Finite Group Databasebeta

← #14676148

Subgroups — #14676148

Order 2816.

2458 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2C2×#10622570C212yesmaximal
3C2×#10622260C212yesmaximal, complemented
4C2×#10622825C211yesmaximal, characteristic, complemented
5C2×#10622280C211yesmaximal, characteristic, complemented
6#13066862C212yesmaximal, complemented
7#13066859C212yesmaximal, complemented
8Dic11⋊#95C211yesmaximal, characteristic, complemented
9(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
10#95×Dic11C211yesmaximal, characteristic, complemented
11C11×C22⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C22×C11×C22⋊C4C2212yes—
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2211yescharacteristic
18C2×C4×C22⋊D11—28no—
19C2×C4×C22⋊D11C418yescomplemented
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×C4⋊Dic11C2212yes—
24C22×Dic11⋊C4C2212yes—
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2211yescharacteristic
27C22×C4×Dic11C2212yes—
28C22×C4×Dic11C2211yescharacteristic
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2212yes—
32#10622825—24no—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38#10622570—28no—
39#10622280—24no—
40#10622260—28no—
41C25×C11C2311yescharacteristic
42C24×D11C2311yescharacteristic
43C23×C4×C11—24no—
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11—42no—
47C23×C4×C11C2×C414yes—
48C23×C4×C11C2312yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C22×C22⋊D11—24no—
53C22×C22⋊D11—24no—
54C22×C22⋊D11C2×C414yes—
55C22×C22⋊D11D414yes—
56C22×C22⋊D11Q814yes—
57C23×Dic11C2312yes—
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2312yes—
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C22×C4×D11—22no—
63C22×C4×D11—22no—
64C22×C4×D11—24no—
65C22×C4×D11—42no—
66C22×C4×D11C2×C414yes—
67C2×C11×C22⋊C4—24no—
68C2×C11×C22⋊C4—24no—
69C2×C11×C22⋊C4—42no—
70C2×C22⋊Dic11—24no—
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11—24no—
73C2×C22⋊Dic11—42no—
74C2×C22⋊Dic11C2×C414yes—
75C4×C22⋊D11—232no—
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—42no—
82C2×(C2×D11)⋊C4—42no—
83C2×(C2×D11)⋊C4C2×C414yes—
84C2×C4⋊Dic11—24no—
85C2×C4⋊Dic11—24no—
86C2×C4⋊Dic11—42no—
87C2×Dic11⋊C4—24no—
88C2×Dic11⋊C4—24no—
89C2×Dic11⋊C4—24no—
90C2×Dic11⋊C4—24no—
91C2×Dic11⋊C4—24no—
92C2×Dic11⋊C4—42no—
93C2×Dic11⋊C4C2×C414yes—
94C2×Dic11⋊C4D418yes—
95C2×C4×Dic11—24no—
96C2×C4×Dic11—24no—
97C2×C4×Dic11—24no—
98C2×C4×Dic11—24no—
99C2×C4×Dic11C2×C414yes—
100C11×#95—24no—
101C11×#95—22no—
102C11×#95—22no—
103C11⋊#95—22no—
104C11⋊#95—24no—
105C11⋊#95—24no—
106C11⋊#95—42no—
107C11⋊#95D414yescomplemented
108#13920—111nomaximal, Sylow
109C24×C11—21no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—21no—
114C24×C11—21no—
115C24×C11—22no—
116C24×C11—21no—
117C24×C11C22×C412yes—
118C24×C11C2×D412yes—
119C24×C11C2×Q812yes—
120C24×C11C2411yescharacteristic
121C23×D11—21no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11—21no—
125C23×D11—22no—
126C23×D11—21no—
127C23×D11—22no—
128C23×D11—21no—
129C23×D11C22×C412yes—
