Finite Group Databasebeta

← C4×C7×#399 #13191078

Subgroups — C4×C7×#399 #13191078

Order 1792.

1966 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#399C211yesmaximal, characteristic
2C2×C4×C7×C4⋊C4C213yesmaximal, complemented
3C2×C4×C7×C22⋊C4C213yesmaximal
4C7×#1445C213yesmaximal, complemented
5C7×#1444C211yesmaximal, characteristic, complemented
6C7×#1439C213yesmaximal
7C4×C7×#95C211yesmaximal, characteristic, complemented
8C24×C4×C7C2211yescharacteristic
9C22×C7×C4⋊C4C2213yes—
10C22×C7×C4⋊C4C2213yes—
11C22×C7×C22⋊C4C2213yes—
12C22×C7×C22⋊C4C2213yes—
13C22×C42×C7C2213yes—
14C22×C42×C7C2213yes—
15C7×#399C418yesdirect product factor
16C4×C7×C4⋊C4—212no—
17C4×C7×C22⋊C4—212no—
18C2×C7×#95C2213yes—
19C2×C7×#95C2213yes—
20C2×C7×#95C2216yes—
21C2×C7×#95C2213yes—
22C2×C7×#95C2211yescharacteristic
23C4×#399C711yesmaximal, characteristic, direct product factor, Sylow
24C25×C7C2311yescharacteristic
25C23×C4×C7—26no—
26C23×C4×C7—26no—
27C23×C4×C7Q814yes—
28C23×C4×C7C2313yes—
29C23×C4×C7C2313yes—
30C23×C4×C7C2311yescharacteristic
31C23×C4×C7C2313yes—
32C23×C4×C7C2313yes—
33C23×C4×C7C2311yescharacteristic
34C2×C7×C4⋊C4—26no—
35C2×C7×C4⋊C4—26no—
36C2×C7×C4⋊C4—212no—
37C2×C7×C4⋊C4—26no—
38C2×C7×C4⋊C4C2×C4112yescomplemented
39C2×C7×C22⋊C4—26no—
40C2×C7×C22⋊C4—26no—
41C2×C7×C22⋊C4—26no—
42C2×C7×C22⋊C4—26no—
43C2×C7×C22⋊C4—26no—
44C2×C7×C22⋊C4C2×C4112yes—
45C2×C42×C7—212no—
46C2×C42×C7—26no—
47C2×C42×C7—212no—
48C2×C42×C7D4112yes—
49C7×#95—26no—
50C7×#95—26no—
51C7×#95—212no—
52C7×#95—26no—
53C7×#95C2×C414yescomplemented
54C2×#399C2×C711yescharacteristic
55C2×C4×C4⋊C4C2×C713yescomplemented
56C2×C4×C22⋊C4C2×C713yes—
57#1445C2×C713yescomplemented
58#1444C2×C711yescharacteristic, complemented
59#1439C2×C713yes—
60C4×#95C2×C711yescharacteristic, complemented
61C24×C7—23no—
62C24×C7—23no—
63C24×C7—23no—
64C24×C7—23no—
65C24×C7C22×C412yes—
66C24×C7C2×Q812yes—
67C24×C7#4112yes—
68C24×C7C2411yescharacteristic
69C22×C4×C7—26no—
70C22×C4×C7—26no—
71C22×C4×C7—23no—
72C22×C4×C7—23no—
73C22×C4×C7—23no—
74C22×C4×C7—26no—
75C22×C4×C7—26no—
76C22×C4×C7—26no—
77C22×C4×C7—26no—
78C22×C4×C7—23no—
79C22×C4×C7—23no—
80C22×C4×C7—23no—
81C22×C4×C7—23no—
82C22×C4×C7—26no—
83C22×C4×C7—26no—
84C22×C4×C7—23no—
85C22×C4×C7—224no—
86C22×C4×C7—412no—
87C22×C4×C7—44no—
88C22×C4×C7C22×C416yes—
89C22×C4×C7C22×C416yes—
90C22×C4×C7C2×D416yes—
91C22×C4×C7C2×D416yes—
92C22×C4×C7C2×D416yes—
93C22×C4×C7C2×Q812yes—
94C22×C4×C7C2×Q812yes—
95C22×C4×C7#4116yes—
96C22×C4×C7#4116yes—
97C22×C4×C7#4116yes—
98C7×C4⋊C4—224no—
99C7×C4⋊C4—224no—
100C7×C22⋊C4—224no—
101C7×C22⋊C4—224no—
102C42×C7—224no—
103C42×C7—412no—
104C24×C4C22×C711yescharacteristic
105C22×C4⋊C4C22×C713yes—
106C22×C4⋊C4C22×C713yes—
107C22×C22⋊C4C22×C713yes—
108C22×C22⋊C4C22×C713yes—
109C22×C42C22×C713yes—
110C22×C42C22×C713yes—
