Finite Group Databasebeta

← C2×C7×#2873 #13237270

Subgroups — C2×C7×#2873 #13237270

Order 1792.

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×C7×M16C212yesmaximal
2C22×C7×#117C211yesmaximal, characteristic
3C7×#2873C2116yesmaximal, direct product factor
4C2×C7×#405C218yesmaximal, complemented
5C2×C4×C7×M16C214yesmaximal, complemented
6C24×C4×C7C2211yescharacteristic
7C22×C7×M16C4132yescomplemented
8C22×C7×M16C2214yes—
9C22×C7×M16C2214yes—
10C22×C7×M16C22116yes—
11C23×C7×C8C2214yes—
12C2×C7×#117C414yes—
13C2×C7×#117C418yes—
14C2×C7×#117C2214yes—
15C2×C7×#117C2218yes—
16C22×C7×C4⋊C4C412yes—
17C22×C7×C22⋊C4C412yes—
18C22×C42×C7C2212yes—
19C7×#405C22164yescomplemented
20C4×C7×M16C22132yescomplemented
21C2×C7×#97C2218yescomplemented
22C2×C4×C7×C8C2218yescomplemented
23C2×#2873C711yesmaximal, characteristic, direct product factor, Sylow
24C25×C7C2×C411yescharacteristic
25C23×C4×C7C2×C414yes—
26C23×C4×C7C2×C411yescharacteristic
27C23×C4×C7C2×C412yes—
28C23×C4×C7C2×C414yes—
29C23×C4×C7C2×C4116yes—
30C23×C4×C7C2314yes—
31C23×C4×C7C2311yescharacteristic
32C23×C4×C7C2312yes—
33C2×C7×M16C2×C4132yes—
34C2×C7×M16C2×C4132yescomplemented
35C2×C7×M16C2×C41128yescomplemented
36C2×C7×M16C23116yes—
37C2×C7×M16C23116yes—
38C22×C7×C8C2×C4132yescomplemented
39C22×C7×C8C2318yes—
40C22×C7×C8C23116yes—
41C7×#117C2×C4116yes—
42C7×#117C2×C4132yes—
43C7×#117C23116yes—
44C2×C7×C4⋊C4C2×C418yes—
45C2×C7×C4⋊C4C2×C4116yes—
46C2×C7×C22⋊C4C2×C418yes—
47C2×C7×C22⋊C4C2×C4116yes—
48C2×C42×C7C2×C414yes—
49C2×C42×C7C2×C418yes—
50C2×C42×C7C2318yes—
51C2×C42×C7C2314yes—
52C7×#97C23132yescomplemented
53C4×C7×C8C23132yescomplemented
54C23×M16C2×C712yes—
55C22×#117C2×C711yescharacteristic
56#2873C2×C7116yesdirect product factor
57C2×#405C2×C718yescomplemented
58C2×C4×M16C2×C714yescomplemented
59C24×C7—44no—
60C24×C7C4218yes—
61C24×C7C22×C412yes—
62C24×C7C22×C411yescharacteristic
63C24×C7C22×C414yes—
64C22×C4×C7—48no—
65C22×C4×C7C4218yes—
66C22×C4×C7C42116yes—
67C22×C4×C7C42132yes—
68C22×C4×C7C22×C418yes—
69C22×C4×C7C22×C4116yes—
70C22×C4×C7C22×C411yescharacteristic
71C22×C4×C7C22×C412yes—
72C22×C4×C7C22×C414yes—
73C22×C4×C7C22×C412yes—
74C22×C4×C7C22×C418yes—
75C22×C4×C7C22×C414yes—
76C22×C4×C7C22×C418yes—
77C22×C4×C7C22×C418yes—
78C22×C4×C7C22×C418yes—
79C22×C4×C7C22×C4132yes—
80C22×C4×C7C2412yes—
81C22×C4×C7C2414yes—
82C22×C4×C7C2411yescharacteristic
83C7×M16C22×C4164yes—
84C7×M16C22×C4164yescomplemented
85C2×C7×C8C22×C4132yes—
86C2×C7×C8C22×C4164yescomplemented
87C2×C7×C8C24116yes—
88C7×C4⋊C4C22×C4132yes—
89C7×C22⋊C4C22×C4132yes—
90C42×C7C22×C4116yes—
91C42×C7C22×C418yes—
92C42×C7C2418yes—
93C24×C4C22×C711yescharacteristic
94C22×M16C4×C7132yescomplemented
95C22×M16C22×C714yes—
96C22×M16C22×C714yes—
