Finite Group Databasebeta

← #14684575

Subgroups — #14684575

Order 2816.

1378 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622561C211yesmaximal, characteristic
2#13066883C211yesmaximal, characteristic, complemented
3#13066882C211yesmaximal, characteristic, complemented
4#13066882C211yesmaximal, characteristic, complemented
5#13066879C211yesmaximal, characteristic, complemented
6#13066876C211yesmaximal, characteristic, complemented
7#13066868C211yesmaximal, characteristic, complemented
8#13066867C211yesmaximal, characteristic, complemented
9#13066866C211yesmaximal, characteristic, complemented
10#13066859C211yesmaximal, characteristic
11#13066859C211yesmaximal, characteristic
12#13066838C211yesmaximal, characteristic
13#13066838C211yesmaximal, characteristic
14#13066838C211yesmaximal, characteristic
15C11×#1439C211yesmaximal, characteristic
16C24×Dic11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
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#10622561C418yescomplemented
52C25×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×Dic11—41no—
60C23×Dic11—41no—
61C23×Dic11—41no—
62C23×Dic11—41no—
63C23×Dic11—41no—
64C23×Dic11—41no—
65C23×Dic11Q814yes—
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C2×C11×C4⋊C4—41no—
75C2×C11×C4⋊C4—41no—
76C2×C11×C4⋊C4—41no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—41no—
80C2×C11×C22⋊C4—41no—
81C2×C11×C22⋊C4—41no—
82C2×C11×C22⋊C4—41no—
83C2×C11×C22⋊C4—41no—
84C2×C11×C22⋊C4—41no—
85C2×C11×C22⋊C4C2×C414yes—
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11—41no—
88C2×C22⋊Dic11—41no—
89C2×C22⋊Dic11—41no—
90C2×C22⋊Dic11—41no—
91C2×C22⋊Dic11—41no—
92C2×C22⋊Dic11—41no—
93C2×C22⋊Dic11C2×C414yes—
94C2×C22⋊Dic11C2×C414yes—
95C2×C4⋊Dic11—41no—
96C2×C4⋊Dic11—41no—
97C2×C4⋊Dic11C2×C414yescomplemented
98C2×Dic11⋊C4—41no—
99C2×Dic11⋊C4—41no—
100C2×Dic11⋊C4—41no—
101C2×Dic11⋊C4—41no—
102C2×Dic11⋊C4—41no—
103C2×Dic11⋊C4—41no—
104C2×Dic11⋊C4—41no—
105C2×Dic11⋊C4—41no—
106C2×Dic11⋊C4—41no—
107C2×Dic11⋊C4—41no—
108C2×Dic11⋊C4C2×C414yescomplemented
109C2×Dic11⋊C4C2×C414yescomplemented
110C11×#95—41no—
111C11×#95—41no—
112C11×#95—41no—
113C11⋊#95—41no—
114C11⋊#95—41no—
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⋊#95—41no—
130C11⋊#95—41no—
131C11⋊#95C2×C414yescomplemented
132#14637—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—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11C22×C412yes—
190C22×C4×C11C22×C412yes—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—21no—
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—44no—
242C22×Dic11—44no—
243C22×Dic11—44no—
244C22×Dic11—44no—
245C22×Dic11—44no—
246C22×Dic11—44no—
247C22×Dic11—44no—
248C22×Dic11C22×C412yes—
249C22×Dic11C22×C412yes—
250C22×Dic11C22×C412yes—
251C22×Dic11C22×C412yes—
252C22×Dic11C2×Q812yes—
253C22×Dic11C2×Q812yes—
254C11×C4⋊C4—44no—
255C11×C22⋊C4—44no—
256C11×C22⋊C4—44no—
257C11×C22⋊C4—44no—
258C22⋊Dic11—44no—
259C22⋊Dic11—44no—
260C22⋊Dic11—44no—
261C4⋊Dic11—44no—
262Dic11⋊C4—44no—
263Dic11⋊C4—44no—
264Dic11⋊C4—44no—
265Dic11⋊C4—44no—
266C2×#396—111no—
267#1445—111no—
268#1445—111no—
269#1445—111no—
270#1444—111no—
271#1443—111no—
272#1441—111no—
273#1441—111no—
274#1441—111no—
275#1439—111no—
276#1439—111no—
277#1439D1111yescharacteristic
278C22⋊#95—111no—
279C22⋊#95—111no—
280C22⋊#95—111no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
