Finite Group Databasebeta

← #14683829

Subgroups — #14683829

Order 2816.

1966 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622285C211yesmaximal, characteristic
2C2×#10622283C211yesmaximal, characteristic, complemented
3C2×#10622603C211yesmaximal, characteristic, complemented
4C2×#10622278C211yesmaximal, characteristic
5C2×#10622278C211yesmaximal, characteristic
6#13066882C211yesmaximal, characteristic, complemented
7#13066873C211yesmaximal, characteristic, complemented
8#13066862C211yesmaximal, characteristic, complemented
9#13066858C211yesmaximal, characteristic, complemented
10#13066847C211yesmaximal, characteristic, complemented
11(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
12(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1442C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C4⋊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×(C2×D11)⋊C4C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
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
51#10622603—24no—
52#10622285C418yescomplemented
53#10622283—24no—
54#10622278—24no—
55#10622278—24no—
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—22no—
72C22×D44—22no—
73C22×D44—22no—
74C22×D44—22no—
75C22×D44—41no—
76C22×D44—41no—
77C22×D44C2×C414yes—
78C22×C4×D11—22no—
79C22×C4×D11—22no—
80C22×C4×D11—22no—
81C22×C4×D11—22no—
82C22×C4×D11—22no—
83C22×C4×D11—22no—
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×D11—41no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—41no—
94C2×C11×C4⋊C4—41no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4—22no—
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—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)⋊C4—41no—
115C2×(C2×D11)⋊C4—41no—
116C2×(C2×D11)⋊C4—41no—
117C2×(C2×D11)⋊C4—41no—
118C2×(C2×D11)⋊C4—41no—
119C2×(C2×D11)⋊C4C2×C414yescomplemented
120C2×(C2×D11)⋊C4C2×C414yescomplemented
121C2×(C2×D11)⋊C4C2×C414yescomplemented
122C2×(C2×D11)⋊C4C2×C414yescomplemented
123C2×(C2×D11)⋊C4D414yes—
124C2×(C2×D11)⋊C4D414yes—
125C2×C4⋊Dic11—22no—
126C2×C4⋊Dic11—41no—
127C2×C4⋊Dic11—41no—
128C2×Dic11⋊C4—41no—
129C2×Dic11⋊C4—41no—
130C2×Dic11⋊C4C2×C414yescomplemented
131C2×C4×Dic11—22no—
132C2×C4×Dic11—22no—
133C2×C4×Dic11—41no—
134C11×#95—22no—
135C11×#95—22no—
136C11×#95—22no—
137C11×#95—41no—
138C11×#95—41no—
139C11×#95C2×C414yescomplemented
140C11⋊#95—22no—
141C11⋊#95—22no—
142C11⋊#95—22no—
143C11⋊#95—22no—
144C11⋊#95—22no—
145C11⋊#95—22no—
146C11⋊#95—22no—
147C11⋊#95—41no—
148C11⋊#95—41no—
149C11⋊#95—41no—
150C11⋊#95—41no—
151C11⋊#95—41no—
152#14571—111nomaximal, Sylow
153C24×C11C2411yescharacteristic
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×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×D11C22×C412yes—
179C23×D11C22×C412yes—
180C23×D11C2×D412yes—
181C23×D11C2×D412yes—
182C23×D11#4112yes—
183C23×D11#4112yes—
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×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×C11C22×C412yes—
228C22×C4×C11C22×C412yes—
229C22×C4×C11C22×C412yes—
230C22×C4×C11C2×D412yes—
231C22×C4×C11C2×D412yes—
232C22×C4×C11#4112yes—
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—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×Dic11C22×C412yes—
271C22×Dic11C22×C412yes—
272C22×Dic11C2×D412yes—
273C22×Dic11C2×D412yes—
274C22×Dic11#4112yes—
275C2×D44—28no—
