Finite Group Databasebeta

← #14677569

Subgroups — #14677569

Order 2816.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66999C211yesmaximal, characteristic
2C2×#10622602C211yesmaximal, characteristic
3C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
4C2×D11×#95C211yesmaximal, characteristic
5#13066887C211yesmaximal, characteristic, complemented
6#13066882C211yesmaximal, characteristic, complemented
7#13066868C211yesmaximal, characteristic, complemented
8#13066866C211yesmaximal, characteristic, complemented
9#13066850C211yesmaximal, characteristic, complemented
10#13066849C211yesmaximal, characteristic, complemented
11Dic11⋊#95C211yesmaximal, characteristic, complemented
12(C2×D11)⋊#95C211yesmaximal, characteristic
13(C2×D11)⋊#95C211yesmaximal, characteristic
14(C2×D11)⋊#95C211yesmaximal, characteristic
15C2×C11×#391C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C2×#66999—24no—
23C2×#66999—24no—
24C2×#66999C418yescomplemented
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C11×#391—24no—
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
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55#10622602—24no—
56C4×(C2×D11)⋊C4—24no—
57D11×#95—24no—
58C24×D11C2311yescharacteristic
59C22×Q8×C11—22no—
60C22×Q8×C11—22no—
61C22×Q8×C11—22no—
62C22×Q8×C11—22no—
63C22×Q8×C11—41no—
64C22×Q8×C11—41no—
65C22×Q8×C11C2×C414yescomplemented
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C22×C4×D11—22no—
81C22×C4×D11—22no—
82C22×C4×D11—22no—
83C22×C4×D11—22no—
84C22×C4×D11—22no—
85C22×C4×D11—22no—
86C22×C4×D11—22no—
87C22×C4×D11—22no—
88C22×C4×D11—22no—
89C22×C4×D11—22no—
90C22×C4×D11—22no—
91C22×C4×D11—22no—
92C22×C4×D11—22no—
93C22×C4×D11—41no—
94C22×C4×D11—41no—
95C22×C4×D11—41no—
96C22×C4×D11—41no—
97C22×C4×D11—41no—
98C22×C4×D11—41no—
99C22×C4×D11C2×C414yes—
100C22×C4×D11Q814yescomplemented
101C2×C11×C4⋊C4—22no—
102C2×C11×C4⋊C4—22no—
103C2×C11×C4⋊C4—41no—
104C2×C42×C11—22no—
105C2×C42×C11—22no—
106C2×C42×C11—41no—
107#66999—232no—
108C2×(C2×D11)⋊C4—22no—
109C2×(C2×D11)⋊C4—22no—
110C2×(C2×D11)⋊C4—22no—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4—22no—
113C2×(C2×D11)⋊C4—22no—
114C2×(C2×D11)⋊C4—22no—
115C2×(C2×D11)⋊C4C2×C414yes—
116C2×(C2×D11)⋊C4C2×C414yes—
117C2×(C2×D11)⋊C4D414yes—
118C2×(C2×D11)⋊C4D414yes—
119C2×(C2×D11)⋊C4Q814yescomplemented
120C2×C4⋊Dic11—22no—
121C2×C4⋊Dic11—22no—
122C2×C4⋊Dic11C2×C414yescomplemented
123C2×Dic11⋊C4—22no—
124C2×Dic11⋊C4—22no—
125C2×Dic11⋊C4—22no—
126C2×Dic11⋊C4—22no—
127C2×Dic11⋊C4—22no—
128C2×Dic11⋊C4—22no—
129C2×Dic11⋊C4—41no—
130C2×Dic11⋊C4C2×C414yescomplemented
131C2×Dic11⋊C4C2×C414yescomplemented
132C2×C4×Dic11—22no—
133C2×C4×Dic11—22no—
134C2×C4×Dic11—41no—
135C11×#95—22no—
136C11×#95—22no—
137C11×#95—22no—
