Finite Group Databasebeta

← C2×C7×#1808 #13197873

Subgroups — C2×C7×#1808 #13197873

Order 1792.

1790 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C7×C8C211yesmaximal, characteristic
2C22×C7×#107C212yesmaximal, complemented
3C2×C7×#380C212yesmaximal
4C7×#1808C218yesmaximal, direct product factor
5C2×C7×#340C212yesmaximal, complemented
6C24×C4×C7C2211yescharacteristic
7C23×C7×C8—28no—
8C23×C7×C8C418yescomplemented
9C23×C7×C8C2211yescharacteristic
10C23×C7×C8C2214yes—
11C23×C7×C8C2211yescharacteristic
12C22×C7×C4⋊C4C2214yes—
13C22×C7×C22⋊C4—22no—
14C2×C7×#107—28no—
15C2×C7×#107C2218yescomplemented
16C7×#380—24no—
17C7×#380C2218yes—
18C2×C7×#95—22no—
19C7×#340C2218yescomplemented
20C2×#1808C711yesmaximal, characteristic, direct product factor, Sylow
21C25×C7D411yescharacteristic
22C23×C4×C7—24no—
23C23×C4×C7—24no—
24C23×C4×C7—24no—
25C23×C4×C7C2×C414yes—
26C23×C4×C7D412yes—
27C23×C4×C7D411yescharacteristic
28C23×C4×C7Q814yes—
29C23×C4×C7C2312yes—
30C23×C4×C7C2311yescharacteristic
31C22×C7×C8—24no—
32C22×C7×C8—232no—
33C22×C7×C8—216no—
34C22×C7×C8C2×C414yes—
35C22×C7×C8C2×C414yes—
36C22×C7×C8C2×C4116yescomplemented
37C22×C7×C8D418yes—
38C22×C7×C8C2312yes—
39C22×C7×C8C2312yes—
40C2×C7×C4⋊C4—28no—
41C2×C7×C4⋊C4—28no—
42C2×C7×C4⋊C4—24no—
43C2×C7×C4⋊C4C2318yes—
44C2×C7×C22⋊C4—28no—
45C2×C7×C22⋊C4—48no—
46C7×#107—216no—
47C7×#95—28no—
48C24×C8C2×C711yescharacteristic
49C22×#107C2×C712yescomplemented
50C2×#380C2×C712yes—
51#1808C2×C718yesdirect product factor
52C2×#340C2×C712yescomplemented
53C24×C7—24no—
54C24×C7—24no—
55C24×C7C4⋊C414yes—
56C24×C7D814yes—
57C24×C7Q1614yes—
58C24×C7C2×D412yes—
59C24×C7C2×D411yescharacteristic
60C22×C4×C7—24no—
61C22×C4×C7—28no—
62C22×C4×C7—28no—
63C22×C4×C7—28no—
64C22×C4×C7—216no—
65C22×C4×C7—24no—
66C22×C4×C7—24no—
67C22×C4×C7—28no—
68C22×C4×C7—48no—
69C22×C4×C7—48no—
70C22×C4×C7—48no—
71C22×C4×C7C4⋊C414yes—
72C22×C4×C7C4⋊C418yes—
73C22×C4×C7C22×C414yes—
74C22×C4×C7C22×C412yes—
75C22×C4×C7C2×D412yes—
76C22×C4×C7C2×D414yes—
77C22×C4×C7C2×D411yescharacteristic
78C22×C4×C7C2×Q814yes—
79C22×C4×C7C2×Q812yes—
80C22×C4×C7#4114yes—
81C22×C4×C7C2411yescharacteristic
82C2×C7×C8—28no—
83C2×C7×C8—24no—
84C2×C7×C8—232no—
85C2×C7×C8C22⋊C4116yescomplemented
86C2×C7×C8C22×C414yes—
87C2×C7×C8C22×C414yes—
88C2×C7×C8C2×D418yes—
89C7×C4⋊C4—28no—
90C7×C4⋊C4—28no—
91C7×C4⋊C4—48no—
92C7×C22⋊C4—416no—
93C24×C4C22×C711yescharacteristic
94C23×C8—28no—
95C23×C8C4×C718yescomplemented
96C23×C8C22×C711yescharacteristic
97C23×C8C22×C714yes—
98C23×C8C22×C711yescharacteristic
99C22×C4⋊C4C22×C714yes—
100C22×C22⋊C4—22no—
101C2×#107—28no—
102C2×#107C22×C718yescomplemented
103#380—24no—
104#380C22×C718yes—
105C2×#95—22no—
106#340C22×C718yescomplemented
107C23×C7—24no—
108C23×C7—24no—
109C23×C7—28no—
