Finite Group Databasebeta

← #11222893

Subgroups — #11222893

Order 768.

1646 conjugacy classes of subgroups.

The subgroup lattice has 1358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2529C211yesmaximal, characteristic, complemented
2#78306C211yesmaximal, characteristic, complemented
3#78249C211yesmaximal, characteristic, complemented
4#77852C211yesmaximal, characteristic, complemented
5#77786C211yesmaximal, characteristic, complemented
6#77618C211yesmaximal, characteristic, complemented
7#77501C211yesmaximal, characteristic
8#77433C211yesmaximal, characteristic
9#77367C211yesmaximal, characteristic, complemented
10#76051C211yesmaximal, characteristic, complemented
11#75989C211yesmaximal, characteristic, complemented
12#75875C211yesmaximal, characteristic
13#75684C211yesmaximal, characteristic, complemented
14#75621C211yesmaximal, characteristic
15#75598C211yesmaximal, characteristic, complemented
16#75593C211yesmaximal, characteristic
17#75564C211yesmaximal, characteristic, complemented
18#75530C211yesmaximal, characteristic
19#75529C211yesmaximal, characteristic
20#75478C211yesmaximal, characteristic, complemented
21#75460C211yesmaximal, characteristic, complemented
22#75098C211yesmaximal, characteristic, complemented
23#75090C211yesmaximal, characteristic, complemented
24#75075C211yesmaximal, characteristic, complemented
25#74947C211yesmaximal, characteristic, complemented
26#74210C211yesmaximal, characteristic, complemented
27#74180C211yesmaximal, characteristic, complemented
28#73659C211yesmaximal, characteristic, complemented
29#73647C211yesmaximal, characteristic, complemented
30#73400C211yesmaximal, characteristic, complemented
31#73397C211yesmaximal, characteristic, complemented
32#44861—31nomaximal, Sylow
33C2×#898C2211yescharacteristic
34C2×#897C2211yescharacteristic
35C2×#896C2211yescharacteristic
36C2×#892C2211yescharacteristic
37C2×#890C2211yescharacteristic
38C2×#890C2211yescharacteristic
39C2×#889C2211yescharacteristic
40C2×#888C2211yescharacteristic
41C2×#887C2211yescharacteristic
42C2×#885C2211yescharacteristic
43C2×#885C2211yescharacteristic
44C2×#879C2211yescharacteristic
45C2×#878C2211yescharacteristic
46C2×#878C2211yescharacteristic
47C2×#877C2211yescharacteristic
48C2×#870C2211yescharacteristic
49C2×C4×Dic6C2211yescharacteristic
50C2×C4×Dic6C2211yescharacteristic
51C3×#400C2211yescharacteristic
52C3×#398C2211yescharacteristic
53C3×#397C2211yescharacteristic
54C3×#396C2211yescharacteristic
55C3×#389C2211yescharacteristic
56C3×#388C2211yescharacteristic
57C3×#388C2211yescharacteristic
58C3×#388C2211yescharacteristic
59C3×#388C2211yescharacteristic
60C3×#388C2211yescharacteristic
61C3×#387C2211yescharacteristic
62C3×#387C2211yescharacteristic
63C3×#382C2211yescharacteristic
64C3×C4×C4⋊C4C2211yescharacteristic
65C3×#376C2211yescharacteristic
66#4994C2211yescharacteristic
67#4994C2211yescharacteristic
68#4994C2211yescharacteristic
69#4993C2211yescharacteristic
70#4990C2211yescharacteristic
71#4984C2211yescharacteristic
72#4984C2211yescharacteristic
73#4982C2211yescharacteristic
