Finite Group Databasebeta

← #16808439

Subgroups — #16808439

Order 3328.

1810 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131634C212yesmaximal, complemented
2#13131634C212yesmaximal, complemented
3#13131633C214yesmaximal, complemented
4#13131632C212yesmaximal, complemented
5#13131631C214yesmaximal, complemented
6#13131630C212yesmaximal, complemented
7#13131629C212yesmaximal, complemented
8#13131628C212yesmaximal, complemented
9#13131626C212yesmaximal, complemented
10#13131625C212yesmaximal, complemented
11#13131479C211yesmaximal, characteristic
12C2×#11719079C211yesmaximal, characteristic
13D13⋊#424C211yesmaximal, characteristic
14#13131402C211yesmaximal, characteristic
15#13131401C211yesmaximal, characteristic
16#13131396C211yesmaximal, characteristic
17#13128240C211yesmaximal, characteristic
18C2×D13⋊M16C2211yescharacteristic
19C2×D13⋊M16C2211yescharacteristic
20C22×#6118C2211yescharacteristic
21C22×D13⋊C8C2211yescharacteristic
22C13×#544C411yescharacteristic
23#11719434C412yes—
24#11719434C412yes—
25#11719433C2212yes—
26#11719433C2212yes—
27#11719394C412yes—
28#11719394C412yes—
29#11719393C2212yes—
30#11719393C2212yes—
31#11719339C414yes—
32#11719327C2214yes—
33D13×#117C2211yescharacteristic
34D13×#117C2211yescharacteristic
35#11719224C411yescharacteristic
36#11719224C411yescharacteristic
37C2×#88146C2211yescharacteristic
38#11719205C411yescharacteristic
39#11719158C2214yescomplemented
40#11719158C2214yescomplemented
41#11719158C2214yescomplemented
42Q8×#1057C2214yescomplemented
43C2×#88112C2212yes—
44C4×#6122C2214yes—
45C2×C4⋊#1057C2212yes—
46#11719080C2214yescomplemented
47#11719080C2214yescomplemented
48#11719080C2214yescomplemented
49#11719079C2211yescharacteristic
50#11719079C2212yes—
51#11719079C2211yescharacteristic
52#11719079C2211yescharacteristic
53#11719079C2212yes—
54#11719079C2211yescharacteristic
55#11719079C2212yes—
56#11719079C2212yes—
57#11719079C2212yes—
58#11719079C2212yes—
59#11719078C2214yescomplemented
60#11719078C2214yescomplemented
61#11719078C2214yescomplemented
62#11719078C2214yescomplemented
63#11719078C2214yescomplemented
64#11719078C2214yescomplemented
65#11719074C2214yescomplemented
66#11719074C2214yescomplemented
67#11719074C2214yescomplemented
68#11719072C2212yes—
69#11719072C2212yes—
70#11719072C2212yes—
71#11719072C2212yes—
72#11719072C2211yescharacteristic
73#11719072C2212yes—
74#11719072C2211yescharacteristic
75#11719072C2212yes—
76#11719072C2211yescharacteristic
77#11719072C2211yescharacteristic
78#11719067C2212yes—
79#11719067C2214yes—
80#11719067C2212yes—
81#11719062C2212yes—
82#11719062C2214yes—
83#11719062C2212yes—
84#11719053C2212yes—
85#11719052C2212yes—
86D13⋊(C4⋊C8)C2212yes—
87D13⋊(C4⋊C8)C2212yes—
88C4×#6118C2212yes—
89C4×#6118C2212yes—
90#11719047C2212yes—
91C4×D13⋊C8C2212yes—
92C22×C4×D13C2311yescharacteristic
93C2×#6122C2312yes—
94C2×#6122C2312yes—
95C22×#1057C2311yescharacteristic
