Finite Group Databasebeta

← #15829763

Subgroups — #15829763

Order 3328.

890 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128263C211yesmaximal, characteristic
2#13123803C211yesmaximal, characteristic, complemented
3#13113308C211yesmaximal, characteristic, complemented
4#13113299C211yesmaximal, characteristic, complemented
5#13113294C211yesmaximal, characteristic, complemented
6#13113290C211yesmaximal, characteristic, complemented
7#13113282C211yesmaximal, characteristic, complemented
8#13113273C211yesmaximal, characteristic, complemented
9#13113268C211yesmaximal, characteristic, complemented
10#13113264C211yesmaximal, characteristic, complemented
11#13113256C211yesmaximal, characteristic, complemented
12#13113247C211yesmaximal, characteristic, complemented
13#13113242C211yesmaximal, characteristic, complemented
14#13113238C211yesmaximal, characteristic, complemented
15C13×#2989C211yesmaximal, characteristic, complemented
16C4×C13×#41C2211yescharacteristic
17#11719538C411yescharacteristic
18#11719530C411yescharacteristic
19#11719288—21no—
20#11719283—21no—
21#11719269—21no—
22#11719269—21no—
23#11719266—21no—
24#11719262—21no—
25#11719243—21no—
26#11719243—21no—
27#11719239C411yescharacteristic
28#11719239C411yescharacteristic
29#11719231C411yescharacteristic
30#11719224C411yescharacteristic
31#11719223C411yescharacteristic
32#11719223C411yescharacteristic
33#11719184C2211yescharacteristic
34#11719184C2211yescharacteristic
35C4×#6127C2211yescharacteristic
36#11719175C2211yescharacteristic
37#11719175C2211yescharacteristic
38C2×C4×Dic26C2211yescharacteristic
39C13×#446—21no—
40C13×#436—21no—
41C13×#435—21no—
42C13×#435—21no—
43C13×#432C2211yescharacteristic
44C13×#432C2211yescharacteristic
45C13×#431C2211yescharacteristic
46C13×#423C2211yescharacteristic
47C13×#423C2211yescharacteristic
48C2×C13×C4⋊C8C2211yescharacteristic
49#11718685—21no—
50#11718673—21no—
51#11718672—21no—
52#11718672—21no—
53#11718586C2211yescharacteristic
54#11718586C2211yescharacteristic
55#11718586C2211yescharacteristic
56C4×#6099C2211yescharacteristic
57C4×#6099C2211yescharacteristic
58C2×C4×#1055C2211yescharacteristic
59#11718076C2211yescharacteristic
60#11718076C2211yescharacteristic
61#11718076C2211yescharacteristic
62#11718076C2211yescharacteristic
63#11718076C2211yescharacteristic
64#11718076C2211yescharacteristic
65#11718076C2211yescharacteristic
66#11718076C2211yescharacteristic
67#11718076C2211yescharacteristic
68#11718076C2211yescharacteristic
69#11718076C2211yescharacteristic
70#11718076C2211yescharacteristic
71#11718075C2211yescharacteristic
72#11718075C2211yescharacteristic
73#11718075C2211yescharacteristic
74#11718075C2211yescharacteristic
75C2×C13×#41C2×C411yescharacteristic
76C2×#6127C2×C411yescharacteristic
77C22×Dic26C2×C411yescharacteristic