74#4982C2211yescharacteristic
75#4982C2211yescharacteristic
76#4980C2211yescharacteristic
77#4979C2211yescharacteristic
78#4978C2211yescharacteristic
79#4978C2211yescharacteristic
80#4978C2211yescharacteristic
81#4978C2211yescharacteristic
82#4976C2211yescharacteristic
83#4976C2211yescharacteristic
84#4976C2211yescharacteristic
85#4976C2211yescharacteristic
86Dic3×C4⋊C4C2211yescharacteristic
87Dic3×C4⋊C4C2211yescharacteristic
88#4973C2211yescharacteristic
89#4972C2211yescharacteristic
90#4972C2211yescharacteristic
91#4972C2211yescharacteristic
92#4972C2211yescharacteristic
93#4961C2211yescharacteristic
94#4961C2211yescharacteristic
95#4958C2211yescharacteristic
96#4957C2211yescharacteristic
97#4956C2211yescharacteristic
98#4953C2211yescharacteristic
99#4951C2211yescharacteristic
100#4951C2211yescharacteristic
101#4951C2211yescharacteristic
102#4951C2211yescharacteristic
103#4950C2211yescharacteristic
104#4949C2211yescharacteristic
105#4948C2211yescharacteristic
106#4948C2211yescharacteristic
107#4948C2211yescharacteristic
108#4948C2211yescharacteristic
109#4944C2211yescharacteristic
110#4944C2211yescharacteristic
111#4944C2211yescharacteristic
112#4944C2211yescharacteristic
113#4942C2211yescharacteristic
114Dic3×C22⋊C4C2211yescharacteristic
115#4940C2211yescharacteristic
116#4940C2211yescharacteristic
117#4940C2211yescharacteristic
118#4940C2211yescharacteristic
119C4×(C2×D3)⋊C4C2211yescharacteristic
120C4×C4⋊Dic3C2211yescharacteristic
121C4×C4⋊Dic3C2211yescharacteristic
122C4×C4⋊Dic3C2211yescharacteristic
123C4×C4⋊Dic3C2211yescharacteristic
124C4×C4⋊Dic3C2211yescharacteristic
125C4×C4⋊Dic3C2211yescharacteristic
126C4×C4⋊Dic3C2211yescharacteristic
127#4933C2211yescharacteristic
128C4×Dic3⋊C4C2211yescharacteristic
129#4929C2211yescharacteristic
130#4928C2211yescharacteristic
131#4928C2211yescharacteristic
132#4676C2211yescharacteristic
133#4676C2211yescharacteristic
134#4675C2211yescharacteristic
135#4674C2211yescharacteristic
136#4670C2211yescharacteristic
137#4670C2211yescharacteristic
138#4670C2211yescharacteristic
139#4670C2211yescharacteristic
140#4670C2211yescharacteristic
141#4670C2211yescharacteristic
142#4669C2211yescharacteristic
143#4669C2211yescharacteristic
144#4668C2211yescharacteristic
145#4667C2211yescharacteristic
146#4661C2211yescharacteristic
147#4661C2211yescharacteristic
148#4661C2211yescharacteristic
149#4661C2211yescharacteristic
150#4660C2211yescharacteristic
151#4658C2211yescharacteristic
152#4658C2211yescharacteristic
153#4657C2211yescharacteristic
154#4657C2211yescharacteristic
155#4656C2211yescharacteristic
156#4656C2211yescharacteristic
157#4656C2211yescharacteristic
158#4656C2211yescharacteristic
159#4656C2211yescharacteristic
160#4656C2211yescharacteristic
161#4656C2211yescharacteristic
162#4654C2211yescharacteristic
163#4654C2211yescharacteristic
164#4654C2211yescharacteristic
165#4653C2211yescharacteristic
166#4653C2211yescharacteristic
167#4653C2211yescharacteristic
168#4652C2211yescharacteristic
169#4652C2211yescharacteristic
170#4650C2211yescharacteristic
