Finite Group Databasebeta

← #15831075

Subgroups — #15831075

Order 3328.

878 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128814C211yesmaximal, characteristic
2#13123850C211yesmaximal, characteristic, complemented
3#13113473C211yesmaximal, characteristic, complemented
4#13113468C211yesmaximal, characteristic, complemented
5#13113465C211yesmaximal, characteristic, complemented
6#13113462C211yesmaximal, characteristic, complemented
7#13113457C211yesmaximal, characteristic, complemented
8#13113454C211yesmaximal, characteristic, complemented
9#13113452C211yesmaximal, characteristic, complemented
10#13113444C211yesmaximal, characteristic, complemented
11#13113439C211yesmaximal, characteristic, complemented
12#13113437C211yesmaximal, characteristic, complemented
13#13113425C211yesmaximal, characteristic, complemented
14C2×#11718057C211yesmaximal, characteristic, complemented
15C13×#2923C211yesmaximal, characteristic, complemented
16C4×C13×#41C2211yescharacteristic
17#11719529—21no—
18#11719288—21no—
19#11719284C411yescharacteristic
20#11719272C411yescharacteristic
21#11719270C411yescharacteristic
22#11719270C411yescharacteristic
23#11719269—21no—
24#11719269—21no—
25#11719260C411yescharacteristic
26#11719251—21no—
27#11719248C411yescharacteristic
28#11719246C411yescharacteristic
29#11719246C411yescharacteristic
30#11719236—21no—
31#11719236—21no—
32#11719234—21no—
33#11719184C2211yescharacteristic
34#11719184C2211yescharacteristic
35#11719184C2211yescharacteristic
36#11719175C2211yescharacteristic
37C2×#88124C2211yescharacteristic
38C2×#88124C2211yescharacteristic
39C13×#433—21no—
40C13×#433—21no—
41C13×#432C2211yescharacteristic
42C13×#432C2211yescharacteristic
43C13×#432C2211yescharacteristic
44C13×#432C2211yescharacteristic
45C13×#424—21no—
46C13×#408—21no—
47C4×C13×M16C2211yescharacteristic
48C2×C13×#97C2211yescharacteristic
49#11718685—21no—
50#11718672—21no—
51#11718672—21no—
52D4×#1055—21no—
53#11718587C2211yescharacteristic
54#11718587C2211yescharacteristic
55#11718587C2211yescharacteristic
56C4×#6099C2211yescharacteristic
57C2×#88043C2211yescharacteristic
58C2×#88043C2211yescharacteristic
59#11718057C2211yescharacteristic
60#11718057C2211yescharacteristic
61#11718057C2211yescharacteristic
62#11718057C2211yescharacteristic
63#11718057C2211yescharacteristic
64#11718057C2211yescharacteristic
65#11718057C2211yescharacteristic
66#11718057C2211yescharacteristic
67#11718057C2211yescharacteristic
68#11718057C2211yescharacteristic
69#11718057C2211yescharacteristic
70#11718057C2211yescharacteristic
71#11718056C2211yescharacteristic
72#11718056C2211yescharacteristic
73#11718056C2211yescharacteristic
74#11718056C2211yescharacteristic
75C2×C13×#41D411yescharacteristic
76C2×#6129—21no—
77C2×C13×M16—21no—
78C22×C8×C13—21no—
79C4×Q8×C13C2×C411yescharacteristic
80C4×Q8×C13D411yescharacteristic
81C4×D4×C13C2×C411yescharacteristic
82C4×D4×C13C2×C411yescharacteristic
