Finite Group Databasebeta

← #16753008

Subgroups — #16753008

Order 3328.

1674 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128701C211yesmaximal, characteristic
2#13127799C214yesmaximal, complemented
3#13127775C214yesmaximal, complemented
4#13127678C214yesmaximal, complemented
5#13127604C214yesmaximal, complemented
6#13126057C212yesmaximal, complemented
7#13126042C211yesmaximal, characteristic, complemented
8#13126026C211yesmaximal, characteristic
9#13126004C212yesmaximal, complemented
10#13125007C212yesmaximal, complemented
11#13124966C211yesmaximal, characteristic, complemented
12#13124958C211yesmaximal, characteristic
13#13124916C212yesmaximal, complemented
14#13123921C211yesmaximal, characteristic, complemented
15C2×C13×#557C211yesmaximal, characteristic, complemented
16C13×#557—22no—
17C13×#557—22no—
18C13×#557C2214yes—
19C13×#557C2214yes—
20C2×C13×C4⋊Q8—21no—
21C2×C13×C4⋊Q8C2211yescharacteristic
22C2×C13×#125—21no—
23C2×C13×#125—21no—
24C2×C13×#125C2211yescharacteristic
25C2×C13×#125C2211yescharacteristic
26C2×C4×Q8×C13—21no—
27C2×C4×Q8×C13C2211yescharacteristic
28C2×C4×Q8×C13C2211yescharacteristic
29C2×C4×Q8×C13C2211yescharacteristic
30C2×C4×Q8×C13C2211yescharacteristic
31#11719521—21no—
32#11719290C2212yes—
33#11719289C2212yes—
34#11719286—22no—
35#11719284C2212yes—
36#11719273—22no—
37#11719272C2212yes—
38#11719220—21no—
39#11719220—21no—
40#11719209—21no—
41#11719184C2212yes—
42#11719184C2212yes—
43#11719182C2211yescharacteristic
44#11719175C2211yescharacteristic
45#11718889C2212yes—
46#11718888C2212yes—
47#11718752C2214yes—
48#11718750C2214yes—
49#11718745C2214yes—
50#11718741C2214yes—
51#11718730C2212yes—
52#11718729C2214yes—
53#11718728C2212yes—
54#11718727C2214yes—
55#11718727C2214yes—
56#11718726C2212yes—
57#11718726C2212yes—
58#11718725C2214yes—
59#11718724C2214yes—
60#11718724C2214yes—
61#11718692C2212yes—
62#11718691C2214yes—
63#11718691C2214yes—
64C4×#6107C2214yes—
65#11718689C2214yes—
66#11718689C2214yes—
67#11718688C2212yes—
68#11718687C2214yes—
69#11718687C2214yes—
70C4×#6106C2214yes—
71#11718685C2214yes—
72#11718685C2214yes—
73#11718683C2214yes—
74#11718683C2214yes—
75#11718682C2212yes—
76#11718681C2212yes—
77#11718632C2212yes—
78#11718632C2212yes—
79#11718631C2212yes—
80#11718629C2212yes—
81#11718628C2212yes—
82#11718628C2212yes—
83#11718587C2211yescharacteristic
84#11718587C2211yescharacteristic
85#11718587C2212yes—
86#11718586C2212yes—
87C22×Q8×C13—21no—
88C22×Q8×C13D411yescharacteristic
89C22×Q8×C13C2311yescharacteristic
90C2×#6127—21no—
91C13×C4⋊Q8—24no—
92C13×C4⋊Q8—24no—
93C13×C4⋊Q8—22no—
94C13×C4⋊Q8C2314yes—
95C13×#125—24no—
96C13×#125—24no—
97C13×#125—24no—
98C13×#125—24no—
