Finite Group Databasebeta

← C2×C7×#3080 #13237699

Subgroups — C2×C7×#3080 #13237699

Order 1792.

2142 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#125C211yesmaximal, characteristic, complemented
2C2×C4×C7×#41C211yesmaximal, characteristic
3C7×#3080C2116yesmaximal, direct product factor
4C2×C7×#479C214yesmaximal, complemented
5C2×C7×#478C214yesmaximal, complemented
6C2×C7×#428C212yesmaximal, complemented
7C2×C7×#423C211yesmaximal, characteristic, complemented
8C2×C7×#417C212yesmaximal
9C22×C7×#41C2211yescharacteristic
10C22×C7×M16C2212yes—
11C2×C7×#125—21no—
12C2×C7×#125—21no—
13C2×C7×#125—24no—
14C2×C7×#125C2214yes—
15C2×C7×#125C2218yescomplemented
16C4×C7×#41—24no—
17C4×C7×#41C2218yes—
18C2×C4×C7×Q8C2212yes—
19C2×C4×C7×D4—22no—
20C2×C4×C7×D4C2212yes—
21C2×C7×#117—21no—
22C2×C7×#117C2211yescharacteristic
23C22×C7×C4⋊C4—22no—
24C22×C7×C4⋊C4C2212yes—
25C22×C42×C7—21no—
26C22×C42×C7C2211yescharacteristic
27C7×#479C22132yescomplemented
28C7×#478C22132yescomplemented
29C7×#428C22116yescomplemented
30C2×C7×#107C2214yes—
31C2×C7×#106C2214yes—
32C7×#423C2218yescomplemented
33C2×C7×C4⋊C8C2214yes—
34C7×#417C22116yes—
35C2×C7×#103C2214yes—
36C2×C7×#102C2214yes—
37C2×#3080C711yesmaximal, characteristic, direct product factor, Sylow
38C2×C7×#41—22no—
39C2×C7×#41—24no—
40C2×C7×#41Q818yes—
41C2×C7×#41C2314yes—
42C22×C7×Q8C2311yescharacteristic
43C22×C7×D4—21no—
44C22×C7×D4C2311yescharacteristic
45C23×C4×C7—21no—
46C23×C4×C7—22no—
47C23×C4×C7—22no—
48C23×C4×C7D412yes—
49C23×C4×C7C2311yescharacteristic
50C2×C7×M16—28no—
51C2×C7×M16C2318yes—
52C22×C7×C8C2314yes—
53C7×#125—28no—
54C7×#125—28no—
55C7×#125—28no—
56C7×#125C23116yes—
57C4×C7×Q8—24no—
58C4×C7×Q8C2318yes—
59C4×C7×D4—216no—
60C4×C7×D4—24no—
61C4×C7×D4C2318yes—
62C7×#117—22no—
63C7×#117—28no—
64C7×#117C2314yes—
65C2×C7×C4⋊C4—24no—
66C2×C7×C4⋊C4—24no—
67C2×C7×C4⋊C4—216no—
68C2×C7×C4⋊C4—24no—
69C2×C7×C4⋊C4—22no—
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4C2314yes—
72C2×C7×C4⋊C4C2318yes—
73C2×C7×C4⋊C4C2312yes—
74C2×C7×C22⋊C4—21no—
75C2×C7×C22⋊C4—22no—
76C2×C42×C7—21no—
77C2×C42×C7—22no—
78C2×C42×C7—28no—
79C2×C42×C7D411yescharacteristic
80C2×C42×C7D411yescharacteristic
81C2×C42×C7D414yes—
82C2×C42×C7C2312yes—
83C2×C42×C7C2314yes—
84C7×#107C23116yes—
85C7×#106C23116yes—
86C7×C4⋊C8C23116yes—
87C7×#103C23116yes—
88C7×#102C23116yes—
89C22×#125C2×C711yescharacteristic, complemented
90C2×C4×#41C2×C711yescharacteristic
91#3080C2×C7116yesdirect product factor
92C2×#479C2×C714yescomplemented
93C2×#478C2×C714yescomplemented
