Finite Group Databasebeta

← #15683328

Subgroups — #15683328

Order 2944.

414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 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#13092928C211yesmaximal, characteristic
2#13092758C214yesmaximal, complemented
3#13092741C214yesmaximal, complemented
4#13092457C212yesmaximal, complemented
5#13092416C212yesmaximal, complemented
6#13092381C211yesmaximal, characteristic, complemented
7C2×C23×#117C211yesmaximal, characteristic, complemented
8C23×C4×C23C2211yescharacteristic
9C2×#67288C2211yescharacteristic
10C23×#117—22no—
11C23×#117C2214yes—
12C2×C4⋊C4×C23C2212yes—
13C2×C22⋊C4×C23—21no—
14C2×C42×C23—21no—
15#10625124—21no—
16#10625101C2212yes—
17#10625100—21no—
18C4×C22⋊D23—22no—
19#10625097C2211yescharacteristic
20#10625095C2212yes—
21C2×#67267C2212yes—
22C22⋊(C23⋊C8)C2214yes—
23#10624992C2214yescomplemented
24#10624991C2214yescomplemented
25#10624990C2214yescomplemented
26#10624989C2214yescomplemented
27C24×C23D411yescharacteristic
28C22×C4×C23—24no—
29C22×C4×C23—22no—
30C22×C4×C23D412yes—
31C22×C4×C23D411yescharacteristic
32C22×C4×C23C2312yes—
33C22×C4×C23C2311yescharacteristic
34C2×C22⋊D23—22no—
35C2×C22⋊D23—21no—
36#67288—24no—
37C2×D92C2311yescharacteristic
38C2×C4×D23—21no—
39C2×Dic46C2311yescharacteristic
40C4⋊C4×C23—22no—
41C4⋊C4×C23C2314yes—
42C22⋊C4×C23—24no—
43C42×C23—24no—
44C22⋊Dic23—22no—
45C22⋊Dic23—21no—
46(C2×D23)⋊C4—22no—
47C4⋊Dic23C2312yes—
48Dic23⋊C4—22no—
49C4×Dic23—21no—
50#67267—24no—
51C2×C23⋊C8C2314yes—
52C23×C23—22no—
53C23×C23—42no—
54C23×C23C2×D412yes—
55C23×C23C2×D411yescharacteristic
56C22×D23—21no—
57C2×C4×C23—22no—
58C2×C4×C23—24no—
59C2×C4×C23—24no—
60C2×C4×C23—24no—
61C2×C4×C23—44no—
62C2×C4×C23C2×D412yes—
63C2×C4×C23C2×D411yescharacteristic
64C2×C4×C23#4114yes—
65C2×C4×C23C2411yescharacteristic
66C22⋊D23—44no—
67C22⋊D23—42no—
68C2×Dic23—22no—
69C2×Dic23—21no—
70D92—22no—
71C4×D23—42no—
72Dic46—22no—
73C23⋊C8—24no—
74#3093—231nomaximal, Sylow
75C22×C23—22no—
76C22×C23—22no—
77C22×C23—22no—
78C22×C23—22no—
79C22×C23—44no—
80C22×C23#12312yes—
81C22×C23C22×D411yescharacteristic
82C2×D23—41no—
83C2×D23—42no—
84C4×C23—22no—
85C4×C23—44no—
86C4×C23#12312yes—
87C4×C23C2×#4112yes—
88Dic23—41no—
89Dic23—42no—
90#525—231no—
91C2×#117D2311yescharacteristic, complemented
92#485—234no—
93#482—234no—
94#428—232no—
95#417—232no—
96#407—231no—
97C2×C23—22no—
98C2×C23—42no—
99C2×C23C2×#12311yescharacteristic
100C2×C23#57512yes—
101D23—81no—
102C2×#41—231no—
103C23×C4C2×D2311yescharacteristic
104C2×M16—232no—
105#123—461no—
106C22⋊Q8—232no—
107#121—232no—
108#120—461no—
109C4×D4—462no—
110#117—22no—
111#117—231no—
112#117C2×D2314yes—
113C2×C4⋊C4C2×D2312yes—
114C2×C22⋊C4—21no—
115C2×C42—21no—
116#107—234no—
117#106—234no—
118#103—234no—
119#102—234no—
120C22⋊C8—234no—
121C23#309311yescharacteristic, complemented, Sylow
122C24C22⋊D2311yescharacteristic
123#41—464no—
124C2×Q8—231no—
125C2×D4—231no—
126C2×D4—462no—
127C2×D4—461no—
128C22×C4—24no—
129C22×C4—22no—
130C22×C4—461no—
131C22×C4C22⋊D2311yescharacteristic
132C22×C4C22⋊D2312yes—
133C22×C4C22×D2312yes—
134C22×C4C22×D2311yescharacteristic
135M16—464no—
136C2×C8—234no—
137C4⋊C4—22no—
138C4⋊C4—232no—
139C4⋊C4—462no—
140C4⋊C4C22×D2314yes—
141C22⋊C4—24no—
142C22⋊C4—461no—
143C22⋊C4—462no—
144C22⋊C4—462no—
145C42—24no—
146C42—461no—
147C23—22no—
148C23—42no—
149C23—461no—
150C23C2×C22⋊D2312yes—
151C23C2×C22⋊D2311yescharacteristic
152Q8—462no—
153D4—462no—
154D4—924no—
155D4—922no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—44no—
161C2×C4—462no—
162C2×C4—461no—
163C2×C4—922no—
164C2×C4#6728814yes—
165C2×C4C2×C22⋊D2312yes—
166C2×C4C2×C22⋊D2311yescharacteristic
167C2×C4C23×D2311yescharacteristic
168C8—464no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—921no—
175C22—922no—
176C22#1062510012yes—
177C22C22×C22⋊D2311yescharacteristic
178C4—22no—
179C4—44no—
180C4—921no—
181C4—922no—
182C4#1062510012yes—
183C4C2×#6728812yes—
184C2—22no—
185C2—42no—
186C2—1841no—
187C2C2×#1062510011yescharacteristic
188C2#1309321512yes—
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC2×C23×#117C2
socleC22×C23C22×D4
prime radical#13092928C2
hypercenterC2×#117D23
hypocenterC23#3093
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #13092758C2semidirect
3. #13092741C2semidirect
4. #13092457C2semidirect
5. #13092416C2semidirect
6. #13092381C2semidirect
7. C2×C23×#117C2semidirect
23. #10624992C22semidirect
24. #10624991C22semidirect
25. #10624990C22semidirect
26. #10624989C22semidirect
91. C2×#117D23semidirect
121. C23#3093semidirect

Maximal subgroups

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

subgroupindex
#130929282
#130927582
#130927412
#130924572
#130924162
#130923812
C2×C23×#1172
#309323