Finite Group Databasebeta

← #11222912

Subgroups — #11222912

Order 768.

1690 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2527C211yesmaximal, characteristic, complemented
2#78425C211yesmaximal, characteristic, complemented
3#78424C211yesmaximal, characteristic, complemented
4#78342C211yesmaximal, characteristic, complemented
5#78308C211yesmaximal, characteristic, complemented
6#77636C211yesmaximal, characteristic, complemented
7#77568C211yesmaximal, characteristic
8#76878C211yesmaximal, characteristic
9#76788C211yesmaximal, characteristic, complemented
10#76637C211yesmaximal, characteristic, complemented
11#76548C211yesmaximal, characteristic, complemented
12#76527C211yesmaximal, characteristic, complemented
13#76491C211yesmaximal, characteristic, complemented
14#75838C211yesmaximal, characteristic
15#75592C211yesmaximal, characteristic
16#75533C211yesmaximal, characteristic, complemented
17#75460C211yesmaximal, characteristic, complemented
18#75328C211yesmaximal, characteristic, complemented
19#75274C211yesmaximal, characteristic, complemented
20#75076C211yesmaximal, characteristic, complemented
21#75040C211yesmaximal, characteristic, complemented
22#75012C211yesmaximal, characteristic, complemented
23#74947C211yesmaximal, characteristic, complemented
24#74500C211yesmaximal, characteristic
25#74472C211yesmaximal, characteristic, complemented
26#74094C211yesmaximal, characteristic
27#74067C211yesmaximal, characteristic, complemented
28#73468C211yesmaximal, characteristic, complemented
29#73464C211yesmaximal, characteristic
30#73422C211yesmaximal, characteristic, complemented
31#73397C211yesmaximal, characteristic, complemented
32#44862—31nomaximal, Sylow
33C2×#946C2211yescharacteristic
34C2×Q8×Dic3C2211yescharacteristic
35C2×#926C2211yescharacteristic
36C2×#924C2211yescharacteristic
37C2×#896C2211yescharacteristic
38C2×#896C2211yescharacteristic
39C2×#892C2211yescharacteristic
40C2×#892C2211yescharacteristic
41C2×#889C2211yescharacteristic
42C2×#886C2211yescharacteristic
43C2×#883C2211yescharacteristic
44C2×#67⋊C4C2211yescharacteristic
45C2×#878C2211yescharacteristic
46C2×#878C2211yescharacteristic
47C2×#877C2211yescharacteristic
48C2×C4×Dic6C2211yescharacteristic
49C2×C4×Dic6C2211yescharacteristic
50C2×C4×Dic6C2211yescharacteristic
51C3×#401C2211yescharacteristic
52C3×#400C2211yescharacteristic
53C3×#397C2211yescharacteristic
54C3×#393C2211yescharacteristic
55C3×#391C2211yescharacteristic
56C3×#391C2211yescharacteristic
57C3×#388C2211yescharacteristic
58C3×#388C2211yescharacteristic
59C3×#387C2211yescharacteristic
60C3×#387C2211yescharacteristic
61C3×#387C2211yescharacteristic
62C3×#385C2211yescharacteristic
63C3×#381C2211yescharacteristic
64C3×C4×C22⋊C4C2211yescharacteristic
65C3×#376C2211yescharacteristic
66#5230C2211yescharacteristic
67#5229C2211yescharacteristic
68#5213C2211yescharacteristic
69C2×C3⋊#95C2211yescharacteristic
70#4994C2211yescharacteristic
71#4984C2211yescharacteristic
72#4984C2211yescharacteristic
73#4983C2211yescharacteristic
74#4982C2211yescharacteristic
75#4982C2211yescharacteristic
76#4980C2211yescharacteristic
77#4979C2211yescharacteristic
78#4978C2211yescharacteristic
79#4978C2211yescharacteristic
80#4978C2211yescharacteristic
81#4976C2211yescharacteristic
82#4975C2211yescharacteristic
83#4972C2211yescharacteristic
