Finite Group Databasebeta

← C7×#19033 #13196249

Subgroups — C7×#19033 #13196249

Order 1792.

948 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3561C211yesmaximal, characteristic
2C7×#3239C211yesmaximal, characteristic, complemented
3C7×#3165C211yesmaximal, characteristic, complemented
4C2×C7×#497C211yesmaximal, characteristic, complemented
5C7×#1661C214yesmaximal, complemented
6C7×#1660C214yesmaximal, complemented
7C7×#1531C211yesmaximal, characteristic, complemented
8C7×#1527C211yesmaximal, characteristic, complemented
9C7×#1524C211yesmaximal, characteristic, complemented
10C22×C7×Q16—21no—
11C22×C7×SD16—21no—
12C7×#563C2212yes—
13C7×#562C2212yes—
14C7×#556—21no—
15C7×#551—22no—
16C7×D4×Q8—21no—
17C7×#548—21no—
18C7×#546—21no—
19C7×#543—21no—
20C7×#542—21no—
21C7×#542—22no—
22C7×#538—21no—
23C7×#536—21no—
24C7×#533C2211yescharacteristic
25C2×C7×C4⋊Q8C2211yescharacteristic
26C7×#529C2211yescharacteristic
27C2×C7×#124C2211yescharacteristic
28C7×#501C2214yescomplemented
29C7×#501C2212yescomplemented
30C7×#500—21no—
31C7×#498—21no—
32C7×#497—22no—
33C7×#497C2214yes—
34C7×#489C2212yescomplemented
35C7×#484—21no—
36C7×#481—21no—
37C7×#475—21no—
38C7×#474—21no—
39C7×#432C2211yescharacteristic
40C7×#428—22no—
41C4×C7×M16C2211yescharacteristic
42C2×C7×#97C2211yescharacteristic
43C7×#330C2212yescomplemented
44C7×#330C2214yescomplemented
45C7×#329C2214yes—
46C7×#329C2212yescomplemented
47#19033C711yesmaximal, characteristic, direct product factor, Sylow
48C2×C7×#41—21no—
49C22×C7×Q8—21no—
50C22×C7×Q8—21no—
51C22×C7×Q8D411yescharacteristic
52C22×C7×D4D411yescharacteristic
53C2×C7×Q16—24no—
54C2×C7×Q16—44no—
55C2×C7×SD16—24no—
56C2×C7×SD16—44no—
57C2×C7×M16—21no—
58C22×C7×C8—21no—
59C7×C4⋊Q8—21no—
60C7×C4⋊Q8—22no—
61C7×C4⋊Q8—21no—
62C7×C4⋊Q8—21no—
63C7×C4⋊Q8—21no—
64C7×C4⋊Q8D411yescharacteristic
65C7×C4⋊Q8D411yescharacteristic
66C7×C4⋊Q8C2312yes—
67C7×#126—22no—
68C7×#126—22no—
69C7×#126—22no—
70C7×#126—21no—
71C7×#125C2311yescharacteristic
72C7×#125C2312yes—
73C7×#124—21no—
74C7×#124—22no—
75C7×#124—22no—
76C7×#124—21no—
77C7×#124—21no—
78C7×#124D412yes—
79C7×#124C2311yescharacteristic
80C7×#124C2312yes—
81C7×#123—22no—
82C7×#123—22no—
83C7×#123—21no—
84C7×#123—22no—
85C7×#123—22no—
86C7×C22⋊Q8—22no—
87C7×C22⋊Q8—22no—
88C7×C22⋊Q8—21no—
89C7×C22⋊Q8—22no—
90C7×C22⋊Q8—22no—
91C7×C22⋊Q8—22no—
92C7×C22⋊Q8—21no—
93C7×C22⋊Q8—21no—
94C7×C22⋊Q8—22no—
95C7×C22⋊Q8—22no—
96C7×C22⋊Q8D411yescharacteristic
97C7×#121—21no—
98C7×#121—22no—
99C7×#121—22no—
100C7×#121D411yescharacteristic
101C7×#120—22no—
102C4×C7×Q8—21no—
103C4×C7×Q8—21no—
104C4×C7×Q8—21no—
105C4×C7×Q8D411yescharacteristic
106C4×C7×D4—22no—
107C4×C7×D4—21no—
108C4×C7×D4—22no—
109C4×C7×D4—21no—
110C4×C7×D4D411yescharacteristic
111C7×#117—22no—
112C7×#117—21no—
113C7×#117D412yes—
114C2×C7×C4⋊C4—21no—
115C2×C7×C4⋊C4—21no—
116C2×C7×C22⋊C4—22no—
117C2×C7×C22⋊C4—21no—
118C2×C7×C22⋊C4—21no—
119C2×C42×C7C2311yescharacteristic
120C7×#107—22no—
121C7×#107—24no—
122C7×#106—22no—
123C7×#106—24no—
124C7×C4⋊C8—21no—
125C7×#103—22no—
126C7×#102—22no—
