Finite Group Databasebeta

← C7×#9332 #13186548

Subgroups — C7×#9332 #13186548

Order 1792.

464 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3194C211yesmaximal, characteristic
2C7×#2978C211yesmaximal, characteristic, complemented
3C7×#1516C211yesmaximal, characteristic, complemented
4C7×#1510C211yesmaximal, characteristic, complemented
5C7×#1471C211yesmaximal, characteristic, complemented
6C7×#1306C211yesmaximal, characteristic, complemented
7C7×#1293C211yesmaximal, characteristic, complemented
8C7×#525C2211yescharacteristic
9C2×C7×#121C2211yescharacteristic
10C7×#483C411yescharacteristic, complemented
11C7×#482—21no—
12C7×#480C411yescharacteristic, complemented
13C7×#469—21no—
14C7×#468—21no—
15C7×#450C411yescharacteristic, complemented
16C7×#449—21no—
17C7×#447C411yescharacteristic, complemented
18C7×#436—21no—
19C7×#436—21no—
20C7×#435—21no—
21C7×#435—21no—
22C7×#433—21no—
23C7×#408—21no—
24C7×#407C2211yescharacteristic
25C7×#407C2211yescharacteristic
26C7×#407C2211yescharacteristic
27C2×C7×C22⋊C8C2211yescharacteristic
28C7×#381C2211yescharacteristic
29C7×#328—21no—
30C7×#327—21no—
31C7×#327—21no—
32C7×#327—21no—
33C7×#323—21no—
34C7×#323—21no—
35#9332C711yesmaximal, characteristic, direct product factor, Sylow
36C2×C7×#41D411yescharacteristic
37C22×C7×D4—21no—
38C22×C7×D4C2×C411yescharacteristic
39C23×C4×C7C2311yescharacteristic
40C2×C7×SD16—21no—
41C2×C7×D8—21no—
42C2×C7×M16—21no—
43C2×C7×M16—21no—
44C2×C7×M16—21no—
45C2×C7×M16—21no—
46C22×C7×C8—21no—
47C22×C7×C8—21no—
48C7×#123—21no—
49C7×C22⋊Q8C2×C411yescharacteristic
50C7×C22⋊Q8D411yescharacteristic
51C7×#121—21no—
52C7×#121—21no—
53C7×#121—21no—
54C7×#121—21no—
55C7×#121C2×C411yescharacteristic
56C7×#121D411yescharacteristic
57C7×#120—21no—
58C4×C7×D4—21no—
59C4×C7×D4—21no—
60C7×#117D411yescharacteristic
61C2×C7×C4⋊C4C2×C411yescharacteristic
62C2×C7×C22⋊C4—21no—
63C2×C7×C22⋊C4—21no—
64C7×#107—21no—
65C7×#106—21no—
66C7×C4⋊C8—21no—
67C7×C4⋊C8—21no—
68C7×#103—21no—
69C7×#102—21no—
70C7×#102—21no—
71C7×#102—21no—
72C7×C22⋊C8—21no—
73C7×C22⋊C8—21no—
74C7×C22⋊C8—21no—
75C7×C22⋊C8—21no—
76C7×C22⋊C8—21no—
77C7×C22⋊C8—21no—
78C7×C22⋊C8—21no—
79C7×C22⋊C8C2×C411yescharacteristic
80C7×C22⋊C8C2×C411yescharacteristic
81C7×C22⋊C8D411yescharacteristic
82C7×C22⋊C8D411yescharacteristic
83C7×C22⋊C8D411yescharacteristic
84C7×C22⋊C8D411yescharacteristic
85C7×#97—21no—
86C4×C7×C8—21no—
87C7×#95—21no—
88C7×#95—21no—
89#3194C2×C711yescharacteristic
90#2978C2×C711yescharacteristic, complemented
91#1516C2×C711yescharacteristic, complemented
92#1510C2×C711yescharacteristic, complemented
93#1471C2×C711yescharacteristic, complemented
94#1306C2×C711yescharacteristic, complemented
95#1293C2×C711yescharacteristic, complemented
96C24×C7—21no—
97C24×C7#4111yescharacteristic
98C7×#41—81no—
99C2×C7×Q8C22⋊C411yescharacteristic
100C2×C7×D4—21no—
101C2×C7×D4—21no—
102C2×C7×D4—21no—
103C2×C7×D4—21no—
104C2×C7×D4—21no—
105C2×C7×D4—41no—
106C2×C7×D4—41no—
107C2×C7×D4—81no—
108C2×C7×D4—82no—
109C2×C7×D4C22⋊C411yescharacteristic
110C22×C4×C7—21no—
111C22×C4×C7—21no—
112C22×C4×C7—41no—
113C22×C4×C7—81no—
114C22×C4×C7C22×C411yescharacteristic
115C22×C4×C7C2×D411yescharacteristic
116C22×C4×C7C2×D411yescharacteristic
117C22×C4×C7C2×D411yescharacteristic
118C22×C4×C7C2×D411yescharacteristic
119C22×C4×C7#4111yescharacteristic
120C7×SD16—81no—
121C7×D8—81no—
122C7×M16—81no—
