Finite Group Databasebeta

← #18010018

Subgroups — #18010018

Order 4736.

208 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 56 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#14558555C211yesmaximal, characteristic
2#14558478C211yesmaximal, characteristic
3#14558387C212yesmaximal
4#14558386C212yesmaximal
5#14558087C211yesmaximal, characteristic
6C4⋊#64438—21no—
7#11924593C2212yes—
8#11924591—21no—
9(C2×#3866)⋊C4—21no—
10(C2×#3866)⋊C4—21no—
11(C2×#3866)⋊C4C2212yes—
12#11924535C411yescharacteristic, complemented
13#11924534C411yescharacteristic, complemented
14#11924526—21no—
15#11924516C2211yescharacteristic
16#11924514—21no—
17#11924512C2211yescharacteristic
18C4×Dic74—21no—
19C4×Dic74C411yescharacteristic, complemented
20#11924493—21no—
21C42×D37C2211yescharacteristic
22C4×Q8×C37C411yescharacteristic, complemented
23C22×#3866—22no—
24C2×Q8×C37C2×C411yescharacteristic
25C2×C4×D37D411yescharacteristic
26C2×C4×D37D411yescharacteristic
27C2×C4×D37C2311yescharacteristic
28C2×Dic74—21no—
29C2×Dic74C2×C411yescharacteristic
30C2×#64438—22no—
31C4⋊C4×C37—21no—
32C4⋊C4×C37C2×C411yescharacteristic
33C42×C37—21no—
34C42×C37C2×C411yescharacteristic
35#10596938—21no—
36#10596938—21no—
37C4⋊Dic37—21no—
38C4⋊Dic37C2×C411yescharacteristic
39#10596936—21no—
40#10596936—21no—
41#10596936—21no—
42#10596936—21no—
43#10596936—21no—
44C4×Dic37—21no—
45C4×Dic37C2×C411yescharacteristic
46C4×Dic37D411yescharacteristic
47C4×Dic37D411yescharacteristic
48C22×D37C2×D411yescharacteristic
49C2×#3866—42no—
50C2×#3866—42no—
51C2×#3866—42no—
52Q8×C37—41no—
53C2×C4×C37—21no—
54C2×C4×C37—21no—
55C2×C4×C37C22⋊C411yescharacteristic
56C2×C4×C37C22⋊C411yescharacteristic
57C2×C4×C37C22×C411yescharacteristic
58C2×Dic37—21no—
59C2×Dic37—21no—
60C2×Dic37C22⋊C411yescharacteristic
61C2×Dic37C22⋊C411yescharacteristic
62C2×Dic37C2×D411yescharacteristic
63C4×D37—22no—
64C4×D37—41no—
65C4×D37—41no—
66Dic74—42no—
67Dic74—41no—
68#64438—42no—
69C22×C37C2×C22⋊C411yescharacteristic
70C2×D37—21no—
71C2×D37—21no—
72C2×D37#13712yes—
73#3866—82no—
74C4×C37—21no—
75C4×C37—21no—
76C4×C37—21no—
77C4×C37—41no—
78C4×C37—41no—
79Dic37—21no—
80Dic37—21no—
81Dic37—21no—
82Dic37—41no—
83Dic37—41no—
84#1515—371nomaximal, Sylow
85C2×C37#41011yescharacteristic
86C2×C37#41911yescharacteristic
87C2×C37#42111yescharacteristic
88D37—22no—
89#533—371no—
90#432—371no—
91#383—371no—
92#328—372no—
93#328—372no—
94C37#151511yescharacteristic, complemented, Sylow
95C4⋊Q8—371no—
96C4⋊Q8—371no—
97#125—741no—
98C22⋊Q8—371no—
99C22⋊Q8—371no—
100C22⋊Q8—741no—
101C4×Q8—371no—
102C4×Q8—741no—
103C4×Q8#386611yescharacteristic, complemented
104#117—741no—
105C2×C42—371no—
106C4⋊C8—741no—
107C22⋊C8—372no—
108#97—741no—
109#95—372no—
110#95—741no—
111#95—741no—
112C2×Q8—371no—
113C2×Q8—741no—
114C2×Q8C2×#386611yescharacteristic
115C22×C4—371no—
116C22×C4—371no—
117C22×C4—371no—
118C22×C4—742no—
119C2×C8—742no—
120C4⋊C4—21no—
121C4⋊C4—371no—
122C4⋊C4—741no—
123C4⋊C4—741no—
124C4⋊C4—741no—
125C4⋊C4—741no—
126C4⋊C4—741no—
127C4⋊C4—741no—
128C4⋊C4C2×#386611yescharacteristic
129C22⋊C4—741no—
130C22⋊C4—741no—
131C42—21no—
132C42—371no—
133C42—371no—
134C42—371no—
135C42—741no—
136C42C2×#386611yescharacteristic
137C23—371no—
138Q8—41no—
139Q8—1481no—
140Q8—1482no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—371no—
144C2×C4—371no—
145C2×C4—371no—
146C2×C4—742no—
147C2×C4—741no—
148C2×C4—741no—
149C2×C4—1481no—
150C2×C4—1481no—
151C2×C4—1482no—
152C2×C4—1482no—
153C2×C4—1482no—
154C2×C4C22⋊#386611yescharacteristic
155C2×C4C22⋊#386611yescharacteristic
156C2×C4C22×#386611yescharacteristic
157C8—1482no—
158C22—372no—
159C22—741no—
160C22—741no—
161C22C2×C22⋊#386611yescharacteristic
162C4—21no—
163C4—21no—
164C4—21no—
165C4—41no—
166C4—41no—
167C4—2962no—
168C4—741no—
169C4—741no—
170C4—741no—
171C4—1481no—
172C4—1481no—
173C2—742no—
174C2#1455851211yescharacteristic
175C2#1455852611yescharacteristic
176C2#1455853011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC4×Q8×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC22×D37C2×D4
cosocleC2×C4×D37C23
hypercenterC4×Q8#3866
hypocenterC37#1515
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
12. #11924535C4semidirect
13. #11924534C4semidirect
19. C4×Dic74C4semidirect
22. C4×Q8×C37C4semidirect
94. C37#1515semidirect
103. C4×Q8#3866semidirect

Maximal subgroups

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

subgroupindex
#145585552
#145584782
#145583872
#145583862
#145580872
#151537