Finite Group Databasebeta

← #14675369

Subgroups — #14675369

Order 2816.

2022 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622283C211yesmaximal, characteristic
2C2×#10622553C211yesmaximal, characteristic
3C2×#10622281C211yesmaximal, characteristic
4C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
5C2×#10622262C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
7C2×#10622279C211yesmaximal, characteristic
8#13066854C211yesmaximal, characteristic
9#13066852C211yesmaximal, characteristic
10#13066851C211yesmaximal, characteristic, complemented
11#13066850C211yesmaximal, characteristic, complemented
12#13066850C211yesmaximal, characteristic, complemented
13#13066849C211yesmaximal, characteristic, complemented
14C4×C11⋊#95C211yesmaximal, characteristic, complemented
15C4×C11×#95C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
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#10622553C418yescomplemented
52C4×(C2×D11)⋊C4—24no—
53C4×C4⋊Dic11—24no—
54#10622283C418yescomplemented
55#10622281C418yescomplemented
56#10622279—24no—
57#10622262—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×D11—41no—
78C22×C4×D11—41no—
79C22×C4×D11C2×C414yes—
80C2×C42×C11—22no—
81C2×C42×C11—22no—
82C2×C42×C11—22no—
83C2×C42×C11—22no—
84C2×C42×C11—22no—
85C2×C42×C11—22no—
86C2×C42×C11—41no—
87C2×C42×C11—41no—
88C2×C42×C11C2×C414yescomplemented
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—41no—
98C2×(C2×D11)⋊C4—41no—
99C2×(C2×D11)⋊C4C2×C414yes—
100C2×(C2×D11)⋊C4C2×C414yes—
101C2×(C2×D11)⋊C4C2×C414yes—
102C2×(C2×D11)⋊C4C2×C414yes—
103C2×(C2×D11)⋊C4C2×C414yes—
104C2×(C2×D11)⋊C4C2×C414yes—
105C2×(C2×D11)⋊C4C2×C414yes—
106C2×(C2×D11)⋊C4C2×C414yes—
107C2×C4⋊Dic11—22no—
108C2×C4⋊Dic11—22no—
109C2×C4⋊Dic11—22no—
110C2×C4⋊Dic11—22no—
111C2×C4⋊Dic11C2×C414yes—
112C2×C4⋊Dic11C2×C414yescomplemented
113C2×Dic11⋊C4—22no—
114C2×Dic11⋊C4—22no—
115C2×Dic11⋊C4—22no—
116C2×Dic11⋊C4—22no—
117C2×Dic11⋊C4C2×C414yes—
118C2×Dic11⋊C4C2×C414yescomplemented
119C2×C4×Dic11—22no—
120C2×C4×Dic11—22no—
121C2×C4×Dic11—22no—
122C2×C4×Dic11—22no—
123C2×C4×Dic11—22no—
124C2×C4×Dic11—22no—
125C2×C4×Dic11—22no—
126C2×C4×Dic11—22no—
127C2×C4×Dic11—22no—
128C2×C4×Dic11—22no—
129C2×C4×Dic11—41no—
130C2×C4×Dic11—41no—
131C2×C4×Dic11—41no—
132C2×C4×Dic11—41no—
133C2×C4×Dic11C2×C414yescomplemented
134C11×#95—22no—
135C11×#95C2×C414yes—
136C11×#95C2×C414yescomplemented
137C11×#95D414yes—
138C11⋊#95—22no—
139C11⋊#95—22no—
140C11⋊#95—22no—
141C11⋊#95—22no—
142C11⋊#95—22no—
143C11⋊#95—41no—
144C11⋊#95—41no—
145C11⋊#95C2×C414yes—
146C11⋊#95C2×C414yescomplemented
147C11⋊#95C2×C414yescomplemented
148C11⋊#95C2×C414yescomplemented
149C11⋊#95D414yes—
150#13823—111nomaximal, Sylow
151C24×C11C2411yescharacteristic
152C23×D11—21no—
153C23×D11—21no—
154C23×D11—21no—
155C23×D11—21no—
156C23×D11—21no—
157C23×D11—21no—
158C23×D11—21no—
159C23×D11—21no—
160C23×D11—21no—
161C23×D11—21no—
162C23×D11—21no—
163C23×D11—21no—
164C23×D11C22×C412yes—
165C23×D11C22×C412yes—
166C23×D11C22×C412yes—
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×C11C22×C412yes—
200C22×C4×C11C22×C412yes—
201C22×C4×C11C22×C412yes—
202C22×C4×C11C22×C412yes—
203C22×C4×C11C22×C412yes—
204C22×C4×C11C22×C412yes—
205C22×C4×C11C22×C412yes—
206C22×C4×C11C22×C412yes—
207C22×C4×C11C22×C412yes—
208C22×C4×C11C2×D412yes—
