Finite Group Databasebeta

← #18010065

Subgroups — #18010065

Order 4736.

256 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 60 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
2C2×#11924591C211yesmaximal, characteristic, complemented
3#14558389C212yesmaximal, complemented
4#14558388C212yesmaximal, complemented
5#14558079C211yesmaximal, characteristic
6C22×#64438—21no—
7#11924603—21no—
8C22⋊#64438—21no—
9#11924591—21no—
10#11924591C2212yes—
11#11924591C2212yes—
12C2×#10596962C411yescharacteristic
13#11924534C411yescharacteristic
14#11924532C411yescharacteristic
15#11924525C2211yescharacteristic
16#11924523C2211yescharacteristic
17#11924508—21no—
18#11924508—21no—
19C4×C22⋊D37—21no—
20C4×C22⋊D37—21no—
21C2×C4×Dic37C2211yescharacteristic
22C2×#41×C37C411yescharacteristic
23#41×C37—42no—
24C2×Q8×C37C2×C411yescharacteristic
25C2×D4×C37—21no—
26C2×D4×C37C2×C411yescharacteristic
27C22×C4×C37—21no—
28C22×C4×C37C2×C411yescharacteristic
29C2×C22⋊D37—21no—
30C2×C22⋊D37—21no—
31C2×C22⋊D37—21no—
32C22×Dic37D411yescharacteristic
33C22×Dic37D411yescharacteristic
34#10596962—42no—
35C2×D148C2×C411yescharacteristic
36C2×C4×D37—21no—
37C2×Dic74C2×C411yescharacteristic
38C2×#64438—24no—
39C2×#64438—22no—
40C2×#64438—22no—
41C22⋊Dic37—21no—
42C22⋊Dic37—21no—
43#10596938—21no—
44#10596938—21no—
45#10596936—21no—
46#10596936—21no—
47C4×Dic37C2×C411yescharacteristic
48C4×Dic37D411yescharacteristic
49C4×Dic37D411yescharacteristic
50C4×Dic37C2311yescharacteristic
51C23×C37—21no—
52C23×C37C22⋊C411yescharacteristic
53C22×D37—21no—
54Q8×C37—41no—
55D4×C37—41no—
56D4×C37—42no—
57C2×C4×C37—22no—
58C2×C4×C37—21no—
59C2×C4×C37—42no—
60C2×C4×C37C22⋊C411yescharacteristic
61C2×C4×C37C22×C411yescharacteristic
62C22⋊D37—42no—
63C22⋊D37—42no—
64C22⋊D37—42no—
65C2×Dic37—22no—
66C2×Dic37—21no—
67C2×Dic37—41no—
68C2×Dic37C22⋊C411yescharacteristic
69C2×Dic37C22⋊C411yescharacteristic
70C2×Dic37C2×D411yescharacteristic
71C2×Dic37C2×D411yescharacteristic
72D148—41no—
73C4×D37—42no—
74Dic74—41no—
75#64438—24no—
76#64438—42no—
77C22×C37—21no—
78C22×C37—21no—
79C22×C37—41no—
80C22×C37—41no—
81C22×C37—41no—
82C22×C37#10012yes—
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—21no—
93Dic37—41no—
94Dic37#10412yes—
95#1530—371nomaximal, Sylow
96C2×C37—22no—
97C2×C37—81no—
98C2×C37C2×#10011yescharacteristic
99C2×C37C2×#10411yescharacteristic
100C2×C37#42111yescharacteristic
101D37—81no—
102#532—371no—
103#432—371no—
104C2×#97—371no—
105#329—372no—
106#329—372no—
107C37#153011yescharacteristic, complemented, Sylow
108C2×#41—371no—
109C2×#41#386611yescharacteristic
110C22×C8—741no—
111C4⋊Q8—371no—
112#127—371no—
113#124—371no—
114#124—371no—
115#121—741no—
116#121—741no—
117C4×D4—741no—
118C4×D4—741no—
119C2×C42—371no—
120C4⋊C8—741no—
121C22⋊C8—741no—
122#97—372no—
123#97—372no—
124#97—741no—
125#41—42no—
126#41—1482no—
127C2×Q8—371no—
128C2×Q8C2×#386611yescharacteristic
129C2×D4—21no—
130C2×D4—371no—
131C2×D4—741no—
132C2×D4—741no—
133C2×D4—741no—
134C2×D4C2×#386611yescharacteristic
135C22×C4—21no—
136C22×C4—371no—
137C22×C4—371no—
138C22×C4—741no—
139C22×C4C2×#386611yescharacteristic
140C2×C8—742no—
141C2×C8—744no—
142C2×C8—742no—
143C4⋊C4—741no—
144C4⋊C4—741no—
145C22⋊C4—741no—
146C22⋊C4—741no—
147C22⋊C4—741no—
148C22⋊C4—741no—
149C42—371no—
150C42—371no—
151C42—371no—
152C42—371no—
153C23—21no—
154C23—741no—
155C23C22⋊#386611yescharacteristic
156Q8—41no—
157Q8—1481no—
158D4—41no—
159D4—42no—
160D4—1481no—
161D4—1482no—
162D4—1482no—
163D4—1482no—
164C2×C4—22no—
165C2×C4—21no—
166C2×C4—42no—
167C2×C4—371no—
168C2×C4—371no—
169C2×C4—371no—
170C2×C4—371no—
171C2×C4—742no—
172C2×C4—741no—
173C2×C4—1482no—
174C2×C4—1481no—
175C2×C4C22⋊#386611yescharacteristic
176C2×C4C22×#386611yescharacteristic
177C8—744no—
178C8—1482no—
179C22—21no—
180C22—21no—
181C22—41no—
182C22—41no—
183C22—41no—
184C22—1481no—
185C22—1481no—
186C22—1481no—
187C22#1192459612yes—
188C22C2×C22⋊#386611yescharacteristic
189C4—21no—
190C4—21no—
191C4—41no—
192C4—372no—
193C4—741no—
194C4—741no—
195C4—741no—
196C4—1481no—
197C2—22no—
198C2—81no—
199C2—2961no—
200C2C2×#1192459611yescharacteristic
201C2D37⋊#10411yescharacteristic
202C2#1455853011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×#41×C37C4
socleC22×C37C2×C22⋊C4
prime radical#14558079C2
cosocleC4×Dic37C23
hypercenterC2×#41#3866
hypocenterC37#1530
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #14558553C2semidirect
2. C2×#11924591C2semidirect
3. #14558389C2semidirect
4. #14558388C2semidirect
107. C37#1530semidirect

Maximal subgroups

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

subgroupindex
#145585532
C2×#119245912
#145583892
#145583882
#145580792
#153037