Finite Group Databasebeta

← #14810977

Subgroups — #14810977

Order 2816.

1162 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622679C211yesmaximal, characteristic, complemented
2C22×#66873C211yesmaximal, characteristic
3C22⋊C4×D44C211yesmaximal, characteristic
4#13070140C211yesmaximal, characteristic, complemented
5#13070001C211yesmaximal, characteristic, complemented
6#13069987C211yesmaximal, characteristic, complemented
7#13069759C211yesmaximal, characteristic, complemented
8#13068876C211yesmaximal, characteristic, complemented
9#13068862C211yesmaximal, characteristic, complemented
10#13068804C211yesmaximal, characteristic, complemented
11#13068796C211yesmaximal, characteristic, complemented
12#13068639C211yesmaximal, characteristic, complemented
13#13068623C211yesmaximal, characteristic, complemented
14#13068546C211yesmaximal, characteristic
15C11×#2442C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C2×C11×#125C2211yescharacteristic, complemented
18C22×C11×C4⋊C4C2211yescharacteristic
19C23×C11⋊C8C2211yescharacteristic
20C2×C22⋊C4×D11—21no—
21C2×C4×D44C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C11×#400—21no—
24C11×#398—21no—
25C11×#389C2211yescharacteristic, complemented
26C11×#389C2211yescharacteristic, complemented
27C11×#385—21no—
28C11×#382C2211yescharacteristic, complemented
29C11×#380—21no—
30C11×#380C2211yescharacteristic
31C4×C11×C22⋊C4C2211yescharacteristic
32#10622825C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34#10622679—24no—
35C2×#66873—24no—
36C2×#66873C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66872C2211yescharacteristic, complemented
45C2×#66872C2211yescharacteristic, complemented
46C2×#66871C2211yescharacteristic, complemented
47C2×#66871C2211yescharacteristic, complemented
48#10622568—21no—
49#10622552C2211yescharacteristic
50#10622552C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
52C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
53#10622278—21no—
54#10622278—21no—
55#10622167C2211yescharacteristic, complemented
56#10622167C2211yescharacteristic, complemented
57#10622167C2211yescharacteristic, complemented
58#10622167C2211yescharacteristic, complemented
59#10622162C2211yescharacteristic, complemented
60#10622162C2211yescharacteristic, complemented
61C24×D11—21no—
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C22×D44—22no—
65C22×D44—22no—
66C22×D44—21no—
67C22×D44—22no—
68C22×D44—41no—
69C22×D44—41no—
70C22×D44Q814yes—
71C22×D44C2311yescharacteristic
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×C4×D11—21no—
75C11×#125—22no—
76C11×#125—41no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—41no—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4D411yescharacteristic
90C2×C11×C22⋊C4D411yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×C42×C11C2311yescharacteristic
93C2×C22⋊Dic11—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C22×C11⋊C8—22no—
103C22×C11⋊C8—22no—
104C22×C11⋊C8—41no—
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22⋊C4×D11—44no—
110C4×D44—22no—
111C4×D44—22no—
112C4×D44—41no—
113C4×D44—41no—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95—21no—
118C11×#95—21no—
119C11×#95D411yescharacteristic
120C11×#95D411yescharacteristic
121C11⋊#95—21no—
122C22⋊(C11⋊C8)—22no—
123#66873—22no—
124#66873—22no—
125#66873—22no—
126#66873—22no—
127#66873—22no—
128#66873—41no—
129#66873—41no—
130#66873D414yes—
131#66872—22no—
132#66872—41no—
133#66871—22no—
134#66871—41no—
135C4⋊(C11⋊C8)—22no—
136C4⋊(C11⋊C8)—41no—
137#25960—111nomaximal, Sylow
138C24×C11C2×D411yescharacteristic
139C23×D11—21no—
140C23×D11—21no—
141C23×D11—24no—
142C23×D11—42no—
143C23×D11—42no—
144C23×D11—42no—
145C23×D11—42no—
146C23×D11—81no—
147C23×D11—81no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—42no—
157C22×C4×C11—42no—
158C22×C4×C11—81no—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×Q812yes—
165C22×C4×C11#4112yes—
166C22×C4×C11C2411yescharacteristic
167C22×Dic11—21no—
168C22×Dic11—21no—
169C2×D44—28no—
170C2×D44—24no—
171C2×D44—21no—
172C2×D44—21no—
173C2×D44—21no—
174C2×D44—21no—
175C2×D44—21no—
176C2×D44—21no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44—42no—
180C2×D44—42no—
181C2×D44—44no—
182C2×D44—44no—
183C2×D44—44no—
184C2×D44C2×D412yes—
185C2×D44C2×Q812yes—
186C2×D44C2×Q812yes—
187C2×D44#4112yes—
188C2×C4×D11—42no—
189C2×C4×D11—42no—
190C2×C4×D11—42no—
191C2×C4×D11—42no—
192C2×C4×D11—81no—
193C2×C4×D11—81no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—42no—
202C11×C4⋊C4—42no—
203C11×C4⋊C4—42no—
204C11×C4⋊C4—81no—
205C11×C4⋊C4—81no—
