Finite Group Databasebeta

← C7×#21827 #13199043

Subgroups — C7×#21827 #13199043

Order 1792.

1130 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 1130 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×#543C211yesmaximal, characteristic
2C7×#2312C212yesmaximal
3C7×#1996C218yesmaximal, complemented
4C7×#1819C214yesmaximal
5C7×#543—28no—
6C2×C7×C22⋊Q8C418yescomplemented
7C2×C7×C22⋊Q8C2214yes—
8C22×C7×C22⋊C4C2212yes—
9C22×C7×C22⋊C4C2211yescharacteristic
10C7×#388—28no—
11C7×#380C2214yes—
12C7×#379C2214yes—
13C4×C7×C22⋊C4C2214yes—
14C7×#342C22116yes—
15#21827C711yesmaximal, characteristic, direct product factor, Sylow
16C25×C7C2311yescharacteristic
17C22×C7×Q8C2×C414yes—
18C23×C4×C7C2×C414yes—
19C23×C4×C7C2312yes—
20C7×C22⋊Q8—28no—
21C7×C22⋊Q8—28no—
22C7×C22⋊Q8—232no—
23C2×C7×C4⋊C4—24no—
24C2×C7×C4⋊C4C2×C4112yes—
25C2×C7×C22⋊C4—28no—
26C2×C7×C22⋊C4—24no—
27C2×C7×C22⋊C4—24no—
28C2×C7×C22⋊C4C2×C414yes—
29C2×C7×C22⋊C4C2×C414yes—
30C2×C7×C22⋊C4D418yes—
31C2×C7×C22⋊C4C2318yes—
32C2×C7×C22⋊C4C2314yes—
33C2×C42×C7—24no—
34C7×#95—24no—
35C7×#95—24no—
36C2×#543C2×C711yescharacteristic
37#2312C2×C712yes—
38#1996C2×C718yescomplemented
39#1819C2×C714yes—
40C24×C7—24no—
41C24×C7—82no—
42C24×C7C22×C412yes—
43C24×C7C2×D414yes—
44C24×C7C2411yescharacteristic
45C2×C7×Q8—28no—
46C2×C7×Q8—84no—
47C22×C4×C7—28no—
48C22×C4×C7—28no—
49C22×C4×C7—82no—
50C22×C4×C7—84no—
51C22×C4×C7C22×C418yes—
52C22×C4×C7C22×C414yes—
53C22×C4×C7C2×D414yes—
54C22×C4×C7C2×D414yes—
55C7×C4⋊C4—224no—
56C7×C4⋊C4—84no—
57C7×C22⋊C4—28no—
58C7×C22⋊C4—28no—
59C7×C22⋊C4—216no—
60C7×C22⋊C4—84no—
61C7×C22⋊C4—84no—
62C7×C22⋊C4C22⋊C4116yes—
63C42×C7—84no—
64#543—28no—
65C2×C22⋊Q8C4×C718yescomplemented
66C2×C22⋊Q8C22×C714yes—
67C22×C22⋊C4C22×C712yes—
68C22×C22⋊C4C22×C711yescharacteristic
69#388—28no—
70#380C22×C714yes—
71#379C22×C714yes—
72C4×C22⋊C4C22×C714yes—
73#342C22×C7116yes—
74C23×C7—24no—
75C23×C7—28no—
76C23×C7—44no—
77C23×C7—42no—
78C23×C7—44no—
79C23×C7—44no—
80C23×C7—88no—
81C23×C7C2×C22⋊C414yes—
82C23×C7C23×C411yescharacteristic
83C23×C7C22×D412yes—
84C23×C72−1+414yes—
85C7×Q8—88no—
86C2×C4×C7—28no—
87C2×C4×C7—44no—
88C2×C4×C7—44no—
89C2×C4×C7—44no—
90C2×C4×C7—48no—
91C2×C4×C7—48no—
92C2×C4×C7—48no—
93C2×C4×C7—48no—
94C2×C4×C7—88no—
95C2×C4×C7C2×C22⋊C418yes—
96C25C23×C711yescharacteristic
97C22×Q8C2×C4×C714yes—
98C23×C4C2×C4×C714yes—