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—41no—
300C23×C11—41no—
301C23×C11—41no—
302C23×C11—41no—
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×C11C4×Q814yes—
316C23×C11C23×C411yescharacteristic
317C23×C11C22×Q811yescharacteristic
318C23×C11C2×#4111yescharacteristic
319C23×C11H(5,𝔽2)11yescharacteristic
320C23×C11H(5,𝔽2)11yescharacteristic
321C23×C11H(5,𝔽2)11yescharacteristic
322C23×C11H(5,𝔽2)11yescharacteristic
323C23×C11H(5,𝔽2)11yescharacteristic
324C23×C11H(5,𝔽2)11yescharacteristic
325C23×C11H(5,𝔽2)11yescharacteristic
326C23×C11H(5,𝔽2)11yescharacteristic
327C23×C11H(5,𝔽2)11yescharacteristic
328C23×C112−1+411yescharacteristic
329C23×C112−1+411yescharacteristic
330C23×C112−1+411yescharacteristic
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
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×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
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—416no—
392C2×Dic11—41no—
393C2×Dic11—41no—
394C2×Dic11—41no—
395C2×Dic11—41no—
396C2×Dic11—41no—
397C2×Dic11—41no—
398C2×Dic11—41no—
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—
430C24×C4—111no—
431C22×C4⋊C4—111no—
432C22×C4⋊C4—111no—
433C22×C4⋊C4—111no—
434C22×C4⋊C4—111no—
435C22×C4⋊C4—111no—
436C22×C4⋊C4C2×D1111yescharacteristic
437C22×C22⋊C4—111no—
438C22×C22⋊C4—111no—
439C22×C22⋊C4—111no—
440C22×C22⋊C4C2×D1111yescharacteristic
441C22×C22⋊C4C2×D1111yescharacteristic
442C22×C22⋊C4C2×D1111yescharacteristic
443#396—118no—
444C2×#95—111no—
445C2×#95—111no—
446C2×#95—111no—
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×#95C2×D1111yescharacteristic
464C2×#95C2×D1111yescharacteristic
465C2×#95C2×D1111yescharacteristic
466C22×C11—24no—
467C22×C11—24no—
468C22×C11—24no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11C2×C4×Q811yescharacteristic
482C22×C11#51811yescharacteristic
483C22×C11#51811yescharacteristic
484C22×C11#51811yescharacteristic
485C22×C11#52011yescharacteristic
486C22×C11#52011yescharacteristic
487C22×C11#52011yescharacteristic
488C22×C11#53811yescharacteristic
489C22×C11#53811yescharacteristic
490C22×C11#53811yescharacteristic
491C22×C11#53911yescharacteristic
492C22×C11#53911yescharacteristic
493C22×C11#53911yescharacteristic
494C22×C11#54311yescharacteristic
495C22×C11#54311yescharacteristic
496C22×C11#54311yescharacteristic
497C22×C11#54411yescharacteristic
498C22×C11#54411yescharacteristic
499C22×C11#54411yescharacteristic
500C22×C11#56011yescharacteristic
501C22×C11#56011yescharacteristic
502C22×C11#56011yescharacteristic
503C22×C11#56011yescharacteristic
504C22×C11#56011yescharacteristic
505C22×C11#56011yescharacteristic
506C22×C11#56011yescharacteristic
507C22×C11#56211yescharacteristic
508C22×C11#56211yescharacteristic
509C22×C11#56211yescharacteristic
510C22×C11#56211yescharacteristic
511C22×C11#56211yescharacteristic
512C22×C11#56211yescharacteristic
513C22×C11#56311yescharacteristic
514C22×C11#56311yescharacteristic
515C22×C11#56311yescharacteristic
516C4×C11—42no—
517C4×C11—42no—
518C4×C11—81no—
519C4×C11—81no—
520C4×C11—81no—
521C4×C11—81no—
522Dic11—42no—
523Dic11—42no—
524Dic11—42no—
525Dic11—42no—
526Dic11—42no—
527Dic11—42no—
528Dic11—81no—
529Dic11—81no—
530C25C22×D1111yescharacteristic
531C23×C4—111no—
532C23×C4—111no—
533C23×C4—111no—
534C23×C4—111no—
535C23×C4—111no—
536C23×C4—111no—
537C23×C4—114no—
538C23×C4—111no—
539C23×C4—111no—
540C23×C4—441no—
541C23×C4—441no—