97C22×M16C22×C7116yes—
98C23×C8C22×C714yes—
99C2×#117C4×C714yes—
100C2×#117C4×C718yes—
101C2×#117C22×C714yes—
102C2×#117C22×C718yes—
103C22×C4⋊C4C4×C712yes—
104C22×C22⋊C4C4×C712yes—
105C22×C42C22×C712yes—
106#405C22×C7164yescomplemented
107C4×M16C22×C7132yescomplemented
108C2×#97C22×C718yescomplemented
109C2×C4×C8C22×C718yescomplemented
110C23×C7—24no—
111C23×C7—28no—
112C23×C7—416no—
113C23×C7—48no—
114C23×C7C2×C4218yes—
115C23×C7C2×C4214yes—
116C23×C7C2×C42116yes—
117C23×C7C23×C414yes—
118C23×C7C23×C412yes—
119C23×C7C23×C411yescharacteristic
120C2×C4×C7—216no—
121C2×C4×C7—416no—
122C2×C4×C7C2×C4218yes—
123C2×C4×C7C2×C42116yes—
124C2×C4×C7C2×C42116yes—
125C2×C4×C7C2×C42132yes—
126C2×C4×C7C2×C4214yes—
127C2×C4×C7C2×C4218yes—
128C2×C4×C7C23×C4116yes—
129C2×C4×C7C23×C414yes—
130C2×C4×C7C23×C418yes—
131C2×C4×C7C23×C418yes—
132C2×C4×C7C23×C418yes—
133C2×C4×C7C23×C412yes—
134C2×C4×C7C23×C411yescharacteristic
135C2×C4×C7C23×C414yes—
136C2×C4×C7C2511yescharacteristic
137C7×C8C23×C4132yes—
138C25C2×C4×C711yescharacteristic
139C23×C4C2×C4×C714yes—
140C23×C4C2×C4×C711yescharacteristic
141C23×C4C2×C4×C712yes—
142C23×C4C2×C4×C714yes—
143C23×C4C2×C4×C7116yes—
144C23×C4C23×C712yes—
145C23×C4C23×C714yes—
146C23×C4C23×C711yescharacteristic
147C2×M16C2×C4×C7132yes—
148C2×M16C2×C4×C7132yescomplemented
149C2×M16C2×C4×C71128yescomplemented
150C2×M16C23×C7116yes—
151C2×M16C23×C7116yes—
152C22×C8C2×C4×C7132yescomplemented
153C22×C8C23×C718yes—
154C22×C8C23×C7116yes—
155#117C2×C4×C7116yes—
156#117C2×C4×C7132yes—
157#117C23×C7116yes—
158C2×C4⋊C4C2×C4×C718yes—
159C2×C4⋊C4C2×C4×C7116yes—
160C2×C22⋊C4C2×C4×C718yes—
161C2×C22⋊C4C2×C4×C7116yes—
162C2×C42C2×C4×C714yes—
163C2×C42C2×C4×C718yes—
164C2×C42C23×C714yes—
165C2×C42C23×C718yes—
166#97C23×C7132yescomplemented
167C4×C8C23×C7132yescomplemented
168C22×C7—28no—
169C22×C7—216no—
170C22×C7—24no—
171C22×C7—28no—
172C22×C7—416no—
173C22×C7C22×C4218yes—
174C22×C7C22×C4214yes—
175C22×C7C22×C4212yes—
176C22×C7#56814yes—
177C22×C7C24×C411yescharacteristic
178C4×C7—216no—
179C4×C7C22×C4212yes—
180C4×C7C22×C4218yes—
181C4×C7C22×C4214yes—
182C4×C7C24×C412yes—
183C24—44no—
184C24C42×C718yes—
185C24C22×C4×C712yes—
186C24C22×C4×C711yescharacteristic
187C24C22×C4×C714yes—
188C22×C4—48no—
189C22×C4C42×C718yes—
190C22×C4C42×C7116yes—
191C22×C4C42×C7132yes—
192C22×C4C22×C4×C718yes—
193C22×C4C22×C4×C7116yes—
194C22×C4C22×C4×C712yes—
195C22×C4C22×C4×C711yescharacteristic
196C22×C4C22×C4×C714yes—
197C22×C4C22×C4×C712yes—
198C22×C4C22×C4×C714yes—
199C22×C4C22×C4×C718yes—
200C22×C4C22×C4×C718yes—
201C22×C4C22×C4×C718yes—
202C22×C4C22×C4×C718yes—
203C22×C4C22×C4×C7132yes—
204C22×C4C24×C711yescharacteristic
205C22×C4C24×C712yes—
206C22×C4C24×C714yes—
207M16C22×C4×C7164yes—
