Finite Group Databasebeta

← C7×#16505 #13193721

Subgroups — C7×#16505 #13193721

Order 1792.

1942 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#124C211yesmaximal, characteristic
2C2×C7×#396C212yesmaximal, complemented
3C2×C7×#395C211yesmaximal, characteristic, complemented
4C2×C7×#394C211yesmaximal, characteristic
5C2×C7×#387C211yesmaximal, characteristic, complemented
6C7×#1446C211yesmaximal, characteristic, complemented
7C7×#1440C212yesmaximal, complemented
8C7×#1439C212yesmaximal, complemented
9C7×#1439C212yesmaximal, complemented
10C7×#1438C211yesmaximal, characteristic
11C7×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C7×Q8C2211yescharacteristic
13C23×C7×D4C2211yescharacteristic
14C2×C7×#124—28no—
15C2×C7×#124—24no—
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C4⋊C4C2212yes—
18C22×C7×C4⋊C4C2212yes—
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2212yes—
21C22×C7×C22⋊C4C2212yes—
22C22×C7×C22⋊C4C2212yes—
23C22×C7×C22⋊C4C2212yes—
24C22×C7×C22⋊C4C2212yes—
25C22×C7×C22⋊C4C2212yes—
26C22×C42×C7C2211yescharacteristic
27C7×#396—28no—
28C7×#395—24no—
29C7×#394—24no—
30C7×#387—24no—
31C2×C7×#95C2211yescharacteristic
32C2×C7×#95C2212yes—
33C2×C7×#95C2212yes—
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2211yescharacteristic
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2211yescharacteristic
38C2×C7×#95C2211yescharacteristic
39C2×C7×#95C2212yes—
40C2×C7×#95C2212yes—
41#16505C711yesmaximal, characteristic, direct product factor, Sylow
42C25×C7C2312yes—
43C22×C7×Q8—24no—
44C22×C7×Q8—22no—
45C22×C7×Q8—22no—
46C22×C7×Q8—22no—
47C22×C7×Q8—42no—
48C22×C7×D4—24no—
49C22×C7×D4—22no—
50C22×C7×D4—22no—
51C22×C7×D4—22no—
52C22×C7×D4—42no—
53C23×C4×C7C2311yescharacteristic
54C23×C4×C7C2311yescharacteristic
55C23×C4×C7C2312yes—
56C23×C4×C7C2312yes—
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2312yes—
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C7×#124—232no—
64C2×C7×C4⋊C4—22no—
65C2×C7×C4⋊C4—22no—
66C2×C7×C4⋊C4—22no—
67C2×C7×C4⋊C4—24no—
68C2×C7×C4⋊C4—24no—
69C2×C7×C4⋊C4—24no—
70C2×C7×C4⋊C4—24no—
71C2×C7×C4⋊C4—24no—
72C2×C7×C4⋊C4—42no—
73C2×C7×C4⋊C4—42no—
74C2×C7×C4⋊C4D414yes—
75C2×C7×C22⋊C4—24no—
76C2×C7×C22⋊C4—24no—
77C2×C7×C22⋊C4—24no—
78C2×C7×C22⋊C4—24no—
79C2×C7×C22⋊C4—24no—
80C2×C7×C22⋊C4—24no—
81C2×C7×C22⋊C4—24no—
82C2×C7×C22⋊C4—24no—
83C2×C7×C22⋊C4—24no—
84C2×C7×C22⋊C4—24no—
85C2×C7×C22⋊C4—24no—
86C2×C7×C22⋊C4—42no—
87C2×C7×C22⋊C4—42no—
88C2×C7×C22⋊C4—42no—
89C2×C7×C22⋊C4—42no—
90C2×C7×C22⋊C4—42no—
91C2×C7×C22⋊C4—42no—
92C2×C7×C22⋊C4D418yes—
93C2×C42×C7—24no—
94C2×C42×C7D414yes—
95C7×#95—22no—
96C7×#95—22no—
97C7×#95—22no—
98C7×#95—22no—
99C7×#95—22no—
100C7×#95—22no—
