Finite Group Databasebeta

← #15830588

Subgroups — #15830588

Order 3328.

944 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128588C211yesmaximal, characteristic
2#13117696C211yesmaximal, characteristic, complemented
3#13113414C211yesmaximal, characteristic, complemented
4#13113401C211yesmaximal, characteristic, complemented
5#13113393C211yesmaximal, characteristic
6#13113388C211yesmaximal, characteristic, complemented
7#13113375C211yesmaximal, characteristic, complemented
8#13113370C211yesmaximal, characteristic, complemented
9#13113362C211yesmaximal, characteristic, complemented
10#13113349C211yesmaximal, characteristic, complemented
11#13113341C211yesmaximal, characteristic
12#13113336C211yesmaximal, characteristic, complemented
13#13113323C211yesmaximal, characteristic, complemented
14C2×#11718059C211yesmaximal, characteristic, complemented
15C13×#2924C211yesmaximal, characteristic, complemented
16C2×C13×#117C2211yescharacteristic
17#11719496C2211yescharacteristic
18C2×#88178C2211yescharacteristic
19#11719239C411yescharacteristic, complemented
20#11719239C411yescharacteristic, complemented
21#11719238—21no—
22#11719236—21no—
23#11719236—21no—
24#11719234—21no—
25#11719231C411yescharacteristic, complemented
26#11719228C411yescharacteristic, complemented
27#11719224C411yescharacteristic, complemented
28#11719223C411yescharacteristic, complemented
29#11719223C411yescharacteristic, complemented
30#11719221C411yescharacteristic, complemented
31#11719218—21no—
32#11719216—21no—
33#11719200—21no—
34#11719200—21no—
35#11719184C2211yescharacteristic
36#11719184C2211yescharacteristic
37#11719175C2211yescharacteristic
38#11719175C2211yescharacteristic
39C13×#433—21no—
40C13×#433—21no—
41C13×#432C2211yescharacteristic
42C13×#432C2211yescharacteristic
43C13×#431C2211yescharacteristic
44C13×#431C2211yescharacteristic
45C13×#424—21no—
46C13×#407C2211yescharacteristic
47C2×C13×C22⋊C8C2211yescharacteristic
48C13×#405—21no—
49#11718872C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51#11718642—21no—
52#11718642—21no—
53#11718611—21no—
54C22⋊C4×Dic13—21no—
55#11718598C2211yescharacteristic
56#11718597C2211yescharacteristic
57C4×C4⋊Dic13C2211yescharacteristic
58#11718593C2211yescharacteristic
59#11718062C2211yescharacteristic
60#11718062C2211yescharacteristic
61#11718062C2211yescharacteristic
62#11718062C2211yescharacteristic
63#11718059C2211yescharacteristic
64#11718059C2211yescharacteristic
65#11718059C2211yescharacteristic
66#11718059C2211yescharacteristic
67#11718059C2211yescharacteristic
68#11718059C2211yescharacteristic
69#11718059C2211yescharacteristic
70#11718059C2211yescharacteristic
71#11718059C2211yescharacteristic
