Finite Group Databasebeta

← C7×#8069 #13185285

Subgroups — C7×#8069 #13185285

Order 1792.

564 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2920C211yesmaximal, characteristic
2C2×C7×#432C211yesmaximal, characteristic
3C7×#2283C211yesmaximal, characteristic
4C7×#1300C214yesmaximal, complemented
5C22×C42×C7C2211yescharacteristic
6C7×#432—21no—
7C7×#432—21no—
8C7×#432C412yescomplemented
9C7×#432C412yescomplemented
10C7×#432C412yescomplemented
11C7×#432C2212yes—
12C7×#431—21no—
13C7×#431—21no—
14C7×#423—21no—
15C2×C7×C4⋊C8C412yescomplemented
16C7×#407—21no—
17C2×C7×C22⋊C8—21no—
18C4×C7×M16C2212yes—
19C2×C7×#97—21no—
20C7×#383—21no—
21C7×#382C412yes—
22C7×#381C412yes—
23C7×#380—21no—
24C4×C7×C4⋊C4—21no—
25C4×C7×C22⋊C4—21no—
26C7×#376C2212yes—
27#8069C711yesmaximal, characteristic, direct product factor, Sylow
28C23×C4×C7C2×C411yescharacteristic
29C23×C4×C7D411yescharacteristic
30C23×C4×C7D411yescharacteristic
31C2×C7×M16—22no—
32C22×C7×C8—22no—
33C2×C7×C4⋊C4—22no—
34C2×C7×C22⋊C4—22no—
35C2×C42×C7—22no—
36C2×C42×C7C2×C411yescharacteristic
37C2×C42×C7C2×C411yescharacteristic
38C2×C42×C7C2×C411yescharacteristic
39C2×C42×C7C2×C411yescharacteristic
40C2×C42×C7C2×C411yescharacteristic
41C2×C42×C7D411yescharacteristic
42C2×C42×C7D411yescharacteristic
43C2×C42×C7D411yescharacteristic
44C2×C42×C7D411yescharacteristic
45C2×C42×C7Q811yescharacteristic
46C2×C42×C7Q811yescharacteristic
47C2×C42×C7C2311yescharacteristic
48C7×C4⋊C8—22no—
49C7×C4⋊C8—22no—
50C7×C4⋊C8—22no—
51C7×C4⋊C8C2×C414yes—
52C7×C22⋊C8—22no—
53C7×C22⋊C8—22no—
54C7×C22⋊C8—22no—
55C7×C22⋊C8—22no—
56C7×#97—22no—
57C7×#97—22no—
58C7×#97C2×C414yes—
59C4×C7×C8—22no—
60C7×#95—22no—
61C7×#95—22no—
62C7×#95—22no—
63C7×#95C2×C414yes—
64#2920C2×C711yescharacteristic
65C2×#432C2×C711yescharacteristic
66#2283C2×C711yescharacteristic
67#1300C2×C714yescomplemented
68C24×C7C22⋊C411yescharacteristic
69C22×C4×C7—24no—
70C22×C4×C7—42no—
71C22×C4×C7—42no—
72C22×C4×C7—42no—
73C22×C4×C7C4211yescharacteristic
74C22×C4×C7C4211yescharacteristic
75C22×C4×C7C22⋊C411yescharacteristic
76C22×C4×C7C22⋊C411yescharacteristic
77C22×C4×C7C22⋊C411yescharacteristic
78C22×C4×C7C22⋊C411yescharacteristic
79C22×C4×C7C22⋊C411yescharacteristic
80C22×C4×C7C22⋊C411yescharacteristic
81C22×C4×C7C22⋊C411yescharacteristic
82C22×C4×C7C4⋊C411yescharacteristic
83C22×C4×C7C4⋊C411yescharacteristic
84C22×C4×C7C4⋊C411yescharacteristic
85C22×C4×C7C4⋊C411yescharacteristic
86C22×C4×C7C4⋊C411yescharacteristic
87C22×C4×C7C4⋊C411yescharacteristic
88C22×C4×C7C22×C411yescharacteristic
89C22×C4×C7C2×D411yescharacteristic
90C22×C4×C7C2×D411yescharacteristic
91C7×M16—44no—
92C2×C7×C8—24no—
93C2×C7×C8—24no—
94C2×C7×C8—44no—
95C7×C4⋊C4—44no—
96C7×C22⋊C4—44no—
97C42×C7—44no—
98C42×C7C4211yescharacteristic
99C42×C7C4211yescharacteristic
100C42×C7C22⋊C411yescharacteristic
101C42×C7C22⋊C411yescharacteristic
102C42×C7C22⋊C411yescharacteristic
103C42×C7C22⋊C411yescharacteristic
104C42×C7C4⋊C411yescharacteristic
105C42×C7C4⋊C411yescharacteristic
106C42×C7C4⋊C411yescharacteristic
107C42×C7C4⋊C411yescharacteristic
108C42×C7C4⋊C411yescharacteristic
