Finite Group Databasebeta

← #14675117

Subgroups — #14675117

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×#10622283C211yesmaximal, characteristic
2C2×#10622282C211yesmaximal, characteristic
3C2×#10622602C211yesmaximal, characteristic
4C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
6#13066852C211yesmaximal, characteristic
7#13066852C211yesmaximal, characteristic
8#13066851C211yesmaximal, characteristic, complemented
9#13066850C211yesmaximal, characteristic, complemented
10#13066849C211yesmaximal, characteristic, complemented
11Dic11⋊#95C211yesmaximal, characteristic, complemented
12#13066841C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic
14#95×Dic11C211yesmaximal, 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×C4×Dic11C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
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#10622602C418yescomplemented
52C4⋊C4×Dic11—24no—
53C4×(C2×D11)⋊C4—24no—
54#10622283C418yescomplemented
55#10622282C418yescomplemented
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⋊C4C2×C414yes—
81C2×C42×C11—22no—
82C2×C42×C11—41no—
83C2×C42×C11—41no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—41no—
89C2×(C2×D11)⋊C4—41no—
90C2×(C2×D11)⋊C4—41no—
91C2×(C2×D11)⋊C4—41no—
92C2×(C2×D11)⋊C4—41no—
93C2×(C2×D11)⋊C4—41no—
94C2×(C2×D11)⋊C4C2×C414yes—
95C2×(C2×D11)⋊C4C2×C414yes—
96C2×(C2×D11)⋊C4C2×C414yes—
97C2×(C2×D11)⋊C4C2×C414yes—
98C2×(C2×D11)⋊C4C2×C414yes—
99C2×(C2×D11)⋊C4C2×C414yes—
100C2×(C2×D11)⋊C4C2×C414yes—
101C2×(C2×D11)⋊C4C2×C414yes—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11C2×C414yescomplemented
105C2×Dic11⋊C4—41no—
106C2×Dic11⋊C4—41no—
107C2×Dic11⋊C4—41no—
108C2×Dic11⋊C4—41no—
109C2×Dic11⋊C4C2×C414yes—
110C2×Dic11⋊C4C2×C414yescomplemented
111C2×C4×Dic11—22no—
112C2×C4×Dic11—22no—
113C2×C4×Dic11—22no—
114C2×C4×Dic11—22no—
115C2×C4×Dic11—41no—
116C2×C4×Dic11—41no—
117C2×C4×Dic11—41no—
118C2×C4×Dic11—41no—
119C2×C4×Dic11—41no—
120C2×C4×Dic11—41no—
121C2×C4×Dic11—41no—
122C2×C4×Dic11—41no—
123C2×C4×Dic11C2×C414yescomplemented
124C2×C4×Dic11C2×C414yescomplemented
125C2×C4×Dic11D414yes—
126C11×#95—22no—
127C11×#95—41no—
128C11×#95—41no—
129C11×#95C2×C414yescomplemented
130C11×#95C2×C414yescomplemented
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95—22no—
134C11⋊#95—22no—
135C11⋊#95—22no—
136C11⋊#95—41no—
137C11⋊#95—41no—
138C11⋊#95—41no—
139C11⋊#95—41no—
140C11⋊#95C2×C414yes—
141C11⋊#95C2×C414yes—
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×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×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×Dic11C22×C412yes—
247C22×Dic11C22×C412yes—
248C22×Dic11C22×C412yes—
249C22×Dic11C22×C412yes—
250C22×Dic11C22×C412yes—
251C22×Dic11C22×C412yes—
252C22×Dic11C22×C412yes—
253C22×Dic11C22×C412yes—
254C22×Dic11C22×C412yes—
255C22×Dic11C2×D412yes—
256C22×Dic11C2×D412yes—
257C22×Dic11#4112yes—
258C22×Dic11#4112yes—
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—
267C42×C11—44no—
268(C2×D11)⋊C4—28no—
269(C2×D11)⋊C4—28no—
270(C2×D11)⋊C4—44no—
271(C2×D11)⋊C4—44no—
272(C2×D11)⋊C4—44no—
273(C2×D11)⋊C4C42116yescomplemented
274C4⋊Dic11—28no—
275Dic11⋊C4—44no—
276Dic11⋊C4—44no—
277C4×Dic11—28no—
278C4×Dic11—44no—
279C4×Dic11—44no—
280C4×Dic11—44no—
281C4×Dic11—44no—
282C2×#388—111no—
283C2×#388—111no—
284C2×#385—111no—
285C2×C4×C4⋊C4—111no—
