Finite Group Databasebeta

← #14684425

Subgroups — #14684425

Order 2816.

1694 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×#10622604C211yesmaximal, characteristic
2C2×#10622278C211yesmaximal, characteristic
3C2×#10622281C211yesmaximal, characteristic, complemented
4#13066874C211yesmaximal, characteristic, complemented
5#13066874C211yesmaximal, characteristic, complemented
6#13066869C211yesmaximal, characteristic, complemented
7#13066864C211yesmaximal, characteristic, complemented
8#13066864C211yesmaximal, characteristic, complemented
9#13066862C211yesmaximal, characteristic, complemented
10#13066860C211yesmaximal, characteristic, complemented
11#13066860C211yesmaximal, characteristic, complemented
12#13066860C211yesmaximal, characteristic, complemented
13#13066856C211yesmaximal, characteristic
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1445C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C22×C11×C4⋊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×(C2×D11)⋊C4C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
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
51#10622604C418yescomplemented
52#10622281—24no—
53#10622278—24no—
54C24×D11C2311yescharacteristic
55C24×D11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C22×D44—22no—
70C22×D44—22no—
71C22×D44—41no—
72C22×D44—41no—
73C22×D44—41no—
74C22×D44—41no—
75C22×D44C2×C414yes—
76C22×C4×D11—41no—
77C22×C4×D11—41no—
78C22×C4×D11—41no—
79C22×C4×D11—41no—
80C22×C4×D11—41no—
81C22×C4×D11—41no—
82C22×C4×D11D414yes—
83C2×C11×C4⋊C4—41no—
84C2×C11×C4⋊C4—41no—
85C2×C11×C4⋊C4C2×C414yescomplemented
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
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×(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)⋊C4C2×C414yes—
116C2×(C2×D11)⋊C4C2×C414yes—
117C2×(C2×D11)⋊C4C2×C414yescomplemented
118C2×(C2×D11)⋊C4C2×C414yescomplemented
119C2×C4⋊Dic11—22no—
120C2×C4⋊Dic11—41no—
121C2×C4⋊Dic11—41no—
122C2×Dic11⋊C4—22no—
123C2×Dic11⋊C4—41no—
124C2×Dic11⋊C4—41no—
125C2×Dic11⋊C4—41no—
126C2×Dic11⋊C4—41no—
127C2×Dic11⋊C4—41no—
128C11×#95—22no—
129C11×#95—22no—
130C11×#95—41no—
131C11×#95—41no—
132C11×#95—41no—
133C11×#95—41no—
134C11⋊#95—22no—
135C11⋊#95—22no—
136C11⋊#95—41no—
137C11⋊#95—41no—
138C11⋊#95—41no—
139C11⋊#95—41no—
140C11⋊#95—41no—
141C11⋊#95—41no—
142C11⋊#95—41no—
143C11⋊#95—41no—
144C11⋊#95—41no—
145C11⋊#95C2×C414yescomplemented
146#14622—111nomaximal, Sylow
147C24×C11C2411yescharacteristic
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×D11—21no—
170C23×D11—21no—
171C23×D11—21no—
172C23×D11—21no—
173C23×D11—21no—
174C23×D11C22×C412yes—
175C23×D11C22×C412yes—
176C23×D11C2×D412yes—
177C23×D11#4112yes—
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×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11C22×C412yes—
224C22×C4×C11C22×C412yes—
225C22×C4×C11C22×C412yes—
226C22×C4×C11C2×D412yes—
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—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
266C22×Dic11C22×C412yes—
267C22×Dic11C22×C412yes—
268C22×Dic11C2×D412yes—
269C2×D44—28no—
270C2×D44—44no—
271C2×D44—44no—
272C2×D44—44no—
273C2×D44—44no—
274C2×D44—44no—
275C2×D44—44no—
276C2×C4×D11—44no—
277C2×C4×D11—44no—
278C2×C4×D11—44no—
279C2×C4×D11—44no—
280C2×C4×D11—44no—
281C2×C4×D11—44no—
282C2×C4×D11—44no—
283C11×C4⋊C4—44no—
284(C2×D11)⋊C4—28no—
285(C2×D11)⋊C4—44no—
286(C2×D11)⋊C4—44no—
287(C2×D11)⋊C4—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—
294(C2×D11)⋊C4—44no—
295C4⋊Dic11—44no—
296Dic11⋊C4—44no—
297Dic11⋊C4—44no—
298C2×#394—111no—
299C2×#386—111no—
300C2×#385—111no—