72#11718059C2211yescharacteristic
73#11718059C2211yescharacteristic
74#11718059C2211yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×Dic13—21no—
77C2×#6127C2×C411yescharacteristic
78C22×Dic26C2×C411yescharacteristic
79C2×C13×M16—21no—
80C22×C8×C13—21no—
81C13×#117C2×C411yescharacteristic
82C13×#117C2×C411yescharacteristic
83C13×#117C2×C411yescharacteristic
84C13×#117C2×C411yescharacteristic
85C13×#117D411yescharacteristic
86C13×#117D411yescharacteristic
87C13×#117D411yescharacteristic
88C13×#117D411yescharacteristic
89C2×C13×C4⋊C4D411yescharacteristic
90C2×C13×C4⋊C4D411yescharacteristic
91C2×C13×C22⋊C4D411yescharacteristic
92C2×C13×C22⋊C4D411yescharacteristic
93C2×C42×C13C2311yescharacteristic
94C2×C42×C13C2311yescharacteristic
95#88207—21no—
96C2×C22⋊Dic13—21no—
97C2×C22⋊Dic13—21no—
98#88184C2×C411yescharacteristic
99#88184C2311yescharacteristic
100#88183—21no—
101#88183—21no—
102#88183—21no—
103C4×C22⋊D13—21no—
104C4×C22⋊D13—21no—
105C4×C22⋊D13—21no—
106C4×C22⋊D13—21no—
107#88180—21no—
108#88180—21no—
109#88180C2×C411yescharacteristic
110C2×C4⋊Dic13—21no—
111C2×C4⋊Dic13—21no—
112C2×C4⋊Dic13C2×C411yescharacteristic
113#88178—21no—
114#88178—21no—
115#88178—21no—
116#88178—21no—
117#88178C2×C411yescharacteristic
118#88178C2×C411yescharacteristic
119#88178C2×C411yescharacteristic
120#88178C2311yescharacteristic
121#88178C2311yescharacteristic
122#88178C2311yescharacteristic
123C2×#6101—21no—
124C2×C4×Dic13—21no—
125C2×C4×Dic13—21no—
126#88152—21no—
127#88152—21no—
128#88151—21no—
129#88151—21no—
130#88150—21no—
131#88150—21no—
132#88146—21no—
133C4⋊C4×D13—21no—
134#88144—21no—
135#88143—21no—
136#88143—21no—
137#88143—21no—
138#88143—21no—
139#88142—21no—
140#88141—21no—
141#88141—21no—
142#88140—21no—
143#88140—21no—
144#88139—21no—
145#88139—21no—
146#88137—21no—
147#88137—21no—
148#88135—21no—
149#88135—21no—
150#88133—21no—
151#88133—21no—
152#88133—21no—
153#88133—21no—
154#88132—21no—
155#88132—21no—
156#88131—21no—
157#88131—21no—
158#88130—21no—
159#88130—21no—
160#88129C2×C411yescharacteristic, complemented
161#88129C2×C411yescharacteristic, complemented
162C4×D52C2×C411yescharacteristic, complemented
163C4×D52C2×C411yescharacteristic, complemented
164#88126—21no—
165#88126—21no—
166#88124—21no—
167#88124—21no—
168#88124C2×C411yescharacteristic, complemented
169#88124C2×C411yescharacteristic, complemented
170#88123C2×C411yescharacteristic, complemented
171#88123C2×C411yescharacteristic, complemented
172#88123C2×C411yescharacteristic, complemented
173#88123C2×C411yescharacteristic, complemented
174C4×Dic26—21no—
175C4×Dic26—21no—
176C4×Dic26C2×C411yescharacteristic, complemented