84#4972C2211yescharacteristic
85#4961C2211yescharacteristic
86#4959C2211yescharacteristic
87#4956C2211yescharacteristic
88#4952C2211yescharacteristic
89#4951C2211yescharacteristic
90#4950C2211yescharacteristic
91#4950C2211yescharacteristic
92#4950C2211yescharacteristic
93#4948C2211yescharacteristic
94#4946C2211yescharacteristic
95#4945C2211yescharacteristic
96#4945C2211yescharacteristic
97#4944C2211yescharacteristic
98#4944C2211yescharacteristic
99#4944C2211yescharacteristic
100#4942C2211yescharacteristic
101#4942C2211yescharacteristic
102Dic3×C22⋊C4C2211yescharacteristic
103#4940C2211yescharacteristic
104#4940C2211yescharacteristic
105C4×(C2×D3)⋊C4C2211yescharacteristic
106C4×(C2×D3)⋊C4C2211yescharacteristic
107C4×C4⋊Dic3C2211yescharacteristic
108C4×C4⋊Dic3C2211yescharacteristic
109C4×C4⋊Dic3C2211yescharacteristic
110C4×C4⋊Dic3C2211yescharacteristic
111#4933C2211yescharacteristic
112#4933C2211yescharacteristic
113#4929C2211yescharacteristic
114#4928C2211yescharacteristic
115#4928C2211yescharacteristic
116#4675C2211yescharacteristic
117#4674C2211yescharacteristic
118#4673C2211yescharacteristic
119#4670C2211yescharacteristic
120#4670C2211yescharacteristic
121#4670C2211yescharacteristic
122#4669C2211yescharacteristic
123#4669C2211yescharacteristic
124#4669C2211yescharacteristic
125#4668C2211yescharacteristic
126#4668C2211yescharacteristic
127#4668C2211yescharacteristic
128#4668C2211yescharacteristic
129#4668C2211yescharacteristic
130#4667C2211yescharacteristic
131#4667C2211yescharacteristic
132#4664C2211yescharacteristic
133D3×#95C2211yescharacteristic
134C3⋊#401C2211yescharacteristic
135#4661C2211yescharacteristic
136#4661C2211yescharacteristic
137#4661C2211yescharacteristic
138#4661C2211yescharacteristic
139#4661C2211yescharacteristic
140#4661C2211yescharacteristic
141#4661C2211yescharacteristic
142#4660C2211yescharacteristic
143#4660C2211yescharacteristic
144#4660C2211yescharacteristic
145#4660C2211yescharacteristic
146#4659C2211yescharacteristic
147#4657C2211yescharacteristic
148#4657C2211yescharacteristic
149#4657C2211yescharacteristic
150#4657C2211yescharacteristic
151#4657C2211yescharacteristic
152#4657C2211yescharacteristic
153#4656C2211yescharacteristic
154#4656C2211yescharacteristic
155#4656C2211yescharacteristic
156#4656C2211yescharacteristic
157#4655C2211yescharacteristic
158#4655C2211yescharacteristic
159#4654C2211yescharacteristic
160#4654C2211yescharacteristic
161#4654C2211yescharacteristic
162#4653C2211yescharacteristic
163#4653C2211yescharacteristic
164#4653C2211yescharacteristic
165#4653C2211yescharacteristic
166#4653C2211yescharacteristic
167#4653C2211yescharacteristic
168#4652C2211yescharacteristic
169#4652C2211yescharacteristic
170#4652C2211yescharacteristic
171#4652C2211yescharacteristic
172#4650C2211yescharacteristic
173#4650C2211yescharacteristic
174#4649C2211yescharacteristic
175#4649C2211yescharacteristic
176#4649C2211yescharacteristic
177#4647C2211yescharacteristic
178#4647C2211yescharacteristic
179#4647C2211yescharacteristic
180#4647C2211yescharacteristic
181#4647C2211yescharacteristic
182#4646C2211yescharacteristic
183#4646C2211yescharacteristic
184#4646C2211yescharacteristic
185#4646C2211yescharacteristic
186#4646C2211yescharacteristic
187#4646C2211yescharacteristic
188#2802—31no—
189#2802—31no—
190#2789—31no—
191#2787—31no—
192#2787—31no—
