Finite Group Databasebeta

← C7×#21828 #13199044

Subgroups — C7×#21828 #13199044

Order 1792.

990 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 990 conjugacy classes of subgroups — too many to draw. Only its 366 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#544C211yesmaximal, characteristic
2C7×#2313C212yesmaximal
3C7×#1996C218yesmaximal
4C7×#1820C214yesmaximal
5C7×#544—28no—
6C2×C7×C4⋊Q8C414yescomplemented
7C2×C7×#125C414yescomplemented
8C2×C7×C22⋊Q8C2214yes—
9C2×C7×#117C2212yes—
10C22×C7×C4⋊C4C2211yescharacteristic
11C7×#387—28no—
12C7×#381C2214yes—
13C7×#380C2214yes—
14C4×C7×C22⋊C4C2214yes—
15C7×#342C22116yes—
16#21828C711yesmaximal, characteristic, direct product factor, Sylow
17C22×C7×Q8C2×C414yes—
18C23×C4×C7C2311yescharacteristic
19C23×C4×C7C2312yes—
20C7×C4⋊Q8—216no—
21C7×#125—216no—
22C7×C22⋊Q8—28no—
23C7×C22⋊Q8—28no—
24C7×#117—28no—
25C2×C7×C4⋊C4—24no—
26C2×C7×C4⋊C4C2×C412yes—
27C2×C7×C4⋊C4C2×C412yes—
28C2×C7×C4⋊C4C2×C414yes—
29C2×C7×C4⋊C4C2×C418yes—
30C2×C7×C4⋊C4C2×C414yes—
31C2×C7×C4⋊C4D418yes—
32C2×C7×C22⋊C4C2318yes—
33C2×C7×C22⋊C4C2314yes—
34C2×C42×C7—24no—
35C2×C42×C7C2×C414yes—
36C7×#95—24no—
37C7×#95—24no—
38C7×#95—28no—
39C2×#544C2×C711yescharacteristic
40#2313C2×C712yes—
41#1996C2×C718yes—
42#1820C2×C714yes—
43C24×C7C2411yescharacteristic
44C2×C7×Q8—28no—
45C2×C7×Q8—84no—
46C22×C4×C7—24no—
47C22×C4×C7—28no—
48C22×C4×C7—82no—
49C22×C4×C7C22×C412yes—
50C22×C4×C7C22×C414yes—
51C22×C4×C7C22×C414yes—
52C22×C4×C7C22×C414yes—
53C22×C4×C7C2×D414yes—
54C22×C4×C7C2×D414yes—
55C22×C4×C7C2×D414yes—
56C7×C4⋊C4—24no—
57C7×C4⋊C4—24no—
58C7×C4⋊C4—28no—
59C7×C4⋊C4—216no—
60C7×C4⋊C4—84no—
61C7×C4⋊C4C22⋊C4116yes—
62C7×C22⋊C4—28no—
63C7×C22⋊C4—216no—
64C42×C7—28no—
65C42×C7—84no—
66#544—28no—
67C2×C4⋊Q8C4×C714yescomplemented
68C2×#125C4×C714yescomplemented
69C2×C22⋊Q8C22×C714yes—
70C2×#117C22×C712yes—
71C22×C4⋊C4C22×C711yescharacteristic
72#387—28no—
73#381C22×C714yes—
74#380C22×C714yes—
75C4×C22⋊C4C22×C714yes—
76#342C22×C7116yes—
77C23×C7—41no—
78C23×C7—41no—
79C23×C7C23×C411yescharacteristic
80C23×C7C22×D412yes—
81C23×C72−1+414yes—
82C7×Q8—88no—
83C2×C4×C7—24no—
84C2×C4×C7—28no—
85C2×C4×C7—24no—
86C2×C4×C7—24no—
87C2×C4×C7—44no—
88C2×C4×C7—44no—
89C2×C4×C7—44no—
90C2×C4×C7—44no—
91C2×C4×C7—44no—
92C2×C4×C7—48no—
93C2×C4×C7—48no—
94C2×C4×C7—48no—
95C2×C4×C7C2×C22⋊C414yes—
96C2×C4×C7C2×C22⋊C418yes—
97C22×Q8C2×C4×C714yes—
98C23×C4C23×C711yescharacteristic