94C2×#428C2×C712yescomplemented
95C2×#423C2×C711yescharacteristic, complemented
96C2×#417C2×C712yes—
97C24×C7—21no—
98C24×C7C2×D411yescharacteristic
99C7×#41—216no—
100C7×#41—28no—
101C7×#41C2×Q8116yes—
102C2×C7×Q8—21no—
103C2×C7×Q8—22no—
104C2×C7×Q8C2×Q814yes—
105C2×C7×Q8C2412yes—
106C2×C7×D4—28no—
107C2×C7×D4—24no—
108C2×C7×D4—21no—
109C2×C7×D4—22no—
110C2×C7×D4C2×Q814yes—
111C2×C7×D4C2412yes—
112C22×C4×C7—21no—
113C22×C4×C7—28no—
114C22×C4×C7—24no—
115C22×C4×C7—28no—
116C22×C4×C7—22no—
117C22×C4×C7—24no—
118C22×C4×C7—28no—
119C22×C4×C7—44no—
120C22×C4×C7—48no—
121C22×C4×C7—48no—
122C22×C4×C7C2×D412yes—
123C22×C4×C7C2×D412yes—
124C22×C4×C7C2×D418yes—
125C22×C4×C7C2×D412yes—
126C22×C4×C7C2×D411yescharacteristic
127C22×C4×C7C2×Q814yes—
128C22×C4×C7#4114yes—
129C22×C4×C7C2412yes—
130C22×C4×C7C2411yescharacteristic
131C7×M16—216no—
132C2×C7×C8—28no—
133C2×C7×C8C2418yes—
134C7×C4⋊C4—216no—
135C7×C4⋊C4—216no—
136C7×C4⋊C4—28no—
137C7×C4⋊C4—24no—
138C7×C4⋊C4—28no—
139C7×C4⋊C4—22no—
140C7×C4⋊C4C2418yes—
141C7×C4⋊C4C2414yes—
142C7×C22⋊C4—24no—
143C7×C22⋊C4—28no—
144C42×C7—24no—
145C42×C7—28no—
146C42×C7C2×D414yes—
147C42×C7C2×D414yes—
148C42×C7C2×D414yes—
149C42×C7C2414yes—
150C22×#41C22×C711yescharacteristic
151C22×M16C22×C712yes—
152C2×#125—21no—
153C2×#125—24no—
154C2×#125—21no—
155C2×#125C22×C714yes—
156C2×#125C22×C718yescomplemented
157C4×#41—24no—
158C4×#41C22×C718yes—
159C2×C4×Q8C22×C712yes—
160C2×C4×D4—22no—
161C2×C4×D4C22×C712yes—
162C2×#117—21no—
163C2×#117C22×C711yescharacteristic
164C22×C4⋊C4—22no—
165C22×C4⋊C4C22×C712yes—
166C22×C42—21no—
167C22×C42C22×C711yescharacteristic
168#479C22×C7132yescomplemented
169#478C22×C7132yescomplemented
170#428C22×C7116yescomplemented
171C2×#107C22×C714yes—
172C2×#106C22×C714yes—
173#423C22×C718yescomplemented
174C2×C4⋊C8C22×C714yes—
175#417C22×C7116yes—
176C2×#103C22×C714yes—
177C2×#102C22×C714yes—
178C23×C7—24no—
179C23×C7—24no—
180C23×C7—22no—
181C23×C7—44no—
182C23×C7C22⋊Q814yes—
183C23×C7C22×D412yes—
184C23×C7C22×D411yescharacteristic
185C7×Q8—24no—
186C7×Q8—22no—
187C7×Q8C22×Q814yes—
188C7×D4—216no—
189C7×D4—24no—
190C7×D4—22no—
191C7×D4C22×Q814yes—
192C2×C4×C7—24no—
193C2×C4×C7—24no—
194C2×C4×C7—24no—
195C2×C4×C7—22no—
196C2×C4×C7—216no—
197C2×C4×C7—24no—
198C2×C4×C7—28no—
199C2×C4×C7—48no—
200C2×C4×C7—416no—
201C2×C4×C7—416no—
202C2×C4×C7—44no—
203C2×C4×C7—48no—
204C2×C4×C7C22⋊Q814yes—
205C2×C4×C7C22⋊Q818yes—
206C2×C4×C7C22×D414yes—
207C2×C4×C7C22×D414yes—
208C2×C4×C7C22×D412yes—
209C2×C4×C7C22×D411yescharacteristic
210C2×C4×C7C22×Q812yes—