193#2687—31no—
194#2687—31no—
195#2680—31no—
196#2609—31no—
197#2582—31no—
198#2565—31no—
199#2549—31no—
200#2549—31no—
201#2536—31no—
202#2527—31no—
203#2527D311yescharacteristic, complemented
204#2520—31no—
205#2520—31no—
206#2475—31no—
207#2475—31no—
208#2465—31no—
209#2465—31no—
210#2438—31no—
211#2438—31no—
212#2399—31no—
213#2362—31no—
214#2362—31no—
215#2359—31no—
216#2359—31no—
217#2323—31no—
218#2323—31no—
219C22×C3×Q8C2311yescharacteristic
220C23×C3×C4C2311yescharacteristic
221C22×#67C2311yescharacteristic
222C23×Dic3C2311yescharacteristic
223C23×Dic3C2311yescharacteristic
224C22×C4×D3C2311yescharacteristic
225C22×C4×D3C2311yescharacteristic
226C22×C4×D3C2311yescharacteristic
227C22×Dic6C2311yescharacteristic
228C22×Dic6C2311yescharacteristic
229C22×Dic6C2311yescharacteristic
230C2×C3×C4⋊C4C2311yescharacteristic
231C2×C3×C4⋊C4C2311yescharacteristic
232C2×C3×C4⋊C4C2311yescharacteristic
233C2×C3×C4⋊C4C2311yescharacteristic
234C2×C3×C4⋊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×#217C2311yescharacteristic
246C2×#217C2311yescharacteristic
247C2×#217C2311yescharacteristic
248C2×#217C2311yescharacteristic
249C2×#217C2311yescharacteristic
250#946—24no—
251Q8×Dic3—42no—
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
263#926—42no—
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×C4⋊Dic3C2311yescharacteristic
274C2×C4⋊Dic3C2311yescharacteristic
275C2×C4⋊Dic3C2311yescharacteristic
276C2×C4⋊Dic3C2311yescharacteristic
277C2×C4⋊Dic3C2311yescharacteristic
278C2×C4⋊Dic3C2311yescharacteristic
279C2×C4⋊Dic3C2311yescharacteristic
280C2×C4⋊Dic3C2311yescharacteristic
281#924—24no—
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×Dic3⋊C4C2311yescharacteristic
300C2×Dic3⋊C4C2311yescharacteristic
301C2×Dic3⋊C4C2311yescharacteristic
302C2×Dic3⋊C4C2311yescharacteristic
303C2×Dic3⋊C4C2311yescharacteristic
304C2×Dic3⋊C4C2311yescharacteristic
305C2×Dic3⋊C4C2311yescharacteristic
306C2×Dic3⋊C4C2311yescharacteristic
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
320#896—24no—
321#896—42no—
322#892—42no—
323#892—42no—
324#889—42no—
325#886—24no—
326#883—24no—
327#67⋊C4—42no—
328#878—24no—
329#878—42no—
330#877—42no—
331C4×Dic6—42no—
332C4×Dic6—42no—
333C4×Dic6—42no—
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
386C3⋊#95C2311yescharacteristic
387C3⋊#95C2311yescharacteristic
388C3⋊#95C2311yescharacteristic
389C3⋊#95C2311yescharacteristic
390C3⋊#95C2311yescharacteristic
391C3⋊#95C2311yescharacteristic
392C2×#125—31no—
393C2×#123—31no—
394C2×#123—31no—
395C2×C22⋊Q8—31no—
396C2×C22⋊Q8—31no—
397C2×C22⋊Q8—31no—
398C2×C22⋊Q8—31no—
399C2×C22⋊Q8—31no—
400C2×C22⋊Q8—31no—
401C2×C4×Q8—31no—
402C2×C4×Q8—31no—
403C2×C4×Q8—31no—
404C2×C4×Q8—31no—
405C2×C4×D4—31no—
406C2×#117—31no—
407C2×#117—31no—
408C2×#117—31no—
409C2×#117—31no—
410#401—31no—
411#401C2×D311yescharacteristic
412#400—31no—
413#400—31no—
414#400—31no—
415#400—31no—
416#400—31no—
417#400C2×D311yescharacteristic
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#398—31no—
427#398—31no—
428#398—31no—
429#398—31no—
430#398—31no—
431#398—31no—
432#398—31no—
433#398—31no—
434#397—31no—
435#397—31no—
436#397—31no—
437#397C2×D311yescharacteristic
438#396—31no—
439#396—31no—
440#395—31no—
441#395—31no—
442#395—31no—
443#395—31no—
444#395—31no—
445#395—31no—
446#394—31no—
447#394—31no—
