Finite Group Databasebeta

← #15672664

Subgroups — #15672664

Order 2944.

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

normal subgroups only

This group has 200 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
2#13092694C211yesmaximal, characteristic
3#13092624C211yesmaximal, characteristic, complemented
4#13092163C211yesmaximal, characteristic, complemented
5#13092149C211yesmaximal, characteristic, complemented
6#13092146C211yesmaximal, characteristic
7C23×#498C211yesmaximal, characteristic, complemented
8C23×C4⋊Q8C2211yescharacteristic
9C23×C4⋊Q8C2211yescharacteristic
10#10625118—21no—
11Q8×Dic23—21no—
12C2×#67275—21no—
13#10625069—22no—
14#10625068—21no—
15#10625063—21no—
16C4×D92C2211yescharacteristic
17C4×Dic46C2211yescharacteristic
18C23×#106—22no—
19C4×C8×C23C2211yescharacteristic
20#10625017—21no—
21#10624991—21no—
22#10624989—21no—
23C4⋊(C23⋊C8)C2211yescharacteristic
24C4⋊(C23⋊C8)C2211yescharacteristic
25C2×Q8×C23—21no—
26C2×Q8×C23—21no—
27C2×D92D411yescharacteristic
28C2×C4×D23—21no—
29C2×Dic46D411yescharacteristic
30C2×C8×C23—21no—
31C4⋊C4×C23—21no—
32C4⋊C4×C23—21no—
33C4⋊C4×C23—21no—
34C4⋊C4×C23D412yes—
35C42×C23C2311yescharacteristic
36#67275—42no—
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—
47C2×C23⋊C8—21no—
48C22×D23—21no—
49Q8×C23—41no—
50Q8×C23—41no—
51Q8×C23—41no—
52Q8×C23—41no—
53C2×C4×C23—22no—
54C2×C4×C23—41no—
55C2×C4×C23C2×D411yescharacteristic
56C2×C4×C23C2×D411yescharacteristic
57C2×C4×C23C2×D411yescharacteristic
58C2×Dic23—21no—
59C2×Dic23—21no—
60C2×Dic23—21no—
61D92—21no—
62D92—21no—
63C4×D23—41no—
64C4×D23—41no—
65Dic46—21no—
66Dic46—21no—
67C8×C23—22no—
68C23⋊C8—41no—
69C23⋊C8—41no—
70#1652—231nomaximal, Sylow
71C22×C23#12011yescharacteristic
72C2×D23—41no—
73C2×D23—41no—
74C2×D23—41no—
75C4×C23—21no—
76C4×C23—42no—
77C4×C23—81no—
78C4×C23#13511yescharacteristic
79C4×C23#13511yescharacteristic
80C4×C23AGL(1,ℤ/8)11yescharacteristic
81C4×C23#13711yescharacteristic
82Dic23—41no—
83Dic23—41no—
84Dic23—41no—
85#556—231no—
86#498D2311yescharacteristic, complemented
87#474—231no—
88#462—231no—
89#332—231no—
90Q8⋊C8—231no—
91D4⋊C8—231no—
92C2×C23#44911yescharacteristic
93C2×C23#45211yescharacteristic
94C2×C23#45611yescharacteristic
95D23—81no—
96C2×Q16—461no—
97C4⋊Q8C2×D2311yescharacteristic
98C4⋊Q8C2×D2311yescharacteristic
99#126—462no—
100#124—461no—
101C22⋊Q8—461no—
102C4×Q8—231no—
103C4×Q8—461no—
104C4×D4—231no—
105#117—461no—
106#107—461no—
107#106—22no—
108C4⋊C8—231no—
109C4⋊C8—231no—
110#103—461no—
111#102—461no—
112C4×C8C2×D2311yescharacteristic
113C23#165211yescharacteristic, complemented, Sylow
114C2×Q8—21no—
115C2×Q8—21no—
116C2×Q8—231no—
117C2×D4—231no—
118C22×C4—461no—
119Q16—922no—
120C2×C8—21no—
121C2×C8—461no—
122C2×C8—461no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—231no—
127C4⋊C4—231no—
128C4⋊C4—462no—
129C4⋊C4—461no—
130C4⋊C4C22⋊D2312yes—
131C22⋊C4—462no—
132C22⋊C4—462no—
133C22⋊C4—461no—
134C42—462no—
135C42—461no—
136C42C22×D2311yescharacteristic
137C23—461no—
138Q8—41no—
139Q8—41no—
140Q8—41no—
141Q8—41no—
142Q8—461no—
143Q8—461no—
144D4—461no—
145D4—461no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—461no—
149C2×C4—461no—
150C2×C4—461no—
151C2×C4—921no—
152C2×C4—921no—
153C2×C4D4×D2311yescharacteristic
154C2×C4D4×D2311yescharacteristic
155C2×C4C2×C22⋊D2311yescharacteristic
156C8—22no—
157C8—921no—
158C8—921no—
159C22—921no—
160C22—921no—
161C22—921no—
162C22#1062510811yescharacteristic
163C4—21no—
164C4—42no—
165C4—81no—
166C4—921no—
167C4—921no—
168C4—921no—
169C4#1062508511yescharacteristic
170C4#1062508611yescharacteristic
171C4#1062508711yescharacteristic
172C4#1062508711yescharacteristic
173C2—1841no—
174C2#1309256111yescharacteristic
175C2#1309257611yescharacteristic
176C2#1309259911yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#498C2
socleC22×C23#120
prime radicalC2×D92D4
hypercenter#498D23
hypocenterC23#1652
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
3. #13092624C2semidirect
4. #13092163C2semidirect
5. #13092149C2semidirect
7. C23×#498C2semidirect
86. #498D23semidirect
113. C23#1652semidirect

Maximal subgroups

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

subgroupindex
#130931412
#130926942
#130926242
#130921632
#130921492
#130921462
C23×#4982
#165223