127C7×C22⋊C8—21no—
128C7×#97—21no—
129C7×#97C2312yes—
130C7×#97C2312yes—
131C7×#97C2312yes—
132C4×C7×C8—21no—
133#3561C2×C711yescharacteristic
134#3239C2×C711yescharacteristic, complemented
135#3165C2×C711yescharacteristic, complemented
136C2×#497C2×C711yescharacteristic, complemented
137#1661C2×C714yescomplemented
138#1660C2×C714yescomplemented
139#1531C2×C711yescharacteristic, complemented
140#1527C2×C711yescharacteristic, complemented
141#1524C2×C711yescharacteristic, complemented
142C24×C7—21no—
143C7×#41—82no—
144C2×C7×Q8—22no—
145C2×C7×Q8—21no—
146C2×C7×Q8—21no—
147C2×C7×Q8—21no—
148C2×C7×Q8—22no—
149C2×C7×Q8—42no—
150C2×C7×Q8—42no—
151C2×C7×Q8—42no—
152C2×C7×Q8—41no—
153C2×C7×Q8—82no—
154C2×C7×Q8C2×D411yescharacteristic
155C2×C7×Q8C2×D412yes—
156C2×C7×D4—21no—
157C2×C7×D4—22no—
158C2×C7×D4—22no—
159C2×C7×D4—21no—
160C2×C7×D4—42no—
161C2×C7×D4C2×D411yescharacteristic
162C2×C7×D4C2×D412yes—
163C22×C4×C7—22no—
164C22×C4×C7—22no—
165C22×C4×C7—22no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—41no—
169C22×C4×C7C2×D411yescharacteristic
170C22×C4×C7C2×D411yescharacteristic
171C22×C4×C7C2×D411yescharacteristic
172C7×Q16—48no—
173C7×SD16—48no—
174C7×M16—24no—
175C2×C7×C8—24no—
176C2×C7×C8—22no—
177C2×C7×C8—22no—
178C2×C7×C8—22no—
179C7×C4⋊C4—22no—
180C7×C4⋊C4—22no—
181C7×C4⋊C4—22no—
182C7×C4⋊C4—22no—
183C7×C4⋊C4—21no—
184C7×C4⋊C4—21no—
185C7×C4⋊C4—21no—
186C7×C4⋊C4—21no—
187C7×C4⋊C4—21no—
188C7×C4⋊C4—21no—
189C7×C4⋊C4—22no—
190C7×C4⋊C4—22no—
191C7×C4⋊C4—22no—
192C7×C4⋊C4—22no—
193C7×C4⋊C4—41no—
194C7×C4⋊C4—41no—
195C7×C4⋊C4C2×D412yes—
196C7×C4⋊C4C2×D411yescharacteristic
197C7×C4⋊C4C2×D412yes—
198C7×C4⋊C4C2×D411yescharacteristic
199C7×C22⋊C4—22no—
200C7×C22⋊C4—22no—
201C7×C22⋊C4—22no—
202C7×C22⋊C4—22no—
203C7×C22⋊C4—22no—
204C7×C22⋊C4—21no—
205C7×C22⋊C4—22no—
206C7×C22⋊C4—22no—
207C7×C22⋊C4—22no—
208C7×C22⋊C4—21no—
209C7×C22⋊C4—21no—
210C7×C22⋊C4—22no—
211C7×C22⋊C4—22no—
212C7×C22⋊C4—21no—
213C7×C22⋊C4—21no—
214C42×C7—22no—
215C42×C7—22no—
216C42×C7—21no—
217C42×C7C2×D411yescharacteristic
218C42×C7C2×D411yescharacteristic
219C42×C7C2×D411yescharacteristic
220C42×C7C2411yescharacteristic
221C22×Q16—21no—
222C22×SD16—21no—
223#563C22×C712yes—
224#562C22×C712yes—
225#556—21no—
226#551—22no—
227D4×Q8—21no—
228#548—21no—
229#546—21no—
230#543—21no—
231#542—21no—
232#542—22no—
233#538—21no—
234#536—21no—
235#533C22×C711yescharacteristic
236C2×C4⋊Q8C22×C711yescharacteristic
237#529C22×C711yescharacteristic
238C2×#124C22×C711yescharacteristic
239#501C22×C714yescomplemented
240#501C22×C712yescomplemented
241#500—21no—
242#498—21no—
243#497—22no—
244#497C22×C714yes—
245#489C22×C712yescomplemented
246#484—21no—
247#481—21no—
248#475—21no—
249#474—21no—
250#432C22×C711yescharacteristic
251#428—22no—
252C4×M16C22×C711yescharacteristic
253C2×#97C22×C711yescharacteristic
254#330C22×C712yescomplemented
255#330C22×C714yescomplemented
256#329C22×C714yes—
257#329C22×C712yescomplemented
258C23×C7—22no—
259C23×C7—21no—
260C23×C7—42no—
261C23×C7—81no—
262C23×C7—81no—
263C23×C7#12011yescharacteristic
264C7×Q8—42no—
