Finite Group Databasebeta

← #323×D37 #17992901

Subgroups — #323×D37 #17992901

Order 4736.

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

normal subgroups only

This group has 456 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×C22⋊C4×D37C211yesmaximal, characteristic
2C22⋊C8×D37C212yesmaximal, complemented
3#14557257C211yesmaximal, characteristic, complemented
4#14557256C212yesmaximal, complemented
5C37×#323C211yesmaximal, characteristic, complemented
6C24×D37C411yescharacteristic
7C22×C4×D37C411yescharacteristic
8C22×C4×D37C2211yescharacteristic
9C2×C8×D37—22no—
10C2×C22⋊Dic37C411yescharacteristic
11C2×#10596938C411yescharacteristic
12C2×#10596938C2211yescharacteristic
13C22⋊C4×D37—22no—
14C22⋊C4×D37—22no—
15C22⋊#64436C2212yescomplemented
16#11924448—22no—
17C2×C22⋊C4×C37C2211yescharacteristic
18C22⋊C8×C37C2212yescomplemented
19C24×C37C2×C411yescharacteristic
20C23×D37—21no—
21C23×D37—21no—
22C23×D37—22no—
23C23×D37—42no—
24C23×D37—42no—
25C23×D37C814yescomplemented
26C23×D37C2×C411yescharacteristic
27C23×D37C2×C411yescharacteristic
28C22×C4×C37C2×C411yescharacteristic
29C22×C4×C37C2311yescharacteristic
30C22×Dic37C2×C411yescharacteristic
31C22×Dic37C2×C411yescharacteristic
32C2×C4×D37—21no—
33C2×C4×D37—21no—
34C2×C4×D37—42no—
35C2×C4×D37—42no—
36C2×C4×D37D412yes—
37C2×C4×D37D412yes—
38C2×C8×C37—22no—
39C22⋊C4×C37—22no—
40C22⋊Dic37—22no—
41#10596938—22no—
42#10596938—22no—
43C2×#64436—22no—
44C8×D37—44no—
45C23×C37—21no—
46C23×C37—21no—
47C23×C37—41no—
48C23×C37—41no—
49C23×C37C2×C812yescomplemented
50C23×C37C22×C411yescharacteristic
51C22×D37—22no—
52C22×D37—22no—
53C22×D37—21no—
54C22×D37—21no—
55C22×D37—24no—
56C22×D37—24no—
57C22×D37—42no—
58C22×D37—42no—
59C22×D37—48no—
60C22×D37—48no—
61C22×D37—42no—
62C22×D37—42no—
63C22×D37—41no—
64C22×D37—41no—
65C22×D37C22⋊C411yescharacteristic
66C22×D37C22⋊C411yescharacteristic
67C22×D37C2×C812yes—
68C22×D37C2×C812yescomplemented
69C22×D37M1612yes—
70C2×C4×C37—21no—
71C2×C4×C37—41no—
72C2×C4×C37—41no—
73C2×C4×C37C2×D412yes—
74C2×Dic37—21no—
75C2×Dic37—41no—
76C2×Dic37—41no—
77C2×Dic37C22⋊C412yes—
78C4×D37—24no—
79C4×D37—42no—
80C4×D37—42no—
81C4×D37—42no—
82C8×C37—42no—
83#64436—42no—
84C22×C37—21no—
85C22×C37—21no—
86C22×C37—22no—
87C22×C37—42no—
88C22×C37—42no—
89C22×C37—41no—
90C22×C37—41no—
91C22×C37C2×C22⋊C411yescharacteristic
92C22×C37C22×C811yescharacteristic
93C22×C37C2×M1611yescharacteristic
94C2×D37—21no—
95C2×D37—21no—
96C2×D37—24no—
97C2×D37—24no—
98C2×D37—22no—
99C2×D37—48no—
100C2×D37—42no—
101C2×D37—41no—
102C2×D37—41no—
103C2×D37—48no—
104C2×D37—42no—
105C2×D37C22⋊C812yes—
106C2×D37C22⋊C812yes—
107C2×D37#9912yes—
108C2×D37#10012yes—
109C4×C37—22no—
110C4×C37—41no—
111Dic37—22no—
112Dic37—41no—
113C2×#323—371nomaximal, Sylow
114C2×C37—21no—
115C2×C37—21no—
116C2×C37—42no—
117C2×C37C2×C22⋊C811yescharacteristic
118C2×C37C2×#9911yescharacteristic
119C2×C37C2×#10011yescharacteristic
120D37—22no—
121D37—42no—