542C23×C4—441no—
543C23×C4—441no—
544C23×C4—441no—
545C23×C4—441no—
546C23×C4C22×D1111yescharacteristic
547C23×C4C22×D1111yescharacteristic
548C23×C4C22×D1111yescharacteristic
549C23×C4C22×D1111yescharacteristic
550C23×C4C22×D1111yescharacteristic
551C23×C4C22×D1111yescharacteristic
552C2×C4⋊C4—41no—
553C2×C4⋊C4—41no—
554C2×C4⋊C4—41no—
555C2×C4⋊C4—114no—
556C2×C4⋊C4—114no—
557C2×C4⋊C4—114no—
558C2×C4⋊C4—441no—
559C2×C4⋊C4—441no—
560C2×C4⋊C4—441no—
561C2×C4⋊C4—441no—
562C2×C4⋊C4—441no—
563C2×C4⋊C4—441no—
564C2×C4⋊C4—441no—
565C2×C4⋊C4—441no—
566C2×C4⋊C4—441no—
567C2×C4⋊C4—441no—
568C2×C4⋊C4—441no—
569C2×C4⋊C4—441no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—41no—
573C2×C22⋊C4—41no—
574C2×C22⋊C4—41no—
575C2×C22⋊C4—41no—
576C2×C22⋊C4—41no—
577C2×C22⋊C4—41no—
578C2×C22⋊C4—114no—
579C2×C22⋊C4—114no—
580C2×C22⋊C4—222no—
581C2×C22⋊C4—441no—
582C2×C22⋊C4—441no—
583C2×C22⋊C4—441no—
584C2×C22⋊C4—441no—
585C2×C22⋊C4—441no—
586C2×C22⋊C4—441no—
587C2×C22⋊C4C4×D1114yes—
588#95—41no—
589#95—41no—
590#95—41no—
591#95—114no—
592#95—441no—
593#95—441no—
594#95—441no—
595#95—441no—
596#95—441no—
597#95—441no—
598#95—441no—
599#95—441no—
600#95—441no—
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—
610C2×C11—44no—
611C2×C11#232911yescharacteristic
612C2×C11#232911yescharacteristic
613C2×C11#232911yescharacteristic
614C2×C11#237711yescharacteristic
615C2×C11#237711yescharacteristic
616C2×C11#237711yescharacteristic
617C2×C11#238311yescharacteristic
618C2×C11#282511yescharacteristic
619C2×C11#282711yescharacteristic
620C2×C11#282711yescharacteristic
621C2×C11#282711yescharacteristic
622C2×C11#284111yescharacteristic
623C2×C11#284111yescharacteristic
624C2×C11#284111yescharacteristic
625C2×C11#284211yescharacteristic
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24C2×C4×D1112yes—
639C24#434112yes—
640C24Q8×D1112yes—
641C24C23×D1111yescharacteristic
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
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—112no—
683C22×C4—112no—
684C22×C4—112no—
685C22×C4—112no—
686C22×C4—112no—
687C22×C4—112no—
688C22×C4—221no—
689C22×C4—221no—
690C22×C4—221no—
691C22×C4—221no—
692C22×C4—221no—
693C22×C4—221no—
694C22×C4—221no—
695C22×C4—221no—
696C22×C4—221no—
697C22×C4—221no—
698C22×C4—221no—
699C22×C4—221no—
700C22×C4—221no—
701C22×C4—221no—
702C22×C4—221no—
703C22×C4—221no—
704C22×C4—221no—
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—444no—
739C22×C4—444no—
740C22×C4—444no—
741C22×C4—444no—
742C22×C4—444no—
743C22×C4—444no—
744C22×C4—444no—
745C22×C4C2×C4×D1112yes—
746C22×C4C2×C4×D1112yes—
747C4⋊C4—44no—
748C4⋊C4—444no—
749C4⋊C4—444no—
750C4⋊C4—444no—
751C4⋊C4—444no—
752C4⋊C4—444no—
753C22⋊C4—44no—
754C22⋊C4—44no—
755C22⋊C4—44no—
756C22⋊C4—444no—
757C22⋊C4—444no—
758C22⋊C4—444no—
759C11#1463711yescharacteristic, complemented, Sylow
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23#6694014yes—
795C23C22×C4×D1111yescharacteristic
796C23C2×#434111yescharacteristic
797C23#6703711yescharacteristic
798C23#6703711yescharacteristic
799C23#6703711yescharacteristic
800C23#6703711yescharacteristic
801C23#6703711yescharacteristic
802C23#6703711yescharacteristic
803C23C2×Q8×D1111yescharacteristic
804C23#6704211yescharacteristic
805C23#6704211yescharacteristic
806C23#6704211yescharacteristic
807C23#6704311yescharacteristic
808C23#6704311yescharacteristic
809C23#6704311yescharacteristic
