Finite Group Databasebeta

← C7×#24041 #13201257

Subgroups — C7×#24041 #13201257

Order 1792.

1338 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×D4×Q8C211yesmaximal, characteristic
2C2×C7×#483C211yesmaximal, characteristic, complemented
3C22×C7×#103C211yesmaximal, characteristic, complemented
4C7×#2486C211yesmaximal, characteristic
5C7×#2043C212yesmaximal, complemented
6C7×#2035C212yesmaximal, complemented
7C7×#1892C211yesmaximal, characteristic, complemented
8C7×#1869C211yesmaximal, characteristic
9C7×#1865C212yesmaximal, complemented
10C7×#1787C212yesmaximal, complemented
11C7×#1787C211yesmaximal, characteristic, complemented
12C23×C7×Q8C2211yescharacteristic
13C23×C7×Q8C2211yescharacteristic
14C23×C7×C8C2211yescharacteristic
15C7×D4×Q8—24no—
16C7×D4×Q8—24no—
17C2×C7×C4⋊Q8—21no—
18C2×C7×C4⋊Q8C2211yescharacteristic
19C2×C7×#123—21no—
20C2×C7×C22⋊Q8—21no—
21C2×C7×C22⋊Q8—21no—
22C2×C7×C22⋊Q8C2211yescharacteristic
23C2×C7×C22⋊Q8C2211yescharacteristic
24C2×C4×C7×Q8C2211yescharacteristic
25C2×C4×C7×D4—21no—
26C2×C4×C7×D4C2211yescharacteristic
27C22×C7×C4⋊C4C2211yescharacteristic
28C7×#483—24no—
29C2×C7×#106C2212yes—
30C2×C7×#103—24no—
31C2×C7×#103C2212yes—
32C2×C7×#103C2212yes—
33C2×C7×#103C2212yes—
34C2×C7×#103C2212yes—
35C2×C7×#103C2212yes—
36C2×C7×#103C2212yes—
37C2×C7×C22⋊C8C2211yescharacteristic
38C2×C7×C22⋊C8C2212yes—
39C7×#398—21no—
40C7×#397—21no—
41C7×#389C2212yes—
42C7×#381—21no—
43C7×#380C2212yes—
44C7×#380C2211yescharacteristic
45C7×#340C2212yes—
46C7×#336C2212yes—
47#24041C711yesmaximal, characteristic, direct product factor, Sylow
48C22×C7×Q8—22no—
49C22×C7×Q8—22no—
50C22×C7×Q8—21no—
51C22×C7×Q8—21no—
52C22×C7×Q8—22no—
53C22×C7×Q8—24no—
54C22×C7×Q8—24no—
55C22×C7×Q8—42no—
56C22×C7×Q8—42no—
57C22×C7×Q8D414yes—
58C22×C7×Q8C2311yescharacteristic
59C22×C7×Q8C2311yescharacteristic
60C22×C7×Q8C2311yescharacteristic
61C22×C7×D4D411yescharacteristic
62C23×C4×C7—21no—
63C23×C4×C7—21no—
64C23×C4×C7—21no—
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C22×C7×C8—22no—
68C22×C7×C8—42no—
69C22×C7×C8C2312yes—
70C22×C7×C8C2312yes—
71C7×C4⋊Q8—28no—
72C7×C4⋊Q8—22no—
73C7×C4⋊Q8—22no—
74C7×#123—44no—
75C7×C22⋊Q8—28no—
76C7×C22⋊Q8—28no—
77C7×C22⋊Q8—22no—
78C7×C22⋊Q8—22no—
79C7×C22⋊Q8—22no—
80C7×C22⋊Q8D414yes—
81C4×C7×Q8—22no—
82C4×C7×Q8—22no—
83C4×C7×D4—28no—
84C4×C7×D4—22no—
85C4×C7×D4—22no—
86C2×C7×C4⋊C4—21no—
87C2×C7×C4⋊C4—21no—
88C2×C7×C4⋊C4—21no—
89C2×C7×C4⋊C4—21no—
90C2×C7×C4⋊C4—21no—
91C2×C7×C4⋊C4—22no—
92C2×C7×C4⋊C4—22no—
93C2×C7×C4⋊C4—21no—
94C2×C7×C4⋊C4—22no—
