Finite Group Databasebeta

← C7×#11562 #13188778

Subgroups — C7×#11562 #13188778

Order 1792.

444 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2486C211yesmaximal, characteristic
2C7×#1465C211yesmaximal, characteristic
3C7×#1460C211yesmaximal, characteristic
4C7×#1317C214yesmaximal, complemented
5C2×C7×#123C412yes—
6C2×C4×C7×D4C2211yescharacteristic
7C22×C7×C4⋊C4C411yescharacteristic
8C7×#431—21no—
9C7×#407—21no—
10C7×#398—21no—
11C7×#397—21no—
12C7×#389—21no—
13C7×#381C2212yes—
14C7×#380—21no—
15C7×#380C411yescharacteristic
16C7×#324—21no—
17C7×#323—21no—
18C7×#323C2212yes—
19C7×#323C2212yes—
20#11562C711yesmaximal, characteristic, direct product factor, Sylow
21C22×C7×D4C2×C411yescharacteristic
22C23×C4×C7C2×C412yes—
23C23×C4×C7C2×C411yescharacteristic
24C23×C4×C7D411yescharacteristic
25C2×C7×M16—41no—
26C7×#123—44no—
27C4×C7×D4—41no—
28C4×C7×D4—41no—
29C2×C7×C4⋊C4—21no—
30C2×C7×C4⋊C4—22no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4—21no—
33C2×C7×C4⋊C4—41no—
34C2×C7×C4⋊C4—41no—
35C2×C7×C4⋊C4D411yescharacteristic
36C2×C7×C22⋊C4—22no—
37C2×C7×C22⋊C4C2×C412yes—
38C2×C7×C22⋊C4D411yescharacteristic
39C2×C7×C22⋊C4C2311yescharacteristic
40C2×C42×C7D411yescharacteristic
41C7×C4⋊C8—41no—
42C7×C22⋊C8—22no—
43C7×C22⋊C8—22no—
44C7×C22⋊C8—41no—
45C4×C7×C8—41no—
46C7×#95—21no—
47C7×#95—22no—
48C7×#95—22no—
49#2486C2×C711yescharacteristic
50#1465C2×C711yescharacteristic
51#1460C2×C711yescharacteristic
52#1317C2×C714yescomplemented
53C24×C7C22⋊C411yescharacteristic
54C24×C7C22×C411yescharacteristic
55C2×C7×D4—22no—
56C2×C7×D4—22no—
57C2×C7×D4—41no—
58C22×C4×C7—21no—
59C22×C4×C7—21no—
60C22×C4×C7—21no—
61C22×C4×C7—21no—
62C22×C4×C7—22no—
63C22×C4×C7—22no—
64C22×C4×C7—24no—
65C22×C4×C7—42no—
66C22×C4×C7—42no—
67C22×C4×C7—42no—
68C22×C4×C7—42no—
69C22×C4×C7C22⋊C411yescharacteristic
70C22×C4×C7C22⋊C411yescharacteristic
71C22×C4×C7C22⋊C411yescharacteristic
72C22×C4×C7C2×D411yescharacteristic
73C22×C4×C7C2×D411yescharacteristic
74C7×M16—82no—
75C2×C7×C8—42no—
76C2×C7×C8—42no—
77C7×C4⋊C4—41no—
78C7×C4⋊C4—42no—
79C7×C4⋊C4—42no—
80C7×C4⋊C4—41no—
81C7×C4⋊C4—41no—
82C7×C4⋊C4—44no—
83C7×C22⋊C4—41no—
84C7×C22⋊C4—41no—
85C7×C22⋊C4—44no—
86C7×C22⋊C4—42no—
87C42×C7—21no—
88C42×C7—21no—
89C2×#123C4×C712yes—
90C2×C4×D4C22×C711yescharacteristic
91C22×C4⋊C4C4×C711yescharacteristic
92#431—21no—
93#407—21no—
94#398—21no—
95#397—21no—
96#389—21no—
97#381C22×C712yes—
98#380—21no—
99#380C4×C711yescharacteristic
100#324—21no—
101#323—21no—
102#323C22×C712yes—
103#323C22×C712yes—
104C23×C7—21no—
105C23×C7—21no—
106C23×C7—21no—
107C23×C7—21no—
108C23×C7—21no—
109C23×C7—41no—
110C23×C7—41no—
111C23×C7—41no—
112C23×C7—41no—
113C23×C7C2×C22⋊C411yescharacteristic
114C23×C7#13112yes—
115C7×D4—44no—
116C2×C4×C7—21no—
117C2×C4×C7—21no—
118C2×C4×C7—22no—
119C2×C4×C7—21no—
120C2×C4×C7—21no—
121C2×C4×C7—21no—
122C2×C4×C7—42no—
123C2×C4×C7—42no—
124C2×C4×C7—42no—
125C2×C4×C7—41no—
126C2×C4×C7—41no—
127C2×C4×C7—41no—
128C2×C4×C7—42no—
129C2×C4×C7—42no—
130C2×C4×C7—42no—
131C2×C4×C7—42no—
132C2×C4×C7—42no—
133C2×C4×C7—42no—
134C2×C4×C7—81no—
135C2×C4×C7—84no—
136C2×C4×C7#9911yescharacteristic
137C2×C4×C7#9911yescharacteristic
