—31no—
442#391—31no—
443#391—31no—
444#391—31no—
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#389C2×D311yescharacteristic
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#388C2×D311yescharacteristic
473#388C2×D311yescharacteristic
474#388C2×D311yescharacteristic
475#388C2×D311yescharacteristic
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#387—31no—
501#387—31no—
502#387—31no—
503#387—31no—
504#387—31no—
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—
541C24×C3C2411yescharacteristic
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×C3×C4C2411yescharacteristic
556C22×Dic3—22no—
557C22×Dic3—22no—
558C22×Dic3—22no—
559C22×Dic3C2411yescharacteristic
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×Dic6—22no—
576C2×Dic6—22no—
577C2×Dic6—22no—
578C2×Dic6—22no—
579C2×Dic6—41no—
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—41no—
589C3×C4⋊C4—41no—
590C3×C4⋊C4—41no—
591C3×C4⋊C4—41no—
592C3×C4⋊C4—41no—
593C3×C4⋊C4—41no—
594C3×C22⋊C4—22no—
595C3×C22⋊C4—22no—
596C3×C22⋊C4—22no—
597C3×C22⋊C4—22no—
598C3×C22⋊C4—41no—
599C3×C22⋊C4—41no—
600C3×C22⋊C4—41no—
601C3×C42—22no—
602C3×C42—22no—
603C3×C42—22no—
604C3×C42—41no—
605C3×C42—41no—
606#217—22no—
607#217—22no—
608#217—22no—
609#217—41no—
610#217—41no—
611#217—41no—
612#217—41no—
613C4⋊Dic3—22no—
614C4⋊Dic3—22no—
615C4⋊Dic3—22no—
616C4⋊Dic3—22no—
617C4⋊Dic3—22no—
618C4⋊Dic3—22no—
619C4⋊Dic3—41no—
620C4⋊Dic3—41no—
621C4⋊Dic3—41no—
622C4⋊Dic3—41no—
623C4⋊Dic3—41no—
624Dic3⋊C4—22no—
625Dic3⋊C4—22no—
626Dic3⋊C4—22no—
627Dic3⋊C4—22no—
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—22no—
645Dic3⋊C4—22no—
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×Q8—31no—
675C23×C4—31no—
676#126—42no—
677#126—122no—
678#125—42no—
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⋊C4C22×D311yescharacteristic
732C2×C4⋊C4C22×D311yescharacteristic
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⋊C4C22×D311yescharacteristic
752C2×C22⋊C4C22×D311yescharacteristic
753C2×C22⋊C4C22×D311yescharacteristic
754C2×C22⋊C4C22×D311yescharacteristic
755C2×C22⋊C4C22×D311yescharacteristic
756C2×C22⋊C4C22×D311yescharacteristic
757C2×C22⋊C4C22×D311yescharacteristic
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#95—31no—
823#95—31no—
824#95—31no—
825#95—31no—
826#95—31no—
827#95—31no—
828#95—31no—
829#95—31no—
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×C3—21no—
841C23×C3—21no—
842C23×C3—21no—
843C23×C3—21no—
844C23×C3—21no—
845C23×C3—21no—
846C23×C3—21no—
847C23×C3C2511yescharacteristic
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×C4C2×#4112yes—
887C2×C3×C4C2×#4112yes—
888C2×C3×C4H(5,𝔽2)12yes—
889C2×C3×C42−1+412yes—
890C2×Dic3—21no—
891C2×Dic3—21no—
892C2×Dic3—21no—
893C2×Dic3—21no—
894C2×Dic3—21no—
895C2×Dic3—21no—
896C2×Dic3—21no—
897C2×Dic3—21no—
898C2×Dic3—21no—
899C2×Dic3—21no—
900C2×Dic3—21no—
901C2×Dic3—21no—
902C2×Dic3—21no—
903C2×Dic3—21no—
904C2×Dic3—21no—
905C2×Dic3—21no—
906C2×Dic3—21no—
907C2×Dic3—21no—
908C2×Dic3—21no—
909C2×Dic3—21no—
910C2×Dic3—21no—
911C2×Dic3—21no—
912C2×Dic3—21no—
913C2×Dic3—21no—
914C2×Dic3—21no—
915C2×Dic3—21no—
916C2×Dic3—21no—
917C2×Dic3—21no—
918C2×Dic3—21no—
919C2×Dic3—21no—
920C2×Dic3—21no—
921C2×Dic3—21no—
922C2×Dic3—21no—
923C2×Dic3—21no—
924C2×Dic3—21no—
925C2×Dic3—21no—
926C2×Dic3—21no—
927C2×Dic3—21no—
928C2×Dic3—21no—
929C2×Dic3—21no—
930C2×Dic3—21no—
931C2×Dic3—21no—
932C2×Dic3—44no—
933C2×Dic3C2×#4112yes—
934C2×Dic3C2×#4112yes—
935C2×Dic3C2×#4112yes—
936C2×Dic3C2×#4112yes—
937C2×Dic32−1+412yes—
938C2×Dic32−1+412yes—
939Dic6—28no—
940Dic6—44no—
941C24C23×D311yescharacteristic
942C2×Q8—34no—
943C2×Q8—62no—
944C2×Q8—62no—
945C2×Q8—62no—
946C2×Q8—62no—
