Finite Group Databasebeta

← #14718913

Subgroups — #14718913

Order 2816.

1426 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13066877C211yesmaximal, characteristic, complemented
2#13066868C211yesmaximal, characteristic, complemented
3#13066867C211yesmaximal, characteristic, complemented
4#13066862C211yesmaximal, characteristic, complemented
5#13066862C211yesmaximal, characteristic, complemented
6#13066860C211yesmaximal, characteristic, complemented
7#13066860C211yesmaximal, characteristic, complemented
8#13066860C211yesmaximal, characteristic, complemented
9#13066860C211yesmaximal, characteristic, complemented
10#13066860C211yesmaximal, characteristic, complemented
11#13066860C211yesmaximal, characteristic, complemented
12#13066856C211yesmaximal, characteristic
13#13066856C211yesmaximal, characteristic
14#13066856C211yesmaximal, characteristic
15C11×#1443C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
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
51C24×D11C2311yescharacteristic
52C24×D11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C22×D44—41no—
67C22×D44—41no—
68C22×D44—41no—
69C22×D44—41no—
70C22×D44—41no—
71C22×D44—41no—
72C22×D44Q814yes—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4—22no—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4—22no—
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)⋊C4—41no—
93C2×(C2×D11)⋊C4—41no—
94C2×(C2×D11)⋊C4—41no—
95C2×(C2×D11)⋊C4—41no—
96C2×(C2×D11)⋊C4—41no—
97C2×(C2×D11)⋊C4—41no—
98C2×(C2×D11)⋊C4—41no—
99C2×(C2×D11)⋊C4—41no—
100C2×(C2×D11)⋊C4—41no—
101C2×(C2×D11)⋊C4—41no—
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×C4⋊Dic11—22no—
110C2×C4⋊Dic11—41no—
111C2×C4⋊Dic11—41no—
112C2×Dic11⋊C4—22no—
113C2×Dic11⋊C4—41no—
114C2×Dic11⋊C4—41no—
115C2×Dic11⋊C4—41no—
116C2×Dic11⋊C4—41no—
117C2×Dic11⋊C4—41no—
118C2×Dic11⋊C4—41no—
119C2×Dic11⋊C4—41no—
120C2×Dic11⋊C4—41no—
121C11×#95—22no—
122C11×#95—41no—
123C11×#95—41no—
124C11×#95—41no—
125C11×#95—41no—
126C11×#95—41no—
127C11×#95—41no—
128C11⋊#95—22no—
129C11⋊#95—41no—
130C11⋊#95—41no—
131C11⋊#95—41no—
132C11⋊#95—41no—
133C11⋊#95—41no—
134C11⋊#95—41no—
135C11⋊#95—41no—
136C11⋊#95—41no—
137C11⋊#95—41no—
138C11⋊#95—41no—
139#17272—111nomaximal, Sylow
140C24×C11C2411yescharacteristic
141C23×D11—21no—
142C23×D11—21no—
143C23×D11—21no—
144C23×D11—21no—
145C23×D11—21no—
146C23×D11—21no—
147C23×D11—21no—
148C23×D11—21no—
149C23×D11—21no—
150C23×D11—21no—
151C23×D11—21no—
152C23×D11—21no—
153C23×D11—21no—
154C23×D11—21no—
155C23×D11—21no—
156C23×D11—21no—
157C23×D11—21no—
158C23×D11—21no—
159C23×D11—21no—
160C23×D11—21no—
161C23×D11—21no—
162C23×D11—21no—
163C23×D11—21no—
164C23×D11—21no—
165C23×D11—21no—
166C23×D11—21no—
167C23×D11—21no—
168C23×D11—21no—
169C23×D11C2×Q812yes—
170C23×D11C2×Q812yes—
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×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—21no—
