Finite Group Databasebeta

← #14680309

Subgroups — #14680309

Order 2816.

1926 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622281C211yesmaximal, characteristic
2C2×#10622602C211yesmaximal, characteristic
3C2×#10622280C211yesmaximal, characteristic
4C2×#10622600C211yesmaximal, characteristic
5C2×D11×#95C211yesmaximal, characteristic
6#13066880C211yesmaximal, characteristic, complemented
7#13066879C211yesmaximal, characteristic, complemented
8#13066874C211yesmaximal, characteristic, complemented
9#13066871C211yesmaximal, characteristic, complemented
10#13066869C211yesmaximal, characteristic, complemented
11#13066868C211yesmaximal, characteristic, complemented
12#13066868C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic
14(C2×D11)⋊#95C211yesmaximal, characteristic
15C11×#1441C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C2×C11×#95C2211yescharacteristic
32C2×C11×#95C2211yescharacteristic
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#10622602—24no—
52#10622600C418yescomplemented
53#10622281—24no—
54#10622280—24no—
55D11×#95—24no—
56C24×D11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C22×C4×D11—22no—
72C22×C4×D11—22no—
73C22×C4×D11—22no—
74C22×C4×D11—22no—
75C22×C4×D11—41no—
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×D11—41no—
83C22×C4×D11—41no—
84C22×C4×D11—41no—
85C22×C4×D11—41no—
86C22×C4×D11—41no—
87C22×C4×D11C2×C414yes—
88C22×C4×D11D414yes—
89C22×C4×D11D414yes—
90C22×C4×D11Q814yes—
91C22×C4×D11Q814yes—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—41no—
94C2×C11×C4⋊C4—41no—
95C2×C11×C4⋊C4—41no—
96C2×C11×C4⋊C4—41no—
97C2×C11×C4⋊C4C2×C414yescomplemented
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—22no—
108C2×(C2×D11)⋊C4C2×C414yes—
109C2×(C2×D11)⋊C4C2×C414yes—
110C2×C4⋊Dic11—22no—
111C2×C4⋊Dic11—41no—
112C2×C4⋊Dic11—41no—
113C2×C4⋊Dic11—41no—
114C2×C4⋊Dic11—41no—
115C2×C4⋊Dic11C2×C414yescomplemented
116C2×Dic11⋊C4—22no—
117C2×Dic11⋊C4—22no—
118C2×Dic11⋊C4—22no—
119C2×Dic11⋊C4—22no—
120C2×Dic11⋊C4—41no—
121C2×Dic11⋊C4—41no—
122C2×Dic11⋊C4—41no—
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—22no—
131C11×#95—41no—
132C11×#95—41no—
133C11⋊#95—22no—
134C11⋊#95—22no—
135C11⋊#95—22no—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—22no—
139C11⋊#95—22no—
140C11⋊#95—41no—
141C11⋊#95—41no—
142C11⋊#95—41no—
143C11⋊#95—41no—
144C11⋊#95—41no—
145C11⋊#95—41no—
146C11⋊#95C2×C414yescomplemented
147C11⋊#95C2×C414yescomplemented
148#14275—111nomaximal, Sylow
149C24×C11C2411yescharacteristic
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×D11C22×C412yes—
159C23×D11C2×D412yes—
160C23×D11C2×D412yes—
161C23×D11C2×Q812yes—
162C23×D11C2×Q812yes—
163C23×D11#4112yes—
164C23×D11#4112yes—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
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×C11C22×C412yes—
208C22×C4×C11C22×C412yes—
209C22×C4×C11C22×C412yes—
210C22×C4×C11C2×D412yes—
211C22×C4×C11C2×D412yes—
212C22×C4×C11C2×Q812yes—
213C22×C4×C11C2×Q812yes—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
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×Dic11C22×C412yes—
257C22×Dic11C22×C412yes—
258C22×Dic11C22×C412yes—
259C22×Dic11C2×D412yes—
260C22×Dic11C2×D412yes—
261C22×Dic11C2×Q812yes—
262C22×Dic11C2×Q812yes—
263C2×C4×D11—28no—
264C2×C4×D11—28no—
265C2×C4×D11—44no—
266C2×C4×D11—44no—
