Finite Group Databasebeta

← #15880290

Subgroups — #15880290

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#13123494C211yesmaximal, characteristic, complemented
2#13123285C211yesmaximal, characteristic
3#13115549C211yesmaximal, characteristic, complemented
4#13115542C211yesmaximal, characteristic, complemented
5#13115486C211yesmaximal, characteristic, complemented
6#13115486C211yesmaximal, characteristic, complemented
7#13115113C211yesmaximal, characteristic, complemented
8#13115113C211yesmaximal, characteristic, complemented
9#13114935C211yesmaximal, characteristic, complemented
10#13114878C211yesmaximal, characteristic, complemented
11#13114780C211yesmaximal, characteristic
12#13114683C211yesmaximal, characteristic, complemented
13#13114676C211yesmaximal, characteristic, complemented
14#13114617C211yesmaximal, characteristic, complemented
15C13×#2896C211yesmaximal, characteristic
16C22×C13×#41C2211yescharacteristic
17C22×C13×M16C2211yescharacteristic
18C2×C13×#117C2211yescharacteristic
19C2×#88202C2211yescharacteristic
20C2×#88202C2211yescharacteristic
21C13×#419C411yescharacteristic, complemented
22C13×#419C411yescharacteristic, complemented
23C13×#418C411yescharacteristic, complemented
24C13×#418C411yescharacteristic, complemented
25C13×#417C411yescharacteristic, complemented
26C13×#417C411yescharacteristic, complemented
27C13×#417C411yescharacteristic, complemented
28C13×#417C411yescharacteristic, complemented
29C13×#416C2211yescharacteristic
30C13×#416C2211yescharacteristic
31C13×#416C2211yescharacteristic
32C13×#416C2211yescharacteristic
33C2×#88077C2211yescharacteristic
34C2×#88077C2211yescharacteristic
35C2×#88077C2211yescharacteristic
36C2×#88077C2211yescharacteristic
37#11718895—21no—
38#11718895—21no—
39#11718895C2211yescharacteristic
40#11718895C2211yescharacteristic
41C4×C22⋊Dic13C2211yescharacteristic
42#11718868—21no—
43#11718868C2211yescharacteristic
44#11718868C2211yescharacteristic
45C2×C22⋊#1055—21no—
46C2×C22⋊#1055C2211yescharacteristic
47C2×#88059C2211yescharacteristic, complemented
48C2×#88059C2211yescharacteristic, complemented
49C2×#88055C2211yescharacteristic, complemented
50C2×C8×Dic13C2211yescharacteristic, complemented
51#11718661—21no—
52#11718661—21no—
53#11718660C2211yescharacteristic, complemented
54#11718660C2211yescharacteristic, complemented
55#11718658C2211yescharacteristic, complemented
56#11718658C2211yescharacteristic, complemented
57#11718587—21no—
58#11718586—21no—
59#11718144C2211yescharacteristic, complemented
60#11718144C2211yescharacteristic, complemented
61#11718142C2211yescharacteristic, complemented
62#11718142C2211yescharacteristic, complemented
63#11718124C2211yescharacteristic, complemented
64#11718124C2211yescharacteristic, complemented
65#11718124C2211yescharacteristic, complemented
66#11718124C2211yescharacteristic, 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
82C2×C13×M16—41no—
83C2×C13×M16—41no—
84C2×C13×M16C2×C411yescharacteristic
85C2×C13×M16C2×C411yescharacteristic
86C2×C13×M16C2×C411yescharacteristic
87C2×C13×M16C2×C411yescharacteristic
88C22×C8×C13C2311yescharacteristic
89C22×C8×C13C2311yescharacteristic
90C13×#117—21no—
91C13×#117—21no—
92C13×#117C2×C411yescharacteristic
93C13×#117C2×C411yescharacteristic
94C13×#117C2311yescharacteristic
95C13×#117C2311yescharacteristic
96C2×C13×C4⋊C4C2×C411yescharacteristic
97C2×C13×C4⋊C4C2×C411yescharacteristic
98C2×C13×C22⋊C4—21no—
99C2×C42×C13—21no—
100C2×C22⋊Dic13—21no—
101#88202—22no—
102#88202—22no—
103#88202—41no—
104#88202—41no—
105C2×C4×Dic13C2311yescharacteristic
106C2×C4×Dic13C2311yescharacteristic
107C2×#6099—21no—
108C2×#6099—21no—
109C2×#6099C2311yescharacteristic
110C2×#6099C2311yescharacteristic
111C2×#6099C2311yescharacteristic
112C2×#6099C2311yescharacteristic
113C22×#1055—21no—
