Finite Group Databasebeta

← #17993636

Subgroups — #17993636

Order 4736.

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

normal subgroups only

This group has 202 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#14557868C211yesmaximal, characteristic
3#14557471C211yesmaximal, characteristic
4#14557271C211yesmaximal, characteristic
5#14557270C211yesmaximal, characteristic
6#14557258C211yesmaximal, characteristic
7C37×#484C211yesmaximal, characteristic
8#11924535—21no—
9#11924534—21no—
10#11924526—21no—
11#11924526—21no—
12#11924515C2211yescharacteristic
13#11924513—21no—
14#11924492—21no—
15C2×#10596936C2211yescharacteristic
16#11924469—21no—
17#11924459—21no—
18C22⋊#64436C2211yescharacteristic
19#11924443—21no—
20#11924443—21no—
21#11924443C2211yescharacteristic
22C22⋊Q8×C37C2211yescharacteristic
23C2×C4⋊C4×C37C2211yescharacteristic
24#107×C37—21no—
25#103×C37—21no—
26C22⋊C8×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×C37—21no—
38C4⋊C4×C37—21no—
39C4⋊C4×C37D411yescharacteristic
40C22⋊C4×C37—21no—
41C22⋊Dic37—21no—
42C4⋊Dic37—21no—
43C4⋊Dic37D411yescharacteristic
44#10596936—21no—
45#10596936—21no—
46#10596936—21no—
47#10596936—21no—
48#10596936—21no—
49#10596936—21no—
50#10596936—21no—
51C4×Dic37—21no—
52C4×Dic37—21no—
53C2×#64436—21no—
54C23×C37C2×D411yescharacteristic
55Q8×C37—41no—
56C2×C4×C37—21no—
57C2×C4×C37—21no—
58C2×C4×C37—41no—
59C2×C4×C37—42no—
60C2×C4×C37—41no—
61C2×C4×C37C2×D411yescharacteristic
62C2×C4×C37C2×D411yescharacteristic
63C2×Dic37—21no—
64C2×Dic37—21no—
65C2×Dic37—21no—
66C2×Dic37—21no—
67C2×Dic37—21no—
68C2×Dic37—41no—
69C2×Dic37—41no—
70C2×Dic37—41no—
71C2×Dic37—41no—
72C2×Dic37Q1612yes—
73Dic74—41no—
74Dic74—81no—
75C8×C37—41no—
76#64436—41no—
77C22×C37—21no—
78C22×C37—21no—
79C22×C37#12011yescharacteristic
80C22×C37C2×Q1611yescharacteristic
81C22×C37#13711yescharacteristic
82C4×C37—21no—
83C4×C37—21no—
84C4×C37—41no—
85C4×C37—41no—
86C4×C37—81no—
87Dic37—22no—
88Dic37—41no—
89Dic37—41no—
90Dic37—41no—
91Dic37—81no—
92#1617—371nomaximal, Sylow
93C2×C37—21no—
94C2×C37—21no—
95C2×C37#45111yescharacteristic
96C2×C37#45411yescharacteristic
97C2×C37#45811yescharacteristic
98#544—371no—
99#484—371no—
100#484D3711yescharacteristic
101#400—371no—
102#328—371no—
103#328—371no—
104#324—371no—
105C37#161711yescharacteristic, complemented, Sylow
106C4⋊Q8—741no—
107C4⋊Q8—741no—
108#125—741no—
109#125—741no—
110C22⋊Q8—371no—
111C22⋊Q8—741no—
112C22⋊Q8C2×D3711yescharacteristic
113#117—741no—
114C2×C4⋊C4—371no—
115C2×C4⋊C4C2×D3711yescharacteristic
116#107—21no—
117#107—741no—
118#103—21no—
119#103—741no—
120C22⋊C8—371no—
121C22⋊C8C2×D3711yescharacteristic
122#95—371no—
123#95—741no—
124#95—741no—
125C2×Q8—371no—
126C2×Q8—741no—
127C2×Q8C22⋊D3711yescharacteristic
128C22×C4—21no—
129C22×C4—371no—
130C22×C4—371no—
131C22×C4—741no—
132C22×C4C22×D3711yescharacteristic
133C2×C8—21no—
134C2×C8—741no—
135C4⋊C4—21no—
136C4⋊C4—21no—
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⋊C4C22⋊D3711yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—741no—
150C42—741no—
151C42—741no—
152C23D4×D3711yescharacteristic
153Q8—41no—
154Q8—2961no—
155Q8—1481no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4—372no—
162C2×C4—741no—
163C2×C4—741no—
164C2×C4—741no—
165C2×C4—741no—
166C2×C4—741no—
167C2×C4—1481no—
168C2×C4—1481no—
169C2×C4—1481no—
170C2×C4—1481no—
171C2×C4D4×D3711yescharacteristic
172C2×C4C2×C22⋊D3711yescharacteristic
173C8—41no—
174C8—1481no—
175C22—21no—
176C22—21no—
177C22#1192450411yescharacteristic
178C22Q16×D3711yescharacteristic
179C22#1192456811yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—2961no—
186C4—742no—
187C4—1481no—
188C4—1481no—
189C4—1481no—
190C2—21no—
191C2—21no—
192C2#1455768711yescharacteristic
193C2#1455770411yescharacteristic
194C2#1455772211yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#484C2
socleC22×C37#120
prime radicalC23×C37C2×D4
hypercenter#484D37
hypocenterC37#1617
LCSG ▷ C22×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
105. C37#1617semidirect

Maximal subgroups

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

subgroupindex
#145581622
#145578682
#145574712
#145572712
#145572702
#145572582
C37×#4842
#161737