Finite Group Databasebeta

← #14667511

Subgroups — #14667511

Order 2816.

294 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 65 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#13081581C211yesmaximal, characteristic, complemented
2#13070857C211yesmaximal, characteristic
3#13068097C211yesmaximal, characteristic
4#13066667C211yesmaximal, characteristic, complemented
5#13066597C211yesmaximal, characteristic, complemented
6#13066586C211yesmaximal, characteristic, complemented
7C11×#2207C211yesmaximal, characteristic
8#10623100—21no—
9C2×C11×SD32—21no—
10C11×#493C2211yescharacteristic
11C4×C11×Q16C2211yescharacteristic
12#10622797—21no—
13#10622688—21no—
14#10622635—21no—
15#10622489—21no—
16#10622409—21no—
17#10622407—21no—
18#10622296C2211yescharacteristic
19#10622292C2211yescharacteristic
20C11×C4⋊C16C2211yescharacteristic
21C11×#357—21no—
22#10622200—21no—
23#10622200—21no—
24#10622182—21no—
25#10622099C2211yescharacteristic
26#10622095C2211yescharacteristic
27C2×C11×Q16D411yescharacteristic
28C2×C11×D8—21no—
29C2×C11×D8—21no—
30C11×#127—21no—
31C4×Q8×C11—21no—
32Q8×Dic11—21no—
33Q8×Dic11—21no—
34C2×#4324—41no—
35#66943—21no—
36#66943—41no—
37#66941—21no—
38#66941—41no—
39#66923—21no—
40#66923—41no—
41C4×Dic22—41no—
42C4×Dic22D411yescharacteristic
43C11×SD32—42no—
44C2×C11×C16—21no—
45C11×#107D411yescharacteristic
46C11×#103—21no—
47C4×C8×C11C2311yescharacteristic
48#66899—21no—
49#66899—21no—
50#66896—41no—
51#66882D411yescharacteristic
52#66882D411yescharacteristic
53#66881—21no—
54#66879—21no—
55Dic11⋊C8—21no—
56C2×C11⋊C16—21no—
57#66872—21no—
58#66871—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)D411yescharacteristic
61#12361—111nomaximal, Sylow
62C2×Q8×C11—21no—
63C2×D4×C11—41no—
64C2×D4×C11—41no—
65C2×D4×C11—41no—
66C2×Dic22—41no—
67C2×Dic22D811yescharacteristic
68C11×Q16—21no—
69C11×Q16SD1612yescomplemented
70C11×D8—42no—
71C11×D8—41no—
72C11×D8—41no—
73C2×C8×C11C2×D411yescharacteristic
74C2×C8×C11C2×D411yescharacteristic
75C11×C4⋊C4—21no—
76C11×C4⋊C4—41no—
77C42×C11—41no—
78C42×C11C2×D411yescharacteristic
79#4324—82no—
80C4⋊Dic11—21no—
81C4⋊Dic11—21no—
82C4⋊Dic11—41no—
83C4⋊Dic11—41no—
84C4⋊Dic11—41no—
85C4⋊Dic11D811yescharacteristic
86Dic11⋊C4—21no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89Dic11⋊C4—41no—
90Dic11⋊C4—41no—
91C4×Dic11—21no—
92C4×Dic11—41no—
93C4×Dic11—41no—
94C2×C11⋊C8—21no—
95C2×C11⋊C8—41no—
96C11×C16—41no—
97C11⋊C16—41no—
98#3390—111no—
99#2244—111no—
100#2207D1111yescharacteristic
101#1688—111no—
102#1363—111no—
103#1338—111no—
104#1334—111no—
105C23×C11—81no—
106Q8×C11—22no—
107Q8×C11—41no—
108D4×C11—81no—
109D4×C11—81no—
110D4×C11—81no—
111D4×C11—81no—
112D4×C11—161no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11#12011yescharacteristic
116C2×C4×C11C2×D811yescharacteristic
117C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—41no—
121C2×Dic11—41no—
122Dic22—41no—
123Dic22—82no—
124C8×C11—21no—
125C8×C11C2×SD1611yescharacteristic
126C8×C11#13711yescharacteristic
127C11⋊C8—41no—
128C11⋊C8—81no—
129#557—221no—
130C2×SD32—21no—
131#501—221no—
132#499—111no—
133#493C2×D1111yescharacteristic
134#479—221no—
135#479—221no—
136#477—221no—
137#460—221no—
138#446—111no—
139#441—221no—
