Finite Group Databasebeta

← #16808443

Subgroups — #16808443

Order 3328.

1882 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131638C211yesmaximal, characteristic, complemented
2#13131637C212yesmaximal, complemented
3#13131634C212yesmaximal, complemented
4#13131633C214yesmaximal, complemented
5#13131632C211yesmaximal, characteristic, complemented
6#13131631C212yesmaximal, complemented
7#13131626C212yesmaximal, complemented
8#13131625C211yesmaximal, characteristic, complemented
9#13131624C214yesmaximal, complemented
10#13131624C212yesmaximal, complemented
11Q8×D13⋊C8C211yesmaximal, characteristic, complemented
12C2×#11719074C212yesmaximal, complemented
13#13131483C212yesmaximal
14#13131481C211yesmaximal, characteristic
15C4×#88238C211yesmaximal, characteristic
16C4×#88238C212yesmaximal
17#13128415C211yesmaximal, characteristic
18C2×#88238C2212yes—
19C2×#88238C2211yescharacteristic
20C2×#88238C2211yescharacteristic
21C13×#554C411yescharacteristic
22#11719433C2211yescharacteristic
23#11719427C411yescharacteristic
24#11719393C2212yes—
25#11719390C412yes—
26#11719341C414yes—
27#11719337C412yes—
28#11719327C2212yes—
29#11719327C2214yes—
30C4×Q8×D13C2211yescharacteristic
31#11719272C411yescharacteristic
32#11719244C412yes—
33D4×Dic26C411yescharacteristic
34C4×#6129C2211yescharacteristic
35C4×#6129C2212yes—
36#11719216C412yes—
37C2×#88141C2212yes—
38#11719158C2212yes—
39#11719158C2214yes—
40#11719158C2212yes—
41Q8×#1057C2211yescharacteristic
42Q8×#1057C2211yescharacteristic
43Q8×#1057C2212yes—
44#11719129C2212yes—
45#11719129C2214yes—
46C2×#88112C2214yes—
47C4×#6122C2212yes—
48C4×#6122C2214yes—
49C2×C4⋊#1057C2212yes—
50C2×C4×#1057C2214yes—
51C2×C4×#1057C2212yes—
52#11719080C2214yes—
53#11719080C2212yes—
54#11719080C2212yes—
55#11719079C2212yes—
56#11719079C2212yes—
57#11719079C2212yes—
58#11719078C2214yes—
59#11719078C2214yes—
60#11719078C2214yes—
61#11719078C2214yes—
62#11719078C2214yes—
63#11719074C2211yescharacteristic
64#11719074C2212yes—
65#11719074C2214yes—
66#11719074C2212yes—
67#11719074C2214yes—
68#11719074C2212yes—
69#11719074C2212yes—
70#11719074C2212yes—
71#11719074C2211yescharacteristic
72#11719074C2214yes—
73#11719072C2212yes—
74#11719072C2211yescharacteristic
75#11719072C2212yes—
76#11719072C2211yescharacteristic
77#11719067C2214yes—
78#11719067C2214yes—
79#11719067C2214yes—
80#11719062C2214yes—
81#11719062C2212yes—
82#11719062C2214yes—
83#11719062C2212yes—
84#11719053C2212yes—
85#11719052C2211yescharacteristic
86D13⋊(C4⋊C8)C2211yescharacteristic
87D13⋊(C4⋊C8)C2212yes—
88C4×#6118C2211yescharacteristic
89C4×#6118C2212yes—
90C4×D13⋊C8C2211yescharacteristic
91C4×D13⋊C8C2212yes—
92C2×Q8×D13C2×C411yescharacteristic
93C2×#6129C2311yescharacteristic
94C22×Dic26C2×C412yes—
95C2×#6122C2312yes—
96C2×#6122C2314yes—
97C2×#6122C2312yes—
98C22×#1057C2314yes—