206C11×C4⋊C4C2×D412yes—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—42no—
210C42×C11—21no—
211C42×C11—21no—
212C42×C11—21no—
213C42×C11—21no—
214C22⋊Dic11—42no—
215(C2×D11)⋊C4—42no—
216(C2×D11)⋊C4—42no—
217(C2×D11)⋊C4—42no—
218(C2×D11)⋊C4—42no—
219(C2×D11)⋊C4—81no—
220(C2×D11)⋊C4—81no—
221C4⋊Dic11—21no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—44no—
237C2×C11⋊C8C2×D412yes—
238C2×#478—111no—
239C22×#102—111no—
240#2442D1111yescharacteristic, complemented
241D4×C22⋊C4—111no—
242#2092—111no—
243#2067—111no—
244#2065—111no—
245#2025—111no—
246#1864—111no—
247#1862—111no—
248#1852—111no—
249#1850—111no—
250#1807—111no—
251#1804—111no—
252#1786—111no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11C22⋊Q812yes—
258C23×C11#13512yes—
259C23×C11AGL(1,ℤ/8)12yes—
260C23×C11C22×D411yescharacteristic
261C22×D11—22no—
262C22×D11—22no—
263C22×D11—22no—
264C22×D11—22no—
265C22×D11—48no—
266C22×D11—41no—
267C22×D11—41no—
268C22×D11—41no—
269C22×D11—41no—
270C22×D11—41no—
271C22×D11—41no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—48no—
277C22×D11—84no—
278C22×D11—84no—
279C22×D11—84no—
280C22×D11—84no—
281C22×D11—84no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—22no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—84no—
313C2×C4×C11C22⋊Q812yes—
314C2×C4×C11C22×D411yescharacteristic
315C2×C4×C11C22×Q811yescharacteristic
316C2×C4×C11C2×#4111yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11H(5,𝔽2)11yescharacteristic
319C2×C4×C11H(5,𝔽2)11yescharacteristic
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326D44—22no—
327D44—22no—
328D44—22no—
329D44—22no—
330D44—22no—
331D44—48no—
332D44—41no—
333D44—41no—
334D44C22⋊Q814yes—
335C4×D11—84no—
336C4×D11—84no—
337C11⋊C8—22no—
338C11⋊C8—41no—
339C11⋊C8—41no—
340C11⋊C8—41no—
341C23×D4—111no—
342C23×C8—111no—
343C2×#125C2×D1111yescharacteristic, complemented
344C2×C4×D4—111no—
345C2×C4×D4—111no—
346C22×C4⋊C4C2×D1111yescharacteristic
347C22×C22⋊C4—221no—
348#478—224no—
349C2×#107—111no—
350C2×#107—111no—
351C2×#106—111no—
352C2×#106—111no—
353C2×C4⋊C8—111no—
354C2×C4⋊C8—111no—
355C2×#102—111no—
356C2×#102—111no—
357C2×#102—111no—
358C2×#102—111no—
359C2×#102—111no—
360C2×#102—111no—
361C2×#102—111no—
362C2×#102—111no—
363C2×#102—224no—
364C2×C22⋊C8—111no—
365#400—21no—
366#398—21no—
367#390—111no—
368#390—111no—
369#389C2×D1111yescharacteristic, complemented
370#389C2×D1111yescharacteristic, complemented
371#386—221no—
372#386—221no—
373#385—21no—
374#382C2×D1111yescharacteristic, complemented
375#380—21no—
376#380—111no—
377#380C2×D1111yescharacteristic
378#379—221no—
379C4×C22⋊C4C2×D1111yescharacteristic
380#340—111no—
381#340—111no—
382#340—111no—
383#340—111no—
384#336—111no—
385#336—111no—
386C22×C11—22no—
387C22×C11—22no—
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11#47814yescomplemented
393C22×C11C2×C22⋊Q811yescharacteristic
394C22×C11D4211yescharacteristic
395C22×C11#54611yescharacteristic
396C22×C11C2×#13511yescharacteristic
397C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
398C22×C11#57611yescharacteristic
399C22×C11#57711yescharacteristic
400C2×D11—24no—
401C2×D11—42no—
402C2×D11—42no—
403C2×D11—42no—
404C2×D11—42no—
405C2×D11—42no—
406C2×D11—42no—
407C2×D11—42no—
408C2×D11—42no—
409C2×D11—42no—
410C2×D11—816no—
411C2×D11—81no—
412C2×D11—81no—
413C2×D11—81no—
414C2×D11—81no—
415C4×C11—22no—
416C4×C11—41no—
417C4×C11—42no—
418C4×C11—41no—
419C4×C11—41no—
420C4×C11—41no—
421C4×C11—81no—
422C4×C11—81no—
423C4×C11—81no—
424C4×C11C2×C22⋊Q811yescharacteristic
425C4×C11#54311yescharacteristic
426C4×C11#54611yescharacteristic
427C4×C11#55111yescharacteristic
428Dic11—81no—
429Dic11—81no—
430C25—221no—
431C22×D4—114no—
432C22×D4—111no—
433C22×D4—111no—
434C22×D4—222no—
435C22×D4—222no—
436C22×D4—222no—
437C22×D4—221no—
438C22×D4—441no—
439C22×D4—441no—
440C23×C4—21no—
441C23×C4—221no—
442C23×C4—221no—
443C23×C4C22×D1111yescharacteristic
444C22×C8—111no—
445C22×C8—111no—
446C22×C8—111no—
447C22×C8—111no—
448C22×C8—222no—
449C22×C8—222no—
450C22×C8—441no—
451#125—22no—
452#125—41no—
453C4×D4—222no—
454C4×D4—222no—
455C4×D4—441no—
456C4×D4—441no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—41no—
464C2×C4⋊C4—111no—
465C2×C4⋊C4—111no—
466C2×C4⋊C4C22×D1111yescharacteristic
467C2×C4⋊C4C22×D1111yescharacteristic
468C2×C4⋊C4C22×D1111yescharacteristic
469C2×C4⋊C4C22×D1111yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—221no—
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—444no—
479C2×C22⋊C4C22⋊D1111yescharacteristic
480C2×C22⋊C4C22⋊D1111yescharacteristic
481C2×C42C22×D1111yescharacteristic