130C23×D11C2×D412yes—
131C23×D11C2×Q812yes—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—28no—
144C22×C4×C11—28no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—44no—
153C22×C4×C11—48no—
154C22×C4×C11—48no—
155C22×C4×C11C22×C412yes—
156C22×C4×C11C22×C412yes—
157C22×C4×C11C2×D414yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11#4114yes—
160C22×C4×C11#4112yes—
161C2×C22⋊D11—28no—
162C2×C22⋊D11—28no—
163C2×C22⋊D11—216no—
164C2×C22⋊D11—216no—
165C2×C22⋊D11C4⋊C4116yescomplemented
166C22×Dic11—21no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—21no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—21no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—21no—
186C22×Dic11C22×C412yes—
187C22×Dic11C22×C412yes—
188C22×Dic11C22×C412yes—
189C22×Dic11C2×D414yes—
190C22×Dic11C2×D414yes—
191C22×Dic11C2×D414yes—
192C22×Dic11C2×D412yes—
193C22×Dic11C2×Q812yes—
194C22×Dic11#4114yes—
195C2×C4×D11—28no—
196C2×C4×D11—28no—
197C2×C4×D11—44no—
198C2×C4×D11—48no—
199C2×C4×D11—48no—
200C11×C22⋊C4—48no—
201C22⋊Dic11—28no—
202C22⋊Dic11—48no—
203(C2×D11)⋊C4—28no—
204(C2×D11)⋊C4—48no—
205(C2×D11)⋊C4—48no—
206C4⋊Dic11—48no—
207Dic11⋊C4—48no—
208Dic11⋊C4—48no—
209Dic11⋊C4C22⋊C4116yescomplemented
210C4×Dic11—28no—
211C4×Dic11—48no—
212C22×C4×D4—111no—
213C2×#390—112no—
214C2×#389—112no—
215C2×#380—111no—
216C2×#380—111no—
217#1439—112no—
218#1439—112no—
219C4⋊#95—111no—
220C22⋊#95—111no—
221C22⋊#95D1111yescharacteristic, complemented
222C4×#95—111no—
223C23×C11—22no—
224C23×C11—22no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—22no—
229C23×C11—24no—
230C23×C11—24no—
231C23×C11—22no—
232C23×C11—24no—
233C23×C11—22no—
234C23×C11—22no—
235C23×C11—24no—
236C23×C11—22no—
237C23×C11—42no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—42no—
244C23×C11—42no—
245C23×C11C2×C4⋊C414yes—
246C23×C11C23×C411yescharacteristic
247C23×C11C22×D412yes—
248C23×C11C22×D411yescharacteristic
249C23×C11C22×D411yescharacteristic
250C23×C11C22×Q811yescharacteristic
251C23×C11C2×#4112yes—
252C23×C11C2×#4111yescharacteristic
253C23×C11C2×#4112yes—
254C23×C11H(5,𝔽2)12yes—
255C23×C11H(5,𝔽2)11yescharacteristic
256C23×C112−1+411yescharacteristic
257C22×D11—22no—
258C22×D11—22no—
259C22×D11—22no—
260C22×D11—22no—
261C22×D11—22no—
262C22×D11—22no—
263C22×D11—24no—
264C22×D11—24no—
265C22×D11—22no—
266C22×D11—24no—
267C22×D11—22no—
268C22×D11—22no—
269C22×D11—24no—
270C22×D11—22no—
271C22×D11—42no—
272C22×D11—42no—
273C22×D11—42no—
274C22×D11—42no—
275C22×D11—42no—
276C22×D11—42no—
277C22×D11—42no—
278C22×D11—42no—
279C22×D11C2×C4⋊C414yes—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—24no—
285C2×C4×C11—24no—
286C2×C4×C11—24no—
287C2×C4×C11—24no—
288C2×C4×C11—24no—
289C2×C4×C11—24no—
290C2×C4×C11—24no—
291C2×C4×C11—416no—
292C2×C4×C11—42no—
293C2×C4×C11—42no—
294C2×C4×C11—42no—
295C2×C4×C11—42no—
296C2×C4×C11—42no—
297C2×C4×C11—42no—
298C2×C4×C11—42no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11C2×C22⋊C414yes—
304C2×C4×C11C4×D414yes—
305C22⋊D11—232no—
