Finite Group Databasebeta

← #16735089

Subgroups — #16735089

Order 3328.

1780 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719175C211yesmaximal, characteristic, complemented
2#13126072C214yesmaximal, complemented
3#13126063C212yesmaximal, complemented
4#13126054C212yesmaximal, complemented
5#13126046C212yesmaximal, complemented
6#13126038C212yesmaximal, complemented
7#13126030C212yesmaximal, complemented
8#13126022C212yesmaximal, complemented
9#13125358C212yesmaximal, complemented
10#13125181C212yesmaximal, complemented
11#13124745C214yesmaximal, complemented
12#13124624C214yesmaximal, complemented
13C2×#11718587C211yesmaximal, characteristic, complemented
14C13×#3444C211yesmaximal, characteristic
15C13×#533C2211yescharacteristic
16C13×#533C2211yescharacteristic
17C13×#533C2211yescharacteristic
18C13×#532C2211yescharacteristic
19C13×#532C2211yescharacteristic
20C13×#532C2211yescharacteristic
21C13×#529—21no—
22C13×#529—21no—
23C13×#529—21no—
24C13×#529—21no—
25C13×#529C2212yes—
26C13×#529C2212yes—
27C13×#525—21no—
28C13×#525—21no—
29C13×#525C2212yes—
30C4×C13×#41—21no—
31C4×C13×#41—21no—
32C4×C13×#41C2212yes—
33C22×C42×C13C2211yescharacteristic
34C2×#88180C2212yes—
35C2×#88178—21no—
36C2×#88178—21no—
37#11719175—21no—
38#11719175—21no—
39#11719175—21no—
40#11719175—21no—
41#11719175C2212yes—
42#11719175C2212yes—
43#11719175C2212yes—
44#11719175C2212yes—
45C2×#88124C2212yes—
46C2×#88123C2211yescharacteristic
47C2×#88123C2211yescharacteristic
48C2×C4×Dic26—21no—
49C2×C4×Dic26—21no—
50#11718894C2218yes—
51C2×C22⋊#1055C2212yes—
52#11718743C2214yescomplemented
53#11718741C2214yescomplemented
54#11718741C2214yescomplemented
55#11718732C2214yescomplemented
56#11718726C2214yescomplemented
57#11718726C2214yescomplemented
58#11718716C2214yescomplemented
59#11718716C2214yescomplemented
60#11718706C2218yes—
61#11718705C2214yes—
62#11718704C2214yes—
63#11718696C2218yes—
64#11718695C2214yes—
65#11718694C2214yes—
66#11718683C2218yescomplemented
67#11718682C2214yescomplemented
68#11718681C2214yescomplemented
69#11718670C2218yescomplemented
70#11718669C2214yescomplemented
71#11718668C2214yescomplemented
72#11718659C2218yes—
73#11718587C2212yes—
74#11718587C2212yes—
75#11718587C2212yes—
76#11718587C2212yes—
77C2×C4⋊#1055C2212yes—
78C2×#88043C2212yes—
79C2×C13×#41—21no—
80C2×C13×#41—21no—
81C2×C13×#41C2312yes—
82C23×C4×C13D411yescharacteristic
83C23×C4×C13D411yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C22×Dic26—21no—
86C22×Dic26—21no—
87C13×C4⋊Q8C2311yescharacteristic
88C13×C4⋊Q8C2311yescharacteristic
89C13×C4⋊Q8C2311yescharacteristic
