Finite Group Databasebeta

← #14770266

Subgroups — #14770266

Order 2816.

1148 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#4318C211yesmaximal, characteristic, complemented
2#13071061C211yesmaximal, characteristic, complemented
3#13069598C211yesmaximal, characteristic, complemented
4#13069561C211yesmaximal, characteristic, complemented
5#13069065C211yesmaximal, characteristic, complemented
6#13069060C211yesmaximal, characteristic, complemented
7#13068919C211yesmaximal, characteristic, complemented
8#13068919C211yesmaximal, characteristic, complemented
9#13068715C211yesmaximal, characteristic, complemented
10#13068715C211yesmaximal, characteristic, complemented
11#13068636C211yesmaximal, characteristic, complemented
12#13068426C211yesmaximal, characteristic, complemented
13#13068325C211yesmaximal, characteristic, complemented
14C2×#10622170C211yesmaximal, characteristic, complemented
15C11×#3475C211yesmaximal, characteristic
16C11×#556C411yescharacteristic, complemented
17C11×#555C411yescharacteristic, complemented
18C11×#554C411yescharacteristic, complemented
19C11×#553C411yescharacteristic, complemented
20C11×#553C411yescharacteristic, complemented
21C11×#552—21no—
22C11×#552C411yescharacteristic, complemented
23C11×#552C411yescharacteristic, complemented
24C11×#551—21no—
25C11×#551—21no—
26C11×#547C411yescharacteristic, complemented
27C11×#546—21no—
28C11×#533C2211yescharacteristic
29C11×#529—21no—
30C11×#529—21no—
31C11×#529—21no—
32C11×#525C2211yescharacteristic
33C11×#525C2211yescharacteristic
34C4×C11×#41—21no—
35C4×C11×#41C2211yescharacteristic
36C2×C4×D4×C11C2211yescharacteristic
37C2×C11×#117C2211yescharacteristic
38C2×C11×#117C2211yescharacteristic
39C2×#66979C2211yescharacteristic
40C22×C4×Dic11C2211yescharacteristic
41C22×#4318C2211yescharacteristic
42C22×#4318C2211yescharacteristic
43C2×#66901C2211yescharacteristic
44C2×#66901C2211yescharacteristic
45C2×#66901C2211yescharacteristic
46C2×#66901C2211yescharacteristic
47#10622833—21no—
48C4×C22⋊Dic11C2211yescharacteristic
49C4×C22⋊Dic11C2211yescharacteristic
50#10622820C2211yescharacteristic
51#10622820C2211yescharacteristic
52#10622625—21no—
53#10622624—21no—
54#10622624—21no—
55D4×C11⋊C8—21no—
56#10622594—21no—
57#10622564—21no—
58#10622563—21no—
59C4×C4⋊Dic11C2211yescharacteristic
60#10622545C2211yescharacteristic
61#10622537C2211yescharacteristic
62C4×#4318C2211yescharacteristic
63#10622170C2211yescharacteristic
64#10622170C2211yescharacteristic
65#10622170C2211yescharacteristic
66#10622170C2211yescharacteristic
67#10622170C2211yescharacteristic
68#10622170C2211yescharacteristic
69#10622170C2211yescharacteristic
70#10622170C2211yescharacteristic
71#10622170C2211yescharacteristic
72#10622170C2211yescharacteristic
73#10622170C2211yescharacteristic
74#10622170C2211yescharacteristic
75C2×C11×#41—21no—
76C2×C11×#41C2311yescharacteristic
77C22×D4×C11D411yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×Dic11—21no—
81C11×C4⋊Q8C2×C411yescharacteristic, complemented
82C11×C4⋊Q8C2×C411yescharacteristic, complemented
83C11×#126—21no—
84C11×#126—21no—
85C11×#126—21no—
86C11×#126—21no—
87C11×#126—21no—
88C11×#126—21no—
89C11×#125—21no—
90C11×#125—21no—
91C11×#125—21no—
