Finite Group Databasebeta

← #17995756

Subgroups — #17995756

Order 4736.

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

normal subgroups only

This group has 246 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
2#14557543C211yesmaximal, characteristic
3#14557541C211yesmaximal, characteristic
4#14557439C211yesmaximal, characteristic
5#14557301C211yesmaximal, characteristic
6#14557293C211yesmaximal, characteristic
7C37×#339C211yesmaximal, characteristic
8C22×Dic74C2211yescharacteristic
9C2×#10596934C2211yescharacteristic
10#11924536—21no—
11#11924535—21no—
12#11924528—21no—
13#11924527—21no—
14#11924513—22no—
15#11924495C2211yescharacteristic
16C2×C4⋊Dic37C2211yescharacteristic
17#11924461—21no—
18#11924461—21no—
19#11924459—21no—
20#11924459—21no—
21#11924443—22no—
22C2×M16×C37C2211yescharacteristic
23#117×C37C2211yescharacteristic
24C2×C42×C37C2211yescharacteristic
25C22×C4×C37—21no—
26C22×C4×C37C2311yescharacteristic
27C22×Dic37—21no—
28C22×Dic37D412yes—
29C2×Dic74—21no—
30C2×Dic74—21no—
31C2×Dic74—21no—
32C2×Dic74—21no—
33C2×Dic74—21no—
34C2×Dic74—22no—
35C2×Dic74Q812yescomplemented
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—
46C4⋊Dic37—22no—
47C4⋊Dic37—21no—
48C4⋊Dic37—21no—
49C4⋊Dic37D411yescharacteristic
50C4⋊Dic37D411yescharacteristic
51#10596936—22no—
52#10596936—22no—
53C4×Dic37—21no—
54#10596934—21no—
55#10596934—21no—
56C2×#64436—21no—
57C23×C37C2×D411yescharacteristic
58C2×C4×C37—22no—
59C2×C4×C37—21no—
60C2×C4×C37—21no—
61C2×C4×C37—41no—
62C2×C4×C37—41no—
63C2×C4×C37C2×D411yescharacteristic
64C2×C4×C37C2×D411yescharacteristic
65C2×C4×C37C2×Q811yescharacteristic
66C2×C4×C37#4111yescharacteristic
67C2×C4×C37#4111yescharacteristic
68C2×C4×C37#4111yescharacteristic
69C2×Dic37—21no—
70C2×Dic37—21no—
71C2×Dic37—22no—
72C2×Dic37—22no—
73C2×Dic37—41no—
74C2×Dic37—41no—
75C2×Dic37—42no—
76Dic74—22no—
77Dic74—22no—
78Dic74—41no—
79Dic74—41no—
80Dic74—82no—
81C8×C37—41no—
82#64436—41no—
83C22×C37—21no—
84C22×C37—21no—
85C22×C37#12011yescharacteristic
86C22×C37C22⋊Q811yescharacteristic
87C22×C37#12411yescharacteristic
88C4×C37—42no—
89C4×C37—41no—
90C4×C37—41no—
91C4×C37C22⋊Q811yescharacteristic
92C4×C37C22⋊Q811yescharacteristic
93C4×C37#12411yescharacteristic
94C4×C37#12411yescharacteristic
95Dic37—42no—
96Dic37—41no—
97Dic37—42no—
98Dic37—41no—
99#2028—371nomaximal, Sylow
100C2×C37—21no—
101C2×C37—21no—
102C2×C37#39311yescharacteristic
103C2×C37#45511yescharacteristic
104C2×C37#45611yescharacteristic
105#544—371no—
106#419—371no—
107#419—371no—
108#391—371no—
109#343—371no—
110#339—371no—
111#339D3711yescharacteristic
112C37#202811yescharacteristic, complemented, Sylow
113C22×Q8—371no—
114C2×M16—371no—
115C2×M16C2×D3711yescharacteristic
116C4⋊Q8—741no—
117C4⋊Q8—741no—
118#125—741no—
119#125—741no—
120C22⋊Q8—742no—
121#117—371no—
122#117C2×D3711yescharacteristic
123C2×C4⋊C4—371no—
124C2×C42C2×D3711yescharacteristic
125#103—741no—
126#103—741no—
127#103—741no—
128#103—741no—
129#95—742no—
130C2×Q8—372no—
131C2×Q8—742no—
132C2×Q8—741no—
133C2×Q8—741no—
134C2×Q8—741no—
135C2×Q8—741no—
136C2×Q8—741no—
137C22×C4—21no—
138C22×C4—372no—
139C22×C4—741no—
140C22×C4C22×D3711yescharacteristic
141M16—21no—
142M16—21no—
143M16—741no—
144M16—741no—
145C2×C8—21no—
146C2×C8—741no—
147C4⋊C4—371no—
148C4⋊C4—371no—
149C4⋊C4—742no—
150C4⋊C4—742no—
151C4⋊C4—742no—
152C4⋊C4—741no—
153C4⋊C4—741no—
154C4⋊C4D14811yescharacteristic
155C4⋊C4D14811yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—741no—
158C42—21no—
159C42—21no—
160C42—21no—
161C42—741no—
162C23D4×D3711yescharacteristic
163Q8—2962no—
164Q8—742no—
165Q8—742no—
166Q8—1481no—
167Q8—1481no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—741no—
174C2×C4—741no—
175C2×C4—742no—
176C2×C4—742no—
177C2×C4—1481no—
178C2×C4—1481no—
179C2×C4—1482no—
180C2×C4C2×D14811yescharacteristic
181C2×C4#1059696211yescharacteristic
182C2×C4#1059696211yescharacteristic
183C2×C4D4×D3711yescharacteristic
184C2×C4#1059696411yescharacteristic
185C2×C4Q8×D3711yescharacteristic
186C8—41no—
187C8—1481no—
188C22—21no—
189C22—21no—
190C22#1192450611yescharacteristic
191C22#1192451411yescharacteristic
192C22#1192452211yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—1482no—
197C4—1482no—
198C4—1481no—
199C4—1481no—
200C4#1192451411yescharacteristic
201C4#1192451611yescharacteristic
202C4#1192452211yescharacteristic
203C4#1192452411yescharacteristic
204C2—21no—
205C2—21no—
206C2#1455744611yescharacteristic
207C2#1455771211yescharacteristic
208C2#1455771711yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#339C2
socleC22×C37#120
prime radicalC23×C37C2×D4
hypercenter#339D37
hypocenterC37#2028
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
35. C2×Dic74Q8semidirect
112. C37#2028semidirect

Maximal subgroups

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

subgroupindex
#145581612
#145575432
#145575412
#145574392
#145573012
#145572932
C37×#3392
#202837