140C4×Q16C2×D1111yescharacteristic
141C4⋊C16C2×D1111yescharacteristic
142#357—21no—
143#357—221no—
144#357—221no—
145#346—111no—
146#334—111no—
147#331—221no—
148C22×C11—161no—
149C22×C11—161no—
150C22×C11—161no—
151C22×C11#44711yescharacteristic
152C4×C11—21no—
153C4×C11—21no—
154C4×C11—42no—
155C4×C11—81no—
156C4×C11#44811yescharacteristic
157C4×C11#45411yescharacteristic
158Dic11—41no—
159Dic11—41no—
160Dic11—81no—
161Dic11—81no—
162C2×Q16C22⋊D1111yescharacteristic
163C2×SD16—441no—
164C2×D8—21no—
165C2×D8—21no—
166C4⋊Q8—221no—
167C4⋊Q8—441no—
168#127—21no—
169#125—221no—
170#125—221no—
171#125—441no—
172#125—441no—
173C4×Q8—21no—
174C4×Q8—111no—
175C4×Q8—221no—
176C4×Q8—221no—
177C4×Q8—441no—
178SD32—42no—
179C2×C16—21no—
180C2×C16—221no—
181#107—111no—
182#107—111no—
183#107—221no—
184#107C22⋊D1111yescharacteristic
185#106—221no—
186#106—221no—
187C4⋊C8—111no—
188C4⋊C8—221no—
189C4⋊C8—221no—
190#103—21no—
191#103—221no—
192#103—221no—
193#102—441no—
194#97—221no—
195C4×C8C22×D1111yescharacteristic
196C2×C11—321no—
197C2×C11#162711yescharacteristic
198C2×C11#219011yescharacteristic
199C2×C11#219311yescharacteristic
200C2×Q8—21no—
201C2×Q8—111no—
202C2×Q8—441no—
203C2×D4—41no—
204C2×D4—41no—
205C2×D4—41no—
206Q16—21no—
207Q16#432412yescomplemented
208SD16—882no—
209D8—42no—
210D8—41no—
211D8—41no—
212C2×C8—221no—
213C2×C8—441no—
214C2×C8D4×D1111yescharacteristic
215C2×C8C2×C22⋊D1111yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—41no—
218C4⋊C4—111no—
219C4⋊C4—221no—
220C4⋊C4—221no—
221C4⋊C4—221no—
222C4⋊C4—441no—
223C4⋊C4—441no—
224C4⋊C4—441no—
225C4⋊C4—441no—
226C4⋊C4—441no—
227C4⋊C4—441no—
228C4⋊C4—441no—
229C42—41no—
230C42—221no—
231C42—441no—
232C42—441no—
233C42D4×D1111yescharacteristic
234C16—41no—
235C16—441no—
236C11#1236111yescharacteristic, complemented, Sylow
237C23—81no—
238Q8—22no—
239Q8—41no—
240Q8—441no—
241Q8—882no—
242D4—81no—
243D4—81no—
244D4—81no—
245D4—81no—
246D4—161no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—221no—
250C2×C4—221no—
251C2×C4—441no—
252C2×C4—441no—
253C2×C4D8×D1111yescharacteristic
254C2×C4#6696411yescharacteristic
255C2×C4#6699011yescharacteristic
256C8—21no—
257C8—441no—
258C8—881no—
259C8C2×#432411yescharacteristic
260C8#6700411yescharacteristic
261C22—161no—
262C22—161no—
263C22—161no—
264C22#1062276911yescharacteristic
265C4—21no—
266C4—21no—
267C4—42no—
268C4—81no—
269C4—441no—
270C4—441no—
271C4—881no—
272C4—881no—
273C4#1062265311yescharacteristic
274C4#1062281411yescharacteristic
275C2—321no—
276C2#1306771811yescharacteristic
277C2#1307056011yescharacteristic
278C2#1307057911yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2207C2
socleC22×C11#447
prime radicalC11×#493C22
hypercenter#2207D11
hypocenterC11#12361
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2207

Complements

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

NH ≅ G/Ntype
1. #13081581C2semidirect
4. #13066667C2semidirect
5. #13066597C2semidirect
6. #13066586C2semidirect
69. C11×Q16SD16semidirect
207. Q16#4324semidirect
236. C11#12361semidirect

Maximal subgroups

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

subgroupindex
#130815812
#130708572
#130680972
#130666672
#130665972
#130665862
C11×#22072
#1236111