Finite Group Databasebeta

← #15672517

Subgroups — #15672517

Order 2944.

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

normal subgroups only

This group has 218 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#13092791C211yesmaximal, characteristic
3#13092709C211yesmaximal, characteristic, complemented
4#13092160C211yesmaximal, characteristic
5Q8⋊(C23⋊C8)C211yesmaximal, characteristic, complemented
6#13092147C211yesmaximal, characteristic, complemented
7C23×#477C211yesmaximal, characteristic, complemented
8C23×C4⋊Q8C2211yescharacteristic
9C4×Q8×C23C2211yescharacteristic
10#10625118—21no—
11C2×#67274—22no—
12#10625065—22no—
13#10625064—21no—
14#10625046—21no—
15#10625045C2211yescharacteristic
16C4×D92—21no—
17C4×Dic46C2211yescharacteristic
18C23×#107—21no—
19C23×C4⋊C8C2211yescharacteristic
20C23×#103—21no—
21#10624992—21no—
22#10624989—21no—
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#67274—44no—
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—42no—
52C2×C4×C23—21no—
53C2×C4×C23—21no—
54C2×C4×C23—41no—
55C2×C4×C23C2×D411yescharacteristic
56C2×C4×C23C2×D411yescharacteristic
57C2×C4×C23C2×D411yescharacteristic
58C2×Dic23—21no—
59C2×Dic23—21no—
60D92—42no—
61D92—41no—
62D92—41no—
63D92—41no—
64D92—41no—
65C4×D23—82no—
66Dic46—21no—
67Dic46—21no—
68C8×C23—41no—
69C23⋊C8—22no—
70C23⋊C8—41no—
71#1630—231nomaximal, Sylow
72C22×C23#12011yescharacteristic
73C2×D23—42no—
74C2×D23—42no—
75C2×D23—42no—
76C4×C23—21no—
77C4×C23—41no—
78C4×C23—41no—
79C4×C23—81no—
80C4×C23#13511yescharacteristic
81C4×C23#13511yescharacteristic
82C4×C23#13711yescharacteristic
83C4×C23#13711yescharacteristic
84Dic23—41no—
85Dic23—41no—
86#559—231no—
87#492—231no—
88#477—231no—
89#477D2311yescharacteristic, complemented
90#331—231no—
91Q8⋊C8—231no—
92Q8⋊C8—231no—
93C2×C23#45211yescharacteristic
94C2×C23#45211yescharacteristic
95C2×C23#45311yescharacteristic
96D23—82no—
97C2×SD16—462no—
98C4⋊Q8C2×D2311yescharacteristic
99#127—231no—
100#124—461no—
101#124—461no—
102#123—462no—
103C4×Q8—231no—
104C4×Q8C2×D2311yescharacteristic
105C4×D4—461no—
106C4×D4—461no—
107#107—21no—
108#107—461no—
109C4⋊C8—231no—
110C4⋊C8C2×D2311yescharacteristic
111#103—21no—
112#103—461no—
113C4×C8—231no—
114C23#163011yescharacteristic, complemented, Sylow
115C2×Q8—21no—
116C2×Q8—231no—
117C2×Q8C22⋊D2311yescharacteristic
118C2×D4—232no—
119C2×D4—461no—
120C2×D4—461no—
121C22×C4—462no—
122SD16—924no—
123C2×C8—21no—
124C2×C8—461no—
125C2×C8—461no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—231no—
130C4⋊C4—461no—
131C4⋊C4C22⋊D2311yescharacteristic
132C22⋊C4—462no—
133C22⋊C4—462no—
134C22⋊C4—462no—
135C42—21no—
136C42—461no—
137C42C22×D2311yescharacteristic
138C23—462no—
139Q8—21no—
140Q8—21no—
141Q8—42no—
142Q8—461no—
143Q8—461no—
144D4—922no—
145D4—921no—
146D4—921no—
147D4—921no—
148D4—921no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—461no—
153C2×C4—461no—
154C2×C4—1842no—
155C2×C4D4×D2311yescharacteristic
156C2×C4D4×D2311yescharacteristic
157C2×C4C2×C22⋊D2311yescharacteristic
158C8—41no—
159C8—462no—
160C8—921no—
161C22—922no—
162C22—922no—
163C22—922no—
164C22#1062510811yescharacteristic
165C4—21no—
166C4—41no—
167C4—41no—
168C4—81no—
169C4—921no—
170C4—921no—
171C4#1062508911yescharacteristic
172C4#1062509011yescharacteristic
173C4#1062511311yescharacteristic
174C4#1062512111yescharacteristic
175C2—1842no—
176C2#1309257711yescharacteristic
177C2#1309257811yescharacteristic
178C2#1309258311yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#477C2
socleC22×C23#120
prime radical#10625045C22
hypercenter#477D23
hypocenterC23#1630
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
3. #13092709C2semidirect
5. Q8⋊(C23⋊C8)C2semidirect
6. #13092147C2semidirect
7. C23×#477C2semidirect
89. #477D23semidirect
114. C23#1630semidirect

Maximal subgroups

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

subgroupindex
#130931522
#130927912
#130927092
#130921602
Q8⋊(C23⋊C8)2
#130921472
C23×#4772
#163023