99C13×#125—21no—
100C13×#125—21no—
101C13×#125—22no—
102C13×#125C2312yes—
103C13×#125C2314yes—
104C13×#125C2312yes—
105C4×Q8×C13—24no—
106C4×Q8×C13—24no—
107C4×Q8×C13—21no—
108C4×Q8×C13—21no—
109C4×Q8×C13—22no—
110C4×Q8×C13—22no—
111C4×Q8×C13D412yes—
112C4×Q8×C13D412yes—
113C4×Q8×C13C2312yes—
114C4×Q8×C13C2312yes—
115C4×Q8×C13C2314yes—
116C4×Q8×C13C2314yes—
117C4×Q8×C13C2312yes—
118C4×Q8×C13C2312yes—
119C2×C13×C4⋊C4—21no—
120C2×C13×C4⋊C4—21no—
121C2×C13×C4⋊C4—21no—
122C2×C13×C4⋊C4—21no—
123C2×C13×C4⋊C4—21no—
124C2×C13×C4⋊C4—21no—
125C2×C13×C4⋊C4—21no—
126C2×C13×C4⋊C4—21no—
127C2×C13×C4⋊C4D411yescharacteristic
128C2×C13×C4⋊C4D411yescharacteristic
129C2×C13×C4⋊C4D411yescharacteristic
130C2×C13×C4⋊C4C2311yescharacteristic
131C2×C13×C4⋊C4C2311yescharacteristic
132C2×C13×C4⋊C4C2311yescharacteristic
133C2×C42×C13—21no—
134C2×C42×C13—21no—
135C2×C42×C13—21no—
136C2×C42×C13C2311yescharacteristic
137C2×C42×C13C2311yescharacteristic
138C2×C42×C13C2311yescharacteristic
139#88201—22no—
140#88200—22no—
141#88200—22no—
142#88198—22no—
143C2×#6107C2314yes—
144C2×#6106C2314yes—
145#88184—21no—
146#88184C2312yes—
147#88183—22no—
148#88183—22no—
149C4×C22⋊D13—22no—
150C4×C22⋊D13—22no—
151#88180—21no—
152#88178—21no—
153#88178C2312yes—
154#88152—22no—
155#88152—22no—
156#88150—22no—
157#88150—22no—
158#88148—22no—
159#88148—22no—
160#88147—22no—
161#88146—22no—
162C4⋊C4×D13—22no—
163#88143—22no—
164#88143—22no—
165#88141—22no—
166#88130—22no—
167#88130—22no—
168#88129—21no—
169#88129C2312yes—
170#88129C2312yes—
171#88128C2311yescharacteristic
172C4×D52—21no—
173C4×D52C2312yes—
174C4×D52C2312yes—
175C4×D52C2312yes—
176#88126—22no—
177#88126—22no—
178#88124—21no—
179#88124C2312yes—
180#88124C2312yes—
181#88123C2311yescharacteristic
182#88123C2311yescharacteristic
183#88123C2311yescharacteristic
184C4×Dic26—21no—
185C4×Dic26C2312yes—
186C4×Dic26C2312yes—
187C4×Dic26C2312yes—
188#88075C2314yes—
189#88075C2314yes—
190C22⋊#1055C2312yes—
191C22⋊#1055C2312yes—
192#88050C2314yes—
193#88050C2314yes—
194#88050C2314yes—
195#88049C2314yes—
196#88049C2314yes—
197#88049C2314yes—
198#88048C2314yes—
199#88048C2314yes—
200#88048C2314yes—
201#88047C2314yes—
202#88047C2314yes—
203#88047C2314yes—
204C4⋊#1055C2312yes—
205C4⋊#1055C2312yes—
206C4⋊#1055C2314yes—
207C4⋊#1055C2314yes—
208#88043C2312yes—
209#88043C2314yes—
210#88043C2312yes—
211C4×#1055C2314yes—
212#61832—131nomaximal, Sylow
213C2×Q8×C13—24no—
214C2×Q8×C13—21no—
215C2×Q8×C13—24no—
216C2×Q8×C13—42no—
217C2×Q8×C13—44no—
218C2×Q8×C13C2×D412yes—
219C2×Q8×C13C2×D412yes—
220C2×Q8×C13C2412yes—
221C22×C4×C13—21no—
222C22×C4×C13—21no—
223C22×C4×C13—21no—
224C22×C4×C13—21no—
225C22×C4×C13C2×D411yescharacteristic
