Finite Group Databasebeta

← #15880291

Subgroups — #15880291

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#13123353C211yesmaximal, characteristic
2#13123282C211yesmaximal, characteristic
3#13115546C211yesmaximal, characteristic, complemented
4#13115539C211yesmaximal, characteristic, complemented
5#13115484C211yesmaximal, characteristic, complemented
6#13115484C211yesmaximal, characteristic, complemented
7#13115110C211yesmaximal, characteristic, complemented
8#13115110C211yesmaximal, characteristic, complemented
9#13114935C211yesmaximal, characteristic, complemented
10#13114876C211yesmaximal, characteristic, complemented
11#13114779C211yesmaximal, characteristic
12#13114682C211yesmaximal, characteristic, complemented
13#13114675C211yesmaximal, characteristic, complemented
14#13114622C211yesmaximal, characteristic, complemented
15C13×#2924C211yesmaximal, characteristic, complemented
16C22×#6127C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C22×#6099C2211yescharacteristic
19C2×#88155C2211yescharacteristic
20C2×#88155C2211yescharacteristic
21C13×#433—21no—
22C13×#433—21no—
23C13×#432—21no—
24C13×#431—21no—
25C13×#424C2211yescharacteristic, complemented
26C13×#424C2211yescharacteristic, complemented
27C13×#407C2211yescharacteristic
28C2×C13×C22⋊C8C2211yescharacteristic
29C13×#405C2211yescharacteristic, complemented
30C13×#405C2211yescharacteristic, complemented
31C4×C22⋊Dic13C2211yescharacteristic
32#11718868C2211yescharacteristic
33C2×#88065C2211yescharacteristic
34C2×#88065C2211yescharacteristic
35C2×#88065C2211yescharacteristic
36C2×#88065C2211yescharacteristic
37C2×#88062C2211yescharacteristic, complemented
38C2×#88062C2211yescharacteristic, complemented
39#11718771C2211yescharacteristic
40#11718771C2211yescharacteristic
41C2×#88055C2211yescharacteristic, complemented
42C2×C8×Dic13C2211yescharacteristic, complemented
43#11718665C411yescharacteristic, complemented
44#11718665C411yescharacteristic, complemented
45#11718663C2211yescharacteristic
46#11718663C2211yescharacteristic
47#11718663C2211yescharacteristic
48#11718663C2211yescharacteristic
49#11718662C411yescharacteristic, complemented
50#11718662C411yescharacteristic, complemented
51#11718627C411yescharacteristic, complemented
52#11718627C411yescharacteristic, complemented
53#11718627C411yescharacteristic, complemented
54#11718627C411yescharacteristic, complemented
55#11718388—21no—
56#11718388—21no—
57#11718387—21no—
58D13×C22⋊C8—21no—
59#11718150C2211yescharacteristic, complemented
60#11718150C2211yescharacteristic, complemented
61#11718142C2211yescharacteristic, complemented
62#11718142C2211yescharacteristic, complemented
63#11718124C2211yescharacteristic, complemented
64#11718124C2211yescharacteristic, complemented
65#11718124C2211yescharacteristic, complemented
66#11718124C2211yescharacteristic, complemented
