Finite Group Databasebeta

← #11233820

Subgroups — #11233820

Order 768.

1502 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2462C211yesmaximal, characteristic
2#83034C211yesmaximal, characteristic
3#83029C211yesmaximal, characteristic
4#82480C211yesmaximal, characteristic
5Q8×Dic3⋊C4C211yesmaximal, characteristic
6#77921C211yesmaximal, characteristic
7#77807C211yesmaximal, characteristic
8#77793C211yesmaximal, characteristic
9#77768C211yesmaximal, characteristic
10#77192C211yesmaximal, characteristic
11#77191C211yesmaximal, characteristic
12#77177C211yesmaximal, characteristic
13#77171C211yesmaximal, characteristic
14#76186C211yesmaximal, characteristic
15#76176C211yesmaximal, characteristic
16#76080C211yesmaximal, characteristic
17#75973C211yesmaximal, characteristic
18#75283C211yesmaximal, characteristic
19#75281C211yesmaximal, characteristic
20#75274C211yesmaximal, characteristic
21#75224C211yesmaximal, characteristic
22#75223C211yesmaximal, characteristic
23#75077C211yesmaximal, characteristic
24#75029C211yesmaximal, characteristic
25#75028C211yesmaximal, characteristic
26#74988C211yesmaximal, characteristic
27#74967C211yesmaximal, characteristic
28#74963C211yesmaximal, characteristic
29#74950C211yesmaximal, characteristic
30#73734C211yesmaximal, characteristic
31#73657C211yesmaximal, characteristic
32#45363—31nomaximal, Sylow
33C2×C3×#125C2211yescharacteristic
34C2×C3×C4×Q8C2211yescharacteristic
35C2×Q8×Dic3C2211yescharacteristic
36C2×Q8×Dic3C2211yescharacteristic
37C2×#889C2211yescharacteristic
38C2×#889C2211yescharacteristic
39C2×#888C2211yescharacteristic
40C2×#887C2211yescharacteristic
41C2×#887C2211yescharacteristic
42C2×C4×Dic6C2211yescharacteristic
43C3×#398C2211yescharacteristic
44C3×#398C2211yescharacteristic
45C3×#395C2211yescharacteristic
46C3×#395C2211yescharacteristic
47C3×#389C2211yescharacteristic
48C3×#389C2211yescharacteristic
49C3×#387C2211yescharacteristic
50C3×#387C2211yescharacteristic
51C3×#387C2211yescharacteristic
52C3×#387C2211yescharacteristic
53C3×#387C2211yescharacteristic
54C3×#387C2211yescharacteristic
55C3×C4×C4⋊C4C2211yescharacteristic
56#5230C2211yescharacteristic
57#5230C2211yescharacteristic
58#4986C2211yescharacteristic
59#4985C2211yescharacteristic
60#4985C2211yescharacteristic
61#4985C2211yescharacteristic
62#4984C2211yescharacteristic
63#4984C2211yescharacteristic
64#4984C2211yescharacteristic
65#4983C2211yescharacteristic
66#4983C2211yescharacteristic
67#4982C2211yescharacteristic
68#4982C2211yescharacteristic
69#4982C2211yescharacteristic
70#4982C2211yescharacteristic
71#4982C2211yescharacteristic
72#4982C2211yescharacteristic
73#4981C2211yescharacteristic
74#4981C2211yescharacteristic
75#4981C2211yescharacteristic
76#4980C2211yescharacteristic
77#4980C2211yescharacteristic
78#4980C2211yescharacteristic
79#4980C2211yescharacteristic
80#4980C2211yescharacteristic
81#4979C2211yescharacteristic
82#4978C2211yescharacteristic
83#4978C2211yescharacteristic
84#4978C2211yescharacteristic
85#4978C2211yescharacteristic
86#4978C2211yescharacteristic
87#4978C2211yescharacteristic
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#4976C2211yescharacteristic
101#4975C2211yescharacteristic
102#4975C2211yescharacteristic
