Finite Group Databasebeta

← #15672530

Subgroups — #15672530

Order 2944.

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

normal subgroups only

This group has 214 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#13093127C211yesmaximal, characteristic
2#13092796C211yesmaximal, characteristic, complemented
3#13092704C211yesmaximal, characteristic
4#13092165C211yesmaximal, characteristic, complemented
5Q8⋊(C23⋊C8)C211yesmaximal, characteristic, complemented
6#13092144C211yesmaximal, characteristic
7C23×#477C211yesmaximal, characteristic, complemented
8C23×C4⋊Q8C2211yescharacteristic
9C4×Q8×C23C2211yescharacteristic
10#10625117—21no—
11C2×#67275—22no—
12#10625067—22no—
13C4⋊C4×D23—21no—
14C4×D92—21no—
15C4×D92C2211yescharacteristic
16#10625041—21no—
17#10625040C2211yescharacteristic
18C23×#107—21no—
19C23×C4⋊C8C2211yescharacteristic
20C23×#103—21no—
21#10624991—21no—
22#10624990—21no—
23C4⋊(C23⋊C8)C2211yescharacteristic
24C4×C23⋊C8C2211yescharacteristic
25C2×Q8×C23—21no—
26C2×Q8×C23D411yescharacteristic
27C2×D92D411yescharacteristic
28C2×C4×D23—21no—
29C2×C4×D23—22no—
30C2×Dic46D412yes—
31C2×C8×C23—21no—
32C4⋊C4×C23—21no—
33C4⋊C4×C23—21no—
34C4⋊C4×C23—21no—
35C4⋊C4×C23D411yescharacteristic
36C42×C23—21no—
37C42×C23C2311yescharacteristic
38#67275—44no—
39(C2×D23)⋊C4—22no—
40(C2×D23)⋊C4—21no—
41C4⋊Dic23—21no—
42C4⋊Dic23—21no—
43C4⋊Dic23D411yescharacteristic
44Dic23⋊C4—22no—
45Dic23⋊C4—22no—
46C2×C23⋊C8—21no—
47C2×C23⋊C8—21no—
48C22×D23—21no—
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—22no—
60D92—21no—
61D92Q1612yescomplemented
62C4×D23—41no—
63C4×D23—41no—
64C4×D23—82no—
65Dic46—42no—
66C8×C23—41no—
67C23⋊C8—22no—
68C23⋊C8—41no—
69#1632—231nomaximal, Sylow
70C22×C23#12011yescharacteristic
71C2×D23—22no—
72C2×D23—41no—
73C2×D23—41no—
74C4×C23—21no—
75C4×C23—41no—
76C4×C23—41no—
77C4×C23—81no—
78C4×C23C2×Q1611yescharacteristic
79C4×C23#13511yescharacteristic
80C4×C23#13711yescharacteristic
81C4×C23#13711yescharacteristic
82Dic23—41no—
83Dic23—42no—
84#554—231no—
85#494—231no—
86#477D2311yescharacteristic, complemented
87#476—231no—
88#333—231no—
89Q8⋊C8—231no—
90D4⋊C8—231no—
91C2×C23#45111yescharacteristic
92C2×C23#45211yescharacteristic
93C2×C23#45311yescharacteristic
94D23—42no—
95C2×Q16—462no—
96C4⋊Q8—231no—
97C4⋊Q8C2×D2311yescharacteristic
98#125—461no—
99C22⋊Q8—462no—
100C22⋊Q8—461no—
101C4×Q8C2×D2311yescharacteristic
102C4×D4—231no—
103C4×D4—461no—
104C2×C4⋊C4—461no—
105#107—21no—
106#106—461no—
107C4⋊C8—231no—
108C4⋊C8C2×D2311yescharacteristic
109#103—21no—
110#102—461no—
111C4×C8—231no—
112C23#163211yescharacteristic, complemented, Sylow
113C2×Q8—21no—
114C2×Q8—232no—
115C2×Q8C22⋊D2311yescharacteristic
116C2×D4—231no—
117C22×C4—462no—
118C22×C4—461no—
119Q16—924no—
120C2×C8—21no—
121C2×C8—461no—
122C2×C8—461no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—231no—
127C4⋊C4—462no—
128C4⋊C4—462no—
129C4⋊C4—461no—
130C4⋊C4—461no—
131C4⋊C4C22⋊D2311yescharacteristic
132C22⋊C4—462no—
133C22⋊C4—461no—
134C42—21no—
135C42C22×D2311yescharacteristic
136C23—461no—
137Q8—21no—
138Q8—21no—
139Q8—42no—
140Q8—922no—
141D4—232no—
142D4—461no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—461no—
147C2×C4—462no—
148C2×C4—921no—
149C2×C4—921no—
150C2×C4—1842no—
151C2×C4D4×D2311yescharacteristic
152C2×C4D4×D2311yescharacteristic
153C2×C4C2×C22⋊D2311yescharacteristic
154C8—41no—
155C8—462no—
156C8—921no—
157C22—462no—
158C22—921no—
159C22—921no—
160C22#1062510811yescharacteristic
161C4—21no—
162C4—41no—
163C4—41no—
164C4—81no—
165C4—921no—
166C4—922no—
167C4Q16×D2311yescharacteristic
168C4#1062508911yescharacteristic
169C4#1062511311yescharacteristic
170C4#1062512111yescharacteristic
171C2—922no—
172C2#1309257111yescharacteristic
173C2#1309257711yescharacteristic
174C2#1309258311yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#477C2
socleC22×C23#120
prime radicalC2×D92D4
hypercenter#477D23
hypocenterC23#1632
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
2. #13092796C2semidirect
4. #13092165C2semidirect
5. Q8⋊(C23⋊C8)C2semidirect
7. C23×#477C2semidirect
61. D92Q16semidirect
86. #477D23semidirect
112. C23#1632semidirect

Maximal subgroups

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

subgroupindex
#130931272
#130927962
#130927042
#130921652
Q8⋊(C23⋊C8)2
#130921442
C23×#4772
#163223