Finite Group Databasebeta

← C2×C7×#2987 #13237463

Subgroups — C2×C7×#2987 #13237463

Order 1792.

1706 conjugacy classes of subgroups.

The subgroup lattice has 224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#533C211yesmaximal, characteristic
2C7×#2987C2116yesmaximal, direct product factor
3C2×C7×#446C218yesmaximal, complemented
4C2×C7×#433C214yesmaximal
5C2×C7×#432C212yesmaximal
6C7×#533C418yes—
7C7×#533C2218yes—
8C2×C7×C4⋊Q8C412yes—
9C2×C7×#125C412yes—
10C2×C7×C22⋊Q8C414yes—
11C2×C4×C7×Q8C2214yes—
12C2×C7×#117C2212yes—
13C22×C42×C7C2211yescharacteristic
14C7×#446C22164yescomplemented
15C7×#433C22132yes—
16C7×#432C22116yes—
17C2×C7×C4⋊C8C2214yes—
18C2×C7×C4⋊C8C2218yes—
19C2×C7×C22⋊C8C2214yes—
20C2×C7×#97C2214yes—
21C2×C7×#97C2214yes—
22C2×C4×C7×C8C2214yes—
23C2×#2987C711yesmaximal, characteristic, direct product factor, Sylow
24C22×C7×Q8C2×C414yes—
25C23×C4×C7C2×C412yes—
26C23×C4×C7C2311yescharacteristic
27C22×C7×C8C2318yes—
28C7×C4⋊Q8C2×C4116yes—
29C7×#125C2×C4116yes—
30C7×C22⋊Q8C2×C4132yes—
31C4×C7×Q8C2×C4116yes—
32C4×C7×Q8C23116yes—
33C7×#117C2×C418yes—
34C7×#117C2318yes—
35C2×C7×C4⋊C4C2×C414yes—
36C2×C7×C4⋊C4C2×C418yes—
37C2×C7×C4⋊C4C2×C414yes—
38C2×C7×C22⋊C4C2×C414yes—
39C2×C42×C7C2×C411yescharacteristic
40C2×C42×C7C2×C411yescharacteristic
41C2×C42×C7C2×C414yes—
42C2×C42×C7C2314yes—
43C2×C42×C7C2312yes—
44C2×C42×C7C2314yes—
45C7×C4⋊C8C23116yes—
46C7×C4⋊C8C23132yes—
47C7×C22⋊C8C23116yes—
48C7×#97C23116yes—
49C7×#97C23116yes—
50C4×C7×C8C23116yes—
51C2×#533C2×C711yescharacteristic
52#2987C2×C7116yesdirect product factor
53C2×#446C2×C718yescomplemented
54C2×#433C2×C714yes—
55C2×#432C2×C712yes—
56C24×C7C22×C411yescharacteristic
57C2×C7×Q8—48no—
58C2×C7×Q8C22×C4116yes—
59C22×C4×C7—24no—
60C22×C4×C7—44no—
61C22×C4×C7C22×C411yescharacteristic
62C22×C4×C7C22×C412yes—
63C22×C4×C7C22×C412yes—
64C22×C4×C7C22×C412yes—
65C22×C4×C7C22×C418yes—
66C22×C4×C7C22×C418yes—
67C22×C4×C7C2412yes—
68C22×C4×C7C2411yescharacteristic
69C2×C7×C8—216no—
70C2×C7×C8C24116yes—
71C7×C4⋊C4C22×C4116yes—
72C7×C4⋊C4C22×C4132yes—
73C7×C4⋊C4C22×C4116yes—
74C7×C22⋊C4C22×C4116yes—
75C42×C7C22×C414yes—
76C42×C7C22×C414yes—
77C42×C7C22×C414yes—
78C42×C7C22×C418yes—
79C42×C7C2418yes—
80C42×C7C2414yes—
81#533C4×C718yes—
82#533C22×C718yes—
83C2×C4⋊Q8C4×C712yes—
84C2×#125C4×C712yes—
85C2×C22⋊Q8C4×C714yes—
86C2×C4×Q8C22×C714yes—
87C2×#117C22×C712yes—
88C22×C42C22×C711yescharacteristic
89#446C22×C7164yescomplemented
90#433C22×C7132yes—
91#432C22×C7116yes—
92C2×C4⋊C8C22×C714yes—
93C2×C4⋊C8C22×C718yes—
94C2×C22⋊C8C22×C714yes—
95C2×#97C22×C714yes—
96C2×#97C22×C714yes—
97C2×C4×C8C22×C714yes—
98C23×C7—22no—
99C23×C7—24no—
100C23×C7C23×C412yes—
101C23×C7C23×C411yescharacteristic
102C7×Q8—416no—
103C2×C4×C7—22no—
104C2×C4×C7—24no—
105C2×C4×C7—24no—
106C2×C4×C7—216no—
107C2×C4×C7—24no—
108C2×C4×C7—24no—
109C2×C4×C7—48no—
110C2×C4×C7C23×C412yes—
111C2×C4×C7C23×C414yes—
112C2×C4×C7C23×C414yes—
113C2×C4×C7C23×C4116yes—
114C2×C4×C7C23×C411yescharacteristic
115C2×C4×C72−1+414yes—