78C2×C13×M16—21no—
79C2×C13×M16—21no—
80C22×C8×C13—21no—
81C4×Q8×C13D411yescharacteristic
82C4×Q8×C13D411yescharacteristic
83C4×D4×C13D411yescharacteristic
84C4×D4×C13D411yescharacteristic
85C4×D4×C13D411yescharacteristic
86C4×D4×C13D411yescharacteristic
87C4×D4×C13D411yescharacteristic
88C4×D4×C13D411yescharacteristic
89C13×#117C2×C411yescharacteristic
90C13×#117C2×C411yescharacteristic
91C13×#117C2×C411yescharacteristic
92C2×C42×C13C2311yescharacteristic
93C2×C42×C13C2311yescharacteristic
94C2×C42×C13C2311yescharacteristic
95#88200—21no—
96#88198—21no—
97#88193—21no—
98#88193—21no—
99#88192—21no—
100#88190—21no—
101#88189—21no—
102#88189—21no—
103#88184C2×C411yescharacteristic
104#88184C2×C411yescharacteristic
105#88183—21no—
106#88183—21no—
107C4×C22⋊D13—21no—
108C4×C22⋊D13—21no—
109C4×C22⋊D13—21no—
110C4×C22⋊D13—21no—
111#88180—21no—
112#88180—21no—
113#88180C2×C411yescharacteristic
114C2×C4⋊Dic13C2×C411yescharacteristic
115#88178—21no—
116#88178—21no—
117#88178C2×C411yescharacteristic
118#88178C2×C411yescharacteristic
119#88178C2×C411yescharacteristic
120#88178C2×C411yescharacteristic
121#88178C2×C411yescharacteristic
122#88178C2×C411yescharacteristic
123C2×#6101—21no—
124C2×C4×Dic13—21no—
125C2×#6099—21no—
126C2×#6099—21no—
127C22×#1055—21no—
128#88152—21no—
129#88152—21no—
130#88151—21no—
131#88151—21no—
132#88150—21no—
133#88150—21no—
134#88144—21no—
135#88143—21no—
136#88143—21no—
137#88143—21no—
138#88143—21no—
139#88142—21no—
140#88140—21no—
141#88140—21no—
142#88139—21no—
143#88139—21no—
144#88137—21no—
145#88137—21no—
146#88133—21no—
147#88133—21no—
148#88133—21no—
149#88133—21no—
150#88132—21no—
151#88132—21no—
152#88130—21no—
153#88130—21no—
154#88129C2×C411yescharacteristic
155#88129C2×C411yescharacteristic
156C4×D52C2×C411yescharacteristic
157C4×D52C2311yescharacteristic
158#88126—21no—
159#88126—21no—
160#88126—21no—
161C42×D13—21no—
162#88124—21no—
163#88124—21no—
164#88124C2×C411yescharacteristic
165#88124C2×C411yescharacteristic
166#88123C2×C411yescharacteristic
167#88123C2×C411yescharacteristic
168#88123C2×C411yescharacteristic
169#88123C2×C411yescharacteristic
170C4×Dic26—21no—
171C4×Dic26—21no—
172C4×Dic26—21no—
173C4×Dic26—21no—
174C4×Dic26C2×C411yescharacteristic
175C4×Dic26C2×C411yescharacteristic
176C4×Dic26C2×C411yescharacteristic
177C4×Dic26C2311yescharacteristic
178C4×Dic26C2311yescharacteristic
179C4×Dic26C2311yescharacteristic
180C13×C4⋊C8—21no—
181C13×C4⋊C8—21no—
182C13×C4⋊C8—21no—
183C13×C4⋊C8C2311yescharacteristic
184C13×C4⋊C8C2311yescharacteristic
185C13×C4⋊C8C2311yescharacteristic
186C13×C4⋊C8C2311yescharacteristic
187C13×C22⋊C8—21no—
188C13×C22⋊C8—21no—
189C13×C22⋊C8—21no—
190C13×#97—21no—
191C13×#97—21no—
192C4×C8×C13—21no—
193C22⋊#1055—21no—
194C22⋊#1055—21no—
195C22⋊#1055—21no—
