Finite Group Databasebeta

← #17995697

Subgroups — #17995697

Order 4736.

370 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C22×Dic148C211yesmaximal, characteristic
2C22×#10596942C211yesmaximal, characteristic
3C2×#11924534C211yesmaximal, characteristic
4C2×#11924459C211yesmaximal, characteristic
5#14557438C211yesmaximal, characteristic
6#14557287C211yesmaximal, characteristic
7C2×#103×C37C211yesmaximal, characteristic
8C22×Dic74C2211yescharacteristic
9C22×Dic74C2211yescharacteristic
10C2×Dic148—22no—
11C2×Dic148—22no—
12C2×Dic148—22no—
13C2×#10596942—22no—
14C2×#10596942—22no—
15C2×#10596942—22no—
16C22×#64436C2211yescharacteristic
17#11924534—22no—
18#11924534—22no—
19C2×#10596936—22no—
20C2×C4×Dic37C2211yescharacteristic
21#11924459—22no—
22#11924443—22no—
23C22×Q8×C37C2211yescharacteristic
24C22×C8×C37C2211yescharacteristic
25C2×C4⋊C4×C37C2211yescharacteristic
26#103×C37—22no—
27C2×Q8×C37—21no—
28C2×Q8×C37—21no—
29C2×Q8×C37—21no—
30C2×Q8×C37—21no—
31C2×Q8×C37—21no—
32C2×Q8×C37D412yes—
33C22×C4×C37—21no—
34C22×C4×C37—21no—
35C22×C4×C37C2311yescharacteristic
36C22×Dic37—21no—
37C22×Dic37—21no—
38C22×Dic37D412yes—
39C2×Dic74—21no—
40C2×Dic74—21no—
41C2×Dic74—21no—
42C2×Dic74—21no—
43C2×Dic74—21no—
44C2×Dic74—21no—
45C2×Dic74—21no—
46C2×Dic74—21no—
47C2×Dic74—21no—
48C2×Dic74—21no—
49C2×Dic74D412yes—
50C2×Dic74D412yes—
51C2×C8×C37—21no—
52C2×C8×C37—21no—
53C2×C8×C37D412yes—
54C4⋊C4×C37—21no—
55C4⋊C4×C37—21no—
56#10596942—28no—
57#10596936—28no—
58C4×Dic37—21no—
59C4×Dic37—21no—
60C2×#64436—21no—
61C2×#64436—21no—
62C2×#64436D412yes—
63Dic148—28no—
64C23×C37C2×D411yescharacteristic
65Q8×C37—22no—
66Q8×C37—22no—
67Q8×C37—41no—
68Q8×C37—41no—
69C2×C4×C37—22no—
70C2×C4×C37—41no—
71C2×C4×C37—41no—
72C2×C4×C37—41no—
73C2×C4×C37—42no—
74C2×C4×C37C2×D411yescharacteristic
75C2×C4×C37C2×D411yescharacteristic
76C2×C4×C37C2×D411yescharacteristic
77C2×C4×C37C2×D411yescharacteristic
78C2×C4×C37C2×D411yescharacteristic
79C2×C4×C37#4111yescharacteristic
80C2×Dic37—22no—
81C2×Dic37—22no—
82C2×Dic37—22no—
83C2×Dic37—22no—
84C2×Dic37—41no—
85C2×Dic37—41no—
86C2×Dic37—41no—
87C2×Dic37—41no—
88C2×Dic37Q1614yescomplemented
89Dic74—22no—
90Dic74—22no—
91Dic74—22no—
92Dic74—22no—
93Dic74—41no—
94Dic74—41no—
95Dic74—41no—
96Dic74—41no—
97C8×C37—22no—
98#64436—22no—
99C22×C37#12011yescharacteristic
100C22×C37#12111yescharacteristic
101C22×C37#12711yescharacteristic
102C22×C37C2×Q1612yes—
103C22×C37#13712yes—
104C4×C37—42no—
105C4×C37—81no—
106C4×C37#12011yescharacteristic
107C4×C37#12011yescharacteristic
108C4×C37#12111yescharacteristic
109C4×C37#12111yescharacteristic
110Dic37—24no—
111Dic37—42no—
112Dic37—42no—
113#2016—371nomaximal, Sylow
114C2×C37#39211yescharacteristic
115C2×C37#45112yes—
116C2×C37#46212yes—
117C2×C37#49411yescharacteristic