101C7×#95—24no—
102C7×#95—24no—
103C7×#95—42no—
104C7×#95—42no—
105C22×#124C2×C711yescharacteristic
106C2×#396C2×C712yescomplemented
107C2×#395C2×C711yescharacteristic, complemented
108C2×#394C2×C711yescharacteristic
109C2×#387C2×C711yescharacteristic, complemented
110#1446C2×C711yescharacteristic, complemented
111#1440C2×C712yescomplemented
112#1439C2×C712yescomplemented
113#1439C2×C712yescomplemented
114#1438C2×C711yescharacteristic
115C4⋊#95C2×C711yescharacteristic, complemented
116C24×C7—22no—
117C24×C7—22no—
118C24×C7—22no—
119C24×C7—22no—
120C24×C7—22no—
121C24×C7—22no—
122C24×C7—22no—
123C24×C7—22no—
124C24×C7—22no—
125C24×C7—22no—
126C24×C7—22no—
127C24×C7—22no—
128C24×C7—22no—
129C24×C7—22no—
130C24×C7C2×D414yes—
131C24×C7C2411yescharacteristic
132C2×C7×Q8—28no—
133C2×C7×Q8—48no—
134C2×C7×Q8—48no—
135C2×C7×Q8—44no—
136C2×C7×Q8—44no—
137C2×C7×D4—28no—
138C2×C7×D4—48no—
139C2×C7×D4—48no—
140C2×C7×D4—44no—
141C2×C7×D4—44no—
142C22×C4×C7—22no—
143C22×C4×C7—22no—
144C22×C4×C7—21no—
145C22×C4×C7—22no—
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7—22no—
149C22×C4×C7—21no—
150C22×C4×C7—22no—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—22no—
154C22×C4×C7—22no—
155C22×C4×C7—22no—
156C22×C4×C7—21no—
157C22×C4×C7—21no—
158C22×C4×C7—22no—
159C22×C4×C7—21no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—22no—
165C22×C4×C7—22no—
166C22×C4×C7—22no—
167C22×C4×C7—22no—
168C22×C4×C7—22no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—22no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—22no—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—22no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—22no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—22no—
190C22×C4×C7C2×D412yes—
191C22×C4×C7C2×D412yes—
192C22×C4×C7C2×D414yes—
193C22×C4×C7C2×D412yes—
194C22×C4×C7C2×D412yes—
195C22×C4×C7C2×D414yes—
196C22×C4×C7C2×D412yes—
197C22×C4×C7C2×D412yes—
198C22×C4×C7#4114yes—
199C22×C4×C7#4112yes—
200C7×C4⋊C4—28no—
201C7×C4⋊C4—48no—
202C7×C4⋊C4—48no—
203C7×C4⋊C4—44no—
204C7×C22⋊C4—216no—
205C7×C22⋊C4—216no—
206C7×C22⋊C4—48no—
207C7×C22⋊C4—48no—
208C7×C22⋊C4—48no—
209C7×C22⋊C4—48no—
210C42×C7—28no—
211C23×Q8C22×C711yescharacteristic
212C23×D4C22×C711yescharacteristic
213C2×#124—28no—
214C2×#124—24no—
215C22×C4⋊C4C22×C711yescharacteristic
216C22×C4⋊C4C22×C712yes—
217C22×C4⋊C4C22×C712yes—
218C22×C4⋊C4C22×C711yescharacteristic
219C22×C22⋊C4C22×C712yes—
220C22×C22⋊C4C22×C712yes—
221C22×C22⋊C4C22×C712yes—
222C22×C22⋊C4C22×C712yes—
223C22×C22⋊C4C22×C712yes—
224C22×C22⋊C4C22×C712yes—
225C22×C42C22×C711yescharacteristic
226#396—28no—
227#395—24no—
228#394—24no—
229#387—24no—
230C2×#95C22×C711yescharacteristic
