Finite Group Databasebeta

← #14764961

Subgroups — #14764961

Order 2816.

1096 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622851C211yesmaximal, characteristic
2#13071122C211yesmaximal, characteristic, complemented
3#13071107C211yesmaximal, characteristic, complemented
4#13069479C211yesmaximal, characteristic, complemented
5#13069467C211yesmaximal, characteristic, complemented
6#13069296C211yesmaximal, characteristic, complemented
7#13069289C211yesmaximal, characteristic, complemented
8#13069260C211yesmaximal, characteristic, complemented
9#13069246C211yesmaximal, characteristic, complemented
10#13068961C211yesmaximal, characteristic, complemented
11#13068947C211yesmaximal, characteristic, complemented
12#13068936C211yesmaximal, characteristic, complemented
13#13068813C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic11C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×#4325C2211yescharacteristic
18C22×#4323C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C2×#66946C2211yescharacteristic
23C2×(C22⋊D11)⋊C4—21no—
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29C11×#380C2211yescharacteristic
30#10622851C418yescomplemented
31#10622843C2211yescharacteristic
32#10622843C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34#10622834C2211yescharacteristic
35#10622834C2211yescharacteristic
36#10622833—21no—
37#10622833—21no—
38C2×#66896C2211yescharacteristic
39C4×C22⋊Dic11—21no—
40C4×C22⋊Dic11—21no—
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×#66885C2211yescharacteristic
43C2×#66885C2211yescharacteristic
44C2×C8×Dic11C2211yescharacteristic
45C2×C8×Dic11C2211yescharacteristic
46#10622601C2211yescharacteristic
47C4⋊C4×Dic11C2211yescharacteristic
48#10622586C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×#66871C2211yescharacteristic
51#10622571—21no—
52#10622282—21no—
53#10622279—21no—
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C2×C11×#41—22no—
61C2×C11×#41—41no—
62C2×C11×#41—41no—
63C2×C11×#41—41no—
64C2×C11×#41—41no—
65C2×C11×#41C2×C414yescomplemented
66C22×Q8×C11C2311yescharacteristic
67C22×D4×C11—21no—
68C22×D4×C11C2311yescharacteristic
69C23×C4×C11—21no—
70C23×C4×C11C2311yescharacteristic
71C22×C22⋊D11—21no—
72C23×Dic11D411yescharacteristic
73C23×Dic11D411yescharacteristic
74C22×D44C2311yescharacteristic
75C22×C4×D11—21no—
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×#4325—41no—
87C2×#4325—41no—
88C2×#4325C2×C414yescomplemented
89C2×#4323—41no—
90C2×#4323—41no—
91C2×#4323C2×C414yescomplemented
92#66983—22no—
93#66983C2×C414yes—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98#66979—41no—
99#66979—41no—
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×Dic11⋊C4—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—41no—
107C2×C4×Dic11—41no—
108C2×C4×Dic11D411yescharacteristic
109C2×C4×Dic11D411yescharacteristic
110C2×C4×Dic11C2311yescharacteristic
111C2×C4×Dic11C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114#66946—41no—
115#66946—41no—
116(C22⋊D11)⋊C4—44no—
117C11×#103—41no—
118C11×#103—41no—
119C11×#102—41no—
120C11×#102—41no—
121C11×C22⋊C8—22no—
122C11×#95—21no—
123#66899C2×C414yescomplemented
124#66896C2×C414yescomplemented
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C22⋊(C11⋊C8)C2×C414yescomplemented
132#66885—41no—
133#66885—41no—
134C8×Dic11—41no—
135C8×Dic11—41no—
136#66872—41no—
137#66871—41no—
138#22045—111nomaximal, Sylow
139C24×C11—21no—
140C24×C11C2×D411yescharacteristic
141C23×D11—21no—
142C11×#41—44no—
143C11×#41—44no—
144C11×#41—44no—
145C11×#41—44no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11C22×C412yes—
152C2×D4×C11—24no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—42no—
159C2×D4×C11—42no—
