Finite Group Databasebeta

← C2×C7×#2943 #13237371

Subgroups — C2×C7×#2943 #13237371

Order 1792.

2854 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#135C211yesmaximal, characteristic
2C2×C4×C7×#41C212yesmaximal, complemented
3C7×#2943C2116yesmaximal, direct product factor
4C2×C7×#442C212yesmaximal, complemented
5C2×C7×#441C212yesmaximal, complemented
6C2×C7×#440C214yesmaximal, complemented
7C2×C7×#427C211yesmaximal, characteristic, complemented
8C2×C7×#416C212yesmaximal, complemented
9C22×C7×#97C211yesmaximal, characteristic, complemented
10C22×C7×#41C2212yes—
11C2×C7×#135C4116yescomplemented
12C2×C7×#135C2218yes—
13C22×C7×Q16C2211yescharacteristic
14C22×C7×SD16C2212yes—
15C22×C7×D8C2211yescharacteristic
16C23×C7×C8C2211yescharacteristic
17C23×C7×C8C2211yescharacteristic
18C4×C7×#41—28no—
19C4×C7×#41C22116yescomplemented
20C2×C4×C7×Q8C2214yes—
21C2×C4×C7×D4—24no—
22C2×C4×C7×D4C2214yes—
23C2×C7×#117—22no—
24C2×C7×#117C2212yes—
25C22×C42×C7—22no—
26C22×C42×C7C2211yescharacteristic
27C7×#442C22116yescomplemented
28C7×#441C22116yescomplemented
29C7×#440C22132yescomplemented
30C7×#427C2218yescomplemented
31C2×C7×#107C2212yes—
32C2×C7×#106C2212yes—
33C7×#416C22116yescomplemented
34C2×C7×#103C2214yes—
35C2×C7×#102C2214yes—
36C2×C7×#97C2212yes—
37C2×C7×#97C2212yes—
38C2×C7×#97C2218yescomplemented
39C2×#2943C711yesmaximal, characteristic, direct product factor, Sylow
40C2×C7×#41—24no—
41C2×C7×#41—28no—
42C2×C7×#41C2×C4116yescomplemented
43C2×C7×#41C2318yes—
44C22×C7×Q8C2312yes—
45C22×C7×D4—22no—
46C22×C7×D4C2312yes—
47C23×C4×C7—22no—
48C23×C4×C7—24no—
49C23×C4×C7D412yes—
50C23×C4×C7C2311yescharacteristic
51C7×#135C2×C4164yescomplemented
52C2×C7×Q16C2×C418yescomplemented
53C2×C7×Q16C2314yes—
54C2×C7×SD16C2×C4116yescomplemented
55C2×C7×SD16C2318yes—
56C2×C7×D8C2×C418yescomplemented
57C2×C7×D8C2314yes—
58C22×C7×C8—24no—
59C22×C7×C8C2×C418yescomplemented
60C22×C7×C8C2312yes—
61C22×C7×C8C2314yes—
62C22×C7×C8C2311yescharacteristic
63C22×C7×C8C2311yescharacteristic
64C22×C7×C8C2314yes—
65C4×C7×Q8—28no—
66C4×C7×Q8C23116yes—
67C4×C7×D4—232no—
68C4×C7×D4—28no—
69C4×C7×D4C23116yes—
70C7×#117—24no—
71C7×#117—216no—
72C7×#117C2318yes—
73C2×C7×C4⋊C4—24no—
74C2×C7×C4⋊C4C2314yes—
75C2×C7×C22⋊C4—22no—
76C2×C7×C22⋊C4—24no—
77C2×C42×C7—24no—
78C2×C42×C7—22no—
79C2×C42×C7—216no—
80C2×C42×C7D414yes—
81C2×C42×C7D412yes—
82C2×C42×C7C2312yes—
83C2×C42×C7C2314yes—
84C7×#107C2318yes—
85C7×#106C2318yes—
86C7×#103C23116yes—
87C7×#102C23116yes—
88C7×#97C2318yes—
89C7×#97C2318yes—
90C22×#135C2×C711yescharacteristic
91C2×C4×#41C2×C712yescomplemented
92#2943C2×C7116yesdirect product factor
93C2×#442C2×C712yescomplemented
94C2×#441C2×C712yescomplemented
95C2×#440C2×C714yescomplemented
96C2×#427C2×C711yescharacteristic, complemented
97C2×#416C2×C712yescomplemented
98C22×#97C2×C711yescharacteristic, complemented