103#4975C2211yescharacteristic
104Dic3×C4⋊C4C2211yescharacteristic
105Dic3×C4⋊C4C2211yescharacteristic
106Dic3×C4⋊C4C2211yescharacteristic
107#4973C2211yescharacteristic
108#4972C2211yescharacteristic
109#4972C2211yescharacteristic
110#4972C2211yescharacteristic
111#4972C2211yescharacteristic
112#4972C2211yescharacteristic
113#4936C2211yescharacteristic
114#4933C2211yescharacteristic
115#4933C2211yescharacteristic
116#4933C2211yescharacteristic
117C4×Dic3⋊C4C2211yescharacteristic
118C4×Dic3⋊C4C2211yescharacteristic
119C4×Dic3⋊C4C2211yescharacteristic
120C4×Dic3⋊C4C2211yescharacteristic
121C4×Dic3⋊C4C2211yescharacteristic
122C4×Dic3⋊C4C2211yescharacteristic
123#4929C2211yescharacteristic
124#4929C2211yescharacteristic
125#4929C2211yescharacteristic
126#4928C2211yescharacteristic
127#4928C2211yescharacteristic
128#4928C2211yescharacteristic
129#4928C2211yescharacteristic
130#4928C2211yescharacteristic
131#4928C2211yescharacteristic
132#4661C2211yescharacteristic
133#4661C2211yescharacteristic
134#4661C2211yescharacteristic
135#4660C2211yescharacteristic
136#4660C2211yescharacteristic
137#4660C2211yescharacteristic
138#4660C2211yescharacteristic
139#4660C2211yescharacteristic
140#4659C2211yescharacteristic
141#4659C2211yescharacteristic
142#4658C2211yescharacteristic
143#4657C2211yescharacteristic
144#4657C2211yescharacteristic
145#4657C2211yescharacteristic
146#4657C2211yescharacteristic
147#4656C2211yescharacteristic
148#4656C2211yescharacteristic
149#4656C2211yescharacteristic
150#4655C2211yescharacteristic
151#4655C2211yescharacteristic
152#4654C2211yescharacteristic
153#4654C2211yescharacteristic
154#4654C2211yescharacteristic
155#4654C2211yescharacteristic
156#4654C2211yescharacteristic
157#4653C2211yescharacteristic
158#4653C2211yescharacteristic
159#4652C2211yescharacteristic
160#4652C2211yescharacteristic
161#4650C2211yescharacteristic
162#4650C2211yescharacteristic
163#4650C2211yescharacteristic
164#4650C2211yescharacteristic
165#4649C2211yescharacteristic
166#4649C2211yescharacteristic
167#4649C2211yescharacteristic
168#4649C2211yescharacteristic
169#4649C2211yescharacteristic
170#4649C2211yescharacteristic
171#4648C2211yescharacteristic
172#4647C2211yescharacteristic
173#4647C2211yescharacteristic
174#4647C2211yescharacteristic
175#4647C2211yescharacteristic
176#4647C2211yescharacteristic
177#4647C2211yescharacteristic
178#4647C2211yescharacteristic
179#4647C2211yescharacteristic
180#4646C2211yescharacteristic
181#4646C2211yescharacteristic
182#4646C2211yescharacteristic
183#4646C2211yescharacteristic
184#4646C2211yescharacteristic
185#4646C2211yescharacteristic
186#4646C2211yescharacteristic
187#4646C2211yescharacteristic
188#2809—31no—
189#2809—31no—
190#2806—31no—
191#2806—31no—
192#2802—31no—
193#2802—31no—
194#2774—31no—
195#2774—31no—
196#2590—31no—
197#2590—31no—
198#2584—31no—
199#2584—31no—
200#2581—31no—
201#2581—31no—
202#2570—31no—
203#2570—31no—
204#2509—31no—
205#2508—31no—
206#2507—31no—
207#2506—31no—
208#2462—31no—
209#2462D311yescharacteristic
210#2453—31no—
211#2453—31no—
212#2399—31no—
213#2369—31no—
214#2365—31no—
215#2355—31no—
216Q8×C4⋊C4—31no—
217#2331—31no—
218#2330—31no—
219C22×C3×Q8C2311yescharacteristic