95C2×C7×C4⋊C4D411yescharacteristic
96C2×C7×C4⋊C4C2312yes—
97C2×C7×C4⋊C4C2312yes—
98C2×C7×C4⋊C4C2311yescharacteristic
99C2×C7×C22⋊C4—21no—
100C2×C7×C22⋊C4—21no—
101C2×C7×C22⋊C4—21no—
102C2×C7×C22⋊C4—22no—
103C2×C7×C22⋊C4D411yescharacteristic
104C2×C7×C22⋊C4D411yescharacteristic
105C2×C42×C7—21no—
106C2×C42×C7C2311yescharacteristic
107C7×#106—24no—
108C7×#103—24no—
109C7×#103—24no—
110C7×#103—24no—
111C7×#103—24no—
112C7×#103—42no—
113C7×#103—42no—
114C7×C22⋊C8—22no—
115C7×C22⋊C8—42no—
116C7×#95—22no—
117C7×#95—21no—
118C7×#95—22no—
119C2×D4×Q8C2×C711yescharacteristic
120C2×#483C2×C711yescharacteristic, complemented
121C22×#103C2×C711yescharacteristic, complemented
122#2486C2×C711yescharacteristic
123#2043C2×C712yescomplemented
124#2035C2×C712yescomplemented
125#1892C2×C711yescharacteristic, complemented
126#1869C2×C711yescharacteristic
127#1865C2×C712yescomplemented
128#1787C2×C712yescomplemented
129#1787C2×C711yescharacteristic, complemented
130C24×C7C2×D411yescharacteristic
131C24×C7C2×D411yescharacteristic
132C2×C7×Q8—24no—
133C2×C7×Q8—24no—
134C2×C7×Q8—21no—
135C2×C7×Q8—21no—
136C2×C7×Q8—21no—
137C2×C7×Q8—22no—
138C2×C7×Q8—28no—
139C2×C7×Q8—22no—
140C2×C7×Q8—22no—
141C2×C7×Q8—22no—
142C2×C7×Q8—22no—
143C2×C7×Q8—44no—
144C2×C7×Q8—44no—
145C2×C7×Q8—44no—
146C2×C7×Q8—48no—
147C2×C7×Q8—48no—
148C2×C7×Q8—44no—
149C2×C7×Q8—44no—
150C2×C7×Q8C2×D412yes—
151C2×C7×Q8C2×D412yes—
152C2×C7×Q8C2×D412yes—
153C2×C7×Q8#4114yes—
154C2×C7×D4—22no—
155C2×C7×D4—22no—
156C2×C7×D4SD1614yes—
157C22×C4×C7—21no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—24no—
161C22×C4×C7—24no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—22no—
168C22×C4×C7—22no—
169C22×C4×C7—22no—
170C22×C4×C7—22no—
171C22×C4×C7—44no—
172C22×C4×C7—44no—
173C22×C4×C7—42no—
174C22×C4×C7—42no—
175C22×C4×C7—42no—
176C22×C4×C7C2×D411yescharacteristic
177C22×C4×C7C2×D411yescharacteristic
178C22×C4×C7C2×D411yescharacteristic
179C22×C4×C7C2×D412yes—
180C22×C4×C7C2×D412yes—
181C22×C4×C7C2×D411yescharacteristic
182C22×C4×C7C2411yescharacteristic
183C2×C7×C8—22no—
184C2×C7×C8—22no—
185C2×C7×C8—22no—
186C2×C7×C8—22no—
187C2×C7×C8—22no—
188C2×C7×C8—22no—
189C2×C7×C8—44no—
190C7×C4⋊C4—24no—
191C7×C4⋊C4—24no—
192C7×C4⋊C4—24no—
193C7×C4⋊C4—24no—
194C7×C4⋊C4—24no—
195C7×C4⋊C4—22no—
196C7×C4⋊C4—21no—
197C7×C4⋊C4—22no—
198C7×C4⋊C4—22no—
199C7×C4⋊C4—22no—
200C7×C4⋊C4—22no—
201C7×C4⋊C4—42no—
202C7×C4⋊C4—44no—
203C7×C4⋊C4C2×D412yes—
204C7×C22⋊C4—24no—
205C7×C22⋊C4—24no—
206C7×C22⋊C4—22no—
207C7×C22⋊C4—22no—
