Finite Group Databasebeta

← #14675747

Subgroups — #14675747

Order 2816.

2006 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66925C211yesmaximal, characteristic
2C2×#10622589C211yesmaximal, characteristic, complemented
3C2×#10622263C211yesmaximal, characteristic, complemented
4C2×#10622280C211yesmaximal, characteristic
5C2×#10622279C211yesmaximal, characteristic
6#13066862C211yesmaximal, characteristic
7#13066860C211yesmaximal, characteristic
8#13066860C211yesmaximal, characteristic
9#13066858C211yesmaximal, characteristic
10#13066850C211yesmaximal, characteristic, complemented
11#13066849C211yesmaximal, characteristic, complemented
12#13066847C211yesmaximal, characteristic, complemented
13Dic11⋊#95C211yesmaximal, characteristic, complemented
14Dic11⋊#95C211yesmaximal, characteristic, complemented
15C11×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×#66925—24no—
36C2×#66925—24no—
37C2×#66925—24no—
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
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54#10622589—24no—
55#10622280—24no—
56#10622279C418yescomplemented
57#10622263—24no—
58C24×D11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C22×C4×D11—22no—
74C22×C4×D11—22no—
75C22×C4×D11—22no—
76C22×C4×D11—22no—
77C22×C4×D11C2×C414yes—
78C22×C4×D11D414yes—
79C22×C4×D11Q814yes—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—41no—
83C2×C42×C11—22no—
84C2×C42×C11—22no—
85C2×C42×C11—22no—
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—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—41no—
99C2×(C2×D11)⋊C4—41no—
100C2×(C2×D11)⋊C4—41no—
101C2×(C2×D11)⋊C4—41no—
102C2×(C2×D11)⋊C4C2×C414yes—
103C2×(C2×D11)⋊C4C2×C414yes—
104C2×C4⋊Dic11—22no—
105C2×C4⋊Dic11—22no—
106C2×C4⋊Dic11—41no—
107C2×Dic11⋊C4—22no—
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4—22no—
110C2×Dic11⋊C4—22no—
111C2×Dic11⋊C4—22no—
112C2×Dic11⋊C4—22no—
113C2×Dic11⋊C4—22no—
114C2×Dic11⋊C4—22no—
115C2×Dic11⋊C4—22no—
116C2×Dic11⋊C4—22no—
117C2×Dic11⋊C4—22no—
118C2×Dic11⋊C4—22no—
119C2×Dic11⋊C4—22no—
120C2×Dic11⋊C4—22no—
121C2×Dic11⋊C4—41no—
122C2×Dic11⋊C4—41no—
123C2×Dic11⋊C4D414yes—
124C2×Dic11⋊C4D414yes—
125C2×C4×Dic11—22no—
126C2×C4×Dic11—22no—
127C2×C4×Dic11—22no—
128C2×C4×Dic11—22no—
129C2×C4×Dic11—22no—
130C2×C4×Dic11—22no—
131C2×C4×Dic11—22no—
132C2×C4×Dic11C2×C414yes—
133C2×C4×Dic11C2×C414yes—
134#66925—232no—
135C11×#95—22no—
136C11×#95—22no—
137C11×#95—22no—
138C11×#95—41no—
139C11×#95C2×C414yes—
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⋊#95C2×C414yes—
151#13879—111nomaximal, Sylow
152C24×C11C2411yescharacteristic
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×D11C22×C412yes—
166C23×D11C2×D412yes—
167C23×D11C2×Q812yes—
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×C11—21no—
208C22×C4×C11C22×C412yes—
209C22×C4×C11C22×C412yes—
210C22×C4×C11C22×C412yes—
211C22×C4×C11C2×D412yes—
212C22×C4×C11C2×D412yes—
213C22×C4×C11C2×D412yes—
214C22×C4×C11C2×Q812yes—
215C22×C4×C11#4112yes—
216C22×C4×C11#4112yes—
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×D412yes—
259C22×Dic11C2×D412yes—
260C22×Dic11C2×D412yes—
261C22×Dic11C2×Q812yes—
262C22×Dic11#4112yes—
263C22×Dic11#4112yes—
264C22×Dic11#4112yes—
265C22×Dic11#4112yes—
266C2×C4×D11—28no—
267C2×C4×D11—28no—
268C2×C4×D11—28no—