92C11×#125C2×C411yescharacteristic, complemented
93C11×#125C2×C411yescharacteristic, complemented
94C11×#124—21no—
95C11×#124—21no—
96C11×#124—21no—
97C11×#123—21no—
98C11×#123—21no—
99C11×#123—21no—
100C11×#123—21no—
101C11×#123—21no—
102C11×#123—21no—
103C11×#123—21no—
104C11×#123—21no—
105C11×C22⋊Q8—21no—
106C11×C22⋊Q8—21no—
107C11×C22⋊Q8—21no—
108C11×C22⋊Q8—21no—
109C11×C22⋊Q8—21no—
110C11×C22⋊Q8C2×C411yescharacteristic
111C11×C22⋊Q8C2×C411yescharacteristic
112C11×C22⋊Q8C2×C411yescharacteristic, complemented
113C11×C22⋊Q8C2×C411yescharacteristic, complemented
114C11×#121—21no—
115C11×#121—21no—
116C11×#121—21no—
117C11×#121C2×C411yescharacteristic
118C11×#121C2×C411yescharacteristic
119C11×#121C2×C411yescharacteristic, complemented
120C11×#121C2×C411yescharacteristic, complemented
121C11×#120—21no—
122C11×#120—21no—
123C4×Q8×C11—21no—
124C4×Q8×C11—21no—
125C4×Q8×C11—21no—
126C4×Q8×C11C2×C411yescharacteristic, complemented
127C4×Q8×C11C2×C411yescharacteristic, complemented
128C4×D4×C11—21no—
129C4×D4×C11—21no—
130C4×D4×C11—21no—
131C4×D4×C11—21no—
132C4×D4×C11—21no—
133C4×D4×C11—21no—
134C4×D4×C11—21no—
135C4×D4×C11—21no—
136C4×D4×C11—21no—
137C4×D4×C11C2×C411yescharacteristic
138C4×D4×C11C2×C411yescharacteristic
139C4×D4×C11C2×C411yescharacteristic
140C4×D4×C11C2×C411yescharacteristic
141C4×D4×C11C2×C411yescharacteristic, complemented
142C4×D4×C11C2×C411yescharacteristic, complemented
143C4×D4×C11D411yescharacteristic
144C4×D4×C11D411yescharacteristic
145C4×D4×C11D411yescharacteristic
146C4×D4×C11D411yescharacteristic
147C11×#117—21no—
148C11×#117—21no—
149C11×#117—21no—
150C11×#117—21no—
151C11×#117—21no—
152C11×#117—21no—
153C11×#117—21no—
154C11×#117—21no—
155C11×#117C2×C411yescharacteristic
156C11×#117C2×C411yescharacteristic
157C11×#117C2×C411yescharacteristic, complemented
158C11×#117C2×C411yescharacteristic, complemented
159C11×#117C2311yescharacteristic
160C11×#117C2311yescharacteristic
161C11×#117C2311yescharacteristic
162C2×C11×C4⋊C4C2×C411yescharacteristic
163C2×C11×C4⋊C4C2×C411yescharacteristic
164C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
165C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
166C2×C11×C4⋊C4D411yescharacteristic
167C2×C11×C22⋊C4—21no—
168C2×C11×C22⋊C4—21no—
169C2×C11×C22⋊C4D411yescharacteristic
170C2×C11×C22⋊C4D411yescharacteristic
171C2×C42×C11—21no—
172C2×C42×C11—21no—
173C2×C42×C11—21no—
174C2×C42×C11C2311yescharacteristic
175C2×C22⋊Dic11—21no—
176C2×C22⋊Dic11—21no—
177C2×C22⋊Dic11—21no—
178#66979—22no—
179#66979—41no—
180C2×C4⋊Dic11—21no—
181C2×C4⋊Dic11—21no—
182C2×C4×Dic11—22no—
183C2×C4×Dic11—21no—
184C2×C4×Dic11—41no—
185C2×C4×Dic11C2311yescharacteristic
186C2×C4×Dic11C2311yescharacteristic
187C2×C4×Dic11C2311yescharacteristic
188C2×C4×Dic11C2311yescharacteristic
189C2×#4318—21no—
190C2×#4318—21no—
191C2×#4318—22no—
192C2×#4318—22no—
193C2×#4318—41no—
194C2×#4318—41no—
195C2×#4318C2311yescharacteristic
196C2×#4318C2311yescharacteristic
197C2×#4318C2311yescharacteristic
198C2×#4318C2311yescharacteristic
199C22×C11⋊C8—21no—
200C22×C11⋊C8—21no—
201#66901—22no—
202#66901—22no—
203#66901—41no—
204#66901—41no—
205C11⋊#95—21no—
206C11⋊#95—21no—
207C11⋊#95—21no—
208C11⋊#95—21no—
209C11⋊#95—21no—
210C22⋊(C11⋊C8)—21no—