99C24×C7—22no—
100C24×C7C2×D411yescharacteristic
101C7×#41—232no—
102C7×#41—216no—
103C7×#41C22×C4132yescomplemented
104C2×C7×Q8—22no—
105C2×C7×Q8—24no—
106C2×C7×Q8C22×C418yes—
107C2×C7×Q8C2414yes—
108C2×C7×D4—216no—
109C2×C7×D4—28no—
110C2×C7×D4—22no—
111C2×C7×D4—24no—
112C2×C7×D4C22×C418yes—
113C2×C7×D4C2414yes—
114C22×C4×C7—22no—
115C22×C4×C7—216no—
116C22×C4×C7—28no—
117C22×C4×C7—24no—
118C22×C4×C7—216no—
119C22×C4×C7—44no—
120C22×C4×C7—416no—
121C22×C4×C7C22×C414yes—
122C22×C4×C7C2×D414yes—
123C22×C4×C7C2×D418yes—
124C22×C4×C7C2×D412yes—
125C22×C4×C7C2×D411yescharacteristic
126C22×C4×C7#4114yes—
127C22×C4×C7C2411yescharacteristic
128C22×C4×C7C2412yes—
129C7×Q16C22×C4116yescomplemented
130C7×SD16C22×C4132yescomplemented
131C7×D8C22×C4116yescomplemented
132C2×C7×C8—24no—
133C2×C7×C8—28no—
134C2×C7×C8C22×C414yes—
135C2×C7×C8C22×C414yes—
136C2×C7×C8C22×C4116yescomplemented
137C2×C7×C8C2414yes—
138C2×C7×C8C2412yes—
139C2×C7×C8C2412yes—
140C7×C4⋊C4—216no—
141C7×C4⋊C4—24no—
142C7×C4⋊C4C2418yes—
143C7×C22⋊C4—28no—
144C7×C22⋊C4—216no—
145C42×C7—28no—
146C42×C7—216no—
147C42×C7C2×D418yes—
148C42×C7C2×D414yes—
149C42×C7C2414yes—
150C22×#41C22×C712yes—
151C2×#135C4×C7116yescomplemented
152C2×#135C22×C718yes—
153C22×Q16C22×C711yescharacteristic
154C22×SD16C22×C712yes—
155C22×D8C22×C711yescharacteristic
156C23×C8C22×C711yescharacteristic
157C23×C8C22×C711yescharacteristic
158C4×#41—28no—
159C4×#41C22×C7116yescomplemented
160C2×C4×Q8C22×C714yes—
161C2×C4×D4—24no—
162C2×C4×D4C22×C714yes—
163C2×#117—22no—
164C2×#117C22×C712yes—
165C22×C42—22no—
166C22×C42C22×C711yescharacteristic
167#442C22×C7116yescomplemented
168#441C22×C7116yescomplemented
169#440C22×C7132yescomplemented
170#427C22×C718yescomplemented
171C2×#107C22×C712yes—
172C2×#106C22×C712yes—
173#416C22×C7116yescomplemented
174C2×#103C22×C714yes—
175C2×#102C22×C714yes—
176C2×#97C22×C712yes—
177C2×#97C22×C712yes—
178C2×#97C22×C718yescomplemented
179C23×C7—24no—
180C23×C7—28no—
181C23×C7—24no—
182C23×C7—48no—
183C23×C7C4×D414yes—
184C23×C7C22×D412yes—
185C23×C7C22×D411yescharacteristic
186C7×Q8—28no—
187C7×Q8—24no—
188C7×Q8C23×C418yes—
189C7×D4—232no—
190C7×D4—28no—
191C7×D4—24no—
192C7×D4C23×C418yes—
193C2×C4×C7—28no—
194C2×C4×C7—28no—
195C2×C4×C7—24no—
196C2×C4×C7—232no—
197C2×C4×C7—28no—
198C2×C4×C7—48no—
199C2×C4×C7—432no—
200C2×C4×C7—48no—
201C2×C4×C7C4×D414yes—
202C2×C4×C7C4×D418yes—
203C2×C4×C7C23×C412yes—
204C2×C4×C7C23×C414yes—
205C2×C4×C7C22×D418yes—
206C2×C4×C7C22×D412yes—
207C2×C4×C7C22×D411yescharacteristic
208C2×C4×C7C2×#4112yes—
209C2×C4×C7C2×#4114yes—
210C2×C4×C7C2511yescharacteristic
211C7×C8—24no—
212C7×C8C23×C414yes—
213C7×C8C23×C414yes—
214C2×#41—24no—
215C2×#41—28no—
216C2×#41C2×C4×C7116yescomplemented
217C2×#41C23×C718yes—
218C22×Q8C23×C712yes—
219C22×D4—22no—
220C22×D4C23×C712yes—
221C23×C4—22no—
