Finite Group Databasebeta

← #14683834

Subgroups — #14683834

Order 2816.

2498 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622836C211yesmaximal, characteristic
2C2×#10622833C211yesmaximal, characteristic, complemented
3C2×#10622826C211yesmaximal, characteristic, complemented
4C2×#10622571C211yesmaximal, characteristic, complemented
5C2×#10622569C211yesmaximal, characteristic, complemented
6C2×#10622569C211yesmaximal, characteristic, complemented
7#13066877C211yesmaximal, characteristic, complemented
8#13066876C211yesmaximal, characteristic, complemented
9#13066860C211yesmaximal, characteristic, complemented
10#13066859C211yesmaximal, characteristic, complemented
11#13066859C211yesmaximal, characteristic, complemented
12#13066839C211yesmaximal, characteristic, complemented
13#13066838C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C2×C11×#386C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C11×#386—24no—
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38#10622836C418yescomplemented
39#10622833—24no—
40#10622826—24no—
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
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55#10622571—24no—
56#10622569—24no—
57#10622569—24no—
58C25×C11C2311yescharacteristic
59C25×C11C2311yescharacteristic
60C24×D11C2311yescharacteristic
61C22×D4×C11—22no—
62C22×D4×C11—22no—
63C22×D4×C11—22no—
64C22×D4×C11—22no—
65C22×D4×C11—41no—
66C22×D4×C11—41no—
67C22×D4×C11C2×C414yescomplemented
68C23×C4×C11—22no—
69C23×C4×C11—22no—
70C23×C4×C11—22no—
71C23×C4×C11—41no—
72C23×C4×C11—41no—
73C23×C4×C11—41no—
74C23×C4×C11—41no—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—22no—
81C22×C22⋊D11—22no—
82C22×C22⋊D11—22no—
83C22×C22⋊D11—22no—
84C22×C22⋊D11—22no—
85C22×C22⋊D11—22no—
86C22×C22⋊D11—22no—
87C22×C22⋊D11—22no—
88C22×C22⋊D11—41no—
89C22×C22⋊D11—41no—
90C22×C22⋊D11—41no—
91C22×C22⋊D11—41no—
92C22×C22⋊D11C2×C414yescomplemented
93C22×C22⋊D11C2×C414yescomplemented
94C23×Dic11—22no—
95C23×Dic11—22no—
96C23×Dic11—22no—
97C23×Dic11—41no—
98C23×Dic11—41no—
99C23×Dic11—41no—
100C23×Dic11—41no—
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C22×C4×D11—22no—
109C22×C4×D11—22no—
110C22×C4×D11—22no—
111C22×C4×D11—41no—
112C22×C4×D11—41no—
113C22×C4×D11—41no—
114C22×C4×D11—41no—
115C2×C11×C22⋊C4—22no—
116C2×C11×C22⋊C4—22no—
117C2×C11×C22⋊C4—22no—
118C2×C11×C22⋊C4—22no—
119C2×C11×C22⋊C4—41no—
120C2×C11×C22⋊C4—41no—
121C2×C11×C22⋊C4—41no—
122C2×C11×C22⋊C4—41no—
123C2×C11×C22⋊C4D414yescomplemented
124C2×C22⋊Dic11—22no—
125C2×C22⋊Dic11—22no—
126C2×C22⋊Dic11—22no—
127C2×C22⋊Dic11—22no—
128C2×C22⋊Dic11—41no—
129C2×C22⋊Dic11—41no—
130C2×C22⋊Dic11—41no—
131C2×C22⋊Dic11—41no—
132C2×C22⋊Dic11—41no—
133C2×C22⋊Dic11—41no—
134C2×C22⋊Dic11—41no—
135C2×C22⋊Dic11—41no—
136C2×C22⋊Dic11C2×C414yescomplemented
137C2×C22⋊Dic11C2×C414yescomplemented
138C2×C22⋊Dic11D414yescomplemented
139C2×(C2×D11)⋊C4—22no—
140C2×(C2×D11)⋊C4—22no—
141C2×(C2×D11)⋊C4—22no—
142C2×(C2×D11)⋊C4—22no—
143C2×(C2×D11)⋊C4—41no—
144C2×(C2×D11)⋊C4—41no—