211C22⋊(C11⋊C8)—21no—
212C22⋊(C11⋊C8)—21no—
213C22⋊(C11⋊C8)—21no—
214C4⋊(C11⋊C8)—21no—
215C4⋊(C11⋊C8)—21no—
216#66867—21no—
217C4×C11⋊C8—21no—
218#22506—111nomaximal, Sylow
219C24×C11C2×D411yescharacteristic
220C24×C11C2×D411yescharacteristic
221C11×#41—21no—
222C11×#41—21no—
223C11×#41—21no—
224C11×#41—21no—
225C11×#41—44no—
226C2×Q8×C11—21no—
227C2×Q8×C11—21no—
228C2×Q8×C11C22×C411yescharacteristic
229C2×D4×C11—21no—
230C2×D4×C11—21no—
231C2×D4×C11—21no—
232C2×D4×C11—21no—
233C2×D4×C11—21no—
234C2×D4×C11—42no—
235C2×D4×C11C22⋊C411yescharacteristic
236C2×D4×C11C22⋊C411yescharacteristic
237C2×D4×C11C22⋊C411yescharacteristic
238C2×D4×C11C22⋊C411yescharacteristic
239C2×D4×C11C22×C411yescharacteristic
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×C11C22×C411yescharacteristic
256C22×C4×C11C22×C411yescharacteristic
257C22×C4×C11C22×C411yescharacteristic
258C22×C4×C11C22×C411yescharacteristic
259C22×C4×C11C2×D411yescharacteristic
260C22×C4×C11C2×D411yescharacteristic
261C22×C4×C11C2×D411yescharacteristic
262C22×C4×C11C2×D411yescharacteristic
263C22×C4×C11C2×D411yescharacteristic
264C22×C4×C11C2×D411yescharacteristic
265C22×C4×C11C2×D411yescharacteristic
266C22×C4×C11C2×D411yescharacteristic
267C22×C4×C11C2411yescharacteristic
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11—21no—
271C22×Dic11—21no—
272C22×Dic11—42no—
273C22×Dic11—42no—
274C22×Dic11—42no—
275C11×C4⋊C4—21no—
276C11×C4⋊C4—21no—
277C11×C4⋊C4—21no—
278C11×C4⋊C4—21no—
279C11×C4⋊C4—21no—
280C11×C4⋊C4—21no—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—21no—
283C11×C4⋊C4—21no—
284C11×C4⋊C4—21no—
285C11×C4⋊C4—21no—
286C11×C4⋊C4—21no—
287C11×C4⋊C4—21no—
288C11×C4⋊C4—21no—
289C11×C4⋊C4—21no—
290C11×C4⋊C4—21no—
291C11×C4⋊C4C22⋊C411yescharacteristic
292C11×C4⋊C4C22⋊C411yescharacteristic
293C11×C4⋊C4C22⋊C411yescharacteristic
294C11×C4⋊C4C22⋊C411yescharacteristic
295C11×C4⋊C4C22×C411yescharacteristic
296C11×C4⋊C4C22×C411yescharacteristic
297C11×C4⋊C4C22×C411yescharacteristic
298C11×C4⋊C4C22×C411yescharacteristic
299C11×C4⋊C4C22×C411yescharacteristic
300C11×C4⋊C4C22×C411yescharacteristic
301C11×C22⋊C4—21no—
302C11×C22⋊C4—21no—
303C11×C22⋊C4—21no—
304C11×C22⋊C4—21no—
305C11×C22⋊C4—21no—
306C11×C22⋊C4—21no—
307C11×C22⋊C4—21no—
308C11×C22⋊C4—21no—
309C11×C22⋊C4—21no—
310C11×C22⋊C4—21no—
311C11×C22⋊C4—21no—
312C11×C22⋊C4—21no—
313C11×C22⋊C4—21no—
314C11×C22⋊C4—21no—
315C11×C22⋊C4—21no—
316C11×C22⋊C4—21no—
317C11×C22⋊C4—21no—
318C11×C22⋊C4C22⋊C411yescharacteristic
319C11×C22⋊C4C22⋊C411yescharacteristic
320C11×C22⋊C4C22⋊C411yescharacteristic
321C11×C22⋊C4C22⋊C411yescharacteristic
322C11×C22⋊C4C22⋊C411yescharacteristic
323C11×C22⋊C4C22⋊C411yescharacteristic
324C11×C22⋊C4C22⋊C411yescharacteristic
325C11×C22⋊C4C22⋊C411yescharacteristic
326C42×C11—21no—
327C42×C11—21no—
328C42×C11—21no—
329C42×C11—21no—
330C42×C11—21no—
331C42×C11—21no—
332C42×C11—21no—
333C42×C11—21no—
334C42×C11—21no—
335C42×C11C22×C411yescharacteristic
336C42×C11C22×C411yescharacteristic
337C42×C11C2×D411yescharacteristic
338C42×C11C2×D411yescharacteristic
339C22⋊Dic11—42no—
340C22⋊Dic11—42no—
341C22⋊Dic11—42no—
342C4⋊Dic11—42no—
343C4⋊Dic11—42no—
344C4×Dic11—21no—
345C4×Dic11—21no—
346C4×Dic11—21no—
347C4×Dic11—21no—
