Finite Group Databasebeta

← #15831141

Subgroups — #15831141

Order 3328.

902 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128732C211yesmaximal, characteristic
2#13123850C211yesmaximal, characteristic, complemented
3#13113468C211yesmaximal, characteristic, complemented
4#13113465C211yesmaximal, characteristic, complemented
5#13113459C211yesmaximal, characteristic, complemented
6#13113457C211yesmaximal, characteristic, complemented
7#13113454C211yesmaximal, characteristic, complemented
8#13113452C211yesmaximal, characteristic, complemented
9#13113450C211yesmaximal, characteristic, complemented
10#13113444C211yesmaximal, characteristic, complemented
11#13113441C211yesmaximal, characteristic, complemented
12#13113425C211yesmaximal, characteristic, complemented
13#13113422C211yesmaximal, characteristic, complemented
14C2×#11718056C211yesmaximal, characteristic, complemented
15C13×#2970C211yesmaximal, characteristic, complemented
16C4×C13×#41C2211yescharacteristic
17#11719535C411yescharacteristic
18#11719530C411yescharacteristic
19#11719273—21no—
20#11719273—21no—
21#11719264—21no—
22#11719264—21no—
23#11719261—21no—
24#11719261—21no—
25#11719261—21no—
26#11719261—21no—
27#11719239C411yescharacteristic
28#11719239C411yescharacteristic
29#11719239C411yescharacteristic
30#11719239C411yescharacteristic
31#11719226C411yescharacteristic
32#11719221C411yescharacteristic
33#11719184C2211yescharacteristic
34#11719184C2211yescharacteristic
35#11719184C2211yescharacteristic
36#11719184C2211yescharacteristic
37C2×#88129C2211yescharacteristic
38#11719175C2211yescharacteristic
39C13×#446—21no—
40C13×#435—21no—
41C13×#435—21no—
42C8×D4×C13—21no—
43C13×#432C2211yescharacteristic
44C13×#432C2211yescharacteristic, complemented
45C13×#432C2211yescharacteristic, complemented
46C4×C13×M16C2211yescharacteristic, complemented
47C2×C13×#97C2211yescharacteristic
48C2×C13×#97C2211yescharacteristic, complemented
49#11718685—21no—
50#11718672—21no—
51#11718672—21no—
52D4×#1055—21no—
53#11718587C2211yescharacteristic
54#11718587C2211yescharacteristic, complemented
55#11718587C2211yescharacteristic, complemented
56C4×#6099C2211yescharacteristic, complemented
57C2×#88043C2211yescharacteristic
58C2×#88043C2211yescharacteristic, complemented
59#11718057C2211yescharacteristic, complemented
60#11718057C2211yescharacteristic, complemented
61#11718057C2211yescharacteristic, complemented
62#11718057C2211yescharacteristic, complemented
63#11718057C2211yescharacteristic, complemented
64#11718057C2211yescharacteristic, complemented
65#11718057C2211yescharacteristic, complemented
66#11718057C2211yescharacteristic, complemented
67#11718056C2211yescharacteristic
68#11718056C2211yescharacteristic
69#11718056C2211yescharacteristic
70#11718056C2211yescharacteristic
71#11718056C2211yescharacteristic
72#11718056C2211yescharacteristic
73#11718056C2211yescharacteristic
74#11718056C2211yescharacteristic
75C2×C13×#41C2×C411yescharacteristic
76C22×D52C2×C411yescharacteristic
77C22×Dic26C2×C411yescharacteristic
78C2×C13×M16—21no—
79C22×C8×C13—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#88201—21no—
96#88198—21no—
97#88194—21no—
98#88191—21no—
99#88191—21no—
100#88190—21no—
101#88189—21no—
