Finite Group Databasebeta

← #15671974

Subgroups — #15671974

Order 2944.

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

normal subgroups only

This group has 218 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#13092470C211yesmaximal, characteristic, complemented
2#13092285C211yesmaximal, characteristic, complemented
3#13092154C212yesmaximal, complemented
4#13092151C212yesmaximal
5C23×#529C211yesmaximal, characteristic
6C23×#126—21no—
7C23×#125C411yescharacteristic, complemented
8C23×#124C411yescharacteristic, complemented
9C23×#123—21no—
10C23×C22⋊Q8C2211yescharacteristic
11C23×#121C2211yescharacteristic
12C4×Q8×C23C411yescharacteristic, complemented
13C4×D4×C23—21no—
14C4×D4×C23C411yescharacteristic, complemented
15C23×#117—21no—
16C2×C42×C23C2211yescharacteristic
17C23⋊#95—21no—
18C23⋊#95—21no—
19C23⋊#95C2212yes—
20C22⋊(C23⋊C8)C2212yes—
21C4⋊(C23⋊C8)—21no—
22C4×C23⋊C8—21no—
23C2×Q8×C23C2×C411yescharacteristic
24C2×D4×C23—21no—
25C2×D4×C23C2×C411yescharacteristic
26C22×C4×C23—21no—
27C22×C4×C23D411yescharacteristic
28C22×C4×C23D411yescharacteristic
29C22×C4×C23C2311yescharacteristic
30C22×Dic23—22no—
31C4⋊C4×C23—21no—
32C4⋊C4×C23—21no—
33C4⋊C4×C23—21no—
34C4⋊C4×C23—21no—
35C4⋊C4×C23C2×C411yescharacteristic
36C4⋊C4×C23C2×C411yescharacteristic
37C22⋊C4×C23—21no—
38C22⋊C4×C23—21no—
39C22⋊C4×C23—21no—
40C22⋊C4×C23—21no—
41C22⋊C4×C23—21no—
42C42×C23—21no—
43C42×C23C2×C411yescharacteristic
44C42×C23C2×C411yescharacteristic
45C42×C23D411yescharacteristic
46C42×C23D411yescharacteristic
47C2×C23⋊C8—22no—
48C23×C23—21no—
49C23×C23C2×D411yescharacteristic
50Q8×C23—41no—
51D4×C23—41no—
52D4×C23—42no—
53C2×C4×C23—22no—
54C2×C4×C23—21no—
55C2×C4×C23—21no—
56C2×C4×C23—21no—
57C2×C4×C23—41no—
58C2×C4×C23—41no—
59C2×C4×C23—42no—
60C2×C4×C23C22⋊C411yescharacteristic
61C2×C4×C23C22⋊C411yescharacteristic
62C2×C4×C23C22⋊C411yescharacteristic
63C2×C4×C23C22⋊C411yescharacteristic
64C2×C4×C23C22×C411yescharacteristic
65C2×C4×C23C2×D411yescharacteristic
66C2×Dic23—42no—
67C2×Dic23—42no—
68C2×Dic23—42no—
69C23⋊C8—42no—
70#1521—231nomaximal, Sylow
71C22×C23—21no—
72C22×C23—21no—
73C22×C23—41no—
74C22×C23—41no—
75C22×C23—41no—
76C22×C23C2×C22⋊C411yescharacteristic
77C22×C23#13512yes—
78C4×C23—21no—
79C4×C23—21no—
80C4×C23—21no—
81C4×C23—21no—
82C4×C23—21no—
83C4×C23—21no—
84C4×C23—41no—
85C4×C23—41no—
86C4×C23—41no—
87Dic23—82no—
88#529D2311yescharacteristic
89#431—231no—
90#383—231no—
91#328—232no—
92#327—232no—
93C2×C23—22no—
94C2×C23—81no—
95C2×C23#41011yescharacteristic
96C2×C23#41611yescharacteristic
97C2×C23#42111yescharacteristic
98#126—21no—
99#125Dic2311yescharacteristic, complemented
100#124Dic2311yescharacteristic, complemented
101#123—21no—
102C22⋊Q8C2×D2311yescharacteristic
103#121C2×D2311yescharacteristic
104C4×Q8Dic2311yescharacteristic, complemented
105C4×D4—21no—
106C4×D4Dic2311yescharacteristic, complemented
107#117—21no—
108C2×C42C2×D2311yescharacteristic
109C4⋊C8—461no—
110C22⋊C8—232no—
111C4×C8—461no—
112#95—232no—
113#95—461no—
114#95—461no—
115C23#152111yescharacteristic, complemented, Sylow
116C2×Q8C2×Dic2311yescharacteristic
117C2×D4—21no—
118C2×D4C2×Dic2311yescharacteristic
119C22×C4—21no—
120C22×C4—462no—
121C22×C4C22⋊D2311yescharacteristic
122C22×C4C22⋊D2311yescharacteristic
123C22×C4C22×D2311yescharacteristic
124C2×C8—462no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4C2×Dic2311yescharacteristic
130C4⋊C4C2×Dic2311yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—21no—
133C22⋊C4—21no—
134C22⋊C4—21no—
135C22⋊C4—21no—
136C42—21no—
137C42C2×Dic2311yescharacteristic
138C42C2×Dic2311yescharacteristic
139C42C22⋊D2311yescharacteristic
140C42C22⋊D2311yescharacteristic
141C23—21no—
142C23C2×C22⋊D2311yescharacteristic
143Q8—41no—
144D4—41no—
145D4—42no—
146C2×C4—22no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—42no—
153C2×C4—922no—
154C2×C4—922no—
155C2×C4—922no—
156C2×C4C22⋊Dic2311yescharacteristic
157C2×C4C22⋊Dic2311yescharacteristic
158C2×C4C22⋊Dic2311yescharacteristic
159C2×C4C22⋊Dic2311yescharacteristic
160C2×C4C22×Dic2311yescharacteristic
161C2×C4C2×C22⋊D2311yescharacteristic
162C8—922no—
163C22—21no—
164C22—21no—
165C22—41no—
166C22—41no—
167C22—41no—
168C22#1062512112yes—
169C22C2×C22⋊Dic2311yescharacteristic
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—41no—
177C4—41no—
178C4—41no—
179C4—1842no—
180C2—22no—
181C2—81no—
182C2#1309239111yescharacteristic
183C2#1309241311yescharacteristic
184C2#1309243411yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#529C2
socleC22×C23C2×C22⋊C4
prime radicalC23×#121C22
cosocleC22×C4×C23C23
hypercenter#529D23
hypocenterC23#1521
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #13092470C2semidirect
2. #13092285C2semidirect
3. #13092154C2semidirect
7. C23×#125C4semidirect
8. C23×#124C4semidirect
12. C4×Q8×C23C4semidirect
14. C4×D4×C23C4semidirect
99. #125Dic23semidirect
100. #124Dic23semidirect
104. C4×Q8Dic23semidirect
106. C4×D4Dic23semidirect
115. C23#1521semidirect

Maximal subgroups

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

subgroupindex
#130924702
#130922852
#130921542
#130921512
C23×#5292
#152123