Finite Group Databasebeta

← #18010499

Subgroups — #18010499

Order 4736.

344 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 84 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#14558406C214yesmaximal, complemented
4C2×C4⋊C4×D37C211yesmaximal, characteristic
5C2×D37⋊C8C2212yes—
6C2×C4⋊#3866C2212yes—
7C2×C22⋊#3866—21no—
8#11924593—21no—
9C22⋊#64438—21no—
10(C2×#3866)⋊C4—21no—
11C22×C4×D37—21no—
12C22×C4×D37C2211yescharacteristic
13C2×C4⋊Dic37C411yescharacteristic, complemented
14C2×#10596936—21no—
15C4⋊C4×D37—21no—
16C4⋊C4×D37—21no—
17C4⋊C4×D37C412yescomplemented
18C4⋊C4×D37C2212yes—
19C2×C4⋊C4×C37C411yescharacteristic, complemented
20C23×D37D411yescharacteristic
21C22×#3866—22no—
22C22×C4×C37—21no—
23C22×C4×C37C2×C411yescharacteristic
24C22×Dic37—21no—
25C22×Dic37D411yescharacteristic
26C2×C4×D37—24no—
27C2×C4×D37—22no—
28C2×C4×D37—22no—
29C2×C4×D37—42no—
30C2×C4×D37—42no—
31C2×C4×D37C2×C411yescharacteristic
32C2×C4×D37D411yescharacteristic
33C2×C4×D37D411yescharacteristic
34C2×C4×D37C2311yescharacteristic
35C22⋊#3866—42no—
36C2×#64438—22no—
37C4⋊#3866—24no—
38D37⋊C8—24no—
39C4⋊C4×C37—21no—
40C4⋊C4×C37C2×C412yes—
41C4⋊Dic37—21no—
42C4⋊Dic37C2×C412yes—
43#10596936—22no—
44#10596936—22no—
45C23×C37C22⋊C411yescharacteristic
46C22×D37—22no—
47C22×D37—22no—
48C22×D37C22⋊C411yescharacteristic
49C22×D37D812yes—
50C22×D37SD1612yes—
51C22×D37C2×D411yescharacteristic
52C2×#3866—42no—
53C2×#3866—42no—
54C2×#3866—42no—
55C2×C4×C37—22no—
56C2×C4×C37—22no—
57C2×C4×C37—42no—
58C2×C4×C37C22⋊C411yescharacteristic
59C2×C4×C37C22×C411yescharacteristic
60C2×Dic37—22no—
61C2×Dic37—22no—
62C2×Dic37—42no—
63C2×Dic37C22⋊C411yescharacteristic
64C2×Dic37C2×D411yescharacteristic
65C4×D37—22no—
66C4×D37—22no—
67C4×D37—22no—
68C4×D37—44no—
69C4×D37—42no—
70C4×D37—42no—
71C4×D37#4114yes—
72#64438—42no—
73C22×C37—21no—
74C22×C37—21no—
75C22×C37#10212yes—
76C22×C37C2×C22⋊C411yescharacteristic
77C2×D37—21no—
78C2×D37—21no—
79C2×D37—24no—
80C2×D37—24no—
81C2×D37#10212yes—
82C2×D37#12312yes—
83C2×D37C2×D811yescharacteristic
84C2×D37C2×SD1611yescharacteristic
85C2×D37#13712yes—
86#3866—82no—
87C4×C37—21no—
88C4×C37—42no—
89C4×C37#11712yes—
90Dic37—21no—
91Dic37—42no—
92Dic37#12312yes—
93#1823—371nomaximal, Sylow
94C2×C37—22no—
95C2×C37#38111yescharacteristic
96C2×C37C2×#10211yescharacteristic
97C2×C37#41911yescharacteristic
98D37—22no—
99D37#48012yes—
100D37#48312yes—
101C22×C4⋊C4—371no—
102C2×C22⋊C8—371no—
103#380—371no—
104#340—374no—
105C37#182311yescharacteristic, complemented, Sylow
106C23×C4—371no—
107C23×C4—741no—
108C22×C8—372no—
109C2×C4⋊C4—371no—
110C2×C4⋊C4—372no—
111C2×C4⋊C4—372no—
112C2×C4⋊C4—372no—
113C2×C4⋊C4—741no—
114C2×C4⋊C4—741no—
115C2×C4⋊C4—741no—
116C2×C4⋊C4#386611yescharacteristic, complemented
117C2×C22⋊C4—741no—
118C22⋊C8—741no—
119C22⋊C8—741no—
120#95—741no—
121C24—371no—
122C22×C4—21no—
123C22×C4—371no—
124C22×C4—371no—
125C22×C4—371no—
126C22×C4—371no—
127C22×C4—371no—
128C22×C4—744no—
129C22×C4—742no—
130C22×C4—742no—
131C22×C4—741no—
132C22×C4—742no—
133C22×C4—1482no—
134C22×C4—1482no—
135C22×C4C2×#386611yescharacteristic
136C2×C8—744no—
137C2×C8—742no—
138C4⋊C4—21no—
139C4⋊C4—372no—
140C4⋊C4—742no—
141C4⋊C4—742no—
142C4⋊C4—744no—
143C4⋊C4—741no—
144C4⋊C4C2×#386612yes—
145C22⋊C4—1482no—
146C23—371no—
147C23—372no—
148C23—372no—
149C23—371no—
150C23—742no—
151C23—742no—
152C23C22⋊#386611yescharacteristic
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—42no—
156C2×C4—371no—
157C2×C4—374no—
158C2×C4—371no—
159C2×C4—742no—
160C2×C4—742no—
161C2×C4—742no—
162C2×C4—742no—
163C2×C4—742no—
164C2×C4—1482no—
165C2×C4—1482no—
166C2×C4—1484no—
167C2×C4—1482no—
168C2×C4—1482no—
169C2×C4—1482no—
170C2×C4—1482no—
171C2×C4C22⋊#386611yescharacteristic
172C2×C4C22×#386611yescharacteristic
173C8—1482no—
174C22—21no—
175C22—21no—
176C22—372no—
177C22—371no—
178C22—371no—
179C22—372no—
180C22—372no—
181C22—744no—
182C22—744no—
183C22—741no—
184C22—741no—
185C22#1192459812yes—
186C22C2×C22⋊#386611yescharacteristic
187C4—21no—
188C4—42no—
189C4—372no—
190C4—2962no—
191C4—741no—
192C4—1482no—
193C4#1192461512yes—
194C2—22no—
195C2—372no—
196C2—372no—
197C2—742no—
198C2#1455847611yescharacteristic
199C2C2×#1192459811yescharacteristic
200C2#1455852611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×C4⋊C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC23×D37D4
cosocleC2×C4×D37C23
hypercenterC2×C4⋊C4#3866
hypocenterC37#1823
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #14558406C2semidirect
13. C2×C4⋊Dic37C4semidirect
17. C4⋊C4×D37C4semidirect
19. C2×C4⋊C4×C37C4semidirect
105. C37#1823semidirect
116. C2×C4⋊C4#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
#145584062
C2×C4⋊C4×D372
#182337