269C2×C4×D11—28no—
270C2×C4×D11—28no—
271C2×C4×D11—28no—
272C2×C4×D11C4⋊C4116yescomplemented
273C11×C4⋊C4—44no—
274C42×C11—28no—
275(C2×D11)⋊C4—28no—
276(C2×D11)⋊C4—28no—
277(C2×D11)⋊C4—28no—
278(C2×D11)⋊C4—28no—
279(C2×D11)⋊C4—44no—
280(C2×D11)⋊C4—44no—
281C4⋊Dic11—44no—
282Dic11⋊C4—28no—
283Dic11⋊C4—28no—
284Dic11⋊C4—44no—
285Dic11⋊C4—44no—
286Dic11⋊C4—44no—
287Dic11⋊C4—44no—
288C4×Dic11—28no—
289C4×Dic11—28no—
290C4×Dic11—28no—
291C22×#117—111no—
292C2×#384—111no—
293C2×#382—111no—
294C2×#380—111no—
295C2×C4×C22⋊C4—111no—
296#1439—111no—
297#1439—111no—
298#1439—111no—
299#1439—111no—
300#1436—111no—
301#1436—111no—
302#1436—111no—
303#1436D1111yescharacteristic, complemented
304C4⋊#95—111no—
305C4⋊#95—111no—
306C23×C11C23×C411yescharacteristic
307C23×C11C22×D411yescharacteristic
308C23×C11C22×D411yescharacteristic
309C23×C11C22×D411yescharacteristic
310C23×C11C22×Q811yescharacteristic
311C23×C11C2×#4111yescharacteristic
312C23×C11C2×#4111yescharacteristic
313C23×C11C2×#4111yescharacteristic
314C23×C11C2×#4111yescharacteristic
315C23×C11C2×#4111yescharacteristic
316C23×C11C2×#4111yescharacteristic
317C23×C11H(5,𝔽2)11yescharacteristic
318C23×C11H(5,𝔽2)11yescharacteristic
319C23×C112−1+411yescharacteristic
320C23×C112−1+411yescharacteristic
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
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—41no—
340C22×D11—41no—
341C22×D11—41no—
342C22×D11—41no—
343C22×D11—41no—
344C22×D11—41no—
345C22×D11—41no—
346C22×D11—41no—
347C22×D11—41no—
348C22×D11—41no—
349C22×D11—41no—
350C22×D11—41no—
351C22×D11—41no—
352C22×D11—41no—
353C22×D11—41no—
354C22×D11—41no—
355C22×D11C2×C4⋊C414yes—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
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—41no—
378C2×C4×C11—41no—
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×C11C2×C4⋊C414yes—
404C2×C4×C11#11714yescomplemented
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—22no—
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—41no—
421C2×Dic11—41no—
422C2×Dic11—41no—
423C2×Dic11—41no—
424C2×Dic11—41no—
425C2×Dic11—41no—
426C2×Dic11—41no—
427C2×Dic11—41no—
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×Dic11C2×C4⋊C414yes—
447C2×Dic11#11714yescomplemented
448C2×Dic11C4×D414yes—
449C2×Dic11C4×D414yes—
450C2×Dic11#12014yes—
451C2×Dic11C22⋊Q814yes—
452C2×Dic11C22⋊Q814yes—
453C2×Dic11#12314yes—
454C4×D11—232no—
455C24×C4—111no—
456C2×#117—224no—
457C2×#117—224no—
458C2×#117—224no—
459C22×C4⋊C4—111no—
460C22×C4⋊C4—111no—
461C22×C4⋊C4—111no—
462C22×C4⋊C4—111no—
463C22×C4⋊C4—111no—
464C22×C4⋊C4—111no—
465C22×C4⋊C4—111no—
466C22×C4⋊C4C2×D1111yescharacteristic
467C22×C22⋊C4—111no—
468C22×C22⋊C4—111no—
469C22×C22⋊C4—111no—
470C22×C22⋊C4—111no—
471C22×C22⋊C4—111no—
472C22×C22⋊C4—111no—
473C22×C42—111no—
474C22×C42—111no—
475C22×C42—111no—
476C22×C42C2×D1111yescharacteristic
477#384—224no—
478#382—224no—
479#380—224no—
480C4×C22⋊C4—118no—
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×#95C2×D1111yescharacteristic
493C2×#95C2×D1111yescharacteristic
494C2×#95C2×D1111yescharacteristic
495C2×#95C2×D1111yescharacteristic
496C2×#95C2×D1111yescharacteristic
497C22×C11C22×C4⋊C411yescharacteristic
498C22×C11C2×#11711yescharacteristic
499C22×C11C2×#11711yescharacteristic