99C22×#1057C2312yes—
100C22×#1057C2312yes—
101#88238—28no—
102#88238—24no—
103#88238Q818yescomplemented
104C2×#6118C2312yes—
105C2×#6118C2311yescharacteristic
106C2×#6118C2311yescharacteristic
107C2×D13⋊C8C2312yes—
108C2×D13⋊C8C2311yescharacteristic
109C2×D13⋊C8C2311yescharacteristic
110C13×C4⋊Q8C2×C411yescharacteristic
111C13×#125C2×C412yes—
112C13×C22⋊Q8C2×C412yes—
113C13×C22⋊Q8C2×C414yes—
114C4×Q8×C13C2×C411yescharacteristic
115C4×D4×C13C2×C411yescharacteristic
116C4×D4×C13C2×C412yes—
117C2×C13×C4⋊C4C2×C412yes—
118#88200C2×C412yes—
119Q8×Dic13C2312yes—
120Q8×Dic13C2311yescharacteristic
121#88198C2×C414yes—
122#88198C2×C412yes—
123D4×Dic13C2×C412yes—
124D4×Dic13C2×C411yescharacteristic
125C4×C22⋊D13C2×C412yes—
126C4×C22⋊D13C2×C414yes—
127#88178C2×C412yes—
128#88178C2×C414yes—
129C2×#6101C2×C414yes—
130C2×C4×Dic13C2312yes—
131C2×C4×Dic13C2314yes—
132#88151C2×C412yes—
133#88150C2×C414yes—
134#88150C2×C414yes—
135#88146C2312yes—
136#88146C2311yescharacteristic
137C4⋊C4×D13C2×C411yescharacteristic
138C4⋊C4×D13C2×C412yes—
139#88144C2×C412yes—
140#88143C2×C414yes—
141#88143C2×C414yes—
142#88143C2×C414yes—
143#88142C2×C412yes—
144#88142C2×C412yes—
145#88142C2×C412yes—
146#88142C2×C414yes—
147#88141C2×C412yes—
148#88141C2×C412yes—
149#88141C2×C412yes—
150#88141C2×C414yes—
151#88141C2×C411yescharacteristic
152#88141C2312yes—
153#88141C2311yescharacteristic
154#88141C2314yes—
155#88141C2312yes—
156#88141C2314yes—
157#88135C2×C414yes—
158#88135C2×C412yes—
159#88132C2×C414yes—
160#88132C2×C414yes—
161#88132C2×C414yes—
162#88131C2314yes—
163#88131C2312yes—
164C42×D13C2311yescharacteristic
165C42×D13C2312yes—
166#88124C2×C412yes—
167#88123C2×C411yescharacteristic
168C4×Dic26C2×C411yescharacteristic
169C4×Dic26C2×C411yescharacteristic
170C4×Dic26C2×C412yes—
171C4×Dic26C2×C412yes—
172#88112C2312yes—
173#88112C2312yes—
174#88112C2312yes—
175#88112C2314yes—
176#88112C2314yes—
177#88112C2314yes—
178#88112C2314yes—
179#88112C2314yes—
180#88110C2314yes—
181#88110C2312yes—
182#88110C2312yes—
183#88110C2312yes—
184#88110C2314yes—
185#88110C2314yes—
186C4⋊#1057C2312yes—
187C4⋊#1057C2312yes—
188C4⋊#1057C2311yescharacteristic
189C4⋊#1057C2311yescharacteristic
190C4⋊#1057C2312yes—
191C4⋊#1057C2312yes—
192C4⋊#1057C2314yes—
193C4⋊#1057C2314yes—
194C4⋊#1057C2314yes—
195C4×#1057C2312yes—
196C4×#1057C2311yescharacteristic
197C4×#1057C2311yescharacteristic
198C4×#1057C2312yes—
199C4×#1057C2312yes—
200C4×#1057C2311yescharacteristic
201C4×#1057C2312yes—
202C4×#1057C2311yescharacteristic
203C4×#1057C2314yes—
204C4×#1057C2312yes—
205C4×#1057C2312yes—
206C4×#1057C2314yes—
207C4×#1057C2312yes—
208C4×#1057C2314yes—
209Q8×#131—131nomaximal, Sylow
210C2×Q8×C13C22×C411yescharacteristic
211C2×Q8×C13C22×C412yes—
212C2×D4×C13C22×C411yescharacteristic
213C22×C4×C13C22×C412yes—
214C22×C4×C13C22×C414yes—
