Finite Group Databasebeta

← #17993605

Subgroups — #17993605

Order 4736.

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

normal subgroups only

This group has 210 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#14557864C211yesmaximal, characteristic
3#14557861C211yesmaximal, characteristic
4#14557465C211yesmaximal, characteristic
5#14557269C211yesmaximal, characteristic
6#14557258C211yesmaximal, characteristic
7C37×#328C211yesmaximal, characteristic
8#11924535—21no—
9#11924534—21no—
10#11924526—21no—
11#11924526—21no—
12#11924515C2211yescharacteristic
13#11924513—21no—
14#11924492—21no—
15C2×C4⋊Dic37—21no—
16C2×C4⋊Dic37C2211yescharacteristic
17C2×#10596936C2211yescharacteristic
18#11924468—21no—
19#11924467—21no—
20#11924461—21no—
21#11924460—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×Dic74D411yescharacteristic
35C2×C8×C37—21no—
36C4⋊C4×C37—21no—
37C4⋊C4×C37D411yescharacteristic
38C22⋊C4×C37—21no—
39C22⋊Dic37—21no—
40C4⋊Dic37—21no—
41C4⋊Dic37—21no—
42C4⋊Dic37—21no—
43C4⋊Dic37—42no—
44C4⋊Dic37D411yescharacteristic
45#10596936—21no—
46#10596936—21no—
47#10596936—21no—
48#10596936—21no—
49#10596936—21no—
50#10596936—21no—
51#10596936—21no—
52C4×Dic37—21no—
53C4×Dic37—21no—
54C2×#64436—21no—
55C23×C37C2×D411yescharacteristic
56Q8×C37—41no—
57C2×C4×C37—22no—
58C2×C4×C37—21no—
59C2×C4×C37—21no—
60C2×C4×C37—41no—
61C2×C4×C37—41no—
62C2×C4×C37—41no—
63C2×C4×C37C2×D411yescharacteristic
64C2×C4×C37C2×D411yescharacteristic
65C2×Dic37—21no—
66C2×Dic37—21no—
67C2×Dic37—21no—
68C2×Dic37—21no—
69C2×Dic37—21no—
70C2×Dic37—41no—
71C2×Dic37—41no—
72C2×Dic37—41no—
73C2×Dic37—41no—
74C2×Dic37SD1612yes—
75Dic74—41no—
76Dic74—81no—
77C8×C37—41no—
78#64436—41no—
79C22×C37—21no—
80C22×C37—21no—
81C22×C37#12011yescharacteristic
82C22×C37C2×SD1611yescharacteristic
83C22×C37#13711yescharacteristic
84C4×C37—21no—
85C4×C37—21no—
86C4×C37—42no—
87C4×C37—41no—
88C4×C37—41no—
89Dic37—22no—
90Dic37—41no—
91Dic37—41no—
92Dic37—41no—
93Dic37—81no—
94#1611—371nomaximal, Sylow
95C2×C37—21no—
96C2×C37—21no—
97C2×C37#44811yescharacteristic
98C2×C37#45611yescharacteristic
99C2×C37#45811yescharacteristic
100#544—371no—
101#483—371no—
102#483—371no—
103#398—371no—
104#328—371no—
105#328D3711yescharacteristic
106#324—371no—
107C37#161111yescharacteristic, complemented, Sylow
108C4⋊Q8—741no—
109C4⋊Q8—741no—
110#125—741no—
111#125—741no—
112C22⋊Q8—371no—
113C22⋊Q8—741no—
114C22⋊Q8C2×D3711yescharacteristic
115#117—741no—
116C2×C4⋊C4—371no—
117C2×C4⋊C4—371no—
118C2×C4⋊C4—741no—
119#106—741no—
120#106—741no—
121#103—741no—
122#103—741no—
123C22⋊C8—371no—
124C22⋊C8C2×D3711yescharacteristic
125#95—741no—
126#95C2×D3711yescharacteristic
127C2×Q8—371no—
128C2×Q8—741no—
129C2×Q8D14811yescharacteristic
130C22×C4—21no—
131C22×C4—371no—
132C22×C4—371no—
133C22×C4—741no—
134C22×C4C22×D3711yescharacteristic
135C2×C8—21no—
136C2×C8—741no—
137C4⋊C4—21no—
138C4⋊C4—371no—
139C4⋊C4—741no—
140C4⋊C4—741no—
141C4⋊C4—741no—
142C4⋊C4—741no—
143C4⋊C4—741no—
144C4⋊C4—741no—
145C4⋊C4—741no—
146C4⋊C4—741no—
147C4⋊C4—741no—
148C4⋊C4—741no—
149C4⋊C4—1482no—
150C4⋊C4D14811yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—741no—
153C42—741no—
154C42—741no—
155C23D4×D3711yescharacteristic
156Q8—41no—
157Q8—2961no—
158Q8—1481no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—372no—
166C2×C4—741no—
167C2×C4—741no—
168C2×C4—741no—
169C2×C4—741no—
170C2×C4—741no—
171C2×C4—1481no—
172C2×C4—1481no—
173C2×C4—1481no—
174C2×C4—1481no—
175C2×C4C2×D14811yescharacteristic
176C2×C4D4×D3711yescharacteristic
177C8—41no—
178C8—1481no—
179C22—21no—
180C22—21no—
181C22#1192450611yescharacteristic
182C22SD16×D3711yescharacteristic
183C22#1192456811yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—2961no—
190C4—742no—
191C4—1481no—
192C4—1481no—
193C4—1481no—
194C2—21no—
195C2—21no—
196C2#1455767311yescharacteristic
197C2#1455771711yescharacteristic
198C2#1455772411yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#328C2
socleC22×C37#120
prime radicalC23×C37C2×D4
hypercenter#328D37
hypocenterC37#1611
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
107. C37#1611semidirect

Maximal subgroups

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

subgroupindex
#145581622
#145578642
#145578612
#145574652
#145572692
#145572582
C37×#3282
#161137