Finite Group Databasebeta

← #14677483

Subgroups — #14677483

Order 2816.

2006 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×#10622602C211yesmaximal, characteristic
4C2×#10622279C211yesmaximal, characteristic
5C2×D11×#95C211yesmaximal, characteristic
6#13066872C211yesmaximal, characteristic, complemented
7#13066871C211yesmaximal, characteristic, complemented
8#13066866C211yesmaximal, characteristic, complemented
9#13066847C211yesmaximal, characteristic, complemented
10#13066847C211yesmaximal, characteristic, complemented
11#13066845C211yesmaximal, characteristic, complemented
12Dic11⋊#95C211yesmaximal, 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×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
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#10622602C418yescomplemented
53#10622281—24no—
54#10622279—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—22no—
76C22×C4×D11—22no—
77C22×C4×D11—22no—
78C22×C4×D11—22no—
79C22×C4×D11—22no—
80C22×C4×D11—22no—
81C22×C4×D11—22no—
82C22×C4×D11—41no—
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×D11C2×C414yes—
91C22×C4×D11D414yes—
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)⋊C4C2×C414yes—
106C2×(C2×D11)⋊C4C2×C414yes—
107C2×(C2×D11)⋊C4D414yes—
108C2×(C2×D11)⋊C4Q814yes—
109C2×(C2×D11)⋊C4Q814yes—
110C2×C4⋊Dic11—22no—
111C2×C4⋊Dic11—22no—
112C2×C4⋊Dic11—41no—
113C2×Dic11⋊C4—22no—
114C2×Dic11⋊C4—22no—
115C2×Dic11⋊C4—22no—
116C2×Dic11⋊C4—22no—
117C2×Dic11⋊C4—22no—
118C2×Dic11⋊C4—41no—
119C2×Dic11⋊C4—41no—
120C2×Dic11⋊C4—41no—
121C2×Dic11⋊C4C2×C414yescomplemented
122C2×C4×Dic11—22no—
123C2×C4×Dic11—22no—
124C2×C4×Dic11—22no—
125C2×C4×Dic11—22no—
126C2×C4×Dic11—41no—
127C2×C4×Dic11—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—22no—
141C11⋊#95—22no—
142C11⋊#95—41no—
143C11⋊#95—41no—
144C11⋊#95—41no—
145C11⋊#95—41no—
146C11⋊#95C2×C414yescomplemented
147C11⋊#95C2×C414yescomplemented
148#14044—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×C11C22×C412yes—
207C22×C4×C11C22×C412yes—
208C22×C4×C11C22×C412yes—
209C22×C4×C11C2×D412yes—
210C22×C4×C11C2×D412yes—
211C22×C4×C11C2×Q812yes—
212C22×C4×C11C2×Q812yes—
213C22×C4×C11#4112yes—
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×Dic11C22×C412yes—
254C22×Dic11C22×C412yes—
255C22×Dic11C22×C412yes—
256C22×Dic11C2×D412yes—
257C22×Dic11C2×D412yes—
258C22×Dic11C2×Q812yes—
259C22×Dic11C2×Q812yes—
260C22×Dic11#4112yes—
261C22×Dic11#4112yes—
262C22×Dic11#4112yes—
263C2×C4×D11—28no—
264C2×C4×D11—28no—
265C2×C4×D11—28no—
266C2×C4×D11—28no—
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×D11—44no—
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)⋊C4C4⋊C4116yescomplemented
290C4⋊Dic11—44no—
291Dic11⋊C4—44no—
292Dic11⋊C4—44no—
293Dic11⋊C4—44no—
294C4×Dic11—44no—
295C4×Dic11—44no—
296C2×#385—111no—
297C2×#385—111no—
298C2×#385—111no—
299C2×C4×C22⋊C4—111no—
300C22×#95—111no—
301#1442—111no—
302#1442—111no—
303#1441—111no—
304#1441D1111yescharacteristic, complemented
305#1436—111no—
306#1436—111no—
307C4⋊#95—111no—
308C4⋊#95—111no—
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×C11C2×#4111yescharacteristic
319C23×C11C2×#4111yescharacteristic
320C23×C11C2×#4111yescharacteristic
321C23×C11C2×#4111yescharacteristic
322C23×C11H(5,𝔽2)11yescharacteristic
323C23×C11H(5,𝔽2)11yescharacteristic
324C23×C11H(5,𝔽2)11yescharacteristic
325C23×C11H(5,𝔽2)11yescharacteristic
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—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
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—22no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
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×Dic11C2×C4⋊C414yes—