83C4×D4×C13C2×C411yescharacteristic
84C4×D4×C13D411yescharacteristic
85C4×D4×C13D411yescharacteristic
86C4×D4×C13D411yescharacteristic
87C13×#117D411yescharacteristic
88C13×#117D411yescharacteristic
89C13×#117D411yescharacteristic
90C2×C42×C13C2311yescharacteristic
91C2×C42×C13C2311yescharacteristic
92C2×C42×C13C2311yescharacteristic
93#88200—21no—
94#88198—21no—
95#88193—21no—
96#88193—21no—
97#88189—21no—
98#88189—21no—
99D4×Dic13—21no—
100#88184C2×C411yescharacteristic
101#88184C2×C411yescharacteristic
102#88184C2×C411yescharacteristic
103#88183—21no—
104#88183—21no—
105#88183—21no—
106C4×C22⋊D13—21no—
107C4×C22⋊D13—21no—
108C4×C22⋊D13—21no—
109#88180C2×C411yescharacteristic
110#88180C2×C411yescharacteristic
111C2×C4⋊Dic13C2×C411yescharacteristic
112C2×C4⋊Dic13C2×C411yescharacteristic
113C2×C4⋊Dic13C2×C411yescharacteristic
114C2×C4⋊Dic13C2×C411yescharacteristic
115#88178—21no—
116#88178—21no—
117#88178C2×C411yescharacteristic
118#88178C2×C411yescharacteristic
119#88178C2×C411yescharacteristic
120C2×#6101—21no—
121C2×#6101—21no—
122C2×#6101—21no—
123C2×#6101—21no—
124C2×#6099—21no—
125C22×#1055—21no—
126C22×#1055—21no—
127#88152—21no—
128#88152—21no—
129#88151—21no—
130#88150—21no—
131#88150—21no—
132C4⋊C4×D13—21no—
133#88144—21no—
134#88143—21no—
135#88143—21no—
136#88143—21no—
137#88143—21no—
138#88141—21no—
139#88140—21no—
140#88140—21no—
141#88137—21no—
142#88137—21no—
143#88135—21no—
144#88135—21no—
145#88133—21no—
146#88133—21no—
147#88132—21no—
148#88132—21no—
149#88131—21no—
150#88131—21no—
151#88130—21no—
152#88130—21no—
153#88130—21no—
154#88129C2311yescharacteristic
155C4×D52C2×C411yescharacteristic
156C4×D52C2×C411yescharacteristic
157C4×D52C2×C411yescharacteristic
158#88126—21no—
159#88126—21no—
160#88126—21no—
161#88124—21no—
162#88124—21no—
163#88124—21no—
164#88124—21no—
165#88124C2×C411yescharacteristic
166#88124C2×C411yescharacteristic
167#88124C2×C411yescharacteristic
168#88124C2×C411yescharacteristic
169#88124C2311yescharacteristic
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
179C13×C4⋊C8—21no—
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×C22⋊C8—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#17680—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—
226C22×Dic13—21no—
227C22×Dic13—21no—
228#6129—44no—
229C2×D52C22×C411yescharacteristic
230C2×C4×D13—21no—
231C2×C4×D13—21no—
232C2×C4×D13—21no—
233C2×Dic26—21no—
234C2×Dic26—21no—
235C2×Dic26C22×C411yescharacteristic
236C13×M16—42no—
237C2×C8×C13—21no—
238C2×C8×C13—21no—
239C2×C8×C13—21no—
240C2×C8×C13—21no—
241C2×C8×C13—42no—
242C13×C4⋊C4C22⋊C411yescharacteristic
243C13×C4⋊C4C22⋊C411yescharacteristic
244C13×C4⋊C4C22⋊C411yescharacteristic
245C13×C4⋊C4C22⋊C411yescharacteristic
246C13×C4⋊C4C22⋊C411yescharacteristic
247C13×C4⋊C4C22⋊C411yescharacteristic
248C13×C22⋊C4C22⋊C411yescharacteristic
249C13×C22⋊C4C22⋊C411yescharacteristic
250C13×C22⋊C4C22⋊C411yescharacteristic
251C13×C22⋊C4C22⋊C411yescharacteristic
