Finite Group Databasebeta

← #11235119

Subgroups — #11235119

Order 768.

1430 conjugacy classes of subgroups.

The subgroup lattice has 1216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2605C211yesmaximal, characteristic
2#78256C211yesmaximal, characteristic
3#78181C211yesmaximal, characteristic
4#78169C211yesmaximal, characteristic
5#78158C211yesmaximal, characteristic
6#77198C211yesmaximal, characteristic
7#77198C211yesmaximal, characteristic
8#77189C211yesmaximal, characteristic
9#77171C211yesmaximal, characteristic
10#76585C211yesmaximal, characteristic
11#76584C211yesmaximal, characteristic
12#76580C211yesmaximal, characteristic
13#76579C211yesmaximal, characteristic
14#76545C211yesmaximal, characteristic
15#76544C211yesmaximal, characteristic
16#76489C211yesmaximal, characteristic
17#76486C211yesmaximal, characteristic
18#75200C211yesmaximal, characteristic
19#75198C211yesmaximal, characteristic
20#75061C211yesmaximal, characteristic
21#75059C211yesmaximal, characteristic
22#75032C211yesmaximal, characteristic
23#75031C211yesmaximal, characteristic
24#74964C211yesmaximal, characteristic
25#74948C211yesmaximal, characteristic
26#74280C211yesmaximal, characteristic
27#74267C211yesmaximal, characteristic
28#73706C211yesmaximal, characteristic
29#73641C211yesmaximal, characteristic
30#73404C211yesmaximal, characteristic
31#73393C211yesmaximal, characteristic
32#45431—31nomaximal, Sylow
33C2×Q8×Dic3C2211yescharacteristic
34C2×#944C2211yescharacteristic
35C2×#888C2211yescharacteristic
36C2×#887C2211yescharacteristic
37C2×#887C2211yescharacteristic
38C2×C4×Dic6C2211yescharacteristic
39C3×#400C2211yescharacteristic
40C3×#400C2211yescharacteristic
41C3×#395C2211yescharacteristic
42C3×#395C2211yescharacteristic
43C3×#391C2211yescharacteristic
44C3×#391C2211yescharacteristic
45C3×#391C2211yescharacteristic
46C3×#391C2211yescharacteristic
47C3×#387C2211yescharacteristic
48C3×#387C2211yescharacteristic
49C3×#387C2211yescharacteristic
50C3×#387C2211yescharacteristic
51C3×#383C2211yescharacteristic
52C3×C4×C4⋊C4C2211yescharacteristic
53C3×#376C2211yescharacteristic
54#5230C2211yescharacteristic
55#5230C2211yescharacteristic
56#5229C2211yescharacteristic
57#5229C2211yescharacteristic
58#5229C2211yescharacteristic
59#5229C2211yescharacteristic
60#4986C2211yescharacteristic
61#4986C2211yescharacteristic
62#4986C2211yescharacteristic
63#4985C2211yescharacteristic
64#4982C2211yescharacteristic
65#4982C2211yescharacteristic
66#4981C2211yescharacteristic
67#4980C2211yescharacteristic
68#4980C2211yescharacteristic
69#4980C2211yescharacteristic
70#4979C2211yescharacteristic
71#4978C2211yescharacteristic
72#4978C2211yescharacteristic
73#4978C2211yescharacteristic
74#4978C2211yescharacteristic
75#4978C2211yescharacteristic
76#4978C2211yescharacteristic
77#4977C2211yescharacteristic
78#4976C2211yescharacteristic
79#4976C2211yescharacteristic
80#4976C2211yescharacteristic
81#4975C2211yescharacteristic
