Finite Group Databasebeta

← #14684647

Subgroups — #14684647

Order 2816.

1226 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×#10622288C211yesmaximal, characteristic
2#13066879C211yesmaximal, characteristic, complemented
3#13066876C211yesmaximal, characteristic, complemented
4#13066874C211yesmaximal, characteristic, complemented
5#13066872C211yesmaximal, characteristic, complemented
6#13066867C211yesmaximal, characteristic, complemented
7#13066864C211yesmaximal, characteristic
8#13066862C211yesmaximal, characteristic
9#13066860C211yesmaximal, characteristic
10#13066860C211yesmaximal, characteristic
11#13066858C211yesmaximal, characteristic
12#13066852C211yesmaximal, characteristic
13#13066851C211yesmaximal, characteristic, complemented
14#13066850C211yesmaximal, characteristic, complemented
15C11×#1442C211yesmaximal, characteristic, complemented
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
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#10622288C418yescomplemented
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—41no—
68C2×C11×C4⋊C4—41no—
69C2×C11×C4⋊C4—41no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—41no—
73C2×(C2×D11)⋊C4—41no—
74C2×(C2×D11)⋊C4—41no—
75C2×(C2×D11)⋊C4—41no—
76C2×(C2×D11)⋊C4—41no—
77C2×(C2×D11)⋊C4—41no—
78C2×(C2×D11)⋊C4—41no—
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)⋊C4C2×C414yes—
89C2×(C2×D11)⋊C4C2×C414yes—
90C2×(C2×D11)⋊C4C2×C414yes—
91C2×C4⋊Dic11—22no—
92C2×C4⋊Dic11—41no—
93C2×C4⋊Dic11—41no—
94C2×Dic11⋊C4—41no—
95C2×Dic11⋊C4—41no—
96C2×Dic11⋊C4—41no—
97C2×Dic11⋊C4—41no—
98C2×Dic11⋊C4—41no—
99C2×Dic11⋊C4—41no—
100C2×Dic11⋊C4—41no—
101C2×Dic11⋊C4—41no—
102C2×Dic11⋊C4C2×C414yes—
103C2×C4×Dic11—41no—
104C2×C4×Dic11—41no—
105C2×C4×Dic11—41no—
106C11×#95—41no—
107C11×#95—41no—
108C11×#95—41no—
109C11×#95—41no—
110C11×#95—41no—
111C11×#95C2×C414yes—
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⋊#95C2×C414yes—
127C11⋊#95C2×C414yes—
128#14643—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×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11C22×C412yes—
192C22×C4×C11C22×C412yes—
193C22×C4×C11C22×C412yes—
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—
244(C2×D11)⋊C4—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—
251C4⋊Dic11—44no—
252Dic11⋊C4—44no—
253Dic11⋊C4—44no—
254Dic11⋊C4—44no—
255C4×Dic11—44no—
256C2×#397—111no—
257#1444—111no—
258#1443—111no—
259#1442—111no—
260#1442—111no—
261#1442D1111yescharacteristic, complemented
262#1441—111no—
263#1440—111no—
264#1439—111no—
265#1439—111no—
266#1439—111no—
267#1439—111no—
268#1437—111no—
269#1436—111no—
270#1436—111no—
271C23×C11C23×C411yescharacteristic
272C23×C11C2×#4111yescharacteristic
273C23×C11C2×#4111yescharacteristic
274C23×C11H(5,𝔽2)11yescharacteristic
275C23×C11H(5,𝔽2)11yescharacteristic
276C23×C11H(5,𝔽2)11yescharacteristic
277C23×C11H(5,𝔽2)11yescharacteristic
278C23×C11H(5,𝔽2)11yescharacteristic
279C23×C11H(5,𝔽2)11yescharacteristic
280C23×C11H(5,𝔽2)11yescharacteristic
281C23×C11H(5,𝔽2)11yescharacteristic
282C23×C112−1+411yescharacteristic
283C23×C112−1+411yescharacteristic
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—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
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×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⋊C4—111no—
422C22×C4⋊C4—111no—
423C22×C4⋊C4C2×D1111yescharacteristic
424C22×C22⋊C4—111no—
425C22×C22⋊C4—111no—
426C22×C22⋊C4—111no—
427C22×C22⋊C4—111no—
428C22×C22⋊C4—111no—