220C22×Dic6C2311yescharacteristic
221C22×Dic6C2311yescharacteristic
222C22×Dic6C2311yescharacteristic
223C3×#125—42no—
224C3×C4×Q8—42no—
225C2×C3×C4⋊C4C2311yescharacteristic
226C2×C3×C4⋊C4C2311yescharacteristic
227C2×C3×C4⋊C4C2311yescharacteristic
228C2×C3×C4⋊C4C2311yescharacteristic
229C2×C3×C4⋊C4C2311yescharacteristic
230C2×C3×C4⋊C4C2311yescharacteristic
231C2×C3×C4⋊C4C2311yescharacteristic
232C2×C3×C4⋊C4C2311yescharacteristic
233C2×C3×C4⋊C4C2311yescharacteristic
234C2×C3×C4⋊C4C2311yescharacteristic
235C2×C3×C4⋊C4C2311yescharacteristic
236C2×C3×C4⋊C4C2311yescharacteristic
237C2×C3×C4⋊C4C2311yescharacteristic
238C2×C3×C4⋊C4C2311yescharacteristic
239C2×C3×C4⋊C4C2311yescharacteristic
240C2×C3×C42C2311yescharacteristic
241C2×C3×C42C2311yescharacteristic
242C2×C3×C42C2311yescharacteristic
243C2×C3×C42C2311yescharacteristic
244C2×C3×C42C2311yescharacteristic
245Q8×Dic3—24no—
246Q8×Dic3—42no—
247C2×C4⋊Dic3C2311yescharacteristic
248C2×C4⋊Dic3C2311yescharacteristic
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×C4⋊Dic3C2311yescharacteristic
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×C4×Dic3C2311yescharacteristic
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
314#889—24no—
315#889—42no—
316#888Q818yescomplemented
317#887—24no—
318#887—42no—
319C4×Dic6—42no—
320C3×#95C2311yescharacteristic
321C3×#95C2311yescharacteristic
322C3×#95C2311yescharacteristic
323C3×#95C2311yescharacteristic
324C3×#95C2311yescharacteristic
325C3×#95C2311yescharacteristic
326C3×#95C2311yescharacteristic
327C3×#95C2311yescharacteristic
328C3×#95C2311yescharacteristic
329C3×#95C2311yescharacteristic
330C3×#95C2311yescharacteristic
331C3×#95C2311yescharacteristic
332C3×#95C2311yescharacteristic
333C3×#95C2311yescharacteristic
334C3⋊#95C2311yescharacteristic
335C3⋊#95C2311yescharacteristic
336C3⋊#95C2311yescharacteristic
337C3⋊#95C2311yescharacteristic
338C3⋊#95C2311yescharacteristic
339C3⋊#95C2311yescharacteristic
340C3⋊#95C2311yescharacteristic
341C3⋊#95C2311yescharacteristic
342C3⋊#95C2311yescharacteristic
343C3⋊#95C2311yescharacteristic
344C3⋊#95C2311yescharacteristic
345C3⋊#95C2311yescharacteristic
346C3⋊#95C2311yescharacteristic
347C3⋊#95C2311yescharacteristic
348C3⋊#95C2311yescharacteristic
349C3⋊#95C2311yescharacteristic
350C3⋊#95C2311yescharacteristic
351C3⋊#95C2311yescharacteristic
352C3⋊#95C2311yescharacteristic
353C3⋊#95C2311yescharacteristic
354C3⋊#95C2311yescharacteristic
355C3⋊#95C2311yescharacteristic
356C3⋊#95C2311yescharacteristic
357C3⋊#95C2311yescharacteristic
358C3⋊#95C2311yescharacteristic
359C3⋊#95C2311yescharacteristic
360C3⋊#95C2311yescharacteristic
361C3⋊#95C2311yescharacteristic
362C3⋊#95C2311yescharacteristic
363C3⋊#95C2311yescharacteristic
364C3⋊#95C2311yescharacteristic
365C3⋊#95C2311yescharacteristic
366C3⋊#95C2311yescharacteristic
367C3⋊#95C2311yescharacteristic
368C3⋊#95C2311yescharacteristic
369C3⋊#95C2311yescharacteristic
370C3⋊#95C2311yescharacteristic
371C3⋊#95C2311yescharacteristic
372C3⋊#95C2311yescharacteristic
373C3⋊#95C2311yescharacteristic
374C3⋊#95C2311yescharacteristic
375C3⋊#95C2311yescharacteristic
376C3⋊#95C2311yescharacteristic
377C3⋊#95C2311yescharacteristic
378C3⋊#95C2311yescharacteristic
379C3⋊#95C2311yescharacteristic