448#393—31no—
449#393C2×D311yescharacteristic
450#391—31no—
451#391—31no—
452#391—31no—
453#391—31no—
454#391—31no—
455#391—31no—
456#391—31no—
457#391—31no—
458#391C2×D311yescharacteristic
459#391C2×D311yescharacteristic
460#389—31no—
461#389—31no—
462#389—31no—
463#389—31no—
464#389—31no—
465#389—31no—
466#389—31no—
467#389—31no—
468#389—31no—
469#389—31no—
470#389—31no—
471#389—31no—
472#388—31no—
473#388—31no—
474#388—31no—
475#388—31no—
476#388—31no—
477#388—31no—
478#388—31no—
479#388—31no—
480#388—31no—
481#388—31no—
482#388—31no—
483#388—31no—
484#388—31no—
485#388—31no—
486#388C2×D311yescharacteristic
487#388C2×D311yescharacteristic
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#387—31no—
506#387—31no—
507#387—31no—
508#387—31no—
509#387C2×D311yescharacteristic
510#387C2×D311yescharacteristic
511#387C2×D311yescharacteristic
512#386—31no—
513#386—31no—
514#385—31no—
515#385—31no—
516#385—31no—
517#385—31no—
518#385—31no—
519#385—31no—
520#385—31no—
521#385—31no—
522#385—31no—
523#385C2×D311yescharacteristic
524#384—31no—
525#382—31no—
526#382—31no—
527#381—31no—
528#381C2×D311yescharacteristic
529#380—31no—
530#380—31no—
531#380—31no—
532#380—31no—
533C4×C4⋊C4—31no—
534C4×C4⋊C4—31no—
535C4×C4⋊C4—31no—
536C4×C4⋊C4—31no—
537C4×C4⋊C4—31no—
538C4×C4⋊C4—31no—
539C4×C4⋊C4—31no—
540C4×C22⋊C4—31no—
541C4×C22⋊C4—31no—
542C4×C22⋊C4—31no—
543C4×C22⋊C4C2×D311yescharacteristic
544#376C2×D311yescharacteristic
545C2×#95—31no—
546C2×#95—31no—
547C24×C3C2411yescharacteristic
548C23×D3C2411yescharacteristic
549C2×C3×Q8—22no—
550C2×C3×Q8—22no—
551C2×C3×Q8—41no—
552C22×C3×C4—22no—
553C22×C3×C4—22no—
554C22×C3×C4—41no—
555C22×C3×C4C2411yescharacteristic
556C22×C3×C4C2411yescharacteristic
557C22×C3×C4C2411yescharacteristic
558C22×C3×C4C2411yescharacteristic
559C22×C3×C4C2411yescharacteristic
560C22×C3×C4C2411yescharacteristic
561C22×C3×C4C2411yescharacteristic
562C22×C3×C4C2411yescharacteristic
563C22×C3×C4C2411yescharacteristic
564C22×C3×C4C2411yescharacteristic
565C22×C3×C4C2411yescharacteristic
566C22×C3×C4C2411yescharacteristic
567C22×C3×C4C2411yescharacteristic
568C22×C3×C4C2411yescharacteristic
569C2×#67—22no—
570C2×#67—22no—
571C2×#67—41no—
572C22×Dic3—22no—
573C22×Dic3—22no—
574C22×Dic3—22no—
575C22×Dic3—41no—
576C22×Dic3—41no—
577C22×Dic3—41no—
578C22×Dic3C2411yescharacteristic
579C22×Dic3C2411yescharacteristic
580C22×Dic3C2411yescharacteristic
581C22×Dic3C2411yescharacteristic
582C22×Dic3C2411yescharacteristic
583C22×Dic3C2411yescharacteristic
584C22×Dic3C2411yescharacteristic
585C22×Dic3C2411yescharacteristic
586C22×Dic3C2411yescharacteristic
587C22×Dic3C2411yescharacteristic
588C22×Dic3C2411yescharacteristic
589C22×Dic3C2411yescharacteristic
590C22×Dic3C2411yescharacteristic
591C22×Dic3C2411yescharacteristic
592C22×Dic3C2411yescharacteristic
593C2×C4×D3—22no—
594C2×C4×D3—22no—
595C2×C4×D3—22no—
596C2×C4×D3—22no—
597C2×C4×D3—22no—
598C2×C4×D3—41no—
599C2×C4×D3—41no—
600C2×C4×D3—41no—
601C2×C4×D3—41no—
602C2×Dic6—22no—
603C2×Dic6—22no—
604C2×Dic6—22no—
605C2×Dic6—22no—
606C2×Dic6—22no—
607C2×Dic6—22no—
608C2×Dic6—41no—
609C2×Dic6—41no—
610C2×Dic6—41no—
611C3×C4⋊C4—22no—
612C3×C4⋊C4—22no—
613C3×C4⋊C4—22no—
614C3×C4⋊C4—41no—
615C3×C4⋊C4—41no—
616C3×C22⋊C4—22no—
617C3×C22⋊C4—22no—
618C3×C22⋊C4—22no—
619C3×C22⋊C4—22no—
620C3×C22⋊C4—22no—
621C3×C22⋊C4—41no—
622C3×C42—22no—
