Finite Group Databasebeta

← #14810980

Subgroups — #14810980

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×#10622622C211yesmaximal, characteristic, complemented
2C22×#66896C211yesmaximal, characteristic
3#13072340C211yesmaximal, characteristic, complemented
4#13070137C211yesmaximal, characteristic, complemented
5#13070004C211yesmaximal, characteristic, complemented
6#13069990C211yesmaximal, characteristic, complemented
7#13069762C211yesmaximal, characteristic, complemented
8#13068877C211yesmaximal, characteristic, complemented
9#13068863C211yesmaximal, characteristic, complemented
10#13068803C211yesmaximal, characteristic, complemented
11#13068796C211yesmaximal, characteristic, complemented
12#13068639C211yesmaximal, characteristic, complemented
13#13068626C211yesmaximal, characteristic, complemented
14#13068547C211yesmaximal, characteristic
15D4×C11×C22⋊C4C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C22×C11×C22⋊C4—21no—
20C22×C4⋊Dic11C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22C2×#66923C2211yescharacteristic, complemented
23C11×#390C2211yescharacteristic
24C11×#390C2211yescharacteristic
25C11×#386—21no—
26C11×#386—21no—
27C11×#380C2211yescharacteristic
28C11×#379—21no—
29C4×C11×C22⋊C4C2211yescharacteristic
30C2×#66896—24no—
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39#10622825C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41#10622622—24no—
42C2×#66872C2211yescharacteristic, complemented
43C2×#66872C2211yescharacteristic, complemented
44C2×#66871C2211yescharacteristic, complemented
45C2×#66871C2211yescharacteristic, complemented
46#10622559—21no—
47#10622555—21no—
48#10622549C2211yescharacteristic, complemented
49#10622541C2211yescharacteristic, complemented
50#10622541C2211yescharacteristic, complemented
51C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
52C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
53#10622273—21no—
54#10622270—21no—
55#10622167C2211yescharacteristic, complemented
56#10622167C2211yescharacteristic, complemented
57#10622167C2211yescharacteristic, complemented
58#10622167C2211yescharacteristic, complemented
59#10622162C2211yescharacteristic, complemented
60#10622162C2211yescharacteristic, complemented
61C25×C11—21no—
62C22×D4×C11—22no—
63C22×D4×C11—22no—
64C22×D4×C11—21no—
65C22×D4×C11—22no—
66C22×D4×C11—41no—
67C22×D4×C11—41no—
68C22×D4×C11Q814yes—
69C22×D4×C11C2311yescharacteristic
70C22×D4×C11C2311yescharacteristic
71C23×C4×C11—21no—
72C23×C4×C11—21no—
73C23×C4×C11C2311yescharacteristic
74C23×Dic11—21no—
75C4×D4×C11—22no—
76C4×D4×C11—22no—
77C4×D4×C11—41no—
78C4×D4×C11—41no—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—44no—
89C2×C11×C22⋊C4D411yescharacteristic
90C2×C11×C22⋊C4D411yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×C42×C11C2311yescharacteristic
93C2×C22⋊Dic11—21no—
94C2×C4⋊Dic11—22no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—41no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C22×C11⋊C8—22no—
106C22×C11⋊C8—22no—
107C22×C11⋊C8—41no—
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112#66923—22no—
113#66923—41no—
114C11×#95—21no—
115C11×#95D411yescharacteristic
116C11×#95D411yescharacteristic
117#66896—22no—
118#66896—22no—
119#66896—22no—
120#66896—22no—
121#66896—22no—
122#66896—41no—
123#66896—41no—
124#66896D414yes—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C22⋊(C11⋊C8)—22no—
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×C11—21no—
139C24×C11—21no—
140C24×C11—24no—
141C24×C11—42no—
142C24×C11—42no—
143C24×C11—42no—
144C24×C11—42no—
145C24×C11—81no—
146C24×C11—81no—
147C24×C11C2×D411yescharacteristic
148C2×D4×C11—28no—
149C2×D4×C11—24no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—44no—
159C2×D4×C11—44no—
160C2×D4×C11—44no—
161C2×D4×C11—42no—
162C2×D4×C11—42no—
163C2×D4×C11C2×D412yes—
164C2×D4×C11C2×Q812yes—
165C2×D4×C11C2×Q812yes—
166C2×D4×C11#4112yes—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—42no—
174C22×C4×C11—42no—
175C22×C4×C11—42no—
176C22×C4×C11—42no—
177C22×C4×C11—81no—
178C22×C4×C11—81no—
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×Q812yes—
185C22×C4×C11#4112yes—
186C22×C4×C11C2411yescharacteristic
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—42no—
192C22×Dic11—42no—
193C22×Dic11—81no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—42no—
