Finite Group Databasebeta

← #11233835

Subgroups — #11233835

Order 768.

1598 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2806C211yesmaximal, characteristic
2#77922C211yesmaximal, characteristic
3#77921C211yesmaximal, characteristic
4#77913C211yesmaximal, characteristic
5#77797C211yesmaximal, characteristic
6#77786C211yesmaximal, characteristic
7#77785C211yesmaximal, characteristic
8#77748C211yesmaximal, characteristic
9#77740C211yesmaximal, characteristic
10#77240C211yesmaximal, characteristic
11#77239C211yesmaximal, characteristic
12#77189C211yesmaximal, characteristic
13#77185C211yesmaximal, characteristic
14#76604C211yesmaximal, characteristic
15#76550C211yesmaximal, characteristic
16#76548C211yesmaximal, characteristic
17#76537C211yesmaximal, characteristic
18#76509C211yesmaximal, characteristic
19#76494C211yesmaximal, characteristic
20#76492C211yesmaximal, characteristic
21#76486C211yesmaximal, characteristic
22#76169C211yesmaximal, characteristic
23#76080C211yesmaximal, characteristic
24#76077C211yesmaximal, characteristic
25#76063C211yesmaximal, characteristic
26#76008C211yesmaximal, characteristic
27#75987C211yesmaximal, characteristic
28#75097C211yesmaximal, characteristic
29#74987C211yesmaximal, characteristic
30#74967C211yesmaximal, characteristic
31#74950C211yesmaximal, characteristic
32#45364—31nomaximal, Sylow
33C2×Q8×Dic3C2211yescharacteristic
34C2×#944C2211yescharacteristic
35C2×#944C2211yescharacteristic
36C2×#889C2211yescharacteristic
37C2×#889C2211yescharacteristic
38C2×#888C2211yescharacteristic
39C2×#888C2211yescharacteristic
40C2×#888C2211yescharacteristic
41C2×#888C2211yescharacteristic
42C2×#887C2211yescharacteristic
43C2×#887C2211yescharacteristic
44C2×#887C2211yescharacteristic
45C2×C4×Dic6C2211yescharacteristic
46C2×C4×Dic6C2211yescharacteristic
47C3×#398C2211yescharacteristic
48C3×#398C2211yescharacteristic
49C3×#398C2211yescharacteristic
50C3×#398C2211yescharacteristic
51C3×#395C2211yescharacteristic
52C3×#395C2211yescharacteristic
53C3×#391C2211yescharacteristic
54C3×#391C2211yescharacteristic
55C3×#391C2211yescharacteristic
56C3×#391C2211yescharacteristic
57C3×#389C2211yescharacteristic
58C3×#389C2211yescharacteristic
59C3×#389C2211yescharacteristic
60C3×#387C2211yescharacteristic
61C3×#387C2211yescharacteristic
62#5230C2211yescharacteristic
63#5230C2211yescharacteristic
64#5229C2211yescharacteristic
65#5229C2211yescharacteristic
66#5229C2211yescharacteristic
67#4984C2211yescharacteristic
68#4983C2211yescharacteristic
69#4983C2211yescharacteristic
70#4983C2211yescharacteristic
71#4983C2211yescharacteristic
72#4982C2211yescharacteristic
73#4982C2211yescharacteristic
74#4982C2211yescharacteristic
75#4981C2211yescharacteristic
76#4981C2211yescharacteristic
77#4980C2211yescharacteristic
78#4980C2211yescharacteristic
79#4979C2211yescharacteristic
80#4979C2211yescharacteristic
81#4979C2211yescharacteristic
82#4979C2211yescharacteristic
83#4979C2211yescharacteristic
84#4979C2211yescharacteristic
85#4979C2211yescharacteristic
86#4979C2211yescharacteristic
87#4979C2211yescharacteristic
88#4978C2211yescharacteristic
89#4976C2211yescharacteristic
90#4976C2211yescharacteristic
91#4976C2211yescharacteristic
92#4976C2211yescharacteristic
93#4976C2211yescharacteristic
94#4976C2211yescharacteristic
95#4976C2211yescharacteristic
96#4976C2211yescharacteristic
97#4976C2211yescharacteristic
98#4976C2211yescharacteristic