217C22×C4×C11—21no—
218C22×C4×C11C2×Q812yes—
219C22×C4×C11#4112yes—
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×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#4112yes—
260C22×Dic11#4112yes—
261C22×Dic11#4112yes—
262C2×D44—44no—
263C2×D44—44no—
264C2×D44—44no—
265C2×D44—44no—
266C2×D44—44no—
267C2×D44—44no—
268C2×D44—44no—
269(C2×D11)⋊C4—44no—
270(C2×D11)⋊C4—44no—
271(C2×D11)⋊C4—44no—
272(C2×D11)⋊C4—44no—
273(C2×D11)⋊C4—44no—
274(C2×D11)⋊C4—44no—
275(C2×D11)⋊C4—44no—
276(C2×D11)⋊C4—44no—
277(C2×D11)⋊C4—44no—
278(C2×D11)⋊C4—44no—
279(C2×D11)⋊C4—44no—
280(C2×D11)⋊C4—44no—
281C4⋊Dic11—44no—
282Dic11⋊C4—44no—
283Dic11⋊C4—44no—
284Dic11⋊C4—44no—
285#1443—111no—
286#1443D1111yescharacteristic, complemented
287#1441—111no—
288#1441—111no—
289#1439—111no—
290#1439—111no—
291#1439—111no—
292#1439—111no—
293#1439—111no—
294#1439—111no—
295#1439—111no—
296#1439—111no—
297#1438—111no—
298#1438—111no—
299#1438—111no—
300C23×C11C22×Q811yescharacteristic
301C23×C11C2×#4111yescharacteristic
302C23×C11C2×#4111yescharacteristic
303C23×C11C2×#4111yescharacteristic
304C23×C11C2×#4111yescharacteristic
305C23×C11H(5,𝔽2)11yescharacteristic
306C23×C11H(5,𝔽2)11yescharacteristic
307C23×C11H(5,𝔽2)11yescharacteristic
308C23×C11H(5,𝔽2)11yescharacteristic
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
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—41no—
330C22×D11—41no—
331C22×D11—41no—
332C22×D11—41no—
333C22×D11—41no—
334C22×D11—41no—
335C22×D11—41no—
336C22×D11—41no—
337C22×D11—41no—
338C22×D11—41no—
339C22×D11—41no—
340C22×D11—41no—
341C22×D11—41no—
342C22×D11—41no—
343C22×D11—41no—
344C22×D11—41no—
345C22×D11—41no—
346C22×D11—41no—
347C22×D11—41no—
348C22×D11—41no—
349C22×D11—41no—
350C22×D11—41no—
351C22×D11—41no—
352C22×D11—41no—
353C22×D11—41no—
354C22×D11—41no—
355C22×D11—41no—
356C22×D11—41no—
357C22×D11—41no—
358C22×D11—41no—
359C22×D11—41no—
360C22×D11—41no—
361C22×D11—41no—
362C22×D11—41no—
363C22×D11—41no—
364C22×D11—41no—
365C22×D11—41no—
366C22×D11—41no—
367C22×D11—41no—
368C22×D11—41no—
369C22×D11—41no—
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—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
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×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—41no—
444C2×Dic11—41no—
445C2×Dic11—41no—
446C2×Dic11—41no—
447C2×Dic11—41no—
448C2×Dic11—41no—
449C2×Dic11—41no—
450C2×Dic11—41no—
451C2×Dic11—41no—
452C2×Dic11—41no—
453C2×Dic11—41no—
454C2×Dic11—41no—
455C2×Dic11—41no—
456C2×Dic11—41no—
457C2×Dic11—41no—
458C2×Dic11—41no—
459C2×Dic11—41no—
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—
476D44—416no—
477C23×D4—111no—
478C22×C4⋊C4—111no—
479C22×C4⋊C4—111no—
480C22×C4⋊C4—111no—
481C22×C4⋊C4—111no—
482C22×C22⋊C4—111no—
483C22×C22⋊C4—111no—
484C22×C22⋊C4—111no—
485C22×C22⋊C4—111no—
486C22×C22⋊C4—111no—
487C22×C22⋊C4—111no—
488C22×C22⋊C4—111no—
