Finite Group Databasebeta

← #14675298

Subgroups — #14675298

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×#10622283C211yesmaximal, characteristic
2C2×#10622603C211yesmaximal, characteristic
3C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
4C2×#10622279C211yesmaximal, characteristic
5C2×#10622261C211yesmaximal, characteristic, complemented
6#13066852C211yesmaximal, characteristic
7#13066852C211yesmaximal, characteristic
8#13066850C211yesmaximal, characteristic, complemented
9#13066845C211yesmaximal, characteristic, complemented
10#13066842C211yesmaximal, characteristic, complemented
11(C2×D11)⋊#95C211yesmaximal, characteristic
12C4×C11⋊#95C211yesmaximal, characteristic, complemented
13#95×Dic11C211yesmaximal, characteristic, complemented
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×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#10622603C418yescomplemented
52C4×(C2×D11)⋊C4—24no—
53#10622283C418yescomplemented
54#10622279C418yescomplemented
55#10622261—24no—
56C24×D11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C22×C4×D11—22no—
72C22×C4×D11—22no—
73C22×C4×D11—22no—
74C22×C4×D11—22no—
75C22×C4×D11—41no—
76C22×C4×D11—41no—
77C22×C4×D11C2×C414yes—
78C2×C11×C4⋊C4—41no—
79C2×C11×C4⋊C4—41no—
80C2×C11×C4⋊C4C2×C414yescomplemented
81C2×C42×C11—22no—
82C2×C42×C11—22no—
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—22no—
89C2×(C2×D11)⋊C4—22no—
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—41no—
103C2×C4⋊Dic11—41no—
104C2×C4⋊Dic11C2×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—22no—
114C2×C4×Dic11—22no—
115C2×C4×Dic11—22no—
116C2×C4×Dic11—22no—
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×#95C2×C414yes—
130C11×#95C2×C414yescomplemented
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95—22no—
134C11⋊#95—22no—
135C11⋊#95—22no—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—41no—
139C11⋊#95C2×C414yes—
140C11⋊#95C2×C414yescomplemented
141C11⋊#95C2×C414yescomplemented
142C11⋊#95C2×C414yescomplemented
143C11⋊#95D414yes—
144#13816—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×C11C22×C412yes—
198C22×C4×C11C22×C412yes—
199C22×C4×C11C22×C412yes—
200C22×C4×C11C22×C412yes—
201C22×C4×C11C22×C412yes—
202C22×C4×C11C22×C412yes—
203C22×C4×C11C22×C412yes—
204C22×C4×C11C22×C412yes—
205C22×C4×C11C22×C412yes—
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×Dic11C22×C412yes—
245C22×Dic11C22×C412yes—
246C22×Dic11C22×C412yes—
247C22×Dic11C22×C412yes—
248C22×Dic11C22×C412yes—
249C22×Dic11C22×C412yes—
250C22×Dic11C22×C412yes—
251C22×Dic11C22×C412yes—
252C22×Dic11C22×C412yes—
253C22×Dic11C2×D412yes—
254C22×Dic11C2×D412yes—
255C22×Dic11#4112yes—
256C22×Dic11#4112yes—
257C22×Dic11#4112yes—
258C22×Dic11#4112yes—
259C2×C4×D11—28no—
260C2×C4×D11—28no—
261C2×C4×D11—44no—
262C2×C4×D11—44no—
263C2×C4×D11—44no—
264C2×C4×D11—44no—
265C2×C4×D11—44no—
266C11×C4⋊C4—44no—
267C42×C11—44no—
268(C2×D11)⋊C4—28no—
269(C2×D11)⋊C4—28no—
270(C2×D11)⋊C4—28no—
271(C2×D11)⋊C4—44no—
272(C2×D11)⋊C4—44no—
273(C2×D11)⋊C4C42116yescomplemented
274C4⋊Dic11—44no—
275C4×Dic11—28no—
276C4×Dic11—28no—
277C4×Dic11—28no—
278C4×Dic11—44no—
279C4×Dic11—44no—
280C4×Dic11—44no—
281C4×Dic11—44no—
282C2×#388—111no—
283C2×#388—111no—
284C2×C4×C22⋊C4—111no—
285C2×C4×C22⋊C4—111no—
286C2×#376—111no—
287#1437—111no—
288#1437—111no—
289#1436—111no—
290#1436D1111yescharacteristic, complemented
291C4⋊#95—111no—
292#1434—111no—
293C22⋊#95—111no—
294C4×#95—111no—
295C4×#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×C11C2×#4111yescharacteristic
305C23×C11C2×#4111yescharacteristic
306C23×C11C2×#4111yescharacteristic
307C23×C11C2×#4111yescharacteristic
308C23×C11H(5,𝔽2)11yescharacteristic
309C23×C11H(5,𝔽2)11yescharacteristic
310C23×C11H(5,𝔽2)11yescharacteristic
311C23×C112−1+411yescharacteristic
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—41no—
331C22×D11—41no—
332C22×D11—41no—
333C22×D11—41no—
334C22×D11—41no—
335C22×D11—41no—
336C22×D11—41no—
337C22×D11—41no—
338C22×D11—41no—
339C22×D11—41no—
340C22×D11—41no—
341C22×D11—41no—
342C22×D11—41no—
343C22×D11—41no—
344C22×D11—41no—