82#4975C2211yescharacteristic
83Dic3×C4⋊C4C2211yescharacteristic
84Dic3×C4⋊C4C2211yescharacteristic
85Dic3×C4⋊C4C2211yescharacteristic
86Dic3×C4⋊C4C2211yescharacteristic
87#4973C2211yescharacteristic
88#4973C2211yescharacteristic
89#4937C2211yescharacteristic
90#4937C2211yescharacteristic
91#4936C2211yescharacteristic
92C4×C4⋊Dic3C2211yescharacteristic
93#4933C2211yescharacteristic
94#4933C2211yescharacteristic
95#4933C2211yescharacteristic
96#4933C2211yescharacteristic
97#4933C2211yescharacteristic
98#4933C2211yescharacteristic
99#4933C2211yescharacteristic
100#4933C2211yescharacteristic
101#4932C2211yescharacteristic
102C4×Dic3⋊C4C2211yescharacteristic
103C4×Dic3⋊C4C2211yescharacteristic
104C4×Dic3⋊C4C2211yescharacteristic
105C4×Dic3⋊C4C2211yescharacteristic
106#4929C2211yescharacteristic
107#4929C2211yescharacteristic
108C3⋊#401C2211yescharacteristic
109C3⋊#401C2211yescharacteristic
110C3⋊#401C2211yescharacteristic
111C3⋊#401C2211yescharacteristic
112#4661C2211yescharacteristic
113#4660C2211yescharacteristic
114#4660C2211yescharacteristic
115#4660C2211yescharacteristic
116#4660C2211yescharacteristic
117#4660C2211yescharacteristic
118#4660C2211yescharacteristic
119#4660C2211yescharacteristic
120#4660C2211yescharacteristic
121#4660C2211yescharacteristic
122#4660C2211yescharacteristic
123#4660C2211yescharacteristic
124#4659C2211yescharacteristic
125#4659C2211yescharacteristic
126#4658C2211yescharacteristic
127#4658C2211yescharacteristic
128#4658C2211yescharacteristic
129#4658C2211yescharacteristic
130#4658C2211yescharacteristic
131#4656C2211yescharacteristic
132#4656C2211yescharacteristic
133#4656C2211yescharacteristic
134#4655C2211yescharacteristic
135#4655C2211yescharacteristic
136#4655C2211yescharacteristic
137#4655C2211yescharacteristic
138#4655C2211yescharacteristic
139#4654C2211yescharacteristic
140#4654C2211yescharacteristic
141#4654C2211yescharacteristic
142#4653C2211yescharacteristic
143#4653C2211yescharacteristic
144#4653C2211yescharacteristic
145#4653C2211yescharacteristic
146#4653C2211yescharacteristic
147#4653C2211yescharacteristic
148#4652C2211yescharacteristic
149#4652C2211yescharacteristic
150#4652C2211yescharacteristic
151#4652C2211yescharacteristic
152#4652C2211yescharacteristic
153#4651C2211yescharacteristic
154#4651C2211yescharacteristic
155#4651C2211yescharacteristic
156#4651C2211yescharacteristic
157#4651C2211yescharacteristic
158#4650C2211yescharacteristic
159#4650C2211yescharacteristic
160#4650C2211yescharacteristic
161#4650C2211yescharacteristic
162#4650C2211yescharacteristic
163#4650C2211yescharacteristic
164#4649C2211yescharacteristic
165#4649C2211yescharacteristic
166#4649C2211yescharacteristic
167#4649C2211yescharacteristic
168#4648C2211yescharacteristic
169#4648C2211yescharacteristic
170#4648C2211yescharacteristic
171#4647C2211yescharacteristic
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#2762—31no—
189#2762—31no—
190#2762—31no—