500C22×C11C2×C4×D411yescharacteristic
501C22×C11C2×C4×D411yescharacteristic
502C22×C11#52011yescharacteristic
503C22×C11#52011yescharacteristic
504C22×C11C2×#12011yescharacteristic
505C22×C11C2×C22⋊Q811yescharacteristic
506C22×C11C2×C22⋊Q811yescharacteristic
507C22×C11C2×#12311yescharacteristic
508C22×C11#53211yescharacteristic
509C22×C11#53211yescharacteristic
510C22×C11#53311yescharacteristic
511C22×C11#53311yescharacteristic
512C22×C11#53511yescharacteristic
513C22×C11#53611yescharacteristic
514C22×C11#54411yescharacteristic
515C22×C11#54411yescharacteristic
516C22×C11#54611yescharacteristic
517C22×C11#54611yescharacteristic
518C22×C11#54711yescharacteristic
519C22×C11#54711yescharacteristic
520C22×C11#54811yescharacteristic
521C22×C11#54811yescharacteristic
522C22×C11#55011yescharacteristic
523C22×C11#55011yescharacteristic
524C22×C11#55211yescharacteristic
525C22×C11#55211yescharacteristic
526C22×C11#55311yescharacteristic
527C22×C11#55311yescharacteristic
528C22×C11#55511yescharacteristic
529C22×C11#55511yescharacteristic
530C22×C11#55611yescharacteristic
531C22×C11#55611yescharacteristic
532C2×D11—24no—
533C2×D11—24no—
534C2×D11—24no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—42no—
539C2×D11—42no—
540C2×D11—42no—
541C2×D11—42no—
542C2×D11—42no—
543C2×D11—42no—
544C2×D11—42no—
545C2×D11—42no—
546C2×D11—42no—
547C4×C11—24no—
548C4×C11—24no—
549C4×C11—42no—
550C4×C11—42no—
551C4×C11—42no—
552C4×C11—81no—
553C4×C11—81no—
554Dic11—24no—
555Dic11—42no—
556Dic11—42no—
557Dic11—42no—
558Dic11—81no—
559Dic11—81no—
560Dic11#38518yes—
561C25—111no—
562C23×C4—111no—
563C23×C4—111no—
564C23×C4—114no—
565C23×C4—114no—
566C23×C4—114no—
567C23×C4—111no—
568C23×C4—111no—
569C23×C4—111no—
570C23×C4—111no—
571C23×C4—111no—
572C23×C4—222no—
573C23×C4—222no—
574C23×C4—222no—
575C23×C4—222no—
576C23×C4C22×D1111yescharacteristic
577C23×C4C22×D1111yescharacteristic
578C23×C4C22×D1111yescharacteristic
579C23×C4C22×D1111yescharacteristic
580C23×C4C22×D1111yescharacteristic
581C23×C4C22×D1111yescharacteristic
582C23×C4C22×D1111yescharacteristic
583#117—2232no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—114no—
588C2×C4⋊C4—114no—
589C2×C4⋊C4—222no—
590C2×C4⋊C4—222no—
591C2×C4⋊C4—222no—
592C2×C4⋊C4—222no—
593C2×C4⋊C4—222no—
594C2×C4⋊C4—222no—
595C2×C4⋊C4—222no—
596C2×C4⋊C4—222no—
597C2×C4⋊C4—222no—
598C2×C4⋊C4—222no—
599C2×C4⋊C4—222no—
600C2×C4⋊C4—222no—
601C2×C4⋊C4—222no—
602C2×C4⋊C4—222no—
603C2×C4⋊C4—222no—
604C2×C4⋊C4—222no—
605C2×C4⋊C4—441no—
606C2×C4⋊C4—441no—
607C2×C4⋊C4—441no—
608C2×C22⋊C4—114no—
609C2×C22⋊C4—114no—
610C2×C22⋊C4—222no—
611C2×C22⋊C4—222no—
612C2×C22⋊C4—222no—
613C2×C22⋊C4—222no—
614C2×C22⋊C4—222no—
615C2×C22⋊C4—222no—
616C2×C22⋊C4—222no—
617C2×C22⋊C4—222no—
618C2×C22⋊C4—222no—
619C2×C22⋊C4—222no—
620C2×C22⋊C4—222no—
621C2×C22⋊C4—222no—
622C2×C22⋊C4—441no—
623C2×C22⋊C4—441no—
624C2×C22⋊C4—441no—
625C2×C22⋊C4—441no—
626C2×C42—22no—
627C2×C42—22no—
628C2×C42—22no—
629C2×C42—114no—
630C2×C42—114no—
631C2×C42—222no—
632C2×C42—222no—
633C2×C42—222no—
634C2×C42—222no—
635C2×C42—222no—
636C2×C42—222no—
637C2×C42—222no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—41no—
642#95—114no—
643#95—222no—
644#95—222no—
645#95—222no—
646#95—222no—
647#95—222no—
648#95—222no—
649#95—222no—
650#95—441no—
