Finite Group Databasebeta

← #14682028

Subgroups — #14682028

Order 2816.

1766 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622570C211yesmaximal, characteristic
2C2×#10622558C211yesmaximal, characteristic, complemented
3C2×#10622826C211yesmaximal, characteristic
4#13066874C211yesmaximal, characteristic, complemented
5#13066864C211yesmaximal, characteristic, complemented
6#13066864C211yesmaximal, characteristic, complemented
7#13066863C211yesmaximal, characteristic, complemented
8#13066860C211yesmaximal, characteristic, complemented
9#13066855C211yesmaximal, characteristic
10#13066852C211yesmaximal, characteristic, complemented
11#13066847C211yesmaximal, characteristic, complemented
12#13066847C211yesmaximal, characteristic, complemented
13#13066842C211yesmaximal, characteristic, complemented
14#13066839C211yesmaximal, characteristic, complemented
15C11×C22⋊#95C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37#10622826C418yescomplemented
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#10622570—24no—
53#10622558—24no—
54C25×C11C2311yescharacteristic
55C24×D11C2311yescharacteristic
56C23×C4×C11—41no—
57C23×C4×C11—41no—
58C23×C4×C11—41no—
59C23×C4×C11—41no—
60C23×C4×C11—41no—
61C23×C4×C11—41no—
62C23×C4×C11C2×C414yes—
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C22×C22⋊D11—22no—
70C22×C22⋊D11—22no—
71C22×C22⋊D11—22no—
72C22×C22⋊D11—22no—
73C22×C22⋊D11—41no—
74C22×C22⋊D11—41no—
75C22×C22⋊D11C2×C414yes—
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—41no—
88C2×C11×C22⋊C4—41no—
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—22no—
92C2×C22⋊Dic11—41no—
93C2×C22⋊Dic11—41no—
94C2×C22⋊Dic11—41no—
95C2×C22⋊Dic11—41no—
96C2×C22⋊Dic11C2×C414yes—
97C2×C22⋊Dic11D414yes—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—41no—
103C2×(C2×D11)⋊C4—41no—
104C2×(C2×D11)⋊C4—41no—
105C2×(C2×D11)⋊C4—41no—
106C2×(C2×D11)⋊C4—41no—
107C2×(C2×D11)⋊C4—41no—
108C2×(C2×D11)⋊C4—41no—
109C2×(C2×D11)⋊C4—41no—
110C2×(C2×D11)⋊C4—41no—
111C2×(C2×D11)⋊C4—41no—
112C2×(C2×D11)⋊C4—41no—
113C2×(C2×D11)⋊C4—41no—
114C2×(C2×D11)⋊C4C2×C414yes—
115C2×(C2×D11)⋊C4C2×C414yes—
116C2×Dic11⋊C4—22no—
117C2×Dic11⋊C4—22no—
118C2×Dic11⋊C4—22no—
119C2×Dic11⋊C4—22no—
120C2×Dic11⋊C4—41no—
121C2×Dic11⋊C4—41no—
122C2×C4×Dic11—22no—
123C2×C4×Dic11—22no—
124C2×C4×Dic11—22no—
125C2×C4×Dic11—41no—
126C2×C4×Dic11—41no—
127C2×C4×Dic11—41no—
128C11×#95—41no—
129C11×#95—41no—
130C11×#95—41no—
131C11×#95—41no—
132C11⋊#95—22no—
133C11⋊#95—22no—
134C11⋊#95—22no—
135C11⋊#95—22no—
136C11⋊#95—22no—
137C11⋊#95—41no—
138C11⋊#95—41no—
139C11⋊#95—41no—
140C11⋊#95—41no—
141C11⋊#95—41no—
142C11⋊#95—41no—
143C11⋊#95—41no—
144C11⋊#95C2×C414yes—
145C11⋊#95C2×C414yes—
146#14428—111nomaximal, Sylow
147C24×C11—21no—
148C24×C11—21no—