145C2×(C2×D11)⋊C4—41no—
146C2×(C2×D11)⋊C4—41no—
147C2×(C2×D11)⋊C4—41no—
148C2×(C2×D11)⋊C4—41no—
149C2×(C2×D11)⋊C4C2×C414yescomplemented
150C2×(C2×D11)⋊C4D414yescomplemented
151C2×Dic11⋊C4—41no—
152C2×Dic11⋊C4—41no—
153C2×Dic11⋊C4—41no—
154C11×#95—22no—
155C11×#95—22no—
156C11⋊#95—22no—
157C11⋊#95—22no—
158C11⋊#95—22no—
159C11⋊#95—22no—
160C11⋊#95—22no—
161C11⋊#95—22no—
162C11⋊#95—22no—
163C11⋊#95—22no—
164C11⋊#95—22no—
165C11⋊#95—22no—
166C11⋊#95—41no—
167C11⋊#95—41no—
168C11⋊#95—41no—
169C11⋊#95C2×C414yescomplemented
170#14572—111nomaximal, Sylow
171C24×C11—21no—
172C24×C11—21no—
173C24×C11—21no—
174C24×C11—21no—
175C24×C11—21no—
176C24×C11—21no—
177C24×C11—21no—
178C24×C11—21no—
179C24×C11—21no—
180C24×C11—21no—
181C24×C11—21no—
182C24×C11—21no—
183C24×C11—21no—
184C24×C11—21no—
185C24×C11—21no—
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—21no—
189C24×C11—21no—
190C24×C11—21no—
191C24×C11—21no—
192C24×C11—21no—
193C24×C11—21no—
194C24×C11—21no—
195C24×C11C22×C412yes—
196C24×C11C22×C412yes—
197C24×C11C2×D412yes—
198C24×C11C2×D412yes—
199C24×C11#4112yes—
200C24×C11#4112yes—
201C24×C11C2411yescharacteristic
202C23×D11—21no—
203C23×D11—21no—
204C23×D11—21no—
205C23×D11—21no—
206C23×D11—21no—
207C23×D11—21no—
208C23×D11—21no—
209C23×D11—21no—
210C23×D11—21no—
211C23×D11—21no—
212C23×D11—21no—
213C23×D11—21no—
214C23×D11C22×C412yes—
215C23×D11C2×D412yes—
216C23×D11#4112yes—
217C2×D4×C11—28no—
218C2×D4×C11—28no—
219C2×D4×C11—44no—
220C2×D4×C11—44no—
221C2×D4×C11—44no—
222C2×D4×C11—44no—
223C2×D4×C11—44no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11—21no—
255C22×C4×C11—44no—
256C22×C4×C11—44no—
257C22×C4×C11—44no—
258C22×C4×C11—44no—
259C22×C4×C11—44no—
260C22×C4×C11—44no—
261C22×C4×C11—44no—
262C22×C4×C11C22×C412yes—
263C22×C4×C11C2×D412yes—
264C22×C4×C11C2×D412yes—
265C22×C4×C11C2×D412yes—
266C2×C22⋊D11—28no—
267C2×C22⋊D11—28no—
268C2×C22⋊D11—28no—
269C2×C22⋊D11—28no—
270C2×C22⋊D11—44no—
271C2×C22⋊D11—44no—
272C2×C22⋊D11—44no—
273C2×C22⋊D11—44no—
274C2×C22⋊D11—44no—
275C2×C22⋊D11—44no—
276C2×C22⋊D11—44no—
277C2×C22⋊D11—44no—
278C2×C22⋊D11—44no—
279C2×C22⋊D11—44no—
280C22×Dic11—21no—
281C22×Dic11—21no—
282C22×Dic11—21no—
283C22×Dic11—21no—
284C22×Dic11—21no—
285C22×Dic11—21no—
286C22×Dic11—21no—
287C22×Dic11—21no—
288C22×Dic11—21no—
289C22×Dic11—21no—
290C22×Dic11—21no—
291C22×Dic11—21no—
292C22×Dic11—21no—
293C22×Dic11—21no—
294C22×Dic11—21no—
295C22×Dic11—21no—
296C22×Dic11—21no—
297C22×Dic11—21no—
298C22×Dic11—21no—
299C22×Dic11—21no—
300C22×Dic11—21no—
301C22×Dic11—21no—
302C22×Dic11—21no—
303C22×Dic11—21no—
304C22×Dic11—21no—
305C22×Dic11—21no—
306C22×Dic11—21no—
307C22×Dic11—21no—
308C22×Dic11—21no—
309C22×Dic11—21no—
310C22×Dic11—21no—
311C22×Dic11—21no—
312C22×Dic11—21no—
313C22×Dic11—21no—
314C22×Dic11—21no—
315C22×Dic11—21no—
316C22×Dic11—21no—
317C22×Dic11—21no—
318C22×Dic11—21no—
319C22×Dic11—21no—
320C22×Dic11—21no—
321C22×Dic11—21no—
322C22×Dic11—21no—
323C22×Dic11—44no—
324C22×Dic11—44no—
325C22×Dic11—44no—
326C22×Dic11—44no—
327C22×Dic11—44no—
