Finite Group Databasebeta

← #18010036

Subgroups — #18010036

Order 4736.

288 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 70 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⋊(C22⋊C8)C211yesmaximal, characteristic
2#14558475C211yesmaximal, characteristic
3#14558387C214yesmaximal, complemented
4C2×#11924512C211yesmaximal, characteristic
5C2×D37⋊C8—21no—
6C2×C4⋊#3866—21no—
7C2×C22⋊#3866—21no—
8#11924593C2212yes—
9C22⋊#64438—21no—
10(C2×#3866)⋊C4C2212yes—
11C22×C4×D37C2211yescharacteristic
12#11924512—21no—
13#11924512—21no—
14#11924512C412yescomplemented
15#11924512C2212yes—
16C2×C4⋊Dic37C411yescharacteristic, complemented
17C2×#10596936—21no—
18C2×#10596938—21no—
19C22×Q8×C37C411yescharacteristic, complemented
20C23×D37D411yescharacteristic
21C22×#3866—22no—
22C2×Q8×C37—21no—
23C2×Q8×C37—42no—
24C2×Q8×C37C2×C412yes—
25C22×C4×C37—21no—
26C22×C4×C37C2×C411yescharacteristic
27C22×Dic37—21no—
28C22×Dic37D411yescharacteristic
29C2×C4×D37—42no—
30C2×C4×D37C2×C411yescharacteristic
31C2×C4×D37D411yescharacteristic
32C2×C4×D37D411yescharacteristic
33C2×C4×D37C2311yescharacteristic
34C22⋊#3866—42no—
35C2×#64438—22no—
36C4⋊#3866—42no—
37D37⋊C8—42no—
38#10596938—22no—
39#10596938—22no—
40C4⋊Dic37—21no—
41C4⋊Dic37C2×C412yes—
42#10596936—22no—
43#10596936—22no—
44C23×C37C22⋊C411yescharacteristic
45C22×D37—41no—
46C22×D37—41no—
47C22×D37C22⋊C411yescharacteristic
48C22×D37SD1612yes—
49C22×D37Q1612yes—
50C22×D37C2×D411yescharacteristic
51C2×#3866—42no—
52C2×#3866—42no—
53C2×#3866—42no—
54Q8×C37—42no—
55Q8×C37—42no—
56C2×C4×C37—22no—
57C2×C4×C37—22no—
58C2×C4×C37—42no—
59C2×C4×C37C22⋊C411yescharacteristic
60C2×C4×C37C22×C411yescharacteristic
61C2×Dic37—22no—
62C2×Dic37—41no—
63C2×Dic37—42no—
64C2×Dic37C22⋊C411yescharacteristic
65C2×Dic37C2×D411yescharacteristic
66C4×D37—22no—
67C4×D37—22no—
68C4×D37—41no—
69C4×D37—41no—
70#64438—42no—
71C22×C37—21no—
72C22×C37—21no—
73C22×C37#10312yes—
74C22×C37C2×C22⋊C411yescharacteristic
75C2×D37—21no—
76C2×D37—21no—
77C2×D37—21no—
78C2×D37—21no—
79C2×D37—42no—
80C2×D37—42no—
81C2×D37#10312yes—
82C2×D37C2×SD1611yescharacteristic
83C2×D37C2×Q1611yescharacteristic
84#3866—82no—
85C4×C37—21no—
86C4×C37—42no—
87C4×C37#9912yes—
88Dic37—21no—
89Dic37—21no—
90Dic37—42no—
91#1520—371nomaximal, Sylow
92C2×C37—22no—
93C2×C37C2×#9911yescharacteristic
94C2×C37C2×#10311yescharacteristic
95C2×C37#42111yescharacteristic
96D37—21no—
97D37—22no—
98D37—21no—
99C2×C22⋊Q8—371no—
100C2×C22⋊C8—371no—
101#380—371no—
102#328—374no—
103C37#152011yescharacteristic, complemented, Sylow
104C22×Q8#386611yescharacteristic, complemented
105C23×C4—371no—
106C22×C8—741no—
107C22⋊Q8—372no—
108C22⋊Q8—372no—
109C22⋊Q8—741no—
110C22⋊Q8—741no—
111C2×C4⋊C4—371no—
112C2×C4⋊C4—741no—
113C2×C4⋊C4—741no—
114C2×C22⋊C4—741no—
115C2×C22⋊C4—741no—
116C22⋊C8—372no—
117C22⋊C8—741no—
118#95—372no—
119C24—371no—
120C2×Q8—21no—
121C2×Q8—42no—
122C2×Q8C2×#386612yes—
123C22×C4—21no—
124C22×C4—371no—
125C22×C4—371no—
126C22×C4—371no—
127C22×C4—371no—
128C22×C4—371no—
129C22×C4—741no—
130C22×C4—742no—
131C22×C4—1482no—
132C22×C4C2×#386611yescharacteristic
133C2×C8—742no—
134C2×C8—1482no—
135C4⋊C4—372no—
136C4⋊C4—742no—
137C4⋊C4—742no—
138C4⋊C4—741no—
139C4⋊C4—1482no—
140C22⋊C4—742no—
141C22⋊C4—742no—
142C22⋊C4—1482no—
143C23—371no—
144C23—371no—
145C23—372no—
146C23—372no—
147C23—1481no—
148C23—1481no—
149C23C22⋊#386611yescharacteristic
150Q8—42no—
151Q8—42no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—42no—
155C2×C4—371no—
156C2×C4—371no—
157C2×C4—742no—
158C2×C4—742no—
159C2×C4—742no—
160C2×C4—1481no—
161C2×C4—1481no—
162C2×C4—1482no—
163C2×C4—1482no—
164C2×C4—1482no—
165C2×C4—1481no—
166C2×C4—1482no—
167C2×C4C22⋊#386611yescharacteristic
168C2×C4C22×#386611yescharacteristic
169C8—1482no—
170C22—21no—
171C22—21no—
172C22—371no—
173C22—372no—
174C22—371no—
175C22—741no—
176C22—741no—
177C22—741no—
178C22—741no—
179C22—1482no—
180C22—1482no—
181C22#1192459912yes—
182C22C2×C22⋊#386611yescharacteristic
183C4—21no—
184C4—42no—
185C4—2962no—
186C4—741no—
187C4—741no—
188C4—1482no—
189C4#1192459412yes—
190C2—22no—
191C2—741no—
192C2—742no—
193C2—741no—
194C2C2×#1192459411yescharacteristic
195C2C2×#1192459911yescharacteristic
196C2#1455853211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC22×Q8×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC23×D37D4
cosocleC2×C4×D37C23
hypercenterC22×Q8#3866
hypocenterC37#1520
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. #14558387C2semidirect
14. #11924512C4semidirect
16. C2×C4⋊Dic37C4semidirect
19. C22×Q8×C37C4semidirect
103. C37#1520semidirect
104. C22×Q8#3866semidirect

Maximal subgroups

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

subgroupindex
D37⋊(C22⋊C8)2
#145584752
#145583872
C2×#119245122
#152037