Finite Group Databasebeta

← C7×#14735 #13191951

Subgroups — C7×#14735 #13191951

Order 1792.

2110 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#397C211yesmaximal, characteristic, complemented
2C2×C7×#386C212yesmaximal
3C2×C7×#386C211yesmaximal, characteristic
4C2×C7×#380C211yesmaximal, characteristic, complemented
5C22×C7×#95C211yesmaximal, characteristic, complemented
6C7×#1445C211yesmaximal, characteristic, complemented
7C7×#1443C212yesmaximal, complemented
8C7×#1442C211yesmaximal, characteristic, complemented
9C7×#1440C212yesmaximal, complemented
10C7×#1439C211yesmaximal, characteristic, complemented
11C7×C22⋊#95C212yesmaximal, complemented
12C23×C7×D4C2211yescharacteristic
13C24×C4×C7C2212yes—
14C24×C4×C7C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2212yes—
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2212yes—
21C22×C7×C22⋊C4C2212yes—
22C22×C7×C22⋊C4C2211yescharacteristic
23C7×#397—24no—
24C7×#386—28no—
25C7×#386—24no—
26C7×#380—24no—
27C2×C7×#95—24no—
28C2×C7×#95C2212yes—
29C2×C7×#95C2211yescharacteristic
30C2×C7×#95C2212yes—
31C2×C7×#95C2212yes—
32C2×C7×#95C2212yes—
33C2×C7×#95C2211yescharacteristic
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2212yes—
36C2×C7×#95C2212yes—
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39C2×C7×#95C2211yescharacteristic
40#14735C711yesmaximal, characteristic, direct product factor, Sylow
41C25×C7C2311yescharacteristic
42C25×C7C2311yescharacteristic
43C22×C7×D4—22no—
44C22×C7×D4—22no—
45C22×C7×D4—24no—
46C22×C7×D4—24no—
47C22×C7×D4D414yes—
48C23×C4×C7—24no—
49C23×C4×C7—24no—
50C23×C4×C7—24no—
51C23×C4×C7—22no—
52C23×C4×C7—24no—
53C23×C4×C7—22no—
54C23×C4×C7—24no—
55C23×C4×C7—24no—
56C23×C4×C7—42no—
57C23×C4×C7—42no—
58C23×C4×C7—42no—
59C23×C4×C7D414yes—
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2312yes—
63C23×C4×C7C2312yes—
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2312yes—
67C23×C4×C7C2312yes—
68C23×C4×C7C2311yescharacteristic
69C2×C7×C4⋊C4—22no—
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4—22no—
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4—42no—
74C2×C7×C22⋊C4—24no—
75C2×C7×C22⋊C4—24no—
76C2×C7×C22⋊C4—24no—
77C2×C7×C22⋊C4—24no—
78C2×C7×C22⋊C4—22no—
79C2×C7×C22⋊C4—24no—
80C2×C7×C22⋊C4—24no—
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—24no—
84C2×C7×C22⋊C4—22no—
85C2×C7×C22⋊C4—24no—
86C2×C7×C22⋊C4—22no—
87C2×C7×C22⋊C4—42no—
88C2×C7×C22⋊C4—42no—
89C2×C7×C22⋊C4—42no—
90C7×#95—24no—
91C7×#95—22no—
92C7×#95—24no—
93C7×#95—22no—
94C7×#95—22no—
95C7×#95—24no—
96C7×#95—24no—
97C7×#95—24no—
98C7×#95—24no—
99C7×#95—42no—
100C7×#95—42no—
101C7×#95D414yescomplemented
102C2×#397C2×C711yescharacteristic, complemented
103C2×#386C2×C711yescharacteristic
104C2×#386C2×C712yes—
105C2×#380C2×C711yescharacteristic, complemented
106C22×#95C2×C711yescharacteristic, complemented
107#1445C2×C711yescharacteristic, complemented
108#1443C2×C712yescomplemented