123C7×M16—81no—
124C7×M16—81no—
125C7×M16—81no—
126C2×C7×C8—21no—
127C2×C7×C8—21no—
128C2×C7×C8—21no—
129C2×C7×C8—21no—
130C2×C7×C8—21no—
131C2×C7×C8—21no—
132C2×C7×C8—41no—
133C2×C7×C8—81no—
134C2×C7×C8—81no—
135C7×C4⋊C4—21no—
136C7×C4⋊C4—21no—
137C7×C4⋊C4—21no—
138C7×C4⋊C4—21no—
139C7×C4⋊C4C22⋊C411yescharacteristic
140C7×C4⋊C4C22⋊C411yescharacteristic
141C7×C22⋊C4—21no—
142C7×C22⋊C4—21no—
143C7×C22⋊C4—21no—
144C7×C22⋊C4—21no—
145C7×C22⋊C4—21no—
146C7×C22⋊C4—41no—
147C7×C22⋊C4—41no—
148C7×C22⋊C4—81no—
149C42×C7—21no—
150#525C22×C711yescharacteristic
151C2×#121C22×C711yescharacteristic
152#483C4×C711yescharacteristic, complemented
153#482—21no—
154#480C4×C711yescharacteristic, complemented
155#469—21no—
156#468—21no—
157#450C4×C711yescharacteristic, complemented
158#449—21no—
159#447C4×C711yescharacteristic, complemented
160#436—21no—
161#436—21no—
162#435—21no—
163#435—21no—
164#433—21no—
165#408—21no—
166#407C22×C711yescharacteristic
167#407C22×C711yescharacteristic
168#407C22×C711yescharacteristic
169C2×C22⋊C8C22×C711yescharacteristic
170#381C22×C711yescharacteristic
171#328—21no—
172#327—21no—
173#327—21no—
174#327—21no—
175#323—21no—
176#323—21no—
177C23×C7—21no—
178C23×C7—41no—
179C23×C7—41no—
180C23×C7—41no—
181C23×C7—42no—
182C23×C7—41no—
183C23×C7—81no—
184C23×C7—81no—
185C23×C7C4×D411yescharacteristic
186C23×C7#12111yescharacteristic
187C23×C7#12311yescharacteristic
188C7×Q8—41no—
189C7×D4—41no—
190C7×D4—41no—
191C7×D4—41no—
192C7×D4—81no—
193C7×D4—81no—
194C7×D4—81no—
195C7×D4—81no—
196C7×D4—82no—
197C7×D4—82no—
198C2×C4×C7—21no—
199C2×C4×C7—21no—
200C2×C4×C7—21no—
201C2×C4×C7—41no—
202C2×C4×C7—41no—
203C2×C4×C7—41no—
204C2×C4×C7—41no—
205C2×C4×C7—41no—
206C2×C4×C7—41no—
207C2×C4×C7—41no—
208C2×C4×C7—41no—
209C2×C4×C7—41no—
210C2×C4×C7—81no—
211C2×C4×C7—81no—
212C2×C4×C7—81no—
213C2×C4×C7—81no—
214C2×C4×C7C2×C22⋊C411yescharacteristic
215C2×C4×C7C4×D411yescharacteristic
216C2×C4×C7#12011yescharacteristic
217C2×C4×C7#12111yescharacteristic
218C7×C8—41no—
219C7×C8—41no—
220C7×C8—41no—
221C7×C8—41no—
222C7×C8—41no—
223C7×C8—41no—
224C7×C8—81no—
225C2×#41C7×D411yescharacteristic
226C22×D4—21no—
227C22×D4C2×C4×C711yescharacteristic
228C23×C4C23×C711yescharacteristic
229C2×SD16—21no—
230C2×D8—21no—
231C2×M16—21no—
232C2×M16—21no—
233C2×M16—21no—
234C2×M16—21no—
235C22×C8—21no—
236C22×C8—21no—
237#123—21no—
238C22⋊Q8C2×C4×C711yescharacteristic
239C22⋊Q8C7×D411yescharacteristic
240#121—21no—
241#121—21no—
242#121—21no—
243#121—21no—
244#121C2×C4×C711yescharacteristic
245#121C7×D411yescharacteristic
246#120—21no—
247C4×D4—21no—
248C4×D4—21no—
249#117C7×D411yescharacteristic
250C2×C4⋊C4C2×C4×C711yescharacteristic
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253#107—21no—
254#106—21no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257#103—21no—
258#102—21no—
259#102—21no—
260#102—21no—
261C22⋊C8—21no—
262C22⋊C8—21no—
263C22⋊C8—21no—
264C22⋊C8—21no—
265C22⋊C8—21no—
266C22⋊C8—21no—
267C22⋊C8—21no—
268C22⋊C8C2×C4×C711yescharacteristic
269C22⋊C8C2×C4×C711yescharacteristic
270C22⋊C8C7×D411yescharacteristic
271C22⋊C8C7×D411yescharacteristic
272C22⋊C8C7×D411yescharacteristic
273C22⋊C8C7×D411yescharacteristic
274#97—21no—
275C4×C8—21no—
276#95—21no—
277#95—21no—
278C22×C7—21no—
279C22×C7—21no—
280C22×C7—21no—
281C22×C7—21no—
282C22×C7—21no—
283C22×C7—21no—
284C22×C7—21no—
285C22×C7—21no—
286C22×C7—21no—