110C23×C7—28no—
111C23×C7—216no—
112C23×C7—216no—
113C23×C7#107116yescomplemented
114C23×C7C2×C4⋊C414yes—
115C23×C7C2×C4⋊C412yes—
116C23×C7#12114yes—
117C23×C7C2×D814yes—
118C23×C7C2×D812yes—
119C23×C7C2×Q1614yes—
120C23×C7C2×Q1612yes—
121C23×C7#13514yes—
122C23×C7C22×D411yescharacteristic
123C2×C4×C7—24no—
124C2×C4×C7—28no—
125C2×C4×C7—24no—
126C2×C4×C7—24no—
127C2×C4×C7—28no—
128C2×C4×C7—216no—
129C2×C4×C7—48no—
130C2×C4×C7—48no—
131C2×C4×C7—48no—
132C2×C4×C7—816no—
133C2×C4×C7C2×C22⋊C414yes—
134C2×C4×C7C2×C4⋊C414yes—
135C2×C4×C7C2×C4⋊C412yes—
136C2×C4×C7#11714yes—
137C2×C4×C7#12114yes—
138C2×C4×C7C22⋊Q818yes—
139C2×C4×C7C23×C411yescharacteristic
140C2×C4×C7C22×D412yes—
141C2×C4×C7C22×Q811yescharacteristic
142C2×C4×C7C2×#4112yes—
143C7×C8—24no—
144C7×C8C2×C22⋊C418yescomplemented
145C25C7×D411yescharacteristic
146C23×C4—24no—
147C23×C4—24no—
148C23×C4—24no—
149C23×C4C2×C4×C714yes—
150C23×C4C7×D411yescharacteristic
151C23×C4C7×D412yes—
152C23×C4C7×Q814yes—
153C23×C4C23×C712yes—
154C23×C4C23×C711yescharacteristic
155C22×C8—24no—
156C22×C8—232no—
157C22×C8—216no—
158C22×C8C2×C4×C714yes—
159C22×C8C2×C4×C714yes—
160C22×C8C2×C4×C7116yescomplemented
161C22×C8C7×D418yes—
162C22×C8C23×C712yes—
163C22×C8C23×C712yes—
164C2×C4⋊C4—28no—
165C2×C4⋊C4—28no—
166C2×C4⋊C4—24no—
167C2×C4⋊C4C23×C718yes—
168C2×C22⋊C4—28no—
169C2×C22⋊C4—48no—
170#107—216no—
171#95—28no—
172C22×C7—232no—
173C22×C7—24no—
174C22×C7—24no—
175C22×C7—28no—
176C22×C7—28no—
177C22×C7#38014yes—
178C22×C7C2×#10714yes—
179C22×C7C2×#10718yescomplemented
180C22×C7#42714yes—
181C22×C7#46618yes—
182C22×C7#46718yes—
183C22×C7C22×C4⋊C411yescharacteristic
184C22×C7C2×#12112yes—
185C22×C7C22×D811yescharacteristic
186C22×C7C22×Q1611yescharacteristic
187C22×C7C2×#13512yes—
188C4×C7—24no—
189C4×C7—88no—
190C4×C7#38014yes—
191C4×C7C22×C22⋊C411yescharacteristic
192C4×C7C2×#11711yescharacteristic
193C4×C7C2×C22⋊Q812yes—
194C24—24no—
195C24—24no—
196C24C7×C4⋊C414yes—
197C24C7×D814yes—
198C24C7×Q1614yes—
199C24C2×C7×D412yes—
200C24C2×C7×D411yescharacteristic
201C22×C4—24no—
202C22×C4—28no—
203C22×C4—28no—
204C22×C4—28no—
205C22×C4—216no—
206C22×C4—24no—
207C22×C4—24no—
208C22×C4—28no—
209C22×C4—48no—
210C22×C4—48no—
211C22×C4—48no—
212C22×C4C7×C4⋊C414yes—
213C22×C4C7×C4⋊C418yes—
214C22×C4C22×C4×C714yes—
215C22×C4C22×C4×C712yes—
216C22×C4C2×C7×D412yes—
217C22×C4C2×C7×D414yes—
218C22×C4C2×C7×D411yescharacteristic
219C22×C4C2×C7×Q814yes—
220C22×C4C2×C7×Q812yes—
221C22×C4C7×#4114yes—
222C22×C4C24×C711yescharacteristic
223C2×C8—28no—
224C2×C8—24no—
225C2×C8—232no—
226C2×C8C7×C22⋊C4116yescomplemented
227C2×C8C22×C4×C714yes—
228C2×C8C22×C4×C714yes—
229C2×C8C2×C7×D418yes—
230C4⋊C4—28no—
231C4⋊C4—28no—
232C4⋊C4—48no—
233C22⋊C4—416no—
234C2×C7—28no—
235C2×C7#180818yesdirect product factor