947C2×Q8—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—31no—
963C22×C4—31no—
964C22×C4—62no—
965C22×C4—62no—
966C22×C4—62no—
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—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—41no—
992C4⋊C4—41no—
993C4⋊C4—41no—
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—62no—
1020C4⋊C4—62no—
1021C4⋊C4—62no—
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—22no—
1038C22⋊C4—22no—
1039C22⋊C4—22no—
1040C22⋊C4—22no—
1041C22⋊C4—41no—
1042C22⋊C4—41no—
1043C22⋊C4—41no—
1044C22⋊C4—62no—
1045C22⋊C4—62no—
1046C22⋊C4—62no—
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×C3—41no—
1074C22×C3—41no—
1075C22×C3—41no—
1076C22×C3—41no—
1077C22×C3—41no—
1078C22×C3—41no—
1079C22×C3—41no—
1080C22×C3C22×#4111yescharacteristic
1081C22×C3C22×#4111yescharacteristic
1082C22×C3C2×H(5,𝔽2)11yescharacteristic
1083C22×C3C2×2−1+411yescharacteristic
1084C22×C3C2×2−1+411yescharacteristic
1085C22×C3C2×2−1+411yescharacteristic
1086C22×C3#58511yescharacteristic
1087C3×C4—22no—
1088C3×C4—22no—
1089C3×C4—22no—
1090C3×C4—22no—
1091C3×C4—41no—
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—
1101Dic3—22no—
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—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23C24×D311yescharacteristic
1125Q8—68no—
1126Q8—124no—
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—32no—
1166C2×C4—32no—
1167C2×C4—32no—
1168C2×C4—32no—
1169C2×C4—32no—
1170C2×C4—32no—
1171C2×C4—61no—
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—61no—
1213C2×C4—124no—
1214C2×C4#100412yes—
1215C2×C4D3×#4112yes—
1216C2×C4D3×#4112yes—
1217C2×C4#101012yes—
1218C2×C3—81no—
1219C2×C3C2×#55211yescharacteristic
1220C2×C3#349511yescharacteristic
1221C2×C3#351111yescharacteristic
1222C2×C3#351611yescharacteristic
1223C2×C3#352211yescharacteristic
1224C2×C3#355411yescharacteristic
1225C2×C3#355611yescharacteristic
1226C22—41no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22C2×#100411yescharacteristic
1234C22C2×D3×#4111yescharacteristic
1235C22C2×D3×#4111yescharacteristic
1236C22C2×#101011yescharacteristic
1237C22#596411yescharacteristic
1238C22D3×2−1+411yescharacteristic
1239C22D3×2−1+411yescharacteristic
1240C4—22no—
1241C4—22no—
1242C4—22no—
1243C4—22no—
1244C4—34no—
1245C4—41no—
1246C4—41no—
1247C4—41no—
1248C4—41no—
1249C4—41no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—62no—
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—81no—
1272C2#8612411yescharacteristic
1273C2#8622611yescharacteristic
1274C2#8650211yescharacteristic
1275C2#8668811yescharacteristic
1276C2#8672911yescharacteristic
1277C2#8682911yescharacteristic
1278C2D3×#55211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2519C2
prime radicalC24×C3C24
hypercenter#2519D3
hypocenterC3#45346
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2519

Complements

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

NH ≅ G/Ntype
4. #83050C2semidirect
5. #83034C2semidirect
8. #77806C2semidirect
9. #77787C2semidirect
10. #77774C2semidirect
11. #77769C2semidirect
14. #76142C2semidirect
15. #76077C2semidirect
24. #75207C2semidirect
25. #74963C2semidirect
26. #74199C2semidirect
27. #74158C2semidirect
28. #73733C2semidirect
29. #73700C2semidirect
30. #73642C2semidirect
31. #73637C2semidirect
1270. C3#45346semidirect

Maximal subgroups

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

subgroupindex
C3×#25192
#830852
#830832
#830502
#830342
#780332
#780182
#778062
#777872
#777742
#777692
#773842
#773052
#761422
#760772
#757572
#757372
#757362
#755642
#754982
#754972
#754602
#754562
#752072
#749632
#741992
#741582
#737332
#737002
#736422
#736372
#453463