Finite Group Databasebeta

← #15672663

Subgroups — #15672663

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#13092815C211yesmaximal, characteristic, complemented
3#13092702C211yesmaximal, characteristic, complemented
4#13092623C211yesmaximal, characteristic
5#13092162C211yesmaximal, characteristic, complemented
6#13092146C211yesmaximal, characteristic
7C23×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×Q8×D23—21no—
9C4×Q8×C23C2211yescharacteristic
10C2×#67263—21no—
11#10625068—21no—
12#10625068—22no—
13C4×D92—21no—
14C4×D92C2211yescharacteristic
15#10625040—21no—
16#10625040C2211yescharacteristic
17#10625040C2211yescharacteristic
18C23×C4⋊C8C2211yescharacteristic
19C4×C8×C23C2211yescharacteristic
20#10625017—21no—
21#10624999—22no—
22#10624998—21no—
23#10624990—21no—
24C4⋊(C23⋊C8)C2211yescharacteristic
25C2×Q8×C23D411yescharacteristic
26Q8×D23—42no—
27Q8×D23—42no—
28C2×D92D411yescharacteristic
29C2×C4×D23—22no—
30C2×C4×D23—21no—
31C2×Dic46—22no—
32C2×Dic46—21no—
33C2×Dic46—21no—
34C2×C8×C23—21no—
35C2×C8×C23—21no—
36C4⋊C4×C23—21no—
37C4⋊C4×C23D411yescharacteristic
38C42×C23—21no—
39C42×C23C2311yescharacteristic
40(C2×D23)⋊C4—22no—
41(C2×D23)⋊C4—21no—
42C4⋊Dic23—22no—
43C4⋊Dic23—21no—
44C4⋊Dic23—21no—
45C4⋊Dic23—21no—
46C4⋊Dic23D411yescharacteristic
47C4⋊Dic23D412yes—
48C2×C23⋊C8—21no—
49#67263—42no—
50C22×D23—21no—
51Q8×C23—21no—
52Q8×C23SD1612yescomplemented
53C2×C4×C23—21no—
54C2×C4×C23—21no—
55C2×C4×C23C2×D411yescharacteristic
56C2×C4×C23C2×D411yescharacteristic
57C2×C4×C23C2×D411yescharacteristic
58C2×Dic23—21no—
59C2×Dic23—22no—
60C2×Dic23—41no—
61D92—21no—
62D92SD1612yes—
63C4×D23—44no—
64C4×D23—41no—
65C4×D23—41no—
66Dic46—44no—
67Dic46—41no—
68Dic46—41no—
69Dic46—41no—
70Dic46—41no—
71C8×C23—22no—
72C8×C23—41no—
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×C23C2×SD1611yescharacteristic
83C4×C23C2×SD1611yescharacteristic
84C4×C23AGL(1,ℤ/8)11yescharacteristic
85C4×C23#13711yescharacteristic
86Dic23—41no—
87Dic23—42no—
88Dic23—81no—
89D4×Q8—231no—
90#498—231no—
91#475—231no—
92#461—231no—
93#332—231no—
94Q8⋊C8D2311yescharacteristic, complemented
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—231no—
104C4⋊Q8—461no—
105C22⋊Q8—462no—
106C22⋊Q8—461no—
107C4×Q8C2×D2311yescharacteristic
108C4×D4—231no—
109C4×D4—461no—
110#106—462no—
111#106—461no—
112C4⋊C8—231no—
113C4⋊C8C2×D2311yescharacteristic
114#103—461no—
115#103—461no—
116C4×C8C2×D2311yescharacteristic
117C23#165111yescharacteristic, complemented, Sylow
118C2×Q8—462no—
119C2×Q8—461no—
120C2×Q8—461no—
121C2×Q8—922no—
122C2×Q8—922no—
123C2×Q8D9211yescharacteristic
124C2×D4—231no—
125C22×C4—462no—
126C22×C4—461no—
127SD16—922no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—461no—
131C4⋊C4—21no—
132C4⋊C4—231no—
133C4⋊C4—232no—
134C4⋊C4—462no—
135C4⋊C4—461no—
136C4⋊C4—461no—
137C4⋊C4—461no—
138C4⋊C4D9211yescharacteristic
139C22⋊C4—462no—
140C22⋊C4—461no—
141C42—21no—
142C42C22×D2311yescharacteristic
143C23—461no—
144Q8—21no—
145Q8—924no—
146Q8—921no—
147Q8—921no—
148Q8—921no—
149Q8—921no—
150Q8#6726312yescomplemented
151D4—232no—
152D4—461no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—462no—
156C2×C4—461no—
157C2×C4—924no—
158C2×C4—921no—
159C2×C4—921no—
160C2×C4—921no—
161C2×C4C2×D9211yescharacteristic
162C2×C4D4×D2311yescharacteristic
163C2×C4D4×D2311yescharacteristic
164C8—22no—
165C8—41no—
166C8—921no—
167C22—462no—
168C22—921no—
169C22—921no—
170C22#1062505311yescharacteristic
171C4—22no—
172C4—21no—
173C4—41no—
174C4—922no—
175C4—921no—
176C4—1841no—
177C4C2×#6726311yescharacteristic
178C4#1062507911yescharacteristic
179C4SD16×D2311yescharacteristic
180C4#1062508911yescharacteristic
181C2—922no—
182C2#1309255711yescharacteristic
183C2#1309257011yescharacteristic
184C2#1309260111yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×Q8⋊C8C2
socleC22×C23#120
prime radicalC2×D92D4
hypercenterQ8⋊C8D23
hypocenterC23#1651
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. #13092815C2semidirect
3. #13092702C2semidirect
5. #13092162C2semidirect
7. C23×Q8⋊C8C2semidirect
52. Q8×C23SD16semidirect
94. Q8⋊C8D23semidirect
117. C23#1651semidirect
150. Q8#67263semidirect

Maximal subgroups

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

subgroupindex
Q8×D922
#130928152
#130927022
#130926232
#130921622
#130921462
C23×Q8⋊C82
#165123