Finite Group Databasebeta

← C7×#9255 #13186471

Subgroups — C7×#9255 #13186471

Order 1792.

924 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#450C211yesmaximal, characteristic
2C7×D4×C22⋊C4C211yesmaximal, characteristic
3C7×#1996C211yesmaximal, characteristic, complemented
4C7×#1786C211yesmaximal, characteristic
5C7×#1520C211yesmaximal, characteristic, complemented
6C7×#1289C211yesmaximal, characteristic, complemented
7C7×#1282C211yesmaximal, characteristic, complemented
8C23×C7×D4C2211yescharacteristic
9C22×C7×SD16C412yescomplemented
10C2×C7×C22⋊Q8C2211yescharacteristic
11C2×C4×C7×D4—21no—
12C22×C7×C22⋊C4—21no—
13C7×#450—21no—
14C7×#450—22no—
15C7×#450—21no—
16C2×C7×#102—22no—
17C2×C7×#102C412yescomplemented
18C2×C7×C22⋊C8C2211yescharacteristic
19C2×C7×C22⋊C8C2211yescharacteristic
20C7×#390—21no—
21C7×#386—22no—
22C7×#380C2211yescharacteristic
23C7×#380C2211yescharacteristic
24C7×#379—21no—
25C4×C7×C22⋊C4C2211yescharacteristic
26C7×#342—21no—
27C7×#342—21no—
28C7×#328—22no—
29#9255C711yesmaximal, characteristic, direct product factor, Sylow
30C25×C7—21no—
31C22×C7×Q8C2×C411yescharacteristic, complemented
32C22×C7×D4—21no—
33C22×C7×D4—21no—
34C22×C7×D4—21no—
35C22×C7×D4—44no—
36C22×C7×D4C2×C412yes—
37C22×C7×D4D411yescharacteristic
38C22×C7×D4D412yes—
39C22×C7×D4D411yescharacteristic
40C23×C4×C7—22no—
41C23×C4×C7C2311yescharacteristic
42C2×C7×SD16—22no—
43C2×C7×SD16—22no—
44C2×C7×SD16—44no—
45C22×C7×C8—21no—
46C22×C7×C8C2×C412yescomplemented
47C7×C22⋊Q8—21no—
48C7×C22⋊Q8—21no—
49C7×C22⋊Q8—21no—
50C7×C22⋊Q8—21no—
51C4×C7×D4—44no—
52C2×C7×C4⋊C4—21no—
53C2×C7×C4⋊C4—21no—
54C2×C7×C4⋊C4—21no—
55C2×C7×C4⋊C4C2×C411yescharacteristic, complemented
56C2×C7×C22⋊C4—22no—
57C2×C7×C22⋊C4—22no—
58C2×C7×C22⋊C4—21no—
59C2×C7×C22⋊C4—21no—
60C2×C7×C22⋊C4—21no—
61C2×C7×C22⋊C4—22no—
62C2×C7×C22⋊C4—42no—
63C2×C7×C22⋊C4—42no—
64C2×C7×C22⋊C4D411yescharacteristic
65C2×C7×C22⋊C4D411yescharacteristic
66C2×C42×C7—21no—
67C7×#102—22no—
68C7×#102—22no—
69C7×#102—44no—
70C7×C22⋊C8—21no—
71C7×C22⋊C8—21no—
72C7×C22⋊C8—21no—
73C7×C22⋊C8—21no—
74C7×#95—21no—
75C7×#95—21no—
76C7×#95D412yes—
77C2×#450C2×C711yescharacteristic
78D4×C22⋊C4C2×C711yescharacteristic
79#1996C2×C711yescharacteristic, complemented
80#1786C2×C711yescharacteristic
81#1520C2×C711yescharacteristic, complemented
82#1289C2×C711yescharacteristic, complemented
83#1282C2×C711yescharacteristic, complemented
84C24×C7—21no—
85C24×C7—21no—
86C24×C7—22no—
87C24×C7—22no—
88C24×C7—44no—
89C24×C7—41no—
90C24×C7—41no—
91C24×C7—41no—
92C24×C7—41no—
93C24×C7—82no—
94C24×C7C2×D411yescharacteristic
95C2×C7×Q8—21no—
96C2×C7×Q8—21no—
97C2×C7×Q8—42no—
98C2×C7×D4—24no—
99C2×C7×D4—24no—
100C2×C7×D4—24no—
101C2×C7×D4—22no—
102C2×C7×D4—22no—
103C2×C7×D4—21no—
104C2×C7×D4—21no—
105C2×C7×D4—42no—
106C2×C7×D4—42no—
107C2×C7×D4—42no—
108C2×C7×D4—44no—
109C2×C7×D4—44no—
110C2×C7×D4—44no—
111C2×C7×D4C22⋊C412yes—
