Finite Group Databasebeta

← #15672634

Subgroups — #15672634

Order 2944.

240 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 57 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#13093071C211yesmaximal, characteristic
2#13092822C211yesmaximal, characteristic, complemented
3#13092698C211yesmaximal, characteristic, complemented
4#13092622C211yesmaximal, characteristic, complemented
5#13092162C211yesmaximal, characteristic, complemented
6#13092146C211yesmaximal, characteristic, complemented
7C23×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#67290—21no—
9C4×D4×C23C2211yescharacteristic
10C2×#67273—21no—
11#10625101—21no—
12C2×C4⋊Dic23—21no—
13#10625068—21no—
14#10625057—22no—
15C4×D92C2211yescharacteristic
16#10625040C2211yescharacteristic
17#10625040C2211yescharacteristic
18C23×C4⋊C8C2211yescharacteristic
19C4×C8×C23C2211yescharacteristic
20#10625003—21no—
21#10625000—21no—
22#10625000—22no—
23#10624992—21no—
24C4⋊(C23⋊C8)C2211yescharacteristic
25C2×D4×C23D411yescharacteristic
26C22×C4×C23—21no—
27C2×C22⋊D23—22no—
28C22×Dic23—22no—
29#67290—42no—
30#67290—42no—
31C2×D92D411yescharacteristic
32C2×C4×D23—21no—
33C2×Dic46—21no—
34C2×Dic46—21no—
35C2×C8×C23—21no—
36C2×C8×C23—21no—
37C4⋊C4×C23D411yescharacteristic
38C22⋊C4×C23—21no—
39C42×C23C2311yescharacteristic
40#67273—42no—
41(C2×D23)⋊C4—22no—
42(C2×D23)⋊C4—21no—
43C4⋊Dic23—22no—
44C4⋊Dic23—21no—
45C4⋊Dic23—21no—
46C4⋊Dic23—21no—
47C4⋊Dic23D412yes—
48C4⋊Dic23D411yescharacteristic
49C2×C23⋊C8—21no—
50C23×C23—21no—
51C22×D23—21no—
52D4×C23—21no—
53D4×C23D812yes—
54C2×C4×C23—21no—
55C2×C4×C23—41no—
56C2×C4×C23—41no—
57C2×C4×C23C2×D411yescharacteristic
58C2×C4×C23C2×D411yescharacteristic
59C2×C4×C23C2×D411yescharacteristic
60C22⋊D23—44no—
61C2×Dic23—22no—
62C2×Dic23—21no—
63C2×Dic23—44no—
64C2×Dic23—41no—
65D92—21no—
66D92—21no—
67C4×D23—41no—
68C4×D23—41no—
69Dic46—41no—
70Dic46—41no—
71Dic46—41no—
72Dic46—41no—
73C8×C23—22no—
74C8×C23—41no—
75C23⋊C8—41no—
76#1647—231nomaximal, Sylow
77C22×C23—22no—
78C22×C23—41no—
79C22×C23—41no—
80C22×C23#12011yescharacteristic
81C2×D23—41no—
82C2×D23—41no—
83C2×D23—41no—
84C4×C23—21no—
85C4×C23—41no—
86C4×C23C2×D811yescharacteristic
87C4×C23#13511yescharacteristic
88C4×C23AGL(1,ℤ/8)11yescharacteristic
89C4×C23#13711yescharacteristic
90Dic23—42no—
91Dic23—41no—
92Dic23—81no—
93#547—231no—
94#500—231no—
95#474—231no—
96#461—231no—
97#332—231no—
98D4⋊C8—231no—
99D4⋊C8D2311yescharacteristic, complemented
100C2×C23—42no—
101C2×C23#44711yescharacteristic
102C2×C23#45211yescharacteristic
103C2×C23#45611yescharacteristic
104D23—81no—
105C2×#41—461no—
106C2×SD16—461no—
107C4⋊Q8—231no—
108C4⋊Q8—231no—
109#123—462no—
110C22⋊Q8—461no—
111#121—461no—
112C4×D4—231no—
113C4×D4C2×D2311yescharacteristic
114C2×C4⋊C4—461no—
115#107—461no—
116#107—462no—
117C4⋊C8—231no—
118C4⋊C8C2×D2311yescharacteristic
119#103—461no—
120#102—461no—
121C4×C8C2×D2311yescharacteristic
122C23#164711yescharacteristic, complemented, Sylow
123#41—922no—
124#41—922no—
125C2×Q8—461no—
126C2×Q8—461no—
127C2×D4—231no—
128C2×D4—462no—
129C2×D4D9211yescharacteristic
130C22×C4—21no—
131C22×C4—462no—
132C22×C4—461no—
133SD16—922no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—461no—
137C4⋊C4—231no—
138C4⋊C4—232no—
139C4⋊C4—462no—
140C4⋊C4—461no—
141C4⋊C4—461no—
142C4⋊C4—461no—
143C4⋊C4D9211yescharacteristic
144C22⋊C4—21no—
145C22⋊C4—462no—
146C22⋊C4—461no—
147C42C22×D2311yescharacteristic
148C23—21no—
149C23—461no—
150Q8—921no—
151Q8—921no—
152Q8—921no—
153Q8—921no—
154D4—21no—
155D4—461no—
156D4—461no—
157D4—924no—
158D4D18412yes—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—461no—
163C2×C4—462no—
164C2×C4—924no—
165C2×C4—921no—
166C2×C4—921no—
167C2×C4—921no—
168C2×C4C2×D9211yescharacteristic
169C2×C4D4×D2311yescharacteristic
170C2×C4D4×D2311yescharacteristic
171C8—22no—
172C8—41no—
173C8—921no—
174C22—22no—
175C22—41no—
176C22—41no—
177C22—921no—
178C22—921no—
179C22—921no—
180C22#1062505311yescharacteristic
181C4—21no—
182C4—41no—
183C4—921no—
184C4—922no—
185C4—1841no—
186C4C2×D18411yescharacteristic
187C4#1062507911yescharacteristic
188C4#1062508311yescharacteristic
189C4#1062508611yescharacteristic
190C2—42no—
191C2—1841no—
192C2#1309255311yescharacteristic
193C2#1309258011yescharacteristic
194C2#1309260111yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×D4⋊C8C2
socleC22×C23#120
prime radical#13093071C2
hypercenterD4⋊C8D23
hypocenterC23#1647
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. #13092822C2semidirect
3. #13092698C2semidirect
4. #13092622C2semidirect
5. #13092162C2semidirect
6. #13092146C2semidirect
7. C23×D4⋊C8C2semidirect
99. D4⋊C8D23semidirect
122. C23#1647semidirect

Maximal subgroups

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

subgroupindex
#130930712
#130928222
#130926982
#130926222
#130921622
#130921462
C23×D4⋊C82
#164723