215C2×C22⋊D13C22×C412yes—
216C22×Dic13C22×C414yes—
217C22×Dic13C22×C412yes—
218C22×Dic13C2412yes—
219Q8×D13—24no—
220#6129C2×Q814yes—
221#6129#4114yes—
222C2×C4×D13C22×C412yes—
223C2×C4×D13C22×C411yescharacteristic
224C2×C4×D13C22×C411yescharacteristic
225C2×C4×D13C22×C412yes—
226C2×C4×D13C2411yescharacteristic
227C2×Dic26—28no—
228C2×Dic26C22×C412yes—
229C2×Dic26C22×C412yes—
230C2×Dic26C22×C414yes—
231C2×Dic26C22×C414yes—
232C2×Dic26C22×C411yescharacteristic
233C2×Dic26C22×C411yescharacteristic
234#6122—24no—
235#6122—28no—
236#6122C2×Q818yescomplemented
237C2×#1057—28no—
238C2×#1057—24no—
239C2×#1057C2×Q818yescomplemented
240C2×#1057C2412yes—
241C2×#1057C2411yescharacteristic
242C2×#1057C2411yescharacteristic
243C2×#1057C2412yes—
244C2×#1057C2414yes—
245C2×#1057C2412yes—
246C2×#1057C2411yescharacteristic
247C2×#1057C2411yescharacteristic
248C2×#1057C2412yes—
249#6118—24no—
250#6118—22no—
251#6118C2×Q814yescomplemented
252D13⋊C8—24no—
253D13⋊C8—22no—
254D13⋊C8C2×Q814yescomplemented
255C13×C4⋊C4C22×C411yescharacteristic
256C13×C4⋊C4C22×C412yes—
257C13×C4⋊C4C22×C414yes—
258C13×C4⋊C4C22×C411yescharacteristic
259C13×C4⋊C4C22×C412yes—
260C13×C4⋊C4C22×C414yes—
261C13×C4⋊C4C22×C412yes—
262C13×C22⋊C4C22×C414yes—
263C13×C22⋊C4C22×C412yes—
264C42×C13C22×C411yescharacteristic
265C42×C13C22×C412yes—
266C22⋊Dic13C22×C412yes—
267C22⋊Dic13C22×C414yes—
268#6103C22×C412yes—
269#6103C22×C414yes—
270C4⋊Dic13C22×C412yes—
271C4⋊Dic13C22×C411yescharacteristic
272C4⋊Dic13C22×C412yes—
273C4⋊Dic13C22×C411yescharacteristic
274C4⋊Dic13C22×C412yes—
275C4⋊Dic13C22×C414yes—
276#6101C22×C414yes—
277#6101C22×C412yes—
278#6101C22×C412yes—
279#6101C22×C412yes—
280#6101C22×C412yes—
281#6101C22×C414yes—
282#6101C22×C414yes—
283#6101C22×C412yes—
284#6101C22×C414yes—
285#6101C22×C414yes—
286#6101C22×C414yes—
287#6101C22×C414yes—
288C4×Dic13C22×C412yes—
289C4×Dic13C22×C411yescharacteristic
290C4×Dic13C22×C412yes—
291C4×Dic13C22×C414yes—
292C4×Dic13C22×C414yes—
293C4×Dic13C22×C412yes—
294C4×Dic13C2411yescharacteristic
295C4×Dic13C2412yes—
296C4×Dic13C2412yes—
297C4×Dic13C2411yescharacteristic
298C4×Dic13C2412yes—
299C4×Dic13C2414yes—
300Q8×#41—131no—
301Q8×M16—132no—
302Q8×M16—131no—
303#2962—132no—
304#2962—131no—
305#2962—134no—
306#2962—132no—
307#2960—134no—
308#2960—132no—
309#2960—131no—
310#2960—132no—
311C2×C8×Q8—132no—
312C2×C8×Q8—131no—
313#2906—131no—
314#2906—132no—
315C4×#131—132no—
316C4×#131—131no—
317C23×C13C23×C412yes—
318C22×D13C23×C411yescharacteristic
319Q8×C13—22no—
320Q8×C13—42no—
321D4×C13C4×Q814yes—
322C2×C4×C13—24no—
323C2×C4×C13—44no—
324C2×C4×C13C23×C412yes—
325C2×C4×C13C23×C414yes—
326C2×C4×C13C23×C412yes—
327C2×C4×C13C23×C411yescharacteristic
328C2×C4×C13C23×C412yes—
329C2×C4×C13C23×C411yescharacteristic
330C2×C4×C13C23×C411yescharacteristic
331C22⋊D13C4×Q818yes—