99#4976C2211yescharacteristic
100#4975C2211yescharacteristic
101#4975C2211yescharacteristic
102Dic3×C4⋊C4C2211yescharacteristic
103Dic3×C4⋊C4C2211yescharacteristic
104Dic3×C4⋊C4C2211yescharacteristic
105#4973C2211yescharacteristic
106#4973C2211yescharacteristic
107#4973C2211yescharacteristic
108#4973C2211yescharacteristic
109#4973C2211yescharacteristic
110#4972C2211yescharacteristic
111#4972C2211yescharacteristic
112#4972C2211yescharacteristic
113#4972C2211yescharacteristic
114C4×C4⋊Dic3C2211yescharacteristic
115#4933C2211yescharacteristic
116C4×Dic3⋊C4C2211yescharacteristic
117C4×Dic3⋊C4C2211yescharacteristic
118C4×Dic3⋊C4C2211yescharacteristic
119C4×Dic3⋊C4C2211yescharacteristic
120#4929C2211yescharacteristic
121#4929C2211yescharacteristic
122#4928C2211yescharacteristic
123#4928C2211yescharacteristic
124#4661C2211yescharacteristic
125#4661C2211yescharacteristic
126#4657C2211yescharacteristic
127#4657C2211yescharacteristic
128#4657C2211yescharacteristic
129#4657C2211yescharacteristic
130#4657C2211yescharacteristic
131#4656C2211yescharacteristic
132#4656C2211yescharacteristic
133#4656C2211yescharacteristic
134#4656C2211yescharacteristic
135#4656C2211yescharacteristic
136#4656C2211yescharacteristic
137#4656C2211yescharacteristic
138#4655C2211yescharacteristic
139#4655C2211yescharacteristic
140#4655C2211yescharacteristic
141#4654C2211yescharacteristic
142#4654C2211yescharacteristic
143#4653C2211yescharacteristic
144#4653C2211yescharacteristic
145#4652C2211yescharacteristic
146#4652C2211yescharacteristic
147#4652C2211yescharacteristic
148#4650C2211yescharacteristic
149#4650C2211yescharacteristic
150#4649C2211yescharacteristic
151#4649C2211yescharacteristic
152#4649C2211yescharacteristic
153#4649C2211yescharacteristic
154#4649C2211yescharacteristic
155#4649C2211yescharacteristic
156#4649C2211yescharacteristic
157#4649C2211yescharacteristic
158#4648C2211yescharacteristic
159#4647C2211yescharacteristic
160#4647C2211yescharacteristic
161#4647C2211yescharacteristic
162#4647C2211yescharacteristic
163#4647C2211yescharacteristic
164#4647C2211yescharacteristic
165#4647C2211yescharacteristic
166#4647C2211yescharacteristic
167#4647C2211yescharacteristic
168#4647C2211yescharacteristic
169#4647C2211yescharacteristic
170#4646C2211yescharacteristic
171#4646C2211yescharacteristic
172#4646C2211yescharacteristic
173#4646C2211yescharacteristic
174#4646C2211yescharacteristic
175#4646C2211yescharacteristic
176#4646C2211yescharacteristic
177#4646C2211yescharacteristic
178#4646C2211yescharacteristic
179#4646C2211yescharacteristic
180#4646C2211yescharacteristic
181#4646C2211yescharacteristic
182#4646C2211yescharacteristic
183#4646C2211yescharacteristic
184#4646C2211yescharacteristic
185#4646C2211yescharacteristic
186#4646C2211yescharacteristic
187#4646C2211yescharacteristic
188#2811—31no—
189#2811—31no—
190#2806—31no—
191#2806—31no—
192#2806—31no—
193#2806D311yescharacteristic
194#2792—31no—
195#2792—31no—
196#2586—31no—
197#2586—31no—
198#2584—31no—
199#2584—31no—
200#2582—31no—
201#2582—31no—
202#2567—31no—
203#2550—31no—
204#2550—31no—
205#2550—31no—
206#2550—31no—
207#2546—31no—
208#2451—31no—
209#2451—31no—
210#2451—31no—
211#2451—31no—
212#2399—31no—
213#2369—31no—
214#2369—31no—
215#2365—31no—
216#2365—31no—
217#2331—31no—
218#2331—31no—
219C22×C3×Q8C2311yescharacteristic
220C22×C3×Q8C2311yescharacteristic
221C22×Dic6C2311yescharacteristic
