Finite Group Databasebeta

← #14675113

Subgroups — #14675113

Order 2816.

1826 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622553C211yesmaximal, characteristic
2C2×#10622603C211yesmaximal, characteristic
3C2×#10622602C211yesmaximal, characteristic
4C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
5#13066854C211yesmaximal, characteristic
6#13066852C211yesmaximal, characteristic
7#13066849C211yesmaximal, characteristic, complemented
8#13066848C211yesmaximal, characteristic, complemented
9#13066848C211yesmaximal, characteristic, complemented
10#13066847C211yesmaximal, characteristic, complemented
11Dic11⋊#95C211yesmaximal, characteristic, complemented
12#13066843C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic
14C4×C11⋊#95C211yesmaximal, characteristic, complemented
15C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C4×C11×C4⋊C4—24no—
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
51C2×C11⋊#95C2211yescharacteristic
52#10622603C418yescomplemented
53#10622602C418yescomplemented
54#10622553C418yescomplemented
55C4×(C2×D11)⋊C4—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—41no—
74C22×C4×D11—41no—
75C22×C4×D11—41no—
76C22×C4×D11—41no—
77C22×C4×D11C2×C414yes—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4C2×C414yes—
83C2×C11×C4⋊C4C2×C414yescomplemented
84C2×C42×C11—22no—
85C2×C42×C11—22no—
86C2×C42×C11—22no—
87C2×C42×C11—41no—
88C2×C42×C11—41no—
89C2×C42×C11—41no—
90C2×C42×C11—41no—
91C2×C42×C11C2×C414yescomplemented
92C2×C42×C11D414yes—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
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)⋊C4C2×C414yes—
104C2×(C2×D11)⋊C4C2×C414yes—
105C2×(C2×D11)⋊C4C2×C414yes—
106C2×(C2×D11)⋊C4C2×C414yes—
107C2×(C2×D11)⋊C4C2×C414yes—
108C2×(C2×D11)⋊C4C2×C414yes—
109C2×(C2×D11)⋊C4C2×C414yes—
110C2×(C2×D11)⋊C4C2×C414yes—
111C2×Dic11⋊C4—41no—
112C2×Dic11⋊C4—41no—
113C2×Dic11⋊C4—41no—
114C2×Dic11⋊C4—41no—
115C2×Dic11⋊C4C2×C414yes—
116C2×Dic11⋊C4C2×C414yescomplemented
117C2×C4×Dic11—22no—
118C2×C4×Dic11—22no—
119C2×C4×Dic11—41no—
120C2×C4×Dic11—41no—
121C2×C4×Dic11—41no—
122C2×C4×Dic11—41no—
123C2×C4×Dic11—41no—
124C2×C4×Dic11—41no—
125C2×C4×Dic11C2×C414yescomplemented
126C11×#95—22no—
127C11×#95—22no—
128C11⋊#95—22no—
129C11⋊#95—22no—
130C11⋊#95—22no—
131C11⋊#95—22no—
132C11⋊#95—41no—
133C11⋊#95—41no—
134C11⋊#95—41no—
135C11⋊#95—41no—
136C11⋊#95—41no—
137C11⋊#95—41no—
138C11⋊#95C2×C414yes—
139C11⋊#95C2×C414yes—
140C11⋊#95C2×C414yescomplemented
141C11⋊#95C2×C414yescomplemented
142C11⋊#95C2×C414yescomplemented
143C11⋊#95C2×C414yescomplemented
144#13789—111nomaximal, Sylow
145C24×C11C2411yescharacteristic
146C23×D11—21no—
147C23×D11—21no—
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×D11C22×C412yes—
159C23×D11C22×C412yes—
160C23×D11C22×C412yes—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
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×C11C22×C412yes—