380C3⋊#95C2311yescharacteristic
381C3⋊#95C2311yescharacteristic
382C3⋊#95C2311yescharacteristic
383C3⋊#95C2311yescharacteristic
384C2×C4⋊Q8—31no—
385C2×#125—31no—
386C2×#125—31no—
387C2×#125C2×D311yescharacteristic
388C2×C4×Q8—31no—
389C2×C4×Q8—31no—
390C2×C4×Q8—31no—
391C2×C4×Q8—31no—
392C2×C4×Q8—31no—
393C2×C4×Q8C2×D311yescharacteristic
394#400—31no—
395#400—31no—
396#400—31no—
397#400—31no—
398#400—31no—
399#400—31no—
400#400—31no—
401#400—31no—
402#400—31no—
403#400—31no—
404#400—31no—
405#400—31no—
406#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#398—31no—
419#398—31no—
420#398—31no—
421#398—31no—
422#398—31no—
423#398—31no—
424#398C2×D311yescharacteristic
425#398C2×D311yescharacteristic
426#395—31no—
427#395—31no—
428#395—31no—
429#395—31no—
430#395—31no—
431#395—31no—
432#395C2×D311yescharacteristic
433#395C2×D311yescharacteristic
434#391—31no—
435#391—31no—
436#391—31no—
437#391—31no—
438#391—31no—
439#391—31no—
440#391—31no—
441#391—31no—
442#391—31no—
443#391—31no—
444#391—31no—
445#391—31no—
446#389—31no—
447#389—31no—
448#389—31no—
449#389—31no—
450#389—31no—
451#389—31no—
452#389—31no—
453#389—31no—
454#389—31no—
455#389—31no—
456#389—31no—
457#389—31no—
458#389—31no—
459#389—31no—
460#389—31no—
461#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#389—31no—
478#389—31no—
479#389—31no—
480#389C2×D311yescharacteristic
481#389C2×D311yescharacteristic
482#387—31no—
483#387—31no—
484#387—31no—
485#387—31no—
486#387—31no—
487#387—31no—
488#387—31no—
489#387—31no—
490#387—31no—
491#387—31no—
492#387—31no—
493#387—31no—
494#387—31no—
495#387—31no—
496#387—31no—
497#387—31no—
498#387—31no—
499#387—31no—
500#387—31no—
501#387—31no—
502#387—31no—
503#387—31no—
504#387—31no—
505#387—31no—
506#387—31no—
507#387—31no—
508#387C2×D311yescharacteristic
509#387C2×D311yescharacteristic
510#387C2×D311yescharacteristic
511#387C2×D311yescharacteristic
512#387C2×D311yescharacteristic
513#387C2×D311yescharacteristic
514#384—31no—
515#384—31no—
516#384—31no—
517#382—31no—
518#382—31no—
519#382—31no—
520#382—31no—
521#382—31no—
522C4×C4⋊C4—31no—
523C4×C4⋊C4—31no—
524C4×C4⋊C4—31no—
525C4×C4⋊C4—31no—
526C4×C4⋊C4—31no—
527C4×C4⋊C4—31no—
528C4×C4⋊C4—31no—
529C4×C4⋊C4—31no—
530C4×C4⋊C4—31no—
531C4×C4⋊C4—31no—
532C4×C4⋊C4—31no—
533C4×C4⋊C4—31no—
534C4×C4⋊C4—31no—
535C4×C4⋊C4—31no—
536C4×C4⋊C4—31no—
537C4×C4⋊C4C2×D311yescharacteristic
538#376—31no—
539C2×C3×Q8—22no—
540C2×C3×Q8—22no—
541C2×C3×Q8—22no—
542C22×C3×C4C2411yescharacteristic
543C22×C3×C4C2411yescharacteristic
544C22×C3×C4C2411yescharacteristic
545C22×C3×C4C2411yescharacteristic
546C22×C3×C4C2411yescharacteristic
547C22×C3×C4C2411yescharacteristic
548C22×C3×C4C2411yescharacteristic
549C22×C3×C4C2411yescharacteristic
550C22×C3×C4C2411yescharacteristic
551C22×C3×C4C2411yescharacteristic
552C22×C3×C4C2411yescharacteristic
553C22×C3×C4C2411yescharacteristic
554C22×C3×C4C2411yescharacteristic
555C22×C3×C4C2411yescharacteristic
556C22×C3×C4C2411yescharacteristic
557C22×Dic3C2411yescharacteristic
558C22×Dic3C2411yescharacteristic
559C22×Dic3C2411yescharacteristic
560C22×Dic3C2411yescharacteristic
561C22×Dic3C2411yescharacteristic
562C22×Dic3C2411yescharacteristic
563C22×Dic3C2411yescharacteristic
