Finite Group Databasebeta

← #15672534

Subgroups — #15672534

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#13092797C211yesmaximal, characteristic, complemented
3#13092712C211yesmaximal, characteristic, complemented
4#13092708C211yesmaximal, characteristic
5#13092165C211yesmaximal, characteristic, complemented
6#13092146C211yesmaximal, characteristic
7C23×Q8⋊C8C211yesmaximal, characteristic, complemented
8C4×Q8×C23C2211yescharacteristic
9#10625117—21no—
10C2×Dic92—22no—
11#10625067—22no—
12C4⋊C4×D23—21no—
13C4×D92—21no—
14C4×D92C2211yescharacteristic
15#10625041—21no—
16#10625040C2211yescharacteristic
17#10625040C2211yescharacteristic
18C23×C4⋊C8C2211yescharacteristic
19C4×C8×C23C2211yescharacteristic
20#10625017—21no—
21#10625003—21no—
22#10624999—21no—
23#10624989—21no—
24C4⋊(C23⋊C8)C2211yescharacteristic
25C2×Q8×C23D411yescharacteristic
26C2×D92D411yescharacteristic
27C2×C4×D23—21no—
28C2×C4×D23—22no—
29C2×Dic46—21no—
30C2×Dic46D412yes—
31C2×C8×C23—21no—
32C2×C8×C23—21no—
33C4⋊C4×C23—21no—
34C4⋊C4×C23D411yescharacteristic
35C42×C23—21no—
36C42×C23C2311yescharacteristic
37(C2×D23)⋊C4—22no—
38(C2×D23)⋊C4—21no—
39C4⋊Dic23—21no—
40C4⋊Dic23—21no—
41C4⋊Dic23—21no—
42C4⋊Dic23—21no—
43C4⋊Dic23D411yescharacteristic
44Dic23⋊C4—22no—
45Dic23⋊C4—22no—
46C2×C23⋊C8—21no—
47Dic92—44no—
48C22×D23—21no—
49Q8×C23—21no—
50Q8×C23—21no—
51C2×C4×C23—21no—
52C2×C4×C23—21no—
53C2×C4×C23C2×D411yescharacteristic
54C2×C4×C23C2×D411yescharacteristic
55C2×C4×C23C2×D411yescharacteristic
56C2×Dic23—21no—
57C2×Dic23—22no—
58C2×Dic23—41no—
59D92—21no—
60D92Q1612yescomplemented
61C4×D23—41no—
62C4×D23—41no—
63C4×D23—82no—
64Dic46—42no—
65Dic46—42no—
66C8×C23—22no—
67C8×C23—41no—
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×C23C2×Q1611yescharacteristic
78C4×C23#13511yescharacteristic
79C4×C23#13711yescharacteristic
80C4×C23#13711yescharacteristic
81Dic23—41no—
82Dic23—42no—
83Dic23—81no—
84#554—231no—
85#494—231no—
86#477—231no—
87#476—231no—
88#333—231no—
89Q8⋊C8D2311yescharacteristic, complemented
90D4⋊C8—231no—
91C2×C23#45111yescharacteristic
92C2×C23#45211yescharacteristic
93C2×C23#45311yescharacteristic
94D23—42no—
95C2×Q16—462no—
96C4⋊Q8—231no—
97C4⋊Q8—231no—
98#125—461no—
99C22⋊Q8—462no—
100C22⋊Q8—461no—
101C4×Q8C2×D2311yescharacteristic
102C4×D4—231no—
103C4×D4—461no—
104C2×C4⋊C4—461no—
105#107—461no—
106#106—461no—
107C4⋊C8—231no—
108C4⋊C8C2×D2311yescharacteristic
109#103—461no—
110#102—461no—
111C4×C8C2×D2311yescharacteristic
112C23#163211yescharacteristic, complemented, Sylow
113C2×Q8—232no—
114C2×Q8—461no—
115C2×Q8D9211yescharacteristic
116C2×D4—231no—
117C22×C4—462no—
118C22×C4—461no—
119Q16—924no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—461no—
123C4⋊C4—21no—
124C4⋊C4—231no—
125C4⋊C4—462no—
126C4⋊C4—462no—
127C4⋊C4—461no—
128C4⋊C4—461no—
129C4⋊C4—461no—
130C4⋊C4—461no—
131C4⋊C4D9211yescharacteristic
132C22⋊C4—462no—
133C22⋊C4—461no—
134C42—21no—
135C42C22×D2311yescharacteristic
136C23—461no—
137Q8—21no—
138Q8—21no—
139Q8—922no—
140Q8—922no—
141D4—232no—
142D4—461no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—461no—
146C2×C4—462no—
147C2×C4—921no—
148C2×C4—921no—
149C2×C4—921no—
150C2×C4—1842no—
151C2×C4C2×D9211yescharacteristic
152C2×C4D4×D2311yescharacteristic
153C2×C4D4×D2311yescharacteristic
154C8—22no—
155C8—41no—
156C8—921no—
157C22—462no—
158C22—921no—
159C22—921no—
160C22#1062505311yescharacteristic
161C4—21no—
162C4—41no—
163C4—41no—
164C4—921no—
165C4—922no—
166C4—1841no—
167C4#1062507511yescharacteristic
168C4#1062508011yescharacteristic
169C4#1062508611yescharacteristic
170C4Q16×D2311yescharacteristic
171C2—922no—
172C2#1309257411yescharacteristic
173C2#1309258111yescharacteristic
174C2#1309258611yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×Q8⋊C8C2
socleC22×C23#120
prime radicalC2×D92D4
hypercenterQ8⋊C8D23
hypocenterC23#1632
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #13092797C2semidirect
3. #13092712C2semidirect
5. #13092165C2semidirect
7. C23×Q8⋊C8C2semidirect
60. D92Q16semidirect
89. Q8⋊C8D23semidirect
112. C23#1632semidirect

Maximal subgroups

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

subgroupindex
#130931272
#130927972
#130927122
#130927082
#130921652
#130921462
C23×Q8⋊C82
#163223