348C4×Dic11—21no—
349C4×Dic11—21no—
350C4×Dic11—21no—
351C4×Dic11—42no—
352C4×Dic11#4112yescomplemented
353#4318—21no—
354#4318—21no—
355#4318—21no—
356#4318—21no—
357#4318—21no—
358#4318—21no—
359#4318—21no—
360#4318—42no—
361#4318—42no—
362#4318#4112yescomplemented
363C2×C11⋊C8—21no—
364C2×C11⋊C8—21no—
365C2×C11⋊C8—21no—
366C2×C11⋊C8—21no—
367C2×C11⋊C8—42no—
368C2×C11⋊C8—42no—
369#3475D1111yescharacteristic
370D4×M16—111no—
371#2290—111no—
372#1995—111no—
373#1986—111no—
374#1897—111no—
375#1896—111no—
376#1871—111no—
377#1871—111no—
378#1826—111no—
379#1826—111no—
380#1806—111no—
381#1759—111no—
382#1733—111no—
383C2×#339—111no—
384C23×C11—21no—
385C23×C11—21no—
386C23×C11—22no—
387C23×C11—21no—
388C23×C11—21no—
389C23×C11—21no—
390C23×C11—41no—
391C23×C11—41no—
392C23×C11—41no—
393C23×C11C2×C22⋊C411yescharacteristic
394C23×C11C2×C22⋊C411yescharacteristic
395C23×C11C2×C22⋊C411yescharacteristic
396C23×C11C2×C22⋊C411yescharacteristic
397C23×C11C22×D411yescharacteristic
398Q8×C11—21no—
399Q8×C11—21no—
400Q8×C11—42no—
401Q8×C11—81no—
402D4×C11—22no—
403D4×C11—22no—
404D4×C11—21no—
405D4×C11—21no—
406D4×C11—41no—
407D4×C11—41no—
408D4×C11—42no—
409D4×C11—41no—
410D4×C11—41no—
411D4×C11—42no—
412D4×C11—81no—
413D4×C11—81no—
414C2×C4×C11—21no—
415C2×C4×C11—21no—
416C2×C4×C11—21no—
417C2×C4×C11—21no—
418C2×C4×C11—21no—
419C2×C4×C11—21no—
420C2×C4×C11—21no—
421C2×C4×C11—21no—
422C2×C4×C11—21no—
423C2×C4×C11—21no—
424C2×C4×C11—21no—
425C2×C4×C11—21no—
426C2×C4×C11—21no—
427C2×C4×C11—21no—
428C2×C4×C11—21no—
429C2×C4×C11—21no—
430C2×C4×C11—21no—
431C2×C4×C11—21no—
432C2×C4×C11—21no—
433C2×C4×C11—21no—
434C2×C4×C11—21no—
435C2×C4×C11—21no—
436C2×C4×C11—21no—
437C2×C4×C11—21no—
438C2×C4×C11—21no—
439C2×C4×C11—21no—
440C2×C4×C11—21no—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
443C2×C4×C11—42no—
444C2×C4×C11—42no—
445C2×C4×C11—42no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C2×C4×C11—81no—
449C2×C4×C11—81no—
450C2×C4×C11—81no—
451C2×C4×C11C2×C22⋊C411yescharacteristic
452C2×C4×C11C2×C22⋊C411yescharacteristic
453C2×C4×C11C2×C22⋊C411yescharacteristic
454C2×C4×C11C2×C22⋊C411yescharacteristic
455C2×C4×C11C2×C22⋊C411yescharacteristic
456C2×C4×C11C2×C22⋊C411yescharacteristic
457C2×C4×C11C2×C22⋊C411yescharacteristic
458C2×C4×C11C2×C22⋊C411yescharacteristic
459C2×C4×C11C23×C411yescharacteristic
460C2×C4×C11C22×D411yescharacteristic
461C2×C4×C11C2×#4111yescharacteristic
462C2×C4×C11C2×#4111yescharacteristic
463C2×C4×C11H(5,𝔽2)11yescharacteristic
464C2×C4×C112−1+411yescharacteristic
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—41no—
468C2×Dic11—41no—
469C2×Dic11—41no—
470C2×Dic11—48no—
471C2×Dic11—41no—
472C2×Dic11—41no—
473C2×Dic11—41no—
474C2×Dic11—41no—
475C2×Dic11—41no—
476C2×Dic11—41no—
477C2×Dic11—41no—
478C11⋊C8—22no—
479C11⋊C8—41no—
480C11⋊C8—41no—
481C11⋊C8—41no—
482C22×M16—111no—
483C22×M16—111no—
484#556Dic1111yescharacteristic, complemented
485#555Dic1111yescharacteristic, complemented
486#554Dic1111yescharacteristic, complemented
487#553Dic1111yescharacteristic, complemented
488#553Dic1111yescharacteristic, complemented
489#552—21no—
490#552Dic1111yescharacteristic, complemented
491#552Dic1111yescharacteristic, complemented
492#551—21no—
