Finite Group Databasebeta

← #11301482

Subgroups — #11301482

Order 768.

1416 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2792C211yesmaximal, characteristic
2#77916C211yesmaximal, characteristic
3#77916C211yesmaximal, characteristic
4#77897C211yesmaximal, characteristic
5#77855C211yesmaximal, characteristic
6#77817C211yesmaximal, characteristic
7#77801C211yesmaximal, characteristic
8#77247C211yesmaximal, characteristic
9#77240C211yesmaximal, characteristic
10#77236C211yesmaximal, characteristic
11#77191C211yesmaximal, characteristic
12#77178C211yesmaximal, characteristic
13#77177C211yesmaximal, characteristic
14#76182C211yesmaximal, characteristic
15#76181C211yesmaximal, characteristic
16#76115C211yesmaximal, characteristic
17#76101C211yesmaximal, characteristic
18#76084C211yesmaximal, characteristic
19#76014C211yesmaximal, characteristic
20#76012C211yesmaximal, characteristic
21#75974C211yesmaximal, characteristic
22#75270C211yesmaximal, characteristic
23#75226C211yesmaximal, characteristic
24#75133C211yesmaximal, characteristic
25#75104C211yesmaximal, characteristic
26#75103C211yesmaximal, characteristic
27#75031C211yesmaximal, characteristic
28#74950C211yesmaximal, characteristic
29#74948C211yesmaximal, characteristic
30#74340C211yesmaximal, characteristic
31#74332C211yesmaximal, characteristic
32#47819—31nomaximal, Sylow
33C2×Q8×Dic3C2211yescharacteristic
34C2×#890C2211yescharacteristic
35C2×#889C2211yescharacteristic
36C2×#888C2211yescharacteristic
37C2×#888C2211yescharacteristic
38C2×#887C2211yescharacteristic
39C2×C4×Dic6C2211yescharacteristic
40C3×#398C2211yescharacteristic
41C3×#398C2211yescharacteristic
42C3×#398C2211yescharacteristic
43C3×#395C2211yescharacteristic
44C3×#395C2211yescharacteristic
45C3×#395C2211yescharacteristic
46C3×#389C2211yescharacteristic
47C3×#389C2211yescharacteristic
48C3×#389C2211yescharacteristic
49C3×#389C2211yescharacteristic
50C3×#387C2211yescharacteristic
51C3×#387C2211yescharacteristic
52C3×#387C2211yescharacteristic
53C3×#387C2211yescharacteristic
54C3×#384C2211yescharacteristic
55#5230C2211yescharacteristic
56#5230C2211yescharacteristic
57#5230C2211yescharacteristic
58#4986C2211yescharacteristic
59#4986C2211yescharacteristic
60#4986C2211yescharacteristic
61#4985C2211yescharacteristic
62#4985C2211yescharacteristic
63#4985C2211yescharacteristic
64#4985C2211yescharacteristic
65#4985C2211yescharacteristic
66#4984C2211yescharacteristic
67#4983C2211yescharacteristic
68#4982C2211yescharacteristic
69#4982C2211yescharacteristic
70#4981C2211yescharacteristic
71#4980C2211yescharacteristic
72#4980C2211yescharacteristic
73#4980C2211yescharacteristic
74#4980C2211yescharacteristic
75#4980C2211yescharacteristic
76#4980C2211yescharacteristic
77#4980C2211yescharacteristic
78#4980C2211yescharacteristic
79#4979C2211yescharacteristic
80#4979C2211yescharacteristic
81#4979C2211yescharacteristic
82#4979C2211yescharacteristic
83#4979C2211yescharacteristic
84#4979C2211yescharacteristic
85#4979C2211yescharacteristic
86#4979C2211yescharacteristic
