Finite Group Databasebeta

← #14680906

Subgroups — #14680906

Order 2816.

1290 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622287C211yesmaximal, characteristic
2#13066878C211yesmaximal, characteristic, complemented
3#13066876C211yesmaximal, characteristic, complemented
4#13066875C211yesmaximal, characteristic, complemented
5#13066868C211yesmaximal, characteristic, complemented
6#13066864C211yesmaximal, characteristic
7#13066860C211yesmaximal, characteristic
8#13066858C211yesmaximal, characteristic
9#13066854C211yesmaximal, characteristic
10#13066852C211yesmaximal, characteristic
11#13066852C211yesmaximal, characteristic
12#13066850C211yesmaximal, characteristic, complemented
13#13066847C211yesmaximal, characteristic, complemented
14C4×C11⋊#95C211yesmaximal, characteristic, complemented
15C11×#1436C211yesmaximal, characteristic, complemented
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
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#10622287C418yescomplemented
52C24×D11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—41no—
69C2×C11×C4⋊C4—41no—
70C2×C42×C11—22no—
71C2×C42×C11—41no—
72C2×C42×C11—41no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4—22no—
79C2×(C2×D11)⋊C4—41no—
80C2×(C2×D11)⋊C4—41no—
81C2×(C2×D11)⋊C4—41no—
82C2×(C2×D11)⋊C4—41no—
83C2×(C2×D11)⋊C4—41no—
84C2×(C2×D11)⋊C4—41no—
85C2×(C2×D11)⋊C4—41no—
86C2×(C2×D11)⋊C4—41no—
87C2×(C2×D11)⋊C4—41no—
88C2×(C2×D11)⋊C4—41no—
89C2×(C2×D11)⋊C4—41no—
90C2×(C2×D11)⋊C4—41no—
91C2×(C2×D11)⋊C4C2×C414yes—
92C2×(C2×D11)⋊C4C2×C414yes—
93C2×(C2×D11)⋊C4C2×C414yes—
94C2×C4⋊Dic11—41no—
95C2×C4⋊Dic11—41no—
96C2×C4⋊Dic11C2×C414yes—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—41no—
99C2×Dic11⋊C4—41no—
100C2×C4×Dic11—22no—
101C2×C4×Dic11—22no—
102C2×C4×Dic11—41no—
103C2×C4×Dic11—41no—
104C2×C4×Dic11—41no—
105C2×C4×Dic11—41no—
106C11×#95—22no—
107C11×#95—22no—
108C11×#95—41no—
109C11×#95—41no—
110C11×#95C2×C414yes—
111C11⋊#95—22no—
112C11⋊#95—22no—
113C11⋊#95—22no—
114C11⋊#95—22no—
115C11⋊#95—22no—
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⋊#95C2×C414yes—
127C11⋊#95C2×C414yes—
128#14332—111nomaximal, Sylow
129C24×C11C2411yescharacteristic
130C23×D11—21no—
131C23×D11—21no—
132C23×D11—21no—
133C23×D11—21no—
134C23×D11—21no—
135C23×D11—21no—
136C23×D11—21no—
137C23×D11—21no—
138C23×D11—21no—
139C23×D11—21no—
140C23×D11—21no—
141C23×D11—21no—
142C23×D11—21no—
143C23×D11—21no—
144C23×D11C22×C412yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
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×C11C22×C412yes—
188C22×C4×C11C22×C412yes—
189C22×C4×C11C22×C412yes—
190C22×C4×C11#4112yes—
191C22×C4×C11#4112yes—
192C22×C4×C11#4112yes—
193C22×C4×C11#4112yes—
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×Dic11C22×C412yes—
239C22×Dic11C22×C412yes—
240C22×Dic11C22×C412yes—
241C22×Dic11#4112yes—
242C22×Dic11#4112yes—
243C11×C4⋊C4—44no—
244C42×C11—44no—
245(C2×D11)⋊C4—44no—
246(C2×D11)⋊C4—44no—
247(C2×D11)⋊C4—44no—
248(C2×D11)⋊C4—44no—
249(C2×D11)⋊C4—44no—