564C22×Dic3C2411yescharacteristic
565C22×Dic3C2411yescharacteristic
566C22×Dic3C2411yescharacteristic
567C22×Dic3C2411yescharacteristic
568C22×Dic3C2411yescharacteristic
569C22×Dic3C2411yescharacteristic
570C22×Dic3C2411yescharacteristic
571C22×Dic3C2411yescharacteristic
572C22×Dic3C2411yescharacteristic
573C2×Dic6—22no—
574C2×Dic6—41no—
575C2×Dic6—41no—
576C2×Dic6—41no—
577C2×Dic6—41no—
578C2×Dic6—41no—
579C2×Dic6—41no—
580C2×Dic6C2×Q814yes—
581C2×Dic6C2×Q814yes—
582C3×C4⋊C4—22no—
583C3×C4⋊C4—22no—
584C3×C4⋊C4—22no—
585C3×C4⋊C4—22no—
586C3×C4⋊C4—22no—
587C3×C4⋊C4—22no—
588C3×C4⋊C4—22no—
589C3×C4⋊C4—41no—
590C3×C4⋊C4—41no—
591C3×C4⋊C4—41no—
592C3×C4⋊C4—41no—
593C3×C4⋊C4—41no—
594C3×C4⋊C4—41no—
595C3×C4⋊C4—41no—
596C3×C4⋊C4C2×Q814yes—
597C3×C42—22no—
598C3×C42—41no—
599C3×C42—41no—
600C3×C42—41no—
601C3×C42—41no—
602C4⋊Dic3—22no—
603C4⋊Dic3—22no—
604C4⋊Dic3—22no—
605C4⋊Dic3—22no—
606C4⋊Dic3—22no—
607C4⋊Dic3—41no—
608C4⋊Dic3—41no—
609C4⋊Dic3—41no—
610C4⋊Dic3—41no—
611C4⋊Dic3—41no—
612C4⋊Dic3—41no—
613C4⋊Dic3—41no—
614C4⋊Dic3—41no—
615C4⋊Dic3—41no—
616C4⋊Dic3C2×Q814yes—
617Dic3⋊C4—22no—
618Dic3⋊C4—22no—
619Dic3⋊C4—22no—
620Dic3⋊C4—22no—
621Dic3⋊C4—22no—
622Dic3⋊C4—22no—
623Dic3⋊C4—22no—
624Dic3⋊C4—22no—
625Dic3⋊C4—22no—
626Dic3⋊C4—22no—
627Dic3⋊C4—22no—
628Dic3⋊C4—22no—
629Dic3⋊C4—22no—
630Dic3⋊C4—22no—
631Dic3⋊C4—41no—
632Dic3⋊C4—41no—
633Dic3⋊C4—41no—
634Dic3⋊C4—41no—
635Dic3⋊C4—41no—
636Dic3⋊C4—41no—
637Dic3⋊C4—41no—
638Dic3⋊C4—41no—
639Dic3⋊C4—41no—
640Dic3⋊C4—41no—
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⋊C4C2×Q814yes—
650Dic3⋊C4C2×Q814yes—
651C4×Dic3—22no—
652C4×Dic3—22no—
653C4×Dic3—22no—
654C4×Dic3—22no—
655C4×Dic3—22no—
656C4×Dic3—22no—
657C4×Dic3—41no—
658C4×Dic3—41no—
659C4×Dic3—41no—
660C4×Dic3—41no—
661C4×Dic3—41no—
662C4×Dic3—41no—
663C4×Dic3—41no—
664C4×Dic3—41no—
665C4×Dic3—41no—
666C4×Dic3—41no—
667C4×Dic3C2×Q814yes—
668C4×Dic3#4114yes—
669C22×Q8—31no—
670C22×Q8—31no—
671C22×Q8—31no—
672C22×Q8C22×D311yescharacteristic
673C4⋊Q8—38no—
674#125—42no—
675#125—64no—
676#125—122no—
677C4×Q8—42no—
678C4×Q8—64no—
679C4×Q8—64no—
680C4×Q8—122no—
681C4×Q8—122no—
682C4×Q8—122no—
683C2×C4⋊C4—31no—
684C2×C4⋊C4—31no—
685C2×C4⋊C4—31no—
686C2×C4⋊C4—31no—
687C2×C4⋊C4—31no—
688C2×C4⋊C4—31no—
689C2×C4⋊C4—31no—
690C2×C4⋊C4—31no—
691C2×C4⋊C4—31no—
692C2×C4⋊C4—31no—
693C2×C4⋊C4—31no—
694C2×C4⋊C4—31no—
695C2×C4⋊C4—31no—
696C2×C4⋊C4—31no—
697C2×C4⋊C4—31no—
698C2×C4⋊C4—31no—
699C2×C4⋊C4—31no—
700C2×C4⋊C4—31no—
701C2×C4⋊C4—31no—
702C2×C4⋊C4—31no—
703C2×C4⋊C4—31no—
704C2×C4⋊C4—31no—
705C2×C4⋊C4—31no—
706C2×C4⋊C4—31no—
707C2×C4⋊C4—31no—
708C2×C4⋊C4—31no—
709C2×C4⋊C4—31no—
710C2×C4⋊C4—31no—
711C2×C4⋊C4—31no—
712C2×C4⋊C4—31no—
713C2×C4⋊C4—31no—
714C2×C4⋊C4—31no—
715C2×C4⋊C4—31no—
716C2×C4⋊C4—31no—
717C2×C4⋊C4—31no—
718C2×C4⋊C4—31no—
719C2×C4⋊C4—31no—
720C2×C4⋊C4—31no—
721C2×C4⋊C4—31no—
722C2×C4⋊C4—31no—
723C2×C4⋊C4—31no—
724C2×C4⋊C4—31no—
725C2×C4⋊C4—31no—
726C2×C4⋊C4—31no—
727C2×C4⋊C4—31no—
728C2×C4⋊C4—31no—
729C2×C4⋊C4—31no—
730C2×C4⋊C4—31no—
731C2×C4⋊C4—31no—
732C2×C4⋊C4C22×D311yescharacteristic
733C2×C4⋊C4C22×D311yescharacteristic
734C2×C4⋊C4C22×D311yescharacteristic
735C2×C4⋊C4C22×D311yescharacteristic
736C2×C4⋊C4C22×D311yescharacteristic
