Finite Group Databasebeta

← C2×C7×#2952 #13237382

Subgroups — C2×C7×#2952 #13237382

Order 1792.

2806 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#135C211yesmaximal, characteristic
2C2×C7×#520C212yesmaximal, complemented
3C7×#2952C2116yesmaximal, direct product factor
4C2×C7×#442C212yesmaximal, complemented
5C2×C7×#441C212yesmaximal, complemented
6C2×C4×C7×SD16C214yesmaximal, complemented
7C22×C7×#106C211yesmaximal, characteristic, complemented
8C2×C7×#417C212yesmaximal, complemented
9C2×C7×#405C211yesmaximal, characteristic, complemented
10C22×C7×#41C2212yes—
11C2×C7×#135C4116yescomplemented
12C2×C7×#135C2218yes—
13C22×C7×Q16C2211yescharacteristic
14C22×C7×SD16C2212yes—
15C22×C7×D8C2211yescharacteristic
16C22×C7×M16C2211yescharacteristic
17C23×C7×C8C2211yescharacteristic
18C7×#520—28no—
19C7×#520C22116yescomplemented
20C2×C4×C7×Q8C2214yes—
21C2×C4×C7×D4—24no—
22C2×C4×C7×D4C2214yes—
23C2×C7×#117—22no—
24C2×C7×#117C2211yescharacteristic
25C22×C7×C4⋊C4—22no—
26C22×C7×C4⋊C4C2212yes—
27C7×#442C22116yescomplemented
28C7×#441C22116yescomplemented
29C4×C7×SD16C22132yescomplemented
30C2×C7×#106C2212yes—
31C2×C7×#106C2212yes—
32C2×C7×#106C2218yescomplemented
33C7×#417C22116yescomplemented
34C2×C7×#103C2214yes—
35C2×C7×#102C2214yes—
36C7×#405C2218yescomplemented
37C2×C7×#97C2212yes—
38C2×C4×C7×C8C2212yes—
39C2×#2952C711yesmaximal, 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—22no—
49C23×C4×C7—24no—
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—
58C2×C7×M16—24no—
59C2×C7×M16C2314yes—
60C22×C7×C8C2×C418yescomplemented
61C22×C7×C8C2312yes—
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—216no—
71C7×#117D414yes—
72C7×#117C2314yes—
73C2×C7×C4⋊C4—22no—
74C2×C7×C4⋊C4—24no—
75C2×C7×C4⋊C4—24no—
76C2×C7×C4⋊C4—216no—
77C2×C7×C4⋊C4D412yes—
78C2×C7×C4⋊C4C2314yes—
79C2×C7×C4⋊C4C2318yes—
80C2×C7×C22⋊C4—24no—
81C2×C7×C22⋊C4D412yes—
82C2×C42×C7—24no—
83C2×C42×C7C2312yes—
84C7×#106C2318yes—
85C7×#106C2318yes—
86C7×#103C23116yes—
87C7×#102C23116yes—
88C7×#97C2318yes—
89C4×C7×C8C2318yes—
90C22×#135C2×C711yescharacteristic
91C2×#520C2×C712yescomplemented
92#2952C2×C7116yesdirect product factor
93C2×#442C2×C712yescomplemented
94C2×#441C2×C712yescomplemented
95C2×C4×SD16C2×C714yescomplemented
96C22×#106C2×C711yescharacteristic, complemented
97C2×#417C2×C712yescomplemented
98C2×#405C2×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—28no—
119C22×C4×C7—216no—
120C22×C4×C7—88no—
121C22×C4×C7—84no—
122C22×C4×C7C22×C414yes—
123C22×C4×C7C2×D414yes—
124C22×C4×C7C2×D412yes—
125C22×C4×C7C2×D411yescharacteristic
126C22×C4×C7#4114yes—