250(C2×D11)⋊C4—44no—
251(C2×D11)⋊C4—44no—
252C4⋊Dic11—44no—
253Dic11⋊C4—44no—
254C4×Dic11—44no—
255C4×Dic11—44no—
256C2×#397—111no—
257#1443—111no—
258#1443—111no—
259#1442—111no—
260#1441—111no—
261#1440—111no—
262#1439—111no—
263#1439—111no—
264#1437—111no—
265#1437—111no—
266#1437—111no—
267#1436—111no—
268#1436—111no—
269#1436D1111yescharacteristic, complemented
270C4×#95—111no—
271C23×C11C23×C411yescharacteristic
272C23×C11C2×#4111yescharacteristic
273C23×C11C2×#4111yescharacteristic
274C23×C11C2×#4111yescharacteristic
275C23×C11C2×#4111yescharacteristic
276C23×C11C2×#4111yescharacteristic
277C23×C11C2×#4111yescharacteristic
278C23×C11H(5,𝔽2)11yescharacteristic
279C23×C11H(5,𝔽2)11yescharacteristic
280C23×C11H(5,𝔽2)11yescharacteristic
281C23×C11H(5,𝔽2)11yescharacteristic
282C23×C11H(5,𝔽2)11yescharacteristic
283C23×C11H(5,𝔽2)11yescharacteristic
284C23×C112−1+411yescharacteristic
285C23×C112−1+411yescharacteristic
286C22×D11—22no—
287C22×D11—22no—
288C22×D11—22no—
289C22×D11—22no—
290C22×D11—22no—
291C22×D11—22no—
292C22×D11—22no—
293C22×D11—41no—
294C22×D11—41no—
295C22×D11—41no—
296C22×D11—41no—
297C22×D11—41no—
298C22×D11—41no—
299C22×D11—41no—
300C22×D11—41no—
301C22×D11—41no—
302C22×D11—41no—
303C22×D11—41no—
304C22×D11—41no—
305C22×D11—41no—
306C22×D11—41no—
307C22×D11—41no—
308C22×D11—41no—
309C22×D11—41no—
310C22×D11—41no—
311C22×D11—41no—
312C22×D11—41no—
313C22×D11—41no—
314C22×D11—41no—
315C22×D11—41no—
316C22×D11—41no—
317C22×D11—41no—
318C22×D11—41no—
319C22×D11—41no—
320C22×D11—41no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
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—22no—
338C2×C4×C11—22no—
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#12614yes—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
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—41no—
386C2×Dic11—41no—
387C2×Dic11—41no—
388C2×Dic11—41no—
389C2×Dic11—41no—
390C2×Dic11—41no—
391C2×Dic11—41no—
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—
419C22×C4⋊C4—111no—
420C22×C4⋊C4—111no—
421C22×C4⋊C4C2×D1111yescharacteristic
422C22×C22⋊C4—111no—
423C22×C22⋊C4—111no—
424C22×C22⋊C4—111no—
425C22×C22⋊C4—111no—
426C22×C22⋊C4—111no—
427C22×C22⋊C4—111no—
428C22×C22⋊C4—111no—
429C22×C42—111no—
430C22×C42—111no—
431C22×C42C2×D1111yescharacteristic
432#397—118no—
433C2×#95—111no—
434C2×#95—111no—
435C2×#95—111no—
436C2×#95—111no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95—111no—
443C2×#95—111no—
444C2×#95—111no—
445C2×#95—111no—
446C2×#95—111no—
447C2×#95—111no—
448C2×#95—111no—
449C2×#95—111no—
450C2×#95C2×D1111yescharacteristic
451C2×#95C2×D1111yescharacteristic
452C2×#95C2×D1111yescharacteristic
453C2×#95C2×D1111yescharacteristic
454C2×#95C2×D1111yescharacteristic
455C22×C11C4×#4111yescharacteristic
456C22×C11C4×#4111yescharacteristic
457C22×C11C4×#4111yescharacteristic
458C22×C11#51811yescharacteristic
459C22×C11#51811yescharacteristic
460C22×C11#52011yescharacteristic
461C22×C11#52011yescharacteristic