208M16C22×C4×C7164yescomplemented
209C2×C8C22×C4×C7132yes—
210C2×C8C22×C4×C7164yescomplemented
211C2×C8C24×C7116yes—
212C4⋊C4C22×C4×C7132yes—
213C22⋊C4C22×C4×C7132yes—
214C42C22×C4×C718yes—
215C42C22×C4×C7116yes—
216C42C24×C718yes—
217C2×C7—24no—
218C2×C7—28no—
219C2×C7#287314yesdirect product factor
220C2×C7C23×C4211yescharacteristic
221C2×C7C2×#56812yes—
222C23—24no—
223C23—28no—
224C23—416no—
225C23—48no—
226C23C2×C42×C718yes—
227C23C2×C42×C714yes—
228C23C2×C42×C7116yes—
229C23C23×C4×C714yes—
230C23C23×C4×C712yes—
231C23C23×C4×C711yescharacteristic
232C2×C4—216no—
233C2×C4—416no—
234C2×C4C2×C42×C718yes—
235C2×C4C2×C42×C7116yes—
236C2×C4C2×C42×C7116yes—
237C2×C4C2×C42×C7132yes—
238C2×C4C2×C42×C714yes—
239C2×C4C2×C42×C718yes—
240C2×C4C23×C4×C7116yes—
241C2×C4C23×C4×C712yes—
242C2×C4C23×C4×C711yescharacteristic
243C2×C4C23×C4×C714yes—
244C2×C4C23×C4×C714yes—
245C2×C4C23×C4×C718yes—
246C2×C4C23×C4×C718yes—
247C2×C4C23×C4×C718yes—
248C2×C4C25×C711yescharacteristic
249C8C23×C4×C7132yes—
250C7C2×#287311yescharacteristic, direct product factor, Sylow
251C22—24no—
252C22—28no—
253C22—28no—
254C22—216no—
255C22—416no—
256C22C22×C42×C718yes—
257C22C22×C42×C714yes—
258C22C22×C42×C712yes—
259C22C7×#56814yes—
260C22C24×C4×C711yescharacteristic
261C4—216no—
262C4C22×C42×C712yes—
263C4C22×C42×C714yes—
264C4C22×C42×C718yes—
265C4C24×C4×C712yes—
266C2—24no—
267C2—28no—
268C2C7×#287314yesdirect product factor
269C2C23×C42×C711yescharacteristic
270C2C2×C7×#56812yes—
subgroupG/H
centerC22×C4×C7C24
commutatorC2C23×C42×C7
Frattini, cosocleC2×C4C25×C7
socleC23×C7C23×C4
prime radicalC25×C7C2×C4
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
3. C7×#2873C2direct (N × H)
4. C2×C7×#405C2semidirect
5. C2×C4×C7×M16C2semidirect
7. C22×C7×M16C4semidirect
19. C7×#405C22semidirect
20. C4×C7×M16C22semidirect
21. C2×C7×#97C22semidirect
22. C2×C4×C7×C8C22semidirect
23. C2×#2873C7direct (N × H)
34. C2×C7×M16C2×C4semidirect
35. C2×C7×M16C2×C4semidirect
38. C22×C7×C8C2×C4semidirect
52. C7×#97C23semidirect
53. C4×C7×C8C23semidirect
56. #2873C2×C7direct (N × H)
57. C2×#405C2×C7semidirect
58. C2×C4×M16C2×C7semidirect
84. C7×M16C22×C4semidirect
86. C2×C7×C8C22×C4semidirect
94. C22×M16C4×C7semidirect
106. #405C22×C7semidirect
107. C4×M16C22×C7semidirect
108. C2×#97C22×C7semidirect
109. C2×C4×C8C22×C7semidirect
148. C2×M16C2×C4×C7semidirect
149. C2×M16C2×C4×C7semidirect
152. C22×C8C2×C4×C7semidirect
166. #97C23×C7semidirect
167. C4×C8C23×C7semidirect
208. M16C22×C4×C7semidirect
210. C2×C8C22×C4×C7semidirect
219. C2×C7#2873direct (N × H)
250. C7C2×#2873direct (N × H)
268. C2C7×#2873direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C7×M162
C22×C7×#1172
C7×#28732
C2×C7×#4052
C2×C4×C7×M162
C2×#28737