96C22×#1057C2311yescharacteristic
97C22×#1057C2312yes—
98D13⋊M16—24no—
99D13⋊M16Q818yescomplemented
100C2×#6118—24no—
101C2×#6118C2312yes—
102C2×#6118C2311yescharacteristic
103C2×#6118C2312yes—
104C2×#6118C2311yescharacteristic
105C2×#6118C2311yescharacteristic
106C2×#6118C2311yescharacteristic
107C2×D13⋊C8—24no—
108C2×D13⋊C8C2311yescharacteristic
109C2×D13⋊C8C2311yescharacteristic
110C2×D13⋊C8C2311yescharacteristic
111C2×D13⋊C8C2311yescharacteristic
112C2×D13⋊C8C2312yes—
113C2×D13⋊C8C2312yes—
114C13×C4⋊Q8C2×C412yes—
115C13×C4⋊Q8C2×C412yes—
116C13×#125C2×C412yes—
117C13×#125C2×C412yes—
118C13×C22⋊Q8C2×C414yes—
119C13×#117C2×C411yescharacteristic
120C13×#117C2×C411yescharacteristic
121C2×C13×C4⋊C4C2×C411yescharacteristic
122#88200C2×C414yes—
123#88200C2×C414yes—
124Q8×Dic13C2314yes—
125#88198C2×C414yes—
126C2×#6103C2×C412yes—
127#88180C2×C411yescharacteristic
128#88180C2×C411yescharacteristic
129C2×C4⋊Dic13C2×C411yescharacteristic
130#88178C2×C414yes—
131C2×C4×Dic13C2312yes—
132#88151C2×C414yes—
133#88151C2×C414yes—
134#88150C2×C414yes—
135#88150C2×C414yes—
136#88150C2×C414yes—
137#88150C2×C414yes—
138#88146C2×C412yes—
139#88146C2×C412yes—
140#88146C2311yescharacteristic
141#88146C2311yescharacteristic
142#88146C2312yes—
143#88146C2312yes—
144#88146C2311yescharacteristic
145#88146C2311yescharacteristic
146C4⋊C4×D13C2×C411yescharacteristic
147C4⋊C4×D13C2×C411yescharacteristic
148C4⋊C4×D13C2×C411yescharacteristic
149C4⋊C4×D13C2×C411yescharacteristic
150#88144C2×C412yes—
151#88144C2×C412yes—
152#88144C2×C412yes—
153#88144C2×C412yes—
154#88143C2×C414yes—
155#88143C2×C414yes—
156#88142C2×C412yes—
157#88142C2×C412yes—
158#88142C2×C412yes—
159#88142C2×C412yes—
160#88142C2×C414yes—
161#88141C2314yes—
162#88141C2314yes—
163#88141C2314yes—
164C22⋊C4×D13C2×C412yes—
165C22⋊C4×D13C2×C412yes—
166#88132C2×C414yes—
167#88132C2×C414yes—
168#88131C2312yes—
169#88131C2312yes—
170#88126C2×C412yes—
171#88126C2×C412yes—
172C42×D13C2312yes—
173C42×D13C2312yes—
174#88124C2×C412yes—
175#88124C2×C412yes—
176#88123C2×C412yes—
177#88123C2×C412yes—
178#88112C2312yes—
179#88112C2312yes—
180#88112C2312yes—
181#88112C2312yes—
182#88112C2314yes—
183#88112C2314yes—
184#88112C2314yes—
185#88112C2314yes—
186#88110C2312yes—
187#88110C2312yes—
188#88110C2312yes—
189#88110C2312yes—
190#88110C2314yes—
191#88110C2314yes—
192#88110C2314yes—
193#88110C2314yes—
194C4⋊#1057C2312yes—
195C4⋊#1057C2312yes—
196C4⋊#1057C2312yes—
197C4⋊#1057C2312yes—
198C4⋊#1057C2314yes—
199C4⋊#1057C2314yes—
200C4⋊#1057C2314yes—
201C4⋊#1057C2314yes—
202C4×#1057C2312yes—
203C4×#1057C2312yes—
204C4×#1057C2312yes—
205C4×#1057C2312yes—
206C4×#1057C2314yes—
207C4×#1057C2314yes—
208C4×#1057C2314yes—
209C4×#1057C2314yes—
210#60193—131nomaximal, Sylow
211C23×D13C22×C411yescharacteristic
212C2×Q8×C13C22×C414yes—
213C22×C4×C13C22×C412yes—
214C22×C4×C13C22×C411yescharacteristic
215C22×Dic13C22×C412yes—
216C22×Dic13C2411yescharacteristic