462C22×C11C2×#12611yescharacteristic
463C22×C11#52911yescharacteristic
464C22×C11#52911yescharacteristic
465C22×C11#52911yescharacteristic
466C22×C11#53811yescharacteristic
467C22×C11#53811yescharacteristic
468C22×C11#53811yescharacteristic
469C22×C11#53811yescharacteristic
470C22×C11#53811yescharacteristic
471C22×C11#53811yescharacteristic
472C22×C11#53811yescharacteristic
473C22×C11#53811yescharacteristic
474C22×C11#53911yescharacteristic
475C22×C11#53911yescharacteristic
476C22×C11#53911yescharacteristic
477C22×C11#53911yescharacteristic
478C22×C11#54011yescharacteristic
479C22×C11#54011yescharacteristic
480C22×C11#54011yescharacteristic
481C22×C11#54011yescharacteristic
482C22×C11#54011yescharacteristic
483C22×C11#54111yescharacteristic
484C22×C11#54211yescharacteristic
485C22×C11#54211yescharacteristic
486C22×C11#54211yescharacteristic
487C22×C11#54211yescharacteristic
488C22×C11#54211yescharacteristic
489C22×C11#54211yescharacteristic
490C2×D11—42no—
491C2×D11—42no—
492C2×D11—42no—
493C2×D11—42no—
494C2×D11—42no—
495C2×D11—42no—
496C2×D11—42no—
497C2×D11—81no—
498C2×D11—81no—
499C2×D11—81no—
500C2×D11—81no—
501C2×D11—81no—
502C2×D11—81no—
503C2×D11—81no—
504C2×D11—81no—
505C4×C11—24no—
506C4×C11—42no—
507C4×C11—42no—
508C4×C11—42no—
509C4×C11—42no—
510C4×C11—81no—
511C4×C11—81no—
512Dic11—42no—
513Dic11—42no—
514Dic11—42no—
515Dic11—42no—
516Dic11—42no—
517Dic11—81no—
518Dic11—81no—
519C25—111no—
520C23×C4—111no—
521C23×C4—111no—
522C23×C4—111no—
523C23×C4—111no—
524C23×C4—111no—
525C23×C4—111no—
526C23×C4—111no—
527C23×C4C22×D1111yescharacteristic
528C23×C4C22×D1111yescharacteristic
529C23×C4C22×D1111yescharacteristic
530C23×C4C22×D1111yescharacteristic
531C23×C4C22×D1111yescharacteristic
532C23×C4C22×D1111yescharacteristic
533C23×C4C22×D1111yescharacteristic
534C2×C4⋊C4—22no—
535C2×C4⋊C4—41no—
536C2×C4⋊C4—41no—
537C2×C4⋊C4—114no—
538C2×C4⋊C4—222no—
539C2×C4⋊C4—441no—
540C2×C4⋊C4—441no—
541C2×C4⋊C4—441no—
542C2×C4⋊C4—441no—
543C2×C22⋊C4—114no—
544C2×C22⋊C4—114no—
545C2×C22⋊C4—114no—
546C2×C22⋊C4—222no—
547C2×C22⋊C4—222no—
548C2×C22⋊C4—222no—
549C2×C22⋊C4—222no—
550C2×C22⋊C4—222no—
551C2×C22⋊C4—222no—
552C2×C22⋊C4—441no—
553C2×C22⋊C4—441no—
554C2×C22⋊C4—441no—
555C2×C22⋊C4—441no—
556C2×C22⋊C4—441no—
557C2×C22⋊C4—441no—
558C2×C22⋊C4—441no—
559C2×C22⋊C4—441no—
560C2×C22⋊C4—441no—
561C2×C22⋊C4—441no—
562C2×C22⋊C4—441no—
563C2×C22⋊C4—441no—
564C2×C42—22no—
565C2×C42—41no—
566C2×C42—41no—
567C2×C42—222no—
568C2×C42—222no—
569C2×C42—441no—
570C2×C42—441no—
571C2×C42—441no—
572C2×C42—441no—
573#95—22no—
574#95—22no—
575#95—41no—
576#95—41no—
577#95—114no—
578#95—114no—
579#95—222no—
580#95—222no—
581#95—222no—
582#95—222no—
583#95—222no—
584#95—441no—
585#95—441no—
586#95—441no—
587#95—441no—
588#95—441no—
589#95—441no—
590#95—441no—
591#95—441no—
592#95—441no—
593#95—441no—
594#95C4×D1114yes—
595C2×C11C4×#12611yescharacteristic
596C2×C11#233311yescharacteristic
597C2×C11#233411yescharacteristic
598C2×C11#233511yescharacteristic
