Finite Group Databasebeta

← #18010006

Subgroups — #18010006

Order 4736.

274 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 60 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#14558505C211yesmaximal, characteristic
2#14558476C211yesmaximal, characteristic
3#14558387C214yesmaximal, complemented
4C2×#11924512C211yesmaximal, characteristic
5C2×#10596957—21no—
6C2×C22⋊#3866—21no—
7#11924593—21no—
8#11924593C2212yes—
9(C2×#3866)⋊C4—21no—
10(C2×#3866)⋊C4C2212yes—
11C22×C4×D37C2211yescharacteristic
12#11924512—21no—
13#11924512—21no—
14#11924512C412yescomplemented
15#11924512C2212yes—
16C2×C4⋊Dic37C411yescharacteristic, complemented
17C2×#10596936—21no—
18C2×#10596938—21no—
19C22×Q8×C37C411yescharacteristic, complemented
20C23×D37D411yescharacteristic
21C22×#3866—22no—
22C2×Q8×C37—21no—
23C2×Q8×C37—42no—
24C2×Q8×C37C2×C412yes—
25C22×C4×C37—21no—
26C22×C4×C37C2×C411yescharacteristic
27C22×Dic37—21no—
28C22×Dic37D411yescharacteristic
29C2×C4×D37—42no—
30C2×C4×D37C2×C411yescharacteristic
31C2×C4×D37D411yescharacteristic
32C2×C4×D37D411yescharacteristic
33C2×C4×D37C2311yescharacteristic
34C22⋊#3866—42no—
35#10596957—42no—
36C2×#64438—22no—
37#10596938—22no—
38#10596938—22no—
39C4⋊Dic37—21no—
40C4⋊Dic37C2×C412yes—
41#10596936—22no—
42#10596936—22no—
43C23×C37C22⋊C411yescharacteristic
44C22×D37—22no—
45C22×D37—22no—
46C22×D37—41no—
47C22×D37C22⋊C411yescharacteristic
48C22×D37C2×D411yescharacteristic
49C2×#3866—42no—
50C2×#3866—42no—
51C2×#3866—42no—
52Q8×C37—42no—
53Q8×C37—42no—
54C2×C4×C37—22no—
55C2×C4×C37—22no—
56C2×C4×C37—42no—
57C2×C4×C37C22⋊C411yescharacteristic
58C2×C4×C37C22×C411yescharacteristic
59C2×Dic37—22no—
60C2×Dic37—22no—
61C2×Dic37—42no—
62C2×Dic37C22⋊C411yescharacteristic
63C2×Dic37C2×D411yescharacteristic
64C4×D37—41no—
65C4×D37—41no—
66C4×D37—41no—
67C4×D37—41no—
68#64438—42no—
69C22×C37—21no—
70C22×C37—21no—
71C22×C37#9912yes—
72C22×C37C2×C22⋊C411yescharacteristic
73C2×D37—21no—
74C2×D37—21no—
75C2×D37—21no—
76C2×D37—21no—
77C2×D37—21no—
78C2×D37—44no—
79C2×D37#13712yes—
80#3866—82no—
81C4×C37—21no—
82C4×C37—21no—
83C4×C37—42no—
84Dic37—21no—
85Dic37—21no—
86Dic37—42no—
87#1511—371nomaximal, Sylow
88C2×C37—22no—
89C2×C37C2×#9911yescharacteristic
90C2×C37#41911yescharacteristic
91C2×C37#42111yescharacteristic
92D37—22no—
93D37—41no—
94C2×C22⋊Q8—371no—
95#407—371no—
96#381—371no—
97#328—374no—
98C37#151111yescharacteristic, complemented, Sylow
99C22×Q8#386611yescharacteristic, complemented
100C23×C4—371no—
101C2×M16—741no—
102C22⋊Q8—372no—
103C22⋊Q8—372no—
104C22⋊Q8—741no—
105C22⋊Q8—741no—
106C2×C4⋊C4—371no—
107C2×C4⋊C4—741no—
108C2×C22⋊C4—741no—
109C2×C22⋊C4—741no—
110C22⋊C8—372no—
111C22⋊C8—741no—
112#95—372no—
113#95—741no—
114C24—371no—
115C2×Q8—21no—
116C2×Q8—42no—
117C2×Q8C2×#386612yes—
118C22×C4—21no—
119C22×C4—371no—
120C22×C4—371no—
121C22×C4—371no—
122C22×C4—371no—
123C22×C4—371no—
124C22×C4—741no—
125C22×C4—742no—
126C22×C4—1482no—
127C22×C4C2×#386611yescharacteristic
128M16—1482no—
129C2×C8—742no—
130C4⋊C4—372no—
131C4⋊C4—742no—
132C4⋊C4—742no—
133C4⋊C4—741no—
134C22⋊C4—742no—
135C22⋊C4—742no—
136C22⋊C4—1482no—
137C23—371no—
138C23—371no—
139C23—742no—
140C23—742no—
141C23—1481no—
142C23C22⋊#386611yescharacteristic
143Q8—42no—
144Q8—42no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—42no—
148C2×C4—371no—
149C2×C4—371no—
150C2×C4—742no—
151C2×C4—742no—
152C2×C4—1481no—
153C2×C4—1481no—
154C2×C4—1481no—
155C2×C4—1481no—
156C2×C4—1482no—
157C2×C4—1482no—
158C2×C4—1482no—
159C2×C4—1482no—
160C2×C4C22⋊#386611yescharacteristic
161C2×C4C22×#386611yescharacteristic
162C8—1482no—
163C22—21no—
164C22—21no—
165C22—372no—
166C22—741no—
167C22—741no—
168C22—741no—
169C22—741no—
170C22—741no—
171C22—1484no—
172C22#1192459412yes—
173C22C2×C22⋊#386611yescharacteristic
174C4—21no—
175C4—21no—
176C4—42no—
177C4—2962no—
178C4—741no—
179C4—741no—
180C4—1482no—
181C2—22no—
182C2—742no—
183C2—1481no—
184C2C2×#1192459411yescharacteristic
185C2#1455852611yescharacteristic
186C2#1455853211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC22×Q8×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC23×D37D4
cosocleC2×C4×D37C23
hypercenterC22×Q8#3866
hypocenterC37#1511
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. #14558387C2semidirect
14. #11924512C4semidirect
16. C2×C4⋊Dic37C4semidirect
19. C22×Q8×C37C4semidirect
98. C37#1511semidirect
99. C22×Q8#3866semidirect

Maximal subgroups

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

subgroupindex
#145585052
#145584762
#145583872
C2×#119245122
#151137