Finite Group Databasebeta

← #15880286

Subgroups — #15880286

Order 3328.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123490C211yesmaximal, characteristic, complemented
2#13123355C211yesmaximal, characteristic
3#13115550C211yesmaximal, characteristic, complemented
4#13115543C211yesmaximal, characteristic, complemented
5#13115481C211yesmaximal, characteristic, complemented
6#13115481C211yesmaximal, characteristic, complemented
7#13115111C211yesmaximal, characteristic, complemented
8#13115111C211yesmaximal, characteristic, complemented
9#13114933C211yesmaximal, characteristic, complemented
10#13114876C211yesmaximal, characteristic, complemented
11#13114780C211yesmaximal, characteristic
12#13114678C211yesmaximal, characteristic, complemented
13#13114671C211yesmaximal, characteristic, complemented
14#13114622C211yesmaximal, characteristic, complemented
15C13×#2880C211yesmaximal, characteristic
16C22×C13×#41C2211yescharacteristic
17C2×C13×#131C2211yescharacteristic
18C2×C13×#131C2211yescharacteristic
19C2×#88180C2211yescharacteristic
20C22×#6099C2211yescharacteristic
21C13×#408—21no—
22C13×#408—21no—
23C13×#408C2211yescharacteristic
24C13×#408C2211yescharacteristic
25C13×#407—21no—
26C13×#407C2211yescharacteristic
27C2×C13×C22⋊C8—21no—
28C2×C13×C22⋊C8C2211yescharacteristic
29C2×#88077C2211yescharacteristic
30C2×#88077C2211yescharacteristic
31C2×#88077C2211yescharacteristic
32C2×#88077C2211yescharacteristic
33#11718894C2211yescharacteristic
34#11718894C2211yescharacteristic
35#11718894C2211yescharacteristic
36#11718894C2211yescharacteristic
37#11718893C411yescharacteristic, complemented
38#11718893C411yescharacteristic, complemented
39#11718893C411yescharacteristic, complemented
40#11718893C411yescharacteristic, complemented
41#11718886C411yescharacteristic, complemented
42#11718886C411yescharacteristic, complemented
43#11718876C411yescharacteristic, complemented
44#11718876C411yescharacteristic, complemented
45C4×C22⋊Dic13C2211yescharacteristic
46#11718868C2211yescharacteristic
47C2×#88062C2211yescharacteristic, complemented
48C2×#88062C2211yescharacteristic, complemented
49#11718763C2211yescharacteristic, complemented
50#11718763C2211yescharacteristic, complemented
51#11718762C2211yescharacteristic, complemented
52#11718762C2211yescharacteristic, complemented
53C2×#88055C2211yescharacteristic, complemented
54C2×C8×Dic13C2211yescharacteristic, complemented
55#11718381—21no—
56#11718381—21no—
57#11718380—21no—
58#11718379—21no—
59#11718150C2211yescharacteristic, complemented
60#11718150C2211yescharacteristic, complemented
61#11718147C2211yescharacteristic, complemented
62#11718147C2211yescharacteristic, complemented
63#11718147C2211yescharacteristic, complemented
64#11718147C2211yescharacteristic, complemented
65#11718142C2211yescharacteristic, complemented
66#11718142C2211yescharacteristic, complemented
67C2×C13×#41—21no—
68C2×C13×#41—21no—
69C2×C13×#41—22no—
70C2×C13×#41—22no—
71C2×C13×#41—41no—
72C2×C13×#41—41no—
73C2×C13×#41C2×C411yescharacteristic
