Finite Group Databasebeta

← #14656955

Subgroups — #14656955

Order 2816.

360 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074265C211yesmaximal, characteristic
2#13069560C211yesmaximal, characteristic
3#13067166C211yesmaximal, characteristic
4#13067129C211yesmaximal, characteristic
5#13066510C211yesmaximal, characteristic
6#13066473C211yesmaximal, characteristic
7C11×#1288C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C11×#432C2211yescharacteristic
10C4×C11×M16C2211yescharacteristic
11C11×#383C2211yescharacteristic
12C4×C4⋊Dic11C2211yescharacteristic
13#10622545C2211yescharacteristic
14#10622539C2211yescharacteristic
15#10622273—21no—
16#10622269—21no—
17#10622268—21no—
18#10622267—21no—
19#10622259—21no—
20#10622259—21no—
21#10622193—21no—
22#10622193—21no—
23#10622105—21no—
24#10622105—21no—
25#10622090—21no—
26#10622090—21no—
27C22×Dic22—21no—
28C2×C11×M16—21no—
29C2×C42×C11C2311yescharacteristic
30#66979—21no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33#66977—21no—
34#66977—21no—
35C2×Dic11⋊C4—21no—
36C2×Dic11⋊C4—21no—
37C2×C4×Dic11—21no—
38C2×C4×Dic11D411yescharacteristic
39C2×C4×Dic11D411yescharacteristic
40#66923—21no—
41#66922Q811yescharacteristic, complemented
42#66922Q811yescharacteristic, complemented
43C4×Dic22—21no—
44C4×Dic22—21no—
45C11×C4⋊C8—21no—
46C11×C22⋊C8—21no—
47C11×#97—21no—
48C11×#97—21no—
49C4×C8×C11—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95D411yescharacteristic
53C11×#95D411yescharacteristic
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95D411yescharacteristic
61C11⋊#95D411yescharacteristic
62C22⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64#66867—21no—
65#10379—111nomaximal, Sylow
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C2×Dic22—21no—
76C2×Dic22—21no—
77C2×Dic22—42no—
78C2×Dic22—42no—
79C2×Dic22—81no—
80C11×M16—22no—
81C11×M16—41no—
82C2×C8×C11—41no—
83C2×C8×C11—41no—
84C42×C11C2×Q811yescharacteristic
85C42×C11#4111yescharacteristic
86C42×C11#4111yescharacteristic
87C42×C11#4111yescharacteristic
88C22⋊Dic11—41no—
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11—42no—
94C4⋊Dic11—42no—
95Dic11⋊C4—42no—
96Dic11⋊C4—41no—
97Dic11⋊C4—41no—
98Dic11⋊C4—81no—
99C4×Dic11—41no—
100C4×Dic11—41no—
101C4×Dic11—42no—
102C4×Dic11—41no—
103C2×C11⋊C8—41no—
104#2605—111no—
105#1986—111no—
106#1515—111no—
107#1506—111no—
108#1300—111no—
109#1288D1111yescharacteristic
110#1285—111no—
111C23×C11#12011yescharacteristic
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11C22⋊Q811yescharacteristic
123C2×C4×C11C22⋊Q811yescharacteristic
124C2×C4×C11C22⋊Q811yescharacteristic
125C2×C4×C11#12411yescharacteristic
126C2×C4×C11#12411yescharacteristic
127C2×C4×C11#12411yescharacteristic
128C2×Dic11—22no—
129C2×Dic11—22no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142Dic22—84no—
143Dic22—81no—
144Dic22—81no—
145C8×C11—42no—
146C8×C11—81no—
147C11⋊C8—81no—
148#533—111no—
149#432—111no—
150#432C2×D1111yescharacteristic
151C4×M16C2×D1111yescharacteristic
152#400—221no—
153#395—221no—
154#391—221no—
155#391—221no—
156#387—221no—
157#387—221no—
158#383C2×D1111yescharacteristic
159C4×C4⋊C4—111no—
160#376—111no—
161#339—221no—
162#339—221no—
163#328—221no—
164#328—221no—
165#328—221no—