102#88189—21no—
103#88184C2×C411yescharacteristic
104#88184C2×C411yescharacteristic
105#88184C2×C411yescharacteristic
106#88184C2×C411yescharacteristic
107#88183—21no—
108#88183—21no—
109#88183—21no—
110#88183—21no—
111C4×C22⋊D13—21no—
112C4×C22⋊D13—21no—
113C4×C22⋊D13—21no—
114C4×C22⋊D13—21no—
115C2×#6103—21no—
116C2×#6103—21no—
117#88180C2×C411yescharacteristic
118#88180C2×C411yescharacteristic
119#88178—21no—
120#88178—21no—
121#88178C2×C411yescharacteristic
122#88178C2×C411yescharacteristic
123#88178C2×C411yescharacteristic
124#88178C2×C411yescharacteristic
125C2×#6099—21no—
126C22×#1055—21no—
127C22×#1055—21no—
128#88152—21no—
129#88152—21no—
130#88152—21no—
131#88152—21no—
132#88150—21no—
133#88150—21no—
134#88150—21no—
135#88150—21no—
136#88147—21no—
137#88147—21no—
138#88141—21no—
139#88141—21no—
140#88139—21no—
141#88139—21no—
142#88139—21no—
143#88139—21no—
144#88137—21no—
145#88137—21no—
146#88137—21no—
147#88137—21no—
148C22⋊C4×D13—21no—
149C22⋊C4×D13—21no—
150#88131—21no—
151#88131—21no—
152#88130—21no—
153#88130—21no—
154#88130—21no—
155#88130—21no—
156#88129—21no—
157#88129—21no—
158#88129C2×C411yescharacteristic
159#88129C2×C411yescharacteristic
160#88129C2311yescharacteristic
161#88129C2311yescharacteristic
162C4×D52C2×C411yescharacteristic
163C4×D52C2×C411yescharacteristic
164C4×D52C2×C411yescharacteristic
165C4×D52C2×C411yescharacteristic
166#88126—21no—
167#88126—21no—
168#88126—21no—
169#88126—21no—
170#88124C2311yescharacteristic
171#88124C2311yescharacteristic
172#88123C2×C411yescharacteristic
173#88123C2×C411yescharacteristic
174C4×Dic26—21no—
175C4×Dic26—21no—
176C4×Dic26C2×C411yescharacteristic
177C4×Dic26C2×C411yescharacteristic
178C4×Dic26C2×C411yescharacteristic
179C4×Dic26C2×C411yescharacteristic
180C13×C4⋊C8—21no—
181C13×C4⋊C8—21no—
182C13×C4⋊C8—21no—
183C13×C22⋊C8—21no—
184C13×C22⋊C8—21no—
185C13×C22⋊C8—21no—
186C13×#97—21no—
187C13×#97—21no—
188C13×#97C2311yescharacteristic
189C13×#97C2311yescharacteristic
190C13×#97C2311yescharacteristic
191C13×#97C2311yescharacteristic
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—
201#88043C2311yescharacteristic
202#88043C2311yescharacteristic
203#88043C2311yescharacteristic
204#88043C2311yescharacteristic
205C4×#1055—21no—
206#17686—131nomaximal, Sylow
207C23×D13—21no—
208C13×#41—42no—
209C2×Q8×C13C22⋊C411yescharacteristic
210C2×D4×C13C22⋊C411yescharacteristic
211C2×D4×C13C22⋊C411yescharacteristic
212C2×D4×C13C22⋊C411yescharacteristic
213C22×C4×C13C22×C411yescharacteristic
214C22×C4×C13C22×C411yescharacteristic
215C22×C4×C13C22×C411yescharacteristic
216C22×C4×C13C2×D411yescharacteristic
217C22×C4×C13C2×D411yescharacteristic
218C22×C4×C13C2×D411yescharacteristic
219C22×C4×C13C2×D411yescharacteristic
220C22×C4×C13C2×D411yescharacteristic
221C22×C4×C13C2×D411yescharacteristic
222C2×C22⋊D13—21no—
223C2×C22⋊D13—21no—
224C2×C22⋊D13—21no—
225C2×C22⋊D13—21no—
226C22×Dic13—21no—
227C2×D52—21no—
228C2×D52—42no—
229C2×D52C22×C411yescharacteristic
230C2×D52C22×C411yescharacteristic
231C2×C4×D13—21no—
232C2×C4×D13—21no—
233C2×C4×D13—21no—
234C2×C4×D13—21no—
235C2×Dic26—21no—
236C2×Dic26—21no—
237C2×Dic26—21no—
238C2×Dic26—42no—
239C2×Dic26C22×C411yescharacteristic