87#4979C2211yescharacteristic
88#4979C2211yescharacteristic
89#4979C2211yescharacteristic
90#4978C2211yescharacteristic
91#4978C2211yescharacteristic
92#4978C2211yescharacteristic
93#4978C2211yescharacteristic
94#4978C2211yescharacteristic
95#4978C2211yescharacteristic
96#4978C2211yescharacteristic
97#4977C2211yescharacteristic
98#4976C2211yescharacteristic
99#4976C2211yescharacteristic
100#4976C2211yescharacteristic
101#4976C2211yescharacteristic
102#4976C2211yescharacteristic
103#4976C2211yescharacteristic
104#4976C2211yescharacteristic
105#4976C2211yescharacteristic
106#4976C2211yescharacteristic
107#4976C2211yescharacteristic
108#4975C2211yescharacteristic
109Dic3×C4⋊C4C2211yescharacteristic
110Dic3×C4⋊C4C2211yescharacteristic
111Dic3×C4⋊C4C2211yescharacteristic
112#4973C2211yescharacteristic
113#4973C2211yescharacteristic
114#4973C2211yescharacteristic
115#4973C2211yescharacteristic
116#4973C2211yescharacteristic
117#4973C2211yescharacteristic
118#4973C2211yescharacteristic
119#4972C2211yescharacteristic
120#4972C2211yescharacteristic
121#4933C2211yescharacteristic
122#4933C2211yescharacteristic
123#4933C2211yescharacteristic
124#4932C2211yescharacteristic
125C4×Dic3⋊C4C2211yescharacteristic
126C4×Dic3⋊C4C2211yescharacteristic
127C4×Dic3⋊C4C2211yescharacteristic
128#4929C2211yescharacteristic
129#4929C2211yescharacteristic
130#4929C2211yescharacteristic
131#4928C2211yescharacteristic
132#4661C2211yescharacteristic
133#4660C2211yescharacteristic
134#4660C2211yescharacteristic
135#4660C2211yescharacteristic
136#4660C2211yescharacteristic
137#4660C2211yescharacteristic
138#4659C2211yescharacteristic
139#4659C2211yescharacteristic
140#4658C2211yescharacteristic
141#4658C2211yescharacteristic
142#4658C2211yescharacteristic
143#4657C2211yescharacteristic
144#4657C2211yescharacteristic
145#4657C2211yescharacteristic
146#4657C2211yescharacteristic
147#4656C2211yescharacteristic
148#4655C2211yescharacteristic
149#4655C2211yescharacteristic
150#4655C2211yescharacteristic
151#4655C2211yescharacteristic
152#4655C2211yescharacteristic
153#4654C2211yescharacteristic
154#4654C2211yescharacteristic
155#4654C2211yescharacteristic
156#4654C2211yescharacteristic
157#4653C2211yescharacteristic
158#4653C2211yescharacteristic
159#4653C2211yescharacteristic
160#4653C2211yescharacteristic
161#4652C2211yescharacteristic
162#4652C2211yescharacteristic
163#4652C2211yescharacteristic
164#4652C2211yescharacteristic
165#4652C2211yescharacteristic
166#4650C2211yescharacteristic
167#4650C2211yescharacteristic
168#4650C2211yescharacteristic
169#4649C2211yescharacteristic
170#4648C2211yescharacteristic
171#4648C2211yescharacteristic
172#4647C2211yescharacteristic
173#4647C2211yescharacteristic
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#2844—31no—
189#2811—31no—
190#2805—31no—
191#2805—31no—
192#2799—31no—
193#2799—31no—
194#2799—31no—
195#2792—31no—
196#2792D311yescharacteristic
197#2774—31no—
198#2774—31no—
199#2713—31no—
200#2713—31no—
201#2612—31no—
202#2612—31no—