599C2×C11#233511yescharacteristic
600C2×C11#233511yescharacteristic
601C2×C11#233711yescharacteristic
602C2×C11#264311yescharacteristic
603C2×C11#264411yescharacteristic
604C2×C11#264811yescharacteristic
605C2×C11#264811yescharacteristic
606C2×C11#265011yescharacteristic
607C2×C11#265111yescharacteristic
608C2×C11#265311yescharacteristic
609C2×C11#265411yescharacteristic
610D11—82no—
611C24—112no—
612C24—221no—
613C24—221no—
614C24—221no—
615C24—221no—
616C24—221no—
617C24—221no—
618C24—221no—
619C24—221no—
620C24—221no—
621C24—221no—
622C24—221no—
623C24—221no—
624C24—221no—
625C24—221no—
626C24C23×D1111yescharacteristic
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
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—112no—
670C22×C4—112no—
671C22×C4—112no—
672C22×C4—112no—
673C22×C4—112no—
674C22×C4—221no—
675C22×C4—221no—
676C22×C4—221no—
677C22×C4—221no—
678C22×C4—221no—
679C22×C4—221no—
680C22×C4—221no—
681C22×C4—221no—
682C22×C4—221no—
683C22×C4—221no—
684C22×C4—221no—
685C22×C4—221no—
686C22×C4—221no—
687C22×C4—221no—
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×C4C2×C4×D1112yes—
719C22×C4C2×C4×D1112yes—
720C22×C4C2×C4×D1112yes—
721C22×C4#433912yes—
722C22×C4#433912yes—
723C22×C4#434112yes—
724C22×C4#434312yes—
725C4⋊C4—44no—
726C4⋊C4—444no—
727C4⋊C4—444no—
728C22⋊C4—444no—
729C22⋊C4—444no—
730C22⋊C4—444no—
731C22⋊C4—444no—
732C22⋊C4—444no—
733C22⋊C4—444no—
734C22⋊C4—444no—
735C42—44no—
736C42—444no—
737C42—444no—
738C11#1433211yescharacteristic, complemented, Sylow
739C23—222no—
740C23—222no—
741C23—222no—
742C23—222no—
743C23—222no—
744C23—222no—
745C23—222no—
746C23—441no—
747C23—441no—
748C23—441no—
749C23—441no—
750C23—441no—
751C23—441no—
752C23—441no—
753C23—441no—
754C23—441no—
755C23—441no—
756C23—441no—
757C23—441no—
758C23—441no—
759C23—441no—
760C23—441no—
761C23—441no—
762C23—441no—
763C23—441no—
764C23—441no—
765C23—441no—
766C23—441no—
767C23—441no—
768C23—441no—
769C23—441no—
770C23—441no—
771C23—441no—
772C23—441no—
773C23—441no—
774C23C22×C4×D1111yescharacteristic
775C23C2×#433911yescharacteristic
776C23C2×#433911yescharacteristic
777C23C2×#434111yescharacteristic
778C23#6703711yescharacteristic
779C23#6703711yescharacteristic
780C23#6703711yescharacteristic
781C23C2×#434311yescharacteristic
782C23#6704011yescharacteristic
783C23#41×D1111yescharacteristic
784C23#41×D1111yescharacteristic
785C23#6704211yescharacteristic
786C23#6704211yescharacteristic
787C23#6704211yescharacteristic
788C23#6704311yescharacteristic
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
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—222no—
838C2×C4—222no—
839C2×C4—222no—
840C2×C4—222no—
841C2×C4—222no—
842C2×C4—222no—
843C2×C4—222no—
844C2×C4—222no—
845C2×C4—222no—
846C2×C4—222no—
847C2×C4—222no—
848C2×C4—222no—
849C2×C4—222no—
850C2×C4—222no—
851C2×C4—222no—
852C2×C4—441no—
853C2×C4—441no—
854C2×C4—441no—
855C2×C4—441no—
856C2×C4—441no—
857C2×C4—441no—
858C2×C4—441no—
859C2×C4—441no—
860C2×C4—441no—
861C2×C4—441no—