138C2×C4×C7#10012yes—
139C7×C8—82no—
140C7×C8—82no—
141C22×D4C2×C4×C711yescharacteristic
142C23×C4C2×C4×C712yes—
143C23×C4C2×C4×C711yescharacteristic
144C23×C4C7×D411yescharacteristic
145C2×M16—41no—
146#123—44no—
147C4×D4—41no—
148C4×D4—41no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—41no—
154C2×C4⋊C4—41no—
155C2×C4⋊C4C7×D411yescharacteristic
156C2×C22⋊C4—22no—
157C2×C22⋊C4C2×C4×C712yes—
158C2×C22⋊C4C7×D411yescharacteristic
159C2×C22⋊C4C23×C711yescharacteristic
160C2×C42C7×D411yescharacteristic
161C4⋊C8—41no—
162C22⋊C8—22no—
163C22⋊C8—22no—
164C22⋊C8—41no—
165C4×C8—41no—
166#95—21no—
167#95—22no—
168#95—22no—
169C22×C7—21no—
170C22×C7—21no—
171C22×C7—22no—
172C22×C7—42no—
173C22×C7—42no—
174C22×C7—42no—
175C22×C7—41no—
176C22×C7—41no—
177C22×C7—41no—
178C22×C7—41no—
179C22×C7—41no—
180C22×C7—81no—
181C22×C7#40811yescharacteristic
182C22×C7C2×#9911yescharacteristic
183C22×C7C2×#10011yescharacteristic
184C4×C7—21no—
185C4×C7—22no—
186C4×C7—41no—
187C4×C7—41no—
188C4×C7—41no—
189C4×C7—82no—
190C4×C7—82no—
191C4×C7#35212yes—
192C24C7×C22⋊C411yescharacteristic
193C24C22×C4×C711yescharacteristic
194C2×D4—22no—
195C2×D4—22no—
196C2×D4—41no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—24no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4C7×C22⋊C411yescharacteristic
209C22×C4C7×C22⋊C411yescharacteristic
210C22×C4C7×C22⋊C411yescharacteristic
211C22×C4C2×C7×D411yescharacteristic
212C22×C4C2×C7×D411yescharacteristic
213M16—82no—
214C2×C8—42no—
215C2×C8—42no—
216C4⋊C4—41no—
217C4⋊C4—42no—
218C4⋊C4—42no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—44no—
222C22⋊C4—41no—
223C22⋊C4—41no—
224C22⋊C4—44no—
225C22⋊C4—42no—
226C42—21no—
227C42—21no—
228C2×C7—21no—
229C2×C7—21no—
230C2×C7—42no—
231C2×C7—81no—
232C2×C7#147111yescharacteristic
233C2×C7C2×#35211yescharacteristic
234C2×C7#212311yescharacteristic
235C23—21no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—41no—
241C23—41no—
242C23—41no—
243C23—41no—
244C23C2×C7×C22⋊C411yescharacteristic
245C23C7×#13112yes—
246D4—44no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—81no—
266C2×C4—84no—
267C2×C4C7×#9911yescharacteristic
268C2×C4C7×#9911yescharacteristic
269C2×C4C7×#10012yes—
270C8—82no—
271C8—82no—
272C7#1156211yescharacteristic, direct product factor, Sylow
273C22—21no—
274C22—21no—
275C22—22no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—81no—
285C22C7×#40811yescharacteristic
286C22C2×C7×#9911yescharacteristic
287C22C2×C7×#10011yescharacteristic
288C4—22no—
289C4—21no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—82no—
294C4—82no—
295C4C7×#35212yes—
296C2—21no—
297C2—21no—
298C2—42no—
299C2—81no—
300C2C7×#147111yescharacteristic
301C2C2×C7×#35211yescharacteristic
302C2C7×#212311yescharacteristic
subgroupG/H
center, socleC22×C7C2×#99
commutatorC24C22×C4×C7
Frattini, cosocleC2×C22⋊C4C23×C7
prime radicalC22×C7×D4C2×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C2×C4×C7×D4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C7×#1317C2semidirect
20. #11562C7direct (N × H)
52. #1317C2×C7semidirect
272. C7#11562direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#24862
C7×#14652
C7×#14602
C7×#13172
#115627