191#2762—31no—
192#2758—31no—
193#2758—31no—
194#2758—31no—
195#2758—31no—
196#2605—31no—
197#2605—31no—
198#2605—31no—
199#2605D311yescharacteristic
200#2568—31no—
201#2568—31no—
202#2568—31no—
203#2567—31no—
204#2528—31no—
205#2528—31no—
206#2528—31no—
207#2528—31no—
208#2514—31no—
209#2514—31no—
210#2511—31no—
211#2511—31no—
212#2399—31no—
213#2356—31no—
214#2356—31no—
215#2355—31no—
216#2355—31no—
217#2331—31no—
218#2327—31no—
219C22×C3×Q8C2311yescharacteristic
220C22×C3×Q8C2311yescharacteristic
221C22×Dic6C2311yescharacteristic
222C22×Dic6C2311yescharacteristic
223C22×Dic6C2311yescharacteristic
224C22×Dic6C2311yescharacteristic
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×C42C2311yescharacteristic
234C2×C3×C42C2311yescharacteristic
235C2×C3×C42C2311yescharacteristic
236C2×C3×C42C2311yescharacteristic
237C2×C3×C42C2311yescharacteristic
238Q8×Dic3—24no—
239#944—24no—
240C2×C4⋊Dic3C2311yescharacteristic
241C2×C4⋊Dic3C2311yescharacteristic
242C2×C4⋊Dic3C2311yescharacteristic
243C2×C4⋊Dic3C2311yescharacteristic
244C2×C4⋊Dic3C2311yescharacteristic
245C2×C4⋊Dic3C2311yescharacteristic
246C2×C4⋊Dic3C2311yescharacteristic
247C2×C4⋊Dic3C2311yescharacteristic
248C2×C4⋊Dic3C2311yescharacteristic
249C2×C4⋊Dic3C2311yescharacteristic
250C2×Dic3⋊C4C2311yescharacteristic
251C2×Dic3⋊C4C2311yescharacteristic
252C2×Dic3⋊C4C2311yescharacteristic
253C2×Dic3⋊C4C2311yescharacteristic
254C2×Dic3⋊C4C2311yescharacteristic
255C2×Dic3⋊C4C2311yescharacteristic
256C2×Dic3⋊C4C2311yescharacteristic
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×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×C4×Dic3C2311yescharacteristic
284C2×C4×Dic3C2311yescharacteristic
285C2×C4×Dic3C2311yescharacteristic
286C2×C4×Dic3C2311yescharacteristic
287C2×C4×Dic3C2311yescharacteristic
288C2×C4×Dic3C2311yescharacteristic
289C2×C4×Dic3C2311yescharacteristic
290C2×C4×Dic3C2311yescharacteristic
291C2×C4×Dic3C2311yescharacteristic
292#888—24no—
293#887—24no—
294#887—24no—
295C4×Dic6—24no—
296C3×#95C2311yescharacteristic
297C3×#95C2311yescharacteristic
298C3×#95C2311yescharacteristic
299C3×#95C2311yescharacteristic
300C3×#95C2311yescharacteristic
301C3×#95C2311yescharacteristic
302C3×#95C2311yescharacteristic
303C3×#95C2311yescharacteristic
304C3×#95C2311yescharacteristic
305C3×#95C2311yescharacteristic
306C3×#95C2311yescharacteristic
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
380C2×C4⋊Q8—31no—
381C2×C4⋊Q8—31no—
382C2×C4×Q8—31no—
383C2×C4×Q8—31no—
384C2×C4×Q8—31no—
385C2×C4×Q8—31no—
386#401—31no—
387#401—31no—
388#401—31no—
389#401—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#400—31no—
407#400—31no—
408#400—31no—
409#400—31no—
410#400—31no—
411#400—31no—
412#400C2×D311yescharacteristic
413#400C2×D311yescharacteristic
414#398—31no—
415#398—31no—
416#398—31no—
417#398—31no—
418#395—31no—
419#395—31no—
420#395—31no—
421#395—31no—
422#395—31no—
423#395—31no—
424#395C2×D311yescharacteristic
425#395C2×D311yescharacteristic
