Finite Group Databasebeta

← #16735247

Subgroups — #16735247

Order 3328.

1788 conjugacy classes of subgroups.

The subgroup lattice has 828 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#13126011C214yesmaximal, complemented
6#13126000C214yesmaximal, complemented
7#13125385C212yesmaximal, complemented
8#13125222C212yesmaximal, complemented
9#13124780C212yesmaximal, complemented
10#13124772C212yesmaximal
11#13124641C212yesmaximal, complemented
12#13124633C212yesmaximal, complemented
13#13123469C211yesmaximal, characteristic, complemented
14C2×C13×#529C211yesmaximal, characteristic
15C13×#529—21no—
16C13×#529—21no—
17C13×#529—21no—
18C13×#529—21no—
19C13×#529C2212yes—
20C13×#529C2212yes—
21C13×#529C2212yes—
22C13×#529C2212yes—
23C2×C13×#126—21no—
24C2×C13×#125C2211yescharacteristic
25C2×C13×#124C2211yescharacteristic
26C2×C13×#123—21no—
27C2×C13×C22⋊Q8C2211yescharacteristic
28C2×C13×#121C2211yescharacteristic
29C2×C4×Q8×C13C2211yescharacteristic
30C2×C4×D4×C13—21no—
31C2×C4×D4×C13C2211yescharacteristic
32C2×C13×#117—21no—
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#11719175C2212yescomplemented
44#11719175C2212yescomplemented
45C2×#88124C2212yescomplemented
46C2×#88123C2211yescharacteristic, complemented
47C2×#88123C2211yescharacteristic, complemented
48C2×C4×Dic26—21no—
49C2×C4×Dic26—21no—
50#11718886C2214yes—
51#11718876C2214yes—
52#11718868C2212yes—
53#11718726C2214yescomplemented
54#11718726C2214yescomplemented
55#11718725C2218yescomplemented
56#11718717C2218yescomplemented
57#11718716C2214yescomplemented
58#11718716C2214yescomplemented
59#11718706C2218yescomplemented
60#11718705C2214yescomplemented
61#11718704C2214yescomplemented
62#11718696C2218yes—
63#11718695C2214yes—
64#11718694C2214yes—
65#11718683C2218yescomplemented
66#11718682C2214yescomplemented
67#11718681C2214yescomplemented
68#11718670C2218yescomplemented
69#11718669C2214yescomplemented
70#11718668C2214yescomplemented
71#11718625C2214yes—
72#11718625C2214yes—
73#11718587C2212yescomplemented
74#11718587C2212yescomplemented
75#11718586C2212yescomplemented
76#11718586C2212yescomplemented
77#11718585C2212yes—
78C4×#6099C2212yes—
79C22×Q8×C13C2311yescharacteristic
80C22×D4×C13—21no—
81C22×D4×C13C2311yescharacteristic
82C23×C4×C13—21no—
83C23×C4×C13D411yescharacteristic
84C23×C4×C13D411yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C22×Dic26—21no—
87C22×Dic26—21no—
88C13×#126—22no—
89C13×#126—22no—
90C13×#126—22no—
91C13×#126—22no—
92C13×#125—21no—
93C13×#125—21no—
94C13×#125C2312yes—
95C13×#125C2312yes—
96C13×#124—21no—
97C13×#124—21no—
98C13×#124C2312yes—
99C13×#124C2312yes—
100C13×#123—22no—
101C13×#123—22no—
102C13×#123—22no—
103C13×#123—22no—
104C13×C22⋊Q8—21no—
105C13×C22⋊Q8—21no—
106C13×C22⋊Q8C2312yes—
107C13×C22⋊Q8C2312yes—
108C13×#121—21no—
109C13×#121—21no—
110C13×#121C2312yes—
111C13×#121C2312yes—
112C4×Q8×C13—21no—
113C4×Q8×C13—21no—
114C4×Q8×C13C2312yes—
115C4×Q8×C13C2312yes—
116C4×D4×C13—22no—
117C4×D4×C13—22no—
118C4×D4×C13—22no—
119C4×D4×C13—22no—
120C4×D4×C13—21no—
121C4×D4×C13—21no—
122C4×D4×C13C2312yes—
123C4×D4×C13C2312yes—
124C13×#117—22no—
125C13×#117—22no—