203#2612—31no—
204#2588—31no—
205#2588—31no—
206#2586—31no—
207#2586—31no—
208#2581—31no—
209#2567—31no—
210#2511—31no—
211#2511—31no—
212#2462—31no—
213#2462—31no—
214#2453—31no—
215#2453—31no—
216#2331—31no—
217#2331—31no—
218#2327—31no—
219C22×C3×Q8C2311yescharacteristic
220C22×Dic6C2311yescharacteristic
221C22×Dic6C2311yescharacteristic
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×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—
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×Dic3⋊C4C2311yescharacteristic
258C2×Dic3⋊C4C2311yescharacteristic
259C2×Dic3⋊C4C2311yescharacteristic
260C2×Dic3⋊C4C2311yescharacteristic
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×C4×Dic3C2311yescharacteristic
286C2×C4×Dic3C2311yescharacteristic
287C2×C4×Dic3C2311yescharacteristic
288C2×C4×Dic3C2311yescharacteristic
289C2×C4×Dic3C2311yescharacteristic
290C2×C4×Dic3C2311yescharacteristic
291C2×C4×Dic3C2311yescharacteristic
292C2×C4×Dic3C2311yescharacteristic
293C2×C4×Dic3C2311yescharacteristic
294C2×C4×Dic3C2311yescharacteristic
295C2×C4×Dic3C2311yescharacteristic
296C2×C4×Dic3C2311yescharacteristic
297C2×C4×Dic3C2311yescharacteristic
298C2×C4×Dic3C2311yescharacteristic
299C2×C4×Dic3C2311yescharacteristic
300C2×C4×Dic3C2311yescharacteristic
301#890—42no—
302#889—42no—
303#888—42no—
304#888Q818yescomplemented
305#887—42no—
306C4×Dic6—42no—
307C3×#95C2311yescharacteristic
308C3×#95C2311yescharacteristic
309C3×#95C2311yescharacteristic
310C3×#95C2311yescharacteristic
311C3×#95C2311yescharacteristic
312C3×#95C2311yescharacteristic
313C3×#95C2311yescharacteristic
314C3×#95C2311yescharacteristic
315C3×#95C2311yescharacteristic
316C3×#95C2311yescharacteristic
317C3×#95C2311yescharacteristic
318C3×#95C2311yescharacteristic
319C3×#95C2311yescharacteristic
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
381C2×C4⋊Q8—31no—
382C2×C4⋊Q8—31no—
383C2×#125—31no—
384C2×#125—31no—
385C2×C4×Q8—31no—
386C2×C4×Q8—31no—
387C2×C4×Q8—31no—
388#400—31no—
389#400—31no—
390#400—31no—
391#400—31no—
392#400—31no—
393#400—31no—
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#398C2×D311yescharacteristic
416#398C2×D311yescharacteristic
417#398C2×D311yescharacteristic
418#395—31no—
419#395—31no—
420#395—31no—
421#395—31no—
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#395C2×D311yescharacteristic
434#395C2×D311yescharacteristic
435#395C2×D311yescharacteristic
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#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#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#389C2×D311yescharacteristic
477#389C2×D311yescharacteristic
478#389C2×D311yescharacteristic
479#389C2×D311yescharacteristic
480#387—31no—
481#387—31no—
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#387—31no—
509#387—31no—
510#387—31no—
511#387—31no—
512#387—31no—
513#387—31no—
514#387—31no—
515#387—31no—
516#387C2×D311yescharacteristic
517#387C2×D311yescharacteristic
518#387C2×D311yescharacteristic
519#387C2×D311yescharacteristic
520#384—31no—