226C22×C4×C13C2×D411yescharacteristic
227C22×C4×C13C2×D411yescharacteristic
228C22×C4×C13C2×D411yescharacteristic
229C22×C4×C13C2×D411yescharacteristic
230C22×C4×C13C2×D411yescharacteristic
231C22×C4×C13C2411yescharacteristic
232C2×C22⋊D13—22no—
233#6127—44no—
234C2×D52—21no—
235C2×D52—21no—
236C2×D52C2412yes—
237C2×C4×D13—22no—
238C2×C4×D13—22no—
239C2×C4×D13—22no—
240C2×Dic26—21no—
241C2×Dic26—21no—
242C2×Dic26C2412yes—
243C13×C4⋊C4—24no—
244C13×C4⋊C4—22no—
245C13×C4⋊C4—22no—
246C13×C4⋊C4—24no—
247C13×C4⋊C4—22no—
248C13×C4⋊C4—24no—
249C13×C4⋊C4—22no—
250C13×C4⋊C4—24no—
251C13×C4⋊C4—22no—
252C13×C4⋊C4—24no—
253C13×C4⋊C4—22no—
254C13×C4⋊C4—21no—
255C13×C4⋊C4—21no—
256C13×C4⋊C4—21no—
257C13×C4⋊C4C2×D412yes—
258C13×C4⋊C4C2×D412yes—
259C13×C4⋊C4C2×D412yes—
260C13×C4⋊C4C2×D412yes—
261C13×C4⋊C4C2×D412yes—
262C13×C4⋊C4C2×D412yes—
263C13×C4⋊C4C2412yes—
264C13×C4⋊C4C2412yes—
265C13×C4⋊C4C2412yes—
266C42×C13—24no—
267C42×C13—22no—
268C42×C13—22no—
269C42×C13—24no—
270C42×C13C2×D411yescharacteristic
271C42×C13C2×D411yescharacteristic
272C42×C13C2×D412yes—
273C42×C13C2×D412yes—
274C42×C13C2411yescharacteristic
275C42×C13C2412yes—
276C42×C13C2412yes—
277C42×C13C2411yescharacteristic
278C22⋊Dic13—22no—
279#6107—28no—
280#6106—28no—
281#6103—22no—
282#6103—22no—
283#6103—22no—
284#6103—22no—
285#6103—22no—
286#6103—22no—
287#6103—22no—
288#6103—22no—
289C4⋊Dic13—21no—
290C4⋊Dic13—21no—
291C4⋊Dic13—21no—
292C4⋊Dic13—21no—
293C4⋊Dic13C2412yes—
294C4⋊Dic13C2412yes—
295#6101—22no—
296#6101—22no—
297#6101—22no—
298#6101—22no—
299#6101—22no—
300#6101—22no—
301#6101—22no—
302#6101—22no—
303C4×Dic13—22no—
304C4×Dic13—22no—
305C4×Dic13—22no—
306C2×#1055C2414yes—
307C2×#1055C2414yes—
308#3507—131no—
309C2×#557D1311yescharacteristic, complemented
310#3390—134no—
311#3388—134no—
312#3377—134no—
313#3371—134no—
314#3238—132no—
315#3236—131no—
316#3234—131no—
317#3232—132no—
318#3117—132no—
319#3113—131no—
320#3112—131no—
321#3108—132no—
322#2983—131no—
323C23×C13C22×D411yescharacteristic
324C22×D13—22no—
325Q8×C13—24no—
326Q8×C13—22no—
327Q8×C13—42no—
328Q8×C13—42no—
329Q8×C13—48no—
330Q8×C132−1+414yes—
331C2×C4×C13—24no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—41no—
341C2×C4×C13—41no—
342C2×C4×C13—41no—
343C2×C4×C13—42no—
344C2×C4×C13—42no—
345C2×C4×C13—42no—
346C2×C4×C13C22×D411yescharacteristic
347C2×C4×C13C22×D412yes—
348C2×C4×C13C22×D412yes—
349C2×C4×C13C22×D411yescharacteristic
350C2×C4×C13C22×D412yes—
351C2×C4×C13C22×D411yescharacteristic
352C2×C4×C13C22×D412yes—
353C2×C4×C13C22×D411yescharacteristic
354C2×C4×C13C22×D411yescharacteristic
355C2×C4×C13C2511yescharacteristic
356C22⋊D13—44no—
357C2×Dic13—22no—