306C2×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—24no—
309C2×Dic11—24no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—24no—
314C2×Dic11—24no—
315C2×Dic11—24no—
316C2×Dic11—42no—
317C2×Dic11—42no—
318C2×Dic11—42no—
319C2×Dic11—42no—
320C2×Dic11—42no—
321C2×Dic11—42no—
322C2×Dic11—42no—
323C2×Dic11—42no—
324C2×Dic11—42no—
325C2×Dic11—42no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11C2×C22⋊C414yes—
330C2×Dic11C2×C22⋊C414yes—
331C2×Dic11C2×C4⋊C414yes—
332C2×Dic11#11714yes—
333C2×Dic11#12118yes—
334C2×Dic11C22⋊Q818yes—
335C4×D11—416no—
336C23×D4—111no—
337C24×C4—111no—
338C24×C4C2×D1111yescharacteristic
339C2×C4×D4—118no—
340C2×C4×D4—228no—
341C22×C4⋊C4—111no—
342C22×C4⋊C4—112no—
343C22×C4⋊C4—112no—
344C22×C4⋊C4—112no—
345C22×C22⋊C4—111no—
346C22×C22⋊C4—111no—
347C22×C22⋊C4—112no—
348C22×C22⋊C4—112no—
349C22×C22⋊C4—112no—
350C22×C22⋊C4C2×D1112yes—
351C22×C42—111no—
352C22×C42—112no—
353#390—228no—
354#389—228no—
355#380—224no—
356#380—224no—
357C2×#95—111no—
358C2×#95—112no—
359C2×#95—111no—
360C2×#95—112no—
361C2×#95—112no—
362C2×#95C2×D1111yescharacteristic
363C2×#95C2×D1111yescharacteristic
364C2×#95C2×D1112yes—
365C22×C11—24no—
366C22×C11—24no—
367C22×C11—24no—
368C22×C11—42no—
369C22×C11—42no—
370C22×C11—42no—
371C22×C11—44no—
372C22×C11—44no—
373C22×C11—44no—
374C22×C11—44no—
375C22×C11—42no—
376C22×C11C22×C22⋊C411yescharacteristic
377C22×C11C22×C4⋊C411yescharacteristic
378C22×C11C2×#11711yescharacteristic
379C22×C11C2×C4×D411yescharacteristic
380C22×C11C4×#4111yescharacteristic
381C22×C11#51811yescharacteristic
382C22×C11#52011yescharacteristic
383C22×C11C2×#12112yes—
384C22×C11C2×C22⋊Q812yes—
385C22×C11#52912yes—
386C22×C11#53212yes—
387C22×C11#54012yes—
388C22×C11#54212yes—
389C22×C11D4212yes—
390C22×C11D4211yescharacteristic
391C22×C11#54612yes—
392C22×C11#54612yes—
393C22×C11#54711yescharacteristic
394C22×C11#54812yes—
395C22×C11D4×Q811yescharacteristic
396C22×C11#55012yes—
397C22×C11#55412yes—
398C22×C11#55411yescharacteristic
399C2×D11—24no—
400C2×D11—24no—
401C2×D11—24no—
402C2×D11—42no—
403C2×D11—42no—
404C2×D11—42no—
405C2×D11—44no—
406C2×D11—44no—
407C2×D11—44no—
408C2×D11—44no—
409C2×D11—42no—
410C4×C11—24no—
411C4×C11—24no—
412C4×C11—44no—
413C4×C11—82no—
414Dic11—24no—
415Dic11—42no—
416Dic11—44no—
417Dic11—82no—
418Dic11#38018yescomplemented
419C25—111no—
420C25C22×D1111yescharacteristic
421C22×D4—114no—
422C22×D4—114no—
423C22×D4—114no—
424C22×D4—224no—
425C22×D4—224no—
426C23×C4—24no—
427C23×C4—22no—
428C23×C4—22no—
429C23×C4—42no—
430C23×C4—111no—
431C23×C4—111no—
432C23×C4—112no—
433C23×C4—111no—
434C23×C4—114no—
435C23×C4—112no—
436C23×C4—224no—
437C23×C4—222no—
438C23×C4—222no—
439C23×C4—442no—
440C23×C4C4×D1114yes—
441C23×C4C22×D1112yes—
442C23×C4C22×D1112yes—
443C23×C4C22×D1111yescharacteristic
444C23×C4C22×D1111yescharacteristic
445C4×D4—2232no—
446C2×C4⋊C4—114no—
447C2×C4⋊C4—118no—
448C2×C4⋊C4—224no—
449C2×C4⋊C4—224no—
450C2×C4⋊C4—224no—
451C2×C4⋊C4—224no—
452C2×C4⋊C4—224no—
453C2×C4⋊C4—224no—
454C2×C4⋊C4—224no—
455C2×C4⋊C4—442no—
