Finite Group Databasebeta

← C22×C7×#407 #13237276

Subgroups — C22×C7×#407 #13237276

Order 1792.

7214 conjugacy classes of subgroups.

The subgroup lattice has 266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×C4×C7C211yesmaximal, characteristic
2C23×C7×M16C212yesmaximal, complemented
3C2×C7×#407C2124yesmaximal, direct product factor
4C22×C7×C22⋊C8C214yesmaximal, complemented
5C26×C7C411yescharacteristic
6C24×C4×C7—216no—
7C24×C4×C7C411yescharacteristic
8C24×C4×C7C4112yes—
9C24×C4×C7C412yes—
10C24×C4×C7C22112yes—
11C24×C4×C7C2212yes—
12C24×C4×C7C2211yescharacteristic
13C22×C7×M16—216no—
14C22×C7×M16C22124yescomplemented
15C23×C7×C8C2214yescomplemented
16C7×#407C22164yesdirect product factor
17C2×C7×C22⋊C8C22148yescomplemented
18C22×#407C711yesmaximal, characteristic, direct product factor, Sylow
19C25×C7—28no—
20C25×C7—216no—
21C25×C7C2×C4112yes—
22C25×C7C2×C411yescharacteristic
23C25×C7C2×C412yes—
24C23×C4×C7—28no—
25C23×C4×C7—296no—
26C23×C4×C7—216no—
27C23×C4×C7—216no—
28C23×C4×C7—296no—
29C23×C4×C7C2×C4112yes—
30C23×C4×C7C2×C412yes—
31C23×C4×C7C2×C4148yes—
32C23×C4×C7C2×C4124yes—
33C23×C4×C7C2×C4112yes—
34C23×C4×C7C2×C411yescharacteristic
35C23×C4×C7C2×C416yes—
36C23×C4×C7D4116yes—
37C23×C4×C7C23112yes—
38C23×C4×C7C23116yes—
39C23×C4×C7C2316yes—
40C23×C4×C7C2311yescharacteristic
41C2×C7×M16—296no—
42C2×C7×M16C23132yescomplemented
43C22×C7×C8—216no—
44C22×C7×C8C23124yescomplemented
45C7×C22⋊C8C23164yescomplemented
46C25×C4C2×C711yescharacteristic
47C23×M16C2×C712yescomplemented
48C2×#407C2×C7124yesdirect product factor
49C22×C22⋊C8C2×C714yescomplemented
50C24×C7—2128no—
51C24×C7—248no—
52C24×C7—28no—
53C24×C7—28no—
54C24×C7—28no—
55C24×C7—296no—
56C24×C7C22⋊C418yes—
57C24×C7M16116yescomplemented
58C24×C7C22×C4116yes—
59C24×C7C22×C416yes—
60C24×C7C22×C4112yes—
61C24×C7C22×C411yescharacteristic
62C22×C4×C7—248no—
63C22×C4×C7—28no—
64C22×C4×C7—2192no—
65C22×C4×C7—296no—
66C22×C4×C7—248no—
67C22×C4×C7—248no—
68C22×C4×C7—264no—
69C22×C4×C7C22⋊C4148yes—
70C22×C4×C7C22⋊C418yes—
71C22×C4×C7C22×C4116yes—
72C22×C4×C7C22×C4112yes—
73C22×C4×C7C22×C4124yes—
74C22×C4×C7C22×C4132yes—
75C22×C4×C7C22×C4112yes—
76C22×C4×C7C22×C416yes—
77C22×C4×C7C22×C413yes—
78C22×C4×C7C2×D418yes—
79C22×C4×C7C2×D4148yes—
80C22×C4×C7C2418yes—
81C22×C4×C7C2413yes—
82C22×C4×C7C2414yes—
83C7×M16—264no—
84C2×C7×C8—248no—
85C2×C7×C8C24116yescomplemented
86C26C4×C711yescharacteristic
87C24×C4—216no—
88C24×C4C4×C711yescharacteristic
89C24×C4C4×C7112yes—
90C24×C4C4×C712yes—
91C24×C4C22×C712yes—
92C24×C4C22×C7112yes—
93C24×C4C22×C711yescharacteristic
