Finite Group Databasebeta

← #14675352

Subgroups — #14675352

Order 2816.

1906 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×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×Dic11C211yesmaximal, characteristic
5C2×C22⋊C4×Dic11C211yesmaximal, characteristic
6#13066853C211yesmaximal, characteristic
7#13066851C211yesmaximal, characteristic, complemented
8#13066847C211yesmaximal, characteristic, complemented
9#13066842C211yesmaximal, characteristic, complemented
10#13066840C211yesmaximal, characteristic, complemented
11#13066838C211yesmaximal, characteristic
12C4×C11⋊#95C211yesmaximal, characteristic, complemented
13#95×Dic11C211yesmaximal, characteristic, complemented
14#95×Dic11C211yesmaximal, characteristic, complemented
15C11×#1437C211yesmaximal, characteristic
16C24×Dic11C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
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#10622558C418yescomplemented
52#10622557C418yescomplemented
53C22⋊C4×Dic11—24no—
54C22⋊C4×Dic11C418yescomplemented
55C4×Dic11⋊C4—24no—
56C25×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11—22no—
64C23×Dic11—22no—
65C23×Dic11—22no—
66C23×Dic11—22no—
67C23×Dic11—41no—
68C23×Dic11—41no—
69C23×Dic11C2×C414yes—
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⋊C4—41no—
83C2×C11×C22⋊C4—41no—
84C2×C11×C22⋊C4C2×C414yes—
85C2×C11×C22⋊C4C2×C414yes—
86C2×C11×C22⋊C4C2×C414yes—
87C2×C42×C11—22no—
88C2×C42×C11—22no—
89C2×C42×C11—41no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—22no—
92C2×C22⋊Dic11—41no—
93C2×C22⋊Dic11—41no—
94C2×C22⋊Dic11C2×C414yes—
95C2×C22⋊Dic11C2×C414yes—
96C2×C22⋊Dic11C2×C414yes—
97C2×C22⋊Dic11C2×C414yes—
98C2×C22⋊Dic11C2×C414yes—
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4—22no—
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4—22no—
103C2×Dic11⋊C4C2×C414yescomplemented
104C2×Dic11⋊C4C2×C414yescomplemented
105C2×C4×Dic11—22no—
106C2×C4×Dic11—22no—
107C2×C4×Dic11—22no—
108C2×C4×Dic11—22no—
109C2×C4×Dic11—22no—
110C2×C4×Dic11—22no—
111C2×C4×Dic11—22no—
112C2×C4×Dic11—22no—
113C2×C4×Dic11—41no—
114C2×C4×Dic11—41no—
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×Dic11C2×C414yes—
123C2×C4×Dic11C2×C414yes—
124C2×C4×Dic11C2×C414yescomplemented
125C2×C4×Dic11C2×C414yescomplemented
126C11×#95—22no—
127C11×#95—22no—
128C11×#95—41no—
129C11⋊#95—22no—
130C11⋊#95—22no—
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95—22no—
134C11⋊#95—22no—
135C11⋊#95—22no—
136C11⋊#95—41no—
137C11⋊#95C2×C414yes—
138C11⋊#95C2×C414yes—
139C11⋊#95C2×C414yescomplemented
140C11⋊#95C2×C414yescomplemented
141C11⋊#95C2×C414yescomplemented
142C11⋊#95C2×C414yescomplemented
143C11⋊#95D414yes—
144#13822—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—21no—
192C22×C4×C11—21no—
193C22×C4×C11C22×C412yes—
194C22×C4×C11C22×C412yes—
195C22×C4×C11C22×C412yes—
196C22×C4×C11C22×C412yes—
197C22×C4×C11C22×C412yes—
198C22×C4×C11C22×C412yes—
199C22×C4×C11C2×D412yes—
200C22×C4×C11#4112yes—
201C22×C4×C11#4112yes—
202C22×C4×C11#4112yes—
203C22×Dic11—28no—
204C22×Dic11—28no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
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—44no—
244C22×Dic11—44no—
245C22×Dic11—44no—
246C22×Dic11—44no—
247C22×Dic11—44no—
248C22×Dic11C22×C412yes—
249C22×Dic11C22×C412yes—
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—