240C2×Dic26C22×C411yescharacteristic
241C13×M16—42no—
242C2×C8×C13—21no—
243C2×C8×C13—21no—
244C2×C8×C13—21no—
245C2×C8×C13—21no—
246C2×C8×C13—42no—
247C2×C8×C13—42no—
248C13×C4⋊C4C22⋊C411yescharacteristic
249C13×C4⋊C4C22⋊C411yescharacteristic
250C13×C4⋊C4C22⋊C411yescharacteristic
251C13×C4⋊C4C22⋊C411yescharacteristic
252C13×C4⋊C4C22⋊C411yescharacteristic
253C13×C4⋊C4C22⋊C411yescharacteristic
254C13×C22⋊C4C22⋊C411yescharacteristic
255C13×C22⋊C4C22⋊C411yescharacteristic
256C13×C22⋊C4C22⋊C411yescharacteristic
257C13×C22⋊C4C22⋊C411yescharacteristic
258C13×C22⋊C4C22⋊C411yescharacteristic
259C13×C22⋊C4C22⋊C411yescharacteristic
260C42×C13C22×C411yescharacteristic
261C42×C13C22×C411yescharacteristic
262C42×C13C22×C411yescharacteristic
263C42×C13C2×D411yescharacteristic
264C42×C13C2×D411yescharacteristic
265C42×C13C2×D411yescharacteristic
266C42×C13C2×D411yescharacteristic
267C42×C13C2×D411yescharacteristic
268C42×C13C2×D411yescharacteristic
269C42×C13C2411yescharacteristic
270C22⋊Dic13—21no—
271C22⋊Dic13—21no—
272C22⋊Dic13—21no—
273C22⋊Dic13—21no—
274C22⋊Dic13—21no—
275C22⋊Dic13—21no—
276#6103—21no—
277#6103—21no—
278#6103—21no—
279#6103—21no—
280#6103—21no—
281#6103—21no—
282#6103—21no—
283#6103—21no—
284#6103—21no—
285#6103—21no—
286#6103—21no—
287#6103—21no—
288#6103—21no—
289#6103—21no—
290#6103—21no—
291#6103—21no—
292C4⋊Dic13—21no—
293C4⋊Dic13—21no—
294C4⋊Dic13C22×C411yescharacteristic
295C4⋊Dic13C22×C411yescharacteristic
296C4⋊Dic13C22×C411yescharacteristic
297C4⋊Dic13C22×C411yescharacteristic
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—
309#6101—21no—
310C4×Dic13—21no—
311C4×Dic13—21no—
312C4×Dic13—21no—
313C4×Dic13—21no—
314C4×Dic13—21no—
315C4×Dic13—21no—
316#6099—42no—
317C2×#1055—21no—
318C2×#1055—21no—
319C2×#1055—21no—
320C2×#1055—21no—
321C2×#1055—42no—
322C2×#1055—42no—
323#3510—131no—
324#2970—131no—
325#2970D1311yescharacteristic, complemented
326#1535—131no—
327#1535—131no—
328#1533—131no—
329#1532—131no—
330#1532—131no—
331#1531—131no—
332#1531—131no—
333#1529—131no—
334#1529—131no—
335#1524—131no—
336#1524—131no—
337C2×#329—131no—
338C23×C13C2×C22⋊C411yescharacteristic
339C23×C13C2×C22⋊C411yescharacteristic
340C23×C13C2×C22⋊C411yescharacteristic
341C22×D13—21no—
342C22×D13—21no—
343C22×D13—42no—
344C22×D13—81no—
345C22×D13—81no—
346Q8×C13—41no—
347D4×C13—22no—
348D4×C13—22no—
349D4×C13—41no—
350C2×C4×C13—22no—
351C2×C4×C13—41no—
352C2×C4×C13—41no—
353C2×C4×C13—41no—
354C2×C4×C13—41no—
355C2×C4×C13—41no—
356C2×C4×C13—41no—
357C2×C4×C13—41no—
358C2×C4×C13—41no—
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×C13C2×C22⋊C411yescharacteristic
368C2×C4×C13C23×C411yescharacteristic
369C2×C4×C13C22×D411yescharacteristic
370C2×C4×C13C22×D411yescharacteristic
371C22⋊D13—81no—
372C22⋊D13—81no—
373C22⋊D13—81no—
374C22⋊D13—81no—
375C2×Dic13—21no—
376C2×Dic13—21no—
377C2×Dic13—21no—
378C2×Dic13—21no—
379C2×Dic13—21no—
380C2×Dic13—21no—
381C2×Dic13—42no—
382D52—42no—
383D52—41no—
384D52—41no—
385C4×D13—81no—
386C4×D13—81no—
387C4×D13—81no—
388C4×D13—81no—
389Dic26—42no—
390Dic26—41no—
391Dic26—41no—
392Dic26—81no—
393Dic26—81no—
394C8×C13—22no—
395C8×C13—41no—
396C8×C13—41no—
397C8×C13—41no—
398#1055—22no—
399#1055—41no—
400#1055—41no—