493#551—21no—
494#547Dic1111yescharacteristic, complemented
495#546—21no—
496#533C2×D1111yescharacteristic
497#529—21no—
498#529—21no—
499#529—21no—
500#525C2×D1111yescharacteristic
501#525C2×D1111yescharacteristic
502C4×#41—21no—
503C4×#41C2×D1111yescharacteristic
504C2×C4×D4C2×D1111yescharacteristic
505C2×#117—111no—
506C2×#117C2×D1111yescharacteristic
507C2×#117C2×D1111yescharacteristic
508C22×C42—111no—
509#436—221no—
510#435—221no—
511#435—221no—
512C8×D4—221no—
513#423—111no—
514C2×#104—111no—
515C2×#104—111no—
516C2×#104—111no—
517C2×#104—111no—
518#407—111no—
519#407—111no—
520C4×M16—111no—
521#388—221no—
522#387—221no—
523#386—221no—
524#385—221no—
525C4×C4⋊C4—111no—
526C4×C22⋊C4—111no—
527C4×C22⋊C4—111no—
528#376—111no—
529#339—111no—
530#339—111no—
531#339—111no—
532#339—111no—
533#339—111no—
534#339—111no—
535#339—111no—
536#339—111no—
537#339—111no—
538#339—111no—
539#339—111no—
540#339—111no—
541C22×C11—21no—
542C22×C11—21no—
543C22×C11—21no—
544C22×C11—21no—
545C22×C11—21no—
546C22×C11—21no—
547C22×C11—21no—
548C22×C11—21no—
549C22×C11—21no—
550C22×C11—21no—
551C22×C11—21no—
552C22×C11—21no—
553C22×C11—21no—
554C22×C11—42no—
555C22×C11—42no—
556C22×C11—41no—
557C22×C11—41no—
558C22×C11—41no—
559C22×C11—81no—
560C22×C11—81no—
561C22×C11#42112yes—
562C22×C11C22×C22⋊C411yescharacteristic
563C22×C11#54611yescharacteristic
564C22×C11#54711yescharacteristic
565C4×C11—21no—
566C4×C11—21no—
567C4×C11—21no—
568C4×C11—21no—
569C4×C11—21no—
570C4×C11—21no—
571C4×C11—21no—
572C4×C11—21no—
573C4×C11—41no—
574C4×C11—41no—
575C4×C11—41no—
576C4×C11—41no—
577C4×C11—41no—
578C4×C11—41no—
579C4×C11—41no—
580C4×C11C4×#4111yescharacteristic
581C4×C11#52011yescharacteristic
582C4×C11#54611yescharacteristic
583C4×C11#54711yescharacteristic
584Dic11—42no—
585Dic11—42no—
586Dic11—81no—
587Dic11—81no—
588C2×#41—21no—
589C2×#41C22×D1111yescharacteristic
590C22×D4C22⋊D1111yescharacteristic
591C23×C4—221no—
592C23×C4C22×D1111yescharacteristic
593C23×C4C22×D1111yescharacteristic
594C2×M16—111no—
595C2×M16—111no—
596C2×M16—111no—
597C2×M16—111no—
598C2×M16—221no—
599C2×M16—221no—
600C2×M16—222no—
601C2×M16—222no—
602C2×M16—441no—
603C2×M16—441no—
604C22×C8—221no—
605C22×C8—221no—
606C4⋊Q8C2×Dic1111yescharacteristic, complemented
607C4⋊Q8C2×Dic1111yescharacteristic, complemented
608#126—21no—
609#126—21no—
610#126—21no—
611#126—21no—
612#126—21no—
613#126—21no—
614#125—21no—
615#125—21no—
616#125—21no—
617#125C2×Dic1111yescharacteristic, complemented
618#125C2×Dic1111yescharacteristic, complemented
619#124—21no—
620#124—21no—
621#124—21no—
622#123—21no—
623#123—21no—
624#123—21no—
625#123—21no—
626#123—21no—
627#123—21no—
628#123—21no—
629#123—21no—
630C22⋊Q8—21no—
631C22⋊Q8—21no—
632C22⋊Q8—21no—
633C22⋊Q8—21no—
634C22⋊Q8—21no—
635C22⋊Q8C2×Dic1111yescharacteristic
636C22⋊Q8C2×Dic1111yescharacteristic
637C22⋊Q8C2×Dic1111yescharacteristic, complemented
638C22⋊Q8C2×Dic1111yescharacteristic, complemented
639#121—21no—
640#121—21no—
641#121—21no—
642#121C2×Dic1111yescharacteristic
643#121C2×Dic1111yescharacteristic
644#121C2×Dic1111yescharacteristic, complemented
645#121C2×Dic1111yescharacteristic, complemented
646#120—21no—
647#120—21no—
648C4×Q8—21no—
649C4×Q8—21no—