114C22×#1055—21no—
115C22×#1055C2311yescharacteristic
116C22×#1055C2311yescharacteristic
117C13×#103C2×C411yescharacteristic
118C13×#103C2×C411yescharacteristic
119C13×#103C2×C411yescharacteristic
120C13×#103C2×C411yescharacteristic
121C13×#103C2×C411yescharacteristic
122C13×#103C2×C411yescharacteristic
123C13×#103C2×C411yescharacteristic
124C13×#103C2×C411yescharacteristic
125C13×#102C2×C411yescharacteristic
126C13×#102C2×C411yescharacteristic
127C13×#102C2×C411yescharacteristic
128C13×#102C2×C411yescharacteristic
129C13×#102C2×C411yescharacteristic
130C13×#102C2×C411yescharacteristic
131C13×#102C2×C411yescharacteristic
132C13×#102C2×C411yescharacteristic
133#88077—22no—
134#88077—22no—
135#88077—41no—
136#88077—41no—
137#88071—21no—
138C22⋊#1055—21no—
139C22⋊#1055—21no—
140C22⋊#1055—21no—
141C22⋊#1055—21no—
142C22⋊#1055—21no—
143C22⋊#1055—21no—
144C22⋊#1055—21no—
145C22⋊#1055—21no—
146C22⋊#1055D411yescharacteristic
147C22⋊#1055D411yescharacteristic
148C22⋊#1055D411yescharacteristic
149C22⋊#1055D411yescharacteristic
150#88059—41no—
151#88059—41no—
152#88055—41no—
153C8×Dic13—41no—
154C4⋊#1055—21no—
155C4⋊#1055—21no—
156C4⋊#1055—21no—
157C4⋊#1055—21no—
158#88043—21no—
159#88043—21no—
160C4×#1055—21no—
161C4×#1055—21no—
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—21no—
207C22×C4×C13—21no—
208C22×C4×C13—42no—
209C22×C4×C13—42no—
210C22×C4×C13C22×C411yescharacteristic
211C22×C4×C13C22×C411yescharacteristic
212C22×C4×C13C2×D411yescharacteristic
213C22×C4×C13C2×D411yescharacteristic
214C22×C4×C13#4111yescharacteristic
215C22×C4×C13C2411yescharacteristic
216C22×Dic13—21no—
217C22×Dic13—21no—
218C13×M16—41no—
219C13×M16—41no—
220C13×M16—41no—
221C13×M16—41no—
222C2×C8×C13—21no—
223C2×C8×C13—21no—
224C2×C8×C13—21no—
225C2×C8×C13—21no—
226C2×C8×C13C22×C411yescharacteristic
227C2×C8×C13C22×C411yescharacteristic
228C2×C8×C13C22×C411yescharacteristic
229C2×C8×C13C22×C411yescharacteristic
230C13×C4⋊C4—21no—
231C13×C4⋊C4—21no—
232C13×C4⋊C4C22×C411yescharacteristic
233C13×C4⋊C4C22×C411yescharacteristic
234C13×C4⋊C4C22×C411yescharacteristic
235C13×C4⋊C4C22×C411yescharacteristic
236C13×C22⋊C4—21no—
237C13×C22⋊C4—21no—
238C13×C22⋊C4—21no—
239C13×C22⋊C4—21no—
240C42×C13—21no—
241C42×C13—21no—
242C42×C13—21no—
243C42×C13—21no—
244C22⋊Dic13—42no—
245C4×Dic13—21no—
246C4×Dic13—21no—
247C4×Dic13—21no—
248C4×Dic13—21no—
249#6099—21no—
250#6099—21no—
251#6099—21no—
252#6099—21no—
253#6099—21no—
254#6099—21no—
255#6099—21no—
256#6099—21no—
257#6099—42no—
258#6099—42no—
259C2×#1055—21no—
260C2×#1055—21no—
261C2×#1055—21no—
262C2×#1055—21no—
263C2×#1055—21no—
264C2×#1055—21no—
265C2×#1055—21no—
266C2×#1055—21no—
267C2×#1055—42no—
268C2×#1055—42no—
269C2×#1055C2×D411yescharacteristic
270C2×#1055C2×D411yescharacteristic
271C2×#1055C2×D411yescharacteristic
272C2×#1055C2×D411yescharacteristic
273#2924—131no—
274#2896D1311yescharacteristic
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—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—21no—
331C2×C4×C13—21no—
332C2×C4×C13—21no—
333C2×C4×C13—21no—
334C2×C4×C13—42no—
335C2×C4×C13—42no—
336C2×C4×C13—42no—
337C2×C4×C13—42no—
338C2×C4×C13—41no—
339C2×C4×C13—41no—
340C2×C4×C13—81no—
341C2×C4×C13C4×D411yescharacteristic
342C2×C4×C13C4×D411yescharacteristic
343C2×C4×C13C23×C411yescharacteristic
344C2×C4×C13C22×D411yescharacteristic
345C2×C4×C13C2×#4111yescharacteristic
346C2×C4×C13C2×#4111yescharacteristic
347C2×C4×C13H(5,𝔽2)11yescharacteristic
348C2×C4×C13H(5,𝔽2)11yescharacteristic
349C2×Dic13—22no—
350C2×Dic13—41no—
351C2×Dic13—41no—
352C2×Dic13—41no—
353C2×Dic13—41no—
354C2×Dic13—41no—
355C8×C13—21no—
356C8×C13—21no—
357C8×C13—21no—
358C8×C13—21no—
359#1055—21no—
360#1055—21no—
361#1055—21no—
362#1055—21no—
363#1055—41no—
364#1055—41no—
365#1055—41no—
366#1055—41no—