328C22×Dic11—44no—
329C22×Dic11—44no—
330C22×Dic11C22×C412yes—
331C22×Dic11C22×C412yes—
332C22×Dic11C22×C412yes—
333C22×Dic11C2×D412yes—
334C22×Dic11C2×D412yes—
335C22×Dic11C2×D412yes—
336C2×C4×D11—44no—
337C2×C4×D11—44no—
338C2×C4×D11—44no—
339C2×C4×D11—44no—
340C2×C4×D11—44no—
341C2×C4×D11—44no—
342C2×C4×D11—44no—
343C11×C22⋊C4—44no—
344C11×C22⋊C4—44no—
345C11×C22⋊C4—44no—
346C22⋊Dic11—44no—
347C22⋊Dic11—44no—
348C22⋊Dic11—44no—
349C22⋊Dic11—44no—
350C22⋊Dic11—44no—
351(C2×D11)⋊C4—44no—
352(C2×D11)⋊C4—44no—
353(C2×D11)⋊C4—44no—
354(C2×D11)⋊C4—44no—
355Dic11⋊C4—44no—
356C2×#392—111no—
357C2×#386—111no—
358C2×#386—111no—
359C2×#386—111no—
360C2×#386—111no—
361C2×#386—111no—
362C2×#386D1111yescharacteristic, complemented
363#1443—111no—
364#1443—111no—
365#1439—111no—
366#1439—111no—
367#1439—111no—
368C22⋊#95—111no—
369C22⋊#95—111no—
370C22⋊#95—111no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—22no—
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—22no—
379C23×C11—22no—
380C23×C11—22no—
381C23×C11—22no—
382C23×C11—22no—
383C23×C11—22no—
384C23×C11—22no—
385C23×C11—22no—
386C23×C11—22no—
387C23×C11—22no—
388C23×C11—22no—
389C23×C11—22no—
390C23×C11—22no—
391C23×C11—22no—
392C23×C11—22no—
393C23×C11—22no—
394C23×C11—22no—
395C23×C11—22no—
396C23×C11—22no—
397C23×C11—22no—
398C23×C11—22no—
399C23×C11—22no—
400C23×C11—22no—
401C23×C11—22no—
402C23×C11—22no—
403C23×C11—22no—
404C23×C11—22no—
405C23×C11—22no—
406C23×C11—22no—
407C23×C11—41no—
408C23×C11—41no—
409C23×C11—41no—
410C23×C11—41no—
411C23×C11—41no—
412C23×C11—41no—
413C23×C11—41no—
414C23×C11—41no—
415C23×C11—41no—
416C23×C11—41no—
417C23×C11—41no—
418C23×C11—41no—
419C23×C11—41no—
420C23×C11—41no—
421C23×C11—41no—
422C23×C11—41no—
423C23×C11—41no—
424C23×C11—41no—
425C23×C11—41no—
426C23×C11—41no—
427C23×C11—41no—
428C23×C11—41no—
429C23×C11—41no—
430C23×C11—41no—
431C23×C11—41no—
432C23×C11—41no—
433C23×C11—41no—
434C23×C11—41no—
435C23×C11—41no—
436C23×C11—41no—
437C23×C11—41no—
438C23×C11—41no—
439C23×C11C4×D414yes—
440C23×C11C4×D414yes—
441C23×C11C23×C411yescharacteristic
442C23×C11C22×D411yescharacteristic
443C23×C11C22×D411yescharacteristic
444C23×C11C22×D411yescharacteristic
445C23×C11C2×#4111yescharacteristic
446C23×C11C2×#4111yescharacteristic
447C23×C11C2×#4111yescharacteristic
448C23×C11H(5,𝔽2)11yescharacteristic
449C23×C11H(5,𝔽2)11yescharacteristic
450C23×C11H(5,𝔽2)11yescharacteristic
451C23×C11H(5,𝔽2)11yescharacteristic
452C23×C11H(5,𝔽2)11yescharacteristic
453C23×C11H(5,𝔽2)11yescharacteristic
454C23×C11H(5,𝔽2)11yescharacteristic
455C23×C112−1+411yescharacteristic
456C22×D11—22no—
457C22×D11—22no—
458C22×D11—22no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—41no—
475C22×D11—41no—
476C22×D11—41no—
477C22×D11—41no—
478C22×D11—41no—
479C22×D11—41no—
480C22×D11—41no—
481C22×D11—41no—
482C22×D11—41no—
483C22×D11—41no—
484C22×D11—41no—
485C22×D11—41no—
486C22×D11—41no—
487C22×D11—41no—
488C22×D11—41no—
489C22×D11—41no—
490C22×D11C4×D414yes—
