Finite Group Databasebeta

← C7×#9275 #13186491

Subgroups — C7×#9275 #13186491

Order 1792.

606 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3187C211yesmaximal, characteristic
2C7×#2364C211yesmaximal, characteristic
3C7×#1996C211yesmaximal, characteristic, complemented
4C7×#1519C211yesmaximal, characteristic
5C2×C7×#328C211yesmaximal, characteristic, complemented
6C7×#1294C211yesmaximal, characteristic, complemented
7C7×#1282C211yesmaximal, characteristic, complemented
8C2×C7×C22⋊Q8C2211yescharacteristic
9C2×C7×#121C2211yescharacteristic
10C2×C4×C7×D4—21no—
11C7×#483—21no—
12C7×#481C412yescomplemented
13C7×#465—22no—
14C7×#450—21no—
15C7×#448C412yescomplemented
16C2×C7×C22⋊C8C2211yescharacteristic
17C2×C7×C22⋊C8C2211yescharacteristic
18C7×#388—21no—
19C7×#387—21no—
20C7×#386—21no—
21C7×#386—21no—
22C7×#380C2211yescharacteristic
23C4×C7×C22⋊C4—21no—
24C4×C7×C22⋊C4C2211yescharacteristic
25C2×C7×#95C2211yescharacteristic
26C7×#342—21no—
27C7×#342—21no—
28C7×#328—21no—
29C7×#328—21no—
30C7×#327—22no—
31#9275C711yesmaximal, characteristic, direct product factor, Sylow
32C22×C7×Q8C2×C411yescharacteristic, complemented
33C22×C7×D4—21no—
34C22×C7×D4D411yescharacteristic
35C23×C4×C7—21no—
36C23×C4×C7—21no—
37C23×C4×C7C2311yescharacteristic
38C2×C7×SD16—22no—
39C22×C7×C8—21no—
40C22×C7×C8—21no—
41C7×C22⋊Q8—21no—
42C7×C22⋊Q8—21no—
43C7×C22⋊Q8—21no—
44C7×C22⋊Q8—21no—
45C7×#121—21no—
46C7×#121—21no—
47C7×#121C2×C412yes—
48C7×#121D412yes—
49C4×C7×D4—42no—
50C4×C7×D4—42no—
51C2×C7×C4⋊C4—21no—
52C2×C7×C4⋊C4—21no—
53C2×C7×C4⋊C4—21no—
54C2×C7×C4⋊C4C2×C411yescharacteristic, complemented
55C2×C7×C4⋊C4D411yescharacteristic
56C2×C7×C22⋊C4—21no—
57C2×C7×C22⋊C4—21no—
58C2×C7×C22⋊C4—21no—
59C2×C7×C22⋊C4—21no—
60C2×C7×C22⋊C4—21no—
61C2×C7×C22⋊C4—21no—
62C2×C7×C22⋊C4D411yescharacteristic
63C2×C7×C22⋊C4D411yescharacteristic
64C2×C42×C7—21no—
65C2×C42×C7—21no—
66C7×#106—22no—
67C7×#103—22no—
68C7×#102—22no—
69C7×C22⋊C8—21no—
70C7×C22⋊C8—21no—
71C7×C22⋊C8—21no—
72C7×C22⋊C8C2×C412yescomplemented
73C7×#95—21no—
74C7×#95—21no—
75C7×#95—21no—
76C7×#95—21no—
77C7×#95—21no—
78C7×#95D411yescharacteristic
79C7×#95D411yescharacteristic
80#3187C2×C711yescharacteristic
81#2364C2×C711yescharacteristic
82#1996C2×C711yescharacteristic, complemented
83#1519C2×C711yescharacteristic
84C2×#328C2×C711yescharacteristic, complemented
85#1294C2×C711yescharacteristic, complemented
86#1282C2×C711yescharacteristic, complemented
87C24×C7—21no—
88C24×C7C2×D411yescharacteristic
89C2×C7×Q8—21no—
90C2×C7×Q8—21no—
91C2×C7×Q8—81no—
92C2×C7×D4—22no—
93C2×C7×D4—22no—
94C2×C7×D4—21no—
95C2×C7×D4—41no—
96C2×C7×D4—41no—