149C24×C11—21no—
150C24×C11—21no—
151C24×C11—21no—
152C24×C11—21no—
153C24×C11—21no—
154C24×C11—21no—
155C24×C11—21no—
156C24×C11—21no—
157C24×C11—21no—
158C24×C11—21no—
159C24×C11C22×C412yes—
160C24×C11C2×D412yes—
161C24×C11#4112yes—
162C24×C11C2411yescharacteristic
163C23×D11—21no—
164C23×D11—21no—
165C23×D11—21no—
166C23×D11—21no—
167C23×D11—21no—
168C23×D11—21no—
169C23×D11—21no—
170C23×D11—21no—
171C23×D11—21no—
172C23×D11—21no—
173C23×D11—21no—
174C23×D11—21no—
175C23×D11—21no—
176C23×D11—21no—
177C23×D11C22×C412yes—
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×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—44no—
217C22×C4×C11—44no—
218C22×C4×C11—44no—
219C22×C4×C11—44no—
220C22×C4×C11—44no—
221C22×C4×C11—44no—
222C22×C4×C11—44no—
223C22×C4×C11C22×C412yes—
224C22×C4×C11C22×C412yes—
225C22×C4×C11#4112yes—
226C22×C4×C11#4112yes—
227C2×C22⋊D11—28no—
228C2×C22⋊D11—28no—
229C2×C22⋊D11—44no—
230C2×C22⋊D11—44no—
231C2×C22⋊D11—44no—
232C2×C22⋊D11—44no—
233C2×C22⋊D11—44no—
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×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11—21no—
271C22×Dic11—21no—
272C22×Dic11—21no—
273C22×Dic11—21no—
274C22×Dic11—21no—
275C22×Dic11—21no—
276C22×Dic11C22×C412yes—
277C22×Dic11C22×C412yes—
278C22×Dic11C22×C412yes—
279C22×Dic11C2×D412yes—
280C22×Dic11C2×D412yes—
281C22×Dic11#4112yes—
282C22×Dic11#4112yes—
283C11×C22⋊C4—44no—
284C11×C22⋊C4—44no—
285C22⋊Dic11—28no—
286C22⋊Dic11—44no—
287C22⋊Dic11—44no—
288(C2×D11)⋊C4—44no—
289(C2×D11)⋊C4—44no—
290(C2×D11)⋊C4—44no—
291(C2×D11)⋊C4—44no—
292(C2×D11)⋊C4—44no—
293(C2×D11)⋊C4—44no—
294Dic11⋊C4—44no—
295Dic11⋊C4—44no—
296C4×Dic11—44no—
297C4×Dic11—44no—
298C2×#390—111no—
299C2×#388—111no—
300C2×#386—111no—
301#1442—111no—
302#1440—111no—
303#1440—111no—
304#1440—111no—
305#1439—111no—
306#1438—111no—
307#1437—111no—
308#1436—111no—
309#1436—111no—
310#1434—111no—
311C22⋊#95—111no—
312C22⋊#95D1111yescharacteristic, complemented
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—41no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11—41no—
337C23×C11—41no—
338C23×C11—41no—
339C23×C11—41no—
340C23×C11—41no—
341C23×C11—41no—
342C23×C11—41no—
343C23×C11—41no—
344C23×C11—41no—
345C23×C11—41no—
346C23×C11—41no—
347C23×C11C4×D414yes—
348C23×C11C23×C411yescharacteristic
349C23×C11C22×D411yescharacteristic
350C23×C11C2×#4111yescharacteristic
351C23×C11C2×#4111yescharacteristic
352C23×C11C2×#4111yescharacteristic
353C23×C11C2×#4111yescharacteristic
354C23×C11C2×#4111yescharacteristic
355C23×C11H(5,𝔽2)11yescharacteristic
356C23×C11H(5,𝔽2)11yescharacteristic
357C23×C11H(5,𝔽2)11yescharacteristic
358C23×C11H(5,𝔽2)11yescharacteristic
359C23×C11H(5,𝔽2)11yescharacteristic
360C23×C11H(5,𝔽2)11yescharacteristic
