Finite Group Databasebeta

← #14675119

Subgroups — #14675119

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×#10622558C211yesmaximal, characteristic
2C2×#10622557C211yesmaximal, characteristic
3C2×#10622823C211yesmaximal, characteristic
4C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
5#13066853C211yesmaximal, characteristic
6#13066853C211yesmaximal, characteristic
7#13066851C211yesmaximal, characteristic, complemented
8#13066849C211yesmaximal, characteristic, complemented
9#13066849C211yesmaximal, characteristic, complemented
10#13066847C211yesmaximal, characteristic, complemented
11Dic11⋊#95C211yesmaximal, characteristic, complemented
12#13066840C211yesmaximal, characteristic, complemented
13#13066839C211yesmaximal, characteristic
14C4×C11⋊#95C211yesmaximal, characteristic, complemented
15C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
16C24×C4×C11C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C4×C11×C22⋊C4—24no—
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36#10622823C418yescomplemented
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
52C2×C11⋊#95C2211yescharacteristic
53#10622558C418yescomplemented
54#10622557C418yescomplemented
55C4×Dic11⋊C4—24no—
56C25×C11C2311yescharacteristic
57C23×C4×C11—22no—
58C23×C4×C11—22no—
59C23×C4×C11—41no—
60C23×C4×C11—41no—
61C23×C4×C11—41no—
62C23×C4×C11—41no—
63C23×C4×C11C2×C414yes—
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4C2×C414yes—
83C2×C11×C22⋊C4C2×C414yes—
84C2×C42×C11—22no—
85C2×C42×C11—41no—
86C2×C42×C11—41no—
87C2×C42×C11—41no—
88C2×C42×C11—41no—
89C2×C42×C11D414yes—
90C2×C22⋊Dic11—41no—
91C2×C22⋊Dic11—41no—
92C2×C22⋊Dic11—41no—
93C2×C22⋊Dic11—41no—
94C2×C22⋊Dic11—41no—
95C2×C22⋊Dic11—41no—
96C2×C22⋊Dic11C2×C414yes—
97C2×C22⋊Dic11C2×C414yes—
98C2×C22⋊Dic11C2×C414yes—
99C2×C22⋊Dic11C2×C414yes—
100C2×C22⋊Dic11C2×C414yes—
101C2×C22⋊Dic11C2×C414yes—
102C2×Dic11⋊C4—22no—
103C2×Dic11⋊C4—22no—
104C2×Dic11⋊C4—22no—
105C2×Dic11⋊C4—22no—
106C2×Dic11⋊C4—41no—
107C2×Dic11⋊C4—41no—
108C2×Dic11⋊C4—41no—
109C2×Dic11⋊C4—41no—
110C2×Dic11⋊C4C2×C414yes—
111C2×Dic11⋊C4C2×C414yes—
112C2×Dic11⋊C4C2×C414yescomplemented
113C2×Dic11⋊C4C2×C414yescomplemented
114C2×C4×Dic11—22no—
115C2×C4×Dic11—22no—
116C2×C4×Dic11—22no—
117C2×C4×Dic11—22no—
118C2×C4×Dic11—41no—
119C2×C4×Dic11—41no—
120C2×C4×Dic11—41no—
121C2×C4×Dic11—41no—
122C2×C4×Dic11—41no—
123C2×C4×Dic11—41no—
124C2×C4×Dic11C2×C414yescomplemented
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×C11—21no—
146C24×C11—21no—
147C24×C11—21no—
148C24×C11—21no—
149C24×C11—21no—
150C24×C11—21no—
151C24×C11—21no—
152C24×C11—21no—
153C24×C11—21no—
154C24×C11—21no—
155C24×C11—21no—
156C24×C11—21no—
157C24×C11C22×C412yes—
158C24×C11C22×C412yes—
159C24×C11C22×C412yes—
160C24×C11C2411yescharacteristic
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—28no—
192C22×C4×C11—44no—
193C22×C4×C11—44no—
194C22×C4×C11—44no—
195C22×C4×C11—44no—
196C22×C4×C11—44no—
197C22×C4×C11—44no—
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×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11C22×C412yes—
255C22×Dic11C22×C412yes—
256C22×Dic11C22×C412yes—
257C22×Dic11C22×C412yes—
258C22×Dic11C22×C412yes—
259C22×Dic11C22×C412yes—
260C22×Dic11C22×C412yes—
261C22×Dic11C22×C412yes—
262C22×Dic11C22×C412yes—
263C22×Dic11C22×C412yes—
264C22×Dic11C22×C412yes—
265C22×Dic11C22×C412yes—
266C11×C22⋊C4—28no—