259C22×Dic11C22×C412yes—
260C22×Dic11C2×D412yes—
261C22×Dic11C2×D412yes—
262C22×Dic11#4112yes—
263C22×Dic11#4112yes—
264C22×Dic11#4112yes—
265C22×Dic11#4112yes—
266C11×C22⋊C4—28no—
267C11×C22⋊C4—28no—
268C11×C22⋊C4—44no—
269C42×C11—44no—
270C22⋊Dic11—28no—
271C22⋊Dic11—44no—
272C22⋊Dic11C42116yescomplemented
273Dic11⋊C4—28no—
274Dic11⋊C4—28no—
275C4×Dic11—28no—
276C4×Dic11—44no—
277C4×Dic11—44no—
278C4×Dic11—44no—
279C4×Dic11—44no—
280C4×Dic11—44no—
281C4×Dic11—44no—
282C2×#388—111no—
283C2×#388—111no—
284C2×C4×C4⋊C4—111no—
285C2×C4×C22⋊C4—111no—
286C2×C4×C22⋊C4—111no—
287#1437—111no—
288#1437D1111yescharacteristic
289#1436—111no—
290#1436—111no—
291#1434—111no—
292#1434—111no—
293C22⋊#95—111no—
294C4×#95—111no—
295C4×#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×C11C2×#4111yescharacteristic
340C23×C11C2×#4111yescharacteristic
341C23×C11C2×#4111yescharacteristic
342C23×C11C2×#4111yescharacteristic
343C23×C11H(5,𝔽2)11yescharacteristic
344C23×C11H(5,𝔽2)11yescharacteristic
345C23×C11H(5,𝔽2)11yescharacteristic
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—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
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#11714yes—
388C2×C4×C11C4×D414yes—
389C2×Dic11—22no—
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—22no—
421C2×Dic11—22no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—416no—
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×Dic11C2×C4214yes—
442C2×Dic11C2×C4214yes—
443C2×Dic11#11714yes—
444C2×Dic11C4×D414yes—
445C2×Dic11C4×D414yes—
446C24×C4—111no—
447C22×C4⋊C4—111no—
448C22×C4⋊C4—111no—
449C22×C22⋊C4—111no—
450C22×C22⋊C4—111no—
451C22×C22⋊C4—111no—
452C22×C22⋊C4C2×D1111yescharacteristic
453C22×C22⋊C4C2×D1111yescharacteristic
454C22×C22⋊C4C2×D1111yescharacteristic
455C22×C42—111no—
456C22×C42—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—
465C4×C4⋊C4—224no—
466C4×C22⋊C4—118no—
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×#95C2×D1111yescharacteristic
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×#11711yescharacteristic
503C22×C11C2×#11711yescharacteristic
504C22×C11C2×C4×D411yescharacteristic
505C22×C11C2×C4×D411yescharacteristic
506C22×C11C2×C4×D411yescharacteristic
507C22×C11C4×#4111yescharacteristic
508C22×C11C4×#4111yescharacteristic
509C22×C11C4×#4111yescharacteristic
510C22×C11C4×#4111yescharacteristic
511C22×C11C4×#4111yescharacteristic
512C22×C11C4×#4111yescharacteristic
513C22×C11C4×#4111yescharacteristic
514C22×C11#51811yescharacteristic
515C22×C11#51811yescharacteristic
516C22×C11#51811yescharacteristic
517C22×C11#52011yescharacteristic
518C22×C11#52011yescharacteristic
519C22×C11#52011yescharacteristic
520C22×C11#54611yescharacteristic
521C22×C11#54611yescharacteristic
522C22×C11#54611yescharacteristic
523C22×C11#54811yescharacteristic
524C22×C11#55111yescharacteristic
525C22×C11#55111yescharacteristic
526C22×C11#55211yescharacteristic
527C22×C11#55311yescharacteristic
528C22×C11#55311yescharacteristic
529C22×C11#55311yescharacteristic
530C22×C11#55311yescharacteristic
531C22×C11#55311yescharacteristic
532C22×C11#55611yescharacteristic
533C22×C11#55611yescharacteristic
534C22×C11#55911yescharacteristic
535C22×C11#55911yescharacteristic
536C4×C11—24no—
537C4×C11—24no—
538C4×C11—42no—
