Finite Group Databasebeta

← C7×#20634 #13197850

Subgroups — C7×#20634 #13197850

Order 1792.

1462 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#520C211yesmaximal, characteristic
2C2×C7×#410C212yesmaximal
3C7×#2316C212yesmaximal, complemented
4C7×#1799C218yesmaximal, complemented
5C7×#1740C212yesmaximal, complemented
6C22×C7×#41C2211yescharacteristic
7C7×#520—28no—
8C2×C4×C7×Q8C412yescomplemented
9C2×C4×C7×D4C412yescomplemented
10C2×C4×C7×D4C2214yes—
11C2×C7×#117C412yescomplemented
12C2×C7×#117C2214yes—
13C2×C7×#117C2211yescharacteristic
14C22×C7×C4⋊C4C412yescomplemented
15C22×C7×C4⋊C4C2211yescharacteristic
16C7×#410—28no—
17C2×C7×#99C2218yes—
18C7×#389—28no—
19C7×#380C2218yes—
20C7×#342C2218yes—
21#20634C711yesmaximal, characteristic, direct product factor, Sylow
22C2×C7×#41—24no—
23C2×C7×#41—24no—
24C2×C7×#41D414yes—
25C2×C7×#41Q814yes—
26C22×C7×Q8C2×C411yescharacteristic
27C22×C7×D4C2×C411yescharacteristic
28C22×C7×D4C2312yes—
29C23×C4×C7C2×C412yes—
30C23×C4×C7C2×C414yes—
31C23×C4×C7C2312yes—
32C23×C4×C7C2311yescharacteristic
33C4×C7×Q8—28no—
34C4×C7×D4—216no—
35C4×C7×D4—28no—
36C7×#117—24no—
37C7×#117—28no—
38C7×#117—28no—
39C7×#117—28no—
40C2×C7×C4⋊C4—28no—
41C2×C7×C4⋊C4—24no—
42C2×C7×C4⋊C4—28no—
43C2×C7×C4⋊C4C2×C411yescharacteristic
44C2×C7×C4⋊C4C2×C414yes—
45C2×C7×C4⋊C4C2×C411yescharacteristic
46C2×C7×C4⋊C4C2×C412yes—
47C2×C7×C4⋊C4C2×C412yes—
48C2×C7×C4⋊C4D418yes—
49C2×C7×C22⋊C4C2×C414yes—
50C2×C7×C22⋊C4C2318yes—
51C2×C7×C22⋊C4C2312yes—
52C2×C42×C7—24no—
53C2×C42×C7C2×C414yes—
54C2×C42×C7C2×C412yes—
55C7×#99—216no—
56C7×#95—28no—
57C2×#520C2×C711yescharacteristic
58C2×#410C2×C712yes—
59#2316C2×C712yescomplemented
60#1799C2×C718yescomplemented
61#1740C2×C712yescomplemented
62C24×C7C22×C412yes—
63C24×C7C2411yescharacteristic
64C7×#41—216no—
65C7×#41—216no—
66C2×C7×Q8—22no—
67C2×C7×Q8—22no—
68C2×C7×Q8C4⋊C414yescomplemented
69C2×C7×D4—24no—
70C2×C7×D4—24no—
71C2×C7×D4—22no—
72C2×C7×D4—22no—
73C2×C7×D4C4⋊C414yescomplemented
74C2×C7×D4C2×D414yes—
75C2×C7×D4C2×Q814yes—
76C22×C4×C7—24no—
77C22×C4×C7—24no—
78C22×C4×C7—28no—
79C22×C4×C7—28no—
80C22×C4×C7—82no—
81C22×C4×C7—84no—
82C22×C4×C7C4⋊C418yescomplemented
83C22×C4×C7C22×C412yes—
84C22×C4×C7C22×C412yes—
85C22×C4×C7C22×C412yes—
86C22×C4×C7C22×C414yes—
87C22×C4×C7C22×C411yescharacteristic
88C22×C4×C7C22×C411yescharacteristic
89C22×C4×C7C2×D418yes—
90C22×C4×C7C2×D414yes—
91C22×C4×C7C2×D412yes—
92C22×C4×C7C2×Q812yes—
93C22×C4×C7#4114yes—
94C7×C4⋊C4—22no—
95C7×C4⋊C4—28no—
96C7×C4⋊C4—22no—
97C7×C4⋊C4—48no—
98C7×C4⋊C4—88no—
99C7×C4⋊C4C22⋊C418yes—
100C7×C4⋊C4C22⋊C418yes—
101C7×C22⋊C4—24no—
102C7×C22⋊C4—28no—
103C7×C22⋊C4—28no—
104C7×C22⋊C4—28no—
105C42×C7—28no—
106C42×C7—24no—
107C42×C7—48no—
108C22×#41C22×C711yescharacteristic
109#520—28no—
110C2×C4×Q8C4×C712yescomplemented
111C2×C4×D4C4×C712yescomplemented
112C2×C4×D4C22×C714yes—
113C2×#117C4×C712yescomplemented