211C2×C4×C7C22×Q814yes—
212C2×C4×C7C2×#4112yes—
213C2×C4×C7C2×#4114yes—
214C2×C4×C7C2511yescharacteristic
215C7×C8—28no—
216C2×#41—22no—
217C2×#41—24no—
218C2×#41C7×Q818yes—
219C2×#41C23×C714yes—
220C22×Q8C23×C711yescharacteristic
221C22×D4—21no—
222C22×D4C23×C711yescharacteristic
223C23×C4—21no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4C7×D412yes—
227C23×C4C23×C711yescharacteristic
228C2×M16—28no—
229C2×M16C23×C718yes—
230C22×C8C23×C714yes—
231#125—28no—
232#125—28no—
233#125—28no—
234#125C23×C7116yes—
235C4×Q8—24no—
236C4×Q8C23×C718yes—
237C4×D4—216no—
238C4×D4—24no—
239C4×D4C23×C718yes—
240#117—22no—
241#117—28no—
242#117C23×C714yes—
243C2×C4⋊C4—24no—
244C2×C4⋊C4—24no—
245C2×C4⋊C4—216no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—24no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4C23×C714yes—
250C2×C4⋊C4C23×C718yes—
251C2×C4⋊C4C23×C712yes—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—22no—
254C2×C42—21no—
255C2×C42—22no—
256C2×C42—28no—
257C2×C42C7×D411yescharacteristic
258C2×C42C7×D414yes—
259C2×C42C7×D411yescharacteristic
260C2×C42C23×C712yes—
261C2×C42C23×C714yes—
262#107C23×C7116yes—
263#106C23×C7116yes—
264C4⋊C8C23×C7116yes—
265#103C23×C7116yes—
266#102C23×C7116yes—
267C22×C7—28no—
268C22×C7—24no—
269C22×C7—24no—
270C22×C7—48no—
271C22×C7—44no—
272C22×C7C2×C22⋊Q814yes—
273C22×C7C2×C22⋊Q812yes—
274C22×C7#57514yes—
275C22×C7C23×D411yescharacteristic
276C4×C7—24no—
277C4×C7—24no—
278C4×C7—24no—
279C4×C7—44no—
280C4×C7—48no—
281C4×C7C2×C22⋊Q814yes—
282C4×C7C2×C22⋊Q812yes—
283C4×C7C23×Q811yescharacteristic
284C4×C7C22×#4111yescharacteristic
285C24—21no—
286C24C2×C7×D411yescharacteristic
287#41—216no—
288#41—28no—
289#41C2×C7×Q8116yes—
290C2×Q8—21no—
291C2×Q8—22no—
292C2×Q8C2×C7×Q814yes—
293C2×Q8C24×C712yes—
294C2×D4—28no—
295C2×D4—24no—
296C2×D4—21no—
297C2×D4—22no—
298C2×D4C2×C7×Q814yes—
299C2×D4C24×C712yes—
300C22×C4—21no—
301C22×C4—28no—
302C22×C4—24no—
303C22×C4—22no—
304C22×C4—28no—
305C22×C4—24no—
306C22×C4—28no—
307C22×C4—44no—
308C22×C4—48no—
309C22×C4—48no—
310C22×C4C2×C7×D412yes—
311C22×C4C2×C7×D412yes—
312C22×C4C2×C7×D418yes—
313C22×C4C2×C7×D411yescharacteristic
314C22×C4C2×C7×D412yes—
315C22×C4C2×C7×Q814yes—
316C22×C4C7×#4114yes—
317C22×C4C24×C711yescharacteristic
318C22×C4C24×C712yes—
319M16—216no—
320C2×C8—28no—
321C2×C8C24×C718yes—
322C4⋊C4—216no—
323C4⋊C4—216no—
324C4⋊C4—28no—
325C4⋊C4—24no—
326C4⋊C4—28no—
327C4⋊C4—22no—
328C4⋊C4C24×C718yes—
329C4⋊C4C24×C714yes—
330C22⋊C4—24no—
331C22⋊C4—28no—
332C42—24no—