367C22×#41C2×D1311yescharacteristic
368C2×#131—131no—
369C2×#131—131no—
370C22×M16C2×D1311yescharacteristic
371C2×#117C2×D1311yescharacteristic
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#419Dic1311yescharacteristic, complemented
385#419Dic1311yescharacteristic, complemented
386#418Dic1311yescharacteristic, complemented
387#418Dic1311yescharacteristic, complemented
388#417Dic1311yescharacteristic, complemented
389#417Dic1311yescharacteristic, complemented
390#417Dic1311yescharacteristic, complemented
391#417Dic1311yescharacteristic, complemented
392#416C2×D1311yescharacteristic
393#416C2×D1311yescharacteristic
394#416C2×D1311yescharacteristic
395#416C2×D1311yescharacteristic
396#408—131no—
397#408—131no—
398#408—261no—
399#408—261no—
400#407—131no—
401#407—131no—
402#407—261no—
403C2×C22⋊C8—131no—
404C2×C22⋊C8—261no—
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×C13—41no—
443C4×C13—41no—
444C4×C13—41no—
445C4×C13—41no—
446C4×C13C2×#11711yescharacteristic
447C4×C13#51811yescharacteristic
448C4×C13#54611yescharacteristic
449C4×C13#54611yescharacteristic
450Dic13—42no—
451Dic13—81no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—22no—
455C2×#41—22no—
456C2×#41—41no—
457C2×#41—41no—
458C2×#41C2×Dic1311yescharacteristic
459C2×#41C2×Dic1311yescharacteristic
460C2×#41C22×D1311yescharacteristic
461C2×#41C22×D1311yescharacteristic
462C22×Q8C2×Dic1311yescharacteristic
463C22×D4—21no—
464C22×D4C2×Dic1311yescharacteristic
465C23×C4—21no—
466C23×C4C22×D1311yescharacteristic
467#131—262no—
468#131—262no—
469#131—521no—
470#131—521no—
471C2×M16—41no—
472C2×M16—41no—
473C2×M16—131no—
474C2×M16—131no—
475C2×M16—131no—
476C2×M16—131no—
477C2×M16—261no—
478C2×M16—261no—
479C2×M16C2×Dic1311yescharacteristic
480C2×M16C2×Dic1311yescharacteristic
481C2×M16C2×Dic1311yescharacteristic
482C2×M16C2×Dic1311yescharacteristic
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#117C2×Dic1311yescharacteristic
492#117C2×Dic1311yescharacteristic
493#117C22×D1311yescharacteristic
494#117C22×D1311yescharacteristic
495C2×C4⋊C4C2×Dic1311yescharacteristic
496C2×C4⋊C4C2×Dic1311yescharacteristic
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—261no—
505C4⋊C8—261no—
506C4⋊C8—261no—
507C4⋊C8—261no—
508#104—262no—
509#104—262no—
510#104—521no—
511#104—521no—
512#103C2×Dic1311yescharacteristic
513#103C2×Dic1311yescharacteristic
514#103C2×Dic1311yescharacteristic
515#103C2×Dic1311yescharacteristic
516#103C2×Dic1311yescharacteristic
517#103C2×Dic1311yescharacteristic
518#103C2×Dic1311yescharacteristic
519#103C2×Dic1311yescharacteristic
520#102C2×Dic1311yescharacteristic
521#102C2×Dic1311yescharacteristic
522#102C2×Dic1311yescharacteristic
523#102C2×Dic1311yescharacteristic
524#102C2×Dic1311yescharacteristic
525#102C2×Dic1311yescharacteristic
526#102C2×Dic1311yescharacteristic
527#102C2×Dic1311yescharacteristic
528C22⋊C8—131no—
529C22⋊C8—131no—
530C22⋊C8—131no—
531C22⋊C8—131no—
532C22⋊C8—261no—
533C22⋊C8—261no—
534C22⋊C8—261no—
535C22⋊C8—261no—
536C22⋊C8—261no—
537C22⋊C8—261no—
538C22⋊C8—261no—
539C22⋊C8—261no—
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#612911yescharacteristic
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#612712yes—
573#41#612712yes—
574C2×Q8—21no—
575C2×Q8—22no—
576C2×Q8—41no—
577C2×Q8C22×Dic1311yescharacteristic
578C2×Q8C22×Dic1311yescharacteristic
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×D4C22×Dic1311yescharacteristic
589C2×D4C22×Dic1311yescharacteristic
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—21no—
600C22×C4—21no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—261no—
604C22×C4—261no—
605C22×C4D4×D1311yescharacteristic
606C22×C4D4×D1311yescharacteristic
607C22×C4#612911yescharacteristic
608C22×C4C22×Dic1311yescharacteristic
609C22×C4C22×Dic1311yescharacteristic
