Finite Group Databasebeta

← #11222909

Subgroups — #11222909

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×#2475C211yesmaximal, characteristic, complemented
2#83039C211yesmaximal, characteristic, complemented
3#83033C211yesmaximal, characteristic, complemented
4#82242C211yesmaximal, characteristic
5#82235C211yesmaximal, characteristic, complemented
6#78309C211yesmaximal, characteristic, complemented
7#78293C211yesmaximal, characteristic, complemented
8#77950C211yesmaximal, characteristic, complemented
9#77796C211yesmaximal, characteristic, complemented
10#77635C211yesmaximal, characteristic, complemented
11#77569C211yesmaximal, characteristic
12#77330C211yesmaximal, characteristic
13#77296C211yesmaximal, characteristic, complemented
14#76244C211yesmaximal, characteristic, complemented
15#76177C211yesmaximal, characteristic, complemented
16#75838C211yesmaximal, characteristic
17#75592C211yesmaximal, characteristic
18#75577C211yesmaximal, characteristic, complemented
19#75478C211yesmaximal, characteristic, complemented
20#75351C211yesmaximal, characteristic, complemented
21#75329C211yesmaximal, characteristic, complemented
22#75246C211yesmaximal, characteristic, complemented
23#75040C211yesmaximal, characteristic, complemented
24#75039C211yesmaximal, characteristic, complemented
25#74947C211yesmaximal, characteristic, complemented
26#74633C211yesmaximal, characteristic
27#74631C211yesmaximal, characteristic
28#74472C211yesmaximal, characteristic, complemented
29#74415C211yesmaximal, characteristic, complemented
30#73669C211yesmaximal, characteristic, complemented
31#73647C211yesmaximal, characteristic, complemented
32#44862—31nomaximal, Sylow
33C2×C3×#125C2211yescharacteristic
34C2×C3×#117C2211yescharacteristic
35C2×#929C2211yescharacteristic
36C2×#924C2211yescharacteristic
37C2×#897C2211yescharacteristic
38C2×#896C2211yescharacteristic
39C2×#896C2211yescharacteristic
40C2×#892C2211yescharacteristic
41C2×#892C2211yescharacteristic
42C2×#887C2211yescharacteristic
43C2×#887C2211yescharacteristic
44C2×#883C2211yescharacteristic
45C2×#67⋊C4C2211yescharacteristic
46C2×#878C2211yescharacteristic
47C2×#878C2211yescharacteristic
48C2×#877C2211yescharacteristic
49C2×C4×Dic6C2211yescharacteristic
50C2×C4×Dic6C2211yescharacteristic
51C3×#400C2211yescharacteristic
52C3×#398C2211yescharacteristic
53C3×#397C2211yescharacteristic
54C3×#396C2211yescharacteristic
55C3×#389C2211yescharacteristic
56C3×#388C2211yescharacteristic
57C3×#388C2211yescharacteristic
58C3×#387C2211yescharacteristic
59C3×#387C2211yescharacteristic
60C3×#387C2211yescharacteristic
61C3×#385C2211yescharacteristic
62C3×#385C2211yescharacteristic
63C3×C4×C4⋊C4C2211yescharacteristic
64#5212C2211yescharacteristic
65C2×C3⋊#95C2211yescharacteristic
66#4994C2211yescharacteristic
67#4992C2211yescharacteristic
68#4990C2211yescharacteristic
69#4989C2211yescharacteristic
70#4989C2211yescharacteristic
71#4989C2211yescharacteristic
72#4989C2211yescharacteristic
73#4986C2211yescharacteristic
74#4984C2211yescharacteristic
75#4984C2211yescharacteristic
76#4982C2211yescharacteristic
77#4982C2211yescharacteristic
78#4982C2211yescharacteristic
79#4982C2211yescharacteristic
