Finite Group Databasebeta

← #14682255

Subgroups — #14682255

Order 2816.

1398 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622564C211yesmaximal, characteristic
2C2×#10622594C211yesmaximal, characteristic, complemented
3#13066878C211yesmaximal, characteristic, complemented
4#13066869C211yesmaximal, characteristic, complemented
5#13066865C211yesmaximal, characteristic
6#13066861C211yesmaximal, characteristic
7#13066861C211yesmaximal, characteristic
8#13066861C211yesmaximal, characteristic
9#13066853C211yesmaximal, characteristic
10#13066850C211yesmaximal, characteristic, complemented
11#13066850C211yesmaximal, characteristic, complemented
12#13066846C211yesmaximal, characteristic, complemented
13#13066846C211yesmaximal, 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
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C11×#388C418yescomplemented
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
52#10622594—24no—
53#10622564—24no—
54C25×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4C2×C414yes—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—41no—
77C2×C11×C22⋊C4—41no—
78C2×C11×C22⋊C4C2×C414yes—
79C2×C11×C22⋊C4C2×C414yes—
80C2×C11×C22⋊C4C2×C414yes—
81C2×C42×C11—41no—
82C2×C42×C11—41no—
83C2×C42×C11C2×C414yes—
84C2×C22⋊Dic11—22no—
85C2×C22⋊Dic11—22no—
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11—22no—
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×C22⋊Dic11—41no—
95C2×C22⋊Dic11—41no—
96C2×C4⋊Dic11—22no—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11—22no—
99C2×C4⋊Dic11—22no—
100C2×C4⋊Dic11—22no—
101C2×C4⋊Dic11—41no—
102C2×C4⋊Dic11—41no—
103C2×C4⋊Dic11—41no—
104C2×C4⋊Dic11—41no—
105C2×C4⋊Dic11—41no—
106C2×C4⋊Dic11—41no—
107C2×C4⋊Dic11D414yes—
108C2×C4×Dic11—22no—
109C2×C4×Dic11—22no—
110C2×C4×Dic11—22no—
111C2×C4×Dic11—41no—
112C2×C4×Dic11—41no—
113C2×C4×Dic11—41no—
114C11×#95C2×C414yes—
115C11×#95C2×C414yes—
116C11⋊#95—22no—
117C11⋊#95—22no—
118C11⋊#95—22no—
119C11⋊#95—22no—
120C11⋊#95—22no—
121C11⋊#95—22no—
122C11⋊#95—22no—
123C11⋊#95—22no—
124C11⋊#95—22no—
125C11⋊#95—41no—
126C11⋊#95—41no—
127C11⋊#95—41no—
128C11⋊#95—41no—
129C11⋊#95—41no—
130C11⋊#95—41no—
131C11⋊#95—41no—
132C11⋊#95—41no—
133C11⋊#95—41no—
134#14447—111nomaximal, Sylow
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×C11—21no—
144C24×C11—21no—
145C24×C11—21no—
146C24×C11—21no—
147C24×C11—21no—
148C24×C11—21no—
149C24×C11C22×C412yes—
150C24×C11C2411yescharacteristic
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×C11C22×C412yes—
186C22×C4×C11C22×C412yes—
187C22×C4×C11C22×C412yes—
188C22×C4×C11C22×C412yes—
189C22×C4×C11C2×D412yes—
190C22×C4×C11#4112yes—
191C22×C4×C11#4112yes—
192C22×C4×C11#4112yes—
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—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11C2×D412yes—
246C22×Dic11C2×D412yes—
247C22×Dic11#4112yes—
248C22×Dic11#4112yes—
249C11×C4⋊C4—28no—
250C11×C22⋊C4—28no—
251C11×C22⋊C4—28no—
252C11×C22⋊C4—44no—
253C42×C11—44no—
254C22⋊Dic11—44no—
255C22⋊Dic11—44no—
256C22⋊Dic11—44no—
257C22⋊Dic11—44no—
258C4⋊Dic11—44no—
259C4⋊Dic11—44no—
260C4⋊Dic11—44no—
261C4⋊Dic11—44no—
262C4×Dic11—44no—
263C4×Dic11—44no—
264C2×#388—111no—
265C2×#388D1111yescharacteristic
266C2×#387—111no—
267#1443—111no—
268#1441—111no—
269#1440—111no—
270#1439—111no—
271#1439—111no—
272#1439—111no—
273#1437—111no—
