Finite Group Databasebeta

← #18010785

Subgroups — #18010785

Order 4736.

324 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 74 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#14558475C211yesmaximal, characteristic
2C4×C22⋊#3866C211yesmaximal, characteristic
3#14558411C214yesmaximal
4C2×#11924512C211yesmaximal, characteristic
5C2×C4⋊#3866—21no—
6C2×C22⋊#3866C2212yes—
7C2×C22⋊#3866C2212yes—
8C2×C4×#3866—21no—
9(C2×#3866)⋊C4—21no—
10(C2×#3866)⋊C4—21no—
11C22×C4×D37C2211yescharacteristic
12#11924512—21no—
13#11924512—21no—
14#11924512—21no—
15#11924512—21no—
16C2×C4⋊Dic37C411yescharacteristic, complemented
17C2×#10596936C412yescomplemented
18C2×#10596938C2212yes—
19C22×Q8×C37C411yescharacteristic, complemented
20C23×D37C2311yescharacteristic
21C22×#3866—22no—
22C22×#3866—22no—
23C2×Q8×C37—21no—
24C2×Q8×C37—21no—
25C2×Q8×C37—42no—
26C22×C4×C37C2×C412yes—
27C22×C4×C37C2×C411yescharacteristic
28C22×Dic37C2×C412yes—
29C22×Dic37C2×C411yescharacteristic
30C2×C4×D37—42no—
31C2×C4×D37D411yescharacteristic
32C2×C4×D37D411yescharacteristic
33C2×C4×D37D411yescharacteristic
34C2×C4×D37D411yescharacteristic
35C22⋊#3866—22no—
36C22⋊#3866—24no—
37C22⋊#3866Q814yescomplemented
38C4⋊#3866—42no—
39C4×#3866—42no—
40#10596938—22no—
41#10596938—22no—
42C4⋊Dic37—21no—
43C4⋊Dic37—21no—
44#10596936—22no—
45#10596936—22no—
46C23×C37C22×C411yescharacteristic
47C22×D37—41no—
48C22×D37—41no—
49C22×D37C2×D411yescharacteristic
50C22×D37C2×D411yescharacteristic
51C22×D37C2×Q812yes—
52C22×D37#4112yes—
53C2×#3866—24no—
54C2×#3866—42no—
55C2×#3866—42no—
56C2×#3866—42no—
57C2×#3866—42no—
58C2×#3866—42no—
59Q8×C37—42no—
60Q8×C37—42no—
61C2×C4×C37—22no—
62C2×C4×C37—22no—
63C2×C4×C37—42no—
64C2×C4×C37C22⋊C411yescharacteristic
65C2×C4×C37C22⋊C411yescharacteristic
66C2×Dic37—22no—
67C2×Dic37—41no—
68C2×Dic37—42no—
69C2×Dic37C22⋊C411yescharacteristic
70C2×Dic37C22⋊C411yescharacteristic
71C4×D37—22no—
72C4×D37—22no—
73C4×D37—41no—
74C4×D37—41no—
75C22×C37—21no—
76C22×C37—21no—
77C22×C37C2×C22⋊C411yescharacteristic
78C22×C37C4×Q812yes—
79C2×D37—21no—
80C2×D37—21no—
81C2×D37—21no—
82C2×D37—21no—
83C2×D37—42no—
84C2×D37—42no—
85C2×D37C22⋊Q812yes—
86C2×D37#12411yescharacteristic
87C2×D37C4⋊Q811yescharacteristic
88#3866—44no—
89#3866—82no—
90C4×C37—21no—
91C4×C37—42no—
92C4×C37#9912yes—
93Dic37—21no—
94Dic37—21no—
95Dic37—42no—
96#1996—371nomaximal, Sylow
97C2×C37—22no—
98C2×C37#39111yescharacteristic
99C2×C37C2×#9911yescharacteristic
100C2×C37#41011yescharacteristic
101D37—22no—
102D37—21no—
103D37—21no—
104C2×C22⋊Q8—371no—
105#380—371no—
106C4×C22⋊C4—371no—
107#342—374no—
108C37#199611yescharacteristic, complemented, Sylow
109C22×Q8#386611yescharacteristic, complemented
110C23×C4—371no—
111C22⋊Q8—741no—
112C22⋊Q8—741no—
113C22⋊Q8—741no—
114C22⋊Q8—741no—
115C2×C4⋊C4—372no—
116C2×C4⋊C4—371no—
117C2×C4⋊C4—741no—
118C2×C22⋊C4—372no—
119C2×C22⋊C4—372no—
120C2×C22⋊C4—372no—
121C2×C42—741no—
122#95—741no—
123#95—741no—
124C24—371no—
125C2×Q8—21no—
126C2×Q8—21no—
127C2×Q8—42no—
128C22×C4—371no—
129C22×C4—371no—
130C22×C4—371no—
131C22×C4—371no—
132C22×C4—371no—
133C22×C4—372no—
134C22×C4—742no—
135C22×C4—742no—
136C22×C4—1482no—
137C22×C4C2×#386612yes—
138C22×C4C2×#386611yescharacteristic
139C4⋊C4—742no—
140C4⋊C4—742no—
141C4⋊C4—741no—
142C4⋊C4—741no—
143C4⋊C4—1482no—
144C22⋊C4—374no—
145C22⋊C4—742no—
146C22⋊C4—742no—
147C22⋊C4—742no—
148C22⋊C4—744no—
149C42—1482no—
150C23—371no—
151C23—371no—
152C23—372no—
153C23—372no—
154C23—1481no—
155C23—1481no—
156C23C22×#386611yescharacteristic
157Q8—42no—
158Q8—42no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—42no—
162C2×C4—371no—
163C2×C4—371no—
164C2×C4—742no—
165C2×C4—742no—
166C2×C4—744no—
167C2×C4—742no—
168C2×C4—1481no—
169C2×C4—1481no—
170C2×C4—1482no—
171C2×C4—1482no—
172C2×C4—1482no—
173C2×C4—1481no—
174C2×C4—1482no—
175C2×C4—1482no—
176C2×C4—1482no—
177C2×C4C22⋊#386611yescharacteristic
178C2×C4C22⋊#386611yescharacteristic
179C22—21no—
180C22—21no—
181C22—372no—
182C22—371no—
183C22—371no—
184C22—741no—
185C22—741no—
186C22—741no—
187C22—741no—
188C22—1482no—
189C22—1482no—
190C22C2×C22⋊#386611yescharacteristic
191C22Q8×#386612yes—
192C4—21no—
193C4—42no—
194C4—2962no—
195C4—741no—
196C4—741no—
197C4—1484no—
198C4—1482no—
199C4#1192459412yes—
200C2—22no—
201C2—741no—
202C2—742no—
203C2—741no—
204C2(C2×#3866)⋊Q811yescharacteristic
205C2C2×#1192459411yescharacteristic
206C2#1455851411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC22×Q8×C37C4
socleC22×C37C2×C22⋊C4
prime radical, cosocleC23×D37C23
hypercenterC22×Q8#3866
hypocenterC37#1996
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
16. C2×C4⋊Dic37C4semidirect
17. C2×#10596936C4semidirect
19. C22×Q8×C37C4semidirect
37. C22⋊#3866Q8semidirect
108. C37#1996semidirect
109. C22×Q8#3866semidirect

Maximal subgroups

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

subgroupindex
#145584752
C4×C22⋊#38662
#145584112
C2×#119245122
#199637