177C4×Dic26C2×C411yescharacteristic, complemented
178C4×Dic26C2×C411yescharacteristic, complemented
179C4×Dic26C2×C411yescharacteristic, complemented
180C4×Dic26C2×C411yescharacteristic, complemented
181C4×Dic26C2×C411yescharacteristic, complemented
182C13×C4⋊C8—21no—
183C13×C4⋊C8—21no—
184C13×C4⋊C8—21no—
185C13×C4⋊C8—21no—
186C13×C22⋊C8—21no—
187C13×C22⋊C8—21no—
188C13×C22⋊C8C2311yescharacteristic
189C13×C22⋊C8C2311yescharacteristic
190C13×C22⋊C8C2311yescharacteristic
191C13×C22⋊C8C2311yescharacteristic
192C13×#97—21no—
193C13×#97—21no—
194C4×C8×C13—21no—
195C4×C8×C13—21no—
196#88071—21no—
197#88071—21no—
198#88071—21no—
199#88071—21no—
200#88071—21no—
201#88071—21no—
202#88071C2311yescharacteristic
203#88071C2311yescharacteristic
204#88071C2311yescharacteristic
205#88071C2311yescharacteristic
206#17609—131nomaximal, Sylow
207C24×C13C2×D411yescharacteristic
208C22×C4×C13—42no—
209C22×C4×C13C22×C411yescharacteristic
210C22×C4×C13C22×C411yescharacteristic
211C22×C4×C13C2×D411yescharacteristic
212C22×C4×C13C2×D411yescharacteristic
213C22×C4×C13C2×D411yescharacteristic
214C22×C4×C13C2×D411yescharacteristic
215C22×C4×C13C2×D411yescharacteristic
216C22×C4×C13C2×D411yescharacteristic
217C22×C4×C13C2×D411yescharacteristic
218C22×C4×C13C2411yescharacteristic
219C2×C22⋊D13—21no—
220C2×C22⋊D13—21no—
221C2×C22⋊D13—21no—
222C22×Dic13—21no—
223C22×Dic13—21no—
224C22×Dic13—21no—
225C22×Dic13—21no—
226C22×Dic13—21no—
227C22×Dic13—21no—
228C22×Dic13—42no—
229C22×Dic13—42no—
230C22×Dic13—81no—
231#6127—42no—
232C2×D52C22×C411yescharacteristic
233C2×C4×D13—21no—
234C2×C4×D13—21no—
235C2×C4×D13—21no—
236C2×Dic26—21no—
237C2×Dic26—21no—
238C2×Dic26—21no—
239C2×Dic26—42no—
240C2×Dic26C22×C411yescharacteristic
241C2×Dic26C22×C411yescharacteristic
242C2×Dic26C22×C411yescharacteristic
243C13×M16—42no—
244C2×C8×C13—21no—
245C2×C8×C13—21no—
246C2×C8×C13—21no—
247C2×C8×C13—21no—
248C2×C8×C13—42no—
249C13×C4⋊C4C22⋊C411yescharacteristic
250C13×C4⋊C4C22⋊C411yescharacteristic
251C13×C4⋊C4C22⋊C411yescharacteristic
252C13×C4⋊C4C22⋊C411yescharacteristic
253C13×C4⋊C4C22⋊C411yescharacteristic
254C13×C4⋊C4C22⋊C411yescharacteristic
255C13×C4⋊C4C22⋊C411yescharacteristic
256C13×C4⋊C4C22⋊C411yescharacteristic
257C13×C22⋊C4C22⋊C411yescharacteristic
258C13×C22⋊C4C22⋊C411yescharacteristic
259C13×C22⋊C4C22⋊C411yescharacteristic
260C13×C22⋊C4C22⋊C411yescharacteristic
261C13×C22⋊C4C22⋊C411yescharacteristic
262C13×C22⋊C4C22⋊C411yescharacteristic
263C13×C22⋊C4C22⋊C411yescharacteristic
264C13×C22⋊C4C22⋊C411yescharacteristic
265C42×C13C22×C411yescharacteristic
266C42×C13C22×C411yescharacteristic
267C42×C13C22×C411yescharacteristic
268C42×C13C22×C411yescharacteristic