118C2×C37#49711yescharacteristic
119C22×Q16—371no—
120C22×Q16—371no—
121C2×C4⋊Q8—371no—
122C2×#103—371no—
123C2×#103D3711yescharacteristic
124#391—371no—
125#336—371no—
126C37#201611yescharacteristic, complemented, Sylow
127C22×Q8—371no—
128C22×Q8—371no—
129C22×Q8C2×D3711yescharacteristic
130C2×Q16—742no—
131C2×Q16—742no—
132C2×Q16—742no—
133C2×Q16—742no—
134C2×Q16—742no—
135C2×Q16—742no—
136C22×C8—371no—
137C22×C8C2×D3711yescharacteristic
138C4⋊Q8—742no—
139C4⋊Q8—742no—
140C2×C4⋊C4—742no—
141C2×C4⋊C4C2×D3711yescharacteristic
142C2×C42—371no—
143#103—22no—
144#103—742no—
145#95—742no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—372no—
152C2×Q8—372no—
153C2×Q8—741no—
154C2×Q8—741no—
155C2×Q8—741no—
156C2×Q8—741no—
157C2×Q8—741no—
158C2×Q8—741no—
159C2×Q8—741no—
160C2×Q8—741no—
161C2×Q8—741no—
162C2×Q8—741no—
163C2×Q8D14812yes—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—372no—
167C22×C4—741no—
168C22×C4—741no—
169C22×C4C22×D3711yescharacteristic
170Q16—748no—
171Q16—748no—
172C2×C8—21no—
173C2×C8—21no—
174C2×C8—372no—
175C2×C8—741no—
176C2×C8—741no—
177C2×C8C22⋊D3712yes—
178C4⋊C4—21no—
179C4⋊C4—21no—
180C4⋊C4—748no—
181C42—741no—
182C42—741no—
183C23D4×D3711yescharacteristic
184Q8—22no—
185Q8—22no—
186Q8—41no—
187Q8—41no—
188Q8—742no—
189Q8—742no—
190Q8—742no—
191Q8—742no—
192Q8—1481no—
193Q8—1481no—
194Q8—1481no—
195Q8—1481no—
196C2×C4—22no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—42no—
201C2×C4—374no—
202C2×C4—742no—
203C2×C4—742no—
204C2×C4—742no—
205C2×C4—742no—
206C2×C4—1481no—
207C2×C4—1481no—
208C2×C4—1481no—
209C2×C4—1481no—
210C2×C4C2×D14811yescharacteristic
211C2×C4#1059696211yescharacteristic
212C2×C4D4×D3711yescharacteristic
213C2×C4D4×D3711yescharacteristic
214C2×C4D4×D3711yescharacteristic
215C2×C4C2×C22⋊D3711yescharacteristic
216C8—22no—
217C8—742no—
218C22#1192450611yescharacteristic
219C22#1192450911yescharacteristic
220C22#1192453211yescharacteristic
221C22Q16×D3712yes—
222C22#1192456512yes—
223C4—42no—
224C4—81no—
225C4—744no—
226C4—1482no—
227C4—1482no—
228C4#1192450411yescharacteristic
229C4#1192450611yescharacteristic
230C4#1192450911yescharacteristic
231C4#1192451011yescharacteristic
232C2#1455744211yescharacteristic
233C2#1455769012yes—
234C2#1455774212yes—
235C2#1455791111yescharacteristic
236C2#1455792411yescharacteristic
subgroupG/H
centerC23D4×D37
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC2×#103×C37C2
socle, prime radicalC23×C37C2×D4
hypercenterC2×#103D37
hypocenterC37#2016
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
88. C2×Dic37Q16semidirect
126. C37#2016semidirect

Maximal subgroups

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

subgroupindex
C22×Dic1482
C22×#105969422
C2×#119245342
C2×#119244592
#145574382
#145572872
C2×#103×C372
#201637