Finite Group Databasebeta

← #14764959

Subgroups — #14764959

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×#10622650C211yesmaximal, characteristic
2#13071106C211yesmaximal, characteristic, complemented
3#13069481C211yesmaximal, characteristic, complemented
4#13069469C211yesmaximal, characteristic, complemented
5#13069298C211yesmaximal, characteristic, complemented
6#13069291C211yesmaximal, characteristic, complemented
7#13069257C211yesmaximal, characteristic, complemented
8#13069243C211yesmaximal, characteristic, complemented
9#13068964C211yesmaximal, characteristic, complemented
10#13068950C211yesmaximal, characteristic, complemented
11#13068939C211yesmaximal, characteristic, complemented
12#13068813C211yesmaximal, characteristic, complemented
13#13068554C211yesmaximal, characteristic, complemented
14C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
15C4×C11×#121C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×C4×D4×C11—21no—
19C2×C4×D4×C11C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×#4324C2211yescharacteristic
22C22×#4323C2211yescharacteristic
23C2×#66979C2211yescharacteristic
24C11×#390C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#388—21no—
27C11×#386—21no—
28C11×#380C2211yescharacteristic
29C4×C11×C4⋊C4C2211yescharacteristic
30C4×C11×C22⋊C4—21no—
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33#10622826—21no—
34#10622826—21no—
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37#10622650C418yescomplemented
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622552C2211yescharacteristic
47#10622552C2211yescharacteristic
48C4×(C2×D11)⋊C4—21no—
49C4×(C2×D11)⋊C4—21no—
50#10622542C2211yescharacteristic
51#10622542C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53C2×C4×C11⋊C8C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D4×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11D411yescharacteristic
64C23×C4×C11D411yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11—21no—
67C2×#4339—22no—
68C2×#4339—41no—
69C2×#4339—41no—
70C2×#4339—41no—
71C2×#4339—41no—
72C2×#4339C2×C414yescomplemented
73C22×D44C2311yescharacteristic
74C22×C4×D11—21no—
75C22×Dic22C2311yescharacteristic
76C11×#121—22no—
77C11×#121C2×C414yes—
78C4×D4×C11—41no—
79C4×D4×C11—41no—
80C4×D4×C11—44no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C42×C11—21no—
91C2×C42×C11—41no—
92C2×C42×C11—41no—
93C2×C42×C11D411yescharacteristic
94C2×C42×C11D411yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C22⋊Dic11—21no—
98C2×#4324—41no—
99C2×#4324—41no—
100C2×#4324C2×C414yescomplemented
101C2×#4323—41no—
102C2×#4323—41no—
103C2×#4323C2×C414yescomplemented
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108#66979—41no—
109#66979—41no—
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4×Dic11—21no—
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C11×#95—21no—
118C11×#95—21no—
119C11×#95—21no—
120#66896—41no—
121#66896—41no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C22⋊(C11⋊C8)—22no—
127C22⋊(C11⋊C8)C2×C414yescomplemented
128#66874—41no—
129#66874—41no—
130#66874C2×C414yescomplemented
131#66873—41no—
132#66873—41no—
133#66873C2×C414yescomplemented
134#66872—41no—
135#66871—41no—
136C4×C11⋊C8—41no—
137C4×C11⋊C8—41no—
138#22045—111nomaximal, Sylow
139C24×C11—21no—
140C24×C11C2×D411yescharacteristic
141C23×D11—21no—
142C2×D4×C11—24no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—42no—
149C2×D4×C11—42no—
150C2×D4×C11C22×C412yes—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—41no—
162C22×C4×C11—41no—
163C22×C4×C11—41no—
164C22×C4×C11—42no—
165C22×C4×C11—42no—
166C22×C4×C11—42no—
167C22×C4×C11C22×C412yes—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
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—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181#4339—44no—
182#4339—44no—
183#4339—44no—
184#4339—44no—
185C2×D44—21no—
186C2×D44—21no—
187C2×D44—21no—
188C2×D44—21no—
189C2×D44—21no—