426#391—31no—
427#391—31no—
428#391—31no—
429#391—31no—
430#391—31no—
431#391—31no—
432#391—31no—
433#391—31no—
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#391—31no—
447#391—31no—
448#391C2×D311yescharacteristic
449#391C2×D311yescharacteristic
450#391C2×D311yescharacteristic
451#391C2×D311yescharacteristic
452#389—31no—
453#389—31no—
454#389—31no—
455#389—31no—
456#389—31no—
457#389—31no—
458#387—31no—
459#387—31no—
460#387—31no—
461#387—31no—
462#387—31no—
463#387—31no—
464#387—31no—
465#387—31no—
466#387—31no—
467#387—31no—
468#387—31no—
469#387—31no—
470#387—31no—
471#387—31no—
472#387—31no—
473#387—31no—
474#387—31no—
475#387—31no—
476#387—31no—
477#387—31no—
478#387—31no—
479#387—31no—
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#387C2×D311yescharacteristic
495#387C2×D311yescharacteristic
496#387C2×D311yescharacteristic
497#387C2×D311yescharacteristic
498#384—31no—
499#384—31no—
500#383—31no—
501#383—31no—
502#383—31no—
503#383—31no—
504#383—31no—
505#383—31no—
506#383—31no—
507#383C2×D311yescharacteristic
508#382—31no—
509#382—31no—
510#382—31no—
511#382—31no—
512#382—31no—
513#382—31no—
514#382—31no—
515#382—31no—
516C4×C4⋊C4—31no—
517C4×C4⋊C4—31no—
518C4×C4⋊C4—31no—
519C4×C4⋊C4—31no—
520C4×C4⋊C4—31no—
521C4×C4⋊C4—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⋊C4C2×D311yescharacteristic
530#376—31no—
531#376—31no—
532#376—31no—
533#376—31no—
534#376C2×D311yescharacteristic
535C2×C3×Q8—22no—
536C2×C3×Q8—22no—
537C2×C3×Q8—22no—
538C2×C3×Q8—41no—
539C2×C3×Q8—41no—
540C2×C3×Q8—41no—
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×C3×C4C2411yescharacteristic
555C22×C3×C4C2411yescharacteristic
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
570C22×Dic3C2411yescharacteristic
571C22×Dic3C2411yescharacteristic
572C2×Dic6—22no—
573C2×Dic6—22no—
574C2×Dic6—22no—
575C2×Dic6—22no—
576C2×Dic6—22no—
577C2×Dic6—22no—
578C2×Dic6—22no—
579C2×Dic6—22no—
580C2×Dic6—22no—
581C2×Dic6—41no—
582C2×Dic6—41no—
583C2×Dic6—41no—
584C3×C4⋊C4—22no—
585C3×C4⋊C4—22no—
586C3×C4⋊C4—22no—
587C3×C4⋊C4—22no—
588C3×C4⋊C4—41no—
589C3×C4⋊C4—41no—
590C3×C4⋊C4—41no—
591C3×C4⋊C4—41no—
592C3×C42—22no—
593C3×C42—22no—
594C3×C42—22no—
595C3×C42—41no—
596C3×C42—41no—
597C4⋊Dic3—22no—
598C4⋊Dic3—22no—
599C4⋊Dic3—22no—
600C4⋊Dic3—22no—
601C4⋊Dic3—22no—
602C4⋊Dic3—41no—
603C4⋊Dic3—41no—
604C4⋊Dic3—41no—
605C4⋊Dic3—41no—
606C4⋊Dic3—41no—
607Dic3⋊C4—22no—
608Dic3⋊C4—22no—
609Dic3⋊C4—22no—
610Dic3⋊C4—22no—
611Dic3⋊C4—22no—
612Dic3⋊C4—22no—
613Dic3⋊C4—22no—
614Dic3⋊C4—22no—
615Dic3⋊C4—22no—
616Dic3⋊C4—22no—
617Dic3⋊C4—22no—
618Dic3⋊C4—22no—
619Dic3⋊C4—22no—
620Dic3⋊C4—22no—
621Dic3⋊C4—22no—
622Dic3⋊C4—22no—
623Dic3⋊C4—22no—
624Dic3⋊C4—41no—
625Dic3⋊C4—41no—
626Dic3⋊C4—41no—
627Dic3⋊C4—41no—
628Dic3⋊C4—41no—
629Dic3⋊C4—41no—
630Dic3⋊C4—41no—
631C4×Dic3—22no—
632C4×Dic3—22no—
633C4×Dic3—22no—
634C4×Dic3—22no—
635C4×Dic3—22no—
636C4×Dic3—22no—
637C4×Dic3—22no—
638C4×Dic3—22no—