109C42×C7C4⋊C411yescharacteristic
110C42×C7C22×C411yescharacteristic
111C42×C7C22×C411yescharacteristic
112C42×C7C2×D411yescharacteristic
113C42×C7C2×Q811yescharacteristic
114C22×C42C22×C711yescharacteristic
115#432—21no—
116#432—21no—
117#432C4×C712yescomplemented
118#432C4×C712yescomplemented
119#432C4×C712yescomplemented
120#432C22×C712yes—
121#431—21no—
122#431—21no—
123#423—21no—
124C2×C4⋊C8C4×C712yescomplemented
125#407—21no—
126C2×C22⋊C8—21no—
127C4×M16C22×C712yes—
128C2×#97—21no—
129#383—21no—
130#382C4×C712yes—
131#381C4×C712yes—
132#380—21no—
133C4×C4⋊C4—21no—
134C4×C22⋊C4—21no—
135#376C22×C712yes—
136C23×C7—22no—
137C23×C7—22no—
138C23×C7—41no—
139C23×C7#9511yescharacteristic
140C23×C7#9511yescharacteristic
141C23×C7C2×C22⋊C411yescharacteristic
142C2×C4×C7—22no—
143C2×C4×C7—22no—
144C2×C4×C7—22no—
145C2×C4×C7—22no—
146C2×C4×C7—22no—
147C2×C4×C7—22no—
148C2×C4×C7—22no—
149C2×C4×C7—41no—
150C2×C4×C7—41no—
151C2×C4×C7—41no—
152C2×C4×C7—41no—
153C2×C4×C7—41no—
154C2×C4×C7—41no—
155C2×C4×C7—41no—
156C2×C4×C7—41no—
157C2×C4×C7—41no—
158C2×C4×C7—41no—
159C2×C4×C7—41no—
160C2×C4×C7—44no—
161C2×C4×C7—44no—
162C2×C4×C7—44no—
163C2×C4×C7#9511yescharacteristic
164C2×C4×C7#9511yescharacteristic
165C2×C4×C7#9511yescharacteristic
166C2×C4×C7#9511yescharacteristic
167C2×C4×C7#9511yescharacteristic
168C2×C4×C7#9511yescharacteristic
169C2×C4×C7C2×C4211yescharacteristic
170C2×C4×C7C2×C22⋊C411yescharacteristic
171C2×C4×C7C2×C22⋊C411yescharacteristic
172C2×C4×C7C2×C4⋊C411yescharacteristic
173C2×C4×C7C2×C4⋊C411yescharacteristic
174C2×C4×C7C2×C4⋊C411yescharacteristic
175C7×C8—44no—
176C7×C8—44no—
177C23×C4C2×C4×C711yescharacteristic
178C23×C4C7×D411yescharacteristic
179C23×C4C7×D411yescharacteristic
180C2×M16—22no—
181C22×C8—22no—
182C2×C4⋊C4—22no—
183C2×C22⋊C4—22no—
184C2×C42—22no—
185C2×C42C2×C4×C711yescharacteristic
186C2×C42C2×C4×C711yescharacteristic
187C2×C42C2×C4×C711yescharacteristic
188C2×C42C2×C4×C711yescharacteristic
189C2×C42C2×C4×C711yescharacteristic
190C2×C42C7×D411yescharacteristic
191C2×C42C7×D411yescharacteristic
192C2×C42C7×D411yescharacteristic
193C2×C42C7×D411yescharacteristic
194C2×C42C7×Q811yescharacteristic
195C2×C42C7×Q811yescharacteristic
196C2×C42C23×C711yescharacteristic
197C4⋊C8—22no—
198C4⋊C8—22no—
199C4⋊C8—22no—
200C4⋊C8C2×C4×C714yes—
201C22⋊C8—22no—
202C22⋊C8—22no—
203C22⋊C8—22no—
204C22⋊C8—22no—
205#97—22no—
206#97—22no—
207#97C2×C4×C714yes—
208C4×C8—22no—
209#95—22no—
210#95—22no—
211#95—22no—
212#95C2×C4×C714yes—
213C22×C7—21no—
214C22×C7—21no—
215C22×C7—21no—
216C22×C7—21no—
217C22×C7—21no—
218C22×C7—21no—
219C22×C7—21no—
220C22×C7—44no—
221C22×C7#34412yes—
222C22×C7C2×#9511yescharacteristic
223C22×C7#42112yes—
224C4×C7—21no—
225C4×C7—21no—
226C4×C7—21no—
227C4×C7—21no—
228C4×C7—21no—
229C4×C7—21no—
230C4×C7—21no—
231C4×C7—21no—
232C4×C7—21no—
233C4×C7—21no—
234C4×C7—21no—
235C4×C7—84no—
236C4×C7#42112yes—
237C24C7×C22⋊C411yescharacteristic
238C22×C4—24no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4C42×C711yescharacteristic
243C22×C4C42×C711yescharacteristic
244C22×C4C7×C22⋊C411yescharacteristic
245C22×C4C7×C22⋊C411yescharacteristic
