Finite Group Databasebeta

← #18010762

Subgroups — #18010762

Order 4736.

324 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 88 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
1D37⋊(C4⋊C8)C211yesmaximal, characteristic
2C2×#11924599C214yesmaximal
3C4×C4⋊#3866C211yesmaximal, characteristic
4C4⋊Q8×D37C211yesmaximal, characteristic
5C2×D37⋊C8C2212yes—
6C2×C4⋊#3866C2212yes—
7C2×C4×#3866—21no—
8#11924603—21no—
9C4⋊#64438—21no—
10#11924599—28no—
11(C2×#3866)⋊C4—21no—
12C2×Q8×D37C2212yes—
13#11924536C411yescharacteristic, complemented
14#11924535—21no—
15#11924535—21no—
16#11924534C412yescomplemented
17C4⋊C4×D37—21no—
18C4⋊C4×D37—21no—
19C42×D37C2211yescharacteristic
20C4⋊Q8×C37C411yescharacteristic, complemented
21C22×#3866—22no—
22C2×Q8×C37C2×C412yes—
23Q8×D37—24no—
24Q8×D37—24no—
25C2×C4×D37—22no—
26C2×C4×D37D411yescharacteristic
27C2×C4×D37D411yescharacteristic
28C2×C4×D37C2311yescharacteristic
29C2×Dic74—22no—
30C2×Dic74C2×C412yes—
31C2×#64438—22no—
32C4⋊#3866—22no—
33C4⋊#3866D414yes—
34C4×#3866—42no—
35D37⋊C8—24no—
36C4⋊C4×C37—21no—
37C4⋊C4×C37—21no—
38C42×C37C2×C411yescharacteristic
39C4⋊Dic37—21no—
40C4⋊Dic37—21no—
41#10596936—22no—
42#10596936—22no—
43C4×Dic37C2×C411yescharacteristic
44C4×Dic37D411yescharacteristic
45C4×Dic37D411yescharacteristic
46C22×D37C2×D411yescharacteristic
47C2×#3866—24no—
48C2×#3866—42no—
49C2×#3866—42no—
50Q8×C37—24no—
51C2×C4×C37—22no—
52C2×C4×C37C22⋊C411yescharacteristic
53C2×C4×C37C22⋊C411yescharacteristic
54C2×C4×C37C22×C411yescharacteristic
55C2×Dic37—22no—
56C2×Dic37C22⋊C411yescharacteristic
57C2×Dic37C22⋊C411yescharacteristic
58C2×Dic37C2×D411yescharacteristic
59C4×D37—22no—
60C4×D37—44no—
61C4×D37SD1612yes—
62C4×D37Q1612yes—
63C4×D37C2×D412yes—
64C4×D37#4112yes—
65Dic74—24no—
66Dic74—42no—
67Dic74—42no—
68#64438—42no—
69C22×C37C2×C22⋊C411yescharacteristic
70C2×D37#12112yes—
71C2×D37C2×SD1611yescharacteristic
72C2×D37C2×Q1611yescharacteristic
73C2×D37#13712yes—
74#3866—44no—
75C4×C37—21no—
76C4×C37—42no—
77C4×C37#10312yescomplemented
78C4×C37C4×D412yes—
79Dic37—21no—
80Dic37—42no—
81Dic37#10312yescomplemented
82Dic37#12411yescharacteristic
83Dic37#12711yescharacteristic
84#1981—371nomaximal, Sylow
85C2×C37#39011yescharacteristic
86C2×C37C2×#10311yescharacteristic
87C2×C37#41911yescharacteristic
88D37#46112yes—
89D37#46212yes—
90C2×C4⋊Q8—371no—
91C2×C4⋊C8—371no—
92C2×#103—374no—
93C4×C4⋊C4—371no—
94C37#198111yescharacteristic, complemented, Sylow
95C22×Q8—372no—
96C22×C8—372no—
97C4⋊Q8—372no—
98C4⋊Q8—371no—
99C4⋊Q8—741no—
100C4⋊Q8—741no—
101C4⋊Q8#386611yescharacteristic, complemented
102C2×C4⋊C4—372no—
103C2×C4⋊C4—741no—
104C2×C4⋊C4—741no—
105C2×C42—371no—
106C2×C42—741no—
107C4⋊C8—741no—
108C4⋊C8—741no—
109#103—748no—
110#95—741no—
111C2×Q8—372no—
112C2×Q8—742no—
113C2×Q8—744no—
114C2×Q8—744no—
115C2×Q8C2×#386612yes—
116C22×C4—371no—
117C22×C4—371no—
118C22×C4—371no—
119C22×C4—742no—
120C22×C4—742no—
121C2×C8—744no—
122C2×C8—742no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—374no—
126C4⋊C4—742no—
127C4⋊C4—742no—
128C4⋊C4—742no—
129C4⋊C4—741no—
130C4⋊C4—741no—
131C42—371no—
132C42—371no—
133C42—371no—
134C42—1482no—
135C42C2×#386611yescharacteristic
136C23—371no—
137Q8—24no—
138Q8—744no—
139Q8—1482no—
140Q8—1482no—
141C2×C4—22no—
142C2×C4—371no—
143C2×C4—371no—
144C2×C4—372no—
145C2×C4—372no—
146C2×C4—372no—
147C2×C4—372no—
148C2×C4—371no—
149C2×C4—742no—
150C2×C4—744no—
151C2×C4—742no—
152C2×C4—1484no—
153C2×C4—1482no—
154C2×C4—1482no—
155C2×C4C22⋊#386611yescharacteristic
156C2×C4C22⋊#386611yescharacteristic
157C2×C4C22×#386611yescharacteristic
158C8—1482no—
159C22—372no—
160C22—371no—
161C22—371no—
162C22—372no—
163C22C2×C22⋊#386611yescharacteristic
164C4—21no—
165C4—42no—
166C4—371no—
167C4—371no—
168C4—372no—
169C4—741no—
170C4—1484no—
171C4—1482no—
172C4#1192459912yescomplemented
173C4D4×#386612yes—
174C2—372no—
175C2—372no—
176C2#1455848511yescharacteristic
177C2C2×#1192459911yescharacteristic
178C2#1455852611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC4⋊Q8×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC22×D37C2×D4
cosocleC2×C4×D37C23
hypercenterC4⋊Q8#3866
hypocenterC37#1981
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
13. #11924536C4semidirect
16. #11924534C4semidirect
20. C4⋊Q8×C37C4semidirect
77. C4×C37#103semidirect
81. Dic37#103semidirect
94. C37#1981semidirect
101. C4⋊Q8#3866semidirect
172. C4#11924599semidirect

Maximal subgroups

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

subgroupindex
D37⋊(C4⋊C8)2
C2×#119245992
C4×C4⋊#38662
C4⋊Q8×D372
#198137