Finite Group Databasebeta

← #15671883

Subgroups — #15671883

Order 2944.

238 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 81 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#13092263C211yesmaximal, 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
17C2×C4×Dic23—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
47C4×Dic23—24no—
48C2×C23⋊C8—22no—
49C23×C23—21no—
50C23×C23C2×D411yescharacteristic
51Q8×C23—41no—
52D4×C23—41no—
53D4×C23—42no—
54C2×C4×C23—22no—
55C2×C4×C23—22no—
56C2×C4×C23—21no—
57C2×C4×C23—21no—
58C2×C4×C23—21no—
59C2×C4×C23—41no—
60C2×C4×C23—42no—
61C2×C4×C23C22⋊C411yescharacteristic
62C2×C4×C23C22⋊C411yescharacteristic
63C2×C4×C23C22⋊C411yescharacteristic
64C2×C4×C23C22⋊C411yescharacteristic
65C2×C4×C23C22×C411yescharacteristic
66C2×C4×C23C2×D411yescharacteristic
67C2×Dic23—24no—
68C2×Dic23—42no—
69C2×Dic23—42no—
70C23⋊C8—42no—
71#1500—231nomaximal, Sylow
72C22×C23—21no—
73C22×C23—21no—
74C22×C23—41no—
75C22×C23—41no—
76C22×C23—41no—
77C22×C23C2×C22⋊C411yescharacteristic
78C22×C23#13512yes—
79C4×C23—21no—
80C4×C23—21no—
81C4×C23—21no—
82C4×C23—21no—
83C4×C23—21no—
84C4×C23—41no—
85C4×C23—41no—
86C4×C23—41no—
87C4×C23#10412yes—
88Dic23—44no—
89#529D2311yescharacteristic
90#431—231no—
91#376—231no—
92#328—232no—
93#327—232no—
94C2×C23—22no—
95C2×C23—81no—
96C2×C23#41011yescharacteristic
97C2×C23#41611yescharacteristic
98C2×C23C2×#10411yescharacteristic
99#126—21no—
100#125Dic2311yescharacteristic, complemented
101#124Dic2311yescharacteristic, complemented
102#123—21no—
103C22⋊Q8C2×D2311yescharacteristic
104#121C2×D2311yescharacteristic
105C4×Q8Dic2311yescharacteristic, complemented
106C4×D4—21no—
107C4×D4Dic2311yescharacteristic, complemented
108#117—21no—
109C2×C42—461no—
110C2×C42C2×D2311yescharacteristic
111C4⋊C8—461no—
112C22⋊C8—232no—
113C4×C8—461no—
114#95—232no—
115#95—461no—
116C23#150011yescharacteristic, complemented, Sylow
117C2×Q8C2×Dic2311yescharacteristic
118C2×D4—21no—
119C2×D4C2×Dic2311yescharacteristic
120C22×C4—21no—
121C22×C4—462no—
122C22×C4C22⋊D2311yescharacteristic
123C22×C4C22⋊D2311yescharacteristic
124C22×C4C22×D2311yescharacteristic
125C2×C8—462no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4C2×Dic2311yescharacteristic
131C4⋊C4C2×Dic2311yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—21no—
134C22⋊C4—21no—
135C22⋊C4—21no—
136C22⋊C4—21no—
137C42—21no—
138C42—464no—
139C42C2×Dic2311yescharacteristic
140C42C2×Dic2311yescharacteristic
141C42C22⋊D2311yescharacteristic
142C42C22⋊D2311yescharacteristic
143C23—21no—
144C23C2×C22⋊D2311yescharacteristic
145Q8—41no—
146D4—41no—
147D4—42no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—42no—
155C2×C4—464no—
156C2×C4—922no—
157C2×C4—922no—
158C2×C4C22⋊Dic2311yescharacteristic
159C2×C4C22⋊Dic2311yescharacteristic
160C2×C4C22⋊Dic2311yescharacteristic
161C2×C4C22⋊Dic2311yescharacteristic
162C2×C4C22×Dic2311yescharacteristic
163C2×C4C2×C22⋊D2311yescharacteristic
164C8—922no—
165C22—21no—
166C22—21no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22#1062512112yes—
171C22C2×C22⋊Dic2311yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—41no—
178C4—41no—
179C4—41no—
180C4—924no—
181C4#1062501912yes—
182C2—22no—
183C2—81no—
184C2#1309239111yescharacteristic
185C2#1309241311yescharacteristic
186C2C2×#1062501911yescharacteristic
subgroupG/H
centerC2×C4C22⋊Dic23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#529C2
socleC22×C23C2×C22⋊C4
prime radicalC23×#121C22
cosocleC22×C4×C23C23
hypercenter#529D23
hypocenterC23#1500
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #13092470C2semidirect
2. #13092263C2semidirect
3. #13092154C2semidirect
7. C23×#125C4semidirect
8. C23×#124C4semidirect
12. C4×Q8×C23C4semidirect
14. C4×D4×C23C4semidirect
100. #125Dic23semidirect
101. #124Dic23semidirect
105. C4×Q8Dic23semidirect
107. C4×D4Dic23semidirect
116. C23#1500semidirect

Maximal subgroups

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

subgroupindex
#130924702
#130922632
#130921542
#130921512
C23×#5292
#150023