Finite Group Databasebeta

← C2×C7×#3162 #13237873

Subgroups — C2×C7×#3162 #13237873

Order 1792.

1902 conjugacy classes of subgroups.

The subgroup lattice has 210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#533C212yesmaximal
2C7×#3162C2116yesmaximal, direct product factor
3C2×C7×#501C218yesmaximal, complemented
4C2×C7×#427C214yesmaximal
5C22×C7×#97C211yesmaximal, characteristic
6C23×C7×C8C2212yes—
7C7×#533—28no—
8C7×#533C22116yes—
9C2×C7×C4⋊Q8C2214yes—
10C2×C7×#125C2214yes—
11C2×C7×C22⋊Q8—24no—
12C2×C4×C7×Q8—24no—
13C2×C7×#117C2214yes—
14C22×C42×C7C2211yescharacteristic
15C7×#501C22164yescomplemented
16C7×#427C22132yes—
17C2×C7×#107C2218yes—
18C2×C7×#106C2218yes—
19C2×C7×#97C2214yes—
20C2×C7×#97C2218yes—
21C2×#3162C711yesmaximal, characteristic, direct product factor, Sylow
22C22×C7×Q8—24no—
23C23×C4×C7D412yes—
24C23×C4×C7C2311yescharacteristic
25C22×C7×C8Q8116yescomplemented
26C22×C7×C8C2314yes—
27C22×C7×C8C2318yes—
28C7×C4⋊Q8—28no—
29C7×C4⋊Q8C23116yes—
30C7×#125—28no—
31C7×#125C23116yes—
32C7×C22⋊Q8—232no—
33C4×C7×Q8—232no—
34C7×#117—28no—
35C7×#117C23116yes—
36C2×C7×C4⋊C4—28no—
37C2×C7×C4⋊C4—24no—
38C2×C7×C4⋊C4C2318yes—
39C2×C7×C22⋊C4—24no—
40C2×C42×C7—24no—
41C2×C42×C7D414yes—
42C2×C42×C7D412yes—
43C2×C42×C7C2312yes—
44C2×C42×C7C2314yes—
45C7×#107C23132yes—
46C7×#106C23132yes—
47C7×#97C23116yes—
48C2×#533C2×C712yes—
49#3162C2×C7116yesdirect product factor
50C2×#501C2×C718yescomplemented
51C2×#427C2×C714yes—
52C22×#97C2×C711yescharacteristic
53C24×C7C2×D411yescharacteristic
54C2×C7×Q8—216no—
55C2×C7×Q8—416no—
56C22×C4×C7—28no—
57C22×C4×C7—44no—
58C22×C4×C7C2×D414yes—
59C22×C4×C7C2×D418yes—
60C22×C4×C7C2×D412yes—
61C22×C4×C7C2×D411yescharacteristic
62C22×C4×C7C2×Q818yes—
63C22×C4×C7C2411yescharacteristic
64C22×C4×C7C2412yes—
65C2×C7×C8C2×Q8116yes—
66C2×C7×C8C2×Q8132yescomplemented
67C2×C7×C8C2418yes—
68C7×C4⋊C4—232no—
69C7×C4⋊C4—216no—
70C7×C4⋊C4—28no—
71C7×C4⋊C4C24116yes—
72C7×C22⋊C4—216no—
73C42×C7—216no—
74C42×C7C2×D418yes—
75C42×C7C2×D414yes—
76C42×C7C2414yes—
77C23×C8C22×C712yes—
78#533—28no—
79#533C22×C7116yes—
80C2×C4⋊Q8C22×C714yes—
81C2×#125C22×C714yes—
82C2×C22⋊Q8—24no—
83C2×C4×Q8—24no—
84C2×#117C22×C714yes—
85C22×C42C22×C711yescharacteristic
86#501C22×C7164yescomplemented
87#427C22×C7132yes—
88C2×#107C22×C718yes—
89C2×#106C22×C718yes—
90C2×#97C22×C714yes—
91C2×#97C22×C718yes—
92C23×C7—24no—
93C23×C7C4⋊Q814yes—
94C23×C7C22×D412yes—
95C23×C7C22×D411yescharacteristic
96C7×Q8—432no—
97C2×C4×C7—28no—
98C2×C4×C7—216no—
99C2×C4×C7—48no—
100C2×C4×C7—416no—
101C2×C4×C7C4⋊Q818yes—
102C2×C4×C7C4⋊Q814yes—
103C2×C4×C7C22×D418yes—
104C2×C4×C7C22×D412yes—
105C2×C4×C7C22×D411yescharacteristic
106C2×C4×C7C22×Q814yes—
107C2×C4×C7C22×Q818yes—
108C2×C4×C7C2511yescharacteristic
109C7×C8C22×Q8116yes—
110C22×Q8—24no—
111C23×C4C7×D412yes—
112C23×C4C23×C711yescharacteristic