109#1442C2×C711yescharacteristic, complemented
110#1440C2×C712yescomplemented
111#1439C2×C711yescharacteristic, complemented
112C22⋊#95C2×C712yescomplemented
113C24×C7—21no—
114C24×C7—21no—
115C24×C7—22no—
116C24×C7—22no—
117C24×C7—21no—
118C24×C7—21no—
119C24×C7—21no—
120C24×C7—21no—
121C24×C7—22no—
122C24×C7—21no—
123C24×C7—21no—
124C24×C7—22no—
125C24×C7—22no—
126C24×C7—21no—
127C24×C7—22no—
128C24×C7—21no—
129C24×C7C2×D412yes—
130C24×C7C2×D412yes—
131C24×C7C2×D412yes—
132C24×C7#4112yes—
133C24×C7#4114yes—
134C24×C7#4114yes—
135C24×C7C2411yescharacteristic
136C2×C7×D4—28no—
137C2×C7×D4—216no—
138C2×C7×D4—44no—
139C2×C7×D4—44no—
140C2×C7×D4—48no—
141C22×C4×C7—22no—
142C22×C4×C7—22no—
143C22×C4×C7—216no—
144C22×C4×C7—28no—
145C22×C4×C7—21no—
146C22×C4×C7—22no—
147C22×C4×C7—21no—
148C22×C4×C7—22no—
149C22×C4×C7—22no—
150C22×C4×C7—21no—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—22no—
154C22×C4×C7—22no—
155C22×C4×C7—22no—
156C22×C4×C7—22no—
157C22×C4×C7—21no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7—22no—
163C22×C4×C7—22no—
164C22×C4×C7—22no—
165C22×C4×C7—28no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—22no—
169C22×C4×C7—22no—
170C22×C4×C7—21no—
171C22×C4×C7—22no—
172C22×C4×C7—22no—
173C22×C4×C7—22no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
176C22×C4×C7—21no—
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—21no—
184C22×C4×C7—22no—
185C22×C4×C7—22no—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—21no—
189C22×C4×C7—22no—
190C22×C4×C7—44no—
191C22×C4×C7—48no—
192C22×C4×C7—48no—
193C22×C4×C7—48no—
194C22×C4×C7—48no—
195C22×C4×C7—48no—
196C22×C4×C7—48no—
197C22×C4×C7—48no—
198C22×C4×C7—48no—
199C22×C4×C7C2×D412yes—
200C22×C4×C7C2×D412yes—
201C22×C4×C7C2×D414yes—
202C22×C4×C7C2×D412yes—
203C22×C4×C7C2×D412yes—
204C22×C4×C7#4114yes—
205C22×C4×C7#4112yes—
206C7×C4⋊C4—44no—
207C7×C4⋊C4—44no—
208C7×C22⋊C4—48no—
209C7×C22⋊C4—48no—
210C7×C22⋊C4—44no—
211C7×C22⋊C4—48no—
212C7×C22⋊C4—44no—
213C7×C22⋊C4—44no—
214C23×D4C22×C711yescharacteristic
215C24×C4C22×C712yes—
216C24×C4C22×C711yescharacteristic
217C22×C4⋊C4C22×C711yescharacteristic
218C22×C4⋊C4C22×C711yescharacteristic
219C22×C22⋊C4C22×C711yescharacteristic
220C22×C22⋊C4C22×C711yescharacteristic
221C22×C22⋊C4C22×C712yes—
222C22×C22⋊C4C22×C712yes—
223C22×C22⋊C4C22×C712yes—
224C22×C22⋊C4C22×C711yescharacteristic
225#397—24no—
226#386—28no—
227#386—24no—
228#380—24no—
229C2×#95—24no—
230C2×#95C22×C712yes—
231C2×#95C22×C712yes—
232C2×#95C22×C711yescharacteristic
233C2×#95C22×C712yes—
234C2×#95C22×C712yes—
235C2×#95C22×C712yes—
236C2×#95C22×C711yescharacteristic
237C2×#95C22×C711yescharacteristic
238C2×#95C22×C712yes—
239C2×#95C22×C712yes—
240C2×#95C22×C712yes—
241C2×#95C22×C711yescharacteristic
242C23×C7—22no—
243C23×C7—24no—
244C23×C7—24no—
245C23×C7—22no—
246C23×C7—22no—
247C23×C7—22no—
248C23×C7—24no—
249C23×C7—24no—
250C23×C7—22no—
251C23×C7—24no—
252C23×C7—24no—