252C13×C22⋊C4C22⋊C411yescharacteristic
253C13×C22⋊C4C22⋊C411yescharacteristic
254C42×C13C22×C411yescharacteristic
255C42×C13C22×C411yescharacteristic
256C42×C13C22×C411yescharacteristic
257C42×C13C2×D411yescharacteristic
258C42×C13C2×D411yescharacteristic
259C42×C13C2×D411yescharacteristic
260C42×C13C2×D411yescharacteristic
261C42×C13C2×D411yescharacteristic
262C42×C13C2×D411yescharacteristic
263C42×C13C2411yescharacteristic
264C22⋊Dic13—21no—
265C22⋊Dic13—21no—
266C22⋊Dic13—21no—
267C22⋊Dic13—21no—
268C22⋊Dic13—21no—
269#6103—21no—
270#6103—21no—
271#6103—21no—
272#6103—21no—
273#6103—21no—
274#6103—21no—
275#6103—21no—
276#6103—21no—
277C4⋊Dic13—21no—
278C4⋊Dic13—21no—
279C4⋊Dic13—21no—
280C4⋊Dic13—21no—
281C4⋊Dic13—21no—
282C4⋊Dic13—21no—
283C4⋊Dic13C22×C411yescharacteristic
284C4⋊Dic13C22×C411yescharacteristic
285C4⋊Dic13C22×C411yescharacteristic
286C4⋊Dic13C22×C411yescharacteristic
287C4⋊Dic13C22×C411yescharacteristic
288C4⋊Dic13C22×C411yescharacteristic
289#6101—21no—
290#6101—21no—
291#6101—21no—
292#6101—21no—
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—
314#6099—42no—
315C2×#1055—21no—
316C2×#1055—21no—
317C2×#1055—21no—
318C2×#1055—21no—
319C2×#1055—42no—
320C2×#1055—42no—
321#3515—131no—
322#2970—131no—
323#2923D1311yescharacteristic, complemented
324#1537—131no—
325#1535—131no—
326#1535—131no—
327#1534—131no—
328#1532—131no—
329#1532—131no—
330#1531—131no—
331#1529—131no—
332#1528—131no—
333#1528—131no—
334#1524—131no—
335C2×#330—131no—
336C23×C13C2×C22⋊C411yescharacteristic
337C23×C13C2×C22⋊C411yescharacteristic
338C23×C13C2×C22⋊C411yescharacteristic
339C22×D13—21no—
340Q8×C13—41no—
341D4×C13—22no—
342D4×C13—22no—
343D4×C13—41no—
344C2×C4×C13—22no—
345C2×C4×C13—41no—
346C2×C4×C13—41no—
347C2×C4×C13—41no—
348C2×C4×C13—41no—
349C2×C4×C13—41no—
350C2×C4×C13—41no—
351C2×C4×C13—41no—
352C2×C4×C13—41no—
353C2×C4×C13C2×C22⋊C411yescharacteristic
354C2×C4×C13C2×C22⋊C411yescharacteristic
355C2×C4×C13C2×C22⋊C411yescharacteristic
356C2×C4×C13C2×C22⋊C411yescharacteristic
357C2×C4×C13C2×C22⋊C411yescharacteristic
358C2×C4×C13C2×C22⋊C411yescharacteristic
359C2×C4×C13C2×C22⋊C411yescharacteristic
360C2×C4×C13C2×C22⋊C411yescharacteristic
361C2×C4×C13C2×C22⋊C411yescharacteristic
362C2×C4×C13C23×C411yescharacteristic
363C2×C4×C13C22×D411yescharacteristic
364C2×C4×C13C22×D411yescharacteristic
365C22⋊D13—42no—
366C22⋊D13—42no—
367C22⋊D13—81no—
368C2×Dic13—21no—
369C2×Dic13—21no—
370C2×Dic13—21no—
371C2×Dic13—21no—
372C2×Dic13—21no—
373C2×Dic13—21no—
374C2×Dic13—21no—
375C2×Dic13—42no—
376C2×Dic13—42no—
377C2×Dic13—81no—
378C2×Dic13—81no—
379D52—41no—
380C4×D13—42no—
381C4×D13—81no—
382C4×D13—81no—
383Dic26—42no—
384Dic26—41no—
385Dic26—81no—
386C8×C13—41no—
387C8×C13—41no—
388C8×C13—41no—
389C8×C13—41no—
390#1055—22no—
391#1055—41no—
392#1055—41no—
393#1055—41no—
394#557—131no—
395#554—131no—
396#554—131no—
397#553—131no—
398#553—131no—
399#552—131no—
400#552—131no—
401#552—261no—