332C2×Dic13—28no—
333C2×Dic13—42no—
334C2×Dic13C23×C411yescharacteristic
335C2×Dic13C23×C412yes—
336C2×Dic13C23×C412yes—
337C2×Dic13C23×C414yes—
338C2×Dic13C23×C411yescharacteristic
339C2×Dic13C23×C412yes—
340C2×Dic13C23×C412yes—
341C2×Dic13C22×Q814yes—
342C2×Dic13C2×#4114yes—
343C2×Dic13C2511yescharacteristic
344C4×D13—22no—
345C4×D13—24no—
346C4×D13—42no—
347C4×D13—41no—
348C4×D13C22×Q812yes—
349C4×D13C2×#4112yes—
350Dic26—24no—
351Dic26—28no—
352Dic26—24no—
353Dic26—44no—
354Dic26C4×Q814yes—
355Dic26#13114yescomplemented
356#1057—22no—
357#1057—21no—
358#1057—21no—
359#1057—22no—
360#1057—24no—
361#1057—22no—
362#1057C22×Q812yes—
363#1057C22×Q812yes—
364#1057C22×Q814yes—
365C2×#131—131no—
366C2×#131—132no—
367C2×#131—131no—
368Q82—131no—
369#557—132no—
370#557—131no—
371#554—134no—
372#554—132no—
373#554—132no—
374#554#26111yescharacteristic
375D4×Q8—132no—
376D4×Q8—131no—
377#533—131no—
378#533—132no—
379#533—132no—
380#533—134no—
381C4×#41—132no—
382C4×#41—131no—
383C2×C4×Q8—131no—
384C2×C4×Q8—132no—
385#446—134no—
386#446—134no—
387#446—134no—
388#446—134no—
389#446—132no—
390#446—134no—
391#446—134no—
392#446—134no—
393#446—132no—
394#446—132no—
395#446—132no—
396C8×Q8—131no—
397C8×Q8—132no—
398C8×Q8—134no—
399C8×Q8—132no—
400C8×Q8—131no—
401C8×Q8—132no—
402C8×Q8—134no—
403C8×Q8—132no—
404C8×Q8—131no—
405C8×Q8—132no—
406C8×Q8—131no—
407C8×Q8—134no—
408C8×Q8—132no—
409#424—134no—
410#424—134no—
411#424—134no—
412#424—132no—
413#424—132no—
414#424—132no—
415#423—131no—
416#423—132no—
417#423—132no—
418#423—134no—
419C2×C4⋊C8—131no—
420C2×C4⋊C8—132no—
421C2×C4⋊C8—132no—
422C2×C4⋊C8—134no—
423#405—134no—
424#405—132no—
425#405—132no—
426#405—131no—
427#405—134no—
428#405—132no—
429#405—132no—
430#405—131no—
431C4×M16—131no—
432C4×M16—132no—
433C4×M16—132no—
434C4×M16—134no—
435C2×C4×C8—131no—
436C2×C4×C8—132no—
437C2×C4×C8—134no—
438C2×C4×C8—132no—
439C22×C13—22no—
440C22×C13—22no—
441C22×C13C2×C4×Q814yes—
442C22×C13C24×C411yescharacteristic
443C2×D13—21no—
444C2×D13—21no—
445C2×D13C2×C4×Q812yes—
446C4×C13—22no—
447C4×C13—22no—
448C4×C13—24no—
449C4×C13—22no—
450C4×C13—21no—
451C4×C13C2×C4×Q812yes—
452C4×C13C2×#13112yes—
453Dic13—21no—
454Dic13—24no—
455Dic13—22no—
456Dic13—22no—
457Dic13—21no—
458Dic13C2×C4×Q814yes—
459Dic13C2×#13114yes—
460Dic13C23×Q811yescharacteristic
461Dic13C22×#4111yescharacteristic
462C2×#41—131no—
463C22×Q8—131no—
464C22×Q8—132no—
465#131—138no—
466#131—268no—
467#131—264no—
468C2×M16—131no—
469C2×M16—132no—
470C2×M16—132no—
471C2×M16—131no—
472C2×M16—134no—
473C2×M16—132no—
474C22×C8—131no—
475C22×C8—132no—
476C22×C8—132no—
477C22×C8—131no—
478C22×C8—134no—
479C22×C8—132no—
480C4⋊Q8—132no—
481C4⋊Q8—134no—
482C4⋊Q8—134no—
483C4⋊Q8—132no—
484C4⋊Q8—132no—
485C4⋊Q8—132no—
486C4⋊Q8—131no—
487C4⋊Q8C2×#26111yescharacteristic
488#125—134no—