361C23×C11H(5,𝔽2)11yescharacteristic
362C23×C112−1+411yescharacteristic
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—41no—
371C22×D11—41no—
372C22×D11—41no—
373C22×D11—41no—
374C22×D11—41no—
375C22×D11—41no—
376C22×D11—41no—
377C22×D11—41no—
378C22×D11—41no—
379C22×D11—41no—
380C22×D11—41no—
381C22×D11—41no—
382C22×D11—41no—
383C22×D11—41no—
384C22×D11—41no—
385C22×D11—41no—
386C22×D11—41no—
387C22×D11—41no—
388C22×D11—41no—
389C22×D11—41no—
390C22×D11—41no—
391C22×D11—41no—
392C22×D11—41no—
393C22×D11—41no—
394C22×D11—41no—
395C22×D11—41no—
396C22×D11—41no—
397C22×D11—41no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—416no—
411C2×C4×C11—41no—
412C2×C4×C11—41no—
413C2×C4×C11—41no—
414C2×C4×C11—41no—
415C2×C4×C11—41no—
416C2×C4×C11—41no—
417C2×C4×C11—41no—
418C2×C4×C11—41no—
419C2×C4×C11—41no—
420C2×C4×C11—41no—
421C2×C4×C11—41no—
422C2×C4×C11—41no—
423C2×C4×C11—41no—
424C2×C4×C11—41no—
425C2×C4×C11—41no—
426C2×C4×C11—41no—
427C2×C4×C11—41no—
428C2×C4×C11—41no—
429C2×C4×C11—41no—
430C2×C4×C11—41no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11—41no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C22⋊D11—416no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—22no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—22no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—22no—
457C2×Dic11—22no—
458C2×Dic11—22no—
459C2×Dic11—22no—
460C2×Dic11—41no—
461C2×Dic11—41no—
462C2×Dic11—41no—
463C2×Dic11—41no—
464C2×Dic11—41no—
465C2×Dic11—41no—
466C2×Dic11—41no—
467C2×Dic11—41no—
468C2×Dic11—41no—
469C2×Dic11—41no—
470C2×Dic11—41no—
471C2×Dic11—41no—
472C2×Dic11—41no—
473C2×Dic11—41no—
474C2×Dic11—41no—
475C2×Dic11—41no—
476C2×Dic11—41no—
477C2×Dic11—41no—
478C2×Dic11—41no—
479C2×Dic11—41no—
480C2×Dic11—41no—
481C2×Dic11—41no—
482C2×Dic11—41no—
483C2×Dic11—41no—
484C2×Dic11—41no—
485C2×Dic11—41no—
486C2×Dic11—41no—
487C2×Dic11—41no—
488C2×Dic11—41no—
489C2×Dic11—41no—
490C2×Dic11#11714yes—
491C23×D4—111no—
492C24×C4C2×D1111yescharacteristic
493C22×C4⋊C4—111no—
494C22×C4⋊C4—111no—
495C22×C22⋊C4—111no—
496C22×C22⋊C4—111no—
497C22×C22⋊C4—111no—
498C22×C22⋊C4—111no—
499C22×C22⋊C4—111no—
500C22×C22⋊C4—111no—
501C22×C22⋊C4—111no—
502C22×C22⋊C4—111no—
503C22×C22⋊C4—111no—
504C22×C22⋊C4C2×D1111yescharacteristic
505C22×C22⋊C4C2×D1111yescharacteristic
506C22×C42—111no—
507C22×C42—111no—
508#390—224no—
509#388—224no—
510#386—118no—
511C2×#95—111no—
512C2×#95—111no—
513C2×#95—111no—
514C2×#95—111no—
515C2×#95—111no—
516C2×#95—111no—
517C2×#95—111no—
518C2×#95—111no—
519C2×#95—111no—
520C2×#95—111no—
521C2×#95—111no—
522C2×#95—111no—
523C2×#95—111no—
524C2×#95—111no—
525C2×#95C2×D1111yescharacteristic
526C2×#95C2×D1111yescharacteristic
527C2×#95C2×D1111yescharacteristic
