Finite Group Databasebeta

← #14682930

Subgroups — #14682930

Order 2816.

1298 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
1#13066884C211yesmaximal, characteristic, complemented
2#13066878C211yesmaximal, characteristic, complemented
3#13066865C211yesmaximal, characteristic
4#13066865C211yesmaximal, characteristic
5#13066861C211yesmaximal, characteristic
6#13066861C211yesmaximal, characteristic
7#13066853C211yesmaximal, characteristic
8#13066853C211yesmaximal, characteristic
9#13066850C211yesmaximal, characteristic, complemented
10#13066850C211yesmaximal, characteristic, complemented
11#13066848C211yesmaximal, characteristic, complemented
12#13066846C211yesmaximal, characteristic, complemented
13#13066843C211yesmaximal, characteristic, complemented
14#13066841C211yesmaximal, characteristic, complemented
15C2×C11×#388C211yesmaximal, characteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C11×#388C418yescomplemented
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
51C2×C11⋊#95C2211yescharacteristic
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×C4⋊C4—41no—
68C2×C11×C4⋊C4—41no—
69C2×C11×C4⋊C4C2×C414yes—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—41no—
73C2×C11×C22⋊C4—41no—
74C2×C11×C22⋊C4—41no—
75C2×C11×C22⋊C4—41no—
76C2×C11×C22⋊C4C2×C414yes—
77C2×C11×C22⋊C4C2×C414yes—
78C2×C11×C22⋊C4C2×C414yes—
79C2×C42×C11—41no—
80C2×C42×C11—41no—
81C2×C42×C11C2×C414yes—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—22no—
85C2×C22⋊Dic11—22no—
86C2×C22⋊Dic11—41no—
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⋊Dic11—41no—
94C2×C4⋊Dic11—22no—
95C2×C4⋊Dic11—22no—
96C2×C4⋊Dic11—22no—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11—41no—
99C2×C4⋊Dic11—41no—
100C2×C4×Dic11—22no—
101C2×C4×Dic11—41no—
102C2×C4×Dic11—41no—
103C2×C4×Dic11—41no—
104C2×C4×Dic11—41no—
105C2×C4×Dic11—41no—
106C11×#95C2×C414yes—
107C11×#95C2×C414yes—
108C11⋊#95—22no—
109C11⋊#95—22no—
110C11⋊#95—22no—
111C11⋊#95—22no—
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⋊#95—41no—
127C11⋊#95—41no—
128#14504—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×C11C22×C412yes—
180C22×C4×C11C22×C412yes—
181C22×C4×C11C22×C412yes—
182C22×C4×C11C22×C412yes—
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×Dic11#4112yes—
240C22×Dic11#4112yes—
241C22×Dic11#4112yes—
242C22×Dic11#4112yes—
243C11×C4⋊C4—44no—
244C11×C22⋊C4—28no—
245C11×C22⋊C4—44no—
246C11×C22⋊C4—44no—
247C42×C11—44no—
248C22⋊Dic11—44no—
249C22⋊Dic11—44no—
250C22⋊Dic11—44no—
251C22⋊Dic11—44no—
252C4⋊Dic11—44no—
253C4⋊Dic11—44no—
254C4×Dic11—44no—
255C4×Dic11—44no—
256C2×#388D1111yescharacteristic
257#1445—111no—
258#1443—111no—
259#1440—111no—
260#1440—111no—
261#1439—111no—
262#1439—111no—
263#1437—111no—
264#1437—111no—
265#1436—111no—
266#1436—111no—
267#1436—111no—
268C4⋊#95—111no—
269#1434—111no—
270#1434—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×C11C2×#4111yescharacteristic
310C23×C11C2×#4111yescharacteristic
311C23×C11C2×#4111yescharacteristic
312C23×C11C2×#4111yescharacteristic
313C23×C11H(5,𝔽2)11yescharacteristic
314C23×C11H(5,𝔽2)11yescharacteristic
315C23×C11H(5,𝔽2)11yescharacteristic
316C23×C11H(5,𝔽2)11yescharacteristic
317C23×C11H(5,𝔽2)11yescharacteristic
318C23×C11H(5,𝔽2)11yescharacteristic
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—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
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#11714yes—
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⋊C4C2×D1111yescharacteristic
422C22×C22⋊C4—111no—
423C22×C22⋊C4—111no—