67C23×C4×C13C2311yescharacteristic
68C22×C22⋊D13—21no—
69C2×#6127—21no—
70C2×#6127—21no—
71C2×#6127—22no—
72C2×#6127—22no—
73C2×#6127—41no—
74C2×#6127—41no—
75C2×#6127C2×C411yescharacteristic
76C2×#6127C2×C411yescharacteristic
77C2×#6127C2311yescharacteristic
78C2×#6127C2311yescharacteristic
79C22×D52C2×C411yescharacteristic
80C22×C4×D13—21no—
81C22×Dic26C2×C411yescharacteristic
82C2×C13×M16C2311yescharacteristic
83C2×C13×M16C2311yescharacteristic
84C22×C8×C13C2311yescharacteristic
85C22×C8×C13C2311yescharacteristic
86C13×#117—21no—
87C13×#117—21no—
88C13×#117C2×C411yescharacteristic
89C13×#117C2×C411yescharacteristic
90C13×#117C2311yescharacteristic
91C13×#117C2311yescharacteristic
92C2×C13×C4⋊C4C2×C411yescharacteristic
93C2×C13×C4⋊C4C2×C411yescharacteristic
94C2×C13×C22⋊C4—21no—
95C2×C42×C13—21no—
96C2×C22⋊Dic13—21no—
97C2×C4×Dic13C2311yescharacteristic
98C2×C4×Dic13C2311yescharacteristic
99C2×#6099—41no—
100C2×#6099—41no—
101C2×#6099C2×C411yescharacteristic
102C2×#6099C2×C411yescharacteristic
103C2×#6099C2×C411yescharacteristic
104C2×#6099C2×C411yescharacteristic
105C2×#6099C2311yescharacteristic
106C2×#6099C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108C22×#1055C2311yescharacteristic
109#88155—22no—
110#88155—22no—
111#88155—41no—
112#88155—41no—
113C2×#6094—21no—
114C2×#6094—21no—
115C2×C8×D13—21no—
116C2×C8×D13—21no—
117C13×C4⋊C8—21no—
118C13×C4⋊C8—21no—
119C13×C4⋊C8—21no—
120C13×C4⋊C8—21no—
121C13×C22⋊C8—21no—
122C13×C22⋊C8—21no—
123C13×C22⋊C8D411yescharacteristic
124C13×C22⋊C8D411yescharacteristic
125C13×C22⋊C8D411yescharacteristic
126C13×C22⋊C8D411yescharacteristic
127C13×#97—21no—
128C13×#97—21no—
129C4×C8×C13—21no—
130C4×C8×C13—21no—
131#88071—21no—
132C22⋊#1055—21no—
133C22⋊#1055—21no—
134#88065—22no—
135#88065—22no—
136#88065—41no—
137#88065—41no—
138#88062—41no—
139#88062—41no—
140#88060—21no—
141#88060—21no—
142#88060—21no—
143#88060—21no—
144#88055—41no—
145C8×Dic13—41no—
146#88050C2×C411yescharacteristic
147#88050C2×C411yescharacteristic
148#88050C2×C411yescharacteristic
149#88050C2×C411yescharacteristic
150#88050C2×C411yescharacteristic
151#88050C2×C411yescharacteristic
152#88050C2×C411yescharacteristic
153#88050C2×C411yescharacteristic
154#88049C2×C411yescharacteristic
155#88049C2×C411yescharacteristic
156#88049C2×C411yescharacteristic
157#88049C2×C411yescharacteristic
158#88049C2×C411yescharacteristic
159#88049C2×C411yescharacteristic
160#88049C2×C411yescharacteristic
161#88049C2×C411yescharacteristic
162#22588—131nomaximal, Sylow
163C24×C13#4111yescharacteristic
164C23×D13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13C22×C411yescharacteristic
172C22×C4×C13C22×C411yescharacteristic
173C22×C4×C13C2×D411yescharacteristic
174C22×C4×C13C2×D411yescharacteristic
175C22×C4×C13#4111yescharacteristic
176C22×C4×C13C2411yescharacteristic
177C2×C22⋊D13—21no—
178C2×C22⋊D13—21no—