114C2×#117C22×C714yes—
115C2×#117C22×C711yescharacteristic
116C22×C4⋊C4C4×C712yescomplemented
117C22×C4⋊C4C22×C711yescharacteristic
118#410—28no—
119C2×#99C22×C718yes—
120#389—28no—
121#380C22×C718yes—
122#342C22×C718yes—
123C23×C7—22no—
124C23×C7—22no—
125C23×C7—41no—
126C23×C7—41no—
127C23×C7—42no—
128C23×C7—42no—
129C23×C7C2×C4⋊C414yes—
130C23×C7C23×C411yescharacteristic
131C23×C7C22×D412yes—
132C23×C7C22×D411yescharacteristic
133C23×C7C22×Q811yescharacteristic
134C23×C7C2×#4112yes—
135C7×Q8—28no—
136C7×D4—28no—
137C7×D4—28no—
138C7×D4—28no—
139C2×C4×C7—22no—
140C2×C4×C7—22no—
141C2×C4×C7—216no—
142C2×C4×C7—22no—
143C2×C4×C7—22no—
144C2×C4×C7—48no—
145C2×C4×C7—44no—
146C2×C4×C7—42no—
147C2×C4×C7—42no—
148C2×C4×C7—48no—
149C2×C4×C7—48no—
150C2×C4×C7—48no—
151C2×C4×C7—88no—
152C2×C4×C7C2×C22⋊C418yes—
153C2×C4×C7C2×C22⋊C412yes—
154C2×C4×C7C2×C22⋊C412yes—
155C2×C4×C7C2×C4⋊C414yes—
156C2×C4×C7C2×C4⋊C412yes—
157C2×C4×C7C2×C4⋊C412yes—
158C2×C4×C7#11712yes—
159C2×C4×C7#11712yes—
160C2×C4×C7#12118yes—
161C2×C4×C7C22⋊Q818yes—
162C2×#41—24no—
163C2×#41—24no—
164C2×#41C7×D414yes—
165C2×#41C7×Q814yes—
166C22×Q8C2×C4×C711yescharacteristic
167C22×D4C2×C4×C711yescharacteristic
168C22×D4C23×C712yes—
169C23×C4C2×C4×C712yes—
170C23×C4C2×C4×C714yes—
171C23×C4C23×C712yes—
172C23×C4C23×C711yescharacteristic
173C4×Q8—28no—
174C4×D4—216no—
175C4×D4—28no—
176#117—24no—
177#117—28no—
178#117—28no—
179#117—28no—
180C2×C4⋊C4—28no—
181C2×C4⋊C4—24no—
182C2×C4⋊C4—28no—
183C2×C4⋊C4C2×C4×C711yescharacteristic
184C2×C4⋊C4C2×C4×C714yes—
185C2×C4⋊C4C2×C4×C711yescharacteristic
186C2×C4⋊C4C2×C4×C712yes—
187C2×C4⋊C4C2×C4×C712yes—
188C2×C4⋊C4C7×D418yes—
189C2×C22⋊C4C2×C4×C714yes—
190C2×C22⋊C4C23×C718yes—
191C2×C22⋊C4C23×C712yes—
192C2×C42—24no—
193C2×C42C2×C4×C714yes—
194C2×C42C2×C4×C712yes—
195#99—216no—
196#95—28no—
197C22×C7—22no—
198C22×C7—21no—
199C22×C7—22no—
200C22×C7—21no—
201C22×C7—24no—
202C22×C7—41no—
203C22×C7—41no—
204C22×C7—42no—
205C22×C7—44no—
206C22×C7—44no—
207C22×C7—42no—
208C22×C7—42no—
209C22×C7C22×C22⋊C411yescharacteristic
210C22×C7C22×C4⋊C411yescharacteristic
211C22×C7C2×#11711yescharacteristic
212C22×C7C2×#12112yes—
213C22×C7C2×C22⋊Q812yes—
214C4×C7—28no—
215C4×C7—24no—
216C4×C7—42no—
217C4×C7—42no—
218C4×C7—88no—
219C4×C7#38014yes—
220C4×C7#38014yes—
221C24C22×C4×C712yes—
222C24C24×C711yescharacteristic
223#41—216no—
224#41—216no—
225C2×Q8—22no—
226C2×Q8—22no—
227C2×Q8C7×C4⋊C414yescomplemented
228C2×D4—24no—
229C2×D4—24no—
230C2×D4—22no—
231C2×D4—22no—
232C2×D4C7×C4⋊C414yescomplemented
233C2×D4C2×C7×D414yes—
234C2×D4C2×C7×Q814yes—
235C22×C4—24no—
236C22×C4—24no—
237C22×C4—28no—
238C22×C4—28no—
239C22×C4—82no—
240C22×C4—84no—
241C22×C4C7×C4⋊C418yescomplemented
242C22×C4C22×C4×C712yes—
243C22×C4C22×C4×C712yes—
244C22×C4C22×C4×C712yes—
245C22×C4C22×C4×C714yes—
246C22×C4C22×C4×C711yescharacteristic
247C22×C4C22×C4×C711yescharacteristic