160C2×D4×C11C22×C412yes—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—24no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—42no—
170C22×C4×C11—42no—
171C22×C4×C11C22×C412yes—
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11#4112yes—
174C22×C4×C11C2411yescharacteristic
175C2×C22⋊D11—24no—
176C2×C22⋊D11—42no—
177C2×C22⋊D11—42no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—41no—
185C22×Dic11—41no—
186C22×Dic11—41no—
187C22×Dic11C2×D411yescharacteristic
188C22×Dic11C2×D411yescharacteristic
189C22×Dic11C2×D411yescharacteristic
190C22×Dic11C2×D411yescharacteristic
191C2×D44—21no—
192C2×D44—21no—
193C2×D44—21no—
194C2×D44—21no—
195C2×D44—21no—
196C2×D44C22×C412yes—
197C2×C4×D11—42no—
198C2×C4×D11—42no—
199C2×C4×D11—42no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C22⋊C4—42no—
211C22⋊Dic11—42no—
212C22⋊Dic11—42no—
213C22⋊Dic11—42no—
214C22⋊Dic11—42no—
215C22⋊Dic11—42no—
216#4325—44no—
217#4323—44no—
218(C2×D11)⋊C4—24no—
219(C2×D11)⋊C4—42no—
220(C2×D11)⋊C4—42no—
221(C2×D11)⋊C4—42no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11C22×C412yes—
228Dic11⋊C4—42no—
229C4×Dic11—21no—
230C4×Dic11—21no—
231C4×Dic11—21no—
232C4×Dic11—21no—
233C4×Dic11—41no—
234C4×Dic11—41no—
235C4×Dic11—42no—
236C4×Dic11—42no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8C22×C412yes—
242C2×C11⋊C8C22×C412yes—
243C2×#449—111no—
244C4×#121—111no—
245#2297—111no—
246#1970—111no—
247#1968—111no—
248#1934—111no—
249#1933—111no—
250#1928—111no—
251#1926—111no—
252#1879—111no—
253#1877—111no—
254#1875—111no—
255#1854—111no—
256#1788D1111yescharacteristic, complemented
257C4×C22⋊C8—111no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—22no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11C4×D412yes—
272C23×C11C22×D411yescharacteristic
273C22×D11—22no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—41no—
279C22×D11—41no—
280Q8×C11—22no—
281Q8×C11—22no—
282Q8×C11—41no—
283Q8×C11—41no—
284D4×C11—22no—
285D4×C11—22no—
286D4×C11—48no—
287D4×C11—41no—
288D4×C11—41no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—48no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11C4×D412yes—
306C2×C4×C11C23×C411yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11H(5,𝔽2)11yescharacteristic
309C2×C4×C11H(5,𝔽2)11yescharacteristic
310C2×C4×C11H(5,𝔽2)11yescharacteristic
311C2×C4×C11H(5,𝔽2)11yescharacteristic
312C22⋊D11—48no—
313C2×Dic11—21no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—22no—
320C2×Dic11—21no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—44no—
324C2×Dic11—44no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11#13512yes—
334C2×Dic11#13512yes—
335C2×Dic11AGL(1,ℤ/8)12yes—
336D44—22no—
337D44—22no—
338D44—41no—
339D44—41no—
340C4×D11—84no—
341C8×C11—41no—
342C8×C11—41no—
343C11⋊C8—22no—
344C11⋊C8—22no—
345C22×#41C2×D1111yescharacteristic
346C22×SD16—111no—
347C22×D8—111no—
348C2×#121—111no—
349C2×C4×D4—111no—
350C2×C4×D4—221no—
351C2×#117—111no—
352C22×C42—111no—
353#449—118no—
354C2×#107—111no—
355C2×#106—111no—
356C2×#103—111no—
357C2×#103C2×D1111yescharacteristic
358C2×#103C2×D1111yescharacteristic
359C2×#102—111no—
360C2×#102—111no—
361C2×#102—111no—
362C2×#102C2×D1111yescharacteristic
363C2×#102C2×D1111yescharacteristic
364C2×C22⋊C8—111no—
365C2×C22⋊C8C2×D1111yescharacteristic
366C2×C4×C8—111no—
367C2×C4×C8—111no—
368#391—111no—
369#391—111no—
370#390—111no—
371#390—111no—
372#390—111no—
373#389—111no—
374#388—221no—
375#386—221no—
376#386—221no—
377#386—221no—
378#380C2×D1111yescharacteristic
379C4×C4⋊C4—111no—
380C4×C22⋊C4—221no—
381C4×C22⋊C4—221no—
382C4×C22⋊C4—221no—
383#340—111no—
384#340—111no—
385#340—111no—
386#340—111no—
387#336—111no—