90C13×#127C2311yescharacteristic
91C13×#126—22no—
92C13×#126—22no—
93C13×#125—21no—
94C13×#125—21no—
95C13×#125C2312yes—
96C13×#124—21no—
97C13×#124—21no—
98C13×#124C2312yes—
99C13×#123—22no—
100C13×#123—22no—
101C13×#123—22no—
102C13×C22⋊Q8—21no—
103C13×C22⋊Q8—21no—
104C13×C22⋊Q8—21no—
105C13×C22⋊Q8—21no—
106C13×C22⋊Q8C2312yes—
107C13×C22⋊Q8C2312yes—
108C13×#121—21no—
109C13×#121—21no—
110C13×#121—21no—
111C13×#121—21no—
112C13×#121C2312yes—
113C13×#121C2312yes—
114C13×#120—22no—
115C4×Q8×C13—21no—
116C4×Q8×C13—21no—
117C4×Q8×C13—21no—
118C4×Q8×C13—21no—
119C4×Q8×C13C2312yes—
120C4×Q8×C13C2312yes—
121C4×D4×C13—22no—
122C4×D4×C13—22no—
123C4×D4×C13—22no—
124C4×D4×C13—22no—
125C4×D4×C13—22no—
126C4×D4×C13—22no—
127C4×D4×C13—21no—
128C4×D4×C13—21no—
129C4×D4×C13—21no—
130C4×D4×C13—21no—
131C4×D4×C13C2312yes—
132C4×D4×C13C2312yes—
133C13×#117—21no—
134C13×#117—21no—
135C13×#117—22no—
136C13×#117—22no—
137C13×#117—22no—
138C13×#117C2312yes—
139C2×C42×C13—22no—
140C2×C42×C13D411yescharacteristic
141C2×C42×C13D411yescharacteristic
142C2×C42×C13D411yescharacteristic
143C2×C42×C13D411yescharacteristic
144C2×C42×C13D411yescharacteristic
145C2×C42×C13D411yescharacteristic
146C2×C42×C13C2311yescharacteristic
147C2×C42×C13C2311yescharacteristic
148C2×C42×C13C2311yescharacteristic
149C2×C42×C13C2311yescharacteristic
150C2×C42×C13C2311yescharacteristic
151C2×C42×C13C2311yescharacteristic
152C2×C22⋊Dic13—22no—
153#88180—22no—
154#88180—22no—
155#88180C2314yes—
156#88180C2314yes—
157C2×C4⋊Dic13—21no—
158C2×C4⋊Dic13—21no—
159C2×C4⋊Dic13C2312yes—
160C2×C4⋊Dic13C2312yes—
161#88178—22no—
162#88178—22no—
163#88178—22no—
164#88178—22no—
165#88178—22no—
166#88178—22no—
167#88178—22no—
168#88178—22no—
169C2×#6101—22no—
170C2×#6101—22no—
171C2×C4×Dic13—22no—
172C22×#1055C2314yes—
173#88124—22no—
174#88124—22no—
175#88124C2314yes—
176#88124C2314yes—
177#88123—21no—
178#88123—21no—
179#88123—21no—
180#88123—21no—
181#88123C2312yes—
182#88123C2312yes—
183#88123C2312yes—
184#88123C2312yes—
185C4×Dic26—22no—
186C4×Dic26—22no—
187C4×Dic26—22no—
188C4×Dic26—22no—
189C4×Dic26—22no—
190C4×Dic26—22no—
191C4×Dic26—22no—
192C4×Dic26—22no—
193#88075C2318yes—
194#88075C2318yes—
195#88072C2318yes—
196#88072C2318yes—
197C22⋊#1055C2314yes—
198C22⋊#1055C2314yes—
199#88048C2318yes—
200#88048C2318yes—
201#88047C2318yes—
202#88047C2318yes—
203C4⋊#1055C2314yes—
204C4⋊#1055C2314yes—
205#88043C2314yes—
206#88043C2314yes—
207#60854—131nomaximal, Sylow
208C24×C13C2×D411yescharacteristic
209C13×#41—28no—
210C13×#41—44no—
211C13×#41—44no—
212C2×Q8×C13—21no—
213C2×Q8×C13—21no—
214C2×Q8×C13C2412yes—
215C2×D4×C13—22no—