179C2×C22⋊D13—21no—
180C2×C22⋊D13—21no—
181C2×C22⋊D13—42no—
182C2×C22⋊D13—42no—
183C22×Dic13—21no—
184C22×Dic13—21no—
185C22×Dic13—21no—
186#6127—21no—
187#6127—21no—
188#6127—21no—
189#6127—21no—
190#6127—21no—
191#6127—21no—
192#6127—22no—
193#6127—22no—
194#6127—41no—
195#6127—41no—
196#6127—42no—
197#6127—42no—
198#6127—42no—
199#6127—42no—
200#6127#4112yes—
201#6127#4112yes—
202C2×D52—22no—
203C2×D52—21no—
204C2×D52—41no—
205C2×D52C22×C411yescharacteristic
206C2×D52C22×C411yescharacteristic
207C2×C4×D13—21no—
208C2×C4×D13—21no—
209C2×C4×D13—21no—
210C2×C4×D13—21no—
211C2×C4×D13—42no—
212C2×C4×D13—42no—
213C2×Dic26—22no—
214C2×Dic26—21no—
215C2×Dic26—41no—
216C2×Dic26C22×C411yescharacteristic
217C2×Dic26C22×C411yescharacteristic
218C13×M16—21no—
219C13×M16—21no—
220C13×M16—21no—
221C13×M16—21no—
222C2×C8×C13—21no—
223C2×C8×C13—21no—
224C2×C8×C13—21no—
225C2×C8×C13—21no—
226C2×C8×C13—21no—
227C2×C8×C13—21no—
228C2×C8×C13C2×D411yescharacteristic
229C2×C8×C13C2×D411yescharacteristic
230C2×C8×C13C2×D411yescharacteristic
231C2×C8×C13C2×D411yescharacteristic
232C13×C4⋊C4—21no—
233C13×C4⋊C4—21no—
234C13×C4⋊C4C22×C411yescharacteristic
235C13×C4⋊C4C22×C411yescharacteristic
236C13×C4⋊C4C22×C411yescharacteristic
237C13×C4⋊C4C22×C411yescharacteristic
238C13×C22⋊C4—21no—
239C13×C22⋊C4—21no—
240C13×C22⋊C4—21no—
241C13×C22⋊C4—21no—
242C42×C13—21no—
243C42×C13—21no—
244C42×C13—21no—
245C42×C13—21no—
246C22⋊Dic13—42no—
247C4×Dic13—21no—
248C4×Dic13—21no—
249C4×Dic13—21no—
250C4×Dic13—21no—
251#6099—21no—
252#6099—21no—
253#6099—21no—
254#6099—21no—
255#6099—41no—
256#6099—41no—
257#6099—41no—
258#6099—41no—
259C2×#1055—21no—
260C2×#1055—21no—
261C2×#1055—21no—
262C2×#1055—21no—
263C2×#1055—21no—
264C2×#1055—21no—
265C2×#1055C22×C411yescharacteristic
266C2×#1055C22×C411yescharacteristic
267C2×#1055C22×C411yescharacteristic
268C2×#1055C22×C411yescharacteristic
269#6094—42no—
270#6094—42no—
271C8×D13—42no—
272C8×D13—42no—
273#2924D1311yescharacteristic, complemented
274#2896—131no—
275#2880—131no—
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—41no—
291C23×C13—41no—
292C23×C13C4×D411yescharacteristic
293C23×C13C4×D411yescharacteristic
294C23×C13C2×#4111yescharacteristic
295C22×D13—21no—
296C22×D13—21no—
297C22×D13—42no—
298C22×D13—42no—
299C22×D13—81no—
300C2×C4×C13—21no—
301C2×C4×C13—21no—
302C2×C4×C13—21no—
303C2×C4×C13—21no—
304C2×C4×C13—21no—
305C2×C4×C13—21no—
306C2×C4×C13—21no—
307C2×C4×C13—21no—
308C2×C4×C13—21no—
309C2×C4×C13—21no—
310C2×C4×C13—21no—
311C2×C4×C13—21no—
312C2×C4×C13—21no—
313C2×C4×C13—21no—
314C2×C4×C13—42no—
315C2×C4×C13—81no—
316C2×C4×C13C4×D411yescharacteristic
317C2×C4×C13C4×D411yescharacteristic
318C2×C4×C13C23×C411yescharacteristic
319C2×C4×C13C22×D411yescharacteristic
320C2×C4×C13C2×#4111yescharacteristic
321C2×C4×C13C2×#4111yescharacteristic
322C2×C4×C13H(5,𝔽2)11yescharacteristic
