Finite Group Databasebeta

← #14681781

Subgroups — #14681781

Order 2816.

2018 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622601C211yesmaximal, characteristic
2C2×#10622278C211yesmaximal, characteristic
3C2×#10622278C211yesmaximal, characteristic
4C2×#10622281C211yesmaximal, characteristic, complemented
5C2×#10622600C211yesmaximal, characteristic, complemented
6#13066875C211yesmaximal, characteristic, complemented
7#13066860C211yesmaximal, characteristic, complemented
8#13066858C211yesmaximal, characteristic, complemented
9#13066858C211yesmaximal, characteristic, complemented
10#13066858C211yesmaximal, characteristic, complemented
11#13066850C211yesmaximal, characteristic, complemented
12#13066847C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1444C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊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×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51#10622601—24no—
52#10622600—24no—
53#10622281—24no—
54#10622278—24no—
55#10622278C418yescomplemented
56C24×D11C2311yescharacteristic
57C24×D11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C22×D44—41no—
72C22×D44—41no—
73C22×D44—41no—
74C22×D44—41no—
75C22×D44C2×C414yes—
76C22×D44D414yes—
77C22×D44Q814yes—
78C22×C4×D11—22no—
79C22×C4×D11—22no—
80C22×C4×D11—22no—
81C22×C4×D11—22no—
82C22×C4×D11—22no—
83C22×C4×D11—41no—
84C22×C4×D11—41no—
85C22×C4×D11—41no—
86C22×C4×D11—41no—
87C22×C4×D11—41no—
88C22×C4×D11—41no—
89C22×C4×D11—41no—
90C22×C4×D11—41no—
91C22×C4×D11C2×C414yescomplemented
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4—41no—
95C2×C11×C4⋊C4—41no—
96C2×C11×C4⋊C4—41no—
97C2×C11×C4⋊C4—41no—
98C2×C11×C4⋊C4—41no—
99C2×C11×C4⋊C4—41no—
100C2×C11×C4⋊C4—41no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—22no—
103C2×(C2×D11)⋊C4—22no—
104C2×(C2×D11)⋊C4—22no—
105C2×(C2×D11)⋊C4—22no—
106C2×(C2×D11)⋊C4—22no—
107C2×(C2×D11)⋊C4—22no—
108C2×(C2×D11)⋊C4—22no—
109C2×(C2×D11)⋊C4—22no—
110C2×(C2×D11)⋊C4—22no—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4—22no—
113C2×(C2×D11)⋊C4—22no—
114C2×(C2×D11)⋊C4—22no—
115C2×(C2×D11)⋊C4—22no—
116C2×(C2×D11)⋊C4—41no—
117C2×(C2×D11)⋊C4—41no—
118C2×(C2×D11)⋊C4—41no—
119C2×(C2×D11)⋊C4—41no—
120C2×(C2×D11)⋊C4—41no—
121C2×(C2×D11)⋊C4—41no—
122C2×(C2×D11)⋊C4—41no—
123C2×(C2×D11)⋊C4—41no—
124C2×(C2×D11)⋊C4—41no—
125C2×(C2×D11)⋊C4—41no—
126C2×(C2×D11)⋊C4—41no—
127C2×(C2×D11)⋊C4—41no—
128C2×(C2×D11)⋊C4C2×C414yes—
129C2×(C2×D11)⋊C4C2×C414yes—
130C2×(C2×D11)⋊C4C2×C414yescomplemented
131C2×C4⋊Dic11—41no—
132C2×C4⋊Dic11—41no—
133C2×C4⋊Dic11D414yescomplemented
134C2×Dic11⋊C4—22no—
135C2×Dic11⋊C4—22no—
136C2×Dic11⋊C4—41no—
137C2×C4×Dic11—22no—
138C2×C4×Dic11—41no—
139C2×C4×Dic11—41no—
140C11×#95—22no—
141C11×#95—22no—
142C11×#95—41no—
143C11×#95C2×C414yescomplemented
144C11⋊#95—22no—