94C22×M16—216no—
95C22×M16C22×C7124yescomplemented
96C23×C8C22×C714yescomplemented
97#407C22×C7164yesdirect product factor
98C2×C22⋊C8C22×C7148yescomplemented
99C23×C7—2384no—
100C23×C7—232no—
101C23×C7—224no—
102C23×C7—224no—
103C23×C7—224no—
104C23×C7—264no—
105C23×C7—232no—
106C23×C7—264no—
107C23×C7C2×C22⋊C4124yes—
108C23×C7C2×C22⋊C414yes—
109C23×C7C2×M1618yes—
110C23×C7C2×M16148yescomplemented
111C23×C7C23×C414yes—
112C23×C7C23×C418yes—
113C23×C7C23×C413yes—
114C2×C4×C7—232no—
115C2×C4×C7—224no—
116C2×C4×C7—248no—
117C2×C4×C7—264no—
118C2×C4×C7—216no—
119C2×C4×C7C2×C22⋊C4148yes—
120C2×C4×C7C2×C22⋊C4124yes—
121C2×C4×C7C2×C22⋊C4112yes—
122C2×C4×C7C23×C418yes—
123C2×C4×C7C23×C414yes—
124C2×C4×C7C23×C413yes—
125C2×C4×C7C22×D4112yes—
126C2×C4×C7C22×D4116yes—
127C2×C4×C7C2511yescharacteristic
128C7×C8—216no—
129C25—28no—
130C25—216no—
131C25C2×C4×C7112yes—
132C25C2×C4×C711yescharacteristic
133C25C2×C4×C712yes—
134C23×C4—28no—
135C23×C4—296no—
136C23×C4—216no—
137C23×C4—216no—
138C23×C4—296no—
139C23×C4C2×C4×C7112yes—
140C23×C4C2×C4×C712yes—
141C23×C4C2×C4×C7148yes—
142C23×C4C2×C4×C7112yes—
143C23×C4C2×C4×C7124yes—
144C23×C4C2×C4×C716yes—
145C23×C4C2×C4×C711yescharacteristic
146C23×C4C7×D4116yes—
147C23×C4C23×C7112yes—
148C23×C4C23×C7116yes—
149C23×C4C23×C711yescharacteristic
150C23×C4C23×C716yes—
151C2×M16—296no—
152C2×M16C23×C7132yescomplemented
153C22×C8—216no—
154C22×C8C23×C7124yescomplemented
155C22⋊C8C23×C7164yescomplemented
156C22×C7—2128no—
157C22×C7—248no—
158C22×C7—296no—
159C22×C7—28no—
160C22×C7—28no—
161C22×C7—28no—
162C22×C7#407116yesdirect product factor
163C22×C7C22×C22⋊C418yes—
164C22×C7C22×C22⋊C416yes—
165C22×C7C22×M16112yes—
166C22×C7C22×M16116yescomplemented
167C22×C7C24×C411yescharacteristic
168C4×C7—28no—
169C4×C7C22×C22⋊C416yes—
170C4×C7C22×C22⋊C418yes—
171C4×C7C23×D412yes—
172C24—2128no—
173C24—248no—
174C24—28no—
175C24—28no—
176C24—28no—
177C24—296no—
178C24C7×C22⋊C418yes—
179C24C7×M16116yescomplemented
180C24C22×C4×C7116yes—
181C24C22×C4×C716yes—
182C24C22×C4×C7112yes—
183C24C22×C4×C711yescharacteristic
184C22×C4—248no—
185C22×C4—28no—
186C22×C4—2192no—
187C22×C4—248no—
188C22×C4—296no—
189C22×C4—248no—
190C22×C4—264no—
191C22×C4C7×C22⋊C4148yes—
192C22×C4C7×C22⋊C418yes—
193C22×C4C22×C4×C7116yes—
194C22×C4C22×C4×C7112yes—
195C22×C4C22×C4×C7124yes—
196C22×C4C22×C4×C7132yes—
197C22×C4C22×C4×C7112yes—
198C22×C4C22×C4×C713yes—
199C22×C4C22×C4×C716yes—
200C22×C4C2×C7×D418yes—
201C22×C4C2×C7×D4148yes—
202C22×C4C24×C718yes—
203C22×C4C24×C713yes—
204C22×C4C24×C714yes—
205M16—264no—
206C2×C8—248no—
