Finite Group Databasebeta

← #15672045

Subgroups — #15672045

Order 2944.

256 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 73 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#13092968C211yesmaximal, characteristic
2#13092469C211yesmaximal, characteristic, complemented
3C4⋊C8×D23C211yesmaximal, characteristic, complemented
4#13092163C211yesmaximal, characteristic, complemented
5#13092160C211yesmaximal, characteristic, complemented
6#13092160C211yesmaximal, characteristic, complemented
7C23×#332C211yesmaximal, characteristic, complemented
8C2×#67292—21no—
9C23×C4⋊Q8C2211yescharacteristic
10#10625118—21no—
11C2×C8×D23—21no—
12#10625066—21no—
13#10625066C412yes—
14#10625064—21no—
15#10625064C412yes—
16#10625045C2211yescharacteristic
17C42×D23C2211yescharacteristic
18C23×C4⋊C8C2211yescharacteristic
19C23×C4⋊C8C2211yescharacteristic
20(C2×D23)⋊C8—21no—
21Dic23⋊C8—21no—
22C8×Dic23—21no—
23C4⋊(C23⋊C8)C2211yescharacteristic
24C4⋊(C23⋊C8)C2211yescharacteristic
25C2×Q8×C23—21no—
26#67292—42no—
27#67292—42no—
28C2×D92—22no—
29C2×D92—21no—
30C2×D92—21no—
31C2×D92C2×C412yes—
32C2×C4×D23—22no—
33C2×C4×D23C2×C411yescharacteristic
34C2×C4×D23D411yescharacteristic
35C2×C4×D23D411yescharacteristic
36C2×C8×C23—21no—
37C2×C8×C23—21no—
38C4⋊C4×C23—21no—
39C4⋊C4×C23C2×C412yes—
40C42×C23C2311yescharacteristic
41(C2×D23)⋊C4—22no—
42(C2×D23)⋊C4—22no—
43C4×Dic23C2×C411yescharacteristic
44C4×Dic23D411yescharacteristic
45C4×Dic23D411yescharacteristic
46C2×C23⋊C8—21no—
47C2×C23⋊C8—21no—
48C8×D23—42no—
49C22×D23—22no—
50C22×D23C22⋊C411yescharacteristic
51Q8×C23—41no—
52Q8×C23—41no—
53C2×C4×C23—22no—
54C2×C4×C23C22×C411yescharacteristic
55C2×C4×C23C2×D411yescharacteristic
56C2×C4×C23C2×D411yescharacteristic
57C2×Dic23C22⋊C411yescharacteristic
58C2×Dic23C22⋊C411yescharacteristic
59C2×Dic23C22⋊C411yescharacteristic
60D92—42no—
61D92—44no—
62D92—41no—
63D92—41no—
64D92—41no—
65D92—41no—
66C4×D23—21no—
67C4×D23—21no—
68C4×D23—41no—
69C4×D23—44no—
70C4×D23D812yes—
71C4×D23SD1612yes—
72C8×C23—41no—
73C8×C23—41no—
74C23⋊C8—41no—
75C23⋊C8—41no—
76#1540—231nomaximal, Sylow
77C22×C23C2×C22⋊C411yescharacteristic
78C2×D23—21no—
79C2×D23—21no—
80C2×D23—42no—
81C2×D23—42no—
82C2×D23—42no—
83C2×D23#10212yes—
84C4×C23—21no—
85C4×C23—42no—
86C4×C23C2×D811yescharacteristic
87C4×C23C2×SD1611yescharacteristic
88C4×C23#13511yescharacteristic
89C4×C23#13511yescharacteristic
90Dic23—21no—
91Dic23—21no—
92Dic23#10212yes—
93#532—231no—
94#431—231no—
95C2×C4⋊C8—231no—
96#332—231no—
97#332D2311yescharacteristic, complemented
98#331—231no—
99#331—231no—
100C2×C23#41311yescharacteristic
101C2×C23C2×#10211yescharacteristic
102C2×C23#41611yescharacteristic
103D23—22no—
104D23—82no—
105C2×#41—461no—
106C22×C8—461no—
107C4⋊Q8C2×D2311yescharacteristic
108#127—231no—
109#124—461no—
110#121—232no—
111#121—461no—
112C4×D4—232no—
113C4×D4—461no—
114C2×C42—231no—
115C4⋊C8—231no—
116C4⋊C8—231no—
117C4⋊C8—461no—
118C4⋊C8C2×D2311yescharacteristic
119C4⋊C8C2×D2311yescharacteristic
120C22⋊C8—461no—
121C4×C8—461no—
122C23#154011yescharacteristic, complemented, Sylow
123#41—922no—
124#41—922no—
125C2×Q8—21no—
126C2×D4—232no—
127C2×D4—462no—
128C2×D4—461no—
129C2×D4—461no—
130C22×C4—231no—
131C22×C4—231no—
132C22×C4—231no—
133C22×C4—462no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—461no—
137C2×C8—461no—
138C2×C8—922no—
139C4⋊C4—21no—
140C4⋊C4C4×D2312yes—
141C22⋊C4—462no—
142C22⋊C4—462no—
143C42—231no—
144C42—231no—
145C42—231no—
146C42C22×D2311yescharacteristic
147C23—231no—
148C23—462no—
149Q8—41no—
150Q8—41no—
151D4—922no—
152D4—924no—
153D4—921no—
154D4—921no—
155D4—921no—
156D4—921no—
157C2×C4—22no—
158C2×C4—231no—
159C2×C4—232no—
160C2×C4—232no—
161C2×C4—231no—
162C2×C4—231no—
163C2×C4—461no—
164C2×C4—461no—
165C2×C4—921no—
166C2×C4—924no—
167C2×C4C2×C4×D2311yescharacteristic
168C2×C4D4×D2311yescharacteristic
169C2×C4D4×D2311yescharacteristic
170C8—41no—
171C8—41no—
172C8—921no—
173C8—921no—
174C22—232no—
175C22—461no—
176C22—461no—
177C22—922no—
178C22—922no—
179C22—922no—
180C22C22⋊C4×D2311yescharacteristic
181C4—21no—
182C4—42no—
183C4—232no—
184C4—461no—
185C4—461no—
186C4D8×D2311yescharacteristic
187C4SD16×D2311yescharacteristic
188C4#1062508711yescharacteristic
189C4#1062509011yescharacteristic
190C2—462no—
191C2—1842no—
192C2#1309240011yescharacteristic
193C2#102×D2311yescharacteristic
194C2#1309241211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutatorC2×C4×C23C22×C4
FrattiniC42C22×D23
FittingC23×#332C2
socleC22×C23C2×C22⋊C4
prime radical#13092968C2
cosocleC42×C23C23
hypercenter#332D23
hypocenterC23#1540
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #13092469C2semidirect
3. C4⋊C8×D23C2semidirect
4. #13092163C2semidirect
5. #13092160C2semidirect
6. #13092160C2semidirect
7. C23×#332C2semidirect
97. #332D23semidirect
122. C23#1540semidirect

Maximal subgroups

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

subgroupindex
#130929682
#130924692
C4⋊C8×D232
#130921632
#130921602
C23×#3322
#154023