458C2×Dic11#12314yes—
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⋊C4C2×D1111yescharacteristic
470C22×C4⋊C4C2×D1111yescharacteristic
471C22×C22⋊C4—111no—
472C22×C22⋊C4—111no—
473C22×C22⋊C4—111no—
474C22×C22⋊C4—111no—
475C22×C42—111no—
476C22×C42—111no—
477#385—118no—
478#385—224no—
479#385—224no—
480C4×C22⋊C4—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×C11C4×#4111yescharacteristic
506C22×C11C4×#4111yescharacteristic
507C22×C11#51811yescharacteristic
508C22×C11#51811yescharacteristic
509C22×C11C2×#12111yescharacteristic
510C22×C11C2×C22⋊Q811yescharacteristic
511C22×C11C2×#12311yescharacteristic
512C22×C11#52511yescharacteristic
513C22×C11C2×#12511yescharacteristic
514C22×C11#52911yescharacteristic
515C22×C11#52911yescharacteristic
516C22×C11C2×C4⋊Q811yescharacteristic
517C22×C11#53411yescharacteristic
518C22×C11#53511yescharacteristic
519C22×C11#53811yescharacteristic
520C22×C11#53811yescharacteristic
521C22×C11#54611yescharacteristic
522C22×C11#54611yescharacteristic
523C22×C11#54611yescharacteristic
524C22×C11#54611yescharacteristic
525C22×C11#55111yescharacteristic
526C22×C11#55111yescharacteristic
527C22×C11#55111yescharacteristic
528C22×C11#55111yescharacteristic
529C22×C11#55411yescharacteristic
530C22×C11#55411yescharacteristic
531C22×C11#55411yescharacteristic
532C22×C11#55411yescharacteristic
533C22×C11#55411yescharacteristic
534C22×C11#55411yescharacteristic
535C22×C11#55411yescharacteristic
536C22×C11#55411yescharacteristic
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—42no—
558C4×C11—81no—
559Dic11—24no—
560Dic11—24no—
561Dic11—42no—
562Dic11—42no—
563Dic11—42no—
564Dic11—42no—
565Dic11—81no—
566C25—111no—
567C23×C4—111no—
568C23×C4—111no—
569C23×C4—111no—
570C23×C4—111no—
571C23×C4—111no—
572C23×C4—111no—
573C23×C4—114no—
574C23×C4—114no—
575C23×C4—111no—
576C23×C4—222no—
577C23×C4—222no—
578C23×C4—222no—
579C23×C4—222no—
580C23×C4—222no—
581C23×C4—222no—
582C23×C4—222no—
583C23×C4—222no—
584C23×C4—222no—
585C23×C4—222no—
586C23×C4—222no—
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—222no—
614C2×C4⋊C4—222no—
615C2×C4⋊C4—441no—
616C2×C4⋊C4—441no—
617C2×C4⋊C4—441no—
618C2×C4⋊C4—441no—
619C2×C4⋊C4C4×D1114yescomplemented
620C2×C22⋊C4—114no—
621C2×C22⋊C4—114no—
622C2×C22⋊C4—114no—
623C2×C22⋊C4—114no—
624C2×C22⋊C4—114no—
625C2×C22⋊C4—222no—
626C2×C22⋊C4—222no—
627C2×C22⋊C4—222no—
628C2×C22⋊C4—222no—
629C2×C22⋊C4—222no—
630C2×C22⋊C4—222no—
631C2×C22⋊C4—222no—
632C2×C42—222no—
633C2×C42—222no—
634C2×C42—222no—
635C2×C42—222no—
636C2×C42—441no—
637C2×C42—441no—
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—222no—
653#95—222no—
654#95—441no—
655#95—441no—
656#95—441no—
657#95—441no—
658C2×C11C2×#38911yescharacteristic
659C2×C11C4×#12311yescharacteristic
660C2×C11#232111yescharacteristic
661C2×C11#234911yescharacteristic
662C2×C11#234911yescharacteristic
663C2×C11#236811yescharacteristic
664C2×C11#236811yescharacteristic
665C2×C11#241111yescharacteristic
666C2×C11#241211yescharacteristic
667C2×C11#245011yescharacteristic
668C2×C11#245011yescharacteristic
669C2×C11#250211yescharacteristic
670C2×C11#250511yescharacteristic
671C2×C11#250511yescharacteristic
672C2×C11#258311yescharacteristic
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—112no—
732C22×C4—112no—
733C22×C4—112no—
734C22×C4—112no—
735C22×C4—112no—
736C22×C4—112no—
737C22×C4—112no—
738C22×C4—112no—
739C22×C4—112no—
740C22×C4—112no—
741C22×C4—228no—
742C22×C4—228no—
743C22×C4—228no—
744C22×C4—228no—
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×C4C2×C4×D1112yes—
802C22×C4C2×C4×D1112yes—
803C22×C4C2×C4×D1112yes—
804C22×C4D4×D1112yes—
805C22×C4D4×D1112yes—
806C22×C4Q8×D1112yes—