231C2×#95C22×C711yescharacteristic
232C2×#95C22×C712yes—
233C2×#95C22×C712yes—
234C2×#95C22×C711yescharacteristic
235C2×#95C22×C711yescharacteristic
236C2×#95C22×C711yescharacteristic
237C2×#95C22×C711yescharacteristic
238C2×#95C22×C712yes—
239C2×#95C22×C712yes—
240C23×C7—24no—
241C23×C7—24no—
242C23×C7—24no—
243C23×C7—24no—
244C23×C7—24no—
245C23×C7—24no—
246C23×C7—24no—
247C23×C7—42no—
248C23×C7—42no—
249C23×C7—42no—
250C23×C7—42no—
251C23×C7—42no—
252C23×C7—42no—
253C23×C7—42no—
254C23×C7—42no—
255C23×C7—42no—
256C23×C7—42no—
257C23×C7—42no—
258C23×C7—42no—
259C23×C7—42no—
260C23×C7—42no—
261C23×C7—42no—
262C23×C7—42no—
263C23×C7—42no—
264C23×C7—42no—
265C23×C7—42no—
266C23×C7—42no—
267C23×C7—42no—
268C23×C7—42no—
269C23×C7—42no—
270C23×C7—42no—
271C23×C7—42no—
272C23×C7—42no—
273C23×C7—42no—
274C23×C7—42no—
275C23×C7C22×D411yescharacteristic
276C23×C7C22×D412yes—
277C23×C7C22×D411yescharacteristic
278C23×C7C2×#4111yescharacteristic
279C23×C7C2×#4112yes—
280C23×C7H(5,𝔽2)11yescharacteristic
281C23×C7H(5,𝔽2)11yescharacteristic
282C23×C7H(5,𝔽2)12yes—
283C23×C72−1+411yescharacteristic
284C23×C72−1+412yes—
285C23×C72−1+411yescharacteristic
286C7×Q8—416no—
287C7×D4—416no—
288C2×C4×C7—22no—
289C2×C4×C7—22no—
290C2×C4×C7—22no—
291C2×C4×C7—22no—
292C2×C4×C7—24no—
293C2×C4×C7—24no—
294C2×C4×C7—24no—
295C2×C4×C7—24no—
296C2×C4×C7—22no—
297C2×C4×C7—24no—
298C2×C4×C7—22no—
299C2×C4×C7—22no—
300C2×C4×C7—22no—
301C2×C4×C7—22no—
302C2×C4×C7—22no—
303C2×C4×C7—22no—
304C2×C4×C7—24no—
305C2×C4×C7—24no—
306C2×C4×C7—24no—
307C2×C4×C7—24no—
308C2×C4×C7—24no—
309C2×C4×C7—24no—
310C2×C4×C7—41no—
311C2×C4×C7—42no—
312C2×C4×C7—41no—
313C2×C4×C7—42no—
314C2×C4×C7—42no—
315C2×C4×C7—42no—
316C2×C4×C7—42no—
317C2×C4×C7—41no—
318C2×C4×C7—41no—
319C2×C4×C7—42no—
320C2×C4×C7—41no—
321C2×C4×C7—41no—
322C2×C4×C7—42no—
323C2×C4×C7—42no—
324C2×C4×C7—42no—
325C2×C4×C7—42no—
326C2×C4×C7—42no—
327C2×C4×C7—41no—
328C2×C4×C7—41no—
329C2×C4×C7—41no—
330C2×C4×C7—42no—
331C2×C4×C7—41no—
332C2×C4×C7—41no—
333C2×C4×C7—42no—
334C2×C4×C7—41no—
335C2×C4×C7—42no—
336C2×C4×C7—42no—
337C2×C4×C7—42no—
338C2×C4×C7—42no—
339C2×C4×C7—42no—
340C2×C4×C7—42no—
341C2×C4×C7—42no—
342C2×C4×C7—42no—
343C2×C4×C7—42no—
344C2×C4×C7#12014yes—
345C2×C4×C7#12114yes—
346C25C23×C712yes—
347C22×Q8—24no—
348C22×Q8—22no—
349C22×Q8—22no—
350C22×Q8—22no—
351C22×Q8—42no—
352C22×D4—24no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—42no—
357C23×C4C23×C711yescharacteristic
358C23×C4C23×C712yes—
359C23×C4C23×C711yescharacteristic
360C23×C4C23×C711yescharacteristic
361C23×C4C23×C712yes—
362C23×C4C23×C711yescharacteristic
363C23×C4C23×C711yescharacteristic
364C23×C4C23×C712yes—
