Finite Group Databasebeta

← #14764966

Subgroups — #14764966

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×#10622771C211yesmaximal, characteristic
2#13071132C211yesmaximal, characteristic, complemented
3#13071103C211yesmaximal, characteristic, complemented
4#13069469C211yesmaximal, characteristic, complemented
5#13069302C211yesmaximal, characteristic, complemented
6#13069292C211yesmaximal, characteristic, complemented
7#13069256C211yesmaximal, characteristic, complemented
8#13069246C211yesmaximal, characteristic, complemented
9#13068966C211yesmaximal, characteristic, complemented
10#13068948C211yesmaximal, characteristic, complemented
11#13068935C211yesmaximal, characteristic, complemented
12#13068812C211yesmaximal, characteristic, complemented
13#13068553C211yesmaximal, characteristic, complemented
14C4×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
15C11×#1970C211yesmaximal, characteristic, complemented
16C22×#4341C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C2×#66991C2211yescharacteristic
19C2×D4×Dic11C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C2×#66945C2211yescharacteristic
22C2×(C22⋊D11)⋊C4—21no—
23C2×C42×D11C2211yescharacteristic
24C2×C11×#107C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28C11×#390C2211yescharacteristic
29C11×#390C2211yescharacteristic
30#10622834C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34#10622771C418yescomplemented
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39#10622600C2211yescharacteristic
40C4⋊C4×Dic11C2211yescharacteristic
41#10622587C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44#10622569—21no—
45#10622569—21no—
46#10622569—21no—
47#10622558—21no—
48C22⋊C4×Dic11—21no—
49C22⋊C4×Dic11—21no—
50C22⋊C4×Dic11—21no—
51#10622542C2211yescharacteristic
52#10622541C2211yescharacteristic
53C2×C4×C11⋊C8C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C22×C22⋊D11—21no—
64C23×Dic11—21no—
65C23×Dic11—21no—
66C2×#4341—22no—
67C2×#4341—41no—
68C2×#4341—41no—
69C2×#4341—41no—
70C2×#4341—41no—
71C2×#4341C2×C414yescomplemented
72C22×C4×D11D411yescharacteristic
73C22×C4×D11D411yescharacteristic
74C22×C4×D11C2311yescharacteristic
75C22×Dic22C2311yescharacteristic
76C2×C11×D8—41no—
77C2×C11×D8—41no—
78C2×C11×D8C2×C414yescomplemented
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C42×C11C2311yescharacteristic
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90C2×C22⋊Dic11—21no—
91C2×C22⋊Dic11—21no—
92#66991—22no—
93#66991C2×C414yes—
94D4×Dic11—41no—
95D4×Dic11—41no—
96C2×#4324—41no—
97C2×#4324—41no—
98C2×#4324C2×C414yescomplemented
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×Dic11⋊C4—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11D411yescharacteristic
108C2×C4×Dic11D411yescharacteristic
109C2×C4×Dic11C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112#66945—41no—
113#66945—41no—
114(C22⋊D11)⋊C4—44no—
115C42×D11—41no—
116C42×D11—41no—
117C11×#107—41no—
118C11×#102—41no—
119C11×#102—41no—
120C4×C8×C11—41no—
121#66896—41no—
122#66896—41no—
123#66896C2×C414yescomplemented
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131(C2×D11)⋊C8—22no—
132(C2×D11)⋊C8C2×C414yescomplemented
133#66880—41no—
134#66880C2×C414yescomplemented
135#66874—41no—
136#66872—41no—
137C4×C11⋊C8—41no—
138#22045—111nomaximal, Sylow
139C24×C11—21no—
140C24×C11—21no—
