Finite Group Databasebeta

← C2×C37×#2873 #22681307

Subgroups — C2×C37×#2873 #22681307

Order 9472.

3342 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×M16×C37C212yesmaximal
2C22×#117×C37C211yesmaximal, characteristic
3C37×#2873C2116yesmaximal, direct product factor
4C2×C37×#405C218yesmaximal, complemented
5C2×C4×M16×C37C214yesmaximal, complemented
6C24×C4×C37C2211yescharacteristic
7C22×M16×C37C4132yescomplemented
8C22×M16×C37C2214yes—
9C22×M16×C37C2214yes—
10C22×M16×C37C22116yes—
11C23×C8×C37C2214yes—
12C2×#117×C37C414yes—
13C2×#117×C37C418yes—
14C2×#117×C37C2214yes—
15C2×#117×C37C2218yes—
16C22×C4⋊C4×C37C412yes—
17C22×C22⋊C4×C37C412yes—
18C22×C42×C37C2212yes—
19C37×#405C22164yescomplemented
20C4×M16×C37C22132yescomplemented
21C2×#97×C37C2218yescomplemented
22C2×C4×C8×C37C2218yescomplemented
23C25×C37C2×C411yescharacteristic
24C23×C4×C37C2×C414yes—
25C23×C4×C37C2×C411yescharacteristic
26C23×C4×C37C2×C412yes—
27C23×C4×C37C2×C414yes—
28C23×C4×C37C2×C4116yes—
29C23×C4×C37C2314yes—
30C23×C4×C37C2312yes—
31C23×C4×C37C2311yescharacteristic
32C2×M16×C37C2×C4132yes—
33C2×M16×C37C2×C4132yescomplemented
34C2×M16×C37C2×C41128yescomplemented
35C2×M16×C37C23116yes—
36C2×M16×C37C23116yes—
37C22×C8×C37C2×C4132yescomplemented
38C22×C8×C37C2318yes—
39C22×C8×C37C23116yes—
40#117×C37C2×C4116yes—
41#117×C37C2×C4132yes—
42#117×C37C23116yes—
43C2×C4⋊C4×C37C2×C418yes—
44C2×C4⋊C4×C37C2×C4116yes—
45C2×C22⋊C4×C37C2×C418yes—
46C2×C22⋊C4×C37C2×C4116yes—
47C2×C42×C37C2×C414yes—
48C2×C42×C37C2×C418yes—
49C2×C42×C37C2318yes—
50C2×C42×C37C2314yes—
51#97×C37C23132yescomplemented
52C4×C8×C37C23132yescomplemented
53C24×C37—44no—
54C24×C37C4218yes—
55C24×C37C22×C412yes—
56C24×C37C22×C411yescharacteristic
57C24×C37C22×C414yes—
58C22×C4×C37—48no—
59C22×C4×C37C4218yes—
60C22×C4×C37C42116yes—
61C22×C4×C37C42132yes—
62C22×C4×C37C22×C418yes—
63C22×C4×C37C22×C4116yes—
64C22×C4×C37C22×C411yescharacteristic
65C22×C4×C37C22×C412yes—
66C22×C4×C37C22×C414yes—
67C22×C4×C37C22×C412yes—
68C22×C4×C37C22×C418yes—
69C22×C4×C37C22×C414yes—
70C22×C4×C37C22×C418yes—
71C22×C4×C37C22×C418yes—
72C22×C4×C37C22×C418yes—
73C22×C4×C37C22×C4132yes—
74C22×C4×C37C2412yes—
75C22×C4×C37C2414yes—
76C22×C4×C37C2411yescharacteristic
77M16×C37C22×C4164yes—
78M16×C37C22×C4164yescomplemented
79C2×C8×C37C22×C4132yes—
80C2×C8×C37C22×C4164yescomplemented
81C2×C8×C37C24116yes—
82C4⋊C4×C37C22×C4132yes—
83C22⋊C4×C37C22×C4132yes—
84C42×C37C22×C4116yes—
85C42×C37C22×C418yes—
86C42×C37C2418yes—
87C23×C37—24no—
88C23×C37—28no—
89C23×C37—416no—
90C23×C37—48no—
91C23×C37C2×C4218yes—
92C23×C37C2×C4214yes—
93C23×C37C2×C42116yes—
94C23×C37C23×C414yes—
95C23×C37C23×C412yes—
96C23×C37C23×C411yescharacteristic
97C2×C4×C37—216no—
98C2×C4×C37—416no—
99C2×C4×C37C2×C4218yes—
100C2×C4×C37C2×C42116yes—
101C2×C4×C37C2×C42116yes—
102C2×C4×C37C2×C42132yes—
103C2×C4×C37C2×C4214yes—