80#4982C2211yescharacteristic
81#4982C2211yescharacteristic
82#4982C2211yescharacteristic
83#4982C2211yescharacteristic
84#4981C2211yescharacteristic
85#4981C2211yescharacteristic
86#4980C2211yescharacteristic
87#4980C2211yescharacteristic
88#4980C2211yescharacteristic
89#4979C2211yescharacteristic
90#4979C2211yescharacteristic
91#4979C2211yescharacteristic
92#4978C2211yescharacteristic
93#4978C2211yescharacteristic
94#4978C2211yescharacteristic
95#4978C2211yescharacteristic
96#4978C2211yescharacteristic
97#4978C2211yescharacteristic
98#4978C2211yescharacteristic
99#4977C2211yescharacteristic
100#4976C2211yescharacteristic
101#4976C2211yescharacteristic
102#4976C2211yescharacteristic
103#4975C2211yescharacteristic
104#4973C2211yescharacteristic
105#4973C2211yescharacteristic
106#4972C2211yescharacteristic
107#4961C2211yescharacteristic
108#4959C2211yescharacteristic
109#4958C2211yescharacteristic
110#4956C2211yescharacteristic
111#4952C2211yescharacteristic
112#4951C2211yescharacteristic
113#4950C2211yescharacteristic
114#4950C2211yescharacteristic
115#4947C2211yescharacteristic
116#4946C2211yescharacteristic
117#4945C2211yescharacteristic
118#4945C2211yescharacteristic
119#4944C2211yescharacteristic
120#4944C2211yescharacteristic
121#4944C2211yescharacteristic
122#4943C2211yescharacteristic
123#4942C2211yescharacteristic
124Dic3×C22⋊C4C2211yescharacteristic
125Dic3×C22⋊C4C2211yescharacteristic
126#4940C2211yescharacteristic
127#4940C2211yescharacteristic
128C4×(C2×D3)⋊C4C2211yescharacteristic
129C4×(C2×D3)⋊C4C2211yescharacteristic
130C4×C4⋊Dic3C2211yescharacteristic
131C4×C4⋊Dic3C2211yescharacteristic
132C4×C4⋊Dic3C2211yescharacteristic
133#4933C2211yescharacteristic
134#4932C2211yescharacteristic
135C4×Dic3⋊C4C2211yescharacteristic
136C4×Dic3⋊C4C2211yescharacteristic
137#4929C2211yescharacteristic
138#4929C2211yescharacteristic
139#4928C2211yescharacteristic
140#4675C2211yescharacteristic
141#4673C2211yescharacteristic
142#4670C2211yescharacteristic
143#4670C2211yescharacteristic
144#4670C2211yescharacteristic
145#4670C2211yescharacteristic
146#4669C2211yescharacteristic
147#4668C2211yescharacteristic
148#4667C2211yescharacteristic
149#4667C2211yescharacteristic
150#4664C2211yescharacteristic
151D3×#95C2211yescharacteristic
152C3⋊#401C2211yescharacteristic
153C3⋊#401C2211yescharacteristic
154#4660C2211yescharacteristic
155#4660C2211yescharacteristic
156#4659C2211yescharacteristic
157#4659C2211yescharacteristic
158#4657C2211yescharacteristic
159#4657C2211yescharacteristic
160#4657C2211yescharacteristic
161#4657C2211yescharacteristic
162#4657C2211yescharacteristic
163#4656C2211yescharacteristic
164#4656C2211yescharacteristic
165#4656C2211yescharacteristic
166#4654C2211yescharacteristic
167#4654C2211yescharacteristic
168#4654C2211yescharacteristic
169#4653C2211yescharacteristic
170#4653C2211yescharacteristic
171#4653C2211yescharacteristic
172#4653C2211yescharacteristic
173#4653C2211yescharacteristic
174#4652C2211yescharacteristic
175#4652C2211yescharacteristic
176#4650C2211yescharacteristic
177#4649C2211yescharacteristic
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#2527—31no—
204#2520—31no—
205#2520—31no—
206#2475—31no—