171#4650C2211yescharacteristic
172#4649C2211yescharacteristic
173#4649C2211yescharacteristic
174#4649C2211yescharacteristic
175#4649C2211yescharacteristic
176#4647C2211yescharacteristic
177#4647C2211yescharacteristic
178#4647C2211yescharacteristic
179#4647C2211yescharacteristic
180#4647C2211yescharacteristic
181#4646C2211yescharacteristic
182#4646C2211yescharacteristic
183#4646C2211yescharacteristic
184#4646C2211yescharacteristic
185#4646C2211yescharacteristic
186#4646C2211yescharacteristic
187#4646C2211yescharacteristic
188#2799—31no—
189#2772—31no—
190#2772—31no—
191#2725—31no—
192#2725—31no—
193#2704—31no—
194#2704—31no—
195#2683—31no—
196#2593—31no—
197#2586—31no—
198#2581—31no—
199#2556—31no—
200#2556—31no—
201#2550—31no—
202#2550—31no—
203#2545—31no—
204#2529—31no—
205#2529D311yescharacteristic, complemented
206#2521—31no—
207#2521—31no—
208#2519—31no—
209#2519—31no—
210#2474—31no—
211#2474—31no—
212#2399—31no—
213#2370—31no—
214#2370—31no—
215#2362—31no—
216#2362—31no—
217#2323—31no—
218#2323—31no—
219C22×#67C2311yescharacteristic
220C23×Dic3C2311yescharacteristic
221C22×C4×D3C2311yescharacteristic
222C22×Dic6C2311yescharacteristic
223C22×Dic6C2311yescharacteristic
224C22×Dic6C2311yescharacteristic
225C22×Dic6C2311yescharacteristic
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×C22⋊C4C2311yescharacteristic
236C2×C3×C22⋊C4C2311yescharacteristic
237C2×C3×C22⋊C4C2311yescharacteristic
238C2×C3×C22⋊C4C2311yescharacteristic
239C2×C3×C22⋊C4C2311yescharacteristic
240C2×C3×C22⋊C4C2311yescharacteristic
241C2×C3×C22⋊C4C2311yescharacteristic
242C2×C3×C42C2311yescharacteristic
243C2×C3×C42C2311yescharacteristic
244C2×C3×C42C2311yescharacteristic
245C2×C3×C42C2311yescharacteristic
246C2×C3×C42C2311yescharacteristic
247C2×#217C2311yescharacteristic
248C2×#217C2311yescharacteristic
249C2×#217C2311yescharacteristic
250C2×#217C2311yescharacteristic
251C2×#217C2311yescharacteristic
252C2×#217C2311yescharacteristic
253C2×(C2×D3)⋊C4C2311yescharacteristic
254C2×(C2×D3)⋊C4C2311yescharacteristic
255C2×(C2×D3)⋊C4C2311yescharacteristic
256C2×(C2×D3)⋊C4C2311yescharacteristic
257C2×(C2×D3)⋊C4C2311yescharacteristic
258C2×(C2×D3)⋊C4C2311yescharacteristic
259C2×(C2×D3)⋊C4C2311yescharacteristic
260C2×(C2×D3)⋊C4C2311yescharacteristic
261C2×(C2×D3)⋊C4C2311yescharacteristic
262C2×(C2×D3)⋊C4C2311yescharacteristic
263C2×(C2×D3)⋊C4C2311yescharacteristic
264C2×(C2×D3)⋊C4C2311yescharacteristic
265C2×(C2×D3)⋊C4C2311yescharacteristic
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
281C2×C4⋊Dic3C2311yescharacteristic
282C2×C4⋊Dic3C2311yescharacteristic
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×Dic3⋊C4C2311yescharacteristic
308C2×C4×Dic3C2311yescharacteristic
309C2×C4×Dic3C2311yescharacteristic
310C2×C4×Dic3C2311yescharacteristic
311C2×C4×Dic3C2311yescharacteristic
312C2×C4×Dic3C2311yescharacteristic
313C2×C4×Dic3C2311yescharacteristic
314C2×C4×Dic3C2311yescharacteristic
315C2×C4×Dic3C2311yescharacteristic
316C2×C4×Dic3C2311yescharacteristic
317C2×C4×Dic3C2311yescharacteristic
318C2×C4×Dic3C2311yescharacteristic
