Finite Group Databasebeta

← #14684723

Subgroups — #14684723

Order 2816.

1290 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622844C211yesmaximal, characteristic
2#13066887C211yesmaximal, characteristic, complemented
3#13066877C211yesmaximal, characteristic, complemented
4#13066876C211yesmaximal, characteristic, complemented
5#13066874C211yesmaximal, characteristic, complemented
6#13066871C211yesmaximal, characteristic, complemented
7#13066864C211yesmaximal, characteristic
8#13066864C211yesmaximal, characteristic
9#13066864C211yesmaximal, characteristic
10#13066860C211yesmaximal, characteristic
11#13066860C211yesmaximal, characteristic
12#13066852C211yesmaximal, characteristic
13#13066851C211yesmaximal, characteristic, complemented
14#13066847C211yesmaximal, characteristic, complemented
15C11×#1446C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2211yescharacteristic
32C2×C11×#95C2211yescharacteristic
33#10622844C418yescomplemented
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
51C2×C11⋊#95C2211yescharacteristic
52C24×D11C2311yescharacteristic
53C22×Q8×C11—41no—
54C22×Q8×C11—41no—
55C22×Q8×C11—41no—
56C22×Q8×C11—41no—
57C22×Q8×C11—41no—
58C22×Q8×C11—41no—
59C22×Q8×C11C2×C414yes—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—22no—
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)⋊C4—41no—
89C2×(C2×D11)⋊C4—41no—
90C2×(C2×D11)⋊C4—41no—
91C2×(C2×D11)⋊C4—41no—
92C2×(C2×D11)⋊C4C2×C414yes—
93C2×(C2×D11)⋊C4C2×C414yes—
94C2×(C2×D11)⋊C4C2×C414yes—
95C2×Dic11⋊C4—22no—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4—41no—
98C2×Dic11⋊C4—41no—
99C2×Dic11⋊C4—41no—
100C2×Dic11⋊C4—41no—
101C2×C4×Dic11—41no—
102C2×C4×Dic11—41no—
103C2×C4×Dic11—41no—
104C11×#95—41no—
105C11×#95—41no—
106C11×#95—41no—
107C11×#95—41no—
108C11×#95—41no—
109C11×#95—41no—
110C11⋊#95—22no—
111C11⋊#95—22no—
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⋊#95C2×C414yes—
126C11⋊#95C2×C414yes—
127C11⋊#95C2×C414yes—
128#14649—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—
145C2×Q8×C11—44no—
146C2×Q8×C11—44no—
147C2×Q8×C11—44no—
148C2×Q8×C11—44no—
149C2×Q8×C11—44no—
150C2×Q8×C11—44no—
151C2×Q8×C11—44no—
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×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11C22×C412yes—
198C22×C4×C11C22×C412yes—
199C22×C4×C11C22×C412yes—
200C22×C4×C11#4112yes—
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×Dic11C22×C412yes—
247C22×Dic11C22×C412yes—
248C22×Dic11C22×C412yes—
249C22×Dic11#4112yes—
250(C2×D11)⋊C4—44no—
251(C2×D11)⋊C4—44no—
252(C2×D11)⋊C4—44no—
253(C2×D11)⋊C4—44no—
254(C2×D11)⋊C4—44no—
255(C2×D11)⋊C4—44no—
256(C2×D11)⋊C4—44no—
257Dic11⋊C4—44no—
258Dic11⋊C4—44no—
259C4×Dic11—44no—
260C2×#393—111no—
261#1446—111no—
262#1446D1111yescharacteristic, complemented
263#1443—111no—
264#1443—111no—
265#1442—111no—
266#1442—111no—
267#1440—111no—
268#1440—111no—
269#1440—111no—
270#1439—111no—
271#1439—111no—
272#1437—111no—
273#1436—111no—
274#1436—111no—
275C23×C11C23×C411yescharacteristic
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×C11H(5,𝔽2)11yescharacteristic
285C23×C11H(5,𝔽2)11yescharacteristic
286C23×C112−1+411yescharacteristic
287C23×C112−1+411yescharacteristic