196C22×C4×C11C22×C412yes—
197C22×C4×C11C22×C412yes—
198C22×C4×C11C22×C412yes—
199C22×C4×C11C22×C412yes—
200C22×C4×C11C22×C412yes—
201C22×C4×C11C22×C412yes—
202C22×C4×C11C22×C412yes—
203C22×C4×C11C22×C412yes—
204C22×C4×C11C2×D412yes—
205C22×C4×C11C2×D412yes—
206C22×C4×C11C2×D412yes—
207C22×C4×C11#4112yes—
208C22×C4×C11#4112yes—
209C22×C4×C11#4112yes—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
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×Dic11C22×C412yes—
251C22×Dic11C22×C412yes—
252C22×Dic11C22×C412yes—
253C22×Dic11C22×C412yes—
254C22×Dic11C22×C412yes—
255C22×Dic11C22×C412yes—
256C22×Dic11C22×C412yes—
257C22×Dic11C22×C412yes—
258C22×Dic11C22×C412yes—
259C2×C4×D11—28no—
260C2×C4×D11—44no—
261C2×C4×D11—44no—
262C2×C4×D11—44no—
263C2×C4×D11—44no—
264C2×C4×D11—44no—
265C2×C4×D11—44no—
266C11×C4⋊C4—28no—
267C11×C4⋊C4—28no—
268C42×C11—28no—
269C42×C11—44no—
270C42×C11—44no—
271(C2×D11)⋊C4—28no—
272(C2×D11)⋊C4—28no—
273(C2×D11)⋊C4—44no—
274(C2×D11)⋊C4—44no—
275(C2×D11)⋊C4—44no—
276(C2×D11)⋊C4C42116yescomplemented
277Dic11⋊C4—44no—
278Dic11⋊C4—44no—
279C4×Dic11—44no—
280C4×Dic11—44no—
281C4×Dic11—44no—
282C2×#388—111no—
283C2×#388—111no—
284C2×#385—111no—
285C2×C4×C4⋊C4D1111yescharacteristic, complemented
286C2×C4×C22⋊C4—111no—
287#1437—111no—
288#1437—111no—
289#1436—111no—
290#1436—111no—
291#1436—111no—
292#1436—111no—
293C4⋊#95—111no—
294#1434—111no—
295C22⋊#95—111no—
296C4×#95—111no—
297C23×C11C23×C411yescharacteristic
298C23×C11C23×C411yescharacteristic
299C23×C11C23×C411yescharacteristic
300C23×C11C22×D411yescharacteristic
301C23×C11C2×#4111yescharacteristic
302C23×C11C2×#4111yescharacteristic
303C23×C11C2×#4111yescharacteristic
304C23×C11H(5,𝔽2)11yescharacteristic
305C23×C11H(5,𝔽2)11yescharacteristic
306C23×C11H(5,𝔽2)11yescharacteristic
307C23×C11H(5,𝔽2)11yescharacteristic
308C23×C11H(5,𝔽2)11yescharacteristic
309C23×C112−1+411yescharacteristic
310C23×C112−1+411yescharacteristic
311C23×C112−1+411yescharacteristic
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
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—41no—
331C22×D11—41no—
332C22×D11—41no—
333C22×D11—41no—
334C22×D11—41no—
335C22×D11—41no—
336C22×D11—41no—
337C22×D11—41no—
338C22×D11—41no—
339C22×D11—41no—
340C22×D11—41no—
341C22×D11—41no—
342C22×D11—41no—
343C22×D11—41no—
344C22×D11—41no—
345C22×D11—41no—
346C22×D11C2×C4214yes—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
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—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
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×C11C2×C4214yes—
393C2×C4×C11C4×D414yes—
394C2×C4×C11C4×D414yes—
395C2×C4×C11C4×D414yes—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—22no—
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×Dic11C2×C4214yes—
445C4×D11—416no—
446C24×C4—111no—
447C22×C4⋊C4—111no—
448C22×C4⋊C4—111no—
449C22×C4⋊C4C2×D1111yescharacteristic