623C3×C42—22no—
624C3×C42—22no—
625C3×C42—41no—
626#217—22no—
627#217—22no—
628#217—41no—
629#217—41no—
630#217#4114yes—
631(C2×D3)⋊C4—22no—
632(C2×D3)⋊C4—22no—
633(C2×D3)⋊C4—22no—
634(C2×D3)⋊C4—22no—
635(C2×D3)⋊C4—22no—
636(C2×D3)⋊C4—22no—
637(C2×D3)⋊C4—22no—
638(C2×D3)⋊C4—41no—
639(C2×D3)⋊C4—41no—
640(C2×D3)⋊C4—41no—
641(C2×D3)⋊C4#4114yes—
642C4⋊Dic3—22no—
643C4⋊Dic3—22no—
644C4⋊Dic3—22no—
645C4⋊Dic3—22no—
646C4⋊Dic3—22no—
647C4⋊Dic3—22no—
648C4⋊Dic3—22no—
649C4⋊Dic3—22no—
650C4⋊Dic3—22no—
651C4⋊Dic3—22no—
652C4⋊Dic3—22no—
653C4⋊Dic3—41no—
654C4⋊Dic3—41no—
655C4⋊Dic3—41no—
656C4⋊Dic3—41no—
657C4⋊Dic3—41no—
658C4⋊Dic3—41no—
659Dic3⋊C4—22no—
660Dic3⋊C4—22no—
661Dic3⋊C4—22no—
662Dic3⋊C4—22no—
663Dic3⋊C4—22no—
664Dic3⋊C4—22no—
665Dic3⋊C4—22no—
666Dic3⋊C4—22no—
667Dic3⋊C4—22no—
668Dic3⋊C4—22no—
669Dic3⋊C4—22no—
670Dic3⋊C4—22no—
671Dic3⋊C4—41no—
672Dic3⋊C4—41no—
673Dic3⋊C4—41no—
674Dic3⋊C4—41no—
675Dic3⋊C4—41no—
676Dic3⋊C4—41no—
677Dic3⋊C4—41no—
678Dic3⋊C4—41no—
679Dic3⋊C4—41no—
680Dic3⋊C4—41no—
681Dic3⋊C4—41no—
682Dic3⋊C4—41no—
683Dic3⋊C4—41no—
684C4×Dic3—22no—
685C4×Dic3—22no—
686C4×Dic3—22no—
687C4×Dic3—22no—
688C4×Dic3—22no—
689C4×Dic3—22no—
690C4×Dic3—41no—
691C4×Dic3—41no—
692C4×Dic3—41no—
693C4×Dic3—41no—
694C4×Dic3—41no—
695C4×Dic3—41no—
696C4×Dic3—41no—
697C22×Q8—31no—
698C22×Q8—31no—
699C22×Q8—31no—
700C22×Q8C22×D311yescharacteristic
701C22×D4—31no—
702C23×C4—31no—
703C23×C4—31no—
704C23×C4—31no—
705C23×C4—31no—
706C23×C4—31no—
707C23×C4C22×D311yescharacteristic
708#125—122no—
709#123—64no—
710#123—64no—
711C22⋊Q8—64no—
712C22⋊Q8—64no—
713C22⋊Q8—64no—
714C22⋊Q8—64no—
715C22⋊Q8—122no—
716C22⋊Q8—122no—
717C4×Q8—122no—
718C4×Q8—122no—
719C4×Q8—122no—
720C4×Q8—122no—
721C4×D4—122no—
722#117—122no—
723#117—122no—
724#117—122no—
725#117—122no—
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⋊C4—31no—
744C2×C4⋊C4—31no—
745C2×C4⋊C4—31no—
746C2×C4⋊C4—31no—
747C2×C4⋊C4—31no—
748C2×C4⋊C4—31no—
749C2×C4⋊C4—31no—
750C2×C4⋊C4—31no—
751C2×C4⋊C4—31no—
752C2×C4⋊C4—31no—
753C2×C4⋊C4—31no—
754C2×C4⋊C4—31no—
755C2×C4⋊C4—31no—
756C2×C4⋊C4—31no—
757C2×C4⋊C4—31no—
758C2×C4⋊C4—31no—
759C2×C4⋊C4—31no—
760C2×C4⋊C4—31no—
761C2×C4⋊C4—31no—
762C2×C4⋊C4—31no—
763C2×C4⋊C4—31no—
764C2×C4⋊C4—31no—
765C2×C4⋊C4—31no—
766C2×C4⋊C4—31no—
767C2×C4⋊C4—31no—
768C2×C4⋊C4C22×D311yescharacteristic
769C2×C4⋊C4C22×D311yescharacteristic
770C2×C4⋊C4C22×D311yescharacteristic
771C2×C4⋊C4C22×D311yescharacteristic
772C2×C4⋊C4C22×D311yescharacteristic
773C2×C22⋊C4—31no—
774C2×C22⋊C4—31no—
775C2×C22⋊C4—31no—
776C2×C22⋊C4—31no—
777C2×C22⋊C4—31no—
778C2×C22⋊C4—31no—
779C2×C22⋊C4—31no—
780C2×C22⋊C4—31no—
781C2×C22⋊C4—31no—
782C2×C22⋊C4—31no—
783C2×C22⋊C4—31no—
784C2×C22⋊C4—31no—
785C2×C22⋊C4—31no—
786C2×C22⋊C4—31no—
787C2×C22⋊C4—31no—
788C2×C22⋊C4—31no—
789C2×C22⋊C4C22×D311yescharacteristic
790C2×C22⋊C4C22×D311yescharacteristic
791C2×C22⋊C4C22×D311yescharacteristic
792C2×C22⋊C4C22×D311yescharacteristic
793C2×C22⋊C4C22×D311yescharacteristic
794C2×C22⋊C4C22×D311yescharacteristic
795C2×C42—31no—
796C2×C42—31no—
797C2×C42—31no—
798C2×C42—31no—
799C2×C42—31no—
800C2×C42—31no—
801C2×C42—31no—
802C2×C42—31no—
803C2×C42—31no—
804C2×C42—31no—
805C2×C42—31no—
806C2×C42—31no—
807C2×C42—31no—
808C2×C42C22×D311yescharacteristic
809C2×C42C22×D311yescharacteristic
810C2×C42C22×D311yescharacteristic