345C22×D11—41no—
346C22×D11C2×C4214yes—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—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×C11C2×C4214yes—
394C2×C4×C11#11714yes—
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—22no—
427C2×Dic11—22no—
428C2×Dic11—22no—
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×Dic11#11714yes—
443C2×Dic11C4×D414yes—
444C2×Dic11C4×D414yes—
445C4×D11—416no—
446C24×C4—111no—
447C22×C4⋊C4—111no—
448C22×C4⋊C4C2×D1111yescharacteristic
449C22×C22⋊C4—111no—
450C22×C22⋊C4—111no—
451C22×C22⋊C4—111no—
452C22×C22⋊C4—111no—
453C22×C22⋊C4—111no—
454C22×C22⋊C4—111no—
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×C22⋊C4—118no—
466C4×C22⋊C4—224no—
467#376—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×#11711yescharacteristic
488C22×C11C2×#11711yescharacteristic
489C22×C11C2×C4×D411yescharacteristic
490C22×C11C2×C4×D411yescharacteristic
491C22×C11C2×C4×D411yescharacteristic
492C22×C11C4×#4111yescharacteristic
493C22×C11C4×#4111yescharacteristic
494C22×C11C4×#4111yescharacteristic
495C22×C11C4×#4111yescharacteristic
496C22×C11C4×#4111yescharacteristic
497C22×C11C4×#4111yescharacteristic
498C22×C11C4×#4111yescharacteristic
499C22×C11#51811yescharacteristic
500C22×C11#51811yescharacteristic
501C22×C11#51811yescharacteristic
502C22×C11#52011yescharacteristic
503C22×C11#52011yescharacteristic
504C22×C11#52011yescharacteristic
505C22×C11#54611yescharacteristic
506C22×C11#54611yescharacteristic
507C22×C11#54711yescharacteristic
508C22×C11#55011yescharacteristic
509C22×C11#55111yescharacteristic
510C22×C11#55111yescharacteristic
511C22×C11#55111yescharacteristic
512C22×C11#55111yescharacteristic
513C22×C11#55211yescharacteristic
514C22×C11#55211yescharacteristic
515C22×C11#55311yescharacteristic
516C22×C11#55311yescharacteristic
517C22×C11#55511yescharacteristic
518C22×C11#55511yescharacteristic
519C22×C11#55511yescharacteristic
520C22×C11#55611yescharacteristic
521C2×D11—24no—
522C2×D11—24no—
523C2×D11—24no—
524C2×D11—42no—
525C2×D11—42no—
526C2×D11—42no—
527C2×D11—42no—
528C2×D11—42no—
529C2×D11—42no—
530C2×D11—42no—
531C2×D11—42no—
532C2×D11—42no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C4×C11—24no—
537C4×C11—24no—
538C4×C11—24no—
539C4×C11—42no—
540C4×C11—42no—
541C4×C11—42no—
542C4×C11—42no—
543Dic11—24no—
544Dic11—24no—
545Dic11—24no—
546Dic11—24no—
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—222no—
562C23×C4—222no—
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—41no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—114no—
575C2×C4⋊C4—441no—
576C2×C4⋊C4—441no—
577C2×C4⋊C4C4×D1114yescomplemented
578C2×C22⋊C4—114no—
579C2×C22⋊C4—114no—
580C2×C22⋊C4—114no—
581C2×C22⋊C4—114no—
582C2×C22⋊C4—114no—
583C2×C22⋊C4—114no—
584C2×C22⋊C4—114no—
585C2×C22⋊C4—114no—
586C2×C22⋊C4—222no—
587C2×C22⋊C4—222no—
588C2×C22⋊C4—222no—
589C2×C22⋊C4—222no—
590C2×C22⋊C4—222no—
591C2×C22⋊C4—222no—
592C2×C22⋊C4—441no—
593C2×C22⋊C4—441no—
594C2×C22⋊C4—441no—
595C2×C22⋊C4—441no—
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—222no—
612C2×C42—222no—
613C2×C42—222no—
614C2×C42—222no—
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—222no—
629#95—222no—
630#95—222no—
631#95—222no—
632#95—222no—
633#95—222no—
634#95—222no—
635#95—441no—
636#95C4×D1114yes—
637#95C4×D1114yescomplemented
638C2×C11C4×#11711yescharacteristic
639C2×C11C42×D411yescharacteristic
640C2×C11#227511yescharacteristic
641C2×C11#234211yescharacteristic
642C2×C11#234611yescharacteristic
643C2×C11#235311yescharacteristic
644C2×C11#235411yescharacteristic
645C2×C11#235911yescharacteristic
646C2×C11#235911yescharacteristic
647C2×C11#236311yescharacteristic
648C2×C11#236311yescharacteristic
649C2×C11#237211yescharacteristic
650C2×C11#237211yescharacteristic
651C2×C11#237311yescharacteristic
652C2×C11#237311yescharacteristic
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—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—112no—
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—228no—
757C22×C4—444no—
758C22×C4—444no—
759C22×C4—444no—
760C22×C4—444no—