265C7×Q8—41no—
266C7×Q8—42no—
267C7×Q8—42no—
268C7×Q8—42no—
269C7×Q8—42no—
270C7×Q8—81no—
271C7×Q8—82no—
272C7×Q8—82no—
273C7×D4—42no—
274C7×D4—41no—
275C7×D4—42no—
276C7×D4—42no—
277C7×D4—82no—
278C7×D4—82no—
279C2×C4×C7—22no—
280C2×C4×C7—22no—
281C2×C4×C7—21no—
282C2×C4×C7—22no—
283C2×C4×C7—21no—
284C2×C4×C7—22no—
285C2×C4×C7—22no—
286C2×C4×C7—21no—
287C2×C4×C7—41no—
288C2×C4×C7—42no—
289C2×C4×C7—42no—
290C2×C4×C7—81no—
291C2×C4×C7—82no—
292C2×C4×C7—82no—
293C2×C4×C7—82no—
294C2×C4×C7—82no—
295C2×C4×C7#12011yescharacteristic
296C2×C4×C7#12011yescharacteristic
297C2×C4×C7#12011yescharacteristic
298C2×C4×C7C22×D411yescharacteristic
299C2×C4×C7C22×D411yescharacteristic
300C2×C4×C7C22×D411yescharacteristic
301C7×C8—24no—
302C7×C8—24no—
303C7×C8—42no—
304C2×#41—21no—
305C22×Q8—21no—
306C22×Q8—21no—
307C22×Q8C7×D411yescharacteristic
308C22×D4C7×D411yescharacteristic
309C2×Q16—24no—
310C2×Q16—44no—
311C2×SD16—24no—
312C2×SD16—44no—
313C2×M16—21no—
314C22×C8—21no—
315C4⋊Q8—21no—
316C4⋊Q8—22no—
317C4⋊Q8—21no—
318C4⋊Q8—21no—
319C4⋊Q8—21no—
320C4⋊Q8C7×D411yescharacteristic
321C4⋊Q8C7×D411yescharacteristic
322C4⋊Q8C23×C712yes—
323#126—22no—
324#126—22no—
325#126—22no—
326#126—21no—
327#125C23×C711yescharacteristic
328#125C23×C712yes—
329#124—21no—
330#124—22no—
331#124—22no—
332#124—21no—
333#124—21no—
334#124C7×D412yes—
335#124C23×C712yes—
336#124C23×C711yescharacteristic
337#123—22no—
338#123—22no—
339#123—21no—
340#123—22no—
341#123—22no—
342C22⋊Q8—22no—
343C22⋊Q8—22no—
344C22⋊Q8—21no—
345C22⋊Q8—22no—
346C22⋊Q8—22no—
347C22⋊Q8—22no—
348C22⋊Q8—21no—
349C22⋊Q8—21no—
350C22⋊Q8—22no—
351C22⋊Q8—22no—
352C22⋊Q8C7×D411yescharacteristic
353#121—21no—
354#121—22no—
355#121—22no—
356#121C7×D411yescharacteristic
357#120—22no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8C7×D411yescharacteristic
362C4×D4—22no—
363C4×D4—21no—
364C4×D4—22no—
365C4×D4—21no—
366C4×D4C7×D411yescharacteristic
367#117—22no—
368#117—21no—
369#117C7×D412yes—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C42C23×C711yescharacteristic
376#107—24no—
377#107—22no—
378#106—24no—
379#106—22no—
380C4⋊C8—21no—
381#103—22no—
382#102—22no—
383C22⋊C8—21no—
384#97—21no—
385#97C23×C712yes—
386#97C23×C712yes—
387#97C23×C712yes—
388C4×C8—21no—
389C22×C7—21no—
390C22×C7—21no—
391C22×C7—41no—
392C22×C7—42no—
393C22×C7—41no—
394C22×C7—42no—
395C22×C7—42no—
396C22×C7—41no—
397C22×C7—162no—
398C22×C7#45612yes—
399C22×C7C2×#12011yescharacteristic
400C4×C7—21no—
401C4×C7—21no—
402C4×C7—21no—
403C4×C7—21no—
404C4×C7—21no—
405C4×C7—41no—
406C4×C7—42no—
407C4×C7—42no—
408C4×C7—41no—
409C4×C7—41no—
410C4×C7—42no—
411C4×C7—82no—
412C4×C7#45312yes—
413C24—21no—
414#41—82no—
415C2×Q8—22no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—22no—
420C2×Q8—42no—
421C2×Q8—42no—
422C2×Q8—42no—
423C2×Q8—41no—
424C2×Q8—82no—
425C2×Q8C2×C7×D411yescharacteristic
426C2×Q8C2×C7×D412yes—
427C2×D4—21no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—21no—
431C2×D4—42no—
432C2×D4C2×C7×D411yescharacteristic
433C2×D4C2×C7×D412yes—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—41no—