113C22×C8C7×Q8116yescomplemented
114C22×C8C23×C714yes—
115C22×C8C23×C718yes—
116C4⋊Q8—28no—
117C4⋊Q8C23×C7116yes—
118#125—28no—
119#125C23×C7116yes—
120C22⋊Q8—232no—
121C4×Q8—232no—
122#117—28no—
123#117C23×C7116yes—
124C2×C4⋊C4—28no—
125C2×C4⋊C4—24no—
126C2×C4⋊C4C23×C718yes—
127C2×C22⋊C4—24no—
128C2×C42—24no—
129C2×C42C7×D412yes—
130C2×C42C7×D414yes—
131C2×C42C23×C712yes—
132C2×C42C23×C714yes—
133#107C23×C7132yes—
134#106C23×C7132yes—
135#97C23×C7116yes—
136C22×C7—28no—
137C22×C7—24no—
138C22×C7C2×C4⋊Q814yes—
139C22×C7C2×C4⋊Q812yes—
140C22×C7#57514yes—
141C22×C7C23×D411yescharacteristic
142C4×C7—28no—
143C4×C7—416no—
144C4×C7C2×C4⋊Q812yes—
145C4×C7C2×C4⋊Q814yes—
146C4×C7C23×Q812yes—
147C24C2×C7×D411yescharacteristic
148C2×Q8—216no—
149C2×Q8—416no—
150C22×C4—28no—
151C22×C4—44no—
152C22×C4C2×C7×D414yes—
153C22×C4C2×C7×D418yes—
154C22×C4C2×C7×D411yescharacteristic
155C22×C4C2×C7×D412yes—
156C22×C4C2×C7×Q818yes—
157C22×C4C24×C711yescharacteristic
158C22×C4C24×C712yes—
159C2×C8C2×C7×Q8116yes—
160C2×C8C2×C7×Q8132yescomplemented
161C2×C8C24×C718yes—
162C4⋊C4—232no—
163C4⋊C4—216no—
164C4⋊C4—28no—
165C4⋊C4C24×C7116yes—
166C22⋊C4—216no—
167C42—216no—
168C42C2×C7×D418yes—
169C42C2×C7×D414yes—
170C42C24×C714yes—
171C2×C7—24no—
172C2×C7#316214yesdirect product factor
173C2×C7C22×C4⋊Q811yescharacteristic
174C2×C7C2×#57512yes—
175C23—24no—
176C23C7×C4⋊Q814yes—
177C23C22×C7×D412yes—
178C23C22×C7×D411yescharacteristic
179Q8—432no—
180C2×C4—28no—
181C2×C4—216no—
182C2×C4—48no—
183C2×C4—416no—
184C2×C4C7×C4⋊Q818yes—
185C2×C4C7×C4⋊Q814yes—
186C2×C4C22×C7×D418yes—
187C2×C4C22×C7×D412yes—
188C2×C4C22×C7×D411yescharacteristic
189C2×C4C22×C7×Q814yes—
190C2×C4C22×C7×Q818yes—
191C2×C4C25×C711yescharacteristic
192C8C22×C7×Q8116yes—
193C7C2×#316211yescharacteristic, direct product factor, Sylow
194C22—28no—
195C22—24no—
196C22C2×C7×C4⋊Q814yes—
197C22C2×C7×C4⋊Q812yes—
198C22C7×#57514yes—
199C22C23×C7×D411yescharacteristic
200C4—28no—
201C4—416no—
202C4C2×C7×C4⋊Q814yes—
203C4C2×C7×C4⋊Q812yes—
204C4C23×C7×Q812yes—
205C2—24no—
206C2C7×#316214yesdirect product factor
207C2C22×C7×C4⋊Q811yescharacteristic
208C2C2×C7×#57512yes—
subgroupG/H
centerC22×C4×C7C2×D4
commutator, Frattini, cosocleC2×C4C25×C7
socleC23×C7C22×D4
prime radicalC24×C7C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C7 ◁ C22×C42×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C7×#3162C2direct (N × H)
3. C2×C7×#501C2semidirect
15. C7×#501C22semidirect
21. C2×#3162C7direct (N × H)
25. C22×C7×C8Q8semidirect
49. #3162C2×C7direct (N × H)
50. C2×#501C2×C7semidirect
66. C2×C7×C8C2×Q8semidirect
86. #501C22×C7semidirect
113. C22×C8C7×Q8semidirect
160. C2×C8C2×C7×Q8semidirect
172. C2×C7#3162direct (N × H)
193. C7C2×#3162direct (N × H)
206. C2C7×#3162direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5332
C7×#31622
C2×C7×#5012
C2×C7×#4272
C22×C7×#972
C2×#31627