209C22×C4×C11C2×D412yes—
210C22×C4×C11C2×D412yes—
211C22×C4×C11C2×D412yes—
212C22×C4×C11#4112yes—
213C22×C4×C11#4112yes—
214C22×C4×C11#4112yes—
215C22×C4×C11#4112yes—
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×Dic11C22×C412yes—
253C22×Dic11C22×C412yes—
254C22×Dic11C22×C412yes—
255C22×Dic11C22×C412yes—
256C22×Dic11C22×C412yes—
257C22×Dic11C22×C412yes—
258C22×Dic11C22×C412yes—
259C22×Dic11C22×C412yes—
260C22×Dic11C22×C412yes—
261C22×Dic11C2×D412yes—
262C22×Dic11C2×D412yes—
263C22×Dic11#4112yes—
264C22×Dic11#4112yes—
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—
272C42×C11—28no—
273C42×C11—44no—
274C42×C11—44no—
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)⋊C4C42116yescomplemented
281C4⋊Dic11—28no—
282C4⋊Dic11—28no—
283Dic11⋊C4—28no—
284Dic11⋊C4—28no—
285C4×Dic11—28no—
286C4×Dic11—44no—
287C4×Dic11—44no—
288C4×Dic11—44no—
289C4×Dic11—44no—
290C2×#388—111no—
291C2×#388—111no—
292C2×#385—111no—
293C2×C4×C4⋊C4—111no—
294C2×C4×C4⋊C4—111no—
295C2×C4×C22⋊C4—111no—
296C2×C4×C22⋊C4—111no—
297#1437—111no—
298#1437—111no—
299#1436—111no—
300#1436—111no—
301#1436—111no—
302#1436—111no—
303C4×#95—111no—
304C4×#95D1111yescharacteristic, complemented
305C23×C11C23×C411yescharacteristic
306C23×C11C23×C411yescharacteristic
307C23×C11C23×C411yescharacteristic
308C23×C11C22×D411yescharacteristic
309C23×C11C22×D411yescharacteristic
310C23×C11C2×#4111yescharacteristic
311C23×C11C2×#4111yescharacteristic
312C23×C11C2×#4111yescharacteristic
313C23×C11C2×#4111yescharacteristic
314C23×C11C2×#4111yescharacteristic
315C23×C11C2×#4111yescharacteristic
316C23×C11H(5,𝔽2)11yescharacteristic
317C23×C11H(5,𝔽2)11yescharacteristic
318C23×C112−1+411yescharacteristic
319C23×C112−1+411yescharacteristic
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—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
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×D11—41no—
347C22×D11—41no—
348C22×D11—41no—
349C22×D11—41no—
350C22×D11—41no—
351C22×D11—41no—
352C22×D11—41no—
353C22×D11—41no—
354C22×D11C2×C4214yes—
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—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
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×C11C2×C4214yes—
400C2×C4×C11C4×D414yes—
401C2×C4×C11C4×D414yes—
402C2×C4×C11C4×D414yes—
403C2×C4×C11C4×D414yes—
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—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×Dic11C2×C4214yes—
451C2×Dic11C4×D414yes—
452C2×Dic11C4×D414yes—
453C4×D11—416no—
454C24×C4—111no—
455C22×C4⋊C4—111no—
456C22×C4⋊C4—111no—
457C22×C4⋊C4—111no—
458C22×C4⋊C4—111no—
459C22×C22⋊C4—111no—
460C22×C22⋊C4—111no—
461C22×C22⋊C4—111no—
462C22×C22⋊C4—111no—
463C22×C22⋊C4—111no—
464C22×C22⋊C4—111no—
465C22×C42—111no—
466C22×C42—111no—
467C22×C42—111no—
468C22×C42—111no—
469C22×C42—111no—
470C22×C42C2×D1111yescharacteristic
471C22×C42C2×D1111yescharacteristic
472C22×C42C2×D1111yescharacteristic
473#388—118no—
474#388—118no—
475#385—118no—
476C4×C4⋊C4—224no—
477C4×C4⋊C4—224no—
478C4×C22⋊C4—224no—
479C4×C22⋊C4—224no—
480C2×#95—111no—
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
496C22×C11C22×C4211yescharacteristic
497C22×C11C2×C4×D411yescharacteristic
498C22×C11C2×C4×D411yescharacteristic
499C22×C11C2×C4×D411yescharacteristic
