Finite Group Databasebeta

← #17995746

Subgroups — #17995746

Order 4736.

258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#11924527C211yesmaximal, characteristic
2C2×#11924461C211yesmaximal, characteristic
3C2×#11924459C211yesmaximal, characteristic
4#14557438C211yesmaximal, characteristic
5#14557295C211yesmaximal, characteristic
6#14557287C211yesmaximal, characteristic
7C37×#340C211yesmaximal, characteristic
8C22×Dic74C2211yescharacteristic
9C22×#64436C2211yescharacteristic
10#11924527—22no—
11#11924527—22no—
12C2×C4⋊Dic37—21no—
13C2×C4⋊Dic37C2211yescharacteristic
14C2×#10596936—21no—
15C2×C4×Dic37C2211yescharacteristic
16#11924461—22no—
17#11924459—22no—
18#11924443—21no—
19#11924443—21no—
20C22×C8×C37C2211yescharacteristic
21C2×C4⋊C4×C37C2211yescharacteristic
22C2×C4⋊C4×C37C2211yescharacteristic
23C22×C4×C37—21no—
24C22×C4×C37—21no—
25C22×C4×C37C2311yescharacteristic
26C22×Dic37—21no—
27C22×Dic37—21no—
28C22×Dic37D411yescharacteristic
29C22×Dic37D411yescharacteristic
30C2×Dic74—21no—
31C2×Dic74—21no—
32C2×Dic74—21no—
33C2×Dic74—21no—
34C2×Dic74—21no—
35C2×Dic74Q812yes—
36C2×C8×C37—21no—
37C2×C8×C37—21no—
38C2×C8×C37—21no—
39C4⋊C4×C37—21no—
40C4⋊C4×C37—21no—
41C4⋊C4×C37—21no—
42C4⋊C4×C37D412yes—
43C4⋊Dic37—24no—
44C4⋊Dic37—21no—
45C4⋊Dic37D412yes—
46#10596936—24no—
47C4×Dic37—21no—
48C4×Dic37—21no—
49C2×#64436—21no—
50C2×#64436—21no—
51C2×#64436—21no—
52C23×C37C2×D411yescharacteristic
53C2×C4×C37—22no—
54C2×C4×C37—41no—
55C2×C4×C37—41no—
56C2×C4×C37—41no—
57C2×C4×C37—41no—
58C2×C4×C37—41no—
59C2×C4×C37C2×D411yescharacteristic
60C2×C4×C37C2×D411yescharacteristic
61C2×C4×C37C2×Q811yescharacteristic
62C2×C4×C37#4111yescharacteristic
63C2×C4×C37#4111yescharacteristic
64C2×C4×C37#4111yescharacteristic
65C2×Dic37—21no—
66C2×Dic37—21no—
67C2×Dic37—22no—
68C2×Dic37—22no—
69C2×Dic37—21no—
70C2×Dic37—21no—
71C2×Dic37—21no—
72C2×Dic37—21no—
73C2×Dic37—41no—
74C2×Dic37—41no—
75C2×Dic37—41no—
76C2×Dic37—41no—
77Dic74—22no—
78Dic74—22no—
79Dic74—41no—
80Dic74—41no—
81C8×C37—41no—
82#64436—41no—
83C22×C37#12011yescharacteristic
84C22×C37C22⋊Q811yescharacteristic
85C22×C37#12411yescharacteristic
86C22×C37#13511yescharacteristic
87C22×C37#13511yescharacteristic
88C22×C37#13711yescharacteristic
89C22×C37#13711yescharacteristic
90C4×C37—42no—
91C4×C37—81no—
92C4×C37C22⋊Q811yescharacteristic
93C4×C37C22⋊Q811yescharacteristic
94C4×C37#12411yescharacteristic
95C4×C37#12411yescharacteristic
96Dic37—42no—
97Dic37—41no—
98Dic37—41no—
99Dic37—42no—
100#2026—371nomaximal, Sylow
101C2×C37#39311yescharacteristic
102C2×C37#45211yescharacteristic
103C2×C37#45211yescharacteristic
104C2×C37#47911yescharacteristic
105C2×C37#47911yescharacteristic
106C2×C37#48811yescharacteristic
107C2×C37#49111yescharacteristic
108C2×#125—371no—
109C2×#103—371no—
110C2×#103—371no—
111#391—371no—
112#340—371no—
113#340D3711yescharacteristic
114#336—371no—
115C37#202611yescharacteristic, complemented, Sylow
116C22×Q8—371no—
117C22×C8—371no—
118C22×C8C2×D3711yescharacteristic
119#125—742no—
120#125—742no—
121C2×C4⋊C4—371no—
122C2×C4⋊C4—741no—
123C2×C4⋊C4—741no—
124C2×C4⋊C4C2×D3711yescharacteristic
125C2×C4⋊C4C2×D3711yescharacteristic
126C2×C42—371no—
127#103—742no—
128#103—742no—
129#95—741no—
130#95—741no—
131C2×Q8—372no—
132C2×Q8—741no—
133C2×Q8—741no—
134C2×Q8—741no—
135C2×Q8—741no—
136C2×Q8—741no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—371no—
140C22×C4—371no—
141C22×C4—741no—
142C22×C4—741no—
143C22×C4C22×D3711yescharacteristic
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—741no—
148C2×C8—741no—
149C2×C8—741no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—372no—
154C4⋊C4—744no—
155C4⋊C4—744no—
156C4⋊C4—741no—
157C4⋊C4D14812yes—
158C42—741no—
159C42—741no—
160C23D4×D3711yescharacteristic
161Q8—742no—
162Q8—742no—
163Q8—1481no—
164Q8—1481no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—741no—
172C2×C4—741no—
173C2×C4—742no—
174C2×C4—742no—
175C2×C4—741no—
176C2×C4—741no—
177C2×C4—741no—
178C2×C4—741no—
179C2×C4—1481no—
180C2×C4—1481no—
181C2×C4—1481no—
182C2×C4—1481no—
183C2×C4C2×D14811yescharacteristic
184C2×C4#1059696211yescharacteristic
185C2×C4#1059696211yescharacteristic
186C2×C4D4×D3711yescharacteristic
187C2×C4#1059696411yescharacteristic
188C2×C4Q8×D3711yescharacteristic
189C8—41no—
190C8—1481no—
191C22#1192450611yescharacteristic
192C22#1192451411yescharacteristic
193C22#1192452211yescharacteristic
194C22#1192455511yescharacteristic
195C22#1192455711yescharacteristic
196C22#1192456511yescharacteristic
197C22#1192456811yescharacteristic
198C4—42no—
199C4—81no—
200C4—1481no—
201C4—1481no—
202C4—1482no—
203C4—1482no—
204C4#1192451411yescharacteristic
205C4#1192451611yescharacteristic
206C4#1192452211yescharacteristic
207C4#1192452411yescharacteristic
208C2#1455744611yescharacteristic
209C2#1455769611yescharacteristic
210C2#1455769811yescharacteristic
211C2#1455783911yescharacteristic
212C2#1455784311yescharacteristic
213C2#1455788611yescharacteristic
214C2#1455790011yescharacteristic
subgroupG/H
centerC23D4×D37
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#340C2
socle, prime radicalC23×C37C2×D4
hypercenter#340D37
hypocenterC37#2026
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
115. C37#2026semidirect

Maximal subgroups

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

subgroupindex
C2×#119245272
C2×#119244612
C2×#119244592
#145574382
#145572952
#145572872
C37×#3402
#202637