528C2×#95C2×D1111yescharacteristic
529C22×C11—24no—
530C22×C11—24no—
531C22×C11—24no—
532C22×C11—42no—
533C22×C11—42no—
534C22×C11—42no—
535C22×C11—42no—
536C22×C11—42no—
537C22×C11—42no—
538C22×C11—42no—
539C22×C11—42no—
540C22×C11—42no—
541C22×C11—42no—
542C22×C11—42no—
543C22×C11—42no—
544C22×C11C2×#11711yescharacteristic
545C22×C11C2×C4×D411yescharacteristic
546C22×C11C4×#4111yescharacteristic
547C22×C11#51811yescharacteristic
548C22×C11#51811yescharacteristic
549C22×C11#51811yescharacteristic
550C22×C11#52011yescharacteristic
551C22×C11#53411yescharacteristic
552C22×C11#53711yescharacteristic
553C22×C11#53811yescharacteristic
554C22×C11#53811yescharacteristic
555C22×C11#53911yescharacteristic
556C22×C11#53911yescharacteristic
557C22×C11#54011yescharacteristic
558C22×C11#54011yescharacteristic
559C22×C11#54011yescharacteristic
560C22×C11#54211yescharacteristic
561C22×C11#54211yescharacteristic
562C22×C11#54211yescharacteristic
563C22×C11#54611yescharacteristic
564C22×C11#54611yescharacteristic
565C22×C11#54611yescharacteristic
566C22×C11#54611yescharacteristic
567C22×C11#55111yescharacteristic
568C22×C11#55111yescharacteristic
569C22×C11#55311yescharacteristic
570C22×C11#55311yescharacteristic
571C22×C11#55311yescharacteristic
572C22×C11#55311yescharacteristic
573C22×C11#55911yescharacteristic
574C22×C11#55911yescharacteristic
575C22×C11#56011yescharacteristic
576C22×C11#56011yescharacteristic
577C22×C11#56011yescharacteristic
578C22×C11H(3,𝔽4)11yescharacteristic
579C2×D11—42no—
580C2×D11—42no—
581C2×D11—42no—
582C2×D11—42no—
583C2×D11—42no—
584C2×D11—42no—
585C2×D11—42no—
586C2×D11—81no—
587C2×D11—81no—
588C2×D11—81no—
589C2×D11—81no—
590C2×D11—81no—
591C2×D11—81no—
592C2×D11—81no—
593C2×D11—81no—
594C4×C11—42no—
595C4×C11—42no—
596C4×C11—42no—
597C4×C11—42no—
598C4×C11—81no—
599C4×C11—81no—
600Dic11—24no—
601Dic11—42no—
602Dic11—42no—
603Dic11—42no—
604Dic11—42no—
605Dic11—81no—
606Dic11—81no—
607C25—111no—
608C25C22×D1111yescharacteristic
609C22×D4—114no—
610C22×D4—222no—
611C22×D4—222no—
612C22×D4—222no—
613C22×D4—222no—
614C22×D4—441no—
615C22×D4—441no—
616C23×C4—41no—
617C23×C4—41no—
618C23×C4—41no—
619C23×C4—41no—
620C23×C4—41no—
621C23×C4—41no—
622C23×C4—111no—
623C23×C4—111no—
624C23×C4—111no—
625C23×C4—111no—
626C23×C4—111no—
627C23×C4—111no—
628C23×C4—111no—
629C23×C4C4×D1114yes—
630C23×C4C22×D1111yescharacteristic
631C23×C4C22×D1111yescharacteristic
632C23×C4C22×D1111yescharacteristic
633C23×C4C22×D1111yescharacteristic
634C23×C4C22×D1111yescharacteristic
635C23×C4C22×D1111yescharacteristic
636C2×C4⋊C4—222no—
637C2×C4⋊C4—222no—
638C2×C4⋊C4—222no—
639C2×C4⋊C4—222no—
640C2×C4⋊C4—441no—
641C2×C4⋊C4—441no—
642C2×C22⋊C4—22no—
643C2×C22⋊C4—22no—
644C2×C22⋊C4—22no—
645C2×C22⋊C4—22no—
646C2×C22⋊C4—41no—