201C11×C22⋊C4—42no—
202C11×C22⋊C4—42no—
203C11×C22⋊C4—42no—
204C11×C22⋊C4—42no—
205C11×C22⋊C4—81no—
206C11×C22⋊C4—81no—
207C42×C11—21no—
208C42×C11—21no—
209C42×C11—21no—
210C42×C11—21no—
211C22⋊Dic11—42no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—21no—
217C4⋊Dic11—21no—
218C4⋊Dic11—21no—
219C4⋊Dic11—42no—
220C4⋊Dic11C2×D412yes—
221Dic11⋊C4—42no—
222Dic11⋊C4—42no—
223Dic11⋊C4—81no—
224Dic11⋊C4—81no—
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#2442—111no—
241D4×C22⋊C4D1111yescharacteristic
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×C11—22no—
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—22no—
261C23×C11—48no—
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×C11—48no—
273C23×C11—84no—
274C23×C11—84no—
275C23×C11—84no—
276C23×C11—84no—
277C23×C11—84no—
278C23×C11C22⋊Q812yes—
279C23×C11#13512yes—
280C23×C11AGL(1,ℤ/8)12yes—
281C23×C11C22×D411yescharacteristic
282D4×C11—22no—
283D4×C11—22no—
284D4×C11—22no—
285D4×C11—22no—
286D4×C11—22no—
287D4×C11—48no—
288D4×C11—41no—
289D4×C11—41no—
290D4×C11C22⋊Q814yes—
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—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—84no—
316C2×C4×C11—84no—
317C2×C4×C11C22⋊Q812yes—
318C2×C4×C11C22×D411yescharacteristic
319C2×C4×C11C22×Q811yescharacteristic
320C2×C4×C11C2×#4111yescharacteristic
321C2×C4×C11C2×#4111yescharacteristic
322C2×C4×C11H(5,𝔽2)11yescharacteristic
323C2×C4×C11H(5,𝔽2)11yescharacteristic
324C2×Dic11—22no—
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—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—84no—
337C11⋊C8—22no—
338C11⋊C8—41no—
339C11⋊C8—41no—
340C11⋊C8—41no—
341C23×D4C2×D1111yescharacteristic
342C23×C8—111no—
343C2×#125—111no—
344C2×C4×D4C2×D1111yescharacteristic
345C2×C4×D4C2×D1111yescharacteristic
346C22×C4⋊C4—111no—
347C22×C22⋊C4—21no—
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—221no—
366#398—221no—
367#390C2×D1111yescharacteristic
368#390C2×D1111yescharacteristic
369#389—111no—
370#389—111no—
371#386—21no—
372#386—21no—
373#385—221no—
374#382—111no—
375#380—111no—
376#380—221no—
377#380C2×D1111yescharacteristic
378#379—21no—
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—24no—
393C22×C11—42no—
394C22×C11—42no—
395C22×C11—42no—
396C22×C11—42no—
397C22×C11—42no—
398C22×C11—42no—
399C22×C11—42no—
400C22×C11—42no—
401C22×C11—42no—
402C22×C11—816no—
403C22×C11—81no—
404C22×C11—81no—
405C22×C11—81no—
406C22×C11—81no—
407C22×C11#47814yescomplemented
408C22×C11C2×C22⋊Q811yescharacteristic
409C22×C11D4211yescharacteristic
410C22×C11#54611yescharacteristic
411C22×C11C2×#13511yescharacteristic
412C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
413C22×C11#57611yescharacteristic
414C22×C11#57711yescharacteristic
415C4×C11—22no—
416C4×C11—41no—
417C4×C11—41no—
418C4×C11—41no—
419C4×C11—41no—
420C4×C11—81no—
421C4×C11—81no—
422C4×C11C2×C22⋊Q811yescharacteristic
423C4×C11#54311yescharacteristic
424C4×C11#54611yescharacteristic
425C4×C11#55111yescharacteristic
426Dic11—42no—
427Dic11—81no—
428Dic11—81no—
429Dic11—81no—
430C25—21no—
431C22×D4—22no—
432C22×D4—22no—
433C22×D4—22no—
434C22×D4—21no—
435C22×D4—41no—
436C22×D4—41no—
437C22×D4Dic2214yes—
438C22×D4C22×D1111yescharacteristic
439C22×D4C22×D1111yescharacteristic
440C23×C4—21no—
441C23×C4—21no—
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—222no—
452#125—441no—
453C4×D4—22no—
454C4×D4—22no—
455C4×D4—41no—
456C4×D4—41no—
457C2×C4⋊C4—111no—
458C2×C4⋊C4—111no—
459C2×C4⋊C4—111no—
460C2×C4⋊C4—111no—
461C2×C4⋊C4—222no—
462C2×C4⋊C4—221no—
463C2×C4⋊C4—221no—
464C2×C4⋊C4—221no—
465C2×C4⋊C4—221no—
466C2×C4⋊C4—221no—
467C2×C4⋊C4—441no—
468C2×C4⋊C4C22×D1111yescharacteristic
469C2×C4⋊C4C22×D1111yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—44no—
478C2×C22⋊C4—221no—
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—221no—
500#95—221no—
501#95—221no—
502#95—221no—
503#95—221no—
504#95C22⋊D1111yescharacteristic
505#95C22⋊D1111yescharacteristic
506C2×C11—24no—
507C2×C11—44no—
508C2×C11—82no—
509C2×C11#243711yescharacteristic
510C2×C11C2×#47811yescharacteristic
511C2×C11#308111yescharacteristic
512C2×C11#326411yescharacteristic
513C2×C11#328211yescharacteristic
514C2×C11#329711yescharacteristic
515C2×C11#331011yescharacteristic
516C24—21no—
517C24—21no—
518C24—24no—
519C24—42no—
520C24—42no—
521C24—42no—
522C24—42no—