141C23×D11C2×D411yescharacteristic
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11C22×C412yes—
153C2×D4×C11C22×C412yes—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2411yescharacteristic
159C2×C22⋊D11—24no—
160C2×C22⋊D11—24no—
161C2×C22⋊D11—42no—
162C2×C22⋊D11—42no—
163C2×C22⋊D11—42no—
164C2×C22⋊D11—42no—
165C22×Dic11—24no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—42no—
171C22×Dic11—42no—
172C22×Dic11—42no—
173C22×Dic11—42no—
174C22×Dic11—42no—
175C22×Dic11C2×D411yescharacteristic
176C22×Dic11C2×D411yescharacteristic
177C22×Dic11C2×D411yescharacteristic
178#4341—44no—
179#4341—44no—
180#4341—44no—
181#4341—44no—
182C2×C4×D11—22no—
183C2×C4×D11—22no—
184C2×C4×D11—22no—
185C2×C4×D11—21no—
186C2×C4×D11—21no—
187C2×C4×D11—21no—
188C2×C4×D11—21no—
189C2×C4×D11—41no—
190C2×C4×D11—41no—
191C2×C4×D11—41no—
192C2×C4×D11C22×C412yes—
193C2×C4×D11#4112yes—
194C2×Dic22—21no—
195C2×Dic22—21no—
196C2×Dic22—21no—
197C2×Dic22—21no—
198C2×Dic22—21no—
199C2×Dic22C22×C412yes—
200C11×D8—44no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11C22×C412yes—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C22⋊C4—42no—
212C11×C22⋊C4—42no—
213C11×C22⋊C4—42no—
214C11×C22⋊C4—42no—
215C42×C11—21no—
216C42×C11—21no—
217C22⋊Dic11—24no—
218C22⋊Dic11—42no—
219C22⋊Dic11—42no—
220C22⋊Dic11—42no—
221#4324—44no—
222(C2×D11)⋊C4—42no—
223(C2×D11)⋊C4—42no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11C22×C412yes—
230Dic11⋊C4—42no—
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⋊C8—21no—
242C2×C11⋊C8C22×C412yes—
243C2×#449—111no—
244C4×#121—111no—
245#2297—111no—
246#1970D1111yescharacteristic, complemented
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#1788—111no—
257C4×C22⋊C8—111no—
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11C22×D411yescharacteristic
273C22×D11—21no—
274C22×D11—21no—
275C22×D11—21no—
276C22×D11—21no—
277C22×D11—21no—
278C22×D11—21no—
279C22×D11C4×D412yes—
280D4×C11—22no—
281D4×C11—22no—
282D4×C11—22no—
283D4×C11—22no—
284D4×C11—41no—
285D4×C11—41no—
286D4×C11—41no—
287D4×C11—41no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11#13512yes—
299C2×C4×C11AGL(1,ℤ/8)12yes—
300C2×C4×C11C23×C411yescharacteristic
301C2×C4×C11C2×#4111yescharacteristic
302C2×C4×C11H(5,𝔽2)11yescharacteristic
303C2×C4×C11H(5,𝔽2)11yescharacteristic
304C2×C4×C11H(5,𝔽2)11yescharacteristic
305C2×C4×C11H(5,𝔽2)11yescharacteristic
306C22⋊D11—48no—
307C22⋊D11—48no—
308C2×Dic11—21no—
309C2×Dic11—21no—
310C2×Dic11—21no—
311C2×Dic11—21no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—48no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—84no—
329C2×Dic11C4×D412yes—
330C2×Dic11#13512yes—
331C4×D11—22no—
332C4×D11—22no—
333C4×D11—22no—
334C4×D11—22no—
335C4×D11—44no—
336C4×D11—44no—
337Dic22—22no—
338Dic22—22no—
339Dic22—41no—
340Dic22—41no—
341C8×C11—22no—
342C8×C11—41no—
343C11⋊C8—22no—
344C11⋊C8—41no—
345C22×#41—111no—
346C22×SD16—111no—
347C22×D8C2×D1111yescharacteristic
348C2×#121—111no—
349C2×C4×D4—111no—
350C2×C4×D4—221no—
351C2×#117—111no—
352C22×C42—111no—
353#449—118no—
354C2×#107C2×D1111yescharacteristic
355C2×#106—111no—
356C2×#103—111no—
357C2×#103—111no—
358C2×#103—111no—
359C2×#102—111no—
360C2×#102—111no—
361C2×#102—111no—
362C2×#102C2×D1111yescharacteristic
363C2×#102C2×D1111yescharacteristic
364C2×C22⋊C8—111no—