737C2×C4⋊C4C22×D311yescharacteristic
738C2×C4⋊C4C22×D311yescharacteristic
739C2×C4⋊C4C22×D311yescharacteristic
740C2×C4⋊C4C22×D311yescharacteristic
741C2×C4⋊C4C22×D311yescharacteristic
742C2×C4⋊C4C22×D311yescharacteristic
743C2×C4⋊C4C22×D311yescharacteristic
744C2×C4⋊C4C22×D311yescharacteristic
745C2×C4⋊C4C22×D311yescharacteristic
746C2×C4⋊C4C22×D311yescharacteristic
747C2×C42—31no—
748C2×C42—31no—
749C2×C42—31no—
750C2×C42—31no—
751C2×C42—31no—
752C2×C42—31no—
753C2×C42—31no—
754C2×C42—31no—
755C2×C42—31no—
756C2×C42—31no—
757C2×C42—31no—
758C2×C42—31no—
759C2×C42—31no—
760C2×C42—31no—
761C2×C42—31no—
762C2×C42—31no—
763C2×C42—31no—
764C2×C42—31no—
765C2×C42C22×D311yescharacteristic
766C2×C42C22×D311yescharacteristic
767C2×C42C22×D311yescharacteristic
768C2×C42C22×D311yescharacteristic
769C2×C42C22×D311yescharacteristic
770#95—31no—
771#95—31no—
772#95—31no—
773#95—31no—
774#95—31no—
775#95—31no—
776#95—31no—
777#95—31no—
778#95—31no—
779#95—31no—
780#95—31no—
781#95—31no—
782#95—31no—
783#95—31no—
784#95—31no—
785#95—31no—
786#95—31no—
787#95—31no—
788#95—31no—
789#95—31no—
790#95—31no—
791#95—31no—
792#95—31no—
793#95—31no—
794#95—31no—
795#95—31no—
796#95—31no—
797#95—31no—
798#95—31no—
799#95—31no—
800#95—31no—
801#95—31no—
802#95—31no—
803#95—31no—
804#95—31no—
805#95—31no—
806#95—31no—
807#95—31no—
808#95—31no—
809#95—31no—
810#95—31no—
811#95—31no—
812#95—31no—
813#95—31no—
814#95—31no—
815#95—31no—
816#95—31no—
817#95—31no—
818#95—31no—
819#95—31no—
820#95C22×D311yescharacteristic
821#95C22×D311yescharacteristic
822#95C22×D311yescharacteristic
823#95C22×D311yescharacteristic
824#95C22×D311yescharacteristic
825#95C22×D311yescharacteristic
826#95C22×D311yescharacteristic
827#95C22×D311yescharacteristic
828#95C22×D311yescharacteristic
829#95C22×D311yescharacteristic
830#95C22×D311yescharacteristic
831#95C22×D311yescharacteristic
832#95C22×D311yescharacteristic
833#95C22×D311yescharacteristic
834C23×C3C2511yescharacteristic
835C3×Q8—28no—
836C2×C3×C4—21no—
837C2×C3×C4—21no—
838C2×C3×C4—21no—
839C2×C3×C4—21no—
840C2×C3×C4—21no—
841C2×C3×C4—21no—
842C2×C3×C4—21no—
843C2×C3×C4—21no—
844C2×C3×C4—21no—
845C2×C3×C4—21no—
846C2×C3×C4—21no—
847C2×C3×C4—21no—
848C2×C3×C4—21no—
849C2×C3×C4—21no—
850C2×C3×C4—21no—
851C2×C3×C4—21no—
852C2×C3×C4—21no—
853C2×C3×C4—21no—
854C2×C3×C4—21no—
855C2×C3×C4—21no—
856C2×C3×C4—21no—
857C2×C3×C4—21no—
858C2×C3×C4—21no—
859C2×C3×C4—21no—
860C2×C3×C4—21no—
861C2×C3×C4—21no—
862C2×C3×C4—21no—
863C2×C3×C4—21no—
864C2×C3×C4—21no—
865C2×C3×C4—21no—
866C2×C3×C4—21no—
867C2×C3×C4—21no—
868C2×C3×C4—21no—
869C2×C3×C4—21no—
870C2×C3×C4—21no—
871C2×C3×C4—21no—
872C2×C3×C4—21no—
873C2×C3×C4—21no—
874C2×C3×C4—21no—
875C2×C3×C4C22×Q812yes—
876C2×C3×C4C22×Q812yes—
877C2×C3×C4C22×Q812yes—
878C2×C3×C4C2×#4112yes—
879C2×C3×C4H(5,𝔽2)12yes—
880C2×C3×C42−1+412yes—
881C2×Dic3—21no—
882C2×Dic3—21no—
883C2×Dic3—21no—
884C2×Dic3—21no—
885C2×Dic3—21no—
886C2×Dic3—21no—
887C2×Dic3—21no—
888C2×Dic3—21no—
889C2×Dic3—21no—
890C2×Dic3—21no—
891C2×Dic3—21no—
892C2×Dic3—21no—
893C2×Dic3—21no—
894C2×Dic3—21no—
895C2×Dic3—21no—
896C2×Dic3—21no—
897C2×Dic3—21no—
898C2×Dic3—21no—
899C2×Dic3—21no—
900C2×Dic3—21no—
901C2×Dic3—21no—
902C2×Dic3—21no—
903C2×Dic3—21no—
