Finite Group Databasebeta

← #17993825

Subgroups — #17993825

Order 4736.

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

normal subgroups only

This group has 212 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#14558249C211yesmaximal, characteristic
2#14557883C211yesmaximal, characteristic, complemented
3#14557814C211yesmaximal, characteristic, complemented
4#14557739C211yesmaximal, characteristic, complemented
5#14557260C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic, complemented
7C37×#333C211yesmaximal, characteristic, complemented
8C2×#10596930—21no—
9#11924536C2211yescharacteristic
10#11924525—22no—
11#11924511—21no—
12#11924511—21no—
13C4×D148C2211yescharacteristic
14C4×D148C2211yescharacteristic
15#11924494—21no—
16#11924494—21no—
17#11924470—21no—
18#11924461—21no—
19#11924460—22no—
20#11924458—21no—
21C4×#64436C2211yescharacteristic
22C4⋊Q8×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4⋊C8×C37C2211yescharacteristic
25C2×Q8×C37D412yes—
26C2×D148—22no—
27C2×D148D411yescharacteristic
28C2×D148D411yescharacteristic
29C2×C4×D37—21no—
30C2×C4×D37—21no—
31C2×Dic74—21no—
32C2×C8×C37—21no—
33C2×C8×C37—21no—
34C4⋊C4×C37—21no—
35C4⋊C4×C37—21no—
36C42×C37C2311yescharacteristic
37#10596938—22no—
38#10596938—22no—
39#10596938—21no—
40#10596938—21no—
41C4⋊Dic37—21no—
42C4⋊Dic37—21no—
43C4⋊Dic37D411yescharacteristic
44C4⋊Dic37D411yescharacteristic
45C4×Dic37—22no—
46C2×#64436—21no—
47#10596930—42no—
48C22×D37—21no—
49C22×D37—21no—
50Q8×C37—42no—
51C2×C4×C37—22no—
52C2×C4×C37C2×D411yescharacteristic
53C2×C4×C37C2×D411yescharacteristic
54C2×C4×C37C2×D411yescharacteristic
55C2×Dic37—21no—
56C2×Dic37—21no—
57C2×Dic37—41no—
58D148—21no—
59D148—21no—
60D148—21no—
61D148—21no—
62D148—82no—
63C4×D37—41no—
64C4×D37—41no—
65C4×D37—41no—
66C4×D37—41no—
67Dic74—41no—
68Dic74—41no—
69C8×C37—41no—
70C8×C37—41no—
71#64436—41no—
72C22×C37#12011yescharacteristic
73C2×D37—41no—
74C2×D37—41no—
75C2×D37—41no—
76C2×D37—41no—
77C2×D37—41no—
78C2×D37—41no—
79C4×C37—21no—
80C4×C37—42no—
81C4×C37#13511yescharacteristic
82C4×C37#13511yescharacteristic
83C4×C37AGL(1,ℤ/8)11yescharacteristic
84C4×C37#13711yescharacteristic
85Dic37—41no—
86Dic37—41no—
87Dic37—81no—
88#1646—371nomaximal, Sylow
89C2×C37#44911yescharacteristic
90C2×C37#45211yescharacteristic
91C2×C37#45511yescharacteristic
92D37—81no—
93D37—81no—
94#555—371no—
95#487—371no—
96#474—371no—
97#461—371no—
98#333D3711yescharacteristic, complemented
99D4⋊C8—371no—
100D4⋊C8—371no—
101C37#164611yescharacteristic, complemented, Sylow
102C2×SD16—741no—
103C4⋊Q8—371no—
104C4⋊Q8C2×D3711yescharacteristic
105#124—742no—
106#121—741no—
107#121—741no—
108C4×D4—371no—
109C4×D4—371no—
110#117—741no—
111#117—741no—
112#107—741no—
113C4⋊C8C2×D3711yescharacteristic
114C4⋊C8C2×D3711yescharacteristic
115#103—741no—
116#103—742no—
117#102—741no—
118C4×C8—371no—
119C2×Q8—741no—
120C2×Q8D14812yes—
121C2×D4—371no—
122C2×D4—371no—
123C2×D4—742no—
124C22×C4—741no—
125C22×C4—741no—
126SD16—1482no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—741no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—371no—
133C4⋊C4—371no—
134C4⋊C4—741no—
135C4⋊C4—741no—
136C22⋊C4—742no—
137C22⋊C4—742no—
138C22⋊C4—741no—
139C22⋊C4—741no—
140C42—742no—
141C42C22×D3711yescharacteristic
142C23—741no—
143C23—741no—
144Q8—42no—
145Q8—1481no—
146Q8—1481no—
147D4—2962no—
148D4—741no—
149D4—741no—
150D4—741no—
151D4—741no—
152C2×C4—22no—
153C2×C4—741no—
154C2×C4—741no—
155C2×C4—1481no—
156C2×C4—1481no—
157C2×C4—1481no—
158C2×C4—1481no—
159C2×C4—1481no—
160C2×C4C2×D14811yescharacteristic
161C2×C4D4×D3711yescharacteristic
162C2×C4D4×D3711yescharacteristic
163C8—41no—
164C8—41no—
165C8—1481no—
166C22—1481no—
167C22—1481no—
168C22—1481no—
169C22—1481no—
170C22—1481no—
171C22—1481no—
172C22#1192450611yescharacteristic
173C4—21no—
174C4—42no—
175C4—2961no—
176C4—1481no—
177C4—1481no—
178C4#1192455711yescharacteristic
179C4#1192455911yescharacteristic
180C4#1192456311yescharacteristic
181C4#1192456811yescharacteristic
182C2—2961no—
183C2—2961no—
184C2#1455768111yescharacteristic
185C2#1455769811yescharacteristic
186C2#1455771311yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#333C2
socleC22×C37#120
prime radical#14558249C2
hypercenter#333D37
hypocenterC37#1646
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #14557883C2semidirect
3. #14557814C2semidirect
4. #14557739C2semidirect
5. #14557260C2semidirect
6. #14557260C2semidirect
7. C37×#333C2semidirect
98. #333D37semidirect
101. C37#1646semidirect

Maximal subgroups

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

subgroupindex
#145582492
#145578832
#145578142
#145577392
#145572602
C37×#3332
#164637