217C2×C4×D13C22×C412yes—
218C2×C4×D13C22×C412yes—
219C2×C4×D13C22×C412yes—
220C2×C4×D13C22×C412yes—
221C2×C4×D13C22×C411yescharacteristic
222C2×C4×D13C22×C411yescharacteristic
223C2×C4×D13C2×Q814yes—
224C2×C4×D13#4114yes—
225C2×C4×D13C2411yescharacteristic
226C2×C4×D13C2411yescharacteristic
227C2×Dic26C22×C414yes—
228C2×Dic26C22×C414yes—
229C2×Dic26C22×C414yes—
230#6122—24no—
231#6122C2×Q818yes—
232C2×#1057—22no—
233C2×#1057—22no—
234C2×#1057—24no—
235C2×#1057C2411yescharacteristic
236C2×#1057C2411yescharacteristic
237C2×#1057C2412yes—
238C2×#1057C2414yes—
239C2×#1057C2412yes—
240C2×#1057C2411yescharacteristic
241C2×#1057C2411yescharacteristic
242C2×#1057C2412yes—
243C2×#1057C2412yes—
244#6118—24no—
245#6118—24no—
246#6118—22no—
247#6118—22no—
248#6118C2×Q814yes—
249#6118C2×Q814yes—
250D13⋊C8—22no—
251D13⋊C8—22no—
252D13⋊C8—22no—
253D13⋊C8—22no—
254D13⋊C8—24no—
255D13⋊C8C2×Q818yes—
256C13×C4⋊C4C22×C414yes—
257C13×C4⋊C4C22×C414yes—
258C13×C4⋊C4C22×C414yes—
259C13×C4⋊C4C22×C411yescharacteristic
260C13×C4⋊C4C22×C411yescharacteristic
261C13×C4⋊C4C22×C412yes—
262C13×C4⋊C4C22×C412yes—
263C13×C4⋊C4C22×C411yescharacteristic
264C13×C4⋊C4C22×C411yescharacteristic
265C13×C22⋊C4C22×C412yes—
266C13×C22⋊C4C22×C412yes—
267C42×C13C22×C412yes—
268C42×C13C22×C412yes—
269C22⋊Dic13C22×C412yes—
270C22⋊Dic13C22×C412yes—
271#6103C22×C412yes—
272#6103C22×C412yes—
273#6103C22×C412yes—
274#6103C22×C412yes—
275#6103C22×C414yes—
276#6103C22×C414yes—
277C4⋊Dic13C22×C411yescharacteristic
278C4⋊Dic13C22×C411yescharacteristic
279C4⋊Dic13C22×C412yes—
280C4⋊Dic13C22×C412yes—
281C4⋊Dic13C22×C414yes—
282C4⋊Dic13C22×C414yes—
283C4⋊Dic13C22×C411yescharacteristic
284C4⋊Dic13C22×C411yescharacteristic
285C4⋊Dic13C22×C414yes—
286#6101C22×C414yes—
287#6101C22×C414yes—
288#6101C22×C414yes—
289#6101C22×C414yes—
290#6101C22×C412yes—
291#6101C22×C412yes—
292#6101C22×C412yes—
293#6101C22×C412yes—
294#6101C22×C414yes—
295#6101C22×C414yes—
296C4×Dic13C22×C412yes—
297C4×Dic13C22×C412yes—
298C4×Dic13C22×C414yes—
299C4×Dic13C2412yes—
300C4×Dic13C2412yes—
301C4×Dic13C2412yes—
302C4×Dic13C2412yes—
303C4×Dic13C2414yes—
304#3458—131no—
305#2962—132no—
306#2962—134no—
307#2962—132no—
308#2962—134no—
309#2962—132no—
310#2962—132no—
311#2961—132no—
312#2961—132no—
313#2960—132no—
314#2960—132no—
315#2905—131no—
316C2×#424—131no—
317C2×#424—131no—
318#2873—131no—
319#2873—131no—
320C2×#405—131no—
321C23×C13C23×C411yescharacteristic
322C22×D13—41no—
323C22×D13—41no—
324C22×D13C4×Q814yes—
325C22×D13C23×C411yescharacteristic
326C22×D13C23×C411yescharacteristic
327Q8×C13—44no—
328C2×C4×C13—42no—
329C2×C4×C13C4×Q814yes—
330C2×C4×C13C23×C414yes—
331C2×C4×C13C23×C412yes—
332C2×C4×C13C23×C412yes—
333C2×C4×C13C23×C412yes—
334C2×C4×C13C23×C412yes—
335C2×C4×C13C23×C411yescharacteristic
336C2×C4×C13C23×C411yescharacteristic
337C2×Dic13—42no—
338C2×Dic13C23×C412yes—
339C2×Dic13C23×C412yes—
340C2×Dic13C23×C414yes—
341C2×Dic13C23×C412yes—