267C2×C4×D11—44no—
268C2×C4×D11—44no—
269C2×C4×D11—44no—
270C2×C4×D11—44no—
271C2×C4×D11—44no—
272C2×C4×D11—44no—
273C2×C4×D11—44no—
274C2×C4×D11—44no—
275C2×C4×D11—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—
283C2×C4×D11C4⋊C4116yescomplemented
284C11×C4⋊C4—44no—
285C11×C4⋊C4—44no—
286(C2×D11)⋊C4—28no—
287(C2×D11)⋊C4—28no—
288(C2×D11)⋊C4—44no—
289(C2×D11)⋊C4—44no—
290C4⋊Dic11—44no—
291C4⋊Dic11—44no—
292Dic11⋊C4—44no—
293Dic11⋊C4—44no—
294Dic11⋊C4—44no—
295Dic11⋊C4—44no—
296C2×#385—111no—
297C2×#385—111no—
298C2×#380—111no—
299C2×#380—111no—
300C22×#95—111no—
301#1444—111no—
302#1444—111no—
303#1442—111no—
304#1442—111no—
305#1441—111no—
306#1441—111no—
307#1441—111no—
308#1441D1111yescharacteristic, complemented
309C22⋊#95—111no—
310C22⋊#95—111no—
311C23×C11C23×C411yescharacteristic
312C23×C11C22×D411yescharacteristic
313C23×C11C22×D411yescharacteristic
314C23×C11C22×Q811yescharacteristic
315C23×C11C22×Q811yescharacteristic
316C23×C11C2×#4111yescharacteristic
317C23×C11C2×#4111yescharacteristic
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×C112−1+411yescharacteristic
325C23×C112−1+411yescharacteristic
326C22×D11—22no—
327C22×D11—22no—
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—22no—
354C22×D11C2×C4⋊C414yes—
355C22×D11C4×D414yes—
356C22×D11C4×Q814yes—
357C22×D11#12114yes—
358C22×D11C22⋊Q814yes—
359C22×D11#12514yes—
360C22×D11C4⋊Q814yes—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
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×C11C2×C4⋊C414yes—
410C2×Dic11—22no—
411C2×Dic11—22no—
412C2×Dic11—22no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—41no—
429C2×Dic11—41no—
430C2×Dic11—41no—
431C2×Dic11—41no—
432C2×Dic11—41no—
433C2×Dic11—41no—
434C2×Dic11—41no—
435C2×Dic11—41no—
436C2×Dic11—41no—
437C2×Dic11—41no—
438C2×Dic11—41no—
439C2×Dic11—41no—
440C2×Dic11—41no—
441C2×Dic11—41no—
442C2×Dic11—41no—
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×Dic11C2×C4⋊C414yes—
459C4×D11—416no—
460C4×D11—416no—
461C4×D11—416no—
462C24×C4—111no—
463C24×C4—111no—
464C24×C4—111no—
465C22×C4⋊C4—111no—
466C22×C4⋊C4—111no—
467C22×C4⋊C4—111no—
468C22×C4⋊C4—111no—
469C22×C4⋊C4—111no—
470C22×C4⋊C4—111no—
471C22×C4⋊C4C2×D1111yescharacteristic
472C22×C4⋊C4C2×D1111yescharacteristic
473C22×C22⋊C4—111no—
474C22×C22⋊C4—111no—
475C22×C22⋊C4—111no—
476C22×C22⋊C4—111no—
477#385—224no—
478#385—224no—
479#380—118no—
480#380—224no—
481C2×#95—111no—
482C2×#95—111no—
483C2×#95—111no—
484C2×#95—111no—
485C2×#95—111no—
486C2×#95—111no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
490C2×#95—111no—
491C2×#95—111no—
492C2×#95—111no—
493C2×#95—111no—
494C2×#95—111no—
495C2×#95—111no—
496C2×#95—224no—
497C2×#95C2×D1111yescharacteristic
498C2×#95C2×D1111yescharacteristic
499C2×#95C2×D1111yescharacteristic
500C2×#95C2×D1111yescharacteristic
501C2×#95C2×D1111yescharacteristic
502C22×C11C22×C4⋊C411yescharacteristic
503C22×C11C2×C4×D411yescharacteristic
504C22×C11C2×C4×Q811yescharacteristic
505C22×C11#51811yescharacteristic
506C22×C11#51811yescharacteristic
507C22×C11#52011yescharacteristic
508C22×C11#52011yescharacteristic
509C22×C11C2×#12111yescharacteristic
510C22×C11C2×C22⋊Q811yescharacteristic
511C22×C11C2×#12511yescharacteristic
512C22×C11C2×C4⋊Q811yescharacteristic
513C22×C11#53411yescharacteristic
514C22×C11#53411yescharacteristic
515C22×C11#53411yescharacteristic