401#1055—41no—
402#559—261no—
403#559—261no—
404#556—261no—
405#556—261no—
406#551—261no—
407#551—261no—
408#551—261no—
409#551—261no—
410#542—131no—
411#542—131no—
412#542—131no—
413#542—131no—
414#536—131no—
415#535—131no—
416#533—131no—
417#529—131no—
418#529—131no—
419#529—131no—
420#529—131no—
421C2×#124—131no—
422#519—131no—
423#518—131no—
424C4×#41C2×D1311yescharacteristic
425#446—21no—
426#446—261no—
427#435—21no—
428#435—21no—
429#435—261no—
430#435—261no—
431C8×D4—21no—
432C8×D4—261no—
433#432—131no—
434#432—131no—
435#432—131no—
436#432C2×D1311yescharacteristic
437#432C2×D1311yescharacteristic, complemented
438#432C2×D1311yescharacteristic, complemented
439C4×M16—131no—
440C4×M16C2×D1311yescharacteristic, complemented
441C2×#97—131no—
442C2×#97—131no—
443C2×#97C2×D1311yescharacteristic
444C2×#97C2×D1311yescharacteristic, complemented
445#330—131no—
446#330—131no—
447#330—131no—
448#330—131no—
449#330—131no—
450#330—131no—
451#330—131no—
452#330—131no—
453#329—131no—
454#329—131no—
455#329—131no—
456#329—131no—
457#329—131no—
458#329—131no—
459#329—131no—
460#329—131no—
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×C13#41312yes—
470C22×C13C22×C22⋊C411yescharacteristic
471C2×D13—41no—
472C2×D13—41no—
473C2×D13—41no—
474C2×D13—41no—
475C2×D13—41no—
476C2×D13—41no—
477C2×D13—162no—
478C4×C13—21no—
479C4×C13—21no—
480C4×C13—21no—
481C4×C13—21no—
482C4×C13—21no—
483C4×C13—21no—
484C4×C13—21no—
485C4×C13—21no—
486C4×C13—21no—
487C4×C13—21no—
488C4×C13—21no—
489C4×C13—21no—
490Dic13—41no—
491Dic13—41no—
492Dic13—41no—
493Dic13—41no—
494Dic13—41no—
495Dic13—41no—
496C2×#41C4×D1311yescharacteristic
497C22×Q8—131no—
498C22×D4—131no—
499C2×M16—21no—
500C2×M16—261no—
501C22×C8—21no—
502C22×C8—21no—
503C22×C8—261no—
504C22×C8—261no—
505C4⋊Q8—131no—
506C4⋊Q8—131no—
507C4⋊Q8—261no—
508#127—261no—
509#126—261no—
510#126—261no—
511#126—261no—
512#126—261no—
513#126—261no—
514#126—261no—
515#126—261no—
516#126—261no—
517#125—131no—
518#125—131no—
519#124—131no—
520#124—131no—
521#124—131no—
522#124—131no—
523#124—261no—
524#124—261no—
525#124—261no—
526#124—261no—
527#124—261no—
528#124—261no—
529#124—261no—
530#124—261no—
531#123—261no—
532#123—261no—
533#123—261no—
534#123—261no—
535#123—261no—
536#123—261no—
537#123—261no—
538#123—261no—
539#123—261no—
540#123—261no—
541C22⋊Q8—131no—
542C22⋊Q8—131no—
543C22⋊Q8—131no—
544C22⋊Q8—131no—
545C22⋊Q8—261no—
546C22⋊Q8—261no—
547C22⋊Q8—261no—
548C22⋊Q8—261no—
549C22⋊Q8—261no—
550C22⋊Q8—261no—
551#121—131no—
552#121—131no—
553#121—131no—
554#121—131no—
555#120—261no—
556#120—261no—
557C4×Q8—131no—
558C4×Q8—131no—
559C4×Q8—131no—
560C4×Q8—131no—
561C4×Q8—261no—
562C4×Q8—261no—
563C4×Q8—261no—
564C4×Q8—261no—
565C4×Q8D5211yescharacteristic
566C4×Q8C22⋊D1311yescharacteristic
567C4×D4—131no—
568C4×D4—131no—
569C4×D4—131no—
570C4×D4—131no—
571C4×D4—261no—
572C4×D4—261no—
573C4×D4—261no—
574C4×D4—261no—
575C4×D4—261no—
576C4×D4—261no—
577C4×D4D5211yescharacteristic
578C4×D4D5211yescharacteristic
579C4×D4D5211yescharacteristic
580C4×D4C22⋊D1311yescharacteristic
581C4×D4C22⋊D1311yescharacteristic
582C4×D4C22⋊D1311yescharacteristic
583#117—131no—
584#117—131no—
585#117—261no—
586#117—261no—
587#117—261no—