216C2×D4×C13—22no—
217C2×D4×C13—22no—
218C2×D4×C13—21no—
219C2×D4×C13—21no—
220C2×D4×C13C2412yes—
221C22×C4×C13—24no—
222C22×C4×C13—22no—
223C22×C4×C13—22no—
224C22×C4×C13—22no—
225C22×C4×C13—42no—
226C22×C4×C13—42no—
227C22×C4×C13C2×D411yescharacteristic
228C22×C4×C13C2×D411yescharacteristic
229C22×C4×C13C2×D411yescharacteristic
230C22×C4×C13C2×D411yescharacteristic
231C22×C4×C13C2×D411yescharacteristic
232C22×C4×C13C2×D411yescharacteristic
233C22×C4×C13C2×D411yescharacteristic
234C22×C4×C13C2×D411yescharacteristic
235C22×C4×C13C2×D411yescharacteristic
236C22×C4×C13C2×D411yescharacteristic
237C22×C4×C13C2×D411yescharacteristic
238C22×C4×C13C2×D411yescharacteristic
239C22×C4×C13C2×D411yescharacteristic
240C22×C4×C13C2×D411yescharacteristic
241C22×C4×C13C2×D411yescharacteristic
242C22×C4×C13C2411yescharacteristic
243C22×C4×C13C2411yescharacteristic
244C22×C4×C13C2411yescharacteristic
245C22×Dic13—22no—
246C22×Dic13—22no—
247C2×Dic26—22no—
248C2×Dic26—22no—
249C2×Dic26—22no—
250C2×Dic26—22no—
251C2×Dic26—44no—
252C2×Dic26—44no—
253C13×C4⋊C4—21no—
254C13×C4⋊C4—21no—
255C13×C4⋊C4—21no—
256C13×C4⋊C4—21no—
257C13×C4⋊C4—22no—
258C13×C4⋊C4—22no—
259C13×C4⋊C4—22no—
260C13×C4⋊C4—22no—
261C13×C4⋊C4—22no—
262C13×C4⋊C4—22no—
263C13×C4⋊C4C2412yes—
264C13×C4⋊C4C2412yes—
265C13×C22⋊C4—22no—
266C13×C22⋊C4—22no—
267C13×C22⋊C4—22no—
268C13×C22⋊C4—22no—
269C13×C22⋊C4—22no—
270C13×C22⋊C4—22no—
271C13×C22⋊C4—22no—
272C13×C22⋊C4—22no—
273C13×C22⋊C4—22no—
274C42×C13—22no—
275C42×C13—22no—
276C42×C13—22no—
277C42×C13C2×D411yescharacteristic
278C42×C13C2×D411yescharacteristic
279C42×C13C2×D411yescharacteristic
280C42×C13C2×D411yescharacteristic
281C42×C13C2×D411yescharacteristic
282C42×C13C2×D411yescharacteristic
283C42×C13C2×D411yescharacteristic
284C42×C13C2×D411yescharacteristic
285C42×C13C2×D411yescharacteristic
286C42×C13C2×D411yescharacteristic
287C42×C13C2×D411yescharacteristic
288C42×C13C2×D411yescharacteristic
289C42×C13C2411yescharacteristic
290C42×C13C2411yescharacteristic
291C42×C13C2411yescharacteristic
292C42×C13C2411yescharacteristic
293C22⋊Dic13—24no—
294C22⋊Dic13—24no—
295C4⋊Dic13—22no—
296C4⋊Dic13—22no—
297C4⋊Dic13—22no—
298C4⋊Dic13—22no—
299C4⋊Dic13—22no—
300C4⋊Dic13—22no—
301C4⋊Dic13C2414yes—
302C4⋊Dic13C2414yes—
303#6101—24no—
304#6101—24no—
305#6101—24no—
306#6101—24no—
307C4×Dic13—24no—
308C4×Dic13—24no—
309C2×#1055—28no—
310C2×#1055C2418yes—
311#3444D1311yescharacteristic
312C2×#533—131no—
313#3240—134no—
314#3239—132no—
315#3238—132no—
316#3237—132no—
317#3236—132no—
318#3235—132no—
319#3234—132no—
320#3162—132no—
321#3135—132no—
322#3091—134no—
323#3076—134no—