456C2×C4⋊C4—442no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—42no—
460C2×C22⋊C4—114no—
461C2×C22⋊C4—114no—
462C2×C22⋊C4—224no—
463C2×C22⋊C4—224no—
464C2×C22⋊C4—224no—
465C2×C22⋊C4—224no—
466C2×C22⋊C4—224no—
467C2×C22⋊C4—224no—
468C2×C22⋊C4—224no—
469C2×C22⋊C4—224no—
470C2×C22⋊C4—442no—
471C2×C22⋊C4—442no—
472C2×C22⋊C4—442no—
473C2×C42—114no—
474C2×C42—224no—
475C2×C42—224no—
476C2×C42—224no—
477C2×C42—224no—
478#95—22no—
479#95—24no—
480#95—22no—
481#95—114no—
482#95—224no—
483#95—224no—
484#95—222no—
485#95—442no—
486C2×C11—44no—
487C2×C11C2×#38011yescharacteristic
488C2×C11#229311yescharacteristic
489C2×C11#231911yescharacteristic
490C2×C11D4×C22⋊C411yescharacteristic
491C2×C11#234111yescharacteristic
492C2×C11D4×C4⋊C411yescharacteristic
493C2×C11#234911yescharacteristic
494C2×C11#242712yes—
495C2×C11#242812yes—
496C2×C11#245212yes—
497C2×C11#245412yes—
498D11—44no—
499C24—22no—
500C24—21no—
501C24—22no—
502C24—21no—
503C24—22no—
504C24—22no—
505C24—21no—
506C24—21no—
507C24—112no—
508C24—112no—
509C24—112no—
510C24—222no—
511C24—221no—
512C24—222no—
513C24—221no—
514C24—222no—
515C24—222no—
516C24—221no—
517C24—221no—
518C24C2×C4×D1112yes—
519C24D4×D1112yes—
520C24Q8×D1112yes—
521C24C23×D1111yescharacteristic
522C2×D4—1116no—
523C2×D4—228no—
524C2×D4—228no—
525C2×D4—2216no—
526C2×D4—2216no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—28no—
539C22×C4—28no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—44no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—112no—
551C22×C4—114no—
552C22×C4—112no—
553C22×C4—112no—
554C22×C4—114no—
555C22×C4—112no—
556C22×C4—114no—
557C22×C4—112no—
558C22×C4—114no—
559C22×C4—228no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—222no—
563C22×C4—222no—
564C22×C4—222no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—221no—
571C22×C4—222no—
572C22×C4—221no—
573C22×C4—228no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—444no—
582C22×C4—448no—
583C22×C4—448no—
584C22×C4C2×C4×D1112yes—
585C22×C4C2×C4×D1112yes—
586C22×C4#433914yes—
587C22×C4D4×D1114yes—
588C22×C4D4×D1112yes—
589C22×C4#434112yes—
590C4⋊C4—1116no—
591C4⋊C4—448no—
592C4⋊C4—448no—
593C4⋊C4—448no—
594C22⋊C4—48no—
595C22⋊C4—228no—
596C22⋊C4—228no—
597C22⋊C4—448no—
598C22⋊C4—448no—
599C22⋊C4—448no—
600C42—228no—
601C42—448no—
602C11#1392011yescharacteristic, complemented, Sylow
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—24no—
608C23—24no—
609C23—22no—
610C23—22no—
611C23—24no—
612C23—22no—
613C23—22no—
614C23—24no—
615C23—22no—
616C23—22no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—114no—
626C23—222no—
627C23—222no—
628C23—222no—
629C23—222no—
630C23—224no—
631C23—224no—
632C23—222no—
633C23—222no—
634C23—224no—
635C23—222no—
636C23—222no—
637C23—224no—
638C23—222no—
639C23—222no—
640C23—442no—
641C23—442no—
642C23—442no—
643C23—442no—
644C23—442no—
645C23—442no—
646C23—442no—
647C23—442no—
648C23C4⋊C4×D1114yes—
649C23C22×C4×D1111yescharacteristic
650C23C2×#433912yes—
651C23C2×D4×D1112yes—
652C23C2×D4×D1111yescharacteristic