112C2×C7×D4C22⋊C412yes—
113C22×C4×C7—21no—
114C22×C4×C7—21no—
115C22×C4×C7—22no—
116C22×C4×C7—21no—
117C22×C4×C7—21no—
118C22×C4×C7—42no—
119C22×C4×C7—44no—
120C22×C4×C7—44no—
121C22×C4×C7—41no—
122C22×C4×C7—82no—
123C22×C4×C7C22×C411yescharacteristic
124C22×C4×C7C2×D411yescharacteristic
125C22×C4×C7C2×D411yescharacteristic
126C22×C4×C7C2×D411yescharacteristic
127C22×C4×C7#4111yescharacteristic
128C22×C4×C7#4111yescharacteristic
129C7×SD16—44no—
130C7×SD16—44no—
131C2×C7×C8—22no—
132C2×C7×C8—42no—
133C2×C7×C8—42no—
134C2×C7×C8—41no—
135C7×C4⋊C4—21no—
136C7×C4⋊C4—21no—
137C7×C4⋊C4—42no—
138C7×C4⋊C4—42no—
139C7×C4⋊C4—41no—
140C7×C4⋊C4—41no—
141C7×C22⋊C4—21no—
142C7×C22⋊C4—21no—
143C7×C22⋊C4—21no—
144C7×C22⋊C4—44no—
145C7×C22⋊C4—44no—
146C7×C22⋊C4—41no—
147C7×C22⋊C4—41no—
148C7×C22⋊C4—41no—
149C7×C22⋊C4—41no—
150C7×C22⋊C4—41no—
151C7×C22⋊C4—41no—
152C7×C22⋊C4—82no—
153C7×C22⋊C4SD1612yescomplemented
154C42×C7—42no—
155C23×D4C22×C711yescharacteristic
156C22×SD16C4×C712yescomplemented
157C2×C22⋊Q8C22×C711yescharacteristic
158C2×C4×D4—21no—
159C22×C22⋊C4—21no—
160#450—21no—
161#450—22no—
162#450—21no—
163C2×#102—22no—
164C2×#102C4×C712yescomplemented
165C2×C22⋊C8C22×C711yescharacteristic
166C2×C22⋊C8C22×C711yescharacteristic
167#390—21no—
168#386—22no—
169#380C22×C711yescharacteristic
170#380C22×C711yescharacteristic
171#379—21no—
172C4×C22⋊C4C22×C711yescharacteristic
173#342—21no—
174#342—21no—
175#328—22no—
176C23×C7—24no—
177C23×C7—22no—
178C23×C7—22no—
179C23×C7—41no—
180C23×C7—41no—
181C23×C7—44no—
182C23×C7—44no—
183C23×C7—42no—
184C23×C7—42no—
185C23×C7—42no—
186C23×C7—41no—
187C23×C7—41no—
188C23×C7—42no—
189C23×C7—42no—
190C23×C7—41no—
191C23×C7—41no—
192C23×C7—42no—
193C23×C7—42no—
194C23×C7—82no—
195C23×C7—82no—
196C23×C7—84no—
197C23×C7—84no—
198C23×C7—84no—
199C23×C7—84no—
200C23×C7C4×D411yescharacteristic
201C23×C7#12011yescharacteristic
202C23×C7#12111yescharacteristic
203C23×C7C2×SD1611yescharacteristic
204C23×C7#13511yescharacteristic
205C23×C7AGL(1,ℤ/8)11yescharacteristic
206C23×C7#13711yescharacteristic
207C7×Q8—42no—
208C7×Q8—81no—
209C7×D4—24no—
210C7×D4—22no—
211C7×D4—22no—
212C7×D4—22no—
213C7×D4—44no—
214C7×D4—44no—
215C7×D4—42no—
216C7×D4#9914yes—
217C2×C4×C7—22no—
218C2×C4×C7—22no—
219C2×C4×C7—22no—
220C2×C4×C7—22no—
221C2×C4×C7—41no—
222C2×C4×C7—41no—
223C2×C4×C7—41no—
224C2×C4×C7—41no—
225C2×C4×C7—41no—
226C2×C4×C7—41no—
227C2×C4×C7—42no—
228C2×C4×C7—41no—
229C2×C4×C7—42no—
230C2×C4×C7—41no—
231C2×C4×C7—41no—
232C2×C4×C7—42no—
233C2×C4×C7—41no—
234C2×C4×C7—88no—
235C2×C4×C7—81no—
236C2×C4×C7—81no—
237C2×C4×C7—81no—
238C2×C4×C7—81no—
239C2×C4×C7—81no—
240C2×C4×C7C2×C22⋊C411yescharacteristic
241C2×C4×C7C4×D411yescharacteristic
242C2×C4×C7#12111yescharacteristic
243C2×C4×C7#12311yescharacteristic
244C7×C8—42no—
245C7×C8—81no—
246C25—21no—
247C22×Q8C2×C4×C711yescharacteristic, complemented
248C22×D4—21no—
