Finite Group Databasebeta

← #14684141

Subgroups — #14684141

Order 2816.

1506 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622560C211yesmaximal, characteristic
2#13066886C211yesmaximal, characteristic, complemented
3#13066886C211yesmaximal, characteristic, complemented
4#13066876C211yesmaximal, characteristic, complemented
5#13066876C211yesmaximal, characteristic, complemented
6#13066859C211yesmaximal, characteristic
7#13066853C211yesmaximal, characteristic
8#13066853C211yesmaximal, characteristic
9#13066851C211yesmaximal, characteristic, complemented
10#13066847C211yesmaximal, characteristic, complemented
11#13066841C211yesmaximal, characteristic, complemented
12#13066840C211yesmaximal, characteristic, complemented
13#13066839C211yesmaximal, characteristic
14#13066839C211yesmaximal, characteristic
15C11×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51#10622560C418yescomplemented
52C25×C11C2311yescharacteristic
53C23×C4×C11—22no—
54C23×C4×C11—22no—
55C23×C4×C11—22no—
56C23×C4×C11—41no—
57C23×C4×C11—41no—
58C23×C4×C11—41no—
59C23×C4×C11—41no—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C22×Dic22—41no—
75C22×Dic22—41no—
76C22×Dic22—41no—
77C22×Dic22—41no—
78C22×Dic22—41no—
79C22×Dic22—41no—
80C22×Dic22C2×C414yescomplemented
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—41no—
84C2×C11×C22⋊C4—41no—
85C2×C11×C22⋊C4—41no—
86C2×C11×C22⋊C4C2×C414yes—
87C2×C22⋊Dic11—22no—
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—41no—
90C2×C22⋊Dic11—41no—
91C2×C22⋊Dic11—41no—
92C2×C22⋊Dic11—41no—
93C2×C22⋊Dic11—41no—
94C2×C22⋊Dic11—41no—
95C2×C22⋊Dic11—41no—
96C2×C22⋊Dic11C2×C414yes—
97C2×C22⋊Dic11C2×C414yes—
98C2×C22⋊Dic11Q814yescomplemented
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4—22no—
101C2×Dic11⋊C4—41no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11—22no—
104C2×C4×Dic11—41no—
105C2×C4×Dic11—41no—
106C2×C4×Dic11—41no—
107C2×C4×Dic11—41no—
108C11×#95—22no—
109C11×#95—41no—
110C11×#95—41no—
111C11×#95—41no—
112C11⋊#95—22no—
113C11⋊#95—22no—
114C11⋊#95—22no—
115C11⋊#95—41no—
116C11⋊#95—41no—
117C11⋊#95—41no—
118C11⋊#95—41no—
119C11⋊#95—41no—
120C11⋊#95—41no—
121C11⋊#95—41no—
122C11⋊#95—41no—
123C11⋊#95—41no—
124C11⋊#95—41no—
125C11⋊#95—41no—
126C11⋊#95—41no—
127C11⋊#95—41no—
128C11⋊#95—41no—
129C11⋊#95C2×C414yescomplemented
130C11⋊#95C2×C414yescomplemented
131C11⋊#95C2×C414yescomplemented
132#14596—111nomaximal, Sylow
133C24×C11—21no—
134C24×C11—21no—
135C24×C11—21no—
136C24×C11—21no—
137C24×C11—21no—
138C24×C11—21no—
139C24×C11—21no—
140C24×C11—21no—
141C24×C11—21no—
142C24×C11—21no—
143C24×C11—21no—
144C24×C11—21no—
145C24×C11C22×C412yes—
146C24×C11C2×Q812yes—
147C24×C11#4112yes—
148C24×C11C2411yescharacteristic
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—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
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—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—44no—
187C22×C4×C11—44no—
188C22×C4×C11—44no—
189C22×C4×C11—44no—
190C22×C4×C11—44no—
191C22×C4×C11—44no—
192C22×C4×C11—44no—
193C22×C4×C11C22×C412yes—