116C2×C4×C7C2511yescharacteristic
117C7×C8—216no—
118C22×Q8C2×C4×C714yes—
119C23×C4C2×C4×C712yes—
120C23×C4C23×C711yescharacteristic
121C22×C8C23×C718yes—
122C4⋊Q8C2×C4×C7116yes—
123#125C2×C4×C7116yes—
124C22⋊Q8C2×C4×C7132yes—
125C4×Q8C2×C4×C7116yes—
126C4×Q8C23×C7116yes—
127#117C2×C4×C718yes—
128#117C23×C718yes—
129C2×C4⋊C4C2×C4×C714yes—
130C2×C4⋊C4C2×C4×C718yes—
131C2×C4⋊C4C2×C4×C714yes—
132C2×C22⋊C4C2×C4×C714yes—
133C2×C42C2×C4×C711yescharacteristic
134C2×C42C2×C4×C711yescharacteristic
135C2×C42C2×C4×C714yes—
136C2×C42C23×C714yes—
137C2×C42C23×C712yes—
138C2×C42C23×C714yes—
139C4⋊C8C23×C7116yes—
140C4⋊C8C23×C7132yes—
141C22⋊C8C23×C7116yes—
142#97C23×C7116yes—
143#97C23×C7116yes—
144C4×C8C23×C7116yes—
145C22×C7—22no—
146C22×C7—24no—
147C22×C7—44no—
148C22×C7#51912yes—
149C22×C7#56814yes—
150C22×C7C24×C411yescharacteristic
151C4×C7—22no—
152C4×C7—24no—
153C4×C7—24no—
154C4×C7—216no—
155C4×C7#51912yes—
156C4×C7C2×2−1+412yes—
157C24C22×C4×C711yescharacteristic
158C2×Q8—48no—
159C2×Q8C22×C4×C7116yes—
160C22×C4—24no—
161C22×C4—44no—
162C22×C4C22×C4×C711yescharacteristic
163C22×C4C22×C4×C712yes—
164C22×C4C22×C4×C712yes—
165C22×C4C22×C4×C712yes—
166C22×C4C22×C4×C718yes—
167C22×C4C22×C4×C718yes—
168C22×C4C24×C712yes—
169C22×C4C24×C711yescharacteristic
170C2×C8—216no—
171C2×C8C24×C7116yes—
172C4⋊C4C22×C4×C7116yes—
173C4⋊C4C22×C4×C7132yes—
174C4⋊C4C22×C4×C7116yes—
175C22⋊C4C22×C4×C7116yes—
176C42C22×C4×C714yes—
177C42C22×C4×C714yes—
178C42C22×C4×C714yes—
179C42C22×C4×C718yes—
180C42C24×C718yes—
181C42C24×C714yes—
182C2×C7—42no—
183C2×C7#298714yesdirect product factor
184C2×C7C2×#51911yescharacteristic
185C2×C7C2×#56812yes—
186C23—22no—
187C23—24no—
188C23C23×C4×C712yes—
189C23C23×C4×C711yescharacteristic
190Q8—416no—
191C2×C4—22no—
192C2×C4—24no—
193C2×C4—24no—
194C2×C4—216no—
195C2×C4—24no—
196C2×C4—24no—
197C2×C4—48no—
198C2×C4C23×C4×C712yes—
199C2×C4C23×C4×C714yes—
200C2×C4C23×C4×C714yes—
201C2×C4C23×C4×C7116yes—
202C2×C4C23×C4×C711yescharacteristic
203C2×C4C7×2−1+414yes—
204C2×C4C25×C711yescharacteristic
205C8—216no—
206C7C2×#298711yescharacteristic, direct product factor, Sylow
207C22—24no—
208C22—22no—
209C22—44no—
210C22C7×#51912yes—
211C22C7×#56814yes—
212C22C24×C4×C711yescharacteristic
213C4—24no—
214C4—24no—
215C4—216no—
216C4—22no—
217C4C7×#51912yes—
218C4C2×C7×2−1+412yes—
219C2—42no—
220C2C7×#298714yesdirect product factor
221C2C2×C7×#51911yescharacteristic
222C2C2×C7×#56812yes—
subgroupG/H
centerC22×C4×C7C24
commutatorC22C24×C4×C7
Frattini, cosocleC2×C4C25×C7
socleC23×C7C23×C4
prime radicalC24×C7C22×C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C7×#2987C2direct (N × H)
3. C2×C7×#446C2semidirect
14. C7×#446C22semidirect
23. C2×#2987C7direct (N × H)
52. #2987C2×C7direct (N × H)
53. C2×#446C2×C7semidirect
89. #446C22×C7semidirect
183. C2×C7#2987direct (N × H)
206. C7C2×#2987direct (N × H)
220. C2C7×#2987direct (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×#29872
C2×C7×#4462
C2×C7×#4332
C2×C7×#4322
C2×#29877