Finite Group Databasebeta

← C7×#14709 #13191925

Subgroups — C7×#14709 #13191925

Order 1792.

1662 conjugacy classes of subgroups.

The subgroup lattice has 242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#125C211yesmaximal, characteristic
2C2×C7×#382C211yesmaximal, characteristic
3C2×C43×C7C211yesmaximal, characteristic
4C7×#1436C218yesmaximal
5C7×C4⋊#95C214yesmaximal
6C2×C7×#125—24no—
7C2×C7×#125—24no—
8C2×C7×#125C418yescomplemented
9C22×C7×C4⋊C4C2212yes—
10C22×C7×C4⋊C4C2212yes—
11C22×C7×C4⋊C4C2214yes—
12C22×C42×C7C2214yes—
13C22×C42×C7C2212yes—
14C22×C42×C7C2211yescharacteristic
15C7×#382—24no—
16C2×C7×#95C2214yes—
17C2×C7×#95C22116yes—
18C43×C7—24no—
19#14709C711yesmaximal, characteristic, direct product factor, Sylow
20C23×C4×C7C2314yes—
21C23×C4×C7C2314yes—
22C23×C4×C7C2312yes—
23C23×C4×C7C2314yes—
24C23×C4×C7C2311yescharacteristic
25C7×#125—232no—
26C2×C7×C4⋊C4—28no—
27C2×C7×C4⋊C4—28no—
28C2×C7×C4⋊C4—24no—
29C2×C7×C4⋊C4—24no—
30C2×C7×C4⋊C4—24no—
31C2×C7×C4⋊C4—28no—
32C2×C7×C4⋊C4C2×C4116yes—
33C2×C7×C4⋊C4C2×C418yes—
34C2×C42×C7—28no—
35C2×C42×C7—24no—
36C2×C42×C7—216no—
37C2×C42×C7—24no—
38C2×C42×C7C2×C414yes—
39C2×C42×C7D414yes—
40C2×C42×C7D414yes—
41C2×C42×C7Q818yes—
42C7×#95—28no—
43C7×#95—232no—
44C22×#125C2×C711yescharacteristic
45C2×#382C2×C711yescharacteristic
46C2×C43C2×C711yescharacteristic
47#1436C2×C718yes—
48C4⋊#95C2×C714yes—
49C24×C7C2411yescharacteristic
50C22×C4×C7—24no—
51C22×C4×C7—28no—
52C22×C4×C7—24no—
53C22×C4×C7—28no—
54C22×C4×C7—24no—
55C22×C4×C7—24no—
56C22×C4×C7—216no—
57C22×C4×C7—24no—
58C22×C4×C7—216no—
59C22×C4×C7—28no—
60C22×C4×C7C22×C418yes—
61C22×C4×C7C22×C414yes—
62C22×C4×C7C22×C412yes—
63C22×C4×C7C2×D414yes—
64C22×C4×C7C2×D414yes—
65C22×C4×C7C2×D412yes—
66C22×C4×C7C2×D412yes—
67C22×C4×C7C2×Q818yes—
68C22×C4×C7C2×Q814yes—
69C22×C4×C7#41116yes—
70C22×C4×C7#4114yes—
71C7×C4⋊C4—232no—
72C7×C4⋊C4—216no—
73C7×C4⋊C4—48no—
74C42×C7—232no—
75C42×C7—216no—
76C42×C7C22⋊C4116yes—
77C2×#125—24no—
78C2×#125—24no—
79C2×#125C4×C718yescomplemented
80C22×C4⋊C4C22×C712yes—
81C22×C4⋊C4C22×C712yes—
82C22×C4⋊C4C22×C714yes—
83C22×C42C22×C714yes—
84C22×C42C22×C712yes—
85C22×C42C22×C711yescharacteristic
86#382—24no—
87C2×#95C22×C7116yes—
88C2×#95C22×C714yes—
89C43—24no—
90C23×C7C23×C411yescharacteristic
91C23×C7C22×D411yescharacteristic
92C23×C7C22×D411yescharacteristic
93C23×C7C22×Q812yes—
94C23×C7C2×#4112yes—
95C23×C7C2×#4118yes—
96C2×C4×C7—28no—
97C2×C4×C7—28no—
98C2×C4×C7—28no—
99C2×C4×C7—216no—
100C2×C4×C7—216no—
101C2×C4×C7—28no—
102C2×C4×C7—28no—
103C2×C4×C7—28no—
104C2×C4×C7—216no—
105C2×C4×C7—48no—
106C2×C4×C7—48no—
107C2×C4×C7—44no—
108C2×C4×C7—416no—
109C2×C4×C7—48no—
110C2×C4×C7C2×C22⋊C418yes—
111C2×C4×C7C2×C22⋊C414yes—
112C2×C4×C7C4×Q818yes—
113C2×C4×C7C22⋊Q818yes—
114C2×C4×C7#12414yes—
115C2×C4×C7#125116yescomplemented
116C2×C4×C7C4⋊Q814yes—
117C23×C4C23×C714yes—
118C23×C4C23×C714yes—
119C23×C4C23×C712yes—
120C23×C4C23×C714yes—