647C2×C22⋊C4—41no—
648C2×C22⋊C4—114no—
649C2×C22⋊C4—114no—
650C2×C22⋊C4—114no—
651C2×C22⋊C4—114no—
652C2×C22⋊C4—222no—
653C2×C22⋊C4—222no—
654C2×C22⋊C4—222no—
655C2×C22⋊C4—222no—
656C2×C22⋊C4—222no—
657C2×C22⋊C4—222no—
658C2×C22⋊C4—222no—
659C2×C22⋊C4—441no—
660C2×C22⋊C4—441no—
661C2×C22⋊C4—441no—
662C2×C22⋊C4—441no—
663C2×C22⋊C4—441no—
664C2×C22⋊C4—441no—
665C2×C22⋊C4—441no—
666C2×C22⋊C4—441no—
667C2×C22⋊C4—441no—
668C2×C22⋊C4—441no—
669C2×C22⋊C4—441no—
670C2×C22⋊C4—441no—
671C2×C22⋊C4—441no—
672C2×C22⋊C4—441no—
673C2×C22⋊C4—441no—
674C2×C22⋊C4—441no—
675C2×C42—222no—
676C2×C42—222no—
677C2×C42—222no—
678C2×C42—441no—
679C2×C42—441no—
680C2×C42—441no—
681#95—41no—
682#95—41no—
683#95—41no—
684#95—41no—
685#95—114no—
686#95—114no—
687#95—222no—
688#95—222no—
689#95—222no—
690#95—222no—
691#95—222no—
692#95—441no—
693#95—441no—
694#95—441no—
695#95—441no—
696#95—441no—
697#95—441no—
698#95—441no—
699C2×C11—44no—
700C2×C11#231911yescharacteristic
701C2×C11#232511yescharacteristic
702C2×C11#233511yescharacteristic
703C2×C11#234211yescharacteristic
704C2×C11#235711yescharacteristic
705C2×C11#236411yescharacteristic
706C2×C11#237511yescharacteristic
707C2×C11#268811yescharacteristic
708C2×C11#269111yescharacteristic
709C2×C11#270911yescharacteristic
710C2×C11#271211yescharacteristic
711C2×C11#275311yescharacteristic
712C2×C11#275711yescharacteristic
713C2×C11#279611yescharacteristic
714C2×C11#279711yescharacteristic
715D11—82no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—112no—
729C24—221no—
730C24—221no—
731C24—221no—
732C24—221no—
733C24—221no—
734C24—221no—
735C24—221no—
736C24—221no—
737C24—221no—
738C24—221no—
739C24—221no—
740C24—221no—
741C24—221no—
742C24—221no—
743C24C2×C4×D1112yes—
744C24D4×D1112yes—
745C24#434312yes—
746C24C23×D1111yescharacteristic
747C2×D4—228no—
748C2×D4—228no—
749C2×D4—444no—
750C2×D4—444no—
751C2×D4—444no—
752C2×D4—444no—
753C2×D4—444no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—112no—
800C22×C4—112no—
801C22×C4—112no—
802C22×C4—112no—
803C22×C4—112no—
804C22×C4—112no—
805C22×C4—112no—
806C22×C4—221no—
807C22×C4—221no—
808C22×C4—221no—
809C22×C4—221no—
810C22×C4—221no—
811C22×C4—221no—
812C22×C4—221no—
813C22×C4—221no—
814C22×C4—221no—
815C22×C4—221no—
816C22×C4—221no—
817C22×C4—221no—
818C22×C4—221no—
819C22×C4—221no—
820C22×C4—221no—
821C22×C4—221no—
822C22×C4—221no—
823C22×C4—221no—
824C22×C4—221no—
825C22×C4—221no—
826C22×C4—221no—
827C22×C4—221no—
828C22×C4—221no—
829C22×C4—221no—
830C22×C4—221no—
831C22×C4—221no—
832C22×C4—221no—
833C22×C4—221no—
834C22×C4—221no—
835C22×C4—221no—
836C22×C4—221no—
837C22×C4—221no—
838C22×C4—221no—
839C22×C4—221no—
840C22×C4—221no—
841C22×C4—221no—
842C22×C4—221no—
843C22×C4—221no—
844C22×C4—221no—
