Finite Group Databasebeta

← #15675070

Subgroups — #15675070

Order 2944.

238 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 55 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#13092987C211yesmaximal, characteristic
2#13092389C212yesmaximal
3#13092212C211yesmaximal, characteristic, complemented
4#13092211C212yesmaximal, complemented
5C23×#354C211yesmaximal, characteristic, complemented
6C2×Q8×D23C411yescharacteristic, complemented
7C2×#67290C2211yescharacteristic
8C23×#124C2211yescharacteristic
9#10625115C411yescharacteristic, complemented
10#10625107C2211yescharacteristic
11#10625054—22no—
12#10625049—22no—
13#10625048—22no—
14#10625043C411yescharacteristic, complemented
15#10625040C411yescharacteristic, complemented
16C23×#99C2212yes—
17#10625016C2212yes—
18#10624988—22no—
19C2×Q8×C23C2×C411yescharacteristic
20C2×D4×C23C2311yescharacteristic
21C2×C22⋊D23D412yes—
22C22×Dic23D412yes—
23Q8×D23—42no—
24#67290—42no—
25C2×C4×D23—21no—
26C2×C4×D23C2×C411yescharacteristic
27C2×Dic46—21no—
28C2×Dic46C2×C411yescharacteristic
29C2×Dic46C2×C411yescharacteristic
30C22⋊C4×C23—22no—
31C22⋊C4×C23—22no—
32C42×C23C2×C411yescharacteristic
33C22⋊Dic23—22no—
34C22⋊Dic23—22no—
35(C2×D23)⋊C4—21no—
36C4⋊Dic23—22no—
37Dic23⋊C4—21no—
38Dic23⋊C4—22no—
39Dic23⋊C4—42no—
40C4×Dic23—42no—
41C4×Dic23C2×C411yescharacteristic
42C23×C23C2×D412yes—
43C22×D23C22⋊C411yescharacteristic
44Q8×C23—41no—
45D4×C23—41no—
46C2×C4×C23—21no—
47C2×C4×C23—21no—
48C2×C4×C23—42no—
49C2×C4×C23C22×C411yescharacteristic
50C22⋊D23—42no—
51C2×Dic23—22no—
52C2×Dic23—22no—
53C2×Dic23—21no—
54C2×Dic23—21no—
55C2×Dic23—42no—
56C2×Dic23C22⋊C412yes—
57C2×Dic23C22⋊C411yescharacteristic
58C4×D23—22no—
59C4×D23—42no—
60Dic46—41no—
61Dic46—42no—
62Dic46—41no—
63#2129—231nomaximal, Sylow
64C22×C23—22no—
65C22×C23—42no—
66C22×C23C2×C22⋊C411yescharacteristic
67C2×D23—21no—
68C2×D23—41no—
69C4×C23—21no—
70C4×C23—41no—
71C4×C23—41no—
72C4×C23—82no—
73Dic23—22no—
74Dic23—41no—
75Dic23—41no—
76Dic23—82no—
77Dic23#9912yes—
78#536—231no—
79#410—232no—
80#354—231no—
81#354—232no—
82#354D2311yescharacteristic, complemented
83C2×C23—21no—
84C2×C23—42no—
85C2×C23C2×#9911yescharacteristic
86D23—41no—
87C2×#41—231no—
88C22×Q8—231no—
89C4⋊Q8—231no—
90C4⋊Q8—231no—
91#124—231no—
92#124C2×D2311yescharacteristic
93#123—462no—
94C22⋊Q8—462no—
95#117—231no—
96#117—462no—
97#99—232no—
98#99—462no—
99#99C2×D2312yes—
100C23#212911yescharacteristic, complemented, Sylow
101#41—922no—
102C2×Q8—231no—
103C2×Q8—231no—
104C2×Q8—461no—
105C2×Q8—922no—
106C2×Q8C4×D2311yescharacteristic
107C2×D4—232no—
108C2×D4C22×D2311yescharacteristic
109C22×C4—232no—
110C22×C4—231no—
111C22×C4—461no—
112C4⋊C4—461no—
113C4⋊C4—462no—
114C4⋊C4—462no—
115C4⋊C4—922no—
116C22⋊C4—22no—
117C22⋊C4—22no—
118C22⋊C4—461no—
119C22⋊C4—462no—
120C22⋊C4—462no—
121C42—231no—
122C42—922no—
123C42C4×D2311yescharacteristic
124C23—231no—
125C23D4×D2312yes—
126Q8—41no—
127Q8—921no—
128Q8—921no—
129Q8—922no—
130D4—41no—
131D4—922no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—42no—
135C2×C4—231no—
136C2×C4—232no—
137C2×C4—462no—
138C2×C4—462no—
139C2×C4—462no—
140C2×C4—461no—
141C2×C4—461no—
142C2×C4—922no—
143C2×C4—922no—
144C2×C4C2×C4×D2311yescharacteristic
145C22—22no—
146C22—42no—
147C22—461no—
148C22—921no—
149C22C22⋊C4×D2311yescharacteristic
150C4—21no—
151C4—41no—
152C4—41no—
153C4—82no—
154C4—232no—
155C4—462no—
156C4—921no—
157C4—921no—
158C4—1842no—
159C2—21no—
160C2—42no—
161C2—921no—
162C2#99×D2311yescharacteristic
subgroupG/H
centerC2#99×D23
commutatorC2×C4×C23C22×C4
FrattiniC2×D4C22×D23
FittingC23×#354C2
socleC2×C23C2×#99
prime radicalC2×#67290C22
cosocleC2×D4×C23C23
hypercenter#354D23
hypocenterC23#2129
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
3. #13092212C2semidirect
4. #13092211C2semidirect
5. C23×#354C2semidirect
6. C2×Q8×D23C4semidirect
9. #10625115C4semidirect
14. #10625043C4semidirect
15. #10625040C4semidirect
82. #354D23semidirect
100. C23#2129semidirect

Maximal subgroups

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

subgroupindex
#130929872
#130923892
#130922122
#130922112
C23×#3542
#212923