208C7×C22⋊C4—42no—
209C7×C22⋊C4—44no—
210C42×C7—24no—
211C42×C7—21no—
212C42×C7—21no—
213C23×Q8C22×C711yescharacteristic
214C23×Q8C22×C711yescharacteristic
215C23×C8C22×C711yescharacteristic
216D4×Q8—24no—
217D4×Q8—24no—
218C2×C4⋊Q8—21no—
219C2×C4⋊Q8C22×C711yescharacteristic
220C2×#123—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8C22×C711yescharacteristic
224C2×C22⋊Q8C22×C711yescharacteristic
225C2×C4×Q8C22×C711yescharacteristic
226C2×C4×D4—21no—
227C2×C4×D4C22×C711yescharacteristic
228C22×C4⋊C4C22×C711yescharacteristic
229#483—24no—
230C2×#106C22×C712yes—
231C2×#103—24no—
232C2×#103C22×C712yes—
233C2×#103C22×C712yes—
234C2×#103C22×C712yes—
235C2×#103C22×C712yes—
236C2×#103C22×C712yes—
237C2×#103C22×C712yes—
238C2×C22⋊C8C22×C711yescharacteristic
239C2×C22⋊C8C22×C712yes—
240#398—21no—
241#397—21no—
242#389C22×C712yes—
243#381—21no—
244#380C22×C711yescharacteristic
245#380C22×C712yes—
246#340C22×C712yes—
247#336C22×C712yes—
248C23×C7—22no—
249C23×C7—22no—
250C23×C7—21no—
251C23×C7—22no—
252C23×C7—21no—
253C23×C7—22no—
254C23×C7#12012yes—
255C23×C7C2×SD1612yes—
256C23×C7C2×SD1612yes—
257C23×C7#13712yes—
258C23×C7C22×D411yescharacteristic
259C7×Q8—22no—
260C7×Q8—24no—
261C7×Q8—22no—
262C7×Q8—22no—
263C7×Q8—24no—
264C7×Q8—48no—
265C7×Q8—48no—
266C7×Q8—41no—
267C7×Q8—41no—
268C7×Q8—42no—
269C7×Q8#12314yescomplemented
270C7×D4—28no—
271C2×C4×C7—21no—
272C2×C4×C7—22no—
273C2×C4×C7—22no—
274C2×C4×C7—24no—
275C2×C4×C7—21no—
276C2×C4×C7—22no—
277C2×C4×C7—22no—
278C2×C4×C7—24no—
279C2×C4×C7—21no—
280C2×C4×C7—22no—
281C2×C4×C7—22no—
282C2×C4×C7—22no—
283C2×C4×C7—21no—
284C2×C4×C7—22no—
285C2×C4×C7—22no—
286C2×C4×C7—48no—
287C2×C4×C7—48no—
288C2×C4×C7—42no—
289C2×C4×C7—42no—
290C2×C4×C7—42no—
291C2×C4×C7—41no—
292C2×C4×C7—41no—
293C2×C4×C7—42no—
294C2×C4×C7—42no—
295C2×C4×C7—42no—
296C2×C4×C7—42no—
297C2×C4×C7—42no—
298C2×C4×C7—42no—
299C2×C4×C7—42no—
300C2×C4×C7—84no—
301C2×C4×C7#12012yes—
302C2×C4×C7C2×SD1612yes—
303C2×C4×C7C22×D411yescharacteristic
304C2×C4×C7C22×D411yescharacteristic
305C2×C4×C7C2×#4112yes—
306C2×C4×C7H(5,𝔽2)12yes—
307C7×C8—42no—
308C7×C8—42no—
309C22×Q8—22no—
310C22×Q8—22no—
311C22×Q8—21no—
312C22×Q8—21no—
313C22×Q8—22no—
314C22×Q8—24no—
315C22×Q8—24no—
316C22×Q8—42no—
317C22×Q8—42no—
318C22×Q8C7×D414yes—
319C22×Q8C23×C711yescharacteristic
320C22×Q8C23×C711yescharacteristic
321C22×Q8C23×C711yescharacteristic
322C22×D4C7×D411yescharacteristic
323C23×C4—21no—
324C23×C4—21no—
325C23×C4—21no—
326C23×C4C23×C711yescharacteristic
327C23×C4C23×C711yescharacteristic