450C22×C4⋊C4C2×D1111yescharacteristic
451C22×C22⋊C4—111no—
452C22×C22⋊C4—111no—
453C22×C22⋊C4—111no—
454C22×C22⋊C4—111no—
455C22×C22⋊C4—111no—
456C22×C22⋊C4—111no—
457C22×C42—111no—
458C22×C42—111no—
459C22×C42—111no—
460C22×C42C2×D1111yescharacteristic
461C22×C42C2×D1111yescharacteristic
462C22×C42C2×D1111yescharacteristic
463#388—118no—
464#388—118no—
465#385—118no—
466C4×C4⋊C4—24no—
467C4×C22⋊C4—224no—
468C2×#95—111no—
469C2×#95—111no—
470C2×#95—111no—
471C2×#95—111no—
472C2×#95—111no—
473C2×#95—111no—
474C2×#95—111no—
475C2×#95—111no—
476C2×#95—111no—
477C2×#95—111no—
478C2×#95—111no—
479C2×#95—111no—
480C2×#95—111no—
481C2×#95—111no—
482C2×#95—111no—
483C2×#95—111no—
484C2×#95C2×D1111yescharacteristic
485C2×#95C2×D1111yescharacteristic
486C22×C11C22×C4211yescharacteristic
487C22×C11C2×C4×D411yescharacteristic
488C22×C11C2×C4×D411yescharacteristic
489C22×C11C2×C4×D411yescharacteristic
490C22×C11C4×#4111yescharacteristic
491C22×C11C4×#4111yescharacteristic
492C22×C11C4×#4111yescharacteristic
493C22×C11#51811yescharacteristic
494C22×C11#51811yescharacteristic
495C22×C11#51811yescharacteristic
496C22×C11#51811yescharacteristic
497C22×C11#51911yescharacteristic
498C22×C11#52011yescharacteristic
499C22×C11#52011yescharacteristic
500C22×C11#52011yescharacteristic
501C22×C11#52011yescharacteristic
502C22×C11#52011yescharacteristic
503C22×C11#52011yescharacteristic
504C22×C11#52011yescharacteristic
505C22×C11#53411yescharacteristic
506C22×C11#53511yescharacteristic
507C22×C11#53611yescharacteristic
508C22×C11#53711yescharacteristic
509C22×C11#53811yescharacteristic
510C22×C11#53811yescharacteristic
511C22×C11#53811yescharacteristic
512C22×C11#53911yescharacteristic
513C22×C11#53911yescharacteristic
514C22×C11#53911yescharacteristic
515C22×C11#54011yescharacteristic
516C22×C11#54111yescharacteristic
517C22×C11#54211yescharacteristic
518C22×C11#54211yescharacteristic
519C22×C11#54211yescharacteristic
520C22×C11#54211yescharacteristic
521C2×D11—24no—
522C2×D11—24no—
523C2×D11—24no—
524C2×D11—42no—
525C2×D11—42no—
526C2×D11—42no—
527C2×D11—42no—
528C2×D11—42no—
529C2×D11—42no—
530C2×D11—42no—
531C2×D11—42no—
532C2×D11—42no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C4×C11—24no—
537C4×C11—24no—
538C4×C11—24no—
539C4×C11—24no—
540C4×C11—42no—
541C4×C11—42no—
542C4×C11—42no—
543Dic11—24no—
544Dic11—42no—
545Dic11—42no—
546Dic11—42no—
547Dic11—42no—
548Dic11—42no—
549Dic11—42no—
550C25—111no—
551C23×C4—111no—
552C23×C4—111no—
553C23×C4—111no—
554C23×C4—111no—
555C23×C4—111no—
556C23×C4—111no—
557C23×C4—111no—
558C23×C4—114no—
559C23×C4—222no—
560C23×C4—222no—
561C23×C4—441no—
562C23×C4—441no—
563C23×C4—441no—
564C23×C4—441no—
565C23×C4C22×D1111yescharacteristic
566C23×C4C22×D1111yescharacteristic
567C23×C4C22×D1111yescharacteristic
568C23×C4C22×D1111yescharacteristic
569C23×C4C22×D1111yescharacteristic
570C23×C4C22×D1111yescharacteristic
571C23×C4C22×D1111yescharacteristic