862C2×C4—441no—
863C2×C4—441no—
864C2×C4—441no—
865C2×C4—441no—
866C2×C4—441no—
867C2×C4—441no—
868C2×C4—441no—
869C2×C4—441no—
870C2×C4—441no—
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#6695114yes—
887C22—442no—
888C22—442no—
889C22—442no—
890C22—442no—
891C22—442no—
892C22—442no—
893C22—442no—
894C22—881no—
895C22—881no—
896C22—881no—
897C22—881no—
898C22—881no—
899C22—881no—
900C22—881no—
901C22—881no—
902C22C4×#433911yescharacteristic
903C22#1062302511yescharacteristic
904C22#1062303511yescharacteristic
905C22C2×#6695111yescharacteristic
906C22#1062305211yescharacteristic
907C22#1062305911yescharacteristic
908C22#1062306511yescharacteristic
909C22C4×#434111yescharacteristic
910C22#1062306911yescharacteristic
911C22#1062307611yescharacteristic
912C22#1062307711yescharacteristic
913C22#1062309111yescharacteristic
914C22#1062309111yescharacteristic
915C22#1062309311yescharacteristic
916C22#1062309511yescharacteristic
917C22C4×#434311yescharacteristic
918C22#1062311111yescharacteristic
919C22#1062311311yescharacteristic
920C22#1062311311yescharacteristic
921C22#1062312411yescharacteristic
922C22#1062314411yescharacteristic
923C22#1062315011yescharacteristic
924C22#1062316911yescharacteristic
925C22#1062317411yescharacteristic
926C22#1062317511yescharacteristic
927C22#1062317611yescharacteristic
928C22#1062319411yescharacteristic
929C22#1062319411yescharacteristic
930C22#1062319611yescharacteristic
931C22#1062320911yescharacteristic
932C22#1062322711yescharacteristic
933C22#1062322911yescharacteristic
934C22#1062323511yescharacteristic
935C22#1062324111yescharacteristic
936C22#1062326411yescharacteristic
937C4—24no—
938C4—42no—
939C4—42no—
940C4—42no—
941C4—42no—
942C4—81no—
943C4—81no—
944C4—442no—
945C4—442no—
946C4—442no—
947C4—442no—
948C4—442no—
949C4—881no—
950C4—881no—
951C2—882no—
952C2C4×#6695111yescharacteristic
953C2#1307138011yescharacteristic
954C2#1307139011yescharacteristic
955C2#1307140111yescharacteristic
956C2#1307140811yescharacteristic
957C2#1307141111yescharacteristic
958C2#1307142911yescharacteristic
959C2#1307457211yescharacteristic
960C2#1307457911yescharacteristic
961C2#1307460211yescharacteristic
962C2#1307460411yescharacteristic
963C2#1307463611yescharacteristic
964C2#1307465511yescharacteristic
965C2#1307468511yescharacteristic
966C2#1307469011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1436D11
hypocenterC11#14332
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. #13066878C2semidirect
3. #13066876C2semidirect
4. #13066875C2semidirect
5. #13066868C2semidirect
12. #13066850C2semidirect
13. #13066847C2semidirect
14. C4×C11⋊#95C2semidirect
15. C11×#1436C2semidirect
51. #10622287C4semidirect
269. #1436D11semidirect
738. C11#14332semidirect

Maximal subgroups

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

subgroupindex
C2×#106222872
#130668782
#130668762
#130668752
#130668682
#130668642
#130668602
#130668582
#130668542
#130668522
#130668502
#130668472
C4×C11⋊#952
C11×#14362
#1433211