328C22×C8—22no—
329C22×C8—42no—
330C22×C8C23×C712yes—
331C22×C8C23×C712yes—
332C4⋊Q8—28no—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335#123—44no—
336C22⋊Q8—28no—
337C22⋊Q8—28no—
338C22⋊Q8—22no—
339C22⋊Q8—22no—
340C22⋊Q8—22no—
341C22⋊Q8C7×D414yes—
342C4×Q8—22no—
343C4×Q8—22no—
344C4×D4—28no—
345C4×D4—22no—
346C4×D4—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4C7×D411yescharacteristic
357C2×C4⋊C4C23×C712yes—
358C2×C4⋊C4C23×C712yes—
359C2×C4⋊C4C23×C711yescharacteristic
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4C7×D411yescharacteristic
365C2×C22⋊C4C7×D411yescharacteristic
366C2×C42—21no—
367C2×C42C23×C711yescharacteristic
368#106—24no—
369#103—24no—
370#103—24no—
371#103—24no—
372#103—24no—
373#103—42no—
374#103—42no—
375C22⋊C8—22no—
376C22⋊C8—42no—
377#95—22no—
378#95—21no—
379#95—22no—
380C22×C7—22no—
381C22×C7—22no—
382C22×C7—24no—
383C22×C7—24no—
384C22×C7—22no—
385C22×C7—24no—
386C22×C7—41no—
387C22×C7—41no—
388C22×C7—42no—
389C22×C7#44814yes—
390C22×C7C2×#12011yescharacteristic
391C22×C7#54612yes—
392C22×C7C22×SD1611yescharacteristic
393C22×C7C2×#13711yescharacteristic
394C22×C7#57812yes—
395C4×C7—22no—
396C4×C7—24no—
397C4×C7—22no—
398C4×C7—41no—
399C4×C7—42no—
400C4×C7—42no—
401C4×C7—41no—
402C4×C7—42no—
403C4×C7—82no—
404C4×C7—82no—
405C4×C7C2×#12311yescharacteristic
406C4×C7#53411yescharacteristic
407C4×C7#54612yes—
408C24C2×C7×D411yescharacteristic
409C24C2×C7×D411yescharacteristic
410C2×Q8—24no—
411C2×Q8—24no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—22no—
416C2×Q8—28no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—44no—
422C2×Q8—44no—
423C2×Q8—44no—
424C2×Q8—48no—
425C2×Q8—48no—
426C2×Q8—44no—
427C2×Q8—44no—
428C2×Q8C2×C7×D412yes—
429C2×Q8C2×C7×D412yes—
430C2×Q8C2×C7×D412yes—
431C2×Q8C7×#4114yes—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4C7×SD1614yes—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—44no—
450C22×C4—44no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4C2×C7×D411yescharacteristic
455C22×C4C2×C7×D411yescharacteristic
456C22×C4C2×C7×D411yescharacteristic
457C22×C4C2×C7×D412yes—
458C22×C4C2×C7×D412yes—
459C22×C4C2×C7×D411yescharacteristic
460C22×C4C24×C711yescharacteristic
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—44no—
468C4⋊C4—24no—
469C4⋊C4—24no—
470C4⋊C4—24no—
471C4⋊C4—24no—
472C4⋊C4—24no—
473C4⋊C4—22no—
474C4⋊C4—21no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—42no—
480C4⋊C4—44no—
481C4⋊C4C2×C7×D412yes—
482C22⋊C4—24no—