482C2×C42C22×D1111yescharacteristic
483#107—222no—
484#107—441no—
485#106—222no—
486#106—441no—
487C4⋊C8—222no—
488C4⋊C8—441no—
489#102—114no—
490#102—222no—
491#102—222no—
492#102—222no—
493#102—222no—
494#102—222no—
495#102—441no—
496#102—441no—
497C22⋊C8—222no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—221no—
504#95C22⋊D1111yescharacteristic
505#95C22⋊D1111yescharacteristic
506C2×C11—24no—
507C2×C11#243711yescharacteristic
508C2×C11C2×#47811yescharacteristic
509C2×C11#308111yescharacteristic
510C2×C11#326411yescharacteristic
511C2×C11#328211yescharacteristic
512C2×C11#329711yescharacteristic
513C2×C11#331011yescharacteristic
514D11—44no—
515D11—82no—
516C24—221no—
517C24—221no—
518C24—224no—
519C24—442no—
520C24—442no—
521C24—442no—
522C24—442no—
523C24—881no—
524C24—881no—
525C24C2×C22⋊D1111yescharacteristic
526C2×D4—112no—
527C2×D4—112no—
528C2×D4—112no—
529C2×D4—112no—
530C2×D4—228no—
531C2×D4—224no—
532C2×D4—221no—
533C2×D4—221no—
534C2×D4—221no—
535C2×D4—221no—
536C2×D4—221no—
537C2×D4—221no—
538C2×D4—221no—
539C2×D4—221no—
540C2×D4—444no—
541C2×D4—444no—
542C2×D4—444no—
543C2×D4—442no—
544C2×D4—442no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—81no—
556C22×C4—221no—
557C22×C4—221no—
558C22×C4—442no—
559C22×C4—442no—
560C22×C4—442no—
561C22×C4—442no—
562C22×C4—881no—
563C22×C4—881no—
564C22×C4Q8×D1112yes—
565C22×C4#434312yes—
566C22×C4C2×C22⋊D1111yescharacteristic
567C22×C4C2×C22⋊D1111yescharacteristic
568C22×C4C2×C22⋊D1111yescharacteristic
569C22×C4C2×C22⋊D1111yescharacteristic
570C22×C4C2×C22⋊D1111yescharacteristic
571C22×C4C23×D1111yescharacteristic
572C2×C8—112no—
573C2×C8—221no—
574C2×C8—221no—
575C2×C8—221no—
576C2×C8—221no—
577C2×C8—221no—
578C2×C8—221no—
579C2×C8—221no—
580C2×C8—221no—
581C2×C8—221no—
582C2×C8—221no—
583C2×C8—221no—
584C2×C8—444no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—81no—
596C4⋊C4—81no—
597C4⋊C4—221no—
598C4⋊C4—221no—
599C4⋊C4—221no—
600C4⋊C4—221no—
601C4⋊C4D4×D1112yes—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—42no—
605C22⋊C4—442no—
606C22⋊C4—442no—
607C22⋊C4—442no—
608C22⋊C4—442no—
609C22⋊C4—442no—
610C22⋊C4—881no—
611C22⋊C4—881no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C11#2596011yescharacteristic, complemented, Sylow
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—222no—
622C23—222no—
623C23—222no—
624C23—222no—
625C23—448no—
626C23—441no—
627C23—441no—
628C23—441no—
629C23—441no—
630C23—441no—
631C23—441no—
632C23—441no—
633C23—441no—
634C23—441no—
635C23—441no—
636C23—448no—
637C23—884no—
638C23—884no—
639C23—884no—
640C23—884no—
641C23—884no—
642C23#6699912yes—
643C23#6700212yes—
644C23#6700312yes—
645C23C22×C22⋊D1111yescharacteristic
646D4—114no—
647D4—222no—
648D4—222no—
649D4—222no—
650D4—222no—
651D4—222no—
652D4—448no—
653D4—441no—
654D4—441no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—84no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—441no—
689C2×C4—441no—
690C2×C4—441no—
691C2×C4—441no—
692C2×C4—884no—
693C2×C4—884no—
694C2×C4#6699912yes—
695C2×C4C2×D4×D1111yescharacteristic
696C2×C4#6703711yescharacteristic
697C2×C4C2×Q8×D1111yescharacteristic
698C2×C4C2×#434311yescharacteristic
699C2×C4#41×D1111yescharacteristic
700C2×C4#6704211yescharacteristic
701C8—222no—
702C8—441no—
703C8—441no—
704C8—441no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—224no—
712C22—442no—
713C22—442no—
714C22—442no—
715C22—442no—
716C22—442no—
717C22—442no—
718C22—442no—
719C22—442no—
720C22—442no—
721C22—8816no—
722C22—881no—
723C22—881no—
724C22—881no—
725C22—881no—
726C22#1062267914yescomplemented
727C22D4×C22⋊D1111yescharacteristic
728C22C2×#6699911yescharacteristic
729C22C2×#6700211yescharacteristic
730C22C2×#6700311yescharacteristic
731C22#1062336011yescharacteristic
732C22#1062336611yescharacteristic
733C22#1062336811yescharacteristic
734C4—22no—
735C4—41no—
736C4—41no—
737C4—42no—
738C4—41no—
739C4—41no—
740C4—81no—
741C4—81no—
742C4—81no—
743C4—881no—
744C4—881no—
745C4D11×C22⋊Q811yescharacteristic
746C4#1062316111yescharacteristic
747C4#1062316511yescharacteristic
748C4#1062316811yescharacteristic
749C2—24no—
750C2—444no—
751C2—882no—
752C2#1307227911yescharacteristic
753C2C2×#1062267911yescharacteristic
754C2#1307844111yescharacteristic
755C2#1308009711yescharacteristic
756C2#1308032411yescharacteristic
757C2#1308046011yescharacteristic
758C2#1308063111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2442C2
socleC23×C11C22×D4
prime radicalC23×D44C22
hypercenter#2442D11
hypocenterC11#25960
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2442