126C13×#117—22no—
127C13×#117—22no—
128C2×C13×C4⋊C4—21no—
129C2×C13×C4⋊C4—21no—
130C2×C13×C4⋊C4—21no—
131C2×C13×C4⋊C4—21no—
132C2×C13×C4⋊C4C2311yescharacteristic
133C2×C13×C4⋊C4C2311yescharacteristic
134C2×C13×C22⋊C4—21no—
135C2×C13×C22⋊C4—21no—
136C2×C13×C22⋊C4—21no—
137C2×C13×C22⋊C4—21no—
138C2×C13×C22⋊C4—21no—
139C2×C42×C13—21no—
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—
172C2×#6099C2314yes—
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—
206C4×#1055C2314yes—
207#60866—131nomaximal, Sylow
208C24×C13—21no—
209C24×C13C2×D411yescharacteristic
210C2×Q8×C13—21no—
211C2×Q8×C13—24no—
212C2×Q8×C13C2412yes—
213C2×D4×C13—22no—
214C2×D4×C13—22no—
215C2×D4×C13—21no—
216C2×D4×C13—24no—
217C2×D4×C13—44no—
218C2×D4×C13C2412yes—
219C22×C4×C13—24no—
220C22×C4×C13—21no—
221C22×C4×C13—21no—
222C22×C4×C13—21no—
223C22×C4×C13—22no—
224C22×C4×C13—22no—
225C22×C4×C13—42no—
226C22×C4×C13—42no—
227C22×C4×C13—44no—
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×C13C2×D411yescharacteristic
243C22×C4×C13C2411yescharacteristic
244C22×C4×C13C2411yescharacteristic
245C22×C4×C13C2411yescharacteristic
246C22×Dic13—22no—
247C22×Dic13—22no—
248C2×Dic26—22no—
249C2×Dic26—22no—
250C2×Dic26—22no—
251C2×Dic26—22no—
252C2×Dic26—44no—
253C2×Dic26—44no—
254C13×C4⋊C4—22no—
255C13×C4⋊C4—22no—
256C13×C4⋊C4—22no—
257C13×C4⋊C4—22no—
258C13×C4⋊C4—22no—
259C13×C4⋊C4—22no—
260C13×C4⋊C4—22no—
261C13×C4⋊C4—22no—
262C13×C4⋊C4—21no—
263C13×C4⋊C4—21no—
264C13×C4⋊C4C2412yes—
265C13×C4⋊C4C2412yes—
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—
274C13×C22⋊C4—22no—
275C13×C22⋊C4—22no—
276C42×C13—22no—
277C42×C13—22no—
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×C13C2×D411yescharacteristic
290C42×C13C2411yescharacteristic
291C42×C13C2411yescharacteristic
292C42×C13C2411yescharacteristic
293C42×C13C2411yescharacteristic
294C22⋊Dic13—24no—
295C22⋊Dic13—24no—
296C4⋊Dic13—22no—
297C4⋊Dic13—22no—
298C4⋊Dic13—22no—
299C4⋊Dic13—22no—
300C4⋊Dic13—22no—
301C4⋊Dic13—22no—
302C4⋊Dic13C2414yes—
303C4⋊Dic13C2414yes—
304#6101—24no—
305#6101—24no—
306#6101—24no—
307#6101—24no—
308C4×Dic13—24no—
309C4×Dic13—24no—
310#6099—28no—
311C2×#1055C2418yes—
312C2×#533—131no—
313C2×#529D1311yescharacteristic
314#3240—134no—
315#3239—132no—
316#3238—132no—
317#3233—134no—
318#3232—134no—
319#3166—132no—
320#3140—132no—
321#3095—132no—
322#3094—132no—
323#3078—132no—
324#3077—132no—
325#2920—131no—
326C23×C13—22no—
327C23×C13—22no—
328C23×C13—22no—
329C23×C13—41no—
330C23×C13—42no—
331C23×C13—42no—
332C23×C13—42no—
333C23×C13C22×D411yescharacteristic
334C23×C13C22×D411yescharacteristic
335C23×C13C22×D411yescharacteristic
336Q8×C13—24no—
337Q8×C13—42no—
338D4×C13—24no—
339D4×C13—44no—
340D4×C13—44no—
341D4×C13—42no—
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—22no—
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—41no—
362C2×C4×C13—44no—
363C2×C4×C13—42no—
364C2×C4×C13—42no—
365C2×C4×C13—42no—
366C2×C4×C13—44no—
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×C13C22×D411yescharacteristic
376C2×C4×C13C22×D411yescharacteristic
377C2×C4×C13C22×D411yescharacteristic
378C2×C4×C132−1+414yes—