365C2×C22⋊C8—111no—
366C2×C4×C8—111no—
367C2×C4×C8C2×D1111yescharacteristic
368#391—111no—
369#391—111no—
370#390—111no—
371#390C2×D1111yescharacteristic
372#390C2×D1111yescharacteristic
373#389—111no—
374#388—221no—
375#386—221no—
376#386—221no—
377#386—221no—
378#380—111no—
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—42no—
390C22×C11—42no—
391C22×C11—42no—
392C22×C11—42no—
393C22×C11—42no—
394C22×C11—42no—
395C22×C11—81no—
396C22×C11—81no—
397C22×C11—81no—
398C22×C11—81no—
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—22no—
411C2×D11—22no—
412C2×D11—22no—
413C2×D11—41no—
414C2×D11—41no—
415C2×D11—41no—
416C2×D11—41no—
417C4×C11—22no—
418C4×C11—22no—
419C4×C11—81no—
420C4×C11—81no—
421C4×C11#51811yescharacteristic
422C4×C11#51811yescharacteristic
423C4×C11#53811yescharacteristic
424C4×C11#53811yescharacteristic
425Dic11—22no—
426Dic11—22no—
427Dic11—42no—
428Dic11—41no—
429Dic11—42no—
430Dic11—81no—
431Dic11—81no—
432C2×#41—114no—
433C2×#41—222no—
434C2×#41—441no—
435C2×#41—441no—
436C2×#41—441no—
437C2×#41—441no—
438C22×Q8—111no—
439C22×D4—221no—
440C22×D4—221no—
441C22×D4C22×D1111yescharacteristic
442C22×D4C22×D1111yescharacteristic
443C23×C4—111no—
444C23×C4—111no—
445C23×C4—111no—
446C23×C4—221no—
447C23×C4—221no—
448C2×SD16—114no—
449C2×SD16—441no—
450C2×SD16—441no—
451C2×D8—41no—
452C2×D8—41no—
453C2×D8C4×D1114yescomplemented
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—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
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—221no—
485C2×C42—221no—
486C2×C42—441no—
487C2×C42—441no—
488C2×C42C22×D1111yescharacteristic
489#107—41no—
490#106—441no—
491#103—114no—
492#103—441no—
493#103—441no—
494#102—41no—
495#102—41no—
496#102—114no—
497#102—441no—
498#102—441no—
499C22⋊C8—114no—
500C22⋊C8—222no—
501C4×C8—41no—
502C4×C8—441no—
503#95—221no—
504#95—221no—
505#95—221no—
506#95—221no—
507#95—221no—
508#95—221no—
509#95—221no—
510C2×C11—82no—
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—42no—
520C24—21no—
521C24—21no—
522C24—111no—
523#41—444no—
524#41—444no—
525#41—444no—
526#41—444no—
527C2×Q8—112no—
528C2×Q8—221no—
529C2×Q8—221no—
530C2×Q8—221no—
531C2×Q8—221no—
532C2×Q8—221no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—224no—
544C2×D4—224no—
545C2×D4—442no—
546C2×D4—442no—
547C2×D4—442no—
548C2×D4—442no—
549C2×D4C2×C4×D1112yes—
550C2×D4C2×C4×D1112yes—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—111no—
554C22×C4—111no—
555C22×C4—112no—
556C22×C4—112no—
557C22×C4—111no—
558C22×C4—222no—
559C22×C4—224no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—441no—
571C22×C4—441no—
572C22×C4—441no—
573C22×C4—442no—
574C22×C4—442no—
575C22×C4—442no—
576C22×C4—442no—
577C22×C4—442no—
578C22×C4D4×D1111yescharacteristic
579C22×C4D4×D1111yescharacteristic
580C22×C4C23×D1111yescharacteristic
581SD16—444no—
582D8—44no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—112no—
589C2×C8—221no—
590C2×C8—221no—
591C2×C8—221no—
592C2×C8—221no—
593C2×C8—221no—
594C2×C8C2×C4×D1112yes—
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—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—224no—
611C22⋊C4—442no—
612C22⋊C4—442no—
613C22⋊C4—442no—
614C22⋊C4—442no—
615C22⋊C4—442no—
616C42—21no—
617C42—21no—
618C42—221no—
619C42—221no—
620C42—441no—
621C42—441no—
622C42—442no—