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
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—222no—
853C2×C4—222no—
854C2×C4—222no—
855C2×C4—222no—
856C2×C4—222no—
857C2×C4—222no—
858C2×C4—222no—
859C2×C4—222no—
860C2×C4—222no—
861C2×C4—222no—
862C2×C4—222no—
863C2×C4—222no—
864C2×C4—222no—
865C2×C4—222no—
866C2×C4—222no—
867C2×C4—222no—
868C2×C4—222no—
869C2×C4—222no—
870C2×C4—4416no—
871C2×C4—441no—
872C2×C4—441no—
873C2×C4—441no—
874C2×C4—441no—
875C2×C4—441no—
876C2×C4—441no—
877C2×C4—441no—
878C2×C4—441no—
879C2×C4—441no—
880C2×C4—441no—
881C2×C4—441no—
882C2×C4—441no—
883C2×C4—441no—
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—
909C22—24no—
910C22—24no—
911C22—24no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22#1062301711yescharacteristic
925C22C2×#6694011yescharacteristic
926C22#1062305411yescharacteristic
927C22#1062307611yescharacteristic
928C22#1062307611yescharacteristic
929C22#1062307711yescharacteristic
930C22#1062307711yescharacteristic
931C22#1062312411yescharacteristic
932C22#1062312411yescharacteristic
933C22#1062312611yescharacteristic
934C22#1062313311yescharacteristic
935C22#1062314811yescharacteristic
936C22#1062315111yescharacteristic
937C22#1062315111yescharacteristic
938C22#1062315111yescharacteristic
939C22#1062315111yescharacteristic
940C22#1062315211yescharacteristic
941C22#1062315211yescharacteristic
942C22#1062315411yescharacteristic
943C22#1062315411yescharacteristic
944C22#1062315411yescharacteristic
945C22#1062316511yescharacteristic
946C22#1062316511yescharacteristic
947C22#1062316511yescharacteristic
948C22#1062318211yescharacteristic
949C22#1062319611yescharacteristic
950C22#1062319611yescharacteristic
951C22#1062319811yescharacteristic
952C22#1062319811yescharacteristic
953C22#1062320311yescharacteristic
954C22#1062321511yescharacteristic
955C22#1062321511yescharacteristic
956C22#1062324211yescharacteristic
957C22#1062324311yescharacteristic
958C22#1062325111yescharacteristic
959C4—42no—
960C4—42no—
961C4—81no—
962C4—81no—
963C4—81no—
964C4—81no—
965C4—442no—
966C4—442no—
967C4—442no—
968C4—442no—
969C4—442no—
970C4—442no—
971C4—881no—
972C4—881no—
973C2—44no—
974C2#1307134611yescharacteristic
975C2#1307134711yescharacteristic
976C2#1307134711yescharacteristic
977C2#1307176711yescharacteristic
978C2#1307176811yescharacteristic
979C2#1307176911yescharacteristic
980C2#1307180311yescharacteristic
981C2#1307670411yescharacteristic
982C2#1307672411yescharacteristic
983C2#1307672611yescharacteristic
984C2#1307672811yescharacteristic
985C2#1307687611yescharacteristic
986C2#1307687711yescharacteristic
987C2#1307687811yescharacteristic
988C2#1307687911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenter#1439D11
hypocenterC11#14637
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. #13066883C2semidirect
3. #13066882C2semidirect
4. #13066882C2semidirect
5. #13066879C2semidirect
6. #13066876C2semidirect
7. #13066868C2semidirect
8. #13066867C2semidirect
9. #13066866C2semidirect
51. #10622561C4semidirect
97. C2×C4⋊Dic11C2×C4semidirect
108. C2×Dic11⋊C4C2×C4semidirect
109. C2×Dic11⋊C4C2×C4semidirect
131. C11⋊#95C2×C4semidirect
759. C11#14637semidirect

Maximal subgroups

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

subgroupindex
C2×#106225612
#130668832
#130668822
#130668792
#130668762
#130668682
#130668672
#130668662
#130668592
#130668382
C11×#14392
#1463711