122D37#32314yesdirect product factor
123C22×C22⋊C4—371no—
124C2×C22⋊C8—372no—
125#323—371no—
126#323—372no—
127#323D3711yescharacteristic, direct product factor
128C37C2×#32311yescharacteristic, complemented, Sylow
129C25—371no—
130C23×C4—371no—
131C23×C4—371no—
132C22×C8—742no—
133C2×C22⋊C4—371no—
134C2×C22⋊C4—371no—
135C2×C22⋊C4—371no—
136C2×C22⋊C4—742no—
137C2×C22⋊C4—742no—
138C2×C22⋊C4C2×D3711yescharacteristic
139C22⋊C8—372no—
140C22⋊C8—742no—
141C22⋊C8C2×D3712yescomplemented
142C24—371no—
143C24—374no—
144C24—371no—
145C24—741no—
146C24—741no—
147C24—742no—
148C24—1482no—
149C24—1482no—
150C24C4×D3711yescharacteristic
151C22×C4—371no—
152C22×C4—372no—
153C22×C4—372no—
154C22×C4—371no—
155C22×C4—741no—
156C22×C4—741no—
157C22×C4—1482no—
158C22×C4—1482no—
159C22×C4C4×D3711yescharacteristic
160C22×C4C22×D3711yescharacteristic
161C2×C8—22no—
162C2×C8—742no—
163C2×C8—1484no—
164C22⋊C4—22no—
165C22⋊C4—742no—
166C22⋊C4—742no—
167C22⋊C4—742no—
168C23—21no—
169C23—21no—
170C23—41no—
171C23—41no—
172C23—371no—
173C23—371no—
174C23—372no—
175C23—372no—
176C23—372no—
177C23—742no—
178C23—742no—
179C23—744no—
180C23—744no—
181C23—741no—
182C23—741no—
183C23—1481no—
184C23—1481no—
185C23—1482no—
186C23—1482no—
187C23—1488no—
188C23—1488no—
189C23—1482no—
190C23—1482no—
191C23C8×D3712yescomplemented
192C23C2×C4×D3711yescharacteristic
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—372no—
197C2×C4—744no—
198C2×C4—741no—
199C2×C4—1482no—
200C2×C4—1482no—
201C2×C4—1482no—
202C2×C4—1481no—
203C2×C4—1481no—
204C2×C4D4×D3712yes—
205C8—42no—
206C8—1482no—
207C22—21no—
208C22—21no—
209C22—22no—
210C22—42no—
211C22—42no—
212C22—41no—
213C22—41no—
214C22—372no—
215C22—372no—
216C22—372no—
217C22—372no—
218C22—744no—
219C22—744no—
220C22—741no—
221C22—741no—
222C22—742no—
223C22—1482no—
224C22—1482no—
225C22—1488no—
226C22—1488no—
227C22—1481no—
228C22—1481no—
229C22C22⋊C4×D3711yescharacteristic
230C22C2×C8×D3711yescharacteristic
231C22M16×D3711yescharacteristic
232C4—22no—
233C4—41no—
234C4—742no—
235C4—1481no—
236C2—21no—
237C2—21no—
238C2—42no—
239C2—374no—
240C2—742no—
241C2—1482no—
242C2C22⋊C8×D3711yescharacteristic
243C2#99×D3711yescharacteristic
244C2#100×D3711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC22×C37C22×C8
FrattiniC22×C4C22×D37
FittingC37×#323C2
socleC22×C37C2×C22⋊C4
prime radicalC24×D37C4
cosocleC22×C4×C37C23
hypercenter#323D37
hypocenterC37C2×#323
LCSG ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D37C2semidirect
3. #14557257C2semidirect
4. #14557256C2semidirect
5. C37×#323C2semidirect
15. C22⋊#64436C22semidirect
18. C22⋊C8×C37C22semidirect
25. C23×D37C8semidirect
49. C23×C37C2×C8semidirect
68. C22×D37C2×C8semidirect
122. D37#323direct (N × H)
127. #323D37direct (N × H)
128. C37C2×#323semidirect
141. C22⋊C8C2×D37semidirect
191. C23C8×D37semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×D372
C22⋊C8×D372
#145572572
#145572562
C37×#3232
C2×#32337