324C2×#432—131no—
325C23×C13—22no—
326C23×C13—22no—
327C23×C13—22no—
328C23×C13—41no—
329C23×C13C22×D411yescharacteristic
330C23×C13C22×D411yescharacteristic
331C23×C13C22×D411yescharacteristic
332Q8×C13—24no—
333Q8×C13—42no—
334Q8×C13—42no—
335D4×C13—24no—
336D4×C13—42no—
337D4×C13—42no—
338D4×C13—44no—
339D4×C13—44no—
340D4×C13—44no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—41no—
355C2×C4×C13—41no—
356C2×C4×C13—41no—
357C2×C4×C13—41no—
358C2×C4×C13—41no—
359C2×C4×C13—41no—
360C2×C4×C13—41no—
361C2×C4×C13—44no—
362C2×C4×C13—44no—
363C2×C4×C13—44no—
364C2×C4×C13C22×D411yescharacteristic
365C2×C4×C13C22×D411yescharacteristic
366C2×C4×C13C22×D411yescharacteristic
367C2×C4×C13C22×D411yescharacteristic
368C2×C4×C13C22×D411yescharacteristic
369C2×C4×C13C22×D411yescharacteristic
370C2×C4×C13C22×D411yescharacteristic
371C2×C4×C13C22×D411yescharacteristic
372C2×C4×C13C22×D411yescharacteristic
373C2×C4×C13C22×D411yescharacteristic
374C2×C4×C13C22×D411yescharacteristic
375C2×C4×C132−1+414yes—
376C2×C4×C13C2511yescharacteristic
377C2×Dic13—24no—
378C2×Dic13—24no—
379C2×Dic13—44no—
380C2×Dic13—44no—
381Dic26—44no—
382Dic26—44no—
383Dic26—44no—
384Dic26—44no—
385#1055—28no—
386#533—132no—
387#533—132no—
388#533—132no—
389#533—132no—
390#533—261no—
391#533—261no—
392#533—261no—
393#533—261no—
394#533C2×D1311yescharacteristic
395#533C2×D1311yescharacteristic
396#533C2×D1311yescharacteristic
397#532C2×D1311yescharacteristic
398#532C2×D1311yescharacteristic
399#532C2×D1311yescharacteristic
400C2×C4⋊Q8—131no—
401C2×C4⋊Q8—131no—
402#529—21no—
403#529—21no—
404#529—21no—
405#529—21no—
406#529C2×D1312yes—
407#529C2×D1312yes—
408C2×#125—132no—
409#525—21no—
410#525—21no—
411#525C2×D1312yes—
412C2×C22⋊Q8—261no—
413C2×C22⋊Q8—261no—
414C4×#41—21no—
415C4×#41—21no—
416C4×#41C2×D1312yes—
417C2×C4×Q8—261no—
418C2×C4×Q8—261no—
419C2×#117—132no—
420C22×C42C2×D1311yescharacteristic
421#501—134no—
422#501—134no—
423#501—134no—
424#501—134no—
425#491—134no—
426#490—134no—
427#489—134no—
428#489—134no—
429#485—138no—
430#484—134no—
431#483—134no—
432#482—138no—
433#481—134no—
434#480—134no—
435#479—138no—
436#478—138no—
437#477—134no—
438#476—134no—
439#475—134no—
440#474—134no—
441#432—132no—
442#432—132no—
443#432—132no—
444#432—132no—
445#427—138no—
446C2×C4⋊C8—132no—
447#416—138no—
448C2×C22⋊C8—132no—
449C2×#97—132no—
450C22×C13—21no—
451C22×C13—21no—
452C22×C13—21no—
453C22×C13—21no—
454C22×C13—21no—
455C22×C13—21no—
456C22×C13—21no—
457C22×C13—44no—
458C22×C13—42no—
459C22×C13—42no—
460C22×C13—42no—
461C22×C13#53612yes—
462C22×C13#57512yes—
463C22×C13C23×D411yescharacteristic
