Finite Group Databasebeta

← #14909467

Subgroups — #14909467

Order 2816.

592 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 147 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#13079193C212yesmaximal, complemented
2#13070898C211yesmaximal, characteristic, complemented
3#13070839C212yesmaximal, complemented
4#13070716C214yesmaximal, complemented
5#13070492C214yesmaximal, complemented
6C4×#66862C211yesmaximal, characteristic, complemented
7C11×#2246C211yesmaximal, characteristic, complemented
8#10623247—22no—
9C2×C11×D16C2214yes—
10C11×#493C2212yes—
11#10622770—22no—
12#10622770C2214yes—
13D8×Dic11—22no—
14D8×Dic11C2214yes—
15#10622683—22no—
16C2×#66862C2212yes—
17C4×C8×D11C2211yescharacteristic
18#10622295C2212yes—
19C4×C11×C16C2211yescharacteristic
20#10622200C2218yes—
21#10622143C2214yes—
22#10622140C2212yes—
23C4×C11⋊C16C2211yescharacteristic
24C2×#4341—42no—
25C2×C11×D8—22no—
26C2×C11×D8C2314yes—
27C11×#127—22no—
28#66991—24no—
29#66991—42no—
30#66989—42no—
31D4×Dic11—24no—
32D4×Dic11—42no—
33C2×C8×D11D411yescharacteristic
34C2×C8×D11C2311yescharacteristic
35C42×D11D411yescharacteristic
36#66922—22no—
37C11×D16—28no—
38C2×C11×C16C2312yes—
39C4×C8×C11C2311yescharacteristic
40#66896—24no—
41#66896—24no—
42#66882—22no—
43#66882C2314yes—
44C8×Dic11D411yescharacteristic
45C8×Dic11C2311yescharacteristic
46C2×C11⋊C16C2312yes—
47C4×C11⋊C8D411yescharacteristic
48#66862—24no—
49#33748—111nomaximal, Sylow
50C2×D4×C11—24no—
51C2×D4×C11—42no—
52C2×D4×C11—42no—
53C2×C22⋊D11—44no—
54C22×Dic11—44no—
55#4341—88no—
56C2×C4×D11D812yes—
57C2×C4×D11C2×D411yescharacteristic
58C2×Dic22—42no—
59C11×D8—28no—
60C11×D8—44no—
61C2×C8×C11C2×D411yescharacteristic
62C2×C8×C11C2411yescharacteristic
63C42×C11C2×D411yescharacteristic
64C22⋊Dic11—44no—
65C22⋊Dic11—44no—
66C4⋊Dic11—24no—
67C4⋊Dic11—42no—
68C4×Dic11D812yes—
69C4×Dic11C2×D411yescharacteristic
70C2×C11⋊C8C2×D411yescharacteristic
71C2×C11⋊C8C2×D411yescharacteristic
72C8×D11—22no—
73C8×D11—22no—
74C11×C16#4114yescomplemented
75C11⋊C16—22no—
76#3169—112no—
77#2254—111no—
78#2246D1111yescharacteristic, complemented
79#2240—112no—
80#2218—114no—
81#2177—114no—
82C4×M32—111no—
83C23×C11—44no—
84C22×D11C2×D811yescharacteristic
85D4×C11—44no—
86D4×C11—44no—
87D4×C11—84no—
88D4×C11—84no—
89C2×C4×C11C2×D812yes—
90C2×C4×C11C22×D411yescharacteristic
91C22⋊D11—88no—
92C2×Dic11—44no—
93C2×Dic11—88no—
94C2×Dic11C2×D811yescharacteristic
95C2×Dic11C2×D812yes—
96C4×D11—21no—
97C4×D11—21no—
98C4×D11—24no—
99Dic22—84no—
100C8×C11#13512yes—
101C8×C11C2×#4112yes—
102C11⋊C8—21no—
103C11⋊C8—21no—
104#532—222no—
105C2×D16C2×D1114yes—
106C2×M32—112no—
107#500—112no—
108#493C2×D1112yes—
109#486—222no—
110#466—114no—
111#466—222no—
112C4×D8—114no—
113C4×D8—222no—