288C23×C112−1+411yescharacteristic
289C23×C112−1+411yescharacteristic
290C22×D11—22no—
291C22×D11—22no—
292C22×D11—22no—
293C22×D11—22no—
294C22×D11—22no—
295C22×D11—22no—
296C22×D11—22no—
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—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325Q8×C11—416no—
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—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×C4×C11—41no—
374C2×C4×C11—41no—
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—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—
419C2×Dic11—41no—
420C2×Dic11—41no—
421C2×Dic11—41no—
422C2×Dic11—41no—
423C2×Dic11—41no—
424C23×Q8C2×D1111yescharacteristic
425C22×C4⋊C4—111no—
426C22×C4⋊C4—111no—
427C22×C22⋊C4—111no—
428C22×C22⋊C4—111no—
429C22×C22⋊C4—111no—
430C22×C22⋊C4—111no—
431C22×C22⋊C4—111no—
432C22×C22⋊C4—111no—
433C22×C22⋊C4—111no—
434C22×C42—111no—
435#393—118no—
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×#95—111no—
451C2×#95—111no—
452C2×#95—111no—
453C2×#95—111no—
454C2×#95C2×D1111yescharacteristic
455C2×#95C2×D1111yescharacteristic
456C2×#95C2×D1111yescharacteristic
457C2×#95C2×D1111yescharacteristic
458C2×#95C2×D1111yescharacteristic
459C2×#95C2×D1111yescharacteristic
460C22×C11C4×#4111yescharacteristic
461C22×C11#51811yescharacteristic
462C22×C11#51811yescharacteristic
463C22×C11#51811yescharacteristic
464C22×C11#51911yescharacteristic
465C22×C11#52011yescharacteristic
466C22×C11#52011yescharacteristic
467C22×C11#53811yescharacteristic
468C22×C11#53811yescharacteristic
469C22×C11#53811yescharacteristic
470C22×C11#53811yescharacteristic
471C22×C11#53911yescharacteristic
472C22×C11#53911yescharacteristic
473C22×C11#54211yescharacteristic
474C22×C11#54211yescharacteristic
475C22×C11#54211yescharacteristic
476C22×C11#54211yescharacteristic
477C22×C11#54211yescharacteristic
478C22×C11#54211yescharacteristic
479C22×C11#56011yescharacteristic
480C22×C11#56011yescharacteristic
481C22×C11#56011yescharacteristic
482C22×C11H(3,𝔽4)11yescharacteristic
483C22×C11H(3,𝔽4)11yescharacteristic
484C22×C11#56211yescharacteristic
485C22×C11#56211yescharacteristic
486C22×C11#56211yescharacteristic
487C22×C11#56211yescharacteristic
488C22×C11#56211yescharacteristic
489C22×C11#56211yescharacteristic
490C22×C11#56311yescharacteristic
491C22×C11#56311yescharacteristic
492C22×C11#56311yescharacteristic
493C22×C11#56311yescharacteristic
494C22×C11#56311yescharacteristic
495C2×D11—42no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—42no—
501C2×D11—42no—
502C2×D11—81no—
503C2×D11—81no—
504C2×D11—81no—
505C2×D11—81no—
506C2×D11—81no—
507C2×D11—81no—
508C2×D11—81no—
509C2×D11—81no—
510C4×C11—42no—
511C4×C11—42no—
512C4×C11—42no—
513C4×C11—42no—
514C4×C11—81no—
515C4×C11—81no—
516C4×C11—81no—
517Dic11—42no—
518Dic11—42no—
519Dic11—42no—
520Dic11—42no—
521Dic11—81no—
522Dic11—81no—
523Dic11—81no—
524C25—111no—
525C22×Q8—41no—
526C22×Q8—41no—
527C22×Q8—41no—
528C22×Q8—41no—
529C22×Q8—41no—
530C22×Q8—41no—
531C22×Q8C4×D1114yes—
532C23×C4—111no—
533C23×C4—111no—
534C23×C4—111no—
535C23×C4—111no—
536C23×C4—111no—
537C23×C4—111no—
538C23×C4—111no—
539C23×C4C22×D1111yescharacteristic
540C23×C4C22×D1111yescharacteristic