269C42×C13C2×D411yescharacteristic
270C42×C13C2×D411yescharacteristic
271C42×C13C2×D411yescharacteristic
272C42×C13C2×D411yescharacteristic
273C22⋊Dic13—21no—
274C22⋊Dic13—21no—
275C22⋊Dic13—21no—
276C22⋊Dic13—21no—
277C22⋊Dic13—21no—
278C22⋊Dic13—21no—
279C22⋊Dic13—21no—
280C22⋊Dic13—42no—
281#6103—21no—
282#6103—21no—
283#6103—21no—
284#6103—21no—
285#6103—21no—
286#6103—21no—
287#6103—21no—
288#6103—21no—
289C4⋊Dic13—21no—
290C4⋊Dic13—21no—
291C4⋊Dic13—21no—
292C4⋊Dic13—21no—
293C4⋊Dic13—21no—
294C4⋊Dic13—21no—
295C4⋊Dic13—21no—
296C4⋊Dic13—42no—
297C4⋊Dic13—81no—
298C4⋊Dic13C22×C411yescharacteristic
299C4⋊Dic13C22×C411yescharacteristic
300C4⋊Dic13C22×C411yescharacteristic
301C4⋊Dic13C22×C411yescharacteristic
302#6101—21no—
303#6101—21no—
304#6101—21no—
305#6101—21no—
306#6101—21no—
307#6101—21no—
308#6101—21no—
309#6101—21no—
310#6101—21no—
311#6101—21no—
312#6101—21no—
313#6101—21no—
314#6101—21no—
315#6101—21no—
316#6101—21no—
317#6101—21no—
318C4×Dic13—21no—
319C4×Dic13—21no—
320C4×Dic13—21no—
321C4×Dic13—21no—
322C4×Dic13—21no—
323C4×Dic13—21no—
324C4×Dic13—21no—
325C4×Dic13—42no—
326C4×Dic13—81no—
327#3495—131no—
328#2924D1311yescharacteristic, complemented
329#2343—131no—
330#1521—131no—
331#1518—131no—
332#1516—131no—
333#1515—131no—
334#1512—131no—
335#1511—131no—
336#1509—131no—
337#1506—131no—
338#1504—131no—
339#1503—131no—
340#1500—131no—
341C2×#328—131no—
342C23×C13—21no—
343C23×C13—21no—
344C23×C13—22no—
345C23×C13—41no—
346C23×C13C2×C22⋊C411yescharacteristic
347C23×C13C2×C22⋊C411yescharacteristic
348C23×C13C22×D411yescharacteristic
349C22×D13—21no—
350C2×C4×C13—21no—
351C2×C4×C13—21no—
352C2×C4×C13—21no—
353C2×C4×C13—21no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—41no—
357C2×C4×C13—41no—
358C2×C4×C13—41no—
359C2×C4×C13—41no—
360C2×C4×C13—41no—
361C2×C4×C13—41no—
362C2×C4×C13C2×C22⋊C411yescharacteristic
363C2×C4×C13C2×C22⋊C411yescharacteristic
364C2×C4×C13C2×C22⋊C411yescharacteristic
365C2×C4×C13C2×C22⋊C411yescharacteristic
366C2×C4×C13C2×C22⋊C411yescharacteristic
367C2×C4×C13C2×C22⋊C411yescharacteristic
368C2×C4×C13C2×C22⋊C411yescharacteristic
369C2×C4×C13C2×C22⋊C411yescharacteristic
370C2×C4×C13C2×C22⋊C411yescharacteristic
371C2×C4×C13C2×C22⋊C411yescharacteristic
372C2×C4×C13C23×C411yescharacteristic
373C2×C4×C13C22×D411yescharacteristic
374C22⋊D13—41no—
375C22⋊D13—41no—
376C22⋊D13—42no—
377C22⋊D13—81no—
378C2×Dic13—22no—
379C2×Dic13—21no—
380C2×Dic13—21no—
381C2×Dic13—21no—
382C2×Dic13—21no—
383C2×Dic13—21no—
384C2×Dic13—21no—
385C2×Dic13—21no—
386C2×Dic13—41no—
387C2×Dic13—41no—
388C2×Dic13—42no—
389C2×Dic13—41no—
390C2×Dic13—41no—
391C2×Dic13—41no—
392C2×Dic13—41no—
393C2×Dic13—41no—