379C2×C4×C13C2511yescharacteristic
380C2×Dic13—24no—
381C2×Dic13—24no—
382C2×Dic13—44no—
383C2×Dic13—44no—
384Dic26—44no—
385Dic26—44no—
386Dic26—44no—
387Dic26—44no—
388#1055—28no—
389#533—132no—
390#533—132no—
391#533—132no—
392#533—132no—
393#533—261no—
394#533—261no—
395#533—261no—
396#533—261no—
397C2×C4⋊Q8—131no—
398C2×C4⋊Q8—131no—
399#529—21no—
400#529—21no—
401#529—21no—
402#529—21no—
403#529C2×D1312yes—
404#529C2×D1312yes—
405#529C2×D1312yes—
406#529C2×D1312yes—
407C2×#126—21no—
408C2×#125—132no—
409C2×#125C2×D1311yescharacteristic
410C2×#124C2×D1311yescharacteristic
411C2×#123—21no—
412C2×C22⋊Q8—261no—
413C2×C22⋊Q8—261no—
414C2×C22⋊Q8C2×D1311yescharacteristic
415C2×#121C2×D1311yescharacteristic
416C2×C4×Q8—261no—
417C2×C4×Q8—261no—
418C2×C4×Q8C2×D1311yescharacteristic
419C2×C4×D4—21no—
420C2×C4×D4C2×D1311yescharacteristic
421C2×#117—21no—
422C2×#117—132no—
423C22×C42C2×D1311yescharacteristic
424#501—134no—
425#501—134no—
426#499—138no—
427#489—134no—
428#489—134no—
429#488—138no—
430#485—138no—
431#484—134no—
432#483—134no—
433#482—138no—
434#481—134no—
435#480—134no—
436#479—138no—
437#478—138no—
438#477—134no—
439#476—134no—
440#475—134no—
441#474—134no—
442#432—132no—
443#432—132no—
444#431—132no—
445#431—132no—
446#428—134no—
447#428—134no—
448#423—132no—
449#419—134no—
450#418—134no—
451#407—132no—
452C4×M16—132no—
453C22×C13—21no—
454C22×C13—21no—
455C22×C13—21no—
456C22×C13—21no—
457C22×C13—21no—
458C22×C13—21no—
459C22×C13—21no—
460C22×C13—44no—
461C22×C13—42no—
462C22×C13—42no—
463C22×C13—42no—
464C22×C13—84no—
465C22×C13#53612yes—
466C22×C13#57512yes—
467C22×C13C23×D411yescharacteristic
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—42no—
478C4×C13—42no—
479C4×C13—42no—
480C4×C13#53612yes—
481C4×C13#57512yes—
482C4×C13C2×2−1+412yes—
483Dic13—44no—
484Dic13—44no—
485C22×Q8—261no—
486C22×Q8—261no—
487C22×Q8C22×D1311yescharacteristic
488C22×D4—21no—
489C22×D4C22×D1311yescharacteristic
490C23×C4—21no—
491C23×C4C22⋊D1311yescharacteristic
492C23×C4C22⋊D1311yescharacteristic
493C23×C4C22×D1311yescharacteristic
494C2×M16—134no—
495C4⋊Q8—132no—
496C4⋊Q8—132no—
497C4⋊Q8—132no—
498C4⋊Q8—132no—
499C4⋊Q8—261no—
500C4⋊Q8—261no—
501C4⋊Q8—261no—
502C4⋊Q8—261no—
503#126—22no—
504#126—22no—
505#126—22no—
506#126—22no—
507#125—21no—
508#125—21no—
509#125—134no—
510#125—134no—
511#125—262no—
512#125—262no—
513#125C22×D1312yes—
514#125C22×D1312yes—
515#124—21no—
516#124—21no—
517#124C22×D1312yes—
518#124C22×D1312yes—
519#123—22no—
520#123—22no—
521#123—22no—
522#123—22no—
523C22⋊Q8—21no—
524C22⋊Q8—21no—
525C22⋊Q8—262no—
526C22⋊Q8—262no—
527C22⋊Q8—262no—
528C22⋊Q8—262no—
529C22⋊Q8—262no—
530C22⋊Q8—262no—
531C22⋊Q8—262no—
532C22⋊Q8—262no—
533C22⋊Q8C22×D1312yes—
534C22⋊Q8C22×D1312yes—
535#121—21no—
536#121—21no—
537#121C22×D1312yes—
538#121C22×D1312yes—
539C4×Q8—21no—
540C4×Q8—21no—
541C4×Q8—262no—
542C4×Q8—262no—
543C4×Q8—262no—
544C4×Q8—262no—
545C4×Q8—262no—
546C4×Q8—262no—
547C4×Q8—262no—
548C4×Q8—262no—
549C4×Q8C22×D1312yes—
550C4×Q8C22×D1312yes—
551C4×D4—22no—
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—21no—
556C4×D4—21no—
557C4×D4C22×D1312yes—
