Finite Group Databasebeta

← C7×#24042 #13201258

Subgroups — C7×#24042 #13201258

Order 1792.

1318 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×D4×Q8C211yesmaximal, characteristic
2C2×C7×#484C211yesmaximal, characteristic, complemented
3C22×C7×#103C211yesmaximal, characteristic, complemented
4C7×#2487C211yesmaximal, characteristic
5C7×#2043C212yesmaximal, complemented
6C7×#2036C212yesmaximal, complemented
7C7×#1892C211yesmaximal, characteristic, complemented
8C7×#1869C211yesmaximal, characteristic
9C7×#1863C212yesmaximal, 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×C22⋊Q8—21no—
20C2×C7×C22⋊Q8—21no—
21C2×C7×C22⋊Q8C2211yescharacteristic
22C2×C7×C22⋊Q8C2211yescharacteristic
23C2×C4×C7×Q8C2211yescharacteristic
24C2×C4×C7×D4—21no—
25C2×C4×C7×D4C2211yescharacteristic
26C22×C7×C4⋊C4C2211yescharacteristic
27C7×#484—24no—
28C2×C7×#107C2212yes—
29C2×C7×#103—24no—
30C2×C7×#103C2212yes—
31C2×C7×#103C2212yes—
32C2×C7×#103C2212yes—
33C2×C7×#103C2212yes—
34C2×C7×#103C2212yes—
35C2×C7×#103C2212yes—
36C2×C7×C22⋊C8C2211yescharacteristic
37C2×C7×C22⋊C8C2212yes—
38C7×#400—21no—
39C7×#399—21no—
40C7×#389C2212yes—
41C7×#386—21no—
42C7×#385—21no—
43C7×#380C2212yes—
44C7×#380C2211yescharacteristic
45C7×#340C2212yes—
46C7×#336C2212yes—
47#24042C711yesmaximal, 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×C22⋊Q8—28no—
75C7×C22⋊Q8—28no—
76C7×C22⋊Q8—22no—
77C7×C22⋊Q8—22no—
78C7×C22⋊Q8—22no—
79C7×C22⋊Q8D414yes—
80C4×C7×Q8—22no—
81C4×C7×Q8—22no—
82C4×C7×D4—28no—
83C4×C7×D4—22no—
84C4×C7×D4—22no—
85C2×C7×C4⋊C4—21no—
86C2×C7×C4⋊C4—21no—
87C2×C7×C4⋊C4—21no—
88C2×C7×C4⋊C4—21no—
89C2×C7×C4⋊C4—21no—
90C2×C7×C4⋊C4—22no—
91C2×C7×C4⋊C4—22no—
92C2×C7×C4⋊C4—21no—
93C2×C7×C4⋊C4—22no—
94C2×C7×C4⋊C4D411yescharacteristic
95C2×C7×C4⋊C4C2312yes—
96C2×C7×C4⋊C4C2312yes—
97C2×C7×C4⋊C4C2311yescharacteristic
98C2×C7×C22⋊C4—21no—
99C2×C7×C22⋊C4—21no—
100C2×C7×C22⋊C4—21no—
101C2×C7×C22⋊C4—22no—
102C2×C7×C22⋊C4D411yescharacteristic
103C2×C7×C22⋊C4D411yescharacteristic
104C2×C42×C7—21no—
105C2×C42×C7C2311yescharacteristic
106C7×#107—24no—
107C7×#103—24no—
108C7×#103—24no—
109C7×#103—24no—
110C7×#103—24no—
111C7×#103—42no—
112C7×#103—42no—
113C7×C22⋊C8—22no—
114C7×C22⋊C8—42no—
115C7×#95—22no—
116C7×#95—21no—
117C7×#95—22no—
118C2×D4×Q8C2×C711yescharacteristic
119C2×#484C2×C711yescharacteristic, complemented
120C22×#103C2×C711yescharacteristic, complemented
121#2487C2×C711yescharacteristic
122#2043C2×C712yescomplemented
123#2036C2×C712yescomplemented
124#1892C2×C711yescharacteristic, complemented
125#1869C2×C711yescharacteristic
126#1863C2×C712yescomplemented
127#1787C2×C712yescomplemented
128#1787C2×C711yescharacteristic, complemented
129C24×C7C2×D411yescharacteristic
130C24×C7C2×D411yescharacteristic
131C2×C7×Q8—24no—
132C2×C7×Q8—24no—
133C2×C7×Q8—21no—
134C2×C7×Q8—21no—
135C2×C7×Q8—21no—
136C2×C7×Q8—22no—
137C2×C7×Q8—28no—
138C2×C7×Q8—22no—
