Finite Group Databasebeta

← C7×#12863 #13190079

Subgroups — C7×#12863 #13190079

Order 1792.

614 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 118 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
1C7×#2311C211yesmaximal, characteristic
2C7×#1785C212yesmaximal
3C7×#1394C214yesmaximal, complemented
4C22×C7×#41C2211yescharacteristic
5C2×C7×#117C411yescharacteristic
6C22×C7×C4⋊C4C411yescharacteristic
7C2×C7×#101C2214yes—
8C2×C7×#100—22no—
9C7×#407—22no—
10C7×#391C2212yes—
11C7×#390C412yes—
12C7×#386—22no—
13C7×#380—22no—
14#12863C711yesmaximal, characteristic, direct product factor, Sylow
15C2×C7×#41—24no—
16C2×C7×#41—42no—
17C2×C7×#41—42no—
18C22×C7×Q8C2311yescharacteristic
19C22×C7×D4C2×C411yescharacteristic
20C22×C7×D4D412yes—
21C23×C4×C7—21no—
22C23×C4×C7C2×C411yescharacteristic
23C23×C4×C7D412yes—
24C2×C7×M16—24no—
25C7×#117—42no—
26C2×C7×C4⋊C4—21no—
27C2×C7×C4⋊C4—21no—
28C2×C7×C4⋊C4—42no—
29C2×C7×C4⋊C4C2×C412yes—
30C2×C7×C22⋊C4—21no—
31C2×C7×C22⋊C4—24no—
32C2×C42×C7C2×C412yes—
33C7×#101—28no—
34C7×#100—44no—
35C7×C22⋊C8—44no—
36C7×#95—24no—
37#2311C2×C711yescharacteristic
38#1785C2×C712yes—
39#1394C2×C714yescomplemented
40C24×C7C22⋊C412yes—
41C24×C7C22⋊C411yescharacteristic
42C7×#41—416no—
43C2×C7×Q8—41no—
44C2×C7×Q8—41no—
45C2×C7×Q8#4114yes—
46C2×C7×D4—24no—
47C2×C7×D4—22no—
48C2×C7×D4—24no—
49C2×C7×D4—41no—
50C2×C7×D4—41no—
51C2×C7×D4—42no—
52C22×C4×C7—22no—
53C22×C4×C7—22no—
54C22×C4×C7—22no—
55C22×C4×C7—24no—
56C22×C4×C7—24no—
57C22×C4×C7—22no—
58C22×C4×C7—22no—
59C22×C4×C7—42no—
60C22×C4×C7—42no—
61C22×C4×C7—82no—
62C22×C4×C7C22⋊C411yescharacteristic
63C22×C4×C7C22×C411yescharacteristic
64C22×C4×C7C2×D412yes—
65C7×M16—44no—
66C7×M16—44no—
67C2×C7×C8—44no—
68C7×C4⋊C4—42no—
69C7×C4⋊C4—42no—
70C7×C4⋊C4—42no—
71C7×C22⋊C4—42no—
72C7×C22⋊C4—84no—
73C42×C7—42no—
74C22×#41C22×C711yescharacteristic
75C2×#117C4×C711yescharacteristic
76C22×C4⋊C4C4×C711yescharacteristic
77C2×#101C22×C714yes—
78C2×#100—22no—
79#407—22no—
80#391C22×C712yes—
81#390C4×C712yes—
82#386—22no—
83#380—22no—
84C23×C7—21no—
85C23×C7—21no—
86C23×C7—22no—
87C23×C7—22no—
88C23×C7—22no—
89C23×C7—41no—
90C23×C7—41no—
91C23×C7—42no—
92C23×C7—42no—
93C23×C7#9912yes—
94C23×C7C2×C22⋊C411yescharacteristic
95C7×Q8—44no—
96C7×D4—48no—
97C7×D4—44no—
98C2×C4×C7—28no—
99C2×C4×C7—21no—
100C2×C4×C7—21no—
101C2×C4×C7—21no—
102C2×C4×C7—22no—
103C2×C4×C7—21no—
104C2×C4×C7—22no—
105C2×C4×C7—48no—
106C2×C4×C7—42no—
107C2×C4×C7—44no—
108C2×C4×C7—42no—
109C2×C4×C7—42no—
110C2×C4×C7—42no—
111C2×C4×C7—84no—
112C2×C4×C7#9912yes—
113C2×C4×C7#11712yes—
114C2×C4×C7#12314yes—
115C7×C8—84no—
116C2×#41—24no—
117C2×#41—42no—
118C2×#41—42no—
119C22×Q8C23×C711yescharacteristic
120C22×D4C2×C4×C711yescharacteristic
121C22×D4C7×D412yes—
122C23×C4—21no—
123C23×C4C2×C4×C711yescharacteristic
124C23×C4C7×D412yes—