811C2×C42C22×D311yescharacteristic
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#95—31no—
847#95—31no—
848#95—31no—
849#95—31no—
850#95—31no—
851#95—31no—
852#95C22×D311yescharacteristic
853#95C22×D311yescharacteristic
854#95C22×D311yescharacteristic
855#95C22×D311yescharacteristic
856#95C22×D311yescharacteristic
857#95C22×D311yescharacteristic
858#95C22×D311yescharacteristic
859#95C22×D311yescharacteristic
860#95C22×D311yescharacteristic
861#95C22×D311yescharacteristic
862#95C22×D311yescharacteristic
863#95C22×D311yescharacteristic
864#95C22×D311yescharacteristic
865#95C22×D311yescharacteristic
866#95C22×D311yescharacteristic
867#95C22×D311yescharacteristic
868#95C22×D311yescharacteristic
869#95C22×D311yescharacteristic
870C23×C3—21no—
871C23×C3—21no—
872C23×C3—21no—
873C23×C3—21no—
874C23×C3—21no—
875C23×C3—21no—
876C23×C3C2×#4112yes—
877C23×C3C2511yescharacteristic
878C22×D3—21no—
879C22×D3—21no—
880C22×D3—21no—
881C22×D3—21no—
882C22×D3—21no—
883C22×D3—21no—
884C22×D3C2×#4112yes—
885C3×Q8—44no—
886C2×C3×C4—21no—
887C2×C3×C4—21no—
888C2×C3×C4—21no—
889C2×C3×C4—21no—
890C2×C3×C4—21no—
891C2×C3×C4—21no—
892C2×C3×C4—21no—
893C2×C3×C4—21no—
894C2×C3×C4—21no—
895C2×C3×C4—21no—
896C2×C3×C4—21no—
897C2×C3×C4—21no—
898C2×C3×C4—21no—
899C2×C3×C4—21no—
900C2×C3×C4—21no—
901C2×C3×C4—21no—
902C2×C3×C4—21no—
903C2×C3×C4—21no—
904C2×C3×C4—21no—
905C2×C3×C4—21no—
906C2×C3×C4—21no—
907C2×C3×C4—21no—
908C2×C3×C4—21no—
909C2×C3×C4—21no—
910C2×C3×C4—21no—
911C2×C3×C4—21no—
912C2×C3×C4—21no—
913C2×C3×C4—21no—
914C2×C3×C4—21no—
915C2×C3×C4—21no—
916C2×C3×C4—21no—
917C2×C3×C4—21no—
918C2×C3×C4—21no—
919C2×C3×C4—21no—
920C2×C3×C4—21no—
921C2×C3×C4—21no—
922C2×C3×C4—21no—
923C2×C3×C4—21no—
924C2×C3×C4—44no—
925C2×C3×C4C2×#4112yes—
926C2×C3×C4H(5,𝔽2)12yes—
927C2×C3×C42−1+412yes—
928C2×C3×C42−1+412yes—
929#67—44no—
930C2×Dic3—21no—
931C2×Dic3—21no—
932C2×Dic3—21no—
933C2×Dic3—21no—
934C2×Dic3—21no—
935C2×Dic3—21no—
936C2×Dic3—21no—
937C2×Dic3—21no—
938C2×Dic3—21no—
939C2×Dic3—21no—
940C2×Dic3—21no—
941C2×Dic3—21no—
942C2×Dic3—21no—
943C2×Dic3—21no—
944C2×Dic3—21no—
945C2×Dic3—21no—
946C2×Dic3—21no—
947C2×Dic3—21no—
948C2×Dic3—21no—
949C2×Dic3—21no—
950C2×Dic3—21no—
951C2×Dic3—21no—
952C2×Dic3—21no—
953C2×Dic3—21no—
954C2×Dic3—21no—
955C2×Dic3—21no—
956C2×Dic3—21no—
957C2×Dic3—21no—
958C2×Dic3—21no—
959C2×Dic3—21no—
960C2×Dic3—21no—
961C2×Dic3—21no—
962C2×Dic3—21no—
963C2×Dic3—21no—
964C2×Dic3—21no—
965C2×Dic3—21no—
966C2×Dic3—21no—
967C2×Dic3—21no—
968C2×Dic3—21no—
969C2×Dic3—21no—
970C2×Dic3—44no—
971C2×Dic3—82no—
972C2×Dic3C2×#4112yes—
973C2×Dic3C2×#4112yes—
974C2×Dic3C2×#4112yes—
975C2×Dic3H(5,𝔽2)12yes—
976C2×Dic32−1+412yes—
977C4×D3—44no—
978C4×D3—44no—
979C4×D3—82no—
980Dic6—44no—
981Dic6—44no—
982Dic6—44no—
983C24—31no—
984C24C23×D311yescharacteristic
985C2×Q8—22no—
986C2×Q8—22no—
987C2×Q8—41no—
988C2×Q8—62no—
989C2×Q8—62no—
990C2×Q8—62no—
991C2×Q8—62no—
992C2×Q8—62no—
993C2×Q8—62no—
994C2×Q8—121no—
995C2×Q8—121no—
996C2×Q8—121no—
997C2×D4—62no—
998C2×D4—62no—
999C2×D4—121no—
1000C22×C4—22no—
1001C22×C4—22no—
1002C22×C4—31no—
1003C22×C4—31no—
1004C22×C4—31no—
1005C22×C4—31no—
1006C22×C4—31no—
1007C22×C4—31no—
1008C22×C4—31no—
1009C22×C4—31no—
1010C22×C4—31no—
1011C22×C4—31no—
1012C22×C4—31no—
1013C22×C4—31no—
1014C22×C4—31no—
1015C22×C4—31no—
1016C22×C4—31no—
1017C22×C4—41no—
