Finite Group Databasebeta

← #15671923

Subgroups — #15671923

Order 2944.

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

normal subgroups only

This group has 242 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
1#13092951C211yesmaximal, characteristic
2C4×C4⋊Dic23C211yesmaximal, characteristic, complemented
3#13092155C212yesmaximal, complemented
4#13092152C212yesmaximal
5C23×#432C211yesmaximal, characteristic, complemented
6C2×C42×C23C2211yescharacteristic
7#10625101C2211yescharacteristic
8#10625100—21no—
9C4×C22⋊D23—21no—
10C2×C4⋊Dic23—21no—
11#10625095C2211yescharacteristic
12C2×C4×Dic23—21no—
13#10625047—21no—
14#10625046C411yescharacteristic, complemented
15C4×D92C411yescharacteristic, complemented
16#10625043—21no—
17#10625041C411yescharacteristic, complemented
18C4×Dic46C411yescharacteristic, complemented
19C23×C4⋊C8—21no—
20C23×C22⋊C8C2212yes—
21C23×#97—21no—
22C23⋊#95C2212yes—
23C22×C4×C23D411yescharacteristic
24C22×C4×C23D411yescharacteristic
25C22×C4×C23C2311yescharacteristic
26C2×C22⋊D23—21no—
27C22×Dic23—22no—
28C2×D92C2×C411yescharacteristic
29C2×C4×D23—21no—
30C2×Dic46C2×C411yescharacteristic
31C2×C8×C23—22no—
32C42×C23C2×C411yescharacteristic
33C42×C23C2×C411yescharacteristic
34C42×C23D411yescharacteristic
35C42×C23D411yescharacteristic
36C22⋊Dic23—21no—
37(C2×D23)⋊C4—21no—
38(C2×D23)⋊C4—21no—
39(C2×D23)⋊C4—21no—
40(C2×D23)⋊C4—21no—
41C4⋊Dic23—24no—
42C4⋊Dic23C2×C411yescharacteristic
43C4⋊Dic23C2×C411yescharacteristic
44Dic23⋊C4—21no—
45Dic23⋊C4—21no—
46Dic23⋊C4—21no—
47Dic23⋊C4—21no—
48C4×Dic23—21no—
49C4×Dic23—42no—
50C23×C23C2×D411yescharacteristic
51C22×D23—21no—
52C2×C4×C23—21no—
53C2×C4×C23—21no—
54C2×C4×C23—22no—
55C2×C4×C23—41no—
56C2×C4×C23C22⋊C411yescharacteristic
57C2×C4×C23C22⋊C411yescharacteristic
58C2×C4×C23C22⋊C411yescharacteristic
59C2×C4×C23C22⋊C411yescharacteristic
60C2×C4×C23C22×C411yescharacteristic
61C2×C4×C23C2×D411yescharacteristic
62C22⋊D23—41no—
63C22⋊D23—41no—
64C2×Dic23—24no—
65C2×Dic23—21no—
66C2×Dic23—21no—
67C2×Dic23—21no—
68C2×Dic23—42no—
69C2×Dic23—42no—
70D92—41no—
71C4×D23—42no—
72Dic46—41no—
73C8×C23—42no—
74#1509—231nomaximal, Sylow
75C22×C23—21no—
76C22×C23—21no—
77C22×C23C2×C22⋊C411yescharacteristic
78C22×C23AGL(1,ℤ/8)11yescharacteristic
79C22×C23#13711yescharacteristic
80C2×D23—41no—
81C2×D23—41no—
82C2×D23—41no—
83C4×C23—21no—
84C4×C23—21no—
85C4×C23—21no—
86C4×C23—21no—
87C4×C23—21no—
88C4×C23#10412yes—
89Dic23—44no—
90Dic23—41no—
91Dic23—41no—
92Dic23—41no—
93#529—231no—
94#432D2311yescharacteristic, complemented
95C4×C4⋊C4—231no—
96#328—232no—
97#327—232no—
98C2×C23—21no—
99C2×C23—21no—
100C2×C23#41011yescharacteristic
101C2×C23#41711yescharacteristic
102C2×C23C2×#10411yescharacteristic
103D23—81no—
104#126—461no—
105#125—231no—
106#124—231no—
107#123—461no—
108C22⋊Q8—231no—
109#121—231no—
110C4×Q8—231no—
111C4×D4—231no—
112C4×D4—461no—
113#117—461no—
114C2×C4⋊C4—461no—
115C2×C42—461no—
116C2×C42C2×D2311yescharacteristic
117C4⋊C8—21no—
118C22⋊C8C2×D2312yes—
119#97—21no—
120#95—232no—
121C23#150911yescharacteristic, complemented, Sylow
122C2×Q8—231no—
123C2×D4—231no—
124C2×D4—461no—
125C22×C4—462no—
126C22×C4—461no—
127C22×C4D9211yescharacteristic
128C22×C4D9211yescharacteristic
129C22×C4C22×D2311yescharacteristic
130C2×C8—22no—
131C4⋊C4—231no—
132C4⋊C4—231no—
133C4⋊C4—464no—
134C4⋊C4—461no—
135C4⋊C4—461no—
136C4⋊C4—461no—
137C4⋊C4—461no—
138C22⋊C4—461no—
139C22⋊C4—461no—
140C22⋊C4—461no—
141C22⋊C4—461no—
142C22⋊C4—461no—
143C42—461no—
144C42—922no—
145C42C4×D2311yescharacteristic
146C42C4×D2311yescharacteristic
147C42C22⋊D2311yescharacteristic
148C42C22⋊D2311yescharacteristic
149C23—461no—
150C23C2×D9211yescharacteristic
151Q8—921no—
152D4—921no—
153D4—921no—
154D4—921no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—41no—
159C2×C4—464no—
160C2×C4—461no—
161C2×C4—461no—
162C2×C4—461no—
163C2×C4—922no—
164C2×C4—922no—
165C2×C4—922no—
166C2×C4(C2×D23)⋊C411yescharacteristic
167C2×C4(C2×D23)⋊C411yescharacteristic
168C2×C4(C2×D23)⋊C411yescharacteristic
169C2×C4(C2×D23)⋊C411yescharacteristic
170C2×C4C2×C4×D2311yescharacteristic
171C2×C4C2×C22⋊D2311yescharacteristic
172C8—42no—
173C22—21no—
174C22—21no—
175C22—921no—
176C22—921no—
177C22—921no—
178C22#1062507911yescharacteristic
179C22#1062508011yescharacteristic
180C22C2×(C2×D23)⋊C411yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—21no—
186C4—924no—
187C4—921no—
188C4—921no—
189C4—921no—
190C4#1062500712yes—
191C2—21no—
192C2—21no—
193C2—1841no—
194C2#1309239011yescharacteristic
195C2#1309241911yescharacteristic
196C2C2×#1062500711yescharacteristic
subgroupG/H
centerC22C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#432C2
socleC22×C23C2×C22⋊C4
prime radical#10625101C22
cosocleC22×C4×C23C23
hypercenter#432D23
hypocenterC23#1509
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊Dic23C2semidirect
3. #13092155C2semidirect
5. C23×#432C2semidirect
14. #10625046C4semidirect
15. C4×D92C4semidirect
17. #10625041C4semidirect
18. C4×Dic46C4semidirect
94. #432D23semidirect
121. C23#1509semidirect

Maximal subgroups

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

subgroupindex
#130929512
C4×C4⋊Dic232
#130921552
#130921522
C23×#4322
#150923