483C22⋊C4—24no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—42no—
487C22⋊C4—44no—
488C42—24no—
489C42—21no—
490C42—21no—
491C2×C7—24no—
492C2×C7—42no—
493C2×C7#240511yescharacteristic
494C2×C7C2×#44811yescharacteristic
495C2×C7#301111yescharacteristic
496C2×C7#329812yes—
497C2×C7#331212yes—
498C23—22no—
499C23—22no—
500C23—21no—
501C23—22no—
502C23—21no—
503C23—22no—
504C23C7×#12012yes—
505C23C2×C7×SD1612yes—
506C23C2×C7×SD1612yes—
507C23C7×#13712yes—
508C23C22×C7×D411yescharacteristic
509Q8—22no—
510Q8—24no—
511Q8—22no—
512Q8—22no—
513Q8—24no—
514Q8—48no—
515Q8—48no—
516Q8—41no—
517Q8—41no—
518Q8—42no—
519Q8C7×#12314yescomplemented
520D4—28no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—48no—
537C2×C4—48no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—84no—
551C2×C4C7×#12012yes—
552C2×C4C2×C7×SD1612yes—
553C2×C4C22×C7×D411yescharacteristic
554C2×C4C22×C7×D411yescharacteristic
555C2×C4C2×C7×#4112yes—
556C2×C4C7×H(5,𝔽2)12yes—
557C8—42no—
558C8—42no—
559C7#2404111yescharacteristic, direct product factor, Sylow
560C22—22no—
561C22—22no—
562C22—24no—
563C22—24no—
564C22—22no—
565C22—24no—
566C22—41no—
567C22—41no—
568C22—42no—
569C22C7×#44814yes—
570C22C2×C7×#12011yescharacteristic
571C22C7×#54612yes—
572C22C22×C7×SD1611yescharacteristic
573C22C2×C7×#13711yescharacteristic
574C22C7×#57812yes—
575C4—22no—
576C4—24no—
577C4—22no—
578C4—41no—
579C4—42no—
580C4—42no—
581C4—41no—
582C4—42no—
583C4—82no—
584C4—82no—
585C4C2×C7×#12311yescharacteristic
586C4C7×#53411yescharacteristic
587C4C7×#54612yes—
588C2—24no—
589C2—42no—
590C2C7×#240511yescharacteristic
591C2C2×C7×#44811yescharacteristic
592C2C7×#301111yescharacteristic
593C2C7×#329812yes—
594C2C7×#331212yes—
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC22×C7×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C2×C4×C7×D4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#483C2semidirect
3. C22×C7×#103C2semidirect
5. C7×#2043C2semidirect
6. C7×#2035C2semidirect
7. C7×#1892C2semidirect
9. C7×#1865C2semidirect
10. C7×#1787C2semidirect
11. C7×#1787C2semidirect
47. #24041C7direct (N × H)
120. C2×#483C2×C7semidirect
121. C22×#103C2×C7semidirect
123. #2043C2×C7semidirect
124. #2035C2×C7semidirect
125. #1892C2×C7semidirect
127. #1865C2×C7semidirect
128. #1787C2×C7semidirect
129. #1787C2×C7semidirect
269. C7×Q8#123semidirect
519. Q8C7×#123semidirect
559. C7#24041direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×D4×Q82
C2×C7×#4832
C22×C7×#1032
C7×#24862
C7×#20432
C7×#20352
C7×#18922
C7×#18692
C7×#18652
C7×#17872
#240417