Finite Group Databasebeta

← #18010867

Subgroups — #18010867

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#14558439C212yesmaximal, complemented
3#14558437C212yesmaximal, complemented
4#14558079C211yesmaximal, characteristic
5#11924615—22no—
6#11924595C2214yes—
7#11924594—22no—
8C2×#10596962C2211yescharacteristic
9#11924534C411yescharacteristic, complemented
10#11924532C2211yescharacteristic
11#11924525C2211yescharacteristic
12#11924523C411yescharacteristic, complemented
13#11924508—22no—
14C4×C22⋊D37—22no—
15C2×C4×Dic37C411yescharacteristic, complemented
16C2×#41×C37C411yescharacteristic, complemented
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×D148C2311yescharacteristic
30C2×C4×D37D412yes—
31C2×Dic74C2×C411yescharacteristic
32C22⋊#3866—24no—
33C4⋊#3866—42no—
34C4×#3866—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×D37C2×D412yes—
44C2×#3866—44no—
45Q8×C37—41no—
46D4×C37—41no—
47D4×C37—42no—
48C2×C4×C37—21no—
49C2×C4×C37—21no—
50C2×C4×C37—21no—
51C2×C4×C37—41no—
52C2×C4×C37—41no—
53C2×C4×C37C22⋊C411yescharacteristic
54C2×C4×C37C22×C411yescharacteristic
55C22⋊D37—42no—
56C22⋊D37—44no—
57C2×Dic37—21no—
58C2×Dic37—21no—
59C2×Dic37—42no—
60C2×Dic37C22⋊C412yes—
61D148—41no—
62C4×D37—22no—
63C4×D37—22no—
64Dic74—41no—
65C22×C37—21no—
66C22×C37—41no—
67C22×C37—42no—
68C22×C37—41no—
69C22×C37C2×C22⋊C411yescharacteristic
70C2×D37—22no—
71C2×D37—42no—
72#3866—84no—
73C4×C37—21no—
74C4×C37—41no—
75C4×C37#9911yescharacteristic
76C4×C37#9911yescharacteristic
77Dic37—22no—
78Dic37—22no—
79Dic37—41no—
80#2126—371nomaximal, Sylow
81C2×C37—21no—
82C2×C37—41no—
83C2×C37—81no—
84C2×C37C2×#9911yescharacteristic
85D37—42no—
86#532—371no—
87#410—372no—
88#354—372no—
89#353—372no—
90C37#212611yescharacteristic, complemented, Sylow
91C2×#41—371no—
92C2×#41#386611yescharacteristic, complemented
93C4⋊Q8—371no—
94#127—371no—
95#124—371no—
96#124—371no—
97#121—742no—
98C4×D4—742no—
99#117—742no—
100C2×C42—371no—
101#99—374no—
102#99—742no—
103#41—41no—
104#41—41no—
105#41—1481no—
106#41—1481no—
107C2×Q8—371no—
108C2×Q8C2×#386611yescharacteristic
109C2×D4—21no—
110C2×D4—372no—
111C2×D4—371no—
112C2×D4—742no—
113C2×D4C2×#386611yescharacteristic
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—371no—
124C42—371no—
125C42—741no—
126C42—1482no—
127C23—21no—
128C23—372no—
129C23C22⋊#386611yescharacteristic
130Q8—41no—
131Q8—1481no—
132D4—41no—
133D4—42no—
134D4—1481no—
135D4—1482no—
136D4—1484no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—372no—
143C2×C4—741no—
144C2×C4—742no—
145C2×C4—742no—
146C2×C4—741no—
147C2×C4—1484no—
148C2×C4—1482no—
149C2×C4C22⋊#386611yescharacteristic
150C2×C4C22×#386611yescharacteristic
151C22—21no—
152C22—41no—
153C22—42no—
154C22—41no—
155C22—742no—
156C22—1482no—
157C22C2×C22⋊#386611yescharacteristic
158C4—21no—
159C4—41no—
160C4—2964no—
161C4—742no—
162C4—742no—
163C4—1481no—
164C4#1192459411yescharacteristic
165C4#1192459411yescharacteristic
166C2—21no—
167C2—41no—
168C2—81no—
169C2—1482no—
170C2C2×#1192459411yescharacteristic
subgroupG/H
centerC4#11924594
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×#41×C37C4
socleC2×C37C2×#99
prime radical#14558079C2
cosocleC2×D148C23
hypercenterC2×#41#3866
hypocenterC37#2126
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. #14558512C2semidirect
2. #14558439C2semidirect
3. #14558437C2semidirect
9. #11924534C4semidirect
12. #11924523C4semidirect
15. C2×C4×Dic37C4semidirect
16. C2×#41×C37C4semidirect
90. C37#2126semidirect
92. C2×#41#3866semidirect

Maximal subgroups

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

subgroupindex
#145585122
#145584392
#145584372
#145580792
#212637