127C22×C4×C7C2412yes—
128C22×C4×C7C2411yescharacteristic
129C7×Q16C22×C4116yescomplemented
130C7×SD16C22×C4132yescomplemented
131C7×D8C22×C4116yescomplemented
132C7×M16—28no—
133C2×C7×C8—24no—
134C2×C7×C8C22×C414yes—
135C2×C7×C8C22×C414yes—
136C2×C7×C8C22×C4116yescomplemented
137C2×C7×C8C2414yes—
138C2×C7×C8C2412yes—
139C2×C7×C8C2412yes—
140C7×C4⋊C4—28no—
141C7×C4⋊C4—216no—
142C7×C4⋊C4—24no—
143C7×C4⋊C4C2×D418yes—
144C7×C4⋊C4C2418yes—
145C7×C22⋊C4—216no—
146C7×C22⋊C4C2×D418yes—
147C42×C7—216no—
148C42×C7C2×D414yes—
149C42×C7C2414yes—
150C22×#41C22×C712yes—
151C2×#135C4×C7116yescomplemented
152C2×#135C22×C718yes—
153C22×Q16C22×C711yescharacteristic
154C22×SD16C22×C712yes—
155C22×D8C22×C711yescharacteristic
156C22×M16C22×C711yescharacteristic
157C23×C8C22×C711yescharacteristic
158#520—28no—
159#520C22×C7116yescomplemented
160C2×C4×Q8C22×C714yes—
161C2×C4×D4—24no—
162C2×C4×D4C22×C714yes—
163C2×#117—22no—
164C2×#117C22×C711yescharacteristic
165C22×C4⋊C4—22no—
166C22×C4⋊C4C22×C712yes—
167#442C22×C7116yescomplemented
168#441C22×C7116yescomplemented
169C4×SD16C22×C7132yescomplemented
170C2×#106C22×C712yes—
171C2×#106C22×C712yes—
172C2×#106C22×C718yescomplemented
173#417C22×C7116yescomplemented
174C2×#103C22×C714yes—
175C2×#102C22×C714yes—
176#405C22×C718yescomplemented
177C2×#97C22×C712yes—
178C2×C4×C8C22×C712yes—
179C23×C7—24no—
180C23×C7—28no—
181C23×C7—24no—
182C23×C7—44no—
183C23×C7—44no—
184C23×C7C4×D414yes—
185C23×C7C22×D412yes—
186C23×C7C22×D411yescharacteristic
187C7×Q8—28no—
188C7×Q8—24no—
189C7×Q8C23×C418yes—
190C7×D4—232no—
191C7×D4—28no—
192C7×D4—24no—
193C7×D4C23×C418yes—
194C2×C4×C7—28no—
195C2×C4×C7—28no—
196C2×C4×C7—24no—
197C2×C4×C7—232no—
198C2×C4×C7—28no—
199C2×C4×C7—48no—
200C2×C4×C7—816no—
201C2×C4×C7—88no—
202C2×C4×C7C4×D414yes—
203C2×C4×C7C4×D418yes—
204C2×C4×C7C23×C412yes—
205C2×C4×C7C23×C414yes—
206C2×C4×C7C22×D418yes—
207C2×C4×C7C22×D411yescharacteristic
208C2×C4×C7C22×D412yes—
209C2×C4×C7C2×#4112yes—
210C2×C4×C7C2×#4114yes—
211C2×C4×C7C2511yescharacteristic
212C7×C8—24no—
213C7×C8C23×C414yes—
214C7×C8C23×C414yes—
215C2×#41—24no—
216C2×#41—28no—
217C2×#41C2×C4×C7116yescomplemented
218C2×#41C23×C718yes—
219C22×Q8C23×C712yes—
220C22×D4—22no—
221C22×D4C23×C712yes—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—24no—
225C23×C4C23×C711yescharacteristic
226#135C2×C4×C7164yescomplemented
227C2×Q16C2×C4×C718yescomplemented
228C2×Q16C23×C714yes—
229C2×SD16C2×C4×C7116yescomplemented
230C2×SD16C23×C718yes—
231C2×D8C2×C4×C718yescomplemented
232C2×D8C23×C714yes—
233C2×M16—24no—
234C2×M16C23×C714yes—
235C22×C8C2×C4×C718yescomplemented
