Finite Group Databasebeta

← C7×#10060 #13187276

Subgroups — C7×#10060 #13187276

Order 1792.

638 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#487C211yesmaximal, characteristic, complemented
2C2×C7×#476C211yesmaximal, characteristic
3C7×#2542C211yesmaximal, characteristic
4C7×#1987C211yesmaximal, characteristic, complemented
5C2×C7×#332C211yesmaximal, characteristic, complemented
6C2×C7×D4⋊C8C211yesmaximal, characteristic
7C7×#1279C211yesmaximal, characteristic, complemented
8C2×C7×C4⋊Q8C2211yescharacteristic
9C2×C7×C4⋊Q8C2211yescharacteristic
10C2×C7×C22⋊Q8—22no—
11C2×C4×C7×D4C2211yescharacteristic
12C7×#487—22no—
13C7×#487—22no—
14C7×#476—22no—
15C7×#476—22no—
16C2×C7×#106—21no—
17C2×C7×C4⋊C8C2211yescharacteristic
18C2×C7×C4⋊C8C2211yescharacteristic
19C2×C7×#103—22no—
20C2×C7×#102—21no—
21C2×C4×C7×C8C2211yescharacteristic
22C7×#399—22no—
23C7×#390—21no—
24C7×#384—21no—
25C4×C7×C4⋊C4C2211yescharacteristic
26C7×#340—22no—
27C7×#332—22no—
28C7×D4⋊C8—22no—
29#10060C711yesmaximal, characteristic, direct product factor, Sylow
30C22×C7×Q8—21no—
31C22×C7×Q8—21no—
32C22×C7×D4D411yescharacteristic
33C23×C4×C7—21no—
34C22×C7×C8—21no—
35C22×C7×C8—21no—
36C22×C7×C8—21no—
37C7×C4⋊Q8—21no—
38C7×C4⋊Q8—21no—
39C7×C4⋊Q8—21no—
40C7×C4⋊Q8—21no—
41C7×C4⋊Q8—21no—
42C7×C4⋊Q8—21no—
43C7×C4⋊Q8—21no—
44C7×C4⋊Q8D412yes—
45C7×C22⋊Q8—44no—
46C7×C22⋊Q8—44no—
47C4×C7×D4—21no—
48C4×C7×D4—21no—
49C4×C7×D4—21no—
50C4×C7×D4—21no—
51C2×C7×C4⋊C4—21no—
52C2×C7×C4⋊C4—21no—
53C2×C7×C4⋊C4—24no—
54C2×C7×C4⋊C4—21no—
55C2×C7×C4⋊C4D411yescharacteristic
56C2×C7×C4⋊C4D412yes—
57C2×C7×C4⋊C4D412yes—
58C2×C7×C22⋊C4—24no—
59C2×C7×C22⋊C4—21no—
60C2×C42×C7—21no—
61C2×C42×C7C2311yescharacteristic
62C7×#106—24no—
63C7×C4⋊C8—21no—
64C7×C4⋊C8—21no—
65C7×C4⋊C8—21no—
66C7×C4⋊C8D412yes—
67C7×#103—28no—
68C7×#102—24no—
69C4×C7×C8—21no—
70C4×C7×C8D412yes—
71C7×#95—21no—
72C2×#487C2×C711yescharacteristic, complemented
73C2×#476C2×C711yescharacteristic
74#2542C2×C711yescharacteristic
75#1987C2×C711yescharacteristic, complemented
76C2×#332C2×C711yescharacteristic, complemented
77C2×D4⋊C8C2×C711yescharacteristic
78#1279C2×C711yescharacteristic, complemented
79C24×C7—21no—
80C2×C7×Q8—22no—
81C2×C7×Q8—44no—
82C2×C7×Q8—41no—
83C2×C7×Q8—41no—
84C2×C7×Q8—41no—
85C2×C7×Q8—42no—
86C2×C7×Q8—42no—
87C2×C7×D4—21no—
88C2×C7×D4—21no—
89C2×C7×D4—21no—
90C2×C7×D4—21no—
91C2×C7×D4—21no—
92C2×C7×D4Q1612yes—
93C22×C4×C7—22no—
94C22×C4×C7—22no—
95C22×C4×C7—21no—
96C22×C4×C7—41no—
97C22×C4×C7—41no—
98C22×C4×C7—41no—
99C22×C4×C7—42no—
100C22×C4×C7—42no—
101C22×C4×C7C2×D411yescharacteristic
102C22×C4×C7C2×D411yescharacteristic
103C22×C4×C7C2×D411yescharacteristic
104C2×C7×C8—22no—
105C2×C7×C8—22no—
106C2×C7×C8—42no—
107C2×C7×C8—41no—
108C2×C7×C8—41no—
109C2×C7×C8—41no—
110C2×C7×C8—42no—
111C7×C4⋊C4—22no—
112C7×C4⋊C4—22no—
113C7×C4⋊C4—22no—
114C7×C4⋊C4—21no—
115C7×C4⋊C4—22no—
116C7×C4⋊C4—21no—
117C7×C4⋊C4—22no—
118C7×C4⋊C4—48no—
119C7×C4⋊C4—41no—
120C7×C4⋊C4—41no—
121C7×C4⋊C4—41no—
122C7×C4⋊C4—41no—
123C7×C4⋊C4SD1614yes—