301#1445D1111yescharacteristic, complemented
302#1442—111no—
303#1442—111no—
304#1441—111no—
305#1440—111no—
306#1440—111no—
307#1439—111no—
308#1439—111no—
309#1439—111no—
310#1439—111no—
311#1438—111no—
312C22⋊#95—111no—
313C23×C11C23×C411yescharacteristic
314C23×C11C22×D411yescharacteristic
315C23×C11C2×#4111yescharacteristic
316C23×C11H(5,𝔽2)11yescharacteristic
317C23×C11H(5,𝔽2)11yescharacteristic
318C23×C11H(5,𝔽2)11yescharacteristic
319C23×C11H(5,𝔽2)11yescharacteristic
320C23×C11H(5,𝔽2)11yescharacteristic
321C23×C11H(5,𝔽2)11yescharacteristic
322C23×C11H(5,𝔽2)11yescharacteristic
323C23×C11H(5,𝔽2)11yescharacteristic
324C23×C11H(5,𝔽2)11yescharacteristic
325C23×C112−1+411yescharacteristic
326C23×C112−1+411yescharacteristic
327C23×C112−1+411yescharacteristic
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
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—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—
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×D11C4×D414yes—
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—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×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×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—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—
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—
489D44—416no—
490C4×D11—416no—
491C23×D4—111no—
492C24×C4—111no—
493C22×C4⋊C4—111no—
494C22×C4⋊C4—111no—
495C22×C4⋊C4—111no—
496C22×C4⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
505C22×C22⋊C4—111no—
506C22×C22⋊C4—111no—
507C22×C22⋊C4—111no—
508#394—118no—
509#386—224no—
510#385—224no—
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×#95C2×D1111yescharacteristic
524C2×#95C2×D1111yescharacteristic
525C2×#95C2×D1111yescharacteristic
526C2×#95C2×D1111yescharacteristic
527C2×#95C2×D1111yescharacteristic
528C2×#95C2×D1111yescharacteristic
529C22×C11C2×C4×D411yescharacteristic
530C22×C11#51811yescharacteristic
531C22×C11#51811yescharacteristic
532C22×C11#51811yescharacteristic
533C22×C11#52011yescharacteristic
534C22×C11#52011yescharacteristic
535C22×C11#52011yescharacteristic
536C22×C11#53411yescharacteristic
537C22×C11#53411yescharacteristic
538C22×C11#53411yescharacteristic
539C22×C11#53511yescharacteristic
540C22×C11#53611yescharacteristic
541C22×C11#53711yescharacteristic
542C22×C11#53811yescharacteristic
543C22×C11#53811yescharacteristic
544C22×C11#53811yescharacteristic
545C22×C11#53911yescharacteristic
546C22×C11#53911yescharacteristic
547C22×C11#53911yescharacteristic
548C22×C11#56011yescharacteristic
549C22×C11#56011yescharacteristic
550C22×C11#56011yescharacteristic
551C22×C11#56011yescharacteristic
552C22×C11#56011yescharacteristic
553C22×C11H(3,𝔽4)11yescharacteristic
554C22×C11#56211yescharacteristic
555C22×C11#56211yescharacteristic
556C22×C11#56211yescharacteristic
557C22×C11#56211yescharacteristic
558C22×C11#56211yescharacteristic
559C22×C11#56211yescharacteristic
560C22×C11#56211yescharacteristic
561C22×C11#56211yescharacteristic
562C22×C11#56311yescharacteristic
563C22×C11#56311yescharacteristic
564C2×D11—24no—
565C2×D11—24no—
566C2×D11—24no—
567C2×D11—42no—
568C2×D11—42no—
569C2×D11—42no—
570C2×D11—42no—
571C2×D11—42no—
572C2×D11—42no—
573C2×D11—42no—
574C2×D11—42no—
575C2×D11—42no—
576C2×D11—42no—
577C2×D11—42no—
578C2×D11—42no—
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—
600C4×C11—81no—
601Dic11—42no—
602Dic11—42no—
603Dic11—42no—
604Dic11—81no—
605Dic11—81no—
606Dic11—81no—
607C25—111no—
608C25—111no—
609C22×D4—114no—
610C22×D4—222no—
611C22×D4—222no—
612C22×D4—441no—
613C22×D4—441no—
614C22×D4—441no—