651#95—441no—
652#95—441no—
653#95C4×D1114yes—
654C2×C11#228511yescharacteristic
655C2×C11C2×#38511yescharacteristic
656C2×C11#231711yescharacteristic
657C2×C11#235211yescharacteristic
658C2×C11#235211yescharacteristic
659C2×C11#235411yescharacteristic
660C2×C11#235411yescharacteristic
661C2×C11#243111yescharacteristic
662C2×C11#243211yescharacteristic
663C2×C11#243911yescharacteristic
664C2×C11#243911yescharacteristic
665C2×C11#244111yescharacteristic
666C2×C11#244111yescharacteristic
667C2×C11#249911yescharacteristic
668C2×C11#250011yescharacteristic
669D11—44no—
670C24—112no—
671C24—112no—
672C24—112no—
673C24—221no—
674C24—221no—
675C24—221no—
676C24—221no—
677C24—221no—
678C24—221no—
679C24—221no—
680C24—221no—
681C24—221no—
682C24—221no—
683C24—221no—
684C24—221no—
685C24C23×D1111yescharacteristic
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
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—112no—
727C22×C4—112no—
728C22×C4—112no—
729C22×C4—112no—
730C22×C4—112no—
731C22×C4—112no—
732C22×C4—112no—
733C22×C4—112no—
734C22×C4—112no—
735C22×C4—112no—
736C22×C4—1116no—
737C22×C4—112no—
738C22×C4—112no—
739C22×C4—112no—
740C22×C4—228no—
741C22×C4—228no—
742C22×C4—228no—
743C22×C4—228no—
744C22×C4—228no—
745C22×C4—228no—
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×C4C2×C4×D1112yes—
783C22×C4C2×C4×D1112yes—
784C22×C4C2×C4×D1112yes—
785C22×C4#433912yes—
786C22×C4#433912yes—
787C22×C4D4×D1112yes—
788C22×C4D4×D1112yes—
789C22×C4D4×D1112yes—
790C22×C4Q8×D1112yes—
791C4⋊C4—44no—
792C4⋊C4—228no—
793C4⋊C4—228no—
794C4⋊C4—444no—
795C4⋊C4—444no—
796C4⋊C4—444no—
797C4⋊C4—444no—
798C4⋊C4—444no—
799C22⋊C4—228no—
800C22⋊C4—228no—
801C22⋊C4—228no—
802C22⋊C4—228no—
803C22⋊C4—444no—
804C22⋊C4—444no—
805C42—28no—
806C42—228no—
807C42—228no—
808C42—228no—
809C11#1387911yescharacteristic, complemented, Sylow
810C23—114no—
811C23—222no—
812C23—222no—
813C23—222no—
814C23—222no—
815C23—222no—
816C23—222no—
817C23—222no—
818C23—222no—
819C23—222no—
820C23—222no—
821C23—222no—
822C23—222no—
823C23—222no—
824C23—222no—
825C23—222no—
826C23—222no—
827C23—222no—
828C23—222no—
829C23—441no—
830C23—441no—
831C23—441no—
832C23—441no—
833C23—441no—
834C23—441no—
835C23—441no—
836C23—441no—
837C23—441no—
838C23—441no—
839C23—441no—
840C23—441no—
841C23—441no—
842C23—441no—
843C23—441no—
844C23—441no—
845C23C22×C4×D1111yescharacteristic
846C23C2×#433911yescharacteristic
847C23C2×#433911yescharacteristic
848C23C2×D4×D1111yescharacteristic
849C23C2×D4×D1111yescharacteristic
850C23C2×D4×D1111yescharacteristic
851C23#6703711yescharacteristic
852C23C2×Q8×D1111yescharacteristic
853C23#6704011yescharacteristic
854C23#41×D1111yescharacteristic
855C23#41×D1111yescharacteristic
856C23#41×D1111yescharacteristic
857C23#41×D1111yescharacteristic
858C23#6704211yescharacteristic
859C23#6704311yescharacteristic
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
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—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
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—114no—
908C2×C4—114no—
909C2×C4—114no—
910C2×C4—114no—
911C2×C4—114no—
912C2×C4—114no—
913C2×C4—114no—
914C2×C4—114no—
915C2×C4—2232no—
916C2×C4—222no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—222no—