276C2×D44—28no—
277C2×D44—44no—
278C2×D44—44no—
279C2×D44—44no—
280C2×D44—44no—
281C2×D44—44no—
282C2×C4×D11—44no—
283C2×C4×D11—44no—
284C2×C4×D11—44no—
285C2×C4×D11—44no—
286C2×C4×D11—44no—
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—
296C11×C4⋊C4—44no—
297(C2×D11)⋊C4—28no—
298(C2×D11)⋊C4—28no—
299(C2×D11)⋊C4—44no—
300(C2×D11)⋊C4—44no—
301(C2×D11)⋊C4—44no—
302(C2×D11)⋊C4—44no—
303(C2×D11)⋊C4—44no—
304(C2×D11)⋊C4—44no—
305(C2×D11)⋊C4—44no—
306(C2×D11)⋊C4—44no—
307C4⋊Dic11—44no—
308Dic11⋊C4—44no—
309C4×Dic11—44no—
310C2×#394—111no—
311C2×#388—111no—
312C2×#388—111no—
313C2×#386—111no—
314C2×#386—111no—
315#1445—111no—
316#1442—111no—
317#1442D1111yescharacteristic, complemented
318#1439—111no—
319#1439—111no—
320#1436—111no—
321C22⋊#95—111no—
322C22⋊#95—111no—
323C22⋊#95—111no—
324C22⋊#95—111no—
325C23×C11C23×C411yescharacteristic
326C23×C11C22×D411yescharacteristic
327C23×C11C22×D411yescharacteristic
328C23×C11C2×#4111yescharacteristic
329C23×C11C2×#4111yescharacteristic
330C23×C11C2×#4111yescharacteristic
331C23×C11C2×#4111yescharacteristic
332C23×C11H(5,𝔽2)11yescharacteristic
333C23×C11H(5,𝔽2)11yescharacteristic
334C23×C11H(5,𝔽2)11yescharacteristic
335C23×C11H(5,𝔽2)11yescharacteristic
336C23×C11H(5,𝔽2)11yescharacteristic
337C23×C11H(5,𝔽2)11yescharacteristic
338C23×C112−1+411yescharacteristic
339C23×C112−1+411yescharacteristic
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
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—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—
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×D11C4×D414yes—
409C22×D11C4×D414yes—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
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—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—
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×Dic11—22no—
460C2×Dic11—22no—
461C2×Dic11—22no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—22no—
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—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—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—
501D44—416no—
502C4×D11—416no—
503C4×D11—416no—
504C23×D4—111no—
505C24×C4—111no—
506C24×C4—111no—
507C22×C4⋊C4—111no—
508C22×C4⋊C4—111no—
509C22×C4⋊C4C2×D1111yescharacteristic
510C22×C22⋊C4—111no—
511C22×C22⋊C4—111no—
512C22×C22⋊C4—111no—
513C22×C22⋊C4—111no—
514C22×C22⋊C4—111no—
515C22×C22⋊C4—111no—
516C22×C22⋊C4—111no—
517C22×C22⋊C4—111no—
518C22×C22⋊C4—111no—
519C22×C22⋊C4—111no—
520C22×C42—111no—
521#394—118no—
522#388—224no—
523#388—224no—
524#386—224no—
525#386—224no—
526C2×#95—111no—
527C2×#95—111no—
528C2×#95—111no—
529C2×#95—111no—
530C2×#95—111no—
531C2×#95—111no—
532C2×#95—111no—
533C2×#95—111no—
534C2×#95—111no—
535C2×#95—111no—
536C2×#95—111no—
537C2×#95—111no—
538C2×#95C2×D1111yescharacteristic
539C2×#95C2×D1111yescharacteristic
540C2×#95C2×D1111yescharacteristic
541C2×#95C2×D1111yescharacteristic
542C2×#95C2×D1111yescharacteristic
543C2×#95C2×D1111yescharacteristic
544C22×C11C2×C4×D411yescharacteristic
545C22×C11C2×C4×D411yescharacteristic
546C22×C11C4×#4111yescharacteristic
547C22×C11#51811yescharacteristic
548C22×C11#51811yescharacteristic
549C22×C11#52011yescharacteristic
550C22×C11#52011yescharacteristic
551C22×C11#53411yescharacteristic
552C22×C11#53411yescharacteristic
