Finite Group Databasebeta

← #15671808

Subgroups — #15671808

Order 2944.

234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 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#13092951C211yesmaximal, characteristic
2C4×#67267C211yesmaximal, characteristic, complemented
3#13092147C212yesmaximal, complemented
4#13092144C212yesmaximal, complemented
5C2×C23×C4⋊C8C211yesmaximal, characteristic, complemented
6C22×C8×C23—21no—
7C2×C42×C23C2211yescharacteristic
8#10625101C411yescharacteristic
9#10625100—21no—
10C4×C22⋊D23—21no—
11#10625095C411yescharacteristic
12C2×#67267—21no—
13#10625047—21no—
14#10625046C411yescharacteristic
15C4×D92C2211yescharacteristic
16#10625043—21no—
17#10625041C411yescharacteristic
18C4×Dic46C2211yescharacteristic
19C23×C4⋊C8—21no—
20C23×C4⋊C8C2212yes—
21#10624985—21no—
22C4×C23⋊C8C2212yes—
23C22×C4×C23C2×C411yescharacteristic
24C22×C4×C23D411yescharacteristic
25C22×C4×C23D411yescharacteristic
26C2×C22⋊D23—21no—
27C2×D92C2×C411yescharacteristic
28C2×C4×D23—21no—
29C2×Dic46C2×C411yescharacteristic
30C2×C8×C23—22no—
31C2×C8×C23—42no—
32C42×C23C2×C411yescharacteristic
33C42×C23D411yescharacteristic
34C42×C23D411yescharacteristic
35C42×C23C2311yescharacteristic
36C22⋊Dic23—21no—
37(C2×D23)⋊C4—21no—
38(C2×D23)⋊C4—21no—
39(C2×D23)⋊C4—21no—
40(C2×D23)⋊C4—21no—
41C4⋊Dic23C2×C411yescharacteristic
42C4⋊Dic23C2×C411yescharacteristic
43Dic23⋊C4—21no—
44Dic23⋊C4—21no—
45Dic23⋊C4—21no—
46Dic23⋊C4—21no—
47C4×Dic23—21no—
48#67267—24no—
49C2×C23⋊C8—22no—
50C23×C23C22⋊C411yescharacteristic
51C22×D23—21no—
52C2×C4×C23—22no—
53C2×C4×C23—22no—
54C2×C4×C23—21no—
55C2×C4×C23—21no—
56C2×C4×C23C22⋊C411yescharacteristic
57C2×C4×C23C22⋊C411yescharacteristic
58C2×C4×C23C22⋊C411yescharacteristic
59C2×C4×C23C22×C411yescharacteristic
60C2×C4×C23C2×D411yescharacteristic
61C2×C4×C23C2×D411yescharacteristic
62C22⋊D23—42no—
63C2×Dic23—21no—
64C2×Dic23—21no—
65C2×Dic23—21no—
66D92—22no—
67C4×D23—41no—
68C4×D23—41no—
69Dic46—22no—
70C8×C23—42no—
71C23⋊C8—24no—
72#1483—231nomaximal, Sylow
73C22×C23—21no—
74C22×C23—21no—
75C22×C23#10412yes—
76C22×C23C2×C22⋊C411yescharacteristic
77C2×D23—41no—
78C2×D23—41no—
79C2×D23—41no—
80C4×C23—21no—
81C4×C23—21no—
82C4×C23—21no—
83C4×C23—21no—
84C4×C23#13112yes—
85C4×C23AGL(1,ℤ/8)11yescharacteristic
86C4×C23#13711yescharacteristic
87Dic23—41no—
88Dic23—41no—
89Dic23—41no—
90#529—231no—
91C2×C4⋊C8D2311yescharacteristic, complemented
92C4×M16—231no—
93Q8⋊C8—232no—
94D4⋊C8—232no—
95C2×C23—22no—
96C2×C23#40811yescharacteristic
97C2×C23#41711yescharacteristic
98C2×C23C2×#10411yescharacteristic
99D23—81no—
100C2×M16—461no—
101C22×C8—21no—
102#126—461no—
103#125—231no—
104#124—231no—
105#123—461no—
106C22⋊Q8—231no—
107#121—231no—
108C4×Q8—231no—
109C4×D4—231no—
110C4×D4—461no—
111#117—461no—
112C2×C42C2×D2311yescharacteristic
113C4⋊C8—21no—
114C4⋊C8C2×D2312yes—
115#97—461no—
116C4×C8—232no—
117C23#148311yescharacteristic, complemented, Sylow
118C2×Q8—231no—
119C2×D4—231no—
120C2×D4—461no—
121C22×C4—461no—
122C22×C4C4×D2311yescharacteristic
123C22×C4D9211yescharacteristic
124C22×C4C22⋊D2311yescharacteristic
125M16—464no—
126C2×C8—22no—
127C2×C8—42no—
128C2×C8—462no—
129C4⋊C4—231no—
130C4⋊C4—231no—
131C4⋊C4—461no—
132C4⋊C4—461no—
133C4⋊C4—461no—
134C4⋊C4—461no—
135C22⋊C4—461no—
136C22⋊C4—461no—
137C22⋊C4—461no—
138C22⋊C4—461no—
139C22⋊C4—461no—
140C42—461no—
141C42C4×D2311yescharacteristic
142C42D9211yescharacteristic
143C42C22⋊D2311yescharacteristic
144C42C22×D2311yescharacteristic
145C23—461no—
146C23(C2×D23)⋊C411yescharacteristic
147Q8—462no—
148D4—462no—
149D4—922no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—461no—
155C2×C4—461no—
156C2×C4—461no—
157C2×C4—921no—
158C2×C4—921no—
159C2×C4(C2×D23)⋊C411yescharacteristic
160C2×C4(C2×D23)⋊C411yescharacteristic
161C2×C4(C2×D23)⋊C411yescharacteristic
162C2×C4C2×C4×D2311yescharacteristic
163C2×C4C2×D9211yescharacteristic
164C2×C4C2×C22⋊D2311yescharacteristic
165C8—42no—
166C8—464no—
167C22—21no—
168C22—21no—
169C22—921no—
170C22—921no—
171C22—921no—
172C22#1062500712yes—
173C22C2×(C2×D23)⋊C411yescharacteristic
174C4—21no—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—921no—
179C4—921no—
180C4—921no—
181C4#1062507212yes—
182C4#1062510311yescharacteristic
183C4#1062511311yescharacteristic
184C2—22no—
185C2—1841no—
186C2#1309238311yescharacteristic
187C2#1309241611yescharacteristic
188C2C2×#1062500711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D23
commutatorC2×C4×C23C22×C4
FrattiniC42C22×D23
FittingC2×C23×C4⋊C8C2
socleC22×C23C2×C22⋊C4
prime radical#10625101C4
cosocleC42×C23C23
hypercenterC2×C4⋊C8D23
hypocenterC23#1483
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C4×#67267C2semidirect
3. #13092147C2semidirect
4. #13092144C2semidirect
5. C2×C23×C4⋊C8C2semidirect
91. C2×C4⋊C8D23semidirect
117. C23#1483semidirect

Maximal subgroups

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

subgroupindex
#130929512
C4×#672672
#130921472
#130921442
C2×C23×C4⋊C82
#148323