Finite Group Databasebeta

← #15675052

Subgroups — #15675052

Order 2944.

234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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#13092988C211yesmaximal, characteristic
2#13092391C211yesmaximal, characteristic
3#13092208C214yesmaximal, complemented
4C23×#413C211yesmaximal, characteristic
5C2×#41×C23C2211yescharacteristic
6C22×Dic46C411yescharacteristic, complemented
7C2×M16×C23—21no—
8#10625115—21no—
9#10625107—21no—
10#10625106C412yescomplemented
11#10625106C2212yes—
12#10625097—21no—
13#10625097C411yescharacteristic, complemented
14#10625095—21no—
15#10625095—21no—
16C23×#101—21no—
17C23×#100C2212yes—
18#10625016—21no—
19#10625016C2212yes—
20#41×C23—41no—
21#41×C23—41no—
22C2×Q8×C23D411yescharacteristic
23C2×D4×C23C2×C411yescharacteristic
24C2×D4×C23D411yescharacteristic
25C2×D4×C23C2311yescharacteristic
26C22×C4×C23C2×C411yescharacteristic
27C22×C4×C23D411yescharacteristic
28C22×C4×C23D411yescharacteristic
29C22×Dic23C2×C412yes—
30C2×Dic46—21no—
31C2×Dic46—21no—
32C2×Dic46—41no—
33C2×Dic46—41no—
34M16×C23—22no—
35M16×C23—41no—
36C2×C8×C23—41no—
37C22⋊Dic23—22no—
38C22⋊Dic23—22no—
39C22⋊Dic23—22no—
40C22⋊Dic23C2×C412yes—
41C4⋊Dic23—21no—
42C4⋊Dic23—41no—
43Dic23⋊C4—22no—
44Dic23⋊C4—22no—
45C4×Dic23—21no—
46C4×Dic23—41no—
47C23×C23C22⋊C411yescharacteristic
48C23×C23C22×C411yescharacteristic
49C23×C23C2×D411yescharacteristic
50Q8×C23—41no—
51D4×C23—41no—
52D4×C23—41no—
53D4×C23—41no—
54C2×C4×C23—21no—
55C2×C4×C23—21no—
56C2×C4×C23—21no—
57C2×C4×C23—21no—
58C2×C4×C23—21no—
59C2×C4×C23—21no—
60C2×C4×C23C22⋊C411yescharacteristic
61C2×C4×C23C22⋊C411yescharacteristic
62C2×C4×C23C22⋊C411yescharacteristic
63C2×C4×C23C2×D411yescharacteristic
64C2×Dic23—22no—
65C2×Dic23—22no—
66C2×Dic23—42no—
67C2×Dic23—42no—
68Dic46—42no—
69Dic46—41no—
70Dic46—41no—
71C8×C23—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#9911yescharacteristic
84C4×C23#9911yescharacteristic
85Dic23—42no—
86Dic23—42no—
87Dic23—82no—
88#536—231no—
89#413D2311yescharacteristic
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×Q8—231no—
99C2×M16—21no—
100C4⋊Q8—461no—
101#124—461no—
102#123—232no—
103#123—232no—
104C22⋊Q8—461no—
105C22⋊Q8—461no—
106#117—231no—
107#117—461no—
108#101—21no—
109#100C2×D2312yes—
110#99—232no—
111#99—461no—
112C23#212311yescharacteristic, complemented, Sylow
113#41—41no—
114#41—41no—
115C2×Q8—461no—
116C2×Q8—461no—
117C2×Q8—921no—
118C2×Q8—921no—
119C2×Q8C22⋊D2311yescharacteristic
120C2×D4C4×D2311yescharacteristic
121C2×D4D9211yescharacteristic
122C2×D4C22×D2311yescharacteristic
123C22×C4—232no—
124C22×C4C4×D2311yescharacteristic
125C22×C4D9211yescharacteristic
126C22×C4C22⋊D2311yescharacteristic
127M16—22no—
128M16—41no—
129C2×C8—41no—
130C4⋊C4—462no—
131C4⋊C4—461no—
132C4⋊C4—462no—
133C4⋊C4—921no—
134C22⋊C4—232no—
135C22⋊C4—462no—
136C22⋊C4—462no—
137C22⋊C4—462no—
138C42—461no—
139C42—921no—
140C23(C2×D23)⋊C411yescharacteristic
141C23C2×C4×D2311yescharacteristic
142C23C2×D9211yescharacteristic
143Q8—41no—
144Q8—922no—
145Q8—921no—
146Q8—921no—
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—462no—
157C2×C4—462no—
158C2×C4—922no—
159C2×C4—922no—
160C2×C4(C2×D23)⋊C411yescharacteristic
161C2×C4(C2×D23)⋊C411yescharacteristic
162C2×C4(C2×D23)⋊C411yescharacteristic
163C2×C4C2×C22⋊D2311yescharacteristic
164C8—42no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—41no—
169C22—41no—
170C22—41no—
171C22C2×(C2×D23)⋊C411yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—922no—
176C4—922no—
177C4—1842no—
178C4#1062498811yescharacteristic
179C4#1062498811yescharacteristic
180C2—21no—
181C2—41no—
182C2—41no—
183C2—41no—
184C2C2×#1062498811yescharacteristic
subgroupG/H
centerC2C2×#10624988
commutatorC23×C23C22×C4
FrattiniC2×D4C22×D23
FittingC23×#413C2
socleC2×C23C2×#99
prime radicalC2×#41×C23C22
cosocleC2×D4×C23C23
hypercenter#413D23
hypocenterC23#2123
LCSG ▷ C23×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
3. #13092208C2semidirect
6. C22×Dic46C4semidirect
10. #10625106C4semidirect
13. #10625097C4semidirect
112. C23#2123semidirect

Maximal subgroups

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

subgroupindex
#130929882
#130923912
#130922082
C23×#4132
#212323