138C11×#95D414yes—
139C11⋊#95—22no—
140C11⋊#95—22no—
141C11⋊#95—22no—
142C11⋊#95—22no—
143C11⋊#95—22no—
144C11⋊#95—22no—
145C11⋊#95—22no—
146C11⋊#95—22no—
147C11⋊#95—22no—
148C11⋊#95—22no—
149C11⋊#95—41no—
150C11⋊#95—41no—
151C11⋊#95—41no—
152C11⋊#95—41no—
153C11⋊#95—41no—
154C11⋊#95—41no—
155#14052—111nomaximal, Sylow
156C24×C11C2411yescharacteristic
157C23×D11—21no—
158C23×D11—21no—
159C23×D11—21no—
160C23×D11—21no—
161C23×D11—21no—
162C23×D11—21no—
163C23×D11—21no—
164C23×D11—21no—
165C23×D11C22×C412yes—
166C23×D11C2×D412yes—
167C23×D11C2×D412yes—
168C23×D11C2×Q812yes—
169C23×D11C2×Q812yes—
170C23×D11#4112yes—
171C23×D11#4112yes—
172C2×Q8×C11—28no—
173C2×Q8×C11—28no—
174C2×Q8×C11—44no—
175C2×Q8×C11—44no—
176C2×Q8×C11—44no—
177C2×Q8×C11—44no—
178C2×Q8×C11—44no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11C22×C412yes—
217C22×C4×C11C22×C412yes—
218C22×C4×C11C22×C412yes—
219C22×C4×C11C2×D412yes—
220C22×C4×C11C2×D412yes—
221C22×C4×C11C2×D412yes—
222C22×C4×C11C2×D412yes—
223C22×C4×C11C2×D412yes—
224C22×C4×C11C2×Q812yes—
225C22×C4×C11C2×Q812yes—
226C22×C4×C11#4112yes—
227C22×C4×C11#4112yes—
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×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11C22×C412yes—
270C22×Dic11C22×C412yes—
271C22×Dic11C22×C412yes—
272C22×Dic11C2×D412yes—
273C22×Dic11C2×D412yes—
274C22×Dic11C2×Q812yes—
275C22×Dic11C2×Q812yes—
276C22×Dic11#4112yes—
277C2×C4×D11—28no—
278C2×C4×D11—28no—
279C2×C4×D11—28no—
280C2×C4×D11—28no—
281C2×C4×D11—28no—
282C2×C4×D11—44no—
283C2×C4×D11—44no—
284C2×C4×D11—44no—
285C2×C4×D11—44no—
286C2×C4×D11—44no—
287C2×C4×D11—44no—
288C2×C4×D11—44no—
289C2×C4×D11—44no—
290C2×C4×D11—44no—
291C2×C4×D11—44no—
292C2×C4×D11—44no—
293C2×C4×D11—44no—
294C2×C4×D11—44no—
295C2×C4×D11—44no—
296C2×C4×D11—44no—
297C2×C4×D11—44no—
298C11×C4⋊C4—44no—
299C42×C11—44no—
300(C2×D11)⋊C4—28no—
301(C2×D11)⋊C4—28no—
302(C2×D11)⋊C4—44no—
303(C2×D11)⋊C4C22⋊C4116yes—
304C4⋊Dic11—28no—
305Dic11⋊C4—28no—
306Dic11⋊C4—28no—
307Dic11⋊C4—44no—
308C4×Dic11—44no—
309C22×C22⋊Q8—111no—
310C2×#391D1111yescharacteristic, complemented
311C2×#385—111no—
312C2×C4×C22⋊C4—111no—
313C22×#95—111no—
314#1446—111no—
315#1445—111no—
316#1441—111no—
317#1441—111no—
318#1436—111no—
319#1436—111no—
320C4⋊#95—111no—
321C22⋊#95—111no—
322C22⋊#95—111no—
323C22⋊#95—111no—
324C23×C11C23×C411yescharacteristic
325C23×C11C22×D411yescharacteristic
326C23×C11C22×D411yescharacteristic
327C23×C11C22×D411yescharacteristic
328C23×C11C22×Q811yescharacteristic
329C23×C11C22×Q811yescharacteristic
330C23×C11C2×#4111yescharacteristic
331C23×C11C2×#4111yescharacteristic
332C23×C11C2×#4111yescharacteristic
333C23×C11C2×#4111yescharacteristic
334C23×C11C2×#4111yescharacteristic
