Finite Group Databasebeta

← #15671828

Subgroups — #15671828

Order 2944.

246 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 71 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×#67290C211yesmaximal, characteristic
2#13092473C211yesmaximal, 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
8C2×#67290C411yescharacteristic
9C4×D4×C23C2211yescharacteristic
10D4×Dic23C411yescharacteristic
11C4×C22⋊D23—21no—
12C2×C4×Dic23—21no—
13#10625063C411yescharacteristic
14#10625058C411yescharacteristic
15(C22⋊D23)⋊C4—21no—
16#10625048—21no—
17C42×D23C2211yescharacteristic
18C4×Dic46C2211yescharacteristic
19C23×C4⋊C8C2211yescharacteristic
20C4×C8×C23C2211yescharacteristic
21(C2×D23)⋊C8—21no—
22(C2×D23)⋊C8—21no—
23#10624997—21no—
24Dic23⋊C8—21no—
25C4⋊(C23⋊C8)C2211yescharacteristic
26C4×C23⋊C8C2211yescharacteristic
27C2×D4×C23C2×C411yescharacteristic
28C22×C4×C23—21no—
29C2×C22⋊D23—21no—
30C22×Dic23—21no—
31C22×Dic23—21no—
32#67290—22no—
33#67290—22no—
34C2×C4×D23C2×C411yescharacteristic
35C2×C4×D23D411yescharacteristic
36C2×C4×D23D411yescharacteristic
37C2×Dic46C2×C411yescharacteristic
38C2×C8×C23—21no—
39C2×C8×C23—21no—
40C4⋊C4×C23C2×C411yescharacteristic
41C22⋊C4×C23—21no—
42C42×C23C2311yescharacteristic
43C22⋊Dic23—21no—
44(C2×D23)⋊C4—21no—
45C4⋊Dic23C2×C411yescharacteristic
46Dic23⋊C4—21no—
47Dic23⋊C4—21no—
48C4×Dic23—21no—
49C4×Dic23—21no—
50C4×Dic23—21no—
51C4×Dic23C2×C411yescharacteristic
52C4×Dic23D411yescharacteristic
53C4×Dic23D411yescharacteristic
54C2×C23⋊C8—21no—
55C2×C23⋊C8—21no—
56C23×C23—21no—
57C22×D23C22⋊C411yescharacteristic
58D4×C23—21no—
59D4×C23M1612yes—
60C2×C4×C23—21no—
61C2×C4×C23—41no—
62C2×C4×C23—41no—
63C2×C4×C23C22×C411yescharacteristic
64C2×C4×C23C2×D411yescharacteristic
65C2×C4×C23C2×D411yescharacteristic
66C22⋊D23—24no—
67C2×Dic23—24no—
68C2×Dic23—21no—
69C2×Dic23—21no—
70C2×Dic23—42no—
71C2×Dic23C22⋊C411yescharacteristic
72C2×Dic23C22⋊C411yescharacteristic
73C2×Dic23C22⋊C411yescharacteristic
74C4×D23—21no—
75C4×D23—21no—
76C4×D23—21no—
77C4×D23—21no—
78C4×D23—41no—
79Dic46—21no—
80Dic46M1612yes—
81C8×C23—41no—
82C8×C23—41no—
83C23⋊C8—41no—
84C23⋊C8—41no—
85#1488—231nomaximal, Sylow
86C22×C23—22no—
87C22×C23—41no—
88C22×C23—41no—
89C22×C23C2×C22⋊C411yescharacteristic
90C2×D23—21no—
91C2×D23—21no—
92C2×D23—21no—
93C4×C23—21no—
94C4×C23—41no—
95C4×C23C2×M1611yescharacteristic
96C4×C23C2×M1611yescharacteristic
97C4×C23#13511yescharacteristic
98C4×C23#13511yescharacteristic
99Dic23—22no—
100Dic23—21no—
101Dic23—21no—
102Dic23—21no—
103Dic23—41no—
104C4×#41—231no—
105#432—231no—
106#431—231no—
107Q8⋊C8—231no—
108Q8⋊C8—231no—
109D4⋊C8—231no—
110D4⋊C8D2311yescharacteristic, complemented