74C2×C13×#41C2×C411yescharacteristic
75C2×C13×#41C2311yescharacteristic
76C2×C13×#41C2311yescharacteristic
77C22×Q8×C13C2×C411yescharacteristic
78C22×D4×C13—21no—
79C22×D4×C13C2×C411yescharacteristic
80C23×C4×C13—21no—
81C23×C4×C13C2311yescharacteristic
82C13×#131—22no—
83C13×#131—22no—
84C13×#131—41no—
85C13×#131—41no—
86C2×C13×M16—21no—
87C2×C13×M16—21no—
88C2×C13×M16C2311yescharacteristic
89C2×C13×M16C2311yescharacteristic
90C22×C8×C13—21no—
91C22×C8×C13—21no—
92C22×C8×C13C2311yescharacteristic
93C22×C8×C13C2311yescharacteristic
94C2×C22⋊Dic13—21no—
95C2×C22⋊Dic13—21no—
96#88180—21no—
97#88180—21no—
98#88180C2×C411yescharacteristic
99#88180C2×C411yescharacteristic
100#88180C2311yescharacteristic
101#88180C2311yescharacteristic
102C2×C4⋊Dic13C2×C411yescharacteristic
103C2×C4⋊Dic13C2×C411yescharacteristic
104C2×C4×Dic13—21no—
105C2×C4×Dic13C2311yescharacteristic
106C2×C4×Dic13C2311yescharacteristic
107C2×#6099—41no—
108C2×#6099—41no—
109C2×#6099C2×C411yescharacteristic
110C2×#6099C2×C411yescharacteristic
111C2×#6099C2×C411yescharacteristic
112C2×#6099C2×C411yescharacteristic
113C2×#6099C2311yescharacteristic
114C2×#6099C2311yescharacteristic
115C22×#1055C2311yescharacteristic
116C22×#1055C2311yescharacteristic
117C13×C22⋊C8—21no—
118C13×C22⋊C8—21no—
119C13×C22⋊C8—21no—
120C13×C22⋊C8—21no—
121C13×C22⋊C8—21no—
122C13×C22⋊C8—21no—
123C13×C22⋊C8D411yescharacteristic
124C13×C22⋊C8D411yescharacteristic
125C13×C22⋊C8D411yescharacteristic
126C13×C22⋊C8D411yescharacteristic
127#88077—22no—
128#88077—22no—
129#88077—41no—
130#88077—41no—
131#88075C2×C411yescharacteristic
132#88075C2×C411yescharacteristic
133#88075C2×C411yescharacteristic
134#88075C2×C411yescharacteristic
135#88075C2×C411yescharacteristic
136#88075C2×C411yescharacteristic
137#88075C2×C411yescharacteristic
138#88075C2×C411yescharacteristic
139#88072C2×C411yescharacteristic
140#88072C2×C411yescharacteristic
141#88072C2×C411yescharacteristic
142#88072C2×C411yescharacteristic
143#88072C2×C411yescharacteristic
144#88072C2×C411yescharacteristic
145#88072C2×C411yescharacteristic
146#88072C2×C411yescharacteristic
147#88071—21no—
148C22⋊#1055—21no—
149C22⋊#1055—21no—
150#88062—41no—
151#88062—41no—
152#88055—21no—
153#88055—21no—
154#88055—41no—
155#88054—21no—
156#88054—21no—
157#88054—21no—
158#88054—21no—
159C8×Dic13—21no—
160C8×Dic13—21no—
161C8×Dic13—41no—
162#22588—131nomaximal, Sylow
163C24×C13—21no—
164C24×C13#4111yescharacteristic
165C13×#41—21no—
166C13×#41—21no—
167C13×#41—22no—
168C13×#41—22no—
169C13×#41—21no—
170C13×#41—21no—
171C13×#41—21no—
172C13×#41—21no—
173C13×#41—42no—
174C13×#41—42no—
175C13×#41—41no—
176C13×#41—41no—
177C13×#41—42no—
178C13×#41—42no—
179C13×#41#4112yes—
180C13×#41#4112yes—
181C2×Q8×C13—21no—
182C2×Q8×C13—22no—
183C2×Q8×C13—41no—
184C2×Q8×C13C22×C411yescharacteristic
185C2×Q8×C13C22×C411yescharacteristic
186C2×D4×C13—21no—
187C2×D4×C13—22no—
188C2×D4×C13—21no—
189C2×D4×C13—21no—
190C2×D4×C13—21no—
191C2×D4×C13—21no—
192C2×D4×C13—41no—
193C2×D4×C13—42no—