166#328—221no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11#39311yescharacteristic
170C22×C11#45511yescharacteristic
171C22×C11#45611yescharacteristic
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—81no—
179C4×C11—81no—
180Dic11—42no—
181Dic11—42no—
182Dic11—81no—
183Dic11—81no—
184Dic11—81no—
185Dic11—81no—
186C22×Q8—221no—
187C2×M16—21no—
188C4⋊Q8—111no—
189C4⋊Q8—111no—
190#125—221no—
191C22⋊Q8—221no—
192C22⋊Q8—221no—
193C4×Q8—221no—
194C4×Q8—221no—
195#117—221no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C42—111no—
201C2×C42—111no—
202C2×C42—221no—
203C2×C42C22×D1111yescharacteristic
204C4⋊C8—21no—
205C4⋊C8—221no—
206C22⋊C8—21no—
207C22⋊C8—221no—
208#97—21no—
209#97—21no—
210#97—221no—
211C4×C8—21no—
212#95—21no—
213#95—21no—
214#95—111no—
215#95—111no—
216#95—221no—
217#95—221no—
218#95—221no—
219#95—221no—
220#95—221no—
221#95—221no—
222#95D4411yescharacteristic
223#95D4411yescharacteristic
224C2×C11—21no—
225C2×C11—21no—
226C2×C11#202811yescharacteristic
227C2×C11#203111yescharacteristic
228C2×C11#203111yescharacteristic
229C2×Q8—221no—
230C2×Q8—221no—
231C2×Q8—442no—
232C2×Q8—442no—
233C2×Q8—881no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—221no—
237C22×C4—221no—
238C22×C4—221no—
239C22×C4—221no—
240C22×C4C2×D4411yescharacteristic
241C22×C4D4×D1111yescharacteristic
242C22×C4D4×D1111yescharacteristic
243M16—22no—
244M16—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—441no—
248C4⋊C4—221no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—442no—
253C4⋊C4—442no—
254C4⋊C4—442no—
255C4⋊C4—441no—
256C4⋊C4—441no—
257C4⋊C4—881no—
258C22⋊C4—441no—
259C42—441no—
260C42—441no—
261C42—442no—
262C42—441no—
263C42#433911yescharacteristic
264C42#433911yescharacteristic
265C42#434111yescharacteristic
266C42Q8×D1111yescharacteristic
267C11#1037911yescharacteristic, complemented, Sylow
268C23#6693511yescharacteristic
269Q8—881no—
270Q8—881no—
271Q8—884no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—222no—
283C2×C4—222no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4—441no—
295C2×C4—441no—
296C2×C4#6692811yescharacteristic
297C2×C4#6693811yescharacteristic
298C2×C4#6693811yescharacteristic
299C2×C4#6694911yescharacteristic
300C2×C4#6694911yescharacteristic
301C2×C4#6695011yescharacteristic
302C8—42no—
303C8—81no—
304C8—881no—
305C22—21no—
306C22—21no—
307C22#1062228611yescharacteristic
308C22#1062243811yescharacteristic
309C22#1062243911yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—81no—
317C4—81no—
318C4—442no—
319C4—442no—
320C4—881no—
321C4—881no—
322C4—881no—
323C4—881no—
324C2—21no—
325C2—21no—
326C2#1306977611yescharacteristic
327C2#1306978711yescharacteristic
328C2#1306979111yescharacteristic
subgroupG/H
centerC22#10622286
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1288C2
socleC22×C11#393
prime radicalC23×C11#120
hypercenter#1288D11
hypocenterC11#10379
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1288

Complements

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

NH ≅ G/Ntype
41. #66922Q8semidirect
42. #66922Q8semidirect
267. C11#10379semidirect

Maximal subgroups

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

subgroupindex
#130742652
#130695602
#130671662
#130671292
#130665102
#130664732
C11×#12882
#1037911