222C23×C4—24no—
223C23×C4C7×D412yes—
224C23×C4C23×C711yescharacteristic
225#135C2×C4×C7164yescomplemented
226C2×Q16C2×C4×C718yescomplemented
227C2×Q16C23×C714yes—
228C2×SD16C2×C4×C7116yescomplemented
229C2×SD16C23×C718yes—
230C2×D8C2×C4×C718yescomplemented
231C2×D8C23×C714yes—
232C22×C8—24no—
233C22×C8C2×C4×C718yescomplemented
234C22×C8C23×C712yes—
235C22×C8C23×C714yes—
236C22×C8C23×C711yescharacteristic
237C22×C8C23×C711yescharacteristic
238C22×C8C23×C714yes—
239C4×Q8—28no—
240C4×Q8C23×C7116yes—
241C4×D4—232no—
242C4×D4—28no—
243C4×D4C23×C7116yes—
244#117—24no—
245#117—216no—
246#117C23×C718yes—
247C2×C4⋊C4—24no—
248C2×C4⋊C4C23×C714yes—
249C2×C22⋊C4—22no—
250C2×C22⋊C4—24no—
251C2×C42—22no—
252C2×C42—24no—
253C2×C42—216no—
254C2×C42C7×D412yes—
255C2×C42C7×D414yes—
256C2×C42C23×C712yes—
257C2×C42C23×C714yes—
258#107C23×C718yes—
259#106C23×C718yes—
260#103C23×C7116yes—
261#102C23×C7116yes—
262#97C23×C718yes—
263#97C23×C718yes—
264C22×C7—28no—
265C22×C7—24no—
266C22×C7—28no—
267C22×C7—416no—
268C22×C7—48no—
269C22×C7C2×C4×D414yes—
270C22×C7C2×C4×D412yes—
271C22×C7#57514yes—
272C22×C7C23×D411yescharacteristic
273C4×C7—28no—
274C4×C7—28no—
275C4×C7—48no—
276C4×C7C2×C4×D414yes—
277C4×C7C2×C4×D412yes—
278C4×C7C24×C411yescharacteristic
279C4×C7C22×#4111yescharacteristic
280C24—22no—
281C24C2×C7×D411yescharacteristic
282#41—232no—
283#41—216no—
284#41C22×C4×C7132yescomplemented
285C2×Q8—22no—
286C2×Q8—24no—
287C2×Q8C22×C4×C718yes—
288C2×Q8C24×C714yes—
289C2×D4—216no—
290C2×D4—28no—
291C2×D4—22no—
292C2×D4—24no—
293C2×D4C22×C4×C718yes—
294C2×D4C24×C714yes—
295C22×C4—22no—
296C22×C4—216no—
297C22×C4—28no—
298C22×C4—24no—
299C22×C4—216no—
300C22×C4—44no—
301C22×C4—416no—
302C22×C4C22×C4×C714yes—
303C22×C4C2×C7×D414yes—
304C22×C4C2×C7×D418yes—
305C22×C4C2×C7×D411yescharacteristic
306C22×C4C2×C7×D412yes—
307C22×C4C7×#4114yes—
308C22×C4C24×C711yescharacteristic
309C22×C4C24×C712yes—
310Q16C22×C4×C7116yescomplemented
311SD16C22×C4×C7132yescomplemented
312D8C22×C4×C7116yescomplemented
313C2×C8—24no—
314C2×C8—28no—
315C2×C8C22×C4×C714yes—
316C2×C8C22×C4×C714yes—
317C2×C8C22×C4×C7116yescomplemented
318C2×C8C24×C714yes—
319C2×C8C24×C712yes—
320C2×C8C24×C712yes—
321C4⋊C4—216no—
322C4⋊C4—24no—
323C4⋊C4C24×C718yes—
324C22⋊C4—28no—
325C22⋊C4—216no—
326C42—28no—
327C42—216no—
328C42C2×C7×D418yes—
329C42C2×C7×D414yes—
330C42C24×C714yes—
331C2×C7—24no—
332C2×C7—48no—
333C2×C7#294314yesdirect product factor
334C2×C7C22×C4×D411yescharacteristic
335C2×C7C2×#57512yes—
336C23—24no—
337C23—24no—
338C23—28no—
339C23—48no—
340C23C4×C7×D414yes—
341C23C22×C7×D412yes—
342C23C22×C7×D411yescharacteristic
343Q8—24no—
344Q8—28no—
345Q8C23×C4×C718yes—
346D4—232no—
347D4—24no—
348D4—28no—
349D4C23×C4×C718yes—
350C2×C4—24no—
351C2×C4—28no—
352C2×C4—28no—
353C2×C4—232no—
354C2×C4—28no—
355C2×C4—48no—
356C2×C4—432no—
357C2×C4—48no—