196C4⋊#1055—21no—
197C4⋊#1055—21no—
198C4⋊#1055—21no—
199#88043—21no—
200#88043—21no—
201C4×#1055—21no—
202C4×#1055C2311yescharacteristic
203C4×#1055C2311yescharacteristic
204C4×#1055C2311yescharacteristic
205C4×#1055C2311yescharacteristic
206#17506—131nomaximal, Sylow
207C13×#41—42no—
208C2×Q8×C13C22⋊C411yescharacteristic
209C2×D4×C13C22⋊C411yescharacteristic
210C2×D4×C13C22⋊C411yescharacteristic
211C2×D4×C13C22⋊C411yescharacteristic
212C22×C4×C13C22×C411yescharacteristic
213C22×C4×C13C22×C411yescharacteristic
214C22×C4×C13C22×C411yescharacteristic
215C22×C4×C13C2×D411yescharacteristic
216C22×C4×C13C2×D411yescharacteristic
217C22×C4×C13C2×D411yescharacteristic
218C22×C4×C13C2×D411yescharacteristic
219C22×C4×C13C2×D411yescharacteristic
220C22×C4×C13C2×D411yescharacteristic
221C2×C22⋊D13—21no—
222C2×C22⋊D13—21no—
223C2×C22⋊D13—21no—
224C22×Dic13—21no—
225C22×Dic13—21no—
226#6127—42no—
227C2×D52C22×C411yescharacteristic
228C2×C4×D13—21no—
229C2×C4×D13—21no—
230C2×C4×D13—21no—
231C2×Dic26—21no—
232C2×Dic26—21no—
233C2×Dic26—21no—
234C2×Dic26—42no—
235C2×Dic26C22×C411yescharacteristic
236C2×Dic26C22×C411yescharacteristic
237C2×Dic26C22×C411yescharacteristic
238C13×M16—81no—
239C13×M16—81no—
240C2×C8×C13—21no—
241C2×C8×C13—21no—
242C2×C8×C13—21no—
243C2×C8×C13—21no—
244C2×C8×C13—81no—
245C13×C4⋊C4C22⋊C411yescharacteristic
246C13×C4⋊C4C22⋊C411yescharacteristic
247C13×C4⋊C4C22⋊C411yescharacteristic
248C13×C4⋊C4C22⋊C411yescharacteristic
249C13×C4⋊C4C22⋊C411yescharacteristic
250C13×C4⋊C4C22⋊C411yescharacteristic
251C13×C22⋊C4C22⋊C411yescharacteristic
252C13×C22⋊C4C22⋊C411yescharacteristic
253C13×C22⋊C4C22⋊C411yescharacteristic
254C13×C22⋊C4C22⋊C411yescharacteristic
255C13×C22⋊C4C22⋊C411yescharacteristic
256C13×C22⋊C4C22⋊C411yescharacteristic
257C42×C13C22×C411yescharacteristic
258C42×C13C22×C411yescharacteristic
259C42×C13C22×C411yescharacteristic
260C42×C13C2×D411yescharacteristic
261C42×C13C2×D411yescharacteristic
262C42×C13C2×D411yescharacteristic
263C42×C13C2×D411yescharacteristic
264C42×C13C2×D411yescharacteristic
265C42×C13C2×D411yescharacteristic
266C42×C13C2411yescharacteristic
267C22⋊Dic13—21no—
268C22⋊Dic13—21no—
269C22⋊Dic13—21no—
270C22⋊Dic13—21no—
271C22⋊Dic13—21no—
272C22⋊Dic13—21no—
273C22⋊Dic13—21no—
274#6103—21no—
275#6103—21no—
276#6103—21no—
277#6103—21no—
278#6103—21no—
279#6103—21no—
280#6103—21no—
281#6103—21no—
282C4⋊Dic13—21no—
283C4⋊Dic13—21no—
284C4⋊Dic13—21no—
285C4⋊Dic13—21no—
286C4⋊Dic13—21no—
287C4⋊Dic13—21no—
288C4⋊Dic13—21no—
289C4⋊Dic13C22×C411yescharacteristic
290C4⋊Dic13C22×C411yescharacteristic
291C4⋊Dic13C22×C411yescharacteristic
292C4⋊Dic13C22×C411yescharacteristic
293#6101—21no—
294#6101—21no—
295#6101—21no—
296#6101—21no—
297#6101—21no—
298#6101—21no—
299#6101—21no—
300#6101—21no—
301#6101—21no—
302#6101—21no—