222C22×Dic6C2311yescharacteristic
223C22×Dic6C2311yescharacteristic
224C22×Dic6C2311yescharacteristic
225C22×Dic6C2311yescharacteristic
226C22×Dic6C2311yescharacteristic
227C22×Dic6C2311yescharacteristic
228C22×Dic6C2311yescharacteristic
229C2×C3×C4⋊C4C2311yescharacteristic
230C2×C3×C4⋊C4C2311yescharacteristic
231C2×C3×C4⋊C4C2311yescharacteristic
232C2×C3×C4⋊C4C2311yescharacteristic
233C2×C3×C4⋊C4C2311yescharacteristic
234C2×C3×C4⋊C4C2311yescharacteristic
235C2×C3×C4⋊C4C2311yescharacteristic
236C2×C3×C4⋊C4C2311yescharacteristic
237C2×C3×C4⋊C4C2311yescharacteristic
238C2×C3×C4⋊C4C2311yescharacteristic
239C2×C3×C4⋊C4C2311yescharacteristic
240C2×C3×C4⋊C4C2311yescharacteristic
241C2×C3×C4⋊C4C2311yescharacteristic
242C2×C3×C4⋊C4C2311yescharacteristic
243C2×C3×C42C2311yescharacteristic
244C2×C3×C42C2311yescharacteristic
245C2×C3×C42C2311yescharacteristic
246Q8×Dic3—42no—
247#944—42no—
248#944Q818yescomplemented
249C2×C4⋊Dic3C2311yescharacteristic
250C2×C4⋊Dic3C2311yescharacteristic
251C2×C4⋊Dic3C2311yescharacteristic
252C2×C4⋊Dic3C2311yescharacteristic
253C2×C4⋊Dic3C2311yescharacteristic
254C2×C4⋊Dic3C2311yescharacteristic
255C2×C4⋊Dic3C2311yescharacteristic
256C2×C4⋊Dic3C2311yescharacteristic
257C2×C4⋊Dic3C2311yescharacteristic
258C2×C4⋊Dic3C2311yescharacteristic
259C2×C4⋊Dic3C2311yescharacteristic
260C2×C4⋊Dic3C2311yescharacteristic
261C2×Dic3⋊C4C2311yescharacteristic
262C2×Dic3⋊C4C2311yescharacteristic
263C2×Dic3⋊C4C2311yescharacteristic
264C2×Dic3⋊C4C2311yescharacteristic
265C2×Dic3⋊C4C2311yescharacteristic
266C2×Dic3⋊C4C2311yescharacteristic
267C2×Dic3⋊C4C2311yescharacteristic
268C2×Dic3⋊C4C2311yescharacteristic
269C2×Dic3⋊C4C2311yescharacteristic
270C2×Dic3⋊C4C2311yescharacteristic
271C2×Dic3⋊C4C2311yescharacteristic
272C2×Dic3⋊C4C2311yescharacteristic
273C2×Dic3⋊C4C2311yescharacteristic
274C2×Dic3⋊C4C2311yescharacteristic
275C2×Dic3⋊C4C2311yescharacteristic
276C2×Dic3⋊C4C2311yescharacteristic
277C2×Dic3⋊C4C2311yescharacteristic
278C2×Dic3⋊C4C2311yescharacteristic
279C2×Dic3⋊C4C2311yescharacteristic
280C2×Dic3⋊C4C2311yescharacteristic
281C2×Dic3⋊C4C2311yescharacteristic
282C2×Dic3⋊C4C2311yescharacteristic
283C2×Dic3⋊C4C2311yescharacteristic
284C2×Dic3⋊C4C2311yescharacteristic
285C2×Dic3⋊C4C2311yescharacteristic
286C2×Dic3⋊C4C2311yescharacteristic
287C2×Dic3⋊C4C2311yescharacteristic
288C2×Dic3⋊C4C2311yescharacteristic
289C2×Dic3⋊C4C2311yescharacteristic
290C2×Dic3⋊C4C2311yescharacteristic
291C2×Dic3⋊C4C2311yescharacteristic
292C2×Dic3⋊C4C2311yescharacteristic
293C2×Dic3⋊C4C2311yescharacteristic
294C2×Dic3⋊C4C2311yescharacteristic
295C2×Dic3⋊C4C2311yescharacteristic
296C2×Dic3⋊C4C2311yescharacteristic
297C2×C4×Dic3C2311yescharacteristic
298C2×C4×Dic3C2311yescharacteristic
299C2×C4×Dic3C2311yescharacteristic
300C2×C4×Dic3C2311yescharacteristic
301C2×C4×Dic3C2311yescharacteristic
302C2×C4×Dic3C2311yescharacteristic
303C2×C4×Dic3C2311yescharacteristic
304C2×C4×Dic3C2311yescharacteristic
305C2×C4×Dic3C2311yescharacteristic
306C2×C4×Dic3C2311yescharacteristic
307C2×C4×Dic3C2311yescharacteristic
308C2×C4×Dic3C2311yescharacteristic
309C2×C4×Dic3C2311yescharacteristic
310C2×C4×Dic3C2311yescharacteristic
311C2×C4×Dic3C2311yescharacteristic
312C2×C4×Dic3C2311yescharacteristic
313C2×C4×Dic3C2311yescharacteristic
314C2×C4×Dic3C2311yescharacteristic
315C2×C4×Dic3C2311yescharacteristic
316C2×C4×Dic3C2311yescharacteristic
317#889—42no—
318#889—42no—