236C22×C8C23×C712yes—
237C22×C8C23×C711yescharacteristic
238C22×C8C23×C711yescharacteristic
239C22×C8C23×C714yes—
240C4×Q8—28no—
241C4×Q8C23×C7116yes—
242C4×D4—232no—
243C4×D4—28no—
244C4×D4C23×C7116yes—
245#117—216no—
246#117C7×D414yes—
247#117C23×C714yes—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—24no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—216no—
252C2×C4⋊C4C7×D412yes—
253C2×C4⋊C4C23×C714yes—
254C2×C4⋊C4C23×C718yes—
255C2×C22⋊C4—24no—
256C2×C22⋊C4C7×D412yes—
257C2×C42—24no—
258C2×C42C23×C712yes—
259#106C23×C718yes—
260#106C23×C718yes—
261#103C23×C7116yes—
262#102C23×C7116yes—
263#97C23×C718yes—
264C4×C8C23×C718yes—
265C22×C7—28no—
266C22×C7—24no—
267C22×C7—28no—
268C22×C7—416no—
269C22×C7—44no—
270C22×C7—44no—
271C22×C7C2×C4×D414yes—
272C22×C7C2×C4×D412yes—
273C22×C7#57714yes—
274C22×C7C23×D411yescharacteristic
275C4×C7—28no—
276C4×C7—28no—
277C4×C7—48no—
278C4×C7C2×C4×D414yes—
279C4×C7C2×C4×D412yes—
280C4×C7C24×C411yescharacteristic
281C4×C7C22×#4111yescharacteristic
282C24—22no—
283C24C2×C7×D411yescharacteristic
284#41—232no—
285#41—216no—
286#41C22×C4×C7132yescomplemented
287C2×Q8—22no—
288C2×Q8—24no—
289C2×Q8C22×C4×C718yes—
290C2×Q8C24×C714yes—
291C2×D4—216no—
292C2×D4—28no—
293C2×D4—22no—
294C2×D4—24no—
295C2×D4C22×C4×C718yes—
296C2×D4C24×C714yes—
297C22×C4—22no—
298C22×C4—216no—
299C22×C4—28no—
300C22×C4—24no—
301C22×C4—28no—
302C22×C4—216no—
303C22×C4—88no—
304C22×C4—84no—
305C22×C4C22×C4×C714yes—
306C22×C4C2×C7×D414yes—
307C22×C4C2×C7×D411yescharacteristic
308C22×C4C2×C7×D412yes—
309C22×C4C7×#4114yes—
310C22×C4C24×C711yescharacteristic
311C22×C4C24×C712yes—
312Q16C22×C4×C7116yescomplemented
313SD16C22×C4×C7132yescomplemented
314D8C22×C4×C7116yescomplemented
315M16—28no—
316C2×C8—24no—
317C2×C8C22×C4×C714yes—
318C2×C8C22×C4×C714yes—
319C2×C8C22×C4×C7116yescomplemented
320C2×C8C24×C714yes—
321C2×C8C24×C712yes—
322C2×C8C24×C712yes—
323C4⋊C4—28no—
324C4⋊C4—216no—
325C4⋊C4—24no—
326C4⋊C4C2×C7×D418yes—
327C4⋊C4C24×C718yes—
328C22⋊C4—216no—
329C22⋊C4C2×C7×D418yes—
330C42—216no—
331C42C2×C7×D414yes—
332C42C24×C714yes—
333C2×C7—24no—
334C2×C7—48no—
335C2×C7#295214yesdirect product factor
336C2×C7C22×C4×D411yescharacteristic
337C2×C7C2×#57712yes—
338C23—24no—
339C23—24no—
340C23—28no—
341C23—44no—
342C23—44no—
343C23C4×C7×D414yes—
344C23C22×C7×D412yes—
345C23C22×C7×D411yescharacteristic
346Q8—24no—
347Q8—28no—
348Q8C23×C4×C718yes—
349D4—232no—
350D4—24no—
351D4—28no—
352D4C23×C4×C718yes—
353C2×C4—24no—
354C2×C4—28no—
355C2×C4—28no—
356C2×C4—232no—
357C2×C4—28no—
358C2×C4—48no—
359C2×C4—816no—
360C2×C4—88no—