267C11×C22⋊C4—28no—
268C42×C11—44no—
269C42×C11—44no—
270C22⋊Dic11—44no—
271C22⋊Dic11—44no—
272C22⋊Dic11—44no—
273C22⋊Dic11C42116yescomplemented
274Dic11⋊C4—28no—
275Dic11⋊C4—28no—
276Dic11⋊C4—44no—
277Dic11⋊C4—44no—
278C4×Dic11—28no—
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⋊C4D1111yescharacteristic
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×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11—41no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11C2×C4214yes—
332C23×C11C23×C411yescharacteristic
333C23×C11C23×C411yescharacteristic
334C23×C11C23×C411yescharacteristic
335C23×C11C22×D411yescharacteristic
336C23×C11C2×#4111yescharacteristic
337C23×C11C2×#4111yescharacteristic
338C23×C11C2×#4111yescharacteristic
339C23×C11H(5,𝔽2)11yescharacteristic
340C23×C11H(5,𝔽2)11yescharacteristic
341C23×C11H(5,𝔽2)11yescharacteristic
342C23×C11H(5,𝔽2)11yescharacteristic
343C23×C11H(5,𝔽2)11yescharacteristic
344C23×C112−1+411yescharacteristic
345C23×C112−1+411yescharacteristic
346C23×C112−1+411yescharacteristic
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—416no—
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×C11C4×D414yes—
388C2×C4×C11C4×D414yes—
389C2×C4×C11C4×D414yes—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
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—
445C2×Dic11C2×C4214yes—
446C24×C4C2×D1111yescharacteristic
447C22×C4⋊C4—111no—
448C22×C4⋊C4—111no—
449C22×C4⋊C4—111no—
450C22×C4⋊C4—111no—
451C22×C22⋊C4—111no—
452C22×C22⋊C4—111no—
453C22×C22⋊C4—111no—
454C22×C22⋊C4—111no—
455C22×C22⋊C4C2×D1111yescharacteristic
456C22×C22⋊C4C2×D1111yescharacteristic
457C22×C42—111no—
458C22×C42—111no—
459C22×C42—111no—
460C22×C42—111no—
461C22×C42C2×D1111yescharacteristic
462C22×C42C2×D1111yescharacteristic
463#388—118no—
464#388—118no—
465#385—118no—
466C4×C4⋊C4—224no—
467C4×C22⋊C4—24no—
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×C11—24no—
487C22×C11—24no—
488C22×C11—24no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11—42no—
495C22×C11—42no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—42no—
501C22×C11C22×C4211yescharacteristic
502C22×C11C2×C4×D411yescharacteristic
503C22×C11C2×C4×D411yescharacteristic
504C22×C11C2×C4×D411yescharacteristic
505C22×C11C4×#4111yescharacteristic
506C22×C11C4×#4111yescharacteristic
507C22×C11C4×#4111yescharacteristic
508C22×C11#51811yescharacteristic
509C22×C11#51811yescharacteristic
510C22×C11#51811yescharacteristic
511C22×C11#51811yescharacteristic
512C22×C11#51911yescharacteristic
513C22×C11#52011yescharacteristic
514C22×C11#52011yescharacteristic
515C22×C11#52011yescharacteristic
516C22×C11#52011yescharacteristic
517C22×C11#52011yescharacteristic
518C22×C11#52011yescharacteristic
519C22×C11#52011yescharacteristic
520C22×C11#53411yescharacteristic
521C22×C11#53511yescharacteristic
522C22×C11#53611yescharacteristic
523C22×C11#53711yescharacteristic
524C22×C11#53811yescharacteristic
525C22×C11#53811yescharacteristic
526C22×C11#53811yescharacteristic
527C22×C11#53911yescharacteristic
528C22×C11#53911yescharacteristic
529C22×C11#53911yescharacteristic
530C22×C11#54011yescharacteristic
531C22×C11#54111yescharacteristic
532C22×C11#54211yescharacteristic
533C22×C11#54211yescharacteristic
534C22×C11#54211yescharacteristic
535C22×C11#54211yescharacteristic
536C4×C11—24no—
537C4×C11—24no—
538C4×C11—24no—
