Finite Group Databasebeta

← #17995722

Subgroups — #17995722

Order 4736.

638 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 73 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#14558095C211yesmaximal, characteristic, complemented
2C2×#11924505C212yesmaximal, complemented
3C2×#11924450C212yesmaximal, complemented
4#14557300C211yesmaximal, characteristic, complemented
5C37×#379C211yesmaximal, characteristic, complemented
6C22×C22⋊D37—22no—
7C22×C22⋊D37C2212yes—
8#11924520—22no—
9#11924510—22no—
10#11924506—22no—
11#11924505—24no—
12#11924505—24no—
13C2×C22⋊Dic37—22no—
14C2×C22⋊Dic37C2212yes—
15#11924450—24no—
16C25×C37C2211yescharacteristic
17C2×C22⋊C4×C37—22no—
18C2×C22⋊C4×C37C2211yescharacteristic
19C2×C22⋊C4×C37C2211yescharacteristic
20C24×C37—22no—
21C24×C37—21no—
22C24×C37—22no—
23C24×C37—21no—
24C24×C37—44no—
25C24×C37D412yescomplemented
26C24×C37C2311yescharacteristic
27C23×D37D412yescomplemented
28C22×C4×C37—21no—
29C22×C4×C37D412yescomplemented
30C2×C22⋊D37—28no—
31C2×C22⋊D37—22no—
32C2×C22⋊D37—22no—
33C2×C22⋊D37—22no—
34C2×C22⋊D37—22no—
35C2×C22⋊D37—22no—
36C2×C22⋊D37—22no—
37C2×C22⋊D37—48no—
38C22×Dic37—22no—
39C22×Dic37D412yescomplemented
40C2×D148—22no—
41C22⋊C4×C37—22no—
42C22⋊C4×C37—22no—
43C22⋊C4×C37—44no—
44C22⋊Dic37—28no—
45C22⋊Dic37—22no—
46C22⋊Dic37D414yescomplemented
47#10596938—24no—
48C4⋊Dic37—22no—
49C23×C37—24no—
50C23×C37—28no—
51C23×C37—24no—
52C23×C37—22no—
53C23×C37—44no—
54C23×C37—42no—
55C23×C37—44no—
56C23×C37—42no—
57C23×C37—48no—
58C23×C37—44no—
59C23×C37—41no—
60C23×C37—42no—
61C23×C37—41no—
62C23×C37C2×D411yescharacteristic
63C23×C37C2×D412yes—
64C23×C37C2×D412yes—
65C23×C37C2×D411yescharacteristic
66C23×C37#4111yescharacteristic
67C22×D37—22no—
68C22×D37—22no—
69C22×D37—22no—
70C22×D37—44no—
71C2×C4×C37—22no—
72C2×C4×C37—42no—
73C2×C4×C37—42no—
74C2×C4×C37—41no—
75C22⋊D37—416no—
76C22⋊D37—42no—
77C22⋊D37—42no—
78C22⋊D37—42no—
79C22⋊D37—42no—
80C2×Dic37—22no—
81C2×Dic37—22no—
82C2×Dic37—24no—
83C2×Dic37—22no—
84C2×Dic37—44no—
85D148—82no—
86C22×C37—24no—
87C22×C37—22no—
88C22×C37—28no—
89C22×C37—24no—
90C22×C37—41no—
91C22×C37—42no—
92C22×C37—41no—
93C22×C37—44no—
94C22×C37—44no—
95C22×C37—48no—
96C22×C37—42no—
97C22×C37—42no—
98C22×C37—44no—
99C22×C37#12011yescharacteristic
100C22×C37#12012yes—
101C22×C37#12112yes—
102C22×C37#12111yescharacteristic
103C22×C37#12711yescharacteristic
104C2×D37—44no—
105C2×D37—42no—
106C2×D37—44no—
107C2×D37—82no—
108C4×C37—42no—
109C4×C37—81no—
110Dic37—44no—
111Dic37—42no—
112#2021—371nomaximal, Sylow
113C2×C37—22no—
114C2×C37—21no—
115C2×C37—22no—
116C2×C37—21no—
117C2×C37—44no—
118C2×C37#39211yescharacteristic
119C2×C37B(4,𝔽2)12yes—
120D37—82no—
121#534—371no—
122C2×#120—372no—
123C2×#99—372no—
124#379D3711yescharacteristic, complemented
125#342—371no—