541C23×C4C22×D1111yescharacteristic
542C23×C4C22×D1111yescharacteristic
543C23×C4C22×D1111yescharacteristic
544C23×C4C22×D1111yescharacteristic
545C23×C4C22×D1111yescharacteristic
546C2×C4⋊C4—222no—
547C2×C4⋊C4—222no—
548C2×C4⋊C4—441no—
549C2×C4⋊C4—441no—
550C2×C4⋊C4—441no—
551C2×C4⋊C4—441no—
552C2×C22⋊C4—114no—
553C2×C22⋊C4—114no—
554C2×C22⋊C4—114no—
555C2×C22⋊C4—222no—
556C2×C22⋊C4—222no—
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×C22⋊C4—441no—
571C2×C22⋊C4—441no—
572C2×C22⋊C4—441no—
573C2×C42—441no—
574C2×C42—441no—
575C2×C42—441no—
576#95—41no—
577#95—41no—
578#95—41no—
579#95—41no—
580#95—41no—
581#95—41no—
582#95—114no—
583#95—114no—
584#95—114no—
585#95—222no—
586#95—222no—
587#95—441no—
588#95—441no—
589#95—441no—
590#95—441no—
591#95—441no—
592#95—441no—
593#95—441no—
594#95—441no—
595#95—441no—
596#95—441no—
597#95—441no—
598#95—441no—
599#95—441no—
600C2×C11#233211yescharacteristic
601C2×C11#233711yescharacteristic
602C2×C11#233711yescharacteristic
603C2×C11#237511yescharacteristic
604C2×C11#237811yescharacteristic
605C2×C11#237811yescharacteristic
606C2×C11#237911yescharacteristic
607C2×C11#282411yescharacteristic
608C2×C11#282411yescharacteristic
609C2×C11#283011yescharacteristic
610C2×C11#283011yescharacteristic
611C2×C11#283211yescharacteristic
612C2×C11#283211yescharacteristic
613C2×C11#283811yescharacteristic
614C2×C11#283811yescharacteristic
615D11—82no—
616C24—112no—
617C24—221no—
618C24—221no—
619C24—221no—
620C24—221no—
621C24—221no—
622C24—221no—
623C24—221no—
624C24—221no—
625C24—221no—
626C24—221no—
627C24—221no—
628C24—221no—
629C24—221no—
630C24—221no—
631C24C23×D1111yescharacteristic
632C2×Q8—44no—
633C2×Q8—44no—
634C2×Q8—44no—
635C2×Q8—44no—
636C2×Q8—44no—
637C2×Q8—44no—
638C2×Q8—44no—
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—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—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×C4C2×C4×D1112yes—
734C22×C4C2×C4×D1112yes—
735C22×C4C2×C4×D1112yes—
736C22×C4#434312yes—
737C4⋊C4—444no—
738C4⋊C4—444no—
739C22⋊C4—444no—
740C22⋊C4—444no—
741C22⋊C4—444no—
742C22⋊C4—444no—
743C22⋊C4—444no—
744C22⋊C4—444no—
745C22⋊C4—444no—
746C42—444no—
747C11#1464911yescharacteristic, complemented, Sylow
748C23—222no—
749C23—222no—
750C23—222no—
751C23—222no—
752C23—222no—
753C23—222no—
754C23—222no—
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—
774C23—441no—
775C23—441no—
776C23—441no—
777C23—441no—
778C23—441no—
779C23—441no—
780C23—441no—
781C23—441no—
782C23—441no—
783C23C22×C4×D1111yescharacteristic
784C23#6703711yescharacteristic
785C23#6703711yescharacteristic
786C23#6703711yescharacteristic
787C23#6703711yescharacteristic
788C23#6703711yescharacteristic
789C23#6703711yescharacteristic
790C23C2×#434311yescharacteristic
791C23#6704011yescharacteristic
792C23#6704011yescharacteristic
793C23#6704011yescharacteristic
794C23#41×D1111yescharacteristic
795C23#6704211yescharacteristic
796C23#6704211yescharacteristic
797C23#6704311yescharacteristic
798Q8—416no—
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—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