253C23×C7—22no—
254C23×C7—22no—
255C23×C7—24no—
256C23×C7—24no—
257C23×C7—24no—
258C23×C7—22no—
259C23×C7—24no—
260C23×C7—22no—
261C23×C7—24no—
262C23×C7—22no—
263C23×C7—24no—
264C23×C7—22no—
265C23×C7—41no—
266C23×C7—41no—
267C23×C7—42no—
268C23×C7—41no—
269C23×C7—42no—
270C23×C7—42no—
271C23×C7—41no—
272C23×C7—41no—
273C23×C7—41no—
274C23×C7—42no—
275C23×C7—42no—
276C23×C7—42no—
277C23×C7—41no—
278C23×C7—42no—
279C23×C7—42no—
280C23×C7—42no—
281C23×C7—41no—
282C23×C7—42no—
283C23×C7#12114yes—
284C23×C7#12314yes—
285C23×C7#12318yes—
286C23×C7#12414yes—
287C23×C7#12618yes—
288C23×C7C22×D411yescharacteristic
289C23×C7C22×D411yescharacteristic
290C23×C7C22×D411yescharacteristic
291C23×C7C2×#4111yescharacteristic
292C23×C7C2×#4111yescharacteristic
293C23×C7C2×#4112yes—
294C23×C7C2×#4112yes—
295C23×C7C2×#4112yes—
296C23×C7H(5,𝔽2)12yes—
297C23×C7H(5,𝔽2)11yescharacteristic
298C23×C72−1+411yescharacteristic
299C7×D4—416no—
300C2×C4×C7—22no—
301C2×C4×C7—22no—
302C2×C4×C7—24no—
303C2×C4×C7—24no—
304C2×C4×C7—22no—
305C2×C4×C7—22no—
306C2×C4×C7—22no—
307C2×C4×C7—24no—
308C2×C4×C7—24no—
309C2×C4×C7—24no—
310C2×C4×C7—22no—
311C2×C4×C7—24no—
312C2×C4×C7—24no—
313C2×C4×C7—24no—
314C2×C4×C7—24no—
315C2×C4×C7—416no—
316C2×C4×C7—432no—
317C2×C4×C7—42no—
318C2×C4×C7—42no—
319C2×C4×C7—41no—
320C2×C4×C7—41no—
321C2×C4×C7—42no—
322C2×C4×C7—42no—
323C2×C4×C7—42no—
324C2×C4×C7—42no—
325C2×C4×C7—42no—
326C2×C4×C7—42no—
327C2×C4×C7—42no—
328C2×C4×C7—42no—
329C2×C4×C7—42no—
330C2×C4×C7—41no—
331C2×C4×C7—42no—
332C2×C4×C7—42no—
333C2×C4×C7—42no—
334C2×C4×C7—42no—
335C2×C4×C7—41no—
336C2×C4×C7—41no—
337C2×C4×C7—42no—
338C2×C4×C7—41no—
339C2×C4×C7—42no—
340C2×C4×C7—41no—
341C2×C4×C7—42no—
342C2×C4×C7—41no—
343C2×C4×C7—42no—
344C2×C4×C7—42no—
345C2×C4×C7—42no—
346C2×C4×C7—42no—
347C2×C4×C7—42no—
348C2×C4×C7—42no—
349C2×C4×C7—42no—
350C2×C4×C7—42no—
351C2×C4×C7—42no—
352C2×C4×C7—42no—
353C2×C4×C7—42no—
354C2×C4×C7#12114yes—
355C25C23×C711yescharacteristic
356C25C23×C711yescharacteristic
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—24no—
360C22×D4—24no—
361C22×D4C7×D414yes—
362C23×C4—24no—
363C23×C4—24no—
364C23×C4—24no—
365C23×C4—22no—
366C23×C4—24no—
367C23×C4—22no—
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—42no—
371C23×C4—42no—
372C23×C4—42no—
373C23×C4C7×D414yes—
374C23×C4C23×C712yes—
375C23×C4C23×C712yes—
376C23×C4C23×C711yescharacteristic
377C23×C4C23×C711yescharacteristic
378C23×C4C23×C711yescharacteristic
379C23×C4C23×C712yes—
380C23×C4C23×C711yescharacteristic
381C23×C4C23×C712yes—
382C23×C4C23×C711yescharacteristic
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—42no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404#95—24no—
405#95—22no—
406#95—24no—
407#95—22no—
408#95—22no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—42no—
414#95—42no—
415#95C7×D414yescomplemented
416C22×C7—24no—
417C22×C7—24no—
418C22×C7—24no—
419C22×C7—24no—
420C22×C7—28no—