365C23×C4C23×C711yescharacteristic
366C23×C4C23×C711yescharacteristic
367#124—232no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—42no—
377C2×C4⋊C4—42no—
378C2×C4⋊C4C7×D414yes—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4C7×D418yes—
397C2×C42—24no—
398C2×C42C7×D414yes—
399#95—22no—
400#95—22no—
401#95—22no—
402#95—22no—
403#95—22no—
404#95—22no—
405#95—24no—
406#95—24no—
407#95—42no—
408#95—42no—
409C22×C7—44no—
410C22×C7—44no—
411C22×C7—44no—
412C22×C7—44no—
413C22×C7—44no—
414C22×C7—44no—
415C22×C7—44no—
416C22×C7—82no—
417C22×C7—82no—
418C22×C7—82no—
419C22×C7—82no—
420C22×C7—82no—
421C22×C7—82no—
422C22×C7—82no—
423C22×C7—82no—
424C22×C7C2×#12011yescharacteristic
425C22×C7C2×#12111yescharacteristic
426C22×C7#53211yescharacteristic
427C22×C7#53511yescharacteristic
428C22×C7#53511yescharacteristic
429C22×C7#53611yescharacteristic
430C22×C7#53612yes—
431C22×C7#53611yescharacteristic
432C22×C7#53711yescharacteristic
433C22×C7#53711yescharacteristic
434C22×C7#53712yes—
435C22×C7#53812yes—
436C22×C7#54211yescharacteristic
437C22×C7#54211yescharacteristic
438C22×C7#54212yes—
439C22×C7D4212yes—
440C22×C7#54612yes—
441C22×C7#54612yes—
442C22×C7#54712yes—
443C22×C7#54812yes—
444C22×C7#55612yes—
445C22×C7#56212yes—
446C22×C7#56312yes—
447C4×C7—24no—
448C4×C7—24no—
449C4×C7—42no—
450C4×C7—42no—
451C4×C7—42no—
452C4×C7—44no—
453C4×C7—44no—
454C4×C7—81no—
455C4×C7—82no—
456C4×C7—81no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24C2×C7×D414yes—
472C24C24×C711yescharacteristic
473C2×Q8—28no—
474C2×Q8—48no—
475C2×Q8—48no—
476C2×Q8—44no—
477C2×Q8—44no—
478C2×D4—28no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—44no—
482C2×D4—44no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4C2×C7×D412yes—
532C22×C4C2×C7×D412yes—
533C22×C4C2×C7×D414yes—
534C22×C4C2×C7×D412yes—
535C22×C4C2×C7×D412yes—
536C22×C4C2×C7×D414yes—
537C22×C4C2×C7×D412yes—
538C22×C4C2×C7×D412yes—
539C22×C4C7×#4114yes—
540C22×C4C7×#4112yes—
541C4⋊C4—28no—
542C4⋊C4—48no—
543C4⋊C4—48no—
544C4⋊C4—44no—
545C22⋊C4—216no—
546C22⋊C4—216no—
547C22⋊C4—48no—
548C22⋊C4—48no—
549C22⋊C4—48no—
550C22⋊C4—48no—
551C42—28no—
552C2×C7—84no—
553C2×C7#240811yescharacteristic
554C2×C7#243011yescharacteristic
555C2×C7#254511yescharacteristic
556C2×C7#261611yescharacteristic
557C2×C7#262011yescharacteristic
558C2×C7#266211yescharacteristic
559C2×C7#267412yes—
560C2×C7#267612yes—
561C2×C7#270012yes—
562C2×C7#271512yes—
563C2×C7#282011yescharacteristic
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—24no—
570C23—24no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23C22×C7×D411yescharacteristic
600C23C22×C7×D412yes—
601C23C22×C7×D411yescharacteristic