246C22×C4C7×C22⋊C411yescharacteristic
247C22×C4C7×C22⋊C411yescharacteristic
248C22×C4C7×C22⋊C411yescharacteristic
249C22×C4C7×C22⋊C411yescharacteristic
250C22×C4C7×C22⋊C411yescharacteristic
251C22×C4C7×C4⋊C411yescharacteristic
252C22×C4C7×C4⋊C411yescharacteristic
253C22×C4C7×C4⋊C411yescharacteristic
254C22×C4C7×C4⋊C411yescharacteristic
255C22×C4C7×C4⋊C411yescharacteristic
256C22×C4C7×C4⋊C411yescharacteristic
257C22×C4C22×C4×C711yescharacteristic
258C22×C4C2×C7×D411yescharacteristic
259C22×C4C2×C7×D411yescharacteristic
260M16—44no—
261C2×C8—24no—
262C2×C8—24no—
263C2×C8—44no—
264C4⋊C4—44no—
265C22⋊C4—44no—
266C42—44no—
267C42C42×C711yescharacteristic
268C42C42×C711yescharacteristic
269C42C7×C22⋊C411yescharacteristic
270C42C7×C22⋊C411yescharacteristic
271C42C7×C22⋊C411yescharacteristic
272C42C7×C22⋊C411yescharacteristic
273C42C7×C4⋊C411yescharacteristic
274C42C7×C4⋊C411yescharacteristic
275C42C7×C4⋊C411yescharacteristic
276C42C7×C4⋊C411yescharacteristic
277C42C7×C4⋊C411yescharacteristic
278C42C7×C4⋊C411yescharacteristic
279C42C22×C4×C711yescharacteristic
280C42C22×C4×C711yescharacteristic
281C42C2×C7×D411yescharacteristic
282C42C2×C7×Q811yescharacteristic
283C2×C7—22no—
284C2×C7—22no—
285C2×C7—41no—
286C2×C7#173311yescharacteristic
287C2×C7#173311yescharacteristic
288C2×C7C2×#34411yescharacteristic
289C23—22no—
290C23—22no—
291C23—41no—
292C23C7×#9511yescharacteristic
293C23C7×#9511yescharacteristic
294C23C2×C7×C22⋊C411yescharacteristic
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—44no—
314C2×C4—44no—
315C2×C4—44no—
316C2×C4C7×#9511yescharacteristic
317C2×C4C7×#9511yescharacteristic
318C2×C4C7×#9511yescharacteristic
319C2×C4C7×#9511yescharacteristic
320C2×C4C7×#9511yescharacteristic
321C2×C4C7×#9511yescharacteristic
322C2×C4C2×C42×C711yescharacteristic
323C2×C4C2×C7×C22⋊C411yescharacteristic
324C2×C4C2×C7×C22⋊C411yescharacteristic
325C2×C4C2×C7×C4⋊C411yescharacteristic
326C2×C4C2×C7×C4⋊C411yescharacteristic
327C2×C4C2×C7×C4⋊C411yescharacteristic
328C8—44no—
329C8—44no—
330C7#806911yescharacteristic, direct product factor, Sylow
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—44no—
339C22C7×#34412yes—
340C22C2×C7×#9511yescharacteristic
341C22C7×#42112yes—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—84no—
354C4C7×#42112yes—
355C2—22no—
356C2—22no—
357C2—41no—
358C2C7×#173311yescharacteristic
359C2C7×#173311yescharacteristic
360C2C2×C7×#34411yescharacteristic
subgroupG/H
centerC2×C4×C7C2×C22⋊C4
commutatorC2×C4C2×C42×C7
Frattini, cosocleC2×C42C23×C7
socleC22×C7C2×#95
prime radicalC24×C7C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C7 ◁ C22×C42×C7 ◁ G

Complements

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

NH ≅ G/Ntype
4. C7×#1300C2semidirect
8. C7×#432C4semidirect
9. C7×#432C4semidirect
10. C7×#432C4semidirect
15. C2×C7×C4⋊C8C4semidirect
27. #8069C7direct (N × H)
67. #1300C2×C7semidirect
117. #432C4×C7semidirect
118. #432C4×C7semidirect
119. #432C4×C7semidirect
124. C2×C4⋊C8C4×C7semidirect
330. C7#8069direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#29202
C2×C7×#4322
C7×#22832
C7×#13002
#80697