342C2×Dic13C23×C412yes—
343C2×Dic13C23×C411yescharacteristic
344C2×Dic13C22×Q812yes—
345C2×Dic13C2×#4112yes—
346C2×Dic13C2511yescharacteristic
347C4×D13—42no—
348C4×D13—42no—
349C4×D13—42no—
350C4×D13—42no—
351C4×D13C4×Q814yes—
352C4×D13C4×Q814yes—
353C4×D13C22×Q812yes—
354C4×D13C22×Q812yes—
355C4×D13C2×#4112yes—
356C4×D13C2×#4112yes—
357Dic26—44no—
358Dic26—44no—
359Dic26—44no—
360#1057—21no—
361#1057—21no—
362#1057—21no—
363#1057—21no—
364#1057—22no—
365#1057—22no—
366#1057—24no—
367#1057C22×Q814yes—
368#1057C22×Q814yes—
369C22×M16—131no—
370C22×M16—131no—
371C22×M16—131no—
372C23×C8—131no—
373#544—132no—
374#544—132no—
375#544—132no—
376#544—132no—
377#544—131no—
378#544—131no—
379#544—131no—
380#544#26111yescharacteristic
381#543—134no—
382#533—132no—
383#533—132no—
384#533—132no—
385#533—132no—
386#533—134no—
387C2×#117—131no—
388C2×#117—131no—
389C2×#117—131no—
390#446—134no—
391#446—134no—
392#446—134no—
393#446—134no—
394#446—134no—
395#446—134no—
396#446—134no—
397#446—134no—
398#446—134no—
399#446—134no—
400#446—134no—
401#446—134no—
402C8×Q8—134no—
403C8×Q8—134no—
404C8×Q8—134no—
405C8×Q8—134no—
406#424—131no—
407#424—131no—
408#424—132no—
409#424—131no—
410#424—131no—
411#424—132no—
412#424—132no—
413#424—132no—
414#424—132no—
415#424—132no—
416#424—134no—
417#424—132no—
418#424—132no—
419#423—132no—
420#423—132no—
421C2×C4⋊C8—132no—
422C2×C4⋊C8—132no—
423C2×C4⋊C8—132no—
424C2×C4⋊C8—132no—
425#405—132no—
426#405—132no—
427#405—131no—
428#405—131no—
429#405—131no—
430#405—131no—
431#405—132no—
432#405—132no—
433#405—132no—
434#405—132no—
435#405—134no—
436#405—132no—
437#405—132no—
438C4×M16—132no—
439C4×M16—132no—
440C4×M16—134no—
441C2×#97—132no—
442C2×C4×C8—132no—
443C22×C13—21no—
444C22×C13—21no—
445C22×C13C2×C4×Q812yes—
446C22×C13C24×C411yescharacteristic
447C2×D13—21no—
448C2×D13—21no—
449C2×D13—21no—
450C2×D13—21no—
451C2×D13—44no—
452C2×D13C2×C4×Q812yes—
453C2×D13C2×C4×Q812yes—
454C4×C13—22no—
455C4×C13—22no—
456C4×C13—24no—
457C4×C13—22no—
458C4×C13—22no—
459C4×C13C2×C4×Q812yes—
460C4×C13C2×C4×Q812yes—
461Dic13—22no—
462Dic13—22no—
463Dic13—22no—
464Dic13—22no—
465Dic13—24no—
466Dic13C2×C4×Q812yes—
467Dic13C23×Q811yescharacteristic
468Dic13C22×#4111yescharacteristic
469C23×C4—131no—
470C2×M16—131no—
471C2×M16—131no—
472C2×M16—132no—
473C2×M16—138no—
474C2×M16—132no—
475C2×M16—132no—
476C2×M16—132no—
477C2×M16—131no—
478C2×M16—131no—
479C2×M16—264no—
480C2×M16—264no—
481C22×C8—132no—
482C22×C8—131no—
483C22×C8—131no—
484C22×C8—131no—
485C22×C8—131no—
486C22×C8—131no—
487C22×C8—131no—
488C22×C8—132no—
489C22×C8—132no—
490C22×C8—264no—
491C4⋊Q8—134no—
492C4⋊Q8—134no—
493C4⋊Q8—132no—
494C4⋊Q8—132no—
495C4⋊Q8—132no—
496C4⋊Q8—132no—
497C4⋊Q8—132no—
498C4⋊Q8—132no—
499C4⋊Q8C2×#26112yes—
500C4⋊Q8C2×#26112yes—
501#125—134no—
502#125—134no—
503#125—132no—
504#125—132no—
505#125—132no—
506#125—132no—
507#125—132no—
508#125—132no—
509#125C2×#26112yes—