274#1436—111no—
275#1436—111no—
276C4⋊#95—111no—
277C4⋊#95—111no—
278#1434—111no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
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×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11C23×C411yescharacteristic
315C23×C11C22×D411yescharacteristic
316C23×C11C2×#4111yescharacteristic
317C23×C11C2×#4111yescharacteristic
318C23×C11C2×#4111yescharacteristic
319C23×C11C2×#4111yescharacteristic
320C23×C11C2×#4111yescharacteristic
321C23×C11H(5,𝔽2)11yescharacteristic
322C23×C11H(5,𝔽2)11yescharacteristic
323C23×C11H(5,𝔽2)11yescharacteristic
324C23×C11H(5,𝔽2)11yescharacteristic
325C23×C11H(5,𝔽2)11yescharacteristic
326C23×C112−1+411yescharacteristic
327C23×C112−1+411yescharacteristic
328C23×C112−1+411yescharacteristic
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—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
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#11714yes—
370C2×C4×C11C4×D414yes—
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—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—
419C2×Dic11—41no—
420C2×Dic11—41no—
421C2×Dic11—41no—
422C2×Dic11—41no—
423C2×Dic11—41no—
424C2×Dic11—41no—
425C2×Dic11—41no—
426C2×Dic11—41no—
427C22×C4⋊C4—111no—
428C22×C4⋊C4—111no—
429C22×C4⋊C4—111no—
430C22×C4⋊C4—111no—
431C22×C4⋊C4C2×D1111yescharacteristic
432C22×C22⋊C4—111no—
433C22×C22⋊C4—111no—
434C22×C22⋊C4—111no—
435C22×C22⋊C4—111no—
436C22×C22⋊C4C2×D1111yescharacteristic
437C22×C22⋊C4C2×D1111yescharacteristic
438C22×C22⋊C4C2×D1111yescharacteristic
439C22×C42—111no—
440C22×C42—111no—
441C22×C42C2×D1111yescharacteristic
442#388—224no—
443#388Dic1118yescomplemented
444#387—224no—
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×#95—111no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95—111no—
460C2×#95—111no—
461C2×#95—111no—
462C2×#95—111no—
463C2×#95C2×D1111yescharacteristic
464C2×#95C2×D1111yescharacteristic
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—81no—
473C22×C11—81no—
474C22×C11—81no—
475C22×C11—81no—
476C22×C11—81no—
477C22×C11—81no—
478C22×C11—81no—
479C22×C11—81no—
480C22×C11C2×#11711yescharacteristic
481C22×C11C2×C4×D411yescharacteristic
482C22×C11C4×#4111yescharacteristic
483C22×C11#51811yescharacteristic
484C22×C11#52011yescharacteristic
485C22×C11#52011yescharacteristic
486C22×C11#52011yescharacteristic
487C22×C11#53411yescharacteristic
488C22×C11#53711yescharacteristic
489C22×C11#53811yescharacteristic
490C22×C11#53811yescharacteristic
491C22×C11#53911yescharacteristic
492C22×C11#53911yescharacteristic
493C22×C11#54011yescharacteristic
494C22×C11#54111yescharacteristic
495C22×C11#54111yescharacteristic
496C22×C11#54211yescharacteristic
497C22×C11#54211yescharacteristic
498C22×C11#54211yescharacteristic
499C22×C11#54611yescharacteristic
500C22×C11#54711yescharacteristic
501C22×C11#54811yescharacteristic
502C22×C11#55011yescharacteristic
503C22×C11#55111yescharacteristic
504C22×C11#55111yescharacteristic
505C22×C11#55311yescharacteristic
506C22×C11#55311yescharacteristic
507C22×C11#55511yescharacteristic
508C22×C11#55611yescharacteristic
509C22×C11#55611yescharacteristic
510C22×C11#55911yescharacteristic
511C22×C11#56011yescharacteristic
512C22×C11#56211yescharacteristic
513C22×C11#56211yescharacteristic
514C22×C11#56311yescharacteristic
515C4×C11—24no—
516C4×C11—24no—