361C2×C4C4×C7×D414yes—
362C2×C4C4×C7×D418yes—
363C2×C4C23×C4×C712yes—
364C2×C4C23×C4×C714yes—
365C2×C4C22×C7×D418yes—
366C2×C4C22×C7×D411yescharacteristic
367C2×C4C22×C7×D412yes—
368C2×C4C2×C7×#4112yes—
369C2×C4C2×C7×#4114yes—
370C2×C4C25×C711yescharacteristic
371C8—24no—
372C8C23×C4×C714yes—
373C8C23×C4×C714yes—
374C7C2×#295211yescharacteristic, direct product factor, Sylow
375C22—24no—
376C22—28no—
377C22—28no—
378C22—44no—
379C22—44no—
380C22—416no—
381C22C2×C4×C7×D414yes—
382C22C2×C4×C7×D412yes—
383C22C7×#57714yes—
384C22C23×C7×D411yescharacteristic
385C4—28no—
386C4—28no—
387C4—48no—
388C4C2×C4×C7×D414yes—
389C4C2×C4×C7×D412yes—
390C4C24×C4×C711yescharacteristic
391C4C22×C7×#4111yescharacteristic
392C2—24no—
393C2—48no—
394C2C7×#295214yesdirect product factor
395C2C22×C4×C7×D411yescharacteristic
396C2C2×C7×#57712yes—
subgroupG/H
center, socleC23×C7C22×D4
commutatorC4C24×C4×C7
Frattini, cosocleC2×C4C25×C7
prime radicalC22×C7×#135C2
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C2×C7×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#520C2semidirect
3. C7×#2952C2direct (N × H)
4. C2×C7×#442C2semidirect
5. C2×C7×#441C2semidirect
6. C2×C4×C7×SD16C2semidirect
7. C22×C7×#106C2semidirect
8. C2×C7×#417C2semidirect
9. C2×C7×#405C2semidirect
11. C2×C7×#135C4semidirect
19. C7×#520C22semidirect
27. C7×#442C22semidirect
28. C7×#441C22semidirect
29. C4×C7×SD16C22semidirect
32. C2×C7×#106C22semidirect
33. C7×#417C22semidirect
36. C7×#405C22semidirect
39. C2×#2952C7direct (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
60. C22×C7×C8C2×C4semidirect
91. C2×#520C2×C7semidirect
92. #2952C2×C7direct (N × H)
93. C2×#442C2×C7semidirect
94. C2×#441C2×C7semidirect
95. C2×C4×SD16C2×C7semidirect
96. C22×#106C2×C7semidirect
97. C2×#417C2×C7semidirect
98. C2×#405C2×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. #520C22×C7semidirect
167. #442C22×C7semidirect
168. #441C22×C7semidirect
169. C4×SD16C22×C7semidirect
172. C2×#106C22×C7semidirect
173. #417C22×C7semidirect
176. #405C22×C7semidirect
217. C2×#41C2×C4×C7semidirect
226. #135C2×C4×C7semidirect
227. C2×Q16C2×C4×C7semidirect
229. C2×SD16C2×C4×C7semidirect
231. C2×D8C2×C4×C7semidirect
235. C22×C8C2×C4×C7semidirect
286. #41C22×C4×C7semidirect
312. Q16C22×C4×C7semidirect
313. SD16C22×C4×C7semidirect
314. D8C22×C4×C7semidirect
319. C2×C8C22×C4×C7semidirect
335. C2×C7#2952direct (N × H)
374. C7C2×#2952direct (N × H)
394. C2C7×#2952direct (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×C7×#5202
C7×#29522
C2×C7×#4422
C2×C7×#4412
C2×C4×C7×SD162
C22×C7×#1062
C2×C7×#4172
C2×C7×#4052
C2×#29527