Finite Group Databasebeta

← #17994675

Subgroups — #17994675

Order 4736.

316 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C2×C4⋊C4×D37C211yesmaximal, characteristic
2#14557496C212yesmaximal
3#14557302C211yesmaximal, characteristic, complemented
4#14557301C212yesmaximal, complemented
5C37×#343C211yesmaximal, characteristic, complemented
6C22×C4×D37C412yes—
7C22×C4×D37C2211yescharacteristic
8C2×#10596934C2212yes—
9C2×C4⋊Dic37C2211yescharacteristic
10C2×#10596936C412yes—
11C4⋊C4×D37—22no—
12C4⋊C4×D37—22no—
13#11924448—22no—
14#11924448—22no—
15C2×M16×C37C2212yes—
16C2×C4⋊C4×C37C2211yescharacteristic
17C23×D37C2×C411yescharacteristic
18C22×C4×C37C2×C412yes—
19C22×C4×C37C2311yescharacteristic
20C22×Dic37C2×C411yescharacteristic
21C22×Dic37C2×C412yes—
22C2×C4×D37—22no—
23C2×C4×D37—21no—
24C2×C4×D37—21no—
25C2×C4×D37—22no—
26C2×C4×D37—22no—
27C2×C4×D37—44no—
28C2×C4×D37D412yes—
29C2×C4×D37D412yes—
30M16×C37—22no—
31M16×C37—22no—
32C2×C8×C37—22no—
33C4⋊C4×C37—22no—
34C4⋊Dic37—22no—
35#10596936—24no—
36#10596934—22no—
37#10596934—22no—
38C2×#64436—22no—
39C23×C37C22×C411yescharacteristic
40C22×D37—21no—
41C22×D37—21no—
42C22×D37—22no—
43C22×D37—22no—
44C22×D37C22⋊C411yescharacteristic
45C22×D37C22⋊C411yescharacteristic
46C2×C4×C37—22no—
47C2×C4×C37—42no—
48C2×C4×C37C2×D412yes—
49C2×C4×C37#4112yes—
50C2×C4×C37#4111yescharacteristic
51C2×C4×C37#4111yescharacteristic
52C2×Dic37—21no—
53C2×Dic37—21no—
54C2×Dic37—22no—
55C2×Dic37—42no—
56C2×Dic37C22⋊C412yes—
57C4×D37—22no—
58C4×D37—22no—
59C4×D37—22no—
60C4×D37—22no—
61C4×D37—44no—
62C4×D37—44no—
63C8×C37—42no—
64#64436—42no—
65C22×C37—21no—
66C22×C37—21no—
67C22×C37C2×C22⋊C411yescharacteristic
68C22×C37#11711yescharacteristic
69C22×C37#11711yescharacteristic
70C2×D37—24no—
71C2×D37—24no—
72C2×D37—21no—
73C2×D37—21no—
74C2×D37—21no—
75C2×D37—21no—
76C2×D37#10012yes—
77C2×D37#10112yes—
78C4×C37—42no—
79C4×C37#12312yes—
80C4×C37#12312yes—
81Dic37—22no—
82Dic37—42no—
83#1821—371nomaximal, Sylow
84C2×C37—21no—
85C2×C37—21no—
86C2×C37#38111yescharacteristic
87C2×C37C2×#10011yescharacteristic
88C2×C37C2×#10111yescharacteristic
89D37—22no—
90D37—22no—
91C22×C4⋊C4—371no—
92#407—372no—
93#343—372no—
94#343—371no—
95#343D3711yescharacteristic, complemented
96C37#182111yescharacteristic, complemented, Sylow
97C23×C4—371no—
98C23×C4—372no—
99C2×M16—372no—
100C2×M16C2×D3712yes—
101C2×C4⋊C4—372no—
102C2×C4⋊C4—371no—
103C2×C4⋊C4—742no—
104C2×C4⋊C4—742no—
105C2×C4⋊C4C2×D3711yescharacteristic
106C22⋊C8—742no—
107C22⋊C8—742no—
108C24—371no—
109C22×C4—371no—
110C22×C4—372no—
111C22×C4—372no—
112C22×C4—372no—
113C22×C4—742no—
114C22×C4—742no—
115C22×C4—742no—
116C22×C4—741no—
117C22×C4—741no—
118C22×C4—1484no—
119C22×C4C4×D3712yes—
120C22×C4C22×D3711yescharacteristic
121M16—22no—
122M16—22no—
123M16—742no—
124M16—742no—
125C2×C8—22no—
126C2×C8—742no—
127C4⋊C4—22no—
128C4⋊C4—744no—
129C4⋊C4—742no—
130C23—371no—
131C23—371no—
132C23—742no—
133C23—742no—
134C23—741no—
135C23—741no—
136C23C2×C4×D3711yescharacteristic
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—372no—
140C2×C4—741no—
141C2×C4—741no—
142C2×C4—742no—
143C2×C4—742no—
144C2×C4—742no—
145C2×C4—742no—
146C2×C4—742no—
147C2×C4—1484no—
148C2×C4—1484no—
149C2×C4—1482no—
150C2×C4#1059696212yes—
151C2×C4D4×D3712yes—
152C2×C4#1059696411yescharacteristic
153C2×C4#1059696611yescharacteristic
154C8—42no—
155C8—1482no—
156C22—21no—
157C22—21no—
158C22—372no—
159C22—372no—
160C22—744no—
161C22—744no—
162C22—741no—
163C22—741no—
164C22—741no—
165C22—741no—
166C22C22⋊C4×D3711yescharacteristic
167C22#1192449311yescharacteristic
168C22#1192449411yescharacteristic
169C4—42no—
170C4—742no—
171C4—1482no—
172C4#1192451812yes—
173C4#1192452112yes—
174C2—21no—
175C2—21no—
176C2—742no—
177C2—742no—
178C2#1455739511yescharacteristic
179C2#100×D3711yescharacteristic
180C2#101×D3711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC23×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#343C2
socleC22×C37C2×C22⋊C4
prime radicalC23×D37C2×C4
cosocleC22×C4×C37C23
hypercenter#343D37
hypocenterC37#1821
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
3. #14557302C2semidirect
4. #14557301C2semidirect
5. C37×#343C2semidirect
95. #343D37semidirect
96. C37#1821semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D372
#145574962
#145573022
#145573012
C37×#3432
#182137