111#399C4×C718yesdirect product factor
112C4×C4⋊C4—212no—
113C4×C22⋊C4—212no—
114C2×#95C22×C713yes—
115C2×#95C22×C716yes—
116C2×#95C22×C713yes—
117C2×#95C22×C713yes—
118C2×#95C22×C711yescharacteristic
119C23×C7—26no—
120C23×C7—26no—
121C23×C7—26no—
122C23×C7—26no—
123C23×C7—26no—
124C23×C7—26no—
125C23×C7—43no—
126C23×C7—43no—
127C23×C7—46no—
128C23×C7—41no—
129C23×C7—43no—
130C23×C7C4×Q814yes—
131C23×C7C23×C411yescharacteristic
132C23×C7C22×D413yes—
133C23×C7C22×Q811yescharacteristic
134C23×C7C2×#4113yes—
135C23×C7C2×#4111yescharacteristic
136C23×C7C2×#4113yes—
137C23×C7C2×#4113yes—
138C2×C4×C7—212no—
139C2×C4×C7—26no—
140C2×C4×C7—26no—
141C2×C4×C7—212no—
142C2×C4×C7—26no—
143C2×C4×C7—212no—
144C2×C4×C7—26no—
145C2×C4×C7—26no—
146C2×C4×C7—26no—
147C2×C4×C7—26no—
148C2×C4×C7—212no—
149C2×C4×C7—26no—
150C2×C4×C7—43no—
151C2×C4×C7—46no—
152C2×C4×C7—43no—
153C2×C4×C7—46no—
154C2×C4×C7—46no—
155C2×C4×C7—43no—
156C2×C4×C7—43no—
157C2×C4×C7—41no—
158C2×C4×C7—43no—
159C2×C4×C7—46no—
160C2×C4×C7—416no—
161C2×C4×C7C4×D4112yes—
162C2×C4×C7C22⋊Q8112yes—
163C2×C4×C7#123112yes—
164C2×C4×C7#12714yes—
165C25C23×C711yescharacteristic
166C23×C4—26no—
167C23×C4—26no—
168C23×C4C7×Q814yes—
169C23×C4C23×C713yes—
170C23×C4C23×C713yes—
171C23×C4C23×C711yescharacteristic
172C23×C4C23×C713yes—
173C23×C4C23×C713yes—
174C23×C4C23×C711yescharacteristic
175C2×C4⋊C4—26no—
176C2×C4⋊C4—26no—
177C2×C4⋊C4—212no—
178C2×C4⋊C4—26no—
179C2×C4⋊C4C2×C4×C7112yescomplemented
180C2×C22⋊C4—26no—
181C2×C22⋊C4—26no—
182C2×C22⋊C4—26no—
183C2×C22⋊C4—26no—
184C2×C22⋊C4—26no—
185C2×C22⋊C4C2×C4×C7112yes—
186C2×C42—212no—
187C2×C42—26no—
188C2×C42—212no—
189C2×C42C7×D4112yes—
190#95—26no—
191#95—26no—
192#95—212no—
193#95—26no—
194#95C2×C4×C714yescomplemented
195C22×C7—212no—
196C22×C7—42no—
197C22×C7—42no—
198C22×C7—46no—
199C22×C7—46no—
200C22×C7—42no—
201C22×C7—46no—
202C22×C7C2×C4×D413yes—
203C22×C7C2×C4×Q811yescharacteristic
204C22×C7C4×#4113yes—
205C22×C7C2×C22⋊Q813yes—
206C22×C7C2×#12313yes—
207C22×C7#52513yes—
208C22×C7#52513yes—
209C22×C7#52913yes—
210C22×C7#52916yes—
211C22×C7C2×#12711yescharacteristic
212C22×C7#53213yes—
213C22×C7#53313yes—
214C4×C7—212no—
215C4×C7—46no—
216C4×C7—42no—
217C4×C7—46no—
218C4×C7—46no—
219C4×C7#39918yesdirect product factor
220C24—23no—
221C24—23no—
222C24—23no—
223C24—23no—
224C24C22×C4×C712yes—
225C24C2×C7×Q812yes—
226C24C7×#4112yes—
227C24C24×C711yescharacteristic
228C22×C4—26no—
229C22×C4—26no—
230C22×C4—23no—
231C22×C4—23no—
232C22×C4—23no—
233C22×C4—26no—
234C22×C4—26no—
235C22×C4—26no—
236C22×C4—26no—
237C22×C4—23no—
238C22×C4—23no—
239C22×C4—23no—
240C22×C4—23no—
241C22×C4—26no—
242C22×C4—26no—
243C22×C4—23no—
244C22×C4—224no—
245C22×C4—412no—
246C22×C4—44no—
247C22×C4C22×C4×C716yes—
248C22×C4C22×C4×C716yes—
249C22×C4C2×C7×D416yes—