553C22×C11#53711yescharacteristic
554C22×C11#53711yescharacteristic
555C22×C11#53811yescharacteristic
556C22×C11#53811yescharacteristic
557C22×C11#53811yescharacteristic
558C22×C11#53811yescharacteristic
559C22×C11#53911yescharacteristic
560C22×C11#53911yescharacteristic
561C22×C11#54011yescharacteristic
562C22×C11#54011yescharacteristic
563C22×C11D4211yescharacteristic
564C22×C11#54611yescharacteristic
565C22×C11#54611yescharacteristic
566C22×C11#54611yescharacteristic
567C22×C11#54611yescharacteristic
568C22×C11#54711yescharacteristic
569C22×C11#54711yescharacteristic
570C22×C11#55111yescharacteristic
571C22×C11#55111yescharacteristic
572C22×C11#55111yescharacteristic
573C22×C11#55211yescharacteristic
574C22×C11#55211yescharacteristic
575C22×C11H(3,𝔽4)11yescharacteristic
576C22×C11#56211yescharacteristic
577C22×C11#56211yescharacteristic
578C22×C11#56311yescharacteristic
579C2×D11—24no—
580C2×D11—24no—
581C2×D11—24no—
582C2×D11—24no—
583C2×D11—24no—
584C2×D11—24no—
585C2×D11—42no—
586C2×D11—42no—
587C2×D11—42no—
588C2×D11—42no—
589C2×D11—42no—
590C2×D11—42no—
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—
609C4×C11—42no—
610C4×C11—42no—
611C4×C11—42no—
612C4×C11—42no—
613C4×C11—42no—
614C4×C11—42no—
615C4×C11—81no—
616Dic11—42no—
617Dic11—42no—
618Dic11—42no—
619Dic11—42no—
620Dic11—42no—
621Dic11—81no—
622C25—111no—
623C25—111no—
624C22×D4—114no—
625C22×D4—222no—
626C22×D4—222no—
627C22×D4—222no—
628C22×D4—222no—
629C22×D4—441no—
630C22×D4—441no—
631C23×C4—111no—
632C23×C4—111no—
633C23×C4—111no—
634C23×C4—111no—
635C23×C4—111no—
636C23×C4—111no—
637C23×C4—222no—
638C23×C4—222no—
639C23×C4—222no—
640C23×C4—222no—
641C23×C4—222no—
642C23×C4—222no—
643C23×C4—441no—
644C23×C4—441no—
645C23×C4—441no—
646C23×C4—441no—
647C23×C4—441no—
648C23×C4—441no—
649C23×C4—441no—
650C23×C4—441no—
651C23×C4C22×D1111yescharacteristic
652C23×C4C22×D1111yescharacteristic
653C23×C4C22×D1111yescharacteristic
654C23×C4C22×D1111yescharacteristic
655C23×C4C22×D1111yescharacteristic
656C23×C4C22×D1111yescharacteristic
657C23×C4C22×D1111yescharacteristic
658C2×C4⋊C4—22no—
659C2×C4⋊C4—41no—
660C2×C4⋊C4—41no—
661C2×C4⋊C4—114no—
662C2×C4⋊C4—222no—
663C2×C4⋊C4—441no—
664C2×C4⋊C4—441no—
665C2×C4⋊C4—441no—
666C2×C4⋊C4—441no—
667C2×C22⋊C4—114no—
668C2×C22⋊C4—114no—
669C2×C22⋊C4—114no—
670C2×C22⋊C4—114no—
671C2×C22⋊C4—114no—
672C2×C22⋊C4—114no—
673C2×C22⋊C4—222no—
674C2×C22⋊C4—222no—
675C2×C22⋊C4—222no—
676C2×C22⋊C4—222no—
677C2×C22⋊C4—222no—
678C2×C22⋊C4—222no—
679C2×C22⋊C4—222no—
680C2×C22⋊C4—222no—
681C2×C22⋊C4—222no—
682C2×C22⋊C4—222no—
683C2×C22⋊C4—222no—
684C2×C22⋊C4—222no—
685C2×C22⋊C4—441no—
686C2×C22⋊C4—441no—
687C2×C22⋊C4—441no—
688C2×C22⋊C4—441no—
689C2×C22⋊C4—441no—
690C2×C22⋊C4—441no—
691C2×C22⋊C4—441no—
692C2×C22⋊C4—441no—
693C2×C22⋊C4—441no—
694C2×C22⋊C4—441no—
695C2×C22⋊C4—441no—
696C2×C22⋊C4—441no—
697C2×C42—222no—
698C2×C42—222no—
699C2×C42—441no—
700#95—22no—
701#95—22no—
702#95—22no—
703#95—41no—
704#95—41no—
705#95—222no—
706#95—222no—
707#95—222no—
708#95—222no—
709#95—222no—
710#95—222no—
711#95—222no—
712#95—441no—
713#95—441no—
714#95—441no—
715#95—441no—
716#95—441no—
717#95C4×D1114yescomplemented
718C2×C11#232511yescharacteristic
719C2×C11#232511yescharacteristic
720C2×C11#233311yescharacteristic
721C2×C11#235811yescharacteristic
722C2×C11#235911yescharacteristic