335C23×C11H(5,𝔽2)11yescharacteristic
336C23×C11H(5,𝔽2)11yescharacteristic
337C23×C11H(5,𝔽2)11yescharacteristic
338C23×C112−1+411yescharacteristic
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—22no—
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—22no—
367C22×D11C2×C22⋊C414yes—
368C22×D11C4×Q814yes—
369C22×D11C4×Q814yes—
370C22×D11C22⋊Q814yes—
371C22×D11C22⋊Q814yes—
372C22×D11#12414yes—
373C22×D11C4⋊Q814yes—
374Q8×C11—416no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
411C2×C4×C11—41no—
412C2×C4×C11—41no—
413C2×C4×C11—41no—
414C2×C4×C11—41no—
415C2×C4×C11—41no—
416C2×C4×C11—41no—
417C2×C4×C11—41no—
418C2×C4×C11—41no—
419C2×C4×C11—41no—
420C2×C4×C11—41no—
421C2×C4×C11C2×C22⋊C414yes—
422C2×C4×C11C4×D414yes—
423C2×C4×C11C22⋊Q814yescomplemented
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—41no—
446C2×Dic11—41no—
447C2×Dic11—41no—
448C2×Dic11—41no—
449C2×Dic11—41no—
450C2×Dic11—41no—
451C2×Dic11—41no—
452C2×Dic11—41no—
453C2×Dic11—41no—
454C2×Dic11—41no—
455C2×Dic11—41no—
456C2×Dic11—41no—
457C2×Dic11—41no—
458C2×Dic11—41no—
459C2×Dic11—41no—
460C2×Dic11—41no—
461C2×Dic11—41no—
462C2×Dic11—41no—
463C2×Dic11—41no—
464C2×Dic11—41no—
465C2×Dic11—41no—
466C2×Dic11—41no—
467C2×Dic11—41no—
468C2×Dic11—41no—
469C2×Dic11—41no—
470C2×Dic11—41no—
471C2×Dic11—41no—
472C2×Dic11C2×C22⋊C414yes—
473C4×D11—416no—
474C4×D11—416no—
475C4×D11—416no—
476C23×Q8C2×D1111yescharacteristic
477C24×C4—111no—
478C24×C4—111no—
479C24×C4—111no—
480C2×C22⋊Q8—118no—
481C2×C22⋊Q8—224no—
482C2×C22⋊Q8—224no—
483C22×C4⋊C4—111no—
484C22×C4⋊C4—111no—
485C22×C4⋊C4—111no—
486C22×C4⋊C4—111no—
487C22×C4⋊C4C2×D1111yescharacteristic
488C22×C22⋊C4—111no—
489C22×C22⋊C4—111no—
490C22×C22⋊C4—111no—
491C22×C22⋊C4—111no—
492C22×C42—111no—
493C22×C42C2×D1111yescharacteristic
494#391—24no—
495#385—224no—
496C4×C22⋊C4—224no—
497C2×#95—111no—
498C2×#95—111no—
499C2×#95—111no—
500C2×#95—111no—
501C2×#95—111no—
502C2×#95—111no—
503C2×#95—111no—
504C2×#95—111no—
505C2×#95—111no—
506C2×#95—111no—
507C2×#95—111no—
508C2×#95—111no—
509C2×#95—111no—
510C2×#95—111no—
511C2×#95—111no—
512C2×#95—111no—
513C2×#95—224no—
514C2×#95C2×D1111yescharacteristic
515C2×#95C2×D1111yescharacteristic
516C2×#95C2×D1111yescharacteristic
517C2×#95C2×D1111yescharacteristic
518C22×C11C22×C22⋊C411yescharacteristic
519C22×C11C2×C4×D411yescharacteristic
520C22×C11C2×C4×Q811yescharacteristic
521C22×C11C2×C4×Q811yescharacteristic
522C22×C11C4×#4111yescharacteristic
523C22×C11#51811yescharacteristic
524C22×C11#52011yescharacteristic
525C22×C11C2×C22⋊Q811yescharacteristic
526C22×C11C2×C22⋊Q811yescharacteristic
527C22×C11C2×C22⋊Q811yescharacteristic
528C22×C11#52511yescharacteristic
529C22×C11C2×#12411yescharacteristic
530C22×C11#52911yescharacteristic