139C2×C7×Q8—22no—
140C2×C7×Q8—22no—
141C2×C7×Q8—22no—
142C2×C7×Q8—44no—
143C2×C7×Q8—44no—
144C2×C7×Q8—44no—
145C2×C7×Q8—48no—
146C2×C7×Q8—48no—
147C2×C7×Q8—44no—
148C2×C7×Q8—44no—
149C2×C7×Q8C2×D412yes—
150C2×C7×Q8C2×D412yes—
151C2×C7×Q8C2×D412yes—
152C2×C7×Q8#4114yes—
153C2×C7×D4—22no—
154C2×C7×D4—22no—
155C2×C7×D4Q1614yes—
156C22×C4×C7—21no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—24no—
160C22×C4×C7—24no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—22no—
167C22×C4×C7—22no—
168C22×C4×C7—22no—
169C22×C4×C7—22no—
170C22×C4×C7—44no—
171C22×C4×C7—44no—
172C22×C4×C7—42no—
173C22×C4×C7—82no—
174C22×C4×C7C2×D411yescharacteristic
175C22×C4×C7C2×D411yescharacteristic
176C22×C4×C7C2×D411yescharacteristic
177C22×C4×C7C2×D412yes—
178C22×C4×C7C2×D412yes—
179C22×C4×C7C2×D411yescharacteristic
180C22×C4×C7C2411yescharacteristic
181C2×C7×C8—22no—
182C2×C7×C8—22no—
183C2×C7×C8—22no—
184C2×C7×C8—22no—
185C2×C7×C8—22no—
186C2×C7×C8—22no—
187C2×C7×C8—44no—
188C7×C4⋊C4—24no—
189C7×C4⋊C4—24no—
190C7×C4⋊C4—24no—
191C7×C4⋊C4—24no—
192C7×C4⋊C4—24no—
193C7×C4⋊C4—22no—
194C7×C4⋊C4—21no—
195C7×C4⋊C4—22no—
196C7×C4⋊C4—22no—
197C7×C4⋊C4—22no—
198C7×C4⋊C4—22no—
199C7×C4⋊C4—42no—
200C7×C4⋊C4—82no—
201C7×C4⋊C4C2×D412yes—
202C7×C22⋊C4—24no—
203C7×C22⋊C4—24no—
204C7×C22⋊C4—22no—
205C7×C22⋊C4—22no—
206C7×C22⋊C4—42no—
207C7×C22⋊C4—82no—
208C42×C7—24no—
209C42×C7—21no—
210C42×C7—21no—
211C23×Q8C22×C711yescharacteristic
212C23×Q8C22×C711yescharacteristic
213C23×C8C22×C711yescharacteristic
214D4×Q8—24no—
215D4×Q8—24no—
216C2×C4⋊Q8—21no—
217C2×C4⋊Q8C22×C711yescharacteristic
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8C22×C711yescharacteristic
221C2×C22⋊Q8C22×C711yescharacteristic
222C2×C4×Q8C22×C711yescharacteristic
223C2×C4×D4—21no—
224C2×C4×D4C22×C711yescharacteristic
225C22×C4⋊C4C22×C711yescharacteristic
226#484—24no—
227C2×#107C22×C712yes—
228C2×#103—24no—
229C2×#103C22×C712yes—
230C2×#103C22×C712yes—
231C2×#103C22×C712yes—
232C2×#103C22×C712yes—
233C2×#103C22×C712yes—
234C2×#103C22×C712yes—
235C2×C22⋊C8C22×C711yescharacteristic
236C2×C22⋊C8C22×C712yes—
237#400—21no—
238#399—21no—
239#389C22×C712yes—
240#386—21no—
241#385—21no—
242#380C22×C711yescharacteristic
243#380C22×C712yes—
244#340C22×C712yes—
245#336C22×C712yes—
246C23×C7—22no—
247C23×C7—22no—
248C23×C7—21no—
249C23×C7—22no—
250C23×C7—21no—
251C23×C7—22no—
252C23×C7#12012yes—
253C23×C7C2×Q1612yes—
254C23×C7C2×Q1612yes—
255C23×C7#13712yes—
256C23×C7C22×D411yescharacteristic
257C7×Q8—22no—
258C7×Q8—24no—
259C7×Q8—22no—
260C7×Q8—22no—
261C7×Q8—24no—
262C7×Q8—48no—
263C7×Q8—48no—
264C7×Q8—41no—
265C7×Q8—41no—
266C7×Q8—42no—
267C7×Q8#12314yes—
268C7×D4—28no—
269C2×C4×C7—21no—
270C2×C4×C7—22no—
271C2×C4×C7—22no—
272C2×C4×C7—24no—
273C2×C4×C7—21no—
274C2×C4×C7—22no—
275C2×C4×C7—22no—
276C2×C4×C7—24no—
277C2×C4×C7—21no—
278C2×C4×C7—22no—
279C2×C4×C7—22no—
280C2×C4×C7—22no—
