Finite Group Databasebeta

← #17993915

Subgroups — #17993915

Order 4736.

208 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 45 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#14558281C211yesmaximal, characteristic
2#14557943C211yesmaximal, characteristic, complemented
3#14557927C211yesmaximal, characteristic, complemented
4#14557893C211yesmaximal, characteristic, complemented
5#14557272C211yesmaximal, characteristic, complemented
6#14557272C211yesmaximal, characteristic, complemented
7C37×#330C211yesmaximal, characteristic, complemented
8C2×Dic148—21no—
9C2×#10596930—21no—
10#11924536C2211yescharacteristic
11#11924524C2211yescharacteristic
12#11924524C2211yescharacteristic
13#11924521—21no—
14#11924521—21no—
15#11924514—21no—
16#11924514—21no—
17#11924511—21no—
18#11924511—21no—
19#11924469—21no—
20#11924467—21no—
21#11924461—21no—
22#11924458—21no—
23#11924447C2211yescharacteristic
24#125×C37C2211yescharacteristic
25#97×C37C2211yescharacteristic
26#97×C37C2211yescharacteristic
27C2×D148—21no—
28C2×D148—21no—
29C2×D148D411yescharacteristic
30C2×D148D411yescharacteristic
31C2×C4×D37—21no—
32C2×C4×D37—21no—
33C2×Dic74—21no—
34C2×Dic74D411yescharacteristic
35C2×Dic74D411yescharacteristic
36C2×C8×C37—21no—
37C2×C8×C37—21no—
38C4⋊C4×C37—21no—
39C4⋊C4×C37—21no—
40C4⋊C4×C37D411yescharacteristic
41C4⋊C4×C37D411yescharacteristic
42C42×C37C2311yescharacteristic
43#10596938—21no—
44#10596938—21no—
45#10596938—21no—
46#10596938—21no—
47#10596938—21no—
48#10596938—21no—
49C4⋊Dic37—21no—
50C4⋊Dic37—21no—
51#10596936—21no—
52#10596936—21no—
53C2×#64436—21no—
54Dic148—42no—
55#10596930—42no—
56C22×D37—21no—
57C22×D37—21no—
58C2×C4×C37—21no—
59C2×C4×C37—21no—
60C2×C4×C37C2×D411yescharacteristic
61C2×C4×C37C2×D411yescharacteristic
62C2×C4×C37C2×D411yescharacteristic
63C2×Dic37—21no—
64C2×Dic37—21no—
65C2×Dic37—41no—
66D148—41no—
67D148—41no—
68D148—81no—
69D148—81no—
70C4×D37—81no—
71C4×D37—81no—
72Dic74—41no—
73Dic74—41no—
74Dic74—41no—
75Dic74—41no—
76C8×C37—22no—
77C8×C37—41no—
78#64436—22no—
79C22×C37#12011yescharacteristic
80C2×D37—41no—
81C2×D37—41no—
82C2×D37—41no—
83C2×D37—41no—
84C2×D37—41no—
85C2×D37—41no—
86C4×C37—21no—
87C4×C37—21no—
88C4×C37—21no—
89C4×C37—41no—
90C4×C37—41no—
91Dic37—41no—
92Dic37—41no—
93Dic37—81no—
94#1661—371nomaximal, Sylow
95C2×C37#45311yescharacteristic
96C2×C37#45511yescharacteristic
97C2×C37#45611yescharacteristic
98D37—81no—
99D37—81no—
100#562—371no—
101#501—371no—
102#497—371no—
103#489—371no—
104#330D3711yescharacteristic, complemented
105#329—371no—
106#329—371no—
107C37#166111yescharacteristic, complemented, Sylow
108C2×Q16—741no—
109C2×SD16—741no—
110C4⋊Q8—371no—
111#125C2×D3711yescharacteristic
112#124—371no—
113#124—371no—
114#123—741no—
115#123—741no—
116C22⋊Q8—741no—
117C22⋊Q8—741no—
118#121—741no—
119#121—741no—
120#107—741no—
121#106—741no—
122#103—741no—
123#102—741no—
124#97—371no—
125#97C2×D3711yescharacteristic
126#97C2×D3711yescharacteristic
127C2×Q8—371no—
128C2×Q8—371no—
129C2×Q8—741no—
130C2×D4—371no—
131C2×D4—371no—
132C2×D4—741no—
133C2×D4—741no—
134C22×C4—741no—
135C22×C4—741no—
136Q16—1482no—
137SD16—1482no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—741no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—741no—
144C4⋊C4—741no—
145C4⋊C4—741no—
146C4⋊C4—741no—
147C4⋊C4D14811yescharacteristic
148C4⋊C4D14811yescharacteristic
149C22⋊C4—741no—
150C22⋊C4—741no—
151C22⋊C4—741no—
152C22⋊C4—741no—
153C22⋊C4—741no—
154C22⋊C4—741no—
155C42C22×D3711yescharacteristic
156C23—741no—
157C23—741no—
158Q8—1481no—
159Q8—1481no—
160Q8—1481no—
161Q8—1481no—
162D4—2961no—
163D4—2961no—
164D4—1481no—
165D4—1481no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—2961no—
169C2×C4—2961no—
170C2×C4—741no—
171C2×C4—741no—
172C2×C4—1481no—
173C2×C4C2×D14811yescharacteristic
174C2×C4D4×D3711yescharacteristic
175C2×C4D4×D3711yescharacteristic
176C8—22no—
177C8—41no—
178C8—742no—
179C22—1481no—
180C22—1481no—
181C22—1481no—
182C22—1481no—
183C22—1481no—
184C22—1481no—
185C22#1192450611yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—41no—
191C4—2961no—
192C4—1481no—
193C4—1481no—
194C2—2961no—
195C2—2961no—
196C2#1455770211yescharacteristic
197C2#1455771211yescharacteristic
198C2#1455771811yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#330C2
socleC22×C37#120
prime radical#14558281C2
hypercenter#330D37
hypocenterC37#1661
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #14557943C2semidirect
3. #14557927C2semidirect
4. #14557893C2semidirect
5. #14557272C2semidirect
6. #14557272C2semidirect
7. C37×#330C2semidirect
104. #330D37semidirect
107. C37#1661semidirect

Maximal subgroups

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

subgroupindex
#145582812
#145579432
#145579272
#145578932
#145572722
C37×#3302
#166137