500C22×C11C2×C4×D411yescharacteristic
501C22×C11C2×C4×D411yescharacteristic
502C22×C11C2×C4×D411yescharacteristic
503C22×C11C4×#4111yescharacteristic
504C22×C11C4×#4111yescharacteristic
505C22×C11C4×#4111yescharacteristic
506C22×C11C4×#4111yescharacteristic
507C22×C11C4×#4111yescharacteristic
508C22×C11C4×#4111yescharacteristic
509C22×C11#51811yescharacteristic
510C22×C11#51911yescharacteristic
511C22×C11#52011yescharacteristic
512C22×C11#52011yescharacteristic
513C22×C11#52011yescharacteristic
514C22×C11#52011yescharacteristic
515C22×C11D4211yescharacteristic
516C22×C11#54611yescharacteristic
517C22×C11#54611yescharacteristic
518C22×C11#54711yescharacteristic
519C22×C11#54711yescharacteristic
520C22×C11#54811yescharacteristic
521C22×C11#54811yescharacteristic
522C22×C11#55111yescharacteristic
523C22×C11#55111yescharacteristic
524C22×C11#55211yescharacteristic
525C22×C11#55211yescharacteristic
526C22×C11#55311yescharacteristic
527C22×C11#55311yescharacteristic
528C22×C11#55611yescharacteristic
529C22×C11#55611yescharacteristic
530C22×C11#55911yescharacteristic
531C2×D11—24no—
532C2×D11—24no—
533C2×D11—24no—
534C2×D11—42no—
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—
546C4×C11—24no—
547C4×C11—24no—
548C4×C11—24no—
549C4×C11—24no—
550C4×C11—24no—
551C4×C11—42no—
552C4×C11—42no—
553Dic11—24no—
554Dic11—24no—
555Dic11—24no—
556Dic11—42no—
557Dic11—42no—
558Dic11—42no—
559Dic11—42no—
560C25—111no—
561C23×C4—111no—
562C23×C4—111no—
563C23×C4—111no—
564C23×C4—111no—
565C23×C4—111no—
566C23×C4—111no—
567C23×C4—111no—
568C23×C4—114no—
569C23×C4—222no—
570C23×C4—222no—
571C23×C4—222no—
572C23×C4—222no—
573C23×C4—441no—
574C23×C4—441no—
575C23×C4C22×D1111yescharacteristic
576C23×C4C22×D1111yescharacteristic
577C23×C4C22×D1111yescharacteristic
578C23×C4C22×D1111yescharacteristic
579C23×C4C22×D1111yescharacteristic
580C23×C4C22×D1111yescharacteristic
581C23×C4C22×D1111yescharacteristic
582C2×C4⋊C4—114no—
583C2×C4⋊C4—114no—
584C2×C4⋊C4—114no—
585C2×C4⋊C4—114no—
586C2×C4⋊C4—222no—
587C2×C4⋊C4—222no—
588C2×C4⋊C4—222no—
589C2×C4⋊C4—222no—
590C2×C4⋊C4—222no—
591C2×C4⋊C4—222no—
592C2×C4⋊C4—222no—
593C2×C4⋊C4—222no—
594C2×C22⋊C4—114no—
595C2×C22⋊C4—114no—
596C2×C22⋊C4—114no—
597C2×C22⋊C4—114no—
598C2×C22⋊C4—114no—
599C2×C22⋊C4—114no—
600C2×C22⋊C4—114no—
601C2×C22⋊C4—114no—
602C2×C22⋊C4—222no—
603C2×C22⋊C4—222no—
604C2×C22⋊C4—222no—
605C2×C22⋊C4—222no—
606C2×C22⋊C4—222no—
607C2×C22⋊C4—222no—
608C2×C22⋊C4—222no—
609C2×C22⋊C4—222no—
610C2×C22⋊C4—441no—
611C2×C22⋊C4—441no—
612C2×C42—22no—
613C2×C42—22no—
614C2×C42—22no—
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—22no—
618C2×C42—41no—
619C2×C42—41no—
620C2×C42—114no—
621C2×C42—222no—
622C2×C42—222no—
623C2×C42—222no—
624C2×C42—222no—
625C2×C42—222no—
626C2×C42—222no—
627C2×C42—222no—
628C2×C42—222no—
629C2×C42—222no—
630C2×C42—222no—
631C2×C42—441no—
632C2×C42—441no—
633C2×C42—441no—
634C2×C42—441no—
635C2×C42C4×D1114yescomplemented
636#95—22no—
637#95—114no—
638#95—114no—
639#95—114no—
640#95—114no—
641#95—114no—
642#95—222no—
643#95—222no—
644#95—222no—
645#95—222no—
646#95—222no—
647#95—441no—
648#95—441no—
649#95C4×D1114yes—
650#95C4×D1114yescomplemented
651#95D4414yes—
652C2×C11C42×D411yescharacteristic
653C2×C11C42×D411yescharacteristic
654C2×C11#227411yescharacteristic
