Finite Group Databasebeta

← #14771128

Subgroups — #14771128

Order 2816.

906 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#13077271C211yesmaximal, characteristic, complemented
2D11×#416C211yesmaximal, characteristic
3#13077064C211yesmaximal, characteristic
4#13069323C211yesmaximal, characteristic, complemented
5#13069317C211yesmaximal, characteristic, complemented
6#13069266C211yesmaximal, characteristic, complemented
7#13068894C211yesmaximal, characteristic, complemented
8#13068888C211yesmaximal, characteristic, complemented
9#13068714C211yesmaximal, characteristic, complemented
10#13068651C211yesmaximal, characteristic, complemented
11#13068558C211yesmaximal, characteristic
12#13068455C211yesmaximal, characteristic, complemented
13#13068450C211yesmaximal, characteristic, complemented
14#13068386C211yesmaximal, characteristic, complemented
15C11×#1929C211yesmaximal, characteristic, complemented
16C2×#41×D11C2211yescharacteristic
17C2×#66960C2211yescharacteristic
18C2×#66954C2211yescharacteristic
19C22×C8×D11C2211yescharacteristic
20D11×#117C2211yescharacteristic
21C2×C11×#108C2211yescharacteristic, complemented
22C2×C11×#104C2211yescharacteristic
23C11×#416C2211yescharacteristic
24C11×#408C2211yescharacteristic
25C11×#405C2211yescharacteristic, complemented
26C2×#66901C2211yescharacteristic
27#10622847C2211yescharacteristic
28#10622846C2211yescharacteristic
29C2×#66889C2211yescharacteristic
30#10622739C2211yescharacteristic
31#10622739C2211yescharacteristic
32#10622732C2211yescharacteristic, complemented
33#10622726C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×#66883C2211yescharacteristic, complemented
36#10622715C2211yescharacteristic, complemented
37C2×C8×Dic11C2211yescharacteristic, complemented
38#10622615C2211yescharacteristic
39#10622610C2211yescharacteristic, complemented
40C4×(C2×D11)⋊C4C2211yescharacteristic
41C2×#66869C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic, complemented
43#10622417C411yescharacteristic, complemented
44#10622417C411yescharacteristic, complemented
45D11×#103C411yescharacteristic, complemented
46D11×#103C411yescharacteristic, complemented
47#10622385C411yescharacteristic, complemented
48#10622385C411yescharacteristic, complemented
49D11×#102C411yescharacteristic, complemented
50D11×#102C411yescharacteristic, complemented
51#10622340—21no—
52#10622340—21no—
53#10622339—21no—
54D11×C22⋊C8—21no—
55#10622322—21no—
56#10622318—21no—
57#10622303—21no—
58#10622298—21no—
59C11×#339C2211yescharacteristic, complemented
60C11×#336C2211yescharacteristic, complemented
61#10622196C2211yescharacteristic, complemented
62#10622196C2211yescharacteristic, complemented
63#10622193C2211yescharacteristic, complemented
64#10622188C2211yescharacteristic, complemented
65#10622170C2211yescharacteristic, complemented
66#10622161C2211yescharacteristic, complemented
67C2×C11×#41C2311yescharacteristic
68#41×D11—22no—
69#41×D11—22no—
70#41×D11—41no—
71#41×D11—41no—
72C2×#4343C2×C411yescharacteristic
73C2×Q8×D11C2×C411yescharacteristic
74C2×#4341—21no—
75C2×#4341C2×C411yescharacteristic