145C11⋊#95—22no—
146C11⋊#95—22no—
147C11⋊#95—22no—
148C11⋊#95—22no—
149C11⋊#95—22no—
150C11⋊#95—41no—
151C11⋊#95—41no—
152C11⋊#95—41no—
153C11⋊#95—41no—
154C11⋊#95—41no—
155C11⋊#95C2×C414yescomplemented
156#14407—111nomaximal, Sylow
157C24×C11C2411yescharacteristic
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×D11—21no—
170C23×D11—21no—
171C23×D11—21no—
172C23×D11—21no—
173C23×D11—21no—
174C23×D11—21no—
175C23×D11—21no—
176C23×D11—21no—
177C23×D11—21no—
178C23×D11—21no—
179C23×D11—21no—
180C23×D11—21no—
181C23×D11—21no—
182C23×D11C22×C412yes—
183C23×D11C22×C412yes—
184C23×D11C2×D412yes—
185C23×D11C2×D412yes—
186C23×D11C2×Q812yes—
187C23×D11C2×Q812yes—
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×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11C22×C412yes—
230C22×C4×C11C22×C412yes—
231C22×C4×C11C22×C412yes—
232C22×C4×C11C2×D412yes—
233C22×C4×C11C2×D412yes—
234C22×C4×C11C2×Q812yes—
235C22×C4×C11#4112yes—
236C22×C4×C11#4112yes—
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×Dic11C22×C412yes—
275C22×Dic11C22×C412yes—
276C22×Dic11C2×D412yes—
277C22×Dic11C2×D412yes—
278C22×Dic11#4112yes—
279C2×D44—44no—
280C2×D44—44no—
281C2×D44—44no—
282C2×D44—44no—
283C2×D44—44no—
284C2×D44—44no—
285C2×D44C4⋊C4116yescomplemented
286C2×C4×D11—28no—
287C2×C4×D11—44no—
288C2×C4×D11—44no—
289C2×C4×D11—44no—
290C2×C4×D11—44no—
291C2×C4×D11—44no—
292C2×C4×D11—44no—
293C2×C4×D11—44no—
294C2×C4×D11—44no—
295C2×C4×D11—44no—
296C2×C4×D11—44no—
297C2×C4×D11—44no—
298C2×C4×D11—44no—
299C2×C4×D11—44no—
300C11×C4⋊C4—44no—
301C11×C4⋊C4—44no—
302C11×C4⋊C4—44no—
303(C2×D11)⋊C4—28no—
304(C2×D11)⋊C4—44no—
305(C2×D11)⋊C4—44no—
306(C2×D11)⋊C4—44no—
307(C2×D11)⋊C4—44no—
308(C2×D11)⋊C4—44no—
309(C2×D11)⋊C4—44no—
310(C2×D11)⋊C4—44no—
311(C2×D11)⋊C4—44no—
312(C2×D11)⋊C4—44no—
313C4⋊Dic11—44no—
314Dic11⋊C4—44no—
315C4×Dic11—44no—
316C2×#390—111no—
317C2×#386—111no—
318C2×#386—111no—
319C2×#385—111no—
320C2×#380—111no—
321#1444D1111yescharacteristic, complemented
322#1442—111no—
323#1439—111no—
324#1439—111no—
325#1439—111no—
326#1439—111no—
327#1436—111no—
328#1436—111no—
329C22⋊#95—111no—
330C22⋊#95—111no—
331C23×C11C23×C411yescharacteristic
332C23×C11C22×D411yescharacteristic
333C23×C11C22×D411yescharacteristic
334C23×C11C22×Q811yescharacteristic
335C23×C11C2×#4111yescharacteristic
336C23×C11C2×#4111yescharacteristic
337C23×C11C2×#4111yescharacteristic
338C23×C11H(5,𝔽2)11yescharacteristic
339C23×C11H(5,𝔽2)11yescharacteristic
340C23×C11H(5,𝔽2)11yescharacteristic
341C23×C11H(5,𝔽2)11yescharacteristic
342C23×C11H(5,𝔽2)11yescharacteristic
343C23×C11H(5,𝔽2)11yescharacteristic
344C23×C11H(5,𝔽2)11yescharacteristic
345C23×C112−1+411yescharacteristic
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—22no—
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—22no—