464C4×C13—21no—
465C4×C13—21no—
466C4×C13—21no—
467C4×C13—21no—
468C4×C13—21no—
469C4×C13—21no—
470C4×C13—21no—
471C4×C13—21no—
472C4×C13—21no—
473C4×C13—42no—
474C4×C13—42no—
475C4×C13—42no—
476C4×C13#53612yes—
477C4×C13#57512yes—
478C4×C13C2×2−1+412yes—
479Dic13—44no—
480Dic13—44no—
481C2×#41—21no—
482C2×#41—21no—
483C2×#41C22×D1312yes—
484C22×Q8—261no—
485C22×Q8—261no—
486C23×C4C22⋊D1311yescharacteristic
487C23×C4C22⋊D1311yescharacteristic
488C23×C4C22×D1311yescharacteristic
489C22×C8—134no—
490C4⋊Q8—132no—
491C4⋊Q8—132no—
492C4⋊Q8—132no—
493C4⋊Q8—132no—
494C4⋊Q8—261no—
495C4⋊Q8—261no—
496C4⋊Q8—261no—
497C4⋊Q8—261no—
498C4⋊Q8C22×D1311yescharacteristic
499C4⋊Q8C22×D1311yescharacteristic
500C4⋊Q8C22×D1311yescharacteristic
501#127C22×D1311yescharacteristic
502#126—22no—
503#126—22no—
504#125—21no—
505#125—21no—
506#125—134no—
507#125—134no—
508#125—262no—
509#125—262no—
510#125C22×D1312yes—
511#124—21no—
512#124—21no—
513#124C22×D1312yes—
514#123—22no—
515#123—22no—
516#123—22no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519C22⋊Q8—21no—
520C22⋊Q8—21no—
521C22⋊Q8—262no—
522C22⋊Q8—262no—
523C22⋊Q8—262no—
524C22⋊Q8—262no—
525C22⋊Q8—262no—
526C22⋊Q8—262no—
527C22⋊Q8—262no—
528C22⋊Q8—262no—
529C22⋊Q8C22×D1312yes—
530C22⋊Q8C22×D1312yes—
531#121—21no—
532#121—21no—
533#121—21no—
534#121—21no—
535#121C22×D1312yes—
536#121C22×D1312yes—
537#120—22no—
538C4×Q8—21no—
539C4×Q8—21no—
540C4×Q8—21no—
541C4×Q8—21no—
542C4×Q8—262no—
543C4×Q8—262no—
544C4×Q8—262no—
545C4×Q8—262no—
546C4×Q8—262no—
547C4×Q8—262no—
548C4×Q8—262no—
549C4×Q8—262no—
550C4×Q8C22×D1312yes—
551C4×Q8C22×D1312yes—
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557C4×D4—22no—
558C4×D4—21no—
559C4×D4—21no—
560C4×D4—21no—
561C4×D4—21no—
562C4×D4C22×D1312yes—
563C4×D4C22×D1312yes—
564#117—21no—
565#117—21no—
566#117—22no—
567#117—22no—
568#117—22no—
569#117—134no—
570#117—134no—
571#117—262no—
572#117—262no—
573#117C22×D1312yes—
574C2×C4⋊C4—132no—
575C2×C4⋊C4—132no—
576C2×C4⋊C4—262no—
577C2×C4⋊C4—262no—
578C2×C4⋊C4—261no—
579C2×C4⋊C4—261no—
580C2×C22⋊C4—262no—
581C2×C42—22no—
582C2×C42—262no—
583C2×C42C22⋊D1311yescharacteristic
584C2×C42C22⋊D1311yescharacteristic
585C2×C42C22⋊D1311yescharacteristic
586C2×C42C22⋊D1311yescharacteristic
587C2×C42C22⋊D1311yescharacteristic
588C2×C42C22⋊D1311yescharacteristic
589C2×C42C22×D1311yescharacteristic
590C2×C42C22×D1311yescharacteristic
591C2×C42C22×D1311yescharacteristic
592C2×C42C22×D1311yescharacteristic
593C2×C42C22×D1311yescharacteristic
594C2×C42C22×D1311yescharacteristic
595#107—138no—
596#107—138no—
597#106—138no—
598#106—138no—