904C2×Dic3—21no—
905C2×Dic3—21no—
906C2×Dic3—21no—
907C2×Dic3—21no—
908C2×Dic3—21no—
909C2×Dic3—21no—
910C2×Dic3—21no—
911C2×Dic3—21no—
912C2×Dic3—21no—
913C2×Dic3—21no—
914C2×Dic3—21no—
915C2×Dic3—21no—
916C2×Dic3—21no—
917C2×Dic3—21no—
918C2×Dic3—21no—
919C2×Dic3—21no—
920C2×Dic3—21no—
921C2×Dic3—21no—
922C2×Dic3C22×Q812yes—
923C2×Dic3C22×Q812yes—
924C2×Dic3C22×Q812yes—
925C2×Dic3C22×Q812yes—
926C2×Dic3C2×#4112yes—
927C2×Dic3C2×#4112yes—
928C2×Dic32−1+412yes—
929Dic6—44no—
930Dic6—44no—
931Dic6—44no—
932C2×Q8—22no—
933C2×Q8—22no—
934C2×Q8—22no—
935C2×Q8—34no—
936C2×Q8—34no—
937C2×Q8—62no—
938C2×Q8—121no—
939C2×Q8—121no—
940C2×Q8—121no—
941C2×Q8—121no—
942C2×Q8—121no—
943C2×Q8—121no—
944C22×C4—31no—
945C22×C4—31no—
946C22×C4—31no—
947C22×C4—31no—
948C22×C4—31no—
949C22×C4—31no—
950C22×C4—31no—
951C22×C4—31no—
952C22×C4—31no—
953C22×C4—31no—
954C22×C4—31no—
955C22×C4—31no—
956C22×C4—31no—
957C22×C4—31no—
958C22×C4—31no—
959C22×C4—31no—
960C22×C4C23×D311yescharacteristic
961C22×C4C23×D311yescharacteristic
962C22×C4C23×D311yescharacteristic
963C22×C4C23×D311yescharacteristic
964C22×C4C23×D311yescharacteristic
965C22×C4C23×D311yescharacteristic
966C22×C4C23×D311yescharacteristic
967C22×C4C23×D311yescharacteristic
968C22×C4C23×D311yescharacteristic
969C22×C4C23×D311yescharacteristic
970C22×C4C23×D311yescharacteristic
971C22×C4C23×D311yescharacteristic
972C22×C4C23×D311yescharacteristic
973C22×C4C23×D311yescharacteristic
974C22×C4C23×D311yescharacteristic
975C4⋊C4—22no—
976C4⋊C4—22no—
977C4⋊C4—22no—
978C4⋊C4—22no—
979C4⋊C4—22no—
980C4⋊C4—22no—
981C4⋊C4—22no—
982C4⋊C4—34no—
983C4⋊C4—34no—
984C4⋊C4—34no—
985C4⋊C4—41no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—41no—
992C4⋊C4—62no—
993C4⋊C4—62no—
994C4⋊C4—62no—
995C4⋊C4—62no—
996C4⋊C4—62no—
997C4⋊C4—62no—
998C4⋊C4—62no—
999C4⋊C4—62no—
1000C4⋊C4—62no—
1001C4⋊C4—62no—
1002C4⋊C4—62no—
1003C4⋊C4—62no—
1004C4⋊C4—62no—
1005C4⋊C4—62no—
1006C4⋊C4—62no—
1007C4⋊C4—62no—
1008C4⋊C4—62no—
1009C4⋊C4—62no—
1010C4⋊C4—62no—
1011C4⋊C4—121no—
1012C4⋊C4—121no—
1013C4⋊C4—121no—
1014C4⋊C4—121no—
1015C4⋊C4—121no—
1016C4⋊C4—121no—
1017C4⋊C4—121no—
1018C4⋊C4—121no—
1019C4⋊C4—121no—
1020C4⋊C4—121no—
1021C4⋊C4—121no—
1022C4⋊C4—121no—
1023C4⋊C4—121no—
1024C4⋊C4—121no—
1025C4⋊C4—121no—
1026C4⋊C4—121no—
1027C4⋊C4—121no—
1028C4⋊C4—121no—
1029C4⋊C4—121no—
1030C4⋊C4—121no—
1031C4⋊C4—121no—
1032C4⋊C4—121no—
1033C4⋊C4—121no—
1034C4⋊C4—121no—
1035C4⋊C4—121no—
1036C4⋊C4—121no—
1037C4⋊C4—121no—
1038C4⋊C4D3×Q814yes—
1039C42—22no—
1040C42—34no—
1041C42—34no—
1042C42—41no—
1043C42—41no—
1044C42—41no—
1045C42—41no—
1046C42—62no—
1047C42—62no—
1048C42—62no—
1049C42—62no—
1050C42—62no—
1051C42—62no—
1052C42—121no—
1053C42—121no—
1054C42—121no—
1055C42—121no—
1056C42—121no—
1057C42—121no—
1058C42—121no—
1059C42—121no—
1060C42—121no—
1061C42—121no—
1062C22×C3C23×Q811yescharacteristic
1063C22×C3C22×#4111yescharacteristic
1064C22×C3C2×H(5,𝔽2)11yescharacteristic
1065C22×C3C2×2−1+411yescharacteristic
1066C22×C3C2×2−1+411yescharacteristic
1067C22×C3#58511yescharacteristic
1068C22×C3#58511yescharacteristic
1069C3×C4—22no—
1070C3×C4—22no—
1071C3×C4—22no—
1072C3×C4—22no—
1073C3×C4—22no—
1074C3×C4—22no—
1075C3×C4—41no—
1076C3×C4—41no—
1077C3×C4—41no—