394C2×Dic13—41no—
395C2×Dic13—41no—
396C2×Dic13—41no—
397C2×Dic13—41no—
398C2×Dic13—81no—
399C2×Dic13—84no—
400D52—41no—
401C4×D13—42no—
402C4×D13—81no—
403C4×D13—81no—
404Dic26—42no—
405Dic26—41no—
406Dic26—41no—
407Dic26—41no—
408Dic26—81no—
409Dic26—81no—
410C8×C13—41no—
411C8×C13—41no—
412C8×C13—41no—
413C8×C13—41no—
414#556—261no—
415#554—261no—
416#552—261no—
417#552—261no—
418#552—261no—
419#552—261no—
420#551—261no—
421#551—261no—
422#544—131no—
423#542—131no—
424#542—131no—
425#541—131no—
426#541—131no—
427#536—131no—
428#533—131no—
429#533—131no—
430#529—131no—
431#529—131no—
432#525—131no—
433C2×C22⋊Q8—131no—
434#520—131no—
435#519—131no—
436C2×#117C2×D1311yescharacteristic
437#433—21no—
438#433—21no—
439#432C2×D1311yescharacteristic
440#432C2×D1311yescharacteristic
441#431C2×D1311yescharacteristic
442#431C2×D1311yescharacteristic
443#424—21no—
444#407C2×D1311yescharacteristic
445C2×C22⋊C8C2×D1311yescharacteristic
446#405—21no—
447#387—261no—
448#387—261no—
449#385—261no—
450#383—131no—
451#382—131no—
452#381—131no—
453C4×C4⋊C4—131no—
454C4×C22⋊C4—261no—
455#376—131no—
456C2×#95—131no—
457#328—131no—
458#328—131no—
459#328—131no—
460#328—131no—
461#328—131no—
462#328—131no—
463#328—131no—
464#328—131no—
465#328—131no—
466#328—131no—
467#328—131no—
468#328—131no—
469#327—131no—
470#327—131no—
471#327—131no—
472#327—131no—
473C22×C13—21no—
474C22×C13—21no—
475C22×C13—21no—
476C22×C13—21no—
477C22×C13—21no—
478C22×C13—21no—
479C22×C13—21no—
480C22×C13—42no—
481C22×C13—42no—
482C22×C13#41012yes—
483C22×C13C22×C22⋊C411yescharacteristic
484C22×C13#57711yescharacteristic
485C22×C13#57811yescharacteristic
486C2×D13—41no—
487C2×D13—41no—
488C2×D13—41no—
489C4×C13—21no—
490C4×C13—21no—
491C4×C13—21no—
492C4×C13—21no—
493C4×C13—21no—
494C4×C13—21no—
495C4×C13—21no—
496C4×C13—21no—
497C4×C13—21no—
498C4×C13—21no—
499C4×C13—21no—
500C4×C13—21no—
501Dic13—42no—
502Dic13—41no—
503Dic13—41no—
504Dic13—41no—
505Dic13—41no—
506Dic13—41no—
507Dic13—41no—
508Dic13—41no—
509Dic13—81no—
510Dic13—81no—
511Dic13—81no—
512C2×#41—131no—
513C22×Q8—131no—
514C23×C4—261no—
515C23×C4C22×D1311yescharacteristic
516C2×M16—21no—
517C22×C8—21no—
518C4⋊Q8—131no—
519C4⋊Q8—131no—
520C4⋊Q8—131no—
521C4⋊Q8—131no—
522C4⋊Q8—261no—
523#126—261no—
524#126—261no—
525#126—261no—
526#126—261no—
527#126—261no—
528#126—261no—
529#126—261no—
530#126—261no—
531#125—131no—
532#125—131no—
533#125—261no—
534#125—261no—
535#125—261no—
536#125—261no—
537#125—261no—
538#125—261no—
539#125—261no—
540#124—131no—
541#124—131no—
542#124—261no—
543#124—261no—
544#123—261no—
545#123—261no—
546#123—261no—
547#123—261no—
548#123—261no—
549#123—261no—
550#123—261no—