489C22×C22⋊C4—111no—
490C22×C22⋊C4—111no—
491C22×C22⋊C4—111no—
492C22×C22⋊C4—111no—
493C22×C22⋊C4—111no—
494C2×#95—111no—
495C2×#95—111no—
496C2×#95—111no—
497C2×#95—111no—
498C2×#95—111no—
499C2×#95—111no—
500C2×#95—111no—
501C2×#95—111no—
502C2×#95—111no—
503C2×#95—111no—
504C2×#95—111no—
505C2×#95C2×D1111yescharacteristic
506C2×#95C2×D1111yescharacteristic
507C2×#95C2×D1111yescharacteristic
508C2×#95C2×D1111yescharacteristic
509C2×#95C2×D1111yescharacteristic
510C2×#95C2×D1111yescharacteristic
511C2×#95C2×D1111yescharacteristic
512C22×C11#53811yescharacteristic
513C22×C11#53811yescharacteristic
514C22×C11#53811yescharacteristic
515C22×C11#53811yescharacteristic
516C22×C11#53811yescharacteristic
517C22×C11#53811yescharacteristic
518C22×C11#53811yescharacteristic
519C22×C11#53811yescharacteristic
520C22×C11#54011yescharacteristic
521C22×C11#54011yescharacteristic
522C22×C11#54011yescharacteristic
523C22×C11#54011yescharacteristic
524C22×C11#54311yescharacteristic
525C22×C11#54311yescharacteristic
526C22×C11#54311yescharacteristic
527C22×C11#55111yescharacteristic
528C22×C11#55311yescharacteristic
529C22×C11#55311yescharacteristic
530C22×C11#55411yescharacteristic
531C22×C11#55411yescharacteristic
532C22×C11#55411yescharacteristic
533C22×C11#55411yescharacteristic
534C22×C11#55511yescharacteristic
535C22×C11#55511yescharacteristic
536C22×C11#55911yescharacteristic
537C22×C11#56011yescharacteristic
538C22×C11#56011yescharacteristic
539C22×C11#56011yescharacteristic
540C22×C11#56011yescharacteristic
541C22×C11#56011yescharacteristic
542C22×C11#56011yescharacteristic
543C22×C11#56011yescharacteristic
544C22×C11#56011yescharacteristic
545C22×C11#56011yescharacteristic
546C22×C11H(3,𝔽4)11yescharacteristic
547C2×D11—42no—
548C2×D11—42no—
549C2×D11—42no—
550C2×D11—42no—
551C2×D11—42no—
552C2×D11—42no—
553C2×D11—42no—
554C2×D11—42no—
555C2×D11—42no—
556C2×D11—42no—
557C2×D11—42no—
558C2×D11—42no—
559C2×D11—42no—
560C2×D11—42no—
561C2×D11—81no—
562C2×D11—81no—
563C2×D11—81no—
564C2×D11—81no—
565C2×D11—81no—
566C2×D11—81no—
567C2×D11—81no—
568C2×D11—81no—
569C2×D11—81no—
570C2×D11—81no—
571C2×D11—81no—
572C2×D11—81no—
573C2×D11—81no—
574C2×D11—81no—
575C2×D11—81no—
576C2×D11—81no—
577C4×C11—42no—
578C4×C11—42no—
579C4×C11—81no—
580C4×C11—81no—
581C4×C11—81no—
582C4×C11—81no—
583C4×C11—81no—
584Dic11—42no—
585Dic11—42no—
586Dic11—42no—
587Dic11—81no—
588Dic11—81no—
589Dic11—81no—
590C25—111no—
591C25—111no—
592C22×D4—114no—
593C22×D4—441no—
594C22×D4—441no—
595C22×D4—441no—
596C22×D4—441no—
597C22×D4—441no—
598C22×D4—441no—
599C23×C4—111no—
600C23×C4—111no—
601C23×C4—111no—
602C23×C4—111no—
603C23×C4—111no—
604C23×C4—111no—
605C23×C4C22×D1111yescharacteristic
606C23×C4C22×D1111yescharacteristic
607C23×C4C22×D1111yescharacteristic
608C23×C4C22×D1111yescharacteristic
609C23×C4C22×D1111yescharacteristic
610C23×C4C22×D1111yescharacteristic
