Finite Group Databasebeta

← #18009989

Subgroups — #18009989

Order 4736.

228 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 58 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#14558556C211yesmaximal, characteristic
2#14558469C211yesmaximal, characteristic
3#14558387C212yesmaximal
4#14558386C212yesmaximal
5#14558087C211yesmaximal, characteristic
6C2×C4×#3866—21no—
7#11924603—21no—
8#11924593C2212yes—
9#11924591—21no—
10(C2×#3866)⋊C4—21no—
11(C2×#3866)⋊C4C2212yes—
12#11924535C411yescharacteristic, complemented
13#11924534C411yescharacteristic, complemented
14#11924526—21no—
15#11924516C2211yescharacteristic
16#11924514—21no—
17#11924512C2211yescharacteristic
18C4×Dic74—21no—
19C4×Dic74C411yescharacteristic, complemented
20#11924493—21no—
21C42×D37C2211yescharacteristic
22C4×Q8×C37C411yescharacteristic, complemented
23C22×#3866—22no—
24C2×Q8×C37C2×C411yescharacteristic
25C2×C4×D37D411yescharacteristic
26C2×C4×D37D411yescharacteristic
27C2×C4×D37C2311yescharacteristic
28C2×Dic74—21no—
29C2×Dic74C2×C411yescharacteristic
30C2×#64438—22no—
31C4×#3866—24no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37C2×C411yescharacteristic
34C42×C37—21no—
35C42×C37C2×C411yescharacteristic
36#10596938—21no—
37#10596938—21no—
38C4⋊Dic37—21no—
39C4⋊Dic37C2×C411yescharacteristic
40#10596936—21no—
41#10596936—21no—
42#10596936—21no—
43#10596936—21no—
44#10596936—21no—
45C4×Dic37—21no—
46C4×Dic37C2×C411yescharacteristic
47C4×Dic37D411yescharacteristic
48C4×Dic37D411yescharacteristic
49C22×D37C2×D411yescharacteristic
50C2×#3866—24no—
51C2×#3866—42no—
52C2×#3866—42no—
53Q8×C37—41no—
54C2×C4×C37—21no—
55C2×C4×C37—21no—
56C2×C4×C37C22⋊C411yescharacteristic
57C2×C4×C37C22⋊C411yescharacteristic
58C2×C4×C37C22×C411yescharacteristic
59C2×Dic37—21no—
60C2×Dic37—21no—
61C2×Dic37C22⋊C411yescharacteristic
62C2×Dic37C22⋊C411yescharacteristic
63C2×Dic37C2×D411yescharacteristic
64C4×D37—22no—
65C4×D37—22no—
66C4×D37—41no—
67Dic74—42no—
68Dic74—41no—
69#64438—42no—
70C22×C37C2×C22⋊C411yescharacteristic
71C2×D37—21no—
72C2×D37—21no—
73C2×D37#13712yes—
74#3866—44no—
75C4×C37—21no—
76C4×C37—21no—
77C4×C37—21no—
78C4×C37—41no—
79C4×C37—41no—
80Dic37—21no—
81Dic37—21no—
82Dic37—41no—
83Dic37—41no—
84Dic37#10412yes—
85#1506—371nomaximal, Sylow
86C2×C37#41011yescharacteristic
87C2×C37#41911yescharacteristic
88C2×C37C2×#10411yescharacteristic
89D37—22no—
90#533—371no—
91#432—371no—
92#376—371no—
93#328—372no—
94#328—372no—
95C37#150611yescharacteristic, complemented, Sylow
96C4⋊Q8—371no—
97C4⋊Q8—371no—
98#125—741no—
99C22⋊Q8—371no—
100C22⋊Q8—371no—
101C22⋊Q8—741no—
102C4×Q8—371no—
103C4×Q8—741no—
104C4×Q8#386611yescharacteristic, complemented
105#117—741no—
106C2×C42—371no—
107C2×C42—741no—
108C4⋊C8—741no—
109C22⋊C8—372no—
110#97—741no—
111#95—372no—
112#95—741no—
113C2×Q8—371no—
114C2×Q8—741no—
115C2×Q8C2×#386611yescharacteristic
116C22×C4—371no—
117C22×C4—371no—
118C22×C4—371no—
119C22×C4—742no—
120C2×C8—742no—
121C4⋊C4—21no—
122C4⋊C4—371no—
123C4⋊C4—741no—
124C4⋊C4—741no—
125C4⋊C4—741no—
126C4⋊C4—741no—
127C4⋊C4—741no—
128C4⋊C4—741no—
129C4⋊C4C2×#386611yescharacteristic
130C22⋊C4—741no—
131C22⋊C4—741no—
132C42—21no—
133C42—371no—
134C42—371no—
135C42—371no—
136C42—744no—
137C42—741no—
138C42C2×#386611yescharacteristic
139C23—371no—
140Q8—41no—
141Q8—1481no—
142Q8—1482no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—371no—
146C2×C4—371no—
147C2×C4—371no—
148C2×C4—742no—
149C2×C4—742no—
150C2×C4—744no—
151C2×C4—741no—
152C2×C4—741no—
153C2×C4—1481no—
154C2×C4—1482no—
155C2×C4—1482no—
156C2×C4C22⋊#386611yescharacteristic
157C2×C4C22⋊#386611yescharacteristic
158C2×C4C22×#386611yescharacteristic
159C8—1482no—
160C22—372no—
161C22—741no—
162C22—741no—
163C22C2×C22⋊#386611yescharacteristic
164C4—21no—
165C4—21no—
166C4—21no—
167C4—41no—
168C4—41no—
169C4—372no—
170C4—741no—
171C4—741no—
172C4—1484no—
173C4—1481no—
174C4—1481no—
175C2—742no—
176C2#1455851211yescharacteristic
177C2#1455852611yescharacteristic
178C2D37⋊#10411yescharacteristic
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#1506
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
12. #11924535C4semidirect
13. #11924534C4semidirect
19. C4×Dic74C4semidirect
22. C4×Q8×C37C4semidirect
95. C37#1506semidirect
104. C4×Q8#3866semidirect

Maximal subgroups

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

subgroupindex
#145585562
#145584692
#145583872
#145583862
#145580872
#150637