104C2×C4×C37C2×C4218yes—
105C2×C4×C37C23×C4116yes—
106C2×C4×C37C23×C414yes—
107C2×C4×C37C23×C418yes—
108C2×C4×C37C23×C418yes—
109C2×C4×C37C23×C418yes—
110C2×C4×C37C23×C412yes—
111C2×C4×C37C23×C411yescharacteristic
112C2×C4×C37C23×C414yes—
113C2×C4×C37C2511yescharacteristic
114C8×C37C23×C4132yes—
115C2×#2873C3711yesmaximal, characteristic, direct product factor, Sylow
116C22×C37—28no—
117C22×C37—216no—
118C22×C37—24no—
119C22×C37—28no—
120C22×C37—416no—
121C22×C37C22×C4218yes—
122C22×C37C22×C4214yes—
123C22×C37C22×C4212yes—
124C22×C37#56814yes—
125C22×C37C24×C411yescharacteristic
126C4×C37—216no—
127C4×C37C22×C4212yes—
128C4×C37C22×C4218yes—
129C4×C37C22×C4214yes—
130C4×C37C24×C412yes—
131C23×M16C2×C3712yes—
132C22×#117C2×C3711yescharacteristic
133#2873C2×C37116yesdirect product factor
134C2×#405C2×C3718yescomplemented
135C2×C4×M16C2×C3714yescomplemented
136C2×C37—24no—
137C2×C37—28no—
138C2×C37#287314yesdirect product factor
139C2×C37C23×C4211yescharacteristic
140C2×C37C2×#56812yes—
141C24×C4C22×C3711yescharacteristic
142C22×M16C4×C37132yescomplemented
143C22×M16C22×C3714yes—
144C22×M16C22×C3714yes—
145C22×M16C22×C37116yes—
146C23×C8C22×C3714yes—
147C2×#117C4×C3714yes—
148C2×#117C4×C3718yes—
149C2×#117C22×C3714yes—
150C2×#117C22×C3718yes—
151C22×C4⋊C4C4×C3712yes—
152C22×C22⋊C4C4×C3712yes—
153C22×C42C22×C3712yes—
154#405C22×C37164yescomplemented
155C4×M16C22×C37132yescomplemented
156C2×#97C22×C3718yescomplemented
157C2×C4×C8C22×C3718yescomplemented
158C37C2×#287311yescharacteristic, direct product factor, Sylow
159C25C2×C4×C3711yescharacteristic
160C23×C4C2×C4×C3714yes—
161C23×C4C2×C4×C3711yescharacteristic
162C23×C4C2×C4×C3712yes—
163C23×C4C2×C4×C3714yes—
164C23×C4C2×C4×C37116yes—
165C23×C4C23×C3712yes—
166C23×C4C23×C3714yes—
167C23×C4C23×C3711yescharacteristic
168C2×M16C2×C4×C37132yes—
169C2×M16C2×C4×C37132yescomplemented
170C2×M16C2×C4×C371128yescomplemented
171C2×M16C23×C37116yes—
172C2×M16C23×C37116yes—
173C22×C8C2×C4×C37132yescomplemented
174C22×C8C23×C3718yes—
175C22×C8C23×C37116yes—
176#117C2×C4×C37116yes—
177#117C2×C4×C37132yes—
178#117C23×C37116yes—
179C2×C4⋊C4C2×C4×C3718yes—
180C2×C4⋊C4C2×C4×C37116yes—
181C2×C22⋊C4C2×C4×C3718yes—
182C2×C22⋊C4C2×C4×C37116yes—
183C2×C42C2×C4×C3714yes—
184C2×C42C2×C4×C3718yes—
185C2×C42C23×C3714yes—
186C2×C42C23×C3718yes—
187#97C23×C37132yescomplemented
188C4×C8C23×C37132yescomplemented
189C24—44no—
190C24C42×C3718yes—
191C24C22×C4×C3712yes—
192C24C22×C4×C3711yescharacteristic
193C24C22×C4×C3714yes—
194C22×C4—48no—
195C22×C4C42×C3718yes—
196C22×C4C42×C37116yes—
197C22×C4C42×C37132yes—
198C22×C4C22×C4×C3718yes—
199C22×C4C22×C4×C37116yes—
200C22×C4C22×C4×C3712yes—
201C22×C4C22×C4×C3711yescharacteristic
202C22×C4C22×C4×C3714yes—
203C22×C4C22×C4×C3712yes—
204C22×C4C22×C4×C3714yes—
205C22×C4C22×C4×C3718yes—
206C22×C4C22×C4×C3718yes—
207C22×C4C22×C4×C3718yes—
