Finite Group Databasebeta

← #17993571

Subgroups — #17993571

Order 4736.

238 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 51 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#14558162C211yesmaximal, characteristic
2#14557691C211yesmaximal, characteristic
3#14557688C211yesmaximal, characteristic
4#14557454C211yesmaximal, characteristic
5#14557269C211yesmaximal, characteristic
6#14557258C211yesmaximal, characteristic
7C37×#328C211yesmaximal, characteristic
8C22×Dic74C2211yescharacteristic
9C2×Dic148—21no—
10C2×#10596942—21no—
11#11924535—21no—
12#11924534—21no—
13#11924526—21no—
14#11924526—21no—
15#11924515C2211yescharacteristic
16#11924513—21no—
17#11924492—21no—
18C2×C4⋊Dic37—21no—
19C2×#10596936C2211yescharacteristic
20#11924461—21no—
21#11924459—21no—
22C22⋊#64436C2211yescharacteristic
23#11924443—21no—
24C22⋊Q8×C37C2211yescharacteristic
25C22⋊C8×C37C2211yescharacteristic
26#95×C37C2211yescharacteristic
27C2×Q8×C37D411yescharacteristic
28C22×C4×C37—21no—
29C22×C4×C37C2311yescharacteristic
30C22×Dic37—21no—
31C22×Dic37D411yescharacteristic
32C22×Dic37D411yescharacteristic
33C2×Dic74—21no—
34C2×Dic74—21no—
35C2×Dic74—21no—
36C2×Dic74—42no—
37C2×Dic74D411yescharacteristic
38C2×C8×C37—21no—
39C4⋊C4×C37—21no—
40C4⋊C4×C37D411yescharacteristic
41C22⋊C4×C37—21no—
42C22⋊Dic37—21no—
43#10596942—42no—
44C4⋊Dic37—21no—
45C4⋊Dic37—42no—
46C4⋊Dic37D411yescharacteristic
47#10596936—21no—
48#10596936—21no—
49#10596936—21no—
50#10596936—21no—
51#10596936—21no—
52#10596936—21no—
53#10596936—21no—
54C4×Dic37—21no—
55C4×Dic37—21no—
56C2×#64436—21no—
57Dic148—42no—
58C23×C37C2×D411yescharacteristic
59Q8×C37—41no—
60C2×C4×C37—22no—
61C2×C4×C37—21no—
62C2×C4×C37—21no—
63C2×C4×C37—41no—
64C2×C4×C37—41no—
65C2×C4×C37—41no—
66C2×C4×C37C2×D411yescharacteristic
67C2×C4×C37C2×D411yescharacteristic
68C2×Dic37—21no—
69C2×Dic37—21no—
70C2×Dic37—22no—
71C2×Dic37—21no—
72C2×Dic37—21no—
73C2×Dic37—21no—
74C2×Dic37—41no—
75C2×Dic37—41no—
76C2×Dic37—41no—
77C2×Dic37Q1612yescomplemented
78Dic74—22no—
79Dic74—22no—
80Dic74—41no—
81Dic74—41no—
82Dic74—41no—
83Dic74—81no—
84C8×C37—41no—
85#64436—41no—
86C22×C37—21no—
87C22×C37—21no—
88C22×C37#12011yescharacteristic
89C22×C37C2×Q1611yescharacteristic
90C22×C37#13711yescharacteristic
91C4×C37—21no—
92C4×C37—21no—
93C4×C37—42no—
94C4×C37—41no—
95C4×C37—41no—
96Dic37—22no—
97Dic37—41no—
98Dic37—42no—
99Dic37—41no—
100Dic37—41no—
101#1605—371nomaximal, Sylow
102C2×C37—21no—
103C2×C37—21no—
104C2×C37#45111yescharacteristic
105C2×C37#45611yescharacteristic
106C2×C37B(4,𝔽2)11yescharacteristic
107#544—371no—
108#451—371no—
109#451—371no—
110#395—371no—
111#328—371no—
112#328D3711yescharacteristic
113#324—371no—
114C37#160511yescharacteristic, complemented, Sylow
115C22×Q8—371no—
116C2×Q16—741no—
117C2×Q16—741no—
118C4⋊Q8—741no—
119C4⋊Q8—741no—
120#125—741no—
121#125—741no—
122C22⋊Q8—371no—
123C22⋊Q8—741no—
124C22⋊Q8C2×D3711yescharacteristic
125#117—741no—
126C2×C4⋊C4—371no—
127C2×C4⋊C4—741no—
128#103—741no—
129#103—741no—
130C22⋊C8—371no—
131C22⋊C8C2×D3711yescharacteristic
132#95—741no—
133#95C2×D3711yescharacteristic
134C2×Q8—371no—
135C2×Q8—741no—
136C2×Q8—741no—
137C2×Q8—741no—
138C2×Q8—1482no—
139C2×Q8D14811yescharacteristic
140C22×C4—21no—
141C22×C4—371no—
142C22×C4—371no—
143C22×C4—741no—
144C22×C4C22×D3711yescharacteristic
145Q16—1482no—
146Q16—1482no—
147C2×C8—21no—
148C2×C8—741no—
149C4⋊C4—21no—
150C4⋊C4—371no—
151C4⋊C4—741no—
152C4⋊C4—741no—
153C4⋊C4—741no—
154C4⋊C4—741no—
155C4⋊C4—741no—
156C4⋊C4—741no—
157C4⋊C4—741no—
158C4⋊C4—741no—
159C4⋊C4—1482no—
160C4⋊C4D14811yescharacteristic
161C22⋊C4—21no—
162C22⋊C4—741no—
163C42—741no—
164C42—741no—
165C23D4×D3711yescharacteristic
166Q8—41no—
167Q8—2961no—
168Q8—742no—
169Q8—742no—
170Q8—1481no—
171Q8—1481no—
172Q8—1481no—
173C2×C4—22no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—372no—
180C2×C4—741no—
181C2×C4—741no—
182C2×C4—742no—
183C2×C4—741no—
184C2×C4—741no—
185C2×C4—741no—
186C2×C4—1481no—
187C2×C4—1481no—
188C2×C4—1481no—
189C2×C4C2×D14811yescharacteristic
190C2×C4D4×D3711yescharacteristic
191C8—41no—
192C8—1481no—
193C22—21no—
194C22—21no—
195C22#1192450611yescharacteristic
196C22Q16×D3711yescharacteristic
197C22#1192456511yescharacteristic
198C4—21no—
199C4—21no—
200C4—42no—
201C4—41no—
202C4—41no—
203C4—742no—
204C4—1481no—
205C4—1482no—
206C4—1481no—
207C4—1481no—
208C2—21no—
209C2—21no—
210C2#1455769011yescharacteristic
211C2#1455771711yescharacteristic
212C2#1455772111yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#328C2
socleC22×C37#120
prime radicalC23×C37C2×D4
hypercenter#328D37
hypocenterC37#1605
LCSG ▷ C22×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
77. C2×Dic37Q16semidirect
114. C37#1605semidirect

Maximal subgroups

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

subgroupindex
#145581622
#145576912
#145576882
#145574542
#145572692
#145572582
C37×#3282
#160537