611C23×C4C22×D1111yescharacteristic
612C2×C4⋊C4—222no—
613C2×C4⋊C4—222no—
614C2×C4⋊C4—441no—
615C2×C4⋊C4—441no—
616C2×C4⋊C4—441no—
617C2×C4⋊C4—441no—
618C2×C4⋊C4—441no—
619C2×C4⋊C4—441no—
620C2×C4⋊C4—441no—
621C2×C4⋊C4—441no—
622C2×C4⋊C4—441no—
623C2×C4⋊C4—441no—
624C2×C22⋊C4—222no—
625C2×C22⋊C4—222no—
626C2×C22⋊C4—222no—
627C2×C22⋊C4—222no—
628C2×C22⋊C4—222no—
629C2×C22⋊C4—222no—
630C2×C22⋊C4—222no—
631C2×C22⋊C4—222no—
632C2×C22⋊C4—441no—
633C2×C22⋊C4—441no—
634C2×C22⋊C4—441no—
635C2×C22⋊C4—441no—
636C2×C22⋊C4—441no—
637C2×C22⋊C4—441no—
638C2×C22⋊C4—441no—
639C2×C22⋊C4—441no—
640C2×C22⋊C4—441no—
641C2×C22⋊C4—441no—
642C2×C22⋊C4—441no—
643C2×C22⋊C4—441no—
644C2×C22⋊C4—441no—
645C2×C22⋊C4—441no—
646C2×C22⋊C4—441no—
647C2×C22⋊C4—441no—
648C2×C22⋊C4—441no—
649C2×C22⋊C4—441no—
650C2×C22⋊C4—441no—
651C2×C22⋊C4—441no—
652C2×C22⋊C4—441no—
653C2×C22⋊C4—441no—
654C2×C22⋊C4—441no—
655C2×C22⋊C4—441no—
656C2×C22⋊C4—441no—
657C2×C22⋊C4—441no—
658C2×C22⋊C4—441no—
659C2×C22⋊C4—441no—
660#95—22no—
661#95—41no—
662#95—41no—
663#95—41no—
664#95—41no—
665#95—41no—
666#95—41no—
667#95—222no—
668#95—441no—
669#95—441no—
670#95—441no—
671#95—441no—
672#95—441no—
673#95—441no—
674#95—441no—
675#95—441no—
676#95—441no—
677#95—441no—
678C2×C11#274811yescharacteristic
679C2×C11#275611yescharacteristic
680C2×C11#275611yescharacteristic
681C2×C11#278011yescharacteristic
682C2×C11#278011yescharacteristic
683C2×C11#278411yescharacteristic
684C2×C11#278411yescharacteristic
685C2×C11#280311yescharacteristic
686C2×C11#280311yescharacteristic
687C2×C11#280411yescharacteristic
688C2×C11#282511yescharacteristic
689C2×C11#282511yescharacteristic
690C2×C11#282811yescharacteristic
691C2×C11#282811yescharacteristic
692C2×C11#284211yescharacteristic
693D11—82no—
694D11—82no—
695C24—112no—
696C24—112no—
697C24—221no—
698C24—221no—
699C24—221no—
700C24—221no—
701C24—221no—
702C24—221no—
703C24—221no—
704C24—221no—
705C24—221no—
706C24—221no—
707C24—221no—
708C24—221no—
709C24—221no—
710C24—221no—
711C24—221no—
712C24—221no—
713C24—221no—
714C24—221no—
715C24—221no—
716C24—221no—
717C24—221no—
718C24—221no—
719C24—221no—
720C24—221no—
721C24—221no—
722C24—221no—
723C24—221no—
724C24—221no—
725C24C23×D1111yescharacteristic
726C2×D4—444no—
727C2×D4—444no—
728C2×D4—444no—
729C2×D4—444no—
730C2×D4—444no—
731C2×D4—444no—
732C2×D4—444no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
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—112no—
781C22×C4—112no—
782C22×C4—112no—
783C22×C4—221no—
784C22×C4—221no—
785C22×C4—221no—
786C22×C4—221no—
787C22×C4—221no—
788C22×C4—221no—
789C22×C4—221no—
790C22×C4—221no—
791C22×C4—221no—
792C22×C4—221no—
793C22×C4—221no—
794C22×C4—221no—
795C22×C4—221no—
796C22×C4—221no—
797C22×C4—221no—
798C22×C4—221no—
799C22×C4—221no—
800C22×C4—221no—
801C22×C4—221no—
802C22×C4—221no—
803C22×C4—221no—
804C22×C4—221no—
805C22×C4—221no—
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#433912yes—