303#6101—21no—
304#6101—21no—
305#6101—21no—
306#6101—21no—
307#6101—21no—
308#6101—21no—
309C4×Dic13—21no—
310C4×Dic13—21no—
311C4×Dic13—21no—
312C4×Dic13—21no—
313C4×Dic13—21no—
314C4×Dic13—21no—
315C4×Dic13—21no—
316#6099—42no—
317#6099—42no—
318C2×#1055—21no—
319C2×#1055—21no—
320C2×#1055—21no—
321C2×#1055—21no—
322C2×#1055—42no—
323#3461—131no—
324#2989D1311yescharacteristic, complemented
325#2965—131no—
326#1497—131no—
327#1495—131no—
328#1494—131no—
329#1493—131no—
330#1491—131no—
331#1489—131no—
332#1488—131no—
333#1487—131no—
334#1485—131no—
335#1483—131no—
336#1482—131no—
337#1481—131no—
338C23×C13C2×C22⋊C411yescharacteristic
339C23×C13C2×C22⋊C411yescharacteristic
340C23×C13C2×C22⋊C411yescharacteristic
341C22×D13—21no—
342Q8×C13—41no—
343D4×C13—41no—
344D4×C13—41no—
345D4×C13—41no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—21no—
350C2×C4×C13—21no—
351C2×C4×C13—21no—
352C2×C4×C13—21no—
353C2×C4×C13—21no—
354C2×C4×C13—21no—
355C2×C4×C13—41no—
356C2×C4×C13—41no—
357C2×C4×C13—41no—
358C2×C4×C13C2×C22⋊C411yescharacteristic
359C2×C4×C13C2×C22⋊C411yescharacteristic
360C2×C4×C13C2×C22⋊C411yescharacteristic
361C2×C4×C13C2×C22⋊C411yescharacteristic
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×C13C23×C411yescharacteristic
368C2×C4×C13C22×D411yescharacteristic
369C2×C4×C13C22×D411yescharacteristic
370C22⋊D13—42no—
371C22⋊D13—81no—
372C22⋊D13—81no—
373C2×Dic13—21no—
374C2×Dic13—21no—
375C2×Dic13—21no—
376C2×Dic13—21no—
377C2×Dic13—21no—
378C2×Dic13—21no—
379C2×Dic13—21no—
380C2×Dic13—42no—
381C2×Dic13—81no—
382D52—22no—
383C4×D13—42no—
384C4×D13—41no—
385C4×D13—41no—
386C4×D13—81no—
387Dic26—22no—
388Dic26—22no—
389Dic26—22no—
390Dic26—42no—
391Dic26—81no—
392Dic26—81no—
393C8×C13—41no—
394C8×C13—41no—
395C8×C13—41no—
396C8×C13—41no—
397#1055—22no—
398#1055—41no—
399#1055—41no—
400#1055—41no—
401#544—131no—
402#542—131no—
403#542—131no—
404#542—261no—
405#541—131no—
406#541—131no—
407#541—261no—
408#539—261no—
409#539—261no—
410#537—131no—
411#536—131no—
412#536—131no—
413#533—131no—
414#533—131no—
415#533—261no—
416#529—131no—
417#529—131no—
418#529—261no—
419#529—261no—
420#529—261no—
421C4×#41—131no—
422C4×#41C2×D1311yescharacteristic
423C2×C4×Q8—131no—
424#446—21no—
425#446—261no—
426#436—21no—
427#436—261no—
428#435—21no—
429#435—21no—
430#435—261no—
431#435—261no—
432#432C2×D1311yescharacteristic
433#432C2×D1311yescharacteristic
434#431—131no—
435#431—131no—
436#431—131no—
437#431C2×D1311yescharacteristic
438#423C2×D1311yescharacteristic
439#423C2×D1311yescharacteristic
440C2×C4⋊C8C2×D1311yescharacteristic
441C4×M16—131no—
442C4×M16—131no—
443C2×C4×C8—131no—
444Q8⋊C8—131no—
445Q8⋊C8—131no—
446Q8⋊C8—131no—
447Q8⋊C8—131no—
448Q8⋊C8—131no—
449Q8⋊C8—131no—
450Q8⋊C8—131no—
451Q8⋊C8—131no—
452Q8⋊C8—131no—
453Q8⋊C8—131no—