521#384C2×D311yescharacteristic
522#382—31no—
523#382—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—
533#376—31no—
534#376—31no—
535#376—31no—
536C2×C3×Q8—41no—
537C2×C3×Q8—41no—
538C2×C3×Q8—41no—
539C22×C3×C4C2411yescharacteristic
540C22×C3×C4C2411yescharacteristic
541C22×C3×C4C2411yescharacteristic
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×Dic3C2411yescharacteristic
555C22×Dic3C2411yescharacteristic
556C22×Dic3C2411yescharacteristic
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
570C2×Dic6—22no—
571C2×Dic6—22no—
572C2×Dic6—41no—
573C2×Dic6—41no—
574C2×Dic6—41no—
575C2×Dic6—41no—
576C2×Dic6—41no—
577C2×Dic6—41no—
578C2×Dic6—41no—
579C2×Dic6—41no—
580C2×Dic6—41no—
581C2×Dic6—41no—
582C2×Dic6—41no—
583C2×Dic6—41no—
584C2×Dic6—41no—
585C2×Dic6—41no—
586C2×Dic6C2×Q814yes—
587C2×Dic6C2×Q814yes—
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⋊C4—41no—
597C3×C4⋊C4—41no—
598C3×C4⋊C4—41no—
599C3×C4⋊C4—41no—
600C3×C4⋊C4—41no—
601C3×C4⋊C4—41no—
602C3×C4⋊C4—41no—
603C3×C4⋊C4—41no—
604C3×C4⋊C4C2×Q814yes—
605C3×C42—41no—
606C3×C42—41no—
607C3×C42—41no—
608C4⋊Dic3—22no—
609C4⋊Dic3—22no—
610C4⋊Dic3—22no—
611C4⋊Dic3—22no—
612C4⋊Dic3—41no—
613C4⋊Dic3—41no—
614C4⋊Dic3—41no—
615C4⋊Dic3—41no—
616C4⋊Dic3—41no—
617C4⋊Dic3C2×Q814yes—
618Dic3⋊C4—22no—
619Dic3⋊C4—22no—
620Dic3⋊C4—22no—
621Dic3⋊C4—22no—
622Dic3⋊C4—22no—
623Dic3⋊C4—22no—
624Dic3⋊C4—22no—
625Dic3⋊C4—41no—
626Dic3⋊C4—41no—
627Dic3⋊C4—41no—
628Dic3⋊C4—41no—
629Dic3⋊C4—41no—
630Dic3⋊C4—41no—
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⋊C4C2×Q814yes—
645Dic3⋊C4C2×Q814yes—
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—41no—
656C4×Dic3—41no—
657C4×Dic3—41no—
658C4×Dic3—41no—
659C4×Dic3—41no—
660C4×Dic3—41no—
661C4×Dic3C2×Q814yes—
662C22×Q8—31no—
663C22×Q8—31no—
664C22×Q8—31no—
665C22×Q8—31no—
666C22×Q8—31no—
667C22×Q8—31no—
668C22×Q8C22×D311yescharacteristic
669C4⋊Q8—38no—
670C4⋊Q8—122no—
671#125—122no—
672#125—122no—
673C4×Q8—122no—
674C4×Q8—122no—
675C4×Q8—122no—
676C2×C4⋊C4—31no—
677C2×C4⋊C4—31no—
678C2×C4⋊C4—31no—
679C2×C4⋊C4—31no—
680C2×C4⋊C4—31no—
681C2×C4⋊C4—31no—
682C2×C4⋊C4—31no—
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⋊C4C22×D311yescharacteristic
715C2×C4⋊C4C22×D311yescharacteristic
716C2×C4⋊C4C22×D311yescharacteristic
717C2×C4⋊C4C22×D311yescharacteristic
718C2×C4⋊C4C22×D311yescharacteristic
719C2×C4⋊C4C22×D311yescharacteristic
720C2×C4⋊C4C22×D311yescharacteristic
721C2×C4⋊C4C22×D311yescharacteristic
722C2×C4⋊C4C22×D311yescharacteristic
723C2×C4⋊C4C22×D311yescharacteristic
724C2×C4⋊C4C22×D311yescharacteristic
725C2×C4⋊C4C22×D311yescharacteristic
726C2×C4⋊C4C22×D311yescharacteristic
727C2×C4⋊C4C22×D311yescharacteristic
728C2×C4⋊C4C22×D311yescharacteristic
729C2×C4⋊C4C22×D311yescharacteristic
730C2×C4⋊C4C22×D311yescharacteristic
731C2×C42—31no—
732C2×C42—31no—
733C2×C42—31no—
734C2×C42—31no—
735C2×C42—31no—
736C2×C42—31no—
737C2×C42—31no—
738C2×C42—31no—
739C2×C42—31no—
740C2×C42—31no—
741C2×C42—31no—
742C2×C42—31no—
743C2×C42—31no—
744C2×C42—31no—
745C2×C42—31no—
746C2×C42—31no—