281C2×C4×C7—21no—
282C2×C4×C7—22no—
283C2×C4×C7—22no—
284C2×C4×C7—48no—
285C2×C4×C7—48no—
286C2×C4×C7—42no—
287C2×C4×C7—42no—
288C2×C4×C7—42no—
289C2×C4×C7—41no—
290C2×C4×C7—41no—
291C2×C4×C7—42no—
292C2×C4×C7—42no—
293C2×C4×C7—42no—
294C2×C4×C7—42no—
295C2×C4×C7—42no—
296C2×C4×C7—42no—
297C2×C4×C7—42no—
298C2×C4×C7—84no—
299C2×C4×C7#12012yes—
300C2×C4×C7C2×Q1612yes—
301C2×C4×C7C22×D411yescharacteristic
302C2×C4×C7C22×D411yescharacteristic
303C2×C4×C7C2×#4112yes—
304C2×C4×C7H(5,𝔽2)12yes—
305C7×C8—42no—
306C7×C8—42no—
307C22×Q8—22no—
308C22×Q8—22no—
309C22×Q8—21no—
310C22×Q8—21no—
311C22×Q8—22no—
312C22×Q8—24no—
313C22×Q8—24no—
314C22×Q8—42no—
315C22×Q8—42no—
316C22×Q8C7×D414yes—
317C22×Q8C23×C711yescharacteristic
318C22×Q8C23×C711yescharacteristic
319C22×Q8C23×C711yescharacteristic
320C22×D4C7×D411yescharacteristic
321C23×C4—21no—
322C23×C4—21no—
323C23×C4—21no—
324C23×C4C23×C711yescharacteristic
325C23×C4C23×C711yescharacteristic
326C22×C8—22no—
327C22×C8—42no—
328C22×C8C23×C712yes—
329C22×C8C23×C712yes—
330C4⋊Q8—28no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C22⋊Q8—28no—
334C22⋊Q8—28no—
335C22⋊Q8—22no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338C22⋊Q8C7×D414yes—
339C4×Q8—22no—
340C4×Q8—22no—
341C4×D4—28no—
342C4×D4—22no—
343C4×D4—22no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4C7×D411yescharacteristic
354C2×C4⋊C4C23×C712yes—
355C2×C4⋊C4C23×C712yes—
356C2×C4⋊C4C23×C711yescharacteristic
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4C7×D411yescharacteristic
362C2×C22⋊C4C7×D411yescharacteristic
363C2×C42—21no—
364C2×C42C23×C711yescharacteristic
365#107—24no—
366#103—24no—
367#103—24no—
368#103—24no—
369#103—24no—
370#103—42no—
371#103—42no—
372C22⋊C8—22no—
373C22⋊C8—42no—
374#95—22no—
375#95—21no—
376#95—22no—
377C22×C7—22no—
378C22×C7—22no—
379C22×C7—24no—
380C22×C7—24no—
381C22×C7—22no—
382C22×C7—24no—
383C22×C7—41no—
384C22×C7—41no—
385C22×C7—42no—
386C22×C7#45114yes—
387C22×C7C2×#12011yescharacteristic
388C22×C7#54612yes—
389C22×C7C22×Q1611yescharacteristic
390C22×C7C2×#13711yescharacteristic
391C22×C7#57712yes—
392C4×C7—22no—
393C4×C7—24no—
394C4×C7—22no—
395C4×C7—41no—
396C4×C7—42no—
397C4×C7—42no—
398C4×C7—41no—
399C4×C7—42no—
400C4×C7—82no—
401C4×C7—82no—
402C4×C7C2×#12311yescharacteristic
403C4×C7#53411yescharacteristic
404C4×C7#54612yes—
405C24C2×C7×D411yescharacteristic
406C24C2×C7×D411yescharacteristic
407C2×Q8—24no—
408C2×Q8—24no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—22no—
413C2×Q8—28no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—44no—
419C2×Q8—44no—
420C2×Q8—44no—
421C2×Q8—48no—
422C2×Q8—48no—
423C2×Q8—44no—
424C2×Q8—44no—
425C2×Q8C2×C7×D412yes—
426C2×Q8C2×C7×D412yes—
427C2×Q8C2×C7×D412yes—
428C2×Q8C7×#4114yes—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4C7×Q1614yes—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—44no—