207C2×C8C24×C7116yescomplemented
208C2×C7—28no—
209C2×C7—216no—
210C2×C7C2×#407112yesdirect product factor
211C2×C7C23×C22⋊C411yescharacteristic
212C2×C7C23×M1612yes—
213C23—2384no—
214C23—232no—
215C23—224no—
216C23—232no—
217C23—264no—
218C23—224no—
219C23—224no—
220C23—264no—
221C23C2×C7×C22⋊C4124yes—
222C23C2×C7×C22⋊C414yes—
223C23C2×C7×M1618yes—
224C23C2×C7×M16148yescomplemented
225C23C23×C4×C714yes—
226C23C23×C4×C718yes—
227C23C23×C4×C713yes—
228C2×C4—232no—
229C2×C4—224no—
230C2×C4—216no—
231C2×C4—248no—
232C2×C4—264no—
233C2×C4C2×C7×C22⋊C4148yes—
234C2×C4C2×C7×C22⋊C4112yes—
235C2×C4C2×C7×C22⋊C4124yes—
236C2×C4C23×C4×C718yes—
237C2×C4C23×C4×C713yes—
238C2×C4C23×C4×C714yes—
239C2×C4C22×C7×D4112yes—
240C2×C4C22×C7×D4116yes—
241C2×C4C25×C711yescharacteristic
242C8—216no—
243C7C22×#40711yescharacteristic, direct product factor, Sylow
244C22—2128no—
245C22—28no—
246C22—28no—
247C22—28no—
248C22—248no—
249C22—296no—
250C22C7×#407116yesdirect product factor
251C22C22×C7×C22⋊C418yes—
252C22C22×C7×C22⋊C416yes—
253C22C22×C7×M16112yes—
254C22C22×C7×M16116yescomplemented
255C22C24×C4×C711yescharacteristic
256C4—28no—
257C4C22×C7×C22⋊C416yes—
258C4C22×C7×C22⋊C418yes—
259C4C23×C7×D412yes—
260C2—28no—
261C2—216no—
262C2C2×C7×#407112yesdirect product factor
263C2C23×C7×C22⋊C411yescharacteristic
264C2C23×C7×M1612yes—
subgroupG/H
centerC23×C4×C7C23
commutatorC22C24×C4×C7
Frattini, cosocleC2×C4C25×C7
socleC24×C7C22×C4
prime radicalC26×C7C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C7×M16C2semidirect
3. C2×C7×#407C2direct (N × H)
4. C22×C7×C22⋊C8C2semidirect
14. C22×C7×M16C22semidirect
15. C23×C7×C8C22semidirect
16. C7×#407C22direct (N × H)
17. C2×C7×C22⋊C8C22semidirect
18. C22×#407C7direct (N × H)
42. C2×C7×M16C23semidirect
44. C22×C7×C8C23semidirect
45. C7×C22⋊C8C23semidirect
47. C23×M16C2×C7semidirect
48. C2×#407C2×C7direct (N × H)
49. C22×C22⋊C8C2×C7semidirect
57. C24×C7M16semidirect
85. C2×C7×C8C24semidirect
95. C22×M16C22×C7semidirect
96. C23×C8C22×C7semidirect
97. #407C22×C7direct (N × H)
98. C2×C22⋊C8C22×C7semidirect
110. C23×C7C2×M16semidirect
152. C2×M16C23×C7semidirect
154. C22×C8C23×C7semidirect
155. C22⋊C8C23×C7semidirect
162. C22×C7#407direct (N × H)
166. C22×C7C22×M16semidirect
179. C24C7×M16semidirect
207. C2×C8C24×C7semidirect
210. C2×C7C2×#407direct (N × H)
224. C23C2×C7×M16semidirect
243. C7C22×#407direct (N × H)
250. C22C7×#407direct (N × H)
254. C22C22×C7×M16semidirect
262. C2C2×C7×#407direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C4×C72
C23×C7×M162
C2×C7×#4072
C22×C7×C22⋊C82
C22×#4077