Finite Group Databasebeta

← #17995736

Subgroups — #17995736

Order 4736.

290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 87 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×#11924535C211yesmaximal, characteristic
2C2×#11924461C211yesmaximal, characteristic
3C2×#11924459C211yesmaximal, characteristic
4#14557438C211yesmaximal, characteristic
5#14557295C211yesmaximal, characteristic
6#14557287C211yesmaximal, characteristic
7C37×#340C211yesmaximal, characteristic
8C22×Dic74—21no—
9C22×Dic74C2211yescharacteristic
10C22×#64436C2211yescharacteristic
11#11924535—22no—
12#11924535—22no—
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—24no—
35C2×Dic74—21no—
36C2×Dic74—42no—
37C2×Dic74—42no—
38C2×Dic74Q812yescomplemented
39C2×C8×C37—21no—
40C2×C8×C37—21no—
41C2×C8×C37—21no—
42C4⋊C4×C37—21no—
43C4⋊C4×C37—21no—
44C4⋊C4×C37—21no—
45C4⋊C4×C37D412yes—
46C4⋊Dic37—21no—
47C4⋊Dic37D412yes—
48#10596936—24no—
49C4×Dic37—21no—
50C4×Dic37—21no—
51C2×#64436—21no—
52C2×#64436—21no—
53C2×#64436—21no—
54C23×C37C2×D411yescharacteristic
55C2×C4×C37—22no—
56C2×C4×C37—41no—
57C2×C4×C37—41no—
58C2×C4×C37—41no—
59C2×C4×C37—41no—
60C2×C4×C37—41no—
61C2×C4×C37C2×D411yescharacteristic
62C2×C4×C37C2×D411yescharacteristic
63C2×C4×C37C2×Q811yescharacteristic
64C2×C4×C37#4111yescharacteristic
65C2×C4×C37#4111yescharacteristic
66C2×C4×C37#4111yescharacteristic
67C2×Dic37—21no—
68C2×Dic37—21no—
69C2×Dic37—21no—
70C2×Dic37—21no—
71C2×Dic37—22no—
72C2×Dic37—22no—
73C2×Dic37—41no—
74C2×Dic37—41no—
75C2×Dic37—41no—
76C2×Dic37—41no—
77C2×Dic37SD1612yes—
78C2×Dic37Q1612yes—
79Dic74—22no—
80Dic74—22no—
81Dic74—48no—
82Dic74—41no—
83Dic74—41no—
84C8×C37—41no—
85#64436—41no—
86C22×C37#12011yescharacteristic
87C22×C37C22⋊Q811yescharacteristic
88C22×C37#12411yescharacteristic
89C22×C37C2×SD1611yescharacteristic
90C22×C37C2×Q1611yescharacteristic
91C22×C37AGL(1,ℤ/8)11yescharacteristic
92C22×C37#13711yescharacteristic
93C4×C37—42no—
94C4×C37—81no—
95C4×C37C22⋊Q811yescharacteristic
96C4×C37C22⋊Q811yescharacteristic
97C4×C37#12411yescharacteristic
98C4×C37#12411yescharacteristic
99Dic37—22no—
100Dic37—22no—
101Dic37—42no—
102Dic37—42no—
103#2024—371nomaximal, Sylow
104C2×C37#39311yescharacteristic
105C2×C37#45011yescharacteristic
106C2×C37#45111yescharacteristic
107C2×C37#47511yescharacteristic
108C2×C37#47711yescharacteristic
109C2×C37#48711yescharacteristic
110C2×C37#48911yescharacteristic
111C2×C4⋊Q8—371no—
112C2×#103—371no—
113C2×#103—371no—
114#391—371no—
115#340—371no—
116#340D3711yescharacteristic
117#336—371no—
118C37#202411yescharacteristic, complemented, Sylow
119C22×Q8—371no—
120C22×Q8—741no—
121C22×C8—371no—
122C22×C8C2×D3711yescharacteristic
123C4⋊Q8—742no—
124C4⋊Q8—742no—
125C2×C4⋊C4—371no—
126C2×C4⋊C4—741no—
127C2×C4⋊C4C2×D3711yescharacteristic
128C2×C4⋊C4C2×D3711yescharacteristic
129C2×C42—371no—
130#103—742no—
131#103—742no—
132#95—741no—
133#95—741no—
134C2×Q8—372no—
135C2×Q8—744no—
136C2×Q8—741no—
137C2×Q8—741no—
138C2×Q8—741no—
139C2×Q8—741no—
140C2×Q8—741no—
141C2×Q8—1482no—
142C2×Q8—1482no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—371no—
146C22×C4—371no—
147C22×C4—741no—
148C22×C4—741no—
149C22×C4C22×D3711yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—741no—
154C2×C8—741no—
155C2×C8—741no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—372no—
160C4⋊C4—744no—
161C4⋊C4—741no—
162C4⋊C4D14812yes—
163C42—741no—
164C42—741no—
165C23D4×D3711yescharacteristic
166Q8—742no—
167Q8—742no—
168Q8—1488no—
169Q8—1481no—
170Q8—1481no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—372no—
178C2×C4—372no—
179C2×C4—741no—
180C2×C4—741no—
181C2×C4—741no—
182C2×C4—741no—
183C2×C4—742no—
184C2×C4—742no—
185C2×C4—1481no—
186C2×C4—1481no—
187C2×C4—1481no—
188C2×C4—1481no—
189C2×C4C2×D14811yescharacteristic
190C2×C4#1059696211yescharacteristic
191C2×C4#1059696211yescharacteristic
192C2×C4D4×D3711yescharacteristic
193C2×C4#1059696411yescharacteristic
194C2×C4Q8×D3711yescharacteristic
195C8—41no—
196C8—1481no—
197C22#1192450611yescharacteristic
198C22#1192451411yescharacteristic
199C22#1192452211yescharacteristic
200C22SD16×D3711yescharacteristic
201C22Q16×D3711yescharacteristic
202C22#1192456011yescharacteristic
203C22#1192456511yescharacteristic
204C4—42no—
205C4—81no—
206C4—742no—
207C4—742no—
208C4—1482no—
209C4—1482no—
210C4#1192451411yescharacteristic
211C4#1192451611yescharacteristic
212C4#1192452211yescharacteristic
213C4#1192452411yescharacteristic
214C2#1455744611yescharacteristic
215C2#1455768511yescharacteristic
216C2#1455769011yescharacteristic
217C2#1455781711yescharacteristic
218C2#1455782711yescharacteristic
219C2#1455788211yescharacteristic
220C2#1455789111yescharacteristic
subgroupG/H
centerC23D4×D37
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#340C2
socle, prime radicalC23×C37C2×D4
hypercenter#340D37
hypocenterC37#2024
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
38. C2×Dic74Q8semidirect
118. C37#2024semidirect

Maximal subgroups

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

subgroupindex
C2×#119245352
C2×#119244612
C2×#119244592
#145574382
#145572952
#145572872
C37×#3402
#202437