558C4×D4C22×D1312yes—
559#117—22no—
560#117—22no—
561#117—22no—
562#117—22no—
563#117—134no—
564#117—134no—
565#117—262no—
566#117—262no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—132no—
572C2×C4⋊C4—132no—
573C2×C4⋊C4—262no—
574C2×C4⋊C4—262no—
575C2×C4⋊C4—261no—
576C2×C4⋊C4—261no—
577C2×C4⋊C4C22×D1311yescharacteristic
578C2×C4⋊C4C22×D1311yescharacteristic
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—262no—
585C2×C42—21no—
586C2×C42—262no—
587C2×C42C22⋊D1311yescharacteristic
588C2×C42C22⋊D1311yescharacteristic
589C2×C42C22⋊D1311yescharacteristic
590C2×C42C22⋊D1311yescharacteristic
591C2×C42C22⋊D1311yescharacteristic
592C2×C42C22⋊D1311yescharacteristic
593C2×C42C22×D1311yescharacteristic
594C2×C42C22×D1311yescharacteristic
595C2×C42C22×D1311yescharacteristic
596C2×C42C22×D1311yescharacteristic
597C2×C42C22×D1311yescharacteristic
598C2×C42C22×D1311yescharacteristic
599#107—138no—
600#107—138no—
601#106—138no—
602#106—138no—
603C4⋊C8—134no—
604C4⋊C8—134no—
605#103—138no—
606#103—138no—
607#102—138no—
608#102—138no—
609C22⋊C8—134no—
610C22⋊C8—134no—
611#97—134no—
612C4×C8—134no—
613C2×C13—22no—
614C2×C13—22no—
615C2×C13—41no—
616C2×C13—82no—
617C2×C13C2×#53611yescharacteristic
618C2×C13C2×#57511yescharacteristic
619C2×C13C2×#57511yescharacteristic
620C24—21no—
621C24C2×C22⋊D1311yescharacteristic
622C2×Q8—21no—
623C2×Q8—24no—
624C2×Q8—262no—
625C2×Q8—262no—
626C2×Q8—262no—
627C2×Q8—262no—
628C2×Q8—524no—
629C2×Q8—524no—
630C2×Q8C23×D1312yes—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—24no—
634C2×D4—21no—
635C2×D4—44no—
636C2×D4C23×D1312yes—
637C22×C4—24no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—44no—
646C22×C4—262no—
647C22×C4—262no—
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×C4C2×C22⋊D1311yescharacteristic
659C22×C4C2×C22⋊D1311yescharacteristic
660C22×C4C2×C22⋊D1311yescharacteristic
661C22×C4C2×C22⋊D1311yescharacteristic
662C22×C4C2×C22⋊D1311yescharacteristic
663C22×C4C23×D1311yescharacteristic
664C22×C4C23×D1311yescharacteristic
665C22×C4C23×D1311yescharacteristic
666M16—268no—
667C2×C8—138no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—134no—
679C4⋊C4—134no—
680C4⋊C4—262no—
681C4⋊C4—262no—
682C4⋊C4—264no—
683C4⋊C4—264no—
684C4⋊C4—264no—
685C4⋊C4—264no—
686C4⋊C4—262no—
687C4⋊C4—262no—
688C4⋊C4—262no—
689C4⋊C4—262no—
690C4⋊C4C23×D1312yes—
691C4⋊C4C23×D1312yes—
692C22⋊C4—22no—
693C22⋊C4—22no—
694C22⋊C4—22no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—22no—
698C22⋊C4—22no—
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—22no—
702C22⋊C4—264no—
703C22⋊C4—264no—
704C42—22no—
705C42—22no—
706C42—264no—
707C42—264no—
708C42C2×C22⋊D1311yescharacteristic
709C42C2×C22⋊D1311yescharacteristic
710C42C2×C22⋊D1311yescharacteristic
711C42C2×C22⋊D1311yescharacteristic
712C42C2×C22⋊D1311yescharacteristic
713C42C2×C22⋊D1311yescharacteristic
714C42C2×C22⋊D1311yescharacteristic
715C42C2×C22⋊D1311yescharacteristic
716C42C2×C22⋊D1311yescharacteristic
717C42C2×C22⋊D1311yescharacteristic
718C42C2×C22⋊D1311yescharacteristic
719C42C2×C22⋊D1311yescharacteristic
720C42C23×D1311yescharacteristic
721C42C23×D1311yescharacteristic
