Finite Group Databasebeta

← #18010029

Subgroups — #18010029

Order 4736.

220 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 66 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
2#14558477C211yesmaximal, characteristic
3#14558387C212yesmaximal
4#14558386C212yesmaximal
5#14558087C211yesmaximal, characteristic
6C2×C4⋊#3866—21no—
7C4⋊#64438—21no—
8#11924593C2212yes—
9C4×#64438—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⋊#3866—42no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37C2×C411yescharacteristic
34C42×C37—21no—
35C42×C37C2×C411yescharacteristic
36#10596938—21no—
37#10596938—21no—
38C4⋊Dic37—21no—
39C4⋊Dic37C2×C411yescharacteristic
40#10596936—21no—
41#10596936—21no—
42#10596936—21no—
43#10596936—21no—
44#10596936—21no—
45C4×Dic37—21no—
46C4×Dic37C2×C411yescharacteristic
47C4×Dic37D411yescharacteristic
48C4×Dic37D411yescharacteristic
49C22×D37C2×D411yescharacteristic
50C2×#3866—42no—
51C2×#3866—42no—
52C2×#3866—42no—
53Q8×C37—41no—
54C2×C4×C37—21no—
55C2×C4×C37—21no—
56C2×C4×C37C22⋊C411yescharacteristic
57C2×C4×C37C22⋊C411yescharacteristic
58C2×C4×C37C22×C411yescharacteristic
59C2×Dic37—21no—
60C2×Dic37—21no—
61C2×Dic37C22⋊C411yescharacteristic
62C2×Dic37C22⋊C411yescharacteristic
63C2×Dic37C2×D411yescharacteristic
64C4×D37—41no—
65C4×D37—41no—
66C4×D37SD1612yes—
67C4×D37Q1612yes—
68Dic74—42no—
69Dic74—41no—
70#64438—42no—
71C22×C37C2×C22⋊C411yescharacteristic
72C2×D37—21no—
73C2×D37—21no—
74C2×D37C2×SD1611yescharacteristic
75C2×D37C2×Q1611yescharacteristic
76#3866—82no—
77C4×C37—21no—
78C4×C37—21no—
79C4×C37—41no—
80C4×C37—41no—
81C4×C37#10312yes—
82Dic37—21no—
83Dic37—21no—
84Dic37—41no—
85Dic37—41no—
86Dic37#10312yes—
87#1518—371nomaximal, Sylow
88C2×C37#41011yescharacteristic
89C2×C37C2×#10311yescharacteristic
90C2×C37#42111yescharacteristic
91D37—21no—
92D37—21no—
93#533—371no—
94#431—371no—
95#382—371no—
96#328—372no—
97#328—372no—
98C37#151811yescharacteristic, complemented, Sylow
99C4⋊Q8—371no—
100C4⋊Q8—371no—
101#125—741no—
102C22⋊Q8—371no—
103C22⋊Q8—371no—
104C22⋊Q8—741no—
105C4×Q8—371no—
106C4×Q8—741no—
107C4×Q8#386611yescharacteristic, complemented
108#117—741no—
109C2×C4⋊C4—741no—
110C2×C42—371no—
111C4⋊C8—741no—
112C22⋊C8—372no—
113C4×C8—741no—
114#95—372no—
115#95—741no—
116C2×Q8—371no—
117C2×Q8—741no—
118C2×Q8C2×#386611yescharacteristic
119C22×C4—371no—
120C22×C4—371no—
121C22×C4—371no—
122C22×C4—742no—
123C2×C8—742no—
124C4⋊C4—21no—
125C4⋊C4—371no—
126C4⋊C4—741no—
127C4⋊C4—741no—
128C4⋊C4—741no—
129C4⋊C4—741no—
130C4⋊C4—741no—
131C4⋊C4—741no—
132C4⋊C4—1482no—
133C4⋊C4C2×#386611yescharacteristic
134C22⋊C4—741no—
135C22⋊C4—741no—
136C42—21no—
137C42—371no—
138C42—371no—
139C42—371no—
140C42—741no—
141C42C2×#386611yescharacteristic
142C23—371no—
143Q8—41no—
144Q8—1481no—
145Q8—1482no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—371no—
149C2×C4—372no—
150C2×C4—372no—
151C2×C4—371no—
152C2×C4—371no—
153C2×C4—741no—
154C2×C4—741no—
155C2×C4—1481no—
156C2×C4—1481no—
157C2×C4—1482no—
158C2×C4—1482no—
159C2×C4—1482no—
160C2×C4C22⋊#386611yescharacteristic
161C2×C4C22⋊#386611yescharacteristic
162C2×C4C22×#386611yescharacteristic
163C8—1482no—
164C22—371no—
165C22—371no—
166C22—741no—
167C22—741no—
168C22C2×C22⋊#386611yescharacteristic
169C4—21no—
170C4—21no—
171C4—41no—
172C4—41no—
173C4—372no—
174C4—2962no—
175C4—741no—
176C4—741no—
177C4—1481no—
178C4—1481no—
179C4#1192459912yes—
180C2—741no—
181C2—741no—
182C2#1455851211yescharacteristic
183C2C2×#1192459911yescharacteristic
184C2#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#1518
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
98. C37#1518semidirect
107. C4×Q8#3866semidirect

Maximal subgroups

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

subgroupindex
#145585522
#145584772
#145583872
#145583862
#145580872
#151837