Finite Group Databasebeta

← #15671833

Subgroups — #15671833

Order 2944.

266 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 73 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#13092439C211yesmaximal, characteristic, complemented
3C4×#67262C211yesmaximal, 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—
13C2×#67262—21no—
14C2×#67262—21no—
15#10625063C411yescharacteristic
16#10625058C411yescharacteristic
17(C22⋊D23)⋊C4—21no—
18#10625048—21no—
19C42×D23C2211yescharacteristic
20C4×Dic46C2211yescharacteristic
21C23×C4⋊C8C2211yescharacteristic
22C4×C8×C23C2211yescharacteristic
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—
56#67262—24no—
57#67262—42no—
58C23×C23—21no—
59C22×D23C22⋊C411yescharacteristic
60D4×C23—21no—
61D4×C23M1612yescomplemented
62C2×C4×C23—21no—
63C2×C4×C23—41no—
64C2×C4×C23—41no—
65C2×C4×C23C22×C411yescharacteristic
66C2×C4×C23C2×D411yescharacteristic
67C2×C4×C23C2×D411yescharacteristic
68C22⋊D23—24no—
69C2×Dic23—24no—
70C2×Dic23—21no—
71C2×Dic23—21no—
72C2×Dic23—42no—
73C2×Dic23C22⋊C411yescharacteristic
74C2×Dic23C22⋊C411yescharacteristic
75C2×Dic23C22⋊C411yescharacteristic
76C4×D23—21no—
77C4×D23—21no—
78C4×D23—21no—
79C4×D23—21no—
80C4×D23—22no—
81Dic46—21no—
82Dic46M1612yescomplemented
83C8×C23—22no—
84C8×C23—41no—
85C23⋊C8—22no—
86C23⋊C8—41no—
87#1489—231nomaximal, Sylow
88C22×C23—22no—
89C22×C23—41no—
90C22×C23—41no—
91C22×C23C2×C22⋊C411yescharacteristic
92C2×D23—21no—
93C2×D23—21no—
94C2×D23—21no—
95C4×C23—21no—
96C4×C23—41no—
97C4×C23C2×M1611yescharacteristic
98C4×C23C2×M1611yescharacteristic
99C4×C23AGL(1,ℤ/8)11yescharacteristic
100C4×C23#13711yescharacteristic
101Dic23—22no—
102Dic23—21no—
103Dic23—21no—
104Dic23—41no—
105Dic23#10412yes—
106C4×#41—231no—
107#423—231no—
108C4×M16—231no—
109Q8⋊C8—231no—
110Q8⋊C8—231no—
111D4⋊C8—231no—
112D4⋊C8D2311yescharacteristic, complemented
113C2×C23—42no—
114C2×C23#40711yescharacteristic
115C2×C23#41711yescharacteristic
116C2×C23C2×#10411yescharacteristic
117D23—41no—
118C2×#41—231no—
119C2×M16—461no—
120C2×M16—461no—
121C4×Q8—231no—
122C4×Q8—231no—
123C4×D4—231no—
124C4×D4—461no—
125C4×D4—461no—
126C4×D4C2×D2311yescharacteristic
127#117—231no—
128#117—461no—
129C2×C42—231no—
130C2×C42—461no—
131C4⋊C8—231no—
132C4⋊C8—461no—
133C4⋊C8C2×D2311yescharacteristic
134#97—461no—
135C4×C8—231no—
136C4×C8C2×D2311yescharacteristic
137C23#148911yescharacteristic, complemented, Sylow
138#41—462no—
139#41—462no—
140C2×Q8—231no—
141C2×D4—461no—
142C2×D4C4×D2311yescharacteristic
143C22×C4—21no—
144C22×C4—231no—
145C22×C4—231no—
146C22×C4—231no—
147C22×C4—461no—
148C22×C4—461no—
149M16—464no—
150M16—922no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—461no—
154C2×C8—461no—
155C4⋊C4—231no—
156C4⋊C4—461no—
157C4⋊C4—461no—
158C4⋊C4C4×D2311yescharacteristic
159C22⋊C4—21no—
160C22⋊C4—461no—
161C22⋊C4—461no—
162C42—231no—
163C42—231no—
164C42—231no—
165C42—461no—
166C42—461no—
167C42—461no—
168C42C22×D2311yescharacteristic
169C23—21no—
170C23—231no—
171Q8—232no—
172Q8—461no—
173D4—21no—
174D4—464no—
175D4#6726212yescomplemented
176C2×C4—21no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—231no—
180C2×C4—231no—
181C2×C4—231no—
182C2×C4—462no—
183C2×C4—464no—
184C2×C4—461no—
185C2×C4—461no—
186C2×C4—461no—
187C2×C4—461no—
188C2×C4—461no—
189C2×C4—461no—
190C2×C4—922no—
191C2×C4C2×C4×D2311yescharacteristic
192C2×C4D4×D2311yescharacteristic
193C2×C4D4×D2311yescharacteristic
194C8—22no—
195C8—41no—
196C8—462no—
197C8—921no—
198C22—22no—
199C22—41no—
200C22—41no—
201C22—461no—
202C22—461no—
203C22—461no—
204C22C22⋊C4×D2311yescharacteristic
205C4—21no—
206C4—41no—
207C4—232no—
208C4—461no—
209C4—462no—
210C4—461no—
211C4—921no—
212C4C2×#6726211yescharacteristic
213C4M16×D2311yescharacteristic
214C4#1062508211yescharacteristic
215C4#1062508611yescharacteristic
216C2—42no—
217C2—921no—
218C2#1309237911yescharacteristic
219C2#1309241511yescharacteristic
220C2#104×D2311yescharacteristic
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#1489
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. #13092439C2semidirect
3. C4×#67262C2semidirect
4. #13092149C2semidirect
5. #13092147C2semidirect
6. D4⋊(C23⋊C8)C2semidirect
7. C23×D4⋊C8C2semidirect
61. D4×C23M16semidirect
82. Dic46M16semidirect
112. D4⋊C8D23semidirect
137. C23#1489semidirect
175. D4#67262semidirect

Maximal subgroups

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

subgroupindex
C4×#672902
#130924392
C4×#672622
#130921492
#130921472
D4⋊(C23⋊C8)2
C23×D4⋊C82
#148923