323C2×C4×C13H(5,𝔽2)11yescharacteristic
324C22⋊D13—22no—
325C22⋊D13—22no—
326C22⋊D13—42no—
327C22⋊D13—42no—
328C22⋊D13—41no—
329C22⋊D13—41no—
330C2×Dic13—21no—
331C2×Dic13—22no—
332C2×Dic13—21no—
333C2×Dic13—42no—
334C2×Dic13—41no—
335C2×Dic13—41no—
336C2×Dic13—41no—
337C2×Dic13—41no—
338C2×Dic13—41no—
339D52—21no—
340D52—21no—
341D52—21no—
342D52—42no—
343D52#11712yes—
344C4×D13—22no—
345C4×D13—22no—
346C4×D13—42no—
347C4×D13—42no—
348C4×D13—41no—
349C4×D13—41no—
350Dic26—21no—
351Dic26—21no—
352Dic26—21no—
353Dic26—42no—
354Dic26#11712yes—
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×#41—131no—
368C2×#131—131no—
369C2×#131—131no—
370C22×M16—131no—
371C2×#117C2×D1311yescharacteristic
372#433—21no—
373#433—21no—
374#432—21no—
375#431—21no—
376C2×#108—131no—
377C2×#108—131no—
378#424C2×D1311yescharacteristic, complemented
379#424C2×D1311yescharacteristic, complemented
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—131no—
397#408—131no—
398#408—261no—
399#408—261no—
400#407—131no—
401#407—261no—
402#407C2×D1311yescharacteristic
403C2×C22⋊C8—261no—
404C2×C22⋊C8C2×D1311yescharacteristic
405#405C2×D1311yescharacteristic, complemented
406#405C2×D1311yescharacteristic, complemented
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—21no—
423C22×C13—21no—
424C22×C13—21no—
425C22×C13—21no—
426C22×C13—81no—
427C22×C13—81no—
428C22×C13C2×C4×D411yescharacteristic
429C22×C13#55111yescharacteristic
430C22×C13#55111yescharacteristic
431C2×D13—22no—
432C2×D13—41no—
433C2×D13—41no—
434C2×D13—41no—
435C2×D13—41no—
436C2×D13—41no—
437C2×D13—84no—
438C4×C13—21no—
439C4×C13—21no—
440C4×C13—41no—
441C4×C13—41no—
442C4×C13—41no—
443C4×C13—41no—
444C4×C13C2×#11711yescharacteristic
445C4×C13#51811yescharacteristic
446C4×C13#54611yescharacteristic
447C4×C13#54611yescharacteristic
448Dic13—22no—
449Dic13—42no—
450Dic13—41no—
451Dic13—81no—
452C2×#41—131no—
453C2×#41—131no—
454C2×#41—131no—
455C2×#41—131no—
456C2×#41—262no—
457C2×#41—262no—
458C2×#41—261no—
459C2×#41—261no—
460C2×#41—521no—
461C2×#41—521no—
462C22×Q8—131no—
463C22×D4—131no—
464C22×D4—261no—
465C23×C4—261no—
466C23×C4C22×D1311yescharacteristic
467#131—262no—
468#131—262no—
469#131—521no—
470#131—521no—
471C2×M16—131no—
472C2×M16—131no—
473C2×M16—131no—
474C2×M16—131no—
475C2×M16—131no—
476C2×M16—131no—
477C2×M16—261no—
478C2×M16—261no—
479C2×M16—521no—
480C2×M16—521no—
481C2×M16C22×D1311yescharacteristic
482C2×M16C22×D1311yescharacteristic
483C22×C8—131no—
484C22×C8—131no—
485C22×C8—261no—
486C22×C8—261no—
487C22×C8C22×D1311yescharacteristic
488C22×C8C22×D1311yescharacteristic
489#117—21no—
490#117—21no—
491#117C4×D1311yescharacteristic
492#117C4×D1311yescharacteristic
493#117C22×D1311yescharacteristic
494#117C22×D1311yescharacteristic
495C2×C4⋊C4C4×D1311yescharacteristic
496C2×C4⋊C4C4×D1311yescharacteristic
497C2×C22⋊C4—21no—
498C2×C22⋊C4—261no—