531C22×C11C2×C4⋊Q811yescharacteristic
532C22×C11#53311yescharacteristic
533C22×C11#53811yescharacteristic
534C22×C11#53911yescharacteristic
535C22×C11#54311yescharacteristic
536C22×C11#54411yescharacteristic
537C22×C11D4211yescharacteristic
538C22×C11D4211yescharacteristic
539C22×C11#54611yescharacteristic
540C22×C11#54611yescharacteristic
541C22×C11#54611yescharacteristic
542C22×C11#54611yescharacteristic
543C22×C11#54611yescharacteristic
544C22×C11#54711yescharacteristic
545C22×C11#54711yescharacteristic
546C22×C11D4×Q811yescharacteristic
547C22×C11#55111yescharacteristic
548C22×C11#55111yescharacteristic
549C22×C11#55211yescharacteristic
550C22×C11#55411yescharacteristic
551C22×C11#55411yescharacteristic
552C22×C11#55411yescharacteristic
553C2×D11—24no—
554C2×D11—24no—
555C2×D11—24no—
556C2×D11—24no—
557C2×D11—24no—
558C2×D11—24no—
559C2×D11—24no—
560C2×D11—24no—
561C2×D11—24no—
562C2×D11—24no—
563C2×D11—24no—
564C2×D11—24no—
565C2×D11—24no—
566C2×D11—24no—
567C2×D11#39118yescomplemented
568C4×C11—24no—
569C4×C11—24no—
570C4×C11—24no—
571C4×C11—42no—
572C4×C11—42no—
573C4×C11—42no—
574C4×C11—81no—
575Dic11—24no—
576Dic11—42no—
577Dic11—42no—
578Dic11—42no—
579Dic11—42no—
580Dic11—42no—
581Dic11—81no—
582C25—111no—
583C22×Q8—22no—
584C22×Q8—22no—
585C22×Q8—22no—
586C22×Q8—22no—
587C22×Q8—41no—
588C22×Q8—41no—
589C22×Q8C4×D1114yescomplemented
590C23×C4—111no—
591C23×C4—111no—
592C23×C4—111no—
593C23×C4—111no—
594C23×C4—111no—
595C23×C4—111no—
596C23×C4—114no—
597C23×C4—114no—
598C23×C4—111no—
599C23×C4—222no—
600C23×C4—222no—
601C23×C4—222no—
602C23×C4—222no—
603C23×C4—222no—
604C23×C4—222no—
605C23×C4—222no—
606C23×C4—222no—
607C23×C4—222no—
608C23×C4—222no—
609C23×C4—222no—
610C23×C4—222no—
611C23×C4—222no—
612C23×C4—441no—
613C23×C4—441no—
614C23×C4—441no—
615C23×C4—441no—
616C23×C4—441no—
617C23×C4—441no—
618C23×C4C22×D1111yescharacteristic
619C23×C4C22×D1111yescharacteristic
620C23×C4C22×D1111yescharacteristic
621C23×C4C22×D1111yescharacteristic
622C23×C4C22×D1111yescharacteristic
623C23×C4C22×D1111yescharacteristic
624C23×C4C22×D1111yescharacteristic
625C22⋊Q8—2232no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—41no—
629C2×C4⋊C4—114no—
630C2×C4⋊C4—114no—
631C2×C4⋊C4—114no—
632C2×C4⋊C4—222no—
633C2×C4⋊C4—222no—
634C2×C4⋊C4—222no—
635C2×C4⋊C4—222no—
636C2×C4⋊C4—222no—
637C2×C4⋊C4—222no—
638C2×C4⋊C4—222no—
639C2×C4⋊C4—222no—
640C2×C4⋊C4—441no—
641C2×C22⋊C4—114no—
642C2×C22⋊C4—114no—
643C2×C22⋊C4—114no—
644C2×C22⋊C4—114no—
645C2×C22⋊C4—114no—
646C2×C22⋊C4—222no—
647C2×C22⋊C4—222no—
648C2×C22⋊C4—222no—
649C2×C22⋊C4—222no—
650C2×C22⋊C4—222no—
651C2×C22⋊C4—222no—
652C2×C22⋊C4—222no—
653C2×C42—22no—
654C2×C42—22no—
655C2×C42—41no—
656C2×C42—222no—
