Finite Group Databasebeta

← C2×C7×#1409 #13190798

Subgroups — C2×C7×#1409 #13190798

Order 1792.

474 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 94 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×#492C211yesmaximal, characteristic
2C2×C7×#353C212yesmaximal
3C7×#1409C214yesmaximal, direct product factor
4C22×C7×SD16—22no—
5C2×C7×C4⋊Q8C411yescharacteristic, complemented
6C2×C7×#127C2211yescharacteristic
7C7×#492—22no—
8C7×#492C412yescomplemented
9C7×#492C2212yes—
10C2×C7×#99—22no—
11C2×C4×C7×C8C411yescharacteristic, complemented
12C7×#353—22no—
13C7×#353C2214yes—
14C2×#1409C711yesmaximal, characteristic, direct product factor, Sylow
15C22×C7×Q8—21no—
16C22×C7×D4—41no—
17C22×C7×D4D412yes—
18C2×C7×SD16—24no—
19C2×C7×SD16—24no—
20C2×C7×SD16—44no—
21C2×C7×SD16—44no—
22C22×C7×C8—21no—
23C7×C4⋊Q8—21no—
24C7×C4⋊Q8—41no—
25C7×C4⋊Q8C2×C412yescomplemented
26C7×#127—41no—
27C7×#127C2×C411yescharacteristic
28C7×#127D412yes—
29C7×#127C2311yescharacteristic
30C2×C7×C4⋊C4—41no—
31C2×C7×C22⋊C4—42no—
32C2×C42×C7C2×C411yescharacteristic
33C7×#99—24no—
34C7×#99—42no—
35C4×C7×C8—21no—
36C4×C7×C8C2×C412yescomplemented
37C2×#492C2×C711yescharacteristic
38C2×#353C2×C712yes—
39#1409C2×C714yesdirect product factor
40C24×C7—22no—
41C2×C7×Q8—22no—
42C2×C7×Q8—42no—
43C2×C7×Q8—42no—
44C2×C7×Q8—41no—
45C2×C7×D4—22no—
46C2×C7×D4—42no—
47C2×C7×D4—42no—
48C2×C7×D4—41no—
49C2×C7×D4—42no—
50C2×C7×D4—41no—
51C2×C7×D4—84no—
52C2×C7×D4C22⋊C412yes—
53C2×C7×D4C2×D412yes—
54C22×C4×C7—21no—
55C22×C4×C7—41no—
56C22×C4×C7—82no—
57C22×C4×C7C22⋊C411yescharacteristic
58C7×SD16—48no—
59C7×SD16—48no—
60C2×C7×C8—22no—
61C2×C7×C8—22no—
62C2×C7×C8—22no—
63C7×C4⋊C4—42no—
64C7×C4⋊C4—42no—
65C7×C22⋊C4—44no—
66C7×C22⋊C4—82no—
67C42×C7—21no—
68C42×C7C22⋊C411yescharacteristic
69C42×C7C22×C411yescharacteristic
70C22×SD16—22no—
71C2×C4⋊Q8C4×C711yescharacteristic, complemented
72C2×#127C22×C711yescharacteristic
73#492—22no—
74#492C4×C712yescomplemented
75#492C22×C712yes—
76C2×#99—22no—
77C2×C4×C8C4×C711yescharacteristic, complemented
78#353—22no—
79#353C22×C714yes—
80C23×C7—22no—
81C23×C7—22no—
82C23×C7—42no—
83C23×C7—42no—
84C23×C7—84no—
85C23×C7#9911yescharacteristic
86C7×Q8—44no—
87C7×Q8—82no—
88C7×D4—42no—
89C7×D4—42no—
90C7×D4—82no—
91C7×D4—82no—
92C7×D4—84no—
93C7×D4—82no—
94C2×C4×C7—24no—
95C2×C4×C7—21no—
96C2×C4×C7—21no—
97C2×C4×C7—21no—
98C2×C4×C7—21no—
99C2×C4×C7—42no—
100C2×C4×C7—81no—
101C2×C4×C7—81no—
102C2×C4×C7—84no—
103C2×C4×C7—164no—
104C2×C4×C7#9911yescharacteristic
105C2×C4×C7C2×C22⋊C411yescharacteristic
106C7×C8—24no—
107C22×Q8—21no—
108C22×D4—41no—
109C22×D4C7×D412yes—
110C2×SD16—24no—
111C2×SD16—24no—
112C2×SD16—44no—
113C2×SD16—44no—
114C22×C8—21no—
115C4⋊Q8—21no—
116C4⋊Q8—41no—
117C4⋊Q8C2×C4×C712yescomplemented
118#127—41no—
119#127C2×C4×C711yescharacteristic