250C22×C4C2×C7×D416yes—
251C22×C4C2×C7×D416yes—
252C22×C4C2×C7×Q812yes—
253C22×C4C2×C7×Q812yes—
254C22×C4C7×#4116yes—
255C22×C4C7×#4116yes—
256C22×C4C7×#4116yes—
257C4⋊C4—224no—
258C4⋊C4—224no—
259C22⋊C4—224no—
260C22⋊C4—224no—
261C42—224no—
262C42—412no—
263C2×C7—44no—
264C2×C7C4×#12313yes—
265C2×C7C4×C22⋊Q813yes—
266C2×C7C4×#12711yescharacteristic
267C2×C7C2×#39911yescharacteristic
268C2×C7#239513yes—
269C2×C7#239613yes—
270C2×C7#239711yescharacteristic
271C23—26no—
272C23—26no—
273C23—26no—
274C23—26no—
275C23—26no—
276C23—26no—
277C23—43no—
278C23—43no—
279C23—46no—
280C23—41no—
281C23—43no—
282C23C4×C7×Q814yes—
283C23C23×C4×C711yescharacteristic
284C23C22×C7×D413yes—
285C23C22×C7×Q811yescharacteristic
286C23C2×C7×#4113yes—
287C23C2×C7×#4111yescharacteristic
288C23C2×C7×#4113yes—
289C23C2×C7×#4113yes—
290C2×C4—212no—
291C2×C4—26no—
292C2×C4—26no—
293C2×C4—212no—
294C2×C4—26no—
295C2×C4—212no—
296C2×C4—26no—
297C2×C4—26no—
298C2×C4—26no—
299C2×C4—26no—
300C2×C4—212no—
301C2×C4—26no—
302C2×C4—43no—
303C2×C4—46no—
304C2×C4—43no—
305C2×C4—46no—
306C2×C4—46no—
307C2×C4—43no—
308C2×C4—43no—
309C2×C4—41no—
310C2×C4—43no—
311C2×C4—46no—
312C2×C4—416no—
313C2×C4C4×C7×D4112yes—
314C2×C4C7×C22⋊Q8112yes—
315C2×C4C7×#123112yes—
316C2×C4C7×#12714yes—
317C7C4×#39911yescharacteristic, direct product factor, Sylow
318C22—212no—
319C22—42no—
320C22—46no—
321C22—46no—
322C22—42no—
323C22—46no—
324C22—42no—
325C22C2×C4×C7×D413yes—
326C22C2×C4×C7×Q811yescharacteristic
327C22C4×C7×#4113yes—
328C22C2×C7×C22⋊Q813yes—
329C22C2×C7×#12313yes—
330C22C7×#52513yes—
331C22C7×#52513yes—
332C22C7×#52913yes—
333C22C7×#52916yes—
334C22C2×C7×#12711yescharacteristic
335C22C7×#53213yes—
336C22C7×#53313yes—
337C4—212no—
338C4—42no—
339C4—46no—
340C4—46no—
341C4—46no—
342C4C7×#39918yesdirect product factor
343C2—44no—
344C2C4×C7×#12313yes—
345C2C4×C7×C22⋊Q813yes—
346C2C4×C7×#12711yescharacteristic
347C2C2×C7×#39911yescharacteristic
348C2C7×#239513yes—
349C2C7×#239613yes—
350C2C7×#239711yescharacteristic
subgroupG/H
centerC23×C4×C7C23
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
socleC24×C7C24
prime radicalC25×C7C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C7×C4⋊C4C2semidirect
4. C7×#1445C2semidirect
5. C7×#1444C2semidirect
7. C4×C7×#95C2semidirect
15. C7×#399C4direct (N × H)
23. C4×#399C7direct (N × H)
38. C2×C7×C4⋊C4C2×C4semidirect
53. C7×#95C2×C4semidirect
55. C2×C4×C4⋊C4C2×C7semidirect
57. #1445C2×C7semidirect
58. #1444C2×C7semidirect
60. C4×#95C2×C7semidirect
111. #399C4×C7direct (N × H)
179. C2×C4⋊C4C2×C4×C7semidirect
194. #95C2×C4×C7semidirect
219. C4×C7#399direct (N × H)
317. C7C4×#399direct (N × H)
342. C4C7×#399direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3992
C2×C4×C7×C4⋊C42
C2×C4×C7×C22⋊C42
C7×#14452
C7×#14442
C7×#14392
C4×C7×#952
C4×#3997