639C4×Dic3—22no—
640C4×Dic3—22no—
641C4×Dic3—41no—
642C4×Dic3—41no—
643C4×Dic3—41no—
644C4×Dic3—41no—
645C4×Dic3—41no—
646C4×Dic3—41no—
647C4×Dic3#4114yes—
648C4×Dic3#4114yes—
649C22×Q8—31no—
650C22×Q8—31no—
651C22×Q8—31no—
652C22×Q8—31no—
653C22×Q8C22×D311yescharacteristic
654C22×Q8C22×D311yescharacteristic
655C4⋊Q8—64no—
656C4⋊Q8—64no—
657C4×Q8—64no—
658C4×Q8—64no—
659C4×Q8—64no—
660C4×Q8—64no—
661C2×C4⋊C4—31no—
662C2×C4⋊C4—31no—
663C2×C4⋊C4—31no—
664C2×C4⋊C4—31no—
665C2×C4⋊C4—31no—
666C2×C4⋊C4—31no—
667C2×C4⋊C4—31no—
668C2×C4⋊C4—31no—
669C2×C4⋊C4—31no—
670C2×C4⋊C4—31no—
671C2×C4⋊C4—31no—
672C2×C4⋊C4—31no—
673C2×C4⋊C4—31no—
674C2×C4⋊C4—31no—
675C2×C4⋊C4—31no—
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⋊C4C22×D311yescharacteristic
696C2×C4⋊C4C22×D311yescharacteristic
697C2×C4⋊C4C22×D311yescharacteristic
698C2×C4⋊C4C22×D311yescharacteristic
699C2×C4⋊C4C22×D311yescharacteristic
700C2×C4⋊C4C22×D311yescharacteristic
701C2×C4⋊C4C22×D311yescharacteristic
702C2×C4⋊C4C22×D311yescharacteristic
703C2×C42—31no—
704C2×C42—31no—
705C2×C42—31no—
706C2×C42—31no—
707C2×C42—31no—
708C2×C42—31no—
709C2×C42—31no—
710C2×C42—31no—
711C2×C42—31no—
712C2×C42—31no—
713C2×C42—31no—
714C2×C42—31no—
715C2×C42—31no—
716C2×C42—31no—
717C2×C42—31no—
718C2×C42—31no—
719C2×C42—31no—
720C2×C42—31no—
721C2×C42C22×D311yescharacteristic
722C2×C42C22×D311yescharacteristic
723C2×C42C22×D311yescharacteristic
724C2×C42C22×D311yescharacteristic
725C2×C42C22×D311yescharacteristic
726#95—31no—
727#95—31no—
728#95—31no—
729#95—31no—
730#95—31no—
731#95—31no—
732#95—31no—
733#95—31no—
734#95—31no—
735#95—31no—
736#95—31no—
737#95—31no—
738#95—31no—
739#95—31no—
740#95—31no—
741#95—31no—
742#95—31no—
743#95—31no—
744#95—31no—
745#95—31no—
746#95—31no—
747#95—31no—
748#95—31no—
749#95—31no—
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#95C22×D311yescharacteristic
791#95C22×D311yescharacteristic
792#95C22×D311yescharacteristic
793#95C22×D311yescharacteristic
794#95C22×D311yescharacteristic
795#95C22×D311yescharacteristic
796#95C22×D311yescharacteristic
797#95C22×D311yescharacteristic
798#95C22×D311yescharacteristic
799#95C22×D311yescharacteristic
800#95C22×D311yescharacteristic
801#95C22×D311yescharacteristic
802#95C22×D311yescharacteristic
803#95C22×D311yescharacteristic
804#95C22×D311yescharacteristic
805#95C22×D311yescharacteristic
806#95C22×D311yescharacteristic
807#95C22×D311yescharacteristic
808#95C22×D311yescharacteristic
809#95C22×D311yescharacteristic
810C23×C3C2511yescharacteristic
811C3×Q8—44no—
812C3×Q8—82no—
813C2×C3×C4—21no—
814C2×C3×C4—21no—
815C2×C3×C4—21no—
816C2×C3×C4—21no—
817C2×C3×C4—21no—
818C2×C3×C4—21no—
819C2×C3×C4—21no—
820C2×C3×C4—21no—
821C2×C3×C4—21no—
822C2×C3×C4—21no—
823C2×C3×C4—21no—
824C2×C3×C4—21no—
825C2×C3×C4—21no—
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×C4C2×#4112yes—
855C2×C3×C4C2×#4112yes—
856C2×C3×C42−1+412yes—
857C2×C3×C42−1+412yes—
858C2×Dic3—21no—