516C22×C11#53411yescharacteristic
517C22×C11#53511yescharacteristic
518C22×C11#53611yescharacteristic
519C22×C11#53711yescharacteristic
520C22×C11#53711yescharacteristic
521C22×C11#53811yescharacteristic
522C22×C11#53811yescharacteristic
523C22×C11#53811yescharacteristic
524C22×C11#53811yescharacteristic
525C22×C11#53911yescharacteristic
526C22×C11#53911yescharacteristic
527C22×C11#53911yescharacteristic
528C22×C11#53911yescharacteristic
529C22×C11#54311yescharacteristic
530C22×C11#54311yescharacteristic
531C22×C11#54311yescharacteristic
532C22×C11#54311yescharacteristic
533C22×C11#54411yescharacteristic
534C22×C11#54411yescharacteristic
535C22×C11#54411yescharacteristic
536C22×C11#54411yescharacteristic
537C2×D11—24no—
538C2×D11—24no—
539C2×D11—24no—
540C2×D11—24no—
541C2×D11—24no—
542C2×D11—24no—
543C2×D11—24no—
544C2×D11—24no—
545C2×D11—24no—
546C2×D11—24no—
547C2×D11—24no—
548C2×D11—24no—
549C2×D11—24no—
550C2×D11—24no—
551C2×D11#38918yes—
552C4×C11—24no—
553C4×C11—42no—
554C4×C11—42no—
555C4×C11—42no—
556C4×C11—42no—
557C4×C11—81no—
558C4×C11—81no—
559Dic11—24no—
560Dic11—42no—
561Dic11—42no—
562Dic11—42no—
563Dic11—42no—
564Dic11—81no—
565Dic11—81no—
566C25—111no—
567C23×C4—111no—
568C23×C4—114no—
569C23×C4—114no—
570C23×C4—114no—
571C23×C4—111no—
572C23×C4—111no—
573C23×C4—111no—
574C23×C4—111no—
575C23×C4—114no—
576C23×C4—114no—
577C23×C4—111no—
578C23×C4—111no—
579C23×C4—222no—
580C23×C4—222no—
581C23×C4—222no—
582C23×C4—222no—
583C23×C4—441no—
584C23×C4—441no—
585C23×C4—441no—
586C23×C4—441no—
587C23×C4—441no—
588C23×C4—441no—
589C23×C4—441no—
590C23×C4—441no—
591C23×C4—441no—
592C23×C4—441no—
593C23×C4—441no—
594C23×C4—441no—
595C23×C4C22×D1111yescharacteristic
596C23×C4C22×D1111yescharacteristic
597C23×C4C22×D1111yescharacteristic
598C23×C4C22×D1111yescharacteristic
599C23×C4C22×D1111yescharacteristic
600C23×C4C22×D1111yescharacteristic
601C23×C4C22×D1111yescharacteristic
602C2×C4⋊C4—22no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—114no—
608C2×C4⋊C4—222no—
609C2×C4⋊C4—222no—
610C2×C4⋊C4—222no—
611C2×C4⋊C4—222no—
612C2×C4⋊C4—222no—
613C2×C4⋊C4—441no—
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×C4⋊C4—441no—
625C2×C4⋊C4C4×D1114yescomplemented
626C2×C22⋊C4—114no—
627C2×C22⋊C4—114no—
628C2×C22⋊C4—222no—
629C2×C22⋊C4—222no—
630C2×C22⋊C4—222no—
631C2×C22⋊C4—222no—
632C2×C22⋊C4—222no—
633C2×C22⋊C4—222no—
634C2×C22⋊C4—222no—
635C2×C22⋊C4—222no—
636C2×C22⋊C4—222no—
637C2×C22⋊C4—222no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—41no—
642#95—41no—
643#95—114no—
644#95—114no—
645#95—222no—
646#95—222no—
647#95—222no—
648#95—222no—
649#95—222no—
650#95—222no—
651#95—222no—
652#95—441no—
653#95—441no—
654#95—441no—
655#95—441no—
656#95—441no—
657#95—441no—
658C2×C11C2×#38911yescharacteristic
659C2×C11#231511yescharacteristic
660C2×C11#231711yescharacteristic
661C2×C11#232511yescharacteristic
662C2×C11#232511yescharacteristic
663C2×C11#232911yescharacteristic
664C2×C11#232911yescharacteristic
665C2×C11#261711yescharacteristic
666C2×C11#261811yescharacteristic
667C2×C11#262611yescharacteristic
668C2×C11#262711yescharacteristic
669C2×C11#264611yescharacteristic
670C2×C11#264611yescharacteristic
671C2×C11#265911yescharacteristic
672C2×C11#265911yescharacteristic
673D11—28no—
674C24—112no—
675C24—112no—
676C24—112no—
677C24—112no—