236C2×C7C2×#38011yescharacteristic
237C2×C7C22×#10711yescharacteristic
238C2×C7C2×#42711yescharacteristic
239C2×C7C2×#46612yes—
240C2×C7C2×#46712yes—
241C23—216no—
242C23—216no—
243C23—28no—
244C23—24no—
245C23—28no—
246C23—24no—
247C23C7×#107116yescomplemented
248C23C2×C7×C4⋊C414yes—
249C23C2×C7×C4⋊C412yes—
250C23C7×#12114yes—
251C23C2×C7×D814yes—
252C23C2×C7×D812yes—
253C23C2×C7×Q1614yes—
254C23C2×C7×Q1612yes—
255C23C7×#13514yes—
256C23C22×C7×D411yescharacteristic
257C2×C4—28no—
258C2×C4—24no—
259C2×C4—24no—
260C2×C4—24no—
261C2×C4—216no—
262C2×C4—28no—
263C2×C4—48no—
264C2×C4—48no—
265C2×C4—48no—
266C2×C4—816no—
267C2×C4C2×C7×C22⋊C414yes—
268C2×C4C2×C7×C4⋊C414yes—
269C2×C4C2×C7×C4⋊C412yes—
270C2×C4C7×#11714yes—
271C2×C4C7×#12114yes—
272C2×C4C7×C22⋊Q818yes—
273C2×C4C23×C4×C711yescharacteristic
274C2×C4C22×C7×D412yes—
275C2×C4C22×C7×Q811yescharacteristic
276C2×C4C2×C7×#4112yes—
277C8—24no—
278C8C2×C7×C22⋊C418yescomplemented
279C7C2×#180811yescharacteristic, direct product factor, Sylow
280C22—24no—
281C22—232no—
282C22—24no—
283C22—28no—
284C22—28no—
285C22C7×#38014yes—
286C22C2×C7×#10714yes—
287C22C2×C7×#10718yescomplemented
288C22C7×#42714yes—
289C22C7×#46618yes—
290C22C7×#46718yes—
291C22C22×C7×C4⋊C411yescharacteristic
292C22C2×C7×#12112yes—
293C22C22×C7×D811yescharacteristic
294C22C22×C7×Q1611yescharacteristic
295C22C2×C7×#13512yes—
296C4—24no—
297C4—88no—
298C4C7×#38014yes—
299C4C22×C7×C22⋊C411yescharacteristic
300C4C2×C7×#11711yescharacteristic
301C4C2×C7×C22⋊Q812yes—
302C2—28no—
303C2C7×#180818yesdirect product factor
304C2C2×C7×#38011yescharacteristic
305C2C22×C7×#10711yescharacteristic
306C2C2×C7×#42711yescharacteristic
307C2C2×C7×#46612yes—
308C2C2×C7×#46712yes—
subgroupG/H
center, socleC24×C7C2×D4
commutatorC2×C4C23×C4×C7
Frattini, cosocleC22×C4C24×C7
prime radicalC25×C7D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C7 ◁ C24×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C7×#107C2semidirect
4. C7×#1808C2direct (N × H)
5. C2×C7×#340C2semidirect
8. C23×C7×C8C4semidirect
15. C2×C7×#107C22semidirect
19. C7×#340C22semidirect
20. C2×#1808C7direct (N × H)
36. C22×C7×C8C2×C4semidirect
49. C22×#107C2×C7semidirect
51. #1808C2×C7direct (N × H)
52. C2×#340C2×C7semidirect
85. C2×C7×C8C22⋊C4semidirect
95. C23×C8C4×C7semidirect
102. C2×#107C22×C7semidirect
106. #340C22×C7semidirect
113. C23×C7#107semidirect
144. C7×C8C2×C22⋊C4semidirect
160. C22×C8C2×C4×C7semidirect
179. C22×C7C2×#107semidirect
226. C2×C8C7×C22⋊C4semidirect
235. C2×C7#1808direct (N × H)
247. C23C7×#107semidirect
278. C8C2×C7×C22⋊C4semidirect
279. C7C2×#1808direct (N × H)
287. C22C2×C7×#107semidirect
303. C2C7×#1808direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C7×C82
C22×C7×#1072
C2×C7×#3802
C7×#18082
C2×C7×#3402
C2×#18087