319C2×C4×Dic3C2311yescharacteristic
320C2×C4×Dic3C2311yescharacteristic
321C2×C4×Dic3C2311yescharacteristic
322C2×C4×Dic3C2311yescharacteristic
323C2×C4×Dic3C2311yescharacteristic
324#898—42no—
325#897—24no—
326#896—24no—
327#892—42no—
328#890—24no—
329#890—42no—
330#889—42no—
331#888—42no—
332#887—42no—
333#885—42no—
334#885—42no—
335#879—42no—
336#878—24no—
337#878—24no—
338#877—42no—
339#870—24no—
340C4×Dic6—42no—
341C4×Dic6—42no—
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×C4⋊Q8—31no—
393C2×#126—31no—
394C2×#126—31no—
395C2×#125—31no—
396C2×#125—31no—
397C2×#125—31no—
398C2×#125—31no—
399C2×#124—31no—
400C2×#124—31no—
401C2×C22⋊Q8—31no—
402C2×C22⋊Q8—31no—
403C2×C22⋊Q8—31no—
404C2×C22⋊Q8—31no—
405C2×C4×Q8—31no—
406C2×C4×Q8—31no—
407C2×C4×Q8—31no—
408C2×#117—31no—
409C2×#117—31no—
410#400—31no—
411#400—31no—
412#400—31no—
413#400C2×D311yescharacteristic
414#399—31no—
415#399—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#398C2×D311yescharacteristic
426#397—31no—
427#397—31no—
428#397—31no—
429#397C2×D311yescharacteristic
430#396—31no—
431#396—31no—
432#396—31no—
433#396—31no—
434#396—31no—
435#396—31no—
436#396—31no—
437#396—31no—
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#395—31no—
447#395—31no—
448#394—31no—
449#394—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#390—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#389—31no—
472#389—31no—
473#389—31no—
474#389—31no—
475#389—31no—
476#389—31no—
477#389C2×D311yescharacteristic
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#388—31no—
487#388—31no—
488#388—31no—
489#388—31no—
490#388—31no—
491#388—31no—
492#388—31no—
493#388—31no—
494#388—31no—
495#388—31no—
496#388—31no—
497#388—31no—
498#388—31no—
499#388C2×D311yescharacteristic
500#388C2×D311yescharacteristic
501#388C2×D311yescharacteristic
502#388C2×D311yescharacteristic
503#388C2×D311yescharacteristic
504#387—31no—
505#387—31no—
506#387—31no—
507#387—31no—
508#387—31no—
509#387—31no—
510#387—31no—
511#387—31no—
512#387—31no—
513#387—31no—
514#387—31no—
515#387—31no—
516#387—31no—
517#387—31no—
518#387C2×D311yescharacteristic
519#387C2×D311yescharacteristic
520#386—31no—
521#386—31no—
522#385—31no—
523#385—31no—
524#382—31no—
525#382—31no—
526#382C2×D311yescharacteristic
527#380—31no—
528#380—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⋊C4—31no—
538C4×C4⋊C4—31no—
539C4×C4⋊C4—31no—
540C4×C4⋊C4—31no—
541C4×C4⋊C4—31no—
542C4×C4⋊C4—31no—
543C4×C4⋊C4C2×D311yescharacteristic
544C4×C22⋊C4—31no—
545C4×C22⋊C4—31no—
546#376C2×D311yescharacteristic
547C24×C3C2411yescharacteristic
548C23×D3C2411yescharacteristic
549C22×C3×C4C2411yescharacteristic
550C22×C3×C4C2411yescharacteristic
551C22×C3×C4C2411yescharacteristic
552C22×C3×C4C2411yescharacteristic
553C22×C3×C4C2411yescharacteristic
554C22×C3×C4C2411yescharacteristic
555C22×C3×C4C2411yescharacteristic
556C22×C3×C4C2411yescharacteristic
557C22×C3×C4C2411yescharacteristic
558C22×C3×C4C2411yescharacteristic
559C22×C3×C4C2411yescharacteristic
560C22×C3×C4C2411yescharacteristic
561C22×C3×C4C2411yescharacteristic