517C4×C11—42no—
518C4×C11—42no—
519C4×C11—42no—
520C4×C11—42no—
521Dic11—42no—
522Dic11—42no—
523Dic11—42no—
524Dic11—42no—
525Dic11—81no—
526Dic11—81no—
527Dic11—81no—
528Dic11—81no—
529C25C22×D1111yescharacteristic
530C23×C4—111no—
531C23×C4—111no—
532C23×C4—111no—
533C23×C4—111no—
534C23×C4—111no—
535C23×C4—111no—
536C23×C4—111no—
537C23×C4—111no—
538C23×C4C22×D1111yescharacteristic
539C23×C4C22×D1111yescharacteristic
540C23×C4C22×D1111yescharacteristic
541C23×C4C22×D1111yescharacteristic
542C23×C4C22×D1111yescharacteristic
543C23×C4C22×D1111yescharacteristic
544C2×C4⋊C4—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—114no—
547C2×C4⋊C4—222no—
548C2×C4⋊C4—222no—
549C2×C4⋊C4—222no—
550C2×C4⋊C4—222no—
551C2×C4⋊C4—222no—
552C2×C4⋊C4—441no—
553C2×C4⋊C4—441no—
554C2×C4⋊C4—441no—
555C2×C4⋊C4—441no—
556C2×C4⋊C4—441no—
557C2×C4⋊C4—441no—
558C2×C4⋊C4C2×Dic1114yes—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—41no—
564C2×C22⋊C4—41no—
565C2×C22⋊C4—222no—
566C2×C22⋊C4—222no—
567C2×C22⋊C4—222no—
568C2×C22⋊C4—222no—
569C2×C22⋊C4—441no—
570C2×C22⋊C4—441no—
571C2×C22⋊C4—441no—
572C2×C22⋊C4—441no—
573C2×C22⋊C4—441no—
574C2×C22⋊C4—441no—
575C2×C22⋊C4—441no—
576C2×C22⋊C4—441no—
577C2×C22⋊C4C2×Dic1114yes—
578C2×C22⋊C4C2×Dic1114yes—
579C2×C22⋊C4C2×Dic1114yes—
580C2×C42—41no—
581C2×C42—41no—
582C2×C42—222no—
583C2×C42—222no—
584C2×C42—222no—
585C2×C42—441no—
586C2×C42—441no—
587C2×C42—441no—
588C2×C42C2×Dic1114yes—
589#95—222no—
590#95—222no—
591#95—222no—
592#95—222no—
593#95—222no—
594#95—222no—
595#95—222no—
596#95—222no—
597#95—222no—
598#95—441no—
599#95—441no—
600#95—441no—
601#95—441no—
602#95—441no—
603#95—441no—
604#95—441no—
605#95—441no—
606#95—441no—
607#95C2×Dic1114yes—
608#95C2×Dic1114yes—
609C2×C11—82no—
610C2×C11#231411yescharacteristic
611C2×C11#232511yescharacteristic
612C2×C11#233411yescharacteristic
613C2×C11#235311yescharacteristic
614C2×C11#235411yescharacteristic
615C2×C11#236711yescharacteristic
616C2×C11#237611yescharacteristic
617C2×C11#270111yescharacteristic
618C2×C11#270511yescharacteristic
619C2×C11#272511yescharacteristic
620C2×C11#273011yescharacteristic
621C2×C11#275911yescharacteristic
622C2×C11#278311yescharacteristic
623C2×C11#279811yescharacteristic
624C2×C11#280311yescharacteristic
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24C22×Dic1112yes—
640C24C23×D1111yescharacteristic
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—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×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#433912yes—
730C22×C4#433912yes—
731C22×C4D4×D1112yes—
732C22×C4#434112yes—
733C22×C4C22×Dic1112yes—
734C22×C4C22×Dic1112yes—
735C22×C4C22×Dic1112yes—
736C22×C4C22×Dic1112yes—
737C22×C4C22×Dic1112yes—
738C22×C4C22×Dic1112yes—
739C4⋊C4—28no—
740C4⋊C4—444no—
741C4⋊C4—444no—
742C4⋊C4—444no—
743C4⋊C4—444no—
744C22⋊C4—28no—
745C22⋊C4—28no—
746C22⋊C4—44no—
747C22⋊C4—444no—
748C22⋊C4—444no—
749C22⋊C4—444no—
750C22⋊C4—444no—
751C42—44no—
752C42—444no—
753C42—444no—
754C11#1444711yescharacteristic, complemented, Sylow
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23C2×#433911yescharacteristic
791C23C2×#433911yescharacteristic
792C23C2×D4×D1111yescharacteristic
793C23C2×#434111yescharacteristic
794C23#6703711yescharacteristic
795C23#6703711yescharacteristic
796C23#41×D1111yescharacteristic