1078C3×C4—41no—
1079C3×C4—41no—
1080C3×C4—41no—
1081C3×C4—41no—
1082C3×C4—41no—
1083C3×C4—41no—
1084Dic3—22no—
1085Dic3—22no—
1086Dic3—22no—
1087Dic3—22no—
1088Dic3—41no—
1089Dic3—41no—
1090Dic3—41no—
1091Dic3—41no—
1092Dic3—41no—
1093Dic3—41no—
1094Dic3—41no—
1095Dic3—41no—
1096Dic3—41no—
1097Dic3—41no—
1098Dic3—41no—
1099Dic3#55714yes—
1100C23C24×D311yescharacteristic
1101Q8—28no—
1102Q8—124no—
1103Q8—124no—
1104Q8—124no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—32no—
1145C2×C4—32no—
1146C2×C4—32no—
1147C2×C4—32no—
1148C2×C4—32no—
1149C2×C4—32no—
1150C2×C4—32no—
1151C2×C4—61no—
1152C2×C4—61no—
1153C2×C4—61no—
1154C2×C4—61no—
1155C2×C4—61no—
1156C2×C4—61no—
1157C2×C4—61no—
1158C2×C4—61no—
1159C2×C4—61no—
1160C2×C4—61no—
1161C2×C4—61no—
1162C2×C4—61no—
1163C2×C4—61no—
1164C2×C4—61no—
1165C2×C4—61no—
1166C2×C4—61no—
1167C2×C4—61no—
1168C2×C4—61no—
1169C2×C4—61no—
1170C2×C4—61no—
1171C2×C4—61no—
1172C2×C4—61no—
1173C2×C4—61no—
1174C2×C4—61no—
1175C2×C4—61no—
1176C2×C4—61no—
1177C2×C4—61no—
1178C2×C4—61no—
1179C2×C4—61no—
1180C2×C4—61no—
1181C2×C4—61no—
1182C2×C4—61no—
1183C2×C4—61no—
1184C2×C4—61no—
1185C2×C4—61no—
1186C2×C4—61no—
1187C2×C4—61no—
1188C2×C4—61no—
1189C2×C4—61no—
1190C2×C4—61no—
1191C2×C4—61no—
1192C2×C4#100412yes—
1193C2×C4C2×D3×Q812yes—
1194C2×C4C2×D3×Q812yes—
1195C2×C4C2×D3×Q812yes—
1196C2×C4D3×#4112yes—
1197C2×C4#101012yes—
1198C2×C3C2×#55711yescharacteristic
1199C2×C3#349211yescharacteristic
1200C2×C3#349311yescharacteristic
1201C2×C3#350111yescharacteristic
1202C2×C3#350211yescharacteristic
1203C2×C3#355411yescharacteristic
1204C2×C3#355511yescharacteristic
1205C22C2×#100411yescharacteristic
1206C22C22×D3×Q811yescharacteristic
1207C22C2×D3×#4111yescharacteristic
1208C22C2×#101011yescharacteristic
1209C22#596411yescharacteristic
1210C22D3×2−1+411yescharacteristic
1211C22#596811yescharacteristic
1212C4—22no—
1213C4—22no—
1214C4—22no—
1215C4—22no—
1216C4—22no—
1217C4—22no—
1218C4—34no—
1219C4—41no—
1220C4—41no—
1221C4—41no—
1222C4—41no—
1223C4—41no—
1224C4—41no—
1225C4—41no—
1226C4—41no—
1227C4—41no—
1228C4—62no—
1229C4—62no—
1230C4—62no—
1231C4—62no—
1232C4—121no—
1233C4—121no—
1234C4—121no—
1235C4—121no—
1236C4—121no—
1237C4—121no—
1238C4—121no—
1239C4—121no—
1240C4—121no—
1241C4—121no—
1242C4—121no—
1243C3#4536311yescharacteristic, complemented, Sylow
1244C2#8602511yescharacteristic
1245C2#8625811yescharacteristic
1246C2#8650011yescharacteristic
1247C2#8669411yescharacteristic
1248C2#8676111yescharacteristic
1249C2#8686111yescharacteristic
1250C2D3×#55711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, prime radical, cosocleC23×C3C25
FittingC3×#2462C2
hypercenter#2462D3
hypocenterC3#45363
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2462

Complements

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

NH ≅ G/Ntype
316. #888Q8semidirect
1243. C3#45363semidirect

Maximal subgroups

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

subgroupindex
C3×#24622
#830342
#830292
#824802
Q8×Dic3⋊C42
#779212
#778072
#777932
#777682
#771922
#771912
#771772
#771712
#761862
#761762
#760802
#759732
#752832
#752812
#752742
#752242
#752232
#750772
#750292
#750282
#749882
#749672
#749632
#749502
#737342
#736572
#453633