402#552—261no—
403#552—261no—
404#547—131no—
405#547—261no—
406#541—261no—
407#539—261no—
408#539—261no—
409#533—131no—
410#529—131no—
411#529—131no—
412#529—131no—
413C2×#125—131no—
414C2×#125—131no—
415#520—261no—
416C4×#41C2×D1311yescharacteristic
417#446—261no—
418#435—261no—
419#435—261no—
420C8×D4—261no—
421#433—21no—
422#433—21no—
423#432—131no—
424#432—131no—
425#432—131no—
426#432C2×D1311yescharacteristic
427#432C2×D1311yescharacteristic
428#432C2×D1311yescharacteristic
429#432C2×D1311yescharacteristic
430#424—21no—
431#408—21no—
432C4×M16—131no—
433C4×M16C2×D1311yescharacteristic
434C2×#97—131no—
435C2×#97—131no—
436C2×#97C2×D1311yescharacteristic
437#330—131no—
438#330—131no—
439#330—131no—
440#330—131no—
441#330—131no—
442#330—131no—
443#330—131no—
444#330—131no—
445#330—131no—
446#330—131no—
447#330—131no—
448#330—131no—
449#329—131no—
450#329—131no—
451#329—131no—
452#329—131no—
453C22×C13—21no—
454C22×C13—21no—
455C22×C13—21no—
456C22×C13—21no—
457C22×C13—21no—
458C22×C13—21no—
459C22×C13—21no—
460C22×C13—21no—
461C22×C13#42112yes—
462C22×C13C22×C22⋊C411yescharacteristic
463C2×D13—41no—
464C2×D13—41no—
465C2×D13—41no—
466C4×C13—21no—
467C4×C13—21no—
468C4×C13—21no—
469C4×C13—21no—
470C4×C13—21no—
471C4×C13—21no—
472C4×C13—21no—
473C4×C13—21no—
474C4×C13—21no—
475C4×C13—21no—
476C4×C13—21no—
477C4×C13—21no—
478Dic13—41no—
479Dic13—41no—
480Dic13—41no—
481Dic13—41no—
482Dic13—41no—
483Dic13—41no—
484Dic13—41no—
485C2×#41—261no—
486C2×#41C22⋊D1311yescharacteristic
487C2×M16—21no—
488C2×M16—261no—
489C22×C8—21no—
490C22×C8—261no—
491C22×C8—261no—
492C4⋊Q8—131no—
493C4⋊Q8—131no—
494C4⋊Q8—261no—
495#126—261no—
496#126—261no—
497#126—261no—
498#126—261no—
499#126—261no—
500#126—261no—
501#126—261no—
502#125—131no—
503#125—131no—
504#125—131no—
505#125—131no—
506#125—131no—
507#125—131no—
508#125—131no—
509#125—261no—
510#125—261no—
511#125—261no—
512#125—261no—
513#125—261no—
514#125—261no—
515#125—261no—
516#125—261no—
517#125—261no—
518#124—131no—
519#123—261no—
520#123—261no—
521#123—261no—
522#123—261no—
523#123—261no—
524#123—261no—
525#123—261no—
526#123—261no—
527#123—261no—
528C22⋊Q8—131no—
529C22⋊Q8—131no—
530C22⋊Q8—131no—
531C22⋊Q8—261no—
532C22⋊Q8—261no—
533C22⋊Q8—261no—
534C22⋊Q8—261no—
535C22⋊Q8—261no—
536C22⋊Q8—261no—
537C22⋊Q8—261no—
538C22⋊Q8—261no—
539#121—131no—
540#121—131no—
541#121—131no—
542#121—261no—
543#121—261no—
544C4×Q8—131no—
545C4×Q8—131no—
546C4×Q8—131no—
547C4×Q8—261no—
548C4×Q8—261no—
549C4×Q8—261no—
550C4×Q8C4×D1311yescharacteristic
551C4×Q8D5211yescharacteristic
552C4×D4—131no—
553C4×D4—131no—
554C4×D4—131no—
555C4×D4—261no—
556C4×D4—261no—
557C4×D4—261no—
558C4×D4—261no—
559C4×D4—261no—
560C4×D4—261no—
561C4×D4C4×D1311yescharacteristic
562C4×D4C4×D1311yescharacteristic
563C4×D4C4×D1311yescharacteristic
564C4×D4D5211yescharacteristic
565C4×D4D5211yescharacteristic
566C4×D4D5211yescharacteristic
567#117—131no—
568#117—131no—
569#117—261no—
