Finite Group Databasebeta

← #18010128

Subgroups — #18010128

Order 4736.

246 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 58 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#14558553C211yesmaximal, characteristic, complemented
2#14558536C211yesmaximal, characteristic, complemented
3#14558392C212yesmaximal, complemented
4#14558391C212yesmaximal, complemented
5#14558078C211yesmaximal, characteristic
6C2×#10596957—21no—
7#11924603C2212yes—
8#11924603C2212yes—
9C4⋊#64438—21no—
10C22⋊#64438—21no—
11#11924591—21no—
12C2×#10596964—21no—
13#11924535C2211yescharacteristic
14#11924532C2211yescharacteristic
15#11924522—21no—
16#11924510C411yescharacteristic
17#11924508—21no—
18D4×Dic37C411yescharacteristic
19#11924498C411yescharacteristic
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—44no—
33C2×D148C2×C411yescharacteristic
34C2×C4×D37—21no—
35C2×Dic74—21no—
36#10596957—42no—
37C2×#64438—22no—
38C2×#64438—22no—
39C4⋊C4×C37C2×C411yescharacteristic
40C22⋊C4×C37—21no—
41C22⋊Dic37—21no—
42#10596938—21no—
43#10596938—21no—
44C4⋊Dic37C2×C411yescharacteristic
45#10596936—21no—
46C4×Dic37C2×C411yescharacteristic
47C4×Dic37D411yescharacteristic
48C4×Dic37D411yescharacteristic
49C4×Dic37C2311yescharacteristic
50C23×C37—21no—
51C23×C37C22⋊C411yescharacteristic
52C22×D37—21no—
53D4×C37—41no—
54D4×C37—42no—
55C2×C4×C37—21no—
56C2×C4×C37—41no—
57C2×C4×C37C22⋊C411yescharacteristic
58C2×C4×C37C22×C411yescharacteristic
59C22⋊D37—42no—
60C22⋊D37—42no—
61C22⋊D37—41no—
62C22⋊D37—41no—
63C2×Dic37—21no—
64C2×Dic37—22no—
65C2×Dic37—21no—
66C2×Dic37—21no—
67C2×Dic37—42no—
68C2×Dic37C22⋊C411yescharacteristic
69C2×Dic37C22⋊C411yescharacteristic
70C2×Dic37C2×D411yescharacteristic
71C2×Dic37C2×D411yescharacteristic
72D148—41no—
73C4×D37—42no—
74Dic74—42no—
75#64438—42no—
76#64438—42no—
77C22×C37—21no—
78C22×C37—21no—
79C22×C37—21no—
80C22×C37—41no—
81C22×C37—41no—
82C22×C37—41no—
83C22×C37C2×C22⋊C411yescharacteristic
84C2×D37—41no—
85C2×D37—41no—
86C2×D37—41no—
87C4×C37—21no—
88C4×C37—21no—
89C4×C37—41no—
90Dic37—21no—
91Dic37—21no—
92Dic37—41no—
93Dic37AGL(1,ℤ/8)11yescharacteristic
94Dic37AGL(1,ℤ/8)12yes—
95Dic37#13711yescharacteristic
96#1557—371nomaximal, Sylow
97C2×C37—41no—
98C2×C37—81no—
99C2×C37#41311yescharacteristic
100C2×C37#41711yescharacteristic
101C2×C37#41811yescharacteristic
102D37—81no—
103#532—371no—
104#432—371no—
105#423—371no—
106#332—372no—
107#331—372no—
108C37#155711yescharacteristic, complemented, Sylow
109C2×#41—741no—
110C2×M16—741no—
111C4⋊Q8—371no—
112#127—371no—
113#124—741no—
114#121—371no—
115#121—741no—
116#121#386611yescharacteristic
117C4×D4—371no—
118C4×D4—371no—
119C4×D4—741no—
120C2×C42—371no—
121C4⋊C8—372no—
122C4⋊C8—372no—
123C4⋊C8—741no—
124C22⋊C8—741no—
125#97—741no—
126#41—1484no—
127C2×Q8—741no—
128C2×D4—21no—
129C2×D4—371no—
130C2×D4—741no—
131C2×D4—741no—
132C2×D4—741no—
133C2×D4C2×#386611yescharacteristic
134C22×C4—371no—
135C22×C4—371no—
136C22×C4—741no—
137C22×C4—741no—
138C22×C4C2×#386611yescharacteristic
139M16—1482no—
140C2×C8—742no—
141C2×C8—742no—
142C4⋊C4—371no—
143C4⋊C4—741no—
144C4⋊C4C2×#386611yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—741no—
147C22⋊C4—741no—
148C22⋊C4—741no—
149C42—371no—
150C42—371no—
151C42—371no—
152C42—371no—
153C23—21no—
154C23—741no—
155C23C22⋊#386611yescharacteristic
156Q8—1482no—
157D4—41no—
158D4—42no—
159D4—1481no—
160D4—1482no—
161D4—1481no—
162D4—1481no—
163D4—1482no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—371no—
167C2×C4—371no—
168C2×C4—371no—
169C2×C4—371no—
170C2×C4—741no—
171C2×C4—742no—
172C2×C4—741no—
173C2×C4—741no—
174C2×C4—1482no—
175C2×C4—1482no—
176C2×C4C22⋊#386611yescharacteristic
177C2×C4C22×#386611yescharacteristic
178C8—1482no—
179C8—1482no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—41no—
184C22—41no—
185C22—41no—
186C22—1481no—
187C22—1481no—
188C22—1481no—
189C22C2×C22⋊#386611yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—371no—
194C4—371no—
195C4—372no—
196C4—741no—
197C4—741no—
198C4—1481no—
199C2—41no—
200C2—81no—
201C2—2961no—
202C2#1455852011yescharacteristic
203C2#1455852411yescharacteristic
204C2#1455852511yescharacteristic
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#1557
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #14558553C2semidirect
2. #14558536C2semidirect
3. #14558392C2semidirect
4. #14558391C2semidirect
108. C37#1557semidirect

Maximal subgroups

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

subgroupindex
#145585532
#145585362
#145583922
#145583912
#145580782
#155737