Finite Group Databasebeta

← #15672678

Subgroups — #15672678

Order 2944.

240 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 55 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#13093070C211yesmaximal, characteristic
2#13092694C211yesmaximal, characteristic, complemented
3#13092619C211yesmaximal, characteristic, complemented
4#13092163C211yesmaximal, characteristic, complemented
5#13092146C211yesmaximal, characteristic, complemented
6#13092146C211yesmaximal, characteristic, complemented
7C23×#498C211yesmaximal, characteristic, complemented
8C2×#67292—21no—
9C23×C4⋊Q8C2211yescharacteristic
10C23×C4⋊Q8C2211yescharacteristic
11#10625117—21no—
12C2×#67274—21no—
13#10625066—21no—
14#10625065—22no—
15C4⋊C4×D23—21no—
16C4×D92C2211yescharacteristic
17C4×D92C2211yescharacteristic
18C23×#106—22no—
19C4×C8×C23C2211yescharacteristic
20#10625017—21no—
21#10624991—21no—
22#10624989—21no—
23C4⋊(C23⋊C8)C2211yescharacteristic
24C4⋊(C23⋊C8)C2211yescharacteristic
25C2×Q8×C23—21no—
26C2×Q8×C23—21no—
27#67292—42no—
28#67292—42no—
29C2×D92—22no—
30C2×D92D411yescharacteristic
31C2×D92D411yescharacteristic
32C2×C4×D23—22no—
33C2×C4×D23—21no—
34C2×C4×D23—21no—
35C2×C8×C23—21no—
36C4⋊C4×C23—21no—
37C4⋊C4×C23—21no—
38C4⋊C4×C23—21no—
39C4⋊C4×C23D412yes—
40C42×C23C2311yescharacteristic
41#67274—42no—
42(C2×D23)⋊C4—22no—
43(C2×D23)⋊C4—21no—
44(C2×D23)⋊C4—21no—
45C4⋊Dic23D411yescharacteristic
46C4⋊Dic23D411yescharacteristic
47Dic23⋊C4—22no—
48C2×C23⋊C8—21no—
49C2×C23⋊C8—21no—
50C22×D23—21no—
51C22×D23—21no—
52Q8×C23—41no—
53Q8×C23—41no—
54Q8×C23—41no—
55Q8×C23—41no—
56C2×C4×C23—22no—
57C2×C4×C23—41no—
58C2×C4×C23C2×D411yescharacteristic
59C2×C4×C23C2×D411yescharacteristic
60C2×C4×C23C2×D411yescharacteristic
61C2×Dic23—21no—
62C2×Dic23—21no—
63D92—21no—
64D92—21no—
65D92—21no—
66D92—44no—
67D92SD1612yescomplemented
68C4×D23—44no—
69C4×D23—41no—
70C4×D23—41no—
71C4×D23—41no—
72C4×D23—41no—
73C8×C23—22no—
74C23⋊C8—41no—
75C23⋊C8—41no—
76#1654—231nomaximal, Sylow
77C22×C23#12011yescharacteristic
78C2×D23—22no—
79C2×D23—41no—
80C2×D23—41no—
81C2×D23—41no—
82C2×D23—41no—
83C2×D23—41no—
84C4×C23—21no—
85C4×C23—42no—
86C4×C23—81no—
87C4×C23C2×SD1611yescharacteristic
88C4×C23#13511yescharacteristic
89C4×C23AGL(1,ℤ/8)11yescharacteristic
90C4×C23AGL(1,ℤ/8)11yescharacteristic
91Dic23—41no—
92Dic23—41no—
93#547—231no—
94#498D2311yescharacteristic, complemented
95#474—231no—
96#461—231no—
97#332—231no—
98D4⋊C8—231no—
99D4⋊C8—231no—
100C2×C23#44911yescharacteristic
101C2×C23#45011yescharacteristic
102C2×C23#45611yescharacteristic
103D23—42no—
104D23—81no—
105C2×#41—461no—
106C2×SD16—461no—
107C4⋊Q8C2×D2311yescharacteristic
108C4⋊Q8C2×D2311yescharacteristic
109#123—462no—
110C22⋊Q8—461no—
111#121—461no—
112C4×D4—231no—
113C4×D4—231no—
114C2×C4⋊C4—461no—
115#107—461no—
116#106—22no—
117C4⋊C8—231no—
118C4⋊C8—231no—
119#103—461no—
120#102—461no—
121C4×C8C2×D2311yescharacteristic
122C23#165411yescharacteristic, complemented, Sylow
123#41—922no—
124#41—922no—
125C2×Q8—21no—
126C2×Q8—21no—
127C2×D4—231no—
128C2×D4—231no—
129C2×D4—462no—
130C22×C4—462no—
131C22×C4—461no—
132C22×C4—461no—
133SD16—922no—
134C2×C8—21no—
135C2×C8—461no—
136C2×C8—461no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—231no—
141C4⋊C4—231no—
142C4⋊C4—462no—
143C4⋊C4C22⋊D2312yes—
144C22⋊C4—462no—
145C22⋊C4—461no—
146C22⋊C4—461no—
147C42C22×D2311yescharacteristic
148C23—461no—
149C23—461no—
150Q8—41no—
151Q8—41no—
152Q8—41no—
153Q8—41no—
154D4—232no—
155D4—461no—
156D4—461no—
157D4—461no—
158D4—924no—
159C2×C4—22no—
160C2×C4—41no—
161C2×C4—461no—
162C2×C4—461no—
163C2×C4—924no—
164C2×C4—921no—
165C2×C4—921no—
166C2×C4—921no—
167C2×C4—921no—
168C2×C4D4×D2311yescharacteristic
169C2×C4D4×D2311yescharacteristic
170C2×C4C2×C22⋊D2311yescharacteristic
171C8—22no—
172C8—921no—
173C8—921no—
174C22—462no—
175C22—921no—
176C22—921no—
177C22—921no—
178C22—921no—
179C22—921no—
180C22#1062510811yescharacteristic
181C4—21no—
182C4—42no—
183C4—81no—
184C4—921no—
185C4—921no—
186C4SD16×D2311yescharacteristic
187C4#1062508511yescharacteristic
188C4#1062508511yescharacteristic
189C4#1062508711yescharacteristic
190C2—922no—
191C2—1841no—
192C2#1309256111yescharacteristic
193C2#1309256611yescharacteristic
194C2#1309259911yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#498C2
socleC22×C23#120
prime radical#13093070C2
hypercenter#498D23
hypocenterC23#1654
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
2. #13092694C2semidirect
3. #13092619C2semidirect
4. #13092163C2semidirect
5. #13092146C2semidirect
6. #13092146C2semidirect
7. C23×#498C2semidirect
67. D92SD16semidirect
94. #498D23semidirect
122. C23#1654semidirect

Maximal subgroups

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

subgroupindex
#130930702
#130926942
#130926192
#130921632
#130921462
C23×#4982
#165423