Finite Group Databasebeta

← #18010063

Subgroups — #18010063

Order 4736.

216 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 58 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#14558555C211yesmaximal, characteristic, complemented
2C4×#10596953C211yesmaximal, characteristic, complemented
3#14558390C212yesmaximal, complemented
4#14558389C212yesmaximal, complemented
5#14558070C211yesmaximal, characteristic
6C2×#10596953—21no—
7C4⋊#64438—21no—
8#11924593—21no—
9#11924591C2212yes—
10#11924591C2212yes—
11C4×#64438—21no—
12#11924531—21no—
13#11924527C2211yescharacteristic
14#11924525C2211yescharacteristic
15#11924521—21no—
16#11924512C411yescharacteristic
17#11924511C411yescharacteristic
18C4×D148—21no—
19C4×D148C411yescharacteristic
20#11924493—21no—
21C42×D37C2211yescharacteristic
22C4×Q8×C37C411yescharacteristic
23C2×Q8×C37C2×C411yescharacteristic
24C2×D148—21no—
25C2×D148C2×C411yescharacteristic
26C2×C4×D37—21no—
27C2×C4×D37C2×C411yescharacteristic
28C2×C4×D37D411yescharacteristic
29C2×C4×D37D411yescharacteristic
30C2×#64438—22no—
31C2×#64438—22no—
32#10596953—24no—
33C4⋊C4×C37—21no—
34C4⋊C4×C37C2×C411yescharacteristic
35C42×C37—21no—
36C42×C37C2×C411yescharacteristic
37#10596938—21no—
38#10596938—21no—
39#10596938—21no—
40#10596938—21no—
41#10596938—21no—
42C4⋊Dic37—21no—
43C4⋊Dic37C2×C411yescharacteristic
44#10596936—21no—
45#10596936—21no—
46C4×Dic37D411yescharacteristic
47C4×Dic37D411yescharacteristic
48C4×Dic37C2311yescharacteristic
49C22×D37—21no—
50C22×D37C22⋊C411yescharacteristic
51Q8×C37—41no—
52C2×C4×C37—21no—
53C2×C4×C37—21no—
54C2×C4×C37C22⋊C411yescharacteristic
55C2×C4×C37C22⋊C411yescharacteristic
56C2×C4×C37C22×C411yescharacteristic
57C2×Dic37—21no—
58C2×Dic37C22⋊C411yescharacteristic
59C2×Dic37C2×D411yescharacteristic
60C2×Dic37C2×D411yescharacteristic
61D148—41no—
62D148—42no—
63C4×D37—22no—
64C4×D37—41no—
65C4×D37—41no—
66C4×D37—42no—
67#64438—24no—
68#64438—42no—
69C22×C37C2×C22⋊C411yescharacteristic
70C2×D37—21no—
71C2×D37—21no—
72C2×D37—21no—
73C2×D37—41no—
74C2×D37—41no—
75C2×D37—41no—
76C4×C37—21no—
77C4×C37—21no—
78C4×C37—41no—
79C4×C37—41no—
80C4×C37#10412yes—
81Dic37—21no—
82Dic37—21no—
83Dic37—21no—
84Dic37—41no—
85#1529—371nomaximal, Sylow
86C2×C37#41311yescharacteristic
87C2×C37C2×#10411yescharacteristic
88C2×C37#42111yescharacteristic
89D37—41no—
90D37—81no—
91#529—371no—
92#432—371no—
93C4×M16—371no—
94#330—372no—
95#329—372no—
96C37#152911yescharacteristic, complemented, Sylow
97C2×M16—741no—
98#126—741no—
99#125—371no—
100#124—371no—
101#123—741no—
102C22⋊Q8—371no—
103#121—371no—
104C4×Q8#386611yescharacteristic
105C4×D4—371no—
106C4×D4—741no—
107#117—741no—
108C2×C42—371no—
109C4⋊C8—741no—
110C22⋊C8—741no—
111#97—372no—
112#97—372no—
113C4×C8—741no—
114C2×Q8C2×#386611yescharacteristic
115C2×D4—371no—
116C2×D4—741no—
117C22×C4—371no—
118C22×C4—371no—
119C22×C4—371no—
120C22×C4—741no—
121M16—744no—
122C2×C8—742no—
123C2×C8—742no—
124C4⋊C4—21no—
125C4⋊C4—371no—
126C4⋊C4—741no—
127C4⋊C4—741no—
128C4⋊C4—741no—
129C4⋊C4C2×#386611yescharacteristic
130C22⋊C4—741no—
131C22⋊C4—741no—
132C22⋊C4—741no—
133C22⋊C4—741no—
134C22⋊C4—741no—
135C42—21no—
136C42—371no—
137C42—371no—
138C42—371no—
139C42C2×#386611yescharacteristic
140C23—371no—
141C23—741no—
142Q8—41no—
143D4—1481no—
144D4—1482no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—371no—
148C2×C4—371no—
149C2×C4—371no—
150C2×C4—742no—
151C2×C4—741no—
152C2×C4—1481no—
153C2×C4—1481no—
154C2×C4—1482no—
155C2×C4C22⋊#386611yescharacteristic
156C2×C4C22⋊#386611yescharacteristic
157C2×C4C22×#386611yescharacteristic
158C8—744no—
159C8—1482no—
160C22—741no—
161C22—741no—
162C22—741no—
163C22—1481no—
164C22—1481no—
165C22—1481no—
166C22C2×C22⋊#386611yescharacteristic
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—741no—
172C4—741no—
173C4—741no—
174C4—1481no—
175C4#1192460112yes—
176C2—2961no—
177C2—1481no—
178C2#1455851911yescharacteristic
179C2C2×#1192460111yescharacteristic
180C2#1455853011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC4×Q8×C37C4
socleC22×C37C2×C22⋊C4
prime radical#11924511C4
cosocleC4×Dic37C23
hypercenterC4×Q8#3866
hypocenterC37#1529
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #14558555C2semidirect
2. C4×#10596953C2semidirect
3. #14558390C2semidirect
4. #14558389C2semidirect
96. C37#1529semidirect

Maximal subgroups

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

subgroupindex
#145585552
C4×#105969532
#145583902
#145583892
#145580702
#152937