Finite Group Databasebeta

← #18010478

Subgroups — #18010478

Order 4736.

260 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 72 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#14558543C212yesmaximal, complemented
2#14558512C212yesmaximal
3#14558401C212yesmaximal, complemented
4C2×#11924542C211yesmaximal, characteristic
5#11924615C2214yes—
6#11924605—22no—
7#11924604—22no—
8#11924595—22no—
9#11924594—22no—
10C2×#10596962C2211yescharacteristic
11#11924542—22no—
12#11924542—22no—
13C2×#10596934C411yescharacteristic, complemented
14C2×#10596929C411yescharacteristic, complemented
15C2×#10596929C2211yescharacteristic
16C2×C8×D37C411yescharacteristic, complemented
17C2×C8×D37C2211yescharacteristic
18C22×C8×C37C411yescharacteristic, complemented
19C22×C4×C37C2×C411yescharacteristic
20C2×C22⋊D37D411yescharacteristic
21C2×C22⋊D37Q811yescharacteristic
22#10596962—22no—
23#10596962—22no—
24C2×D148D411yescharacteristic
25C2×C4×D37C2×C411yescharacteristic
26C2×C4×D37C2311yescharacteristic
27C2×Dic74Q811yescharacteristic
28C22⋊#3866—24no—
29C4⋊#3866—24no—
30C4×#3866—24no—
31C2×C8×C37—21no—
32C2×C8×C37—21no—
33C2×C8×C37C2×C411yescharacteristic
34C2×C8×C37C2×C411yescharacteristic
35#10596934—22no—
36C2×#64436C2×C411yescharacteristic
37C2×#64436C2×C411yescharacteristic
38#10596929—22no—
39#10596929—22no—
40C8×D37—21no—
41C8×D37—21no—
42C8×D37D412yes—
43C8×D37D412yes—
44C23×C37C4⋊C411yescharacteristic
45C22×D37C4⋊C411yescharacteristic
46C22×D37C2×D411yescharacteristic
47C2×#3866—44no—
48C2×C4×C37—21no—
49C2×C4×C37—21no—
50C2×C4×C37C4⋊C411yescharacteristic
51C2×C4×C37C22×C411yescharacteristic
52C22⋊D37—22no—
53C22⋊D37—22no—
54C2×Dic37C4⋊C411yescharacteristic
55C2×Dic37C2×Q811yescharacteristic
56D148—22no—
57C4×D37—21no—
58C4×D37—21no—
59C4×D37C2×D412yes—
60C4×D37#4112yes—
61Dic74—22no—
62C8×C37—21no—
63C8×C37C22⋊C411yescharacteristic
64C8×C37C22⋊C411yescharacteristic
65#64436—21no—
66#64436C22⋊C412yes—
67C22×C37—21no—
68C22×C37—41no—
69C22×C37C2×C4⋊C411yescharacteristic
70C2×D37—21no—
71C2×D37—41no—
72C2×D37—41no—
73C2×D37#12112yes—
74#3866—84no—
75C4×C37—21no—
76C4×C37C2×C22⋊C411yescharacteristic
77C4×C37#11711yescharacteristic
78Dic37—21no—
79Dic37C22⋊Q812yes—
80#1812—371nomaximal, Sylow
81C2×C37—21no—
82C2×C37—41no—
83C2×C37#38011yescharacteristic
84D37—22no—
85D37—41no—
86C2×#131—371no—
87#427—372no—
88#410—372no—
89H(3,ℤ/4)—372no—
90C37#181211yescharacteristic, complemented, Sylow
91C2×#41—371no—
92#131—742no—
93#131—742no—
94C2×M16—371no—
95C2×M16—371no—
96C2×M16—371no—
97C22×C8—371no—
98C22×C8—371no—
99C22×C8#386611yescharacteristic, complemented
100#117—374no—
101#107—742no—
102#106—742no—
103#99—742no—
104#99—742no—
105#41—742no—
106#41—742no—
107C2×Q8—371no—
108C2×D4—371no—
109C2×D4—371no—
110C2×D4—371no—
111C22×C4—371no—
112C22×C4—371no—
113C22×C4C2×#386611yescharacteristic
114M16—742no—
115M16—742no—
116M16—742no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—371no—
120C2×C8—372no—
121C2×C8—372no—
122C2×C8—371no—
123C2×C8—741no—
124C2×C8—741no—
125C2×C8C2×#386611yescharacteristic
126C2×C8C2×#386611yescharacteristic
127C4⋊C4—744no—
128C22⋊C4—744no—
129C42—744no—
130C23—371no—
131C23—371no—
132C23C4⋊#386611yescharacteristic
133Q8—742no—
134D4—742no—
135D4—742no—
136D4—742no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—371no—
140C2×C4—372no—
141C2×C4—372no—
142C2×C4—371no—
143C2×C4—741no—
144C2×C4—741no—
145C2×C4—1484no—
146C2×C4C4⋊#386611yescharacteristic
147C2×C4C22×#386611yescharacteristic
148C8—21no—
149C8—372no—
150C8—741no—
151C8C22⋊#386611yescharacteristic
152C8C22⋊#386611yescharacteristic
153C22—21no—
154C22—41no—
155C22—372no—
156C22—741no—
157C22—1481no—
158C22—1481no—
159C22C2×C4⋊#386611yescharacteristic
160C4—21no—
161C4—372no—
162C4—2964no—
163C4—741no—
164C4C2×C22⋊#386611yescharacteristic
165C4#1192461511yescharacteristic
166C2—21no—
167C2—41no—
168C2—742no—
169C2—1481no—
170C2#1455847511yescharacteristic
subgroupG/H
centerC4#11924615
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC22×C8×C37C4
socleC2×C37#380
prime radicalC2×#10596962C22
cosocleC2×C4×D37C23
hypercenterC22×C8#3866
hypocenterC37#1812
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C2×C8 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. #14558543C2semidirect
3. #14558401C2semidirect
13. C2×#10596934C4semidirect
14. C2×#10596929C4semidirect
16. C2×C8×D37C4semidirect
18. C22×C8×C37C4semidirect
90. C37#1812semidirect
99. C22×C8#3866semidirect

Maximal subgroups

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

subgroupindex
#145585432
#145585122
#145584012
C2×#119245422
#181237