Finite Group Databasebeta

← #17993896

Subgroups — #17993896

Order 4736.

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

normal subgroups only

This group has 206 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#14558287C211yesmaximal, characteristic, complemented
2#14557922C211yesmaximal, characteristic
3#14557899C211yesmaximal, characteristic, complemented
4#14557898C211yesmaximal, characteristic, complemented
5#14557274C211yesmaximal, characteristic, complemented
6#14557272C211yesmaximal, characteristic, complemented
7C37×#330C211yesmaximal, characteristic, complemented
8C2×#10596930—21no—
9C2×D296—21no—
10#11924535—21no—
11#11924533C2211yescharacteristic
12#11924531—21no—
13#11924531—21no—
14#11924528C2211yescharacteristic
15#11924524C2211yescharacteristic
16#11924521—21no—
17#11924516—21no—
18#11924514—21no—
19#11924458—21no—
20#11924458—21no—
21#11924456—21no—
22#11924456—21no—
23#11924447C2211yescharacteristic
24#125×C37C2211yescharacteristic
25#97×C37C2211yescharacteristic
26#97×C37C2211yescharacteristic
27C2×D148—21no—
28C2×D148—21no—
29C2×D148—21no—
30C2×D148D411yescharacteristic
31C2×C4×D37—21no—
32C2×Dic74—21no—
33C2×Dic74D411yescharacteristic
34C2×C8×C37—21no—
35C2×C8×C37—21no—
36C4⋊C4×C37—21no—
37C4⋊C4×C37—21no—
38C4⋊C4×C37D411yescharacteristic
39C4⋊C4×C37D411yescharacteristic
40C42×C37C2311yescharacteristic
41#10596938—21no—
42#10596938—21no—
43#10596938—21no—
44#10596938—21no—
45#10596938—21no—
46C4⋊Dic37—21no—
47C4⋊Dic37D411yescharacteristic
48C4⋊Dic37D411yescharacteristic
49#10596936—21no—
50#10596936—21no—
51#10596936—21no—
52C4×Dic37—21no—
53C2×#64436—21no—
54D296—42no—
55#10596930—42no—
56C22×D37—21no—
57C22×D37—41no—
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—21no—
66D148—41no—
67D148—41no—
68D148—41no—
69D148—42no—
70D148—42no—
71C4×D37—81no—
72Dic74—41no—
73Dic74—81no—
74C8×C37—22no—
75C8×C37—41no—
76#64436—41no—
77C22×C37#12011yescharacteristic
78C2×D37—41no—
79C2×D37—41no—
80C2×D37—41no—
81C2×D37—81no—
82C2×D37—81no—
83C2×D37—81no—
84C4×C37—21no—
85C4×C37—21no—
86C4×C37—21no—
87C4×C37—41no—
88C4×C37—41no—
89Dic37—41no—
90Dic37—41no—
91Dic37—41no—
92#1657—371nomaximal, Sylow
93C2×C37#45311yescharacteristic
94C2×C37#45411yescharacteristic
95C2×C37#45411yescharacteristic
96D37—81no—
97D37—161no—
98#563—371no—
99#496—371no—
100#490—371no—
101#490—371no—
102#330—371no—
103#330D3711yescharacteristic, complemented
104#329—371no—
105C37#165711yescharacteristic, complemented, Sylow
106C2×SD16—741no—
107C2×D8—741no—
108C4⋊Q8—741no—
109#127—371no—
110#126—741no—
111#126—741no—
112#125—371no—
113#125C2×D3711yescharacteristic
114#124—371no—
115#123—741no—
116C22⋊Q8—741no—
117C22⋊Q8—741no—
118#102—741no—
119#102—741no—
120#102—741no—
121#102—741no—
122#97—371no—
123#97C2×D3711yescharacteristic
124#97C2×D3711yescharacteristic
125C2×Q8—371no—
126C2×Q8—741no—
127C2×D4—371no—
128C2×D4—741no—
129C2×D4—741no—
130C2×D4—741no—
131C22×C4—741no—
132SD16—1482no—
133D8—1482no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—741no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—371no—
140C4⋊C4—371no—
141C4⋊C4—741no—
142C4⋊C4—741no—
143C4⋊C4—741no—
144C4⋊C4—741no—
145C4⋊C4D14811yescharacteristic
146C4⋊C4D14811yescharacteristic
147C22⋊C4—741no—
148C22⋊C4—741no—
149C22⋊C4—741no—
150C22⋊C4—741no—
151C22⋊C4—741no—
152C42—741no—
153C42C22×D3711yescharacteristic
154C23—741no—
155C23—1481no—
156Q8—2961no—
157Q8—1481no—
158D4—1481no—
159D4—1481no—
160D4—1482no—
161D4—1482no—
162D4—1481no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—2961no—
166C2×C4—741no—
167C2×C4—741no—
168C2×C4—741no—
169C2×C4C2×D14811yescharacteristic
170C2×C4D4×D3711yescharacteristic
171C2×C4D4×D3711yescharacteristic
172C8—22no—
173C8—41no—
174C8—1481no—
175C22—2961no—
176C22—2961no—
177C22—2961no—
178C22—1481no—
179C22—1481no—
180C22—1481no—
181C22#1192450611yescharacteristic
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—1481no—
188C4—1481no—
189C4—1481no—
190C2—2961no—
191C2—5921no—
192C2#1455770211yescharacteristic
193C2#1455770711yescharacteristic
194C2#1455770811yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#330C2
socleC22×C37#120
prime radical#14557922C2
hypercenter#330D37
hypocenterC37#1657
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. #14558287C2semidirect
3. #14557899C2semidirect
4. #14557898C2semidirect
5. #14557274C2semidirect
6. #14557272C2semidirect
7. C37×#330C2semidirect
103. #330D37semidirect
105. C37#1657semidirect

Maximal subgroups

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

subgroupindex
#145582872
#145579222
#145578992
#145578982
#145572742
#145572722
C37×#3302
#165737