797C23#41×D1111yescharacteristic
798C23#6704211yescharacteristic
799C23#6704211yescharacteristic
800C23#6704211yescharacteristic
801C23#6704311yescharacteristic
802C23#6704311yescharacteristic
803C23#6704311yescharacteristic
804C23C23×Dic1111yescharacteristic
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
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—222no—
846C2×C4—222no—
847C2×C4—222no—
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—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—
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—
897C2×C4—441no—
898C2×C4—441no—
899C2×C4—441no—
900C2×C4—441no—
901C2×C4#6697914yes—
902C2×C4D4×Dic1114yes—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22#1062304911yescharacteristic
919C22#1062306511yescharacteristic
920C22#1062306511yescharacteristic
921C22#1062306611yescharacteristic
922C22#1062307111yescharacteristic
923C22#1062307111yescharacteristic
924C22#1062307311yescharacteristic
925C22#1062308211yescharacteristic
926C22#1062308411yescharacteristic
927C22#1062308711yescharacteristic
928C22#1062308711yescharacteristic
929C22#1062309411yescharacteristic
930C22#1062312811yescharacteristic
931C22#1062313311yescharacteristic
932C22#1062313611yescharacteristic
933C22#1062314811yescharacteristic
934C22#1062318211yescharacteristic
935C22#1062319711yescharacteristic
936C22#1062319811yescharacteristic
937C22#1062319811yescharacteristic
938C22#1062320211yescharacteristic
939C22#1062320711yescharacteristic
940C22#1062320811yescharacteristic
941C22#1062321211yescharacteristic
942C22#1062323211yescharacteristic
943C22#1062323511yescharacteristic
944C22#1062323811yescharacteristic
945C22#1062324111yescharacteristic
946C22C2×#6697911yescharacteristic
947C22C2×D4×Dic1111yescharacteristic
948C22#1062332911yescharacteristic
949C22#41×Dic1111yescharacteristic
950C22#1062335811yescharacteristic
951C22#1062335811yescharacteristic
952C22#1062335811yescharacteristic
953C4—24no—
954C4—24no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—42no—
959C4—442no—
960C4—442no—
961C4—442no—
962C4—442no—
963C4—881no—
964C4—881no—
965C4—881no—
966C4—881no—
967C2—82no—
968C2#1307122511yescharacteristic
969C2#1307132111yescharacteristic
970C2#1307139511yescharacteristic
971C2#1307155611yescharacteristic
972C2#1307156511yescharacteristic
973C2#1307169111yescharacteristic
974C2#1307176411yescharacteristic
975C2#1307522611yescharacteristic
976C2#1307528611yescharacteristic
977C2#1307555111yescharacteristic
978C2#1307561011yescharacteristic
979C2#1307598611yescharacteristic
980C2#1307630611yescharacteristic
981C2#1307648411yescharacteristic
982C2#1307655211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#388C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#388D11
hypocenterC11#14447
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#10622594C2semidirect
3. #13066878C2semidirect
4. #13066869C2semidirect
10. #13066850C2semidirect
11. #13066850C2semidirect
12. #13066846C2semidirect
13. #13066846C2semidirect
14. #13066841C2semidirect
31. C11×#388C4semidirect
443. #388Dic11semidirect
754. C11#14447semidirect

Maximal subgroups

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

subgroupindex
C2×#106225642
C2×#106225942
#130668782
#130668692
#130668652
#130668612
#130668532
#130668502
#130668462
#130668412
C2×C11×#3882
#1444711