Finite Group Databasebeta

← #14658271

Subgroups — #14658271

Order 2816.

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

normal subgroups only

This group has 406 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#13068784C212yesmaximal
4#13066498C212yesmaximal
5C11×#1295C211yesmaximal, characteristic
6C2×C11×#97C2212yes—
7C11×#382C2211yescharacteristic
8C2×#66882—22no—
9C2×#66881—22no—
10#10622599—21no—
11#10622592—21no—
12C2×#66872—21no—
13C2×#66871—21no—
14#10622549C2212yes—
15#10622548C2211yescharacteristic
16C2×#66867C2211yescharacteristic
17#10622273—22no—
18#10622269—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#66882—44no—
40#66881—44no—
41#66872—42no—
42#66871—42no—
43#66867—21no—
44#66867Q812yescomplemented
45#10583—111nomaximal, Sylow
46C22×C4×C11—21no—
47C22×C4×C11—21no—
48C22×C4×C11C2×D411yescharacteristic
49C22×C4×C11C2×D412yes—
50C22×Dic11—22no—
51C22×Dic11—22no—
52C22×Dic11—41no—
53C2×Dic22—82no—
54C2×Dic22—81no—
55C2×C8×C11—24no—
56C2×C8×C11—24no—
57C2×C8×C11—24no—
58C11×C4⋊C4—41no—
59C11×C4⋊C4—41no—
60C42×C11C2×Q812yes—
61C42×C11C2×Q811yescharacteristic
62C42×C11#4111yescharacteristic
63C4⋊Dic11—42no—
64C4⋊Dic11—42no—
65C4⋊Dic11—41no—
66C4⋊Dic11—41no—
67C4⋊Dic11—42no—
68C4⋊Dic11—42no—
69C4⋊Dic11—81no—
70Dic11⋊C4—82no—
71C2×C11⋊C8—22no—
72C2×C11⋊C8—22no—
73C2×C11⋊C8—22no—
74#2844—111no—
75#1847—112no—
76#1847—111no—
77#1295—112no—
78#1295D1111yescharacteristic
79C23×C11#12011yescharacteristic
80C2×C4×C11—21no—
81C2×C4×C11—22no—
82C2×C4×C11—21no—
83C2×C4×C11—22no—
84C2×C4×C11—42no—
85C2×C4×C11—41no—
86C2×C4×C11—41no—
87C2×C4×C11—42no—
88C2×C4×C11C22⋊Q812yes—
89C2×C4×C11C22⋊Q811yescharacteristic
90C2×C4×C11C4⋊Q811yescharacteristic
91C2×C4×C11C4⋊Q812yes—
92C2×Dic11—42no—
93C2×Dic11—42no—
94C2×Dic11—42no—
95C2×Dic11—42no—
96C2×Dic11—42no—
97C2×Dic11—42no—
98C2×Dic11—81no—
99C2×Dic11—82no—
100Dic22—84no—
101C8×C11—28no—
102C11⋊C8—24no—
103C2×#107—222no—
104C2×#107—221no—
105C2×#106—222no—
106C2×#106—221no—
107C2×#97—111no—
108C2×#97C2×D1112yes—
109#400—222no—
110#400—221no—
111#395—222no—
112#395—221no—
113#384—111no—
114#382—112no—
115#382C2×D1111yescharacteristic
116C22×C11#39511yescharacteristic
117C22×C11#45311yescharacteristic
118C22×C11#45312yes—
119C22×C11#45611yescharacteristic
120C22×C11#45612yes—
121C4×C11—21no—
122C4×C11—22no—
123C4×C11—22no—
124C4×C11—21no—
125C4×C11—81no—
126C4×C11—81no—
127Dic11—82no—
128Dic11—82no—
129Dic11—161no—
130C22×Q8—221no—
131C22×C8—22no—
132C22×C8—221no—
133C2×C4⋊C4—112no—
134C2×C4⋊C4—112no—
135C2×C4⋊C4—221no—
136C2×C4⋊C4—222no—
137C2×C4⋊C4—222no—
138C2×C4⋊C4—221no—
139C2×C4⋊C4D4411yescharacteristic
140C2×C4⋊C4D4411yescharacteristic
141C2×C42C22×D1111yescharacteristic
142#107—442no—
143#107—444no—
144#106—442no—
145#106—444no—
146#97—22no—
147#97—112no—
148#97—221no—
149#97Dic2214yescomplemented
150#95—22no—
151#95—222no—
152#95—221no—
153#95—221no—
154#95—222no—
155#95—222no—
156C2×C11#165511yescharacteristic
157C2×C11#166011yescharacteristic
158C2×C11#166012yes—
159C2×C11#206012yes—
160C2×C11#206011yescharacteristic
161C2×Q8—881no—
162C2×Q8—882no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—222no—
166C22×C4—222no—
167C22×C4—441no—
168C22×C4C2×D4411yescharacteristic
169C22×C4D4×D1112yes—
170C2×C8—24no—
171C2×C8—24no—
172C2×C8—24no—
173C2×C8—222no—
174C2×C8—222no—
175C2×C8—222no—
176C4⋊C4—41no—
177C4⋊C4—41no—
178C4⋊C4—442no—
179C4⋊C4—442no—
180C4⋊C4—441no—
181C4⋊C4—442no—
182C4⋊C4—441no—
183C4⋊C4—442no—
184C4⋊C4—882no—
185C4⋊C4—881no—
186C42C2×Dic2212yes—
187C42#434111yescharacteristic
188C42Q8×D1111yescharacteristic
189C11#1058311yescharacteristic, complemented, Sylow
190C23#6693511yescharacteristic
191Q8—884no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—442no—
201C2×C4—442no—
202C2×C4—442no—
203C2×C4—442no—
204C2×C4—442no—
205C2×C4—442no—
206C2×C4—881no—
207C2×C4—882no—
208C2×C4#6692211yescharacteristic
209C2×C4#6693112yes—
210C2×C4#6694112yes—
211C2×C4#6695011yescharacteristic
212C8—28no—
213C8—224no—
214C22#1062226911yescharacteristic
215C22#1062236011yescharacteristic
216C22#1062236511yescharacteristic
217C22#1062243512yes—
218C22#1062243912yes—
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—81no—
224C4—81no—
225C4—882no—
226C4—882no—
227C4—1761no—
228C2#1306790611yescharacteristic
229C2#1306792811yescharacteristic
230C2#1306792912yes—
231C2#1306996012yes—
232C2#1306996211yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1295C2
socle, prime radicalC23×C11#120
hypercenter#1295D11
hypocenterC11#10583
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
44. #66867Q8semidirect
149. #97Dic22semidirect
189. C11#10583semidirect

Maximal subgroups

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

subgroupindex
#130768882
#130687852
#130687842
#130664982
C11×#12952
#1058311