333C42—28no—
334C42C2×C7×D414yes—
335C42C2×C7×D414yes—
336C42C2×C7×D414yes—
337C42C24×C714yes—
338C2×C7—24no—
339C2×C7—44no—
340C2×C7#308014yesdirect product factor
341C2×C7C22×C22⋊Q811yescharacteristic
342C2×C7C2×#57512yes—
343C23—24no—
344C23—22no—
345C23—24no—
346C23—44no—
347C23C7×C22⋊Q814yes—
348C23C22×C7×D412yes—
349C23C22×C7×D411yescharacteristic
350Q8—22no—
351Q8—24no—
352Q8C22×C7×Q814yes—
353D4—216no—
354D4—22no—
355D4—24no—
356D4C22×C7×Q814yes—
357C2×C4—22no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—24no—
361C2×C4—216no—
362C2×C4—24no—
363C2×C4—28no—
364C2×C4—48no—
365C2×C4—416no—
366C2×C4—416no—
367C2×C4—44no—
368C2×C4—48no—
369C2×C4C7×C22⋊Q814yes—
370C2×C4C7×C22⋊Q818yes—
371C2×C4C22×C7×D414yes—
372C2×C4C22×C7×D414yes—
373C2×C4C22×C7×D412yes—
374C2×C4C22×C7×D411yescharacteristic
375C2×C4C22×C7×Q812yes—
376C2×C4C22×C7×Q814yes—
377C2×C4C2×C7×#4112yes—
378C2×C4C2×C7×#4114yes—
379C2×C4C25×C711yescharacteristic
380C8—28no—
381C7C2×#308011yescharacteristic, direct product factor, Sylow
382C22—24no—
383C22—28no—
384C22—24no—
385C22—44no—
386C22—48no—
387C22C2×C7×C22⋊Q814yes—
388C22C2×C7×C22⋊Q812yes—
389C22C7×#57514yes—
390C22C23×C7×D411yescharacteristic
391C4—24no—
392C4—24no—
393C4—24no—
394C4—44no—
395C4—48no—
396C4C2×C7×C22⋊Q814yes—
397C4C2×C7×C22⋊Q812yes—
398C4C23×C7×Q811yescharacteristic
399C4C22×C7×#4111yescharacteristic
400C2—24no—
401C2—44no—
402C2C7×#308014yesdirect product factor
403C2C22×C7×C22⋊Q811yescharacteristic
404C2C2×C7×#57512yes—
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC2×C4C25×C7
prime radicalC22×C7×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C22×C42×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C7×#125C2semidirect
3. C7×#3080C2direct (N × H)
4. C2×C7×#479C2semidirect
5. C2×C7×#478C2semidirect
6. C2×C7×#428C2semidirect
7. C2×C7×#423C2semidirect
15. C2×C7×#125C22semidirect
27. C7×#479C22semidirect
28. C7×#478C22semidirect
29. C7×#428C22semidirect
32. C7×#423C22semidirect
37. C2×#3080C7direct (N × H)
89. C22×#125C2×C7semidirect
91. #3080C2×C7direct (N × H)
92. C2×#479C2×C7semidirect
93. C2×#478C2×C7semidirect
94. C2×#428C2×C7semidirect
95. C2×#423C2×C7semidirect
156. C2×#125C22×C7semidirect
168. #479C22×C7semidirect
169. #478C22×C7semidirect
170. #428C22×C7semidirect
173. #423C22×C7semidirect
340. C2×C7#3080direct (N × H)
381. C7C2×#3080direct (N × H)
402. C2C7×#3080direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1252
C2×C4×C7×#412
C7×#30802
C2×C7×#4792
C2×C7×#4782
C2×C7×#4282
C2×C7×#4232
C2×C7×#4172
C2×#30807