Finite Group Databasebeta

← #18010888

Subgroups — #18010888

Order 4736.

250 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 52 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#14558520C212yesmaximal, complemented
2#14558444C212yesmaximal, complemented
3#14558441C212yesmaximal, complemented
4#14558081C211yesmaximal, characteristic
5C2×#10596957—22no—
6#11924597C2214yes—
7#11924596—22no—
8C2×#10596964C411yescharacteristic
9C2×#10596964C2211yescharacteristic
10#11924536C2211yescharacteristic
11#11924523C411yescharacteristic
12#11924523C2211yescharacteristic
13#11924507—22no—
14D4×Dic37—22no—
15C42×D37C411yescharacteristic
16#127×C37C411yescharacteristic
17C2×D4×C37—22no—
18C2×D4×C37C2×C411yescharacteristic
19C2×D4×C37C2×C411yescharacteristic
20C2×C22⋊D37—21no—
21C2×C22⋊D37D412yes—
22C22×Dic37—21no—
23C22×Dic37D412yes—
24#10596964—41no—
25#10596964—41no—
26#10596964—41no—
27#10596964—41no—
28C2×C4×D37—21no—
29C2×C4×D37C2×C411yescharacteristic
30C2×Dic74C2×C411yescharacteristic
31C2×Dic74C2311yescharacteristic
32#10596957—24no—
33#10596957—42no—
34C2×#64438—42no—
35C42×C37C2×C411yescharacteristic
36C22⋊Dic37—22no—
37C22⋊Dic37—22no—
38C4⋊Dic37—22no—
39C4×Dic37—21no—
40C4×Dic37C2×C411yescharacteristic
41C23×C37—21no—
42C23×C37C22⋊C412yes—
43C22×D37C22⋊C411yescharacteristic
44D4×C37—41no—
45D4×C37—41no—
46D4×C37—44no—
47C2×C4×C37—21no—
48C2×C4×C37C22×C411yescharacteristic
49C22⋊D37—42no—
50C22⋊D37—42no—
51C2×Dic37—22no—
52C2×Dic37—22no—
53C2×Dic37—21no—
54C2×Dic37—21no—
55C2×Dic37—41no—
56C2×Dic37—41no—
57C2×Dic37C22⋊C411yescharacteristic
58C2×Dic37C2×D412yes—
59C4×D37—21no—
60C4×D37—21no—
61C4×D37—42no—
62Dic74—41no—
63Dic74—41no—
64#64438—44no—
65C22×C37—22no—
66C22×C37—42no—
67C22×C37—42no—
68C22×C37—41no—
69C22×C37C2×C22⋊C411yescharacteristic
70C2×D37—21no—
71C2×D37—41no—
72C4×C37—22no—
73C4×C37—21no—
74Dic37—22no—
75Dic37—41no—
76Dic37—41no—
77Dic37#9911yescharacteristic
78Dic37#9911yescharacteristic
79#2132—371nomaximal, Sylow
80C2×C37—21no—
81C2×C37—42no—
82C2×C37—81no—
83C2×C37C2×#9911yescharacteristic
84D37—41no—
85#532—371no—
86#413—372no—
87#356—372no—
88#355—372no—
89C37#213211yescharacteristic, complemented, Sylow
90C2×#41—371no—
91C2×#41—371no—
92C2×M16—742no—
93C4⋊Q8—371no—
94#127#386611yescharacteristic
95#124—371no—
96#124—371no—
97#121—742no—
98C4×D4—742no—
99C2×C42—371no—
100#101—374no—
101#100—742no—
102#41—1481no—
103#41—1481no—
104#41—1481no—
105#41—1481no—
106C2×Q8—371no—
107C2×Q8—371no—
108C2×D4—22no—
109C2×D4—372no—
110C2×D4—741no—
111C2×D4C2×#386611yescharacteristic
112C2×D4C2×#386611yescharacteristic
113C22×C4—372no—
114C22×C4—371no—
115C22×C4—741no—
116C22×C4—741no—
117M16—744no—
118M16—1482no—
119C2×C8—1482no—
120C4⋊C4—742no—
121C22⋊C4—742no—
122C22⋊C4—742no—
123C42—371no—
124C42—741no—
125C42C2×#386611yescharacteristic
126C23—21no—
127C23—371no—
128C23C22⋊#386612yes—
129Q8—1481no—
130Q8—1481no—
131D4—41no—
132D4—41no—
133D4—44no—
134D4—1482no—
135D4—1482no—
136C2×C4—21no—
137C2×C4—371no—
138C2×C4—372no—
139C2×C4—741no—
140C2×C4—741no—
141C2×C4—742no—
142C2×C4—742no—
143C2×C4—741no—
144C2×C4—741no—
145C2×C4—1482no—
146C2×C4—1481no—
147C2×C4—1481no—
148C2×C4C22×#386611yescharacteristic
149C8—1484no—
150C22—22no—
151C22—42no—
152C22—42no—
153C22—41no—
154C22—741no—
155C22—1481no—
156C22C2×C22⋊#386611yescharacteristic
157C4—22no—
158C4—21no—
159C4—371no—
160C4—371no—
161C4—742no—
162C4—1481no—
163C4—1481no—
164C2—21no—
165C2—42no—
166C2—81no—
167C2—1481no—
168C2D37⋊#9911yescharacteristic
subgroupG/H
centerC2D37⋊#99
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#127×C37C4
socleC2×C37C2×#99
prime radical#14558081C2
cosocleC2×Dic74C23
hypercenter#127#3866
hypocenterC37#2132
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #14558520C2semidirect
2. #14558444C2semidirect
3. #14558441C2semidirect
89. C37#2132semidirect

Maximal subgroups

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

subgroupindex
#145585202
#145584442
#145584412
#145580812
#213237