Finite Group Databasebeta

← #18010890

Subgroups — #18010890

Order 4736.

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

normal subgroups only

This group has 250 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#14558443C212yesmaximal, complemented
3#14558442C212yesmaximal, complemented
4#14558082C211yesmaximal, characteristic
5C2×#10596957—22no—
6#11924597C2214yes—
7#11924596—22no—
8C2×#10596966C411yescharacteristic
9C2×#10596964C2211yescharacteristic
10#11924534C2211yescharacteristic
11#11924532C411yescharacteristic
12#11924524C2211yescharacteristic
13#11924509—22no—
14#11924496—22no—
15C42×D37C411yescharacteristic
16#124×C37C411yescharacteristic
17C2×Q8×C37C2×C411yescharacteristic
18C2×D4×C37C2×C411yescharacteristic
19C2×C22⋊D37—22no—
20C2×C22⋊D37D412yes—
21C22×Dic37D412yes—
22#10596966—41no—
23#10596966—41no—
24#10596964—41no—
25#10596964—41no—
26C2×D148—21no—
27C2×D148C2×C411yescharacteristic
28C2×C4×D37—21no—
29C2×C4×D37—21no—
30C2×C4×D37C2×C411yescharacteristic
31C2×Dic74C2311yescharacteristic
32#10596957—24no—
33#10596957—42no—
34C2×#64438—42no—
35C22⋊C4×C37—22no—
36C42×C37C2×C411yescharacteristic
37#10596938—22no—
38#10596936—22no—
39C4×Dic37—21no—
40C4×Dic37C2×C411yescharacteristic
41C23×C37C22⋊C412yes—
42C22×D37—21no—
43C22×D37C22⋊C411yescharacteristic
44Q8×C37—41no—
45D4×C37—41no—
46C2×C4×C37—21no—
47C2×C4×C37—21no—
48C2×C4×C37C22×C411yescharacteristic
49C22⋊D37—42no—
50C22⋊D37—44no—
51C2×Dic37—21no—
52C2×Dic37—22no—
53C2×Dic37—22no—
54C2×Dic37C22⋊C411yescharacteristic
55C2×Dic37C2×D412yes—
56D148—41no—
57D148—42no—
58C4×D37—21no—
59C4×D37—21no—
60C4×D37—42no—
61C4×D37—41no—
62C4×D37—41no—
63Dic74—41no—
64#64438—44no—
65C22×C37—22no—
66C22×C37—42no—
67C22×C37C2×C22⋊C411yescharacteristic
68C2×D37—21no—
69C2×D37—41no—
70C2×D37—42no—
71C2×D37—41no—
72C4×C37—21no—
73C4×C37—41no—
74C4×C37—41no—
75Dic37—22no—
76Dic37—22no—
77Dic37#9911yescharacteristic
78Dic37#9911yescharacteristic
79#2132—371nomaximal, Sylow
80C2×C37—21no—
81C2×C37—42no—
82C2×C37C2×#9911yescharacteristic
83D37—41no—
84D37—81no—
85#532—371no—
86#413—372no—
87#356—372no—
88#355—372no—
89C37#213211yescharacteristic, complemented, Sylow
90C2×#41—371no—
91C2×#41—371no—
92C2×M16—742no—
93C4⋊Q8—371no—
94#127—371no—
95#124—371no—
96#124#386611yescharacteristic
97#121—742no—
98C4×D4—742no—
99C2×C42—371no—
100#101—374no—
101#100—742no—
102#41—1481no—
103#41—1481no—
104#41—1481no—
105#41—1481no—
106C2×Q8—371no—
107C2×Q8C2×#386611yescharacteristic
108C2×D4—372no—
109C2×D4—371no—
110C2×D4—741no—
111C2×D4—742no—
112C2×D4C2×#386611yescharacteristic
113C22×C4—372no—
114C22×C4—371no—
115C22×C4—741no—
116C22×C4—741no—
117M16—744no—
118M16—1482no—
119C2×C8—1482no—
120C4⋊C4—742no—
121C22⋊C4—22no—
122C22⋊C4—742no—
123C42—371no—
124C42—741no—
125C42C2×#386611yescharacteristic
126C23—371no—
127C23—741no—
128C23C22⋊#386612yes—
129Q8—41no—
130Q8—1481no—
131D4—41no—
132D4—1481no—
133D4—1482no—
134D4—1482no—
135D4—1484no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—371no—
139C2×C4—372no—
140C2×C4—741no—
141C2×C4—741no—
142C2×C4—742no—
143C2×C4—742no—
144C2×C4—741no—
145C2×C4—1481no—
146C2×C4—1481no—
147C2×C4—1482no—
148C2×C4C22×#386611yescharacteristic
149C8—1484no—
150C22—22no—
151C22—42no—
152C22—741no—
153C22—1482no—
154C22—1481no—
155C22—1481no—
156C22C2×C22⋊#386611yescharacteristic
157C4—21no—
158C4—41no—
159C4—41no—
160C4—371no—
161C4—371no—
162C4—742no—
163C4—742no—
164C2—21no—
165C2—42no—
166C2—2961no—
167C2—1481no—
168C2D37⋊#9911yescharacteristic
subgroupG/H
centerC2D37⋊#99
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#124×C37C4
socleC2×C37C2×#99
prime radical#14558082C2
cosocleC2×Dic74C23
hypercenter#124#3866
hypocenterC37#2132
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #14558520C2semidirect
2. #14558443C2semidirect
3. #14558442C2semidirect
89. C37#2132semidirect

Maximal subgroups

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

subgroupindex
#145585202
#145584432
#145584422
#145580822
#213237