Finite Group Databasebeta

← #18010869

Subgroups — #18010869

Order 4736.

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

normal subgroups only

This group has 258 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#14558512C212yesmaximal, complemented
2#14558440C212yesmaximal, complemented
3#14558438C212yesmaximal, complemented
4#14558083C211yesmaximal, characteristic
5#11924615—22no—
6#11924595C2214yes—
7#11924594—22no—
8C2×#10596962C411yescharacteristic, complemented
9C2×#10596962C2211yescharacteristic
10#11924536C411yescharacteristic, complemented
11#11924533C2211yescharacteristic
12#11924524C411yescharacteristic, complemented
13#11924524C2211yescharacteristic
14#11924510—22no—
15C4×D148—22no—
16C2×C42×C37C411yescharacteristic, complemented
17C22×C4×C37—21no—
18C22×C4×C37C2×C411yescharacteristic
19C2×C22⋊D37—21no—
20C2×C22⋊D37D412yes—
21#10596962—41no—
22#10596962—41no—
23#10596962—41no—
24#10596962—41no—
25C2×D148—22no—
26C2×D148C2×C411yescharacteristic
27C2×D148C2311yescharacteristic
28C2×C4×D37—21no—
29C2×C4×D37D412yes—
30C2×Dic74C2×C411yescharacteristic
31C2×Dic74C2×C411yescharacteristic
32C22⋊#3866—24no—
33C4⋊#3866—42no—
34C4×#3866—42no—
35C42×C37—21no—
36C42×C37C2×C411yescharacteristic
37C42×C37C2×C411yescharacteristic
38#10596938—22no—
39#10596938—22no—
40C4⋊Dic37—22no—
41C23×C37C22⋊C411yescharacteristic
42C22×D37—21no—
43C22×D37C2×D412yes—
44C2×#3866—44no—
45C2×C4×C37—21no—
46C2×C4×C37—21no—
47C2×C4×C37—21no—
48C2×C4×C37—21no—
49C2×C4×C37—42no—
50C2×C4×C37C22⋊C411yescharacteristic
51C2×C4×C37C22×C411yescharacteristic
52C22⋊D37—42no—
53C22⋊D37—42no—
54C2×Dic37—21no—
55C2×Dic37C22⋊C412yes—
56D148—41no—
57D148—41no—
58D148—44no—
59C4×D37—22no—
60C4×D37—22no—
61C4×D37—41no—
62C4×D37—41no—
63Dic74—41no—
64Dic74—41no—
65C22×C37—21no—
66C22×C37—41no—
67C22×C37C2×C22⋊C411yescharacteristic
68C2×D37—22no—
69C2×D37—42no—
70C2×D37—42no—
71C2×D37—41no—
72#3866—84no—
73C4×C37—22no—
74C4×C37—21no—
75C4×C37—41no—
76C4×C37#9911yescharacteristic
77C4×C37#9911yescharacteristic
78Dic37—22no—
79Dic37—41no—
80#2126—371nomaximal, Sylow
81C2×C37—21no—
82C2×C37—41no—
83C2×C37C2×#9911yescharacteristic
84D37—42no—
85D37—81no—
86#532—371no—
87#410—372no—
88#354—372no—
89#353—372no—
90C37#212611yescharacteristic, complemented, Sylow
91C2×#41—371no—
92C2×#41—371no—
93C4⋊Q8—371no—
94#127—371no—
95#124—371no—
96#124—371no—
97#121—742no—
98C4×D4—742no—
99#117—742no—
100C2×C42#386611yescharacteristic, complemented
101#99—374no—
102#99—742no—
103#41—1481no—
104#41—1481no—
105#41—1481no—
106#41—1481no—
107C2×Q8—371no—
108C2×Q8—371no—
109C2×D4—372no—
110C2×D4—371no—
111C2×D4—371no—
112C2×D4—742no—
113C2×D4—741no—
114C22×C4—21no—
115C22×C4—372no—
116C22×C4—741no—
117C22×C4C2×#386611yescharacteristic
118C4⋊C4—742no—
119C4⋊C4—1482no—
120C22⋊C4—742no—
121C22⋊C4—742no—
122C22⋊C4—744no—
123C42—21no—
124C42—1482no—
125C42C2×#386611yescharacteristic
126C42C2×#386611yescharacteristic
127C23—372no—
128C23—741no—
129C23C22⋊#386611yescharacteristic
130Q8—1481no—
131Q8—1481no—
132D4—1481no—
133D4—1481no—
134D4—1484no—
135D4—1482no—
136D4—1482no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—42no—
142C2×C4—372no—
143C2×C4—742no—
144C2×C4—742no—
145C2×C4—741no—
146C2×C4—1484no—
147C2×C4—1481no—
148C2×C4—1481no—
149C2×C4C22⋊#386611yescharacteristic
150C2×C4C22×#386611yescharacteristic
151C22—21no—
152C22—41no—
153C22—742no—
154C22—1482no—
155C22—1482no—
156C22—1481no—
157C22C2×C22⋊#386611yescharacteristic
158C4—22no—
159C4—21no—
160C4—41no—
161C4—2964no—
162C4—742no—
163C4—1481no—
164C4#1192459511yescharacteristic
165C4#1192459511yescharacteristic
166C2—21no—
167C2—41no—
168C2—2961no—
169C2—1482no—
170C2C2×#1192459511yescharacteristic
subgroupG/H
centerC4#11924595
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×C42×C37C4
socleC2×C37C2×#99
prime radical#14558083C2
cosocleC2×D148C23
hypercenterC2×C42#3866
hypocenterC37#2126
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #14558512C2semidirect
2. #14558440C2semidirect
3. #14558438C2semidirect
8. C2×#10596962C4semidirect
10. #11924536C4semidirect
12. #11924524C4semidirect
16. C2×C42×C37C4semidirect
90. C37#2126semidirect
100. C2×C42#3866semidirect

Maximal subgroups

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

subgroupindex
#145585122
#145584402
#145584382
#145580832
#212637