920C2×C4—222no—
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—441no—
932C2×C4—441no—
933C2×C4—441no—
934C2×C4—441no—
935C2×C4—441no—
936C2×C4—441no—
937C2×C4—441no—
938C2×C4—441no—
939C2×C4—441no—
940C2×C4—441no—
941C2×C4—441no—
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#6692514yescomplemented
958C2×C4C4⋊C4×D1114yes—
959C22—224no—
960C22—224no—
961C22—224no—
962C22—442no—
963C22—442no—
964C22—442no—
965C22—442no—
966C22—442no—
967C22—442no—
968C22—442no—
969C22—442no—
970C22—442no—
971C22—442no—
972C22—442no—
973C22—442no—
974C22C2×#6692511yescharacteristic
975C22#1062302111yescharacteristic
976C22C2×C4⋊C4×D1111yescharacteristic
977C22#1062303811yescharacteristic
978C22D11×#11711yescharacteristic
979C22#1062306211yescharacteristic
980C22#1062306311yescharacteristic
981C22#1062307111yescharacteristic
982C22C4×D4×D1111yescharacteristic
983C22C4×D4×D1111yescharacteristic
984C22#1062307711yescharacteristic
985C22#1062307911yescharacteristic
986C22#1062307911yescharacteristic
987C22#1062308311yescharacteristic
988C22#1062308411yescharacteristic
989C22#1062309911yescharacteristic
990C22#1062310511yescharacteristic
991C22#1062310911yescharacteristic
992C22#1062310911yescharacteristic
993C22D11×#12011yescharacteristic
994C22#1062313011yescharacteristic
995C22#1062313811yescharacteristic
996C22D11×C22⋊Q811yescharacteristic
997C22D11×C22⋊Q811yescharacteristic
998C22#1062315911yescharacteristic
999C22#1062316411yescharacteristic
1000C22D11×#12311yescharacteristic
1001C22#1062318511yescharacteristic
1002C22#1062318611yescharacteristic
1003C22#1062320111yescharacteristic
1004C22#1062322011yescharacteristic
1005C22#1062322411yescharacteristic
1006C22#1062323311yescharacteristic
1007C22#1062324011yescharacteristic
1008C22#1062326011yescharacteristic
1009C4—24no—
1010C4—24no—
1011C4—42no—
1012C4—42no—
1013C4—42no—
1014C4—81no—
1015C4—81no—
1016C4—118no—
1017C4—224no—
1018C4—442no—
1019C4—442no—
1020C4—442no—
1021C4—881no—
1022C4—881no—
1023C2—444no—
1024C2#1307102011yescharacteristic
1025C2D11×#38511yescharacteristic
1026C2#1307123811yescharacteristic
1027C2#1307153911yescharacteristic
1028C2#1307154011yescharacteristic
1029C2#1307156111yescharacteristic
1030C2#1307156211yescharacteristic
1031C2#1307223311yescharacteristic
1032C2#1307224211yescharacteristic
1033C2#1307230411yescharacteristic
1034C2#1307230611yescharacteristic
1035C2#1307232611yescharacteristic
1036C2#1307232811yescharacteristic
1037C2#1307306711yescharacteristic
1038C2#1307307611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1436D11
hypocenterC11#13879
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#10622589C2semidirect
3. C2×#10622263C2semidirect
10. #13066850C2semidirect
11. #13066849C2semidirect
12. #13066847C2semidirect
13. Dic11⋊#95C2semidirect
14. Dic11⋊#95C2semidirect
15. C11×#1436C2semidirect
56. #10622279C4semidirect
272. C2×C4×D11C4⋊C4semidirect
303. #1436D11semidirect
404. C2×C4×C11#117semidirect
447. C2×Dic11#117semidirect
809. C11#13879semidirect
957. C2×C4#66925semidirect

Maximal subgroups

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

subgroupindex
C22×#669252
C2×#106225892
C2×#106222632
C2×#106222802
C2×#106222792
#130668622
#130668602
#130668582
#130668502
#130668492
#130668472
Dic11⋊#952
C11×#14362
#1387911