Finite Group Databasebeta

← #14658274

Subgroups — #14658274

Order 2816.

374 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 97 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#13076888C211yesmaximal, characteristic
2#13068785C211yesmaximal, characteristic
3#13068750C212yesmaximal
4#13066498C212yesmaximal
5C11×#1295C211yesmaximal, characteristic
6C2×C11×#97C2212yes—
7C11×#382C2211yescharacteristic
8#10622599—21no—
9#10622592—21no—
10C2×#66872—21no—
11C2×#66871—21no—
12#10622549C2212yes—
13#10622548C2211yescharacteristic
14C2×#66867C2211yescharacteristic
15#10622273—22no—
16#10622269—22no—
17#10622189—22no—
18#10622189—22no—
19C22×Dic22—21no—
20C22×C8×C11—22no—
21C2×C11×C4⋊C4D411yescharacteristic
22C2×C11×C4⋊C4D411yescharacteristic
23C2×C42×C11C2311yescharacteristic
24C2×C4⋊Dic11—21no—
25C2×C4⋊Dic11—22no—
26C2×C4⋊Dic11—21no—
27C2×C4⋊Dic11D412yes—
28C2×C4⋊Dic11D412yes—
29C2×Dic11⋊C4—22no—
30C22×C11⋊C8—21no—
31C11×#97—22no—
32C11×#97Q814yescomplemented
33C11×#95—22no—
34C11⋊#95—22no—
35C11⋊#95—21no—
36C11⋊#95—21no—
37C11⋊#95—22no—
38C11⋊#95—22no—
39#66872—42no—
40#66871—42no—
41#66867—21no—
42#66867Q812yescomplemented
43#10584—111nomaximal, Sylow
44C22×C4×C11—21no—
45C22×C4×C11—21no—
46C22×C4×C11C2×D411yescharacteristic
47C22×C4×C11C2×D412yes—
48C22×Dic11—22no—
49C22×Dic11—22no—
50C22×Dic11—41no—
51C2×Dic22—81no—
52C2×Dic22—82no—
53C2×C8×C11—24no—
54C2×C8×C11—42no—
55C2×C8×C11—42no—
56C11×C4⋊C4—41no—
57C11×C4⋊C4—41no—
58C42×C11C2×Q812yes—
59C42×C11C2×Q811yescharacteristic
60C42×C11#4111yescharacteristic
61C4⋊Dic11—42no—
62C4⋊Dic11—42no—
63C4⋊Dic11—41no—
64C4⋊Dic11—41no—
65C4⋊Dic11—44no—
66C4⋊Dic11—81no—
67Dic11⋊C4—82no—
68C2×C11⋊C8—22no—
69C2×C11⋊C8—22no—
70C2×C11⋊C8—22no—
71#2844—111no—
72#1847—111no—
73#1836—112no—
74#1295—112no—
75#1295D1111yescharacteristic
76C23×C11#12011yescharacteristic
77C2×C4×C11—21no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—21no—
81C2×C4×C11—41no—
82C2×C4×C11—41no—
83C2×C4×C11—42no—
84C2×C4×C11—42no—
85C2×C4×C11C22⋊Q812yes—
86C2×C4×C11C22⋊Q811yescharacteristic
87C2×C4×C11C4⋊Q811yescharacteristic
88C2×C4×C11C4⋊Q812yes—
89C2×Dic11—42no—
90C2×Dic11—42no—
91C2×Dic11—42no—
92C2×Dic11—42no—
93C2×Dic11—42no—
94C2×Dic11—42no—
95C2×Dic11—81no—
96C2×Dic11—82no—
97Dic22—84no—
98C8×C11—44no—
99C11⋊C8—24no—
100C2×#107—221no—
101C2×#106—221no—
102C2×#97—111no—
103C2×#97C2×D1112yes—
104#400—222no—
105#400—221no—
106#395—222no—
107#395—221no—
108#384—111no—
109#382—112no—
110#382C2×D1111yescharacteristic
111#340—222no—
112#340—222no—
113C22×C11#39511yescharacteristic
114C22×C11#45311yescharacteristic
115C22×C11#45412yes—
116C22×C11#45512yes—
117C22×C11#45611yescharacteristic
118C4×C11—21no—
119C4×C11—21no—
120C4×C11—22no—
121C4×C11—22no—
122C4×C11—81no—
123C4×C11—81no—
124Dic11—82no—
125Dic11—82no—
126Dic11—161no—
127C22×Q8—221no—
128C22×C8—22no—
129C22×C8—221no—
130C2×C4⋊C4—112no—
131C2×C4⋊C4—112no—
132C2×C4⋊C4—221no—
133C2×C4⋊C4—222no—
134C2×C4⋊C4—222no—
135C2×C4⋊C4—221no—
136C2×C4⋊C4D4411yescharacteristic
137C2×C4⋊C4D4411yescharacteristic
138C2×C42C22×D1111yescharacteristic
139#107—442no—
140#106—442no—
141#97—22no—
142#97—112no—
143#97—221no—
144#97Dic2214yescomplemented
145#95—22no—
146#95—222no—
147#95—221no—
148#95—221no—
149#95—222no—
150#95—222no—
151C2×C11#165711yescharacteristic
152C2×C11#165911yescharacteristic
153C2×C11#166412yes—
154C2×C11#206011yescharacteristic
155C2×C11#206112yes—
156C2×Q8—881no—
157C2×Q8—882no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—222no—
161C22×C4—222no—
162C22×C4—441no—
163C22×C4C2×D4411yescharacteristic
164C22×C4D4×D1112yes—
165C2×C8—24no—
166C2×C8—42no—
167C2×C8—42no—
168C2×C8—222no—
169C2×C8—222no—
170C2×C8—222no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—442no—
174C4⋊C4—442no—
175C4⋊C4—441no—
176C4⋊C4—441no—
177C4⋊C4—444no—
178C4⋊C4—882no—
179C4⋊C4—881no—
180C42C2×Dic2212yes—
181C42#434111yescharacteristic
182C42Q8×D1111yescharacteristic
183C11#1058411yescharacteristic, complemented, Sylow
184C23#6693511yescharacteristic
185Q8—884no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—442no—
195C2×C4—442no—
196C2×C4—442no—
197C2×C4—442no—
198C2×C4—442no—
199C2×C4—442no—
200C2×C4—881no—
201C2×C4—882no—
202C2×C4#6692211yescharacteristic
203C2×C4#6693112yes—
204C2×C4#6694112yes—
205C2×C4#6695011yescharacteristic
206C8—44no—
207C8—224no—
208C22#1062226911yescharacteristic
209C22#1062236011yescharacteristic
210C22#1062236511yescharacteristic
211C22#1062243812yes—
212C22#1062244012yes—
213C4—21no—
214C4—21no—
215C4—22no—
216C4—22no—
217C4—81no—
218C4—81no—
219C4—882no—
220C4—882no—
221C4—1761no—
222C2#1306791511yescharacteristic
223C2#1306792311yescharacteristic
224C2#1306795212yes—
225C2#1306996211yescharacteristic
226C2#1306996512yes—
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1295C2
socle, prime radicalC23×C11#120
hypercenter#1295D11
hypocenterC11#10584
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
32. C11×#97Q8semidirect
42. #66867Q8semidirect
144. #97Dic22semidirect
183. C11#10584semidirect

Maximal subgroups

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

subgroupindex
#130768882
#130687852
#130687502
#130664982
C11×#12952
#1058411