845C22×C4—221no—
846C22×C4—221no—
847C22×C4—221no—
848C22×C4C2×C4×D1112yes—
849C22×C4C2×C4×D1112yes—
850C22×C4#433912yes—
851C22×C4#433912yes—
852C4⋊C4—444no—
853C4⋊C4—444no—
854C22⋊C4—44no—
855C22⋊C4—44no—
856C22⋊C4—228no—
857C22⋊C4—444no—
858C22⋊C4—444no—
859C22⋊C4—444no—
860C22⋊C4—444no—
861C22⋊C4—444no—
862C22⋊C4—444no—
863C22⋊C4—444no—
864C22⋊C4—444no—
865C42—444no—
866C42—444no—
867C11#1442811yescharacteristic, complemented, Sylow
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—222no—
903C23—222no—
904C23—222no—
905C23—222no—
906C23—222no—
907C23—222no—
908C23—222no—
909C23—441no—
910C23—441no—
911C23—441no—
912C23—441no—
913C23—441no—
914C23—441no—
915C23—441no—
916C23—441no—
917C23—441no—
918C23—441no—
919C23—441no—
920C23—441no—
921C23—441no—
922C23—441no—
923C23—441no—
924C23—441no—
925C23—441no—
926C23—441no—
927C23—441no—
928C23—441no—
929C23—441no—
930C23—441no—
931C23—441no—
932C23—441no—
933C23—441no—
934C23—441no—
935C23—441no—
936C23—441no—
937C23#6694614yes—
938C23C22×C4×D1111yescharacteristic
939C23C2×#433911yescharacteristic
940C23C2×#433911yescharacteristic
941C23C2×D4×D1111yescharacteristic
942C23#6703711yescharacteristic
943C23#6703711yescharacteristic
944C23#6703711yescharacteristic
945C23#6703711yescharacteristic
946C23#6703711yescharacteristic
947C23#6703711yescharacteristic
948C23C2×#434311yescharacteristic
949C23#41×D1111yescharacteristic
950C23#41×D1111yescharacteristic
951C23#6704211yescharacteristic
952C23#6704311yescharacteristic
953D4—4416no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—416no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—114no—
998C2×C4—222no—
999C2×C4—222no—
1000C2×C4—222no—
1001C2×C4—222no—
1002C2×C4—222no—
1003C2×C4—222no—
1004C2×C4—222no—
1005C2×C4—222no—
1006C2×C4—222no—
1007C2×C4—222no—
1008C2×C4—222no—
1009C2×C4—222no—
1010C2×C4—222no—
1011C2×C4—222no—
1012C2×C4—222no—
1013C2×C4—222no—
1014C2×C4—222no—
1015C2×C4—222no—
1016C2×C4—441no—
1017C2×C4—441no—
1018C2×C4—441no—
1019C2×C4—441no—
1020C2×C4—441no—
1021C2×C4—441no—
1022C2×C4—441no—
1023C2×C4—441no—
1024C2×C4—441no—
1025C2×C4—441no—
1026C2×C4—441no—
1027C2×C4—441no—
1028C2×C4—441no—
1029C2×C4—441no—
1030C2×C4—441no—
1031C2×C4—441no—
1032C2×C4—441no—
1033C2×C4—441no—
1034C2×C4—441no—
1035C2×C4—441no—
1036C2×C4—441no—
1037C2×C4—441no—
1038C2×C4—441no—
1039C2×C4—441no—
1040C2×C4—441no—
1041C2×C4—441no—
1042C2×C4—441no—
1043C2×C4—441no—
1044C2×C4—441no—
1045C2×C4—441no—
1046C22—24no—
1047C22—24no—
1048C22—24no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—442no—
1062C22—442no—
1063C22—442no—
1064C22—442no—
1065C22—442no—
1066C22—442no—
1067C22—442no—
1068C22—881no—
1069C22—881no—
1070C22—881no—
1071C22—881no—
1072C22—881no—
1073C22—881no—
1074C22—881no—
1075C22—881no—
