Finite Group Databasebeta

← #18009894

Subgroups — #18009894

Order 4736.

264 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 78 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#14558551C211yesmaximal, characteristic, complemented
2D37⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
3Q8⋊#64438C212yesmaximal, complemented
4#14558381C212yesmaximal, complemented
5C4×#10596966C211yesmaximal, characteristic
6C2×D37⋊C8—21no—
7#11924603—21no—
8#11924603—21no—
9C4⋊#64438C2212yes—
10#11924593—21no—
11C4×#64438C2212yes—
12C2×#10596966C411yescharacteristic
13Q8×Dic37C2211yescharacteristic
14C4×D148—21no—
15C4×D148C411yescharacteristic
16#11924498—21no—
17#11924498C2211yescharacteristic
18#11924494—21no—
19#11924494C411yescharacteristic
20C42×D37—21no—
21C42×D37C2211yescharacteristic
22C4×Q8×C37C411yescharacteristic
23C2×Q8×C37C2×C411yescharacteristic
24#10596966—22no—
25#10596966C814yescomplemented
26C2×D148—21no—
27C2×D148C2×C411yescharacteristic
28C2×C4×D37—21no—
29C2×C4×D37—21no—
30C2×C4×D37—21no—
31C2×C4×D37C2×C411yescharacteristic
32C2×C4×D37D411yescharacteristic
33C2×C4×D37D411yescharacteristic
34C2×#64438—22no—
35C2×#64438—22no—
36D37⋊C8—42no—
37C4⋊C4×C37—21no—
38C4⋊C4×C37C2×C411yescharacteristic
39C42×C37—21no—
40C42×C37C2×C411yescharacteristic
41#10596938—21no—
42#10596938—21no—
43#10596938—21no—
44C4⋊Dic37—21no—
45C4⋊Dic37C2×C411yescharacteristic
46C4×Dic37—21no—
47C4×Dic37—21no—
48C4×Dic37D411yescharacteristic
49C4×Dic37D411yescharacteristic
50C4×Dic37C2311yescharacteristic
51C22×D37—21no—
52C22×D37C22⋊C411yescharacteristic
53Q8×C37—21no—
54Q8×C37C2×C812yescomplemented
55C2×C4×C37—21no—
56C2×C4×C37—21no—
57C2×C4×C37C22⋊C411yescharacteristic
58C2×C4×C37C22⋊C411yescharacteristic
59C2×C4×C37C22×C411yescharacteristic
60C2×Dic37—21no—
61C2×Dic37C22⋊C411yescharacteristic
62C2×Dic37C2×D411yescharacteristic
63C2×Dic37C2×D411yescharacteristic
64D148—24no—
65D148—21no—
66D148C2×C812yescomplemented
67C4×D37—24no—
68C4×D37—21no—
69C4×D37—21no—
70C4×D37—41no—
71C4×D37—42no—
72C4×D37—41no—
73C4×D37—41no—
74C4×D37C2×C812yes—
75C4×D37M1612yes—
76#64438—42no—
77#64438—42no—
78C22×C37C2×C22⋊C411yescharacteristic
79C2×D37—21no—
80C2×D37—21no—
81C2×D37—22no—
82C2×D37—41no—
83C2×D37—41no—
84C2×D37C22⋊C812yes—
85C4×C37—22no—
86C4×C37—21no—
87C4×C37—21no—
88C4×C37—41no—
89C4×C37C22×C811yescharacteristic
90C4×C37C2×M1611yescharacteristic
91Dic37—21no—
92Dic37—41no—
93Dic37C22⋊C812yes—
94Dic37AGL(1,ℤ/8)11yescharacteristic
95Dic37#13711yescharacteristic
96#1477—371nomaximal, Sylow
97C2×C37C2×C22⋊C811yescharacteristic
98C2×C37#41711yescharacteristic
99C2×C37#42111yescharacteristic
100D37—22no—
101D37—42no—
102C4×#41—371no—
103#431—371no—
104C2×C4⋊C8—371no—
105Q8⋊C8—372no—
106D4⋊C8—372no—
107C37#147711yescharacteristic, complemented, Sylow
108C2×#41—371no—
109C22×C8—741no—
110C4×Q8—371no—
111C4×Q8#386611yescharacteristic
112C4×D4—371no—
113C4×D4—371no—
114C4×D4—741no—
115C4×D4—741no—
116#117—371no—
117#117—741no—
118C2×C42—371no—
119C2×C42—741no—
120C4⋊C8—372no—
121C4⋊C8—741no—
122C4⋊C8—741no—
123C22⋊C8—741no—
124C4×C8—372no—
125#41—374no—
126#41—742no—
127C2×Q8C2×#386611yescharacteristic
128C2×D4—371no—
129C2×D4—741no—
130C22×C4—371no—
131C22×C4—371no—
132C22×C4—371no—
133C22×C4—741no—
134C22×C4—741no—
135C22×C4—741no—
136C2×C8—742no—
137C2×C8—742no—
138C2×C8—1482no—
139C4⋊C4—21no—
140C4⋊C4—371no—
141C4⋊C4—741no—
142C4⋊C4C2×#386611yescharacteristic
143C22⋊C4—741no—
144C22⋊C4—741no—
145C22⋊C4—741no—
146C42—21no—
147C42—371no—
148C42—371no—
149C42—371no—
150C42—741no—
151C42—741no—
152C42C2×#386611yescharacteristic
153C23—371no—
154C23—741no—
155Q8—21no—
156Q8D37⋊C812yescomplemented
157D4—372no—
158D4—744no—
159D4—741no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—371no—
163C2×C4—371no—
164C2×C4—372no—
165C2×C4—372no—
166C2×C4—371no—
167C2×C4—741no—
168C2×C4—741no—
169C2×C4—744no—
170C2×C4—741no—
171C2×C4—1481no—
172C2×C4—1482no—
173C2×C4—1481no—
174C2×C4—1481no—
175C2×C4C22⋊#386611yescharacteristic
176C2×C4C22⋊#386611yescharacteristic
177C2×C4C22×#386611yescharacteristic
178C8—1482no—
179C8—1482no—
180C22—372no—
181C22—741no—
182C22—741no—
183C22—742no—
184C22—1481no—
185C22—1481no—
186C22C2×C22⋊#386611yescharacteristic
187C4—22no—
188C4—21no—
189C4—21no—
190C4—41no—
191C4—372no—
192C4—371no—
193C4—371no—
194C4—741no—
195C4—1481no—
196C4C2×D37⋊C811yescharacteristic
197C4D37⋊M1611yescharacteristic
198C2—742no—
199C2—1482no—
200C2D37⋊(C22⋊C8)11yescharacteristic
201C2#1455852411yescharacteristic
202C2#1455853211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC4×C37C22×C8
FrattiniC2×C4C22×#3866
FittingC4×Q8×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC2×#10596966C4
cosocleC4×Dic37C23
hypercenterC4×Q8#3866
hypocenterC37#1477
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #14558551C2semidirect
2. D37⋊(C4⋊C8)C2semidirect
3. Q8⋊#64438C2semidirect
4. #14558381C2semidirect
25. #10596966C8semidirect
54. Q8×C37C2×C8semidirect
66. D148C2×C8semidirect
107. C37#1477semidirect
156. Q8D37⋊C8semidirect

Maximal subgroups

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

subgroupindex
#145585512
D37⋊(C4⋊C8)2
Q8⋊#644382
#145583812
C4×#105969662
#147737