388#336—111no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—42no—
397C22×C11—42no—
398C22×C11—42no—
399C22×C11—81no—
400C22×C11—81no—
401C22×C11—81no—
402C22×C11—81no—
403C22×C11C2×C4×D411yescharacteristic
404C22×C11#53411yescharacteristic
405C22×C11#53511yescharacteristic
406C22×C11C2×#13511yescharacteristic
407C22×C11C2×#13511yescharacteristic
408C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C11#57511yescharacteristic
410C2×D11—42no—
411C2×D11—42no—
412C2×D11—42no—
413C2×D11—81no—
414C2×D11—81no—
415C2×D11—81no—
416C2×D11—81no—
417C4×C11—22no—
418C4×C11—42no—
419C4×C11—81no—
420C4×C11—81no—
421C4×C11#51811yescharacteristic
422C4×C11#51811yescharacteristic
423C4×C11#53811yescharacteristic
424C4×C11#53811yescharacteristic
425Dic11—22no—
426Dic11—22no—
427Dic11—22no—
428Dic11—41no—
429Dic11—42no—
430Dic11—81no—
431Dic11—81no—
432C2×#41—22no—
433C2×#41—41no—
434C2×#41—41no—
435C2×#41—41no—
436C2×#41—41no—
437C2×#41C4×D1114yescomplemented
438C22×Q8C22×D1111yescharacteristic
439C22×D4—21no—
440C22×D4—111no—
441C22×D4—221no—
442C22×D4C22×D1111yescharacteristic
443C23×C4—21no—
444C23×C4—111no—
445C23×C4—111no—
446C23×C4—221no—
447C23×C4C22×D1111yescharacteristic
448C2×SD16—114no—
449C2×SD16—441no—
450C2×SD16—441no—
451C2×D8—114no—
452C2×D8—441no—
453C2×D8—441no—
454C22×C8—111no—
455C22×C8—111no—
456C22×C8C22×D1111yescharacteristic
457C22×C8C22×D1111yescharacteristic
458#121—114no—
459#121—222no—
460C4×D4—441no—
461C4×D4—441no—
462C4×D4—444no—
463#117—441no—
464#117—441no—
465C2×C4⋊C4—111no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—111no—
468C2×C4⋊C4—221no—
469C2×C4⋊C4C22×D1111yescharacteristic
470C2×C4⋊C4C22×D1111yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—221no—
473C2×C22⋊C4—221no—
474C2×C22⋊C4—221no—
475C2×C22⋊C4—221no—
476C2×C22⋊C4—221no—
477C2×C22⋊C4—221no—
478C2×C22⋊C4—221no—
479C2×C22⋊C4—221no—
480C2×C22⋊C4—221no—
481C2×C42—111no—
482C2×C42—111no—
483C2×C42—111no—
484C2×C42—111no—
485C2×C42—221no—
486C2×C42—221no—
487C2×C42—441no—
488C2×C42—441no—
489#107—441no—
490#106—441no—
491#103—41no—
492#103—41no—
493#103—114no—
494#102—41no—
495#102—41no—
496#102—114no—
497#102—441no—
498#102—441no—
499C22⋊C8—22no—
500C22⋊C8—114no—
501C4×C8—441no—
502C4×C8—441no—
503#95—21no—
504#95—221no—
505#95—221no—
506#95—221no—
507#95—221no—
508#95—221no—
509#95—221no—
510C2×C11—42no—
511C2×C11—82no—
512C2×C11#232111yescharacteristic
513C2×C11C4×#13511yescharacteristic
514C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
515C2×C11#318811yescharacteristic
516C2×C11#319111yescharacteristic
517C2×C11#320711yescharacteristic
518C2×C11#321211yescharacteristic
519D11—82no—
520C24—21no—
521C24—221no—
522C24D4×D1111yescharacteristic
523#41—44no—
524#41—44no—
525#41—44no—
526#41—44no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8C2×C4×D1112yes—
533C2×D4—24no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—112no—
542C2×D4—224no—
543C2×D4—221no—
544C2×D4—221no—
545C2×D4—221no—
546C2×D4—221no—
547C2×D4—221no—
548C2×D4—442no—
549C2×D4—442no—
550C2×D4C2×C4×D1112yes—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—24no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—111no—
562C22×C4—111no—
563C22×C4—111no—
564C22×C4—111no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—442no—
572C22×C4—442no—
573C22×C4—442no—
574C22×C4—441no—
575C22×C4—441no—
576C22×C4—441no—
577C22×C4C2×C4×D1112yes—
578C22×C4D4×D1111yescharacteristic
579C22×C4#434112yes—
580C22×C4C23×D1111yescharacteristic
581SD16—444no—
582D8—444no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—112no—
590C2×C8—112no—
591C2×C8—221no—
592C2×C8—221no—
593C2×C8—221no—
594C2×C8—221no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—112no—
600C4⋊C4—221no—