248C22×C4C2×C7×D418yes—
249C22×C4C2×C7×D414yes—
250C22×C4C2×C7×D412yes—
251C22×C4C2×C7×Q812yes—
252C22×C4C7×#4114yes—
253C4⋊C4—22no—
254C4⋊C4—28no—
255C4⋊C4—22no—
256C4⋊C4—48no—
257C4⋊C4—88no—
258C4⋊C4C7×C22⋊C418yes—
259C4⋊C4C7×C22⋊C418yes—
260C22⋊C4—24no—
261C22⋊C4—28no—
262C22⋊C4—28no—
263C22⋊C4—28no—
264C42—28no—
265C42—24no—
266C42—48no—
267C2×C7—22no—
268C2×C7—21no—
269C2×C7—21no—
270C2×C7—22no—
271C2×C7—44no—
272C2×C7C2×#38011yescharacteristic
273C2×C7#288311yescharacteristic
274C2×C7#288411yescharacteristic
275C23—22no—
276C23—22no—
277C23—41no—
278C23—41no—
279C23—42no—
280C23—42no—
281C23C2×C7×C4⋊C414yes—
282C23C23×C4×C711yescharacteristic
283C23C22×C7×D412yes—
284C23C22×C7×D411yescharacteristic
285C23C22×C7×Q811yescharacteristic
286C23C2×C7×#4112yes—
287Q8—28no—
288D4—28no—
289D4—28no—
290D4—28no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—216no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—48no—
297C2×C4—44no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—48no—
301C2×C4—48no—
302C2×C4—48no—
303C2×C4—88no—
304C2×C4C2×C7×C22⋊C418yes—
305C2×C4C2×C7×C22⋊C412yes—
306C2×C4C2×C7×C22⋊C412yes—
307C2×C4C2×C7×C4⋊C414yes—
308C2×C4C2×C7×C4⋊C412yes—
309C2×C4C2×C7×C4⋊C412yes—
310C2×C4C7×#11712yes—
311C2×C4C7×#11712yes—
312C2×C4C7×#12118yes—
313C2×C4C7×C22⋊Q818yes—
314C7#2063411yescharacteristic, direct product factor, Sylow
315C22—22no—
316C22—21no—
317C22—22no—
318C22—21no—
319C22—24no—
320C22—41no—
321C22—41no—
322C22—42no—
323C22—44no—
324C22—44no—
325C22—42no—
326C22—42no—
327C22C22×C7×C22⋊C411yescharacteristic
328C22C22×C7×C4⋊C411yescharacteristic
329C22C2×C7×#11711yescharacteristic
330C22C2×C7×#12112yes—
331C22C2×C7×C22⋊Q812yes—
332C4—24no—
333C4—28no—
334C4—42no—
335C4—42no—
336C4—88no—
337C4C7×#38014yes—
338C4C7×#38014yes—
339C2—22no—
340C2—21no—
341C2—21no—
342C2—22no—
343C2—44no—
344C2C2×C7×#38011yescharacteristic
345C2C7×#288311yescharacteristic
346C2C7×#288411yescharacteristic
subgroupG/H
center, socleC22×C7C22×C22⋊C4
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC22×C7×#41C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C22×C7×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C7×#2316C2semidirect
4. C7×#1799C2semidirect
5. C7×#1740C2semidirect
8. C2×C4×C7×Q8C4semidirect
9. C2×C4×C7×D4C4semidirect
11. C2×C7×#117C4semidirect
14. C22×C7×C4⋊C4C4semidirect
21. #20634C7direct (N × H)
59. #2316C2×C7semidirect
60. #1799C2×C7semidirect
61. #1740C2×C7semidirect
68. C2×C7×Q8C4⋊C4semidirect
73. C2×C7×D4C4⋊C4semidirect
82. C22×C4×C7C4⋊C4semidirect
110. C2×C4×Q8C4×C7semidirect
111. C2×C4×D4C4×C7semidirect
113. C2×#117C4×C7semidirect
116. C22×C4⋊C4C4×C7semidirect
227. C2×Q8C7×C4⋊C4semidirect
232. C2×D4C7×C4⋊C4semidirect
241. C22×C4C7×C4⋊C4semidirect
314. C7#20634direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5202
C2×C7×#4102
C7×#23162
C7×#17992
C7×#17402
#206347