287C22×C7—41no—
288C22×C7—41no—
289C22×C7—41no—
290C22×C7—82no—
291C22×C7—81no—
292C22×C7—81no—
293C22×C7—81no—
294C22×C7—162no—
295C22×C7#38611yescharacteristic
296C4×C7—21no—
297C4×C7—21no—
298C4×C7—21no—
299C4×C7—21no—
300C4×C7—41no—
301C4×C7—41no—
302C4×C7—41no—
303C4×C7—81no—
304C4×C7—161no—
305C24—21no—
306C24C7×#4111yescharacteristic
307#41—81no—
308C2×Q8C7×C22⋊C411yescharacteristic
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—81no—
317C2×D4—82no—
318C2×D4C7×C22⋊C411yescharacteristic
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—41no—
322C22×C4—81no—
323C22×C4C22×C4×C711yescharacteristic
324C22×C4C2×C7×D411yescharacteristic
325C22×C4C2×C7×D411yescharacteristic
326C22×C4C2×C7×D411yescharacteristic
327C22×C4C2×C7×D411yescharacteristic
328C22×C4C7×#4111yescharacteristic
329SD16—81no—
330D8—81no—
331M16—81no—
332M16—81no—
333M16—81no—
334M16—81no—
335C2×C8—21no—
336C2×C8—21no—
337C2×C8—21no—
338C2×C8—21no—
339C2×C8—21no—
340C2×C8—21no—
341C2×C8—41no—
342C2×C8—81no—
343C2×C8—81no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4C7×C22⋊C411yescharacteristic
349C4⋊C4C7×C22⋊C411yescharacteristic
350C22⋊C4—21no—
351C22⋊C4—21no—
352C22⋊C4—21no—
353C22⋊C4—21no—
354C22⋊C4—21no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—81no—
358C42—21no—
359C2×C7—41no—
360C2×C7—41no—
361C2×C7—41no—
362C2×C7—81no—
363C2×C7—161no—
364C2×C7#188111yescharacteristic
365C2×C7#190311yescharacteristic
366C2×C7#191311yescharacteristic
367C23—21no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—42no—
372C23—41no—
373C23—81no—
374C23—81no—
375C23C4×C7×D411yescharacteristic
376C23C7×#12111yescharacteristic
377C23C7×#12311yescharacteristic
378Q8—41no—
379D4—41no—
380D4—41no—
381D4—41no—
382D4—81no—
383D4—81no—
384D4—81no—
385D4—81no—
386D4—82no—
387D4—82no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4C2×C7×C22⋊C411yescharacteristic
405C2×C4C4×C7×D411yescharacteristic
406C2×C4C7×#12011yescharacteristic
407C2×C4C7×#12111yescharacteristic
408C8—41no—
409C8—41no—
410C8—41no—
411C8—41no—
412C8—41no—
413C8—41no—
414C8—81no—
415C7#933211yescharacteristic, direct product factor, Sylow
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—82no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22—162no—
433C22C7×#38611yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—41no—
439C4—41no—
440C4—41no—
441C4—81no—
442C4—161no—
443C2—41no—
444C2—41no—
445C2—41no—
446C2—81no—
447C2—161no—
448C2C7×#188111yescharacteristic
449C2C7×#190311yescharacteristic
450C2C7×#191311yescharacteristic
subgroupG/H
center, socleC22×C7#386
commutatorC22×C4C22×C4×C7
Frattini, cosocleC23×C4C23×C7
prime radicalC7×#3194C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C7×#2978C2semidirect
3. C7×#1516C2semidirect
4. C7×#1510C2semidirect
5. C7×#1471C2semidirect
6. C7×#1306C2semidirect
7. C7×#1293C2semidirect
10. C7×#483C4semidirect
12. C7×#480C4semidirect
15. C7×#450C4semidirect
17. C7×#447C4semidirect
35. #9332C7direct (N × H)
90. #2978C2×C7semidirect
91. #1516C2×C7semidirect
92. #1510C2×C7semidirect
93. #1471C2×C7semidirect
94. #1306C2×C7semidirect
95. #1293C2×C7semidirect
152. #483C4×C7semidirect
154. #480C4×C7semidirect
157. #450C4×C7semidirect
159. #447C4×C7semidirect
415. C7#9332direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#31942
C7×#29782
C7×#15162
C7×#15102
C7×#14712
C7×#13062
C7×#12932
#93327