194C2×D4×C13—42no—
195C2×D4×C13C22×C411yescharacteristic
196C2×D4×C13C22×C411yescharacteristic
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—42no—
207C22×C4×C13—42no—
208C22×C4×C13C22×C411yescharacteristic
209C22×C4×C13C22×C411yescharacteristic
210C22×C4×C13C2×D411yescharacteristic
211C22×C4×C13C2×D411yescharacteristic
212C22×C4×C13#4111yescharacteristic
213C22×C4×C13C2411yescharacteristic
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C22×Dic13—21no—
218C13×M16—21no—
219C13×M16—21no—
220C13×M16—21no—
221C13×M16—21no—
222C13×M16—42no—
223C13×M16—42no—
224C2×C8×C13—21no—
225C2×C8×C13—21no—
226C2×C8×C13—21no—
227C2×C8×C13—21no—
228C2×C8×C13—21no—
229C2×C8×C13—21no—
230C2×C8×C13—42no—
231C2×C8×C13—42no—
232C2×C8×C13C2×D411yescharacteristic
233C2×C8×C13C2×D411yescharacteristic
234C2×C8×C13C2×D411yescharacteristic
235C2×C8×C13C2×D411yescharacteristic
236C22⋊Dic13—21no—
237C22⋊Dic13—21no—
238C22⋊Dic13—21no—
239C22⋊Dic13—21no—
240C22⋊Dic13—42no—
241C4⋊Dic13—21no—
242C4⋊Dic13—21no—
243C4⋊Dic13C22×C411yescharacteristic
244C4⋊Dic13C22×C411yescharacteristic
245C4⋊Dic13C22×C411yescharacteristic
246C4⋊Dic13C22×C411yescharacteristic
247C4×Dic13—21no—
248C4×Dic13—21no—
249C4×Dic13—21no—
250C4×Dic13—21no—
251C4×Dic13—21no—
252C4×Dic13—21no—
253C4×Dic13—21no—
254C4×Dic13—21no—
255#6099—21no—
256#6099—21no—
257#6099—21no—
258#6099—21no—
259#6099—41no—
260#6099—41no—
261#6099—41no—
262#6099—41no—
263C2×#1055—21no—
264C2×#1055—21no—
265C2×#1055—21no—
266C2×#1055—21no—
267C2×#1055—21no—
268C2×#1055—21no—
269C2×#1055C22×C411yescharacteristic
270C2×#1055C22×C411yescharacteristic
271C2×#1055C22×C411yescharacteristic
272C2×#1055C22×C411yescharacteristic
273#2924—131no—
274#2896—131no—
275#2880D1311yescharacteristic
276#1938—131no—
277#1937—131no—
278#1929—131no—
279#1929—131no—
280#1866—131no—
281#1866—131no—
282#1826—131no—
283#1811—131no—
284#1789—131no—
285#1765—131no—
286#1764—131no—
287#1753—131no—
288C23×C13—21no—
289C23×C13—21no—
290C23×C13—21no—
291C23×C13—21no—
292C23×C13—41no—
293C23×C13—41no—
294C23×C13—42no—
295C23×C13—42no—
296C23×C13—81no—
297C23×C13C4×D411yescharacteristic
298C23×C13C4×D411yescharacteristic
299C23×C13C2×#4111yescharacteristic
300Q8×C13—21no—
301Q8×C13—21no—
302Q8×C13—21no—
303Q8×C13—42no—
304Q8×C13#11712yes—
305D4×C13—22no—
306D4×C13—22no—
307D4×C13—21no—
308D4×C13—21no—
309D4×C13—21no—
310D4×C13—42no—
311D4×C13—42no—
312D4×C13—42no—
313D4×C13—41no—
314D4×C13—41no—
315D4×C13#11712yes—
316C2×C4×C13—21no—
317C2×C4×C13—21no—
318C2×C4×C13—21no—
319C2×C4×C13—21no—
320C2×C4×C13—21no—
321C2×C4×C13—21no—
322C2×C4×C13—21no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—21no—
326C2×C4×C13—21no—
327C2×C4×C13—21no—
328C2×C4×C13—21no—
329C2×C4×C13—21no—
330C2×C4×C13—42no—
331C2×C4×C13—42no—
332C2×C4×C13—42no—
333C2×C4×C13—41no—
334C2×C4×C13—41no—
335C2×C4×C13C4×D411yescharacteristic
336C2×C4×C13C4×D411yescharacteristic
337C2×C4×C13C23×C411yescharacteristic
338C2×C4×C13C22×D411yescharacteristic
339C2×C4×C13C2×#4111yescharacteristic