510#125C2×#26112yes—
511C22⋊Q8—134no—
512C22⋊Q8—134no—
513C22⋊Q8—134no—
514C22⋊Q8—134no—
515C22⋊Q8—134no—
516C22⋊Q8—134no—
517C22⋊Q8—134no—
518C22⋊Q8—134no—
519C22⋊Q8—134no—
520C22⋊Q8—134no—
521C22⋊Q8—134no—
522C22⋊Q8C2×#26114yes—
523C4×Q8—134no—
524C4×Q8—134no—
525C4×Q8—134no—
526C4×Q8—134no—
527#117—131no—
528#117—131no—
529#117—131no—
530#117—131no—
531#117—131no—
532#117—131no—
533#117—132no—
534#117—132no—
535#117—132no—
536#117—132no—
537#117—132no—
538#117—132no—
539#117—132no—
540#117—132no—
541#117C2×#26111yescharacteristic
542#117C2×#26111yescharacteristic
543C2×C4⋊C4—131no—
544C2×C4⋊C4—131no—
545C2×C4⋊C4—131no—
546C2×C4⋊C4—131no—
547C2×C4⋊C4—131no—
548C2×C4⋊C4C2×#26111yescharacteristic
549C2×C22⋊C4—132no—
550C2×C22⋊C4—132no—
551C2×C22⋊C4—132no—
552C2×C42—132no—
553C2×C42—132no—
554C2×C42—132no—
555C4⋊C8—132no—
556C4⋊C8—132no—
557C4⋊C8—134no—
558C4⋊C8—132no—
559C4⋊C8—132no—
560C4⋊C8—134no—
561C4⋊C8—134no—
562C4⋊C8—134no—
563C4⋊C8—132no—
564C4⋊C8—132no—
565C4⋊C8—134no—
566C4⋊C8—132no—
567C4⋊C8—132no—
568C4⋊C8—134no—
569C4⋊C8—134no—
570C4⋊C8—134no—
571#97—132no—
572#97—132no—
573#97—132no—
574#97—132no—
575#97—134no—
576#97—134no—
577#97—134no—
578#97—134no—
579C4×C8—132no—
580C4×C8—132no—
581C4×C8—132no—
582C4×C8—132no—
583C4×C8—134no—
584C4×C8—134no—
585C4×C8—134no—
586C4×C8—134no—
587C2×C13—22no—
588C2×C13C22×C4×Q811yescharacteristic
589C2×C13#357311yescharacteristic
590C2×C13#357311yescharacteristic
591D13—22no—
592D13—22no—
593C24—131no—
594C2×Q8—134no—
595C2×Q8—134no—
596C2×Q8—134no—
597C2×Q8C22×#26114yes—
598C22×C4—131no—
599C22×C4—134no—
600C22×C4—134no—
601C22×C4—131no—
602C22×C4—131no—
603C22×C4—131no—
604C22×C4—131no—
605C22×C4—132no—
606C22×C4—132no—
607C22×C4—132no—
608C22×C4—132no—
609C22×C4—132no—
610C22×C4C22×#26112yes—
611C22×C4C22×#26111yescharacteristic
612M16—134no—
613M16—134no—
614M16—138no—
615M16—264no—
616M16—264no—
617M16—262no—
618M16—262no—
619M16—264no—
620C2×C8—132no—
621C2×C8—132no—
622C2×C8—138no—
623C2×C8—131no—
624C2×C8—131no—
625C2×C8—132no—
626C2×C8—134no—
627C2×C8—132no—
628C2×C8—131no—
629C2×C8—131no—
630C2×C8—262no—
631C2×C8—262no—
632C2×C8—262no—
633C2×C8—262no—
634C2×C8—262no—
635C2×C8—262no—
636C2×C8—264no—
637C2×C8—264no—
638C4⋊C4—132no—
639C4⋊C4—132no—
640C4⋊C4—132no—
641C4⋊C4—132no—
642C4⋊C4—132no—
643C4⋊C4—132no—
644C4⋊C4—131no—
645C4⋊C4—131no—
646C4⋊C4—131no—
647C4⋊C4—131no—
648C4⋊C4—134no—
649C4⋊C4—134no—
650C4⋊C4—134no—
651C4⋊C4—134no—
652C4⋊C4—134no—
653C4⋊C4—134no—
654C4⋊C4—134no—
655C4⋊C4—134no—
656C4⋊C4—134no—
657C4⋊C4C22×#26111yescharacteristic
658C4⋊C4C22×#26111yescharacteristic
659C4⋊C4C22×#26111yescharacteristic
660C4⋊C4C22×#26111yescharacteristic
661C4⋊C4C22×#26112yes—
662C4⋊C4C22×#26112yes—
663C4⋊C4C22×#26114yes—
664C4⋊C4C22×#26114yes—
665C4⋊C4C22×#26114yes—
666C22⋊C4—132no—
667C22⋊C4—132no—
668C22⋊C4—134no—
669C22⋊C4—134no—
670C22⋊C4—132no—
671C22⋊C4—132no—
672C22⋊C4—132no—
673C22⋊C4—132no—