551C22⋊Q8—131no—
552C22⋊Q8—131no—
553C22⋊Q8—131no—
554C22⋊Q8—131no—
555C22⋊Q8—131no—
556C22⋊Q8—131no—
557C22⋊Q8—261no—
558C22⋊Q8—261no—
559C22⋊Q8—261no—
560C22⋊Q8—261no—
561C22⋊Q8—261no—
562C22⋊Q8—261no—
563C22⋊Q8—261no—
564C22⋊Q8—261no—
565C22⋊Q8—261no—
566C22⋊Q8—261no—
567#121—131no—
568#121—131no—
569#120—261no—
570C4×Q8—131no—
571C4×Q8—131no—
572C4×Q8—131no—
573C4×Q8—131no—
574C4×Q8—131no—
575C4×Q8—131no—
576C4×Q8—261no—
577C4×Q8—261no—
578C4×Q8—261no—
579C4×Q8—261no—
580C4×D4—131no—
581C4×D4—131no—
582C4×D4—261no—
583C4×D4—261no—
584C4×D4—261no—
585C4×D4—261no—
586C4×D4—261no—
587C4×D4—261no—
588#117—131no—
589#117—261no—
590#117—261no—
591#117—261no—
592#117—261no—
593#117—261no—
594#117—261no—
595#117—261no—
596#117C4×D1311yescharacteristic
597#117C4×D1311yescharacteristic
598#117C4×D1311yescharacteristic
599#117C4×D1311yescharacteristic
600#117C22⋊D1311yescharacteristic
601#117C22⋊D1311yescharacteristic
602#117C22⋊D1311yescharacteristic
603#117C22⋊D1311yescharacteristic
604C2×C4⋊C4—131no—
605C2×C4⋊C4—261no—
606C2×C4⋊C4—261no—
607C2×C4⋊C4—261no—
608C2×C4⋊C4—261no—
609C2×C4⋊C4D5211yescharacteristic
610C2×C4⋊C4D5211yescharacteristic
611C2×C22⋊C4—261no—
612C2×C22⋊C4—261no—
613C2×C22⋊C4D5211yescharacteristic
614C2×C22⋊C4D5211yescharacteristic
615C2×C42—261no—
616C2×C42—261no—
617C2×C42C22×D1311yescharacteristic
618C2×C42C22×D1311yescharacteristic
619C4⋊C8—21no—
620C4⋊C8—21no—
621C4⋊C8—21no—
622C4⋊C8—21no—
623C22⋊C8—21no—
624C22⋊C8—21no—
625C22⋊C8C22×D1311yescharacteristic
626C22⋊C8C22×D1311yescharacteristic
627C22⋊C8C22×D1311yescharacteristic
628C22⋊C8C22×D1311yescharacteristic
629#97—21no—
630#97—21no—
631C4×C8—21no—
632C4×C8—21no—
633#95—131no—
634#95—131no—
635#95—131no—
636#95—131no—
637#95—261no—
638#95—261no—
639#95—261no—
640#95—261no—
641#95—261no—
642#95—261no—
643C2×C13—21no—
644C2×C13—21no—
645C2×C13—22no—
646C2×C13—41no—
647C2×C13C2×#41011yescharacteristic
648C2×C13#289811yescharacteristic
649C2×C13#290111yescharacteristic
650D13—81no—
651C24C2×D5211yescharacteristic
652#41—522no—
653C2×Q8—131no—
654C2×Q8—131no—
655C2×Q8—131no—
656C2×Q8—261no—
657C2×Q8—261no—
658C2×Q8—261no—
659C2×Q8—522no—
660C2×D4—131no—
661C2×D4—261no—
662C2×D4—261no—
663C2×D4—261no—
664C22×C4—42no—
665C22×C4—261no—
666C22×C4—261no—
667C22×C4—261no—
668C22×C4—261no—
669C22×C4—261no—
670C22×C4—261no—
671C22×C4—261no—
672C22×C4—261no—
673C22×C4—261no—
674C22×C4—522no—
675C22×C4—522no—
676C22×C4—1041no—
677C22×C4C2×C4×D1311yescharacteristic
678C22×C4C2×C4×D1311yescharacteristic
679C22×C4C2×D5211yescharacteristic
680C22×C4C2×D5211yescharacteristic
681C22×C4C2×D5211yescharacteristic
682C22×C4C2×D5211yescharacteristic