447C22×C4—44no—
448C22×C4—42no—
449C22×C4—82no—
450C22×C4C2×C7×D411yescharacteristic
451C22×C4C2×C7×D411yescharacteristic
452C22×C4C2×C7×D411yescharacteristic
453C22×C4C2×C7×D412yes—
454C22×C4C2×C7×D412yes—
455C22×C4C2×C7×D411yescharacteristic
456C22×C4C24×C711yescharacteristic
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—44no—
464C4⋊C4—24no—
465C4⋊C4—24no—
466C4⋊C4—24no—
467C4⋊C4—24no—
468C4⋊C4—24no—
469C4⋊C4—22no—
470C4⋊C4—21no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—42no—
476C4⋊C4—82no—
477C4⋊C4C2×C7×D412yes—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—42no—
483C22⋊C4—82no—
484C42—24no—
485C42—21no—
486C42—21no—
487C2×C7—24no—
488C2×C7—42no—
489C2×C7#240511yescharacteristic
490C2×C7C2×#45111yescharacteristic
491C2×C7#301011yescharacteristic
492C2×C7#329912yes—
493C2×C7#332012yes—
494C23—22no—
495C23—22no—
496C23—21no—
497C23—22no—
498C23—21no—
499C23—22no—
500C23C7×#12012yes—
501C23C2×C7×Q1612yes—
502C23C2×C7×Q1612yes—
503C23C7×#13712yes—
504C23C22×C7×D411yescharacteristic
505Q8—22no—
506Q8—24no—
507Q8—22no—
508Q8—22no—
509Q8—24no—
510Q8—48no—
511Q8—48no—
512Q8—41no—
513Q8—41no—
514Q8—42no—
515Q8C7×#12314yes—
516D4—28no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—48no—
533C2×C4—48no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—84no—
547C2×C4C7×#12012yes—
548C2×C4C2×C7×Q1612yes—
549C2×C4C22×C7×D411yescharacteristic
550C2×C4C22×C7×D411yescharacteristic
551C2×C4C2×C7×#4112yes—
552C2×C4C7×H(5,𝔽2)12yes—
553C8—42no—
554C8—42no—
555C7#2404211yescharacteristic, direct product factor, Sylow
556C22—22no—
557C22—22no—
558C22—24no—
559C22—24no—
560C22—22no—
561C22—24no—
562C22—41no—
563C22—41no—
564C22—42no—
565C22C7×#45114yes—
566C22C2×C7×#12011yescharacteristic
567C22C7×#54612yes—
568C22C22×C7×Q1611yescharacteristic
569C22C2×C7×#13711yescharacteristic
570C22C7×#57712yes—
571C4—22no—
572C4—24no—
573C4—22no—
574C4—41no—
575C4—42no—
576C4—42no—
577C4—41no—
578C4—42no—
579C4—82no—
580C4—82no—
581C4C2×C7×#12311yescharacteristic
582C4C7×#53411yescharacteristic
583C4C7×#54612yes—
584C2—24no—
585C2—42no—
586C2C7×#240511yescharacteristic
587C2C2×C7×#45111yescharacteristic
588C2C7×#301011yescharacteristic
589C2C7×#329912yes—
590C2C7×#332012yes—
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×#484C2semidirect
3. C22×C7×#103C2semidirect
5. C7×#2043C2semidirect
6. C7×#2036C2semidirect
7. C7×#1892C2semidirect
9. C7×#1863C2semidirect
10. C7×#1787C2semidirect
11. C7×#1787C2semidirect
47. #24042C7direct (N × H)
119. C2×#484C2×C7semidirect
120. C22×#103C2×C7semidirect
122. #2043C2×C7semidirect
123. #2036C2×C7semidirect
124. #1892C2×C7semidirect
126. #1863C2×C7semidirect
127. #1787C2×C7semidirect
128. #1787C2×C7semidirect
555. C7#24042direct (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×#4842
C22×C7×#1032
C7×#24872
C7×#20432
C7×#20362
C7×#18922
C7×#18692
C7×#18632
C7×#17872
#240427