650C4×Q8—21no—
651C4×Q8C2×Dic1111yescharacteristic, complemented
652C4×Q8C2×Dic1111yescharacteristic, complemented
653C4×D4—21no—
654C4×D4—21no—
655C4×D4—21no—
656C4×D4—21no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—21no—
660C4×D4—21no—
661C4×D4—21no—
662C4×D4C2×Dic1111yescharacteristic
663C4×D4C2×Dic1111yescharacteristic
664C4×D4C2×Dic1111yescharacteristic
665C4×D4C2×Dic1111yescharacteristic
666C4×D4C2×Dic1111yescharacteristic, complemented
667C4×D4C2×Dic1111yescharacteristic, complemented
668C4×D4C22⋊D1111yescharacteristic
669C4×D4C22⋊D1111yescharacteristic
670C4×D4C22⋊D1111yescharacteristic
671C4×D4C22⋊D1111yescharacteristic
672#117—21no—
673#117—21no—
674#117—21no—
675#117—21no—
676#117—21no—
677#117—21no—
678#117—21no—
679#117—21no—
680#117—222no—
681#117—441no—
682#117C2×Dic1111yescharacteristic
683#117C2×Dic1111yescharacteristic
684#117C2×Dic1111yescharacteristic, complemented
685#117C2×Dic1111yescharacteristic, complemented
686#117C22×D1111yescharacteristic
687#117C22×D1111yescharacteristic
688#117C22×D1111yescharacteristic
689C2×C4⋊C4—221no—
690C2×C4⋊C4—221no—
691C2×C4⋊C4C2×Dic1111yescharacteristic
692C2×C4⋊C4C2×Dic1111yescharacteristic
693C2×C4⋊C4C2×Dic1111yescharacteristic, complemented
694C2×C4⋊C4C2×Dic1111yescharacteristic, complemented
695C2×C4⋊C4C22⋊D1111yescharacteristic
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—221no—
699C2×C22⋊C4—221no—
700C2×C22⋊C4—221no—
701C2×C22⋊C4C22⋊D1111yescharacteristic
702C2×C22⋊C4C22⋊D1111yescharacteristic
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—111no—
707C2×C42—111no—
708C2×C42—111no—
709C2×C42—111no—
710C2×C42—222no—
711C2×C42—221no—
712C2×C42—441no—
713C2×C42C22×D1111yescharacteristic
714C4⋊C8—221no—
715C4⋊C8—221no—
716#104—222no—
717#104—222no—
718#104—441no—
719#104—441no—
720C22⋊C8—221no—
721C22⋊C8—221no—
722C22⋊C8—221no—
723C22⋊C8—221no—
724#97—221no—
725C4×C8—221no—
726#95—221no—
727#95—221no—
728#95—221no—
729#95—221no—
730#95—221no—
731C2×C11—21no—
732C2×C11—21no—
733C2×C11—22no—
734C2×C11—41no—
735C2×C11—41no—
736C2×C11—41no—
737C2×C11—81no—
738C2×C11#233911yescharacteristic
739C2×C11C2×#42111yescharacteristic
740C2×C11#290111yescharacteristic
741C24C2×C22⋊D1111yescharacteristic
742C24C2×C22⋊D1111yescharacteristic
743#41—21no—
744#41—21no—
745#41—21no—
746#41—21no—
747#41—44no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8C22×Dic1111yescharacteristic
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—42no—
757C2×D4C22⋊Dic1111yescharacteristic
758C2×D4C22⋊Dic1111yescharacteristic
759C2×D4C22⋊Dic1111yescharacteristic
760C2×D4C22⋊Dic1111yescharacteristic
761C2×D4C22×Dic1111yescharacteristic
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—221no—
778C22×C4—221no—
779C22×C4—221no—
780C22×C4—221no—
781C22×C4—442no—
782C22×C4—442no—
783C22×C4—442no—
784C22×C4C22×Dic1111yescharacteristic
785C22×C4C22×Dic1111yescharacteristic
786C22×C4C22×Dic1111yescharacteristic
787C22×C4C22×Dic1111yescharacteristic
788C22×C4C2×C22⋊D1111yescharacteristic
789C22×C4C2×C22⋊D1111yescharacteristic
790C22×C4C2×C22⋊D1111yescharacteristic
791C22×C4C2×C22⋊D1111yescharacteristic
792C22×C4C2×C22⋊D1111yescharacteristic
793C22×C4C2×C22⋊D1111yescharacteristic
794C22×C4C2×C22⋊D1111yescharacteristic