249C22×D4—21no—
250C22×D4—21no—
251C22×D4—44no—
252C22×D4C2×C4×C712yes—
253C22×D4C7×D411yescharacteristic
254C22×D4C7×D412yes—
255C22×D4C7×D411yescharacteristic
256C23×C4—22no—
257C23×C4C23×C711yescharacteristic
258C2×SD16—22no—
259C2×SD16—22no—
260C2×SD16—44no—
261C22×C8—21no—
262C22×C8C2×C4×C712yescomplemented
263C22⋊Q8—21no—
264C22⋊Q8—21no—
265C22⋊Q8—21no—
266C22⋊Q8—21no—
267C4×D4—44no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4C2×C4×C711yescharacteristic, complemented
272C2×C22⋊C4—22no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—42no—
279C2×C22⋊C4—42no—
280C2×C22⋊C4C7×D411yescharacteristic
281C2×C22⋊C4C7×D411yescharacteristic
282C2×C42—21no—
283#102—22no—
284#102—22no—
285#102—44no—
286C22⋊C8—21no—
287C22⋊C8—21no—
288C22⋊C8—21no—
289C22⋊C8—21no—
290#95—21no—
291#95—21no—
292#95C7×D412yes—
293C22×C7—21no—
294C22×C7—21no—
295C22×C7—21no—
296C22×C7—21no—
297C22×C7—21no—
298C22×C7—21no—
299C22×C7—24no—
300C22×C7—41no—
301C22×C7—41no—
302C22×C7—41no—
303C22×C7—41no—
304C22×C7—44no—
305C22×C7—44no—
306C22×C7—42no—
307C22×C7—42no—
308C22×C7—42no—
309C22×C7—42no—
310C22×C7—42no—
311C22×C7—84no—
312C22×C7—84no—
313C22×C7—84no—
314C22×C7—84no—
315C22×C7—82no—
316C22×C7—82no—
317C22×C7#38611yescharacteristic
318C22×C7C4×SD1611yescharacteristic
319C22×C7#44011yescharacteristic
320C22×C7#45011yescharacteristic
321C22×C7#45211yescharacteristic
322C22×C7#46111yescharacteristic
323C22×C7#46311yescharacteristic
324C4×C7—21no—
325C4×C7—21no—
326C4×C7—21no—
327C4×C7—42no—
328C4×C7—81no—
329C4×C7—82no—
330C4×C7—81no—
331C4×C7—81no—
332C4×C7—161no—
333C4×C7C2×#9912yes—
334C24—21no—
335C24—21no—
336C24—22no—
337C24—22no—
338C24—44no—
339C24—41no—
340C24—41no—
341C24—41no—
342C24—41no—
343C24—82no—
344C24C2×C7×D411yescharacteristic
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—42no—
348C2×D4—24no—
349C2×D4—24no—
350C2×D4—24no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—42no—
356C2×D4—42no—
357C2×D4—42no—
358C2×D4—44no—
359C2×D4—44no—
360C2×D4—44no—
361C2×D4C7×C22⋊C412yes—
362C2×D4C7×C22⋊C412yes—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—42no—
369C22×C4—44no—
370C22×C4—44no—
371C22×C4—41no—
372C22×C4—82no—
373C22×C4C22×C4×C711yescharacteristic
374C22×C4C2×C7×D411yescharacteristic
375C22×C4C2×C7×D411yescharacteristic
376C22×C4C2×C7×D411yescharacteristic
377C22×C4C7×#4111yescharacteristic
378C22×C4C7×#4111yescharacteristic
379SD16—44no—
380SD16—44no—
381C2×C8—22no—
382C2×C8—42no—
383C2×C8—42no—
384C2×C8—41no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—42no—
388C4⋊C4—42no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C22⋊C4—21no—
392C22⋊C4—21no—
393C22⋊C4—21no—
394C22⋊C4—44no—
395C22⋊C4—44no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4—82no—
403C22⋊C4C7×SD1612yescomplemented
404C42—42no—
405C2×C7—21no—
406C2×C7—21no—
407C2×C7—21no—
408C2×C7—21no—
409C2×C7—21no—
410C2×C7—21no—
