Finite Group Databasebeta

← #18010454

Subgroups — #18010454

Order 4736.

312 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 92 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×#11924603C211yesmaximal, characteristic, complemented
2C2×C4⋊#64438C211yesmaximal, characteristic, complemented
3C2×C22⋊#64438C212yesmaximal
4#14558399C212yesmaximal, complemented
5C2×#11924492C211yesmaximal, characteristic
6C22×#64438C2212yes—
7C22×#64438C2212yes—
8#11924603—22no—
9C4⋊#64438—22no—
10C22⋊#64438—24no—
11C23×Dic37C2211yescharacteristic
12#11924492—22no—
13#11924492—22no—
14C2×#10596936C411yescharacteristic
15C2×#10596936C411yescharacteristic
16C2×C22⋊Dic37C411yescharacteristic
17C2×C4×Dic37C2211yescharacteristic
18C2×C4×Dic37C2211yescharacteristic
19C2×C22⋊C4×C37C411yescharacteristic
20C24×C37C2×C411yescharacteristic
21C22×C4×C37C2×C411yescharacteristic
22C22×C4×C37C2×C411yescharacteristic
23C22×Dic37—21no—
24C22×Dic37—21no—
25C22×Dic37—21no—
26C22×Dic37—21no—
27C22×Dic37C2×C411yescharacteristic
28C22×Dic37C2×C411yescharacteristic
29C22×Dic37C2×C411yescharacteristic
30C22×Dic37D412yes—
31C22×Dic37Q812yes—
32C22×Dic37C2311yescharacteristic
33C2×#64438—22no—
34C2×#64438—22no—
35C2×#64438—22no—
36C2×#64438—22no—
37C2×#64438—22no—
38C2×#64438—22no—
39C22⋊C4×C37—22no—
40C22⋊Dic37—22no—
41#10596936—22no—
42#10596936—22no—
43C4×Dic37—21no—
44C4×Dic37—21no—
45C4×Dic37D412yes—
46C4×Dic37D412yes—
47C23×C37—21no—
48C23×C37—21no—
49C23×C37—22no—
50C23×C37—22no—
51C23×C37C4⋊C412yes—
52C23×C37C22×C411yescharacteristic
53C2×C4×C37—22no—
54C2×C4×C37—21no—
55C2×C4×C37—22no—
56C2×C4×C37C22⋊C412yes—
57C2×Dic37—21no—
58C2×Dic37—21no—
59C2×Dic37—22no—
60C2×Dic37—22no—
61C2×Dic37—22no—
62C2×Dic37—22no—
63C2×Dic37—22no—
64C2×Dic37—21no—
65C2×Dic37—22no—
66C2×Dic37C22⋊C412yes—
67C2×Dic37C4⋊C412yes—
68C2×Dic37C2×D411yescharacteristic
69C2×Dic37C2×D411yescharacteristic
70C2×Dic37C2×D411yescharacteristic
71C2×Dic37C2×Q811yescharacteristic
72C2×Dic37#4111yescharacteristic
73C2×Dic37#4111yescharacteristic
74#64438—42no—
75#64438—42no—
76C22×C37—22no—
77C22×C37—24no—
78C22×C37—41no—
79C22×C37—41no—
80C22×C37—42no—
81C22×C37C2×C22⋊C411yescharacteristic
82C22×C37C2×C4⋊C411yescharacteristic
83C22×C37#11711yescharacteristic
84C22×C37#13112yes—
85C22×C37#13112yes—
86C4×C37—22no—
87C4×C37—41no—
88Dic37—22no—
89Dic37—22no—
90Dic37—41no—
91Dic37#12111yescharacteristic
92Dic37#12111yescharacteristic
93Dic37C22⋊Q811yescharacteristic
94Dic37C22⋊Q811yescharacteristic
95#1798—371nomaximal, Sylow
96C2×C37—42no—
97C2×C37#38011yescharacteristic
98C2×C37#40811yescharacteristic
99C2×C37#40811yescharacteristic
100C2×C37#42412yes—
101C2×C37#43312yes—
102C2×#117—371no—
103C2×C4⋊C8—371no—
104C2×C4⋊C8—371no—
105C2×C22⋊C8—372no—
106#336—372no—
107C37#179811yescharacteristic, complemented, Sylow
108C23×C4—371no—
109C22×C8—372no—
110C22×C8—372no—
111#117—742no—
112#117—742no—
113C2×C4⋊C4—371no—
114C2×C4⋊C4—371no—
115C2×C22⋊C4—371no—
116C2×C22⋊C4#386611yescharacteristic
117C2×C42—371no—
118C2×C42—371no—
119C4⋊C8—742no—
120C4⋊C8—742no—
121C22⋊C8—744no—
122C24C2×#386611yescharacteristic
123C22×C4—371no—
124C22×C4—372no—
125C22×C4—372no—
126C22×C4—371no—
127C22×C4—371no—
128C22×C4—371no—
129C22×C4—741no—
130C22×C4—741no—
131C22×C4—741no—
132C22×C4—741no—
133C22×C4C2×#386611yescharacteristic
134C22×C4C2×#386611yescharacteristic
135C2×C8—742no—
136C2×C8—742no—
137C2×C8—742no—
138C2×C8—742no—
139C2×C8—742no—
140C2×C8—742no—
141C4⋊C4—742no—
142C4⋊C4—742no—
143C22⋊C4—22no—
144C22⋊C4—742no—
145C42—372no—
146C42—372no—
147C42—741no—
148C42—741no—
149C23—21no—
150C23—21no—
151C23—22no—
152C23—22no—
153C23C4⋊#386612yes—
154C23C22×#386611yescharacteristic
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—371no—
159C2×C4—371no—
160C2×C4—371no—
161C2×C4—371no—
162C2×C4—371no—
163C2×C4—371no—
164C2×C4—372no—
165C2×C4—372no—
166C2×C4—742no—
167C2×C4—742no—
168C2×C4—742no—
169C2×C4—742no—
170C2×C4—741no—
171C2×C4—741no—
172C2×C4—742no—
173C2×C4—741no—
174C2×C4—742no—
175C2×C4C22⋊#386612yes—
176C8—1482no—
177C8—1482no—
178C22—22no—
179C22—24no—
180C22—41no—
181C22—41no—
182C22—42no—
183C22C2×C22⋊#386611yescharacteristic
184C22C2×C4⋊#386611yescharacteristic
185C22#1192461511yescharacteristic
186C22#1192462312yes—
187C22#1192462312yes—
188C4—22no—
189C4—41no—
190C4—371no—
191C4—371no—
192C4—371no—
193C4—371no—
194C4—742no—
195C4—742no—
196C4—1481no—
197C2—42no—
198C2#1455847511yescharacteristic
199C2#1455850611yescharacteristic
200C2#1455850711yescharacteristic
201C2#1455853912yes—
202C2#1455855712yes—
subgroupG/H
center, FrattiniC23C22×#3866
commutator, socleC23×C37C22×C4
FittingC2×C22⋊C4×C37C4
prime radicalC24×C37C2×C4
cosocleC22×Dic37C23
hypercenterC2×C22⋊C4#3866
hypocenterC37#1798
LCSG ▷ C23×C37 ▷ C37
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11924603C2semidirect
2. C2×C4⋊#64438C2semidirect
4. #14558399C2semidirect
107. C37#1798semidirect

Maximal subgroups

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

subgroupindex
C2×#119246032
C2×C4⋊#644382
C2×C22⋊#644382
#145583992
C2×#119244922
#179837