286C2×C4×C22⋊C4—111no—
287#1437—111no—
288#1437—111no—
289#1436—111no—
290#1436—111no—
291#1436—111no—
292#1436D1111yescharacteristic, complemented
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—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
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×C11C2×C4214yes—
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—22no—
421C2×Dic11—22no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—22no—
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×Dic11C2×C4214yes—
443C2×Dic11C4×D414yes—
444C2×Dic11C4×D414yes—
445C4×D11—416no—
446C24×C4—111no—
447C22×C4⋊C4—111no—
448C22×C4⋊C4—111no—
449C22×C4⋊C4—111no—
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×C42—111no—
461C22×C42—111no—
462C22×C42C2×D1111yescharacteristic
463#388—118no—
464#388—118no—
465#385—118no—
466C4×C4⋊C4—224no—
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×#95C2×D1111yescharacteristic
482C2×#95C2×D1111yescharacteristic
483C2×#95C2×D1111yescharacteristic
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—42no—
539C4×C11—42no—
540C4×C11—42no—
541C4×C11—42no—
542C4×C11—42no—
543Dic11—24no—
544Dic11—24no—
545Dic11—24no—
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—114no—
575C2×C4⋊C4—114no—
576C2×C4⋊C4—114no—
577C2×C4⋊C4—222no—
578C2×C4⋊C4—222no—
579C2×C4⋊C4—441no—
580C2×C4⋊C4—441no—
581C2×C4⋊C4—441no—
582C2×C4⋊C4—441no—
583C2×C4⋊C4C4×D1114yes—
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—41no—
604C2×C42—41no—
605C2×C42—114no—
606C2×C42—114no—
607C2×C42—114no—
608C2×C42—222no—
609C2×C42—222no—
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×C42—441no—
619C2×C42—441no—
620#95—22no—
621#95—41no—
622#95—41no—
623#95—114no—
624#95—114no—
625#95—114no—
626#95—114no—
627#95—222no—
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#95C4×D1114yescomplemented
637#95C4×D1114yescomplemented
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—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—112no—
709C22×C4—112no—
710C22×C4—112no—
711C22×C4—112no—
712C22×C4—112no—
713C22×C4—112no—
714C22×C4—112no—
715C22×C4—112no—
716C22×C4—112no—
717C22×C4—112no—
718C22×C4—112no—
719C22×C4—112no—
720C22×C4—112no—
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—221no—
754C22×C4—221no—
755C22×C4—221no—
756C22×C4—221no—
757C22×C4—228no—
758C22×C4—444no—
759C22×C4—444no—
760C22×C4—444no—
761C22×C4—444no—
762C22×C4—444no—
763C22×C4—444no—
764C22×C4C2×C4×D1112yes—
765C22×C4C2×C4×D1112yes—
766C22×C4C2×C4×D1112yes—
767C22×C4C2×C4×D1112yes—
768C22×C4C2×C4×D1112yes—
769C22×C4C2×C4×D1112yes—
770C22×C4C2×C4×D1112yes—
771C22×C4C2×C4×D1112yes—
772C22×C4C2×C4×D1112yes—
773C22×C4D4×D1112yes—
774C22×C4#434112yes—
775C4⋊C4—28no—
776C4⋊C4—228no—
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—44no—
786C42—228no—
787C42—444no—
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×D4×D1111yescharacteristic
831C23C2×#434111yescharacteristic
832C23#6703711yescharacteristic
833C23#6703711yescharacteristic
834C23#6704011yescharacteristic
835C23#6704011yescharacteristic
836C23#41×D1111yescharacteristic
837C23#41×D1111yescharacteristic
838C23#6704211yescharacteristic
839C23#6704211yescharacteristic
840C23#6704211yescharacteristic
841C23#6704311yescharacteristic
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—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