562C22×C3×C4C2411yescharacteristic
563C2×#67—22no—
564C2×#67—41no—
565C2×#67—41no—
566C22×Dic3—22no—
567C22×Dic3—22no—
568C22×Dic3—41no—
569C22×Dic3C2411yescharacteristic
570C22×Dic3C2411yescharacteristic
571C22×Dic3C2411yescharacteristic
572C22×Dic3C2411yescharacteristic
573C22×Dic3C2411yescharacteristic
574C22×Dic3C2411yescharacteristic
575C22×Dic3C2411yescharacteristic
576C22×Dic3C2411yescharacteristic
577C22×Dic3C2411yescharacteristic
578C22×Dic3C2411yescharacteristic
579C22×Dic3C2411yescharacteristic
580C22×Dic3C2411yescharacteristic
581C22×Dic3C2411yescharacteristic
582C22×Dic3C2411yescharacteristic
583C22×Dic3C2411yescharacteristic
584C2×C4×D3—22no—
585C2×C4×D3—22no—
586C2×C4×D3—41no—
587C2×Dic6—22no—
588C2×Dic6—22no—
589C2×Dic6—22no—
590C2×Dic6—22no—
591C2×Dic6—22no—
592C2×Dic6—22no—
593C2×Dic6—22no—
594C2×Dic6—41no—
595C2×Dic6—41no—
596C2×Dic6—41no—
597C2×Dic6—41no—
598C2×Dic6—41no—
599C3×C4⋊C4—22no—
600C3×C4⋊C4—22no—
601C3×C4⋊C4—22no—
602C3×C4⋊C4—22no—
603C3×C4⋊C4—22no—
604C3×C4⋊C4—41no—
605C3×C4⋊C4—41no—
606C3×C4⋊C4—41no—
607C3×C4⋊C4—41no—
608C3×C22⋊C4—22no—
609C3×C22⋊C4—22no—
610C3×C22⋊C4—22no—
611C3×C22⋊C4—22no—
612C3×C22⋊C4—22no—
613C3×C22⋊C4—41no—
614C3×C22⋊C4—41no—
615C3×C42—22no—
616C3×C42—22no—
617C3×C42—22no—
618C3×C42—22no—
619C3×C42—22no—
620#217—22no—
621#217—22no—
622#217—22no—
623#217—41no—
624#217—41no—
625#217—41no—
626(C2×D3)⋊C4—22no—
627(C2×D3)⋊C4—22no—
628(C2×D3)⋊C4—22no—
629(C2×D3)⋊C4—22no—
630(C2×D3)⋊C4—22no—
631(C2×D3)⋊C4—22no—
632(C2×D3)⋊C4—22no—
633(C2×D3)⋊C4—22no—
634(C2×D3)⋊C4—41no—
635(C2×D3)⋊C4—41no—
636(C2×D3)⋊C4—41no—
637(C2×D3)⋊C4—41no—
638(C2×D3)⋊C4—41no—
639C4⋊Dic3—22no—
640C4⋊Dic3—22no—
641C4⋊Dic3—22no—
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—41no—
652C4⋊Dic3—41no—
653C4⋊Dic3—41no—
654C4⋊Dic3—41no—
655C4⋊Dic3#4114yes—
656Dic3⋊C4—22no—
657Dic3⋊C4—22no—
658Dic3⋊C4—22no—
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—41no—
670Dic3⋊C4—41no—
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#4114yes—
681C4×Dic3—22no—
682C4×Dic3—22no—
683C4×Dic3—22no—
684C4×Dic3—22no—
685C4×Dic3—22no—
686C4×Dic3—22no—
687C4×Dic3—41no—
688C4×Dic3—41no—
689C4×Dic3—41no—
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—
704C4⋊Q8—122no—
705#126—122no—
706#126—122no—
707#125—64no—
708#125—64no—
709#125—122no—
710#125—122no—
711#124—122no—
712#124—122no—
713C22⋊Q8—64no—
714C22⋊Q8—64no—
715C22⋊Q8—64no—
716C22⋊Q8—64no—
717C4×Q8—122no—
718C4×Q8—122no—
719C4×Q8—122no—
720#117—122no—
721#117—122no—
722C2×C4⋊C4—31no—
723C2×C4⋊C4—31no—
724C2×C4⋊C4—31no—
725C2×C4⋊C4—31no—
726C2×C4⋊C4—31no—
727C2×C4⋊C4—31no—
728C2×C4⋊C4—31no—
729C2×C4⋊C4—31no—
730C2×C4⋊C4—31no—
731C2×C4⋊C4—31no—
732C2×C4⋊C4—31no—
733C2×C4⋊C4—31no—
734C2×C4⋊C4—31no—
735C2×C4⋊C4—31no—
736C2×C4⋊C4—31no—
737C2×C4⋊C4—31no—
738C2×C4⋊C4—31no—
739C2×C4⋊C4—31no—
740C2×C4⋊C4—31no—
741C2×C4⋊C4—31no—
742C2×C4⋊C4—31no—
743C2×C4⋊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⋊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⋊C4—31no—
790C2×C22⋊C4—31no—
791C2×C22⋊C4—31no—