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—
398C22×D11—41no—
399C22×D11—41no—
400C22×D11—41no—
401C22×D11—41no—
402C22×D11—41no—
403C22×D11—41no—
404C22×D11—41no—
405C22×D11—41no—
406C22×D11—41no—
407C22×D11—41no—
408C22×D11—41no—
409C22×D11—41no—
410C22×D11—41no—
411C22×D11—41no—
412C22×D11—41no—
413C22×D11—41no—
414C22×D11C2×C4⋊C414yes—
415C22×D11C2×C4⋊C414yes—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
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—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
452C2×C4×C11—41no—
453C2×C4×C11—41no—
454C2×C4×C11—41no—
455C2×C4×C11—41no—
456C2×C4×C11—41no—
457C2×C4×C11—41no—
458C2×C4×C11—41no—
459C2×C4×C11—41no—
460C2×C4×C11—41no—
461C2×C4×C11—41no—
462C2×C4×C11—41no—
463C2×C4×C11C2×C4⋊C414yes—
464C2×C4×C11C4×D414yes—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
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—41no—
491C2×Dic11—41no—
492C2×Dic11—41no—
493C2×Dic11—41no—
494C2×Dic11—41no—
495C2×Dic11—41no—
496C2×Dic11—41no—
497C2×Dic11—41no—
498C2×Dic11—41no—
499C2×Dic11—41no—
500C2×Dic11—41no—
501C2×Dic11—41no—
502C2×Dic11—41no—
503C2×Dic11—41no—
504C2×Dic11—41no—
505C2×Dic11—41no—
506C2×Dic11—41no—
507D44—416no—
508C4×D11—416no—
509C4×D11—416no—
510C23×D4—111no—
511C24×C4—111no—
512C24×C4—111no—
513C22×C4⋊C4—111no—
514C22×C4⋊C4—111no—
515C22×C4⋊C4C2×D1111yescharacteristic
516C22×C4⋊C4C2×D1111yescharacteristic
517C22×C4⋊C4C2×D1111yescharacteristic
518C22×C22⋊C4—111no—
519C22×C22⋊C4—111no—
520C22×C22⋊C4—111no—
521C22×C22⋊C4—111no—
522C22×C22⋊C4—111no—
523C22×C22⋊C4—111no—
524C22×C22⋊C4—111no—
525C22×C22⋊C4—111no—
526C22×C22⋊C4—111no—
527C22×C22⋊C4—111no—
528C22×C42—111no—
529#390—224no—
530#386—118no—
531#386—224no—
532#385—224no—
533#380—224no—
534C2×#95—111no—
535C2×#95—111no—
536C2×#95—111no—
537C2×#95—111no—
538C2×#95—111no—
539C2×#95—111no—
540C2×#95—111no—
541C2×#95—111no—
542C2×#95—111no—
543C2×#95—111no—
544C2×#95—111no—
545C2×#95—111no—
546C2×#95C2×D1111yescharacteristic
547C2×#95C2×D1111yescharacteristic
548C2×#95C2×D1111yescharacteristic
549C2×#95C2×D1111yescharacteristic
550C22×C11C22×C4⋊C411yescharacteristic
551C22×C11C2×C4×D411yescharacteristic
552C22×C11C4×#4111yescharacteristic
553C22×C11#51811yescharacteristic
554C22×C11#51811yescharacteristic
555C22×C11#51811yescharacteristic
556C22×C11#52011yescharacteristic
557C22×C11#53411yescharacteristic
558C22×C11#53411yescharacteristic
559C22×C11#53411yescharacteristic
560C22×C11#53511yescharacteristic
561C22×C11#53811yescharacteristic
562C22×C11#53811yescharacteristic
563C22×C11#53811yescharacteristic
564C22×C11#53911yescharacteristic
565C22×C11#54011yescharacteristic
566C22×C11#54211yescharacteristic
567C22×C11#54311yescharacteristic
568C22×C11#54311yescharacteristic
569C22×C11D4211yescharacteristic
570C22×C11#54611yescharacteristic