440C22×C4C2×C7×D411yescharacteristic
441C22×C4C2×C7×D411yescharacteristic
442C22×C4C2×C7×D411yescharacteristic
443Q16—48no—
444SD16—48no—
445M16—24no—
446C2×C8—24no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—22no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4C2×C7×D412yes—
467C4⋊C4C2×C7×D411yescharacteristic
468C4⋊C4C2×C7×D412yes—
469C4⋊C4C2×C7×D411yescharacteristic
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—21no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C42—22no—
486C42—22no—
487C42—21no—
488C42C2×C7×D411yescharacteristic
489C42C2×C7×D411yescharacteristic
490C42C2×C7×D411yescharacteristic
491C42C24×C711yescharacteristic
492C2×C7—22no—
493C2×C7—81no—
494C2×C7—82no—
495C2×C7C2×#45311yescharacteristic
496C2×C7C2×#45611yescharacteristic
497C2×C7#302211yescharacteristic
498C23—22no—
499C23—21no—
500C23—42no—
501C23—81no—
502C23—81no—
503C23C7×#12011yescharacteristic
504Q8—42no—
505Q8—41no—
506Q8—42no—
507Q8—42no—
508Q8—42no—
509Q8—42no—
510Q8—81no—
511Q8—82no—
512Q8—82no—
513D4—42no—
514D4—41no—
515D4—42no—
516D4—42no—
517D4—82no—
518D4—82no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—81no—
531C2×C4—82no—
532C2×C4—82no—
533C2×C4—82no—
534C2×C4—82no—
535C2×C4C7×#12011yescharacteristic
536C2×C4C7×#12011yescharacteristic
537C2×C4C7×#12011yescharacteristic
538C2×C4C22×C7×D411yescharacteristic
539C2×C4C22×C7×D411yescharacteristic
540C2×C4C22×C7×D411yescharacteristic
541C8—24no—
542C8—24no—
543C8—42no—
544C7#1903311yescharacteristic, direct product factor, Sylow
545C22—21no—
546C22—21no—
547C22—41no—
548C22—42no—
549C22—41no—
550C22—42no—
551C22—42no—
552C22—41no—
553C22—162no—
554C22C7×#45612yes—
555C22C2×C7×#12011yescharacteristic
556C4—21no—
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—41no—
562C4—42no—
563C4—42no—
564C4—41no—
565C4—41no—
566C4—42no—
567C4—82no—
568C4C7×#45312yes—
569C2—22no—
570C2—82no—
571C2—81no—
572C2C2×C7×#45311yescharacteristic
573C2C2×C7×#45611yescharacteristic
574C2C7×#302211yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC42C24×C7
prime radicalC7×#3561C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C7×#3239C2semidirect
3. C7×#3165C2semidirect
4. C2×C7×#497C2semidirect
5. C7×#1661C2semidirect
6. C7×#1660C2semidirect
7. C7×#1531C2semidirect
8. C7×#1527C2semidirect
9. C7×#1524C2semidirect
28. C7×#501C22semidirect
29. C7×#501C22semidirect
34. C7×#489C22semidirect
43. C7×#330C22semidirect
44. C7×#330C22semidirect
46. C7×#329C22semidirect
47. #19033C7direct (N × H)
134. #3239C2×C7semidirect
135. #3165C2×C7semidirect
136. C2×#497C2×C7semidirect
137. #1661C2×C7semidirect
138. #1660C2×C7semidirect
139. #1531C2×C7semidirect
140. #1527C2×C7semidirect
141. #1524C2×C7semidirect
239. #501C22×C7semidirect
240. #501C22×C7semidirect
245. #489C22×C7semidirect
254. #330C22×C7semidirect
255. #330C22×C7semidirect
257. #329C22×C7semidirect
544. C7#19033direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#35612
C7×#32392
C7×#31652
C2×C7×#4972
C7×#16612
C7×#16602
C7×#15312
C7×#15272
C7×#15242
#190337