340C2×C4×C13C2×#4111yescharacteristic
341C2×C4×C13H(5,𝔽2)11yescharacteristic
342C2×C4×C13H(5,𝔽2)11yescharacteristic
343C2×Dic13—22no—
344C2×Dic13—21no—
345C2×Dic13—21no—
346C2×Dic13—21no—
347C2×Dic13—21no—
348C2×Dic13—41no—
349C2×Dic13—42no—
350C2×Dic13—41no—
351C2×Dic13—41no—
352C2×Dic13—41no—
353C2×Dic13—41no—
354C2×Dic13—81no—
355C8×C13—21no—
356C8×C13—21no—
357C8×C13—21no—
358C8×C13—21no—
359C8×C13—41no—
360C8×C13—41no—
361#1055—21no—
362#1055—21no—
363#1055—21no—
364#1055—21no—
365#1055—41no—
366#1055—41no—
367C22×#41C2×D1311yescharacteristic
368C2×#131C2×D1311yescharacteristic
369C2×#131C2×D1311yescharacteristic
370C22×M16—131no—
371C2×#117—131no—
372#433—261no—
373#433—261no—
374#432—261no—
375#431—261no—
376C2×#108—131no—
377C2×#108—131no—
378#424—131no—
379#424—131no—
380C2×#104—131no—
381C2×#104—131no—
382C2×#104—131no—
383C2×#104—131no—
384#419—131no—
385#419—131no—
386#418—131no—
387#418—131no—
388#417—131no—
389#417—131no—
390#417—131no—
391#417—131no—
392#416—131no—
393#416—131no—
394#416—131no—
395#416—131no—
396#408—21no—
397#408—21no—
398#408C2×D1311yescharacteristic
399#408C2×D1311yescharacteristic
400#407—21no—
401#407—131no—
402#407C2×D1311yescharacteristic
403C2×C22⋊C8—21no—
404C2×C22⋊C8C2×D1311yescharacteristic
405#405—131no—
406#405—131no—
407C2×#97—131no—
408C2×C4×C8—131no—
409C4×C22⋊C4—131no—
410#341—131no—
411#341—131no—
412#339—131no—
413#339—131no—
414#339—131no—
415#339—131no—
416#336—131no—
417#336—131no—
418C22×C13—21no—
419C22×C13—21no—
420C22×C13—21no—
421C22×C13—21no—
422C22×C13—22no—
423C22×C13—21no—
424C22×C13—21no—
425C22×C13—21no—
426C22×C13—21no—
427C22×C13—41no—
428C22×C13—41no—
429C22×C13—41no—
430C22×C13—41no—
431C22×C13—41no—
432C22×C13—81no—
433C22×C13—81no—
434C22×C13—84no—
435C22×C13C2×C4×D411yescharacteristic
436C22×C13#55111yescharacteristic
437C22×C13#55111yescharacteristic
438C4×C13—21no—
439C4×C13—21no—
440C4×C13—22no—
441C4×C13—41no—
442C4×C13C2×#11711yescharacteristic
443C4×C13#51811yescharacteristic
444C4×C13#54611yescharacteristic
445C4×C13#54611yescharacteristic
446Dic13—42no—
447Dic13—41no—
448Dic13—41no—
449Dic13—41no—
450Dic13—41no—
451Dic13—81no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—22no—
455C2×#41—22no—
456C2×#41—41no—
457C2×#41—41no—
458C2×#41C4×D1311yescharacteristic
459C2×#41C4×D1311yescharacteristic
460C2×#41C22×D1311yescharacteristic
461C2×#41C22×D1311yescharacteristic
462C22×Q8C4×D1311yescharacteristic
463C22×D4—21no—
464C22×D4C4×D1311yescharacteristic
465C23×C4—21no—
466C23×C4C22×D1311yescharacteristic
467#131—22no—
468#131—22no—
469#131—41no—
470#131—41no—
471C2×M16—21no—
472C2×M16—21no—
473C2×M16—131no—
474C2×M16—131no—
475C2×M16—131no—
476C2×M16—131no—
477C2×M16—131no—
478C2×M16—131no—
479C2×M16—521no—
480C2×M16—521no—
481C2×M16C22×D1311yescharacteristic
482C2×M16C22×D1311yescharacteristic
483C22×C8—21no—
484C22×C8—21no—
485C22×C8—131no—
486C22×C8—131no—
487C22×C8C22×D1311yescharacteristic
488C22×C8C22×D1311yescharacteristic
489#117—131no—
490#117—131no—
