Finite Group Databasebeta

← #14648156

Subgroups — #14648156

Order 2816.

396 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 111 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#13071802C211yesmaximal, characteristic
2#13068751C212yesmaximal
3C2×#10622181C211yesmaximal, characteristic
4#13066498C212yesmaximal
5C11×#1992C211yesmaximal, characteristic
6C2×C11×#125C2211yescharacteristic
7C2×C11×#97C2211yescharacteristic
8C11×#384C2211yescharacteristic
9#10622598—22no—
10#10622594—22no—
11#10622594—22no—
12#10622549C2212yes—
13C2×#66867C2212yes—
14C11×#340—22no—
15#10622181C414yescomplemented
16#10622167—22no—
17#10622167—22no—
18C22×C8×C11—21no—
19C11×#125—22no—
20C11×#125C2×C412yes—
21C11×#125Q812yes—
22C2×C11×C4⋊C4—22no—
23C2×C11×C4⋊C4—21no—
24C2×C11×C4⋊C4—22no—
25C2×C11×C4⋊C4D412yes—
26C2×C42×C11C2311yescharacteristic
27C2×C4⋊Dic11—22no—
28C2×C4⋊Dic11D412yes—
29C2×C4⋊Dic11D412yes—
30C2×C4×Dic11—22no—
31C22×C11⋊C8—22no—
32C11×#97—22no—
33C11⋊#95—22no—
34C11⋊#95—22no—
35C11⋊#95—22no—
36C11⋊#95—22no—
37#66867—22no—
38#66867C2×C414yes—
39#8915—111nomaximal, Sylow
40C22×C4×C11—22no—
41C22×C4×C11—41no—
42C22×C4×C11C2×D411yescharacteristic
43C22×C4×C11C2×D412yes—
44C22×Dic11—22no—
45C22×Dic11—22no—
46C2×C8×C11—22no—
47C2×C8×C11—41no—
48C2×C8×C11—41no—
49C11×C4⋊C4—24no—
50C11×C4⋊C4—24no—
51C11×C4⋊C4—22no—
52C11×C4⋊C4—44no—
53C11×C4⋊C4—42no—
54C11×C4⋊C4C4⋊C414yes—
55C42×C11C22×C411yescharacteristic
56C42×C11C2×Q811yescharacteristic
57C42×C11#4112yes—
58C4⋊Dic11—42no—
59C4⋊Dic11—42no—
60C4⋊Dic11—82no—
61C4×Dic11—82no—
62C2×C11⋊C8—24no—
63C2×C11⋊C8—42no—
64C2×C11⋊C8—42no—
65#2382—111no—
66#1992D1111yescharacteristic
67#1836—112no—
68C2×#330—111no—
69#1295—112no—
70C23×C11#12011yescharacteristic
71C2×C4×C11—22no—
72C2×C4×C11—21no—
73C2×C4×C11—22no—
74C2×C4×C11—21no—
75C2×C4×C11—24no—
76C2×C4×C11—42no—
77C2×C4×C11—42no—
78C2×C4×C11—82no—
79C2×C4×C11—81no—
80C2×C4×C11C2×C4⋊C411yescharacteristic
81C2×C4×C11C4×D412yes—
82C2×C4×C11C22⋊Q812yes—
83C2×C4×C11#12311yescharacteristic
84C2×Dic11—42no—
85C2×Dic11—42no—
86C2×Dic11—42no—
87C2×Dic11—42no—
88C2×Dic11—42no—
89C2×Dic11—42no—
90C8×C11—42no—
91C11⋊C8—44no—
92C2×#125C2×D1111yescharacteristic
93C2×#97—112no—
94C2×#97C2×D1111yescharacteristic
95#389—222no—
96#387—222no—
97#387—222no—
98#384C2×D1111yescharacteristic
99#382—112no—
100#340—22no—
101#340—222no—
102#340—222no—
103#330—114no—
104C22×C11#38511yescharacteristic
105C22×C11#45412yes—
106C22×C11#45411yescharacteristic
107C22×C11#45512yes—
108C22×C11#45611yescharacteristic
109C4×C11—21no—
110C4×C11—21no—
111C4×C11—22no—
112C4×C11—22no—
113C4×C11—44no—
114C4×C11—161no—
115Dic11—82no—
116Dic11—82no—
117C22×C8—21no—
118C22×C8—222no—
119#125—22no—
120#125Dic2212yes—
121#125C4×D1112yes—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—112no—
126C2×C4⋊C4—112no—
127C2×C4⋊C4—222no—
128C2×C4⋊C4C22⋊D1112yes—
129C2×C42—222no—
130C2×C42C22×D1111yescharacteristic
131#97—22no—
132#97—114no—
133#97—222no—
134#95—222no—
135#95—222no—
136#95—222no—
137#95—222no—
138C2×C11#165811yescharacteristic
139C2×C11#166211yescharacteristic
140C2×C11#166412yes—
141C2×C11#185711yescharacteristic
142C2×C11#186012yes—
143C22×C4—22no—
144C22×C4—41no—
145C22×C4—222no—
146C22×C4—222no—
147C22×C4D4×D1112yes—
148C22×C4C2×C22⋊D1111yescharacteristic
149C2×C8—22no—
150C2×C8—41no—
151C2×C8—41no—
152C2×C8—224no—
153C2×C8—442no—
154C2×C8—442no—
155C4⋊C4—24no—
156C4⋊C4—24no—
157C4⋊C4—22no—
158C4⋊C4—44no—
159C4⋊C4—42no—
160C4⋊C4—442no—
161C4⋊C4—442no—
162C4⋊C4—882no—
163C4⋊C4Dic11⋊C414yes—
164C42—882no—
165C42C2×Dic2211yescharacteristic
166C42C2×C4×D1111yescharacteristic
167C42#434112yes—
168C11#891511yescharacteristic, complemented, Sylow
169C23#6699011yescharacteristic
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—24no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—82no—
178C2×C4—81no—
179C2×C4—442no—
180C2×C4—442no—
181C2×C4—442no—
182C2×C4—442no—
183C2×C4—442no—
184C2×C4—442no—
185C2×C4#6693112yes—
186C2×C4(C22⋊D11)⋊C412yes—
187C2×C4C2×Dic11⋊C411yescharacteristic
188C2×C4#6698811yescharacteristic
189C8—42no—
190C8—444no—
191C22#1062255911yescharacteristic
192C22#1062267511yescharacteristic
193C22#1062270811yescharacteristic
194C22#1062281412yes—
195C22#1062281512yes—
196C4—21no—
197C4—21no—
198C4—22no—
199C4—22no—
200C4—44no—
201C4—161no—
202C4—882no—
203C4—882no—
204C2#1306791711yescharacteristic
205C2#1306793711yescharacteristic
206C2#1306794812yes—
207C2#1306883011yescharacteristic
208C2#1306884712yes—
subgroupG/H
centerC23#66990
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1992C2
socle, prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenter#1992D11
hypocenterC11#8915
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1992

Complements

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

NH ≅ G/Ntype
15. #10622181C4semidirect
168. C11#8915semidirect

Maximal subgroups

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

subgroupindex
#130718022
#130687512
C2×#106221812
#130664982
C11×#19922
#891511