653C23C2×D4×D1111yescharacteristic
654C23C2×#434111yescharacteristic
655C23#6703712yes—
656C23C2×Q8×D1111yescharacteristic
657C23#41×D1112yes—
658C23#6704211yescharacteristic
659C23#6704311yescharacteristic
660D4—2232no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—416no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—114no—
685C2×C4—114no—
686C2×C4—114no—
687C2×C4—118no—
688C2×C4—118no—
689C2×C4—114no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—224no—
693C2×C4—224no—
694C2×C4—222no—
695C2×C4—222no—
696C2×C4—222no—
697C2×C4—224no—
698C2×C4—224no—
699C2×C4—224no—
700C2×C4—4416no—
701C2×C4—442no—
702C2×C4—442no—
703C2×C4—442no—
704C2×C4—442no—
705C2×C4—442no—
706C2×C4—442no—
707C2×C4—442no—
708C2×C4—442no—
709C2×C4—442no—
710C2×C4—442no—
711C2×C4—442no—
712C2×C4—442no—
713C2×C4—442no—
714C2×C4C22⋊C4×D1114yes—
715C2×C4(C22⋊D11)⋊C414yes—
716C22—24no—
717C22—24no—
718C22—24no—
719C22—44no—
720C22—42no—
721C22—44no—
722C22—44no—
723C22—42no—
724C22—44no—
725C22—42no—
726C22—42no—
727C22—224no—
728C22—224no—
729C22—224no—
730C22—444no—
731C22—442no—
732C22—444no—
733C22—444no—
734C22—442no—
735C22—444no—
736C22—442no—
737C22—442no—
738C22C4×#433911yescharacteristic
739C22C2×C22⋊C4×D1111yescharacteristic
740C22C2×(C22⋊D11)⋊C411yescharacteristic
741C22#1062301711yescharacteristic
742C22#1062302112yes—
743C22C2×C4⋊C4×D1111yescharacteristic
744C22#1062304212yes—
745C22D11×#11711yescharacteristic
746C22#1062305411yescharacteristic
747C22#1062306912yes—
748C22#1062307912yes—
749C22#1062308312yes—
750C22#1062308412yes—
751C22#1062312112yes—
752C22#1062312212yes—
753C22D11×#12112yes—
754C22#1062314011yescharacteristic
755C22#1062314211yescharacteristic
756C22D11×C22⋊Q812yes—
757C22#1062316311yescharacteristic
758C22#1062316611yescharacteristic
759C22#1062319312yes—
760C22#1062319412yes—
761C4—24no—
762C4—24no—
763C4—44no—
764C4—82no—
765C4—118no—
766C4—224no—
767C4—444no—
768C4—442no—
769C4—882no—
770C2—44no—
771C2—444no—
772C2D11×#38011yescharacteristic
773C2#1307107911yescharacteristic
774C2#1307125611yescharacteristic
775C2#1307143211yescharacteristic
776C2#1307145611yescharacteristic
777C2#1307151211yescharacteristic
778C2#1307152311yescharacteristic
779C2#1307219012yes—
780C2#1307220312yes—
781C2#1307246312yes—
782C2#1307248512yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22⋊#95D11
hypocenterC11#13920
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#10622260C2semidirect
4. C2×#10622825C2semidirect
5. C2×#10622280C2semidirect
6. #13066862C2semidirect
7. #13066859C2semidirect
8. Dic11⋊#95C2semidirect
9. (C2×D11)⋊#95C2semidirect
10. #95×Dic11C2semidirect
11. C11×C22⋊#95C2semidirect
19. C2×C4×C22⋊D11C4semidirect
107. C11⋊#95D4semidirect
165. C2×C22⋊D11C4⋊C4semidirect
209. Dic11⋊C4C22⋊C4semidirect
221. C22⋊#95D11semidirect
418. Dic11#380semidirect
602. C11#13920semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
C2×#106225702
C2×#106222602
C2×#106228252
C2×#106222802
#130668622
#130668592
Dic11⋊#952
(C2×D11)⋊#952
#95×Dic112
C11×C22⋊#952
#1392011