570#117—261no—
571#117—261no—
572#117—261no—
573#117—261no—
574#117C22⋊D1311yescharacteristic
575#117C22⋊D1311yescharacteristic
576#117C22⋊D1311yescharacteristic
577C2×C4⋊C4—131no—
578C2×C4⋊C4—131no—
579C2×C4⋊C4—131no—
580C2×C4⋊C4—131no—
581C2×C4⋊C4—261no—
582C2×C4⋊C4—261no—
583C2×C4⋊C4—261no—
584C2×C4⋊C4—261no—
585C2×C4⋊C4—261no—
586C2×C42C22×D1311yescharacteristic
587C2×C42C22×D1311yescharacteristic
588C2×C42C22×D1311yescharacteristic
589C4⋊C8—21no—
590C4⋊C8—21no—
591C4⋊C8—21no—
592C4⋊C8—21no—
593C4⋊C8—261no—
594C4⋊C8—261no—
595C4⋊C8—261no—
596C22⋊C8—21no—
597C22⋊C8—21no—
598C22⋊C8—21no—
599C22⋊C8—21no—
600C22⋊C8—261no—
601C22⋊C8—261no—
602C22⋊C8—261no—
603#97—21no—
604#97—131no—
605#97—131no—
606#97—131no—
607#97—131no—
608#97—261no—
609#97—261no—
610#97C22×D1311yescharacteristic
611#97C22×D1311yescharacteristic
612#97C22×D1311yescharacteristic
613#97C22×D1311yescharacteristic
614C4×C8—21no—
615C4×C8—261no—
616C2×C13—22no—
617C2×C13—41no—
618C2×C13—41no—
619C2×C13#288911yescharacteristic
620C2×C13C2×#42111yescharacteristic
621C2×C13#290111yescharacteristic
622D13—81no—
623#41—42no—
624#41—524no—
625C2×Q8—131no—
626C2×Q8—261no—
627C2×Q8—261no—
628C2×Q8#610311yescharacteristic
629C2×D4—131no—
630C2×D4—261no—
631C2×D4—261no—
632C2×D4—261no—
633C2×D4#610311yescharacteristic
634C2×D4#610311yescharacteristic
635C2×D4#610311yescharacteristic
636C22×C4—261no—
637C22×C4—261no—
638C22×C4—261no—
639C22×C4—261no—
640C22×C4—261no—
641C22×C4—261no—
642C22×C4—261no—
643C22×C4C2×C4×D1311yescharacteristic
644C22×C4C2×C4×D1311yescharacteristic
645C22×C4C2×C4×D1311yescharacteristic
646C22×C4C2×D5211yescharacteristic
647C22×C4C2×D5211yescharacteristic
648C22×C4C2×D5211yescharacteristic
649C22×C4C2×C22⋊D1311yescharacteristic
650C22×C4C2×C22⋊D1311yescharacteristic
651C22×C4C2×C22⋊D1311yescharacteristic
652M16—42no—
653M16—522no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—42no—
659C2×C8—261no—
660C2×C8—261no—
661C2×C8—261no—
662C2×C8—261no—
663C2×C8—522no—
664C2×C8—522no—
665C4⋊C4—131no—
666C4⋊C4—131no—
667C4⋊C4—131no—
668C4⋊C4—131no—
669C4⋊C4—131no—
670C4⋊C4—131no—
671C4⋊C4—261no—
672C4⋊C4—261no—
673C4⋊C4—261no—
674C4⋊C4—261no—
675C4⋊C4—261no—
676C4⋊C4—261no—
677C4⋊C4—261no—
678C4⋊C4—261no—
679C4⋊C4—261no—
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#610311yescharacteristic
698C4⋊C4#610311yescharacteristic
699C4⋊C4#610311yescharacteristic
700C4⋊C4#610311yescharacteristic
701C4⋊C4#610311yescharacteristic
702C4⋊C4#610311yescharacteristic
703C22⋊C4—261no—
704C22⋊C4—261no—
705C22⋊C4—261no—
706C22⋊C4—261no—
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#610311yescharacteristic
717C22⋊C4#610311yescharacteristic
718C22⋊C4#610311yescharacteristic
719C22⋊C4#610311yescharacteristic
720C22⋊C4#610311yescharacteristic
721C22⋊C4#610311yescharacteristic
722C42—261no—
723C42—261no—
724C42—261no—
725C42—261no—
726C42—261no—
727C42C2×C4×D1311yescharacteristic
728C42C2×C4×D1311yescharacteristic