489#125—134no—
490#125—134no—
491#125—132no—
492#125—132no—
493#125C2×#26112yes—
494C22⋊Q8—132no—
495C22⋊Q8—132no—
496C22⋊Q8—134no—
497C22⋊Q8—134no—
498C22⋊Q8—132no—
499C22⋊Q8—134no—
500C22⋊Q8—134no—
501C22⋊Q8—134no—
502C22⋊Q8—134no—
503C22⋊Q8C2×#26112yes—
504C22⋊Q8C2×#26114yes—
505C4×Q8—131no—
506C4×Q8—132no—
507C4×Q8—131no—
508C4×Q8—132no—
509C4×Q8—132no—
510C4×Q8—134no—
511C4×Q8—132no—
512C4×Q8—134no—
513C4×Q8—132no—
514C4×Q8—131no—
515C4×Q8—132no—
516C4×Q8—134no—
517C4×Q8—131no—
518C4×Q8—132no—
519C4×Q8—132no—
520C4×Q8—131no—
521C4×Q8C2×#26111yescharacteristic
522C4×D4—132no—
523C4×D4—131no—
524C4×D4—132no—
525C4×D4—134no—
526C4×D4—134no—
527C4×D4—132no—
528C4×D4C2×#26111yescharacteristic
529C4×D4C2×#26112yes—
530#117—132no—
531#117—131no—
532#117—134no—
533#117—132no—
534C2×C4⋊C4—134no—
535C2×C4⋊C4—132no—
536C2×C4⋊C4—131no—
537C2×C4⋊C4C2×#26112yes—
538C2×C42—134no—
539C2×C42—132no—
540C2×C42—131no—
541C2×C42—132no—
542C4⋊C8—131no—
543C4⋊C8—131no—
544C4⋊C8—132no—
545C4⋊C8—132no—
546C4⋊C8—132no—
547C4⋊C8—134no—
548C4⋊C8—132no—
549C4⋊C8—134no—
550C4⋊C8—134no—
551C4⋊C8—132no—
552C4⋊C8—132no—
553C4⋊C8—134no—
554C4⋊C8—132no—
555C4⋊C8—134no—
556C4⋊C8—134no—
557C4⋊C8—134no—
558C4⋊C8—134no—
559#97—134no—
560#97—132no—
561#97—132no—
562#97—132no—
563#97—134no—
564#97—134no—
565C4×C8—132no—
566C4×C8—131no—
567C4×C8—132no—
568C4×C8—131no—
569C4×C8—134no—
570C4×C8—132no—
571C4×C8—132no—
572C4×C8—131no—
573C4×C8—132no—
574C4×C8—134no—
575C4×C8—131no—
576C4×C8—132no—
577C4×C8—132no—
578C4×C8—134no—
579C2×C13—24no—
580C2×C13C22×C4×Q811yescharacteristic
581C2×C13C22×#13111yescharacteristic
582C2×C13#357311yescharacteristic
583D13—22no—
584#41—134no—
585#41—134no—
586C2×Q8—131no—
587C2×Q8—131no—
588C2×Q8—134no—
589C2×Q8—132no—
590C2×Q8—132no—
591C2×Q8—134no—
592C2×Q8—268no—
593C2×Q8—264no—
594C2×Q8C22×#26111yescharacteristic
595C2×Q8C22×#26112yes—
596C2×D4—132no—
597C2×D4C22×#26111yescharacteristic
598C22×C4—132no—
599C22×C4—131no—
600C22×C4—134no—
601C22×C4—132no—
602C22×C4—132no—
603C22×C4—131no—
604C22×C4—131no—
605C22×C4—132no—
606C22×C4C22×#26112yes—
607C22×C4C22×#26114yes—
608M16—134no—
609M16—138no—
610M16—264no—
611M16—262no—
612M16—268no—
613M16—264no—
614C2×C8—131no—
615C2×C8—131no—
616C2×C8—132no—
617C2×C8—134no—
618C2×C8—138no—
619C2×C8—132no—
620C2×C8—131no—
621C2×C8—132no—
622C2×C8—134no—
623C2×C8—131no—
624C2×C8—132no—
625C2×C8—264no—
626C2×C8—262no—
627C2×C8—268no—
628C2×C8—264no—
629C4⋊C4—132no—
630C4⋊C4—134no—
631C4⋊C4—134no—
632C4⋊C4—132no—
633C4⋊C4—132no—
634C4⋊C4—134no—
635C4⋊C4—132no—
636C4⋊C4—131no—
637C4⋊C4—134no—
638C4⋊C4—132no—
639C4⋊C4—132no—
640C4⋊C4—134no—
641C4⋊C4—132no—
642C4⋊C4—131no—
643C4⋊C4—134no—
644C4⋊C4—134no—
645C4⋊C4—134no—
646C4⋊C4—132no—
647C4⋊C4C22×#26111yescharacteristic
648C4⋊C4C22×#26112yes—
649C4⋊C4C22×#26114yes—
650C4⋊C4C22×#26112yes—