571C22×C11#54611yescharacteristic
572C22×C11#54611yescharacteristic
573C22×C11#54711yescharacteristic
574C22×C11D4×Q811yescharacteristic
575C22×C11#55011yescharacteristic
576C22×C11#55311yescharacteristic
577C22×C11#55411yescharacteristic
578C22×C11#55411yescharacteristic
579C22×C11#55411yescharacteristic
580C22×C11#55511yescharacteristic
581C22×C11#56011yescharacteristic
582C22×C11#56011yescharacteristic
583C22×C11#56211yescharacteristic
584C22×C11#56211yescharacteristic
585C2×D11—24no—
586C2×D11—24no—
587C2×D11—24no—
588C2×D11—24no—
589C2×D11—24no—
590C2×D11—24no—
591C2×D11—42no—
592C2×D11—42no—
593C2×D11—42no—
594C2×D11—42no—
595C2×D11—42no—
596C2×D11—42no—
597C2×D11—42no—
598C2×D11—42no—
599C2×D11—42no—
600C2×D11—42no—
601C2×D11—42no—
602C2×D11—42no—
603C2×D11—42no—
604C2×D11—42no—
605C2×D11—42no—
606C2×D11—42no—
607C2×D11—42no—
608C2×D11—42no—
609C2×D11—42no—
610C2×D11—42no—
611C2×D11—42no—
612C2×D11—42no—
613C2×D11—42no—
614C2×D11—42no—
615C4×C11—24no—
616C4×C11—24no—
617C4×C11—42no—
618C4×C11—42no—
619C4×C11—81no—
620C4×C11—81no—
621C4×C11—81no—
622Dic11—42no—
623Dic11—42no—
624Dic11—42no—
625Dic11—42no—
626Dic11—42no—
627Dic11—81no—
628C25—111no—
629C25—111no—
630C22×D4—114no—
631C22×D4—114no—
632C22×D4—114no—
633C22×D4—441no—
634C22×D4—441no—
635C22×D4—441no—
636C22×D4—441no—
637C23×C4—111no—
638C23×C4—111no—
639C23×C4—111no—
640C23×C4—111no—
641C23×C4—111no—
642C23×C4—114no—
643C23×C4—111no—
644C23×C4—222no—
645C23×C4—222no—
646C23×C4—222no—
647C23×C4—222no—
648C23×C4—222no—
649C23×C4—441no—
650C23×C4—441no—
651C23×C4—441no—
652C23×C4—441no—
653C23×C4—441no—
654C23×C4—441no—
655C23×C4—441no—
656C23×C4—441no—
657C23×C4C22×D1111yescharacteristic
658C23×C4C22×D1111yescharacteristic
659C23×C4C22×D1111yescharacteristic
660C23×C4C22×D1111yescharacteristic
661C23×C4C22×D1111yescharacteristic
662C23×C4C22×D1111yescharacteristic
663C23×C4C22×D1111yescharacteristic
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—41no—
667C2×C4⋊C4—41no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4—41no—
672C2×C4⋊C4—41no—
673C2×C4⋊C4—114no—
674C2×C4⋊C4—222no—
675C2×C4⋊C4—222no—
676C2×C4⋊C4—441no—
677C2×C4⋊C4—441no—
678C2×C4⋊C4—441no—
679C2×C22⋊C4—114no—
680C2×C22⋊C4—114no—
681C2×C22⋊C4—114no—
682C2×C22⋊C4—222no—
683C2×C22⋊C4—222no—
684C2×C22⋊C4—222no—
685C2×C22⋊C4—222no—
686C2×C22⋊C4—222no—
687C2×C22⋊C4—222no—
688C2×C22⋊C4—222no—
689C2×C22⋊C4—222no—
690C2×C22⋊C4—222no—
691C2×C22⋊C4—222no—
692C2×C22⋊C4—222no—
693C2×C22⋊C4—222no—
694C2×C22⋊C4—222no—
695C2×C22⋊C4—222no—
696C2×C22⋊C4—222no—
697C2×C22⋊C4—441no—
698C2×C22⋊C4—441no—
699C2×C22⋊C4—441no—
700C2×C22⋊C4—441no—
701C2×C22⋊C4—441no—
702C2×C22⋊C4—441no—
703C2×C22⋊C4—441no—
704C2×C22⋊C4—441no—
705C2×C22⋊C4—441no—
706C2×C22⋊C4—441no—
707C2×C22⋊C4—441no—
708C2×C22⋊C4—441no—
709C2×C42—222no—
