Finite Group Databasebeta

← #15675051

Subgroups — #15675051

Order 2944.

234 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 73 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#13092401C211yesmaximal, characteristic
2#13092391C211yesmaximal, characteristic
3#13092207C214yesmaximal, complemented
4C23×#536C211yesmaximal, characteristic
5C2×#41×C23C2211yescharacteristic
6C22×Q8×C23C411yescharacteristic, complemented
7C23×C4⋊Q8—21no—
8C23×#124—21no—
9C23×#123C412yescomplemented
10C23×#123C2212yes—
11C23×C22⋊Q8—21no—
12C23×C22⋊Q8—21no—
13C23×#117C411yescharacteristic, complemented
14#10625097—21no—
15C2×#67267—21no—
16#10625018—21no—
17#10625016—21no—
18#10625016C2212yes—
19#10625015C2212yes—
20#41×C23—41no—
21#41×C23—41no—
22C2×Q8×C23—21no—
23C2×Q8×C23—21no—
24C2×Q8×C23—41no—
25C2×Q8×C23—41no—
26C2×Q8×C23D411yescharacteristic
27C2×D4×C23C2×C411yescharacteristic
28C2×D4×C23D411yescharacteristic
29C2×D4×C23C2311yescharacteristic
30C22×C4×C23C2×C411yescharacteristic
31C22×C4×C23C2×C412yes—
32C22×C4×C23D411yescharacteristic
33C22×C4×C23D411yescharacteristic
34C4⋊C4×C23—21no—
35C4⋊C4×C23—22no—
36C4⋊C4×C23—22no—
37C22⋊C4×C23—22no—
38C22⋊C4×C23—22no—
39C22⋊C4×C23C2×C412yes—
40C42×C23—21no—
41C22⋊Dic23—22no—
42C4⋊Dic23—41no—
43C4×Dic23—41no—
44#67267—22no—
45#67267—41no—
46C2×C23⋊C8—41no—
47C23×C23C22⋊C411yescharacteristic
48C23×C23C22×C411yescharacteristic
49C23×C23C2×D411yescharacteristic
50Q8×C23—41no—
51Q8×C23—42no—
52Q8×C23—41no—
53Q8×C23—41no—
54D4×C23—41no—
55D4×C23—41no—
56D4×C23—41no—
57C2×C4×C23—21no—
58C2×C4×C23—21no—
59C2×C4×C23—21no—
60C2×C4×C23—21no—
61C2×C4×C23—21no—
62C2×C4×C23—21no—
63C2×C4×C23—22no—
64C2×C4×C23—22no—
65C2×C4×C23—42no—
66C2×C4×C23C22⋊C411yescharacteristic
67C2×C4×C23C22⋊C411yescharacteristic
68C2×C4×C23C22⋊C411yescharacteristic
69C2×C4×C23C2×D411yescharacteristic
70C2×Dic23—42no—
71C23⋊C8—42no—
72#2123—231nomaximal, Sylow
73C22×C23—21no—
74C22×C23—21no—
75C22×C23—21no—
76C22×C23—41no—
77C22×C23—41no—
78C22×C23—41no—
79C22×C23C2×C22⋊C411yescharacteristic
80C4×C23—21no—
81C4×C23—21no—
82C4×C23—21no—
83C4×C23—42no—
84C4×C23—42no—
85C4×C23#9911yescharacteristic
86C4×C23#9911yescharacteristic
87Dic23—82no—
88#536D2311yescharacteristic
89#413—231no—
90#410—231no—
91#352—234no—
92C2×C23—21no—
93C2×C23—41no—
94C2×C23—41no—
95C2×C23—41no—
96C2×C23C2×#9911yescharacteristic
97C2×#41C2×D2311yescharacteristic
98C22×Q8Dic2311yescharacteristic, complemented
99C2×M16—461no—
100C4⋊Q8—21no—
101#124—21no—
102#123Dic2312yescomplemented
103#123C2×D2312yes—
104C22⋊Q8—21no—
105C22⋊Q8—21no—
106#117—461no—
107#117Dic2311yescharacteristic, complemented
108#101—461no—
109#100—232no—
110#99—232no—
111#99—461no—
112C23#212311yescharacteristic, complemented, Sylow
113#41—41no—
114#41—41no—
115C2×Q8—21no—
116C2×Q8—21no—
117C2×Q8—41no—
118C2×Q8—41no—
119C2×Q8C22⋊D2311yescharacteristic
120C2×D4C2×Dic2311yescharacteristic
121C2×D4C22⋊D2311yescharacteristic
122C2×D4C22×D2311yescharacteristic
123C22×C4C2×Dic2311yescharacteristic
124C22×C4C2×Dic2312yes—
125C22×C4C22⋊D2311yescharacteristic
126C22×C4C22⋊D2311yescharacteristic
127M16—462no—
128M16—921no—
129C2×C8—921no—
130C4⋊C4—22no—
131C4⋊C4—21no—
132C4⋊C4—22no—
133C4⋊C4—921no—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C22⋊C4—462no—
137C22⋊C4C2×Dic2312yes—
138C42—21no—
139C42—921no—
140C23C22⋊Dic2311yescharacteristic
141C23C22×Dic2311yescharacteristic
142C23C2×C22⋊D2311yescharacteristic
143Q8—41no—
144Q8—42no—
145Q8—41no—
146Q8—41no—
147D4—41no—
148D4—41no—
149D4—41no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—42no—
159C2×C4—922no—
160C2×C4C22⋊Dic2311yescharacteristic
161C2×C4C22⋊Dic2311yescharacteristic
162C2×C4C22⋊Dic2311yescharacteristic
163C2×C4C2×C22⋊D2311yescharacteristic
164C8—922no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—41no—
169C22—41no—
170C22—41no—
171C22C2×C22⋊Dic2311yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—42no—
176C4—42no—
177C4—1842no—
178C4#1062501611yescharacteristic
179C4#1062501611yescharacteristic
180C2—21no—
181C2—41no—
182C2—41no—
183C2—41no—
184C2C2×#1062501611yescharacteristic
subgroupG/H
centerC2C2×#10625016
commutatorC23×C23C22×C4
FrattiniC2×D4C22×D23
FittingC23×#536C2
socleC2×C23C2×#99
prime radicalC2×#41×C23C22
cosocleC2×D4×C23C23
hypercenter#536D23
hypocenterC23#2123
LCSG ▷ C23×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
3. #13092207C2semidirect
6. C22×Q8×C23C4semidirect
9. C23×#123C4semidirect
13. C23×#117C4semidirect
98. C22×Q8Dic23semidirect
102. #123Dic23semidirect
107. #117Dic23semidirect
112. C23#2123semidirect

Maximal subgroups

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

subgroupindex
#130924012
#130923912
#130922072
C23×#5362
#212323