747C2×C42C22×D311yescharacteristic
748C2×C42C22×D311yescharacteristic
749C2×C42C22×D311yescharacteristic
750#95—31no—
751#95—31no—
752#95—31no—
753#95—31no—
754#95—31no—
755#95—31no—
756#95—31no—
757#95—31no—
758#95—31no—
759#95—31no—
760#95—31no—
761#95—31no—
762#95—31no—
763#95—31no—
764#95—31no—
765#95—31no—
766#95—31no—
767#95—31no—
768#95—31no—
769#95—31no—
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#95C22×D311yescharacteristic
811#95C22×D311yescharacteristic
812#95C22×D311yescharacteristic
813#95C22×D311yescharacteristic
814#95C22×D311yescharacteristic
815#95C22×D311yescharacteristic
816#95C22×D311yescharacteristic
817#95C22×D311yescharacteristic
818#95C22×D311yescharacteristic
819#95C22×D311yescharacteristic
820#95C22×D311yescharacteristic
821#95C22×D311yescharacteristic
822#95C22×D311yescharacteristic
823#95C22×D311yescharacteristic
824C23×C3C2511yescharacteristic
825C3×Q8—44no—
826C2×C3×C4—21no—
827C2×C3×C4—21no—
828C2×C3×C4—21no—
829C2×C3×C4—21no—
830C2×C3×C4—21no—
831C2×C3×C4—21no—
832C2×C3×C4—21no—
833C2×C3×C4—21no—
834C2×C3×C4—21no—
835C2×C3×C4—21no—
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×C4C22×Q812yes—
868C2×C3×C4C22×Q812yes—
869C2×C3×C4C22×Q812yes—
870C2×C3×C42−1+412yes—
871C2×Dic3—21no—
872C2×Dic3—21no—
873C2×Dic3—21no—
874C2×Dic3—21no—
875C2×Dic3—21no—
876C2×Dic3—21no—
877C2×Dic3—21no—
878C2×Dic3—21no—
879C2×Dic3—21no—
880C2×Dic3—21no—
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×Dic3C22×Q812yes—
914C2×Dic3C22×Q812yes—
915C2×Dic3C22×Q812yes—
916C2×Dic3C22×Q812yes—
917C2×Dic3H(5,𝔽2)12yes—
918C2×Dic32−1+412yes—
919Dic6—44no—
920Dic6—44no—
921Dic6—82no—
922Dic6—82no—
923Dic6—82no—
924Dic6—82no—
925C2×Q8—34no—
926C2×Q8—34no—
927C2×Q8—41no—
928C2×Q8—41no—
929C2×Q8—41no—
930C2×Q8—62no—
931C2×Q8—62no—
932C2×Q8—121no—
933C2×Q8—121no—
934C2×Q8—121no—
935C2×Q8—121no—
936C2×Q8—121no—
937C2×Q8—121no—
938C2×Q8—121no—
939C2×Q8—121no—
940C2×Q8—121no—
941C2×Q8—121no—
942C2×Q8—121no—
943C2×Q8—121no—
944C2×Q8—121no—
945C2×Q8—121no—
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×C4—31no—
961C22×C4—31no—
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
975C22×C4C23×D311yescharacteristic
976C22×C4C23×D311yescharacteristic
977C4⋊C4—22no—
978C4⋊C4—34no—
979C4⋊C4—34no—
980C4⋊C4—34no—
981C4⋊C4—41no—
982C4⋊C4—41no—
983C4⋊C4—41no—
984C4⋊C4—41no—
985C4⋊C4—41no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—41no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—41no—
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—121no—
1008C4⋊C4—121no—
1009C4⋊C4—121no—
1010C4⋊C4—121no—
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⋊C4D3×Q814yes—
1032C42—34no—
1033C42—41no—
1034C42—41no—
1035C42—41no—
1036C42—62no—
1037C42—62no—
1038C42—62no—
1039C42—62no—
1040C42—62no—
1041C42—121no—
1042C42—121no—
1043C42—121no—
1044C42—121no—
1045C42—121no—
1046C42—121no—
1047C42—121no—
1048C42—121no—
1049C42—121no—
1050C42—121no—
1051C22×C3C23×Q811yescharacteristic
1052C22×C3C2×H(5,𝔽2)11yescharacteristic
1053C22×C3C2×2−1+411yescharacteristic