124C7×C22⋊C4—48no—
125C7×C22⋊C4—41no—
126C7×C22⋊C4—41no—
127C42×C7—41no—
128C42×C7—41no—
129C42×C7C2×D411yescharacteristic
130C42×C7C2×D411yescharacteristic
131C42×C7C2×D411yescharacteristic
132C42×C7#4111yescharacteristic
133C2×C4⋊Q8C22×C711yescharacteristic
134C2×C4⋊Q8C22×C711yescharacteristic
135C2×C22⋊Q8—22no—
136C2×C4×D4C22×C711yescharacteristic
137#487—22no—
138#487—22no—
139#476—22no—
140#476—22no—
141C2×#106—21no—
142C2×C4⋊C8C22×C711yescharacteristic
143C2×C4⋊C8C22×C711yescharacteristic
144C2×#103—22no—
145C2×#102—21no—
146C2×C4×C8C22×C711yescharacteristic
147#399—22no—
148#390—21no—
149#384—21no—
150C4×C4⋊C4C22×C711yescharacteristic
151#340—22no—
152#332—22no—
153D4⋊C8—22no—
154C23×C7—22no—
155C23×C7—41no—
156C23×C7—42no—
157C23×C7—41no—
158C23×C7—42no—
159C23×C7#12011yescharacteristic
160C7×Q8—44no—
161C7×Q8—82no—
162C7×Q8—82no—
163C7×Q8—81no—
164C7×Q8—81no—
165C7×D4—22no—
166C7×D4—22no—
167C7×D4—41no—
168C7×D4—41no—
169C2×C4×C7—22no—
170C2×C4×C7—24no—
171C2×C4×C7—42no—
172C2×C4×C7—42no—
173C2×C4×C7—41no—
174C2×C4×C7—42no—
175C2×C4×C7—42no—
176C2×C4×C7—44no—
177C2×C4×C7—42no—
178C2×C4×C7—82no—
179C2×C4×C7—82no—
180C2×C4×C7—81no—
181C2×C4×C7—81no—
182C2×C4×C7#12011yescharacteristic
183C2×C4×C7#12011yescharacteristic
184C2×C4×C7#12111yescharacteristic
185C2×C4×C7#12111yescharacteristic
186C2×C4×C7#12111yescharacteristic
187C2×C4×C7#12711yescharacteristic
188C2×C4×C7C2×SD1612yes—
189C2×C4×C7C2×Q1611yescharacteristic
190C2×C4×C7#13511yescharacteristic
191C2×C4×C7AGL(1,ℤ/8)12yes—
192C2×C4×C7#13711yescharacteristic
193C2×C4×C7#13711yescharacteristic
194C7×C8—42no—
195C7×C8—42no—
196C7×C8—81no—
197C22×Q8—21no—
198C22×Q8—21no—
199C22×D4C7×D411yescharacteristic
200C23×C4—21no—
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8C7×D412yes—
212C22⋊Q8—44no—
213C22⋊Q8—44no—
214C4×D4—21no—
215C4×D4—21no—
216C4×D4—21no—
217C4×D4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—24no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4C7×D411yescharacteristic
223C2×C4⋊C4C7×D412yes—
224C2×C4⋊C4C7×D412yes—
225C2×C22⋊C4—24no—
226C2×C22⋊C4—21no—
227C2×C42—21no—
228C2×C42C23×C711yescharacteristic
229#106—24no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8C7×D412yes—
234#103—28no—
235#102—24no—
236C4×C8—21no—
237C4×C8C7×D412yes—
238#95—21no—
239C22×C7—44no—
240C22×C7—42no—
241C22×C7—82no—
242C22×C7—81no—
243C22×C7—81no—
244C22×C7#39211yescharacteristic
245C22×C7#45012yes—
246C22×C7#45111yescharacteristic
247C22×C7#45211yescharacteristic
248C22×C7#45412yes—
249C4×C7—21no—
250C4×C7—21no—
251C4×C7—44no—
252C4×C7—82no—
253C4×C7—81no—
254C4×C7—82no—
255C4×C7#45111yescharacteristic
256C4×C7#45211yescharacteristic
257C4×C7#46012yes—
258C4×C7#46711yescharacteristic
259C4×C7#47011yescharacteristic
260C4×C7#49211yescharacteristic
261C4×C7#49611yescharacteristic
262C24—21no—
263C2×Q8—22no—
264C2×Q8—44no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×Q8—41no—
268C2×Q8—42no—