792C2×C22⋊C4C22×D311yescharacteristic
793C2×C22⋊C4C22×D311yescharacteristic
794C2×C22⋊C4C22×D311yescharacteristic
795C2×C22⋊C4C22×D311yescharacteristic
796C2×C22⋊C4C22×D311yescharacteristic
797C2×C22⋊C4C22×D311yescharacteristic
798C2×C22⋊C4C22×D311yescharacteristic
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×C42—31no—
809C2×C42—31no—
810C2×C42—31no—
811C2×C42—31no—
812C2×C42—31no—
813C2×C42—31no—
814C2×C42—31no—
815C2×C42C22×D311yescharacteristic
816C2×C42C22×D311yescharacteristic
817C2×C42C22×D311yescharacteristic
818C2×C42C22×D311yescharacteristic
819C2×C42C22×D311yescharacteristic
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#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×C3—21no—
877C23×C3C2511yescharacteristic
878C22×D3—21no—
879C22×D3—21no—
880C22×D3—21no—
881C22×D3—21no—
882C22×D3—21no—
883C22×D3—21no—
884C22×D3—21no—
885C2×C3×C4—21no—
886C2×C3×C4—21no—
887C2×C3×C4—21no—
888C2×C3×C4—21no—
889C2×C3×C4—21no—
890C2×C3×C4—21no—
891C2×C3×C4—21no—
892C2×C3×C4—21no—
893C2×C3×C4—21no—
894C2×C3×C4—21no—
895C2×C3×C4—21no—
896C2×C3×C4—21no—
897C2×C3×C4—21no—
898C2×C3×C4—21no—
899C2×C3×C4—21no—
900C2×C3×C4—21no—
901C2×C3×C4—21no—
902C2×C3×C4—21no—
903C2×C3×C4—21no—
904C2×C3×C4—21no—
905C2×C3×C4—21no—
906C2×C3×C4—21no—
907C2×C3×C4—21no—
908C2×C3×C4—21no—
909C2×C3×C4—21no—
910C2×C3×C4—21no—
911C2×C3×C4—21no—
912C2×C3×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×C4C2×#4112yes—
923C2×C3×C4C2×#4112yes—
924C2×C3×C4H(5,𝔽2)12yes—
925C2×C3×C42−1+412yes—
926C2×C3×C42−1+412yes—
927#67—82no—
928C2×Dic3—21no—
929C2×Dic3—21no—
930C2×Dic3—21no—
931C2×Dic3—21no—
932C2×Dic3—21no—
933C2×Dic3—21no—
934C2×Dic3—21no—
935C2×Dic3—21no—
936C2×Dic3—21no—
937C2×Dic3—21no—
938C2×Dic3—21no—
939C2×Dic3—21no—
940C2×Dic3—21no—
941C2×Dic3—21no—
942C2×Dic3—21no—
943C2×Dic3—21no—
944C2×Dic3—21no—
945C2×Dic3—21no—
946C2×Dic3—21no—
947C2×Dic3—21no—
948C2×Dic3—21no—
949C2×Dic3—21no—
950C2×Dic3—21no—
951C2×Dic3—21no—
952C2×Dic3—21no—
953C2×Dic3—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—44no—
968C2×Dic3C2×#4112yes—
969C2×Dic3C2×#4112yes—
970C2×Dic3C2×#4112yes—
971C2×Dic3C2×#4112yes—
972C2×Dic3H(5,𝔽2)12yes—
973C2×Dic32−1+412yes—
974C4×D3—44no—
975Dic6—44no—
976Dic6—44no—
977Dic6—44no—
978Dic6—82no—
979C24—31no—
980C24C23×D311yescharacteristic
981C2×Q8—62no—
982C2×Q8—62no—
983C2×Q8—62no—
984C2×Q8—62no—
985C2×Q8—62no—
986C2×Q8—62no—
987C2×Q8—62no—
988C2×Q8—121no—
989C2×Q8—121no—
990C2×Q8—121no—
991C2×Q8—121no—
992C2×Q8—121no—
993C2×D4—62no—
994C2×D4—121no—
995C2×D4—121no—
996C22×C4—31no—
997C22×C4—31no—
998C22×C4—31no—
999C22×C4—31no—
1000C22×C4—31no—
1001C22×C4—31no—
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—62no—
1012C22×C4—62no—
1013C22×C4—62no—
1014C22×C4—62no—
1015C22×C4—121no—
1016C22×C4—121no—
1017C22×C4C23×D311yescharacteristic
1018C22×C4C23×D311yescharacteristic
1019C22×C4C23×D311yescharacteristic
1020C22×C4C23×D311yescharacteristic
1021C22×C4C23×D311yescharacteristic
1022C22×C4C23×D311yescharacteristic
1023C22×C4C23×D311yescharacteristic
1024C22×C4C23×D311yescharacteristic
1025C22×C4C23×D311yescharacteristic