194C22×C4×C11C22×C412yes—
195C22×C4×C11#4112yes—
196C22×C4×C11#4112yes—
197C22×C4×C11#4112yes—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11C22×C412yes—
248C22×Dic11C22×C412yes—
249C22×Dic11C22×C412yes—
250C22×Dic11C22×C412yes—
251C22×Dic11C2×Q812yes—
252C22×Dic11C2×Q812yes—
253C22×Dic11#4112yes—
254C2×Dic22—44no—
255C2×Dic22—44no—
256C2×Dic22—44no—
257C2×Dic22—44no—
258C2×Dic22—44no—
259C2×Dic22—44no—
260C2×Dic22—44no—
261C11×C22⋊C4—44no—
262C11×C22⋊C4—44no—
263C22⋊Dic11—44no—
264C22⋊Dic11—44no—
265C22⋊Dic11—44no—
266C22⋊Dic11—44no—
267Dic11⋊C4—44no—
268C4×Dic11—44no—
269C4×Dic11—44no—
270C2×#393—111no—
271#1446—111no—
272#1446—111no—
273#1443—111no—
274#1443—111no—
275#1439—111no—
276#1437—111no—
277#1437—111no—
278#1436—111no—
279#1436—111no—
280#1434—111no—
281#1434—111no—
282C22⋊#95—111no—
283C22⋊#95—111no—
284C22⋊#95D1111yescharacteristic
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11C4×Q814yes—
320C23×C11C23×C411yescharacteristic
321C23×C11C22×Q811yescharacteristic
322C23×C11C2×#4111yescharacteristic
323C23×C11C2×#4111yescharacteristic
324C23×C11C2×#4111yescharacteristic
325C23×C11C2×#4111yescharacteristic
326C23×C11C2×#4111yescharacteristic
327C23×C11H(5,𝔽2)11yescharacteristic
328C23×C11H(5,𝔽2)11yescharacteristic
329C23×C11H(5,𝔽2)11yescharacteristic
330C23×C11H(5,𝔽2)11yescharacteristic
331C23×C11H(5,𝔽2)11yescharacteristic
332C23×C11H(5,𝔽2)11yescharacteristic
333C23×C11H(5,𝔽2)11yescharacteristic
334C23×C112−1+411yescharacteristic
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—416no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—41no—
400C2×Dic11—41no—
401C2×Dic11—41no—
402C2×Dic11—41no—
403C2×Dic11—41no—
404C2×Dic11—41no—
405C2×Dic11—41no—
406C2×Dic11—41no—
407C2×Dic11—41no—
408C2×Dic11—41no—
409C2×Dic11—41no—
410C2×Dic11—41no—
411C2×Dic11—41no—
412C2×Dic11—41no—
413C2×Dic11—41no—
414C2×Dic11—41no—
415C2×Dic11—41no—
416C2×Dic11—41no—
417C2×Dic11—41no—
418C2×Dic11—41no—
419C2×Dic11—41no—
420C2×Dic11—41no—
421C2×Dic11—41no—
422C2×Dic11—41no—
423C2×Dic11—41no—
424C2×Dic11—41no—
425C2×Dic11—41no—
426C2×Dic11—41no—
427C2×Dic11—41no—
428C2×Dic11—41no—
429C2×Dic11—41no—
430C2×Dic11—41no—
431C2×Dic11—41no—
432C2×Dic11—41no—
433C2×Dic11—41no—
434Dic22—416no—
435C23×Q8—111no—
436C24×C4C2×D1111yescharacteristic
437C22×C4⋊C4—111no—
438C22×C22⋊C4—111no—
439C22×C22⋊C4—111no—
440C22×C22⋊C4—111no—
441C22×C22⋊C4—111no—
442C22×C22⋊C4C2×D1111yescharacteristic
443C22×C22⋊C4C2×D1111yescharacteristic
444C22×C42—111no—
445C22×C42—111no—
446#393—118no—
447C2×#95—111no—
448C2×#95—111no—
449C2×#95—111no—
450C2×#95—111no—
451C2×#95—111no—
452C2×#95—111no—
453C2×#95—111no—
454C2×#95—111no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95—111no—
460C2×#95—111no—
461C2×#95—111no—
462C2×#95—111no—
463C2×#95—111no—
464C2×#95—111no—
465C2×#95—111no—
466C2×#95—111no—
467C2×#95C2×D1111yescharacteristic
468C2×#95C2×D1111yescharacteristic
469C2×#95C2×D1111yescharacteristic
470C2×#95C2×D1111yescharacteristic
471C22×C11—24no—
472C22×C11—24no—
473C22×C11—24no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11C2×C4×Q811yescharacteristic