539C4×C11—42no—
540C4×C11—42no—
541C4×C11—42no—
542Dic11—24no—
543Dic11—24no—
544Dic11—24no—
545Dic11—24no—
546Dic11—24no—
547Dic11—42no—
548Dic11—42no—
549Dic11—42no—
550C25C22×D1111yescharacteristic
551C23×C4—111no—
552C23×C4—111no—
553C23×C4—111no—
554C23×C4—111no—
555C23×C4—111no—
556C23×C4—111no—
557C23×C4—111no—
558C23×C4—111no—
559C23×C4—114no—
560C23×C4—222no—
561C23×C4—222no—
562C23×C4—222no—
563C23×C4—222no—
564C23×C4—441no—
565C23×C4—441no—
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—222no—
575C2×C4⋊C4—222no—
576C2×C4⋊C4—222no—
577C2×C4⋊C4—222no—
578C2×C22⋊C4—22no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—41no—
583C2×C22⋊C4—41no—
584C2×C22⋊C4—114no—
585C2×C22⋊C4—114no—
586C2×C22⋊C4—114no—
587C2×C22⋊C4—114no—
588C2×C22⋊C4—114no—
589C2×C22⋊C4—222no—
590C2×C22⋊C4—222no—
591C2×C22⋊C4—441no—
592C2×C22⋊C4—441no—
593C2×C22⋊C4C4×D1114yes—
594C2×C22⋊C4C4×D1114yes—
595C2×C22⋊C4C4×D1114yes—
596C2×C42—22no—
597C2×C42—22no—
598C2×C42—41no—
599C2×C42—114no—
600C2×C42—114no—
601C2×C42—114no—
602C2×C42—114no—
603C2×C42—222no—
604C2×C42—222no—
605C2×C42—222no—
606C2×C42—222no—
607C2×C42—222no—
608C2×C42—222no—
609C2×C42—222no—
610C2×C42—222no—
611C2×C42—441no—
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—22no—
622#95—41no—
623#95—114no—
624#95—114no—
625#95—114no—
626#95—114no—
627#95—114no—
628#95—114no—
629#95—114no—
630#95—222no—
631#95—222no—
632#95—222no—
633#95—222no—
634#95—222no—
635#95—222no—
636#95—222no—
637#95—441no—
638C2×C11—44no—
639C2×C11C4×#11711yescharacteristic
640C2×C11C42×D411yescharacteristic
641C2×C11#227511yescharacteristic
642C2×C11#234211yescharacteristic
643C2×C11#234711yescharacteristic
644C2×C11#235211yescharacteristic
645C2×C11#235711yescharacteristic
646C2×C11#236411yescharacteristic
647C2×C11#236411yescharacteristic
648C2×C11#236711yescharacteristic
649C2×C11#236711yescharacteristic
650C2×C11#237311yescharacteristic
651C2×C11#237311yescharacteristic
652C2×C11#237411yescharacteristic
653C2×C11#237411yescharacteristic
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—21no—
701C22×C4—21no—
702C22×C4—112no—
703C22×C4—112no—
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—112no—
714C22×C4—112no—
715C22×C4—112no—
716C22×C4—112no—
717C22×C4—112no—
718C22×C4—112no—
719C22×C4—112no—
720C22×C4—228no—
721C22×C4—228no—
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—444no—
761C22×C4—444no—
762C22×C4—444no—
763C22×C4—444no—
764C22×C4—444no—
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×C4D4×D1112yes—
772C22×C4#434112yes—
773C22×C4#434112yes—
774C22×C4#434112yes—
775C4⋊C4—228no—
776C4⋊C4—228no—
777C22⋊C4—28no—
778C22⋊C4—28no—
779C22⋊C4—44no—
780C22⋊C4—1116no—
781C22⋊C4—228no—
782C22⋊C4—444no—
783C42—44no—
784C42—228no—
785C42—444no—
786C42—444no—
787C42—444no—
788C42—444no—
789C42—444no—
790C42—444no—
791C11#1382211yescharacteristic, 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×D4×D1111yescharacteristic
831C23C2×#434111yescharacteristic
832C23C2×#434111yescharacteristic
833C23C2×#434111yescharacteristic
834C23#6703711yescharacteristic
835C23#6703711yescharacteristic
836C23#41×D1111yescharacteristic
837C23#41×D1111yescharacteristic
838C23#41×D1111yescharacteristic
839C23#41×D1111yescharacteristic
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—41no—