572C2×C4⋊C4—22no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—114no—
577C2×C4⋊C4—114no—
578C2×C4⋊C4—441no—
579C2×C4⋊C4—441no—
580C2×C4⋊C4—441no—
581C2×C4⋊C4—441no—
582C2×C4⋊C4C4×D1114yes—
583C2×C4⋊C4C4×D1114yescomplemented
584C2×C22⋊C4—114no—
585C2×C22⋊C4—114no—
586C2×C22⋊C4—114no—
587C2×C22⋊C4—114no—
588C2×C22⋊C4—114no—
589C2×C22⋊C4—114no—
590C2×C22⋊C4—114no—
591C2×C22⋊C4—114no—
592C2×C22⋊C4—222no—
593C2×C22⋊C4—222no—
594C2×C22⋊C4—222no—
595C2×C22⋊C4—222no—
596C2×C22⋊C4—441no—
597C2×C22⋊C4—441no—
598C2×C22⋊C4—441no—
599C2×C22⋊C4—441no—
600C2×C22⋊C4—441no—
601C2×C22⋊C4—441no—
602C2×C42—22no—
603C2×C42—22no—
604C2×C42—22no—
605C2×C42—41no—
606C2×C42—41no—
607C2×C42—41no—
608C2×C42—41no—
609C2×C42—114no—
610C2×C42—222no—
611C2×C42—222no—
612C2×C42—441no—
613C2×C42—441no—
614C2×C42—441no—
615C2×C42—441no—
616C2×C42—441no—
617C2×C42—441no—
618C2×C42C4×D1114yescomplemented
619C2×C42C22⋊D1114yes—
620#95—22no—
621#95—22no—
622#95—114no—
623#95—114no—
624#95—114no—
625#95—114no—
626#95—114no—
627#95—114no—
628#95—222no—
629#95—222no—
630#95—222no—
631#95—222no—
632#95—441no—
633#95—441no—
634#95—441no—
635#95—441no—
636#95—441no—
637#95—441no—
638C2×C11C42×D411yescharacteristic
639C2×C11#227411yescharacteristic
640C2×C11#227511yescharacteristic
641C2×C11#232111yescharacteristic
642C2×C11#232211yescharacteristic
643C2×C11#232311yescharacteristic
644C2×C11#232411yescharacteristic
645C2×C11#232511yescharacteristic
646C2×C11#232611yescharacteristic
647C2×C11#233211yescharacteristic
648C2×C11#233411yescharacteristic
649C2×C11#233411yescharacteristic
650C2×C11#233511yescharacteristic
651C2×C11#233511yescharacteristic
652C2×C11#233711yescharacteristic
653D11—44no—
654C24—112no—
655C24—112no—
656C24—112no—
657C24—221no—
658C24—221no—
659C24—221no—
660C24—221no—
661C24—221no—
662C24—221no—
663C24—221no—
664C24—221no—
665C24—221no—
666C24—221no—
667C24—221no—
668C24—221no—
669C24C23×D1111yescharacteristic
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
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—112no—
705C22×C4—112no—
706C22×C4—112no—
707C22×C4—112no—
708C22×C4—112no—
709C22×C4—112no—
710C22×C4—112no—
711C22×C4—112no—
712C22×C4—112no—
713C22×C4—221no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—221no—
726C22×C4—221no—
727C22×C4—221no—
728C22×C4—221no—
729C22×C4—221no—
730C22×C4—221no—
731C22×C4—221no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4—221no—
735C22×C4—221no—
736C22×C4—221no—
737C22×C4—221no—
738C22×C4—221no—
739C22×C4—221no—
740C22×C4—221no—
741C22×C4—221no—
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—228no—
754C22×C4—444no—
755C22×C4—444no—
756C22×C4—444no—
757C22×C4—444no—
758C22×C4—444no—
759C22×C4—444no—
760C22×C4C2×C4×D1112yes—
761C22×C4C2×C4×D1112yes—
762C22×C4C2×C4×D1112yes—
763C22×C4C2×C4×D1112yes—
764C22×C4C2×C4×D1112yes—
765C22×C4C2×C4×D1112yes—
766C22×C4C2×C4×D1112yes—
767C22×C4C2×C4×D1112yes—