601C4⋊C4—221no—
602C4⋊C4—221no—
603C4⋊C4—221no—
604C4⋊C4—221no—
605C4⋊C4—442no—
606C22⋊C4—42no—
607C22⋊C4—224no—
608C22⋊C4—442no—
609C22⋊C4—442no—
610C22⋊C4—442no—
611C22⋊C4—442no—
612C22⋊C4—442no—
613C22⋊C4—442no—
614C22⋊C4—442no—
615C22⋊C4—442no—
616C42—221no—
617C42—221no—
618C42—221no—
619C42—221no—
620C42—441no—
621C42—441no—
622C42—442no—
623C42—442no—
624C11#2204511yescharacteristic, complemented, Sylow
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—22no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—222no—
639C23—441no—
640C23—441no—
641C23—441no—
642C23—441no—
643C23—441no—
644C23—441no—
645C23(C22⋊D11)⋊C412yes—
646C23C2×D4×D1111yescharacteristic
647Q8—22no—
648Q8—22no—
649Q8—41no—
650Q8—41no—
651D4—22no—
652D4—22no—
653D4—48no—
654D4—41no—
655D4—41no—
656D4—222no—
657D4—222no—
658D4—448no—
659D4—441no—
660D4—441no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—48no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—112no—
678C2×C4—112no—
679C2×C4—112no—
680C2×C4—221no—
681C2×C4—221no—
682C2×C4—221no—
683C2×C4—221no—
684C2×C4—221no—
685C2×C4—221no—
686C2×C4—222no—
687C2×C4—221no—
688C2×C4—221no—
689C2×C4—221no—
690C2×C4—444no—
691C2×C4—444no—
692C2×C4—441no—
693C2×C4—441no—
694C2×C4—441no—
695C2×C4—441no—
696C2×C4—441no—
697C2×C4—441no—
698C2×C4—441no—
699C2×C4—441no—
700C2×C4—884no—
701C2×C4(C22⋊D11)⋊C412yes—
702C2×C4C22×C4×D1111yescharacteristic
703C2×C4C2×#434111yescharacteristic
704C2×C4#6703711yescharacteristic
705C2×C4#6703711yescharacteristic
706C2×C4#6703711yescharacteristic
707C2×C4#6703711yescharacteristic
708C8—41no—
709C8—41no—
710C8—222no—
711C8—222no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—442no—
727C22—442no—
728C22—442no—
729C22—881no—
730C22—881no—
731C22—881no—
732C22—881no—
733C22C2×(C22⋊D11)⋊C411yescharacteristic
734C22#1062312011yescharacteristic
735C22#1062312311yescharacteristic
736C22D11×#13511yescharacteristic
737C22D11×#13511yescharacteristic
738C22D11×AGL(1,ℤ/8)11yescharacteristic
739C22#1062330811yescharacteristic
740C4—22no—
741C4—42no—
742C4—81no—
743C4—81no—
744C4—222no—
745C4—222no—
746C4—222no—
747C4—441no—
748C4—442no—
749C4—881no—
750C4—881no—
751C4#1062301711yescharacteristic
752C4#1062301711yescharacteristic
753C4#1062312411yescharacteristic
754C4#1062312411yescharacteristic
755C2—42no—
756C2—82no—
757C2—882no—
758C2#1307127111yescharacteristic
759C2#1307738411yescharacteristic
760C2#1307742911yescharacteristic
761C2#1307937911yescharacteristic
762C2#1307940811yescharacteristic
763C2#1307954711yescharacteristic
764C2#1307959511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1788C2
socleC23×C11C22×D4
prime radicalC2×#10622851C2
cosocleC22×C4×C11C24
hypercenter#1788D11
hypocenterC11#22045
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. #13071122C2semidirect
3. #13071107C2semidirect
4. #13069479C2semidirect
5. #13069467C2semidirect
6. #13069296C2semidirect
7. #13069289C2semidirect
8. #13069260C2semidirect
9. #13069246C2semidirect
10. #13068961C2semidirect
11. #13068947C2semidirect
12. #13068936C2semidirect
13. #13068813C2semidirect
14. C22⋊C8×Dic11C2semidirect
15. C11×#1788C2semidirect
30. #10622851C4semidirect
65. C2×C11×#41C2×C4semidirect
88. C2×#4325C2×C4semidirect
91. C2×#4323C2×C4semidirect
123. #66899C2×C4semidirect
124. #66896C2×C4semidirect
131. C22⋊(C11⋊C8)C2×C4semidirect
256. #1788D11semidirect
437. C2×#41C4×D11semidirect
624. C11#22045semidirect

Maximal subgroups

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

subgroupindex
C2×#106228512
#130711222
#130711072
#130694792
#130694672
#130692962
#130692892
#130692602
#130692462
#130689612
#130689472
#130689362
#130688132
C22⋊C8×Dic112
C11×#17882
#2204511