487C22×C11C4×#4111yescharacteristic
488C22×C11C4×#4111yescharacteristic
489C22×C11#51811yescharacteristic
490C22×C11#51811yescharacteristic
491C22×C11#51811yescharacteristic
492C22×C11#52011yescharacteristic
493C22×C11#53811yescharacteristic
494C22×C11#53811yescharacteristic
495C22×C11#53811yescharacteristic
496C22×C11#53811yescharacteristic
497C22×C11#53811yescharacteristic
498C22×C11#53911yescharacteristic
499C22×C11#54211yescharacteristic
500C22×C11#54211yescharacteristic
501C22×C11#54211yescharacteristic
502C22×C11#54211yescharacteristic
503C22×C11#54311yescharacteristic
504C22×C11#54411yescharacteristic
505C22×C11#55111yescharacteristic
506C22×C11#55111yescharacteristic
507C22×C11#55111yescharacteristic
508C22×C11#55111yescharacteristic
509C22×C11#55111yescharacteristic
510C22×C11#55111yescharacteristic
511C22×C11#55411yescharacteristic
512C22×C11#55411yescharacteristic
513C22×C11#55411yescharacteristic
514C22×C11#55411yescharacteristic
515C22×C11#55511yescharacteristic
516C22×C11#55511yescharacteristic
517C22×C11#56011yescharacteristic
518C22×C11#56011yescharacteristic
519C22×C11#56011yescharacteristic
520C22×C11H(3,𝔽4)11yescharacteristic
521C4×C11—42no—
522C4×C11—42no—
523C4×C11—42no—
524C4×C11—42no—
525C4×C11—42no—
526C4×C11—81no—
527Dic11—42no—
528Dic11—42no—
529Dic11—42no—
530Dic11—42no—
531Dic11—42no—
532Dic11—42no—
533Dic11—42no—
534Dic11—81no—
535C25C22×D1111yescharacteristic
536C22×Q8—114no—
537C22×Q8—441no—
538C22×Q8—441no—
539C22×Q8—441no—
540C22×Q8—441no—
541C22×Q8—441no—
542C22×Q8—441no—
543C23×C4—22no—
544C23×C4—22no—
545C23×C4—22no—
546C23×C4—41no—
547C23×C4—41no—
548C23×C4—41no—
549C23×C4—41no—
550C23×C4—111no—
551C23×C4—111no—
552C23×C4—111no—
553C23×C4—111no—
554C23×C4—111no—
555C23×C4—111no—
556C23×C4—111no—
557C23×C4—111no—
558C23×C4C22×D1111yescharacteristic
559C23×C4C22×D1111yescharacteristic
560C23×C4C22×D1111yescharacteristic
561C23×C4C22×D1111yescharacteristic
562C23×C4C22×D1111yescharacteristic
563C23×C4C22×D1111yescharacteristic
564C2×C4⋊C4—222no—
565C2×C4⋊C4—222no—
566C2×C4⋊C4—441no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—41no—
570C2×C22⋊C4—41no—
571C2×C22⋊C4—41no—
572C2×C22⋊C4—114no—
573C2×C22⋊C4—114no—
574C2×C22⋊C4—114no—
575C2×C22⋊C4—222no—
576C2×C22⋊C4—222no—
577C2×C22⋊C4—441no—
578C2×C22⋊C4—441no—
579C2×C22⋊C4—441no—
580C2×C22⋊C4—441no—
581C2×C22⋊C4—441no—
582C2×C22⋊C4—441no—
583C2×C22⋊C4—441no—
584C2×C22⋊C4C4×D1114yes—
585C2×C42—222no—
586C2×C42—222no—
587C2×C42—441no—
588C2×C42—441no—
589C2×C42—441no—
590C2×C42—441no—
591#95—22no—
592#95—41no—
593#95—41no—
594#95—41no—
595#95—114no—
596#95—114no—
597#95—114no—
598#95—222no—
599#95—222no—
600#95—222no—
601#95—441no—
602#95—441no—
603#95—441no—
604#95—441no—
605#95—441no—
606#95—441no—
607#95—441no—
608#95—441no—
609#95—441no—
610#95—441no—
611#95—441no—
612#95—441no—
613#95—441no—
614#95—441no—
615C2×C11—44no—
616C2×C11#232911yescharacteristic
617C2×C11#233711yescharacteristic
618C2×C11#233711yescharacteristic
619C2×C11#236811yescharacteristic
620C2×C11#236811yescharacteristic