539C4×C11—42no—
540C4×C11—42no—
541C4×C11—42no—
542Dic11—24no—
543Dic11—24no—
544Dic11—42no—
545Dic11—42no—
546Dic11—42no—
547Dic11—42no—
548Dic11—42no—
549Dic11—42no—
550C25C22×D1111yescharacteristic
551C23×C4—22no—
552C23×C4—22no—
553C23×C4—41no—
554C23×C4—41no—
555C23×C4—41no—
556C23×C4—41no—
557C23×C4—111no—
558C23×C4—111no—
559C23×C4—111no—
560C23×C4—111no—
561C23×C4—111no—
562C23×C4—111no—
563C23×C4—111no—
564C23×C4—111no—
565C23×C4C4×D1114yes—
566C23×C4C22×D1111yescharacteristic
567C23×C4C22×D1111yescharacteristic
568C23×C4C22×D1111yescharacteristic
569C23×C4C22×D1111yescharacteristic
570C23×C4C22×D1111yescharacteristic
571C23×C4C22×D1111yescharacteristic
572C2×C4⋊C4—114no—
573C2×C4⋊C4—114no—
574C2×C4⋊C4—114no—
575C2×C4⋊C4—114no—
576C2×C4⋊C4—222no—
577C2×C4⋊C4—222no—
578C2×C4⋊C4—222no—
579C2×C4⋊C4—222no—
580C2×C4⋊C4—441no—
581C2×C4⋊C4—441no—
582C2×C4⋊C4—441no—
583C2×C4⋊C4—441no—
584C2×C22⋊C4—22no—
585C2×C22⋊C4—22no—
586C2×C22⋊C4—22no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—114no—
589C2×C22⋊C4—114no—
590C2×C22⋊C4—114no—
591C2×C22⋊C4—114no—
592C2×C22⋊C4—114no—
593C2×C22⋊C4—114no—
594C2×C22⋊C4—441no—
595C2×C22⋊C4—441no—
596C2×C22⋊C4—441no—
597C2×C22⋊C4—441no—
598C2×C22⋊C4—441no—
599C2×C22⋊C4—441no—
600C2×C22⋊C4C4×D1114yes—
601C2×C22⋊C4C4×D1114yes—
602C2×C42—22no—
603C2×C42—41no—
604C2×C42—41no—
605C2×C42—41no—
606C2×C42—41no—
607C2×C42—114no—
608C2×C42—114no—
609C2×C42—222no—
610C2×C42—222no—
611C2×C42—222no—
612C2×C42—222no—
613C2×C42—441no—
614C2×C42—441no—
615C2×C42—441no—
616C2×C42—441no—
617C2×C42—441no—
618C2×C42—441no—
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×C11—44no—
639C2×C11C42×D411yescharacteristic
640C2×C11#227411yescharacteristic
641C2×C11#227511yescharacteristic
642C2×C11#232111yescharacteristic
643C2×C11#232211yescharacteristic
644C2×C11#232311yescharacteristic
645C2×C11#232411yescharacteristic
646C2×C11#232511yescharacteristic
647C2×C11#232611yescharacteristic
648C2×C11#233211yescharacteristic
649C2×C11#233411yescharacteristic
650C2×C11#233411yescharacteristic
651C2×C11#233511yescharacteristic
652C2×C11#233511yescharacteristic
653C2×C11#233711yescharacteristic
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24C2×C4×D1112yes—
667C24C2×C4×D1112yes—
668C24C2×C4×D1112yes—
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—28no—
701C22×C4—44no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—112no—
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—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—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×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—228no—
776C4⋊C4—228no—
777C4⋊C4—444no—
778C4⋊C4—444no—
779C22⋊C4—28no—
780C22⋊C4—28no—
781C22⋊C4—1116no—
782C22⋊C4—444no—
783C22⋊C4—444no—
784C22⋊C4—444no—
785C42—44no—
786C42—44no—
787C42—228no—
788C42—444no—
789C42—444no—
790C42—444no—
791C11#1378911yescharacteristic, complemented, Sylow
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C42×D1114yes—
827C23C22×C4×D1111yescharacteristic
828C23C22×C4×D1111yescharacteristic
829C23C22×C4×D1111yescharacteristic
830C23C2×#433911yescharacteristic
831C23C2×#433911yescharacteristic
832C23C2×#433911yescharacteristic
833C23#6703711yescharacteristic
834C23#6703711yescharacteristic
835C23#6703711yescharacteristic
836C23#6703711yescharacteristic
837C23#6704211yescharacteristic
838C23#6704311yescharacteristic