424C22×C22⋊C4—111no—
425C22×C22⋊C4—111no—
426C22×C22⋊C4C2×D1111yescharacteristic
427C22×C22⋊C4C2×D1111yescharacteristic
428C22×C22⋊C4C2×D1111yescharacteristic
429C22×C42—111no—
430C22×C42—111no—
431C22×C42C2×D1111yescharacteristic
432#388Dic1118yescomplemented
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×#95—111no—
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×C11C2×#11711yescharacteristic
471C22×C11C4×#4111yescharacteristic
472C22×C11C4×#4111yescharacteristic
473C22×C11#51811yescharacteristic
474C22×C11#51811yescharacteristic
475C22×C11#52011yescharacteristic
476C22×C11#52011yescharacteristic
477C22×C11#53811yescharacteristic
478C22×C11#53811yescharacteristic
479C22×C11#53811yescharacteristic
480C22×C11#53911yescharacteristic
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#55111yescharacteristic
490C22×C11#55111yescharacteristic
491C22×C11#55111yescharacteristic
492C22×C11#55211yescharacteristic
493C22×C11#55311yescharacteristic
494C22×C11#55311yescharacteristic
495C22×C11#55311yescharacteristic
496C22×C11#55311yescharacteristic
497C22×C11#55311yescharacteristic
498C22×C11#55611yescharacteristic
499C22×C11#55911yescharacteristic
500C22×C11#55911yescharacteristic
501C22×C11#56011yescharacteristic
502C22×C11#56011yescharacteristic
503C22×C11#56211yescharacteristic
504C22×C11#56211yescharacteristic
505C4×C11—24no—
506C4×C11—42no—
507C4×C11—42no—
508C4×C11—42no—
509C4×C11—42no—
510C4×C11—42no—
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—41no—
535C2×C4⋊C4—41no—
536C2×C4⋊C4—222no—
537C2×C4⋊C4—222no—
538C2×C4⋊C4—222no—
539C2×C4⋊C4—222no—
540C2×C4⋊C4—441no—
541C2×C4⋊C4—441no—
542C2×C4⋊C4C2×Dic1114yes—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—41no—
546C2×C22⋊C4—41no—
547C2×C22⋊C4—41no—
548C2×C22⋊C4—41no—
549C2×C22⋊C4—222no—
550C2×C22⋊C4—222no—
551C2×C22⋊C4—222no—
552C2×C22⋊C4—222no—
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⋊C4C2×Dic1114yes—
562C2×C22⋊C4C2×Dic1114yes—
563C2×C22⋊C4C2×Dic1114yes—
564C2×C42—41no—
565C2×C42—41no—
566C2×C42—222no—
567C2×C42—441no—
568C2×C42—441no—
569C2×C42—441no—
570C2×C42—441no—
571C2×C42—441no—
572C2×C42C2×Dic1114yes—
573#95—222no—
574#95—222no—
575#95—222no—
576#95—222no—
577#95—222no—
578#95—222no—
579#95—222no—
580#95—441no—
581#95—441no—
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#95C2×Dic1114yes—
594#95C2×Dic1114yes—
595C2×C11—82no—
596C2×C11#231411yescharacteristic
597C2×C11#233511yescharacteristic
598C2×C11#233711yescharacteristic
599C2×C11#235311yescharacteristic
600C2×C11#235711yescharacteristic
601C2×C11#237311yescharacteristic
602C2×C11#237711yescharacteristic
603C2×C11#275211yescharacteristic
604C2×C11#275411yescharacteristic
605C2×C11#275711yescharacteristic
606C2×C11#277911yescharacteristic
607C2×C11#279711yescharacteristic
608C2×C11#279811yescharacteristic
609C2×C11#280011yescharacteristic
610C2×C11#280111yescharacteristic
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—
625C24C22×Dic1112yes—
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—112no—
662C22×C4—112no—
663C22×C4—112no—
664C22×C4—112no—
665C22×C4—221no—
666C22×C4—221no—
667C22×C4—221no—
668C22×C4—221no—
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#433912yes—
718C22×C4#433912yes—
719C22×C4C22×Dic1112yes—
720C22×C4C22×Dic1112yes—
721C22×C4C22×Dic1112yes—
722C22×C4C22×Dic1112yes—
723C22×C4C22×Dic1112yes—
724C22×C4C22×Dic1112yes—
725C4⋊C4—44no—
726C4⋊C4—444no—
727C4⋊C4—444no—
728C22⋊C4—28no—
729C22⋊C4—44no—
730C22⋊C4—44no—
731C22⋊C4—444no—
732C22⋊C4—444no—
733C22⋊C4—444no—
734C22⋊C4—444no—
735C42—44no—