421C22×C7—28no—
422C22×C7—28no—
423C22×C7—24no—
424C22×C7—28no—
425C22×C7—24no—
426C22×C7—42no—
427C22×C7—42no—
428C22×C7—44no—
429C22×C7—44no—
430C22×C7—42no—
431C22×C7—81no—
432C22×C7—81no—
433C22×C7—81no—
434C22×C7—82no—
435C22×C7—81no—
436C22×C7—82no—
437C22×C7#39718yescomplemented
438C22×C7C2×#12111yescharacteristic
439C22×C7C2×#12111yescharacteristic
440C22×C7C2×#12311yescharacteristic
441C22×C7C2×#12312yes—
442C22×C7#52512yes—
443C22×C7C2×#12411yescharacteristic
444C22×C7C2×#12612yes—
445C22×C7#52912yes—
446C22×C7#53211yescharacteristic
447C22×C7#53411yescharacteristic
448C22×C7#53711yescharacteristic
449C22×C7#53812yes—
450C22×C7#53912yes—
451C22×C7D4211yescharacteristic
452C22×C7#54612yes—
453C22×C7#54612yes—
454C22×C7#54711yescharacteristic
455C22×C7#54811yescharacteristic
456C22×C7#55112yes—
457C22×C7#55112yes—
458C22×C7#55212yes—
459C22×C7#55311yescharacteristic
460C22×C7#55312yes—
461C4×C7—24no—
462C4×C7—42no—
463C4×C7—42no—
464C4×C7—44no—
465C4×C7—44no—
466C4×C7—81no—
467C4×C7—81no—
468C4×C7—82no—
469C4×C7—82no—
470C24—21no—
471C24—21no—
472C24—22no—
473C24—22no—
474C24—21no—
475C24—21no—
476C24—21no—
477C24—21no—
478C24—22no—
479C24—21no—
480C24—21no—
481C24—22no—
482C24—22no—
483C24—21no—
484C24—22no—
485C24—21no—
486C24C2×C7×D412yes—
487C24C2×C7×D412yes—
488C24C2×C7×D412yes—
489C24C7×#4112yes—
490C24C7×#4114yes—
491C24C7×#4114yes—
492C24C24×C711yescharacteristic
493C2×D4—28no—
494C2×D4—216no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—48no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—216no—
501C22×C4—28no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—28no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—44no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—48no—
551C22×C4—48no—
552C22×C4—48no—
553C22×C4—48no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4C2×C7×D412yes—
557C22×C4C2×C7×D412yes—
558C22×C4C2×C7×D414yes—
559C22×C4C2×C7×D412yes—
560C22×C4C2×C7×D412yes—
561C22×C4C7×#4114yes—
562C22×C4C7×#4112yes—
563C4⋊C4—44no—
564C4⋊C4—44no—
565C22⋊C4—48no—
566C22⋊C4—48no—
567C22⋊C4—44no—
568C22⋊C4—48no—
569C22⋊C4—44no—
570C22⋊C4—44no—
571C2×C7—28no—
572C2×C7—82no—
573C2×C7C2×#39711yescharacteristic
574C2×C7#241211yescharacteristic
575C2×C7#241611yescharacteristic
576C2×C7#241812yes—
577C2×C7#241912yes—
578C2×C7#248112yes—
579C2×C7#249811yescharacteristic
580C2×C7#251012yes—
581C2×C7#254311yescharacteristic
582C2×C7#263911yescharacteristic
583C2×C7#285011yescharacteristic
584C23—22no—
585C23—24no—
586C23—24no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—24no—
591C23—24no—
592C23—22no—
593C23—24no—
594C23—24no—
595C23—22no—
596C23—22no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—22no—
601C23—24no—
602C23—22no—
603C23—24no—
604C23—22no—
605C23—24no—
606C23—22no—
607C23—41no—
608C23—41no—
609C23—42no—
610C23—41no—
611C23—42no—
612C23—42no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—41no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—41no—
