Finite Group Databasebeta

← #14656877

Subgroups — #14656877

Order 2816.

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

normal subgroups only

This group has 400 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#13076979C211yesmaximal, characteristic
2#13069593C211yesmaximal, characteristic
3#13067181C212yesmaximal
4#13066475C212yesmaximal
5C11×#1276C211yesmaximal, characteristic
6#10623001C2211yescharacteristic
7C2×#66923—21no—
8C11×#431C2212yes—
9C43×C11C2211yescharacteristic
10#10622549C2212yes—
11#10622548—21no—
12#10622541—24no—
13#10622537C2211yescharacteristic
14#10622161—21no—
15#10622161—21no—
16#10622105—24no—
17C2×C42×C11—22no—
18C2×C42×C11D411yescharacteristic
19C2×C42×C11D411yescharacteristic
20C2×C42×C11C2311yescharacteristic
21#66979—21no—
22C2×C4⋊Dic11—24no—
23C2×C4⋊Dic11—22no—
24#66977—22no—
25C2×Dic11⋊C4—24no—
26C2×#4318—21no—
27#66923—21no—
28#66923—42no—
29#66923—42no—
30#66922Q812yes—
31C4×Dic22—22no—
32C11×C4⋊C8—22no—
33C11×C22⋊C8—22no—
34C4×C8×C11—22no—
35C11⋊#95—22no—
36C11⋊#95D414yes—
37C4⋊(C11⋊C8)—22no—
38#10365—111nomaximal, Sylow
39C22×C4×C11—21no—
40C22×C4×C11—21no—
41C22×C4×C11C2×D412yes—
42C22×C4×C11C2×D411yescharacteristic
43C22×Dic11—24no—
44C2×Dic22—22no—
45C2×C8×C11—42no—
46C42×C11—21no—
47C42×C11—21no—
48C42×C11—44no—
49C42×C11SD1612yes—
50C42×C11Q1612yes—
51C42×C11C2×Q811yescharacteristic
52C42×C11#4112yes—
53C42×C11#4111yescharacteristic
54C22⋊Dic11—41no—
55C4⋊Dic11—22no—
56C4⋊Dic11—22no—
57C4⋊Dic11—48no—
58C4⋊Dic11—42no—
59C4⋊Dic11—42no—
60Dic11⋊C4—48no—
61Dic11⋊C4—42no—
62C4×Dic11—41no—
63#4318—41no—
64#4318—41no—
65C2×C11⋊C8—41no—
66#2859—111no—
67#1994—111no—
68#1518—112no—
69#1286—112no—
70#1276D1111yescharacteristic
71C23×C11#12011yescharacteristic
72C2×C4×C11—24no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—42no—
76C2×C4×C11—42no—
77C2×C4×C11C22⋊Q812yes—
78C2×C4×C11C22⋊Q811yescharacteristic
79C2×C4×C11#12411yescharacteristic
80C2×C4×C11#12412yes—
81C2×C4×C11C2×SD1611yescharacteristic
82C2×C4×C11C2×Q1611yescharacteristic
83C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
84C2×C4×C11#13711yescharacteristic
85C2×Dic11—48no—
86C2×Dic11—42no—
87C2×Dic11—44no—
88Dic22—82no—
89C8×C11—82no—
90C11⋊C8—81no—
91#533—111no—
92C2×#125—221no—
93#431C2×D1112yes—
94#423—111no—
95#389—224no—
96#384—221no—
97#382—112no—
98C43C2×D1111yescharacteristic
99#339—221no—
100#339—221no—
101#328—224no—
102C22×C11—22no—
103C22×C11#39311yescharacteristic
104C22×C11#45011yescharacteristic
105C22×C11#45111yescharacteristic
106C4×C11—24no—
107C4×C11—22no—
108C4×C11—22no—
109C4×C11—42no—
110C4×C11#47511yescharacteristic
111C4×C11#47711yescharacteristic
112C4×C11#48711yescharacteristic
113C4×C11#48911yescharacteristic
114Dic11—84no—
115Dic11—82no—
116C2×M16—221no—
117C4⋊Q8—112no—
118#125—221no—
119#125—442no—
120#125—442no—
121C22⋊Q8—222no—
122C4×Q8—222no—
123#117—221no—
124C2×C4⋊C4—224no—
125C2×C4⋊C4—224no—
126C2×C4⋊C4—222no—
127C2×C42—22no—
128C2×C42D4411yescharacteristic
129C2×C42D4411yescharacteristic
130C2×C42C22×D1111yescharacteristic
131C4⋊C8—22no—
132C4⋊C8—222no—
133C22⋊C8—22no—
134C4×C8—22no—
135#95—114no—
136#95—222no—
137C2×C11—21no—
138C2×C11—21no—
139C2×C11#202411yescharacteristic
140C2×C11#203112yes—
141C2×Q8—222no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—224no—
145C22×C4C2×D4411yescharacteristic
146C22×C4D4×D1112yes—
147M16—441no—
148M16—441no—
149C2×C8—42no—
150C2×C8—441no—
151C4⋊C4—222no—
152C4⋊C4—222no—
153C4⋊C4—448no—
154C4⋊C4—448no—
155C4⋊C4—442no—
156C4⋊C4—442no—
157C4⋊C4—442no—
158C22⋊C4—441no—
159C42—21no—
160C42—21no—
161C42—44no—
162C42—441no—
163C42#431412yes—
164C42Dic4412yes—
165C42#433912yes—
166C42#434111yescharacteristic
167C42Q8×D1111yescharacteristic
168C11#1036511yescharacteristic, complemented, Sylow
169C23#6693511yescharacteristic
170Q8—882no—
171C2×C4—24no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—448no—
177C2×C4—442no—
178C2×C4—444no—
179C2×C4#6692811yescharacteristic
180C2×C4#6693812yes—
181C2×C4#6694912yes—
182C2×C4#6695011yescharacteristic
183C2×C4C2×#431411yescharacteristic
184C2×C4C2×Dic4411yescharacteristic
185C2×C4#6696111yescharacteristic
186C2×C4#6696211yescharacteristic
187C8—82no—
188C8—881no—
189C22—22no—
190C22#1062228611yescharacteristic
191C22#1062234411yescharacteristic
192C22#1062235211yescharacteristic
193C4—24no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—884no—
198C4—882no—
199C4#1062229411yescharacteristic
200C4#1062232711yescharacteristic
201C4#1062246311yescharacteristic
202C4#1062246411yescharacteristic
203C2—21no—
204C2—21no—
205C2#1306975811yescharacteristic
206C2#1306978912yes—
subgroupG/H
centerC22#10622286
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1276C2
socleC22×C11#393
prime radicalC23×C11#120
hypercenter#1276D11
hypocenterC11#10365
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
168. C11#10365semidirect

Maximal subgroups

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

subgroupindex
#130769792
#130695932
#130671812
#130664752
C11×#12762
#1036511