615C22×D4—441no—
616C23×C4—111no—
617C23×C4—111no—
618C23×C4—111no—
619C23×C4—114no—
620C23×C4—111no—
621C23×C4—111no—
622C23×C4—111no—
623C23×C4—441no—
624C23×C4—441no—
625C23×C4—441no—
626C23×C4—441no—
627C23×C4—441no—
628C23×C4—441no—
629C23×C4C22×D1111yescharacteristic
630C23×C4C22×D1111yescharacteristic
631C23×C4C22×D1111yescharacteristic
632C23×C4C22×D1111yescharacteristic
633C23×C4C22×D1111yescharacteristic
634C23×C4C22×D1111yescharacteristic
635C23×C4C22×D1111yescharacteristic
636C2×C4⋊C4—41no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4—222no—
639C2×C4⋊C4—222no—
640C2×C4⋊C4—441no—
641C2×C4⋊C4—441no—
642C2×C4⋊C4—441no—
643C2×C4⋊C4—441no—
644C2×C4⋊C4—441no—
645C2×C4⋊C4—441no—
646C2×C4⋊C4—441no—
647C2×C4⋊C4C4×D1114yescomplemented
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×C22⋊C4—441no—
676C2×C22⋊C4—441no—
677C2×C22⋊C4—441no—
678C2×C22⋊C4—441no—
679C2×C22⋊C4—441no—
680C2×C22⋊C4—441no—
681#95—22no—
682#95—22no—
683#95—41no—
684#95—41no—
685#95—41no—
686#95—41no—
687#95—114no—
688#95—222no—
689#95—222no—
690#95—441no—
691#95—441no—
692#95—441no—
693#95—441no—
694#95—441no—
695#95—441no—
696#95—441no—
697#95—441no—
698#95—441no—
699C2×C11#232111yescharacteristic
700C2×C11#232211yescharacteristic
701C2×C11#232511yescharacteristic
702C2×C11#237611yescharacteristic
703C2×C11#237711yescharacteristic
704C2×C11#237711yescharacteristic
705C2×C11#237911yescharacteristic
706C2×C11#281211yescharacteristic
707C2×C11#281311yescharacteristic
708C2×C11#281411yescharacteristic
709C2×C11#281611yescharacteristic
710C2×C11#282411yescharacteristic
711C2×C11#282611yescharacteristic
712C2×C11#282711yescharacteristic
713C2×C11#282711yescharacteristic
714D11—44no—
715D11—82no—
716C24—112no—
717C24—112no—
718C24—112no—
719C24—112no—
720C24—221no—
721C24—221no—
722C24—221no—
723C24—221no—
724C24—221no—
725C24—221no—
726C24—221no—
727C24—221no—
728C24—221no—
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—
743C24—221no—
744C24—221no—
745C24—221no—
746C24C23×D1111yescharacteristic
747C2×D4—228no—
748C2×D4—444no—
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—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—112no—
800C22×C4—112no—
801C22×C4—112no—
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—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—444no—
842C22×C4—444no—
843C22×C4—444no—
844C22×C4—444no—
845C22×C4—444no—
846C22×C4—444no—
847C22×C4—444no—
848C22×C4C2×C4×D1112yes—
849C22×C4C2×C4×D1112yes—
850C22×C4C2×C4×D1112yes—
851C22×C4D4×D1112yes—
852C4⋊C4—44no—
853C4⋊C4—444no—
854C4⋊C4—444no—
855C4⋊C4—444no—
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—
865C22⋊C4—444no—
866C22⋊C4—444no—
867C11#1462211yescharacteristic, complemented, Sylow
868C23—114no—
869C23—222no—
870C23—222no—
871C23—222no—
872C23—222no—
873C23—222no—
874C23—222no—
875C23—222no—
876C23—222no—
877C23—222no—
878C23—222no—
879C23—222no—
880C23—222no—
881C23—222no—
882C23—222no—
883C23—222no—
884C23—222no—
885C23—222no—
886C23—222no—
887C23—222no—
888C23—222no—
889C23—222no—
890C23—222no—
891C23—222no—
892C23—222no—
893C23—222no—
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—
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—441no—
938C23C22×C4×D1111yescharacteristic
939C23C2×D4×D1111yescharacteristic
940C23#6703711yescharacteristic
941C23#6703711yescharacteristic
942C23#6703711yescharacteristic
943C23#6704011yescharacteristic
944C23#6704011yescharacteristic
945C23#41×D1111yescharacteristic
946C23#6704211yescharacteristic
947C23#6704211yescharacteristic
948C23#6704211yescharacteristic
949C23#6704211yescharacteristic
950C23#6704211yescharacteristic
