Finite Group Databasebeta

← #15672564

Subgroups — #15672564

Order 2944.

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

normal subgroups only

This group has 228 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#13092768C211yesmaximal, characteristic, complemented
3#13092712C211yesmaximal, characteristic, complemented
4#13092708C211yesmaximal, characteristic
5#13092162C211yesmaximal, characteristic, complemented
6#13092146C211yesmaximal, characteristic
7C23×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×Q8×D23—21no—
9C4×Q8×C23C2211yescharacteristic
10#10625068—21no—
11#10625068—22no—
12C4×D92—21no—
13C4×D92C2211yescharacteristic
14#10625040—21no—
15#10625040C2211yescharacteristic
16#10625040C2211yescharacteristic
17C23×C4⋊C8C2211yescharacteristic
18C4×C8×C23C2211yescharacteristic
19#10625017—21no—
20#10625003—21no—
21#10624999—21no—
22#10624998—22no—
23#10624989—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—
49C22×D23—21no—
50Q8×C23—21no—
51Q8×C23SD1612yes—
52C2×C4×C23—21no—
53C2×C4×C23—21no—
54C2×C4×C23C2×D411yescharacteristic
55C2×C4×C23C2×D411yescharacteristic
56C2×C4×C23C2×D411yescharacteristic
57C2×Dic23—21no—
58C2×Dic23—22no—
59C2×Dic23—41no—
60D92—21no—
61D92Q1612yes—
62C4×D23—44no—
63C4×D23—41no—
64C4×D23—41no—
65Dic46—44no—
66Dic46—41no—
67Dic46—41no—
68Dic46—42no—
69C8×C23—41no—
70C8×C23—41no—
71C23⋊C8—41no—
72#1637—231nomaximal, Sylow
73C22×C23#12011yescharacteristic
74C2×D23—22no—
75C2×D23—41no—
76C2×D23—41no—
77C4×C23—22no—
78C4×C23—21no—
79C4×C23—41no—
80C4×C23C2×SD1611yescharacteristic
81C4×C23C2×Q1611yescharacteristic
82C4×C23AGL(1,ℤ/8)11yescharacteristic
83C4×C23#13711yescharacteristic
84Dic23—41no—
85Dic23—42no—
86Dic23—81no—
87D4×Q8—231no—
88#487—231no—
89#477—231no—
90#476—231no—
91#332—231no—
92Q8⋊C8D2311yescharacteristic, complemented
93D4⋊C8—231no—
94C2×C23#45011yescharacteristic
95C2×C23#45111yescharacteristic
96C2×C23#45411yescharacteristic
97D23—42no—
98C22×Q8—461no—
99C4⋊Q8—231no—
100C4⋊Q8—231no—
101C4⋊Q8—461no—
102C22⋊Q8—462no—
103C22⋊Q8—461no—
104C4×Q8C2×D2311yescharacteristic
105C4×D4—231no—
106C4×D4—461no—
107#107—461no—
108#106—461no—
109C4⋊C8—231no—
110C4⋊C8C2×D2311yescharacteristic
111#103—462no—
112#103—461no—
113#102—461no—
114C4×C8C2×D2311yescharacteristic
115C23#163711yescharacteristic, complemented, Sylow
116C2×Q8—462no—
117C2×Q8—461no—
118C2×Q8—461no—
119C2×Q8—922no—
120C2×Q8—922no—
121C2×Q8D9211yescharacteristic
122C2×D4—231no—
123C22×C4—462no—
124C22×C4—461no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—461no—
128C4⋊C4—21no—
129C4⋊C4—232no—
130C4⋊C4—231no—
131C4⋊C4—462no—
132C4⋊C4—461no—
133C4⋊C4—461no—
134C4⋊C4—461no—
135C4⋊C4D9211yescharacteristic
136C22⋊C4—462no—
137C22⋊C4—461no—
138C42—21no—
139C42C22×D2311yescharacteristic
140C23—461no—
141Q8—21no—
142Q8—924no—
143Q8—922no—
144Q8—921no—
145Q8—921no—
146Q8#6726312yes—
147D4—232no—
148D4—461no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—462no—
152C2×C4—461no—
153C2×C4—924no—
154C2×C4—921no—
155C2×C4—921no—
156C2×C4—921no—
157C2×C4C2×D9211yescharacteristic
158C2×C4D4×D2311yescharacteristic
159C2×C4D4×D2311yescharacteristic
160C8—41no—
161C8—41no—
162C8—921no—
163C22—462no—
164C22—921no—
165C22—921no—
166C22#1062505311yescharacteristic
167C4—22no—
168C4—21no—
169C4—41no—
170C4—922no—
171C4—921no—
172C4—1841no—
173C4C2×#6726311yescharacteristic
174C4#1062507911yescharacteristic
175C4#1062508611yescharacteristic
176C4Q16×D2311yescharacteristic
177C2—922no—
178C2#1309257011yescharacteristic
179C2#1309257411yescharacteristic
180C2#1309259111yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×Q8⋊C8C2
socleC22×C23#120
prime radicalC2×D92D4
hypercenterQ8⋊C8D23
hypocenterC23#1637
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. #13092768C2semidirect
3. #13092712C2semidirect
5. #13092162C2semidirect
7. C23×Q8⋊C8C2semidirect
92. Q8⋊C8D23semidirect
115. C23#1637semidirect

Maximal subgroups

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

subgroupindex
Q8×D922
#130927682
#130927122
#130927082
#130921622
#130921462
C23×Q8⋊C82
#163723