683C22×C4C2×D5211yescharacteristic
684C22×C4C2×C22⋊D1311yescharacteristic
685C22×C4C2×C22⋊D1311yescharacteristic
686C22×C4C23×D1311yescharacteristic
687M16—42no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—42no—
693C4⋊C4—131no—
694C4⋊C4—131no—
695C4⋊C4—131no—
696C4⋊C4—131no—
697C4⋊C4—261no—
698C4⋊C4—261no—
699C4⋊C4—261no—
700C4⋊C4—261no—
701C4⋊C4—261no—
702C4⋊C4—261no—
703C4⋊C4—261no—
704C4⋊C4—261no—
705C4⋊C4—261no—
706C4⋊C4—261no—
707C4⋊C4—261no—
708C4⋊C4—261no—
709C4⋊C4—261no—
710C4⋊C4—261no—
711C4⋊C4—261no—
712C4⋊C4—261no—
713C4⋊C4—261no—
714C4⋊C4—261no—
715C4⋊C4—261no—
716C4⋊C4—261no—
717C4⋊C4—261no—
718C4⋊C4—261no—
719C4⋊C4—261no—
720C4⋊C4—522no—
721C4⋊C4—1041no—
722C4⋊C4#610311yescharacteristic
723C4⋊C4#610311yescharacteristic
724C4⋊C4#610311yescharacteristic
725C4⋊C4#610311yescharacteristic
726C4⋊C4#610311yescharacteristic
727C4⋊C4#610311yescharacteristic
728C4⋊C4#610311yescharacteristic
729C4⋊C4#610311yescharacteristic
730C22⋊C4—261no—
731C22⋊C4—261no—
732C22⋊C4—261no—
733C22⋊C4—261no—
734C22⋊C4—261no—
735C22⋊C4—261no—
736C22⋊C4—261no—
737C22⋊C4—261no—
738C22⋊C4—261no—
739C22⋊C4—261no—
740C22⋊C4—261no—
741C22⋊C4—261no—
742C22⋊C4—261no—
743C22⋊C4—261no—
744C22⋊C4—261no—
745C22⋊C4—522no—
746C22⋊C4#610311yescharacteristic
747C22⋊C4#610311yescharacteristic
748C22⋊C4#610311yescharacteristic
749C22⋊C4#610311yescharacteristic
750C22⋊C4#610311yescharacteristic
751C22⋊C4#610311yescharacteristic
752C22⋊C4#610311yescharacteristic
753C22⋊C4#610311yescharacteristic
754C42—261no—
755C42—261no—
756C42—261no—
757C42—261no—
758C42—261no—
759C42—261no—
760C42—261no—
761C42—522no—
762C42—1041no—
763C42C2×C4×D1311yescharacteristic
764C42C2×C4×D1311yescharacteristic
765C42C2×C4×D1311yescharacteristic
766C42C2×C4×D1311yescharacteristic
767C42C2×C22⋊D1311yescharacteristic
768C42C2×C22⋊D1311yescharacteristic
769C42C2×C22⋊D1311yescharacteristic
770C42C2×C22⋊D1311yescharacteristic
771C13#1760911yescharacteristic, complemented, Sylow
772C23—22no—
773C23—21no—
774C23—21no—
775C23—41no—
776C23—261no—
777C23C2×#610311yescharacteristic
778C23C2×#610311yescharacteristic
779C23C22×D5211yescharacteristic
780Q8—521no—
781Q8—521no—
782Q8—521no—
783Q8—522no—
784Q8—1041no—
785Q8—1041no—
786D4—521no—
787D4—522no—
788D4—521no—
789D4—521no—
790D4—1041no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—262no—
804C2×C4—261no—
805C2×C4—261no—
806C2×C4—261no—
807C2×C4—261no—
808C2×C4—261no—
809C2×C4—261no—
810C2×C4—261no—
811C2×C4—522no—
812C2×C4—521no—
813C2×C4—522no—
814C2×C4—521no—
815C2×C4—521no—
816C2×C4—521no—
817C2×C4—521no—
818C2×C4—521no—
819C2×C4—521no—
820C2×C4—521no—
821C2×C4—521no—
822C2×C4—521no—
823C2×C4—521no—
824C2×C4—1041no—