207#2475D311yescharacteristic, complemented
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—
219C23×C3×C4C2311yescharacteristic
220C22×#67C2311yescharacteristic
221C23×Dic3C2311yescharacteristic
222C23×Dic3C2311yescharacteristic
223C22×C4×D3C2311yescharacteristic
224C22×C4×D3C2311yescharacteristic
225C22×C4×D3C2311yescharacteristic
226C22×Dic6C2311yescharacteristic
227C22×Dic6C2311yescharacteristic
228C22×Dic6C2311yescharacteristic
229C22×Dic6C2311yescharacteristic
230C3×#125—42no—
231C3×#117—42no—
232C2×C3×C4⋊C4C2311yescharacteristic
233C2×C3×C4⋊C4C2311yescharacteristic
234C2×C3×C4⋊C4C2311yescharacteristic
235C2×C3×C4⋊C4C2311yescharacteristic
236C2×C3×C4⋊C4C2311yescharacteristic
237C2×C3×C4⋊C4C2311yescharacteristic
238C2×C3×C4⋊C4C2311yescharacteristic
239C2×C3×C4⋊C4C2311yescharacteristic
240C2×C3×C4⋊C4C2311yescharacteristic
241C2×C3×C4⋊C4C2311yescharacteristic
242C2×C3×C4⋊C4C2311yescharacteristic
243C2×C3×C4⋊C4C2311yescharacteristic
244C2×C3×C22⋊C4C2311yescharacteristic
245C2×C3×C22⋊C4C2311yescharacteristic
246C2×C3×C22⋊C4C2311yescharacteristic
247C2×C3×C22⋊C4C2311yescharacteristic
248C2×C3×C22⋊C4C2311yescharacteristic
249C2×C3×C22⋊C4C2311yescharacteristic
250C2×C3×C42C2311yescharacteristic
251C2×C3×C42C2311yescharacteristic
252C2×C3×C42C2311yescharacteristic
253C2×C3×C42C2311yescharacteristic
254C2×#217C2311yescharacteristic
255C2×#217C2311yescharacteristic
256C2×#217C2311yescharacteristic
257C2×#217C2311yescharacteristic
258C2×#217C2311yescharacteristic
259#929—24no—
260C2×(C2×D3)⋊C4C2311yescharacteristic
261C2×(C2×D3)⋊C4C2311yescharacteristic
262C2×(C2×D3)⋊C4C2311yescharacteristic
263C2×(C2×D3)⋊C4C2311yescharacteristic
264C2×(C2×D3)⋊C4C2311yescharacteristic
265C2×(C2×D3)⋊C4C2311yescharacteristic
266C2×(C2×D3)⋊C4C2311yescharacteristic
267C2×(C2×D3)⋊C4C2311yescharacteristic
268C2×(C2×D3)⋊C4C2311yescharacteristic
269C2×(C2×D3)⋊C4C2311yescharacteristic
270C2×(C2×D3)⋊C4C2311yescharacteristic
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
281C2×C4⋊Dic3C2311yescharacteristic
282C2×C4⋊Dic3C2311yescharacteristic
283#924—24no—
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#897—24no—
321#896—24no—
322#896—42no—
323#892—42no—
324#892—42no—
325#887—42no—
326#887—42no—
327#883—24no—
328#67⋊C4—42no—
329#878—24no—
330#878—42no—
331#877—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×#125C2×D311yescharacteristic
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×#117C2×D311yescharacteristic
410#401—31no—
411#401—31no—
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#398C2×D311yescharacteristic
434#397—31no—
435#397—31no—
436#397—31no—
437#397C2×D311yescharacteristic
438#396—31no—
439#396C2×D311yescharacteristic
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#393—31no—
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#391—31no—
459#391—31no—
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#389C2×D311yescharacteristic
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#385C2×D311yescharacteristic
523#385C2×D311yescharacteristic
524#384—31no—
525#382—31no—
526#382—31no—
527#381—31no—
528#381—31no—
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⋊C4C2×D311yescharacteristic
540C4×C22⋊C4—31no—
541C4×C22⋊C4—31no—