319#888—42no—
320#888—42no—
321#888—42no—
322#888Q818yescomplemented
323#887—42no—
324#887—42no—
325#887—42no—
326C4×Dic6—42no—
327C4×Dic6—42no—
328C3×#95C2311yescharacteristic
329C3×#95C2311yescharacteristic
330C3×#95C2311yescharacteristic
331C3×#95C2311yescharacteristic
332C3×#95C2311yescharacteristic
333C3×#95C2311yescharacteristic
334C3×#95C2311yescharacteristic
335C3×#95C2311yescharacteristic
336C3×#95C2311yescharacteristic
337C3×#95C2311yescharacteristic
338C3×#95C2311yescharacteristic
339C3×#95C2311yescharacteristic
340C3×#95C2311yescharacteristic
341C3×#95C2311yescharacteristic
342C3×#95C2311yescharacteristic
343C3×#95C2311yescharacteristic
344C3⋊#95C2311yescharacteristic
345C3⋊#95C2311yescharacteristic
346C3⋊#95C2311yescharacteristic
347C3⋊#95C2311yescharacteristic
348C3⋊#95C2311yescharacteristic
349C3⋊#95C2311yescharacteristic
350C3⋊#95C2311yescharacteristic
351C3⋊#95C2311yescharacteristic
352C3⋊#95C2311yescharacteristic
353C3⋊#95C2311yescharacteristic
354C3⋊#95C2311yescharacteristic
355C3⋊#95C2311yescharacteristic
356C3⋊#95C2311yescharacteristic
357C3⋊#95C2311yescharacteristic
358C3⋊#95C2311yescharacteristic
359C3⋊#95C2311yescharacteristic
360C3⋊#95C2311yescharacteristic
361C3⋊#95C2311yescharacteristic
362C3⋊#95C2311yescharacteristic
363C3⋊#95C2311yescharacteristic
364C3⋊#95C2311yescharacteristic
365C3⋊#95C2311yescharacteristic
366C3⋊#95C2311yescharacteristic
367C3⋊#95C2311yescharacteristic
368C3⋊#95C2311yescharacteristic
369C3⋊#95C2311yescharacteristic
370C3⋊#95C2311yescharacteristic
371C3⋊#95C2311yescharacteristic
372C3⋊#95C2311yescharacteristic
373C3⋊#95C2311yescharacteristic
374C3⋊#95C2311yescharacteristic
375C3⋊#95C2311yescharacteristic
376C3⋊#95C2311yescharacteristic
377C3⋊#95C2311yescharacteristic
378C3⋊#95C2311yescharacteristic
379C3⋊#95C2311yescharacteristic
380C3⋊#95C2311yescharacteristic
381C3⋊#95C2311yescharacteristic
382C3⋊#95C2311yescharacteristic
383C3⋊#95C2311yescharacteristic
384C3⋊#95C2311yescharacteristic
385C3⋊#95C2311yescharacteristic
386C3⋊#95C2311yescharacteristic
387C3⋊#95C2311yescharacteristic
388C2×C4⋊Q8—31no—
389C2×C4⋊Q8—31no—
390C2×C4⋊Q8—31no—
391C2×C4⋊Q8—31no—
392C2×C4⋊Q8—31no—
393C2×C4⋊Q8—31no—
394C2×#125—31no—
395C2×#125—31no—
396C2×C4×Q8—31no—
397C2×C4×Q8—31no—
398C2×C4×Q8—31no—
399C2×C4×Q8—31no—
400C2×C4×Q8—31no—
401C2×C4×Q8—31no—
402#398—31no—
403#398—31no—
404#398—31no—
405#398—31no—
406#398—31no—
407#398—31no—
408#398—31no—
409#398—31no—
410#398—31no—
411#398—31no—
412#398—31no—
413#398—31no—
414#398—31no—
415#398—31no—
416#398—31no—
417#398—31no—
418#398C2×D311yescharacteristic
419#398C2×D311yescharacteristic
420#398C2×D311yescharacteristic
421#398C2×D311yescharacteristic
422#395—31no—
423#395—31no—
424#395—31no—
425#395—31no—
426#395—31no—
427#395—31no—
428#395—31no—
429#395—31no—
430#395—31no—
431#395—31no—
432#395—31no—
433#395—31no—
434#395—31no—
435#395—31no—
436#395—31no—
437#395—31no—
438#395—31no—
439#395—31no—
440#395C2×D311yescharacteristic
441#395C2×D311yescharacteristic
442#391—31no—
443#391—31no—
444#391—31no—
445#391—31no—
446#391—31no—
447#391—31no—
448#391—31no—
449#391—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#391—31no—
461#391—31no—
462#391—31no—
463#391—31no—
464#391—31no—
465#391—31no—
466#391—31no—
467#391—31no—
468#391—31no—
469#391—31no—
470#391C2×D311yescharacteristic
471#391C2×D311yescharacteristic
472#391C2×D311yescharacteristic
473#391C2×D311yescharacteristic