97C2×C7×D4—41no—
98C2×C7×D4—41no—
99C2×C7×D4—81no—
100C2×C7×D4C22⋊C412yes—
101C22×C4×C7—21no—
102C22×C4×C7—21no—
103C22×C4×C7—21no—
104C22×C4×C7—21no—
105C22×C4×C7—21no—
106C22×C4×C7—21no—
107C22×C4×C7—21no—
108C22×C4×C7—42no—
109C22×C4×C7—42no—
110C22×C4×C7—42no—
111C22×C4×C7—41no—
112C22×C4×C7—41no—
113C22×C4×C7—41no—
114C22×C4×C7—81no—
115C22×C4×C7—81no—
116C22×C4×C7—81no—
117C22×C4×C7C22×C411yescharacteristic
118C22×C4×C7C2×D411yescharacteristic
119C22×C4×C7C2×D411yescharacteristic
120C22×C4×C7C2×D411yescharacteristic
121C22×C4×C7#4111yescharacteristic
122C22×C4×C7#4111yescharacteristic
123C7×SD16—82no—
124C2×C7×C8—22no—
125C2×C7×C8—41no—
126C2×C7×C8—81no—
127C2×C7×C8—81no—
128C7×C4⋊C4—21no—
129C7×C4⋊C4—21no—
130C7×C4⋊C4—21no—
131C7×C4⋊C4—42no—
132C7×C4⋊C4—41no—
133C7×C4⋊C4—41no—
134C7×C4⋊C4—81no—
135C7×C4⋊C4C22⋊C412yes—
136C7×C22⋊C4—21no—
137C7×C22⋊C4—22no—
138C7×C22⋊C4—22no—
139C7×C22⋊C4—21no—
140C7×C22⋊C4—21no—
141C7×C22⋊C4—42no—
142C7×C22⋊C4—42no—
143C7×C22⋊C4—41no—
144C7×C22⋊C4—41no—
145C7×C22⋊C4—41no—
146C7×C22⋊C4—41no—
147C7×C22⋊C4—81no—
148C7×C22⋊C4SD1612yescomplemented
149C42×C7—42no—
150C42×C7—81no—
151C2×C22⋊Q8C22×C711yescharacteristic
152C2×#121C22×C711yescharacteristic
153C2×C4×D4—21no—
154#483—21no—
155#481C4×C712yescomplemented
156#465—22no—
157#450—21no—
158#448C4×C712yescomplemented
159C2×C22⋊C8C22×C711yescharacteristic
160C2×C22⋊C8C22×C711yescharacteristic
161#388—21no—
162#387—21no—
163#386—21no—
164#386—21no—
165#380C22×C711yescharacteristic
166C4×C22⋊C4—21no—
167C4×C22⋊C4C22×C711yescharacteristic
168C2×#95C22×C711yescharacteristic
169#342—21no—
170#342—21no—
171#328—21no—
172#328—21no—
173#327—22no—
174C23×C7—22no—
175C23×C7—41no—
176C23×C7—41no—
177C23×C7—41no—
178C23×C7—41no—
179C23×C7—41no—
180C23×C7—41no—
181C23×C7—41no—
182C23×C7—41no—
183C23×C7C4×D411yescharacteristic
184C23×C7#12011yescharacteristic
185C23×C7#12111yescharacteristic
186C23×C7C2×SD1611yescharacteristic
187C23×C7#13511yescharacteristic
188C23×C7AGL(1,ℤ/8)11yescharacteristic
189C23×C7#13711yescharacteristic
190C7×Q8—42no—
191C7×Q8—81no—
192C7×D4—42no—
193C7×D4—42no—
194C7×D4—42no—
195C7×D4—42no—
196C7×D4—42no—
197C7×D4—81no—
198C2×C4×C7—22no—
199C2×C4×C7—22no—
200C2×C4×C7—22no—
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—41no—
211C2×C4×C7—41no—
212C2×C4×C7—41no—
213C2×C4×C7—41no—
214C2×C4×C7—41no—
215C2×C4×C7—41no—
216C2×C4×C7—41no—
217C2×C4×C7—41no—
218C2×C4×C7—41no—
219C2×C4×C7—41no—
220C2×C4×C7—41no—
221C2×C4×C7—84no—
222C2×C4×C7—82no—
223C2×C4×C7—82no—
224C2×C4×C7—81no—
225C2×C4×C7—81no—
226C2×C4×C7—81no—
227C2×C4×C7—81no—
228C2×C4×C7—81no—
229C2×C4×C7C2×C22⋊C411yescharacteristic
