Finite Group Databasebeta

← #18009901

Subgroups — #18009901

Order 4736.

260 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 70 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#14558550C211yesmaximal, characteristic, complemented
2C2×C4⋊#64438C211yesmaximal, characteristic, complemented
3#14558381C212yesmaximal, complemented
4D4⋊#64438C212yesmaximal, complemented
5#14558078C211yesmaximal, characteristic
6C22×#64438—21no—
7#11924603—21no—
8C4⋊#64438—21no—
9C4⋊#64438C2212yes—
10C22⋊#64438—21no—
11C4×#64438C2212yes—
12C2×#10596964—21no—
13#11924535C411yescharacteristic
14#11924532C411yescharacteristic
15#11924522—21no—
16#11924510C411yescharacteristic
17#11924508—21no—
18D4×Dic37C2211yescharacteristic
19#11924498C2211yescharacteristic
20#11924496—21no—
21C2×C4×Dic37C2211yescharacteristic
22#121×C37C411yescharacteristic
23C2×D4×C37—21no—
24C2×D4×C37C2×C411yescharacteristic
25C22×C4×C37C2×C411yescharacteristic
26C2×C22⋊D37—21no—
27C2×C22⋊D37—21no—
28C2×C22⋊D37—21no—
29C22×Dic37—21no—
30C22×Dic37D411yescharacteristic
31C22×Dic37D411yescharacteristic
32#10596964—42no—
33#10596964—42no—
34C2×D148C2×C411yescharacteristic
35C2×C4×D37—21no—
36C2×Dic74—21no—
37C2×#64438—22no—
38C2×#64438—22no—
39C2×#64438—42no—
40C4⋊C4×C37C2×C411yescharacteristic
41C22⋊C4×C37—21no—
42C22⋊Dic37—21no—
43#10596938—21no—
44#10596938—21no—
45C4⋊Dic37C2×C411yescharacteristic
46#10596936—21no—
47C4×Dic37C2×C411yescharacteristic
48C4×Dic37D411yescharacteristic
49C4×Dic37D411yescharacteristic
50C4×Dic37C2311yescharacteristic
51C23×C37—21no—
52C23×C37C22⋊C411yescharacteristic
53C22×D37—21no—
54D4×C37—22no—
55D4×C37—42no—
56C2×C4×C37—22no—
57C2×C4×C37—21no—
58C2×C4×C37C22⋊C411yescharacteristic
59C2×C4×C37C22×C411yescharacteristic
60C22⋊D37—42no—
61C22⋊D37—42no—
62C22⋊D37—42no—
63C2×Dic37—21no—
64C2×Dic37—41no—
65C2×Dic37—41no—
66C2×Dic37—41no—
67C2×Dic37C22⋊C411yescharacteristic
68C2×Dic37C22⋊C411yescharacteristic
69C2×Dic37D812yes—
70C2×Dic37SD1612yes—
71C2×Dic37C2×D411yescharacteristic
72C2×Dic37C2×D411yescharacteristic
73D148—22no—
74C4×D37—41no—
75C4×D37—41no—
76Dic74—42no—
77#64438—42no—
78#64438—42no—
79C22×C37—21no—
80C22×C37—21no—
81C22×C37—41no—
82C22×C37—41no—
83C22×C37—41no—
84C22×C37#10212yes—
85C22×C37C2×C22⋊C411yescharacteristic
86C2×D37—41no—
87C2×D37—41no—
88C2×D37—41no—
89C4×C37—21no—
90C4×C37—41no—
91C4×C37#13112yes—
92Dic37—21no—
93Dic37—21no—
94Dic37—41no—
95Dic37#10212yes—
96Dic37C2×D811yescharacteristic
97Dic37C2×SD1611yescharacteristic
98#1480—371nomaximal, Sylow
99C2×C37—22no—
100C2×C37—81no—
101C2×C37#40811yescharacteristic
102C2×C37C2×#10211yescharacteristic
103C2×C37#42111yescharacteristic
104D37—81no—
105#532—371no—
106#431—371no—
107C2×C4⋊C8—371no—
108D4⋊C8—372no—
109D4⋊C8—372no—
110C37#148011yescharacteristic, complemented, Sylow
111C2×#41—741no—
112C22×C8—741no—
113C4⋊Q8—371no—
114#127—371no—
115#124—741no—
116#121—371no—
117#121—741no—
118#121#386611yescharacteristic
119C4×D4—371no—
120C4×D4—371no—
121C4×D4—741no—
122C2×C42—371no—
123C4⋊C8—372no—
124C4⋊C8—741no—
125C4⋊C8—741no—
126C22⋊C8—741no—
127C4×C8—372no—
128#41—1482no—
129#41—1482no—
130C2×Q8—741no—
131C2×D4—21no—
132C2×D4—371no—
133C2×D4—741no—
134C2×D4—741no—
135C2×D4—741no—
136C2×D4C2×#386611yescharacteristic
137C22×C4—371no—
138C22×C4—371no—
139C22×C4—741no—
140C22×C4—741no—
141C22×C4C2×#386611yescharacteristic
142C2×C8—742no—
143C2×C8—742no—
144C2×C8—1482no—
145C4⋊C4—371no—
146C4⋊C4—741no—
147C4⋊C4C2×#386611yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—741no—
150C22⋊C4—741no—
151C22⋊C4—741no—
152C42—371no—
153C42—371no—
154C42—371no—
155C42—371no—
156C23—21no—
157C23—741no—
158C23C22⋊#386611yescharacteristic
159Q8—1482no—
160D4—22no—
161D4—42no—
162D4—742no—
163D4—1482no—
164D4—1482no—
165D4—1482no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—372no—
169C2×C4—372no—
170C2×C4—371no—
171C2×C4—371no—
172C2×C4—371no—
173C2×C4—371no—
174C2×C4—741no—
175C2×C4—1481no—
176C2×C4—1481no—
177C2×C4—1481no—
178C2×C4—1481no—
179C2×C4—1481no—
180C2×C4C22⋊#386611yescharacteristic
181C2×C4C22×#386611yescharacteristic
182C8—1482no—
183C8—1482no—
184C22—21no—
185C22—21no—
186C22—41no—
187C22—41no—
188C22—41no—
189C22—1481no—
190C22—1481no—
191C22—1481no—
192C22#1192459812yes—
193C22C2×C22⋊#386611yescharacteristic
194C4—21no—
195C4—41no—
196C4—371no—
197C4—371no—
198C4—372no—
199C4—741no—
200C4—741no—
201C4—1481no—
202C4#1192462312yes—
203C2—22no—
204C2—81no—
205C2—2961no—
206C2#1455850611yescharacteristic
207C2C2×#1192459811yescharacteristic
208C2#1455853011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#121×C37C4
socleC22×C37C2×C22⋊C4
prime radical#14558078C2
cosocleC4×Dic37C23
hypercenter#121#3866
hypocenterC37#1480
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #14558550C2semidirect
2. C2×C4⋊#64438C2semidirect
3. #14558381C2semidirect
4. D4⋊#64438C2semidirect
110. C37#1480semidirect

Maximal subgroups

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

subgroupindex
#145585502
C2×C4⋊#644382
#145583812
D4⋊#644382
#145580782
#148037