491D4×C11—416no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—416no—
505C2×C4×C11—41no—
506C2×C4×C11—41no—
507C2×C4×C11—41no—
508C2×C4×C11—41no—
509C2×C4×C11—41no—
510C2×C4×C11—41no—
511C2×C4×C11—41no—
512C2×C4×C11—41no—
513C2×C4×C11—41no—
514C2×C4×C11—41no—
515C2×C4×C11—41no—
516C2×C4×C11—41no—
517C2×C4×C11—41no—
518C2×C4×C11—41no—
519C2×C4×C11—41no—
520C2×C4×C11—41no—
521C2×C4×C11—41no—
522C2×C4×C11—41no—
523C2×C4×C11—41no—
524C2×C4×C11—41no—
525C2×C4×C11—41no—
526C2×C4×C11—41no—
527C2×C4×C11—41no—
528C22⋊D11—416no—
529C22⋊D11—416no—
530C2×Dic11—22no—
531C2×Dic11—22no—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—22no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—22no—
543C2×Dic11—22no—
544C2×Dic11—22no—
545C2×Dic11—22no—
546C2×Dic11—22no—
547C2×Dic11—22no—
548C2×Dic11—416no—
549C2×Dic11—41no—
550C2×Dic11—41no—
551C2×Dic11—41no—
552C2×Dic11—41no—
553C2×Dic11—41no—
554C2×Dic11—41no—
555C2×Dic11—41no—
556C2×Dic11—41no—
557C2×Dic11—41no—
558C2×Dic11—41no—
559C2×Dic11—41no—
560C2×Dic11—41no—
561C2×Dic11—41no—
562C2×Dic11—41no—
563C2×Dic11—41no—
564C2×Dic11—41no—
565C2×Dic11—41no—
566C2×Dic11—41no—
567C2×Dic11—41no—
568C2×Dic11—41no—
569C2×Dic11—41no—
570C2×Dic11—41no—
571C2×Dic11—41no—
572C2×Dic11—41no—
573C2×Dic11—41no—
574C2×Dic11—41no—
575C2×Dic11—41no—
576C2×Dic11—41no—
577C2×Dic11—41no—
578C2×Dic11—41no—
579C2×Dic11—41no—
580C4×D11—416no—
581C23×D4—111no—
582C23×D4—111no—
583C23×D4C2×D1111yescharacteristic
584C24×C4—111no—
585C24×C4—111no—
586C24×C4C2×D1111yescharacteristic
587C22×C4⋊C4—111no—
588C22×C22⋊C4—111no—
589C22×C22⋊C4—111no—
590C22×C22⋊C4—111no—
591C22×C22⋊C4—111no—
592C22×C22⋊C4—111no—
593C22×C22⋊C4—111no—
594C22×C22⋊C4—111no—
595C22×C22⋊C4—111no—
596C22×C22⋊C4—111no—
597C22×C22⋊C4C2×D1111yescharacteristic
598C22×C22⋊C4C2×D1111yescharacteristic
599C22×C22⋊C4C2×D1111yescharacteristic
600#392—118no—
601#386—24no—
602#386—224no—
603#386—224no—
604#386—224no—
605#386—224no—
606#386—224no—
607C2×#95—111no—
608C2×#95—111no—
609C2×#95—111no—
610C2×#95—111no—
611C2×#95—111no—
612C2×#95—111no—
613C2×#95—111no—
614C2×#95—111no—
615C2×#95—111no—
616C2×#95—111no—
617C2×#95—111no—
618C2×#95—111no—
619C2×#95—111no—
620C2×#95—111no—
621C2×#95C2×D1111yescharacteristic
622C2×#95C2×D1111yescharacteristic
623C22×C11—24no—
624C22×C11—24no—
625C22×C11—24no—
626C22×C11—24no—
627C22×C11—24no—
628C22×C11—24no—
629C22×C11—42no—
630C22×C11—42no—
631C22×C11—42no—
632C22×C11—42no—
633C22×C11—42no—
634C22×C11—42no—
635C22×C11—42no—
636C22×C11—42no—
637C22×C11—42no—
638C22×C11—42no—
639C22×C11—42no—
640C22×C11—42no—
641C22×C11—42no—
642C22×C11—42no—
643C22×C11—42no—
644C22×C11—42no—
645C22×C11—42no—
646C22×C11—42no—
647C22×C11—42no—
648C22×C11—42no—
649C22×C11—42no—
650C22×C11—42no—
651C22×C11—42no—
652C22×C11—42no—
653C22×C11C2×C4×D411yescharacteristic
654C22×C11C2×C4×D411yescharacteristic
655C22×C11C2×C4×D411yescharacteristic
656C22×C11#51811yescharacteristic
657C22×C11#51811yescharacteristic
658C22×C11#51811yescharacteristic
659C22×C11#52011yescharacteristic
660C22×C11#53411yescharacteristic