454Q8⋊C8—131no—
455Q8⋊C8—131no—
456D4⋊C8—131no—
457D4⋊C8—131no—
458D4⋊C8—131no—
459D4⋊C8—131no—
460C22×C13—21no—
461C22×C13—21no—
462C22×C13—21no—
463C22×C13—21no—
464C22×C13—21no—
465C22×C13—21no—
466C22×C13—21no—
467C22×C13—21no—
468C22×C13—21no—
469C22×C13C22×C22⋊C411yescharacteristic
470C2×D13—41no—
471C2×D13—41no—
472C2×D13—41no—
473C4×C13—21no—
474C4×C13—21no—
475C4×C13—21no—
476C4×C13—21no—
477C4×C13—21no—
478C4×C13—21no—
479C4×C13—21no—
480C4×C13—21no—
481C4×C13—21no—
482C4×C13—21no—
483C4×C13#56812yes—
484C4×C13#57711yescharacteristic
485C4×C13#57811yescharacteristic
486Dic13—41no—
487Dic13—41no—
488Dic13—41no—
489Dic13—41no—
490Dic13—41no—
491Dic13—41no—
492Dic13—41no—
493C2×#41—131no—
494C2×#41C4×D1311yescharacteristic
495C22×Q8—131no—
496C2×M16—21no—
497C2×M16—21no—
498C2×M16—261no—
499C2×M16—261no—
500C22×C8—21no—
501C22×C8—261no—
502C4⋊Q8—131no—
503C4⋊Q8—131no—
504C4⋊Q8—131no—
505C4⋊Q8—131no—
506C4⋊Q8—261no—
507C4⋊Q8—261no—
508#126—261no—
509#126—261no—
510#126—261no—
511#126—261no—
512#126—261no—
513#126—261no—
514#126—261no—
515#126—261no—
516#125—131no—
517#125—131no—
518#125—261no—
519#125—261no—
520#125—261no—
521#125—261no—
522#125—261no—
523#125—261no—
524#125—261no—
525#124—131no—
526#124—131no—
527#124—261no—
528#124—261no—
529#124—261no—
530#123—261no—
531#123—261no—
532#123—261no—
533#123—261no—
534#123—261no—
535#123—261no—
536#123—261no—
537#123—261no—
538C22⋊Q8—131no—
539C22⋊Q8—131no—
540C22⋊Q8—131no—
541C22⋊Q8—131no—
542C22⋊Q8—131no—
543C22⋊Q8—131no—
544C22⋊Q8—261no—
545C22⋊Q8—261no—
546C22⋊Q8—261no—
547C22⋊Q8—261no—
548C22⋊Q8—261no—
549C22⋊Q8—261no—
550C22⋊Q8—261no—
551C22⋊Q8—261no—
552C22⋊Q8—261no—
553#121—131no—
554#121—131no—
555#121—261no—
556#121—261no—
557#121—261no—
558C4×Q8—131no—
559C4×Q8—131no—
560C4×Q8—131no—
561C4×Q8—131no—
562C4×Q8—131no—
563C4×Q8—131no—
564C4×Q8—261no—
565C4×Q8—261no—
566C4×Q8—261no—
567C4×Q8—261no—
568C4×Q8D5211yescharacteristic
569C4×Q8C22⋊D1311yescharacteristic
570C4×D4—131no—
571C4×D4—131no—
572C4×D4—261no—
573C4×D4—261no—
574C4×D4—261no—
575C4×D4—261no—
576C4×D4D5211yescharacteristic
577C4×D4D5211yescharacteristic
578C4×D4D5211yescharacteristic
579C4×D4C22⋊D1311yescharacteristic
580C4×D4C22⋊D1311yescharacteristic
581C4×D4C22⋊D1311yescharacteristic
582#117—131no—
583#117—261no—
584#117—261no—
585#117—261no—
586#117—261no—
587#117—261no—
588#117C4×D1311yescharacteristic
589#117C4×D1311yescharacteristic
590#117C4×D1311yescharacteristic
591C2×C4⋊C4—131no—
592C2×C4⋊C4—261no—
593C2×C42—261no—
594C2×C42—261no—
595C2×C42C22×D1311yescharacteristic
596C2×C42C22×D1311yescharacteristic
597C2×C42C22×D1311yescharacteristic
598C4⋊C8—21no—
599C4⋊C8—21no—
600C4⋊C8—21no—
601C4⋊C8—261no—
602C4⋊C8—261no—
603C4⋊C8—261no—
604C4⋊C8C22×D1311yescharacteristic
605C4⋊C8C22×D1311yescharacteristic