839C23#6704311yescharacteristic
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—416no—
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—114no—
883C2×C4—114no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—222no—
887C2×C4—222no—
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—222no—
913C2×C4—222no—
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×C4—441no—
938C2×C4C4×C22⋊D1114yes—
939C2×C4C4×C22⋊D1114yes—
940C2×C4C4×C22⋊D1114yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C2×C42×D1111yescharacteristic
957C22C4×#433911yescharacteristic
958C22C4×#433911yescharacteristic
959C22C4×#433911yescharacteristic
960C22#1062301711yescharacteristic
961C22#1062301711yescharacteristic
962C22#1062302511yescharacteristic
963C22#1062302511yescharacteristic
964C22#1062304711yescharacteristic
965C22#1062304911yescharacteristic
966C22#1062305411yescharacteristic
967C22#1062306511yescharacteristic
968C22#1062307611yescharacteristic
969C22#1062307611yescharacteristic
970C22#1062307711yescharacteristic
971C22#1062307711yescharacteristic
972C22#1062307711yescharacteristic
973C22#1062307711yescharacteristic
974C22#1062307711yescharacteristic
975C22#1062307711yescharacteristic
976C22#1062309111yescharacteristic
977C22#1062309211yescharacteristic
978C22#1062309211yescharacteristic
979C22#1062309211yescharacteristic
980C22#1062309311yescharacteristic
981C22#1062309511yescharacteristic
982C22#1062309511yescharacteristic
983C22#1062309511yescharacteristic
984C22C2×C4×C22⋊D1111yescharacteristic
985C22C2×C4×C22⋊D1111yescharacteristic
986C22C2×C4×C22⋊D1111yescharacteristic
987C22#1062333511yescharacteristic
988C22#1062333611yescharacteristic
989C22#1062335611yescharacteristic
990C22#1062336411yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—224no—
998C4—224no—
999C4—442no—
1000C4—442no—
1001C4—442no—
1002C4—442no—
1003C4—442no—
1004C4—442no—
1005C2—44no—
1006C2C42×C22⋊D1111yescharacteristic
1007C2#1307097111yescharacteristic
1008C2#1307097511yescharacteristic
1009C2#1307127411yescharacteristic
1010C2#1307128111yescharacteristic
1011C2#1307129811yescharacteristic
1012C2#1307130311yescharacteristic
1013C2#1307131411yescharacteristic
1014C2#1307132811yescharacteristic
1015C2#1307137211yescharacteristic
1016C2#1307139311yescharacteristic
1017C2#1307139311yescharacteristic
1018C2#1307140611yescharacteristic
1019C2#1307140811yescharacteristic
1020C2#1307142411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#13789
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C4×Dic11⋊C4C2semidirect
7. #13066851C2semidirect
8. #13066849C2semidirect
9. #13066849C2semidirect
10. #13066847C2semidirect
11. Dic11⋊#95C2semidirect
12. #13066840C2semidirect
14. C4×C11⋊#95C2semidirect
36. #10622823C4semidirect
53. #10622558C4semidirect
54. #10622557C4semidirect
112. C2×Dic11⋊C4C2×C4semidirect
113. C2×Dic11⋊C4C2×C4semidirect
124. C2×C4×Dic11C2×C4semidirect
125. C2×C4×Dic11C2×C4semidirect
140. C11⋊#95C2×C4semidirect
141. C11⋊#95C2×C4semidirect
142. C11⋊#95C2×C4semidirect
143. C11⋊#95C2×C4semidirect
273. C22⋊Dic11C42semidirect
791. C11#13789semidirect

Maximal subgroups

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

subgroupindex
C2×#106225582
C2×#106225572
C2×#106228232
C2×C4×Dic11⋊C42
#130668532
#130668512
#130668492
#130668472
Dic11⋊#952
#130668402
#130668392
C4×C11⋊#952
C2×C4×C11×C22⋊C42
#1378911