710C2×C42—441no—
711C2×C42—441no—
712#95—22no—
713#95—22no—
714#95—41no—
715#95—114no—
716#95—222no—
717#95—222no—
718#95—222no—
719#95—222no—
720#95—222no—
721#95—222no—
722#95—441no—
723#95—441no—
724#95—441no—
725#95—441no—
726#95—441no—
727#95C4×D1114yescomplemented
728C2×C11#231511yescharacteristic
729C2×C11#232111yescharacteristic
730C2×C11#233511yescharacteristic
731C2×C11D4×C4⋊C411yescharacteristic
732C2×C11#234911yescharacteristic
733C2×C11#236311yescharacteristic
734C2×C11#237711yescharacteristic
735C2×C11#266811yescharacteristic
736C2×C11#267311yescharacteristic
737C2×C11#268611yescharacteristic
738C2×C11#269211yescharacteristic
739C2×C11#270811yescharacteristic
740C2×C11#273211yescharacteristic
741C2×C11#278011yescharacteristic
742C2×C11#278411yescharacteristic
743D11—44no—
744D11—44no—
745C24—112no—
746C24—112no—
747C24—112no—
748C24—112no—
749C24—112no—
750C24—112no—
751C24—221no—
752C24—221no—
753C24—221no—
754C24—221no—
755C24—221no—
756C24—221no—
757C24—221no—
758C24—221no—
759C24—221no—
760C24—221no—
761C24—221no—
762C24—221no—
763C24—221no—
764C24—221no—
765C24—221no—
766C24—221no—
767C24—221no—
768C24—221no—
769C24—221no—
770C24—221no—
771C24—221no—
772C24—221no—
773C24—221no—
774C24—221no—
775C24C23×D1111yescharacteristic
776C2×D4—1116no—
777C2×D4—444no—
778C2×D4—444no—
779C2×D4—444no—
780C2×D4—444no—
781C2×D4—444no—
782C2×D4—444no—
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—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—112no—
825C22×C4—112no—
826C22×C4—112no—
827C22×C4—112no—
828C22×C4—112no—
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×C4—221no—
849C22×C4—221no—
850C22×C4—221no—
851C22×C4—221no—
852C22×C4—221no—
853C22×C4—221no—
854C22×C4—221no—
855C22×C4—221no—
856C22×C4—221no—
857C22×C4—221no—
858C22×C4—221no—
859C22×C4—228no—
860C22×C4—221no—
861C22×C4—221no—
862C22×C4—221no—
863C22×C4—221no—
864C22×C4—221no—
865C22×C4—221no—
866C22×C4—221no—
867C22×C4—444no—
868C22×C4—444no—
869C22×C4—444no—
870C22×C4—444no—
871C22×C4—444no—
872C22×C4—444no—
873C22×C4—444no—
874C22×C4—444no—
875C22×C4—444no—
876C22×C4—444no—
877C22×C4—444no—
878C22×C4—444no—
879C22×C4—444no—
880C22×C4C2×C4×D1112yes—
881C22×C4C2×C4×D1112yes—
882C22×C4C2×C4×D1112yes—
883C22×C4D4×D1112yes—
884C22×C4D4×D1112yes—
885C22×C4Q8×D1112yes—
886C22×C4#434312yes—
887C22×C4#434312yes—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—444no—
892C4⋊C4—444no—
893C22⋊C4—228no—
894C22⋊C4—444no—
895C22⋊C4—444no—
896C22⋊C4—444no—
897C22⋊C4—444no—
898C22⋊C4—444no—
899C22⋊C4—444no—
900C22⋊C4—444no—
901C22⋊C4—444no—
902C22⋊C4—444no—
903C42—444no—
904C11#1440711yescharacteristic, complemented, Sylow
905C23—114no—
906C23—114no—
907C23—222no—
908C23—222no—
909C23—222no—
910C23—222no—
911C23—222no—
912C23—222no—
913C23—222no—
914C23—222no—
915C23—222no—