610C22×C4C23×D1311yescharacteristic
611M16—41no—
612M16—41no—
613M16—41no—
614M16—41no—
615M16—261no—
616M16—261no—
617M16—261no—
618M16—261no—
619M16—261no—
620M16—261no—
621M16—261no—
622M16—261no—
623M16—522no—
624M16—522no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—131no—
630C2×C8—131no—
631C2×C8—131no—
632C2×C8—131no—
633C2×C8—261no—
634C2×C8—261no—
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×C8C22×Dic1311yescharacteristic
644C2×C8C22×Dic1311yescharacteristic
645C2×C8C22×Dic1311yescharacteristic
646C2×C8C22×Dic1311yescharacteristic
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4C22×Dic1311yescharacteristic
650C4⋊C4C22×Dic1311yescharacteristic
651C4⋊C4C22×Dic1311yescharacteristic
652C4⋊C4C22×Dic1311yescharacteristic
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—21no—
670C23—21no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—81no—
676C23D4×Dic1311yescharacteristic
677C23D4×Dic1311yescharacteristic
678C23C2×#612911yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—42no—
683Q8#8818012yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4#8818012yes—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
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—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—81no—
720C2×C4—262no—
721C2×C4—521no—
722C2×C4—521no—
723C2×C4—521no—
724C2×C4—521no—
725C2×C4—521no—
726C2×C4D4×Dic1311yescharacteristic
727C2×C4D4×Dic1311yescharacteristic
728C2×C4C2×#612711yescharacteristic
729C2×C4C2×#612711yescharacteristic
730C2×C4C2×D4×D1311yescharacteristic
731C2×C4#8825111yescharacteristic
732C2×C4#8825111yescharacteristic
733C2×C4C23×Dic1311yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—261no—
739C8—261no—
740C8—261no—
741C8—261no—
742C8—521no—
743C8—521no—
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×D4×Dic1311yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—522no—
775C4—1041no—
776C4#1171919511yescharacteristic
777C4#1171919511yescharacteristic
778C4C2×#8818011yescharacteristic
779C4#1171950311yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2#1311768511yescharacteristic
787C2#1312373911yescharacteristic
788C2#1312374611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2896C2
socleC22×C13C2×C4×D4
prime radicalC22×C13×#41C22
cosocleC22×C4×C13C24
hypercenter#2896D13
hypocenterC13#22588
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
1. #13123494C2semidirect
3. #13115549C2semidirect
4. #13115542C2semidirect
5. #13115486C2semidirect
6. #13115486C2semidirect
7. #13115113C2semidirect
8. #13115113C2semidirect
9. #13114935C2semidirect
10. #13114878C2semidirect
12. #13114683C2semidirect
13. #13114676C2semidirect
14. #13114617C2semidirect
21. C13×#419C4semidirect
22. C13×#419C4semidirect
23. C13×#418C4semidirect
24. C13×#418C4semidirect
25. C13×#417C4semidirect
26. C13×#417C4semidirect
27. C13×#417C4semidirect
28. C13×#417C4semidirect
47. C2×#88059C22semidirect
48. C2×#88059C22semidirect
49. C2×#88055C22semidirect
50. C2×C8×Dic13C22semidirect
53. #11718660C22semidirect
54. #11718660C22semidirect
55. #11718658C22semidirect
56. #11718658C22semidirect
59. #11718144C22semidirect
60. #11718144C22semidirect
61. #11718142C22semidirect
62. #11718142C22semidirect
63. #11718124C22semidirect
64. #11718124C22semidirect
65. #11718124C22semidirect
66. #11718124C22semidirect
384. #419Dic13semidirect
385. #419Dic13semidirect
386. #418Dic13semidirect
387. #418Dic13semidirect
388. #417Dic13semidirect
389. #417Dic13semidirect
390. #417Dic13semidirect
391. #417Dic13semidirect
666. C13#22588semidirect

Maximal subgroups

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

subgroupindex
#131234942
#131232852
#131155492
#131155422
#131154862
#131151132
#131149352
#131148782
#131147802
#131146832
#131146762
#131146172
C13×#28962
#2258813