76C2×D4×D11—21no—
77C2×D4×D11C2×C411yescharacteristic
78C2×#4339—21no—
79C2×#4339C2311yescharacteristic
80C22×C4×D11—21no—
81C22×C4×D11C2311yescharacteristic
82C2×C11×M16C2311yescharacteristic
83C2×C11×M16C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C11×#117C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×(C2×D11)⋊C4—21no—
89#66979C2311yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C2×#4318C2311yescharacteristic
92C2×#4318C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95#66960—22no—
96#66960—41no—
97#66954—22no—
98#66954—41no—
99C2×#4313—21no—
100C2×#4313—21no—
101C2×C8×D11—21no—
102C2×C8×D11—21no—
103C2×C8×D11—41no—
104C2×C8×D11—41no—
105C2×C8×D11C2×C411yescharacteristic
106C2×C8×D11C2×C411yescharacteristic
107C2×C8×D11C2×C411yescharacteristic
108C2×C8×D11C2×C411yescharacteristic
109#66945C2×C411yescharacteristic
110#66945C2×C411yescharacteristic
111C4⋊C4×D11C2×C411yescharacteristic
112C4⋊C4×D11C2×C411yescharacteristic
113C22⋊C4×D11—21no—
114#66930—21no—
115#66925—21no—
116C42×D11—21no—
117C11×#108—41no—
118C11×#104—41no—
119C11×#103C2×C411yescharacteristic
120C11×#103C2×C411yescharacteristic
121C11×#102C2×C411yescharacteristic
122C11×#102C2×C411yescharacteristic
123C11×C22⋊C8—21no—
124C11×C22⋊C8—21no—
125C11×#97—21no—
126C4×C8×C11—21no—
127#66901—41no—
128#66899C2×C411yescharacteristic
129#66899C2×C411yescharacteristic
130#66896C2×C411yescharacteristic
131#66896C2×C411yescharacteristic
132C11⋊#95—21no—
133C22⋊(C11⋊C8)—21no—
134C22⋊(C11⋊C8)—21no—
135#66889—22no—
136#66885C2×C411yescharacteristic
137#66885C2×C411yescharacteristic
138(C2×D11)⋊C8—21no—
139(C2×D11)⋊C8—21no—
140(C2×D11)⋊C8—21no—
141(C2×D11)⋊C8—21no—
142(C2×D11)⋊C8D411yescharacteristic
143(C2×D11)⋊C8D411yescharacteristic
144(C2×D11)⋊C8D411yescharacteristic
145(C2×D11)⋊C8D411yescharacteristic
146#66883—41no—
147#66880C2×C411yescharacteristic
148#66880C2×C411yescharacteristic
149Dic11⋊C8—21no—
150Dic11⋊C8—21no—
151Dic11⋊C8—21no—
152Dic11⋊C8—21no—
153C8×Dic11—41no—
154#66874C2×C411yescharacteristic
155#66874C2×C411yescharacteristic
156#66873C2×C411yescharacteristic
157#66873C2×C411yescharacteristic
158#66869—22no—
159#66867—21no—
160C4×C11⋊C8—21no—
161C4×C11⋊C8—41no—
162#22587—111nomaximal, Sylow
163C23×D11—21no—
164C23×D11#4111yescharacteristic
165C11×#41—21no—
166C11×#41—21no—
167C11×#41—21no—
168C11×#41—21no—
169C2×Q8×C11C22×C411yescharacteristic
170C2×D4×C11—21no—
171C2×D4×C11C22×C411yescharacteristic
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11C2411yescharacteristic
175C2×C22⋊D11—21no—
176C2×C22⋊D11—21no—
177C2×C22⋊D11—21no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11#4111yescharacteristic
181#4343—22no—
182#4343—41no—
183Q8×D11—22no—
184Q8×D11—41no—
185#4341—22no—
186#4341—41no—
187#4341—42no—
188#4341—42no—
189D4×D11—22no—
190D4×D11—41no—
191D4×D11—42no—
192D4×D11—42no—
193#4339—21no—
194#4339—21no—
195#4339—42no—
196#4339—42no—
197#4339#4112yes—
198#4339#4112yes—
199C2×D44—21no—
200C2×D44C22×C411yescharacteristic
201C2×C4×D11—21no—
202C2×C4×D11—21no—
203C2×C4×D11—21no—
204C2×C4×D11—21no—
205C2×C4×D11—21no—