358C2×Dic13—22no—
359C2×Dic13—22no—
360D52—24no—
361D52—42no—
362D52—81no—
363C4×D13—44no—
364C4×D13—82no—
365C4×D13—82no—
366Dic26—24no—
367Dic26—42no—
368Dic26—81no—
369#1055—24no—
370#1055—24no—
371#559—132no—
372#557—22no—
373#557—22no—
374#557—132no—
375#557C2×D1314yes—
376#557C2×D1314yes—
377#556—132no—
378#556—262no—
379#554—132no—
380#552—262no—
381#539—261no—
382#539—261no—
383#536—261no—
384#533—131no—
385#532—131no—
386C2×C4⋊Q8—21no—
387C2×C4⋊Q8C2×D1311yescharacteristic
388#529—132no—
389#529—132no—
390C2×#125—21no—
391C2×#125—21no—
392C2×#125C2×D1311yescharacteristic
393C2×#125C2×D1311yescharacteristic
394#520—261no—
395C2×C4×Q8—21no—
396C2×C4×Q8C2×D1311yescharacteristic
397C2×C4×Q8C2×D1311yescharacteristic
398C2×C4×Q8C2×D1311yescharacteristic
399C2×C4×Q8C2×D1311yescharacteristic
400#501—134no—
401#501—132no—
402#501—132no—
403#499—134no—
404#491—132no—
405#490—132no—
406#489—134no—
407#488—134no—
408#484—132no—
409#483—132no—
410#483—132no—
411#481—132no—
412#480—132no—
413#480—132no—
414#479—134no—
415#479—134no—
416#479—134no—
417#479—134no—
418#478—134no—
419#478—134no—
420#477—134no—
421#477—132no—
422#476—134no—
423#475—132no—
424#464—134no—
425#464—134no—
426#462—132no—
427#460—132no—
428#451—132no—
429#448—132no—
430#446—134no—
431#446—134no—
432#441—134no—
433#441—134no—
434#440—134no—
435#440—134no—
436C4×Q16—134no—
437C4×SD16—134no—
438#432—131no—
439#432—131no—
440#432—132no—
441#431—132no—
442C22×C13—21no—
443C22×C13—21no—
444C22×C13#57512yes—
445C22×C13C23×D411yescharacteristic
446C2×D13—42no—
447C2×D13—42no—
448C2×D13—42no—
449C4×C13—21no—
450C4×C13—22no—
451C4×C13—22no—
452C4×C13—21no—
453C4×C13—24no—
454C4×C13—21no—
455C4×C13—21no—
456C4×C13—21no—
457C4×C13—22no—
458C4×C13—22no—
459C4×C13—42no—
460C4×C13—42no—
461C4×C13—42no—
462C4×C13C2×2−1+412yes—
463Dic13—42no—
464Dic13—42no—
465Dic13—42no—
466C2×#41—261no—
467C22×Q8—21no—
468C22×Q8C22⋊D1311yescharacteristic
469C22×Q8C22×D1311yescharacteristic
470C2×Q16—134no—
471C2×SD16—134no—
472C4⋊Q8—24no—
473C4⋊Q8—24no—
474C4⋊Q8—22no—
475C4⋊Q8—131no—
476C4⋊Q8—131no—
477C4⋊Q8—131no—
478C4⋊Q8—262no—
479C4⋊Q8C22×D1314yes—
480#127—131no—
481#126—262no—
482#126—262no—
483#126—262no—
484#126—262no—
485#125—24no—
486#125—24no—
487#125—24no—
488#125—24no—
489#125—22no—
490#125—21no—
491#125—21no—
492#125—132no—
493#125—132no—
494#125—262no—
495#125—262no—
496#125—261no—
497#125C22×D1312yes—
498#125C22×D1314yes—
499#125C22×D1312yes—
500#124—132no—
501#124—132no—
502#124—262no—
503#124—261no—
504#123—262no—
505#123—262no—
506#123—262no—
507#123—262no—
508C22⋊Q8—132no—
509C22⋊Q8—262no—
510C22⋊Q8—262no—
511C22⋊Q8—261no—
512C22⋊Q8—262no—
513C22⋊Q8—262no—
514#121—132no—