125C2×M16—24no—
126#117—42no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—42no—
130C2×C4⋊C4C2×C4×C712yes—
131C2×C22⋊C4—21no—
132C2×C22⋊C4—24no—
133C2×C42C2×C4×C712yes—
134#101—28no—
135#100—44no—
136C22⋊C8—44no—
137#95—24no—
138C22×C7—21no—
139C22×C7—21no—
140C22×C7—22no—
141C22×C7—42no—
142C22×C7—42no—
143C22×C7—44no—
144C22×C7—41no—
145C22×C7—41no—
146C22×C7—42no—
147C22×C7—42no—
148C22×C7—42no—
149C22×C7—82no—
150C22×C7#38111yescharacteristic
151C22×C7C2×#9911yescharacteristic
152C22×C7C2×#9911yescharacteristic
153C4×C7—24no—
154C4×C7—22no—
155C4×C7—22no—
156C4×C7—82no—
157C4×C7—82no—
158C24C7×C22⋊C412yes—
159C24C7×C22⋊C411yescharacteristic
160#41—416no—
161C2×Q8—41no—
162C2×Q8—41no—
163C2×Q8C7×#4114yes—
164C2×D4—24no—
165C2×D4—22no—
166C2×D4—24no—
167C2×D4—41no—
168C2×D4—41no—
169C2×D4—42no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—24no—
174C22×C4—24no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—42no—
178C22×C4—42no—
179C22×C4—82no—
180C22×C4C7×C22⋊C411yescharacteristic
181C22×C4C22×C4×C711yescharacteristic
182C22×C4C2×C7×D412yes—
183M16—44no—
184M16—44no—
185C2×C8—44no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C22⋊C4—42no—
190C22⋊C4—84no—
191C42—42no—
192C2×C7—21no—
193C2×C7—21no—
194C2×C7—42no—
195C2×C7—82no—
196C2×C7#181911yescharacteristic
197C2×C7#213411yescharacteristic
198C2×C7#213511yescharacteristic
199C23—21no—
200C23—21no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—41no—
205C23—41no—
206C23—42no—
207C23—42no—
208C23C7×#9912yes—
209C23C2×C7×C22⋊C411yescharacteristic
210Q8—44no—
211D4—48no—
212D4—44no—
213C2×C4—28no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—48no—
221C2×C4—42no—
222C2×C4—44no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—84no—
227C2×C4C7×#9912yes—
228C2×C4C7×#11712yes—
229C2×C4C7×#12314yes—
230C8—84no—
231C7#1286311yescharacteristic, direct product factor, Sylow
232C22—21no—
233C22—21no—
234C22—22no—
235C22—42no—
236C22—42no—
237C22—44no—
238C22—41no—
239C22—41no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—82no—
244C22C7×#38111yescharacteristic
245C22C2×C7×#9911yescharacteristic
246C22C2×C7×#9911yescharacteristic
247C4—24no—
248C4—22no—
249C4—22no—
250C4—82no—
251C4—82no—
252C2—21no—
253C2—21no—
254C2—42no—
255C2—82no—
256C2C7×#181911yescharacteristic
257C2C7×#213411yescharacteristic
258C2C7×#213511yescharacteristic
subgroupG/H
center, socleC22×C7C2×#99
commutatorC22×C4C22×C4×C7
Frattini, cosocleC22×Q8C23×C7
prime radicalC22×C7×#41C22
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C22×C7×#41 ◁ G

Complements

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

NH ≅ G/Ntype
3. C7×#1394C2semidirect
14. #12863C7direct (N × H)
39. #1394C2×C7semidirect
231. C7#12863direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#23112
C7×#17852
C7×#13942
#128637