Finite Group Databasebeta

← #15671972

Subgroups — #15671972

Order 2944.

218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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
2#13092470C211yesmaximal, characteristic, complemented
3#13092153C212yesmaximal, complemented
4#13092150C212yesmaximal
5C23×#383C211yesmaximal, characteristic, complemented
6C2×C42×C23C2211yescharacteristic
7#10625101C2211yescharacteristic
8#10625100—21no—
9C4×C22⋊D23—21no—
10#10625095C2211yescharacteristic
11#10625047—21no—
12#10625046C411yescharacteristic, complemented
13C4×D92C411yescharacteristic, complemented
14#10625043—21no—
15#10625041C411yescharacteristic, complemented
16C4×Dic46C411yescharacteristic, complemented
17C23×#95—21no—
18C23×#95—21no—
19C23×#95C2212yes—
20C22⋊(C23⋊C8)C2212yes—
21C4⋊(C23⋊C8)—21no—
22C4×C23⋊C8—21no—
23C22×C4×C23—22no—
24C22×C4×C23D411yescharacteristic
25C22×C4×C23D411yescharacteristic
26C22×C4×C23C2311yescharacteristic
27C2×C22⋊D23—21no—
28C2×D92C2×C411yescharacteristic
29C2×C4×D23—21no—
30C2×Dic46C2×C411yescharacteristic
31C42×C23C2×C411yescharacteristic
32C42×C23C2×C411yescharacteristic
33C42×C23D411yescharacteristic
34C42×C23D411yescharacteristic
35C22⋊Dic23—21no—
36(C2×D23)⋊C4—21no—
37(C2×D23)⋊C4—21no—
38(C2×D23)⋊C4—21no—
39(C2×D23)⋊C4—21no—
40C4⋊Dic23C2×C411yescharacteristic
41C4⋊Dic23C2×C411yescharacteristic
42Dic23⋊C4—21no—
43Dic23⋊C4—21no—
44Dic23⋊C4—21no—
45Dic23⋊C4—21no—
46C4×Dic23—21no—
47C2×C23⋊C8—22no—
48C23×C23C2×D411yescharacteristic
49C22×D23—21no—
50C2×C4×C23—22no—
51C2×C4×C23—41no—
52C2×C4×C23—41no—
53C2×C4×C23—42no—
54C2×C4×C23—42no—
55C2×C4×C23—42no—
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—42no—
63C2×Dic23—21no—
64C2×Dic23—21no—
65C2×Dic23—21no—
66D92—41no—
67C4×D23—42no—
68Dic46—41no—
69C23⋊C8—42no—
70#1521—231nomaximal, Sylow
71C22×C23—21no—
72C22×C23—21no—
73C22×C23C2×C22⋊C411yescharacteristic
74C22×C23#13512yes—
75C2×D23—41no—
76C2×D23—41no—
77C2×D23—41no—
78C4×C23—21no—
79C4×C23—21no—
80C4×C23—21no—
81C4×C23—21no—
82C4×C23—21no—
83C4×C23—21no—
84C4×C23—82no—
85Dic23—41no—
86Dic23—41no—
87Dic23—41no—
88#529—231no—
89#431—231no—
90#383D2311yescharacteristic, complemented
91#328—232no—
92#327—232no—
93C2×C23—22no—
94C2×C23#41011yescharacteristic
95C2×C23#41611yescharacteristic
96C2×C23#42111yescharacteristic
97D23—81no—
98#126—461no—
99#125—231no—
100#124—231no—
101#123—461no—
102C22⋊Q8—231no—
103#121—231no—
104C4×Q8—231no—
105C4×D4—231no—
106C4×D4—461no—
107#117—461no—
108C2×C42C2×D2311yescharacteristic
109C4⋊C8—461no—
110C22⋊C8—232no—
111C4×C8—461no—
112#95—21no—
113#95—21no—
114#95C2×D2312yes—
115C23#152111yescharacteristic, complemented, Sylow
116C2×Q8—231no—
117C2×D4—231no—
118C2×D4—461no—
119C22×C4—22no—
120C22×C4—461no—
121C22×C4C22⋊D2311yescharacteristic
122C22×C4C22⋊D2311yescharacteristic
123C22×C4C22×D2311yescharacteristic
124C2×C8—462no—
125C4⋊C4—231no—
126C4⋊C4—231no—
127C4⋊C4—461no—
128C4⋊C4—461no—
129C4⋊C4—461no—
130C4⋊C4—461no—
131C22⋊C4—461no—
132C22⋊C4—461no—
133C22⋊C4—461no—
134C22⋊C4—461no—
135C22⋊C4—461no—
136C42—461no—
137C42C4×D2311yescharacteristic
138C42C4×D2311yescharacteristic
139C42D9211yescharacteristic
140C42D9211yescharacteristic
141C23—461no—
142C23C2×C22⋊D2311yescharacteristic
143Q8—921no—
144D4—921no—
145D4—922no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—42no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4—461no—
153C2×C4—461no—
154C2×C4—461no—
155C2×C4—922no—
156C2×C4(C2×D23)⋊C411yescharacteristic
157C2×C4(C2×D23)⋊C411yescharacteristic
158C2×C4(C2×D23)⋊C411yescharacteristic
159C2×C4(C2×D23)⋊C411yescharacteristic
160C2×C4C2×C4×D2311yescharacteristic
161C2×C4C2×D9211yescharacteristic
162C8—922no—
163C22—21no—
164C22—21no—
165C22—921no—
166C22—921no—
167C22—921no—
168C22C2×(C2×D23)⋊C411yescharacteristic
169C22#1062512112yes—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—82no—
177C4—921no—
178C4—921no—
179C4—921no—
180C2—22no—
181C2—1841no—
182C2#1309239011yescharacteristic
183C2#1309241111yescharacteristic
184C2#1309243511yescharacteristic
subgroupG/H
centerC22C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#383C2
socleC22×C23C2×C22⋊C4
prime radical#10625101C22
cosocleC22×C4×C23C23
hypercenter#383D23
hypocenterC23#1521
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×C42 ◁ #383

Complements

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

NH ≅ G/Ntype
2. #13092470C2semidirect
3. #13092153C2semidirect
5. C23×#383C2semidirect
12. #10625046C4semidirect
13. C4×D92C4semidirect
15. #10625041C4semidirect
16. C4×Dic46C4semidirect
90. #383D23semidirect
115. C23#1521semidirect

Maximal subgroups

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

subgroupindex
#130929512
#130924702
#130921532
#130921502
C23×#3832
#152123