429C22×C22⋊C4—111no—
430C22×C22⋊C4—111no—
431C22×C42—111no—
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×#95C2×D1111yescharacteristic
450C2×#95C2×D1111yescharacteristic
451C2×#95C2×D1111yescharacteristic
452C2×#95C2×D1111yescharacteristic
453C2×#95C2×D1111yescharacteristic
454C2×#95C2×D1111yescharacteristic
455C22×C11C4×#4111yescharacteristic
456C22×C11#51811yescharacteristic
457C22×C11#51811yescharacteristic
458C22×C11#52011yescharacteristic
459C22×C11#52011yescharacteristic
460C22×C11#52011yescharacteristic
461C22×C11#52011yescharacteristic
462C22×C11#53811yescharacteristic
463C22×C11#53811yescharacteristic
464C22×C11#53811yescharacteristic
465C22×C11#53911yescharacteristic
466C22×C11#53911yescharacteristic
467C22×C11#53911yescharacteristic
468C22×C11#54011yescharacteristic
469C22×C11#54011yescharacteristic
470C22×C11#54111yescharacteristic
471C22×C11#54211yescharacteristic
472C22×C11#54211yescharacteristic
473C22×C11#54211yescharacteristic
474C22×C11#56011yescharacteristic
475C22×C11#56011yescharacteristic
476C22×C11#56011yescharacteristic
477C22×C11#56011yescharacteristic
478C22×C11H(3,𝔽4)11yescharacteristic
479C22×C11#56211yescharacteristic
480C22×C11#56211yescharacteristic
481C22×C11#56211yescharacteristic
482C22×C11#56211yescharacteristic
483C22×C11#56211yescharacteristic
484C22×C11#56211yescharacteristic
485C22×C11#56311yescharacteristic
486C22×C11#56311yescharacteristic
487C22×C11#56311yescharacteristic
488C22×C11#56311yescharacteristic
489C22×C11#56311yescharacteristic
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—42no—
506C4×C11—42no—
507C4×C11—42no—
508C4×C11—81no—
509C4×C11—81no—
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—41no—
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×C4⋊C4—441no—
544C2×C4⋊C4—441no—
545C2×C4⋊C4—441no—
546C2×C4⋊C4—441no—
547C2×C4⋊C4—441no—
548C2×C4⋊C4—441no—
549C2×C22⋊C4—114no—
550C2×C22⋊C4—114no—
551C2×C22⋊C4—114no—
552C2×C22⋊C4—222no—
553C2×C22⋊C4—222no—
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×C22⋊C4—441no—
565C2×C22⋊C4—441no—
566C2×C22⋊C4—441no—
567C2×C22⋊C4—441no—
568C2×C22⋊C4—441no—
569C2×C22⋊C4—441no—
570C2×C42—441no—
571C2×C42—441no—
572C2×C42—441no—
573#95—41no—
574#95—41no—
575#95—41no—
576#95—41no—
577#95—41no—
578#95—114no—
579#95—114no—
580#95—222no—
581#95—222no—
582#95—222no—
583#95—441no—
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×C11#233411yescharacteristic
596C2×C11#233511yescharacteristic
597C2×C11#233511yescharacteristic
598C2×C11#237611yescharacteristic
599C2×C11#237711yescharacteristic
600C2×C11#237911yescharacteristic
601C2×C11#238311yescharacteristic
602C2×C11#282611yescharacteristic
603C2×C11#282711yescharacteristic
604C2×C11#282811yescharacteristic
605C2×C11#283011yescharacteristic
606C2×C11#283211yescharacteristic
607C2×C11#283611yescharacteristic
608C2×C11#283611yescharacteristic
609C2×C11#283811yescharacteristic
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—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—112no—
674C22×C4—112no—
675C22×C4—112no—
676C22×C4—112no—
677C22×C4—112no—
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×C4—221no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4C2×C4×D1112yes—
723C22×C4C2×C4×D1112yes—
724C22×C4C2×C4×D1112yes—
725C4⋊C4—44no—
726C4⋊C4—444no—
727C4⋊C4—444no—
728C4⋊C4—444no—
729C4⋊C4—444no—
730C22⋊C4—444no—
731C22⋊C4—444no—
732C22⋊C4—444no—
733C22⋊C4—444no—
734C22⋊C4—444no—
735C22⋊C4—444no—
736C22⋊C4—444no—
737C42—444no—