599C4⋊C8—134no—
600C4⋊C8—134no—
601#103—138no—
602#103—138no—
603#102—138no—
604#102—138no—
605C22⋊C8—134no—
606C22⋊C8—134no—
607#97—134no—
608#97—134no—
609C2×C13—22no—
610C2×C13—22no—
611C2×C13—41no—
612C2×C13—82no—
613C2×C13C2×#53611yescharacteristic
614C2×C13C2×#57511yescharacteristic
615C2×C13C2×#57511yescharacteristic
616C24C2×C22⋊D1311yescharacteristic
617#41—28no—
618#41—44no—
619#41—44no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—262no—
623C2×Q8—262no—
624C2×Q8—262no—
625C2×Q8—262no—
626C2×Q8—524no—
627C2×Q8—524no—
628C2×Q8C23×D1312yes—
629C2×D4—22no—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4C23×D1312yes—
635C22×C4—24no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—262no—
642C22×C4—262no—
643C22×C4C2×C22⋊D1311yescharacteristic
644C22×C4C2×C22⋊D1311yescharacteristic
645C22×C4C2×C22⋊D1311yescharacteristic
646C22×C4C2×C22⋊D1311yescharacteristic
647C22×C4C2×C22⋊D1311yescharacteristic
648C22×C4C2×C22⋊D1311yescharacteristic
649C22×C4C2×C22⋊D1311yescharacteristic
650C22×C4C2×C22⋊D1311yescharacteristic
651C22×C4C2×C22⋊D1311yescharacteristic
652C22×C4C2×C22⋊D1311yescharacteristic
653C22×C4C2×C22⋊D1311yescharacteristic
654C22×C4C2×C22⋊D1311yescharacteristic
655C22×C4C2×C22⋊D1311yescharacteristic
656C22×C4C2×C22⋊D1311yescharacteristic
657C22×C4C2×C22⋊D1311yescharacteristic
658C22×C4C23×D1311yescharacteristic
659C22×C4C23×D1311yescharacteristic
660C22×C4C23×D1311yescharacteristic
661C2×C8—138no—
662C2×C8—268no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—134no—
674C4⋊C4—134no—
675C4⋊C4—262no—
676C4⋊C4—262no—
677C4⋊C4—264no—
678C4⋊C4—264no—
679C4⋊C4—264no—
680C4⋊C4—264no—
681C4⋊C4—262no—
682C4⋊C4—262no—
683C4⋊C4—262no—
684C4⋊C4—262no—
685C4⋊C4C23×D1312yes—
686C4⋊C4C23×D1312yes—
687C22⋊C4—22no—
688C22⋊C4—22no—
689C22⋊C4—22no—
690C22⋊C4—22no—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—22no—
694C22⋊C4—22no—
695C22⋊C4—22no—
696C22⋊C4—264no—
697C22⋊C4—264no—
698C42—22no—
699C42—22no—
700C42—22no—
701C42—264no—
702C42—264no—
703C42C2×C22⋊D1311yescharacteristic
704C42C2×C22⋊D1311yescharacteristic
705C42C2×C22⋊D1311yescharacteristic
706C42C2×C22⋊D1311yescharacteristic
707C42C2×C22⋊D1311yescharacteristic
708C42C2×C22⋊D1311yescharacteristic
709C42C2×C22⋊D1311yescharacteristic
710C42C2×C22⋊D1311yescharacteristic
711C42C2×C22⋊D1311yescharacteristic
712C42C2×C22⋊D1311yescharacteristic
713C42C2×C22⋊D1311yescharacteristic
714C42C2×C22⋊D1311yescharacteristic
715C42C23×D1311yescharacteristic
716C42C23×D1311yescharacteristic
717C42C23×D1311yescharacteristic
718C42C23×D1311yescharacteristic
719C13#6085411yescharacteristic, complemented, Sylow