230C2×C4×C7C4×D411yescharacteristic
231C2×C4×C7#12111yescharacteristic
232C2×C4×C7#12311yescharacteristic
233C7×C8—42no—
234C7×C8—81no—
235C22×Q8C2×C4×C711yescharacteristic, complemented
236C22×D4—21no—
237C22×D4C7×D411yescharacteristic
238C23×C4—21no—
239C23×C4—21no—
240C23×C4C23×C711yescharacteristic
241C2×SD16—22no—
242C22×C8—21no—
243C22×C8—21no—
244C22⋊Q8—21no—
245C22⋊Q8—21no—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248#121—21no—
249#121—21no—
250#121C2×C4×C712yes—
251#121C7×D412yes—
252C4×D4—42no—
253C4×D4—42no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4C2×C4×C711yescharacteristic, complemented
258C2×C4⋊C4C7×D411yescharacteristic
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4C7×D411yescharacteristic
266C2×C22⋊C4C7×D411yescharacteristic
267C2×C42—21no—
268C2×C42—21no—
269#106—22no—
270#103—22no—
271#102—22no—
272C22⋊C8—21no—
273C22⋊C8—21no—
274C22⋊C8—21no—
275C22⋊C8C2×C4×C712yescomplemented
276#95—21no—
277#95—21no—
278#95—21no—
279#95—21no—
280#95—21no—
281#95C7×D411yescharacteristic
282#95C7×D411yescharacteristic
283C22×C7—21no—
284C22×C7—21no—
285C22×C7—21no—
286C22×C7—21no—
287C22×C7—21no—
288C22×C7—21no—
289C22×C7—41no—
290C22×C7—41no—
291C22×C7—41no—
292C22×C7—41no—
293C22×C7—42no—
294C22×C7—42no—
295C22×C7—42no—
296C22×C7—81no—
297C22×C7—81no—
298C22×C7—81no—
299C22×C7—81no—
300C22×C7#38611yescharacteristic
301C22×C7C4×SD1611yescharacteristic
302C22×C7#44011yescharacteristic
303C22×C7#45011yescharacteristic
304C22×C7#45211yescharacteristic
305C22×C7#46111yescharacteristic
306C22×C7#46311yescharacteristic
307C4×C7—21no—
308C4×C7—21no—
309C4×C7—21no—
310C4×C7—21no—
311C4×C7—42no—
312C4×C7—42no—
313C4×C7—42no—
314C4×C7—81no—
315C4×C7—81no—
316C4×C7—81no—
317C4×C7—81no—
318C4×C7—161no—
319C24—21no—
320C24C2×C7×D411yescharacteristic
321C2×Q8—21no—
322C2×Q8—21no—
323C2×Q8—81no—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—21no—
327C2×D4—41no—
328C2×D4—41no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—81no—
332C2×D4C7×C22⋊C412yes—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—81no—
347C22×C4—81no—
348C22×C4—81no—
349C22×C4C22×C4×C711yescharacteristic
350C22×C4C2×C7×D411yescharacteristic
351C22×C4C2×C7×D411yescharacteristic
352C22×C4C2×C7×D411yescharacteristic
353C22×C4C7×#4111yescharacteristic
354C22×C4C7×#4111yescharacteristic
355SD16—82no—
356C2×C8—22no—
357C2×C8—41no—
358C2×C8—81no—
359C2×C8—81no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—42no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—81no—
367C4⋊C4C7×C22⋊C412yes—
368C22⋊C4—21no—
369C22⋊C4—22no—
370C22⋊C4—22no—
371C22⋊C4—21no—
