Finite Group Databasebeta

← #15683215

Subgroups — #15683215

Order 2944.

384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C4×#67288C211yesmaximal, characteristic
2#13092721C214yesmaximal, complemented
3#13092714C214yesmaximal, complemented
4#13092457C212yesmaximal, complemented
5#13092441C211yesmaximal, characteristic, complemented
6#13092416C212yesmaximal
7C2×C23×#125C211yesmaximal, characteristic, complemented
8C2×#67288C2211yescharacteristic
9C23×#125—21no—
10C23×#125—21no—
11C23×#125C2214yes—
12C2×C4⋊C4×C23—22no—
13C2×C4⋊C4×C23C2212yes—
14C2×C42×C23C2211yescharacteristic
15C4×C22⋊D23—22no—
16#10625097C2211yescharacteristic
17C2×#67267C2212yes—
18C4×D92C2212yes—
19#10625043—21no—
20C42×D23—21no—
21C4×Dic46C2212yes—
22#10624992C2214yes—
23#10624991C2214yes—
24#10624990C2214yes—
25#10624989C2214yes—
26C4⋊(C23⋊C8)C2214yes—
27C22×C4×C23—22no—
28C22×C4×C23D412yes—
29C22×C4×C23C2311yescharacteristic
30C2×C22⋊D23—21no—
31#67288—22no—
32#67288Q814yes—
33C2×D92C2311yescharacteristic
34C2×C4×D23—21no—
35C2×C4×D23—22no—
36C2×Dic46C2311yescharacteristic
37C4⋊C4×C23—24no—
38C4⋊C4×C23—24no—
39C4⋊C4×C23—22no—
40C4⋊C4×C23C2314yes—
41C42×C23D411yescharacteristic
42C42×C23D411yescharacteristic
43C42×C23C2312yes—
44C22⋊Dic23—21no—
45(C2×D23)⋊C4—22no—
46C4⋊Dic23C2312yes—
47Dic23⋊C4—22no—
48C4×Dic23—22no—
49C4×Dic23—21no—
50#67267—24no—
51C2×C23⋊C8C2314yes—
52C23×C23C2×D411yescharacteristic
53C22×D23—21no—
54C2×C4×C23—24no—
55C2×C4×C23—42no—
56C2×C4×C23—44no—
57C2×C4×C23C2×D412yes—
58C2×C4×C23C2×D412yes—
59C2×C4×C23C2×D411yescharacteristic
60C2×C4×C23C2×Q812yes—
61C2×C4×C23#4112yes—
62C2×C4×C23C2411yescharacteristic
63C22⋊D23—24no—
64C2×Dic23—21no—
65C2×Dic23—22no—
66D92—21no—
67D92C2×Q812yes—
68C4×D23—24no—
69C4×D23—44no—
70Dic46—21no—
71Dic46C2×Q812yes—
72C23⋊C8—24no—
73#3080—231nomaximal, Sylow
74C22×C23—22no—
75C22×C23C22⋊Q812yes—
76C22×C23C22×D411yescharacteristic
77C2×D23—22no—
78C2×D23—42no—
79C4×C23—22no—
80C4×C23—22no—
81C4×C23—44no—
82C4×C23C22⋊Q812yes—
83C4×C23C22×Q811yescharacteristic
84C4×C23C2×#4111yescharacteristic
85Dic23—22no—
86Dic23—42no—
87C2×#125D2311yescharacteristic, complemented
88C4×#41—231no—
89#479—234no—
90#478—234no—
91#428—232no—
92#423—231no—
93#417—232no—
94C2×C23—22no—
95C2×C23C2×C22⋊Q811yescharacteristic
96C2×C23#57512yes—
97D23—42no—
98C2×#41—231no—
99C2×M16—232no—
100#125—21no—
101#125—21no—
102#125C2×D2314yes—
103C4×Q8—232no—
104C4×D4—232no—
105C4×D4—462no—
106#117—231no—
107#117—461no—
108C2×C4⋊C4—22no—
109C2×C4⋊C4C2×D2312yes—
110C2×C42—461no—
111C2×C42C2×D2311yescharacteristic
112#107—234no—
113#106—234no—
114C4⋊C8—234no—
115#103—234no—
116#102—234no—
117C23#308011yescharacteristic, complemented, Sylow
118#41—234no—
119#41—462no—
120C2×Q8—231no—
121C2×D4—231no—
122C2×D4—461no—
123C22×C4—22no—
124C22×C4—461no—
125C22×C4—462no—
126C22×C4C22⋊D2312yes—
127C22×C4C22×D2311yescharacteristic
128M16—464no—
129C2×C8—234no—
130C4⋊C4—24no—
131C4⋊C4—24no—
132C4⋊C4—22no—
133C4⋊C4—232no—
134C4⋊C4—462no—
135C4⋊C4C22×D2314yes—
136C22⋊C4—461no—
137C22⋊C4—462no—
138C42—461no—
139C42—462no—
140C42C22⋊D2311yescharacteristic
141C42C22⋊D2311yescharacteristic
142C42C22×D2312yes—
143C23—461no—
144C23C2×C22⋊D2311yescharacteristic
145Q8—232no—
146Q8—461no—
147D4—232no—
148D4—464no—
149D4—461no—
150C2×C4—24no—
151C2×C4—42no—
152C2×C4—44no—
153C2×C4—461no—
154C2×C4—464no—
155C2×C4—462no—
156C2×C4—924no—
157C2×C4Q8×D2312yes—
158C2×C4#6729212yes—
159C2×C4C2×C22⋊D2312yes—
160C2×C4C2×C22⋊D2312yes—
161C2×C4C2×C22⋊D2311yescharacteristic
162C2×C4C23×D2311yescharacteristic
163C8—464no—
164C22—22no—
165C22—462no—
166C22—922no—
167C22#1062511712yes—
168C22C22×C22⋊D2311yescharacteristic
169C4—22no—
170C4—22no—
171C4—44no—
172C4—462no—
173C4—922no—
174C4#1062511712yes—
175C4C2×Q8×D2311yescharacteristic
176C4C2×#6729211yescharacteristic
177C2—22no—
178C2—922no—
179C2C2×#1062511711yescharacteristic
180C2#1309321512yes—
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC2×C23×#125C2
socleC22×C23C22×D4
prime radicalC2×#67288C22
hypercenterC2×#125D23
hypocenterC23#3080
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #13092721C2semidirect
3. #13092714C2semidirect
4. #13092457C2semidirect
5. #13092441C2semidirect
7. C2×C23×#125C2semidirect
87. C2×#125D23semidirect
117. C23#3080semidirect

Maximal subgroups

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

subgroupindex
C4×#672882
#130927212
#130927142
#130924572
#130924412
#130924162
C2×C23×#1252
#308023