723C2×C11#235911yescharacteristic
724C2×C11#237911yescharacteristic
725C2×C11#267111yescharacteristic
726C2×C11#267111yescharacteristic
727C2×C11#268411yescharacteristic
728C2×C11#268411yescharacteristic
729C2×C11#269511yescharacteristic
730C2×C11#269511yescharacteristic
731C2×C11#274311yescharacteristic
732C2×C11#274311yescharacteristic
733D11—44no—
734D11—44no—
735C24—112no—
736C24—112no—
737C24—112no—
738C24—112no—
739C24—112no—
740C24—112no—
741C24—221no—
742C24—221no—
743C24—221no—
744C24—221no—
745C24—221no—
746C24—221no—
747C24—221no—
748C24—221no—
749C24—221no—
750C24—221no—
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—
765C24C23×D1111yescharacteristic
766C2×D4—228no—
767C2×D4—228no—
768C2×D4—444no—
769C2×D4—444no—
770C2×D4—444no—
771C2×D4—444no—
772C2×D4—444no—
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—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—112no—
817C22×C4—112no—
818C22×C4—112no—
819C22×C4—112no—
820C22×C4—112no—
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×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—444no—
859C22×C4—444no—
860C22×C4—444no—
861C22×C4—444no—
862C22×C4—444no—
863C22×C4—444no—
864C22×C4—444no—
865C22×C4—444no—
866C22×C4—444no—
867C22×C4—444no—
868C22×C4—444no—
869C22×C4—444no—
870C22×C4—444no—
871C22×C4—444no—
872C22×C4C2×C4×D1112yes—
873C22×C4C2×C4×D1112yes—
874C22×C4C2×C4×D1112yes—
875C22×C4D4×D1112yes—
876C22×C4D4×D1112yes—
877C22×C4#434312yes—
878C4⋊C4—44no—
879C4⋊C4—444no—
880C4⋊C4—444no—
881C22⋊C4—228no—
882C22⋊C4—228no—
883C22⋊C4—444no—
884C22⋊C4—444no—
885C22⋊C4—444no—
886C22⋊C4—444no—
887C22⋊C4—444no—
888C22⋊C4—444no—
889C22⋊C4—444no—
890C22⋊C4—444no—
891C42—444no—
892C11#1457111yescharacteristic, complemented, Sylow
893C23—114no—
894C23—114no—
895C23—222no—
896C23—222no—
897C23—222no—
898C23—222no—
899C23—222no—
900C23—222no—
901C23—222no—
902C23—222no—
903C23—222no—
904C23—222no—
905C23—222no—
906C23—222no—
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—441no—
932C23—441no—
933C23—441no—
934C23—441no—
935C23—441no—
936C23—441no—
937C23—441no—
938C23—441no—
939C23—441no—
940C23—441no—
941C23—441no—
942C23—441no—
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—
963C23C22×C4×D1111yescharacteristic
964C23C2×D4×D1111yescharacteristic
965C23C2×D4×D1111yescharacteristic
966C23#6703711yescharacteristic
967C23#6703711yescharacteristic
968C23C2×#434311yescharacteristic
969C23#6704011yescharacteristic
970C23#41×D1111yescharacteristic
971C23#41×D1111yescharacteristic
972C23#41×D1111yescharacteristic
973C23#6704211yescharacteristic
974C23#6704211yescharacteristic
975C23#6704211yescharacteristic
976C23#6704211yescharacteristic
977C23#6704311yescharacteristic
978D4—4416no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
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—222no—
1029C2×C4—222no—
1030C2×C4—222no—
1031C2×C4—222no—
1032C2×C4—222no—
1033C2×C4—222no—
1034C2×C4—222no—
1035C2×C4—222no—
1036C2×C4—222no—
1037C2×C4—222no—
1038C2×C4—222no—
1039C2×C4—222no—
1040C2×C4—222no—
1041C2×C4—222no—
1042C2×C4—222no—
1043C2×C4—4416no—
1044C2×C4—4416no—
1045C2×C4—441no—
1046C2×C4—441no—
1047C2×C4—441no—
1048C2×C4—441no—
1049C2×C4—441no—
1050C2×C4—441no—
1051C2×C4—441no—
1052C2×C4—441no—
1053C2×C4—441no—
1054C2×C4—441no—
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—