859C2×Dic3—21no—
860C2×Dic3—21no—
861C2×Dic3—21no—
862C2×Dic3—21no—
863C2×Dic3—21no—
864C2×Dic3—21no—
865C2×Dic3—21no—
866C2×Dic3—21no—
867C2×Dic3—21no—
868C2×Dic3—21no—
869C2×Dic3—21no—
870C2×Dic3—21no—
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×Dic3C2×#4112yes—
902C2×Dic3C2×#4112yes—
903C2×Dic3C2×#4112yes—
904C2×Dic3C2×#4112yes—
905C2×Dic32−1+412yes—
906Dic6—44no—
907Dic6—44no—
908Dic6—44no—
909Dic6—82no—
910C2×Q8—22no—
911C2×Q8—22no—
912C2×Q8—22no—
913C2×Q8—41no—
914C2×Q8—41no—
915C2×Q8—41no—
916C2×Q8—62no—
917C2×Q8—62no—
918C2×Q8—62no—
919C2×Q8—62no—
920C2×Q8—62no—
921C2×Q8—62no—
922C2×Q8—62no—
923C2×Q8—62no—
924C2×Q8—62no—
925C2×Q8—121no—
926C2×Q8—121no—
927C2×Q8—121no—
928C22×C4—31no—
929C22×C4—31no—
930C22×C4—31no—
931C22×C4—31no—
932C22×C4—31no—
933C22×C4—31no—
934C22×C4—31no—
935C22×C4—31no—
936C22×C4—31no—
937C22×C4—31no—
938C22×C4—31no—
939C22×C4—31no—
940C22×C4—31no—
941C22×C4—31no—
942C22×C4—31no—
943C22×C4—31no—
944C22×C4C23×D311yescharacteristic
945C22×C4C23×D311yescharacteristic
946C22×C4C23×D311yescharacteristic
947C22×C4C23×D311yescharacteristic
948C22×C4C23×D311yescharacteristic
949C22×C4C23×D311yescharacteristic
950C22×C4C23×D311yescharacteristic
951C22×C4C23×D311yescharacteristic
952C22×C4C23×D311yescharacteristic
953C22×C4C23×D311yescharacteristic
954C22×C4C23×D311yescharacteristic
955C22×C4C23×D311yescharacteristic
956C22×C4C23×D311yescharacteristic
957C22×C4C23×D311yescharacteristic
958C22×C4C23×D311yescharacteristic
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—22no—
963C4⋊C4—41no—
964C4⋊C4—41no—
965C4⋊C4—41no—
966C4⋊C4—41no—
967C4⋊C4—62no—
968C4⋊C4—62no—
969C4⋊C4—62no—
970C4⋊C4—62no—
971C4⋊C4—62no—
972C4⋊C4—62no—
973C4⋊C4—62no—
974C4⋊C4—62no—
975C4⋊C4—62no—
976C4⋊C4—62no—
977C4⋊C4—62no—
978C4⋊C4—62no—
979C4⋊C4—62no—
980C4⋊C4—62no—
981C4⋊C4—62no—
982C4⋊C4—62no—
983C4⋊C4—62no—
984C4⋊C4—62no—
985C4⋊C4—62no—
986C4⋊C4—62no—
987C4⋊C4—62no—
988C4⋊C4—62no—
989C4⋊C4—121no—
990C4⋊C4—121no—
991C4⋊C4—121no—
992C4⋊C4—121no—
993C4⋊C4—121no—
994C4⋊C4—121no—
995C4⋊C4—121no—
996C4⋊C4—121no—
997C4⋊C4—121no—
998C4⋊C4—121no—
999C4⋊C4—121no—
1000C4⋊C4—121no—
1001C42—22no—
1002C42—22no—
1003C42—22no—
1004C42—34no—
1005C42—34no—
1006C42—41no—
1007C42—41no—
1008C42—62no—
1009C42—62no—
1010C42—62no—
1011C42—62no—
1012C42—62no—
1013C42—62no—
1014C42—62no—
1015C42—62no—
1016C42—62no—
1017C42—62no—
1018C42—121no—
1019C42—121no—
1020C42—121no—
1021C42—121no—
1022C42—121no—
1023C42—121no—
1024C22×C3C22×#4111yescharacteristic
1025C22×C3C22×#4111yescharacteristic
1026C22×C3C2×2−1+411yescharacteristic
1027C22×C3C2×2−1+411yescharacteristic
1028C22×C3C2×2−1+411yescharacteristic
1029C22×C3#58511yescharacteristic
1030C22×C3#58511yescharacteristic
1031C3×C4—22no—
1032C3×C4—22no—
1033C3×C4—22no—
1034C3×C4—22no—
1035C3×C4—41no—
1036C3×C4—41no—
1037C3×C4—41no—
1038C3×C4—41no—
1039C3×C4—41no—
1040C3×C4—41no—
1041C3×C4—41no—
1042C3×C4—41no—
1043C3×C4—41no—
1044C3×C4—41no—
1045C3×C4—41no—
