Finite Group Databasebeta

← #14667525

Subgroups — #14667525

Order 2816.

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

normal subgroups only

This group has 278 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
2#13070861C211yesmaximal, characteristic
3#13068107C211yesmaximal, characteristic
4#13066667C211yesmaximal, characteristic
5#13066597C211yesmaximal, characteristic
6#13066586C211yesmaximal, characteristic
7C11×#2209C211yesmaximal, characteristic
8#10623100—21no—
9C2×C11×Q32—21no—
10C11×#494C2211yescharacteristic
11C4×C11×Q16C2211yescharacteristic
12#10622797—21no—
13#10622707—21no—
14#10622635—21no—
15#10622489—21no—
16#10622409—21no—
17#10622407—21no—
18#10622296C2211yescharacteristic
19#10622292C2211yescharacteristic
20C11×C4⋊C16C2211yescharacteristic
21C11×#358—21no—
22#10622202—21no—
23#10622202—21no—
24#10622185—21no—
25#10622099C2211yescharacteristic
26#10622095C2211yescharacteristic
27C2×C11×Q16—21no—
28C2×C11×Q16—21no—
29C2×C11×Q16D411yescharacteristic
30C11×C4⋊Q8—21no—
31C4×Q8×C11—21no—
32Q8×Dic11—21no—
33Q8×Dic11—21no—
34#66943—21no—
35#66943—41no—
36#66941—21no—
37#66941—41no—
38#66923—21no—
39#66923—41no—
40C4×Dic22—41no—
41C4×Dic22D411yescharacteristic
42C11×Q32—42no—
43C2×C11×C16—21no—
44C11×#107D411yescharacteristic
45C11×#103—21no—
46C4×C8×C11C2311yescharacteristic
47#66899—21no—
48#66899—21no—
49#66882D411yescharacteristic
50#66882D411yescharacteristic
51#66881—21no—
52#66879—21no—
53Dic11⋊C8—21no—
54C2×C11⋊C16—21no—
55#66874—41no—
56#66872—21no—
57#66872—41no—
58#66871—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)D411yescharacteristic
61#12363—111nomaximal, Sylow
62C2×Q8×C11—21no—
63C2×Q8×C11—41no—
64C2×Dic22—41no—
65C2×Dic22D811yescharacteristic
66C11×Q16—21no—
67C11×Q16—42no—
68C11×Q16—41no—
69C11×Q16—41no—
70C11×Q16SD1612yes—
71C2×C8×C11C2×D411yescharacteristic
72C2×C8×C11C2×D411yescharacteristic
73C11×C4⋊C4—21no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C42×C11—41no—
78C42×C11C2×D411yescharacteristic
79C4⋊Dic11—21no—
80C4⋊Dic11—21no—
81C4⋊Dic11—41no—
82C4⋊Dic11—41no—
83C4⋊Dic11—41no—
84C4⋊Dic11D811yescharacteristic
85Dic11⋊C4—21no—
86Dic11⋊C4—41no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89Dic11⋊C4—41no—
90C4×Dic11—21no—
91C4×Dic11—41no—
92C4×Dic11—41no—
93C2×C11⋊C8—21no—
94C2×C11⋊C8—41no—
95C11×C16—41no—
96C11⋊C16—41no—
97#3390—111no—
98#2245—111no—
99#2209D1111yescharacteristic
100#1690—111no—
101#1363—111no—
102#1338—111no—
103#1334—111no—
104Q8×C11—22no—
105Q8×C11—41no—
106Q8×C11—81no—
107Q8×C11—81no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11—81no—
111C2×C4×C11#12011yescharacteristic
112C2×C4×C11C2×D811yescharacteristic
113C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
114C2×Dic11—21no—
115C2×Dic11—21no—
116C2×Dic11—41no—
117C2×Dic11—41no—
118Dic22—41no—
119Dic22—82no—
120C8×C11—21no—
121C8×C11C2×SD1611yescharacteristic
122C8×C11#13711yescharacteristic
123C11⋊C8—41no—
124C11⋊C8—81no—
125#557—221no—
126C2×Q32—21no—
127#501—221no—
128#499—111no—