491#117—131no—
492#117—131no—
493#117—261no—
494#117—261no—
495C2×C4⋊C4—131no—
496C2×C4⋊C4—131no—
497C2×C22⋊C4—261no—
498C2×C22⋊C4—261no—
499C2×C42—131no—
500C2×C42—131no—
501C2×C42—261no—
502#108—521no—
503#108—521no—
504C4⋊C8—261no—
505C4⋊C8—261no—
506C4⋊C8—261no—
507C4⋊C8—261no—
508#104—262no—
509#104—262no—
510#104—521no—
511#104—521no—
512#103—131no—
513#103—131no—
514#103—131no—
515#103—131no—
516#103—131no—
517#103—131no—
518#103—131no—
519#103—131no—
520#102—131no—
521#102—131no—
522#102—131no—
523#102—131no—
524#102—131no—
525#102—131no—
526#102—131no—
527#102—131no—
528C22⋊C8—21no—
529C22⋊C8—21no—
530C22⋊C8—21no—
531C22⋊C8—21no—
532C22⋊C8—21no—
533C22⋊C8—21no—
534C22⋊C8—261no—
535C22⋊C8—261no—
536C22⋊C8C22⋊D1311yescharacteristic
537C22⋊C8C22⋊D1311yescharacteristic
538C22⋊C8C22⋊D1311yescharacteristic
539C22⋊C8C22⋊D1311yescharacteristic
540#97—261no—
541#97—261no—
542#97—521no—
543C4×C8—261no—
544C4×C8—261no—
545C4×C8—521no—
546#95—261no—
547C2×C13—21no—
548C2×C13—21no—
549C2×C13—41no—
550C2×C13—41no—
551C2×C13—42no—
552C2×C13—81no—
553C2×C13#234211yescharacteristic
554C2×C13#295511yescharacteristic
555C2×C13#295611yescharacteristic
556C24—21no—
557C24#612711yescharacteristic
558#41—21no—
559#41—21no—
560#41—22no—
561#41—22no—
562#41—21no—
563#41—21no—
564#41—21no—
565#41—21no—
566#41—42no—
567#41—42no—
568#41—41no—
569#41—41no—
570#41—42no—
571#41—42no—
572#41#612912yes—
573#41#612912yes—
574C2×Q8—21no—
575C2×Q8—22no—
576C2×Q8—41no—
577C2×Q8C2×C4×D1311yescharacteristic
578C2×Q8C2×C4×D1311yescharacteristic
579C2×D4—21no—
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—41no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4C2×C4×D1311yescharacteristic
589C2×D4C2×C4×D1311yescharacteristic
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—261no—
602C22×C4—261no—
603C22×C4—261no—
604C22×C4—261no—
605C22×C4C2×C4×D1311yescharacteristic
606C22×C4C2×C4×D1311yescharacteristic
607C22×C4#612711yescharacteristic
608C22×C4C2×C22⋊D1311yescharacteristic
609C22×C4C2×C22⋊D1311yescharacteristic
610C22×C4C23×D1311yescharacteristic
611M16—21no—
612M16—21no—
613M16—21no—
614M16—21no—
615M16—42no—
616M16—42no—
617M16—261no—
618M16—261no—
619M16—261no—
620M16—261no—
621M16—521no—
622M16—521no—
623M16—521no—
624M16—521no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—42no—
632C2×C8—42no—
633C2×C8—131no—
634C2×C8—131no—
635C2×C8—131no—
636C2×C8—131no—
637C2×C8—261no—
638C2×C8—261no—
639C2×C8—261no—
640C2×C8—261no—
641C2×C8—261no—
642C2×C8—261no—
643C2×C8C2×C22⋊D1311yescharacteristic
644C2×C8C2×C22⋊D1311yescharacteristic
645C2×C8C2×C22⋊D1311yescharacteristic
646C2×C8C2×C22⋊D1311yescharacteristic
647C4⋊C4—131no—
648C4⋊C4—131no—
649C4⋊C4—131no—
650C4⋊C4—131no—
651C4⋊C4—261no—
652C4⋊C4—261no—
653C22⋊C4—261no—
654C22⋊C4—261no—
655C22⋊C4—261no—
656C22⋊C4—261no—
657C22⋊C4—522no—
658C42—261no—
659C42—261no—
660C42—261no—
661C42—261no—
662C42—261no—
663C42—261no—
664C42—261no—
665C42—261no—
666C13#2258811yescharacteristic, complemented, Sylow