678C24—112no—
679C24—112no—
680C24—112no—
681C24—221no—
682C24—221no—
683C24—221no—
684C24—221no—
685C24—221no—
686C24—221no—
687C24—221no—
688C24—221no—
689C24C23×D1111yescharacteristic
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—112no—
733C22×C4—112no—
734C22×C4—112no—
735C22×C4—1116no—
736C22×C4—112no—
737C22×C4—112no—
738C22×C4—112no—
739C22×C4—112no—
740C22×C4—228no—
741C22×C4—228no—
742C22×C4—221no—
743C22×C4—221no—
744C22×C4—221no—
745C22×C4—221no—
746C22×C4—221no—
747C22×C4—221no—
748C22×C4—221no—
749C22×C4—221no—
750C22×C4—221no—
751C22×C4—221no—
752C22×C4—221no—
753C22×C4—221no—
754C22×C4—221no—
755C22×C4—221no—
756C22×C4—221no—
757C22×C4—221no—
758C22×C4—221no—
759C22×C4—221no—
760C22×C4—221no—
761C22×C4—221no—
762C22×C4—221no—
763C22×C4—221no—
764C22×C4—221no—
765C22×C4—221no—
766C22×C4—221no—
767C22×C4—221no—
768C22×C4—221no—
769C22×C4—221no—
770C22×C4—221no—
771C22×C4—221no—
772C22×C4—221no—
773C22×C4—221no—
774C22×C4—221no—
775C22×C4—221no—
776C22×C4—221no—
777C22×C4—221no—
778C22×C4—221no—
779C22×C4—221no—
780C22×C4—221no—
781C22×C4—221no—
782C22×C4—221no—
783C22×C4—221no—
784C22×C4—444no—
785C22×C4—444no—
786C22×C4—444no—
787C22×C4—444no—
788C22×C4—444no—
789C22×C4—444no—
790C22×C4—444no—
791C22×C4—444no—
792C22×C4—444no—
793C22×C4—444no—
794C22×C4—444no—
795C22×C4—444no—
796C22×C4—444no—
797C22×C4—444no—
798C22×C4—444no—
799C22×C4—444no—
800C22×C4—444no—
801C22×C4—444no—
802C22×C4C2×C4×D1112yes—
803C22×C4C2×C4×D1112yes—
804C22×C4C2×C4×D1112yes—
805C22×C4D4×D1112yes—
806C22×C4D4×D1112yes—
807C22×C4Q8×D1112yes—
808C22×C4Q8×D1112yes—
809C4⋊C4—44no—
810C4⋊C4—44no—
811C4⋊C4—444no—
812C4⋊C4—444no—
813C4⋊C4—444no—
814C4⋊C4—444no—
815C4⋊C4—444no—
816C4⋊C4—444no—
817C22⋊C4—228no—
818C22⋊C4—228no—
819C22⋊C4—444no—
820C22⋊C4—444no—
821C11#1427511yescharacteristic, complemented, Sylow
822C23—114no—
823C23—114no—
824C23—114no—
825C23—114no—
826C23—114no—
827C23—114no—
828C23—114no—
829C23—222no—
830C23—222no—
831C23—222no—
832C23—222no—
833C23—222no—
834C23—222no—
835C23—222no—
836C23—222no—
837C23—222no—
838C23—222no—
839C23—222no—
840C23—222no—
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—222no—
856C23—222no—
857C23C22×C4×D1111yescharacteristic
858C23C2×D4×D1111yescharacteristic
859C23C2×D4×D1111yescharacteristic
860C23#6703711yescharacteristic
861C23#6703711yescharacteristic
862C23#6703711yescharacteristic
863C23C2×Q8×D1111yescharacteristic
864C23C2×Q8×D1111yescharacteristic
865C23#6704011yescharacteristic
866C23#41×D1111yescharacteristic
867C23#41×D1111yescharacteristic
868C23#6704211yescharacteristic
869C23#6704211yescharacteristic
870C23#6704211yescharacteristic
871C23#6704311yescharacteristic
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—114no—
921C2×C4—222no—
922C2×C4—222no—
923C2×C4—222no—
924C2×C4—222no—
925C2×C4—222no—
926C2×C4—222no—
927C2×C4—222no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—222no—
932C2×C4—222no—
933C2×C4—222no—
934C2×C4—222no—
935C2×C4—222no—
936C2×C4—222no—
937C2×C4—222no—
938C2×C4—222no—
939C2×C4—4416no—
940C2×C4—4416no—
941C2×C4—4416no—
942C2×C4—441no—
943C2×C4—441no—
944C2×C4—441no—
945C2×C4—441no—
946C2×C4—441no—
947C2×C4—441no—
948C2×C4—441no—
949C2×C4—441no—
950C2×C4—441no—
951C2×C4—441no—
952C2×C4—441no—
953C2×C4—441no—
954C2×C4—441no—
955C2×C4—441no—
956C2×C4—441no—
957C2×C4—441no—
