Finite Group Databasebeta

← #15672582

Subgroups — #15672582

Order 2944.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#13093152C211yesmaximal, characteristic
2#13092765C211yesmaximal, characteristic
3#13092624C211yesmaximal, characteristic, complemented
4#13092160C211yesmaximal, characteristic
5Q8⋊(C23⋊C8)C211yesmaximal, characteristic, complemented
6#13092147C211yesmaximal, characteristic, complemented
7C23×#475C211yesmaximal, characteristic, complemented
8C23×C4⋊Q8C2211yescharacteristic
9C4×Q8×C23C2211yescharacteristic
10#10625118—21no—
11C2×#67275—21no—
12#10625065—22no—
13#10625064—21no—
14#10625046—21no—
15#10625045C2211yescharacteristic
16C4×D92—21no—
17C4×Dic46C2211yescharacteristic
18C23×#106—21no—
19C23×C4⋊C8C2211yescharacteristic
20C23×#103—21no—
21#10625017—21no—
22#10624991—22no—
23C4⋊(C23⋊C8)C2211yescharacteristic
24C4×C23⋊C8C2211yescharacteristic
25C2×Q8×C23—21no—
26C2×Q8×C23D411yescharacteristic
27C2×D92—21no—
28C2×D92—21no—
29C2×D92D412yes—
30C2×C4×D23—22no—
31C2×Dic46D411yescharacteristic
32C2×C8×C23—21no—
33C4⋊C4×C23—21no—
34C4⋊C4×C23—21no—
35C4⋊C4×C23—21no—
36C4⋊C4×C23D411yescharacteristic
37C42×C23—21no—
38C42×C23C2311yescharacteristic
39#67275—42no—
40(C2×D23)⋊C4—22no—
41(C2×D23)⋊C4—22no—
42(C2×D23)⋊C4—22no—
43C4⋊Dic23D411yescharacteristic
44Dic23⋊C4—21no—
45C4×Dic23—21no—
46C2×C23⋊C8—21no—
47C2×C23⋊C8—21no—
48C22×D23—22no—
49Q8×C23—21no—
50Q8×C23—21no—
51Q8×C23—41no—
52Q8×C23—41no—
53C2×C4×C23—21no—
54C2×C4×C23—21no—
55C2×C4×C23—41no—
56C2×C4×C23C2×D411yescharacteristic
57C2×C4×C23C2×D411yescharacteristic
58C2×C4×C23C2×D411yescharacteristic
59C2×Dic23—21no—
60C2×Dic23—21no—
61D92—42no—
62D92—41no—
63D92—41no—
64D92—41no—
65D92—41no—
66C4×D23—82no—
67Dic46—21no—
68Dic46—21no—
69C8×C23—41no—
70C23⋊C8—41no—
71C23⋊C8—41no—
72#1640—231nomaximal, Sylow
73C22×C23#12011yescharacteristic
74C2×D23—42no—
75C2×D23—42no—
76C2×D23—42no—
77C4×C23—21no—
78C4×C23—41no—
79C4×C23—41no—
80C4×C23—81no—
81C4×C23#13511yescharacteristic
82C4×C23#13511yescharacteristic
83C4×C23AGL(1,ℤ/8)11yescharacteristic
84C4×C23#13711yescharacteristic
85Dic23—41no—
86Dic23—41no—
87#559—231no—
88#486—231no—
89#475D2311yescharacteristic, complemented
90#462—231no—
91#331—231no—
92Q8⋊C8—231no—
93Q8⋊C8—231no—
94C2×C23#44911yescharacteristic
95C2×C23#45211yescharacteristic
96C2×C23#45511yescharacteristic
97D23—82no—
98C2×Q16—461no—
99C4⋊Q8C2×D2311yescharacteristic
100#127—231no—
101#124—461no—
102#124—461no—
103#123—462no—
104C4×Q8—231no—
105C4×Q8C2×D2311yescharacteristic
106C4×D4—461no—
107C4×D4—461no—
108#106—21no—
109C4⋊C8—231no—
110C4⋊C8C2×D2311yescharacteristic
111#103—21no—
112#103—461no—
113#102—462no—
114C4×C8—231no—
115C23#164011yescharacteristic, complemented, Sylow
116C2×Q8—21no—
117C2×Q8—231no—
118C2×Q8C22⋊D2311yescharacteristic
119C2×D4—232no—
120C2×D4—461no—
121C2×D4—461no—
122C22×C4—462no—
123Q16—922no—
124C2×C8—21no—
125C2×C8—461no—
126C2×C8—461no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—231no—
131C4⋊C4—461no—
132C4⋊C4C22⋊D2311yescharacteristic
133C22⋊C4—462no—
134C22⋊C4—462no—
135C22⋊C4—462no—
136C42—21no—
137C42—461no—
138C42C22×D2311yescharacteristic
139C23—462no—
140Q8—21no—
141Q8—21no—
142Q8—41no—
143Q8—41no—
144Q8—461no—
145Q8—461no—
146D4—922no—
147D4—921no—
148D4—921no—
149D4—921no—
150D4—921no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—461no—
155C2×C4—461no—
156C2×C4—1842no—
157C2×C4D4×D2311yescharacteristic
158C2×C4D4×D2311yescharacteristic
159C2×C4C2×C22⋊D2311yescharacteristic
160C8—41no—
161C8—921no—
162C8—921no—
163C22—922no—
164C22—922no—
165C22—922no—
166C22#1062510811yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—81no—
171C4—921no—
172C4—921no—
173C4#1062508511yescharacteristic
174C4#1062508711yescharacteristic
175C4#1062511311yescharacteristic
176C4#1062512111yescharacteristic
177C2—1842no—
178C2#1309256111yescharacteristic
179C2#1309257711yescharacteristic
180C2#1309259311yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#475C2
socleC22×C23#120
prime radical#10625045C22
hypercenter#475D23
hypocenterC23#1640
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
3. #13092624C2semidirect
5. Q8⋊(C23⋊C8)C2semidirect
6. #13092147C2semidirect
7. C23×#475C2semidirect
89. #475D23semidirect
115. C23#1640semidirect

Maximal subgroups

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

subgroupindex
#130931522
#130927652
#130926242
#130921602
Q8⋊(C23⋊C8)2
#130921472
C23×#4752
#164023