190C2×D44C22×C412yes—
191C2×C4×D11—24no—
192C2×C4×D11—42no—
193C2×C4×D11—42no—
194C2×Dic22—21no—
195C2×Dic22—21no—
196C2×Dic22—21no—
197C2×Dic22—21no—
198C2×Dic22—21no—
199C2×Dic22C22×C412yes—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—42no—
206C11×C4⋊C4C22×C412yes—
207C11×C22⋊C4—24no—
208C11×C22⋊C4—42no—
209C11×C22⋊C4—42no—
210C11×C22⋊C4—42no—
211C11×C22⋊C4—42no—
212C42×C11—21no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—41no—
217C42×C11—41no—
218C42×C11—42no—
219C22⋊Dic11—42no—
220#4324—44no—
221#4323—44no—
222(C2×D11)⋊C4—42no—
223(C2×D11)⋊C4—42no—
224(C2×D11)⋊C4—42no—
225(C2×D11)⋊C4—42no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4×Dic11—42no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
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×#121D1111yescharacteristic, complemented
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#1788—111no—
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—
280D4×C11—22no—
281D4×C11—22no—
282D4×C11—48no—
283D4×C11—41no—
284D4×C11—41no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—44no—
302C2×C4×C11—44no—
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—84no—
312C2×C4×C11C4×D412yes—
313C2×C4×C11#13512yes—
314C2×C4×C11#13512yes—
315C2×C4×C11AGL(1,ℤ/8)12yes—
316C2×C4×C11C23×C411yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11H(5,𝔽2)11yescharacteristic
319C2×C4×C11H(5,𝔽2)11yescharacteristic
320C2×C4×C11H(5,𝔽2)11yescharacteristic
321C2×C4×C11H(5,𝔽2)11yescharacteristic
322C22⋊D11—48no—
323C2×Dic11—22no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332D44—22no—
333D44—22no—
334D44—41no—
335D44—41no—
336C4×D11—48no—
337Dic22—22no—
338Dic22—22no—
339Dic22—41no—
340Dic22—41no—
341C11⋊C8—22no—
342C11⋊C8—22no—
343C11⋊C8—41no—
344C11⋊C8—41no—
345C22×#41—111no—
346C22×SD16—111no—
347C22×D8—111no—
348C2×#121C2×D1111yescharacteristic
349C2×C4×D4—21no—
350C2×C4×D4C2×D1111yescharacteristic
351C2×#117—111no—
352C22×C42C2×D1111yescharacteristic
353#449—118no—
354C2×#107—111no—
355C2×#106—111no—
356C2×#103—111no—
357C2×#103—111no—
358C2×#103—111no—
359C2×#102—111no—
360C2×#102—111no—
361C2×#102—111no—
362C2×#102—111no—
363C2×#102—111no—
364C2×C22⋊C8—111no—
365C2×C22⋊C8—111no—
366C2×C4×C8—111no—
367C2×C4×C8—111no—
368#391—111no—
369#391—111no—
370#390—111no—
371#390—111no—
372#390C2×D1111yescharacteristic
373#389C2×D1111yescharacteristic
374#388—21no—
375#386—21no—
376#386—221no—
377#386—221no—
378#380C2×D1111yescharacteristic
379C4×C4⋊C4C2×D1111yescharacteristic
380C4×C22⋊C4—21no—
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—22no—
419C4×C11—22no—
420C4×C11—22no—
421C4×C11—41no—
422C4×C11—42no—
423C4×C11—81no—
424C4×C11—81no—
425C4×C11#51811yescharacteristic
426C4×C11#51811yescharacteristic
427C4×C11#53811yescharacteristic
428C4×C11#53811yescharacteristic
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—21no—
440C22×D4—111no—
441C22×D4—221no—
442C22×D4C22×D1111yescharacteristic
443C23×C4—21no—
444C23×C4—221no—
445C23×C4C22⋊D1111yescharacteristic
446C23×C4C22⋊D1111yescharacteristic
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×C8—111no—
457C22×C8—111no—
458#121—22no—
459#121C4×D1114yes—
460C4×D4—41no—
461C4×D4—41no—
462C4×D4—44no—
463#117—441no—
464#117—441no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—111no—
468C2×C4⋊C4C22×D1111yescharacteristic
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—21no—
476C2×C22⋊C4—221no—
477C2×C22⋊C4—221no—
478C2×C22⋊C4—221no—
479C2×C22⋊C4—221no—
480C2×C22⋊C4—221no—
481C2×C42—21no—
482C2×C42—41no—
483C2×C42—41no—
484C2×C42—221no—
485C2×C42C22⋊D1111yescharacteristic
486C2×C42C22⋊D1111yescharacteristic
487C2×C42C22×D1111yescharacteristic
488C2×C42C22×D1111yescharacteristic
489#107—441no—
490#106—441no—
491#103—114no—
492#103—441no—
493#103—441no—
494#102—114no—
495#102—441no—
496#102—441no—
497#102—441no—
498#102—441no—
499C22⋊C8—114no—
500C22⋊C8—222no—
501C4×C8—441no—
502C4×C8—441no—
503#95—21no—