1076C22C4×#433911yescharacteristic
1077C22#1062301711yescharacteristic
1078C22#1062301711yescharacteristic
1079C22#1062301711yescharacteristic
1080C22#1062302111yescharacteristic
1081C22#1062302111yescharacteristic
1082C22C2×#6694611yescharacteristic
1083C22#1062304511yescharacteristic
1084C22#1062304511yescharacteristic
1085C22D11×#11711yescharacteristic
1086C22#1062305411yescharacteristic
1087C22#1062307111yescharacteristic
1088C22#1062307111yescharacteristic
1089C22#1062309011yescharacteristic
1090C22#1062309011yescharacteristic
1091C22#1062309111yescharacteristic
1092C22#1062309211yescharacteristic
1093C22#1062309311yescharacteristic
1094C22#1062309511yescharacteristic
1095C22#1062312511yescharacteristic
1096C22#1062312611yescharacteristic
1097C22#1062312611yescharacteristic
1098C22#1062312611yescharacteristic
1099C22#1062312811yescharacteristic
1100C22#1062313611yescharacteristic
1101C22#1062314111yescharacteristic
1102C22#1062314111yescharacteristic
1103C22#1062316811yescharacteristic
1104C22#1062316811yescharacteristic
1105C22#1062317511yescharacteristic
1106C22#1062317611yescharacteristic
1107C22#1062319311yescharacteristic
1108C22#1062319311yescharacteristic
1109C22#1062319411yescharacteristic
1110C22#1062319411yescharacteristic
1111C4—42no—
1112C4—42no—
1113C4—42no—
1114C4—42no—
1115C4—81no—
1116C4—81no—
1117C4—224no—
1118C4—442no—
1119C4—442no—
1120C4—442no—
1121C4—442no—
1122C4—881no—
1123C4—881no—
1124C2—44no—
1125C2—882no—
1126C2#1307125611yescharacteristic
1127C2#1307131611yescharacteristic
1128C2#1307140611yescharacteristic
1129C2#1307146211yescharacteristic
1130C2#1307159011yescharacteristic
1131C2#1307166311yescharacteristic
1132C2#1307175511yescharacteristic
1133C2#1307504911yescharacteristic
1134C2#1307509411yescharacteristic
1135C2#1307534411yescharacteristic
1136C2#1307538311yescharacteristic
1137C2#1307589411yescharacteristic
1138C2#1307595411yescharacteristic
1139C2#1307646211yescharacteristic
1140C2#1307647711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22⋊#95D11
hypocenterC11#14428
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622558C2semidirect
4. #13066874C2semidirect
5. #13066864C2semidirect
6. #13066864C2semidirect
7. #13066863C2semidirect
8. #13066860C2semidirect
10. #13066852C2semidirect
11. #13066847C2semidirect
12. #13066847C2semidirect
13. #13066842C2semidirect
14. #13066839C2semidirect
15. C11×C22⋊#95C2semidirect
37. #10622826C4semidirect
312. C22⋊#95D11semidirect
867. C11#14428semidirect

Maximal subgroups

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

subgroupindex
C2×#106225702
C2×#106225582
C2×#106228262
#130668742
#130668642
#130668632
#130668602
#130668552
#130668522
#130668472
#130668422
#130668392
C11×C22⋊#952
#1442811