Finite Group Databasebeta

← #14684635

Subgroups — #14684635

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×#10622565C211yesmaximal, characteristic
2#13066880C211yesmaximal, characteristic, complemented
3#13066877C211yesmaximal, characteristic, complemented
4#13066872C211yesmaximal, characteristic, complemented
5#13066871C211yesmaximal, characteristic, complemented
6#13066871C211yesmaximal, characteristic, complemented
7#13066867C211yesmaximal, characteristic, complemented
8#13066863C211yesmaximal, characteristic
9#13066861C211yesmaximal, characteristic
10#13066859C211yesmaximal, characteristic
11#13066859C211yesmaximal, characteristic
12#13066859C211yesmaximal, characteristic
13#13066849C211yesmaximal, characteristic, complemented
14#13066849C211yesmaximal, characteristic, complemented
15C11×#1437C211yesmaximal, characteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
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#10622565C418yescomplemented
52C25×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—41no—
70C2×C11×C22⋊C4—41no—
71C2×C11×C22⋊C4—41no—
72C2×C11×C22⋊C4—41no—
73C2×C11×C22⋊C4—41no—
74C2×C11×C22⋊C4—41no—
75C2×C11×C22⋊C4C2×C414yes—
76C2×C42×C11—41no—
77C2×C42×C11—41no—
78C2×C42×C11—41no—
79C2×C22⋊Dic11—41no—
80C2×C22⋊Dic11—41no—
81C2×C22⋊Dic11—41no—
82C2×C22⋊Dic11—41no—
83C2×C22⋊Dic11—41no—
84C2×C22⋊Dic11—41no—
85C2×C22⋊Dic11—41no—
86C2×C22⋊Dic11—41no—
87C2×C22⋊Dic11—41no—
88C2×C22⋊Dic11—41no—
89C2×C22⋊Dic11C2×C414yes—
90C2×C22⋊Dic11C2×C414yes—
91C2×C4⋊Dic11—41no—
92C2×C4⋊Dic11—41no—
93C2×C4⋊Dic11—41no—
94C2×Dic11⋊C4—22no—
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⋊C4—41no—
103C2×Dic11⋊C4—41no—
104C2×Dic11⋊C4—41no—
105C2×Dic11⋊C4C2×C414yes—
106C11×#95—41no—
107C11×#95—41no—
108C11×#95—41no—
109C11⋊#95—22no—
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#14643—111nomaximal, Sylow
129C24×C11—21no—
130C24×C11—21no—
131C24×C11—21no—
132C24×C11—21no—
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×C11C22×C412yes—
144C24×C11C2411yescharacteristic
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×C11C22×C412yes—
184C22×C4×C11C22×C412yes—
185C22×C4×C11#4112yes—
186C22×C4×C11#4112yes—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
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×Dic11C22×C412yes—
240C22×Dic11C22×C412yes—
241C22×Dic11C22×C412yes—
242C22×Dic11C22×C412yes—
243C11×C22⋊C4—44no—
244C11×C22⋊C4—44no—
245C11×C22⋊C4—44no—
246C42×C11—44no—
247C22⋊Dic11—44no—
248C22⋊Dic11—44no—
249C22⋊Dic11—44no—
250C22⋊Dic11—44no—
251C4⋊Dic11—44no—
252Dic11⋊C4—44no—
253Dic11⋊C4—44no—
254Dic11⋊C4—44no—
255Dic11⋊C4—44no—
256C2×#397—111no—
257#1444—111no—
258#1443—111no—
259#1442—111no—
260#1442—111no—
261#1442—111no—
262#1441—111no—
263#1440—111no—
264#1439—111no—
265#1439—111no—
266#1439—111no—
267#1439—111no—
268#1437D1111yescharacteristic
269#1436—111no—
270#1436—111no—
271C23×C11—22no—
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—41no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11—41no—
294C23×C11—41no—
295C23×C11—41no—
296C23×C11—41no—
297C23×C11—41no—
298C23×C11—41no—
299C23×C11—41no—
300C23×C11—41no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11C23×C411yescharacteristic
307C23×C11C2×#4111yescharacteristic
308C23×C11C2×#4111yescharacteristic
309C23×C11H(5,𝔽2)11yescharacteristic
310C23×C11H(5,𝔽2)11yescharacteristic
311C23×C11H(5,𝔽2)11yescharacteristic
312C23×C11H(5,𝔽2)11yescharacteristic
313C23×C11H(5,𝔽2)11yescharacteristic
314C23×C11H(5,𝔽2)11yescharacteristic
315C23×C11H(5,𝔽2)11yescharacteristic
316C23×C11H(5,𝔽2)11yescharacteristic
317C23×C112−1+411yescharacteristic
318C23×C112−1+411yescharacteristic
319C23×C112−1+411yescharacteristic
320C23×C112−1+411yescharacteristic
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—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×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383C2×Dic11—41no—
384C2×Dic11—41no—
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⋊C4—111no—
424C22×C22⋊C4—111no—