722C42C23×D1311yescharacteristic
723C42C23×D1311yescharacteristic
724C13#6086611yescharacteristic, complemented, Sylow
725C23—22no—
726C23—22no—
727C23—22no—
728C23—41no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23C22×C22⋊D1311yescharacteristic
733C23C22×C22⋊D1311yescharacteristic
734C23C22×C22⋊D1311yescharacteristic
735Q8—24no—
736Q8—42no—
737Q8—524no—
738Q8—524no—
739Q8—524no—
740Q8—524no—
741D4—24no—
742D4—44no—
743D4—44no—
744D4—42no—
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—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—44no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—44no—
770C2×C4—264no—
771C2×C4—264no—
772C2×C4—524no—
773C2×C4—524no—
774C2×C4#8825714yes—
775C2×C4C22×C22⋊D1311yescharacteristic
776C2×C4C22×C22⋊D1311yescharacteristic
777C2×C4C22×C22⋊D1311yescharacteristic
778C2×C4C22×C22⋊D1311yescharacteristic
779C2×C4C22×C22⋊D1311yescharacteristic
780C2×C4C22×C22⋊D1311yescharacteristic
781C2×C4C22×C22⋊D1311yescharacteristic
782C2×C4C22×C22⋊D1311yescharacteristic
783C2×C4C22×C22⋊D1311yescharacteristic
784C2×C4C22×C22⋊D1311yescharacteristic
785C2×C4C22×C22⋊D1311yescharacteristic
786C2×C4C24×D1311yescharacteristic
787C8—268no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—44no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—84no—
800C22#1171952712yes—
801C22#1171953012yes—
802C22C23×C22⋊D1311yescharacteristic
803C4—21no—
804C4—21no—
805C4—21no—
806C4—21no—
807C4—21no—
808C4—21no—
809C4—21no—
810C4—21no—
811C4—21no—
812C4—42no—
813C4—42no—
814C4—42no—
815C4—524no—
816C4—524no—
817C4#1171952712yes—
818C4#1171953012yes—
819C4C2×#8825712yes—
820C2—22no—
821C2—22no—
822C2—41no—
823C2—82no—
824C2C2×#1171953011yescharacteristic
825C2C2×#1171952711yescharacteristic
826C2C2×#1171952711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#529C2
socleC22×C13C23×D4
prime radicalC2×C13×#121C22
hypercenterC2×#529D13
hypocenterC13#60866
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#11719175C2semidirect
2. #13126072C2semidirect
3. #13126063C2semidirect
4. #13126054C2semidirect
5. #13126011C2semidirect
6. #13126000C2semidirect
7. #13125385C2semidirect
8. #13125222C2semidirect
9. #13124780C2semidirect
11. #13124641C2semidirect
12. #13124633C2semidirect
13. #13123469C2semidirect
43. #11719175C22semidirect
44. #11719175C22semidirect
45. C2×#88124C22semidirect
46. C2×#88123C22semidirect
47. C2×#88123C22semidirect
53. #11718726C22semidirect
54. #11718726C22semidirect
55. #11718725C22semidirect
56. #11718717C22semidirect
57. #11718716C22semidirect
58. #11718716C22semidirect
59. #11718706C22semidirect
60. #11718705C22semidirect
61. #11718704C22semidirect
65. #11718683C22semidirect
66. #11718682C22semidirect
67. #11718681C22semidirect
68. #11718670C22semidirect
69. #11718669C22semidirect
70. #11718668C22semidirect
73. #11718587C22semidirect
74. #11718587C22semidirect
75. #11718586C22semidirect
76. #11718586C22semidirect
724. C13#60866semidirect

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
#131260112
#131260002
#131253852
#131252222
#131247802
#131247722
#131246412
#131246332
#131234692
C2×C13×#5292
#6086613