661C22×C11#53411yescharacteristic
662C22×C11#53411yescharacteristic
663C22×C11#53711yescharacteristic
664C22×C11#53711yescharacteristic
665C22×C11#53711yescharacteristic
666C22×C11#53811yescharacteristic
667C22×C11#53811yescharacteristic
668C22×C11#53811yescharacteristic
669C22×C11#53911yescharacteristic
670C22×C11#53911yescharacteristic
671C22×C11#53911yescharacteristic
672C22×C11D4211yescharacteristic
673C22×C11D4211yescharacteristic
674C22×C11D4211yescharacteristic
675C22×C11#54611yescharacteristic
676C22×C11#54611yescharacteristic
677C22×C11#54611yescharacteristic
678C22×C11#54611yescharacteristic
679C22×C11#54611yescharacteristic
680C22×C11#54611yescharacteristic
681C22×C11#55111yescharacteristic
682C22×C11#55111yescharacteristic
683C22×C11#55111yescharacteristic
684C22×C11#56011yescharacteristic
685C22×C11#56011yescharacteristic
686C22×C11#56011yescharacteristic
687C22×C11#56011yescharacteristic
688C2×D11—24no—
689C2×D11—24no—
690C2×D11—24no—
691C2×D11—42no—
692C2×D11—42no—
693C2×D11—42no—
694C2×D11—42no—
695C2×D11—42no—
696C2×D11—42no—
697C2×D11—42no—
698C2×D11—42no—
699C2×D11—42no—
700C2×D11—42no—
701C2×D11—42no—
702C2×D11—42no—
703C4×C11—42no—
704C4×C11—42no—
705C4×C11—42no—
706C4×C11—42no—
707C4×C11—81no—
708Dic11—42no—
709Dic11—42no—
710Dic11—42no—
711Dic11—42no—
712Dic11—42no—
713Dic11—42no—
714Dic11—81no—
715C25—111no—
716C25C22×D1111yescharacteristic
717C25C22×D1111yescharacteristic
718C22×D4—22no—
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—41no—
723C22×D4—41no—
724C22×D4—114no—
725C22×D4—114no—
726C22×D4—222no—
727C22×D4—222no—
728C22×D4—222no—
729C22×D4—222no—
730C22×D4—222no—
731C22×D4—222no—
732C22×D4—222no—
733C22×D4—222no—
734C22×D4—441no—
735C22×D4—441no—
736C22×D4—441no—
737C22×D4—441no—
738C22×D4C4×D1114yescomplemented
739C23×C4—22no—
740C23×C4—22no—
741C23×C4—22no—
742C23×C4—41no—
743C23×C4—41no—
744C23×C4—41no—
745C23×C4—41no—
746C23×C4—111no—
747C23×C4—111no—
748C23×C4—111no—
749C23×C4—111no—
750C23×C4—111no—
751C23×C4—111no—
752C23×C4—111no—
753C23×C4—222no—
754C23×C4—222no—
755C23×C4—222no—
756C23×C4—222no—
757C23×C4—222no—
758C23×C4—222no—
759C23×C4—441no—
760C23×C4—441no—
761C23×C4—441no—
762C23×C4—441no—
763C23×C4—441no—
764C23×C4—441no—
765C23×C4—441no—
766C23×C4—441no—
767C23×C4C22×D1111yescharacteristic
768C23×C4C22×D1111yescharacteristic
769C23×C4C22×D1111yescharacteristic
770C23×C4C22×D1111yescharacteristic
771C23×C4C22×D1111yescharacteristic
772C2×C4⋊C4—441no—
773C2×C4⋊C4—441no—
774C2×C4⋊C4—441no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—41no—
780C2×C22⋊C4—41no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—114no—
784C2×C22⋊C4—114no—
785C2×C22⋊C4—114no—
786C2×C22⋊C4—114no—
787C2×C22⋊C4—114no—
788C2×C22⋊C4—222no—
789C2×C22⋊C4—222no—
790C2×C22⋊C4—222no—
791C2×C22⋊C4—222no—
792C2×C22⋊C4—222no—
793C2×C22⋊C4—222no—
794C2×C22⋊C4—222no—
795C2×C22⋊C4—222no—
796C2×C22⋊C4—441no—
797C2×C22⋊C4—441no—
798C2×C22⋊C4—441no—
799C2×C22⋊C4—441no—
800C2×C22⋊C4—441no—
801C2×C22⋊C4—441no—
802C2×C22⋊C4—441no—
