Finite Group Databasebeta

← #17995745

Subgroups — #17995745

Order 4736.

258 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 85 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×#11924460C211yesmaximal, characteristic
3#14557440C211yesmaximal, characteristic
4#14557296C211yesmaximal, characteristic
5#14557295C211yesmaximal, characteristic
6#14557287C211yesmaximal, characteristic
7C2×#103×C37C211yesmaximal, characteristic
8C22×#64436C2211yescharacteristic
9#11924527—22no—
10#11924527—22no—
11C2×C4⋊Dic37—21no—
12C2×C4⋊Dic37C2211yescharacteristic
13C2×C4⋊Dic37C2211yescharacteristic
14C2×#10596936—21no—
15C2×C4×Dic37C2211yescharacteristic
16#11924460—22no—
17#11924443—21no—
18#11924443—21no—
19C22×Q8×C37C2211yescharacteristic
20C22×C8×C37C2211yescharacteristic
21C2×C4⋊C4×C37C2211yescharacteristic
22#103×C37—22no—
23C2×Q8×C37—21no—
24C2×Q8×C37—21no—
25C2×Q8×C37—21no—
26C2×Q8×C37—21no—
27C2×Q8×C37—21no—
28C2×Q8×C37Q812yes—
29C22×C4×C37—21no—
30C22×C4×C37—21no—
31C22×C4×C37C2311yescharacteristic
32C22×Dic37—21no—
33C22×Dic37—21no—
34C22×Dic37D411yescharacteristic
35C22×Dic37D411yescharacteristic
36C2×C8×C37—21no—
37C2×C8×C37—21no—
38C2×C8×C37—21no—
39C4⋊C4×C37—21no—
40C4⋊C4×C37D412yes—
41C4⋊Dic37—24no—
42C4⋊Dic37—21no—
43C4⋊Dic37—21no—
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
53Q8×C37—22no—
54Q8×C37—22no—
55Q8×C37—41no—
56Q8×C37—41no—
57C2×C4×C37—22no—
58C2×C4×C37—22no—
59C2×C4×C37—41no—
60C2×C4×C37—41no—
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—21no—
73C2×Dic37—21no—
74C2×Dic37—21no—
75C2×Dic37—21no—
76C2×Dic37—41no—
77C2×Dic37—41no—
78C2×Dic37—41no—
79C2×Dic37—41no—
80C2×Dic37—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—42no—
92C4×C37C22⋊Q811yescharacteristic
93C4×C37C22⋊Q811yescharacteristic
94C4×C37#12411yescharacteristic
95C4×C37#12411yescharacteristic
96Dic37—41no—
97Dic37—41no—
98Dic37—42no—
99Dic37—81no—
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×#103D3711yescharacteristic
111#391—371no—
112#340—371no—
113#340—371no—
114#336—371no—
115C37#202611yescharacteristic, complemented, Sylow
116C22×Q8C2×D3711yescharacteristic
117C22×C8—371no—
118C22×C8C2×D3711yescharacteristic
119#125—742no—
120#125—742no—
121C2×C4⋊C4—371no—
122C2×C4⋊C4—371no—
123C2×C4⋊C4—741no—
124C2×C4⋊C4—741no—
125C2×C4⋊C4C2×D3711yescharacteristic
126C2×C42—371no—
127#103—22no—
128#103—742no—
129#95—741no—
130#95—741no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8Dic7412yes—
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—372no—
152C4⋊C4—744no—
153C4⋊C4—744no—
154C4⋊C4—741no—
155C4⋊C4—741no—
156C4⋊C4—741no—
157C4⋊C4C22⋊D3712yes—
158C42—741no—
159C42—741no—
160C23D4×D3711yescharacteristic
161Q8—22no—
162Q8—22no—
163Q8—41no—
164Q8—41no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—741no—
172C2×C4—741no—
173C2×C4—742no—
174C2×C4—741no—
175C2×C4—741no—
176C2×C4—741no—
177C2×C4—741no—
178C2×C4—1481no—
179C2×C4—1481no—
180C2×C4—1481no—
181C2×C4—1481no—
182C2×C4—1481no—
183C2×C4C2×Dic7411yescharacteristic
184C2×C4#1059696211yescharacteristic
185C2×C4D4×D3711yescharacteristic
186C2×C4#1059696411yescharacteristic
187C2×C4#1059696411yescharacteristic
188C2×C4C2×C22⋊D3711yescharacteristic
189C8—41no—
190C8—1481no—
191C22#1192450411yescharacteristic
192C22#1192451311yescharacteristic
193C22#1192452211yescharacteristic
194C22#1192455711yescharacteristic
195C22#1192455911yescharacteristic
196C22#1192456511yescharacteristic
197C22#1192456811yescharacteristic
198C4—42no—
199C4—42no—
200C4—2961no—
201C4—1481no—
202C4—1481no—
203C4—1482no—
204C4#1192451311yescharacteristic
205C4#1192451511yescharacteristic
206C4#1192452211yescharacteristic
207C4#1192452311yescharacteristic
208C2#1455744511yescharacteristic
209C2#1455769211yescharacteristic
210C2#1455769411yescharacteristic
211C2#1455783811yescharacteristic
212C2#1455784211yescharacteristic
213C2#1455788911yescharacteristic
214C2#1455790011yescharacteristic
subgroupG/H
centerC23D4×D37
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC2×#103×C37C2
socle, prime radicalC23×C37C2×D4
hypercenterC2×#103D37
hypocenterC37#2026
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

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×#119244602
#145574402
#145572962
#145572952
#145572872
C2×#103×C372
#202637