867C2×C4—41no—
868C2×C4—41no—
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—114no—
883C2×C4—114no—
884C2×C4—114no—
885C2×C4—114no—
886C2×C4—114no—
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—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—4416no—
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×C4#6693014yes—
940C2×C4(C22⋊D11)⋊C414yes—
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
957C22C2×#6693011yescharacteristic
958C22C2×(C22⋊D11)⋊C411yescharacteristic
959C22#1062301711yescharacteristic
960C22D11×#11711yescharacteristic
961C22#1062305311yescharacteristic
962C22#1062305411yescharacteristic
963C22C4×#434111yescharacteristic
964C22C4×#434111yescharacteristic
965C22C4×#434111yescharacteristic
966C22C4×#434111yescharacteristic
967C22C4×#434111yescharacteristic
968C22C4×#434111yescharacteristic
969C22C4×D4×D1111yescharacteristic
970C22C4×D4×D1111yescharacteristic
971C22#1062307611yescharacteristic
972C22#1062307611yescharacteristic
973C22#1062307711yescharacteristic
974C22#1062307711yescharacteristic
975C22#1062312211yescharacteristic
976C22#1062312911yescharacteristic
977C22#1062313211yescharacteristic
978C22#1062313211yescharacteristic
979C22#1062314311yescharacteristic
980C22#1062314511yescharacteristic
981C22#1062314911yescharacteristic
982C22#1062318111yescharacteristic
983C22#1062318511yescharacteristic
984C22#1062319211yescharacteristic
985C22#1062320211yescharacteristic
986C22#1062321011yescharacteristic
987C22#1062321211yescharacteristic
988C22#1062323311yescharacteristic
989C22#1062323611yescharacteristic
990C22#1062324411yescharacteristic
991C4—24no—
992C4—24no—
993C4—42no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—224no—
998C4—224no—
999C4—224no—
1000C4—224no—
1001C4—224no—
1002C4—442no—
1003C4—442no—
1004C4—442no—
1005C2—44no—
1006C2C4×#6693011yescharacteristic
1007C2C4×(C22⋊D11)⋊C411yescharacteristic
1008C2#1307097511yescharacteristic
1009C2#1307146011yescharacteristic
1010C2#1307150611yescharacteristic
1011C2#1307154311yescharacteristic
1012C2#1307158811yescharacteristic
1013C2#1307166411yescharacteristic
1014C2#1307166511yescharacteristic
1015C2#1307168611yescharacteristic
1016C2#1307169011yescharacteristic
1017C2#1307173311yescharacteristic
1018C2#1307174311yescharacteristic
1019C2#1307174411yescharacteristic
1020C2#1307175111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC11×#1437C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenter#1437D11
hypocenterC11#13822
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic11⋊C4C2semidirect
7. #13066851C2semidirect
8. #13066847C2semidirect
9. #13066842C2semidirect
10. #13066840C2semidirect
12. C4×C11⋊#95C2semidirect
13. #95×Dic11C2semidirect
14. #95×Dic11C2semidirect
51. #10622558C4semidirect
52. #10622557C4semidirect
54. C22⋊C4×Dic11C4semidirect
103. C2×Dic11⋊C4C2×C4semidirect
104. C2×Dic11⋊C4C2×C4semidirect
124. C2×C4×Dic11C2×C4semidirect
125. C2×C4×Dic11C2×C4semidirect
139. C11⋊#95C2×C4semidirect
140. C11⋊#95C2×C4semidirect
141. C11⋊#95C2×C4semidirect
142. C11⋊#95C2×C4semidirect
272. C22⋊Dic11C42semidirect
791. C11#13822semidirect

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×C4×Dic11⋊C42
C2×C22⋊C4×Dic112
#130668532
#130668512
#130668472
#130668422
#130668402
#130668382
C4×C11⋊#952
#95×Dic112
C11×#14372
#1382211