474#389—31no—
475#389—31no—
476#389—31no—
477#389—31no—
478#389—31no—
479#389—31no—
480#389—31no—
481#389—31no—
482#389—31no—
483#389—31no—
484#389—31no—
485#389—31no—
486#389—31no—
487#389—31no—
488#389—31no—
489#389—31no—
490#389—31no—
491#389—31no—
492#389—31no—
493#389—31no—
494#389—31no—
495#389—31no—
496#389—31no—
497#389—31no—
498#389—31no—
499#389—31no—
500#389—31no—
501#389—31no—
502#389—31no—
503#389C2×D311yescharacteristic
504#389C2×D311yescharacteristic
505#389C2×D311yescharacteristic
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#387—31no—
519#387—31no—
520#387C2×D311yescharacteristic
521#387C2×D311yescharacteristic
522#384—31no—
523#384—31no—
524#382—31no—
525#382—31no—
526C4×C4⋊C4—31no—
527C4×C4⋊C4—31no—
528C4×C4⋊C4—31no—
529C4×C4⋊C4—31no—
530C4×C4⋊C4—31no—
531C4×C4⋊C4—31no—
532C4×C4⋊C4—31no—
533C4×C4⋊C4—31no—
534C4×C4⋊C4—31no—
535C4×C4⋊C4—31no—
536C4×C4⋊C4—31no—
537C4×C4⋊C4—31no—
538C4×C4⋊C4—31no—
539C4×C4⋊C4—31no—
540C4×C4⋊C4—31no—
541C4×C4⋊C4—31no—
542#376—31no—
543C2×C3×Q8—41no—
544C2×C3×Q8—41no—
545C2×C3×Q8—41no—
546C2×C3×Q8—41no—
547C2×C3×Q8—41no—
548C2×C3×Q8C2×Q814yes—
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
563C22×C3×C4C2411yescharacteristic
564C22×Dic3C2411yescharacteristic
565C22×Dic3C2411yescharacteristic
566C22×Dic3C2411yescharacteristic
567C22×Dic3C2411yescharacteristic
568C22×Dic3C2411yescharacteristic
569C22×Dic3C2411yescharacteristic
570C22×Dic3C2411yescharacteristic
571C22×Dic3C2411yescharacteristic
572C22×Dic3C2411yescharacteristic
573C22×Dic3C2411yescharacteristic
574C22×Dic3C2411yescharacteristic
575C22×Dic3C2411yescharacteristic
576C22×Dic3C2411yescharacteristic
577C22×Dic3C2411yescharacteristic
578C22×Dic3C2411yescharacteristic
579C22×Dic3C2411yescharacteristic
580C2×Dic6—22no—
581C2×Dic6—22no—
582C2×Dic6—22no—
583C2×Dic6—22no—
584C2×Dic6—41no—
585C2×Dic6—41no—
586C2×Dic6—41no—
587C2×Dic6—41no—
588C2×Dic6—41no—
589C2×Dic6—41no—
590C2×Dic6—41no—
591C2×Dic6—41no—
592C2×Dic6—41no—
593C2×Dic6—41no—
594C2×Dic6—41no—
595C2×Dic6—41no—
596C2×Dic6—41no—
597C2×Dic6—41no—
598C2×Dic6—41no—
599C2×Dic6—41no—
600C2×Dic6—41no—
601C2×Dic6C2×Q814yes—
602C2×Dic6C2×Q814yes—
603C2×Dic6C2×Q814yes—
604C3×C4⋊C4—41no—
605C3×C4⋊C4—41no—
606C3×C4⋊C4—41no—
607C3×C4⋊C4—41no—
608C3×C4⋊C4—41no—
609C3×C4⋊C4—41no—
610C3×C4⋊C4—41no—
611C3×C4⋊C4—41no—
612C3×C4⋊C4—41no—
613C3×C4⋊C4—41no—
614C3×C4⋊C4—41no—
615C3×C4⋊C4—41no—
616C3×C4⋊C4—41no—
617C3×C4⋊C4C2×Q814yes—
618C3×C42—41no—
619C3×C42—41no—
620C3×C42—41no—
621C4⋊Dic3—22no—
622C4⋊Dic3—22no—
623C4⋊Dic3—22no—
624C4⋊Dic3—22no—
625C4⋊Dic3—41no—
626C4⋊Dic3—41no—
627C4⋊Dic3—41no—
628C4⋊Dic3—41no—
629C4⋊Dic3—41no—
630C4⋊Dic3—41no—
631C4⋊Dic3—41no—
632C4⋊Dic3C2×Q814yes—
633Dic3⋊C4—22no—
634Dic3⋊C4—22no—
635Dic3⋊C4—22no—
636Dic3⋊C4—22no—
637Dic3⋊C4—22no—
638Dic3⋊C4—22no—
639Dic3⋊C4—22no—
640Dic3⋊C4—22no—
641Dic3⋊C4—41no—
642Dic3⋊C4—41no—
643Dic3⋊C4—41no—
644Dic3⋊C4—41no—
645Dic3⋊C4—41no—
646Dic3⋊C4—41no—
647Dic3⋊C4—41no—
648Dic3⋊C4—41no—
649Dic3⋊C4—41no—
650Dic3⋊C4—41no—
651Dic3⋊C4—41no—
652Dic3⋊C4—41no—
653Dic3⋊C4—41no—
654Dic3⋊C4—41no—
655Dic3⋊C4—41no—
656Dic3⋊C4—41no—
657Dic3⋊C4—41no—
658Dic3⋊C4—41no—
659Dic3⋊C4—41no—
660Dic3⋊C4—41no—
661Dic3⋊C4—41no—
662Dic3⋊C4—41no—
663Dic3⋊C4C2×Q814yes—
664Dic3⋊C4C2×Q814yes—
665Dic3⋊C4C2×Q814yes—
666Dic3⋊C4C2×Q814yes—
667Dic3⋊C4C2×Q814yes—
668Dic3⋊C4C2×Q814yes—
669C4×Dic3—22no—
670C4×Dic3—22no—
671C4×Dic3—22no—