542C4×C22⋊C4—31no—
543C4×C22⋊C4—31no—
544#376—31no—
545C2×#95—31no—
546C2×#95—31no—
547C24×C3C2411yescharacteristic
548C23×D3C2411yescharacteristic
549C22×C3×C4—22no—
550C22×C3×C4—22no—
551C22×C3×C4—41no—
552C22×C3×C4C2411yescharacteristic
553C22×C3×C4C2411yescharacteristic
554C22×C3×C4C2411yescharacteristic
555C22×C3×C4C2411yescharacteristic
556C22×C3×C4C2411yescharacteristic
557C22×C3×C4C2411yescharacteristic
558C22×C3×C4C2411yescharacteristic
559C22×C3×C4C2411yescharacteristic
560C22×C3×C4C2411yescharacteristic
561C22×C3×C4C2411yescharacteristic
562C22×C3×C4C2411yescharacteristic
563C22×C3×C4C2411yescharacteristic
564C22×C3×C4C2411yescharacteristic
565C22×C3×C4C2411yescharacteristic
566C2×#67—22no—
567C2×#67—22no—
568C2×#67—41no—
569C22×Dic3—22no—
570C22×Dic3—22no—
571C22×Dic3—22no—
572C22×Dic3—41no—
573C22×Dic3—41no—
574C22×Dic3—41no—
575C22×Dic3C2411yescharacteristic
576C22×Dic3C2411yescharacteristic
577C22×Dic3C2411yescharacteristic
578C22×Dic3C2411yescharacteristic
579C22×Dic3C2411yescharacteristic
580C22×Dic3C2411yescharacteristic
581C22×Dic3C2411yescharacteristic
582C22×Dic3C2411yescharacteristic
583C22×Dic3C2411yescharacteristic
584C22×Dic3C2411yescharacteristic
585C22×Dic3C2411yescharacteristic
586C22×Dic3C2411yescharacteristic
587C22×Dic3C2411yescharacteristic
588C22×Dic3C2411yescharacteristic
589C22×Dic3C2411yescharacteristic
590C2×C4×D3—22no—
591C2×C4×D3—22no—
592C2×C4×D3—22no—
593C2×C4×D3—22no—
594C2×C4×D3—22no—
595C2×C4×D3—41no—
596C2×C4×D3—41no—
597C2×C4×D3—41no—
598C2×C4×D3—41no—
599C2×Dic6—22no—
600C2×Dic6—22no—
601C2×Dic6—22no—
602C2×Dic6—22no—
603C2×Dic6—22no—
604C2×Dic6—22no—
605C2×Dic6—22no—
606C2×Dic6—22no—
607C2×Dic6—41no—
608C2×Dic6—41no—
609C2×Dic6—41no—
610C2×Dic6—41no—
611C3×C4⋊C4—22no—
612C3×C4⋊C4—22no—
613C3×C4⋊C4—22no—
614C3×C4⋊C4—22no—
615C3×C4⋊C4—22no—
616C3×C4⋊C4—22no—
617C3×C4⋊C4—22no—
618C3×C4⋊C4—41no—
619C3×C4⋊C4—41no—
620C3×C4⋊C4—41no—
621C3×C4⋊C4—41no—
622C3×C4⋊C4—41no—
623C3×C22⋊C4—22no—
624C3×C22⋊C4—22no—
625C3×C22⋊C4—22no—
626C3×C22⋊C4—22no—
627C3×C22⋊C4—22no—
628C3×C22⋊C4—41no—
629C3×C42—22no—
630C3×C42—22no—
631C3×C42—22no—
632C3×C42—41no—
633#217—22no—
634#217—22no—
635#217—41no—
636#217—41no—
637#217#4114yes—
638(C2×D3)⋊C4—22no—
639(C2×D3)⋊C4—22no—
640(C2×D3)⋊C4—22no—
641(C2×D3)⋊C4—22no—
642(C2×D3)⋊C4—22no—
643(C2×D3)⋊C4—22no—
644(C2×D3)⋊C4—22no—
645(C2×D3)⋊C4—41no—
646(C2×D3)⋊C4—41no—
647(C2×D3)⋊C4—41no—
648(C2×D3)⋊C4#4114yes—
649C4⋊Dic3—22no—
650C4⋊Dic3—22no—
651C4⋊Dic3—22no—
652C4⋊Dic3—22no—
653C4⋊Dic3—22no—
654C4⋊Dic3—22no—
655C4⋊Dic3—22no—
656C4⋊Dic3—41no—
657C4⋊Dic3—41no—
658C4⋊Dic3—41no—
659C4⋊Dic3—41no—
660C4⋊Dic3—41no—
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—22no—
672Dic3⋊C4—22no—
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×Q8—31no—
701C22×D4—31no—
702C23×C4—31no—
703C23×C4—31no—
704C23×C4—31no—
705C23×C4—31no—
706C23×C4—31no—
707C23×C4C22×D311yescharacteristic
708#125—42no—
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—42no—
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⋊C4C22×D311yescharacteristic
762C2×C4⋊C4C22×D311yescharacteristic
763C2×C4⋊C4C22×D311yescharacteristic
764C2×C4⋊C4C22×D311yescharacteristic
765C2×C4⋊C4C22×D311yescharacteristic
