Finite Group Databasebeta

← #15672089

Subgroups — #15672089

Order 2944.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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#13092965C211yesmaximal, characteristic
2#13092473C211yesmaximal, characteristic, complemented
3C4⋊C8×D23C211yesmaximal, characteristic, complemented
4#13092165C211yesmaximal, characteristic, complemented
5#13092165C211yesmaximal, characteristic, complemented
6#13092161C211yesmaximal, characteristic, complemented
7C23×#331C211yesmaximal, characteristic, complemented
8C2×#67290C412yes—
9C23×#127C2211yescharacteristic
10#10625109—21no—
11#10625109—21no—
12#10625107C412yes—
13D4×Dic23—21no—
14D4×Dic23—21no—
15C2×C8×D23—21no—
16C42×D23C2211yescharacteristic
17#10625040C2211yescharacteristic
18C23×C4⋊C8C2211yescharacteristic
19C23×C4⋊C8C2211yescharacteristic
20(C2×D23)⋊C8—21no—
21#10624997—21no—
22Dic23⋊C8—21no—
23C4⋊(C23⋊C8)C2211yescharacteristic
24C4⋊(C23⋊C8)C2211yescharacteristic
25C2×D4×C23—21no—
26C2×D4×C23—21no—
27C2×D4×C23C2×C412yes—
28C2×C22⋊D23—22no—
29C22×Dic23—22no—
30#67290—44no—
31C2×C4×D23C2×C411yescharacteristic
32C2×C4×D23D411yescharacteristic
33C2×C4×D23D411yescharacteristic
34C2×Dic46C2×C412yes—
35C2×C8×C23—21no—
36C2×C8×C23—21no—
37C42×C23C2311yescharacteristic
38C22⋊Dic23—22no—
39C22⋊Dic23—22no—
40C4⋊Dic23—21no—
41C4⋊Dic23—21no—
42C4×Dic23C2×C411yescharacteristic
43C4×Dic23D411yescharacteristic
44C4×Dic23D411yescharacteristic
45C2×C23⋊C8—21no—
46C2×C23⋊C8—21no—
47C8×D23—42no—
48C23×C23—22no—
49C22×D23C22⋊C411yescharacteristic
50D4×C23—42no—
51D4×C23—41no—
52D4×C23—41no—
53D4×C23—41no—
54D4×C23—41no—
55C2×C4×C23C22×C411yescharacteristic
56C2×C4×C23C2×D411yescharacteristic
57C2×C4×C23C2×D411yescharacteristic
58C22⋊D23—44no—
59C2×Dic23—22no—
60C2×Dic23—44no—
61C2×Dic23C22⋊C411yescharacteristic
62C2×Dic23C22⋊C411yescharacteristic
63C2×Dic23C22⋊C411yescharacteristic
64C4×D23—22no—
65C4×D23—21no—
66C4×D23—21no—
67C4×D23—21no—
68C4×D23—21no—
69Dic46—42no—
70C8×C23—41no—
71C8×C23—41no—
72C23⋊C8—41no—
73C23⋊C8—41no—
74#1551—231nomaximal, Sylow
75C22×C23—42no—
76C22×C23—42no—
77C22×C23—42no—
78C22×C23C2×C22⋊C411yescharacteristic
79C2×D23—21no—
80C2×D23—21no—
81C2×D23#10012yes—
82C4×C23—21no—
83C4×C23#13511yescharacteristic
84C4×C23#13511yescharacteristic
85C4×C23AGL(1,ℤ/8)11yescharacteristic
86C4×C23#13711yescharacteristic
87Dic23—21no—
88Dic23—21no—
89Dic23—21no—
90Dic23—42no—
91#532—231no—
92#432—231no—
93C2×C4⋊C8—231no—
94#333—231no—
95#333—231no—
96#331—231no—
97#331D2311yescharacteristic, complemented
98C2×C23—82no—
99C2×C23C2×#10011yescharacteristic
100C2×C23#41611yescharacteristic
101C2×C23#41711yescharacteristic
102D23—22no—
103C2×#41—232no—
104C22×C8—461no—
105C4⋊Q8—231no—
106#127C2×D2311yescharacteristic
107#124—232no—
108#121—461no—
109#121—461no—
110C4×D4—461no—
111C4×D4—461no—
112C2×C42—231no—
113C4⋊C8—231no—
114C4⋊C8—231no—
115C4⋊C8—461no—
116C4⋊C8C2×D2311yescharacteristic
117C4⋊C8C2×D2311yescharacteristic
118C22⋊C8—461no—
119#97—461no—
120C23#155111yescharacteristic, complemented, Sylow
121#41—924no—
122C2×Q8—232no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—462no—
126C2×D4C4×D2312yes—
127C22×C4—231no—
128C22×C4—231no—
129C22×C4—231no—
130C22×C4—462no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—461no—
134C2×C8—461no—
135C2×C8—922no—
136C4⋊C4—461no—
137C4⋊C4—461no—
138C22⋊C4—462no—
139C22⋊C4—462no—
140C42—231no—
141C42—231no—
142C42—231no—
143C42C22×D2311yescharacteristic
144C23—22no—
145C23—231no—
146Q8—922no—
147D4—42no—
148D4—41no—
149D4—41no—
150D4—41no—
151D4—41no—
152D4—924no—
153C2×C4—231no—
154C2×C4—231no—
155C2×C4—231no—
156C2×C4—462no—
157C2×C4—461no—
158C2×C4—461no—
159C2×C4—461no—
160C2×C4—461no—
161C2×C4—462no—
162C2×C4—924no—
163C2×C4C2×C4×D2311yescharacteristic
164C2×C4D4×D2311yescharacteristic
165C2×C4D4×D2311yescharacteristic
166C8—41no—
167C8—41no—
168C8—921no—
169C8—921no—
170C22—42no—
171C22—42no—
172C22—42no—
173C22—232no—
174C22—461no—
175C22—461no—
176C22C22⋊C4×D2311yescharacteristic
177C4—21no—
178C4—461no—
179C4—461no—
180C4—461no—
181C4—922no—
182C4#1062508211yescharacteristic
183C4#1062508311yescharacteristic
184C4#1062508611yescharacteristic
185C4#1062508711yescharacteristic
186C2—82no—
187C2—462no—
188C2#100×D2311yescharacteristic
189C2#1309241011yescharacteristic
190C2#1309241511yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutatorC2×C4×C23C22×C4
FrattiniC42C22×D23
FittingC23×#331C2
socleC22×C23C2×C22⋊C4
prime radical#13092965C2
cosocleC42×C23C23
hypercenter#331D23
hypocenterC23#1551
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #13092473C2semidirect
3. C4⋊C8×D23C2semidirect
4. #13092165C2semidirect
5. #13092165C2semidirect
6. #13092161C2semidirect
7. C23×#331C2semidirect
97. #331D23semidirect
120. C23#1551semidirect

Maximal subgroups

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

subgroupindex
#130929652
#130924732
C4⋊C8×D232
#130921652
#130921612
C23×#3312
#155123