Complements

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

NH ≅ G/Ntype
1. C2×#10622679C2semidirect
4. #13070140C2semidirect
5. #13070001C2semidirect
6. #13069987C2semidirect
7. #13069759C2semidirect
8. #13068876C2semidirect
9. #13068862C2semidirect
10. #13068804C2semidirect
11. #13068796C2semidirect
12. #13068639C2semidirect
13. #13068623C2semidirect
15. C11×#2442C2semidirect
17. C2×C11×#125C22semidirect
25. C11×#389C22semidirect
26. C11×#389C22semidirect
28. C11×#382C22semidirect
44. C2×#66872C22semidirect
45. C2×#66872C22semidirect
46. C2×#66871C22semidirect
47. C2×#66871C22semidirect
51. C2×C4⋊(C11⋊C8)C22semidirect
52. C2×C4⋊(C11⋊C8)C22semidirect
55. #10622167C22semidirect
56. #10622167C22semidirect
57. #10622167C22semidirect
58. #10622167C22semidirect
59. #10622162C22semidirect
60. #10622162C22semidirect
240. #2442D11semidirect
343. C2×#125C2×D11semidirect
369. #389C2×D11semidirect
370. #389C2×D11semidirect
374. #382C2×D11semidirect
392. C22×C11#478semidirect
616. C11#25960semidirect
726. C22#10622679semidirect

Maximal subgroups

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

subgroupindex
C2×#106226792
C22×#668732
C22⋊C4×D442
#130701402
#130700012
#130699872
#130697592
#130688762
#130688622
#130688042
#130687962
#130686392
#130686232
#130685462
C11×#24422
#2596011