358C2×C4C4×C7×D414yes—
359C2×C4C4×C7×D418yes—
360C2×C4C23×C4×C712yes—
361C2×C4C23×C4×C714yes—
362C2×C4C22×C7×D418yes—
363C2×C4C22×C7×D412yes—
364C2×C4C22×C7×D411yescharacteristic
365C2×C4C2×C7×#4112yes—
366C2×C4C2×C7×#4114yes—
367C2×C4C25×C711yescharacteristic
368C8—24no—
369C8C23×C4×C714yes—
370C8C23×C4×C714yes—
371C7C2×#294311yescharacteristic, direct product factor, Sylow
372C22—24no—
373C22—28no—
374C22—28no—
375C22—48no—
376C22—416no—
377C22C2×C4×C7×D414yes—
378C22C2×C4×C7×D412yes—
379C22C7×#57514yes—
380C22C23×C7×D411yescharacteristic
381C4—28no—
382C4—28no—
383C4—48no—
384C4C2×C4×C7×D414yes—
385C4C2×C4×C7×D412yes—
386C4C24×C4×C711yescharacteristic
387C4C22×C7×#4111yescharacteristic
388C2—24no—
389C2—48no—
390C2C7×#294314yesdirect product factor
391C2C22×C4×C7×D411yescharacteristic
392C2C2×C7×#57512yes—
subgroupG/H
centerC22×C4×C7C2×D4
commutatorC4C24×C4×C7
Frattini, cosocleC2×C4C25×C7
socleC23×C7C22×D4
prime radicalC22×C7×#135C2
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C7 ◁ C22×C42×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C7×#41C2semidirect
3. C7×#2943C2direct (N × H)
4. C2×C7×#442C2semidirect
5. C2×C7×#441C2semidirect
6. C2×C7×#440C2semidirect
7. C2×C7×#427C2semidirect
8. C2×C7×#416C2semidirect
9. C22×C7×#97C2semidirect
11. C2×C7×#135C4semidirect
19. C4×C7×#41C22semidirect
27. C7×#442C22semidirect
28. C7×#441C22semidirect
29. C7×#440C22semidirect
30. C7×#427C22semidirect
33. C7×#416C22semidirect
38. C2×C7×#97C22semidirect
39. C2×#2943C7direct (N × H)
42. C2×C7×#41C2×C4semidirect
51. C7×#135C2×C4semidirect
52. C2×C7×Q16C2×C4semidirect
54. C2×C7×SD16C2×C4semidirect
56. C2×C7×D8C2×C4semidirect
59. C22×C7×C8C2×C4semidirect
91. C2×C4×#41C2×C7semidirect
92. #2943C2×C7direct (N × H)
93. C2×#442C2×C7semidirect
94. C2×#441C2×C7semidirect
95. C2×#440C2×C7semidirect
96. C2×#427C2×C7semidirect
97. C2×#416C2×C7semidirect
98. C22×#97C2×C7semidirect
103. C7×#41C22×C4semidirect
129. C7×Q16C22×C4semidirect
130. C7×SD16C22×C4semidirect
131. C7×D8C22×C4semidirect
136. C2×C7×C8C22×C4semidirect
151. C2×#135C4×C7semidirect
159. C4×#41C22×C7semidirect
167. #442C22×C7semidirect
168. #441C22×C7semidirect
169. #440C22×C7semidirect
170. #427C22×C7semidirect
173. #416C22×C7semidirect
178. C2×#97C22×C7semidirect
216. C2×#41C2×C4×C7semidirect
225. #135C2×C4×C7semidirect
226. C2×Q16C2×C4×C7semidirect
228. C2×SD16C2×C4×C7semidirect
230. C2×D8C2×C4×C7semidirect
233. C22×C8C2×C4×C7semidirect
284. #41C22×C4×C7semidirect
310. Q16C22×C4×C7semidirect
311. SD16C22×C4×C7semidirect
312. D8C22×C4×C7semidirect
317. C2×C8C22×C4×C7semidirect
333. C2×C7#2943direct (N × H)
371. C7C2×#2943direct (N × H)
390. C2C7×#2943direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1352
C2×C4×C7×#412
C7×#29432
C2×C7×#4422
C2×C7×#4412
C2×C7×#4402
C2×C7×#4272
C2×C7×#4162
C22×C7×#972
C2×#29437