803C2×C22⋊C4—441no—
804C2×C22⋊C4—441no—
805C2×C22⋊C4—441no—
806C2×C22⋊C4—441no—
807C2×C22⋊C4—441no—
808C2×C22⋊C4—441no—
809C2×C22⋊C4—441no—
810C2×C22⋊C4C22⋊D1114yescomplemented
811#95—22no—
812#95—22no—
813#95—114no—
814#95—222no—
815#95—222no—
816#95—222no—
817#95—222no—
818#95—222no—
819#95—222no—
820#95—222no—
821#95—222no—
822#95—222no—
823#95—222no—
824#95—441no—
825#95—441no—
826#95—441no—
827C2×C11—44no—
828C2×C11—44no—
829C2×C11#232511yescharacteristic
830C2×C11#232511yescharacteristic
831C2×C11#232511yescharacteristic
832C2×C11#235811yescharacteristic
833C2×C11#235811yescharacteristic
834C2×C11#235811yescharacteristic
835C2×C11#238011yescharacteristic
836C2×C11#266811yescharacteristic
837C2×C11#266811yescharacteristic
838C2×C11#266811yescharacteristic
839C2×C11#267511yescharacteristic
840C2×C11#269311yescharacteristic
841C2×C11#269311yescharacteristic
842C2×C11#269311yescharacteristic
843C2×C11#276011yescharacteristic
844D11—44no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—112no—
870C24—112no—
871C24—112no—
872C24—221no—
873C24—221no—
874C24—221no—
875C24—221no—
876C24—221no—
877C24—221no—
878C24—221no—
879C24—221no—
880C24—221no—
881C24—221no—
882C24—221no—
883C24—221no—
884C24C2×C4×D1112yes—
885C24C2×C4×D1112yes—
886C24#433912yes—
887C24D4×D1112yes—
888C24#434112yes—
889C24C2×C22⋊D1112yes—
890C24C23×D1111yescharacteristic
891C2×D4—28no—
892C2×D4—28no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—228no—
899C2×D4—228no—
900C2×D4—228no—
901C2×D4—228no—
902C2×D4—444no—
903C2×D4—444no—
904C2×D4—444no—
905C2×D4—444no—
906C2×D4—444no—
907C2×D4—444no—
908C2×D4—444no—
909C2×D4—444no—
910C2×D4—444no—
911C2×D4—444no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—44no—
944C22×C4—44no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4—44no—
950C22×C4—112no—
951C22×C4—112no—
952C22×C4—112no—
953C22×C4—112no—
954C22×C4—112no—
955C22×C4—112no—
956C22×C4—221no—
957C22×C4—221no—
958C22×C4—221no—
959C22×C4—221no—
960C22×C4—221no—
961C22×C4—221no—
962C22×C4—221no—
963C22×C4—221no—
964C22×C4—221no—
965C22×C4—221no—
966C22×C4—221no—
967C22×C4—221no—
968C22×C4—221no—
969C22×C4—221no—
970C22×C4—221no—
971C22×C4—221no—
972C22×C4—221no—
973C22×C4—221no—
974C22×C4—221no—
975C22×C4—221no—
976C22×C4—221no—
977C22×C4—221no—
978C22×C4—221no—
979C22×C4—221no—
980C22×C4—221no—
981C22×C4—221no—
982C22×C4—221no—
983C22×C4—221no—
984C22×C4—221no—
985C22×C4—221no—
986C22×C4—221no—
987C22×C4—221no—
988C22×C4—221no—
989C22×C4—221no—
990C22×C4—221no—
991C22×C4—221no—
992C22×C4—221no—
993C22×C4—221no—
994C22×C4—221no—
995C22×C4—221no—
996C22×C4—221no—
997C22×C4—221no—
998C22×C4—221no—
999C22×C4—444no—
1000C22×C4—444no—
1001C22×C4—444no—
1002C22×C4—444no—
1003C22×C4—444no—
1004C22×C4—444no—
1005C22×C4—444no—
1006C22×C4—444no—
1007C22×C4—444no—
1008C22×C4—444no—
1009C22×C4—444no—
1010C22×C4—444no—
1011C22×C4—444no—
1012C22×C4—444no—
1013C22×C4C2×C4×D1112yes—
1014C22×C4D4×D1112yes—
1015C22×C4C2×C22⋊D1112yes—
1016C22×C4C2×C22⋊D1112yes—