1026C22×C4C23×D311yescharacteristic
1027C22×C4C23×D311yescharacteristic
1028C22×C4C23×D311yescharacteristic
1029C22×C4C23×D311yescharacteristic
1030C22×C4C23×D311yescharacteristic
1031C4⋊C4—22no—
1032C4⋊C4—22no—
1033C4⋊C4—22no—
1034C4⋊C4—22no—
1035C4⋊C4—22no—
1036C4⋊C4—34no—
1037C4⋊C4—34no—
1038C4⋊C4—41no—
1039C4⋊C4—41no—
1040C4⋊C4—41no—
1041C4⋊C4—41no—
1042C4⋊C4—62no—
1043C4⋊C4—62no—
1044C4⋊C4—62no—
1045C4⋊C4—62no—
1046C4⋊C4—62no—
1047C4⋊C4—62no—
1048C4⋊C4—62no—
1049C4⋊C4—62no—
1050C4⋊C4—62no—
1051C4⋊C4—62no—
1052C4⋊C4—62no—
1053C4⋊C4—62no—
1054C4⋊C4—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—121no—
1068C4⋊C4—121no—
1069C4⋊C4—121no—
1070C4⋊C4—121no—
1071C4⋊C4—121no—
1072C4⋊C4—121no—
1073C4⋊C4—121no—
1074C4⋊C4—121no—
1075C4⋊C4—121no—
1076C4⋊C4—121no—
1077C4⋊C4—121no—
1078C4⋊C4—121no—
1079C4⋊C4—121no—
1080C4⋊C4—121no—
1081C4⋊C4—121no—
1082C22⋊C4—22no—
1083C22⋊C4—22no—
1084C22⋊C4—22no—
1085C22⋊C4—22no—
1086C22⋊C4—22no—
1087C22⋊C4—41no—
1088C22⋊C4—41no—
1089C22⋊C4—62no—
1090C22⋊C4—62no—
1091C22⋊C4—62no—
1092C22⋊C4—62no—
1093C22⋊C4—62no—
1094C22⋊C4—62no—
1095C22⋊C4—62no—
1096C22⋊C4—62no—
1097C22⋊C4—62no—
1098C22⋊C4—62no—
1099C22⋊C4—62no—
1100C22⋊C4—121no—
1101C22⋊C4—121no—
1102C22⋊C4—121no—
1103C22⋊C4—121no—
1104C22⋊C4—121no—
1105C22⋊C4—121no—
1106C22⋊C4—121no—
1107C22⋊C4—121no—
1108C42—22no—
1109C42—22no—
1110C42—22no—
1111C42—22no—
1112C42—22no—
1113C42—62no—
1114C42—62no—
1115C42—62no—
1116C42—62no—
1117C42—62no—
1118C42—62no—
1119C42—121no—
1120C42—121no—
1121C42—121no—
1122C42—121no—
1123C42—121no—
1124C42—121no—
1125C42—121no—
1126C42—121no—
1127C42—121no—
1128C42—121no—
1129C22×C3—41no—
1130C22×C3—41no—
1131C22×C3—41no—
1132C22×C3—41no—
1133C22×C3—41no—
1134C22×C3—41no—
1135C22×C3—41no—
1136C22×C3C22×#4111yescharacteristic
1137C22×C3C22×#4111yescharacteristic
1138C22×C3C2×H(5,𝔽2)11yescharacteristic
1139C22×C3C2×H(5,𝔽2)11yescharacteristic
1140C22×C3C2×2−1+411yescharacteristic
1141C22×C3C2×2−1+411yescharacteristic
1142C22×C3C2×2−1+411yescharacteristic
1143C2×D3—41no—
1144C2×D3—41no—
1145C2×D3—41no—
1146C2×D3—41no—
1147C2×D3—41no—
1148C2×D3—41no—
1149C2×D3—41no—
1150C3×C4—22no—
1151C3×C4—22no—
1152C3×C4—22no—
1153C3×C4—22no—
1154C3×C4—22no—
1155C3×C4—41no—
1156C3×C4—41no—
1157C3×C4—41no—
1158C3×C4—41no—
1159C3×C4—41no—
1160C3×C4—41no—
1161C3×C4—41no—
1162C3×C4—41no—
1163C3×C4—41no—
1164Dic3—22no—
1165Dic3—22no—
1166Dic3—22no—
1167Dic3—22no—
1168Dic3—22no—
1169Dic3—22no—
1170Dic3—41no—
1171Dic3—41no—
1172Dic3—41no—
1173Dic3—41no—
1174Dic3—41no—
1175Dic3—41no—
1176Dic3—41no—
1177Dic3—41no—
1178Dic3—41no—
1179C23—21no—
1180C23—21no—
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23—21no—
1185C23—21no—
1186C23—61no—
1187C23—61no—
1188C23—61no—
1189C23—61no—
1190C23—61no—
1191C23—61no—
1192C23—61no—
1193C23C24×D311yescharacteristic
1194Q8—124no—
1195Q8—124no—
1196Q8—124no—
1197Q8—242no—
1198D4—242no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—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—32no—
1237C2×C4—32no—
1238C2×C4—32no—
1239C2×C4—32no—
1240C2×C4—32no—