372C22⋊C4—21no—
373C22⋊C4—42no—
374C22⋊C4—42no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—81no—
380C22⋊C4C7×SD1612yescomplemented
381C42—42no—
382C42—81no—
383C2×C7—21no—
384C2×C7—21no—
385C2×C7—21no—
386C2×C7—21no—
387C2×C7—21no—
388C2×C7—21no—
389C2×C7—82no—
390C2×C7#187711yescharacteristic
391C2×C7#190611yescharacteristic
392C2×C7#191311yescharacteristic
393C23—22no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23C4×C7×D411yescharacteristic
403C23C7×#12011yescharacteristic
404C23C7×#12111yescharacteristic
405C23C2×C7×SD1611yescharacteristic
406C23C7×#13511yescharacteristic
407C23C7×AGL(1,ℤ/8)11yescharacteristic
408C23C7×#13711yescharacteristic
409Q8—42no—
410Q8—81no—
411D4—42no—
412D4—42no—
413D4—42no—
414D4—42no—
415D4—42no—
416D4—81no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—84no—
441C2×C4—82no—
442C2×C4—82no—
443C2×C4—81no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4C2×C7×C22⋊C411yescharacteristic
449C2×C4C4×C7×D411yescharacteristic
450C2×C4C7×#12111yescharacteristic
451C2×C4C7×#12311yescharacteristic
452C8—42no—
453C8—81no—
454C7#927511yescharacteristic, direct product factor, Sylow
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22C7×#38611yescharacteristic
473C22C4×C7×SD1611yescharacteristic
474C22C7×#44011yescharacteristic
475C22C7×#45011yescharacteristic
476C22C7×#45211yescharacteristic
477C22C7×#46111yescharacteristic
478C22C7×#46311yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—42no—
484C4—42no—
485C4—42no—
486C4—81no—
487C4—81no—
488C4—81no—
489C4—81no—
490C4—161no—
491C2—21no—
492C2—21no—
493C2—21no—
494C2—21no—
495C2—21no—
496C2—21no—
497C2—82no—
498C2C7×#187711yescharacteristic
499C2C7×#190611yescharacteristic
500C2C7×#191311yescharacteristic
subgroupG/H
center, socleC22×C7#386
commutatorC22×C4C22×C4×C7
Frattini, cosocleC23×C4C23×C7
prime radicalC2×C7×#121C22
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
3. C7×#1996C2semidirect
5. C2×C7×#328C2semidirect
6. C7×#1294C2semidirect
7. C7×#1282C2semidirect
12. C7×#481C4semidirect
15. C7×#448C4semidirect
31. #9275C7direct (N × H)
32. C22×C7×Q8C2×C4semidirect
54. C2×C7×C4⋊C4C2×C4semidirect
72. C7×C22⋊C8C2×C4semidirect
82. #1996C2×C7semidirect
84. C2×#328C2×C7semidirect
85. #1294C2×C7semidirect
86. #1282C2×C7semidirect
148. C7×C22⋊C4SD16semidirect
155. #481C4×C7semidirect
158. #448C4×C7semidirect
235. C22×Q8C2×C4×C7semidirect
257. C2×C4⋊C4C2×C4×C7semidirect
275. C22⋊C8C2×C4×C7semidirect
380. C22⋊C4C7×SD16semidirect
454. C7#9275direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#31872
C7×#23642
C7×#19962
C7×#15192
C2×C7×#3282
C7×#12942
C7×#12822
#92757