807C22×C4Q8×D1112yes—
808C22×C4#434312yes—
809C4⋊C4—44no—
810C4⋊C4—44no—
811C4⋊C4—444no—
812C4⋊C4—444no—
813C4⋊C4—444no—
814C4⋊C4—444no—
815C22⋊C4—1116no—
816C22⋊C4—228no—
817C22⋊C4—228no—
818C22⋊C4—444no—
819C42—444no—
820C42—444no—
821C11#1404411yescharacteristic, 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
865C23C2×#434311yescharacteristic
866C23#41×D1111yescharacteristic
867C23#41×D1111yescharacteristic
868C23#41×D1111yescharacteristic
869C23#41×D1111yescharacteristic
870C23#41×D1111yescharacteristic
871C23#6704211yescharacteristic
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—22no—
891C2×C4—22no—
892C2×C4—22no—
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—114no—
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—222no—
940C2×C4—222no—
941C2×C4—222no—
942C2×C4—222no—
943C2×C4—222no—
944C2×C4—222no—
945C2×C4—222no—
946C2×C4—4416no—
947C2×C4—4416no—
948C2×C4—4416no—
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#1062305311yescharacteristic
991C22C4×D4×D1111yescharacteristic
992C22#1062307611yescharacteristic
993C22C4×Q8×D1111yescharacteristic
994C22C4×#434311yescharacteristic
995C22#1062312011yescharacteristic
996C22D11×#12111yescharacteristic
997C22#1062313811yescharacteristic
998C22#1062314111yescharacteristic
999C22#1062314111yescharacteristic
1000C22#1062314311yescharacteristic
1001C22#1062314411yescharacteristic
1002C22D11×C22⋊Q811yescharacteristic
1003C22#1062315811yescharacteristic
1004C22#1062316111yescharacteristic
1005C22#1062316711yescharacteristic
1006C22#1062316711yescharacteristic
1007C22#1062316711yescharacteristic
1008C22#1062316711yescharacteristic
1009C22#1062316811yescharacteristic
1010C22D11×#12311yescharacteristic
1011C22#1062318811yescharacteristic
1012C22#1062319011yescharacteristic
1013C22#1062321011yescharacteristic
1014C22D11×#12511yescharacteristic
1015C22#1062322111yescharacteristic
1016C22#1062322111yescharacteristic
1017C22#1062322211yescharacteristic
1018C22#1062323611yescharacteristic
1019C22#1062323711yescharacteristic
1020C22D11×C4⋊Q811yescharacteristic
1021C22#1062326111yescharacteristic
1022C22#1062326111yescharacteristic
1023C4—24no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—42no—
1029C4—81no—
1030C4—224no—
1031C4—224no—
1032C4—442no—
1033C4—442no—
1034C4—442no—
1035C4—442no—
1036C4—881no—
1037C2—228no—
1038C2D11×#38911yescharacteristic
1039C2#1307113711yescharacteristic
1040C2#1307127211yescharacteristic
1041C2#1307152011yescharacteristic
1042C2#1307152511yescharacteristic
1043C2#1307169311yescharacteristic
1044C2#1307169511yescharacteristic
1045C2#1307199611yescharacteristic
1046C2#1307200711yescharacteristic
1047C2#1307243511yescharacteristic
1048C2#1307244111yescharacteristic
1049C2#1307308911yescharacteristic
1050C2#1307311211yescharacteristic
1051C2#1307311811yescharacteristic
1052C2#1307399211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1441C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1441D11
hypocenterC11#14044
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
6. #13066872C2semidirect
7. #13066871C2semidirect
8. #13066866C2semidirect
9. #13066847C2semidirect
10. #13066847C2semidirect
11. #13066845C2semidirect
12. Dic11⋊#95C2semidirect
15. C11×#1441C2semidirect
52. #10622602C4semidirect
97. C2×C11×C4⋊C4C2×C4semidirect
121. C2×Dic11⋊C4C2×C4semidirect
146. C11⋊#95C2×C4semidirect
147. C11⋊#95C2×C4semidirect
289. (C2×D11)⋊C4C4⋊C4semidirect
304. #1441D11semidirect
619. C2×C4⋊C4C4×D11semidirect
821. C11#14044semidirect

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×#106222792
C2×D11×#952
#130668722
#130668712
#130668662
#130668472
#130668452
Dic11⋊#952
(C2×D11)⋊#952
C11×#14412
#1404411