621C2×C11#237211yescharacteristic
622C2×C11#237511yescharacteristic
623C2×C11#273611yescharacteristic
624C2×C11#273711yescharacteristic
625C2×C11#273711yescharacteristic
626C2×C11#274211yescharacteristic
627C2×C11#276011yescharacteristic
628C2×C11#276311yescharacteristic
629C2×C11#278411yescharacteristic
630C2×C11#278411yescharacteristic
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24C2×C4×D1112yes—
644C24#434112yes—
645C24Q8×D1112yes—
646C24C23×D1111yescharacteristic
647C2×Q8—444no—
648C2×Q8—444no—
649C2×Q8—444no—
650C2×Q8—444no—
651C2×Q8—444no—
652C2×Q8—444no—
653C2×Q8—444no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—44no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—112no—
699C22×C4—112no—
700C22×C4—112no—
701C22×C4—112no—
702C22×C4—112no—
703C22×C4—112no—
704C22×C4—112no—
705C22×C4—221no—
706C22×C4—221no—
707C22×C4—221no—
708C22×C4—221no—
709C22×C4—221no—
710C22×C4—221no—
711C22×C4—221no—
712C22×C4—221no—
713C22×C4—221no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—221no—
726C22×C4—221no—
727C22×C4—221no—
728C22×C4—221no—
729C22×C4—221no—
730C22×C4—221no—
731C22×C4—221no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4—221no—
735C22×C4—221no—
736C22×C4—221no—
737C22×C4—221no—
738C22×C4—221no—
739C22×C4—221no—
740C22×C4—221no—
741C22×C4—221no—
742C22×C4—221no—
743C22×C4—221no—
744C22×C4—221no—
745C22×C4—221no—
746C22×C4—221no—
747C22×C4—221no—
748C22×C4—221no—
749C22×C4—221no—
750C22×C4—221no—
751C22×C4—221no—
752C22×C4—221no—
753C22×C4—221no—
754C22×C4C2×C4×D1112yes—
755C22×C4C2×C4×D1112yes—
756C22×C4#433912yes—
757C22×C4#433912yes—
758C22×C4#434112yes—
759C4⋊C4—444no—
760C22⋊C4—44no—
761C22⋊C4—44no—
762C22⋊C4—444no—
763C22⋊C4—444no—
764C22⋊C4—444no—
765C22⋊C4—444no—
766C42—444no—
767C42—444no—
768C11#1459611yescharacteristic, complemented, Sylow
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23#6694014yes—
804C23C22×C4×D1111yescharacteristic
805C23C2×#433911yescharacteristic
806C23C2×#433911yescharacteristic
807C23C2×#434111yescharacteristic
808C23C2×#434111yescharacteristic
809C23#6703711yescharacteristic
810C23#6703711yescharacteristic
811C23#6703711yescharacteristic
812C23#6703711yescharacteristic
813C23#6703711yescharacteristic
814C23C2×Q8×D1111yescharacteristic
815C23#41×D1111yescharacteristic
816C23#6704211yescharacteristic
817C23#6704211yescharacteristic
818C23#6704311yescharacteristic
819Q8—4416no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—416no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—222no—
864C2×C4—222no—
865C2×C4—222no—
866C2×C4—222no—
867C2×C4—222no—
868C2×C4—222no—
869C2×C4—222no—
870C2×C4—222no—
871C2×C4—222no—
872C2×C4—222no—
873C2×C4—222no—
874C2×C4—222no—
875C2×C4—222no—
876C2×C4—222no—
877C2×C4—222no—
878C2×C4—222no—
879C2×C4—222no—
880C2×C4—222no—
881C2×C4—222no—
882C2×C4—222no—
883C2×C4—222no—
884C2×C4—441no—
885C2×C4—441no—
886C2×C4—441no—
887C2×C4—441no—
888C2×C4—441no—
889C2×C4—441no—
890C2×C4—441no—
891C2×C4—441no—
892C2×C4—441no—
893C2×C4—441no—
894C2×C4—441no—
895C2×C4—441no—
896C2×C4—441no—
897C2×C4—441no—
898C2×C4—441no—