1072C22—224no—
1073C22—224no—
1074C22—224no—
1075C22—224no—
1076C22—224no—
1077C22—224no—
1078C22—442no—
1079C22—442no—
1080C22—442no—
1081C22—442no—
1082C22—442no—
1083C22—442no—
1084C22—442no—
1085C22—442no—
1086C22—442no—
1087C22—442no—
1088C22—442no—
1089C22—442no—
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#1062303511yescharacteristic
1103C22#1062305211yescharacteristic
1104C22#1062305411yescharacteristic
1105C22C4×D4×D1111yescharacteristic
1106C22C4×D4×D1111yescharacteristic
1107C22#1062307611yescharacteristic
1108C22C4×#434311yescharacteristic
1109C22#1062312011yescharacteristic
1110C22#1062313911yescharacteristic
1111C22#1062314011yescharacteristic
1112C22#1062314111yescharacteristic
1113C22#1062316011yescharacteristic
1114C22#1062316111yescharacteristic
1115C22#1062316811yescharacteristic
1116C22#1062316911yescharacteristic
1117C22#1062317511yescharacteristic
1118C22#1062318411yescharacteristic
1119C22#1062318511yescharacteristic
1120C22#1062318611yescharacteristic
1121C22#1062318811yescharacteristic
1122C22#1062319411yescharacteristic
1123C22#1062320711yescharacteristic
1124C22#1062320911yescharacteristic
1125C22#1062321411yescharacteristic
1126C22#1062321511yescharacteristic
1127C22#1062322411yescharacteristic
1128C22#1062322511yescharacteristic
1129C22#1062322911yescharacteristic
1130C22#1062323011yescharacteristic
1131C22#1062323111yescharacteristic
1132C22#1062323511yescharacteristic
1133C22#1062323611yescharacteristic
1134C22#1062323611yescharacteristic
1135C22#1062323811yescharacteristic
1136C22#1062325711yescharacteristic
1137C4—42no—
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—42no—
1143C4—81no—
1144C4—442no—
1145C4—442no—
1146C4—442no—
1147C4—442no—
1148C4—442no—
1149C4—881no—
1150C2—444no—
1151C2—444no—
1152C2#1307131311yescharacteristic
1153C2#1307132011yescharacteristic
1154C2#1307138011yescharacteristic
1155C2#1307159411yescharacteristic
1156C2#1307160311yescharacteristic
1157C2#1307161511yescharacteristic
1158C2#1307178711yescharacteristic
1159C2#1307485811yescharacteristic
1160C2#1307485911yescharacteristic
1161C2#1307499811yescharacteristic
1162C2#1307499911yescharacteristic
1163C2#1307515311yescharacteristic
1164C2#1307515611yescharacteristic
1165C2#1307575411yescharacteristic
1166C2#1307576011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1442C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1442D11
hypocenterC11#14571
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
2. C2×#10622283C2semidirect
3. C2×#10622603C2semidirect
6. #13066882C2semidirect
7. #13066873C2semidirect
8. #13066862C2semidirect
9. #13066858C2semidirect
10. #13066847C2semidirect
11. (C2×D11)⋊#95C2semidirect
12. (C2×D11)⋊#95C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1442C2semidirect
52. #10622285C4semidirect
119. C2×(C2×D11)⋊C4C2×C4semidirect
120. C2×(C2×D11)⋊C4C2×C4semidirect
121. C2×(C2×D11)⋊C4C2×C4semidirect
122. C2×(C2×D11)⋊C4C2×C4semidirect
130. C2×Dic11⋊C4C2×C4semidirect
139. C11×#95C2×C4semidirect
317. #1442D11semidirect
717. #95C4×D11semidirect
892. C11#14571semidirect

Maximal subgroups

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

subgroupindex
C2×#106222852
C2×#106222832
C2×#106226032
C2×#106222782
#130668822
#130668732
#130668622
#130668582
#130668472
(C2×D11)⋊#952
C11×#14422
#1457111