651C4⋊C4C22×#26112yes—
652C4⋊C4C22×#26111yescharacteristic
653C4⋊C4C22×#26114yes—
654C22⋊C4—134no—
655C22⋊C4—132no—
656C22⋊C4—134no—
657C22⋊C4—132no—
658C22⋊C4C22×#26114yes—
659C22⋊C4C22×#26112yes—
660C42—132no—
661C42—131no—
662C42—134no—
663C42—132no—
664C42—131no—
665C42—132no—
666C42—132no—
667C42—134no—
668C42—131no—
669C42—134no—
670C42—132no—
671C42—132no—
672C42C22×#26112yes—
673C42C22×#26111yescharacteristic
674C13Q8×#13111yescharacteristic, complemented, Sylow
675C23—131no—
676C23C23×#26112yes—
677Q8—22no—
678Q8—42no—
679Q8—134no—
680Q8—134no—
681Q8—268no—
682Q8—264no—
683Q8—264no—
684Q8—524no—
685D4—138no—
686D4Q8×#26114yes—
687C2×C4—24no—
688C2×C4—44no—
689C2×C4—134no—
690C2×C4—134no—
691C2×C4—131no—
692C2×C4—132no—
693C2×C4—132no—
694C2×C4—132no—
695C2×C4—132no—
696C2×C4—131no—
697C2×C4—131no—
698C2×C4—134no—
699C2×C4—132no—
700C2×C4—132no—
701C2×C4—264no—
702C2×C4—268no—
703C2×C4—262no—
704C2×C4—522no—
705C2×C4—521no—
706C2×C4—522no—
707C2×C4C23×#26112yes—
708C2×C4C23×#26114yes—
709C2×C4C23×#26112yes—
710C2×C4C23×#26111yescharacteristic
711C2×C4C23×#26112yes—
712C2×C4C23×#26111yescharacteristic
713C2×C4C23×#26111yescharacteristic
714C8—132no—
715C8—132no—
716C8—134no—
717C8—262no—
718C8—261no—
719C8—262no—
720C8—261no—
721C8—264no—
722C8—262no—
723C22—22no—
724C22—22no—
725C22—132no—
726C22—261no—
727C22—261no—
728C22C2×Q8×#26114yes—
729C22C24×#26111yescharacteristic
730C4—22no—
731C4—22no—
732C4—22no—
733C4—24no—
734C4—21no—
735C4—134no—
736C4—131no—
737C4—131no—
738C4—134no—
739C4—261no—
740C4—264no—
741C4—261no—
742C4—262no—
743C4—262no—
744C4C2×Q8×#26112yes—
745C4D13⋊#13112yes—
746C2—24no—
747C2—262no—
748C2C22×Q8×#26111yescharacteristic
749C2C2×D13⋊#13111yescharacteristic
750C2#1313183111yescharacteristic
subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingC13×#554C4
prime radicalC2×#6129C23
cosocleC2×Dic13C25
hypercenter#554#261
hypocenterC13Q8×#131
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #554

Complements

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

NH ≅ G/Ntype
1. #13131638C2semidirect
2. #13131637C2semidirect
3. #13131634C2semidirect
4. #13131633C2semidirect
5. #13131632C2semidirect
6. #13131631C2semidirect
7. #13131626C2semidirect
8. #13131625C2semidirect
9. #13131624C2semidirect
10. #13131624C2semidirect
11. Q8×D13⋊C8C2semidirect
12. C2×#11719074C2semidirect
103. #88238Q8semidirect
236. #6122C2×Q8semidirect
239. C2×#1057C2×Q8semidirect
251. #6118C2×Q8semidirect
254. D13⋊C8C2×Q8semidirect
355. Dic26#131semidirect
674. C13Q8×#131semidirect

Maximal subgroups

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

subgroupindex
#131316382
#131316372
#131316342
#131316332
#131316322
#131316312
#131316262
#131316252
#131316242
Q8×D13⋊C82
C2×#117190742
#131314832
#131314812
C4×#882382
#131284152
Q8×#13113