655C2×C11#235811yescharacteristic
656C2×C11#235911yescharacteristic
657C2×C11#235911yescharacteristic
658C2×C11#236111yescharacteristic
659C2×C11#236111yescharacteristic
660C2×C11#236211yescharacteristic
661C2×C11#236211yescharacteristic
662C2×C11#236711yescharacteristic
663C2×C11#236711yescharacteristic
664C2×C11#237311yescharacteristic
665C2×C11#237311yescharacteristic
666C2×C11#237411yescharacteristic
667D11—44no—
668C24—112no—
669C24—112no—
670C24—112no—
671C24—221no—
672C24—221no—
673C24—221no—
674C24—221no—
675C24—221no—
676C24—221no—
677C24—221no—
678C24—221no—
679C24—221no—
680C24—221no—
681C24—221no—
682C24—221no—
683C24C23×D1111yescharacteristic
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—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—112no—
717C22×C4—112no—
718C22×C4—112no—
719C22×C4—112no—
720C22×C4—112no—
721C22×C4—112no—
722C22×C4—112no—
723C22×C4—112no—
724C22×C4—112no—
725C22×C4—112no—
726C22×C4—112no—
727C22×C4—112no—
728C22×C4—112no—
729C22×C4—228no—
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—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—228no—
767C22×C4—444no—
768C22×C4—444no—
769C22×C4—444no—
770C22×C4—444no—
771C22×C4—444no—
772C22×C4C2×C4×D1112yes—
773C22×C4C2×C4×D1112yes—
774C22×C4C2×C4×D1112yes—
775C22×C4C2×C4×D1112yes—
776C22×C4C2×C4×D1112yes—
777C22×C4C2×C4×D1112yes—
778C22×C4C2×C4×D1112yes—
779C22×C4C2×C4×D1112yes—
780C22×C4C2×C4×D1112yes—
781C22×C4C2×D4412yes—
782C22×C4C2×D4412yes—
783C22×C4C2×D4412yes—
784C22×C4#433912yes—
785C22×C4#433912yes—
786C22×C4#433912yes—
787C22×C4D4×D1112yes—
788C22×C4#434112yes—
789C4⋊C4—228no—
790C4⋊C4—228no—
791C4⋊C4—228no—
792C4⋊C4—228no—
793C22⋊C4—1116no—
794C22⋊C4—228no—
795C22⋊C4—228no—
796C22⋊C4—228no—
797C22⋊C4—228no—
798C22⋊C4—444no—
799C42—28no—
800C42—44no—
801C42—44no—
802C42—228no—
803C42—444no—
804C42—444no—
805C42—444no—
806C42—444no—
807C11#1382311yescharacteristic, complemented, Sylow
808C23—114no—
809C23—222no—
810C23—222no—
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—441no—
828C23—441no—
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—
843C23C22×C4×D1111yescharacteristic
844C23C22×C4×D1111yescharacteristic
845C23C22×C4×D1111yescharacteristic
846C23C22×D4411yescharacteristic
847C23C2×#433911yescharacteristic
848C23C2×#433911yescharacteristic
849C23C2×#433911yescharacteristic
850C23C2×D4×D1111yescharacteristic
851C23C2×#434111yescharacteristic
852C23#6703711yescharacteristic
853C23#6704011yescharacteristic
854C23#41×D1111yescharacteristic
855C23#41×D1111yescharacteristic
856C23#6704211yescharacteristic
857C23#6704311yescharacteristic
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—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—22no—
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—114no—
903C2×C4—114no—
904C2×C4—114no—
905C2×C4—222no—
906C2×C4—222no—
907C2×C4—222no—
908C2×C4—222no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—222no—
912C2×C4—222no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—222no—
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—222no—
932C2×C4—222no—
933C2×C4—222no—
934C2×C4—222no—
935C2×C4—4416no—
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×C4C42×D1114yes—
953C2×C4C4×D4414yes—
954C2×C4C4×D4414yes—
955C2×C4C4×D4414yes—
956C2×C4(C22⋊D11)⋊C414yes—
