Finite Group Databasebeta

← #18010500

Subgroups — #18010500

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—44no—
30C2×C4×D37C2×C411yescharacteristic
31C2×C4×D37D411yescharacteristic
32C2×C4×D37D411yescharacteristic
33C2×C4×D37C2311yescharacteristic
34C22⋊#3866—42no—
35C2×#64438—22no—
36C4⋊#3866—24no—
37D37⋊C8—24no—
38C4⋊C4×C37—21no—
39C4⋊C4×C37C2×C412yes—
40C4⋊Dic37—21no—
41C4⋊Dic37C2×C412yes—
42#10596936—22no—
43#10596936—22no—
44C23×C37C22⋊C411yescharacteristic
45C22×D37—22no—
46C22×D37—22no—
47C22×D37C22⋊C411yescharacteristic
48C22×D37SD1612yes—
49C22×D37Q1612yes—
50C22×D37C2×D411yescharacteristic
51C2×#3866—42no—
52C2×#3866—42no—
53C2×#3866—42no—
54C2×C4×C37—22no—
55C2×C4×C37—22no—
56C2×C4×C37—42no—
57C2×C4×C37C22⋊C411yescharacteristic
58C2×C4×C37C22×C411yescharacteristic
59C2×Dic37—22no—
60C2×Dic37—22no—
61C2×Dic37—42no—
62C2×Dic37C22⋊C411yescharacteristic
63C2×Dic37C2×D411yescharacteristic
64C4×D37—22no—
65C4×D37—22no—
66C4×D37—22no—
67C4×D37—44no—
68C4×D37—44no—
69C4×D37#4114yes—
70#64438—42no—
71C22×C37—21no—
72C22×C37—21no—
73C22×C37#10312yes—
74C22×C37C2×C22⋊C411yescharacteristic
75C2×D37—21no—
76C2×D37—21no—
77C2×D37—24no—
78C2×D37—24no—
79C2×D37#10312yes—
80C2×D37#12312yes—
81C2×D37C2×SD1611yescharacteristic
82C2×D37C2×Q1611yescharacteristic
83C2×D37AGL(1,ℤ/8)12yes—
84#3866—82no—
85C4×C37—21no—
86C4×C37—42no—
87C4×C37#11712yes—
88Dic37—21no—
89Dic37—42no—
90Dic37#12312yes—
91#1824—371nomaximal, Sylow
92C2×C37—22no—
93C2×C37#38111yescharacteristic
94C2×C37C2×#10311yescharacteristic
95C2×C37#41811yescharacteristic
96D37—22no—
97D37#48112yes—
98D37#48412yes—
99C22×C4⋊C4—371no—
100C2×C22⋊C8—371no—
101#380—371no—
102#340—374no—
103C37#182411yescharacteristic, complemented, Sylow
104C23×C4—371no—
105C23×C4—741no—
106C22×C8—372no—
107C2×C4⋊C4—371no—
108C2×C4⋊C4—372no—
109C2×C4⋊C4—372no—
110C2×C4⋊C4—372no—
111C2×C4⋊C4—741no—
112C2×C4⋊C4—741no—
113C2×C4⋊C4—741no—
114C2×C4⋊C4#386611yescharacteristic, complemented
115C2×C22⋊C4—741no—
116C22⋊C8—741no—
117C22⋊C8—741no—
118#95—741no—
119C24—371no—
120C22×C4—21no—
121C22×C4—371no—
122C22×C4—371no—
123C22×C4—371no—
124C22×C4—371no—
125C22×C4—371no—
126C22×C4—744no—
127C22×C4—742no—
128C22×C4—742no—
129C22×C4—741no—
130C22×C4—742no—
131C22×C4—1484no—
132C22×C4C2×#386611yescharacteristic
133C2×C8—744no—
134C2×C8—742no—
135C4⋊C4—21no—
136C4⋊C4—372no—
137C4⋊C4—742no—
138C4⋊C4—742no—
139C4⋊C4—744no—
140C4⋊C4—741no—
141C4⋊C4C2×#386612yes—
142C22⋊C4—1482no—
143C23—371no—
144C23—372no—
145C23—372no—
146C23—371no—
147C23—742no—
148C23—742no—
149C23C22⋊#386611yescharacteristic
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—42no—
153C2×C4—371no—
154C2×C4—374no—
155C2×C4—371no—
156C2×C4—742no—
157C2×C4—742no—
158C2×C4—742no—
159C2×C4—742no—
160C2×C4—742no—
161C2×C4—1484no—
162C2×C4—1484no—
163C2×C4—1482no—
164C2×C4—1482no—
165C2×C4—1482no—
166C2×C4—1482no—
167C2×C4C22⋊#386611yescharacteristic
168C2×C4C22×#386611yescharacteristic
169C8—1482no—
170C22—21no—
171C22—21no—
172C22—372no—
173C22—371no—
174C22—371no—
175C22—372no—
176C22—372no—
177C22—744no—
178C22—744no—
179C22—741no—
180C22—741no—
181C22#1192459912yes—
182C22C2×C22⋊#386611yescharacteristic
183C4—21no—
184C4—42no—
185C4—372no—
186C4—2962no—
187C4—741no—
188C4—1482no—
189C4#1192461512yes—
190C2—22no—
191C2—372no—
192C2—372no—
193C2—742no—
194C2#1455847611yescharacteristic
195C2C2×#1192459911yescharacteristic
196C2#1455852511yescharacteristic
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#1824
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
103. C37#1824semidirect
114. 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
#182437