624C23—42no—
625C23C7×#12114yes—
626C23C7×#12314yes—
627C23C7×#12318yes—
628C23C7×#12414yes—
629C23C7×#12618yes—
630C23C22×C7×D411yescharacteristic
631C23C22×C7×D411yescharacteristic
632C23C22×C7×D411yescharacteristic
633C23C2×C7×#4111yescharacteristic
634C23C2×C7×#4111yescharacteristic
635C23C2×C7×#4112yes—
636C23C2×C7×#4112yes—
637C23C2×C7×#4112yes—
638C23C7×H(5,𝔽2)12yes—
639C23C7×H(5,𝔽2)11yescharacteristic
640C23C7×2−1+411yescharacteristic
641D4—416no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—416no—
658C2×C4—432no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4C7×#12114yes—
697C7#1473511yescharacteristic, direct product factor, Sylow
698C22—24no—
699C22—24no—
700C22—28no—
701C22—28no—
702C22—28no—
703C22—24no—
704C22—28no—
705C22—24no—
706C22—24no—
707C22—24no—
708C22—42no—
709C22—42no—
710C22—44no—
711C22—44no—
712C22—42no—
713C22—81no—
714C22—82no—
715C22—81no—
716C22—82no—
717C22—81no—
718C22—81no—
719C22C7×#39718yescomplemented
720C22C2×C7×#12111yescharacteristic
721C22C2×C7×#12111yescharacteristic
722C22C2×C7×#12311yescharacteristic
723C22C2×C7×#12312yes—
724C22C7×#52512yes—
725C22C2×C7×#12411yescharacteristic
726C22C2×C7×#12612yes—
727C22C7×#52912yes—
728C22C7×#53211yescharacteristic
729C22C7×#53411yescharacteristic
730C22C7×#53711yescharacteristic
731C22C7×#53812yes—
732C22C7×#53912yes—
733C22C7×D4211yescharacteristic
734C22C7×#54612yes—
735C22C7×#54612yes—
736C22C7×#54711yescharacteristic
737C22C7×#54811yescharacteristic
738C22C7×#55112yes—
739C22C7×#55112yes—
740C22C7×#55212yes—
741C22C7×#55311yescharacteristic
742C22C7×#55312yes—
743C4—24no—
744C4—42no—
745C4—42no—
746C4—44no—
747C4—44no—
748C4—82no—
749C4—82no—
750C4—81no—
751C4—81no—
752C2—28no—
753C2—82no—
754C2C2×C7×#39711yescharacteristic
755C2C7×#241211yescharacteristic
756C2C7×#241611yescharacteristic
757C2C7×#241812yes—
758C2C7×#241912yes—
759C2C7×#248112yes—
760C2C7×#249811yescharacteristic
761C2C7×#251012yes—
762C2C7×#254311yescharacteristic
763C2C7×#263911yescharacteristic
764C2C7×#285011yescharacteristic
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
1. C2×C7×#397C2semidirect
4. C2×C7×#380C2semidirect
5. C22×C7×#95C2semidirect
6. C7×#1445C2semidirect
7. C7×#1443C2semidirect
8. C7×#1442C2semidirect
9. C7×#1440C2semidirect
10. C7×#1439C2semidirect
11. C7×C22⋊#95C2semidirect
40. #14735C7direct (N × H)
101. C7×#95D4semidirect
102. C2×#397C2×C7semidirect
105. C2×#380C2×C7semidirect
106. C22×#95C2×C7semidirect
107. #1445C2×C7semidirect
108. #1443C2×C7semidirect
109. #1442C2×C7semidirect
110. #1440C2×C7semidirect
111. #1439C2×C7semidirect
112. C22⋊#95C2×C7semidirect
415. #95C7×D4semidirect
437. C22×C7#397semidirect
697. C7#14735direct (N × H)
719. C22C7×#397semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3972
C2×C7×#3862
C2×C7×#3802
C22×C7×#952
C7×#14452
C7×#14432
C7×#14422
C7×#14402
C7×#14392
C7×C22⋊#952
#147357