729C42C2×C4×D1311yescharacteristic
730C42C2×D5211yescharacteristic
731C42C2×D5211yescharacteristic
732C42C2×D5211yescharacteristic
733C42C2×C22⋊D1311yescharacteristic
734C42C2×C22⋊D1311yescharacteristic
735C42C2×C22⋊D1311yescharacteristic
736C42C23×D1311yescharacteristic
737C13#1768011yescharacteristic, complemented, Sylow
738C23—261no—
739C23C2×#610311yescharacteristic
740C23C2×#610311yescharacteristic
741C23C2×#610311yescharacteristic
742Q8—41no—
743Q8—521no—
744Q8—522no—
745Q8—1041no—
746D4—22no—
747D4—22no—
748D4—41no—
749D4—521no—
750D4—522no—
751D4—522no—
752D4—1041no—
753C2×C4—22no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—261no—
763C2×C4—261no—
764C2×C4—261no—
765C2×C4—261no—
766C2×C4—261no—
767C2×C4—261no—
768C2×C4—261no—
769C2×C4—522no—
770C2×C4—522no—
771C2×C4—522no—
772C2×C4—1041no—
773C2×C4—1041no—
774C2×C4—1041no—
775C2×C4—1041no—
776C2×C4C2×#610311yescharacteristic
777C2×C4C2×#610311yescharacteristic
778C2×C4C2×#610311yescharacteristic
779C2×C4C2×#610311yescharacteristic
780C2×C4C2×#610311yescharacteristic
781C2×C4C2×#610311yescharacteristic
782C2×C4C2×#610311yescharacteristic
783C2×C4C2×#610311yescharacteristic
784C2×C4C2×#610311yescharacteristic
785C2×C4C22×C4×D1311yescharacteristic
786C2×C4C22×D5211yescharacteristic
787C2×C4C22×C22⋊D1311yescharacteristic
788C8—41no—
789C8—41no—
790C8—41no—
791C8—41no—
792C8—262no—
793C8—521no—
794C8—521no—
795C8—521no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—521no—
805C22—521no—
806C22—521no—
807C22#1171866612yes—
808C22C22×#610311yescharacteristic
809C4—21no—
810C4—21no—
811C4—21no—
812C4—21no—
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—21no—
820C4—21no—
821C4—521no—
822C4—521no—
823C4—521no—
824C4—521no—
825C4—521no—
826C4—521no—
827C4—521no—
828C2—22no—
829C2—41no—
830C2—41no—
831C2—1041no—
832C2#1312331811yescharacteristic
833C2C2×#1171866611yescharacteristic
834C2#1312338111yescharacteristic
subgroupG/H
centerC22C22×#6103
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2923C2
socleC22×C13C22×C22⋊C4
prime radical#13128814C2
cosocleC42×C13C24
hypercenter#2923D13
hypocenterC13#17680
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2923

Complements

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

NH ≅ G/Ntype
2. #13123850C2semidirect
3. #13113473C2semidirect
4. #13113468C2semidirect
5. #13113465C2semidirect
6. #13113462C2semidirect
7. #13113457C2semidirect
8. #13113454C2semidirect
9. #13113452C2semidirect
10. #13113444C2semidirect
11. #13113439C2semidirect
12. #13113437C2semidirect
13. #13113425C2semidirect
14. C2×#11718057C2semidirect
15. C13×#2923C2semidirect
323. #2923D13semidirect
737. C13#17680semidirect

Maximal subgroups

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

subgroupindex
#131288142
#131238502
#131134732
#131134682
#131134652
#131134622
#131134572
#131134542
#131134522
#131134442
#131134392
#131134372
#131134252
C2×#117180572
C13×#29232
#1768013