Finite Group Databasebeta

← #17995139

Subgroups — #17995139

Order 4736.

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

normal subgroups only

This group has 380 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
1#14558008C211yesmaximal, characteristic, complemented
2C2×#11924451C211yesmaximal, characteristic, complemented
3C2×#11924451C212yesmaximal, complemented
4#14557299C212yesmaximal, complemented
5C37×#534C211yesmaximal, characteristic
6D4×Dic37—24no—
7#11924495—21no—
8C2×C22⋊Dic37—21no—
9C2×C22⋊Dic37C2212yes—
10C2×C22⋊Dic37C2212yes—
11#11924451—22no—
12#11924451—24no—
13C22×D4×C37C2211yescharacteristic
14C22×D4×C37C2211yescharacteristic
15#123×C37—21no—
16#123×C37C412yescomplemented
17#121×C37—22no—
18#120×C37—21no—
19#120×C37C412yescomplemented
20C2×C22⋊C4×C37C2211yescharacteristic
21C24×C37C2×C411yescharacteristic, complemented
22C24×C37D411yescharacteristic
23C24×C37C2311yescharacteristic
24C2×D4×C37—22no—
25C2×D4×C37—22no—
26C2×D4×C37—21no—
27C2×D4×C37—21no—
28C2×D4×C37—22no—
29C2×D4×C37—22no—
30C2×D4×C37—22no—
31C2×D4×C37C2×C412yes—
32C2×D4×C37D412yes—
33C22×C4×C37—21no—
34C22×C4×C37C2×C411yescharacteristic, complemented
35C22×C4×C37D411yescharacteristic
36C22×Dic37—22no—
37C22×Dic37—22no—
38C22×Dic37—22no—
39C4⋊C4×C37—22no—
40C22⋊C4×C37—22no—
41C22⋊C4×C37—21no—
42C22⋊C4×C37—22no—
43C22⋊C4×C37C2×C412yescomplemented
44C22⋊Dic37—22no—
45C22⋊Dic37—22no—
46C22⋊Dic37—22no—
47C22⋊Dic37—22no—
48C22⋊Dic37D414yescomplemented
49C4⋊Dic37—22no—
50C4×Dic37—22no—
51C23×C37—21no—
52C23×C37—21no—
53C23×C37—21no—
54C23×C37—22no—
55C23×C37—81no—
56C23×C37—81no—
57C23×C37—81no—
58C23×C37C22⋊C412yes—
59C23×C37C22×C411yescharacteristic
60C23×C37C2×D412yes—
61C23×C37C2×D411yescharacteristic
62C23×C37C2×D411yescharacteristic
63C23×C37#4112yes—
64D4×C37—24no—
65D4×C37—24no—
66D4×C37—41no—
67D4×C37—42no—
68D4×C37—41no—
69D4×C37—82no—
70C2×C4×C37—21no—
71C2×C4×C37—21no—
72C2×C4×C37—22no—
73C2×C4×C37—21no—
74C2×C4×C37—22no—
75C2×C4×C37—81no—
76C2×C4×C37C22⋊C412yes—
77C2×Dic37—24no—
78C2×Dic37—42no—
79C2×Dic37—82no—
80C2×Dic37—82no—
81C2×Dic37—82no—
82C22×C37—22no—
83C22×C37—42no—
84C22×C37—42no—
85C22×C37—41no—
86C22×C37—41no—
87C22×C37—41no—
88C22×C37—42no—
89C22×C37—42no—
90C22×C37—42no—
91C22×C37—41no—
92C22×C37—81no—
93C22×C37—82no—
94C22×C37C2×C22⋊C411yescharacteristic
95C22×C37C4×D412yes—
96C22×C37#12011yescharacteristic
97C22×C37#12112yes—
98C22×C37#12311yescharacteristic
99C4×C37—22no—
100C4×C37—42no—
101C4×C37—41no—
102Dic37—44no—
103Dic37—82no—
104#1913—371nomaximal, Sylow
105C2×C37—21no—
106C2×C37—22no—
107C2×C37—21no—
108C2×C37—22no—
109C2×C37—21no—
110C2×C37—42no—
111C2×C37—81no—
112C2×C37#38611yescharacteristic
113#534D3711yescharacteristic
114#518—371no—
115C2×#99—372no—
116C2×#99—371no—
117#342—372no—
118C37#191311yescharacteristic, complemented, Sylow
119C22×D4C2×D3711yescharacteristic