121C23×C4C23×C711yescharacteristic
122#125—232no—
123C2×C4⋊C4—28no—
124C2×C4⋊C4—28no—
125C2×C4⋊C4—24no—
126C2×C4⋊C4—24no—
127C2×C4⋊C4—24no—
128C2×C4⋊C4—28no—
129C2×C4⋊C4C2×C4×C7116yes—
130C2×C4⋊C4C2×C4×C718yes—
131C2×C42—28no—
132C2×C42—24no—
133C2×C42—216no—
134C2×C42—24no—
135C2×C42C2×C4×C714yes—
136C2×C42C7×D414yes—
137C2×C42C7×D414yes—
138C2×C42C7×Q818yes—
139#95—28no—
140#95—232no—
141C22×C7C22×C22⋊C411yescharacteristic
142C22×C7C2×C4×Q812yes—
143C22×C7C4×#4114yes—
144C22×C7C2×C22⋊Q812yes—
145C22×C7#52514yes—
146C22×C7C2×#12411yescharacteristic
147C22×C7C2×#12514yes—
148C22×C7#52918yes—
149C22×C7C2×C4⋊Q811yescharacteristic
150C22×C7#53214yes—
151C22×C7#53314yes—
152C4×C7—216no—
153C4×C7—28no—
154C4×C7—48no—
155C4×C7—84no—
156C4×C7#39118yes—
157C24C24×C711yescharacteristic
158C22×C4—24no—
159C22×C4—28no—
160C22×C4—24no—
161C22×C4—28no—
162C22×C4—24no—
163C22×C4—24no—
164C22×C4—216no—
165C22×C4—24no—
166C22×C4—216no—
167C22×C4—28no—
168C22×C4C22×C4×C718yes—
169C22×C4C22×C4×C714yes—
170C22×C4C22×C4×C712yes—
171C22×C4C2×C7×D414yes—
172C22×C4C2×C7×D414yes—
173C22×C4C2×C7×D412yes—
174C22×C4C2×C7×D412yes—
175C22×C4C2×C7×Q818yes—
176C22×C4C2×C7×Q814yes—
177C22×C4C7×#41116yes—
178C22×C4C7×#4114yes—
179C4⋊C4—232no—
180C4⋊C4—216no—
181C4⋊C4—48no—
182C42—232no—
183C42—216no—
184C42C7×C22⋊C4116yes—
185C2×C7C2×#39111yescharacteristic
186C2×C7#229712yes—
187C2×C7C4×#12514yes—
188C2×C7#285114yes—
189C2×C7#285912yes—
190C2×C7#286112yes—
191C23C23×C4×C711yescharacteristic
192C23C22×C7×D411yescharacteristic
193C23C22×C7×D411yescharacteristic
194C23C22×C7×Q812yes—
195C23C2×C7×#4112yes—
196C23C2×C7×#4118yes—
197C2×C4—28no—
198C2×C4—28no—
199C2×C4—28no—
200C2×C4—216no—
201C2×C4—216no—
202C2×C4—28no—
203C2×C4—28no—
204C2×C4—28no—
205C2×C4—216no—
206C2×C4—48no—
207C2×C4—48no—
208C2×C4—44no—
209C2×C4—416no—
210C2×C4—48no—
211C2×C4C2×C7×C22⋊C418yes—
212C2×C4C2×C7×C22⋊C414yes—
213C2×C4C4×C7×Q818yes—
214C2×C4C7×C22⋊Q818yes—
215C2×C4C7×#12414yes—
216C2×C4C7×#125116yescomplemented
217C2×C4C7×C4⋊Q814yes—
218C7#1470911yescharacteristic, direct product factor, Sylow
219C22C22×C7×C22⋊C411yescharacteristic
220C22C2×C4×C7×Q812yes—
221C22C4×C7×#4114yes—
222C22C2×C7×C22⋊Q812yes—
223C22C7×#52514yes—
224C22C2×C7×#12411yescharacteristic
225C22C2×C7×#12514yes—
226C22C7×#52918yes—
227C22C2×C7×C4⋊Q811yescharacteristic
228C22C7×#53214yes—
229C22C7×#53314yes—
230C4—28no—
231C4—216no—
232C4—48no—
233C4—84no—
234C4C7×#39118yes—
235C2C2×C7×#39111yescharacteristic
236C2C7×#229712yes—
237C2C4×C7×#12514yes—
238C2C7×#285114yes—
239C2C7×#285912yes—
240C2C7×#286112yes—
subgroupG/H
center, socle, prime radicalC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
8. C2×C7×#125C4semidirect
19. #14709C7direct (N × H)
79. C2×#125C4×C7semidirect
115. C2×C4×C7#125semidirect
216. C2×C4C7×#125semidirect
218. C7#14709direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1252
C2×C7×#3822
C2×C43×C72
C7×#14362
C7×C4⋊#952
#147097