672C4×Dic3—22no—
673C4×Dic3—22no—
674C4×Dic3—22no—
675C4×Dic3—22no—
676C4×Dic3—41no—
677C4×Dic3—41no—
678C4×Dic3—41no—
679C4×Dic3—41no—
680C4×Dic3—41no—
681C4×Dic3—41no—
682C4×Dic3—41no—
683C4×Dic3—41no—
684C4×Dic3—41no—
685C4×Dic3—41no—
686C4×Dic3—41no—
687C4×Dic3C2×Q814yes—
688C4×Dic3C2×Q814yes—
689C22×Q8—31no—
690C22×Q8—31no—
691C22×Q8—31no—
692C22×Q8—31no—
693C22×Q8—31no—
694C22×Q8—31no—
695C22×Q8—31no—
696C22×Q8—31no—
697C22×Q8C22×D311yescharacteristic
698C22×Q8C22×D311yescharacteristic
699C4⋊Q8—38no—
700C4⋊Q8—38no—
701C4⋊Q8—122no—
702C4⋊Q8—122no—
703C4⋊Q8—122no—
704C4⋊Q8—122no—
705#125—122no—
706#125—122no—
707C4×Q8—122no—
708C4×Q8—122no—
709C4×Q8—122no—
710C4×Q8—122no—
711C4×Q8—122no—
712C4×Q8—122no—
713C2×C4⋊C4—31no—
714C2×C4⋊C4—31no—
715C2×C4⋊C4—31no—
716C2×C4⋊C4—31no—
717C2×C4⋊C4—31no—
718C2×C4⋊C4—31no—
719C2×C4⋊C4—31no—
720C2×C4⋊C4—31no—
721C2×C4⋊C4—31no—
722C2×C4⋊C4—31no—
723C2×C4⋊C4—31no—
724C2×C4⋊C4—31no—
725C2×C4⋊C4—31no—
726C2×C4⋊C4—31no—
727C2×C4⋊C4—31no—
728C2×C4⋊C4—31no—
729C2×C4⋊C4—31no—
730C2×C4⋊C4—31no—
731C2×C4⋊C4—31no—
732C2×C4⋊C4—31no—
733C2×C4⋊C4—31no—
734C2×C4⋊C4—31no—
735C2×C4⋊C4—31no—
736C2×C4⋊C4—31no—
737C2×C4⋊C4—31no—
738C2×C4⋊C4—31no—
739C2×C4⋊C4—31no—
740C2×C4⋊C4—31no—
741C2×C4⋊C4—31no—
742C2×C4⋊C4—31no—
743C2×C4⋊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×C4⋊C4C22×D311yescharacteristic
774C2×C4⋊C4C22×D311yescharacteristic
775C2×C42—31no—
776C2×C42—31no—
777C2×C42—31no—
778C2×C42—31no—
779C2×C42—31no—
780C2×C42—31no—
781C2×C42—31no—
782C2×C42—31no—
783C2×C42—31no—
784C2×C42—31no—
785C2×C42—31no—
786C2×C42—31no—
787C2×C42—31no—
788C2×C42—31no—
789C2×C42—31no—
790C2×C42—31no—
791C2×C42—31no—
792C2×C42—31no—
793C2×C42—31no—
794C2×C42—31no—
795C2×C42C22×D311yescharacteristic
796C2×C42C22×D311yescharacteristic
797C2×C42C22×D311yescharacteristic
798#95—31no—
799#95—31no—
800#95—31no—
801#95—31no—
802#95—31no—
803#95—31no—
804#95—31no—
805#95—31no—
806#95—31no—
807#95—31no—
808#95—31no—
809#95—31no—
810#95—31no—
811#95—31no—
812#95—31no—
813#95—31no—
814#95—31no—
815#95—31no—
816#95—31no—
817#95—31no—
818#95—31no—
819#95—31no—
820#95—31no—
821#95—31no—
822#95—31no—
823#95—31no—
824#95—31no—
825#95—31no—
826#95—31no—
827#95—31no—
828#95—31no—
829#95—31no—
830#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#95C22×D311yescharacteristic
843#95C22×D311yescharacteristic
844#95C22×D311yescharacteristic
845#95C22×D311yescharacteristic
846#95C22×D311yescharacteristic
847#95C22×D311yescharacteristic
848#95C22×D311yescharacteristic
849#95C22×D311yescharacteristic
850#95C22×D311yescharacteristic
851#95C22×D311yescharacteristic
852#95C22×D311yescharacteristic
853#95C22×D311yescharacteristic
854#95C22×D311yescharacteristic
855#95C22×D311yescharacteristic
856#95C22×D311yescharacteristic
857#95C22×D311yescharacteristic
858C23×C3C2511yescharacteristic
859C3×Q8—44no—
860C3×Q8—82no—
861C2×C3×C4—21no—
862C2×C3×C4—21no—
863C2×C3×C4—21no—
864C2×C3×C4—21no—
865C2×C3×C4—21no—
866C2×C3×C4—21no—
867C2×C3×C4—21no—
868C2×C3×C4—21no—
869C2×C3×C4—21no—
870C2×C3×C4—21no—
871C2×C3×C4—21no—
872C2×C3×C4—21no—
873C2×C3×C4—21no—
874C2×C3×C4—21no—
875C2×C3×C4—21no—
876C2×C3×C4—21no—
877C2×C3×C4—21no—
878C2×C3×C4—21no—
879C2×C3×C4—21no—
880C2×C3×C4—21no—
881C2×C3×C4—21no—
882C2×C3×C4—21no—
883C2×C3×C4—21no—
884C2×C3×C4—21no—
885C2×C3×C4—21no—
886C2×C3×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×C4C22×Q812yes—
901C2×C3×C4C22×Q812yes—