657C2×C42—222no—
658C2×C42—441no—
659#95—22no—
660#95—22no—
661#95—22no—
662#95—222no—
663#95—222no—
664#95—222no—
665#95—222no—
666#95—222no—
667#95—222no—
668#95—222no—
669#95—222no—
670#95—222no—
671#95—222no—
672#95—441no—
673#95—441no—
674#95—441no—
675#95—441no—
676#95—441no—
677#95—441no—
678#95C22⋊D1114yes—
679C2×C11C2×#39111yescharacteristic
680C2×C11C4×C22⋊Q811yescharacteristic
681C2×C11#232911yescharacteristic
682C2×C11D4×C22⋊C411yescharacteristic
683C2×C11#233911yescharacteristic
684C2×C11#236011yescharacteristic
685C2×C11#236811yescharacteristic
686C2×C11#243711yescharacteristic
687C2×C11#243811yescharacteristic
688C2×C11#244011yescharacteristic
689C2×C11#244911yescharacteristic
690C2×C11#245011yescharacteristic
691C2×C11#247211yescharacteristic
692C2×C11#248811yescharacteristic
693C2×C11#254911yescharacteristic
694D11—28no—
695C24—112no—
696C24—112no—
697C24—112no—
698C24—112no—
699C24—112no—
700C24—112no—
701C24—112no—
702C24—221no—
703C24—221no—
704C24—221no—
705C24—221no—
706C24—221no—
707C24—221no—
708C24—221no—
709C24—221no—
710C24C23×D1111yescharacteristic
711C2×Q8—28no—
712C2×Q8—28no—
713C2×Q8—44no—
714C2×Q8—44no—
715C2×Q8—44no—
716C2×Q8—44no—
717C2×Q8—44no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—112no—
756C22×C4—112no—
757C22×C4—112no—
758C22×C4—112no—
759C22×C4—112no—
760C22×C4—112no—
761C22×C4—112no—
762C22×C4—112no—
763C22×C4—228no—
764C22×C4—228no—
765C22×C4—228no—
766C22×C4—221no—
767C22×C4—221no—
768C22×C4—221no—
769C22×C4—221no—
770C22×C4—221no—
771C22×C4—221no—
772C22×C4—221no—
773C22×C4—221no—
774C22×C4—221no—
775C22×C4—221no—
776C22×C4—221no—
777C22×C4—221no—
778C22×C4—221no—
779C22×C4—221no—
780C22×C4—221no—
781C22×C4—221no—
782C22×C4—221no—
783C22×C4—221no—
784C22×C4—221no—
785C22×C4—221no—
786C22×C4—221no—
787C22×C4—221no—
788C22×C4—221no—
789C22×C4—221no—
790C22×C4—221no—
791C22×C4—221no—
792C22×C4—221no—
793C22×C4—221no—
794C22×C4—221no—
795C22×C4—221no—
796C22×C4—221no—
797C22×C4—221no—
798C22×C4—221no—
799C22×C4—221no—
800C22×C4—228no—
801C22×C4—228no—
802C22×C4—221no—
803C22×C4—221no—
804C22×C4—221no—
805C22×C4—221no—
806C22×C4—221no—
807C22×C4—221no—
808C22×C4—221no—
809C22×C4—444no—
810C22×C4—444no—
811C22×C4—444no—
812C22×C4—444no—
813C22×C4—444no—
814C22×C4—444no—
815C22×C4—444no—
816C22×C4—444no—
817C22×C4—444no—
818C22×C4—444no—
819C22×C4—444no—
820C22×C4—444no—
821C22×C4—444no—
822C22×C4—444no—
823C22×C4—444no—
824C22×C4—444no—
825C22×C4C2×C4×D1112yes—
826C22×C4C2×C4×D1112yes—
827C22×C4C2×C4×D1112yes—
828C22×C4#433912yes—
829C22×C4D4×D1112yes—
830C22×C4D4×D1112yes—
831C22×C4Q8×D1112yes—
832C22×C4Q8×D1112yes—
833C22×C4#434312yes—
834C22×C4C2×C22⋊D1112yes—
835C22×C4C2×C22⋊D1112yes—
836C22×C4C2×C22⋊D1112yes—