206C2×C4×D11—21no—
207C2×C4×D11—21no—
208C2×C4×D11—21no—
209C2×C4×D11—21no—
210C2×C4×D11—42no—
211C2×C4×D11—42no—
212C2×C4×D11C22×C411yescharacteristic
213C2×C4×D11C22×C411yescharacteristic
214C2×C4×D11C2×D411yescharacteristic
215C2×C4×D11C2×D411yescharacteristic
216C2×Dic22—21no—
217C2×Dic22C22×C411yescharacteristic
218C11×M16—21no—
219C11×M16—21no—
220C11×M16—21no—
221C11×M16—21no—
222C2×C8×C11—21no—
223C2×C8×C11—21no—
224C2×C8×C11—21no—
225C2×C8×C11—21no—
226C2×C8×C11—21no—
227C2×C8×C11—21no—
228C2×C8×C11C22×C411yescharacteristic
229C2×C8×C11C22×C411yescharacteristic
230C2×C8×C11C2×D411yescharacteristic
231C2×C8×C11C2×D411yescharacteristic
232C11×C4⋊C4C22×C411yescharacteristic
233C11×C4⋊C4C22×C411yescharacteristic
234C11×C22⋊C4—21no—
235C42×C11—21no—
236C42×C11—21no—
237C42×C11—21no—
238C22⋊Dic11—21no—
239(C2×D11)⋊C4—24no—
240(C2×D11)⋊C4—21no—
241(C2×D11)⋊C4—21no—
242C4⋊Dic11C22×C411yescharacteristic
243C4⋊Dic11C22×C411yescharacteristic
244Dic11⋊C4—21no—
245Dic11⋊C4—21no—
246C4×Dic11—21no—
247C4×Dic11—21no—
248C4×Dic11—21no—
249C4×Dic11—21no—
250C4×Dic11—21no—
251#4318—21no—
252#4318—21no—
253#4318—21no—
254#4318—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8—21no—
261C2×C11⋊C8C22×C411yescharacteristic
262C2×C11⋊C8C22×C411yescharacteristic
263C2×C11⋊C8C2×D411yescharacteristic
264C2×C11⋊C8C2×D411yescharacteristic
265#4313—42no—
266#4313—42no—
267C8×D11—41no—
268C8×D11—41no—
269C8×D11—41no—
270C8×D11—41no—
271C8×D11—42no—
272C8×D11—42no—
273#2924—111no—
274C2×#416—111no—
275#2880—111no—
276#1937—111no—
277#1937—111no—
278#1929—111no—
279#1929D1111yescharacteristic, complemented
280#1866—111no—
281#1866—111no—
282#1826—111no—
283#1810—111no—
284#1789—111no—
285#1764—111no—
286#1764—111no—
287C8×C22⋊C4—111no—
288C23×C11—21no—
289C23×C11C2×#4111yescharacteristic
290C22×D11—21no—
291C22×D11—21no—
292C22×D11—21no—
293C22×D11—22no—
294C22×D11—41no—
295C22×D11—42no—
296C22×D11—42no—
297C22×D11—81no—
298C22×D11C4×D411yescharacteristic
299C22×D11C4×D411yescharacteristic
300Q8×C11—21no—
301Q8×C11—21no—
302D4×C11—21no—
303D4×C11—21no—
304D4×C11—41no—
305D4×C11—41no—
306C2×C4×C11—22no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11C23×C411yescharacteristic
315C2×C4×C11C22×D411yescharacteristic
316C2×C4×C11C2×#4111yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11H(5,𝔽2)11yescharacteristic
319C2×C4×C11H(5,𝔽2)11yescharacteristic
320C22⋊D11—22no—
321C22⋊D11—22no—
322C22⋊D11—42no—
323C22⋊D11—42no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—21no—
327C2×Dic11—22no—
328C2×Dic11—21no—
329C2×Dic11—21no—
330C2×Dic11—42no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11C4×D411yescharacteristic
334C2×Dic11C4×D411yescharacteristic
335D44—21no—
336D44—42no—
337D44#11712yes—
338C4×D11—21no—
339C4×D11—21no—
340C4×D11—21no—
341C4×D11—21no—
342C4×D11—22no—
343C4×D11—22no—
344C4×D11—21no—
345C4×D11—21no—
346C4×D11—21no—
347C4×D11—21no—
348C4×D11—42no—
349C4×D11—42no—
350C4×D11—42no—
351C4×D11—81no—
352Dic22—21no—
353Dic22—42no—
354Dic22#11712yes—
355C8×C11—21no—
356C8×C11—21no—
357C8×C11—21no—
358C8×C11—21no—