425C22×C22⋊C4—111no—
426C22×C22⋊C4—111no—
427C22×C22⋊C4—111no—
428C22×C22⋊C4C2×D1111yescharacteristic
429C22×C22⋊C4C2×D1111yescharacteristic
430C22×C22⋊C4C2×D1111yescharacteristic
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×#95—111no—
451C2×#95—111no—
452C2×#95C2×D1111yescharacteristic
453C2×#95C2×D1111yescharacteristic
454C2×#95C2×D1111yescharacteristic
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—81no—
463C22×C11—81no—
464C22×C11—81no—
465C22×C11—81no—
466C22×C11—81no—
467C22×C11—81no—
468C22×C11—81no—
469C22×C11—81no—
470C22×C11C4×#4111yescharacteristic
471C22×C11#51811yescharacteristic
472C22×C11#51811yescharacteristic
473C22×C11#52011yescharacteristic
474C22×C11#52011yescharacteristic
475C22×C11#52011yescharacteristic
476C22×C11#52011yescharacteristic
477C22×C11#53811yescharacteristic
478C22×C11#53811yescharacteristic
479C22×C11#53811yescharacteristic
480C22×C11#53911yescharacteristic
481C22×C11#53911yescharacteristic
482C22×C11#53911yescharacteristic
483C22×C11#54011yescharacteristic
484C22×C11#54011yescharacteristic
485C22×C11#54111yescharacteristic
486C22×C11#54211yescharacteristic
487C22×C11#54211yescharacteristic
488C22×C11#54211yescharacteristic
489C22×C11#56011yescharacteristic
490C22×C11#56011yescharacteristic
491C22×C11#56011yescharacteristic
492C22×C11#56011yescharacteristic
493C22×C11H(3,𝔽4)11yescharacteristic
494C22×C11#56211yescharacteristic
495C22×C11#56211yescharacteristic
496C22×C11#56211yescharacteristic
497C22×C11#56211yescharacteristic
498C22×C11#56211yescharacteristic
499C22×C11#56211yescharacteristic
500C22×C11#56311yescharacteristic
501C22×C11#56311yescharacteristic
502C22×C11#56311yescharacteristic
503C22×C11#56311yescharacteristic
504C22×C11#56311yescharacteristic
505C4×C11—42no—
506C4×C11—42no—
507C4×C11—42no—
508C4×C11—42no—
509C4×C11—81no—
510C4×C11—81no—
511Dic11—42no—
512Dic11—42no—
513Dic11—42no—
514Dic11—42no—
515Dic11—81no—
516Dic11—81no—
517Dic11—81no—
518Dic11—81no—
519C25C22×D1111yescharacteristic
520C23×C4—111no—
521C23×C4—111no—
522C23×C4—111no—
523C23×C4—111no—
524C23×C4—111no—
525C23×C4—111no—
526C23×C4—111no—
527C23×C4—111no—
528C23×C4C22×D1111yescharacteristic
529C23×C4C22×D1111yescharacteristic
530C23×C4C22×D1111yescharacteristic
531C23×C4C22×D1111yescharacteristic
532C23×C4C22×D1111yescharacteristic
533C23×C4C22×D1111yescharacteristic
534C2×C4⋊C4—114no—
535C2×C4⋊C4—222no—
536C2×C4⋊C4—441no—
537C2×C4⋊C4—441no—
538C2×C4⋊C4—441no—
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—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—41no—
552C2×C22⋊C4—41no—
553C2×C22⋊C4—41no—
554C2×C22⋊C4—41no—
555C2×C22⋊C4—41no—
556C2×C22⋊C4—41no—
557C2×C22⋊C4—114no—
558C2×C22⋊C4—114no—
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⋊C4C4×D1114yes—
570C2×C42—41no—
571C2×C42—41no—
572C2×C42—41no—
573#95—41no—
574#95—41no—
575#95—41no—
576#95—114no—
577#95—114no—
578#95—114no—
579#95—222no—
580#95—222no—
581#95—222no—
582#95—441no—
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#95—441no—
595C2×C11—82no—
596C2×C11#233411yescharacteristic
597C2×C11#233511yescharacteristic
598C2×C11#233511yescharacteristic
599C2×C11#237611yescharacteristic
600C2×C11#237711yescharacteristic
601C2×C11#237911yescharacteristic
602C2×C11#238311yescharacteristic
603C2×C11#282611yescharacteristic
604C2×C11#282711yescharacteristic
605C2×C11#282811yescharacteristic
606C2×C11#283011yescharacteristic
607C2×C11#283211yescharacteristic
608C2×C11#283611yescharacteristic
609C2×C11#283611yescharacteristic
610C2×C11#283811yescharacteristic
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24C2×C4×D1112yes—
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—112no—
666C22×C4—112no—
667C22×C4—112no—
668C22×C4—112no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4—221no—
672C22×C4—221no—
673C22×C4—221no—
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×C4—221no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4C2×C4×D1112yes—
722C22×C4C2×C4×D1112yes—
723C22×C4#433912yes—
724C22×C4#433912yes—
