Finite Group Databasebeta

← #18009977

Subgroups — #18009977

Order 4736.

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

normal subgroups only

This group has 284 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#14558552C211yesmaximal, characteristic, complemented
2C4×C4⋊#3866C211yesmaximal, characteristic, complemented
3#14558385C214yesmaximal, complemented
4#14558084C211yesmaximal, characteristic
5C2×C4⋊#3866—21no—
6C2×C4×#3866—21no—
7C4⋊#64438—21no—
8#11924593C2212yes—
9C4×#64438—21no—
10(C2×#3866)⋊C4C2212yes—
11C2×#10596966—21no—
12#11924533C411yescharacteristic, complemented
13#11924525—21no—
14#11924511—21no—
15#11924511C2212yes—
16#11924498—21no—
17#11924498C412yescomplemented
18C42×D37C2211yescharacteristic
19C4⋊Q8×C37C411yescharacteristic, complemented
20C22×#3866—22no—
21C2×Q8×C37—21no—
22#10596966—42no—
23#10596966—42no—
24C2×D148—22no—
25C2×D148—21no—
26C2×D148—21no—
27C2×D148C2×C412yes—
28C2×C4×D37—22no—
29C2×C4×D37D411yescharacteristic
30C2×C4×D37D411yescharacteristic
31C2×C4×D37C2311yescharacteristic
32C2×#64438—22no—
33C4⋊#3866—24no—
34C4×#3866—42no—
35C4⋊C4×C37—21no—
36C4⋊C4×C37C2×C412yes—
37C42×C37C2×C411yescharacteristic
38#10596938—22no—
39#10596938—22no—
40C4×Dic37C2×C411yescharacteristic
41C4×Dic37D411yescharacteristic
42C4×Dic37D411yescharacteristic
43C22×D37—22no—
44C22×D37C2×D411yescharacteristic
45C2×#3866—24no—
46C2×#3866—42no—
47C2×#3866—42no—
48Q8×C37—42no—
49C2×C4×C37—22no—
50C2×C4×C37C22⋊C411yescharacteristic
51C2×C4×C37C22⋊C411yescharacteristic
52C2×C4×C37C22×C411yescharacteristic
53C2×Dic37C22⋊C411yescharacteristic
54C2×Dic37C22⋊C411yescharacteristic
55C2×Dic37C2×D411yescharacteristic
56D148—42no—
57D148—42no—
58D148—42no—
59D148—42no—
60D148—42no—
61C4×D37—22no—
62C4×D37—41no—
63C4×D37—44no—
64C4×D37D812yes—
65C4×D37SD1612yes—
66#64438—42no—
67C22×C37C2×C22⋊C411yescharacteristic
68C2×D37—21no—
69C2×D37—21no—
70C2×D37—42no—
71C2×D37—42no—
72C2×D37—42no—
73C2×D37C2×D811yescharacteristic
74C2×D37C2×SD1611yescharacteristic
75#3866—44no—
76C4×C37—21no—
77C4×C37—42no—
78C4×C37#10212yes—
79C4×C37#10412yes—
80Dic37—21no—
81Dic37—21no—
82Dic37#10212yes—
83#1502—371nomaximal, Sylow
84C2×C37#41011yescharacteristic
85C2×C37C2×#10211yescharacteristic
86C2×C37C2×#10411yescharacteristic
87D37—21no—
88D37—21no—
89D37—82no—
90#532—371no—
91#431—371no—
92C4×C4⋊C4—371no—
93#327—374no—
94C37#150211yescharacteristic, complemented, Sylow
95C2×#41—741no—
96C4⋊Q8#386611yescharacteristic, complemented
97#127—371no—
98#124—741no—
99#121—372no—
100#121—741no—
101C4×D4—372no—
102C4×D4—741no—
103C2×C4⋊C4—741no—
104C2×C42—371no—
105C2×C42—741no—
106C4⋊C8—741no—
107C22⋊C8—372no—
108C4×C8—741no—
109#95—372no—
110#41—1482no—
111#41—1482no—
112C2×Q8—21no—
113C2×D4—372no—
114C2×D4—742no—
115C2×D4—741no—
116C2×D4—741no—
117C22×C4—371no—
118C22×C4—371no—
119C22×C4—371no—
120C22×C4—742no—
121C22×C4—742no—
122C2×C8—742no—
123C4⋊C4—21no—
124C4⋊C4—744no—
125C4⋊C4C2×#386612yes—
126C22⋊C4—742no—
127C22⋊C4—742no—
128C42—371no—
129C42—371no—
130C42—371no—
131C42—1482no—
132C42C2×#386611yescharacteristic
133C23—371no—
134C23—742no—
135Q8—42no—
136D4—1482no—
137D4—1482no—
138D4—1482no—
139D4—1482no—
140D4—1482no—
141C2×C4—22no—
142C2×C4—371no—
143C2×C4—372no—
144C2×C4—372no—
145C2×C4—371no—
146C2×C4—371no—
147C2×C4—742no—
148C2×C4—744no—
149C2×C4—1481no—
150C2×C4—1484no—
151C2×C4—1482no—
152C2×C4—1482no—
153C2×C4C22⋊#386611yescharacteristic
154C2×C4C22⋊#386611yescharacteristic
155C2×C4C22×#386611yescharacteristic
156C8—1482no—
157C22—371no—
158C22—371no—
159C22—741no—
160C22—741no—
161C22—1482no—
162C22—1482no—
163C22—1482no—
164C22C2×C22⋊#386611yescharacteristic
165C4—21no—
166C4—42no—
167C4—372no—
168C4—741no—
169C4—741no—
170C4—1484no—
171C4#1192459812yes—
172C4#1192460112yes—
173C2—2962no—
174C2—741no—
175C2—741no—
176C2#1455851411yescharacteristic
177C2C2×#1192459811yescharacteristic
178C2C2×#1192460111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC4⋊Q8×C37C4
socleC22×C37C2×C22⋊C4
prime radical#14558084C2
cosocleC2×C4×D37C23
hypercenterC4⋊Q8#3866
hypocenterC37#1502
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #14558552C2semidirect
2. C4×C4⋊#3866C2semidirect
3. #14558385C2semidirect
12. #11924533C4semidirect
17. #11924498C4semidirect
19. C4⋊Q8×C37C4semidirect
94. C37#1502semidirect
96. C4⋊Q8#3866semidirect

Maximal subgroups

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

subgroupindex
#145585522
C4×C4⋊#38662
#145583852
#145580842
#150237