129#494C2×D1111yescharacteristic
130#479—221no—
131#479—221no—
132#477—221no—
133#475—221no—
134#446—111no—
135#441—221no—
136C4×Q16C2×D1111yescharacteristic
137C4⋊C16C2×D1111yescharacteristic
138#358—21no—
139#358—221no—
140#358—221no—
141#346—111no—
142#334—111no—
143#332—221no—
144C22×C11#44711yescharacteristic
145C4×C11—21no—
146C4×C11—21no—
147C4×C11—42no—
148C4×C11—81no—
149C4×C11—161no—
150C4×C11#44811yescharacteristic
151C4×C11#45411yescharacteristic
152Dic11—41no—
153Dic11—41no—
154Dic11—81no—
155Dic11—81no—
156C2×Q16—21no—
157C2×Q16—21no—
158C2×Q16C22⋊D1111yescharacteristic
159C4⋊Q8—21no—
160C4⋊Q8—221no—
161C4⋊Q8—441no—
162#125—221no—
163#125—221no—
164#125—441no—
165#125—441no—
166C4×Q8—21no—
167C4×Q8—111no—
168C4×Q8—221no—
169C4×Q8—221no—
170C4×Q8—441no—
171Q32—42no—
172C2×C16—21no—
173C2×C16—221no—
174#107—111no—
175#107—111no—
176#107—221no—
177#107C22⋊D1111yescharacteristic
178#106—221no—
179#106—221no—
180#106—441no—
181C4⋊C8—111no—
182C4⋊C8—221no—
183C4⋊C8—221no—
184#103—21no—
185#103—221no—
186#103—221no—
187#103—441no—
188#97—221no—
189C4×C8C22×D1111yescharacteristic
190C2×C11#162711yescharacteristic
191C2×C11#219111yescharacteristic
192C2×C11#219511yescharacteristic
193C2×Q8—21no—
194C2×Q8—41no—
195C2×Q8—111no—
196C2×Q8—441no—
197Q16—21no—
198Q16—42no—
199Q16—41no—
200Q16—41no—
201Q16#432412yes—
202C2×C8—221no—
203C2×C8—441no—
204C2×C8D4×D1111yescharacteristic
205C2×C8C2×C22⋊D1111yescharacteristic
206C4⋊C4—21no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—111no—
211C4⋊C4—221no—
212C4⋊C4—221no—
213C4⋊C4—221no—
214C4⋊C4—441no—
215C4⋊C4—441no—
216C4⋊C4—441no—
217C4⋊C4—441no—
218C4⋊C4—441no—
219C4⋊C4—441no—
220C4⋊C4—441no—
221C42—41no—
222C42—221no—
223C42—441no—
224C42—441no—
225C42D4×D1111yescharacteristic
226C16—41no—
227C16—441no—
228C11#1236311yescharacteristic, complemented, Sylow
229Q8—22no—
230Q8—41no—
231Q8—81no—
232Q8—81no—
233Q8—441no—
234Q8—882no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—81no—
238C2×C4—221no—
239C2×C4—221no—
240C2×C4—441no—
241C2×C4—441no—
242C2×C4D8×D1111yescharacteristic
243C2×C4#6696411yescharacteristic
244C2×C4#6699011yescharacteristic
245C8—21no—
246C8—441no—
247C8—881no—
248C8C2×#432411yescharacteristic
249C8#6700411yescharacteristic
250C22#1062276911yescharacteristic
251C4—21no—
252C4—21no—
253C4—42no—
254C4—81no—
255C4—161no—
256C4—441no—
257C4—441no—
258C4—881no—
259C4—881no—
260C4#1062265311yescharacteristic
261C4#1062281411yescharacteristic
262C2#1306771811yescharacteristic
263C2#1307056511yescharacteristic
264C2#1307059311yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2209C2
socle, prime radicalC22×C11#447
hypercenter#2209D11
hypocenterC11#12363
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2209

Complements

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

NH ≅ G/Ntype
228. C11#12363semidirect

Maximal subgroups

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

subgroupindex
#130815812
#130708612
#130681072
#130666672
#130665972
#130665862
C11×#22092
#1236311