504#95—21no—
505#95—21no—
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—
522C24C2×C22⋊D1111yescharacteristic
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—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—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—221no—
568C22×C4—224no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—442no—
572C22×C4—442no—
573C22×C4C2×C4×D1112yes—
574C22×C4#433912yes—
575C22×C4C2×C22⋊D1111yescharacteristic
576C22×C4C2×C22⋊D1111yescharacteristic
577C22×C4C2×C22⋊D1111yescharacteristic
578C22×C4C2×C22⋊D1111yescharacteristic
579C22×C4C2×C22⋊D1111yescharacteristic
580C22×C4C23×D1111yescharacteristic
581SD16—444no—
582D8—444no—
583C2×C8—112no—
584C2×C8—112no—
585C2×C8—221no—
586C2×C8—221no—
587C2×C8—221no—
588C2×C8—221no—
589C2×C8—221no—
590C2×C8—221no—
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—21no—
600C4⋊C4—42no—
601C4⋊C4—221no—
602C4⋊C4—221no—
603C4⋊C4—221no—
604C4⋊C4—221no—
605C4⋊C4C2×C4×D1112yes—
606C22⋊C4—24no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—442no—
612C22⋊C4—442no—
613C22⋊C4—442no—
614C22⋊C4—442no—
615C22⋊C4—442no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—41no—
621C42—41no—
622C42—42no—
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—
645C23C4×C22⋊D1112yes—
646C23C22×C22⋊D1111yescharacteristic
647Q8—222no—
648Q8—222no—
649Q8—441no—
650Q8—441no—
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—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—44no—
678C2×C4—44no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—84no—
688C2×C4—222no—
689C2×C4—448no—
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×C4C4×C22⋊D1112yes—
699C2×C4#6698512yes—
700C2×C4#6700312yes—
701C2×C4#6700312yes—
702C2×C4C22×C4×D1111yescharacteristic
703C2×C4C2×#433911yescharacteristic
704C2×C4#6703711yescharacteristic
705C2×C4#6703711yescharacteristic
706C2×C4#6704211yescharacteristic
707C2×C4#6704211yescharacteristic
708C8—222no—
709C8—222no—
710C8—441no—
711C8—441no—
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×C4×C22⋊D1111yescharacteristic
734C22C2×#6698511yescharacteristic
735C22#1062333511yescharacteristic
736C22C2×#6700311yescharacteristic
737C22C2×#6700311yescharacteristic
738C22#1062335311yescharacteristic
739C22#1062336111yescharacteristic
740C4—22no—
741C4—22no—
742C4—22no—
743C4—22no—
744C4—41no—
745C4—42no—
746C4—81no—
747C4—81no—
748C4—442no—
749C4—881no—
750C4—881no—
751C4#1062307611yescharacteristic
752C4#1062307611yescharacteristic
753C4#1062309111yescharacteristic
754C4#1062309111yescharacteristic
755C2—42no—
756C2—82no—
757C2—882no—
758C2#1307127011yescharacteristic
759C2C4×#6700311yescharacteristic
760C2C4×#6698511yescharacteristic
761C2#1307938111yescharacteristic
762C2#1307940411yescharacteristic
763C2#1307954511yescharacteristic
764C2#1307958811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#121C2
socleC23×C11C22×D4
prime radicalC2×#10622650C2
cosocleC22×C4×C11C24
hypercenterC4×#121D11
hypocenterC11#22045
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
2. #13071106C2semidirect
3. #13069481C2semidirect
4. #13069469C2semidirect
5. #13069298C2semidirect
6. #13069291C2semidirect
7. #13069257C2semidirect
8. #13069243C2semidirect
9. #13068964C2semidirect
10. #13068950C2semidirect
11. #13068939C2semidirect
12. #13068813C2semidirect
13. #13068554C2semidirect
14. C4×C22⋊(C11⋊C8)C2semidirect
15. C4×C11×#121C2semidirect
37. #10622650C4semidirect
72. C2×#4339C2×C4semidirect
100. C2×#4324C2×C4semidirect
103. C2×#4323C2×C4semidirect
127. C22⋊(C11⋊C8)C2×C4semidirect
130. #66874C2×C4semidirect
133. #66873C2×C4semidirect
244. C4×#121D11semidirect
624. C11#22045semidirect

Maximal subgroups

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

subgroupindex
C2×#106226502
#130711062
#130694812
#130694692
#130692982
#130692912
#130692572
#130692432
#130689642
#130689502
#130689392
#130688132
#130685542
C4×C22⋊(C11⋊C8)2
C4×C11×#1212
#2204511