Finite Group Databasebeta

← #17995755

Subgroups — #17995755

Order 4736.

246 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 69 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#14557542C211yesmaximal, characteristic
3#14557440C211yesmaximal, characteristic
4#14557301C211yesmaximal, characteristic
5#14557294C211yesmaximal, characteristic
6#14557292C211yesmaximal, characteristic
7C37×#419C211yesmaximal, characteristic
8C2×#10596934C2211yescharacteristic
9#11924536—21no—
10#11924535—21no—
11#11924528—21no—
12#11924527—21no—
13#11924513—22no—
14#11924495C2211yescharacteristic
15C2×C4⋊Dic37C2211yescharacteristic
16C2×C4×Dic37C2211yescharacteristic
17#11924460—21no—
18#11924460—21no—
19#11924443—22no—
20C22×Q8×C37C2211yescharacteristic
21C2×M16×C37C2211yescharacteristic
22#117×C37C2211yescharacteristic
23#103×C37—21no—
24#103×C37—21no—
25C2×Q8×C37—21no—
26C2×Q8×C37—21no—
27C2×Q8×C37—21no—
28C2×Q8×C37—21no—
29C2×Q8×C37—21no—
30C2×Q8×C37Q812yescomplemented
31C22×C4×C37—21no—
32C22×C4×C37C2311yescharacteristic
33C22×Dic37—21no—
34C22×Dic37D412yes—
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—
43C22⋊Dic37—21no—
44C4⋊Dic37—22no—
45C4⋊Dic37—21no—
46C4⋊Dic37—21no—
47C4⋊Dic37D411yescharacteristic
48C4⋊Dic37D411yescharacteristic
49#10596936—22no—
50#10596936—22no—
51C4×Dic37—21no—
52C4×Dic37—21no—
53C4×Dic37—21no—
54#10596934—21no—
55#10596934—21no—
56C2×#64436—21no—
57C23×C37C2×D411yescharacteristic
58Q8×C37—22no—
59Q8×C37—22no—
60Q8×C37—41no—
61Q8×C37—41no—
62C2×C4×C37—21no—
63C2×C4×C37—21no—
64C2×C4×C37—22no—
65C2×C4×C37—41no—
66C2×C4×C37—41no—
67C2×C4×C37C2×D411yescharacteristic
68C2×C4×C37C2×D411yescharacteristic
69C2×C4×C37C2×Q811yescharacteristic
70C2×C4×C37#4111yescharacteristic
71C2×C4×C37#4111yescharacteristic
72C2×C4×C37#4111yescharacteristic
73C2×Dic37—22no—
74C2×Dic37—21no—
75C2×Dic37—21no—
76C2×Dic37—22no—
77C2×Dic37—41no—
78C2×Dic37—41no—
79C2×Dic37—42no—
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#419D3711yescharacteristic
108#391—371no—
109#343—371no—
110#339—371no—
111#339—371no—
112C37#202811yescharacteristic, complemented, Sylow
113C22×Q8C2×D3711yescharacteristic
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×C42—371no—
125#103—21no—
126#103—21no—
127#103—741no—
128#103—741no—
129#95—742no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—742no—
136C2×Q8Dic7412yescomplemented
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⋊C4C22⋊D3711yescharacteristic
155C4⋊C4C22⋊D3711yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—741no—
158C42—21no—
159C42—741no—
160C42—741no—
161C42—741no—
162C23D4×D3711yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—41no—
166Q8—41no—
167Q8—2962no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—742no—
174C2×C4—741no—
175C2×C4—741no—
176C2×C4—742no—
177C2×C4—1481no—
178C2×C4—1481no—
179C2×C4—1482no—
180C2×C4C2×Dic7411yescharacteristic
181C2×C4#1059696211yescharacteristic
182C2×C4D4×D3711yescharacteristic
183C2×C4#1059696411yescharacteristic
184C2×C4#1059696411yescharacteristic
185C2×C4C2×C22⋊D3711yescharacteristic
186C8—41no—
187C8—1481no—
188C22—21no—
189C22—21no—
190C22#1192450411yescharacteristic
191C22#1192451311yescharacteristic
192C22#1192452211yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—1482no—
197C4—1482no—
198C4—1481no—
199C4—1481no—
200C4#1192451311yescharacteristic
201C4#1192451511yescharacteristic
202C4#1192452211yescharacteristic
203C4#1192452311yescharacteristic
204C2—21no—
205C2—21no—
206C2#1455744511yescharacteristic
207C2#1455770911yescharacteristic
208C2#1455771411yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#419C2
socleC22×C37#120
prime radicalC23×C37C2×D4
hypercenter#419D37
hypocenterC37#2028
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
30. C2×Q8×C37Q8semidirect
112. C37#2028semidirect
136. C2×Q8Dic74semidirect

Maximal subgroups

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

subgroupindex
#145581612
#145575422
#145574402
#145573012
#145572942
#145572922
C37×#4192
#202837