359C8×C11—41no—
360C8×C11—41no—
361C11⋊C8—21no—
362C11⋊C8—21no—
363C11⋊C8—21no—
364C11⋊C8—21no—
365C11⋊C8—41no—
366C11⋊C8—41no—
367C22×#41—111no—
368C2×#131—111no—
369C2×#131—111no—
370C23×C8—111no—
371C2×#117—111no—
372#433—221no—
373#433—221no—
374#432—221no—
375#431—221no—
376C2×#108—111no—
377C2×#108C2×D1111yescharacteristic, complemented
378#424—111no—
379#424—111no—
380C2×#104—111no—
381C2×#104—111no—
382C2×#104—111no—
383C2×#104C2×D1111yescharacteristic
384#416—111no—
385#416—111no—
386#416—111no—
387#416—111no—
388#416—111no—
389#416—111no—
390#416—111no—
391#416C2×D1111yescharacteristic
392C2×#103—111no—
393C2×#103—111no—
394C2×#102—111no—
395C2×#102—111no—
396#408—111no—
397#408—221no—
398#408—221no—
399#408C2×D1111yescharacteristic
400#407—111no—
401#407—111no—
402#407—221no—
403C2×C22⋊C8—111no—
404C2×C22⋊C8—221no—
405#405—111no—
406#405C2×D1111yescharacteristic, complemented
407C2×C4×C8—111no—
408C2×C4×C8—111no—
409C4×C22⋊C4—111no—
410#341—111no—
411#341—111no—
412#339—111no—
413#339—111no—
414#339—111no—
415#339C2×D1111yescharacteristic, complemented
416#336—111no—
417#336C2×D1111yescharacteristic, complemented
418C22×C11—21no—
419C22×C11—21no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—41no—
423C22×C11C2×C4×D411yescharacteristic
424C22×C11#55111yescharacteristic
425C22×C11#55111yescharacteristic
426C2×D11—21no—
427C2×D11—21no—
428C2×D11—21no—
429C2×D11—22no—
430C2×D11—21no—
431C2×D11—21no—
432C2×D11—42no—
433C2×D11—42no—
434C2×D11—41no—
435C2×D11—41no—
436C2×D11—84no—
437C2×D11#44312yes—
438C4×C11—42no—
439C4×C11—41no—
440C4×C11—41no—
441C4×C11—41no—
442C4×C11C2×#11711yescharacteristic
443C4×C11#51811yescharacteristic
444C4×C11#54611yescharacteristic
445C4×C11#54611yescharacteristic
446Dic11—22no—
447Dic11—21no—
448Dic11—21no—
449Dic11—42no—
450Dic11—41no—
451Dic11—41no—
452C2×#41—111no—
453C2×#41—111no—
454C2×#41—111no—
455C2×#41—221no—
456C2×#41—221no—
457C2×#41—222no—
458C2×#41—222no—
459C2×#41—441no—
460C2×#41—441no—
461C2×#41C22×D1111yescharacteristic
462C22×Q8—111no—
463C22×D4—111no—
464C22×D4—221no—
465C23×C4—111no—
466C23×C4—221no—
467#131—222no—
468#131—222no—
469#131—441no—
470#131—441no—
471C2×M16—111no—
472C2×M16—111no—
473C2×M16—221no—
474C2×M16—221no—
475C2×M16C22×D1111yescharacteristic
476C2×M16C22×D1111yescharacteristic
477C22×C8—111no—
478C22×C8—111no—
479C22×C8—111no—
480C22×C8—111no—
481C22×C8—111no—
482C22×C8—111no—
483C22×C8—221no—
484C22×C8—221no—
485C22×C8—441no—
486C22×C8—441no—
487C22×C8C22×D1111yescharacteristic
488C22×C8C22×D1111yescharacteristic
489#117—111no—
490#117—111no—
491#117—111no—
492#117—221no—
493#117—221no—
494#117C22×D1111yescharacteristic
495C2×C4⋊C4—111no—
496C2×C4⋊C4—111no—
497C2×C22⋊C4—221no—
498C2×C22⋊C4—221no—
499C2×C42—111no—
500C2×C42—221no—
501C2×C42C22×D1111yescharacteristic
502#108—41no—
503#108—441no—
504C4⋊C8—221no—
505C4⋊C8—221no—
506C4⋊C8—221no—
507C4⋊C8—221no—
508#104—41no—
509#104—222no—
510#104—222no—
511#104—441no—
512#103—111no—
513#103—111no—
514#103—111no—
515#103—111no—
516#103—111no—
517#103—111no—
518#103C4×D1111yescharacteristic