515#121—261no—
516C4×Q8—24no—
517C4×Q8—24no—
518C4×Q8—22no—
519C4×Q8—21no—
520C4×Q8—21no—
521C4×Q8—22no—
522C4×Q8—132no—
523C4×Q8—132no—
524C4×Q8—132no—
525C4×Q8—262no—
526C4×Q8—261no—
527C4×Q8C22⋊D1312yes—
528C4×Q8C22⋊D1312yes—
529C4×Q8C22×D1314yes—
530C4×Q8C22×D1312yes—
531C4×Q8C22×D1314yes—
532C4×Q8C22×D1312yes—
533C4×Q8C22×D1312yes—
534C4×Q8C22×D1312yes—
535C4×D4—132no—
536C4×D4—132no—
537C4×D4—132no—
538C4×D4—262no—
539C4×D4—262no—
540C4×D4—262no—
541C4×D4—261no—
542#117—261no—
543#117—262no—
544#117—262no—
545#117—262no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—262no—
555C2×C4⋊C4C22⋊D1311yescharacteristic
556C2×C4⋊C4C22⋊D1311yescharacteristic
557C2×C4⋊C4C22⋊D1311yescharacteristic
558C2×C4⋊C4C22×D1311yescharacteristic
559C2×C4⋊C4C22×D1311yescharacteristic
560C2×C4⋊C4C22×D1311yescharacteristic
561C2×C42—21no—
562C2×C42—21no—
563C2×C42—21no—
564C2×C42C22×D1311yescharacteristic
565C2×C42C22×D1311yescharacteristic
566C2×C42C22×D1311yescharacteristic
567#107—134no—
568#107—134no—
569#107—134no—
570#106—134no—
571#106—134no—
572#106—134no—
573C4⋊C8—134no—
574C4⋊C8—132no—
575C4⋊C8—132no—
576C4⋊C8—134no—
577#103—134no—
578#103—134no—
579#103—134no—
580#103—134no—
581#103—134no—
582#102—134no—
583#102—134no—
584#102—134no—
585C22⋊C8—132no—
586C22⋊C8—132no—
587#97—132no—
588#97—134no—
589#97—132no—
590C4×C8—134no—
591C2×C13—22no—
592C2×C13#348611yescharacteristic
593C2×C13C2×#57511yescharacteristic
594C2×C13#358611yescharacteristic
595D13—82no—
596#41—524no—
597C2×Q8—24no—
598C2×Q8—21no—
599C2×Q8—24no—
600C2×Q8—42no—
601C2×Q8—44no—
602C2×Q8—132no—
603C2×Q8—261no—
604C2×Q8—261no—
605C2×Q8C2×C22⋊D1312yes—
606C2×Q8C2×C22⋊D1312yes—
607C2×Q8C23×D1312yes—
608C2×D4—132no—
609C2×D4—262no—
610C2×D4—261no—
611C2×D4—261no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—262no—
617C22×C4—262no—
618C22×C4—262no—
619C22×C4C2×C22⋊D1311yescharacteristic
620C22×C4C2×C22⋊D1311yescharacteristic
621C22×C4C2×C22⋊D1311yescharacteristic
622C22×C4C2×C22⋊D1311yescharacteristic
623C22×C4C2×C22⋊D1311yescharacteristic
624C22×C4C2×C22⋊D1311yescharacteristic
625C22×C4C23×D1311yescharacteristic
626Q16—268no—
627SD16—268no—
628C2×C8—134no—
629C2×C8—134no—
630C4⋊C4—24no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—24no—
634C4⋊C4—22no—
635C4⋊C4—24no—
636C4⋊C4—22no—
637C4⋊C4—24no—
638C4⋊C4—22no—
639C4⋊C4—24no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—132no—
645C4⋊C4—132no—
646C4⋊C4—261no—
647C4⋊C4—262no—
648C4⋊C4—262no—
649C4⋊C4—261no—
650C4⋊C4—262no—
651C4⋊C4—262no—
652C4⋊C4—262no—
653C4⋊C4—261no—
654C4⋊C4—262no—
655C4⋊C4—262no—
656C4⋊C4—262no—
657C4⋊C4—261no—
658C4⋊C4C2×C22⋊D1312yes—
659C4⋊C4C2×C22⋊D1312yes—
