Finite Group Databasebeta

← #15671802

Subgroups — #15671802

Order 2944.

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

normal subgroups only

This group has 212 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#13092949C211yesmaximal, characteristic
2#13092469C211yesmaximal, characteristic, complemented
3#13092468C211yesmaximal, characteristic, complemented
4#13092149C211yesmaximal, characteristic, complemented
5#13092147C211yesmaximal, characteristic, complemented
6D4⋊(C23⋊C8)C211yesmaximal, characteristic, complemented
7C23×D4⋊C8C211yesmaximal, characteristic, complemented
8C4×D4×C23C2211yescharacteristic
9#10625109C411yescharacteristic
10#10625107C411yescharacteristic
11C4×C22⋊D23—21no—
12#10625097—21no—
13#10625068C411yescharacteristic
14#10625061C411yescharacteristic
15#10625054—21no—
16#10625050—21no—
17C42×D23C2211yescharacteristic
18C4×Dic46C2211yescharacteristic
19C23×C4⋊C8C2211yescharacteristic
20C4×C8×C23C2211yescharacteristic
21(C2×D23)⋊C8—21no—
22(C2×D23)⋊C8—21no—
23Dic23⋊C8—21no—
24C8×Dic23—21no—
25C4⋊(C23⋊C8)C2211yescharacteristic
26C4×C23⋊C8C2211yescharacteristic
27C2×D4×C23C2×C411yescharacteristic
28C22×C4×C23—21no—
29C2×C22⋊D23—21no—
30C2×C4×D23C2×C411yescharacteristic
31C2×C4×D23D411yescharacteristic
32C2×C4×D23D411yescharacteristic
33C2×Dic46C2×C411yescharacteristic
34C2×C8×C23—21no—
35C2×C8×C23—21no—
36C4⋊C4×C23C2×C411yescharacteristic
37C22⋊C4×C23—21no—
38C42×C23C2311yescharacteristic
39C22⋊Dic23—21no—
40C22⋊Dic23—21no—
41C22⋊Dic23—21no—
42(C2×D23)⋊C4—21no—
43C4⋊Dic23—21no—
44C4⋊Dic23—21no—
45C4⋊Dic23C2×C411yescharacteristic
46Dic23⋊C4—21no—
47Dic23⋊C4—21no—
48C4×Dic23—21no—
49C4×Dic23C2×C411yescharacteristic
50C4×Dic23D411yescharacteristic
51C4×Dic23D411yescharacteristic
52C2×C23⋊C8—21no—
53C2×C23⋊C8—21no—
54C23×C23—21no—
55C22×D23C22⋊C411yescharacteristic
56D4×C23—21no—
57D4×C23—21no—
58C2×C4×C23—21no—
59C2×C4×C23—41no—
60C2×C4×C23—41no—
61C2×C4×C23C22×C411yescharacteristic
62C2×C4×C23C2×D411yescharacteristic
63C2×C4×C23C2×D411yescharacteristic
64C22⋊D23—42no—
65C2×Dic23—21no—
66C2×Dic23—21no—
67C2×Dic23C22⋊C411yescharacteristic
68C2×Dic23C22⋊C411yescharacteristic
69C2×Dic23C22⋊C411yescharacteristic
70C4×D23—21no—
71C4×D23—21no—
72C4×D23—21no—
73C4×D23—21no—
74C4×D23—41no—
75Dic46—21no—
76Dic46—21no—
77C8×C23—41no—
78C8×C23—41no—
79C23⋊C8—41no—
80C23⋊C8—41no—
81#1482—231nomaximal, Sylow
82C22×C23—41no—
83C22×C23—41no—
84C22×C23—41no—
85C22×C23C2×C22⋊C411yescharacteristic
86C2×D23—21no—
87C2×D23—21no—
88C2×D23—21no—
89C4×C23—21no—
90C4×C23—41no—
91C4×C23#13111yescharacteristic
92C4×C23#13111yescharacteristic
93C4×C23#13511yescharacteristic
94C4×C23#13511yescharacteristic
95Dic23—21no—
96Dic23—21no—
97Dic23—21no—
98Dic23—41no—
99Dic23—41no—