916C23—222no—
917C23—222no—
918C23—222no—
919C23—222no—
920C23—222no—
921C23—222no—
922C23—222no—
923C23—222no—
924C23—222no—
925C23—222no—
926C23—222no—
927C23—222no—
928C23—222no—
929C23—222no—
930C23—222no—
931C23—222no—
932C23—222no—
933C23—222no—
934C23—222no—
935C23—222no—
936C23—222no—
937C23—222no—
938C23—222no—
939C23—222no—
940C23—222no—
941C23—222no—
942C23—222no—
943C23—441no—
944C23—441no—
945C23—441no—
946C23—441no—
947C23—441no—
948C23—441no—
949C23—441no—
950C23—441no—
951C23—441no—
952C23—441no—
953C23—441no—
954C23—441no—
955C23—441no—
956C23—441no—
957C23—441no—
958C23—441no—
959C23—441no—
960C23—441no—
961C23—441no—
962C23—441no—
963C23—441no—
964C23—441no—
965C23—441no—
966C23—441no—
967C23—441no—
968C23—441no—
969C23—441no—
970C23—441no—
971C23—441no—
972C23—441no—
973C23—441no—
974C23—441no—
975C23C22×C4×D1111yescharacteristic
976C23C2×D4×D1111yescharacteristic
977C23C2×D4×D1111yescharacteristic
978C23#6703711yescharacteristic
979C23#6703711yescharacteristic
980C23#6703711yescharacteristic
981C23#6703711yescharacteristic
982C23C2×Q8×D1111yescharacteristic
983C23C2×#434311yescharacteristic
984C23C2×#434311yescharacteristic
985C23#6704011yescharacteristic
986C23#41×D1111yescharacteristic
987C23#6704211yescharacteristic
988C23#6704211yescharacteristic
989C23#6704211yescharacteristic
990D4—4416no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—222no—
1039C2×C4—222no—
1040C2×C4—222no—
1041C2×C4—222no—
1042C2×C4—222no—
1043C2×C4—222no—
1044C2×C4—222no—
1045C2×C4—222no—
1046C2×C4—222no—
1047C2×C4—222no—
1048C2×C4—222no—
1049C2×C4—222no—
1050C2×C4—222no—
1051C2×C4—222no—
1052C2×C4—222no—
1053C2×C4—4416no—
1054C2×C4—4416no—
1055C2×C4—441no—
1056C2×C4—441no—
1057C2×C4—441no—
1058C2×C4—441no—
1059C2×C4—441no—
1060C2×C4—441no—
1061C2×C4—441no—
1062C2×C4—441no—
1063C2×C4—441no—
1064C2×C4—441no—
1065C2×C4—441no—
1066C2×C4—441no—
1067C2×C4—441no—
1068C2×C4—441no—
1069C2×C4—441no—
1070C2×C4—441no—
1071C2×C4—441no—
1072C2×C4—441no—
1073C2×C4—441no—
1074C2×C4—441no—
1075C2×C4—441no—
1076C2×C4—441no—
1077C2×C4—441no—
1078C2×C4—441no—
1079C2×C4—441no—
1080C2×C4—441no—
1081C2×C4—441no—
1082C2×C4C4⋊C4×D1114yes—
1083C2×C4#6694614yes—
1084C22—224no—
1085C22—224no—
1086C22—224no—
1087C22—224no—
1088C22—224no—
1089C22—224no—
1090C22—442no—
1091C22—442no—
1092C22—442no—
1093C22—442no—
1094C22—442no—
1095C22—442no—
1096C22—442no—
1097C22—442no—
1098C22—442no—
1099C22—442no—
1100C22—442no—
1101C22—442no—
1102C22—442no—
1103C22—442no—
1104C22—442no—
1105C22—442no—
1106C22—442no—
1107C22—442no—
1108C22—442no—
1109C22—442no—
1110C22—442no—
1111C22—442no—
1112C22—442no—
1113C22—442no—
1114C22C2×C4⋊C4×D1111yescharacteristic
1115C22C2×#6694611yescharacteristic
1116C22#1062303511yescharacteristic
1117C22#1062307611yescharacteristic
1118C22#1062307611yescharacteristic