120#127C7×D412yes—
121#127C23×C711yescharacteristic
122C2×C4⋊C4—41no—
123C2×C22⋊C4—42no—
124C2×C42C2×C4×C711yescharacteristic
125#99—24no—
126#99—42no—
127C4×C8—21no—
128C4×C8C2×C4×C712yescomplemented
129C22×C7—22no—
130C22×C7—42no—
131C22×C7—42no—
132C22×C7—82no—
133C22×C7—82no—
134C22×C7—84no—
135C22×C7—162no—
136C22×C7#35311yescharacteristic
137C22×C7#35311yescharacteristic
138C22×C7C2×#9911yescharacteristic
139C4×C7—22no—
140C4×C7—22no—
141C4×C7—21no—
142C4×C7—21no—
143C4×C7—82no—
144C4×C7—164no—
145C24—22no—
146C2×Q8—22no—
147C2×Q8—42no—
148C2×Q8—42no—
149C2×Q8—41no—
150C2×D4—22no—
151C2×D4—42no—
152C2×D4—42no—
153C2×D4—41no—
154C2×D4—42no—
155C2×D4—41no—
156C2×D4—84no—
157C2×D4C7×C22⋊C412yes—
158C2×D4C2×C7×D412yes—
159C22×C4—21no—
160C22×C4—41no—
161C22×C4—82no—
162C22×C4C7×C22⋊C411yescharacteristic
163SD16—48no—
164SD16—48no—
165C2×C8—22no—
166C2×C8—22no—
167C2×C8—22no—
168C4⋊C4—42no—
169C4⋊C4—42no—
170C22⋊C4—44no—
171C22⋊C4—82no—
172C42—21no—
173C42C7×C22⋊C411yescharacteristic
174C42C22×C4×C711yescharacteristic
175C2×C7—21no—
176C2×C7—21no—
177C2×C7—82no—
178C2×C7—82no—
179C2×C7#140912yesdirect product factor
180C2×C7C2×#35311yescharacteristic
181C23—22no—
182C23—22no—
183C23—42no—
184C23—42no—
185C23—84no—
186C23C7×#9911yescharacteristic
187Q8—44no—
188Q8—82no—
189D4—42no—
190D4—42no—
191D4—82no—
192D4—82no—
193D4—84no—
194D4—82no—
195C2×C4—24no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—42no—
201C2×C4—81no—
202C2×C4—81no—
203C2×C4—84no—
204C2×C4—164no—
205C2×C4C7×#9911yescharacteristic
206C2×C4C2×C7×C22⋊C411yescharacteristic
207C8—24no—
208C7C2×#140911yescharacteristic, direct product factor, Sylow
209C22—22no—
210C22—42no—
211C22—42no—
212C22—82no—
213C22—82no—
214C22—84no—
215C22—162no—
216C22C7×#35311yescharacteristic
217C22C7×#35311yescharacteristic
218C22C2×C7×#9911yescharacteristic
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—82no—
224C4—164no—
225C2—21no—
226C2—21no—
227C2—82no—
228C2—82no—
229C2C7×#140912yesdirect product factor
230C2C2×C7×#35311yescharacteristic
subgroupG/H
center, socleC22×C7#353
commutatorC42C22×C4×C7
Frattini, cosocle#127C23×C7
prime radicalC2×C7×#127C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C23×C7 ◁ C22×C4×C7 ◁ C2×C7×#127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C7×#1409C2direct (N × H)
5. C2×C7×C4⋊Q8C4semidirect
8. C7×#492C4semidirect
11. C2×C4×C7×C8C4semidirect
14. C2×#1409C7direct (N × H)
25. C7×C4⋊Q8C2×C4semidirect
36. C4×C7×C8C2×C4semidirect
39. #1409C2×C7direct (N × H)
71. C2×C4⋊Q8C4×C7semidirect
74. #492C4×C7semidirect
77. C2×C4×C8C4×C7semidirect
117. C4⋊Q8C2×C4×C7semidirect
128. C4×C8C2×C4×C7semidirect
179. C2×C7#1409direct (N × H)
208. C7C2×#1409direct (N × H)
229. C2C7×#1409direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#4922
C2×C7×#3532
C7×#14092
C2×#14097