1046Dic3—22no—
1047Dic3—22no—
1048Dic3—41no—
1049Dic3—41no—
1050Dic3—41no—
1051Dic3—41no—
1052Dic3—41no—
1053Dic3—41no—
1054Dic3—41no—
1055Dic3—41no—
1056Dic3—41no—
1057Dic3—41no—
1058Dic3—41no—
1059Dic3—41no—
1060Dic3—41no—
1061Dic3#55614yes—
1062C23C24×D311yescharacteristic
1063Q8—44no—
1064Q8—82no—
1065Q8—124no—
1066Q8—124no—
1067Q8—124no—
1068Q8—242no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
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—32no—
1111C2×C4—32no—
1112C2×C4—32no—
1113C2×C4—32no—
1114C2×C4—32no—
1115C2×C4—61no—
1116C2×C4—61no—
1117C2×C4—61no—
1118C2×C4—61no—
1119C2×C4—61no—
1120C2×C4—61no—
1121C2×C4—61no—
1122C2×C4—61no—
1123C2×C4—61no—
1124C2×C4—61no—
1125C2×C4—61no—
1126C2×C4—61no—
1127C2×C4—61no—
1128C2×C4—61no—
1129C2×C4—61no—
1130C2×C4—61no—
1131C2×C4—61no—
1132C2×C4—61no—
1133C2×C4—61no—
1134C2×C4—61no—
1135C2×C4—61no—
1136C2×C4—61no—
1137C2×C4—61no—
1138C2×C4—61no—
1139C2×C4—61no—
1140C2×C4—61no—
1141C2×C4—61no—
1142C2×C4—61no—
1143C2×C4—61no—
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#100712yes—
1159C2×C4D3×#4112yes—
1160C2×C4D3×#4112yes—
1161C2×C4#101012yes—
1162C2×C3C2×#55611yescharacteristic
1163C2×C3#349511yescharacteristic
1164C2×C3#349511yescharacteristic
1165C2×C3#350911yescharacteristic
1166C2×C3#351011yescharacteristic
1167C2×C3#355511yescharacteristic
1168C2×C3#355511yescharacteristic
1169C22C2×#100711yescharacteristic
1170C22C2×D3×#4111yescharacteristic
1171C22C2×D3×#4111yescharacteristic
1172C22C2×#101011yescharacteristic
1173C22#596411yescharacteristic
1174C22#596611yescharacteristic
1175C22D3×2−1+411yescharacteristic
1176C4—22no—
1177C4—22no—
1178C4—22no—
1179C4—22no—
1180C4—34no—
1181C4—41no—
1182C4—41no—
1183C4—41no—
1184C4—41no—
1185C4—41no—
1186C4—41no—
1187C4—41no—
1188C4—41no—
1189C4—41no—
1190C4—41no—
1191C4—41no—
1192C4—62no—
1193C4—62no—
1194C4—121no—
1195C4—121no—
1196C4—121no—
1197C4—121no—
1198C4—121no—
1199C4—121no—
1200C4—121no—
1201C4—121no—
1202C4—121no—
1203C4—121no—
1204C4—121no—
1205C4—121no—
1206C4—121no—
1207C3#4543111yescharacteristic, complemented, Sylow
1208C2#8627911yescharacteristic
1209C2#8628311yescharacteristic
1210C2#8659011yescharacteristic
1211C2#8679311yescharacteristic
1212C2#8679411yescharacteristic
1213C2#8699611yescharacteristic
1214C2D3×#55611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, prime radical, cosocleC23×C3C25
FittingC3×#2605C2
hypercenter#2605D3
hypocenterC3#45431
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2605

Complements

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

NH ≅ G/Ntype
1207. C3#45431semidirect

Maximal subgroups

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

subgroupindex
C3×#26052
#782562
#781812
#781692
#781582
#771982
#771892
#771712
#765852
#765842
#765802
#765792
#765452
#765442
#764892
#764862
#752002
#751982
#750612
#750592
#750322
#750312
#749642
#749482
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