Finite Group Databasebeta

← #17993766

Subgroups — #17993766

Order 4736.

194 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 53 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#14558253C211yesmaximal, characteristic
2#14557883C211yesmaximal, characteristic, complemented
3#14557825C211yesmaximal, characteristic, complemented
4#14557280C211yesmaximal, characteristic, complemented
5#14557263C211yesmaximal, characteristic, complemented
6D4⋊#64436C211yesmaximal, characteristic
7C37×#476C211yesmaximal, characteristic
8#11924536C2211yescharacteristic
9#11924529—22no—
10#11924523—21no—
11#11924515—21no—
12C4×Dic74C2211yescharacteristic
13#11924501—21no—
14#11924495—21no—
15#11924469—21no—
16C4⋊#64436C2211yescharacteristic
17#11924460—22no—
18#11924459—21no—
19C4×#64436C2211yescharacteristic
20C4⋊Q8×C37C2211yescharacteristic
21C4×D4×C37C2211yescharacteristic
22#106×C37—21no—
23C4⋊C8×C37C2211yescharacteristic
24#102×C37—21no—
25C2×Q8×C37—21no—
26C2×D4×C37D411yescharacteristic
27C22×C4×C37—21no—
28C2×Dic74—21no—
29C2×Dic74D411yescharacteristic
30C2×C8×C37—21no—
31C4⋊C4×C37—21no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37D411yescharacteristic
34C22⋊C4×C37—21no—
35C42×C37C2311yescharacteristic
36C22⋊Dic37—22no—
37C22⋊Dic37—22no—
38C4⋊Dic37—21no—
39C4⋊Dic37D411yescharacteristic
40C4⋊Dic37D412yes—
41#10596936—22no—
42#10596936—21no—
43C4×Dic37—22no—
44C4×Dic37—21no—
45C2×#64436—21no—
46C2×#64436—21no—
47C23×C37—21no—
48Q8×C37—42no—
49D4×C37—21no—
50D4×C37—21no—
51C2×C4×C37—21no—
52C2×C4×C37—41no—
53C2×C4×C37—41no—
54C2×C4×C37—41no—
55C2×C4×C37C2×D411yescharacteristic
56C2×C4×C37C2×D411yescharacteristic
57C2×C4×C37C2×D411yescharacteristic
58C2×Dic37—21no—
59C2×Dic37—21no—
60C2×Dic37—22no—
61Dic74—21no—
62Dic74—21no—
63Dic74—41no—
64Dic74—41no—
65C8×C37—41no—
66#64436—41no—
67#64436—41no—
68C22×C37—41no—
69C22×C37—41no—
70C22×C37—41no—
71C22×C37#12011yescharacteristic
72C4×C37—21no—
73C4×C37—41no—
74C4×C37—81no—
75C4×C37#13511yescharacteristic
76C4×C37#13511yescharacteristic
77C4×C37#13711yescharacteristic
78C4×C37#13711yescharacteristic
79Dic37—41no—
80Dic37—42no—
81Dic37—41no—
82#1638—371nomaximal, Sylow
83C2×C37—81no—
84C2×C37#45211yescharacteristic
85C2×C37#45211yescharacteristic
86C2×C37#45411yescharacteristic
87#556—371no—
88#487—371no—
89#477—371no—
90#476D3711yescharacteristic
91#332—371no—
92Q8⋊C8—371no—
93D4⋊C8—371no—
94C37#163811yescharacteristic, complemented, Sylow
95C4⋊Q8—371no—
96C4⋊Q8C2×D3711yescharacteristic
97#126—742no—
98#124—741no—
99C22⋊Q8—741no—
100C4×Q8—371no—
101C4×Q8—741no—
102C4×D4C2×D3711yescharacteristic
103#117—741no—
104#107—741no—
105#106—21no—
106C4⋊C8—371no—
107C4⋊C8C2×D3711yescharacteristic
108#103—741no—
109#103—742no—
110#102—21no—
111C4×C8—371no—
112C2×Q8—21no—
113C2×Q8—371no—
114C2×Q8—741no—
115C2×D4C22⋊D3711yescharacteristic
116C22×C4—21no—
117C2×C8—21no—
118C2×C8—741no—
119C2×C8—741no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—372no—
123C4⋊C4—371no—
124C4⋊C4—742no—
125C4⋊C4—741no—
126C4⋊C4—741no—
127C4⋊C4C22⋊D3711yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—742no—
130C22⋊C4—742no—
131C42—742no—
132C42—741no—
133C42C22×D3711yescharacteristic
134C23—21no—
135Q8—42no—
136Q8—741no—
137Q8—741no—
138Q8—1481no—
139Q8—1481no—
140D4—21no—
141D4—21no—
142C2×C4—21no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—741no—
147C2×C4—742no—
148C2×C4—741no—
149C2×C4D4×D3711yescharacteristic
150C2×C4D4×D3711yescharacteristic
151C2×C4C2×C22⋊D3711yescharacteristic
152C8—41no—
153C8—1481no—
154C8—1481no—
155C22—41no—
156C22—41no—
157C22—41no—
158C22#1192450411yescharacteristic
159C4—21no—
160C4—41no—
161C4—81no—
162C4—1481no—
163C4—1481no—
164C4—1482no—
165C4#1192455611yescharacteristic
166C4#1192455711yescharacteristic
167C4#1192456511yescharacteristic
168C4#1192456711yescharacteristic
169C2—81no—
170C2#1455769211yescharacteristic
171C2#1455769311yescharacteristic
172C2#1455770411yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#476C2
socleC22×C37#120
prime radicalC2×D4×C37D4
hypercenter#476D37
hypocenterC37#1638
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #14557883C2semidirect
3. #14557825C2semidirect
4. #14557280C2semidirect
5. #14557263C2semidirect
94. C37#1638semidirect

Maximal subgroups

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

subgroupindex
#145582532
#145578832
#145578252
#145572802
#145572632
D4⋊#644362
C37×#4762
#163837