519#103C4×D1111yescharacteristic
520#102—111no—
521#102—111no—
522#102—111no—
523#102—111no—
524#102—111no—
525#102—111no—
526#102C4×D1111yescharacteristic
527#102C4×D1111yescharacteristic
528C22⋊C8—21no—
529C22⋊C8—21no—
530C22⋊C8—111no—
531C22⋊C8—111no—
532C22⋊C8—111no—
533C22⋊C8—111no—
534C22⋊C8—221no—
535C22⋊C8—221no—
536C22⋊C8—221no—
537C22⋊C8—221no—
538C22⋊C8—221no—
539C22⋊C8—221no—
540#97—21no—
541#97—221no—
542C4×C8—21no—
543C4×C8—221no—
544C4×C8—441no—
545C4×C8—441no—
546#95—221no—
547C2×C11—21no—
548C2×C11—21no—
549C2×C11—81no—
550C2×C11#234211yescharacteristic
551C2×C11C2×#44311yescharacteristic
552C2×C11#295711yescharacteristic
553D11—22no—
554D11—41no—
555D11—42no—
556C24—111no—
557C24—221no—
558#41—21no—
559#41—21no—
560#41—21no—
561#41—21no—
562#41—112no—
563#41—112no—
564#41—221no—
565#41—221no—
566#41—222no—
567#41—222no—
568#41—442no—
569#41—442no—
570#41—441no—
571#41—442no—
572#41—442no—
573#41—441no—
574C2×Q8—111no—
575C2×Q8—221no—
576C2×Q8—222no—
577C2×Q8—441no—
578C2×Q8C2×C4×D1111yescharacteristic
579C2×D4—21no—
580C2×D4—111no—
581C2×D4—221no—
582C2×D4—221no—
583C2×D4—222no—
584C2×D4—221no—
585C2×D4—221no—
586C2×D4—441no—
587C2×D4—442no—
588C2×D4—442no—
589C2×D4C2×C4×D1111yescharacteristic
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—111no—
593C22×C4—111no—
594C22×C4—111no—
595C22×C4—111no—
596C22×C4—111no—
597C22×C4—221no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—221no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4—442no—
609C22×C4—442no—
610C22×C4C23×D1111yescharacteristic
611M16—21no—
612M16—21no—
613M16—21no—
614M16—21no—
615M16—221no—
616M16—221no—
617M16—221no—
618M16—221no—
619M16—442no—
620M16—442no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—111no—
628C2×C8—111no—
629C2×C8—111no—
630C2×C8—111no—
631C2×C8—221no—
632C2×C8—221no—
633C2×C8—221no—
634C2×C8—221no—
635C2×C8—221no—
636C2×C8—221no—
637C2×C8—441no—
638C2×C8—441no—
639C2×C8—441no—
640C2×C8—441no—
641C2×C8—442no—
642C2×C8—442no—
643C2×C8C2×C4×D1111yescharacteristic
644C2×C8C2×C4×D1111yescharacteristic
645C2×C8D4×D1111yescharacteristic
646C2×C8D4×D1111yescharacteristic
647C4⋊C4—111no—
648C4⋊C4—111no—
649C4⋊C4—221no—
650C4⋊C4—221no—
651C4⋊C4C2×C4×D1111yescharacteristic
652C4⋊C4C2×C4×D1111yescharacteristic
653C22⋊C4—21no—
654C22⋊C4—221no—
655C22⋊C4—221no—
656C22⋊C4—224no—
657C22⋊C4—221no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—221no—
662C42—221no—
663C42—221no—
664C42—221no—
665C42—221no—
666C11#2258711yescharacteristic, complemented, Sylow
667C23—21no—
668C23—111no—
669C23—111no—
670C23—222no—
671C23—221no—
672C23—221no—
673C23—221no—
674C23—441no—
675C23—442no—
676C23—442no—
677C23—881no—
678C23#41×D1111yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—112no—
682Q8—221no—
683Q8—442no—
684D4—21no—
685D4—21no—
686D4—41no—
687D4—41no—
688D4—112no—
689D4—222no—
690D4—222no—
691D4—221no—
692D4—442no—
693D4—442no—
694D4—442no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—111no—
704C2×C4—111no—
705C2×C4—221no—
706C2×C4—221no—
707C2×C4—221no—
708C2×C4—221no—
709C2×C4—221no—