1018C22×C4—62no—
1019C22×C4—62no—
1020C22×C4—62no—
1021C22×C4—62no—
1022C22×C4—62no—
1023C22×C4—62no—
1024C22×C4—62no—
1025C22×C4—62no—
1026C22×C4—121no—
1027C22×C4—121no—
1028C22×C4—121no—
1029C22×C4—121no—
1030C22×C4—121no—
1031C22×C4—121no—
1032C22×C4—121no—
1033C22×C4C23×D311yescharacteristic
1034C22×C4C23×D311yescharacteristic
1035C22×C4C23×D311yescharacteristic
1036C22×C4C23×D311yescharacteristic
1037C22×C4C23×D311yescharacteristic
1038C22×C4C23×D311yescharacteristic
1039C22×C4C23×D311yescharacteristic
1040C22×C4C23×D311yescharacteristic
1041C22×C4C23×D311yescharacteristic
1042C22×C4C23×D311yescharacteristic
1043C22×C4C23×D311yescharacteristic
1044C22×C4C23×D311yescharacteristic
1045C22×C4C23×D311yescharacteristic
1046C22×C4C23×D311yescharacteristic
1047C4⋊C4—22no—
1048C4⋊C4—22no—
1049C4⋊C4—22no—
1050C4⋊C4—41no—
1051C4⋊C4—41no—
1052C4⋊C4—62no—
1053C4⋊C4—62no—
1054C4⋊C4—62no—
1055C4⋊C4—62no—
1056C4⋊C4—62no—
1057C4⋊C4—62no—
1058C4⋊C4—62no—
1059C4⋊C4—62no—
1060C4⋊C4—62no—
1061C4⋊C4—62no—
1062C4⋊C4—62no—
1063C4⋊C4—62no—
1064C4⋊C4—62no—
1065C4⋊C4—62no—
1066C4⋊C4—62no—
1067C4⋊C4—62no—
1068C4⋊C4—62no—
1069C4⋊C4—62no—
1070C4⋊C4—62no—
1071C4⋊C4—62no—
1072C4⋊C4—62no—
1073C4⋊C4—62no—
1074C4⋊C4—62no—
1075C4⋊C4—121no—
1076C4⋊C4—121no—
1077C4⋊C4—121no—
1078C4⋊C4—121no—
1079C4⋊C4—121no—
1080C4⋊C4—121no—
1081C4⋊C4—121no—
1082C4⋊C4—121no—
1083C4⋊C4—121no—
1084C4⋊C4—121no—
1085C4⋊C4—121no—
1086C4⋊C4—121no—
1087C4⋊C4—121no—
1088C4⋊C4—121no—
1089C4⋊C4—121no—
1090C4⋊C4—121no—
1091C4⋊C4—121no—
1092C4⋊C4—121no—
1093C4⋊C4—121no—
1094C22⋊C4—22no—
1095C22⋊C4—22no—
1096C22⋊C4—22no—
1097C22⋊C4—22no—
1098C22⋊C4—22no—
1099C22⋊C4—34no—
1100C22⋊C4—34no—
1101C22⋊C4—41no—
1102C22⋊C4—62no—
1103C22⋊C4—62no—
1104C22⋊C4—62no—
1105C22⋊C4—62no—
1106C22⋊C4—62no—
1107C22⋊C4—62no—
1108C22⋊C4—62no—
1109C22⋊C4—62no—
1110C22⋊C4—62no—
1111C22⋊C4—121no—
1112C22⋊C4—121no—
1113C22⋊C4—121no—
1114C22⋊C4—121no—
1115C22⋊C4—121no—
1116C42—22no—
1117C42—22no—
1118C42—22no—
1119C42—41no—
1120C42—62no—
1121C42—62no—
1122C42—62no—
1123C42—62no—
1124C42—62no—
1125C42—62no—
1126C42—121no—
1127C42—121no—
1128C42—121no—
1129C42—121no—
1130C42—121no—
1131C42—121no—
1132C42—121no—
1133C22×C3—22no—
1134C22×C3—22no—
1135C22×C3—22no—
1136C22×C3—41no—
1137C22×C3—41no—
1138C22×C3—41no—
1139C22×C3—41no—
1140C22×C3C22×#4111yescharacteristic
1141C22×C3C22×#4111yescharacteristic
1142C22×C3C2×H(5,𝔽2)11yescharacteristic
1143C22×C3C2×H(5,𝔽2)11yescharacteristic
1144C22×C3C2×2−1+411yescharacteristic
1145C22×C3C2×2−1+411yescharacteristic
1146C22×C3C2×2−1+411yescharacteristic
1147C2×D3—22no—
1148C2×D3—22no—
1149C2×D3—22no—
1150C2×D3—41no—
1151C2×D3—41no—
1152C2×D3—41no—
1153C2×D3—41no—
1154C3×C4—22no—
1155C3×C4—22no—
1156C3×C4—22no—
1157C3×C4—22no—
1158C3×C4—41no—
1159C3×C4—41no—
1160C3×C4—41no—
1161C3×C4—41no—
1162C3×C4—41no—
1163C3×C4—41no—
1164C3×C4—41no—
1165C3×C4—41no—
1166C3×C4—41no—
1167C3×C4—41no—
1168Dic3—22no—
1169Dic3—22no—
1170Dic3—22no—
1171Dic3—22no—
1172Dic3—22no—
1173Dic3—41no—
1174Dic3—41no—
1175Dic3—41no—
1176Dic3—41no—
1177Dic3—41no—
1178Dic3—41no—
1179Dic3—41no—
1180Dic3—41no—
1181Dic3—41no—
1182Dic3—41no—
1183C23—21no—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—32no—
1190C23—61no—
1191C23—61no—
1192C23—61no—
1193C23—61no—
1194C23—61no—
1195C23—61no—
1196C23D3×#4112yes—
1197C23C24×D311yescharacteristic