720C23—22no—
721C23—22no—
722C23—22no—
723C23—41no—
724C23C22×C22⋊D1311yescharacteristic
725C23C22×C22⋊D1311yescharacteristic
726C23C22×C22⋊D1311yescharacteristic
727Q8—24no—
728Q8—42no—
729Q8—42no—
730Q8—524no—
731Q8—524no—
732Q8—524no—
733Q8—524no—
734D4—24no—
735D4—42no—
736D4—42no—
737D4—44no—
738D4—44no—
739D4—44no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—264no—
764C2×C4—264no—
765C2×C4—524no—
766C2×C4—524no—
767C2×C4#8825714yes—
768C2×C4C22×C22⋊D1311yescharacteristic
769C2×C4C22×C22⋊D1311yescharacteristic
770C2×C4C22×C22⋊D1311yescharacteristic
771C2×C4C22×C22⋊D1311yescharacteristic
772C2×C4C22×C22⋊D1311yescharacteristic
773C2×C4C22×C22⋊D1311yescharacteristic
774C2×C4C22×C22⋊D1311yescharacteristic
775C2×C4C22×C22⋊D1311yescharacteristic
776C2×C4C22×C22⋊D1311yescharacteristic
777C2×C4C22×C22⋊D1311yescharacteristic
778C2×C4C22×C22⋊D1311yescharacteristic
779C2×C4C24×D1311yescharacteristic
780C8—268no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—44no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22#1171952712yes—
793C22#1171953012yes—
794C22C23×C22⋊D1311yescharacteristic
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—524no—
808C4—524no—
809C4#1171952712yes—
810C4#1171953012yes—
811C4C2×#8825712yes—
812C2—22no—
813C2—22no—
814C2—41no—
815C2—82no—
816C2C2×#1171953011yescharacteristic
817C2C2×#1171952711yescharacteristic
818C2C2×#1171952711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
Fitting, prime radicalC13×#3444C2
socleC22×C13C23×D4
hypercenter#3444D13
hypocenterC13#60854
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. C2×#11719175C2semidirect
2. #13126072C2semidirect
3. #13126063C2semidirect
4. #13126054C2semidirect
5. #13126046C2semidirect
6. #13126038C2semidirect
7. #13126030C2semidirect
8. #13126022C2semidirect
9. #13125358C2semidirect
10. #13125181C2semidirect
11. #13124745C2semidirect
12. #13124624C2semidirect
13. C2×#11718587C2semidirect
52. #11718743C22semidirect
53. #11718741C22semidirect
54. #11718741C22semidirect
55. #11718732C22semidirect
56. #11718726C22semidirect
57. #11718726C22semidirect
58. #11718716C22semidirect
59. #11718716C22semidirect
66. #11718683C22semidirect
67. #11718682C22semidirect
68. #11718681C22semidirect
69. #11718670C22semidirect
70. #11718669C22semidirect
71. #11718668C22semidirect
719. C13#60854semidirect

Maximal subgroups

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

subgroupindex
C2×#117191752
#131260722
#131260632
#131260542
#131260462
#131260382
#131260302
#131260222
#131253582
#131251812
#131247452
#131246242
C2×#117185872
C13×#34442
#6085413