957C22—224no—
958C22—224no—
959C22—224no—
960C22—442no—
961C22—442no—
962C22—442no—
963C22—442no—
964C22—442no—
965C22—442no—
966C22—442no—
967C22—442no—
968C22—442no—
969C22—442no—
970C22—442no—
971C22—442no—
972C22C2×C42×D1111yescharacteristic
973C22C2×C4×D4411yescharacteristic
974C22C2×C4×D4411yescharacteristic
975C22C2×C4×D4411yescharacteristic
976C22C4×#433911yescharacteristic
977C22C4×#433911yescharacteristic
978C22C4×#433911yescharacteristic
979C22C2×(C22⋊D11)⋊C411yescharacteristic
980C22#1062302111yescharacteristic
981C22#1062302611yescharacteristic
982C22#1062303511yescharacteristic
983C22#1062303811yescharacteristic
984C22#1062304411yescharacteristic
985C22#1062305311yescharacteristic
986C22#1062305411yescharacteristic
987C22#1062305811yescharacteristic
988C22#1062306111yescharacteristic
989C22#1062306211yescharacteristic
990C22#1062306411yescharacteristic
991C22C4×#434111yescharacteristic
992C22C4×#434111yescharacteristic
993C22C4×D4×D1111yescharacteristic
994C22C4×D4×D1111yescharacteristic
995C22#1062307611yescharacteristic
996C22#1062307711yescharacteristic
997C22D4×D4411yescharacteristic
998C22#1062308311yescharacteristic
999C22#1062308511yescharacteristic
1000C22#1062308611yescharacteristic
1001C22#1062309011yescharacteristic
1002C22#1062309611yescharacteristic
1003C22#1062309911yescharacteristic
1004C22#1062310311yescharacteristic
1005C22#1062310511yescharacteristic
1006C22#1062310711yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—24no—
1012C4—42no—
1013C4—42no—
1014C4—224no—
1015C4—224no—
1016C4—224no—
1017C4—442no—
1018C4—442no—
1019C4—442no—
1020C4—442no—
1021C2—444no—
1022C2C4×(C22⋊D11)⋊C411yescharacteristic
1023C2C42×D4411yescharacteristic
1024C2#1307097011yescharacteristic
1025C2#1307159811yescharacteristic
1026C2#1307160411yescharacteristic
1027C2#1307161011yescharacteristic
1028C2#1307163011yescharacteristic
1029C2#1307163411yescharacteristic
1030C2#1307164411yescharacteristic
1031C2#1307164511yescharacteristic
1032C2#1307168711yescharacteristic
1033C2#1307168811yescharacteristic
1034C2#1307173611yescharacteristic
1035C2#1307174111yescharacteristic
1036C2#1307175011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC4×C11×#95C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC4×#95D11
hypocenterC11#13823
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
4. C2×C4×C4⋊Dic11C2semidirect
5. C2×#10622262C2semidirect
10. #13066851C2semidirect
11. #13066850C2semidirect
12. #13066850C2semidirect
13. #13066849C2semidirect
14. C4×C11⋊#95C2semidirect
15. C4×C11×#95C2semidirect
51. #10622553C4semidirect
54. #10622283C4semidirect
55. #10622281C4semidirect
88. C2×C42×C11C2×C4semidirect
112. C2×C4⋊Dic11C2×C4semidirect
118. C2×Dic11⋊C4C2×C4semidirect
133. C2×C4×Dic11C2×C4semidirect
136. C11×#95C2×C4semidirect
146. C11⋊#95C2×C4semidirect
147. C11⋊#95C2×C4semidirect
148. C11⋊#95C2×C4semidirect
280. (C2×D11)⋊C4C42semidirect
304. C4×#95D11semidirect
635. C2×C42C4×D11semidirect
650. #95C4×D11semidirect
807. C11#13823semidirect

Maximal subgroups

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

subgroupindex
C2×#106222832
C2×#106225532
C2×#106222812
C2×C4×C4⋊Dic112
C2×#106222622
C2×C4×(C2×D11)⋊C42
C2×#106222792
#130668542
#130668522
#130668512
#130668502
#130668492
C4×C11⋊#952
C4×C11×#952
#1382311