411C2×C7—44no—
412C2×C7—82no—
413C2×C7#187711yescharacteristic
414C2×C7#189811yescharacteristic
415C2×C7#190411yescharacteristic
416C23—24no—
417C23—22no—
418C23—22no—
419C23—41no—
420C23—41no—
421C23—44no—
422C23—44no—
423C23—42no—
424C23—42no—
425C23—42no—
426C23—41no—
427C23—41no—
428C23—42no—
429C23—42no—
430C23—41no—
431C23—41no—
432C23—42no—
433C23—42no—
434C23—82no—
435C23—82no—
436C23—84no—
437C23—84no—
438C23—84no—
439C23—84no—
440C23C4×C7×D411yescharacteristic
441C23C7×#12011yescharacteristic
442C23C7×#12111yescharacteristic
443C23C2×C7×SD1611yescharacteristic
444C23C7×#13511yescharacteristic
445C23C7×AGL(1,ℤ/8)11yescharacteristic
446C23C7×#13711yescharacteristic
447Q8—42no—
448Q8—81no—
449D4—24no—
450D4—22no—
451D4—22no—
452D4—22no—
453D4—44no—
454D4—44no—
455D4—42no—
456D4C7×#9914yes—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—41no—
474C2×C4—88no—
475C2×C4—81no—
476C2×C4—81no—
477C2×C4—81no—
478C2×C4—81no—
479C2×C4—81no—
480C2×C4C2×C7×C22⋊C411yescharacteristic
481C2×C4C4×C7×D411yescharacteristic
482C2×C4C7×#12111yescharacteristic
483C2×C4C7×#12311yescharacteristic
484C8—42no—
485C8—81no—
486C7#925511yescharacteristic, direct product factor, Sylow
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—24no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—44no—
499C22—44no—
500C22—42no—
501C22—42no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—84no—
506C22—84no—
507C22—84no—
508C22—84no—
509C22—82no—
510C22—82no—
511C22C7×#38611yescharacteristic
512C22C4×C7×SD1611yescharacteristic
513C22C7×#44011yescharacteristic
514C22C7×#45011yescharacteristic
515C22C7×#45211yescharacteristic
516C22C7×#46111yescharacteristic
517C22C7×#46311yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—42no—
522C4—82no—
523C4—81no—
524C4—81no—
525C4—81no—
526C4—161no—
527C4C2×C7×#9912yes—
528C2—21no—
529C2—21no—
530C2—21no—
531C2—21no—
532C2—21no—
533C2—21no—
534C2—44no—
535C2—82no—
536C2C7×#187711yescharacteristic
537C2C7×#189811yescharacteristic
538C2C7×#190411yescharacteristic
subgroupG/H
center, socleC22×C7#386
commutatorC22×C4C22×C4×C7
Frattini, cosocleC23×C4C23×C7
prime radicalC23×C7×D4C22
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. C7×#1520C2semidirect
6. C7×#1289C2semidirect
7. C7×#1282C2semidirect
9. C22×C7×SD16C4semidirect
17. C2×C7×#102C4semidirect
29. #9255C7direct (N × H)
31. C22×C7×Q8C2×C4semidirect
46. C22×C7×C8C2×C4semidirect
55. C2×C7×C4⋊C4C2×C4semidirect
79. #1996C2×C7semidirect
81. #1520C2×C7semidirect
82. #1289C2×C7semidirect
83. #1282C2×C7semidirect
153. C7×C22⋊C4SD16semidirect
156. C22×SD16C4×C7semidirect
164. C2×#102C4×C7semidirect
247. C22×Q8C2×C4×C7semidirect
262. C22×C8C2×C4×C7semidirect
271. C2×C4⋊C4C2×C4×C7semidirect
403. C22⋊C4C7×SD16semidirect
486. C7#9255direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#4502
C7×D4×C22⋊C42
C7×#19962
C7×#17862
C7×#15202
C7×#12892
C7×#12822
#92557