499C2×C42—21no—
500C2×C42—131no—
501C2×C42—131no—
502#108—521no—
503#108—521no—
504C4⋊C8—21no—
505C4⋊C8—21no—
506C4⋊C8—21no—
507C4⋊C8—21no—
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—261no—
531C22⋊C8—261no—
532C22⋊C8—261no—
533C22⋊C8—261no—
534C22⋊C8—261no—
535C22⋊C8—261no—
536C22⋊C8C22⋊D1311yescharacteristic
537C22⋊C8C22⋊D1311yescharacteristic
538C22⋊C8C22⋊D1311yescharacteristic
539C22⋊C8C22⋊D1311yescharacteristic
540#97—21no—
541#97—21no—
542#97—521no—
543C4×C8—21no—
544C4×C8—21no—
545C4×C8—521no—
546#95—261no—
547C2×C13—21no—
548C2×C13—21no—
549C2×C13—41no—
550C2×C13—41no—
551C2×C13#234211yescharacteristic
552C2×C13#295511yescharacteristic
553C2×C13#295611yescharacteristic
554D13—42no—
555D13—81no—
556C24—261no—
557C24#612711yescharacteristic
558#41—132no—
559#41—132no—
560#41—262no—
561#41—262no—
562#41—261no—
563#41—261no—
564#41—261no—
565#41—261no—
566#41—261no—
567#41—261no—
568#41—522no—
569#41—522no—
570#41—521no—
571#41—521no—
572#41—522no—
573#41—522no—
574C2×Q8—131no—
575C2×Q8—131no—
576C2×Q8—262no—
577C2×Q8—261no—
578C2×Q8—521no—
579C2×D4—131no—
580C2×D4—131no—
581C2×D4—262no—
582C2×D4—261no—
583C2×D4—261no—
584C2×D4—261no—
585C2×D4—261no—
586C2×D4—261no—
587C2×D4—521no—
588C2×D4—522no—
589C2×D4—522no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—261no—
597C22×C4—261no—
598C22×C4—261no—
599C22×C4—261no—
600C22×C4—261no—
601C22×C4—261no—
602C22×C4—261no—
603C22×C4—522no—
604C22×C4—522no—
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—261no—
616M16—261no—
617M16—261no—
618M16—261no—
619M16—522no—
620M16—522no—
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—131no—
632C2×C8—131no—
633C2×C8—131no—
634C2×C8—131no—
635C2×C8—261no—
636C2×C8—261no—
637C2×C8—261no—
638C2×C8—261no—
639C2×C8—261no—
640C2×C8—261no—
641C2×C8—522no—
642C2×C8—522no—
643C2×C8C2×C22⋊D1311yescharacteristic
644C2×C8C2×C22⋊D1311yescharacteristic
645C2×C8C2×C22⋊D1311yescharacteristic
646C2×C8C2×C22⋊D1311yescharacteristic
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4C2×C4×D1311yescharacteristic
650C4⋊C4C2×C4×D1311yescharacteristic
651C4⋊C4C2×C4×D1311yescharacteristic
652C4⋊C4C2×C4×D1311yescharacteristic
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—522no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—261no—
663C42—261no—
664C42—261no—
665C42—261no—
666C13#2258811yescharacteristic, complemented, Sylow
667C23—21no—
668C23—21no—
669C23—41no—
670C23—41no—
671C23—261no—
672C23—261no—
673C23—522no—
674C23—522no—
675C23—1041no—
676C23C4×C22⋊D1311yescharacteristic
677C23C4×C22⋊D1311yescharacteristic
678C23C2×#612711yescharacteristic
679Q8—132no—
680Q8—261no—
681Q8—261no—
682Q8—261no—
683Q8—522no—
684D4—132no—
685D4—262no—
686D4—262no—
687D4—261no—
688D4—261no—
689D4—261no—
690D4—522no—
691D4—522no—
692D4—522no—
693D4—521no—
694D4—521no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—42no—