768C22×C4C2×C4×D1112yes—
769C22×C4#433912yes—
770C22×C4#433912yes—
771C22×C4#433912yes—
772C22×C4C2×C22⋊D1112yes—
773C22×C4C2×C22⋊D1112yes—
774C22×C4C2×C22⋊D1112yes—
775C4⋊C4—28no—
776C4⋊C4—28no—
777C4⋊C4—444no—
778C4⋊C4—444no—
779C22⋊C4—1116no—
780C22⋊C4—228no—
781C22⋊C4—228no—
782C22⋊C4—444no—
783C22⋊C4—444no—
784C22⋊C4—444no—
785C42—28no—
786C42—44no—
787C42—44no—
788C42—444no—
789C42—444no—
790C42—444no—
791C11#1378911yescharacteristic, complemented, Sylow
792C23—114no—
793C23—222no—
794C23—222no—
795C23—222no—
796C23—222no—
797C23—222no—
798C23—222no—
799C23—222no—
800C23—222no—
801C23—222no—
802C23—222no—
803C23—222no—
804C23—222no—
805C23—222no—
806C23—222no—
807C23—222no—
808C23—222no—
809C23—222no—
810C23—222no—
811C23—441no—
812C23—441no—
813C23—441no—
814C23—441no—
815C23—441no—
816C23—441no—
817C23—441no—
818C23—441no—
819C23—441no—
820C23—441no—
821C23—441no—
822C23—441no—
823C23—441no—
824C23—441no—
825C23—441no—
826C23—441no—
827C23C22×C4×D1111yescharacteristic
828C23C22×C4×D1111yescharacteristic
829C23C22×C4×D1111yescharacteristic
830C23C2×#433911yescharacteristic
831C23C2×#433911yescharacteristic
832C23C2×#433911yescharacteristic
833C23#6703711yescharacteristic
834C23#6703711yescharacteristic
835C23#6704011yescharacteristic
836C23#6704011yescharacteristic
837C23#6704211yescharacteristic
838C23#6704211yescharacteristic
839C23#6704211yescharacteristic
840C23#6704311yescharacteristic
841C23C22×C22⋊D1111yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
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—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—114no—
888C2×C4—222no—
889C2×C4—222no—
890C2×C4—222no—
891C2×C4—222no—
892C2×C4—222no—
893C2×C4—222no—
894C2×C4—222no—
895C2×C4—222no—
896C2×C4—222no—
897C2×C4—222no—
898C2×C4—222no—
899C2×C4—222no—
900C2×C4—222no—
901C2×C4—222no—
902C2×C4—222no—
903C2×C4—222no—
904C2×C4—222no—
905C2×C4—222no—
906C2×C4—222no—
907C2×C4—222no—
908C2×C4—222no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—222no—
912C2×C4—4416no—
913C2×C4—441no—
914C2×C4—441no—
915C2×C4—441no—
916C2×C4—441no—
917C2×C4—441no—
918C2×C4—441no—
919C2×C4—441no—
920C2×C4—441no—
921C2×C4—441no—
922C2×C4—441no—
923C2×C4—441no—
924C2×C4—441no—
925C2×C4—441no—
926C2×C4—441no—
927C2×C4—441no—
928C2×C4—441no—
929C2×C4—441no—
930C2×C4—441no—
931C2×C4—441no—
932C2×C4—441no—
933C2×C4—441no—
934C2×C4—441no—
935C2×C4—441no—
936C2×C4—441no—
937C2×C4C42×D1114yes—
938C2×C4C4×C22⋊D1114yes—
939C2×C4C4×C22⋊D1114yes—
940C2×C4C4×C22⋊D1114yes—
941C22—224no—
942C22—224no—
943C22—224no—
944C22—442no—
945C22—442no—
946C22—442no—
947C22—442no—
948C22—442no—
949C22—442no—
950C22—442no—
951C22—442no—
952C22—442no—
953C22—442no—
954C22—442no—
955C22—442no—
956C22C2×C42×D1111yescharacteristic
957C22C4×#433911yescharacteristic
958C22C4×#433911yescharacteristic
959C22C4×#433911yescharacteristic
960C22#1062303511yescharacteristic
961C22#1062303511yescharacteristic
