Finite Group Databasebeta

← #18010896

Subgroups — #18010896

Order 4736.

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

normal subgroups only

This group has 262 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#14558442C212yesmaximal, complemented
3#14558441C212yesmaximal, complemented
4#14558096C211yesmaximal, characteristic
5C2×#10596957—22no—
6#11924597C2214yescomplemented
7#11924596—22no—
8C2×#10596964C2211yescharacteristic
9C2×D4×D37C411yescharacteristic
10#11924532C411yescharacteristic
11#11924524C2211yescharacteristic
12#11924523C2211yescharacteristic
13#11924508—22no—
14#11924504—22no—
15#11924493C411yescharacteristic
16#127×C37C411yescharacteristic
17C23×D37—21no—
18C2×D4×C37—22no—
19C2×D4×C37C2×C411yescharacteristic
20C2×D4×C37C2×C411yescharacteristic
21C2×C22⋊D37—22no—
22C2×C22⋊D37—21no—
23C2×C22⋊D37D412yes—
24C22×Dic37D412yes—
25#10596964—42no—
26D4×D37—42no—
27C2×D148C2×C411yescharacteristic
28C2×C4×D37C2×C411yescharacteristic
29C2×Dic74C2311yescharacteristic
30#10596957—24no—
31#10596957—42no—
32C2×#64438—42no—
33C42×C37C2×C411yescharacteristic
34C22⋊Dic37—22no—
35#10596938—21no—
36#10596938—22no—
37#10596936—21no—
38C4×Dic37C2×C411yescharacteristic
39C23×C37—21no—
40C23×C37C22⋊C412yes—
41C22×D37—21no—
42C22×D37—42no—
43C22×D37—82no—
44C22×D37C22⋊C411yescharacteristic
45D4×C37—41no—
46D4×C37—41no—
47D4×C37—82no—
48C2×C4×C37—21no—
49C2×C4×C37C22×C411yescharacteristic
50C22⋊D37—42no—
51C22⋊D37—42no—
52C22⋊D37—82no—
53C2×Dic37—22no—
54C2×Dic37—22no—
55C2×Dic37—21no—
56C2×Dic37C22⋊C411yescharacteristic
57C2×Dic37C2×D412yes—
58D148—41no—
59C4×D37—22no—
60Dic74—41no—
61#64438—44no—
62C22×C37—22no—
63C22×C37—42no—
64C22×C37—42no—
65C22×C37—41no—
66C22×C37C2×C22⋊C411yescharacteristic
67C2×D37—21no—
68C2×D37—41no—
69C2×D37—42no—
70C2×D37—41no—
71C2×D37—84no—
72C4×C37—21no—
73C4×C37—41no—
74Dic37—22no—
75Dic37—41no—
76Dic37#9912yes—
77#2134—371nomaximal, Sylow
78C2×C37—21no—
79C2×C37—42no—
80C2×C37—81no—
81C2×C37C2×#9911yescharacteristic
82D37—41no—
83D37—81no—
84#535—371no—
85#413—372no—
86#355—372no—
87#355—372no—
88C37#213411yescharacteristic, complemented, Sylow
89C2×#41—371no—
90C22×D4—371no—
91C2×M16—742no—
92#127—371no—
93#127#386611yescharacteristic
94#124—371no—
95#124—371no—
96#121—742no—
97#120—742no—
98#117—371no—
99#101—374no—
100#100—742no—
101C24—741no—
102#41—1482no—
103C2×Q8—371no—
104C2×D4—22no—
105C2×D4—372no—
106C2×D4—371no—
107C2×D4—741no—
108C2×D4—742no—
109C2×D4—1482no—
110C2×D4C2×#386611yescharacteristic
111C2×D4C2×#386611yescharacteristic
112C22×C4—372no—
113C22×C4—371no—
114M16—744no—
115M16—1482no—
116C2×C8—1482no—
117C4⋊C4—741no—
118C22⋊C4—742no—
119C22⋊C4—741no—
120C22⋊C4—742no—
121C42—371no—
122C42C2×#386611yescharacteristic
123C23—21no—
124C23—371no—
125C23—2962no—
126C23—741no—
127C23—1482no—
128C23C22⋊#386612yes—
129Q8—1481no—
130D4—41no—
131D4—41no—
132D4—82no—
133D4—2962no—
134D4—1481no—
135D4—1482no—
136D4—1482no—
137C2×C4—21no—
138C2×C4—371no—
139C2×C4—372no—
140C2×C4—742no—
141C2×C4—742no—
142C2×C4—742no—
143C2×C4—741no—
144C2×C4C22×#386611yescharacteristic
145C8—1484no—
146C22—22no—
147C22—42no—
148C22—42no—
149C22—41no—
150C22—2964no—
151C22—741no—
152C22—1482no—
153C22—1481no—
154C22—1481no—
155C22C2×C22⋊#386611yescharacteristic
156C4—21no—
157C4—41no—
158C4—372no—
159C4—742no—
160C4—1481no—
161C2—21no—
162C2—42no—
163C2—81no—
164C2—2961no—
165C2—1481no—
166C2D37⋊#9911yescharacteristic
subgroupG/H
centerC2D37⋊#99
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#127×C37C4
socleC2×C37C2×#99
prime radical#14558096C2
cosocleC2×Dic74C23
hypercenter#127#3866
hypocenterC37#2134
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. #14558442C2semidirect
3. #14558441C2semidirect
6. #11924597C22semidirect
88. C37#2134semidirect

Maximal subgroups

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

subgroupindex
#145585202
#145584422
#145584412
#145580962
#213437