710C2×C4—81no—
711C2×C4—261no—
712C2×C4—262no—
713C2×C4—262no—
714C2×C4—262no—
715C2×C4—261no—
716C2×C4—522no—
717C2×C4—522no—
718C2×C4—522no—
719C2×C4—521no—
720C2×C4—521no—
721C2×C4—521no—
722C2×C4—521no—
723C2×C4—521no—
724C2×C4—521no—
725C2×C4—521no—
726C2×C4C4×C22⋊D1311yescharacteristic
727C2×C4C4×C22⋊D1311yescharacteristic
728C2×C4C22×C4×D1311yescharacteristic
729C2×C4#41×D1311yescharacteristic
730C2×C4#41×D1311yescharacteristic
731C2×C4#8825611yescharacteristic
732C2×C4#8825611yescharacteristic
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—81no—
755C22—81no—
756C22—262no—
757C22—521no—
758C22—521no—
759C22—521no—
760C22—521no—
761C22—521no—
762C22—1044no—
763C22#1171923211yescharacteristic
764C22#1171923211yescharacteristic
765C22C2×C4×C22⋊D1311yescharacteristic
766C4—21no—
767C4—21no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—262no—
773C4—522no—
774C4—521no—
775C4—1041no—
776C4D13×#11711yescharacteristic
777C4#1171922611yescharacteristic
778C4#1171953411yescharacteristic
779C4#1171953411yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—522no—
785C2—1041no—
786C2#1311768611yescharacteristic
787C2#1312373711yescharacteristic
788C2#1312374311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2924C2
socleC22×C13C2×C4×D4
prime radicalC22×#6127C22
cosocleC22×C4×C13C24
hypercenter#2924D13
hypocenterC13#22588
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2924

Complements

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

NH ≅ G/Ntype
3. #13115546C2semidirect
4. #13115539C2semidirect
5. #13115484C2semidirect
6. #13115484C2semidirect
7. #13115110C2semidirect
8. #13115110C2semidirect
9. #13114935C2semidirect
10. #13114876C2semidirect
12. #13114682C2semidirect
13. #13114675C2semidirect
14. #13114622C2semidirect
15. C13×#2924C2semidirect
25. C13×#424C22semidirect
26. C13×#424C22semidirect
29. C13×#405C22semidirect
30. C13×#405C22semidirect
37. C2×#88062C22semidirect
38. C2×#88062C22semidirect
41. C2×#88055C22semidirect
42. C2×C8×Dic13C22semidirect
43. #11718665C4semidirect
44. #11718665C4semidirect
49. #11718662C4semidirect
50. #11718662C4semidirect
51. #11718627C4semidirect
52. #11718627C4semidirect
53. #11718627C4semidirect
54. #11718627C4semidirect
59. #11718150C22semidirect
60. #11718150C22semidirect
61. #11718142C22semidirect
62. #11718142C22semidirect
63. #11718124C22semidirect
64. #11718124C22semidirect
65. #11718124C22semidirect
66. #11718124C22semidirect
273. #2924D13semidirect
378. #424C2×D13semidirect
379. #424C2×D13semidirect
405. #405C2×D13semidirect
406. #405C2×D13semidirect
666. C13#22588semidirect

Maximal subgroups

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

subgroupindex
#131233532
#131232822
#131155462
#131155392
#131154842
#131151102
#131149352
#131148762
#131147792
#131146822
#131146752
#131146222
C13×#29242
#2258813