823C22×C4Q8×D1112yes—
824C4⋊C4—444no—
825C4⋊C4—444no—
826C4⋊C4—444no—
827C4⋊C4—444no—
828C22⋊C4—444no—
829C22⋊C4—444no—
830C22⋊C4—444no—
831C22⋊C4—444no—
832C22⋊C4—444no—
833C22⋊C4—444no—
834C22⋊C4—444no—
835C22⋊C4—444no—
836C22⋊C4—444no—
837C22⋊C4—444no—
838C22⋊C4—444no—
839C22⋊C4—444no—
840C11#1727211yescharacteristic, complemented, Sylow
841C23—222no—
842C23—222no—
843C23—222no—
844C23—222no—
845C23—222no—
846C23—222no—
847C23—222no—
848C23—222no—
849C23—222no—
850C23—222no—
851C23—222no—
852C23—222no—
853C23—222no—
854C23—222no—
855C23—441no—
856C23—441no—
857C23—441no—
858C23—441no—
859C23—441no—
860C23—441no—
861C23—441no—
862C23—441no—
863C23—441no—
864C23—441no—
865C23—441no—
866C23—441no—
867C23—441no—
868C23—441no—
869C23—441no—
870C23—441no—
871C23—441no—
872C23—441no—
873C23—441no—
874C23—441no—
875C23—441no—
876C23—441no—
877C23—441no—
878C23—441no—
879C23—441no—
880C23—441no—
881C23—441no—
882C23—441no—
883C23—441no—
884C23—441no—
885C23—441no—
886C23—441no—
887C23—441no—
888C23—441no—
889C23—441no—
890C23—441no—
891C23—441no—
892C23—441no—
893C23—441no—
894C23—441no—
895C23—441no—
896C23—441no—
897C23—441no—
898C23—441no—
899C23—441no—
900C23—441no—
901C23—441no—
902C23—441no—
903C23—441no—
904C23—441no—
905C23—441no—
906C23—441no—
907C23—441no—
908C23—441no—
909C23—441no—
910C23—441no—
911C23C2×#433911yescharacteristic
912C23#6703711yescharacteristic
913C23#6703711yescharacteristic
914C23#6703711yescharacteristic
915C23C2×Q8×D1111yescharacteristic
916C23#41×D1111yescharacteristic
917C23#41×D1111yescharacteristic
918C23#41×D1111yescharacteristic
919C23#6704211yescharacteristic
920C23#6704211yescharacteristic
921C23#6704211yescharacteristic
922C23#6704211yescharacteristic
923C23#6704211yescharacteristic
924C23#6704211yescharacteristic
925C23#6704211yescharacteristic
926D4—4416no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
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—222no—
977C2×C4—222no—
978C2×C4—222no—
979C2×C4—222no—
980C2×C4—222no—
981C2×C4—222no—
982C2×C4—222no—
983C2×C4—222no—
984C2×C4—222no—
985C2×C4—441no—
986C2×C4—441no—
987C2×C4—441no—
988C2×C4—441no—
989C2×C4—441no—
990C2×C4—441no—
991C2×C4—441no—
992C2×C4—441no—
993C2×C4—441no—
994C2×C4—441no—
995C2×C4—441no—
996C2×C4—441no—
997C2×C4—441no—
998C2×C4—441no—
999C2×C4—441no—
1000C2×C4—441no—
1001C2×C4—441no—
1002C2×C4—441no—
1003C2×C4—441no—
1004C2×C4—441no—
1005C2×C4—441no—
1006C2×C4—441no—
1007C2×C4—441no—
1008C2×C4—441no—
1009C2×C4—441no—
1010C2×C4—441no—
1011C2×C4—441no—
1012C2×C4—441no—
1013C2×C4—441no—
1014C2×C4—441no—
1015C2×C4—441no—
1016C2×C4—441no—
1017C2×C4—441no—
1018C22—442no—
1019C22—442no—
1020C22—442no—
1021C22—442no—
1022C22—442no—
1023C22—442no—
1024C22—442no—
1025C22—442no—
1026C22—442no—
1027C22—442no—
1028C22—442no—
1029C22—442no—
1030C22—442no—
1031C22—442no—
1032C22—881no—
1033C22—881no—