674C22⋊C4C22×#26112yes—
675C22⋊C4C22×#26112yes—
676C42—134no—
677C42—132no—
678C42—132no—
679C42—132no—
680C42—132no—
681C42—134no—
682C42—132no—
683C42—132no—
684C42C22×#26112yes—
685C42C22×#26112yes—
686C13#6019311yescharacteristic, complemented, Sylow
687C23—131no—
688C23—131no—
689C23—134no—
690C23—521no—
691C23—521no—
692C23C23×#26111yescharacteristic
693Q8—44no—
694Q8—524no—
695Q8—524no—
696Q8—524no—
697C2×C4—42no—
698C2×C4—132no—
699C2×C4—132no—
700C2×C4—131no—
701C2×C4—131no—
702C2×C4—132no—
703C2×C4—132no—
704C2×C4—132no—
705C2×C4—132no—
706C2×C4—134no—
707C2×C4—134no—
708C2×C4—132no—
709C2×C4—132no—
710C2×C4—132no—
711C2×C4—132no—
712C2×C4—134no—
713C2×C4—522no—
714C2×C4—522no—
715C2×C4—522no—
716C2×C4—522no—
717C2×C4—522no—
718C2×C4Q8×#26114yes—
719C2×C4C23×#26114yes—
720C2×C4C23×#26112yes—
721C2×C4C23×#26112yes—
722C2×C4C23×#26112yes—
723C2×C4C23×#26112yes—
724C2×C4C23×#26111yescharacteristic
725C2×C4C23×#26111yescharacteristic
726C8—134no—
727C8—134no—
728C8—261no—
729C8—261no—
730C8—261no—
731C8—261no—
732C8—262no—
733C8—262no—
734C8—264no—
735C22—21no—
736C22—21no—
737C22—132no—
738C22—132no—
739C22—261no—
740C22—261no—
741C22—261no—
742C22—261no—
743C22—524no—
744C22C2×Q8×#26112yes—
745C22C24×#26111yescharacteristic
746C4—24no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—132no—
752C4—131no—
753C4—131no—
754C4—262no—
755C4—262no—
756C4—262no—
757C4—262no—
758C4—264no—
759C4C2×Q8×#26112yes—
760C4C2×Q8×#26112yes—
761C2—22no—
762C2—262no—
763C2—262no—
764C2C22×Q8×#26111yescharacteristic
765C2#1313183111yescharacteristic
766C2#1313183211yescharacteristic
subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingC13×#544C4
prime radicalC23×D13C22×C4
cosocleC2×Dic13C25
hypercenter#544#261
hypocenterC13#60193
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #544

Complements

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

NH ≅ G/Ntype
1. #13131634C2semidirect
2. #13131634C2semidirect
3. #13131633C2semidirect
4. #13131632C2semidirect
5. #13131631C2semidirect
6. #13131630C2semidirect
7. #13131629C2semidirect
8. #13131628C2semidirect
9. #13131626C2semidirect
10. #13131625C2semidirect
39. #11719158C22semidirect
40. #11719158C22semidirect
41. #11719158C22semidirect
42. Q8×#1057C22semidirect
46. #11719080C22semidirect
47. #11719080C22semidirect
48. #11719080C22semidirect
59. #11719078C22semidirect
60. #11719078C22semidirect
61. #11719078C22semidirect
62. #11719078C22semidirect
63. #11719078C22semidirect
64. #11719078C22semidirect
65. #11719074C22semidirect
66. #11719074C22semidirect
67. #11719074C22semidirect
99. D13⋊M16Q8semidirect
686. C13#60193semidirect

Maximal subgroups

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

subgroupindex
#131316342
#131316332
#131316322
#131316312
#131316302
#131316292
#131316282
#131316262
#131316252
#131314792
C2×#117190792
D13⋊#4242
#131314022
#131314012
#131313962
#131282402
#6019313