Finite Group Databasebeta

← #17993156

Subgroups — #17993156

Order 4736.

264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 93 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#14557586C211yesmaximal, characteristic, complemented
2#14557399C211yesmaximal, characteristic, complemented
3#14557267C214yesmaximal, complemented
4C37×#532C211yesmaximal, characteristic
5C2×C4⋊Dic37—21no—
6C4⋊#64436—21no—
7C22⋊#64436C2212yes—
8C4×#64436—21no—
9#11924443—21no—
10#11924443C2212yes—
11C2×#41×C37—21no—
12C4⋊Q8×C37C411yescharacteristic, complemented
13#127×C37C411yescharacteristic, complemented
14#124×C37—21no—
15#121×C37—21no—
16#121×C37C2212yes—
17C4×D4×C37—21no—
18C4×D4×C37C412yescomplemented
19C2×C42×C37C2211yescharacteristic
20#41×C37—42no—
21#41×C37—42no—
22C2×Q8×C37—21no—
23C2×D4×C37—22no—
24C2×D4×C37—21no—
25C2×D4×C37—21no—
26C2×D4×C37C2×C412yes—
27C22×C4×C37—22no—
28C22×C4×C37D411yescharacteristic
29C22×C4×C37D411yescharacteristic
30C22×C4×C37C2311yescharacteristic
31C22×Dic37—22no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37C2×C412yes—
34C22⋊C4×C37—22no—
35C22⋊C4×C37—22no—
36C42×C37C2×C411yescharacteristic
37C42×C37C2×C411yescharacteristic
38C42×C37D411yescharacteristic
39C42×C37D411yescharacteristic
40C4⋊Dic37—42no—
41C2×#64436—22no—
42C23×C37—22no—
43C23×C37C2×D411yescharacteristic
44Q8×C37—42no—
45D4×C37—42no—
46D4×C37—42no—
47D4×C37—42no—
48D4×C37—42no—
49D4×C37—42no—
50C2×C4×C37—22no—
51C2×C4×C37—41no—
52C2×C4×C37—41no—
53C2×C4×C37—44no—
54C2×C4×C37C22⋊C411yescharacteristic
55C2×C4×C37C22⋊C411yescharacteristic
56C2×C4×C37C22⋊C411yescharacteristic
57C2×C4×C37C22⋊C411yescharacteristic
58C2×C4×C37D812yes—
59C2×C4×C37SD1612yes—
60C2×C4×C37C22×C411yescharacteristic
61C2×C4×C37C2×D411yescharacteristic
62C2×Dic37—42no—
63C2×Dic37—42no—
64C2×Dic37—42no—
65#64436—42no—
66C22×C37—21no—
67C22×C37—21no—
68C22×C37—42no—
69C22×C37—42no—
70C22×C37—42no—
71C22×C37C2×C22⋊C411yescharacteristic
72C22×C37C2×D811yescharacteristic
73C22×C37C2×SD1611yescharacteristic
74C4×C37—21no—
75C4×C37—21no—
76C4×C37—21no—
77C4×C37—21no—
78C4×C37—42no—
79C4×C37#10212yes—
80C4×C37#10212yes—
81Dic37—82no—
82#1517—371nomaximal, Sylow
83C2×C37—21no—
84C2×C37—21no—
85C2×C37—82no—
86C2×C37#41011yescharacteristic
87C2×C37C2×#10211yescharacteristic
88C2×C37#42111yescharacteristic
89#532D3711yescharacteristic
90#431—371no—
91#382—371no—
92#327—374no—
93C37#151711yescharacteristic, complemented, Sylow
94C2×#41—21no—
95C4⋊Q8Dic3711yescharacteristic, complemented
96#127Dic3711yescharacteristic, complemented
97#124—21no—
98#121—21no—
99#121C2×D3712yes—
100C4×D4—21no—
101C4×D4Dic3712yescomplemented
102C2×C4⋊C4—741no—
103C2×C42C2×D3711yescharacteristic
104C4⋊C8—741no—
105C22⋊C8—372no—
106C4×C8—741no—
107#95—372no—
108#95—741no—
109#41—42no—
110#41—42no—
111C2×Q8—21no—
112C2×D4—22no—
113C2×D4—21no—
114C2×D4—21no—
115C2×D4C2×Dic3712yes—
116C22×C4—22no—
117C22×C4—742no—
118C22×C4C22⋊D3711yescharacteristic
119C22×C4C22⋊D3711yescharacteristic
120C22×C4C22×D3711yescharacteristic
121C2×C8—742no—
122C4⋊C4—21no—
123C4⋊C4—1482no—
124C4⋊C4C2×Dic3712yes—
125C22⋊C4—22no—
126C22⋊C4—22no—
127C42C2×Dic3711yescharacteristic
128C42C2×Dic3711yescharacteristic
129C42C22⋊D3711yescharacteristic
130C42C22⋊D3711yescharacteristic
131C23—22no—
132C23C2×C22⋊D3711yescharacteristic
133Q8—42no—
134D4—42no—
135D4—42no—
136D4—42no—
137D4—42no—
138D4—42no—
139C2×C4—22no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—44no—
143C2×C4—1482no—
144C2×C4—1482no—
145C2×C4—1482no—
146C2×C4#1059693912yes—
147C2×C4#1059694012yes—
148C2×C4C22⋊Dic3711yescharacteristic
149C2×C4C22⋊Dic3711yescharacteristic
150C2×C4C22⋊Dic3711yescharacteristic
151C2×C4C22⋊Dic3711yescharacteristic
152C2×C4C22×Dic3711yescharacteristic
153C2×C4C2×C22⋊D3711yescharacteristic
154C8—1482no—
155C22—21no—
156C22—21no—
157C22—42no—
158C22—42no—
159C22—42no—
160C22C2×C22⋊Dic3711yescharacteristic
161C22C2×#1059693911yescharacteristic
162C22C2×#1059694011yescharacteristic
163C4—21no—
164C4—21no—
165C4—21no—
166C4—21no—
167C4—42no—
168C4—2962no—
169C4#1192445712yes—
170C4#1192445712yes—
171C2—21no—
172C2—21no—
173C2—82no—
174C2#1455750711yescharacteristic
175C2C2×#1192445711yescharacteristic
176C2#1455755011yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
Fitting, prime radicalC37×#532C2
socleC22×C37C2×C22⋊C4
cosocleC22×C4×C37C23
hypercenter#532D37
hypocenterC37#1517
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #14557586C2semidirect
2. #14557399C2semidirect
3. #14557267C2semidirect
12. C4⋊Q8×C37C4semidirect
13. #127×C37C4semidirect
18. C4×D4×C37C4semidirect
93. C37#1517semidirect
95. C4⋊Q8Dic37semidirect
96. #127Dic37semidirect
101. C4×D4Dic37semidirect

Maximal subgroups

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

subgroupindex
#145575862
#145573992
#145572672
C37×#5322
#151737