588#117—261no—
589#117—261no—
590#117—261no—
591#117C4×D1311yescharacteristic
592#117C4×D1311yescharacteristic
593#117C4×D1311yescharacteristic
594C2×C22⋊C4—261no—
595C2×C22⋊C4—261no—
596C2×C22⋊C4—261no—
597C2×C22⋊C4—261no—
598C2×C42C22×D1311yescharacteristic
599C2×C42C22×D1311yescharacteristic
600C2×C42C22×D1311yescharacteristic
601C4⋊C8—21no—
602C4⋊C8—21no—
603C4⋊C8—21no—
604C4⋊C8—261no—
605C4⋊C8—261no—
606C4⋊C8—261no—
607C22⋊C8—21no—
608C22⋊C8—21no—
609C22⋊C8—21no—
610C22⋊C8—261no—
611C22⋊C8—261no—
612C22⋊C8—261no—
613#97—21no—
614#97—21no—
615#97—131no—
616#97—131no—
617#97—131no—
618#97—131no—
619#97—261no—
620#97—261no—
621#97C22×D1311yescharacteristic
622#97C22×D1311yescharacteristic
623#97C22×D1311yescharacteristic
624#97C22×D1311yescharacteristic
625C4×C8—21no—
626C4×C8—261no—
627C2×C13—22no—
628C2×C13—41no—
629C2×C13—41no—
630C2×C13C2×#41311yescharacteristic
631C2×C13#290111yescharacteristic
632C2×C13#290111yescharacteristic
633D13—81no—
634D13—81no—
635C24—261no—
636#41—42no—
637C2×Q8—131no—
638C2×Q8—131no—
639C2×Q8—261no—
640C2×Q8—261no—
641C2×Q8—261no—
642C2×Q8—522no—
643C2×Q8#610311yescharacteristic
644C2×D4—131no—
645C2×D4—131no—
646C2×D4—261no—
647C2×D4—261no—
648C2×D4—261no—
649C2×D4—261no—
650C2×D4—261no—
651C2×D4—522no—
652C2×D4#610311yescharacteristic
653C2×D4#610311yescharacteristic
654C2×D4#610311yescharacteristic
655C22×C4—261no—
656C22×C4—261no—
657C22×C4—261no—
658C22×C4—261no—
659C22×C4—261no—
660C22×C4C2×C4×D1311yescharacteristic
661C22×C4C2×C4×D1311yescharacteristic
662C22×C4C2×C4×D1311yescharacteristic
663C22×C4C2×D5211yescharacteristic
664C22×C4C2×D5211yescharacteristic
665C22×C4C2×D5211yescharacteristic
666C22×C4C2×C22⋊D1311yescharacteristic
667C22×C4C2×C22⋊D1311yescharacteristic
668C22×C4C2×C22⋊D1311yescharacteristic
669M16—42no—
670M16—522no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—42no—
676C2×C8—42no—
677C2×C8—261no—
678C2×C8—261no—
679C2×C8—261no—
680C2×C8—261no—
681C2×C8—522no—
682C2×C8—522no—
683C4⋊C4—131no—
684C4⋊C4—131no—
685C4⋊C4—131no—
686C4⋊C4—131no—
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#610311yescharacteristic
702C4⋊C4#610311yescharacteristic
703C4⋊C4#610311yescharacteristic
704C4⋊C4#610311yescharacteristic
705C4⋊C4#610311yescharacteristic
706C4⋊C4#610311yescharacteristic
707C22⋊C4—261no—
708C22⋊C4—261no—
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—261no—
725C22⋊C4—261no—
726C22⋊C4—261no—
727C22⋊C4—261no—
728C22⋊C4—261no—
729C22⋊C4#610311yescharacteristic
730C22⋊C4#610311yescharacteristic
731C22⋊C4#610311yescharacteristic
732C22⋊C4#610311yescharacteristic
733C22⋊C4#610311yescharacteristic
734C22⋊C4#610311yescharacteristic
735C42—261no—
736C42—261no—
737C42—261no—
738C42—261no—
739C42—261no—
740C42—261no—
741C42C2×C4×D1311yescharacteristic
742C42C2×C4×D1311yescharacteristic
743C42C2×C4×D1311yescharacteristic
744C42C2×D5211yescharacteristic
745C42C2×D5211yescharacteristic
746C42C2×D5211yescharacteristic
747C42C2×C22⋊D1311yescharacteristic
748C42C2×C22⋊D1311yescharacteristic
749C42C2×C22⋊D1311yescharacteristic
750C42C23×D1311yescharacteristic
751C13#1768611yescharacteristic, complemented, Sylow
752C23—261no—
753C23—261no—
754C23—522no—
755C23—1041no—
756C23—1041no—