837C4⋊C4—44no—
838C4⋊C4—228no—
839C4⋊C4—228no—
840C4⋊C4—228no—
841C4⋊C4—444no—
842C22⋊C4—1116no—
843C22⋊C4—228no—
844C22⋊C4—228no—
845C22⋊C4—444no—
846C42—44no—
847C42—444no—
848C11#1405211yescharacteristic, complemented, Sylow
849C23—114no—
850C23—114no—
851C23—114no—
852C23—114no—
853C23—114no—
854C23—114no—
855C23—114no—
856C23—222no—
857C23—222no—
858C23—222no—
859C23—222no—
860C23—222no—
861C23—222no—
862C23—222no—
863C23—222no—
864C23—222no—
865C23—222no—
866C23—222no—
867C23—222no—
868C23—222no—
869C23—222no—
870C23—222no—
871C23—222no—
872C23—222no—
873C23—222no—
874C23—222no—
875C23—222no—
876C23—222no—
877C23—222no—
878C23—222no—
879C23—222no—
880C23—222no—
881C23—222no—
882C23—222no—
883C23—222no—
884C23C22×C4×D1111yescharacteristic
885C23C2×#433911yescharacteristic
886C23C2×D4×D1111yescharacteristic
887C23C2×D4×D1111yescharacteristic
888C23#6703711yescharacteristic
889C23#6703711yescharacteristic
890C23C2×Q8×D1111yescharacteristic
891C23C2×Q8×D1111yescharacteristic
892C23C2×#434311yescharacteristic
893C23#6704011yescharacteristic
894C23#41×D1111yescharacteristic
895C23#41×D1111yescharacteristic
896C23#41×D1111yescharacteristic
897C23#6704211yescharacteristic
898C23C22×C22⋊D1111yescharacteristic
899Q8—416no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—114no—
947C2×C4—222no—
948C2×C4—222no—
949C2×C4—222no—
950C2×C4—222no—
951C2×C4—222no—
952C2×C4—222no—
953C2×C4—222no—
954C2×C4—222no—
955C2×C4—222no—
956C2×C4—222no—
957C2×C4—222no—
958C2×C4—222no—
959C2×C4—222no—
960C2×C4—222no—
961C2×C4—222no—
962C2×C4—222no—
963C2×C4—222no—
964C2×C4—222no—
965C2×C4—222no—
966C2×C4—222no—
967C2×C4—222no—
968C2×C4—4416no—
969C2×C4—4416no—
970C2×C4—4416no—
971C2×C4—441no—
972C2×C4—441no—
973C2×C4—441no—
974C2×C4—441no—
975C2×C4—441no—
976C2×C4—441no—
977C2×C4—441no—
978C2×C4—441no—
979C2×C4—441no—
980C2×C4—441no—
981C2×C4—441no—
982C2×C4—441no—
983C2×C4—441no—
984C2×C4—441no—
985C2×C4—441no—
986C2×C4—441no—
987C2×C4—441no—
988C2×C4—441no—
989C2×C4—441no—
990C2×C4—441no—
991C2×C4—441no—
992C2×C4—441no—
993C2×C4—441no—
994C2×C4—441no—
995C2×C4—441no—
996C2×C4—441no—
997C2×C4—441no—
998C2×C4C22⋊C4×D1114yes—
999C2×C4C4×C22⋊D1114yes—
1000C2×C4#6699914yescomplemented
1001C22—118no—
1002C22—224no—
1003C22—224no—
1004C22—224no—
1005C22—224no—
1006C22—224no—
1007C22—224no—
1008C22—224no—
1009C22—224no—
1010C22—224no—
1011C22—224no—
1012C22—224no—
1013C22—224no—
1014C22—224no—
1015C22—224no—
1016C22C2×C22⋊C4×D1111yescharacteristic
1017C22#1062301711yescharacteristic
1018C22#1062302111yescharacteristic
1019C22#1062302111yescharacteristic
1020C22C4×Q8×D1111yescharacteristic
1021C22C4×Q8×D1111yescharacteristic
1022C22C4×#434311yescharacteristic
1023C22#1062310511yescharacteristic
