Finite Group Databasebeta

← #18009978

Subgroups — #18009978

Order 4736.

240 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 68 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
2C4×C4⋊#3866C211yesmaximal, characteristic
3#14558387C212yesmaximal
4#14558386C212yesmaximal
5#14558087C211yesmaximal, characteristic
6C2×C4⋊#3866—21no—
7C2×C4×#3866—21no—
8#11924603—21no—
9#11924593C2212yes—
10C4×#64438—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⋊#3866—24no—
32C4×#3866—42no—
33C4⋊C4×C37—21no—
34C4⋊C4×C37C2×C411yescharacteristic
35C42×C37—21no—
36C42×C37C2×C411yescharacteristic
37#10596938—21no—
38#10596938—21no—
39C4⋊Dic37—21no—
40C4⋊Dic37C2×C411yescharacteristic
41#10596936—21no—
42#10596936—21no—
43#10596936—21no—
44#10596936—21no—
45#10596936—21no—
46C4×Dic37—21no—
47C4×Dic37C2×C411yescharacteristic
48C4×Dic37D411yescharacteristic
49C4×Dic37D411yescharacteristic
50C22×D37C2×D411yescharacteristic
51C2×#3866—24no—
52C2×#3866—42no—
53C2×#3866—42no—
54Q8×C37—41no—
55C2×C4×C37—21no—
56C2×C4×C37—21no—
57C2×C4×C37C22⋊C411yescharacteristic
58C2×C4×C37C22⋊C411yescharacteristic
59C2×C4×C37C22×C411yescharacteristic
60C2×Dic37—21no—
61C2×Dic37—21no—
62C2×Dic37C22⋊C411yescharacteristic
63C2×Dic37C22⋊C411yescharacteristic
64C2×Dic37C2×D411yescharacteristic
65C4×D37—22no—
66C4×D37—41no—
67C4×D37SD1612yes—
68C4×D37Q1612yes—
69Dic74—42no—
70Dic74—41no—
71#64438—42no—
72C22×C37C2×C22⋊C411yescharacteristic
73C2×D37—21no—
74C2×D37—21no—
75C2×D37C2×SD1611yescharacteristic
76C2×D37C2×Q1611yescharacteristic
77#3866—44no—
78C4×C37—21no—
79C4×C37—21no—
80C4×C37—41no—
81C4×C37—41no—
82C4×C37#10312yes—
83Dic37—21no—
84Dic37—41no—
85Dic37—41no—
86Dic37#10312yes—
87Dic37#10412yes—
88#1503—371nomaximal, Sylow
89C2×C37#41011yescharacteristic
90C2×C37C2×#10311yescharacteristic
91C2×C37C2×#10411yescharacteristic
92D37—21no—
93D37—21no—
94#533—371no—
95#431—371no—
96C4×C4⋊C4—371no—
97#328—372no—
98#328—372no—
99C37#150311yescharacteristic, complemented, Sylow
100C4⋊Q8—371no—
101C4⋊Q8—371no—
102#125—741no—
103C22⋊Q8—371no—
104C22⋊Q8—371no—
105C22⋊Q8—741no—
106C4×Q8—371no—
107C4×Q8—741no—
108C4×Q8#386611yescharacteristic, complemented
109#117—741no—
110C2×C4⋊C4—741no—
111C2×C42—371no—
112C2×C42—741no—
113C4⋊C8—741no—
114C22⋊C8—372no—
115C4×C8—741no—
116#95—372no—
117C2×Q8—371no—
118C2×Q8—741no—
119C2×Q8C2×#386611yescharacteristic
120C22×C4—371no—
121C22×C4—371no—
122C22×C4—371no—
123C22×C4—742no—
124C2×C8—742no—
125C4⋊C4—21no—
126C4⋊C4—371no—
127C4⋊C4—741no—
128C4⋊C4—741no—
129C4⋊C4—741no—
130C4⋊C4—741no—
131C4⋊C4—741no—
132C4⋊C4—744no—
133C4⋊C4—741no—
134C4⋊C4C2×#386611yescharacteristic
135C22⋊C4—741no—
136C22⋊C4—741no—
137C42—21no—
138C42—371no—
139C42—371no—
140C42—371no—
141C42—741no—
142C42—1482no—
143C42C2×#386611yescharacteristic
144C23—371no—
145Q8—41no—
146Q8—1481no—
147Q8—1482no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—371no—
151C2×C4—371no—
152C2×C4—372no—
153C2×C4—372no—
154C2×C4—371no—
155C2×C4—742no—
156C2×C4—744no—
157C2×C4—741no—
158C2×C4—741no—
159C2×C4—1481no—
160C2×C4—1482no—
161C2×C4—1482no—
162C2×C4C22⋊#386611yescharacteristic
163C2×C4C22⋊#386611yescharacteristic
164C2×C4C22×#386611yescharacteristic
165C8—1482no—
166C22—371no—
167C22—371no—
168C22—741no—
169C22—741no—
170C22C2×C22⋊#386611yescharacteristic
171C4—21no—
172C4—21no—
173C4—41no—
174C4—41no—
175C4—372no—
176C4—372no—
177C4—741no—
178C4—1484no—
179C4—1481no—
180C4—1481no—
181C4#1192459912yes—
182C2—741no—
183C2—741no—
184C2#1455851211yescharacteristic
185C2C2×#1192459911yescharacteristic
186C2D37⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#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#1503
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ 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
99. C37#1503semidirect
108. C4×Q8#3866semidirect

Maximal subgroups

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

subgroupindex
#145585512
C4×C4⋊#38662
#145583872
#145583862
#145580872
#150337