710C2×C4—221no—
711C2×C4—221no—
712C2×C4—222no—
713C2×C4—221no—
714C2×C4—221no—
715C2×C4—222no—
716C2×C4—221no—
717C2×C4—221no—
718C2×C4—222no—
719C2×C4—221no—
720C2×C4—221no—
721C2×C4—442no—
722C2×C4—442no—
723C2×C4—442no—
724C2×C4—442no—
725C2×C4—441no—
726C2×C4—441no—
727C2×C4—881no—
728C2×C4C22×C4×D1111yescharacteristic
729C2×C4C2×D4×D1111yescharacteristic
730C2×C4#6703711yescharacteristic
731C2×C4#41×D1111yescharacteristic
732C2×C4#41×D1111yescharacteristic
733C2×C4#6704211yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—41no—
739C8—41no—
740C8—221no—
741C8—221no—
742C8—221no—
743C8—221no—
744C8—441no—
745C8—441no—
746C22—21no—
747C22—21no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—112no—
752C22—221no—
753C22—221no—
754C22—221no—
755C22—221no—
756C22—222no—
757C22—221no—
758C22—442no—
759C22—442no—
760C22—441no—
761C22—441no—
762C22—884no—
763C22C4×D4×D1111yescharacteristic
764C22#1062321011yescharacteristic
765C22#1062323611yescharacteristic
766C4—42no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—221no—
771C4—221no—
772C4—222no—
773C4—442no—
774C4—441no—
775C4—441no—
776C4D11×#11711yescharacteristic
777C4#1062307611yescharacteristic
778C4#1062314311yescharacteristic
779C4#1062318511yescharacteristic
780C2—21no—
781C2—21no—
782C2—81no—
783C2—222no—
784C2—441no—
785C2—442no—
786C2#1307146011yescharacteristic
787C2D11×#44311yescharacteristic
788C2#1307753011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1929C2
socleC22×C11C2×C4×D4
prime radicalC2×#41×D11C22
cosocleC22×C4×C11C24
hypercenter#1929D11
hypocenterC11#22587
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1929

Complements

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

NH ≅ G/Ntype
1. #13077271C2semidirect
4. #13069323C2semidirect
5. #13069317C2semidirect
6. #13069266C2semidirect
7. #13068894C2semidirect
8. #13068888C2semidirect
9. #13068714C2semidirect
10. #13068651C2semidirect
12. #13068455C2semidirect
13. #13068450C2semidirect
14. #13068386C2semidirect
15. C11×#1929C2semidirect
21. C2×C11×#108C22semidirect
25. C11×#405C22semidirect
32. #10622732C22semidirect
35. C2×#66883C22semidirect
36. #10622715C22semidirect
37. C2×C8×Dic11C22semidirect
39. #10622610C22semidirect
42. C2×C4×C11⋊C8C22semidirect
43. #10622417C4semidirect
44. #10622417C4semidirect
45. D11×#103C4semidirect
46. D11×#103C4semidirect
47. #10622385C4semidirect
48. #10622385C4semidirect
49. D11×#102C4semidirect
50. D11×#102C4semidirect
59. C11×#339C22semidirect
60. C11×#336C22semidirect
61. #10622196C22semidirect
62. #10622196C22semidirect
63. #10622193C22semidirect
64. #10622188C22semidirect
65. #10622170C22semidirect
66. #10622161C22semidirect
279. #1929D11semidirect
377. C2×#108C2×D11semidirect
406. #405C2×D11semidirect
415. #339C2×D11semidirect
417. #336C2×D11semidirect
666. C11#22587semidirect

Maximal subgroups

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

subgroupindex
#130772712
D11×#4162
#130770642
#130693232
#130693172
#130692662
#130688942
#130688882
#130687142
#130686512
#130685582
#130684552
#130684502
#130683862
C11×#19292
#2258711