Finite Group Databasebeta

← #17997314

Subgroups — #17997314

Order 4736.

516 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 197 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
1C2×#11924534C211yesmaximal, characteristic
2C2×Q8×Dic37C211yesmaximal, characteristic
3C2×#11924501C211yesmaximal, characteristic
4#14557439C211yesmaximal, characteristic
5#14557420C214yesmaximal
6#14557415C214yesmaximal
7#14557398C211yesmaximal, characteristic
8#14557379C211yesmaximal, characteristic
9C37×#391C211yesmaximal, characteristic
10C22×Dic74C2211yescharacteristic
11#11924534C418yescomplemented
12Q8×Dic37—24no—
13#11924501—24no—
14C2×C4⋊Dic37C2211yescharacteristic
15C2×C4⋊Dic37C2212yes—
16C2×#10596936C2212yes—
17C2×#10596936C2214yes—
18C2×C4×Dic37C2212yes—
19C2×C4×Dic37C2212yes—
20C2×C4×Dic37C2211yescharacteristic
21C2×C4×Dic37C2211yescharacteristic
22#11924443C2212yes—
23#11924443C2212yes—
24#11924443C2214yes—
25#11924443C2214yes—
26C22×Q8×C37C2211yescharacteristic
27C2×C4⋊C4×C37C2211yescharacteristic
28C2×C42×C37C2211yescharacteristic
29#95×C37C2214yes—
30C2×Q8×C37—22no—
31C2×Q8×C37—22no—
32C2×Q8×C37C2×C414yes—
33C22×C4×C37C2312yes—
34C22×C4×C37C2312yes—
35C22×C4×C37C2312yes—
36C22×C4×C37C2311yescharacteristic
37C22×Dic37C2312yes—
38C22×Dic37C2312yes—
39C22×Dic37C2312yes—
40C22×Dic37C2311yescharacteristic
41C22×Dic37C2311yescharacteristic
42C2×Dic74—22no—
43C2×Dic74—22no—
44C2×Dic74C2×C414yes—
45C4⋊C4×C37—22no—
46C42×C37—22no—
47C4⋊Dic37—22no—
48C4⋊Dic37—24no—
49#10596936—24no—
50#10596936C2×C4116yes—
51C4×Dic37—24no—
52C4×Dic37—24no—
53C4×Dic37C2×C414yes—
54C4×Dic37D414yes—
55C23×C37C2411yescharacteristic
56Q8×C37—28no—
57C2×C4×C37—22no—
58C2×C4×C37—22no—
59C2×C4×C37—22no—
60C2×C4×C37—22no—
61C2×C4×C37—24no—
62C2×C4×C37—22no—
63C2×C4×C37—22no—
64C2×C4×C37C22×C414yes—
65C2×C4×C37C22×C412yes—
66C2×C4×C37C2×D412yes—
67C2×C4×C37#4112yes—
68C2×Dic37—22no—
69C2×Dic37—22no—
70C2×Dic37—22no—
71C2×Dic37—22no—
72C2×Dic37—22no—
73C2×Dic37—22no—
74C2×Dic37—22no—
75C2×Dic37—24no—
76C2×Dic37C22×C414yes—
77C2×Dic37C22×C414yes—
78C2×Dic37C2×D412yes—
79C2×Dic37C2×D412yes—
80Dic74—28no—
81C22×C37C23×C411yescharacteristic
82C22×C37C22×D411yescharacteristic
83C22×C37C2×#4111yescharacteristic
84C22×C372−1+412yes—
85C22×C372−1+412yes—
86C4×C37—24no—
87C4×C37—42no—
88C4×C37—42no—
89C4×C37C4×D414yes—
90Dic37—24no—
91Dic37—24no—
92Dic37—22no—
93Dic37—22no—
94Dic37—42no—
95#2327—371nomaximal, Sylow
96C2×C37C2×C4×D411yescharacteristic
97C2×C37#51912yes—
98C2×C37#53611yescharacteristic
99C2×C37#53611yescharacteristic
100C2×C37#54112yes—
101C2×C4⋊Q8—371no—
102C2×C4×Q8—371no—
103C2×C4×Q8—371no—
104#391—371no—
105#391D3711yescharacteristic
106#387—374no—
107#387—374no—
108#382—371no—
109#376—371no—
110C37#232711yescharacteristic, complemented, Sylow
111C22×Q8—371no—
112C22×Q8C2×D3711yescharacteristic
113C4⋊Q8—378no—
114C4×Q8—744no—
115C4×Q8—744no—
116C2×C4⋊C4—374no—
117C2×C4⋊C4—372no—
118C2×C4⋊C4—371no—
119C2×C4⋊C4—372no—
120C2×C4⋊C4C2×D3711yescharacteristic
121C2×C42—371no—
122C2×C42—371no—
123C2×C42—372no—
124C2×C42—372no—
125C2×C42C2×D3711yescharacteristic
126#95—372no—
127#95—372no—
128#95—374no—
129#95—374no—
130#95C2×D3714yes—
131C2×Q8—22no—
132C2×Q8—22no—
133C2×Q8—374no—
134C2×Q8—742no—
135C2×Q8—742no—
136C2×Q8C4×D3714yes—
137C22×C4—372no—
138C22×C4—371no—
139C22×C4—371no—
140C22×C4—372no—
141C22×C4—372no—
142C22×C4C22×D3712yes—
143C22×C4C22×D3712yes—
144C22×C4C22×D3712yes—
145C22×C4C22×D3711yescharacteristic
146C4⋊C4—22no—
147C4⋊C4—3716no—
148C4⋊C4—744no—
149C4⋊C4—744no—
150C4⋊C4—742no—
151C42—22no—
152C42—374no—
153C42—374no—
154C42—744no—
155C42—744no—
156C23C23×D3711yescharacteristic
157Q8—28no—
158Q8—748no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—24no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—374no—
167C2×C4—374no—
168C2×C4—372no—
169C2×C4—372no—
170C2×C4—742no—
171C2×C4—742no—
172C2×C4—742no—
173C2×C4—742no—
174C2×C4—742no—
175C2×C4—742no—
176C2×C4—742no—
177C2×C4—744no—
178C2×C4C2×C4×D3714yes—
179C2×C4C2×C4×D3712yes—
180C2×C4D4×D3712yes—
181C2×C4#1059696412yes—
182C22C22×C4×D3711yescharacteristic
183C22C2×D4×D3711yescharacteristic
184C22C2×#1059696411yescharacteristic
185C22#1192458312yes—
186C22#1192458412yes—
187C4—24no—
188C4—42no—
189C4—42no—
190C4—744no—
191C4—744no—
192C4—742no—
193C4—742no—
194C4—1482no—
195C4#1192449614yes—
196C2C2×#1192449611yescharacteristic
197C2#1455800912yes—
198C2#1455810311yescharacteristic
199C2#1455810811yescharacteristic
200C2#1455814312yes—
subgroupG/H
center, FrattiniC23C23×D37
commutatorC22×C37C23×C4
FittingC37×#391C2
socle, prime radical, cosocleC23×C37C24
hypercenter#391D37
hypocenterC37#2327
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
11. #11924534C4semidirect
110. C37#2327semidirect

Maximal subgroups

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

subgroupindex
C2×#119245342
C2×Q8×Dic372
C2×#119245012
#145574392
#145574202
#145574152
#145573982
#145573792
C37×#3912
#232737