606C4⋊C8C22×D1311yescharacteristic
607C4⋊C8C22×D1311yescharacteristic
608C22⋊C8—21no—
609C22⋊C8—21no—
610C22⋊C8—21no—
611C22⋊C8—261no—
612C22⋊C8—261no—
613C22⋊C8—261no—
614#97—21no—
615#97—21no—
616#97—261no—
617#97—261no—
618C4×C8—21no—
619C4×C8—131no—
620C4×C8—131no—
621C4×C8—131no—
622C4×C8—131no—
623C4×C8—261no—
624C2×C13—41no—
625C2×C13—41no—
626C2×C13—41no—
627C2×C13#287911yescharacteristic
628C2×C13#289811yescharacteristic
629C2×C13#290111yescharacteristic
630D13—81no—
631#41—42no—
632#41—522no—
633C2×Q8—131no—
634C2×Q8—131no—
635C2×Q8—131no—
636C2×Q8—261no—
637C2×Q8—261no—
638C2×Q8—261no—
639C2×Q8—522no—
640C2×Q8#610311yescharacteristic
641C2×D4—131no—
642C2×D4—261no—
643C2×D4—261no—
644C2×D4—261no—
645C2×D4#610311yescharacteristic
646C2×D4#610311yescharacteristic
647C2×D4#610311yescharacteristic
648C22×C4—261no—
649C22×C4—261no—
650C22×C4—261no—
651C22×C4—261no—
652C22×C4—261no—
653C22×C4C2×C4×D1311yescharacteristic
654C22×C4C2×C4×D1311yescharacteristic
655C22×C4C2×C4×D1311yescharacteristic
656C22×C4C2×D5211yescharacteristic
657C22×C4C2×D5211yescharacteristic
658C22×C4C2×D5211yescharacteristic
659C22×C4C2×C22⋊D1311yescharacteristic
660C22×C4C2×C22⋊D1311yescharacteristic
661C22×C4C2×C22⋊D1311yescharacteristic
662M16—81no—
663M16—81no—
664M16—522no—
665M16—522no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—81no—
671C2×C8—261no—
672C2×C8—261no—
673C2×C8—261no—
674C2×C8—261no—
675C2×C8—522no—
676C4⋊C4—131no—
677C4⋊C4—131no—
678C4⋊C4—131no—
679C4⋊C4—131no—
680C4⋊C4—261no—
681C4⋊C4—261no—
682C4⋊C4—261no—
683C4⋊C4—261no—
684C4⋊C4—261no—
685C4⋊C4—261no—
686C4⋊C4—261no—
687C4⋊C4—261no—
688C4⋊C4—261no—
689C4⋊C4—261no—
690C4⋊C4—261no—
691C4⋊C4—261no—
692C4⋊C4—261no—
693C4⋊C4—261no—
694C4⋊C4—261no—
695C4⋊C4—261no—
696C4⋊C4—261no—
697C4⋊C4—261no—
698C4⋊C4—261no—
699C4⋊C4—261no—
700C4⋊C4—261no—
701C4⋊C4—261no—
702C4⋊C4—261no—
703C4⋊C4#610311yescharacteristic
704C4⋊C4#610311yescharacteristic
705C4⋊C4#610311yescharacteristic
706C4⋊C4#610311yescharacteristic
707C4⋊C4#610311yescharacteristic
708C4⋊C4#610311yescharacteristic
709C22⋊C4—261no—
710C22⋊C4—261no—
711C22⋊C4—261no—
712C22⋊C4—261no—
713C22⋊C4—261no—
714C22⋊C4—261no—
715C22⋊C4—261no—
716C22⋊C4—261no—
717C22⋊C4—261no—
718C22⋊C4—261no—
719C22⋊C4—261no—
720C22⋊C4—261no—
721C22⋊C4—261no—
722C22⋊C4—261no—
723C22⋊C4—261no—
724C22⋊C4#610311yescharacteristic
725C22⋊C4#610311yescharacteristic
726C22⋊C4#610311yescharacteristic
727C22⋊C4#610311yescharacteristic
728C22⋊C4#610311yescharacteristic
729C22⋊C4#610311yescharacteristic
730C42—261no—
731C42—261no—
732C42—261no—
733C42—261no—
734C42—261no—
735C42—261no—
736C42—261no—
737C42C2×C4×D1311yescharacteristic
738C42C2×C4×D1311yescharacteristic
739C42C2×C4×D1311yescharacteristic
740C42C2×D5211yescharacteristic
741C42C2×D5211yescharacteristic
