Finite Group Databasebeta

← #15672112

Subgroups — #15672112

Order 2944.

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

normal subgroups only

This group has 228 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
1C4⋊Q8×D23C211yesmaximal, characteristic
2#13092473C211yesmaximal, characteristic
3#13092473C211yesmaximal, characteristic
4#13092164C211yesmaximal, characteristic, complemented
5#13092163C211yesmaximal, characteristic, complemented
6#13092162C211yesmaximal, characteristic, complemented
7C23×#332C211yesmaximal, characteristic, complemented
8C2×Q8×D23—21no—
9C23×C4⋊Q8C2211yescharacteristic
10#10625115—21no—
11C4⋊C4×D23—21no—
12C4⋊C4×D23C412yes—
13#10625059—21no—
14#10625059C412yes—
15C42×D23C2211yescharacteristic
16#10625040C2211yescharacteristic
17C23×C4⋊C8C2211yescharacteristic
18C23×C4⋊C8C2211yescharacteristic
19(C2×D23)⋊C8—21no—
20(C2×D23)⋊C8—21no—
21#10624997—21no—
22#10624997—21no—
23C4⋊(C23⋊C8)C2211yescharacteristic
24C4⋊(C23⋊C8)C2211yescharacteristic
25C2×Q8×C23—21no—
26Q8×D23—42no—
27Q8×D23—42no—
28C2×C4×D23—22no—
29C2×C4×D23C2×C411yescharacteristic
30C2×C4×D23D411yescharacteristic
31C2×C4×D23D411yescharacteristic
32C2×Dic46—21no—
33C2×Dic46—22no—
34C2×C8×C23—21no—
35C2×C8×C23—21no—
36C4⋊C4×C23—21no—
37C4⋊C4×C23C2×C412yes—
38C42×C23C2311yescharacteristic
39C4⋊Dic23—21no—
40C4⋊Dic23C2×C412yes—
41Dic23⋊C4—22no—
42Dic23⋊C4—22no—
43C4×Dic23C2×C411yescharacteristic
44C4×Dic23D411yescharacteristic
45C4×Dic23D411yescharacteristic
46C2×C23⋊C8—21no—
47C2×C23⋊C8—21no—
48C22×D23C22⋊C411yescharacteristic
49Q8×C23—41no—
50Q8×C23—41no—
51C2×C4×C23—22no—
52C2×C4×C23C22×C411yescharacteristic
53C2×C4×C23C2×D411yescharacteristic
54C2×C4×C23C2×D411yescharacteristic
55C2×Dic23—22no—
56C2×Dic23C22⋊C411yescharacteristic
57C2×Dic23C22⋊C411yescharacteristic
58C2×Dic23C22⋊C411yescharacteristic
59C4×D23—22no—
60C4×D23—21no—
61C4×D23—21no—
62C4×D23—21no—
63C4×D23—21no—
64C4×D23—44no—
65Dic46—44no—
66Dic46—41no—
67Dic46—41no—
68C8×C23—41no—
69C8×C23—41no—
70C23⋊C8—41no—
71C23⋊C8—41no—
72#1556—231nomaximal, Sylow
73C22×C23C2×C22⋊C411yescharacteristic
74C2×D23—21no—
75C2×D23—21no—
76C2×D23#10112yes—
77C4×C23—21no—
78C4×C23—42no—
79C4×C23AGL(1,ℤ/8)11yescharacteristic
80C4×C23AGL(1,ℤ/8)11yescharacteristic
81C4×C23#13711yescharacteristic
82C4×C23#13711yescharacteristic
83Dic23—21no—
84Dic23—21no—
85Dic23—21no—
86Dic23—42no—
87C2×C4⋊Q8—231no—
88#432—231no—
89#432—231no—
90#332—231no—
91#332—231no—
92#332—231no—
93#332D2311yescharacteristic, complemented
94C2×C23C2×#10111yescharacteristic
95C2×C23#41811yescharacteristic
96C2×C23#41911yescharacteristic
97D23—22no—
98C22×Q8—461no—
99C4⋊Q8—232no—
100C4⋊Q8—231no—
101C4⋊Q8—461no—
102C4⋊Q8—461no—
103C4⋊Q8C2×D2311yescharacteristic
104C2×C4⋊C4—232no—
105C2×C4⋊C4—461no—
106C2×C42—231no—
107C4⋊C8—231no—
108C4⋊C8—231no—
109C4⋊C8C2×D2311yescharacteristic
110C4⋊C8C2×D2311yescharacteristic
111C22⋊C8—461no—
112C22⋊C8—461no—
113#97—461no—
114#97—461no—
115C23#155611yescharacteristic, complemented, Sylow
116C2×Q8—21no—
117C2×Q8—462no—
118C2×Q8—461no—
119C2×Q8—922no—
120C2×Q8—922no—
121C22×C4—231no—
122C22×C4—231no—
123C22×C4—231no—
124C22×C4—462no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—461no—
128C2×C8—461no—
129C4⋊C4—21no—
130C4⋊C4—232no—
131C4⋊C4—462no—
132C4⋊C4—462no—
133C4⋊C4—461no—
134C4⋊C4C4×D2312yes—
135C42—231no—
136C42—231no—
137C42—231no—
138C42C22×D2311yescharacteristic
139C23—231no—
140Q8—41no—
141Q8—41no—
142Q8—924no—
143Q8—921no—
144Q8—921no—
145C2×C4—22no—
146C2×C4—231no—
147C2×C4—231no—
148C2×C4—231no—
149C2×C4—462no—
150C2×C4—461no—
151C2×C4—461no—
152C2×C4—461no—
153C2×C4—461no—
154C2×C4—462no—
155C2×C4—924no—
156C2×C4C2×C4×D2311yescharacteristic
157C2×C4D4×D2311yescharacteristic
158C2×C4D4×D2311yescharacteristic
159C8—41no—
160C8—41no—
161C8—921no—
162C8—921no—
163C22—232no—
164C22—461no—
165C22—461no—
166C22C22⋊C4×D2311yescharacteristic
167C4—21no—
168C4—42no—
169C4—461no—
170C4—461no—
171C4—461no—
172C4—922no—
173C4#1062508211yescharacteristic
174C4#1062508511yescharacteristic
175C4#1062508611yescharacteristic
176C4#1062508911yescharacteristic
177C2—462no—
178C2#101×D2311yescharacteristic
179C2#1309242011yescharacteristic
180C2#1309242411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutatorC2×C4×C23C22×C4
FrattiniC42C22×D23
FittingC23×#332C2
socleC22×C23C2×C22⋊C4
prime radicalC22×D23C22⋊C4
cosocleC42×C23C23
hypercenter#332D23
hypocenterC23#1556
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
4. #13092164C2semidirect
5. #13092163C2semidirect
6. #13092162C2semidirect
7. C23×#332C2semidirect
93. #332D23semidirect
115. C23#1556semidirect

Maximal subgroups

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

subgroupindex
C4⋊Q8×D232
#130924732
#130921642
#130921632
#130921622
C23×#3322
#155623