523C24—81no—
524C24—81no—
525C24C2×C22⋊D1111yescharacteristic
526C2×D4—28no—
527C2×D4—24no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—44no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4C2×Dic2212yes—
542C2×D4C2×Dic2212yes—
543C2×D4D4×D1112yes—
544C2×D4#434112yes—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—81no—
556C22×C4—81no—
557C22×C4—221no—
558C22×C4—221no—
559C22×C4—221no—
560C22×C4—221no—
561C22×C4—442no—
562C22×C4—442no—
563C22×C4—881no—
564C22×C4C2×Dic2212yes—
565C22×C4#433912yes—
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—112no—
590C4⋊C4—221no—
591C4⋊C4—221no—
592C4⋊C4—221no—
593C4⋊C4—221no—
594C4⋊C4—221no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—442no—
598C4⋊C4—442no—
599C4⋊C4—442no—
600C4⋊C4—881no—
601C4⋊C4—881no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C22⋊C4—442no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C11#2596011yescharacteristic, complemented, Sylow
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—48no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—48no—
637C23—84no—
638C23—84no—
639C23—84no—
640C23—84no—
641C23—84no—
642C23#6697712yes—
643C23#6698512yes—
644C23#6700312yes—
645C23C22×C22⋊D1111yescharacteristic
646D4—22no—
647D4—22no—
648D4—22no—
649D4—22no—
650D4—22no—
651D4—48no—
652D4—41no—
653D4—41no—
654D4#6693114yes—
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—21no—
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—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—84no—
680C2×C4—84no—
681C2×C4—222no—
682C2×C4—441no—
683C2×C4—441no—
684C2×C4—441no—
685C2×C4—441no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—441no—
689C2×C4—441no—
690C2×C4—441no—
691C2×C4—441no—
692C2×C4—441no—
693C2×C4—884no—
694C2×C4#6697712yes—
695C2×C4C22×Dic2211yescharacteristic
696C2×C4C2×#433911yescharacteristic
697C2×C4C2×D4×D1111yescharacteristic
698C2×C4C2×#434111yescharacteristic
699C2×C4#6703711yescharacteristic
700C2×C4#6703711yescharacteristic
701C8—222no—
702C8—441no—
703C8—441no—
704C8—441no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—24no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—816no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22#1062262214yescomplemented
727C22C2×#6697711yescharacteristic
728C22C2×#6698511yescharacteristic
729C22D4×C22⋊D1111yescharacteristic
730C22#1062333711yescharacteristic
731C22C2×#6700311yescharacteristic
732C22#1062336611yescharacteristic
733C22#1062336711yescharacteristic
734C4—22no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—81no—
740C4—81no—
741C4—442no—
742C4—881no—
743C4—881no—
744C4—881no—
745C4C2×#6693111yescharacteristic
746C4#1062301411yescharacteristic
747C4#1062302111yescharacteristic
748C4#1062302611yescharacteristic
749C2—24no—
750C2—44no—
751C2—82no—
752C2#1307227711yescharacteristic
753C2C2×#1062262211yescharacteristic
754C2#1307844711yescharacteristic
755C2#1308009211yescharacteristic
756C2#1308031911yescharacteristic
757C2#1308046611yescharacteristic
758C2#1308063711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingD4×C11×C22⋊C4C2
socleC23×C11C22×D4
prime radicalC23×D4×C11C22
hypercenterD4×C22⋊C4D11
hypocenterC11#25960
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622622C2semidirect
3. #13072340C2semidirect
4. #13070137C2semidirect
5. #13070004C2semidirect
6. #13069990C2semidirect
7. #13069762C2semidirect
8. #13068877C2semidirect
9. #13068863C2semidirect
10. #13068803C2semidirect
11. #13068796C2semidirect
12. #13068639C2semidirect
13. #13068626C2semidirect
22. C2×#66923C22semidirect
42. C2×#66872C22semidirect
43. C2×#66872C22semidirect
44. C2×#66871C22semidirect
45. C2×#66871C22semidirect
48. #10622549C22semidirect
49. #10622541C22semidirect
50. #10622541C22semidirect
51. C2×C4⋊(C11⋊C8)C22semidirect
52. C2×C4⋊(C11⋊C8)C22semidirect
55. #10622167C22semidirect
56. #10622167C22semidirect
57. #10622167C22semidirect
58. #10622167C22semidirect
59. #10622162C22semidirect
60. #10622162C22semidirect
407. C22×C11#478semidirect
616. C11#25960semidirect
726. C22#10622622semidirect

Maximal subgroups

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

subgroupindex
C2×#106226222
C22×#668962
#130723402
#130701372
#130700042
#130699902
#130697622
#130688772
#130688632
#130688032
#130687962
#130686392
#130686262
#130685472
D4×C11×C22⋊C42
#2596011