742C42C2×D5211yescharacteristic
743C42C2×C22⋊D1311yescharacteristic
744C42C2×C22⋊D1311yescharacteristic
745C42C2×C22⋊D1311yescharacteristic
746C42C23×D1311yescharacteristic
747C13#1750611yescharacteristic, complemented, Sylow
748C23—261no—
749C23C2×#610311yescharacteristic
750C23C2×#610311yescharacteristic
751C23C2×#610311yescharacteristic
752Q8—41no—
753Q8—262no—
754Q8—262no—
755Q8—262no—
756Q8—522no—
757Q8—1041no—
758Q8—1041no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—262no—
763D4—522no—
764D4—1041no—
765D4—1041no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—261no—
779C2×C4—261no—
780C2×C4—261no—
781C2×C4—261no—
782C2×C4—261no—
783C2×C4—261no—
784C2×C4—261no—
785C2×C4—522no—
786C2×C4—522no—
787C2×C4—521no—
788C2×C4—521no—
789C2×C4—1041no—
790C2×C4—1041no—
791C2×C4C2×#610311yescharacteristic
792C2×C4C2×#610311yescharacteristic
793C2×C4C2×#610311yescharacteristic
794C2×C4C2×#610311yescharacteristic
795C2×C4C2×#610311yescharacteristic
796C2×C4C2×#610311yescharacteristic
797C2×C4C2×#610311yescharacteristic
798C2×C4C2×#610311yescharacteristic
799C2×C4C2×#610311yescharacteristic
800C2×C4C22×C4×D1311yescharacteristic
801C2×C4C22×D5211yescharacteristic
802C2×C4C22×C22⋊D1311yescharacteristic
803C8—41no—
804C8—41no—
805C8—41no—
806C8—41no—
807C8—262no—
808C8—521no—
809C8—521no—
810C8—521no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—521no—
821C22—521no—
822C22—521no—
823C22C22×#610311yescharacteristic
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—521no—
835C4—521no—
836C4—521no—
837C4—521no—
838C4—521no—
839C4—521no—
840C4—521no—
841C4#1171945012yes—
842C4#1171954111yescharacteristic
843C4#1171954311yescharacteristic
844C2—41no—
845C2—41no—
846C2—41no—
847C2—1041no—
848C2#1312328011yescharacteristic
849C2#1312336611yescharacteristic
850C2#1312338111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2989C2
socleC22×C13C22×C22⋊C4
prime radical#11719538C4
cosocleC42×C13C24
hypercenter#2989D13
hypocenterC13#17506
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2989

Complements

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

NH ≅ G/Ntype
2. #13123803C2semidirect
3. #13113308C2semidirect
4. #13113299C2semidirect
5. #13113294C2semidirect
6. #13113290C2semidirect
7. #13113282C2semidirect
8. #13113273C2semidirect
9. #13113268C2semidirect
10. #13113264C2semidirect
11. #13113256C2semidirect
12. #13113247C2semidirect
13. #13113242C2semidirect
14. #13113238C2semidirect
15. C13×#2989C2semidirect
324. #2989D13semidirect
747. C13#17506semidirect

Maximal subgroups

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

subgroupindex
#131282632
#131238032
#131133082
#131132992
#131132942
#131132902
#131132822
#131132732
#131132682
#131132642
#131132562
#131132472
#131132422
#131132382
C13×#29892
#1750613