1054C22×C3C2×2−1+411yescharacteristic
1055C22×C3#58511yescharacteristic
1056C22×C3#58511yescharacteristic
1057C22×C3#58511yescharacteristic
1058C3×C4—22no—
1059C3×C4—22no—
1060C3×C4—22no—
1061C3×C4—22no—
1062C3×C4—41no—
1063C3×C4—41no—
1064C3×C4—41no—
1065C3×C4—41no—
1066C3×C4—41no—
1067C3×C4—41no—
1068C3×C4—41no—
1069C3×C4—41no—
1070C3×C4—41no—
1071C3×C4—41no—
1072C3×C4—41no—
1073Dic3—22no—
1074Dic3—22no—
1075Dic3—22no—
1076Dic3—22no—
1077Dic3—22no—
1078Dic3—22no—
1079Dic3—41no—
1080Dic3—41no—
1081Dic3—41no—
1082Dic3—41no—
1083Dic3—41no—
1084Dic3—41no—
1085Dic3—41no—
1086Dic3—41no—
1087Dic3—41no—
1088Dic3—41no—
1089C23C24×D311yescharacteristic
1090Q8—44no—
1091Q8—124no—
1092Q8—124no—
1093Q8—242no—
1094Q8—242no—
1095Q8—242no—
1096Q8—242no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
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—32no—
1139C2×C4—32no—
1140C2×C4—32no—
1141C2×C4—32no—
1142C2×C4—32no—
1143C2×C4—32no—
1144C2×C4—61no—
1145C2×C4—61no—
1146C2×C4—61no—
1147C2×C4—61no—
1148C2×C4—61no—
1149C2×C4—61no—
1150C2×C4—61no—
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×C4C2×D3×Q812yes—
1187C2×C4C2×D3×Q812yes—
1188C2×C4C2×D3×Q812yes—
1189C2×C4#100712yes—
1190C2×C3#350111yescharacteristic
1191C2×C3#350211yescharacteristic
1192C2×C3#350211yescharacteristic
1193C2×C3#354011yescharacteristic
1194C2×C3#354411yescharacteristic
1195C2×C3#356411yescharacteristic
1196C2×C3#356411yescharacteristic
1197C22C22×D3×Q811yescharacteristic
1198C22C2×#100711yescharacteristic
1199C22#596411yescharacteristic
1200C22D3×H(5,𝔽2)11yescharacteristic
1201C22#596611yescharacteristic
1202C22#596611yescharacteristic
1203C22D3×2−1+411yescharacteristic
1204C4—22no—
1205C4—22no—
1206C4—22no—
1207C4—22no—
1208C4—41no—
1209C4—41no—
1210C4—41no—
1211C4—41no—
1212C4—41no—
1213C4—41no—
1214C4—41no—
1215C4—41no—
1216C4—41no—
1217C4—41no—
1218C4—41no—
1219C4—62no—
1220C4—62no—
1221C4—62no—
1222C4—62no—
1223C4—62no—
1224C4—62no—
1225C4—121no—
1226C4—121no—
1227C4—121no—
1228C4—121no—
1229C4—121no—
1230C4—121no—
1231C4—121no—
1232C4—121no—
1233C4—121no—
1234C4—121no—
1235C3#4781911yescharacteristic, complemented, Sylow
1236C2#8646611yescharacteristic
1237C2#8658511yescharacteristic
1238C2#8660111yescharacteristic
1239C2#8694411yescharacteristic
1240C2#8694911yescharacteristic
1241C2#8704611yescharacteristic
1242C2#8707311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, prime radical, cosocleC23×C3C25
FittingC3×#2792C2
hypercenter#2792D3
hypocenterC3#47819
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2792

Complements

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

NH ≅ G/Ntype
304. #888Q8semidirect
1235. C3#47819semidirect

Maximal subgroups

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

subgroupindex
C3×#27922
#779162
#778972
#778552
#778172
#778012
#772472
#772402
#772362
#771912
#771782
#771772
#761822
#761812
#761152
#761012
#760842
#760142
#760122
#759742
#752702
#752262
#751332
#751042
#751032
#750312
#749502
#749482
#743402
#743322
#478193