126C37#202111yescharacteristic, complemented, Sylow
127C25C2×D3711yescharacteristic
128C22×D4—372no—
129C22×D4—742no—
130#123—742no—
131#121—742no—
132#120—742no—
133#120—744no—
134#120—744no—
135C2×C22⋊C4—22no—
136C2×C22⋊C4—372no—
137C2×C22⋊C4—742no—
138C2×C22⋊C4C2×D3711yescharacteristic
139C2×C22⋊C4C2×D3711yescharacteristic
140#99—744no—
141C24—22no—
142C24—21no—
143C24—21no—
144C24—22no—
145C24—44no—
146C24—372no—
147C24D14812yescomplemented
148C24C22×D3711yescharacteristic
149C2×D4—742no—
150C2×D4—748no—
151C2×D4—742no—
152C2×D4—742no—
153C2×D4—742no—
154C2×D4—742no—
155C2×D4—742no—
156C2×D4—742no—
157C2×D4—1488no—
158C22×C4—21no—
159C22×C4—372no—
160C22×C4—742no—
161C22×C4C22⋊D3712yescomplemented
162C4⋊C4—742no—
163C22⋊C4—22no—
164C22⋊C4—22no—
165C22⋊C4—44no—
166C22⋊C4—374no—
167C22⋊C4—744no—
168C22⋊C4—748no—
169C22⋊C4—742no—
170C23—24no—
171C23—28no—
172C23—24no—
173C23—22no—
174C23—44no—
175C23—42no—
176C23—42no—
177C23—44no—
178C23—48no—
179C23—44no—
180C23—41no—
181C23—42no—
182C23—41no—
183C23—742no—
184C23—742no—
185C23—742no—
186C23—1484no—
187C23C2×D14811yescharacteristic
188C23#1059696211yescharacteristic
189C23D4×D3712yes—
190C23D4×D3712yes—
191C23C2×C22⋊D3711yescharacteristic
192D4—2962no—
193D4—14816no—
194D4—1482no—
195D4—1482no—
196D4—1482no—
197D4—1482no—
198C2×C4—22no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—41no—
202C2×C4—742no—
203C2×C4—744no—
204C2×C4—742no—
205C2×C4—742no—
206C2×C4—1484no—
207C22—22no—
208C22—24no—
209C22—28no—
210C22—24no—
211C22—41no—
212C22—41no—
213C22—42no—
214C22—44no—
215C22—44no—
216C22—42no—
217C22—48no—
218C22—42no—
219C22—44no—
220C22—2962no—
221C22—1484no—
222C22—1482no—
223C22—1484no—
224C22#1192450411yescharacteristic
225C22#1192450612yes—
226C22#1192450912yes—
227C22#1192451011yescharacteristic
228C22#1192453211yescharacteristic
229C4—42no—
230C4—81no—
231C4—1484no—
232C4—1482no—
233C2—21no—
234C2—22no—
235C2—21no—
236C2—22no—
237C2—44no—
238C2—2962no—
239C2#1455744211yescharacteristic
240C2#1455771912yes—
subgroupG/H
centerC22#11924504
commutator, cosocleC24×C37C23
FrattiniC24C22×D37
FittingC37×#379C2
socleC22×C37#120
hypercenter#379D37
hypocenterC37#2021
LCSG ▷ C24×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C24 ◁ #379

Complements

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

NH ≅ G/Ntype
1. #14558095C2semidirect
2. C2×#11924505C2semidirect
3. C2×#11924450C2semidirect
4. #14557300C2semidirect
5. C37×#379C2semidirect
25. C24×C37D4semidirect
27. C23×D37D4semidirect
29. C22×C4×C37D4semidirect
39. C22×Dic37D4semidirect
46. C22⋊Dic37D4semidirect
124. #379D37semidirect
126. C37#2021semidirect
147. C24D148semidirect
161. C22×C4C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145580952
C2×#119245052
C2×#119244502
#145573002
C37×#3792
#202137