761C22×C4—444no—
762C22×C4C2×C4×D1112yes—
763C22×C4C2×C4×D1112yes—
764C22×C4C2×C4×D1112yes—
765C22×C4C2×C4×D1112yes—
766C22×C4C2×C4×D1112yes—
767C22×C4C2×C4×D1112yes—
768C22×C4C2×C4×D1112yes—
769C22×C4C2×C4×D1112yes—
770C22×C4C2×C4×D1112yes—
771C22×C4D4×D1112yes—
772C22×C4#434112yes—
773C22×C4#434312yes—
774C22×C4#434312yes—
775C4⋊C4—44no—
776C4⋊C4—444no—
777C22⋊C4—1116no—
778C22⋊C4—228no—
779C22⋊C4—228no—
780C22⋊C4—228no—
781C22⋊C4—444no—
782C22⋊C4—444no—
783C42—44no—
784C42—228no—
785C42—228no—
786C42—228no—
787C42—444no—
788C42—444no—
789C42—444no—
790C42—444no—
791C11#1381611yescharacteristic, 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
834C23C2×#434311yescharacteristic
835C23C2×#434311yescharacteristic
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—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
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—114no—
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—222no—
923C2×C4—222no—
924C2×C4—222no—
925C2×C4—4416no—
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×C4C42×D1114yes—
939C2×C4#6694514yes—
940C2×C4#6694614yes—
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
957C22#1062301711yescharacteristic
958C22C2×#6694511yescharacteristic
959C22C2×#6694611yescharacteristic
960C22D11×#11711yescharacteristic
961C22#1062305311yescharacteristic
962C22#1062305411yescharacteristic
963C22C4×#434111yescharacteristic
964C22C4×#434111yescharacteristic
965C22C4×D4×D1111yescharacteristic
966C22C4×D4×D1111yescharacteristic
967C22#1062307611yescharacteristic
968C22#1062307611yescharacteristic
969C22#1062307711yescharacteristic
970C22#1062307711yescharacteristic
971C22C4×#434311yescharacteristic
972C22C4×#434311yescharacteristic
973C22C4×#434311yescharacteristic
974C22C4×#434311yescharacteristic
975C22#1062312211yescharacteristic
976C22#1062313011yescharacteristic
977C22#1062314711yescharacteristic
978C22#1062316111yescharacteristic
979C22#1062316811yescharacteristic
980C22#1062316811yescharacteristic
981C22#1062317311yescharacteristic
982C22#1062318611yescharacteristic
983C22#1062318911yescharacteristic
984C22#1062319211yescharacteristic
985C22#1062320111yescharacteristic
986C22#1062322511yescharacteristic
987C22#1062322611yescharacteristic
988C22#1062323311yescharacteristic
989C22#1062323611yescharacteristic
990C22#1062326511yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—224no—
999C4—224no—
1000C4—224no—
1001C4—224no—
1002C4—442no—
1003C4—442no—
1004C4—442no—
1005C2—444no—
1006C2C4×#6694511yescharacteristic
1007C2C4×#6694611yescharacteristic
1008C2#1307097511yescharacteristic
1009C2#1307146311yescharacteristic
1010C2#1307150011yescharacteristic
1011C2#1307155511yescharacteristic
1012C2#1307156211yescharacteristic
1013C2#1307160611yescharacteristic
1014C2#1307161511yescharacteristic
1015C2#1307165311yescharacteristic
1016C2#1307165711yescharacteristic
1017C2#1307172311yescharacteristic
1018C2#1307172711yescharacteristic
1019C2#1307173511yescharacteristic
1020C2#1307174211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1436D11
hypocenterC11#13816
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
5. C2×#10622261C2semidirect
8. #13066850C2semidirect
9. #13066845C2semidirect
10. #13066842C2semidirect
12. C4×C11⋊#95C2semidirect
13. #95×Dic11C2semidirect
14. #95×Dic11C2semidirect
15. C11×#1436C2semidirect
51. #10622603C4semidirect
53. #10622283C4semidirect
54. #10622279C4semidirect
80. C2×C11×C4⋊C4C2×C4semidirect
104. C2×C4⋊Dic11C2×C4semidirect
124. C2×C4×Dic11C2×C4semidirect
125. C2×C4×Dic11C2×C4semidirect
130. C11×#95C2×C4semidirect
140. C11⋊#95C2×C4semidirect
141. C11⋊#95C2×C4semidirect
142. C11⋊#95C2×C4semidirect
273. (C2×D11)⋊C4C42semidirect
290. #1436D11semidirect
577. C2×C4⋊C4C4×D11semidirect
637. #95C4×D11semidirect
791. C11#13816semidirect

Maximal subgroups

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

subgroupindex
C2×#106222832
C2×#106226032
C2×C4×(C2×D11)⋊C42
C2×#106222792
C2×#106222612
#130668522
#130668502
#130668452
#130668422
(C2×D11)⋊#952
C4×C11⋊#952
#95×Dic112
C11×#14362
#1381611