738C11#1464311yescharacteristic, 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
775C23#6703711yescharacteristic
776C23#6703711yescharacteristic
777C23#6703711yescharacteristic
778C23#6703711yescharacteristic
779C23#6704011yescharacteristic
780C23#6704011yescharacteristic
781C23#41×D1111yescharacteristic
782C23#41×D1111yescharacteristic
783C23#6704211yescharacteristic
784C23#6704211yescharacteristic
785C23#6704211yescharacteristic
786C23#6704211yescharacteristic
787C23#6704311yescharacteristic
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—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
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—41no—
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—222no—
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—441no—
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—
902C22#1062303511yescharacteristic
903C22#1062305311yescharacteristic
904C22#1062305411yescharacteristic
905C22#1062307611yescharacteristic
906C22#1062307611yescharacteristic
907C22#1062307711yescharacteristic
908C22#1062310511yescharacteristic
909C22#1062312511yescharacteristic
910C22#1062314611yescharacteristic
911C22#1062315111yescharacteristic
912C22#1062315111yescharacteristic
913C22#1062317111yescharacteristic
914C22#1062317711yescharacteristic
915C22#1062317711yescharacteristic
916C22#1062317811yescharacteristic
917C22#1062317811yescharacteristic
918C22#1062319311yescharacteristic
919C22#1062319411yescharacteristic
920C22#1062319711yescharacteristic
921C22#1062319811yescharacteristic
922C22#1062319811yescharacteristic
923C22#1062320011yescharacteristic
924C22#1062320911yescharacteristic
925C22#1062320911yescharacteristic
926C22#1062321511yescharacteristic
927C22#1062322311yescharacteristic
928C22#1062322311yescharacteristic
929C22#1062322711yescharacteristic
930C22#1062323011yescharacteristic
931C22#1062323111yescharacteristic
932C22#1062323511yescharacteristic
933C22#1062323811yescharacteristic
934C22#1062324211yescharacteristic
935C22#1062324311yescharacteristic
936C22#1062326611yescharacteristic
937C4—42no—
938C4—42no—
939C4—42no—
940C4—81no—
941C4—81no—
942C4—81no—
943C4—81no—
944C4—442no—
945C4—442no—
946C4—442no—
947C4—442no—
948C4—442no—
949C4—881no—
950C4—881no—
951C2—882no—
952C2#1307138711yescharacteristic
953C2#1307140411yescharacteristic
954C2#1307141211yescharacteristic
955C2#1307176111yescharacteristic
956C2#1307176911yescharacteristic
957C2#1307178911yescharacteristic
958C2#1307180611yescharacteristic
959C2#1307671311yescharacteristic
960C2#1307672711yescharacteristic
961C2#1307673611yescharacteristic
962C2#1307676111yescharacteristic
963C2#1307678411yescharacteristic
964C2#1307681411yescharacteristic
965C2#1307682211yescharacteristic
966C2#1307684211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1442C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1442D11
hypocenterC11#14643
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
2. #13066879C2semidirect
3. #13066876C2semidirect
4. #13066874C2semidirect
5. #13066872C2semidirect
6. #13066867C2semidirect
13. #13066851C2semidirect
14. #13066850C2semidirect
15. C11×#1442C2semidirect
51. #10622288C4semidirect
261. #1442D11semidirect
738. C11#14643semidirect

Maximal subgroups

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

subgroupindex
C2×#106222882
#130668792
#130668762
#130668742
#130668722
#130668672
#130668642
#130668622
#130668602
#130668582
#130668522
#130668512
#130668502
C11×#14422
#1464311