766C2×C4⋊C4C22×D311yescharacteristic
767C2×C4⋊C4C22×D311yescharacteristic
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#95—31no—
853#95—31no—
854#95—31no—
855#95—31no—
856#95—31no—
857#95—31no—
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—
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×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—44no—
924C2×C3×C4C2×#4112yes—
925C2×C3×C4H(5,𝔽2)12yes—
926C2×C3×C4H(5,𝔽2)12yes—
927C2×C3×C42−1+412yes—
928#67—44no—
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—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—44no—
970C2×Dic3—82no—
971C2×Dic3C2×#4112yes—
972C2×Dic3C2×#4112yes—
973C2×Dic3C2×#4112yes—
974C2×Dic32−1+412yes—
975C2×Dic32−1+412yes—
976C4×D3—44no—
977C4×D3—44no—
978C4×D3—82no—
979Dic6—44no—
980Dic6—44no—
981Dic6—44no—
982Dic6—44no—
983C24—31no—
984C24C23×D311yescharacteristic
985C2×Q8—62no—
986C2×Q8—62no—
987C2×Q8—62no—
988C2×Q8—62no—
989C2×Q8—62no—
990C2×Q8—62no—
991C2×Q8—62no—
992C2×Q8—62no—
993C2×Q8—121no—
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—22no—
1051C4⋊C4—22no—
1052C4⋊C4—22no—
1053C4⋊C4—22no—
1054C4⋊C4—41no—
1055C4⋊C4—41no—
1056C4⋊C4—41no—
1057C4⋊C4—41no—
1058C4⋊C4—41no—
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—62no—
1076C4⋊C4—62no—
1077C4⋊C4—62no—
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—124no—
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×C4#100412yes—
1293C2×C4D3×#4112yes—
1294C2×C4#100912yes—
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×#100411yescharacteristic
1320C22C2×D3×#4111yescharacteristic
1321C22C2×D3×#4111yescharacteristic
1322C22C2×#100911yescharacteristic
1323C22C2×#101011yescharacteristic
1324C22D3×2−1+411yescharacteristic
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#8603811yescharacteristic
1359C2#8616711yescharacteristic
1360C2#8651011yescharacteristic
1361C2#8669211yescharacteristic
1362C2#8673911yescharacteristic
1363C2#8683211yescharacteristic
1364C2#8683911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2475C2
prime radicalC22×#67C23
hypercenter#2475D3
hypocenterC3#44862
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2475

Complements

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

NH ≅ G/Ntype
1. C3×#2475C2semidirect
2. #83039C2semidirect
3. #83033C2semidirect
5. #82235C2semidirect
6. #78309C2semidirect
7. #78293C2semidirect
8. #77950C2semidirect
9. #77796C2semidirect
10. #77635C2semidirect
13. #77296C2semidirect
14. #76244C2semidirect
15. #76177C2semidirect
18. #75577C2semidirect
19. #75478C2semidirect
20. #75351C2semidirect
21. #75329C2semidirect
22. #75246C2semidirect
23. #75040C2semidirect
24. #75039C2semidirect
25. #74947C2semidirect
28. #74472C2semidirect
29. #74415C2semidirect
30. #73669C2semidirect
31. #73647C2semidirect
207. #2475D3semidirect
1355. C3#44862semidirect

Maximal subgroups

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

subgroupindex
C3×#24752
#830392
#830332
#822422
#822352
#783092
#782932
#779502
#777962
#776352
#775692
#773302
#772962
#762442
#761772
#758382
#755922
#755772
#754782
#753512
#753292
#752462
#750402
#750392
#749472
#746332
#746312
#744722
#744152
#736692
#736472
#448623