Finite Group Databasebeta

← #15672508

Subgroups — #15672508

Order 2944.

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

normal subgroups only

This group has 216 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#13093141C211yesmaximal, characteristic, complemented
2#13092765C211yesmaximal, characteristic, complemented
3#13092618C211yesmaximal, characteristic, complemented
4#13092613C211yesmaximal, characteristic
5#13092147C211yesmaximal, characteristic, complemented
6#13092144C211yesmaximal, characteristic, complemented
7C23×#332C211yesmaximal, characteristic, complemented
8C23×C4⋊Q8C2211yescharacteristic
9#10625118—21no—
10Q8×Dic23—21no—
11C2×D184—21no—
12C2×#67263—21no—
13#10625069—22no—
14#10625068—21no—
15#10625063—21no—
16#10625045C2211yescharacteristic
17C4×D92C2211yescharacteristic
18C4×Dic46C2211yescharacteristic
19C23×C4⋊C8C2211yescharacteristic
20C23×C4⋊C8C2211yescharacteristic
21#10625003—21no—
22#10625003—21no—
23#10624991—22no—
24C4×C23⋊C8C2211yescharacteristic
25C2×Q8×C23—21no—
26C2×D92—21no—
27C2×D92—21no—
28C2×D92—21no—
29C2×D92D411yescharacteristic
30C2×C4×D23—21no—
31C2×Dic46D411yescharacteristic
32C2×C8×C23—21no—
33C2×C8×C23—21no—
34C4⋊C4×C23—21no—
35C4⋊C4×C23D412yes—
36C42×C23C2311yescharacteristic
37(C2×D23)⋊C4—22no—
38(C2×D23)⋊C4—22no—
39(C2×D23)⋊C4—21no—
40C4⋊Dic23—22no—
41C4⋊Dic23D411yescharacteristic
42C4⋊Dic23D411yescharacteristic
43Dic23⋊C4—21no—
44C4×Dic23—22no—
45C4×Dic23—21no—
46C2×C23⋊C8—21no—
47D184—42no—
48#67263—42no—
49C22×D23—21no—
50C22×D23—41no—
51Q8×C23—41no—
52Q8×C23—41no—
53C2×C4×C23—22no—
54C2×C4×C23C2×D411yescharacteristic
55C2×C4×C23C2×D411yescharacteristic
56C2×C4×C23C2×D411yescharacteristic
57C2×Dic23—21no—
58C2×Dic23—21no—
59C2×Dic23—21no—
60D92—21no—
61D92—21no—
62D92—42no—
63D92—41no—
64D92—41no—
65D92—41no—
66D92—41no—
67C4×D23—41no—
68C4×D23—41no—
69Dic46—21no—
70Dic46—21no—
71C8×C23—41no—
72C8×C23—41no—
73C23⋊C8—41no—
74#1628—231nomaximal, Sylow
75C22×C23#12011yescharacteristic
76C2×D23—41no—
77C2×D23—41no—
78C2×D23—41no—
79C2×D23—81no—
80C2×D23—81no—
81C2×D23—81no—
82C4×C23—21no—
83C4×C23—42no—
84C4×C23#13511yescharacteristic
85C4×C23#13511yescharacteristic
86C4×C23AGL(1,ℤ/8)11yescharacteristic
87C4×C23AGL(1,ℤ/8)11yescharacteristic
88Dic23—41no—
89Dic23—41no—
90Dic23—41no—
91#556—231no—
92#486—231no—
93#460—231no—
94#459—231no—
95#332D2311yescharacteristic, complemented
96Q8⋊C8—231no—
97D4⋊C8—231no—
98C2×C23#44911yescharacteristic
99C2×C23#44911yescharacteristic
100C2×C23#45411yescharacteristic
101D23—81no—
102D23—161no—
103C2×SD16—461no—
104C2×D8—461no—
105C4⋊Q8C2×D2311yescharacteristic
106#127—231no—
107#126—462no—
108#124—461no—
109C22⋊Q8—461no—
110C4×Q8—231no—
111C4×Q8—461no—
112C4×D4—231no—
113#117—461no—
114C4⋊C8C2×D2311yescharacteristic
115C4⋊C8C2×D2311yescharacteristic
116#102—461no—
117#102—461no—
118#102—462no—
119C4×C8—231no—
120C23#162811yescharacteristic, complemented, Sylow
121C2×Q8—21no—
122C2×Q8—231no—
123C2×D4—231no—
124C2×D4—461no—
125C2×D4—461no—
126C2×D4—461no—
127C22×C4—461no—
128SD16—922no—
129D8—922no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—461no—
133C4⋊C4—21no—
134C4⋊C4—231no—
135C4⋊C4—231no—
136C4⋊C4—462no—
137C4⋊C4—461no—
138C4⋊C4D9212yes—
139C22⋊C4—462no—
140C22⋊C4—462no—
141C22⋊C4—461no—
142C42—462no—
143C42—461no—
144C42C22×D2311yescharacteristic
145C23—461no—
146C23—921no—
147Q8—41no—
148Q8—41no—
149Q8—461no—
150Q8—461no—
151D4—461no—
152D4—461no—
153D4—922no—
154D4—921no—
155D4—921no—
156D4—921no—
157D4—921no—
158C2×C4—22no—
159C2×C4—461no—
160C2×C4—461no—
161C2×C4—461no—
162C2×C4—921no—
163C2×C4—921no—
164C2×C4C2×D9211yescharacteristic
165C2×C4D4×D2311yescharacteristic
166C2×C4D4×D2311yescharacteristic
167C8—41no—
168C8—41no—
169C8—921no—
170C22—921no—
171C22—921no—
172C22—921no—
173C22—1841no—
174C22—1841no—
175C22—1841no—
176C22#1062505311yescharacteristic
177C4—21no—
178C4—42no—
179C4—921no—
180C4—921no—
181C4—921no—
182C4#1062508211yescharacteristic
183C4#1062508511yescharacteristic
184C4#1062508711yescharacteristic
185C4#1062509011yescharacteristic
186C2—3681no—
187C2—1841no—
188C2#1309256311yescharacteristic
189C2#1309256511yescharacteristic
190C2#1309259211yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#332C2
socleC22×C23#120
prime radical#13092613C2
hypercenter#332D23
hypocenterC23#1628
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #13093141C2semidirect
2. #13092765C2semidirect
3. #13092618C2semidirect
5. #13092147C2semidirect
6. #13092144C2semidirect
7. C23×#332C2semidirect
95. #332D23semidirect
120. C23#1628semidirect

Maximal subgroups

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

subgroupindex
#130931412
#130927652
#130926182
#130926132
#130921472
#130921442
C23×#3322
#162823