114C2×C4×C8—111no—
115#367—114no—
116#357—118no—
117#346—112no—
118C4×C16—111no—
119C4×C16C2×D1111yescharacteristic
120C22×C11—84no—
121C22×C11—84no—
122C22×C11—84no—
123C22×C11C22×D811yescharacteristic
124C2×D11—22no—
125C2×D11—21no—
126C4×C11#50914yes—
127C4×C11#53211yescharacteristic
128C4×C11C2×#13511yescharacteristic
129Dic11—22no—
130Dic11—21no—
131Dic11—84no—
132C2×#41—442no—
133C2×D8—22no—
134C2×D8C22×D1114yes—
135C22×C8—111no—
136C22×C8—111no—
137C4⋊Q8—222no—
138#127—22no—
139#124—442no—
140#121—224no—
141#121—442no—
142C4×D4—224no—
143C4×D4—442no—
144C2×C42—111no—
145D16—28no—
146M32—224no—
147C2×C16—112no—
148C2×C16C22×D1112yes—
149#107—114no—
150#107—222no—
151#102—224no—
152#102—224no—
153C4×C8—111no—
154C4×C8—111no—
155C4×C8—111no—
156C4×C8C22×D1111yescharacteristic
157C2×C11—164no—
158C2×C11#316911yescharacteristic
159C2×C11C2×#50912yes—
160D11—41no—
161#41—888no—
162C2×Q8—442no—
163C2×D4—24no—
164C2×D4—42no—
165C2×D4—42no—
166C2×D4—444no—
167C22×C4—112no—
168C22×C4—111no—
169C22×C4—444no—
170D8—28no—
171D8—44no—
172C2×C8—111no—
173C2×C8—111no—
174C2×C8—222no—
175C2×C8—222no—
176C2×C8D4×D1111yescharacteristic
177C2×C8C23×D1111yescharacteristic
178C4⋊C4—224no—
179C4⋊C4—442no—
180C22⋊C4—444no—
181C22⋊C4—444no—
182C42—112no—
183C42—111no—
184C42D4×D1111yescharacteristic
185C16—222no—
186C16#434114yescomplemented
187C11#3374811yescharacteristic, complemented, Sylow
188C23—44no—
189C23—111no—
190Q8—884no—
191D4—44no—
192D4—44no—
193D4—84no—
194D4—84no—
195D4—888no—
196C2×C4—111no—
197C2×C4—112no—
198C2×C4—221no—
199C2×C4—221no—
200C2×C4—224no—
201C2×C4—444no—
202C2×C4—888no—
203C2×C4D8×D1112yes—
204C2×C4C2×D4×D1111yescharacteristic
205C8—221no—
206C8—221no—
207C8#6696512yes—
208C8C2×#434112yes—
209C22—84no—
210C22—84no—
211C22—84no—
212C22—222no—
213C22—221no—
214C22C2×D8×D1111yescharacteristic
215C4—222no—
216C4—221no—
217C4—884no—
218C4#1062252414yes—
219C4#1062324711yescharacteristic
220C4C2×#6696511yescharacteristic
221C2—164no—
222C2—441no—
223C2#1307919311yescharacteristic
224C2C2×#1062252412yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2246C2
socleC22×C11C22×D8
hypercenter#2246D11
hypocenterC11#33748
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2246

Complements

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

NH ≅ G/Ntype
1. #13079193C2semidirect
2. #13070898C2semidirect
3. #13070839C2semidirect
4. #13070716C2semidirect
5. #13070492C2semidirect
6. C4×#66862C2semidirect
7. C11×#2246C2semidirect
74. C11×C16#41semidirect
78. #2246D11semidirect
186. C16#4341semidirect
187. C11#33748semidirect

Maximal subgroups

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

subgroupindex
#130791932
#130708982
#130708392
#130707162
#130704922
C4×#668622
C11×#22462
#3374811