120C22×D4C2×D3711yescharacteristic
121#123—21no—
122#123Dic3712yescomplemented
123#121—22no—
124#120—21no—
125#120Dic3712yescomplemented
126C4×D4—744no—
127#117—741no—
128C2×C22⋊C4—372no—
129C2×C22⋊C4—372no—
130C2×C22⋊C4—741no—
131C2×C22⋊C4C2×D3711yescharacteristic
132#99—744no—
133#99—742no—
134C24C2×Dic3711yescharacteristic, complemented
135C24C22⋊D3711yescharacteristic
136C24C22×D3711yescharacteristic
137C2×D4—22no—
138C2×D4—22no—
139C2×D4—22no—
140C2×D4—22no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4—22no—
144C2×D4C2×Dic3712yes—
145C2×D4C22⋊D3712yes—
146C22×C4—21no—
147C22×C4—742no—
148C22×C4—742no—
149C22×C4—742no—
150C22×C4C2×Dic3711yescharacteristic, complemented
151C22×C4C22⋊D3711yescharacteristic
152C4⋊C4—22no—
153C4⋊C4—742no—
154C22⋊C4—22no—
155C22⋊C4—21no—
156C22⋊C4—22no—
157C22⋊C4—374no—
158C22⋊C4—742no—
159C22⋊C4—742no—
160C22⋊C4—742no—
161C22⋊C4—742no—
162C22⋊C4C2×Dic3712yescomplemented
163C42—742no—
164C23—21no—
165C23—21no—
166C23—21no—
167C23—22no—
168C23—81no—
169C23—81no—
170C23—81no—
171C23C22⋊Dic3712yes—
172C23D4×D3712yes—
173C23#1059696412yes—
174C23C22×Dic3711yescharacteristic
175C23C2×C22⋊D3711yescharacteristic
176C23C2×C22⋊D3711yescharacteristic
177D4—24no—
178D4—24no—
179D4—41no—
180D4—42no—
181D4—41no—
182D4—82no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—81no—
189C2×C4—2962no—
190C2×C4—2962no—
191C2×C4—2962no—
192C2×C4—744no—
193C2×C4—1482no—
194C2×C4C22⋊Dic3712yes—
195C22—22no—
196C22—41no—
197C22—42no—
198C22—42no—
199C22—41no—
200C22—41no—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—41no—
205C22—81no—
206C22—82no—
207C22C2×C22⋊Dic3711yescharacteristic
208C22D4×Dic3712yes—
209C22#1192450411yescharacteristic
210C22#1192450812yes—
211C22#1192451711yescharacteristic
212C4—22no—
213C4—42no—
214C4—41no—
215C4—2962no—
216C4—1484no—
217C2—21no—
218C2—22no—
219C2—21no—
220C2—22no—
221C2—21no—
222C2—42no—
223C2—81no—
224C2#1455741311yescharacteristic
subgroupG/H
centerC2#14557413
commutatorC23×C37C22×C4
FrattiniC24C22×D37
Fitting, prime radicalC37×#534C2
socleC2×C37#386
cosocleC24×C37C23
hypercenter#534D37
hypocenterC37#1913
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C24 ◁ #534

Complements

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

NH ≅ G/Ntype
1. #14558008C2semidirect
2. C2×#11924451C2semidirect
3. C2×#11924451C2semidirect
4. #14557299C2semidirect
16. #123×C37C4semidirect
19. #120×C37C4semidirect
21. C24×C37C2×C4semidirect
34. C22×C4×C37C2×C4semidirect
43. C22⋊C4×C37C2×C4semidirect
48. C22⋊Dic37D4semidirect
118. C37#1913semidirect
122. #123Dic37semidirect
125. #120Dic37semidirect
134. C24C2×Dic37semidirect
150. C22×C4C2×Dic37semidirect
162. C22⋊C4C2×Dic37semidirect

Maximal subgroups

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

subgroupindex
#145580082
C2×#119244512
#145572992
C37×#5342
#191337