Finite Group Databasebeta

← #18010104

Subgroups — #18010104

Order 4736.

344 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 70 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, complemented
2#14558538C211yesmaximal, characteristic, complemented
3#14558391C214yesmaximal, complemented
4#127×D37C211yesmaximal, characteristic
5C2×#10596953—21no—
6#11924603—21no—
7#11924603C2212yescomplemented
8#11924603C2212yescomplemented
9#11924593—21no—
10C4×#64438—21no—
11C2×D4×D37—21no—
12C2×D4×D37—21no—
13C2×D4×D37C412yes—
14#11924533C411yescharacteristic
15#11924532—21no—
16#11924532—21no—
17#11924532C2212yes—
18C42×D37C2211yescharacteristic
19#127×C37C411yescharacteristic
20C23×D37—22no—
21C2×D4×C37—21no—
22C2×D4×C37—21no—
23C2×D4×C37C2×C412yes—
24C2×C22⋊D37—22no—
25C2×C22⋊D37—22no—
26C2×C22⋊D37—22no—
27D4×D37—44no—
28D4×D37—44no—
29D4×D37—42no—
30D4×D37—42no—
31C2×D148—21no—
32C2×D148—21no—
33C2×D148C2×C412yes—
34C2×C4×D37C2×C411yescharacteristic
35C2×C4×D37D411yescharacteristic
36C2×C4×D37D411yescharacteristic
37C2×#64438—22no—
38C2×#64438—22no—
39#10596953—42no—
40C42×C37C2×C411yescharacteristic
41C4×Dic37D411yescharacteristic
42C4×Dic37D411yescharacteristic
43C4×Dic37C2311yescharacteristic
44C23×C37—22no—
45C22×D37—22no—
46C22×D37—44no—
47C22×D37—44no—
48C22×D37—44no—
49C22×D37C22⋊C411yescharacteristic
50D4×C37—42no—
51D4×C37—42no—
52D4×C37—42no—
53C2×C4×C37C22⋊C411yescharacteristic
54C2×C4×C37C22⋊C411yescharacteristic
55C2×C4×C37C22×C411yescharacteristic
56C22⋊D37—44no—
57C22⋊D37—42no—
58C22⋊D37—42no—
59C22⋊D37—44no—
60C2×Dic37C22⋊C411yescharacteristic
61C2×Dic37C2×D411yescharacteristic
62C2×Dic37C2×D411yescharacteristic
63D148—42no—
64D148—42no—
65D148—42no—
66C4×D37—22no—
67C4×D37—22no—
68C4×D37D812yes—
69C4×D37SD1612yes—
70#64438—42no—
71#64438—42no—
72C22×C37—42no—
73C22×C37—42no—
74C22×C37—42no—
75C22×C37C2×C22⋊C411yescharacteristic
76C2×D37—21no—
77C2×D37—21no—
78C2×D37—42no—
79C2×D37—42no—
80C2×D37—42no—
81C2×D37—88no—
82C2×D37#10212yes—
83C4×C37—21no—
84C4×C37—21no—
85C4×C37#10212yes—
86Dic37#10012yes—
87Dic37C2×D811yescharacteristic
88Dic37C2×SD1611yescharacteristic
89Dic37AGL(1,ℤ/8)12yes—
90#1545—371nomaximal, Sylow
91C2×C37—82no—
92C2×C37C2×#10011yescharacteristic
93C2×C37C2×#10211yescharacteristic
94C2×C37#41811yescharacteristic
95D37—22no—
96D37—82no—
97C2×#127—371no—
98#431—371no—
99#423—371no—
100#331—374no—
101C37#154511yescharacteristic, complemented, Sylow
102C22×D4—372no—
103C22×D4—741no—
104C22×D4—741no—
105C2×M16—741no—
106#127—372no—
107#127—371no—
108#127—741no—
109#127—741no—
110#127#386611yescharacteristic
111C2×C42—371no—
112C4⋊C8—372no—
113C4⋊C8—372no—
114C4⋊C8—741no—
115C22⋊C8—741no—
116C4×C8—741no—
117C24—742no—
118C2×D4—21no—
119C2×D4—21no—
120C2×D4—372no—
121C2×D4—742no—
122C2×D4—742no—
123C2×D4—742no—
124C2×D4—741no—
125C2×D4—741no—
126C2×D4—1482no—
127C2×D4—1482no—
128C2×D4—1484no—
129C2×D4—1484no—
130C2×D4C2×#386612yes—
131C22×C4—371no—
132C22×C4—371no—
133C22×C4—371no—
134M16—1482no—
135C2×C8—742no—
136C2×C8—742no—
137C42—371no—
138C42—371no—
139C42—371no—
140C42C2×#386611yescharacteristic
141C23—22no—
142C23—371no—
143C23—742no—
144C23—1484no—
145C23—1484no—
146C23—1484no—
147D4—42no—
148D4—42no—
149D4—42no—
150D4—1482no—
151D4—1482no—
152D4—1482no—
153D4—1482no—
154D4—1484no—
155D4—1484no—
156D4—1482no—
157C2×C4—371no—
158C2×C4—371no—
159C2×C4—371no—
160C2×C4—372no—
161C2×C4—372no—
162C2×C4—742no—
163C2×C4—742no—
164C2×C4C22⋊#386611yescharacteristic
165C2×C4C22⋊#386611yescharacteristic
166C2×C4C22×#386611yescharacteristic
167C8—1482no—
168C8—1482no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22—372no—
173C22—2968no—
174C22—741no—
175C22—741no—
176C22—1482no—
177C22—1482no—
178C22—1482no—
179C22C2×C22⋊#386611yescharacteristic
180C4—21no—
181C4—21no—
182C4—372no—
183C4—371no—
184C4—371no—
185C4—372no—
186C4#1192459812yes—
187C2—82no—
188C2—2962no—
189C2—742no—
190C2D37⋊#10011yescharacteristic
191C2C2×#1192459811yescharacteristic
192C2#1455852511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#127×C37C4
socleC22×C37C2×C22⋊C4
prime radical#127×D37C2
cosocleC4×Dic37C23
hypercenter#127#3866
hypocenterC37#1545
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #14558551C2semidirect
2. #14558538C2semidirect
3. #14558391C2semidirect
7. #11924603C22semidirect
8. #11924603C22semidirect
101. C37#1545semidirect

Maximal subgroups

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

subgroupindex
#145585512
#145585382
#145583912
#127×D372
#154537