1198Q8—44no—
1199Q8—124no—
1200Q8—124no—
1201Q8—124no—
1202D4—124no—
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—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—32no—
1242C2×C4—32no—
1243C2×C4—32no—
1244C2×C4—32no—
1245C2×C4—32no—
1246C2×C4—44no—
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—61no—
1266C2×C4—61no—
1267C2×C4—61no—
1268C2×C4—61no—
1269C2×C4—61no—
1270C2×C4—61no—
1271C2×C4—61no—
1272C2×C4—61no—
1273C2×C4—61no—
1274C2×C4—61no—
1275C2×C4—61no—
1276C2×C4—61no—
1277C2×C4—61no—
1278C2×C4—61no—
1279C2×C4—61no—
1280C2×C4—61no—
1281C2×C4—61no—
1282C2×C4—61no—
1283C2×C4—61no—
1284C2×C4—61no—
1285C2×C4—61no—
1286C2×C4—61no—
1287C2×C4—124no—
1288C2×C4—124no—
1289C2×C4—124no—
1290C2×C4—242no—
1291C2×C4—242no—
1292C2×C4D3×#4112yes—
1293C2×C4#100912yes—
1294C2×C4#101012yes—
1295C2×C4#101012yes—
1296C2×C3—42no—
1297C2×C3#348111yescharacteristic
1298C2×C3#350911yescharacteristic
1299C2×C3#350911yescharacteristic
1300C2×C3#352011yescharacteristic
1301C2×C3#352011yescharacteristic
1302C2×C3#353611yescharacteristic
1303C2×C3#354411yescharacteristic
1304D3—42no—
1305C22—22no—
1306C22—22no—
1307C22—22no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—62no—
1313C22—62no—
1314C22—62no—
1315C22—121no—
1316C22—121no—
1317C22—121no—
1318C22—121no—
1319C22C2×D3×#4111yescharacteristic
1320C22C2×D3×#4111yescharacteristic
1321C22C2×#100911yescharacteristic
1322C22C2×#101011yescharacteristic
1323C22C2×#101011yescharacteristic
1324C22D3×H(5,𝔽2)11yescharacteristic
1325C22D3×2−1+411yescharacteristic
1326C4—22no—
1327C4—22no—
1328C4—22no—
1329C4—22no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—62no—
1341C4—62no—
1342C4—62no—
1343C4—62no—
1344C4—62no—
1345C4—121no—
1346C4—121no—
1347C4—121no—
1348C4—121no—
1349C4—121no—
1350C4—121no—
1351C4—121no—
1352C4—121no—
1353C4—121no—
1354C4—121no—
1355C3#4486211yescharacteristic, complemented, Sylow
1356C2—42no—
1357C2—122no—
1358C2#8613311yescharacteristic
1359C2#8615311yescharacteristic
1360C2#8656111yescharacteristic
1361C2#8679811yescharacteristic
1362C2#8679811yescharacteristic
1363C2#8683211yescharacteristic
1364C2#8698311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2527C2
prime radicalC22×#67C23
hypercenter#2527D3
hypocenterC3#44862
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2527

Complements

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

NH ≅ G/Ntype
1. C3×#2527C2semidirect
2. #78425C2semidirect
3. #78424C2semidirect
4. #78342C2semidirect
5. #78308C2semidirect
6. #77636C2semidirect
9. #76788C2semidirect
10. #76637C2semidirect
11. #76548C2semidirect
12. #76527C2semidirect
13. #76491C2semidirect
16. #75533C2semidirect
17. #75460C2semidirect
18. #75328C2semidirect
19. #75274C2semidirect
20. #75076C2semidirect
21. #75040C2semidirect
22. #75012C2semidirect
23. #74947C2semidirect
25. #74472C2semidirect
27. #74067C2semidirect
28. #73468C2semidirect
30. #73422C2semidirect
31. #73397C2semidirect
203. #2527D3semidirect
1355. C3#44862semidirect

Maximal subgroups

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

subgroupindex
C3×#25272
#784252
#784242
#783422
#783082
#776362
#775682
#768782
#767882
#766372
#765482
#765272
#764912
#758382
#755922
#755332
#754602
#753282
#752742
#750762
#750402
#750122
#749472
#745002
#744722
#740942
#740672
#734682
#734642
#734222
#733972
#448623