Finite Group Databasebeta

← #18010887

Subgroups — #18010887

Order 4736.

250 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 54 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#14558519C212yesmaximal, complemented
2#14558443C212yesmaximal, complemented
3#14558441C212yesmaximal, complemented
4#14558079C211yesmaximal, characteristic
5D37⋊M16—22no—
6#11924597C2214yes—
7#11924596—22no—
8C2×#10596962C2211yescharacteristic
9#11924534C2211yescharacteristic
10#11924532C411yescharacteristic
11#11924525C411yescharacteristic
12#11924523C2211yescharacteristic
13#11924508—22no—
14C4×C22⋊D37—22no—
15C2×C4×Dic37C411yescharacteristic
16C2×#41×C37C411yescharacteristic
17#41×C37—41no—
18#41×C37—41no—
19C2×Q8×C37C2×C411yescharacteristic
20C2×D4×C37—21no—
21C2×D4×C37C2×C411yescharacteristic
22C22×C4×C37—21no—
23C22×C4×C37C2×C411yescharacteristic
24C2×C22⋊D37—22no—
25C2×C22⋊D37D412yes—
26C22×Dic37—21no—
27#10596962—41no—
28#10596962—41no—
29C2×D148C2×C411yescharacteristic
30C2×C4×D37D412yes—
31C2×Dic74C2311yescharacteristic
32#10596957—24no—
33#10596953—42no—
34D37⋊C8—42no—
35C22⋊Dic37—22no—
36#10596938—22no—
37#10596936—22no—
38C4×Dic37—21no—
39C4×Dic37C2×C411yescharacteristic
40C4×Dic37C2×C411yescharacteristic
41C23×C37—21no—
42C23×C37C22⋊C411yescharacteristic
43C22×D37C22⋊C412yes—
44Q8×C37—41no—
45D4×C37—41no—
46D4×C37—42no—
47C2×C4×C37—21no—
48C2×C4×C37—21no—
49C2×C4×C37—21no—
50C2×C4×C37—41no—
51C2×C4×C37—41no—
52C2×C4×C37C22⋊C411yescharacteristic
53C2×C4×C37C22×C411yescharacteristic
54C22⋊D37—42no—
55C22⋊D37—44no—
56C2×Dic37—21no—
57C2×Dic37—21no—
58C2×Dic37—42no—
59C2×Dic37C2×D412yes—
60D148—41no—
61C4×D37—22no—
62C4×D37—22no—
63Dic74—41no—
64#64438—44no—
65C22×C37—21no—
66C22×C37—41no—
67C22×C37—42no—
68C22×C37—41no—
69C22×C37C2×C22⋊C411yescharacteristic
70C2×D37—22no—
71C2×D37—42no—
72C4×C37—21no—
73C4×C37—41no—
74C4×C37#9911yescharacteristic
75C4×C37#9911yescharacteristic
76Dic37—22no—
77Dic37—22no—
78Dic37—41no—
79#2132—371nomaximal, Sylow
80C2×C37—21no—
81C2×C37—41no—
82C2×C37—81no—
83C2×C37C2×#9911yescharacteristic
84D37—42no—
85#532—371no—
86#413—372no—
87#356—372no—
88#355—372no—
89C37#213211yescharacteristic, complemented, Sylow
90C2×#41—371no—
91C2×#41#386611yescharacteristic
92C2×M16—742no—
93C4⋊Q8—371no—
94#127—371no—
95#124—371no—
96#124—371no—
97#121—742no—
98C4×D4—742no—
99C2×C42—371no—
100#101—374no—
101#100—742no—
102#41—41no—
103#41—41no—
104#41—1481no—
105#41—1481no—
106C2×Q8—371no—
107C2×Q8C2×#386611yescharacteristic
108C2×D4—21no—
109C2×D4—372no—
110C2×D4—371no—
111C2×D4—742no—
112C2×D4C2×#386611yescharacteristic
113C22×C4—21no—
114C22×C4—372no—
115C22×C4—741no—
116C22×C4C2×#386611yescharacteristic
117M16—744no—
118M16—1482no—
119C2×C8—1482no—
120C4⋊C4—742no—
121C22⋊C4—742no—
122C22⋊C4—742no—
123C42—371no—
124C42—371no—
125C42—741no—
126C23—21no—
127C23—372no—
128C23C22⋊#386611yescharacteristic
129Q8—41no—
130Q8—1481no—
131D4—41no—
132D4—42no—
133D4—1481no—
134D4—1482no—
135D4—1484no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—372no—
142C2×C4—741no—
143C2×C4—742no—
144C2×C4—742no—
145C2×C4—741no—
146C2×C4—1482no—
147C2×C4C22⋊#386611yescharacteristic
148C2×C4C22×#386611yescharacteristic
149C8—1484no—
150C22—21no—
151C22—41no—
152C22—42no—
153C22—41no—
154C22—742no—
155C22—1482no—
156C22C2×C22⋊#386611yescharacteristic
157C4—21no—
158C4—41no—
159C4—742no—
160C4—742no—
161C4—1481no—
162C4#1192459411yescharacteristic
163C4#1192459411yescharacteristic
164C2—21no—
165C2—41no—
166C2—81no—
167C2—1482no—
168C2C2×#1192459411yescharacteristic
subgroupG/H
centerC4#11924594
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×#41×C37C4
socleC2×C37C2×#99
prime radical#14558079C2
cosocleC2×Dic74C23
hypercenterC2×#41#3866
hypocenterC37#2132
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #14558519C2semidirect
2. #14558443C2semidirect
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
#145585192
#145584432
#145584412
#145580792
#213237