99C23×C4C23×C712yes—
100C4⋊Q8—216no—
101#125—216no—
102C22⋊Q8—28no—
103C22⋊Q8—28no—
104#117—28no—
105C2×C4⋊C4—24no—
106C2×C4⋊C4C2×C4×C712yes—
107C2×C4⋊C4C2×C4×C712yes—
108C2×C4⋊C4C2×C4×C714yes—
109C2×C4⋊C4C2×C4×C718yes—
110C2×C4⋊C4C2×C4×C714yes—
111C2×C4⋊C4C7×D418yes—
112C2×C22⋊C4C23×C718yes—
113C2×C22⋊C4C23×C714yes—
114C2×C42—24no—
115C2×C42C2×C4×C714yes—
116#95—24no—
117#95—24no—
118#95—28no—
119C22×C7—21no—
120C22×C7—22no—
121C22×C7—21no—
122C22×C7—22no—
123C22×C7—44no—
124C22×C7C22×C22⋊C411yescharacteristic
125C22×C7#51912yes—
126C22×C7#53614yes—
127C4×C7—24no—
128C4×C7—28no—
129C4×C7—44no—
130C4×C7—44no—
131C4×C7—88no—
132C24C24×C711yescharacteristic
133C2×Q8—28no—
134C2×Q8—84no—
135C22×C4—24no—
136C22×C4—28no—
137C22×C4—82no—
138C22×C4C22×C4×C712yes—
139C22×C4C22×C4×C714yes—
140C22×C4C22×C4×C714yes—
141C22×C4C22×C4×C714yes—
142C22×C4C2×C7×D414yes—
143C22×C4C2×C7×D414yes—
144C22×C4C2×C7×D414yes—
145C4⋊C4—24no—
146C4⋊C4—24no—
147C4⋊C4—28no—
148C4⋊C4—216no—
149C4⋊C4—84no—
150C4⋊C4C7×C22⋊C4116yes—
151C22⋊C4—28no—
152C22⋊C4—216no—
153C42—28no—
154C42—84no—
155C2×C7—24no—
156C2×C7—22no—
157C2×C7#231011yescharacteristic
158C2×C7#288311yescharacteristic
159C2×C7#288411yescharacteristic
160C23—41no—
161C23—41no—
162C23C23×C4×C711yescharacteristic
163C23C22×C7×D412yes—
164C23C7×2−1+414yes—
165Q8—88no—
166C2×C4—24no—
167C2×C4—28no—
168C2×C4—24no—
169C2×C4—24no—
170C2×C4—44no—
171C2×C4—44no—
172C2×C4—44no—
173C2×C4—44no—
174C2×C4—44no—
175C2×C4—48no—
176C2×C4—48no—
177C2×C4—48no—
178C2×C4C2×C7×C22⋊C414yes—
179C2×C4C2×C7×C22⋊C418yes—
180C7#2182811yescharacteristic, direct product factor, Sylow
181C22—21no—
182C22—22no—
183C22—21no—
184C22—22no—
185C22—44no—
186C22C22×C7×C22⋊C411yescharacteristic
187C22C7×#51912yes—
188C22C7×#53614yes—
189C4—24no—
190C4—28no—
191C4—44no—
192C4—44no—
193C4—88no—
194C2—24no—
195C2—22no—
196C2C7×#231011yescharacteristic
197C2C7×#288311yescharacteristic
198C2C7×#288411yescharacteristic
subgroupG/H
center, socleC22×C7C22×C22⋊C4
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC24×C7C24
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C22×C7×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
6. C2×C7×C4⋊Q8C4semidirect
7. C2×C7×#125C4semidirect
16. #21828C7direct (N × H)
67. C2×C4⋊Q8C4×C7semidirect
68. C2×#125C4×C7semidirect
180. C7#21828direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5442
C7×#23132
C7×#19962
C7×#18202
#218287