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—41no—
888C2×C4—41no—
889C2×C4—114no—
890C2×C4—114no—
891C2×C4—114no—
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—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—4416no—
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×C4—441no—
938C2×C4—441no—
939C2×C4C42×D1114yes—
940C2×C4(C22⋊D11)⋊C414yes—
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
957C22C2×(C22⋊D11)⋊C411yescharacteristic
958C22#1062303511yescharacteristic
959C22#1062303511yescharacteristic
960C22#1062305211yescharacteristic
961C22#1062305311yescharacteristic
962C22#1062305411yescharacteristic
963C22C4×#434111yescharacteristic
964C22C4×#434111yescharacteristic
965C22C4×D4×D1111yescharacteristic
966C22C4×D4×D1111yescharacteristic
967C22#1062307611yescharacteristic
968C22#1062307611yescharacteristic
969C22#1062307611yescharacteristic
970C22#1062307711yescharacteristic
971C22#1062310311yescharacteristic
972C22#1062310511yescharacteristic
973C22#1062310511yescharacteristic
974C22#1062310511yescharacteristic
975C22#1062312311yescharacteristic
976C22#1062314811yescharacteristic
977C22#1062314811yescharacteristic
978C22#1062315911yescharacteristic
979C22#1062316011yescharacteristic
980C22#1062317111yescharacteristic
981C22#1062317111yescharacteristic
982C22#1062318411yescharacteristic
983C22#1062319311yescharacteristic
984C22#1062319411yescharacteristic
985C22#1062321311yescharacteristic
986C22#1062322311yescharacteristic
987C22#1062322311yescharacteristic
988C22#1062323511yescharacteristic
989C22#1062323811yescharacteristic
990C22#1062326211yescharacteristic
991C4—24no—
992C4—24no—
993C4—42no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—224no—
999C4—224no—
1000C4—224no—
1001C4—442no—
1002C4—442no—
1003C4—442no—
1004C4—442no—
1005C2—444no—
1006C2C4×(C22⋊D11)⋊C411yescharacteristic
1007C2#1307097011yescharacteristic
1008C2#1307097611yescharacteristic
1009C2#1307127911yescharacteristic
1010C2#1307128911yescharacteristic
1011C2#1307130111yescharacteristic
1012C2#1307130811yescharacteristic
1013C2#1307131511yescharacteristic
1014C2#1307132211yescharacteristic
1015C2#1307137011yescharacteristic
1016C2#1307138411yescharacteristic
1017C2#1307138411yescharacteristic
1018C2#1307139911yescharacteristic
1019C2#1307141211yescharacteristic
1020C2#1307142311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1436D11
hypocenterC11#13789
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊C4×Dic11C2semidirect
8. #13066851C2semidirect
9. #13066850C2semidirect
10. #13066849C2semidirect
11. Dic11⋊#95C2semidirect
12. #13066841C2semidirect
14. #95×Dic11C2semidirect
15. C11×#1436C2semidirect
51. #10622602C4semidirect
54. #10622283C4semidirect
55. #10622282C4semidirect
104. C2×C4⋊Dic11C2×C4semidirect
110. C2×Dic11⋊C4C2×C4semidirect
123. C2×C4×Dic11C2×C4semidirect
124. C2×C4×Dic11C2×C4semidirect
129. C11×#95C2×C4semidirect
130. C11×#95C2×C4semidirect
142. C11⋊#95C2×C4semidirect
143. C11⋊#95C2×C4semidirect
273. (C2×D11)⋊C4C42semidirect
292. #1436D11semidirect
636. #95C4×D11semidirect
637. #95C4×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×#106222832
C2×#106222822
C2×#106226022
C2×C4⋊C4×Dic112
C2×C4×(C2×D11)⋊C42
#130668522
#130668512
#130668502
#130668492
Dic11⋊#952
#130668412
(C2×D11)⋊#952
#95×Dic112
C11×#14362
#1378911