795C22×C4C2×C22⋊D1111yescharacteristic
796C22×C4C23×D1111yescharacteristic
797M16—112no—
798M16—221no—
799M16—221no—
800M16—221no—
801M16—221no—
802M16—221no—
803M16—221no—
804M16—221no—
805M16—442no—
806M16—442no—
807C2×C8—221no—
808C2×C8—221no—
809C2×C8—221no—
810C2×C8—221no—
811C2×C8—442no—
812C2×C8—442no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—442no—
830C4⋊C4—442no—
831C4⋊C4C22⋊Dic1111yescharacteristic
832C4⋊C4C22⋊Dic1111yescharacteristic
833C4⋊C4C22⋊Dic1111yescharacteristic
834C4⋊C4C22⋊Dic1111yescharacteristic
835C4⋊C4C22×Dic1111yescharacteristic
836C4⋊C4C22×Dic1111yescharacteristic
837C4⋊C4C22×Dic1111yescharacteristic
838C4⋊C4C22×Dic1111yescharacteristic
839C4⋊C4C22×Dic1111yescharacteristic
840C4⋊C4C22×Dic1111yescharacteristic
841C22⋊C4—21no—
842C22⋊C4—21no—
843C22⋊C4—21no—
844C22⋊C4—21no—
845C22⋊C4—21no—
846C22⋊C4—21no—
847C22⋊C4—21no—
848C22⋊C4—21no—
849C22⋊C4—21no—
850C22⋊C4—21no—
851C22⋊C4—21no—
852C22⋊C4—21no—
853C22⋊C4—21no—
854C22⋊C4—21no—
855C22⋊C4—21no—
856C22⋊C4—21no—
857C22⋊C4—21no—
858C22⋊C4—442no—
859C22⋊C4—442no—
860C22⋊C4—442no—
861C22⋊C4C22⋊Dic1111yescharacteristic
862C22⋊C4C22⋊Dic1111yescharacteristic
863C22⋊C4C22⋊Dic1111yescharacteristic
864C22⋊C4C22⋊Dic1111yescharacteristic
865C22⋊C4C22⋊Dic1111yescharacteristic
866C22⋊C4C22⋊Dic1111yescharacteristic
867C22⋊C4C22⋊Dic1111yescharacteristic
868C22⋊C4C22⋊Dic1111yescharacteristic
869C42—21no—
870C42—21no—
871C42—21no—
872C42—21no—
873C42—21no—
874C42—21no—
875C42—21no—
876C42—21no—
877C42—21no—
878C42—112no—
879C42—221no—
880C42—221no—
881C42—221no—
882C42—221no—
883C42—221no—
884C42—221no—
885C42—221no—
886C42—442no—
887C42C22×Dic1111yescharacteristic
888C42C22×Dic1111yescharacteristic
889C42C2×C22⋊D1111yescharacteristic
890C42C2×C22⋊D1111yescharacteristic
891C11#2250611yescharacteristic, complemented, Sylow
892C23—21no—
893C23—21no—
894C23—22no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23C2×C22⋊Dic1111yescharacteristic
902C23C2×C22⋊Dic1111yescharacteristic
903C23C2×C22⋊Dic1111yescharacteristic
904C23C2×C22⋊Dic1111yescharacteristic
905C23C22×C22⋊D1111yescharacteristic
906Q8—21no—
907Q8—21no—
908Q8—42no—
909Q8—81no—
910D4—22no—
911D4—22no—
912D4—21no—
913D4—21no—
914D4—41no—
915D4—41no—
916D4—42no—
917D4—41no—
918D4—41no—
919D4—42no—
920D4—81no—
921D4—81no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—81no—
957C2×C4—81no—
958C2×C4—81no—
959C2×C4—222no—
960C2×C4—222no—
961C2×C4—441no—
962C2×C4—441no—
963C2×C4—441no—
964C2×C4—448no—
965C2×C4—441no—
966C2×C4—441no—
967C2×C4—441no—
968C2×C4—441no—
969C2×C4—441no—
970C2×C4—441no—
971C2×C4—441no—
972C2×C4C2×C22⋊Dic1111yescharacteristic
973C2×C4C2×C22⋊Dic1111yescharacteristic
974C2×C4C2×C22⋊Dic1111yescharacteristic
975C2×C4C2×C22⋊Dic1111yescharacteristic
976C2×C4C2×C22⋊Dic1111yescharacteristic
977C2×C4C2×C22⋊Dic1111yescharacteristic
978C2×C4C2×C22⋊Dic1111yescharacteristic
979C2×C4C2×C22⋊Dic1111yescharacteristic
980C2×C4#41×D1111yescharacteristic
981C2×C4#41×D1111yescharacteristic
982C2×C4#6704211yescharacteristic
983C2×C4#6704311yescharacteristic
984C2×C4C23×Dic1111yescharacteristic
985C2×C4C22×C22⋊D1111yescharacteristic
986C8—222no—
987C8—441no—
988C8—441no—
989C8—441no—
990C22—21no—
991C22—21no—
