Finite Group Databasebeta

← #15672020

Subgroups — #15672020

Order 2944.

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

normal subgroups only

This group has 248 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
1C2×#10625046C211yesmaximal, characteristic
2#13092474C211yesmaximal, characteristic, complemented
3#13092156C214yesmaximal, complemented
4C23×#432C211yesmaximal, characteristic, complemented
5C22×D92C411yescharacteristic
6C22×Dic46C411yescharacteristic
7C2×C42×C23C2211yescharacteristic
8C2×(C2×D23)⋊C4—21no—
9C2×(C2×D23)⋊C4—21no—
10#10625046—21no—
11#10625046—21no—
12#10625046C412yes—
13#10625046C2212yes—
14C23×C4⋊C8—21no—
15C23×C22⋊C8—21no—
16C23×#97C2212yescomplemented
17C22⋊(C23⋊C8)—21no—
18C4⋊(C23⋊C8)—21no—
19#10624985C2212yescomplemented
20C23×D23—21no—
21C22×C4×C23C2×C411yescharacteristic
22C22×C4×C23D411yescharacteristic
23C22×C4×C23D411yescharacteristic
24C22×Dic23—21no—
25C2×D92—21no—
26C2×D92—42no—
27C2×D92C2×C412yes—
28C2×Dic46—21no—
29C2×Dic46—42no—
30C2×Dic46C2×C412yes—
31C2×C8×C23—22no—
32C42×C23C2×C411yescharacteristic
33C42×C23D411yescharacteristic
34C42×C23D411yescharacteristic
35C42×C23C2311yescharacteristic
36(C2×D23)⋊C4—22no—
37(C2×D23)⋊C4—22no—
38(C2×D23)⋊C4—22no—
39(C2×D23)⋊C4—22no—
40C2×C23⋊C8—22no—
41C23×C23C22⋊C411yescharacteristic
42C22×D23—22no—
43C22×D23—42no—
44C22×D23—42no—
45C22×D23—42no—
46C2×C4×C23—22no—
47C2×C4×C23—41no—
48C2×C4×C23—41no—
49C2×C4×C23C22⋊C411yescharacteristic
50C2×C4×C23C22⋊C411yescharacteristic
51C2×C4×C23C22⋊C411yescharacteristic
52C2×C4×C23C22×C411yescharacteristic
53C2×C4×C23C2×D411yescharacteristic
54C2×C4×C23C2×D411yescharacteristic
55C2×Dic23—22no—
56C2×Dic23—42no—
57D92—42no—
58D92—42no—
59Dic46—42no—
60Dic46—42no—
61C8×C23—42no—
62C23⋊C8—42no—
63#1533—231nomaximal, Sylow
64C22×C23—21no—
65C22×C23—21no—
66C22×C23#10012yes—
67C22×C23C2×C22⋊C411yescharacteristic
68C2×D23—42no—
69C2×D23—42no—
70C2×D23—42no—
71C2×D23—84no—
72C4×C23—21no—
73C4×C23—21no—
74C4×C23—21no—
75C4×C23—21no—
76C4×C23—21no—
77C4×C23—21no—
78Dic23—42no—
79C2×#124—231no—
80#432—231no—
81#432D2311yescharacteristic, complemented
82#329—234no—
83C2×C23—22no—
84C2×C23C2×#10011yescharacteristic
85C2×C23#42111yescharacteristic
86C2×C23#42111yescharacteristic
87D23—82no—
88C22×Q8—231no—
89C22×D4—231no—
90#124—232no—
91#124—232no—
92#124—461no—
93#124—461no—
94C2×C22⋊C4—461no—
95C2×C22⋊C4—461no—
96C2×C42C2×D2311yescharacteristic
97C4⋊C8—21no—
98C4⋊C8—461no—
99C22⋊C8—21no—
100C22⋊C8—461no—
101#97—232no—
102#97C2×D2312yescomplemented
103C23#153311yescharacteristic, complemented, Sylow
104C24—461no—
105C2×Q8—232no—
106C2×Q8—461no—
107C2×Q8—922no—
108C2×D4—232no—
109C2×D4—461no—
110C2×D4—922no—
111C22×C4—461no—
112C22×C4C4×D2311yescharacteristic
113C22×C4D9211yescharacteristic
114C22×C4C22⋊D2311yescharacteristic
115C2×C8—22no—
116C2×C8—462no—
117C22⋊C4—462no—
118C22⋊C4—462no—
119C22⋊C4—462no—
120C22⋊C4—462no—
121C42C4×D2311yescharacteristic
122C42D9211yescharacteristic
123C42C22⋊D2311yescharacteristic
124C42C22×D2311yescharacteristic
125C23—462no—
126C23—922no—
127C23—922no—
128C23—922no—
129C23(C2×D23)⋊C411yescharacteristic
130Q8—922no—
131Q8—922no—
132D4—922no—
133D4—922no—
134C2×C4—22no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—462no—
138C2×C4—922no—
139C2×C4(C2×D23)⋊C411yescharacteristic
140C2×C4(C2×D23)⋊C411yescharacteristic
141C2×C4(C2×D23)⋊C411yescharacteristic
142C2×C4C2×C4×D2311yescharacteristic
143C2×C4C2×D9211yescharacteristic
144C2×C4C2×C22⋊D2311yescharacteristic
145C8—42no—
146C8—922no—
147C22—21no—
148C22—21no—
149C22—922no—
150C22—922no—
151C22—922no—
152C22—1844no—
153C22#1062500512yes—
154C22C2×(C2×D23)⋊C411yescharacteristic
155C4—21no—
156C4—21no—
157C4—21no—
158C4—21no—
159C4—21no—
160C4—21no—
161C4—922no—
162C2—22no—
163C2—1842no—
164C2C2×#1062500511yescharacteristic
165C2#1309243311yescharacteristic
166C2#1309243511yescharacteristic
subgroupG/H
centerC22C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C4
FrattiniC42C22×D23
FittingC23×#432C2
socleC22×C23C2×C22⋊C4
prime radicalC22×D92C4
cosocleC42×C23C23
hypercenter#432D23
hypocenterC23#1533
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. #13092474C2semidirect
3. #13092156C2semidirect
4. C23×#432C2semidirect
16. C23×#97C22semidirect
19. #10624985C22semidirect
81. #432D23semidirect
102. #97C2×D23semidirect
103. C23#1533semidirect

Maximal subgroups

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

subgroupindex
C2×#106250462
#130924742
#130921562
C23×#4322
#153323