1034C22—881no—
1035C22—881no—
1036C22—881no—
1037C22—881no—
1038C22—881no—
1039C22—881no—
1040C22—881no—
1041C22—881no—
1042C22—881no—
1043C22—881no—
1044C22—881no—
1045C22—881no—
1046C22—881no—
1047C22—881no—
1048C22#1062305811yescharacteristic
1049C22#1062306311yescharacteristic
1050C22#1062306611yescharacteristic
1051C22#1062307111yescharacteristic
1052C22#1062309111yescharacteristic
1053C22#1062309311yescharacteristic
1054C22#1062311011yescharacteristic
1055C22#1062315111yescharacteristic
1056C22#1062315111yescharacteristic
1057C22#1062315111yescharacteristic
1058C22#1062316511yescharacteristic
1059C22#1062316511yescharacteristic
1060C22#1062316511yescharacteristic
1061C22#1062318811yescharacteristic
1062C22#1062319411yescharacteristic
1063C22#1062319411yescharacteristic
1064C22#1062319511yescharacteristic
1065C22#1062319711yescharacteristic
1066C22#1062319711yescharacteristic
1067C22#1062320111yescharacteristic
1068C22#1062320911yescharacteristic
1069C22#1062321411yescharacteristic
1070C22#1062322111yescharacteristic
1071C22#1062322111yescharacteristic
1072C22#1062322111yescharacteristic
1073C22#1062323511yescharacteristic
1074C22#1062323511yescharacteristic
1075C22#1062323511yescharacteristic
1076C22#1062323511yescharacteristic
1077C22#1062323511yescharacteristic
1078C22#1062324011yescharacteristic
1079C22#1062324211yescharacteristic
1080C22#1062324211yescharacteristic
1081C22#1062324211yescharacteristic
1082C22#1062324211yescharacteristic
1083C4—42no—
1084C4—42no—
1085C4—81no—
1086C4—81no—
1087C4—81no—
1088C4—81no—
1089C4—81no—
1090C4—442no—
1091C4—442no—
1092C4—442no—
1093C4—881no—
1094C4—881no—
1095C4—881no—
1096C2—882no—
1097C2—882no—
1098C2#1307582411yescharacteristic
1099C2#1307593311yescharacteristic
1100C2#1307593411yescharacteristic
1101C2#1307626311yescharacteristic
1102C2#1307626711yescharacteristic
1103C2#1307631211yescharacteristic
1104C2#1307631611yescharacteristic
1105C2#1307654411yescharacteristic
1106C2#1307655411yescharacteristic
1107C2#1307656111yescharacteristic
1108C2#1307670311yescharacteristic
1109C2#1307670611yescharacteristic
1110C2#1307673311yescharacteristic
1111C2#1307673711yescharacteristic
1112C2#1307687911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC11×#1443C2
prime radicalC23×D44C22
hypercenter#1443D11
hypocenterC11#17272
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
1. #13066877C2semidirect
2. #13066868C2semidirect
3. #13066867C2semidirect
4. #13066862C2semidirect
5. #13066862C2semidirect
6. #13066860C2semidirect
7. #13066860C2semidirect
8. #13066860C2semidirect
9. #13066860C2semidirect
10. #13066860C2semidirect
11. #13066860C2semidirect
15. C11×#1443C2semidirect
286. #1443D11semidirect
840. C11#17272semidirect

Maximal subgroups

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

subgroupindex
#130668772
#130668682
#130668672
#130668622
#130668602
#130668562
C11×#14432
#1727211