Finite Group Databasebeta

← #17993728

Subgroups — #17993728

Order 4736.

214 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 57 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#14558240C211yesmaximal, characteristic
2#14557912C211yesmaximal, characteristic, complemented
3#14557825C211yesmaximal, characteristic, complemented
4#14557281C211yesmaximal, characteristic, complemented
5#14557263C211yesmaximal, characteristic, complemented
6D4⋊#64436C211yesmaximal, characteristic
7C37×#476C211yesmaximal, characteristic
8C2×#10596942—22no—
9#11924536C2211yescharacteristic
10#11924527—21no—
11#11924515—21no—
12#11924513—22no—
13C4×Dic74C2211yescharacteristic
14D4×Dic37—21no—
15C2×C4⋊Dic37—21no—
16#11924469—21no—
17C4⋊#64436C2211yescharacteristic
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—
28C22×Dic37—22no—
29C2×Dic74D411yescharacteristic
30C2×Dic74D412yes—
31C2×C8×C37—21no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37—21no—
34C4⋊C4×C37D411yescharacteristic
35C22⋊C4×C37—21no—
36C42×C37C2311yescharacteristic
37C22⋊Dic37—22no—
38#10596942—44no—
39C4⋊Dic37—22no—
40C4⋊Dic37—21no—
41C4⋊Dic37—21no—
42C4⋊Dic37D411yescharacteristic
43#10596936—22no—
44#10596936—21no—
45C4×Dic37—21no—
46C2×#64436—21no—
47C2×#64436—21no—
48C23×C37—21no—
49Q8×C37—42no—
50D4×C37—21no—
51D4×C37Q1612yescomplemented
52C2×C4×C37—21no—
53C2×C4×C37—41no—
54C2×C4×C37—41no—
55C2×C4×C37—41no—
56C2×C4×C37C2×D411yescharacteristic
57C2×C4×C37C2×D411yescharacteristic
58C2×C4×C37C2×D411yescharacteristic
59C2×Dic37—21no—
60C2×Dic37—21no—
61C2×Dic37—22no—
62C2×Dic37—82no—
63Dic74—21no—
64Dic74—21no—
65Dic74—42no—
66C8×C37—41no—
67#64436—22no—
68#64436—41no—
69C22×C37—22no—
70C22×C37—41no—
71C22×C37—41no—
72C22×C37#12011yescharacteristic
73C4×C37—21no—
74C4×C37—41no—
75C4×C37—81no—
76C4×C37C2×Q1611yescharacteristic
77C4×C37#13511yescharacteristic
78C4×C37#13711yescharacteristic
79C4×C37#13711yescharacteristic
80Dic37—41no—
81Dic37—42no—
82Dic37—41no—
83#1632—371nomaximal, Sylow
84C2×C37—42no—
85C2×C37#45111yescharacteristic
86C2×C37#45211yescharacteristic
87C2×C37#45311yescharacteristic
88#554—371no—
89#494—371no—
90#477—371no—
91#476D3711yescharacteristic
92#333—371no—
93Q8⋊C8—371no—
94D4⋊C8—371no—
95C37#163211yescharacteristic, complemented, Sylow
96C2×Q16—742no—
97C4⋊Q8—371no—
98C4⋊Q8C2×D3711yescharacteristic
99#125—741no—
100C22⋊Q8—742no—
101C22⋊Q8—741no—
102C4×Q8—371no—
103C4×D4—741no—
104C4×D4C2×D3711yescharacteristic
105C2×C4⋊C4—741no—
106#107—741no—
107#106—21no—
108C4⋊C8—371no—
109C4⋊C8C2×D3711yescharacteristic
110#103—741no—
111#102—21no—
112C4×C8—371no—
113C2×Q8—21no—
114C2×Q8—371no—
115C2×Q8—372no—
116C2×D4C22⋊D3711yescharacteristic
117C22×C4—21no—
118C22×C4—742no—
119Q16—1484no—
120C2×C8—21no—
121C2×C8—741no—
122C2×C8—741no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—371no—
126C4⋊C4—742no—
127C4⋊C4—742no—
128C4⋊C4—741no—
129C4⋊C4—741no—
130C4⋊C4—741no—
131C4⋊C4C22⋊D3711yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—742no—
134C42—741no—
135C42C22×D3711yescharacteristic
136C23—21no—
137Q8—42no—
138Q8—741no—
139Q8—741no—
140Q8—1482no—
141D4—21no—
142D4#1059694212yescomplemented
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—2962no—
148C2×C4—741no—
149C2×C4—741no—
150C2×C4—742no—
151C2×C4D4×D3711yescharacteristic
152C2×C4D4×D3711yescharacteristic
153C2×C4C2×C22⋊D3711yescharacteristic
154C8—41no—
155C8—742no—
156C8—1481no—
157C22—22no—
158C22—41no—
159C22—41no—
160C22#1192450411yescharacteristic
161C4—21no—
162C4—41no—
163C4—81no—
164C4—1481no—
165C4—1482no—
166C4—1481no—
167C4C2×#1059694211yescharacteristic
168C4#1192455711yescharacteristic
169C4#1192456511yescharacteristic
170C4#1192456611yescharacteristic
171C2—42no—
172C2#1455768811yescharacteristic
173C2#1455769211yescharacteristic
174C2#1455769911yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#476C2
socleC22×C37#120
prime radicalC2×D4×C37D4
hypercenter#476D37
hypocenterC37#1632
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. #14557912C2semidirect
3. #14557825C2semidirect
4. #14557281C2semidirect
5. #14557263C2semidirect
51. D4×C37Q16semidirect
95. C37#1632semidirect
142. D4#10596942semidirect

Maximal subgroups

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

subgroupindex
#145582402
#145579122
#145578252
#145572812
#145572632
D4⋊#644362
C37×#4762
#163237