736C42—444no—
737C42—444no—
738C11#1450411yescharacteristic, 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—
774C23C2×#433911yescharacteristic
775C23C2×#433911yescharacteristic
776C23#6703711yescharacteristic
777C23#6703711yescharacteristic
778C23#6703711yescharacteristic
779C23#6703711yescharacteristic
780C23#41×D1111yescharacteristic
781C23#41×D1111yescharacteristic
782C23#41×D1111yescharacteristic
783C23#41×D1111yescharacteristic
784C23#6704211yescharacteristic
785C23#6704211yescharacteristic
786C23#6704311yescharacteristic
787C23#6704311yescharacteristic
788C23C23×Dic1111yescharacteristic
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—22no—
808C2×C4—22no—
809C2×C4—22no—
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—222no—
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—441no—
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#6697914yes—
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—
902C22#1062304911yescharacteristic
903C22#1062306511yescharacteristic
904C22#1062306511yescharacteristic
905C22#1062306611yescharacteristic
906C22#1062307111yescharacteristic
907C22#1062307111yescharacteristic
908C22#1062308711yescharacteristic
909C22#1062308711yescharacteristic
910C22#1062308911yescharacteristic
911C22#1062308911yescharacteristic
912C22#1062309011yescharacteristic
913C22#1062309011yescharacteristic
914C22#1062315111yescharacteristic
915C22#1062315111yescharacteristic
916C22#1062315211yescharacteristic
917C22#1062315211yescharacteristic
918C22#1062318811yescharacteristic
919C22#1062319111yescharacteristic
920C22#1062319311yescharacteristic
921C22#1062319411yescharacteristic
922C22#1062320011yescharacteristic
923C22#1062320011yescharacteristic
924C22#1062320911yescharacteristic
925C22#1062320911yescharacteristic
926C22#1062323311yescharacteristic
927C22#1062323611yescharacteristic
928C22#1062323911yescharacteristic
929C22#1062324011yescharacteristic
930C22C2×#6697911yescharacteristic
931C22#1062332911yescharacteristic
932C22#1062332911yescharacteristic
933C22#41×Dic1111yescharacteristic
934C22#41×Dic1111yescharacteristic
935C22#1062335811yescharacteristic
936C22#1062335811yescharacteristic
937C4—24no—
938C4—42no—
939C4—42no—
940C4—42no—
941C4—42no—
942C4—42no—
943C4—442no—
944C4—442no—
945C4—442no—
946C4—442no—
947C4—881no—
948C4—881no—
949C4—881no—
950C4—881no—
951C2—82no—
952C2#1307122511yescharacteristic
953C2#1307141011yescharacteristic
954C2#1307143111yescharacteristic
955C2#1307155611yescharacteristic
956C2#1307158911yescharacteristic
957C2#1307174011yescharacteristic
958C2#1307177311yescharacteristic
959C2#1307588111yescharacteristic
960C2#1307591111yescharacteristic
961C2#1307595011yescharacteristic
962C2#1307625211yescharacteristic
963C2#1307647611yescharacteristic
964C2#1307649111yescharacteristic
965C2#1307650811yescharacteristic
966C2#1307652211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#388C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#388D11
hypocenterC11#14504
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. #13066884C2semidirect
2. #13066878C2semidirect
9. #13066850C2semidirect
10. #13066850C2semidirect
11. #13066848C2semidirect
12. #13066846C2semidirect
13. #13066843C2semidirect
14. #13066841C2semidirect
29. C11×#388C4semidirect
432. #388Dic11semidirect
738. C11#14504semidirect

Maximal subgroups

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

subgroupindex
#130668842
#130668782
#130668652
#130668612
#130668532
#130668502
#130668482
#130668462
#130668432
#130668412
C2×C11×#3882
#1450411