962C22#1062304611yescharacteristic
963C22#1062304611yescharacteristic
964C22#1062305211yescharacteristic
965C22#1062305411yescharacteristic
966C22#1062306511yescharacteristic
967C22#1062306611yescharacteristic
968C22#1062307611yescharacteristic
969C22#1062307611yescharacteristic
970C22#1062307611yescharacteristic
971C22#1062307711yescharacteristic
972C22#1062309111yescharacteristic
973C22#1062309111yescharacteristic
974C22#1062309111yescharacteristic
975C22#1062309511yescharacteristic
976C22#1062310311yescharacteristic
977C22#1062310511yescharacteristic
978C22#1062310511yescharacteristic
979C22#1062310511yescharacteristic
980C22#1062311311yescharacteristic
981C22#1062311311yescharacteristic
982C22#1062311311yescharacteristic
983C22#1062311411yescharacteristic
984C22C2×C4×C22⋊D1111yescharacteristic
985C22C2×C4×C22⋊D1111yescharacteristic
986C22C2×C4×C22⋊D1111yescharacteristic
987C22#1062333511yescharacteristic
988C22#1062334711yescharacteristic
989C22#1062336111yescharacteristic
990C22#1062336411yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—24no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—224no—
999C4—442no—
1000C4—442no—
1001C4—442no—
1002C4—442no—
1003C4—442no—
1004C4—442no—
1005C2—444no—
1006C2C42×C22⋊D1111yescharacteristic
1007C2#1307097011yescharacteristic
1008C2#1307097611yescharacteristic
1009C2#1307127011yescharacteristic
1010C2#1307128511yescharacteristic
1011C2#1307129211yescharacteristic
1012C2#1307130911yescharacteristic
1013C2#1307131411yescharacteristic
1014C2#1307132311yescharacteristic
1015C2#1307136711yescharacteristic
1016C2#1307138511yescharacteristic
1017C2#1307139111yescharacteristic
1018C2#1307140011yescharacteristic
1019C2#1307140011yescharacteristic
1020C2#1307142911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC2×C4×C11×C4⋊C4C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×C4×C4⋊C4D11
hypocenterC11#13789
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
7. #13066849C2semidirect
8. #13066848C2semidirect
9. #13066848C2semidirect
10. #13066847C2semidirect
11. Dic11⋊#95C2semidirect
12. #13066843C2semidirect
14. C4×C11⋊#95C2semidirect
15. C2×C4×C11×C4⋊C4C2semidirect
52. #10622603C4semidirect
53. #10622602C4semidirect
54. #10622553C4semidirect
83. C2×C11×C4⋊C4C2×C4semidirect
91. C2×C42×C11C2×C4semidirect
116. C2×Dic11⋊C4C2×C4semidirect
125. C2×C4×Dic11C2×C4semidirect
140. C11⋊#95C2×C4semidirect
141. C11⋊#95C2×C4semidirect
142. C11⋊#95C2×C4semidirect
143. C11⋊#95C2×C4semidirect
276. (C2×D11)⋊C4C42semidirect
285. C2×C4×C4⋊C4D11semidirect
583. C2×C4⋊C4C4×D11semidirect
618. C2×C42C4×D11semidirect
791. C11#13789semidirect

Maximal subgroups

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

subgroupindex
C2×#106225532
C2×#106226032
C2×#106226022
C2×C4×(C2×D11)⋊C42
#130668542
#130668522
#130668492
#130668482
#130668472
Dic11⋊#952
#130668432
(C2×D11)⋊#952
C4×C11⋊#952
C2×C4×C11×C4⋊C42
#1378911