208C22×C4C22×C4×C3718yes—
209C22×C4C22×C4×C37132yes—
210C22×C4C24×C3712yes—
211C22×C4C24×C3714yes—
212C22×C4C24×C3711yescharacteristic
213M16C22×C4×C37164yes—
214M16C22×C4×C37164yescomplemented
215C2×C8C22×C4×C37132yes—
216C2×C8C22×C4×C37164yescomplemented
217C2×C8C24×C37116yes—
218C4⋊C4C22×C4×C37132yes—
219C22⋊C4C22×C4×C37132yes—
220C42C22×C4×C3718yes—
221C42C22×C4×C37116yes—
222C42C24×C3718yes—
223C23—24no—
224C23—28no—
225C23—416no—
226C23—48no—
227C23C2×C42×C3718yes—
228C23C2×C42×C3714yes—
229C23C2×C42×C37116yes—
230C23C23×C4×C3714yes—
231C23C23×C4×C3712yes—
232C23C23×C4×C3711yescharacteristic
233C2×C4—216no—
234C2×C4—416no—
235C2×C4C2×C42×C3718yes—
236C2×C4C2×C42×C37116yes—
237C2×C4C2×C42×C37116yes—
238C2×C4C2×C42×C37132yes—
239C2×C4C2×C42×C3714yes—
240C2×C4C2×C42×C3718yes—
241C2×C4C23×C4×C37116yes—
242C2×C4C23×C4×C3714yes—
243C2×C4C23×C4×C3718yes—
244C2×C4C23×C4×C3718yes—
245C2×C4C23×C4×C3718yes—
246C2×C4C23×C4×C3712yes—
247C2×C4C23×C4×C3711yescharacteristic
248C2×C4C23×C4×C3714yes—
249C2×C4C25×C3711yescharacteristic
250C8C23×C4×C37132yes—
251C22—28no—
252C22—216no—
253C22—24no—
254C22—28no—
255C22—416no—
256C22C22×C42×C3718yes—
257C22C22×C42×C3714yes—
258C22C22×C42×C3712yes—
259C22C37×#56814yes—
260C22C24×C4×C3711yescharacteristic
261C4—216no—
262C4C22×C42×C3712yes—
263C4C22×C42×C3718yes—
264C4C22×C42×C3714yes—
265C4C24×C4×C3712yes—
266C2—24no—
267C2—28no—
268C2C37×#287314yesdirect product factor
269C2C23×C42×C3711yescharacteristic
270C2C2×C37×#56812yes—
subgroupG/H
centerC22×C4×C37C24
commutatorC2C23×C42×C37
Frattini, cosocleC2×C4C25×C37
socleC23×C37C23×C4
prime radicalC25×C37C2×C4
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
3. C37×#2873C2direct (N × H)
4. C2×C37×#405C2semidirect
5. C2×C4×M16×C37C2semidirect
7. C22×M16×C37C4semidirect
19. C37×#405C22semidirect
20. C4×M16×C37C22semidirect
21. C2×#97×C37C22semidirect
22. C2×C4×C8×C37C22semidirect
33. C2×M16×C37C2×C4semidirect
34. C2×M16×C37C2×C4semidirect
37. C22×C8×C37C2×C4semidirect
51. #97×C37C23semidirect
52. C4×C8×C37C23semidirect
78. M16×C37C22×C4semidirect
80. C2×C8×C37C22×C4semidirect
115. C2×#2873C37direct (N × H)
133. #2873C2×C37direct (N × H)
134. C2×#405C2×C37semidirect
135. C2×C4×M16C2×C37semidirect
138. C2×C37#2873direct (N × H)
142. C22×M16C4×C37semidirect
154. #405C22×C37semidirect
155. C4×M16C22×C37semidirect
156. C2×#97C22×C37semidirect
157. C2×C4×C8C22×C37semidirect
158. C37C2×#2873direct (N × H)
169. C2×M16C2×C4×C37semidirect
170. C2×M16C2×C4×C37semidirect
173. C22×C8C2×C4×C37semidirect
187. #97C23×C37semidirect
188. C4×C8C23×C37semidirect
214. M16C22×C4×C37semidirect
216. C2×C8C22×C4×C37semidirect
268. C2C37×#2873direct (N × H)

Maximal subgroups

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

subgroupindex
C23×M16×C372
C22×#117×C372
C37×#28732
C2×C37×#4052
C2×C4×M16×C372
C2×#287337