958C2×C4—441no—
959C2×C4—441no—
960C2×C4—441no—
961C2×C4—441no—
962C2×C4—441no—
963C2×C4—441no—
964C2×C4—441no—
965C2×C4—441no—
966C2×C4—441no—
967C2×C4—441no—
968C2×C4—441no—
969C2×C4—441no—
970C2×C4—441no—
971C2×C4—441no—
972C2×C4C4⋊C4×D1114yes—
973C22—118no—
974C22—224no—
975C22—224no—
976C22—224no—
977C22—224no—
978C22—224no—
979C22—224no—
980C22—224no—
981C22—224no—
982C22—224no—
983C22—224no—
984C22—224no—
985C22—224no—
986C22—224no—
987C22—224no—
988C22#1062301711yescharacteristic
989C22C2×C4⋊C4×D1111yescharacteristic
990C22#1062305211yescharacteristic
991C22C4×D4×D1111yescharacteristic
992C22#1062307711yescharacteristic
993C22C4×Q8×D1111yescharacteristic
994C22#1062310511yescharacteristic
995C22#1062312011yescharacteristic
996C22D11×#12111yescharacteristic
997C22#1062313611yescharacteristic
998C22#1062313611yescharacteristic
999C22#1062313811yescharacteristic
1000C22#1062313911yescharacteristic
1001C22#1062314411yescharacteristic
1002C22D11×C22⋊Q811yescharacteristic
1003C22#1062315911yescharacteristic
1004C22#1062316011yescharacteristic
1005C22#1062316511yescharacteristic
1006C22#1062316511yescharacteristic
1007C22#1062316511yescharacteristic
1008C22#1062316511yescharacteristic
1009C22#1062316911yescharacteristic
1010C22#1062318411yescharacteristic
1011C22#1062318811yescharacteristic
1012C22#1062319111yescharacteristic
1013C22#1062320911yescharacteristic
1014C22D11×#12511yescharacteristic
1015C22#1062322011yescharacteristic
1016C22#1062322011yescharacteristic
1017C22#1062322311yescharacteristic
1018C22#1062323511yescharacteristic
1019C22#1062323811yescharacteristic
1020C22D11×C4⋊Q811yescharacteristic
1021C22#1062326011yescharacteristic
1022C22#1062326011yescharacteristic
1023C4—24no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—81no—
1029C4—81no—
1030C4—224no—
1031C4—442no—
1032C4—442no—
1033C4—442no—
1034C4—442no—
1035C4—881no—
1036C4—881no—
1037C2—228no—
1038C2D11×#38911yescharacteristic
1039C2#1307122911yescharacteristic
1040C2#1307123811yescharacteristic
1041C2#1307131511yescharacteristic
1042C2#1307131811yescharacteristic
1043C2#1307134511yescharacteristic
1044C2#1307134811yescharacteristic
1045C2#1307435511yescharacteristic
1046C2#1307436311yescharacteristic
1047C2#1307442611yescharacteristic
1048C2#1307443411yescharacteristic
1049C2#1307458511yescharacteristic
1050C2#1307458711yescharacteristic
1051C2#1307472911yescharacteristic
1052C2#1307473111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1441C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1441D11
hypocenterC11#14275
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
6. #13066880C2semidirect
7. #13066879C2semidirect
8. #13066874C2semidirect
9. #13066871C2semidirect
10. #13066869C2semidirect
11. #13066868C2semidirect
12. #13066868C2semidirect
15. C11×#1441C2semidirect
52. #10622600C4semidirect
97. C2×C11×C4⋊C4C2×C4semidirect
115. C2×C4⋊Dic11C2×C4semidirect
146. C11⋊#95C2×C4semidirect
147. C11⋊#95C2×C4semidirect
283. C2×C4×D11C4⋊C4semidirect
308. #1441D11semidirect
625. C2×C4⋊C4C4×D11semidirect
821. C11#14275semidirect

Maximal subgroups

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

subgroupindex
C2×#106222812
C2×#106226022
C2×#106222802
C2×#106226002
C2×D11×#952
#130668802
#130668792
#130668742
#130668712
#130668692
#130668682
(C2×D11)⋊#952
C11×#14412
#1427511