757C23C2×#610311yescharacteristic
758C23C2×#610311yescharacteristic
759C23C2×#610311yescharacteristic
760Q8—41no—
761Q8—521no—
762Q8—521no—
763Q8—522no—
764Q8—1041no—
765Q8—1041no—
766D4—22no—
767D4—22no—
768D4—41no—
769D4—521no—
770D4—521no—
771D4—522no—
772D4—1041no—
773D4—1041no—
774D4—1041no—
775D4—1041no—
776C2×C4—22no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—261no—
786C2×C4—261no—
787C2×C4—261no—
788C2×C4—261no—
789C2×C4—261no—
790C2×C4—261no—
791C2×C4—522no—
792C2×C4—1041no—
793C2×C4—1041no—
794C2×C4—1041no—
795C2×C4—1041no—
796C2×C4C2×#610311yescharacteristic
797C2×C4C2×#610311yescharacteristic
798C2×C4C2×#610311yescharacteristic
799C2×C4C2×#610311yescharacteristic
800C2×C4C2×#610311yescharacteristic
801C2×C4C2×#610311yescharacteristic
802C2×C4C2×#610311yescharacteristic
803C2×C4C2×#610311yescharacteristic
804C2×C4C2×#610311yescharacteristic
805C2×C4C22×C4×D1311yescharacteristic
806C2×C4C22×D5211yescharacteristic
807C2×C4C22×C22⋊D1311yescharacteristic
808C8—22no—
809C8—41no—
810C8—41no—
811C8—41no—
812C8—262no—
813C8—521no—
814C8—521no—
815C8—521no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—521no—
825C22—521no—
826C22—521no—
827C22—521no—
828C22—521no—
829C22—521no—
830C22—2082no—
831C22#1171879312yes—
832C22C22×#610311yescharacteristic
833C4—21no—
834C4—21no—
835C4—21no—
836C4—21no—
837C4—21no—
838C4—21no—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—521no—
846C4—521no—
847C4—521no—
848C4—521no—
849C4—521no—
850C4—521no—
851C2—22no—
852C2—41no—
853C2—41no—
854C2—1041no—
855C2—1041no—
856C2C2×#1171879311yescharacteristic
857C2#1312338111yescharacteristic
858C2#1312338411yescharacteristic
subgroupG/H
centerC22C22×#6103
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2970C2
socleC22×C13C22×C22⋊C4
prime radical#11719535C4
cosocleC42×C13C24
hypercenter#2970D13
hypocenterC13#17686
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2970

Complements

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

NH ≅ G/Ntype
2. #13123850C2semidirect
3. #13113468C2semidirect
4. #13113465C2semidirect
5. #13113459C2semidirect
6. #13113457C2semidirect
7. #13113454C2semidirect
8. #13113452C2semidirect
9. #13113450C2semidirect
10. #13113444C2semidirect
11. #13113441C2semidirect
12. #13113425C2semidirect
13. #13113422C2semidirect
14. C2×#11718056C2semidirect
15. C13×#2970C2semidirect
44. C13×#432C22semidirect
45. C13×#432C22semidirect
46. C4×C13×M16C22semidirect
48. C2×C13×#97C22semidirect
54. #11718587C22semidirect
55. #11718587C22semidirect
56. C4×#6099C22semidirect
58. C2×#88043C22semidirect
59. #11718057C22semidirect
60. #11718057C22semidirect
61. #11718057C22semidirect
62. #11718057C22semidirect
63. #11718057C22semidirect
64. #11718057C22semidirect
65. #11718057C22semidirect
66. #11718057C22semidirect
325. #2970D13semidirect
437. #432C2×D13semidirect
438. #432C2×D13semidirect
440. C4×M16C2×D13semidirect
444. C2×#97C2×D13semidirect
751. C13#17686semidirect

Maximal subgroups

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

subgroupindex
#131287322
#131238502
#131134682
#131134652
#131134592
#131134572
#131134542
#131134522
#131134502
#131134442
#131134412
#131134252
#131134222
C2×#117180562
C13×#29702
#1768613