Finite Group Databasebeta

← #15675071

Subgroups — #15675071

Order 2944.

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

normal subgroups only

This group has 238 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#13092211C214yesmaximal, complemented
4C23×#410C211yesmaximal, characteristic
5C2×#41×C23C2211yescharacteristic
6C22×Dic46C411yescharacteristic, complemented
7C23×#117—21no—
8#10625115C412yescomplemented
9#10625107C2212yes—
10#10625106—21no—
11#10625106—21no—
12#10625097—21no—
13#10625097C411yescharacteristic, complemented
14#10625095—21no—
15#10625095—21no—
16C23×#99—21no—
17C23×#99C2212yes—
18#10625016—21no—
19#10625016C2212yes—
20#41×C23—41no—
21#41×C23—41no—
22C2×Q8×C23C2×C411yescharacteristic
23C2×D4×C23D411yescharacteristic
24C2×D4×C23D411yescharacteristic
25C2×D4×C23C2311yescharacteristic
26C22×C4×C23C2×C411yescharacteristic
27C22×C4×C23D411yescharacteristic
28C22×C4×C23D411yescharacteristic
29C22×Dic23—21no—
30C2×Dic46—21no—
31C2×Dic46—41no—
32C2×Dic46—41no—
33C2×Dic46C2×C412yes—
34C4⋊C4×C23—41no—
35C22⋊C4×C23—22no—
36C42×C23—41no—
37C22⋊Dic23—21no—
38C22⋊Dic23—22no—
39C22⋊Dic23—22no—
40C22⋊Dic23—22no—
41C4⋊Dic23—21no—
42C4⋊Dic23—41no—
43Dic23⋊C4—22no—
44Dic23⋊C4—22no—
45C4×Dic23—41no—
46C4×Dic23C2×C412yes—
47C23×C23C22⋊C411yescharacteristic
48C23×C23C2×D411yescharacteristic
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×C23—42no—
61C2×C4×C23C22⋊C411yescharacteristic
62C2×C4×C23C22⋊C411yescharacteristic
63C2×C4×C23C22⋊C411yescharacteristic
64C2×C4×C23C22×C411yescharacteristic
65C2×Dic23—22no—
66C2×Dic23—22no—
67C2×Dic23—42no—
68C2×Dic23—42no—
69Dic46—41no—
70Dic46—41no—
71Dic46—42no—
72#2129—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—82no—
84C4×C23#9911yescharacteristic
85C4×C23#9911yescharacteristic
86Dic23—42no—
87Dic23—42no—
88Dic23—82no—
89#536—231no—
90#410—231no—
91#410D2311yescharacteristic
92#354—234no—
93C2×C23—21no—
94C2×C23—41no—
95C2×C23—41no—
96C2×C23—41no—
97C2×C23C2×#9911yescharacteristic
98C2×#41C2×D2311yescharacteristic
99C22×Q8—231no—
100C4⋊Q8—232no—
101#124—232no—
102#123—461no—
103#123—461no—
104C22⋊Q8—461no—
105C22⋊Q8—461no—
106#117—21no—
107#117—231no—
108#117—461no—
109#99—21no—
110#99—232no—
111#99—461no—
112#99C2×D2312yes—
113C23#212911yescharacteristic, complemented, Sylow
114#41—41no—
115#41—41no—
116C2×Q8—232no—
117C2×Q8—461no—
118C2×Q8—921no—
119C2×Q8—921no—
120C2×Q8C4×D2311yescharacteristic
121C2×D4D9211yescharacteristic
122C2×D4C22⋊D2311yescharacteristic
123C2×D4C22×D2311yescharacteristic
124C22×C4—461no—
125C22×C4C4×D2311yescharacteristic
126C22×C4D9211yescharacteristic
127C22×C4C22⋊D2311yescharacteristic
128C4⋊C4—41no—
129C4⋊C4—462no—
130C4⋊C4—462no—
131C4⋊C4—461no—
132C4⋊C4—921no—
133C22⋊C4—22no—
134C22⋊C4—461no—
135C22⋊C4—462no—
136C22⋊C4—462no—
137C22⋊C4—462no—
138C42—41no—
139C42—232no—
140C42—921no—
141C23(C2×D23)⋊C411yescharacteristic
142C23C2×D9211yescharacteristic
143C23C2×C22⋊D2311yescharacteristic
144Q8—41no—
145Q8—922no—
146Q8—921no—
147Q8—921no—
148D4—41no—
149D4—41no—
150D4—41no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—42no—
158C2×C4—462no—
159C2×C4—462no—
160C2×C4—922no—
161C2×C4—922no—
162C2×C4(C2×D23)⋊C411yescharacteristic
163C2×C4(C2×D23)⋊C411yescharacteristic
164C2×C4(C2×D23)⋊C411yescharacteristic
165C2×C4C2×C4×D2311yescharacteristic
166C22—21no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22C2×(C2×D23)⋊C411yescharacteristic
173C4—21no—
174C4—21no—
175C4—21no—
176C4—82no—
177C4—922no—
178C4—922no—
179C4—1842no—
180C4#1062498811yescharacteristic
181C4#1062498811yescharacteristic
182C2—21no—
183C2—41no—
184C2—41no—
185C2—41no—
186C2C2×#1062498811yescharacteristic
subgroupG/H
centerC2C2×#10624988
commutatorC2×C4×C23C22×C4
FrattiniC2×D4C22×D23
FittingC23×#410C2
socleC2×C23C2×#99
prime radicalC2×#41×C23C22
cosocleC2×D4×C23C23
hypercenter#410D23
hypocenterC23#2129
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #13092211C2semidirect
6. C22×Dic46C4semidirect
8. #10625115C4semidirect
13. #10625097C4semidirect
113. C23#2129semidirect

Maximal subgroups

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

subgroupindex
#130929882
#130923912
#130922112
C23×#4102
#212923