Finite Group Databasebeta

← #18010113

Subgroups — #18010113

Order 4736.

216 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 68 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#14558538C211yesmaximal, characteristic
2D37⋊(C4⋊C8)C211yesmaximal, characteristic
3#14558393C212yesmaximal, complemented
4#14558392C212yesmaximal, complemented
5#14558087C211yesmaximal, characteristic
6C2×#10596953—21no—
7C2×D37⋊C8—21no—
8#11924603—21no—
9#11924603C2212yes—
10#11924603C2212yes—
11C4⋊#64438—21no—
12#11924535C2211yescharacteristic
13#11924534C2211yescharacteristic
14#11924526—21no—
15#11924516C411yescharacteristic
16#11924514—21no—
17#11924512C411yescharacteristic
18C4×Dic74—21no—
19C4×Dic74C411yescharacteristic
20#11924493—21no—
21C42×D37C2211yescharacteristic
22C4×Q8×C37C411yescharacteristic
23C2×Q8×C37C2×C411yescharacteristic
24C2×C4×D37C2×C411yescharacteristic
25C2×C4×D37D411yescharacteristic
26C2×C4×D37D411yescharacteristic
27C2×Dic74—21no—
28C2×Dic74C2×C411yescharacteristic
29C2×#64438—22no—
30C2×#64438—22no—
31#10596953—42no—
32D37⋊C8—42no—
33C4⋊C4×C37—21no—
34C4⋊C4×C37C2×C411yescharacteristic
35C42×C37—21no—
36C42×C37C2×C411yescharacteristic
37#10596938—21no—
38#10596938—21no—
39C4⋊Dic37—21no—
40C4⋊Dic37C2×C411yescharacteristic
41#10596936—21no—
42#10596936—21no—
43#10596936—21no—
44#10596936—21no—
45#10596936—21no—
46C4×Dic37—21no—
47C4×Dic37D411yescharacteristic
48C4×Dic37D411yescharacteristic
49C4×Dic37C2311yescharacteristic
50C22×D37C22⋊C411yescharacteristic
51Q8×C37—41no—
52C2×C4×C37—21no—
53C2×C4×C37—21no—
54C2×C4×C37C22⋊C411yescharacteristic
55C2×C4×C37C22⋊C411yescharacteristic
56C2×C4×C37C22×C411yescharacteristic
57C2×Dic37—21no—
58C2×Dic37—21no—
59C2×Dic37C22⋊C411yescharacteristic
60C2×Dic37C2×D411yescharacteristic
61C2×Dic37C2×D411yescharacteristic
62C4×D37—21no—
63C4×D37—21no—
64C4×D37—41no—
65C4×D37SD1612yes—
66C4×D37Q1612yes—
67Dic74—41no—
68Dic74—41no—
69Dic74—41no—
70#64438—42no—
71#64438—42no—
72C22×C37C2×C22⋊C411yescharacteristic
73C2×D37—21no—
74C2×D37—21no—
75C2×D37#10312yes—
76C4×C37—21no—
77C4×C37—21no—
78C4×C37—41no—
79C4×C37—41no—
80C4×C37#10312yes—
81Dic37—21no—
82Dic37—41no—
83Dic37—41no—
84Dic37C2×SD1611yescharacteristic
85Dic37C2×Q1611yescharacteristic
86Dic37AGL(1,ℤ/8)11yescharacteristic
87Dic37#13711yescharacteristic
88#1550—371nomaximal, Sylow
89C2×C37#41311yescharacteristic
90C2×C37C2×#10311yescharacteristic
91C2×C37#41711yescharacteristic
92D37—22no—
93#533—371no—
94#423—371no—
95C2×C4⋊C8—371no—
96#333—372no—
97#332—372no—
98C37#155011yescharacteristic, complemented, Sylow
99C2×M16—741no—
100C22×C8—741no—
101C4⋊Q8—371no—
102C4⋊Q8—371no—
103#125—741no—
104C22⋊Q8—371no—
105C22⋊Q8—371no—
106C22⋊Q8—741no—
107C4×Q8—371no—
108C4×Q8—741no—
109C4×Q8#386611yescharacteristic
110#117—741no—
111C2×C42—371no—
112C4⋊C8—372no—
113C4⋊C8—372no—
114C4⋊C8—741no—
115C4⋊C8—741no—
116C2×Q8—371no—
117C2×Q8—741no—
118C2×Q8C2×#386611yescharacteristic
119C22×C4—371no—
120C22×C4—371no—
121C22×C4—371no—
122M16—1482no—
123C2×C8—742no—
124C2×C8—742no—
125C2×C8—1482no—
126C4⋊C4—21no—
127C4⋊C4—371no—
128C4⋊C4—741no—
129C4⋊C4—741no—
130C4⋊C4—741no—
131C4⋊C4—741no—
132C4⋊C4—741no—
133C4⋊C4—741no—
134C4⋊C4C2×#386611yescharacteristic
135C22⋊C4—741no—
136C22⋊C4—741no—
137C42—21no—
138C42—371no—
139C42—371no—
140C42—371no—
141C42—741no—
142C42C2×#386611yescharacteristic
143C23—371no—
144Q8—41no—
145Q8—1481no—
146Q8—1481no—
147Q8—1481no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—371no—
151C2×C4—371no—
152C2×C4—372no—
153C2×C4—372no—
154C2×C4—371no—
155C2×C4—741no—
156C2×C4—741no—
157C2×C4—741no—
158C2×C4—741no—
159C2×C4—1481no—
160C2×C4C22⋊#386611yescharacteristic
161C2×C4C22⋊#386611yescharacteristic
162C2×C4C22×#386611yescharacteristic
163C8—1482no—
164C8—1482no—
165C22—372no—
166C22—741no—
167C22—741no—
168C22C2×C22⋊#386611yescharacteristic
169C4—21no—
170C4—21no—
171C4—41no—
172C4—41no—
173C4—371no—
174C4—371no—
175C4—371no—
176C4—371no—
177C4—741no—
178C4—1481no—
179C4—1481no—
180C4#1192459912yes—
181C2—742no—
182C2#1455851911yescharacteristic
183C2C2×#1192459911yescharacteristic
184C2#1455852411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC4×Q8×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC22×D37C22⋊C4
cosocleC4×Dic37C23
hypercenterC4×Q8#3866
hypocenterC37#1550
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
3. #14558393C2semidirect
4. #14558392C2semidirect
98. C37#1550semidirect

Maximal subgroups

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

subgroupindex
#145585382
D37⋊(C4⋊C8)2
#145583932
#145583922
#145580872
#155037