902C2×C3×C4C22×Q812yes—
903C2×C3×C4C22×Q812yes—
904C2×C3×C4C22×Q812yes—
905C2×C3×C4C22×Q812yes—
906C2×Dic3—21no—
907C2×Dic3—21no—
908C2×Dic3—21no—
909C2×Dic3—21no—
910C2×Dic3—21no—
911C2×Dic3—21no—
912C2×Dic3—21no—
913C2×Dic3—21no—
914C2×Dic3—21no—
915C2×Dic3—21no—
916C2×Dic3—21no—
917C2×Dic3—21no—
918C2×Dic3—21no—
919C2×Dic3—21no—
920C2×Dic3—21no—
921C2×Dic3—21no—
922C2×Dic3—21no—
923C2×Dic3—21no—
924C2×Dic3—21no—
925C2×Dic3—21no—
926C2×Dic3—21no—
927C2×Dic3—21no—
928C2×Dic3—21no—
929C2×Dic3—21no—
930C2×Dic3—21no—
931C2×Dic3—21no—
932C2×Dic3—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×Dic3C22×Q812yes—
944C2×Dic3C22×Q812yes—
945C2×Dic3C22×Q812yes—
946C2×Dic3C22×Q812yes—
947C2×Dic3C22×Q812yes—
948C2×Dic3C22×Q812yes—
949C2×Dic3C22×Q812yes—
950C2×Dic3C22×Q812yes—
951C2×Dic3H(5,𝔽2)12yes—
952C2×Dic3H(5,𝔽2)12yes—
953C2×Dic32−1+412yes—
954Dic6—44no—
955Dic6—44no—
956Dic6—44no—
957Dic6—44no—
958Dic6—44no—
959Dic6—82no—
960Dic6—82no—
961Dic6—82no—
962C2×Q8—34no—
963C2×Q8—34no—
964C2×Q8—34no—
965C2×Q8—41no—
966C2×Q8—41no—
967C2×Q8—41no—
968C2×Q8—41no—
969C2×Q8—41no—
970C2×Q8—62no—
971C2×Q8—62no—
972C2×Q8—62no—
973C2×Q8—62no—
974C2×Q8—121no—
975C2×Q8—121no—
976C2×Q8—121no—
977C2×Q8—121no—
978C2×Q8—121no—
979C2×Q8—121no—
980C2×Q8—121no—
981C2×Q8—121no—
982C2×Q8—121no—
983C2×Q8—121no—
984C2×Q8—121no—
985C2×Q8—121no—
986C2×Q8—121no—
987C2×Q8—121no—
988C2×Q8—121no—
989C2×Q8—121no—
990C2×Q8—121no—
991C2×Q8D3×Q814yes—
992C22×C4—31no—
993C22×C4—31no—
994C22×C4—31no—
995C22×C4—31no—
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×C4C23×D311yescharacteristic
1009C22×C4C23×D311yescharacteristic
1010C22×C4C23×D311yescharacteristic
1011C22×C4C23×D311yescharacteristic
1012C22×C4C23×D311yescharacteristic
1013C22×C4C23×D311yescharacteristic
1014C22×C4C23×D311yescharacteristic
1015C22×C4C23×D311yescharacteristic
1016C22×C4C23×D311yescharacteristic
1017C22×C4C23×D311yescharacteristic
1018C22×C4C23×D311yescharacteristic
1019C22×C4C23×D311yescharacteristic
1020C22×C4C23×D311yescharacteristic
1021C22×C4C23×D311yescharacteristic
1022C22×C4C23×D311yescharacteristic
1023C4⋊C4—34no—
1024C4⋊C4—34no—
1025C4⋊C4—34no—
1026C4⋊C4—34no—
1027C4⋊C4—34no—
1028C4⋊C4—34no—
1029C4⋊C4—34no—
1030C4⋊C4—41no—
1031C4⋊C4—41no—
1032C4⋊C4—41no—
1033C4⋊C4—41no—
1034C4⋊C4—41no—
1035C4⋊C4—41no—
1036C4⋊C4—41no—
1037C4⋊C4—41no—
1038C4⋊C4—41no—
1039C4⋊C4—41no—
1040C4⋊C4—41no—
1041C4⋊C4—41no—
1042C4⋊C4—41no—
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—121no—
1056C4⋊C4—121no—
1057C4⋊C4—121no—
1058C4⋊C4—121no—
1059C4⋊C4—121no—
1060C4⋊C4—121no—
1061C4⋊C4—121no—
1062C4⋊C4—121no—
1063C4⋊C4—121no—
1064C4⋊C4—121no—
1065C4⋊C4—121no—
1066C4⋊C4—121no—
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—
1082C4⋊C4—121no—
1083C4⋊C4—121no—
1084C4⋊C4D3×Q814yes—
1085C42—34no—
1086C42—34no—
1087C42—41no—
1088C42—41no—
1089C42—41no—
1090C42—62no—
1091C42—62no—
1092C42—62no—
1093C42—62no—
1094C42—62no—
1095C42—62no—
1096C42—62no—
1097C42—121no—
1098C42—121no—
1099C42—121no—
1100C42—121no—
1101C42—121no—
1102C42—121no—
1103C42—121no—
1104C42—121no—
1105C42—121no—
1106C42—121no—
1107C42—121no—
1108C22×C3C23×Q811yescharacteristic
1109C22×C3C23×Q811yescharacteristic
1110C22×C3C2×H(5,𝔽2)11yescharacteristic
1111C22×C3C2×H(5,𝔽2)11yescharacteristic
1112C22×C3C2×2−1+411yescharacteristic
1113C22×C3#58511yescharacteristic
1114C22×C3#58511yescharacteristic
1115C3×C4—22no—
1116C3×C4—22no—