100#529—231no—
101#431—231no—
102#431—231no—
103Q8⋊C8—231no—
104Q8⋊C8—231no—
105D4⋊C8—231no—
106D4⋊C8D2311yescharacteristic, complemented
107C2×C23—81no—
108C2×C23#40811yescharacteristic
109C2×C23#41611yescharacteristic
110C2×C23#42111yescharacteristic
111D23—41no—
112#126—461no—
113#125—231no—
114#124—231no—
115#123—461no—
116C22⋊Q8—231no—
117#121—231no—
118C4×Q8—231no—
119C4×D4—461no—
120C4×D4C2×D2311yescharacteristic
121#117—461no—
122C2×C42—231no—
123C4⋊C8—231no—
124C4⋊C8—461no—
125C4⋊C8C2×D2311yescharacteristic
126C22⋊C8—461no—
127C22⋊C8—461no—
128C4×C8—231no—
129C4×C8—461no—
130C4×C8C2×D2311yescharacteristic
131C23#148211yescharacteristic, complemented, Sylow
132C2×Q8—231no—
133C2×D4—461no—
134C2×D4C4×D2311yescharacteristic
135C22×C4—21no—
136C22×C4—231no—
137C22×C4—231no—
138C22×C4—231no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—461no—
142C2×C8—461no—
143C4⋊C4—231no—
144C4⋊C4—461no—
145C4⋊C4—461no—
146C4⋊C4—461no—
147C4⋊C4—461no—
148C4⋊C4C4×D2311yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—461no—
151C22⋊C4—461no—
152C22⋊C4—461no—
153C22⋊C4—461no—
154C42—231no—
155C42—231no—
156C42—231no—
157C42—461no—
158C42C22×D2311yescharacteristic
159C23—21no—
160C23—231no—
161Q8—461no—
162Q8—461no—
163D4—21no—
164D4—21no—
165D4—922no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—231no—
170C2×C4—231no—
171C2×C4—231no—
172C2×C4—461no—
173C2×C4—461no—
174C2×C4—461no—
175C2×C4—461no—
176C2×C4—461no—
177C2×C4—461no—
178C2×C4—921no—
179C2×C4C2×C4×D2311yescharacteristic
180C2×C4D4×D2311yescharacteristic
181C2×C4D4×D2311yescharacteristic
182C8—41no—
183C8—41no—
184C8—921no—
185C8—921no—
186C22—41no—
187C22—41no—
188C22—41no—
189C22—461no—
190C22—461no—
191C22—461no—
192C22C22⋊C4×D2311yescharacteristic
193C4—21no—
194C4—41no—
195C4—461no—
196C4—461no—
197C4—461no—
198C4—921no—
199C4—921no—
200C4#1062507211yescharacteristic
201C4#1062507811yescharacteristic
202C4#1062508311yescharacteristic
203C4#1062508711yescharacteristic
204C2—81no—
205C2—921no—
206C2#1309238211yescharacteristic
207C2#1309241011yescharacteristic
208C2#1309243211yescharacteristic
subgroupG/H
centerC2×C4D4×D23
commutatorC2×C4×C23C22×C4
FrattiniC42C22×D23
FittingC23×D4⋊C8C2
socleC22×C23C2×C22⋊C4
prime radical#10625109C4
cosocleC42×C23C23
hypercenterD4⋊C8D23
hypocenterC23#1482
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #13092469C2semidirect
3. #13092468C2semidirect
4. #13092149C2semidirect
5. #13092147C2semidirect
6. D4⋊(C23⋊C8)C2semidirect
7. C23×D4⋊C8C2semidirect
106. D4⋊C8D23semidirect
131. C23#1482semidirect

Maximal subgroups

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

subgroupindex
#130929492
#130924692
#130924682
#130921492
#130921472
D4⋊(C23⋊C8)2
C23×D4⋊C82
#148223