269C2×Q8—42no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4C7×Q1612yes—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—21no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4C2×C7×D411yescharacteristic
285C22×C4C2×C7×D411yescharacteristic
286C22×C4C2×C7×D411yescharacteristic
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—42no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—42no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—22no—
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—48no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4C7×SD1614yes—
307C22⋊C4—48no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C42—41no—
311C42—41no—
312C42C2×C7×D411yescharacteristic
313C42C2×C7×D411yescharacteristic
314C42C2×C7×D411yescharacteristic
315C42C7×#4111yescharacteristic
316C2×C7—82no—
317C2×C7#163512yes—
318C2×C7#163712yes—
319C2×C7#200111yescharacteristic
320C2×C7#200311yescharacteristic
321C2×C7#201411yescharacteristic
322C23—22no—
323C23—41no—
324C23—42no—
325C23—41no—
326C23—42no—
327C23C7×#12011yescharacteristic
328Q8—44no—
329Q8—82no—
330Q8—81no—
331Q8—81no—
332Q8—82no—
333D4—22no—
334D4—22no—
335D4—41no—
336D4—41no—
337C2×C4—22no—
338C2×C4—24no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—44no—
345C2×C4—42no—
346C2×C4—82no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—82no—
350C2×C4C7×#12011yescharacteristic
351C2×C4C7×#12011yescharacteristic
352C2×C4C7×#12111yescharacteristic
353C2×C4C7×#12111yescharacteristic
354C2×C4C7×#12111yescharacteristic
355C2×C4C7×#12711yescharacteristic
356C2×C4C2×C7×SD1612yes—
357C2×C4C2×C7×Q1611yescharacteristic
358C2×C4C7×#13511yescharacteristic
359C2×C4C7×AGL(1,ℤ/8)12yes—
360C2×C4C7×#13711yescharacteristic
361C2×C4C7×#13711yescharacteristic
362C8—42no—
363C8—42no—
364C8—81no—
365C7#1006011yescharacteristic, direct product factor, Sylow
366C22—42no—
367C22—44no—
368C22—81no—
369C22—81no—
370C22—82no—
371C22C7×#39211yescharacteristic
372C22C7×#45012yes—
373C22C7×#45111yescharacteristic
374C22C7×#45211yescharacteristic
375C22C7×#45412yes—
376C4—21no—
377C4—21no—
378C4—44no—
379C4—82no—
380C4—81no—
381C4—82no—
382C4C7×#45111yescharacteristic
383C4C7×#45211yescharacteristic
384C4C7×#46012yes—
385C4C7×#46711yescharacteristic
386C4C7×#47011yescharacteristic
387C4C7×#49211yescharacteristic
388C4C7×#49611yescharacteristic
389C2—82no—
390C2C7×#163512yes—
391C2C7×#163712yes—
392C2C7×#200111yescharacteristic
393C2C7×#200311yescharacteristic
394C2C7×#201411yescharacteristic
subgroupG/H
center, socleC23×C7#120
commutator, Frattini, cosocleC2×C42C23×C7
prime radicalC22×C7×D4D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C7 ◁ C2×C42×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C7×#487C2semidirect
4. C7×#1987C2semidirect
5. C2×C7×#332C2semidirect
7. C7×#1279C2semidirect
29. #10060C7direct (N × H)
72. C2×#487C2×C7semidirect
75. #1987C2×C7semidirect
76. C2×#332C2×C7semidirect
78. #1279C2×C7semidirect
365. C7#10060direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#4872
C2×C7×#4762
C7×#25422
C7×#19872
C2×C7×#3322
C2×C7×D4⋊C82
C7×#12792
#100607