623C42—442no—
624C11#2204511yescharacteristic, complemented, Sylow
625C23—22no—
626C23—22no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—112no—
640C23—221no—
641C23—221no—
642C23—221no—
643C23—221no—
644C23—221no—
645C23—221no—
646C23C2×D4×D1111yescharacteristic
647Q8—222no—
648Q8—222no—
649Q8—441no—
650Q8—441no—
651D4—22no—
652D4—22no—
653D4—22no—
654D4—22no—
655D4—41no—
656D4—41no—
657D4—41no—
658D4—41no—
659D4—448no—
660D4—448no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—112no—
672C2×C4—112no—
673C2×C4—221no—
674C2×C4—221no—
675C2×C4—221no—
676C2×C4—221no—
677C2×C4—222no—
678C2×C4—222no—
679C2×C4—222no—
680C2×C4—222no—
681C2×C4—221no—
682C2×C4—221no—
683C2×C4—222no—
684C2×C4—222no—
685C2×C4—221no—
686C2×C4—444no—
687C2×C4—444no—
688C2×C4—448no—
689C2×C4—441no—
690C2×C4—441no—
691C2×C4—441no—
692C2×C4—441no—
693C2×C4—441no—
694C2×C4—441no—
695C2×C4—441no—
696C2×C4—441no—
697C2×C4—441no—
698C2×C4—441no—
699C2×C4—884no—
700C2×C4#6696412yes—
701C2×C4#6696512yes—
702C2×C4C22×C4×D1111yescharacteristic
703C2×C4#6703711yescharacteristic
704C2×C4#6703711yescharacteristic
705C2×C4#6703711yescharacteristic
706C2×C4#41×D1111yescharacteristic
707C2×C4#6704211yescharacteristic
708C8—22no—
709C8—41no—
710C8—222no—
711C8—441no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—222no—
727C22—222no—
728C22—222no—
729C22—441no—
730C22—441no—
731C22—441no—
732C22—441no—
733C22C4×D4×D1111yescharacteristic
734C22#1062313611yescharacteristic
735C22#1062324611yescharacteristic
736C22C2×#6696411yescharacteristic
737C22C2×#6696511yescharacteristic
738C22D11×#13511yescharacteristic
739C22#1062329911yescharacteristic
740C4—22no—
741C4—22no—
742C4—81no—
743C4—81no—
744C4—222no—
745C4—222no—
746C4—441no—
747C4—442no—
748C4—442no—
749C4—881no—
750C4—881no—
751C4#1062301711yescharacteristic
752C4#1062307611yescharacteristic
753C4#1062314411yescharacteristic
754C4#1062320911yescharacteristic
755C2—82no—
756C2—82no—
757C2—442no—
758C2#1307127511yescharacteristic
759C2C4×#6696511yescharacteristic
760C2C4×#6696411yescharacteristic
761C2#1307937611yescharacteristic
762C2#1307940311yescharacteristic
763C2#1307954411yescharacteristic
764C2#1307958711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1970C2
socleC23×C11C22×D4
prime radicalC2×#10622771C2
cosocleC22×C4×C11C24
hypercenter#1970D11
hypocenterC11#22045
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1970

Complements

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

NH ≅ G/Ntype
2. #13071132C2semidirect
3. #13071103C2semidirect
4. #13069469C2semidirect
5. #13069302C2semidirect
6. #13069292C2semidirect
7. #13069256C2semidirect
8. #13069246C2semidirect
9. #13068966C2semidirect
10. #13068948C2semidirect
11. #13068935C2semidirect
12. #13068812C2semidirect
13. #13068553C2semidirect
14. C4×(C2×D11)⋊C8C2semidirect
15. C11×#1970C2semidirect
34. #10622771C4semidirect
71. C2×#4341C2×C4semidirect
78. C2×C11×D8C2×C4semidirect
98. C2×#4324C2×C4semidirect
123. #66896C2×C4semidirect
132. (C2×D11)⋊C8C2×C4semidirect
134. #66880C2×C4semidirect
246. #1970D11semidirect
453. C2×D8C4×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×#106227712
#130711322
#130711032
#130694692
#130693022
#130692922
#130692562
#130692462
#130689662
#130689482
#130689352
#130688122
#130685532
C4×(C2×D11)⋊C82
C11×#19702
#2204511