Finite Group Databasebeta

← #15683799

Subgroups — #15683799

Order 2944.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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#13092968C211yesmaximal, characteristic
2#125×D23C211yesmaximal, characteristic, complemented
3#13092785C211yesmaximal, characteristic, complemented
4#13092783C211yesmaximal, characteristic, complemented
5#13092782C211yesmaximal, characteristic, complemented
6#13092773C214yesmaximal, complemented
7#13092417C214yesmaximal, complemented
8#13092369C211yesmaximal, characteristic, complemented
9C23×#491C211yesmaximal, characteristic, complemented
10C2×#67292C2212yes—
11C23×C4⋊Q8C2211yescharacteristic
12C23×#125C2211yescharacteristic
13#10625118C2212yes—
14C2×#67262C2212yes—
15#10625066—22no—
16#10625064—22no—
17C4⋊C4×D23—22no—
18C4⋊C4×D23C2212yes—
19#10625061C2212yes—
20#10625060—22no—
21#10625045C2211yescharacteristic
22C42×D23C2211yescharacteristic
23#10625041C2211yescharacteristic
24C23×#103C2214yes—
25C23×#97C2211yescharacteristic
26#10625017C2214yes—
27#10625003C2214yes—
28C8×Dic23C2212yes—
29#10624991C2214yes—
30#10624985C2211yescharacteristic
31C2×Q8×C23C2312yes—
32#67292—28no—
33C2×D92—22no—
34C2×D92—22no—
35C2×D92C2312yes—
36C2×C4×D23—22no—
37C2×C4×D23—22no—
38C2×C4×D23D412yes—
39C2×C4×D23C2311yescharacteristic
40C2×C8×C23C2312yes—
41C4⋊C4×C23—22no—
42C4⋊C4×C23—22no—
43C4⋊C4×C23C2312yes—
44C42×C23C2311yescharacteristic
45(C2×D23)⋊C4—24no—
46C4⋊Dic23—22no—
47C4⋊Dic23C2312yes—
48Dic23⋊C4—22no—
49Dic23⋊C4—22no—
50Dic23⋊C4—22no—
51C4×Dic23D412yes—
52C4×Dic23C2311yescharacteristic
53C2×C23⋊C8C2312yes—
54#67262—24no—
55C22×D23—22no—
56C22×D23C2×D411yescharacteristic
57Q8×C23—24no—
58C2×C4×C23—22no—
59C2×C4×C23—22no—
60C2×C4×C23C2×D412yes—
61C2×C4×C23C2411yescharacteristic
62C2×Dic23—22no—
63C2×Dic23C2×D412yes—
64C2×Dic23C2×D411yescharacteristic
65D92—24no—
66D92—44no—
67D92—44no—
68C4×D23—42no—
69C4×D23—44no—
70C4×D23—44no—
71C4×D23#4114yes—
72C8×C23—22no—
73C23⋊C8—22no—
74#3142—231nomaximal, Sylow
75C22×C23C22×D411yescharacteristic
76C2×D23—22no—
77C2×D23—42no—
78C2×D23—44no—
79C2×D23#12412yes—
80C4×C23—22no—
81C4×C23—42no—
82C4×C23—42no—
83C4×C23C2×#4112yes—
84Dic23—22no—
85Dic23—42no—
86Dic23#12412yes—
87#532—231no—
88C2×#125—231no—
89#491—231no—
90#491D2311yescharacteristic, complemented
91#490—231no—
92#490—231no—
93#488—234no—
94#417—234no—
95C4×M16—231no—
96C2×C23C2×#12411yescharacteristic
97C2×C23#57512yes—
98D23—22no—
99D23—82no—
100C2×#41—232no—
101C2×M16—232no—
102C4⋊Q8C2×D2311yescharacteristic
103#127—231no—
104#125—232no—
105#125—231no—
106#125—462no—
107#125C2×D2311yescharacteristic
108#124—232no—
109#121—462no—
110C4×D4—462no—
111C2×C4⋊C4—232no—
112C2×C4⋊C4—462no—
113C2×C42—231no—
114#103—234no—
115#103C2×D2314yes—
116#102—234no—
117#102—234no—
118#97—231no—
119#97C2×D2311yescharacteristic
120C4×C8—232no—
121C23#314211yescharacteristic, complemented, Sylow
122#41—468no—
123C2×Q8C22×D2312yes—
124C2×D4—232no—
125C2×D4—462no—
126C2×D4—462no—
127C22×C4—231no—
128C22×C4—232no—
129C22×C4—462no—
130C22×C4—462no—
131M16—464no—
132C2×C8—232no—
133C2×C8C22×D2312yes—
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—232no—
137C4⋊C4—462no—
138C4⋊C4—462no—
139C4⋊C4—462no—
140C4⋊C4—462no—
141C4⋊C4C22×D2312yes—
142C22⋊C4—464no—
143C42—232no—
144C42—231no—
145C42C22×D2311yescharacteristic
146C23—231no—
147C23—462no—
148Q8—24no—
149D4—464no—
150D4—924no—
151D4—924no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—231no—
155C2×C4—234no—
156C2×C4—232no—
157C2×C4—462no—
158C2×C4—922no—
159C2×C4—924no—
160C2×C4—924no—
161C2×C4D4×D2312yes—
162C2×C4C23×D2311yescharacteristic
163C8—22no—
164C8—462no—
165C22—232no—
166C22—462no—
167C22—922no—
168C22—924no—
169C22C2×D4×D2311yescharacteristic
170C4—22no—
171C4—42no—
172C4—42no—
173C4—232no—
174C4—462no—
175C4—922no—
176C4#41×D2312yes—
177C2—462no—
178C2—1842no—
179C2#124×D2311yescharacteristic
180C2#1309321612yes—
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#491C2
socleC22×C23C22×D4
prime radical#13092968C2
hypercenter#491D23
hypocenterC23#3142
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #125×D23C2semidirect
3. #13092785C2semidirect
4. #13092783C2semidirect
5. #13092782C2semidirect
6. #13092773C2semidirect
7. #13092417C2semidirect
8. #13092369C2semidirect
9. C23×#491C2semidirect
90. #491D23semidirect
121. C23#3142semidirect

Maximal subgroups

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

subgroupindex
#130929682
#125×D232
#130927852
#130927832
#130927822
#130927732
#130924172
#130923692
C23×#4912
#314223