Finite Group Databasebeta

← #15671930

Subgroups — #15671930

Order 2944.

274 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 81 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#13092381C211yesmaximal, characteristic
2#13092280C211yesmaximal, characteristic
3#13092154C214yesmaximal, complemented
4C2×C23×C22⋊Q8C211yesmaximal, characteristic
5C22×Q8×C23C411yescharacteristic, complemented
6C23×C4×C23C2211yescharacteristic
7C23×C22⋊Q8—21no—
8C23×C22⋊Q8—21no—
9C23×C22⋊Q8C412yescomplemented
10C23×C22⋊Q8C2212yes—
11C2×C4⋊C4×C23—21no—
12C2×C4⋊C4×C23C411yescharacteristic, complemented
13C2×C22⋊C4×C23—21no—
14C2×C22⋊Dic23—21no—
15C2×#67267—21no—
16C23⋊#95—21no—
17C23⋊#95C2212yes—
18C22⋊(C23⋊C8)—21no—
19C22⋊(C23⋊C8)C2212yes—
20C24×C23D411yescharacteristic
21C2×Q8×C23—21no—
22C2×Q8×C23—42no—
23C2×Q8×C23C2×C412yes—
24C22×C4×C23—21no—
25C22×C4×C23—21no—
26C22×C4×C23—42no—
27C22×C4×C23C2×C411yescharacteristic
28C22×C4×C23C2×C411yescharacteristic
29C22×C4×C23D411yescharacteristic
30C22×C4×C23D411yescharacteristic
31C22×C4×C23D411yescharacteristic
32C22×C4×C23C2311yescharacteristic
33C22×Dic23—22no—
34C4⋊C4×C23—22no—
35C4⋊C4×C23—21no—
36C4⋊C4×C23—22no—
37C4⋊C4×C23C2×C412yes—
38C22⋊C4×C23—22no—
39C22⋊C4×C23—22no—
40C22⋊Dic23—42no—
41#67267—42no—
42C2×C23⋊C8—22no—
43C23×C23—22no—
44C23×C23—22no—
45C23×C23—41no—
46C23×C23C22⋊C411yescharacteristic
47C23×C23C22⋊C411yescharacteristic
48C23×C23C2×D411yescharacteristic
49Q8×C23—42no—
50Q8×C23—42no—
51C2×C4×C23—22no—
52C2×C4×C23—22no—
53C2×C4×C23—22no—
54C2×C4×C23—22no—
55C2×C4×C23—41no—
56C2×C4×C23—41no—
57C2×C4×C23—41no—
58C2×C4×C23—41no—
59C2×C4×C23—42no—
60C2×C4×C23—42no—
61C2×C4×C23C22⋊C411yescharacteristic
62C2×C4×C23C22⋊C411yescharacteristic
63C2×C4×C23C22×C411yescharacteristic
64C2×C4×C23C2×D411yescharacteristic
65C2×Dic23—42no—
66C2×Dic23—42no—
67C2×Dic23—42no—
68C23⋊C8—42no—
69#1511—231nomaximal, Sylow
70C22×C23—21no—
71C22×C23—21no—
72C22×C23—21no—
73C22×C23—21no—
74C22×C23—21no—
75C22×C23—21no—
76C22×C23—21no—
77C22×C23—44no—
78C22×C23#9912yes—
79C22×C23C2×C22⋊C411yescharacteristic
80C22×C23#13712yes—
81C4×C23—21no—
82C4×C23—21no—
83C4×C23—21no—
84C4×C23—21no—
85C4×C23—42no—
86C4×C23—42no—
87Dic23—82no—
88C2×C22⋊Q8D2311yescharacteristic
89#407—231no—
90#381—231no—
91#328—234no—
92C2×C23—22no—
93C2×C23—22no—
94C2×C23—41no—
95C2×C23C2×#9911yescharacteristic
96C2×C23#41911yescharacteristic
97C2×C23#42111yescharacteristic
98C22×Q8Dic2311yescharacteristic, complemented
99C23×C4C2×D2311yescharacteristic
100C2×M16—461no—
101C22⋊Q8—21no—
102C22⋊Q8—21no—
103C22⋊Q8Dic2312yescomplemented
104C22⋊Q8C2×D2312yes—
105C2×C4⋊C4—21no—
106C2×C4⋊C4Dic2311yescharacteristic, complemented
107C2×C22⋊C4—21no—
108C2×C22⋊C4—461no—
109C22⋊C8—232no—
110C22⋊C8—461no—
111#95—232no—
112#95—461no—
113C23#151111yescharacteristic, complemented, Sylow
114C24C22⋊D2311yescharacteristic
115C2×Q8—21no—
116C2×Q8—42no—
117C2×Q8C2×Dic2312yes—
118C22×C4—21no—
119C22×C4—21no—
120C22×C4—42no—
121C22×C4—462no—
122C22×C4C2×Dic2311yescharacteristic
123C22×C4C2×Dic2311yescharacteristic
124C22×C4C22⋊D2311yescharacteristic
125C22×C4C22⋊D2311yescharacteristic
126C22×C4C22⋊D2311yescharacteristic
127C22×C4C22×D2311yescharacteristic
128M16—922no—
129C2×C8—462no—
130C4⋊C4—22no—
131C4⋊C4—21no—
132C4⋊C4—22no—
133C4⋊C4C2×Dic2312yes—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C22⋊C4—922no—
137C23—22no—
138C23—22no—
139C23—41no—
140C23C22⋊Dic2311yescharacteristic
141C23C22⋊Dic2311yescharacteristic
142C23C2×C22⋊D2311yescharacteristic
143Q8—42no—
144Q8—42no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—922no—
156C2×C4—922no—
157C2×C4—922no—
158C2×C4C22⋊Dic2311yescharacteristic
159C2×C4C22⋊Dic2311yescharacteristic
160C2×C4C22×Dic2311yescharacteristic
161C2×C4C2×C22⋊D2311yescharacteristic
162C8—922no—
163C22—21no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—44no—
171C22#1062501612yes—
172C22#1062511312yes—
173C22C2×C22⋊Dic2311yescharacteristic
174C4—21no—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—42no—
179C4—42no—
180C4—1842no—
181C2—22no—
182C2—22no—
183C2—41no—
184C2C2×#1062501611yescharacteristic
185C2#1309242611yescharacteristic
186C2#1309243411yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC2×C23×C22⋊Q8C2
socleC22×C23C2×C22⋊C4
prime radicalC24×C23D4
cosocleC22×C4×C23C23
hypercenterC2×C22⋊Q8D23
hypocenterC23#1511
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13092154C2semidirect
5. C22×Q8×C23C4semidirect
9. C23×C22⋊Q8C4semidirect
12. C2×C4⋊C4×C23C4semidirect
98. C22×Q8Dic23semidirect
103. C22⋊Q8Dic23semidirect
106. C2×C4⋊C4Dic23semidirect
113. C23#1511semidirect

Maximal subgroups

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

subgroupindex
#130923812
#130922802
#130921542
C2×C23×C22⋊Q82
#151123