111C2×C23—42no—
112C2×C23#40711yescharacteristic
113C2×C23#41611yescharacteristic
114C2×C23#42111yescharacteristic
115D23—41no—
116C2×#41—231no—
117C4×Q8—231no—
118C4×Q8—231no—
119C4×D4—231no—
120C4×D4—461no—
121C4×D4—461no—
122C4×D4C2×D2311yescharacteristic
123#117—231no—
124#117—461no—
125C2×C42—231no—
126C2×C42—461no—
127C4⋊C8—231no—
128C4⋊C8—461no—
129C4⋊C8C2×D2311yescharacteristic
130C22⋊C8—461no—
131C22⋊C8—461no—
132#97—461no—
133C4×C8—231no—
134C4×C8C2×D2311yescharacteristic
135C23#148811yescharacteristic, complemented, Sylow
136#41—462no—
137#41—462no—
138C2×Q8—231no—
139C2×D4—461no—
140C2×D4C4×D2311yescharacteristic
141C22×C4—21no—
142C22×C4—231no—
143C22×C4—231no—
144C22×C4—231no—
145C22×C4—461no—
146C22×C4—461no—
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—461no—
150C2×C8—461no—
151C4⋊C4—231no—
152C4⋊C4—461no—
153C4⋊C4—461no—
154C4⋊C4C4×D2311yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—461no—
157C22⋊C4—461no—
158C42—231no—
159C42—231no—
160C42—231no—
161C42—461no—
162C42—461no—
163C42—461no—
164C42C22×D2311yescharacteristic
165C23—21no—
166C23—231no—
167Q8—232no—
168Q8—461no—
169D4—21no—
170D4—464no—
171D4#6726212yes—
172C2×C4—21no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—231no—
176C2×C4—231no—
177C2×C4—231no—
178C2×C4—464no—
179C2×C4—461no—
180C2×C4—461no—
181C2×C4—461no—
182C2×C4—461no—
183C2×C4—461no—
184C2×C4—461no—
185C2×C4—921no—
186C2×C4—922no—
187C2×C4C2×C4×D2311yescharacteristic
188C2×C4D4×D2311yescharacteristic
189C2×C4D4×D2311yescharacteristic
190C8—41no—
191C8—41no—
192C8—921no—
193C8—921no—
194C22—22no—
195C22—41no—
196C22—41no—
197C22—461no—
198C22—461no—
199C22—461no—
200C22C22⋊C4×D2311yescharacteristic
201C4—21no—
202C4—41no—
203C4—461no—
204C4—462no—
205C4—461no—
206C4—461no—
207C4—921no—
208C4C2×#6726211yescharacteristic
209C4M16×D2311yescharacteristic
210C4#1062508311yescharacteristic
211C4#1062508711yescharacteristic
212C2—42no—
213C2—921no—
214C2#1309237911yescharacteristic
215C2#1309241011yescharacteristic
216C2#1309243211yescharacteristic
subgroupG/H
centerC2×C4D4×D23
commutatorC2×C4×C23C22×C4
FrattiniC42C22×D23
FittingC23×D4⋊C8C2
socleC22×C23C2×C22⋊C4
prime radicalC2×#67290C4
cosocleC42×C23C23
hypercenterD4⋊C8D23
hypocenterC23#1488
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. #13092473C2semidirect
3. #13092468C2semidirect
4. #13092149C2semidirect
5. #13092147C2semidirect
6. D4⋊(C23⋊C8)C2semidirect
7. C23×D4⋊C8C2semidirect
110. D4⋊C8D23semidirect
135. C23#1488semidirect

Maximal subgroups

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

subgroupindex
C4×#672902
#130924732
#130924682
#130921492
#130921472
D4⋊(C23⋊C8)2
C23×D4⋊C82
#148823