Finite Group Databasebeta

← #15672116

Subgroups — #15672116

Order 2944.

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

normal subgroups only

This group has 246 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#13092965C211yesmaximal, characteristic
2#13092473C211yesmaximal, characteristic, complemented
3#13092439C211yesmaximal, characteristic, complemented
4#13092164C211yesmaximal, characteristic, complemented
5#13092162C211yesmaximal, characteristic, complemented
6#13092161C211yesmaximal, characteristic, complemented
7C23×#331C211yesmaximal, characteristic, complemented
8C2×#67290—21no—
9C23×#127C2211yescharacteristic
10#10625109—21no—
11#10625109C412yes—
12#10625107—21no—
13D4×Dic23—21no—
14D4×Dic23C412yes—
15C2×#67262—21no—
16C42×D23C2211yescharacteristic
17#10625040C2211yescharacteristic
18C23×C4⋊C8C2211yescharacteristic
19C23×C4⋊C8C2211yescharacteristic
20(C2×D23)⋊C8—21no—
21#10624997—21no—
22Dic23⋊C8—21no—
23C4⋊(C23⋊C8)C2211yescharacteristic
24C4⋊(C23⋊C8)C2211yescharacteristic
25C2×D4×C23—21no—
26C2×D4×C23—21no—
27C2×D4×C23C2×C412yes—
28C2×C22⋊D23—22no—
29C22×Dic23—22no—
30#67290—42no—
31#67290—42no—
32C2×C4×D23C2×C411yescharacteristic
33C2×C4×D23D411yescharacteristic
34C2×C4×D23D411yescharacteristic
35C2×Dic46—21no—
36C2×C8×C23—21no—
37C2×C8×C23—21no—
38C42×C23C2311yescharacteristic
39C22⋊Dic23—22no—
40C22⋊Dic23—22no—
41C4⋊Dic23—21no—
42C4⋊Dic23C2×C412yes—
43C4×Dic23C2×C411yescharacteristic
44C4×Dic23D411yescharacteristic
45C4×Dic23D411yescharacteristic
46C2×C23⋊C8—21no—
47C2×C23⋊C8—21no—
48#67262—42no—
49C23×C23—22no—
50C22×D23C22⋊C411yescharacteristic
51D4×C23—42no—
52D4×C23—41no—
53D4×C23—41no—
54D4×C23—41no—
55D4×C23—41no—
56C2×C4×C23C22×C411yescharacteristic
57C2×C4×C23C2×D411yescharacteristic
58C2×C4×C23C2×D411yescharacteristic
59C22⋊D23—44no—
60C2×Dic23—22no—
61C2×Dic23—44no—
62C2×Dic23C22⋊C411yescharacteristic
63C2×Dic23C22⋊C411yescharacteristic
64C2×Dic23C22⋊C411yescharacteristic
65C4×D23—21no—
66C4×D23—21no—
67C4×D23—21no—
68C4×D23—21no—
69C4×D23—41no—
70Dic46—41no—
71Dic46—41no—
72C8×C23—41no—
73C8×C23—41no—
74C23⋊C8—41no—
75C23⋊C8—41no—
76#1557—231nomaximal, Sylow
77C22×C23—42no—
78C22×C23—42no—
79C22×C23—42no—
80C22×C23C2×C22⋊C411yescharacteristic
81C2×D23—21no—
82C2×D23—21no—
83C2×D23—21no—
84C4×C23—21no—
85C4×C23AGL(1,ℤ/8)11yescharacteristic
86C4×C23AGL(1,ℤ/8)11yescharacteristic
87C4×C23AGL(1,ℤ/8)11yescharacteristic
88C4×C23#13711yescharacteristic
89Dic23—21no—
90Dic23—21no—
91Dic23—21no—
92Dic23—42no—
93#532—231no—
94#432—231no—
95#423—231no—
96#332—231no—
97#332—231no—
98#331—231no—
99#331D2311yescharacteristic, complemented
100C2×C23—82no—
101C2×C23#41311yescharacteristic
102C2×C23#41711yescharacteristic
103C2×C23#41811yescharacteristic
104D23—41no—
105C2×#41—461no—
106C2×M16—461no—
107C4⋊Q8—231no—
108#127C2×D2311yescharacteristic
109#124—461no—
110#121—232no—
111#121—461no—
112C4×D4—232no—
113C4×D4—461no—
114C2×C42—231no—
115C4⋊C8—231no—
116C4⋊C8—231no—
117C4⋊C8—461no—
118C4⋊C8C2×D2311yescharacteristic
119C4⋊C8C2×D2311yescharacteristic
120C22⋊C8—461no—
121#97—461no—
122C23#155711yescharacteristic, complemented, Sylow
123#41—922no—
124#41—922no—
125C2×Q8—461no—
126C2×D4—21no—
127C2×D4—21no—
128C2×D4—462no—
129C2×D4C4×D2312yes—
130C22×C4—231no—
131C22×C4—231no—
132C22×C4—231no—
133C22×C4—462no—
134M16—922no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—461no—
138C2×C8—461no—
139C4⋊C4—232no—
140C4⋊C4—461no—
141C22⋊C4—462no—
142C22⋊C4—462no—
143C42—231no—
144C42—231no—
145C42—231no—
146C42C22×D2311yescharacteristic
147C23—22no—
148C23—231no—
149Q8—921no—
150Q8—921no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—924no—
157C2×C4—231no—
158C2×C4—231no—
159C2×C4—231no—
160C2×C4—461no—
161C2×C4—461no—
162C2×C4—461no—
163C2×C4—461no—
164C2×C4—462no—
165C2×C4—921no—
166C2×C4—924no—
167C2×C4C2×C4×D2311yescharacteristic
168C2×C4D4×D2311yescharacteristic
169C2×C4D4×D2311yescharacteristic
170C8—41no—
171C8—41no—
172C8—921no—
173C8—921no—
174C22—42no—
175C22—42no—
176C22—42no—
177C22—461no—
178C22—461no—
179C22—461no—
180C22C22⋊C4×D2311yescharacteristic
181C4—21no—
182C4—461no—
183C4—461no—
184C4—461no—
185C4—922no—
186C4#1062508211yescharacteristic
187C4#1062508211yescharacteristic
188C4#1062508511yescharacteristic
189C4#1062508611yescharacteristic
190C2—82no—
191C2—921no—
192C2#1309239811yescharacteristic
193C2#1309241511yescharacteristic
194C2#1309242011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutatorC2×C4×C23C22×C4
FrattiniC42C22×D23
FittingC23×#331C2
socleC22×C23C2×C22⋊C4
prime radical#13092965C2
cosocleC42×C23C23
hypercenter#331D23
hypocenterC23#1557
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #13092473C2semidirect
3. #13092439C2semidirect
4. #13092164C2semidirect
5. #13092162C2semidirect
6. #13092161C2semidirect
7. C23×#331C2semidirect
99. #331D23semidirect
122. C23#1557semidirect

Maximal subgroups

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

subgroupindex
#130929652
#130924732
#130924392
#130921642
#130921622
#130921612
C23×#3312
#155723