725C4⋊C4—444no—
726C4⋊C4—444no—
727C4⋊C4—444no—
728C4⋊C4—444no—
729C4⋊C4—444no—
730C22⋊C4—44no—
731C22⋊C4—44no—
732C22⋊C4—44no—
733C22⋊C4—444no—
734C22⋊C4—444no—
735C22⋊C4—444no—
736C22⋊C4—444no—
737C42—44no—
738C11#1464311yescharacteristic, complemented, Sylow
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23C22×C4×D1111yescharacteristic
775C23C2×#433911yescharacteristic
776C23C2×#433911yescharacteristic
777C23#6703711yescharacteristic
778C23#6703711yescharacteristic
779C23#6703711yescharacteristic
780C23#6703711yescharacteristic
781C23#6703711yescharacteristic
782C23#6703711yescharacteristic
783C23#6704211yescharacteristic
784C23#6704211yescharacteristic
785C23#6704311yescharacteristic
786C23#6704311yescharacteristic
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—22no—
799C2×C4—22no—
800C2×C4—22no—
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—222no—
832C2×C4—222no—
833C2×C4—222no—
834C2×C4—222no—
835C2×C4—222no—
836C2×C4—222no—
837C2×C4—222no—
838C2×C4—222no—
839C2×C4—222no—
840C2×C4—222no—
841C2×C4—222no—
842C2×C4—222no—
843C2×C4—441no—
844C2×C4—441no—
845C2×C4—441no—
846C2×C4—441no—
847C2×C4—441no—
848C2×C4—441no—
849C2×C4—441no—
850C2×C4—441no—
851C2×C4—441no—
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—441no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—81no—
895C22—81no—
896C22—81no—
897C22—81no—
898C22—81no—
899C22—81no—
900C22—81no—
901C22—81no—
902C22C4×#433911yescharacteristic
903C22#1062301711yescharacteristic
904C22#1062302511yescharacteristic
905C22#1062302511yescharacteristic
906C22#1062304911yescharacteristic
907C22#1062305411yescharacteristic
908C22#1062306511yescharacteristic
909C22#1062307611yescharacteristic
910C22#1062307711yescharacteristic
911C22#1062307711yescharacteristic
912C22#1062307711yescharacteristic
913C22#1062309111yescharacteristic
914C22#1062309211yescharacteristic
915C22#1062309211yescharacteristic
916C22#1062309311yescharacteristic
917C22#1062309311yescharacteristic
918C22#1062309511yescharacteristic
919C22#1062309511yescharacteristic
920C22#1062309511yescharacteristic
921C22#1062312611yescharacteristic
922C22#1062315111yescharacteristic
923C22#1062315111yescharacteristic
924C22#1062315211yescharacteristic
925C22#1062315211yescharacteristic
926C22#1062315211yescharacteristic
927C22#1062315211yescharacteristic
928C22#1062318211yescharacteristic
929C22#1062319811yescharacteristic
930C22#1062319811yescharacteristic
931C22#1062320311yescharacteristic
932C22#1062320311yescharacteristic
933C22#1062321411yescharacteristic
934C22#1062324311yescharacteristic
935C22#1062324311yescharacteristic
936C22#1062325111yescharacteristic
937C4—42no—
938C4—42no—
939C4—42no—
940C4—42no—
941C4—81no—
942C4—81no—
943C4—442no—
944C4—442no—
945C4—442no—
946C4—442no—
947C4—881no—
948C4—881no—
949C4—881no—
950C4—881no—
951C2—82no—
952C2#1307139311yescharacteristic
953C2#1307140611yescharacteristic
954C2#1307140811yescharacteristic
955C2#1307176611yescharacteristic
956C2#1307177411yescharacteristic
957C2#1307178511yescharacteristic
958C2#1307180311yescharacteristic
959C2#1307671111yescharacteristic
960C2#1307672011yescharacteristic
961C2#1307673511yescharacteristic
962C2#1307675911yescharacteristic
963C2#1307678111yescharacteristic
964C2#1307680911yescharacteristic
965C2#1307680911yescharacteristic
966C2#1307684311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1437C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenter#1437D11
hypocenterC11#14643
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. #13066880C2semidirect
3. #13066877C2semidirect
4. #13066872C2semidirect
5. #13066871C2semidirect
6. #13066871C2semidirect
7. #13066867C2semidirect
13. #13066849C2semidirect
14. #13066849C2semidirect
51. #10622565C4semidirect
738. C11#14643semidirect

Maximal subgroups

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

subgroupindex
C2×#106225652
#130668802
#130668772
#130668722
#130668712
#130668672
#130668632
#130668612
#130668592
#130668492
C11×#14372
#1464311