1117C3×C4—22no—
1118C3×C4—22no—
1119C3×C4—22no—
1120C3×C4—22no—
1121C3×C4—41no—
1122C3×C4—41no—
1123C3×C4—41no—
1124C3×C4—41no—
1125C3×C4—41no—
1126C3×C4—41no—
1127C3×C4—41no—
1128C3×C4—41no—
1129C3×C4—41no—
1130Dic3—22no—
1131Dic3—22no—
1132Dic3—22no—
1133Dic3—22no—
1134Dic3—22no—
1135Dic3—22no—
1136Dic3—22no—
1137Dic3—22no—
1138Dic3—41no—
1139Dic3—41no—
1140Dic3—41no—
1141Dic3—41no—
1142Dic3—41no—
1143Dic3—41no—
1144Dic3—41no—
1145Dic3Q8214yes—
1146C23C24×D311yescharacteristic
1147Q8—44no—
1148Q8—82no—
1149Q8—124no—
1150Q8—124no—
1151Q8—124no—
1152Q8—124no—
1153Q8—124no—
1154Q8—242no—
1155Q8—242no—
1156Q8—242no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—32no—
1197C2×C4—32no—
1198C2×C4—32no—
1199C2×C4—32no—
1200C2×C4—32no—
1201C2×C4—32no—
1202C2×C4—32no—
1203C2×C4—32no—
1204C2×C4—32no—
1205C2×C4—32no—
1206C2×C4—32no—
1207C2×C4—61no—
1208C2×C4—61no—
1209C2×C4—61no—
1210C2×C4—61no—
1211C2×C4—61no—
1212C2×C4—61no—
1213C2×C4—61no—
1214C2×C4—61no—
1215C2×C4—61no—
1216C2×C4—61no—
1217C2×C4—61no—
1218C2×C4—61no—
1219C2×C4—61no—
1220C2×C4—61no—
1221C2×C4—61no—
1222C2×C4—61no—
1223C2×C4—61no—
1224C2×C4—61no—
1225C2×C4—61no—
1226C2×C4—61no—
1227C2×C4—61no—
1228C2×C4—61no—
1229C2×C4—61no—
1230C2×C4—61no—
1231C2×C4—61no—
1232C2×C4—61no—
1233C2×C4—61no—
1234C2×C4—61no—
1235C2×C4—61no—
1236C2×C4—61no—
1237C2×C4—61no—
1238C2×C4—61no—
1239C2×C4—61no—
1240C2×C4—61no—
1241C2×C4—61no—
1242C2×C4—61no—
1243C2×C4—61no—
1244C2×C4C2×D3×Q812yes—
1245C2×C4C2×D3×Q812yes—
1246C2×C4C2×D3×Q812yes—
1247C2×C4C2×D3×Q812yes—
1248C2×C4C2×D3×Q812yes—
1249C2×C4C2×D3×Q812yes—
1250C2×C3C2×Q8211yescharacteristic
1251C2×C3#350111yescharacteristic
1252C2×C3#350111yescharacteristic
1253C2×C3#350211yescharacteristic
1254C2×C3#350211yescharacteristic
1255C2×C3#353611yescharacteristic
1256C2×C3#354011yescharacteristic
1257C22C22×D3×Q811yescharacteristic
1258C22C22×D3×Q811yescharacteristic
1259C22#596411yescharacteristic
1260C22D3×H(5,𝔽2)11yescharacteristic
1261C22D3×H(5,𝔽2)11yescharacteristic
1262C22#596611yescharacteristic
1263C22D3×2−1+411yescharacteristic
1264C4—22no—
1265C4—22no—
1266C4—22no—
1267C4—22no—
1268C4—22no—
1269C4—22no—
1270C4—34no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—41no—
1278C4—41no—
1279C4—41no—
1280C4—62no—
1281C4—62no—
1282C4—62no—
1283C4—62no—
1284C4—62no—
1285C4—62no—
1286C4—62no—
1287C4—62no—
1288C4—121no—
1289C4—121no—
1290C4—121no—
1291C4—121no—
1292C4—121no—
1293C4—121no—
1294C4—121no—
1295C3#4536411yescharacteristic, complemented, Sylow
1296C2#8639711yescharacteristic
1297C2#8657411yescharacteristic
1298C2#8658511yescharacteristic
1299C2#8694911yescharacteristic
1300C2#8703211yescharacteristic
1301C2D3×Q8211yescharacteristic
1302C2#8709511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, prime radical, cosocleC23×C3C25
FittingC3×#2806C2
hypercenter#2806D3
hypocenterC3#45364
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2806

Complements

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

NH ≅ G/Ntype
248. #944Q8semidirect
322. #888Q8semidirect
1295. C3#45364semidirect

Maximal subgroups

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

subgroupindex
C3×#28062
#779222
#779212
#779132
#777972
#777862
#777852
#777482
#777402
#772402
#772392
#771892
#771852
#766042
#765502
#765482
#765372
#765092
#764942
#764922
#764862
#761692
#760802
#760772
#760632
#760082
#759872
#750972
#749872
#749672
#749502
#453643