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—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—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—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
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—4416no—
1013C2×C4—441no—
1014C2×C4—441no—
1015C2×C4—441no—
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—224no—
1047C22—224no—
1048C22—224no—
1049C22—442no—
1050C22—442no—
1051C22—442no—
1052C22—442no—
1053C22—442no—
1054C22—442no—
1055C22—442no—
1056C22—442no—
1057C22—442no—
1058C22—442no—
1059C22—442no—
1060C22—442no—
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—
1076C22#1062301711yescharacteristic
1077C22#1062305211yescharacteristic
1078C22#1062305411yescharacteristic
1079C22C4×D4×D1111yescharacteristic
1080C22#1062307611yescharacteristic
1081C22#1062310511yescharacteristic
1082C22#1062310511yescharacteristic
1083C22#1062313611yescharacteristic
1084C22#1062314411yescharacteristic
1085C22#1062315911yescharacteristic
1086C22#1062316011yescharacteristic
1087C22#1062317811yescharacteristic
1088C22#1062317811yescharacteristic
1089C22#1062317811yescharacteristic
1090C22#1062317811yescharacteristic
1091C22#1062318411yescharacteristic
1092C22#1062318411yescharacteristic
1093C22#1062319711yescharacteristic
1094C22#1062319711yescharacteristic
1095C22#1062319711yescharacteristic
1096C22#1062319811yescharacteristic
1097C22#1062319811yescharacteristic
1098C22#1062319811yescharacteristic
1099C22#1062320911yescharacteristic
1100C22#1062321411yescharacteristic
1101C22#1062322311yescharacteristic
1102C22#1062322311yescharacteristic
1103C22#1062323011yescharacteristic
1104C22#1062323111yescharacteristic
1105C22#1062323511yescharacteristic
1106C22#1062323811yescharacteristic
1107C22#1062324211yescharacteristic
1108C22#1062324211yescharacteristic
1109C22#1062324611yescharacteristic
1110C22#1062326611yescharacteristic
1111C4—42no—
1112C4—42no—
1113C4—42no—
1114C4—42no—
1115C4—81no—
1116C4—81no—
1117C4—81no—
1118C4—442no—
1119C4—442no—
1120C4—442no—
1121C4—881no—
1122C4—881no—
1123C4—881no—
1124C2—444no—
1125C2—882no—
1126C2#1307127511yescharacteristic
1127C2#1307128911yescharacteristic
1128C2#1307131511yescharacteristic
1129C2#1307176311yescharacteristic
1130C2#1307177111yescharacteristic
1131C2#1307177511yescharacteristic
1132C2#1307178811yescharacteristic
1133C2#1307661411yescharacteristic
1134C2#1307661911yescharacteristic
1135C2#1307663611yescharacteristic
1136C2#1307664511yescharacteristic
1137C2#1307669411yescharacteristic
1138C2#1307671311yescharacteristic
1139C2#1307671911yescharacteristic
1140C2#1307672711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1445C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1445D11
hypocenterC11#14622
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
3. C2×#10622281C2semidirect
4. #13066874C2semidirect
5. #13066874C2semidirect
6. #13066869C2semidirect
7. #13066864C2semidirect
8. #13066864C2semidirect
9. #13066862C2semidirect
10. #13066860C2semidirect
11. #13066860C2semidirect
12. #13066860C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1445C2semidirect
51. #10622604C4semidirect
85. C2×C11×C4⋊C4C2×C4semidirect
117. C2×(C2×D11)⋊C4C2×C4semidirect
118. C2×(C2×D11)⋊C4C2×C4semidirect
145. C11⋊#95C2×C4semidirect
301. #1445D11semidirect
647. C2×C4⋊C4C4×D11semidirect
867. C11#14622semidirect

Maximal subgroups

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

subgroupindex
C2×#106226042
C2×#106222782
C2×#106222812
#130668742
#130668692
#130668642
#130668622
#130668602
#130668562
(C2×D11)⋊#952
C11×#14452
#1462211