Finite Group Databasebeta

← #14909476

Subgroups — #14909476

Order 2816.

504 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 163 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#13079202C212yesmaximal
2#13070898C211yesmaximal, characteristic, complemented
3#13070869C211yesmaximal, characteristic, complemented
4#13070844C212yesmaximal, complemented
5#13070724C214yesmaximal
6#13070488C214yesmaximal, complemented
7C4×C11×M32C211yesmaximal, characteristic
8#10623001—22no—
9C2×C11×M32C2212yes—
10C2×C4×C8×C11C2211yescharacteristic
11#10622729—22no—
12#10622729C2214yes—
13C2×Dic88C2214yes—
14#10622312C2212yes—
15C4×Dic44—22no—
16C4×Dic44C2214yes—
17#10622295C2212yes—
18#10622294—22no—
19C11×#346C2212yes—
20C4×C11×C16C2211yescharacteristic
21C4×C11×C16C2211yescharacteristic
22#10622143C2214yes—
23#10622141C2218yes—
24C22×C8×C11D411yescharacteristic
25C22×C8×C11C2311yescharacteristic
26C2×C42×C11D411yescharacteristic
27#66979—42no—
28#66977—24no—
29#66977—42no—
30C2×Dic44—22no—
31C2×Dic44C2314yes—
32#66923—42no—
33#66922—22no—
34#66922—22no—
35C4×Dic22—24no—
36C4×Dic22—42no—
37C11×M32—24no—
38C2×C11×C16C2312yes—
39C2×C11×C16C2312yes—
40C4×C8×C11D411yescharacteristic
41C4×C8×C11D411yescharacteristic
42C4×C8×C11C2311yescharacteristic
43C4×C8×C11C2311yescharacteristic
44#66882—22no—
45#66882C2314yes—
46#66880—24no—
47#66880—24no—
48Dic88—28no—
49#33749—111nomaximal, Sylow
50C22×C4×C11D812yes—
51C22×C4×C11C2×D411yescharacteristic
52C2×Dic22—24no—
53C2×Dic22—42no—
54C2×C8×C11—22no—
55C2×C8×C11—22no—
56C2×C8×C11C2×D411yescharacteristic
57C2×C8×C11C2×D411yescharacteristic
58C2×C8×C11C2×D411yescharacteristic
59C2×C8×C11C2411yescharacteristic
60C42×C11D812yes—
61C42×C11C2×D411yescharacteristic
62C42×C11C2×D411yescharacteristic
63C22⋊Dic11—44no—
64C4⋊Dic11—24no—
65C4⋊Dic11—42no—
66C4⋊Dic11—42no—
67C4⋊Dic11—42no—
68Dic11⋊C4—44no—
69Dic11⋊C4—44no—
70C4×Dic11—44no—
71Dic44—28no—
72Dic44—44no—
73C11×C16—22no—
74C11×C16#4114yes—
75#3170—112no—
76#2254—111no—
77#2247—111no—
78#2241—112no—
79#2219—114no—
80#2176—114no—
81C4×M32D1111yescharacteristic
82C23×C11C2×D811yescharacteristic
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—24no—
86C2×C4×C11C2×D812yes—
87C2×C4×C11C2×D811yescharacteristic
88C2×C4×C11C2×D812yes—
89C2×C4×C11C22×D411yescharacteristic
90C2×Dic11—44no—
91C2×Dic11—44no—
92Dic22—44no—
93Dic22—44no—
94Dic22—84no—
95C8×C11—21no—
96C8×C11—21no—
97C8×C11#13512yes—
98C8×C11C2×#4112yes—
99#533—222no—
100C2×Q32—114no—
101C2×M32C2×D1112yes—
102#500—112no—
103#494—112no—
104#487—222no—
105#467—114no—
106#467—222no—
107C4×Q16—114no—
108C4×Q16—222no—
109C2×C4×C8C2×D1111yescharacteristic
110#367—114no—
111#358—118no—
112#346C2×D1112yes—
113C4×C16C2×D1111yescharacteristic
114C4×C16C2×D1111yescharacteristic
115C22×C11—22no—
116C22×C11—21no—
117C22×C11C22×D811yescharacteristic
118C4×C11—22no—
119C4×C11—21no—
120C4×C11#51014yes—
121C4×C11#53211yescharacteristic
122C4×C11C2×#13511yescharacteristic
123Dic11—84no—
124Dic11—84no—
125C2×Q16—114no—
126C2×Q16—222no—
127C22×C8D4411yescharacteristic
128C22×C8C22×D1111yescharacteristic
129C4⋊Q8—222no—
130C4⋊Q8—222no—
131#125—442no—
132C22⋊Q8—224no—
133C22⋊Q8—442no—
134C4×Q8—224no—
135C4×Q8—442no—
136#117—442no—
137C2×C42D4411yescharacteristic
138Q32—228no—
139M32—24no—
140C2×C16C22×D1112yes—
141C2×C16C22×D1112yes—
142#107—114no—
143#107—222no—
144#103—224no—
145#103—224no—
146C4×C8D4411yescharacteristic
147C4×C8D4411yescharacteristic
148C4×C8C22×D1111yescharacteristic
149C4×C8C22×D1111yescharacteristic
150C2×C11—41no—
151C2×C11#316911yescharacteristic
152C2×C11C2×#51012yes—
153C2×Q8—224no—
154C2×Q8—442no—
155C22×C4D8812yes—
156C22×C4C2×D4411yescharacteristic
157Q16—228no—
158Q16—444no—
159C2×C8—22no—
160C2×C8—22no—
161C2×C8C2×D4411yescharacteristic
162C2×C8C2×D4411yescharacteristic
163C2×C8C2×D4411yescharacteristic
164C2×C8C23×D1111yescharacteristic
165C4⋊C4—224no—
166C4⋊C4—442no—
167C4⋊C4—442no—
168C4⋊C4—444no—
169C4⋊C4—444no—
170C4⋊C4—442no—
171C22⋊C4—444no—
172C42—444no—
173C42D8812yes—
174C42C2×D4411yescharacteristic
175C42C2×D4411yescharacteristic
176C16—22no—
177C16#433914yes—
178C11#3374911yescharacteristic, complemented, Sylow
179C23C2×D8811yescharacteristic
180Q8—444no—
181Q8—444no—
182Q8—884no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—24no—
186C2×C4—444no—
187C2×C4—444no—
188C2×C4C2×D8812yes—
189C2×C4C2×D8811yescharacteristic
190C2×C4C2×D8812yes—
191C2×C4C22×D4411yescharacteristic
192C8—21no—
193C8—21no—
194C8#6695712yes—
195C8C2×#433912yes—
196C22—22no—
197C22—21no—
198C22C22×D8811yescharacteristic
199C4—22no—
200C4—21no—
201C4—884no—
202C4—884no—
203C4#1062252214yes—
204C4#1062300811yescharacteristic
205C4C2×#6695711yescharacteristic
206C2—41no—
207C2#1307919511yescharacteristic
208C2C2×#1062252212yes—
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×M32C2
socleC22×C11C22×D8
prime radicalC23×C11C2×D8
hypercenterC4×M32D11
hypocenterC11#33749
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×M32

Complements

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

NH ≅ G/Ntype
2. #13070898C2semidirect
3. #13070869C2semidirect
4. #13070844C2semidirect
6. #13070488C2semidirect
178. C11#33749semidirect

Maximal subgroups

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

subgroupindex
#130792022
#130708982
#130708692
#130708442
#130707242
#130704882
C4×C11×M322
#3374911