99C23×C4C23×C712yes—
100C22⋊Q8—28no—
101C22⋊Q8—28no—
102C22⋊Q8—232no—
103C2×C4⋊C4—24no—
104C2×C4⋊C4C2×C4×C7112yes—
105C2×C22⋊C4—28no—
106C2×C22⋊C4—24no—
107C2×C22⋊C4—24no—
108C2×C22⋊C4C2×C4×C714yes—
109C2×C22⋊C4C2×C4×C714yes—
110C2×C22⋊C4C7×D418yes—
111C2×C22⋊C4C23×C718yes—
112C2×C22⋊C4C23×C714yes—
113C2×C42—24no—
114#95—24no—
115#95—24no—
116C22×C7—22no—
117C22×C7—22no—
118C22×C7—22no—
119C22×C7—24no—
120C22×C7—28no—
121C22×C7—44no—
122C22×C7—48no—
123C22×C7—88no—
124C22×C7C22×C22⋊C411yescharacteristic
125C22×C7#51912yes—
126C22×C7#53614yes—
127C4×C7—28no—
128C4×C7—48no—
129C4×C7—88no—
130C24—24no—
131C24—82no—
132C24C22×C4×C712yes—
133C24C2×C7×D414yes—
134C24C24×C711yescharacteristic
135C2×Q8—28no—
136C2×Q8—84no—
137C22×C4—28no—
138C22×C4—28no—
139C22×C4—82no—
140C22×C4—84no—
141C22×C4C22×C4×C718yes—
142C22×C4C22×C4×C714yes—
143C22×C4C2×C7×D414yes—
144C22×C4C2×C7×D414yes—
145C4⋊C4—224no—
146C4⋊C4—84no—
147C22⋊C4—28no—
148C22⋊C4—28no—
149C22⋊C4—216no—
150C22⋊C4—84no—
151C22⋊C4—84no—
152C22⋊C4C7×C22⋊C4116yes—
153C42—84no—
154C2×C7—24no—
155C2×C7—22no—
156C2×C7—44no—
157C2×C7#231011yescharacteristic
158C2×C7#288312yes—
159C23—24no—
160C23—28no—
161C23—44no—
162C23—42no—
163C23—44no—
164C23—44no—
165C23—88no—
166C23C2×C7×C22⋊C414yes—
167C23C23×C4×C711yescharacteristic
168C23C22×C7×D412yes—
169C23C7×2−1+414yes—
170Q8—88no—
171C2×C4—28no—
172C2×C4—44no—
173C2×C4—44no—
174C2×C4—44no—
175C2×C4—48no—
176C2×C4—48no—
177C2×C4—48no—
178C2×C4—48no—
179C2×C4—88no—
180C2×C4C2×C7×C22⋊C418yes—
181C7#2182711yescharacteristic, direct product factor, Sylow
182C22—22no—
183C22—22no—
184C22—22no—
185C22—24no—
186C22—28no—
187C22—44no—
188C22—48no—
189C22—88no—
190C22C22×C7×C22⋊C411yescharacteristic
191C22C7×#51912yes—
192C22C7×#53614yes—
193C4—28no—
194C4—48no—
195C4—88no—
196C2—24no—
197C2—22no—
198C2—44no—
199C2C7×#231011yescharacteristic
200C2C7×#288312yes—
subgroupG/H
center, socleC22×C7C22×C22⋊C4
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC25×C7C23
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C22×C7×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C7×#1996C2semidirect
6. C2×C7×C22⋊Q8C4semidirect
15. #21827C7direct (N × H)
38. #1996C2×C7semidirect
65. C2×C22⋊Q8C4×C7semidirect
181. C7#21827direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5432
C7×#23122
C7×#19962
C7×#18192
#218277