Finite Group Databasebeta

← #15672659

Subgroups — #15672659

Order 2944.

234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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
1Q8×D92C211yesmaximal, characteristic
2#13092813C211yesmaximal, characteristic, complemented
3#13092619C211yesmaximal, characteristic
4#13092164C211yesmaximal, characteristic, complemented
5Q8⋊(C23⋊C8)C211yesmaximal, characteristic, complemented
6#13092144C211yesmaximal, characteristic
7C23×#475C211yesmaximal, characteristic, complemented
8C2×Q8×D23—21no—
9C23×C4⋊Q8C2211yescharacteristic
10C4×Q8×C23C2211yescharacteristic
11C2×#67274—21no—
12#10625068—21no—
13#10625068—22no—
14C4×D92—21no—
15C4×D92C2211yescharacteristic
16#10625040—21no—
17#10625040C2211yescharacteristic
18C23×#106—21no—
19C23×C4⋊C8C2211yescharacteristic
20C23×#103—21no—
21#10625017—21no—
22#10624990—22no—
23C4⋊(C23⋊C8)C2211yescharacteristic
24C4×C23⋊C8C2211yescharacteristic
25C2×Q8×C23—21no—
26C2×Q8×C23D411yescharacteristic
27Q8×D23—42no—
28Q8×D23—42no—
29C2×D92D411yescharacteristic
30C2×C4×D23—22no—
31C2×C4×D23—21no—
32C2×Dic46—22no—
33C2×Dic46—21no—
34C2×C8×C23—21no—
35C4⋊C4×C23—21no—
36C4⋊C4×C23—21no—
37C4⋊C4×C23—21no—
38C4⋊C4×C23D411yescharacteristic
39C42×C23—21no—
40C42×C23C2311yescharacteristic
41#67274—42no—
42(C2×D23)⋊C4—22no—
43(C2×D23)⋊C4—21no—
44C4⋊Dic23—22no—
45C4⋊Dic23—21no—
46C4⋊Dic23D411yescharacteristic
47C4⋊Dic23D412yes—
48C2×C23⋊C8—21no—
49C2×C23⋊C8—21no—
50C22×D23—21no—
51Q8×C23—21no—
52Q8×C23—41no—
53Q8×C23—41no—
54Q8×C23SD1612yescomplemented
55C2×C4×C23—21no—
56C2×C4×C23—21no—
57C2×C4×C23—41no—
58C2×C4×C23C2×D411yescharacteristic
59C2×C4×C23C2×D411yescharacteristic
60C2×C4×C23C2×D411yescharacteristic
61C2×Dic23—21no—
62C2×Dic23—22no—
63D92—21no—
64D92SD1612yes—
65C4×D23—44no—
66C4×D23—41no—
67C4×D23—41no—
68Dic46—44no—
69Dic46—41no—
70Dic46—41no—
71C8×C23—41no—
72C23⋊C8—22no—
73C23⋊C8—41no—
74#1651—231nomaximal, Sylow
75C22×C23#12011yescharacteristic
76C2×D23—22no—
77C2×D23—41no—
78C2×D23—41no—
79C4×C23—22no—
80C4×C23—21no—
81C4×C23—41no—
82C4×C23—81no—
83C4×C23C2×SD1611yescharacteristic
84C4×C23C2×SD1611yescharacteristic
85C4×C23AGL(1,ℤ/8)11yescharacteristic
86C4×C23#13711yescharacteristic
87Dic23—41no—
88Dic23—42no—
89D4×Q8—231no—
90#498—231no—
91#475D2311yescharacteristic, complemented
92#461—231no—
93#332—231no—
94Q8⋊C8—231no—
95D4⋊C8—231no—
96C2×C23#44811yescharacteristic
97C2×C23#45011yescharacteristic
98C2×C23#45611yescharacteristic
99D23—42no—
100C22×Q8—461no—
101C2×SD16—461no—
102C4⋊Q8—231no—
103C4⋊Q8—461no—
104C4⋊Q8C2×D2311yescharacteristic
105C22⋊Q8—462no—
106C22⋊Q8—461no—
107C4×Q8C2×D2311yescharacteristic
108C4×D4—231no—
109C4×D4—461no—
110#106—21no—
111#106—462no—
112C4⋊C8—231no—
113C4⋊C8C2×D2311yescharacteristic
114#103—21no—
115#103—461no—
116C4×C8—231no—
117C23#165111yescharacteristic, complemented, Sylow
118C2×Q8—21no—
119C2×Q8—462no—
120C2×Q8—461no—
121C2×Q8—922no—
122C2×Q8—922no—
123C2×Q8C22⋊D2311yescharacteristic
124C2×D4—231no—
125C22×C4—462no—
126C22×C4—461no—
127SD16—922no—
128C2×C8—21no—
129C2×C8—461no—
130C2×C8—461no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—231no—
135C4⋊C4—232no—
136C4⋊C4—462no—
137C4⋊C4—461no—
138C4⋊C4C22⋊D2311yescharacteristic
139C22⋊C4—462no—
140C22⋊C4—461no—
141C42—21no—
142C42C22×D2311yescharacteristic
143C23—461no—
144Q8—21no—
145Q8—41no—
146Q8—41no—
147Q8—924no—
148Q8—921no—
149Q8—921no—
150Q8#6727412yescomplemented
151D4—232no—
152D4—461no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—462no—
157C2×C4—461no—
158C2×C4—924no—
159C2×C4—921no—
160C2×C4—921no—
161C2×C4D4×D2311yescharacteristic
162C2×C4D4×D2311yescharacteristic
163C2×C4C2×C22⋊D2311yescharacteristic
164C8—41no—
165C8—462no—
166C8—921no—
167C22—462no—
168C22—921no—
169C22—921no—
170C22#1062510811yescharacteristic
171C4—22no—
172C4—21no—
173C4—41no—
174C4—81no—
175C4—922no—
176C4—921no—
177C4SD16×D2311yescharacteristic
178C4#1062508611yescharacteristic
179C4C2×#6727411yescharacteristic
180C4#1062512011yescharacteristic
181C2—922no—
182C2#1309255411yescharacteristic
183C2#1309256711yescharacteristic
184C2#1309259811yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#475C2
socleC22×C23#120
prime radicalC2×D92D4
hypercenter#475D23
hypocenterC23#1651
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #13092813C2semidirect
4. #13092164C2semidirect
5. Q8⋊(C23⋊C8)C2semidirect
7. C23×#475C2semidirect
54. Q8×C23SD16semidirect
91. #475D23semidirect
117. C23#1651semidirect
150. Q8#67274semidirect

Maximal subgroups

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

subgroupindex
Q8×D922
#130928132
#130926192
#130921642
Q8⋊(C23⋊C8)2
#130921442
C23×#4752
#165123