Finite Group Databasebeta

← #17995751

Subgroups — #17995751

Order 4736.

282 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 67 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#14558161C211yesmaximal, characteristic, complemented
2#14557539C211yesmaximal, characteristic
3#14557537C211yesmaximal, characteristic
4#14557435C211yesmaximal, characteristic
5#14557301C211yesmaximal, characteristic, complemented
6#14557293C211yesmaximal, characteristic, complemented
7C37×#339C211yesmaximal, characteristic, complemented
8C22×D148C2211yescharacteristic
9C2×#10596934C2211yescharacteristic
10#11924536—21no—
11#11924535—21no—
12#11924528—21no—
13#11924527—21no—
14#11924513—22no—
15#11924495C2211yescharacteristic
16C2×C4⋊Dic37C2211yescharacteristic
17C2×#10596938—22no—
18#11924458—21no—
19#11924458—21no—
20#11924456—21no—
21#11924456—21no—
22C2×M16×C37C2211yescharacteristic
23#117×C37C2211yescharacteristic
24C2×C42×C37C2211yescharacteristic
25C23×D37—21no—
26C22×C4×C37—21no—
27C22×C4×C37C2311yescharacteristic
28C22×Dic37D412yes—
29C2×D148—21no—
30C2×D148—21no—
31C2×D148—21no—
32C2×D148—21no—
33C2×D148—21no—
34C2×D148Q812yescomplemented
35C2×Dic74—22no—
36M16×C37—21no—
37M16×C37—21no—
38C2×C8×C37—21no—
39C4⋊C4×C37D411yescharacteristic
40C4⋊C4×C37D411yescharacteristic
41C22⋊C4×C37—21no—
42C42×C37—21no—
43C42×C37—21no—
44C42×C37—21no—
45C22⋊Dic37—21no—
46#10596938—44no—
47C4⋊Dic37—22no—
48C4⋊Dic37—21no—
49C4⋊Dic37—21no—
50C4⋊Dic37D411yescharacteristic
51C4⋊Dic37D411yescharacteristic
52#10596936—22no—
53#10596936—22no—
54C4×Dic37—21no—
55#10596934—21no—
56#10596934—21no—
57C2×#64436—21no—
58C23×C37C2×D411yescharacteristic
59C22×D37—22no—
60C22×D37—42no—
61C22×D37—42no—
62C22×D37—41no—
63C22×D37—41no—
64C2×C4×C37—22no—
65C2×C4×C37—21no—
66C2×C4×C37—21no—
67C2×C4×C37—41no—
68C2×C4×C37—41no—
69C2×C4×C37C2×D411yescharacteristic
70C2×C4×C37C2×D411yescharacteristic
71C2×C4×C37C2×Q811yescharacteristic
72C2×C4×C37#4111yescharacteristic
73C2×C4×C37#4111yescharacteristic
74C2×C4×C37#4111yescharacteristic
75C2×Dic37—21no—
76C2×Dic37—21no—
77C2×Dic37—22no—
78C2×Dic37—42no—
79D148—22no—
80D148—22no—
81D148—41no—
82D148—41no—
83Dic74—82no—
84C8×C37—41no—
85#64436—41no—
86C22×C37—21no—
87C22×C37—21no—
88C22×C37#12011yescharacteristic
89C22×C37C22⋊Q811yescharacteristic
90C22×C37#12411yescharacteristic
91C2×D37—44no—
92C2×D37—42no—
93C2×D37—82no—
94C2×D37—81no—
95C2×D37—81no—
96C4×C37—42no—
97C4×C37—41no—
98C4×C37—41no—
99C4×C37C22⋊Q811yescharacteristic
100C4×C37C22⋊Q811yescharacteristic
101C4×C37#12411yescharacteristic
102C4×C37#12411yescharacteristic
103Dic37—41no—
104Dic37—42no—
105Dic37—41no—
106#2027—371nomaximal, Sylow
107C2×C37—21no—
108C2×C37—21no—
109C2×C37#39311yescharacteristic
110C2×C37#45311yescharacteristic
111C2×C37#45411yescharacteristic
112D37—82no—
113#544—371no—
114#418—371no—
115#418—371no—
116#390—371no—
117#343—371no—
118#339—371no—
119#339D3711yescharacteristic, complemented
120C37#202711yescharacteristic, complemented, Sylow
121C22×D4—371no—
122C2×M16—371no—
123C2×M16C2×D3711yescharacteristic
124C4⋊Q8—741no—
125C4⋊Q8—741no—
126#125—741no—
127#125—741no—
128C22⋊Q8—742no—
129#117—371no—
130#117C2×D3711yescharacteristic
131C2×C4⋊C4—371no—
132C2×C22⋊C4—742no—
133C2×C42C2×D3711yescharacteristic
134#102—741no—
135#102—741no—
136#102—741no—
137#102—741no—
138C24—741no—
139C2×Q8—742no—
140C2×D4—372no—
141C2×D4—741no—
142C2×D4—741no—
143C2×D4—741no—
144C2×D4—741no—
145C2×D4—741no—
146C22×C4—21no—
147C22×C4—372no—
148C22×C4C22×D3711yescharacteristic
149M16—21no—
150M16—21no—
151M16—741no—
152M16—741no—
153C2×C8—21no—
154C2×C8—741no—
155C4⋊C4—371no—
156C4⋊C4—371no—
157C4⋊C4—742no—
158C4⋊C4—742no—
159C4⋊C4—742no—
160C4⋊C4—741no—
161C4⋊C4—741no—
162C4⋊C4D14811yescharacteristic
163C4⋊C4D14811yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—741no—
166C22⋊C4—1484no—
167C42—21no—
168C42—21no—
169C42—21no—
170C42—741no—
171C23—742no—
172C23—1482no—
173C23—1482no—
174C23—1481no—
175C23—1481no—
176C23D4×D3711yescharacteristic
177Q8—2962no—
178D4—742no—
179D4—742no—
180D4—1481no—
181D4—1481no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—741no—
188C2×C4—741no—
189C2×C4—742no—
190C2×C4—1482no—
191C2×C4C2×D14811yescharacteristic
192C2×C4#1059696211yescharacteristic
193C2×C4#1059696211yescharacteristic
194C2×C4D4×D3711yescharacteristic
195C2×C4#1059696411yescharacteristic
196C2×C4Q8×D3711yescharacteristic
197C8—41no—
198C8—1481no—
199C22—21no—
200C22—21no—
201C22—2962no—
202C22—2961no—
203C22—2961no—
204C22—1484no—
205C22—1482no—
206C22#1192450611yescharacteristic
207C22#1192451411yescharacteristic
208C22#1192452211yescharacteristic
209C4—42no—
210C4—41no—
211C4—41no—
212C4—1482no—
213C4—1481no—
214C4—1481no—
215C4#1192451411yescharacteristic
216C4#1192451611yescharacteristic
217C4#1192452211yescharacteristic
218C4#1192452411yescharacteristic
219C2—21no—
220C2—21no—
221C2—2962no—
222C2#1455744611yescharacteristic
223C2#1455770211yescharacteristic
224C2#1455770711yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#339C2
socleC22×C37#120
prime radicalC22×D148C22
hypercenter#339D37
hypocenterC37#2027
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. #14558161C2semidirect
5. #14557301C2semidirect
6. #14557293C2semidirect
7. C37×#339C2semidirect
34. C2×D148Q8semidirect
119. #339D37semidirect
120. C37#2027semidirect

Maximal subgroups

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

subgroupindex
#145581612
#145575392
#145575372
#145574352
#145573012
#145572932
C37×#3392
#202737