825C2×C4—1041no—
826C2×C4—1041no—
827C2×C4—1044no—
828C2×C4C2×#610311yescharacteristic
829C2×C4C2×#610311yescharacteristic
830C2×C4C2×#610311yescharacteristic
831C2×C4C2×#610311yescharacteristic
832C2×C4C2×#610311yescharacteristic
833C2×C4C2×#610311yescharacteristic
834C2×C4C2×#610311yescharacteristic
835C2×C4C2×#610311yescharacteristic
836C2×C4C2×#610311yescharacteristic
837C2×C4C2×#610311yescharacteristic
838C2×C4C22×C4×D1311yescharacteristic
839C2×C4C22×C22⋊D1311yescharacteristic
840C8—41no—
841C8—41no—
842C8—41no—
843C8—41no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—42no—
852C22—42no—
853C22—521no—
854C22—521no—
855C22—521no—
856C22#1171866712yes—
857C22#1171945611yescharacteristic
858C22#1171945811yescharacteristic
859C22C22×#610311yescharacteristic
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—522no—
873C4—521no—
874C4—521no—
875C4—521no—
876C4—521no—
877C4—521no—
878C4—521no—
879C4—521no—
880C4—1041no—
881C4—1041no—
882C4—1041no—
883C2—21no—
884C2—21no—
885C2—22no—
886C2—41no—
887C2—1041no—
888C2C2×#1171866711yescharacteristic
889C2#1312337011yescharacteristic
890C2#1312338111yescharacteristic
subgroupG/H
centerC22C22×#6103
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2924C2
socleC22×C13C22×C22⋊C4
prime radical#11719496C22
cosocleC22×C4×C13C24
hypercenter#2924D13
hypocenterC13#17609
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #13117696C2semidirect
3. #13113414C2semidirect
4. #13113401C2semidirect
6. #13113388C2semidirect
7. #13113375C2semidirect
8. #13113370C2semidirect
9. #13113362C2semidirect
10. #13113349C2semidirect
12. #13113336C2semidirect
13. #13113323C2semidirect
14. C2×#11718059C2semidirect
15. C13×#2924C2semidirect
19. #11719239C4semidirect
20. #11719239C4semidirect
25. #11719231C4semidirect
26. #11719228C4semidirect
27. #11719224C4semidirect
28. #11719223C4semidirect
29. #11719223C4semidirect
30. #11719221C4semidirect
160. #88129C2×C4semidirect
161. #88129C2×C4semidirect
162. C4×D52C2×C4semidirect
163. C4×D52C2×C4semidirect
168. #88124C2×C4semidirect
169. #88124C2×C4semidirect
170. #88123C2×C4semidirect
171. #88123C2×C4semidirect
172. #88123C2×C4semidirect
173. #88123C2×C4semidirect
176. C4×Dic26C2×C4semidirect
177. C4×Dic26C2×C4semidirect
178. C4×Dic26C2×C4semidirect
179. C4×Dic26C2×C4semidirect
180. C4×Dic26C2×C4semidirect
181. C4×Dic26C2×C4semidirect
328. #2924D13semidirect
771. C13#17609semidirect

Maximal subgroups

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

subgroupindex
#131285882
#131176962
#131134142
#131134012
#131133932
#131133882
#131133752
#131133702
#131133622
#131133492
#131133412
#131133362
#131133232
C2×#117180592
C13×#29242
#1760913