1119C22#1062307611yescharacteristic
1120C22C4×#434311yescharacteristic
1121C22#1062312011yescharacteristic
1122C22#1062312311yescharacteristic
1123C22#1062312611yescharacteristic
1124C22#1062313011yescharacteristic
1125C22#1062314311yescharacteristic
1126C22#1062314611yescharacteristic
1127C22#1062316111yescharacteristic
1128C22#1062316111yescharacteristic
1129C22#1062316511yescharacteristic
1130C22#1062316511yescharacteristic
1131C22#1062317511yescharacteristic
1132C22#1062317511yescharacteristic
1133C22#1062317511yescharacteristic
1134C22#1062317811yescharacteristic
1135C22#1062317811yescharacteristic
1136C22#1062318411yescharacteristic
1137C22#1062318411yescharacteristic
1138C22#1062319711yescharacteristic
1139C22#1062322111yescharacteristic
1140C22#1062322311yescharacteristic
1141C22#1062322611yescharacteristic
1142C22#1062324811yescharacteristic
1143C22#1062325711yescharacteristic
1144C22#1062325811yescharacteristic
1145C22#1062326111yescharacteristic
1146C22#1062326111yescharacteristic
1147C22#1062326411yescharacteristic
1148C22#1062326511yescharacteristic
1149C4—24no—
1150C4—24no—
1151C4—42no—
1152C4—42no—
1153C4—81no—
1154C4—81no—
1155C4—81no—
1156C4—442no—
1157C4—442no—
1158C4—442no—
1159C4—442no—
1160C4—442no—
1161C4—881no—
1162C2—444no—
1163C2—444no—
1164C2#1307122711yescharacteristic
1165C2#1307127311yescharacteristic
1166C2#1307140911yescharacteristic
1167C2#1307151611yescharacteristic
1168C2#1307152511yescharacteristic
1169C2#1307165311yescharacteristic
1170C2#1307177211yescharacteristic
1171C2#1307482511yescharacteristic
1172C2#1307488711yescharacteristic
1173C2#1307502911yescharacteristic
1174C2#1307511911yescharacteristic
1175C2#1307534111yescharacteristic
1176C2#1307563711yescharacteristic
1177C2#1307627011yescharacteristic
1178C2#1307631911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1444C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1444D11
hypocenterC11#14407
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
4. C2×#10622281C2semidirect
5. C2×#10622600C2semidirect
6. #13066875C2semidirect
7. #13066860C2semidirect
8. #13066858C2semidirect
9. #13066858C2semidirect
10. #13066858C2semidirect
11. #13066850C2semidirect
12. #13066847C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1444C2semidirect
55. #10622278C4semidirect
91. C22×C4×D11C2×C4semidirect
130. C2×(C2×D11)⋊C4C2×C4semidirect
133. C2×C4⋊Dic11D4semidirect
143. C11×#95C2×C4semidirect
155. C11⋊#95C2×C4semidirect
285. C2×D44C4⋊C4semidirect
321. #1444D11semidirect
727. #95C4×D11semidirect
904. C11#14407semidirect

Maximal subgroups

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

subgroupindex
C2×#106226012
C2×#106222782
C2×#106222812
C2×#106226002
#130668752
#130668602
#130668582
#130668502
#130668472
(C2×D11)⋊#952
C11×#14442
#1440711