1017C4⋊C4—444no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—444no—
1022C22⋊C4—444no—
1023C22⋊C4—444no—
1024C22⋊C4—444no—
1025C22⋊C4—444no—
1026C22⋊C4—444no—
1027C22⋊C4—444no—
1028C22⋊C4—444no—
1029C22⋊C4—444no—
1030C11#1457211yescharacteristic, complemented, Sylow
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—114no—
1100C23—222no—
1101C23—222no—
1102C23—222no—
1103C23—222no—
1104C23—222no—
1105C23—222no—
1106C23—222no—
1107C23—222no—
1108C23—222no—
1109C23—222no—
1110C23—222no—
1111C23—222no—
1112C23—222no—
1113C23—222no—
1114C23—222no—
1115C23—222no—
1116C23—222no—
1117C23—222no—
1118C23—441no—
1119C23—441no—
1120C23—441no—
1121C23—441no—
1122C23—441no—
1123C23—441no—
1124C23—441no—
1125C23—441no—
1126C23—441no—
1127C23—441no—
1128C23—441no—
1129C23—441no—
1130C23—441no—
1131C23—441no—
1132C23—441no—
1133C23—441no—
1134C23(C22⋊D11)⋊C414yes—
1135C23C4×C22⋊D1114yes—
1136C23C22×C4×D1111yescharacteristic
1137C23C2×#433911yescharacteristic
1138C23C2×D4×D1111yescharacteristic
1139C23C2×D4×D1111yescharacteristic
1140C23C2×#434111yescharacteristic
1141C23#6703711yescharacteristic
1142C23#6703711yescharacteristic
1143C23#6703711yescharacteristic
1144C23#6703711yescharacteristic
1145C23#6703711yescharacteristic
1146C23#41×D1111yescharacteristic
1147C23#6704211yescharacteristic
1148C23#6704211yescharacteristic
1149C23#6704311yescharacteristic
1150C23C22×C22⋊D1111yescharacteristic
1151D4—416no—
1152D4—4416no—
1153D4—4416no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—416no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—222no—
1191C2×C4—222no—
1192C2×C4—222no—
1193C2×C4—222no—
1194C2×C4—222no—
1195C2×C4—222no—
1196C2×C4—222no—
1197C2×C4—222no—
1198C2×C4—222no—
1199C2×C4—222no—
1200C2×C4—222no—
1201C2×C4—222no—
1202C2×C4—222no—
1203C2×C4—222no—
1204C2×C4—222no—
1205C2×C4—222no—
1206C2×C4—222no—
1207C2×C4—222no—
1208C2×C4—4416no—
1209C2×C4—4416no—
1210C2×C4—441no—
1211C2×C4—441no—
1212C2×C4—441no—
1213C2×C4—441no—
1214C2×C4—441no—
1215C2×C4—441no—
1216C2×C4—441no—
1217C2×C4—441no—
1218C2×C4—441no—
1219C2×C4—441no—
1220C2×C4—441no—
1221C2×C4—441no—
1222C2×C4—441no—
1223C2×C4—441no—
1224C2×C4—441no—
1225C2×C4—441no—
1226C2×C4—441no—
1227C2×C4—441no—
1228C2×C4—441no—
1229C2×C4—441no—
1230C2×C4—441no—
1231C2×C4—441no—
1232C2×C4—441no—
1233C2×C4—441no—
1234C2×C4—441no—
1235C2×C4—441no—
1236C2×C4—441no—
1237C2×C4—441no—
1238C2×C4—441no—
1239C2×C4—441no—
1240C2×C4—441no—
1241C22—24no—
1242C22—24no—
1243C22—24no—
1244C22—24no—
1245C22—24no—
1246C22—24no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—224no—
1272C22—224no—
1273C22—224no—
1274C22—442no—
1275C22—442no—
1276C22—442no—
1277C22—442no—
1278C22—442no—
1279C22—442no—
1280C22—442no—
1281C22—442no—
1282C22—442no—
1283C22—442no—
1284C22—442no—
1285C22—442no—
1286C22C2×(C22⋊D11)⋊C411yescharacteristic
1287C22#1062301711yescharacteristic
1288C22#1062302111yescharacteristic
1289C22#1062302611yescharacteristic
1290C22C4×D4×D1111yescharacteristic
1291C22#1062307611yescharacteristic
1292C22#1062307611yescharacteristic