1024C22#1062310911yescharacteristic
1025C22#1062311011yescharacteristic
1026C22#1062311111yescharacteristic
1027C22#1062311211yescharacteristic
1028C22D11×C22⋊Q811yescharacteristic
1029C22D11×C22⋊Q811yescharacteristic
1030C22#1062316111yescharacteristic
1031C22#1062316211yescharacteristic
1032C22#1062316511yescharacteristic
1033C22#1062316711yescharacteristic
1034C22#1062316811yescharacteristic
1035C22#1062316911yescharacteristic
1036C22D11×#12411yescharacteristic
1037C22#1062320711yescharacteristic
1038C22#1062320911yescharacteristic
1039C22#1062321011yescharacteristic
1040C22D11×C4⋊Q811yescharacteristic
1041C22#1062325711yescharacteristic
1042C22#1062326011yescharacteristic
1043C22#1062326111yescharacteristic
1044C22C2×C4×C22⋊D1111yescharacteristic
1045C22D4×C22⋊D1111yescharacteristic
1046C22D4×C22⋊D1111yescharacteristic
1047C22C2×#6699911yescharacteristic
1048C22Q8×C22⋊D1111yescharacteristic
1049C22#1062335911yescharacteristic
1050C22#1062336011yescharacteristic
1051C4—24no—
1052C4—24no—
1053C4—24no—
1054C4—42no—
1055C4—42no—
1056C4—42no—
1057C4—81no—
1058C4—224no—
1059C4—442no—
1060C4—442no—
1061C4—442no—
1062C4—442no—
1063C4—442no—
1064C4—881no—
1065C2—228no—
1066C2D11×#39111yescharacteristic
1067C2C4×#6699911yescharacteristic
1068C2#1307134811yescharacteristic
1069C2C22⋊C4×C22⋊D1111yescharacteristic
1070C2#1307144511yescharacteristic
1071C2#1307161711yescharacteristic
1072C2#1307169511yescharacteristic
1073C2#1307227911yescharacteristic
1074C2#1307228911yescharacteristic
1075C2#1307231411yescharacteristic
1076C2#1307242211yescharacteristic
1077C2#1307243711yescharacteristic
1078C2#1307273811yescharacteristic
1079C2#1307294911yescharacteristic
1080C2#1307362511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#391C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#391D11
hypocenterC11#14052
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
5. #13066887C2semidirect
6. #13066882C2semidirect
7. #13066868C2semidirect
8. #13066866C2semidirect
9. #13066850C2semidirect
10. #13066849C2semidirect
11. Dic11⋊#95C2semidirect
15. C2×C11×#391C2semidirect
24. C2×#66999C4semidirect
65. C22×Q8×C11C2×C4semidirect
100. C22×C4×D11Q8semidirect
119. C2×(C2×D11)⋊C4Q8semidirect
122. C2×C4⋊Dic11C2×C4semidirect
130. C2×Dic11⋊C4C2×C4semidirect
131. C2×Dic11⋊C4C2×C4semidirect
310. C2×#391D11semidirect
423. C2×C4×C11C22⋊Q8semidirect
567. C2×D11#391semidirect
589. C22×Q8C4×D11semidirect
848. C11#14052semidirect
1000. C2×C4#66999semidirect

Maximal subgroups

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

subgroupindex
C22×#669992
C2×#106226022
C2×C4×(C2×D11)⋊C42
C2×D11×#952
#130668872
#130668822
#130668682
#130668662
#130668502
#130668492
Dic11⋊#952
(C2×D11)⋊#952
C2×C11×#3912
#1405211