1241C2×C4—32no—
1242C2×C4—61no—
1243C2×C4—61no—
1244C2×C4—61no—
1245C2×C4—61no—
1246C2×C4—61no—
1247C2×C4—61no—
1248C2×C4—61no—
1249C2×C4—61no—
1250C2×C4—61no—
1251C2×C4—61no—
1252C2×C4—61no—
1253C2×C4—61no—
1254C2×C4—61no—
1255C2×C4—61no—
1256C2×C4—61no—
1257C2×C4—61no—
1258C2×C4—61no—
1259C2×C4—61no—
1260C2×C4—61no—
1261C2×C4—61no—
1262C2×C4—61no—
1263C2×C4—61no—
1264C2×C4—61no—
1265C2×C4—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—124no—
1282C2×C4—124no—
1283C2×C4D3×#4112yes—
1284C2×C4D3×#4112yes—
1285C2×C4#100912yes—
1286C2×C4#101012yes—
1287C2×C4#101012yes—
1288C2×C3—81no—
1289C2×C3#348111yescharacteristic
1290C2×C3#351111yescharacteristic
1291C2×C3#351111yescharacteristic
1292C2×C3#352311yescharacteristic
1293C2×C3#352311yescharacteristic
1294C2×C3#353611yescharacteristic
1295C2×C3#354411yescharacteristic
1296D3—81no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—121no—
1305C22—121no—
1306C22—121no—
1307C22—121no—
1308C22—121no—
1309C22—121no—
1310C22—121no—
1311C22C2×D3×#4111yescharacteristic
1312C22C2×D3×#4111yescharacteristic
1313C22C2×#100911yescharacteristic
1314C22C2×#101011yescharacteristic
1315C22C2×#101011yescharacteristic
1316C22D3×H(5,𝔽2)11yescharacteristic
1317C22D3×2−1+411yescharacteristic
1318C4—22no—
1319C4—22no—
1320C4—22no—
1321C4—22no—
1322C4—22no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—62no—
1333C4—62no—
1334C4—62no—
1335C4—62no—
1336C4—62no—
1337C4—62no—
1338C4—121no—
1339C4—121no—
1340C4—121no—
1341C4—121no—
1342C4—121no—
1343C4—121no—
1344C4—121no—
1345C4—121no—
1346C4—121no—
1347C3#4486111yescharacteristic, complemented, Sylow
1348C2—81no—
1349C2—241no—
1350C2#8613311yescharacteristic
1351C2#8615311yescharacteristic
1352C2#8656111yescharacteristic
1353C2#8684211yescharacteristic
1354C2#8684211yescharacteristic
1355C2#8687911yescharacteristic
1356C2#8696111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2529C2
prime radicalC22×#67C23
hypercenter#2529D3
hypocenterC3#44861
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2529

Complements

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

NH ≅ G/Ntype
1. C3×#2529C2semidirect
2. #78306C2semidirect
3. #78249C2semidirect
4. #77852C2semidirect
5. #77786C2semidirect
6. #77618C2semidirect
9. #77367C2semidirect
10. #76051C2semidirect
11. #75989C2semidirect
13. #75684C2semidirect
15. #75598C2semidirect
17. #75564C2semidirect
20. #75478C2semidirect
21. #75460C2semidirect
22. #75098C2semidirect
23. #75090C2semidirect
24. #75075C2semidirect
25. #74947C2semidirect
26. #74210C2semidirect
27. #74180C2semidirect
28. #73659C2semidirect
29. #73647C2semidirect
30. #73400C2semidirect
31. #73397C2semidirect
205. #2529D3semidirect
1347. C3#44861semidirect

Maximal subgroups

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

subgroupindex
C3×#25292
#783062
#782492
#778522
#777862
#776182
#775012
#774332
#773672
#760512
#759892
#758752
#756842
#756212
#755982
#755932
#755642
#755302
#755292
#754782
#754602
#750982
#750902
#750752
#749472
#742102
#741802
#736592
#736472
#734002
#733972
#448613