602C23C2×C7×#4111yescharacteristic
603C23C2×C7×#4112yes—
604C23C7×H(5,𝔽2)11yescharacteristic
605C23C7×H(5,𝔽2)11yescharacteristic
606C23C7×H(5,𝔽2)12yes—
607C23C7×2−1+411yescharacteristic
608C23C7×2−1+412yes—
609C23C7×2−1+411yescharacteristic
610Q8—416no—
611D4—416no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—22no—
621C2×C4—24no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—41no—
635C2×C4—42no—
636C2×C4—41no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—42no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—42no—
658C2×C4—41no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4C7×#12014yes—
669C2×C4C7×#12114yes—
670C7#1650511yescharacteristic, direct product factor, Sylow
671C22—44no—
672C22—44no—
673C22—44no—
674C22—44no—
675C22—44no—
676C22—44no—
677C22—44no—
678C22—82no—
679C22—82no—
680C22—82no—
681C22—82no—
682C22—82no—
683C22—82no—
684C22—82no—
685C22—82no—
686C22C2×C7×#12011yescharacteristic
687C22C2×C7×#12111yescharacteristic
688C22C7×#53211yescharacteristic
689C22C7×#53511yescharacteristic
690C22C7×#53511yescharacteristic
691C22C7×#53611yescharacteristic
692C22C7×#53612yes—
693C22C7×#53611yescharacteristic
694C22C7×#53711yescharacteristic
695C22C7×#53712yes—
696C22C7×#53711yescharacteristic
697C22C7×#53812yes—
698C22C7×#54212yes—
699C22C7×#54211yescharacteristic
700C22C7×#54211yescharacteristic
701C22C7×D4212yes—
702C22C7×#54612yes—
703C22C7×#54612yes—
704C22C7×#54712yes—
705C22C7×#54812yes—
706C22C7×#55612yes—
707C22C7×#56212yes—
708C22C7×#56312yes—
709C4—24no—
710C4—24no—
711C4—44no—
712C4—42no—
713C4—44no—
714C4—42no—
715C4—42no—
716C4—81no—
717C4—82no—
718C4—81no—
719C2—84no—
720C2C7×#240811yescharacteristic
721C2C7×#243011yescharacteristic
722C2C7×#254511yescharacteristic
723C2C7×#261611yescharacteristic
724C2C7×#262011yescharacteristic
725C2C7×#266211yescharacteristic
726C2C7×#267412yes—
727C2C7×#267612yes—
728C2C7×#270012yes—
729C2C7×#271512yes—
730C2C7×#282011yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC23×C7×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#396C2semidirect
3. C2×C7×#395C2semidirect
5. C2×C7×#387C2semidirect
6. C7×#1446C2semidirect
7. C7×#1440C2semidirect
8. C7×#1439C2semidirect
9. C7×#1439C2semidirect
11. C7×C4⋊#95C2semidirect
41. #16505C7direct (N × H)
106. C2×#396C2×C7semidirect
107. C2×#395C2×C7semidirect
109. C2×#387C2×C7semidirect
110. #1446C2×C7semidirect
111. #1440C2×C7semidirect
112. #1439C2×C7semidirect
113. #1439C2×C7semidirect
115. C4⋊#95C2×C7semidirect
670. C7#16505direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1242
C2×C7×#3962
C2×C7×#3952
C2×C7×#3942
C2×C7×#3872
C7×#14462
C7×#14402
C7×#14392
C7×#14382
C7×C4⋊#952
#165057