Finite Group Databasebeta

← #15672662

Subgroups — #15672662

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
1D4×Dic46C211yesmaximal, characteristic
2#13092815C211yesmaximal, characteristic, complemented
3#13092703C211yesmaximal, characteristic, complemented
4#13092622C211yesmaximal, characteristic
5#13092164C211yesmaximal, characteristic, complemented
6#13092149C211yesmaximal, characteristic, complemented
7C23×D4⋊C8C211yesmaximal, characteristic
8C22×Dic46—21no—
9C4×D4×C23C2211yescharacteristic
10D4×Dic23—21no—
11C2×#67273—21no—
12#10625095—21no—
13#10625059—21no—
14#10625049—22no—
15#10625040C2211yescharacteristic
16#10625040C2211yescharacteristic
17C4×Dic46C2211yescharacteristic
18C23×C4⋊C8C2211yescharacteristic
19C4×C8×C23C2211yescharacteristic
20#10624999—21no—
21#10624999—22no—
22#10624998—21no—
23#10624992—21no—
24C4⋊(C23⋊C8)C2211yescharacteristic
25C2×D4×C23D411yescharacteristic
26C22×C4×C23—21no—
27C22×Dic23—22no—
28C2×Dic46—22no—
29C2×Dic46—21no—
30C2×Dic46—21no—
31C2×Dic46—42no—
32C2×Dic46—42no—
33C2×Dic46D411yescharacteristic
34C2×C8×C23—21no—
35C2×C8×C23—21no—
36C4⋊C4×C23D411yescharacteristic
37C22⋊C4×C23—21no—
38C42×C23C2311yescharacteristic
39C22⋊Dic23—22no—
40#67273—42no—
41C4⋊Dic23—21no—
42C4⋊Dic23—21no—
43C4⋊Dic23—21no—
44C4⋊Dic23D411yescharacteristic
45C4⋊Dic23D412yes—
46Dic23⋊C4—22no—
47Dic23⋊C4—21no—
48C4×Dic23—21no—
49C2×C23⋊C8—21no—
50C23×C23—21no—
51D4×C23—21no—
52D4×C23SD1612yes—
53C2×C4×C23—21no—
54C2×C4×C23—41no—
55C2×C4×C23—41no—
56C2×C4×C23C2×D411yescharacteristic
57C2×C4×C23C2×D411yescharacteristic
58C2×C4×C23C2×D411yescharacteristic
59C2×Dic23—21no—
60C2×Dic23—21no—
61C2×Dic23—22no—
62C2×Dic23—44no—
63C2×Dic23—41no—
64Dic46—21no—
65Dic46—44no—
66Dic46—41no—
67Dic46—41no—
68Dic46—41no—
69Dic46—41no—
70Dic46SD1612yescomplemented
71C8×C23—22no—
72C8×C23—41no—
73C23⋊C8—41no—
74#1651—231nomaximal, Sylow
75C22×C23—22no—
76C22×C23—41no—
77C22×C23—41no—
78C22×C23#12011yescharacteristic
79C4×C23—21no—
80C4×C23—41no—
81C4×C23C2×SD1611yescharacteristic
82C4×C23C2×SD1611yescharacteristic
83C4×C23AGL(1,ℤ/8)11yescharacteristic
84C4×C23#13711yescharacteristic
85Dic23—22no—
86Dic23—42no—
87Dic23—41no—
88Dic23—81no—
89D4×Q8—231no—
90#498—231no—
91#475—231no—
92#461—231no—
93#332—231no—
94Q8⋊C8—231no—
95D4⋊C8D2311yescharacteristic
96C2×C23—42no—
97C2×C23#44811yescharacteristic
98C2×C23#45011yescharacteristic
99C2×C23#45611yescharacteristic
100C22×Q8—461no—
101C2×SD16—461no—
102C4⋊Q8—231no—
103C4⋊Q8—231no—
104C4⋊Q8—461no—
105C22⋊Q8—462no—
106C22⋊Q8—461no—
107C4×Q8—231no—
108C4×D4—461no—
109C4×D4C2×D2311yescharacteristic
110#106—461no—
111#106—462no—
112C4⋊C8—231no—
113C4⋊C8C2×D2311yescharacteristic
114#103—461no—
115#103—461no—
116C4×C8C2×D2311yescharacteristic
117C23#165111yescharacteristic, complemented, Sylow
118C2×Q8—231no—
119C2×Q8—462no—
120C2×Q8—461no—
121C2×Q8—461no—
122C2×Q8—922no—
123C2×Q8—922no—
124C2×D4D9211yescharacteristic
125C22×C4—21no—
126C22×C4—462no—
127SD16—922no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—461no—
131C4⋊C4—231no—
132C4⋊C4—232no—
133C4⋊C4—462no—
134C4⋊C4—461no—
135C4⋊C4—461no—
136C4⋊C4—461no—
137C4⋊C4—461no—
138C4⋊C4D9211yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—462no—
141C42—461no—
142C42C22×D2311yescharacteristic
143C23—21no—
144Q8—232no—
145Q8—461no—
146Q8—924no—
147Q8—921no—
148Q8—921no—
149Q8—921no—
150Q8—921no—
151D4—21no—
152D4#6726312yes—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—461no—
157C2×C4—461no—
158C2×C4—462no—
159C2×C4—924no—
160C2×C4—921no—
161C2×C4C2×D9211yescharacteristic
162C2×C4D4×D2311yescharacteristic
163C2×C4D4×D2311yescharacteristic
164C8—22no—
165C8—41no—
166C8—921no—
167C22—22no—
168C22—41no—
169C22—41no—
170C22#1062505311yescharacteristic
171C4—21no—
172C4—41no—
173C4—462no—
174C4—922no—
175C4—921no—
176C4—1841no—
177C4C2×#6726311yescharacteristic
178C4#1062508011yescharacteristic
179C4#1062508211yescharacteristic
180C4SD16×D2311yescharacteristic
181C2—42no—
182C2#1309255811yescharacteristic
183C2#1309256911yescharacteristic
184C2#1309260111yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×D4⋊C8C2
socleC22×C23#120
prime radicalC2×D4×C23D4
hypercenterD4⋊C8D23
hypocenterC23#1651
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #13092815C2semidirect
3. #13092703C2semidirect
5. #13092164C2semidirect
6. #13092149C2semidirect
70. Dic46SD16semidirect
117. C23#1651semidirect

Maximal subgroups

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

subgroupindex
D4×Dic462
#130928152
#130927032
#130926222
#130921642
#130921492
C23×D4⋊C82
#165123