1293C22#1062307711yescharacteristic
1294C22#1062308111yescharacteristic
1295C22#1062308711yescharacteristic
1296C22#1062309111yescharacteristic
1297C22#1062309511yescharacteristic
1298C22#1062312011yescharacteristic
1299C22#1062312211yescharacteristic
1300C22#1062312411yescharacteristic
1301C22#1062312611yescharacteristic
1302C22#1062312811yescharacteristic
1303C22#1062313611yescharacteristic
1304C22#1062313911yescharacteristic
1305C22#1062314011yescharacteristic
1306C22#1062314111yescharacteristic
1307C22#1062314411yescharacteristic
1308C22#1062315111yescharacteristic
1309C22#1062315111yescharacteristic
1310C22#1062318911yescharacteristic
1311C22#1062319111yescharacteristic
1312C22#1062319611yescharacteristic
1313C22#1062319711yescharacteristic
1314C22C2×C4×C22⋊D1111yescharacteristic
1315C22D4×C22⋊D1111yescharacteristic
1316C22D4×C22⋊D1111yescharacteristic
1317C22#1062333511yescharacteristic
1318C22#1062333711yescharacteristic
1319C22#1062336011yescharacteristic
1320C22#1062336411yescharacteristic
1321C4—42no—
1322C4—42no—
1323C4—42no—
1324C4—42no—
1325C4—81no—
1326C4—442no—
1327C4—442no—
1328C4—442no—
1329C4—442no—
1330C4—442no—
1331C4—442no—
1332C4—881no—
1333C2—44no—
1334C2—44no—
1335C2—444no—
1336C2#1307131411yescharacteristic
1337C2#1307131711yescharacteristic
1338C2#1307131811yescharacteristic
1339C2#1307159311yescharacteristic
1340C2#1307159511yescharacteristic
1341C2#1307159611yescharacteristic
1342C2#1307179111yescharacteristic
1343C2#1307481911yescharacteristic
1344C2#1307482011yescharacteristic
1345C2#1307482111yescharacteristic
1346C2#1307490611yescharacteristic
1347C2#1307512111yescharacteristic
1348C2#1307512211yescharacteristic
1349C2#1307512711yescharacteristic
1350C2#1307599211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#386C2
socle, cosocleC24×C11C24
prime radicalC2×#10622836C2
hypercenterC2×#386D11
hypocenterC11#14572
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×#10622833C2semidirect
3. C2×#10622826C2semidirect
4. C2×#10622571C2semidirect
5. C2×#10622569C2semidirect
6. C2×#10622569C2semidirect
7. #13066877C2semidirect
8. #13066876C2semidirect
9. #13066860C2semidirect
10. #13066859C2semidirect
11. #13066859C2semidirect
12. #13066839C2semidirect
13. #13066838C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C2×C11×#386C2semidirect
38. #10622836C4semidirect
67. C22×D4×C11C2×C4semidirect
92. C22×C22⋊D11C2×C4semidirect
93. C22×C22⋊D11C2×C4semidirect
123. C2×C11×C22⋊C4D4semidirect
136. C2×C22⋊Dic11C2×C4semidirect
137. C2×C22⋊Dic11C2×C4semidirect
138. C2×C22⋊Dic11D4semidirect
149. C2×(C2×D11)⋊C4C2×C4semidirect
150. C2×(C2×D11)⋊C4D4semidirect
169. C11⋊#95C2×C4semidirect
362. C2×#386D11semidirect
738. C22×D4C4×D11semidirect
810. C2×C22⋊C4C22⋊D11semidirect
1030. C11#14572semidirect

Maximal subgroups

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

subgroupindex
C2×#106228362
C2×#106228332
C2×#106228262
C2×#106225712
C2×#106225692
#130668772
#130668762
#130668602
#130668592
#130668392
#130668382
(C2×D11)⋊#952
C2×C11×#3862
#1457211