992C22—21no—
993C22—21no—
994C22—21no—
995C22—21no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—42no—
1004C22—42no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—81no—
1009C22—81no—
1010C22#1062284912yes—
1011C22#1062335511yescharacteristic
1012C22#1062336011yescharacteristic
1013C22C22×C22⋊Dic1111yescharacteristic
1014C4—21no—
1015C4—21no—
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—21no—
1021C4—21no—
1022C4—41no—
1023C4—41no—
1024C4—41no—
1025C4—41no—
1026C4—41no—
1027C4—41no—
1028C4—41no—
1029C4—442no—
1030C4—442no—
1031C4—881no—
1032C4—881no—
1033C4#1062335511yescharacteristic
1034C4#41×Dic1111yescharacteristic
1035C4#1062335811yescharacteristic
1036C4#1062336011yescharacteristic
1037C2—21no—
1038C2—21no—
1039C2—22no—
1040C2—41no—
1041C2—41no—
1042C2—41no—
1043C2—81no—
1044C2#1307144611yescharacteristic
1045C2C2×#1062284911yescharacteristic
1046C2#1307716311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3475C2
socleC22×C11C22×C22⋊C4
cosocleC22×C4×C11C24
hypercenter#3475D11
hypocenterC11#22506
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ #3475

Complements

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

NH ≅ G/Ntype
1. D4×#4318C2semidirect
2. #13071061C2semidirect
3. #13069598C2semidirect
4. #13069561C2semidirect
5. #13069065C2semidirect
6. #13069060C2semidirect
7. #13068919C2semidirect
8. #13068919C2semidirect
9. #13068715C2semidirect
10. #13068715C2semidirect
11. #13068636C2semidirect
12. #13068426C2semidirect
13. #13068325C2semidirect
14. C2×#10622170C2semidirect
16. C11×#556C4semidirect
17. C11×#555C4semidirect
18. C11×#554C4semidirect
19. C11×#553C4semidirect
20. C11×#553C4semidirect
22. C11×#552C4semidirect
23. C11×#552C4semidirect
26. C11×#547C4semidirect
81. C11×C4⋊Q8C2×C4semidirect
82. C11×C4⋊Q8C2×C4semidirect
92. C11×#125C2×C4semidirect
93. C11×#125C2×C4semidirect
112. C11×C22⋊Q8C2×C4semidirect
113. C11×C22⋊Q8C2×C4semidirect
119. C11×#121C2×C4semidirect
120. C11×#121C2×C4semidirect
126. C4×Q8×C11C2×C4semidirect
127. C4×Q8×C11C2×C4semidirect
141. C4×D4×C11C2×C4semidirect
142. C4×D4×C11C2×C4semidirect
157. C11×#117C2×C4semidirect
158. C11×#117C2×C4semidirect
164. C2×C11×C4⋊C4C2×C4semidirect
165. C2×C11×C4⋊C4C2×C4semidirect
352. C4×Dic11#41semidirect
362. #4318#41semidirect
484. #556Dic11semidirect
485. #555Dic11semidirect
486. #554Dic11semidirect
487. #553Dic11semidirect
488. #553Dic11semidirect
490. #552Dic11semidirect
491. #552Dic11semidirect
494. #547Dic11semidirect
606. C4⋊Q8C2×Dic11semidirect
607. C4⋊Q8C2×Dic11semidirect
617. #125C2×Dic11semidirect
618. #125C2×Dic11semidirect
637. C22⋊Q8C2×Dic11semidirect
638. C22⋊Q8C2×Dic11semidirect
644. #121C2×Dic11semidirect
645. #121C2×Dic11semidirect
651. C4×Q8C2×Dic11semidirect
652. C4×Q8C2×Dic11semidirect
666. C4×D4C2×Dic11semidirect
667. C4×D4C2×Dic11semidirect
684. #117C2×Dic11semidirect
685. #117C2×Dic11semidirect
693. C2×C4⋊C4C2×Dic11semidirect
694. C2×C4⋊C4C2×Dic11semidirect
891. C11#22506semidirect

Maximal subgroups

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

subgroupindex
D4×#43182
#130710612
#130695982
#130695612
#130690652
#130690602
#130689192
#130687152
#130686362
#130684262
#130683252
C2×#106221702
C11×#34752
#2250611