660C4⋊C4C2×C22⋊D1312yes—
661C4⋊C4C2×C22⋊D1312yes—
662C4⋊C4C2×C22⋊D1312yes—
663C4⋊C4C2×C22⋊D1312yes—
664C4⋊C4C23×D1312yes—
665C4⋊C4C23×D1312yes—
666C4⋊C4C23×D1312yes—
667C22⋊C4—262no—
668C22⋊C4—262no—
669C22⋊C4—262no—
670C22⋊C4—262no—
671C22⋊C4—262no—
672C22⋊C4—262no—
673C22⋊C4—262no—
674C22⋊C4—262no—
675C22⋊C4—262no—
676C42—24no—
677C42—22no—
678C42—22no—
679C42—24no—
680C42—262no—
681C42—262no—
682C42—262no—
683C42C2×C22⋊D1312yes—
684C42C2×C22⋊D1312yes—
685C42C2×C22⋊D1311yescharacteristic
686C42C2×C22⋊D1311yescharacteristic
687C42C23×D1312yes—
688C42C23×D1311yescharacteristic
689C42C23×D1312yes—
690C42C23×D1311yescharacteristic
691C13#6183211yescharacteristic, complemented, Sylow
692C23—262no—
693C23C22×C22⋊D1311yescharacteristic
694Q8—24no—
695Q8—22no—
696Q8—42no—
697Q8—42no—
698Q8—48no—
699Q8—264no—
700Q8—522no—
701Q8—1041no—
702Q8#8825414yes—
703D4—264no—
704D4—522no—
705D4—524no—
706D4—1041no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—262no—
723C2×C4—262no—
724C2×C4—262no—
725C2×C4—524no—
726C2×C4—1042no—
727C2×C4—1042no—
728C2×C4C22×C22⋊D1312yes—
729C2×C4C22×C22⋊D1311yescharacteristic
730C2×C4C22×C22⋊D1312yes—
731C2×C4C22×C22⋊D1311yescharacteristic
732C2×C4C22×C22⋊D1311yescharacteristic
733C2×C4C22×C22⋊D1312yes—
734C2×C4C22×C22⋊D1311yescharacteristic
735C2×C4C22×C22⋊D1312yes—
736C2×C4C22×C22⋊D1311yescharacteristic
737C2×C4C24×D1311yescharacteristic
738C8—264no—
739C8—264no—
740C22—21no—
741C22—21no—
742C22—522no—
743C22—522no—
744C22—522no—
745C22#1171952712yes—
746C22C23×C22⋊D1311yescharacteristic
747C4—24no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—22no—
755C4—21no—
756C4—21no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—522no—
761C4—522no—
762C4—522no—
763C4C2×#8825412yes—
764C2—22no—
765C2—1042no—
766C2#1312848711yescharacteristic
767C2C2×#1171952711yescharacteristic
768C2#1312962311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#557C2
socleC22×C13C23×D4
prime radical#11719182C22
hypercenterC2×#557D13
hypocenterC13#61832
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #13127799C2semidirect
3. #13127775C2semidirect
4. #13127678C2semidirect
5. #13127604C2semidirect
6. #13126057C2semidirect
7. #13126042C2semidirect
9. #13126004C2semidirect
10. #13125007C2semidirect
11. #13124966C2semidirect
13. #13124916C2semidirect
14. #13123921C2semidirect
15. C2×C13×#557C2semidirect
309. C2×#557D13semidirect
691. C13#61832semidirect

Maximal subgroups

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

subgroupindex
#131287012
#131277992
#131277752
#131276782
#131276042
#131260572
#131260422
#131260262
#131260042
#131250072
#131249662
#131249582
#131249162
#131239212
C2×C13×#5572
#6183213