Finite Group Databasebeta

← #15671996

Subgroups — #15671996

Order 2944.

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

normal subgroups only

This group has 264 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
1C2×#10625046C211yesmaximal, characteristic
2C4×#67267C211yesmaximal, 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—
10C2×#67267—21no—
11#10625046—21no—
12#10625046—21no—
13#10625046C412yes—
14#10625046C2212yes—
15C23×C4⋊C8—21no—
16C23×C22⋊C8—21no—
17C23×#97C2212yescomplemented
18#10624985C2212yescomplemented
19C4×C23⋊C8—21no—
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—
40#67267—24no—
41C2×C23⋊C8—22no—
42C23×C23C22⋊C411yescharacteristic
43C22×D23—22no—
44C22×D23—42no—
45C22×D23—42no—
46C22×D23—42no—
47C2×C4×C23—22no—
48C2×C4×C23—22no—
49C2×C4×C23—41no—
50C2×C4×C23C22⋊C411yescharacteristic
51C2×C4×C23C22⋊C411yescharacteristic
52C2×C4×C23C22⋊C411yescharacteristic
53C2×C4×C23C22×C411yescharacteristic
54C2×C4×C23C2×D411yescharacteristic
55C2×C4×C23C2×D411yescharacteristic
56C2×Dic23—22no—
57C2×Dic23—42no—
58D92—42no—
59D92—42no—
60Dic46—42no—
61Dic46—42no—
62C8×C23—42no—
63C23⋊C8—24no—
64#1527—231nomaximal, Sylow
65C22×C23—21no—
66C22×C23—21no—
67C22×C23#10412yes—
68C22×C23C2×C22⋊C411yescharacteristic
69C2×D23—42no—
70C2×D23—42no—
71C2×D23—42no—
72C2×D23—84no—
73C4×C23—21no—
74C4×C23—21no—
75C4×C23—21no—
76C4×C23—21no—
77C4×C23—21no—
78C4×C23#10012yes—
79Dic23—42no—
80C2×#124—231no—
81#432D2311yescharacteristic, complemented
82C4×M16—231no—
83#329—234no—
84C2×C23—22no—
85C2×C23C2×#10011yescharacteristic
86C2×C23C2×#10411yescharacteristic
87C2×C23#42111yescharacteristic
88D23—82no—
89C22×Q8—231no—
90C22×D4—231no—
91C2×M16—461no—
92#124—232no—
93#124—232no—
94#124—461no—
95#124—461no—
96C2×C22⋊C4—461no—
97C2×C22⋊C4—461no—
98C2×C42C2×D2311yescharacteristic
99C4⋊C8—21no—
100C22⋊C8—21no—
101#97—232no—
102#97C2×D2312yescomplemented
103C4×C8—461no—
104C23#152711yescharacteristic, complemented, Sylow
105C24—461no—
106C2×Q8—232no—
107C2×Q8—461no—
108C2×Q8—922no—
109C2×D4—232no—
110C2×D4—461no—
111C2×D4—922no—
112C22×C4—461no—
113C22×C4C4×D2311yescharacteristic
114C22×C4D9211yescharacteristic
115C22×C4C22⋊D2311yescharacteristic
116M16—464no—
117C2×C8—22no—
118C2×C8—462no—
119C22⋊C4—462no—
120C22⋊C4—462no—
121C22⋊C4—462no—
122C22⋊C4—462no—
123C42C4×D2311yescharacteristic
124C42D9211yescharacteristic
125C42C22⋊D2311yescharacteristic
126C42C22×D2311yescharacteristic
127C23—462no—
128C23—922no—
129C23—922no—
130C23—922no—
131C23(C2×D23)⋊C411yescharacteristic
132Q8—922no—
133Q8—922no—
134D4—922no—
135D4—922no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—41no—
139C2×C4—462no—
140C2×C4—922no—
141C2×C4(C2×D23)⋊C411yescharacteristic
142C2×C4(C2×D23)⋊C411yescharacteristic
143C2×C4(C2×D23)⋊C411yescharacteristic
144C2×C4C2×C4×D2311yescharacteristic
145C2×C4C2×D9211yescharacteristic
146C2×C4C2×C22⋊D2311yescharacteristic
147C8—42no—
148C8—464no—
149C22—21no—
150C22—21no—
151C22—922no—
152C22—922no—
153C22—922no—
154C22—1844no—
155C22#1062500712yes—
156C22C2×(C2×D23)⋊C411yescharacteristic
157C4—21no—
158C4—21no—
159C4—21no—
160C4—21no—
161C4—21no—
162C4—922no—
163C4#1062500512yes—
164C2—22no—
165C2—1842no—
166C2C2×#1062500511yescharacteristic
167C2C2×#1062500711yescharacteristic
168C2#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#1527
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×#67267C2semidirect
3. #13092156C2semidirect
4. C23×#432C2semidirect
17. C23×#97C22semidirect
18. #10624985C22semidirect
81. #432D23semidirect
102. #97C2×D23semidirect
104. C23#1527semidirect

Maximal subgroups

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

subgroupindex
C2×#106250462
C4×#672672
#130921562
C23×#4322
#152723