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—81no—
676C23C4×C22⋊D1311yescharacteristic
677C23C4×C22⋊D1311yescharacteristic
678C23C2×#612711yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—42no—
683Q8#8813112yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4#8813112yes—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—262no—
715C2×C4—261no—
716C2×C4—261no—
717C2×C4—261no—
718C2×C4—261no—
719C2×C4—521no—
720C2×C4—522no—
721C2×C4—521no—
722C2×C4—521no—
723C2×C4—521no—
724C2×C4—521no—
725C2×C4—1041no—
726C2×C4C4×C22⋊D1311yescharacteristic
727C2×C4C4×C22⋊D1311yescharacteristic
728C2×C4C22×C4×D1311yescharacteristic
729C2×C4C2×#612911yescharacteristic
730C2×C4C2×#612911yescharacteristic
731C2×C4#8825111yescharacteristic
732C2×C4#8825111yescharacteristic
733C2×C4C22×C22⋊D1311yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—41no—
739C8—41no—
740C8—261no—
741C8—261no—
742C8—261no—
743C8—261no—
744C8—521no—
745C8—521no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—84no—
763C22#1171920011yescharacteristic
764C22#1171920011yescharacteristic
765C22C2×C4×C22⋊D1311yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—41no—
770C4—522no—
771C4—521no—
772C4—521no—
773C4—521no—
774C4—521no—
775C4—1041no—
776C4C2×#8813111yescharacteristic
777C4#1171919111yescharacteristic
778C4#1171951111yescharacteristic
779C4#1171951111yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2#1311768111yescharacteristic
787C2#1312373711yescharacteristic
788C2#1312374311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2880C2
socleC22×C13C2×C4×D4
prime radicalC22×C13×#41C22
cosocleC22×C4×C13C24
hypercenter#2880D13
hypocenterC13#22588
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2880

Complements

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

NH ≅ G/Ntype
1. #13123490C2semidirect
3. #13115550C2semidirect
4. #13115543C2semidirect
5. #13115481C2semidirect
6. #13115481C2semidirect
7. #13115111C2semidirect
8. #13115111C2semidirect
9. #13114933C2semidirect
10. #13114876C2semidirect
12. #13114678C2semidirect
13. #13114671C2semidirect
14. #13114622C2semidirect
37. #11718893C4semidirect
38. #11718893C4semidirect
39. #11718893C4semidirect
40. #11718893C4semidirect
41. #11718886C4semidirect
42. #11718886C4semidirect
43. #11718876C4semidirect
44. #11718876C4semidirect
47. C2×#88062C22semidirect
48. C2×#88062C22semidirect
49. #11718763C22semidirect
50. #11718763C22semidirect
51. #11718762C22semidirect
52. #11718762C22semidirect
53. C2×#88055C22semidirect
54. C2×C8×Dic13C22semidirect
59. #11718150C22semidirect
60. #11718150C22semidirect
61. #11718147C22semidirect
62. #11718147C22semidirect
63. #11718147C22semidirect
64. #11718147C22semidirect
65. #11718142C22semidirect
66. #11718142C22semidirect
666. C13#22588semidirect

Maximal subgroups

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

subgroupindex
#131234902
#131233552
#131155502
#131155432
#131154812
#131151112
#131149332
#131148762
#131147802
#131146782
#131146712
#131146222
C13×#28802
#2258813