899C2×C4—441no—
900C2×C4—441no—
901C2×C4—441no—
902C2×C4—441no—
903C2×C4—441no—
904C2×C4—441no—
905C2×C4—441no—
906C2×C4—441no—
907C2×C4—441no—
908C2×C4—441no—
909C2×C4—441no—
910C2×C4—441no—
911C2×C4—441no—
912C2×C4—441no—
913C2×C4—441no—
914C2×C4—441no—
915C2×C4—441no—
916C2×C4—441no—
917C2×C4—441no—
918C2×C4—441no—
919C22—24no—
920C22—24no—
921C22—24no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22C4×#433911yescharacteristic
935C22#1062301711yescharacteristic
936C22#1062302511yescharacteristic
937C22#1062302611yescharacteristic
938C22#1062302611yescharacteristic
939C22#1062302611yescharacteristic
940C22C2×#6694011yescharacteristic
941C22#1062304211yescharacteristic
942C22#1062304211yescharacteristic
943C22#1062306311yescharacteristic
944C22#1062306511yescharacteristic
945C22C4×#434111yescharacteristic
946C22#1062307611yescharacteristic
947C22#1062307611yescharacteristic
948C22#1062307711yescharacteristic
949C22#1062308711yescharacteristic
950C22#1062309111yescharacteristic
951C22#1062309211yescharacteristic
952C22#1062309411yescharacteristic
953C22#1062311811yescharacteristic
954C22#1062312411yescharacteristic
955C22#1062312411yescharacteristic
956C22#1062312511yescharacteristic
957C22#1062313411yescharacteristic
958C22#1062314411yescharacteristic
959C22#1062315111yescharacteristic
960C22#1062315111yescharacteristic
961C22#1062315411yescharacteristic
962C22#1062316511yescharacteristic
963C22#1062316611yescharacteristic
964C22#1062316711yescharacteristic
965C22#1062318911yescharacteristic
966C22#1062319311yescharacteristic
967C22#1062319611yescharacteristic
968C22#1062319711yescharacteristic
969C4—42no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—42no—
974C4—81no—
975C4—442no—
976C4—442no—
977C4—442no—
978C4—442no—
979C4—442no—
980C4—442no—
981C4—442no—
982C4—881no—
983C2—44no—
984C2#1307134711yescharacteristic
985C2#1307142411yescharacteristic
986C2#1307142511yescharacteristic
987C2#1307169611yescharacteristic
988C2#1307169711yescharacteristic
989C2#1307172411yescharacteristic
990C2#1307175411yescharacteristic
991C2#1307566211yescharacteristic
992C2#1307567111yescharacteristic
993C2#1307567511yescharacteristic
994C2#1307574111yescharacteristic
995C2#1307599211yescharacteristic
996C2#1307602811yescharacteristic
997C2#1307631311yescharacteristic
998C2#1307631511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC22⋊#95D11
hypocenterC11#14596
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. #13066886C2semidirect
3. #13066886C2semidirect
4. #13066876C2semidirect
5. #13066876C2semidirect
9. #13066851C2semidirect
10. #13066847C2semidirect
11. #13066841C2semidirect
12. #13066840C2semidirect
51. #10622560C4semidirect
80. C22×Dic22C2×C4semidirect
98. C2×C22⋊Dic11Q8semidirect
129. C11⋊#95C2×C4semidirect
130. C11⋊#95C2×C4semidirect
131. C11⋊#95C2×C4semidirect
768. C11#14596semidirect

Maximal subgroups

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

subgroupindex
C2×#106225602
#130668862
#130668762
#130668592
#130668532
#130668512
#130668472
#130668412
#130668402
#130668392
C11×C22⋊#952
#1459611