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—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—222no—
849C2×C4—222no—
850C2×C4—222no—
851C2×C4—222no—
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—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—
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—
897C22—442no—
898C22—442no—
899C22—442no—
900C22—442no—
901C22—442no—
902C22—442no—
903C22—442no—
904C22—881no—
905C22—881no—
906C22—881no—
907C22—881no—
908C22—881no—
909C22—881no—
910C22—881no—
911C22—881no—
912C22#1062301711yescharacteristic
913C22#1062301711yescharacteristic
914C22#1062301711yescharacteristic
915C22#1062310311yescharacteristic
916C22C4×#434311yescharacteristic
917C22#1062310511yescharacteristic
918C22#1062310511yescharacteristic
919C22#1062312511yescharacteristic
920C22#1062312611yescharacteristic
921C22#1062312611yescharacteristic
922C22#1062312611yescharacteristic
923C22#1062316911yescharacteristic
924C22#1062317111yescharacteristic
925C22#1062317111yescharacteristic
926C22#1062317511yescharacteristic
927C22#1062317511yescharacteristic
928C22#1062317611yescharacteristic
929C22#1062317711yescharacteristic
930C22#1062317711yescharacteristic
931C22#1062317811yescharacteristic
932C22#1062317811yescharacteristic
933C22#1062317811yescharacteristic
934C22#1062317811yescharacteristic
935C22#1062320011yescharacteristic
936C22#1062320911yescharacteristic
937C22#1062320911yescharacteristic
938C22#1062321411yescharacteristic
939C22#1062321511yescharacteristic
940C22#1062321511yescharacteristic
941C22#1062326411yescharacteristic
942C22#1062326411yescharacteristic
943C22#1062326411yescharacteristic
944C22#1062326611yescharacteristic
945C22#1062326611yescharacteristic
946C22#1062326611yescharacteristic
947C4—42no—
948C4—42no—
949C4—42no—
950C4—42no—
951C4—81no—
952C4—81no—
953C4—81no—
954C4—442no—
955C4—442no—
956C4—442no—
957C4—442no—
958C4—881no—
959C4—881no—
960C4—881no—
961C2—882no—
962C2#1307137111yescharacteristic
963C2#1307142811yescharacteristic
964C2#1307142811yescharacteristic
965C2#1307175511yescharacteristic
966C2#1307177711yescharacteristic
967C2#1307177711yescharacteristic
968C2#1307178811yescharacteristic
969C2#1307669511yescharacteristic
970C2#1307670011yescharacteristic
971C2#1307676011yescharacteristic
972C2#1307676411yescharacteristic
973C2#1307678411yescharacteristic
974C2#1307678811yescharacteristic
975C2#1307684011yescharacteristic
976C2#1307685111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1446C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1446D11
hypocenterC11#14649
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1446

Complements

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

NH ≅ G/Ntype
2. #13066887C2semidirect
3. #13066877C2semidirect
4. #13066876C2semidirect
5. #13066874C2semidirect
6. #13066871C2semidirect
13. #13066851C2semidirect
14. #13066847C2semidirect
15. C11×#1446C2semidirect
33. #10622844C4semidirect
262. #1446D11semidirect
747. C11#14649semidirect

Maximal subgroups

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

subgroupindex
C2×#106228442
#130668872
#130668772
#130668762
#130668742
#130668712
#130668642
#130668602
#130668522
#130668512
#130668472
C11×#14462
#1464911