Finite Group Databasebeta

← C7×#24056 #13201272

Subgroups — C7×#24056 #13201272

Order 1792.

1820 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3484C211yesmaximal, characteristic
2C7×#2849C212yesmaximal, complemented
3C2×C7×#386C211yesmaximal, characteristic, complemented
4C7×#2044C214yesmaximal, complemented
5C7×#1898C212yesmaximal, complemented
6C7×#1867C212yesmaximal, complemented
7C7×#1790C212yesmaximal, complemented
8C7×#1781C211yesmaximal, characteristic, complemented
9C2×C7×H(5,𝔽2)C2211yescharacteristic
10C23×C7×D4C2211yescharacteristic
11C24×C4×C7C2211yescharacteristic, complemented
12C7×#546—22no—
13C7×#546—22no—
14C7×D42—22no—
15C7×D42—22no—
16C7×#535—21no—
17C7×#534—21no—
18C7×#534C2212yes—
19C7×#525—21no—
20C2×C7×#123—22no—
21C2×C7×#120—21no—
22C2×C7×#120C2212yes—
23C7×#518C2211yescharacteristic
24C22×C7×C22⋊C4—21no—
25C22×C7×C22⋊C4C2211yescharacteristic, complemented
26C2×C7×#99C2212yes—
27C2×C7×#99C2212yescomplemented
28C2×C7×#99C2214yescomplemented
29C7×#386—21no—
30C7×#386—21no—
31C7×#386—22no—
32C7×#386C2212yes—
33C7×#386C2212yescomplemented
34C7×#386C2214yescomplemented
35C7×#385—22no—
36C7×#385C2214yescomplemented
37C7×#381—22no—
38C7×#379C2212yescomplemented
39C2×C7×#95—21no—
40C7×#342C2214yescomplemented
41#24056C711yesmaximal, characteristic, direct product factor, Sylow
42C25×C7D411yescharacteristic
43C25×C7C2311yescharacteristic
44C7×H(5,𝔽2)—24no—
45C7×H(5,𝔽2)—42no—
46C2×C7×#41—21no—
47C2×C7×#41—22no—
48C22×C7×D4—22no—
49C22×C7×D4—22no—
50C22×C7×D4—21no—
51C22×C7×D4—22no—
52C22×C7×D4—21no—
53C22×C7×D4—21no—
54C22×C7×D4—24no—
55C22×C7×D4—42no—
56C22×C7×D4D411yescharacteristic
57C22×C7×D4D411yescharacteristic
58C22×C7×D4D412yes—
59C22×C7×D4D412yes—
60C22×C7×D4C2311yescharacteristic
61C22×C7×D4C2312yes—
62C22×C7×D4C2311yescharacteristic
63C23×C4×C7—21no—
64C23×C4×C7—22no—
65C23×C4×C7—21no—
66C23×C4×C7—22no—
67C23×C4×C7—21no—
68C23×C4×C7—44no—
69C23×C4×C7D411yescharacteristic
70C23×C4×C7C2312yes—
71C7×#127—22no—
72C7×#124—22no—
73C7×#123—22no—
74C7×#123—22no—
75C7×#123—22no—
76C7×#123—48no—
77C7×C22⋊Q8—21no—
78C7×C22⋊Q8—21no—
79C7×#121—21no—
80C7×#121—21no—
81C7×#121—22no—
82C7×#121—22no—
83C7×#121—22no—
84C7×#121—22no—
85C7×#121—22no—
86C7×#121—22no—
87C7×#120—22no—
88C7×#120—22no—
89C7×#120—22no—
90C7×#120—22no—
91C7×#120—22no—
92C7×#120—22no—
93C7×#120—22no—
94C7×#120—22no—
95C7×#120—22no—
96C4×C7×D4—22no—
97C4×C7×D4—22no—
98C4×C7×D4—22no—
99C4×C7×D4—22no—
100C7×#117—21no—
101C2×C7×C4⋊C4—24no—
102C2×C7×C22⋊C4—21no—
103C2×C7×C22⋊C4—21no—
104C2×C7×C22⋊C4—21no—
105C2×C7×C22⋊C4—22no—
106C2×C7×C22⋊C4—22no—
107C2×C7×C22⋊C4—21no—
108C2×C7×C22⋊C4—22no—
109C2×C7×C22⋊C4—22no—
110C2×C7×C22⋊C4—24no—
111C2×C7×C22⋊C4—42no—
112C2×C7×C22⋊C4—44no—
113C2×C7×C22⋊C4D412yes—
114C2×C7×C22⋊C4D412yes—
115C2×C7×C22⋊C4C2312yes—
116C2×C7×C22⋊C4C2314yes—
117C2×C7×C22⋊C4C2312yes—
118C7×#99—24no—
119C7×#99—42no—
120C7×#99—44no—
121C7×#95—22no—
122C7×#95—22no—
123C7×#95—24no—
124C7×#95—24no—
125#3484C2×C711yescharacteristic
126#2849C2×C712yescomplemented
127C2×#386C2×C711yescharacteristic, complemented
128#2044C2×C714yescomplemented
129#1898C2×C712yescomplemented
130#1867C2×C712yescomplemented
131#1790C2×C712yescomplemented
132#1781C2×C711yescharacteristic, complemented
133C24×C7—22no—
134C24×C7—22no—
135C24×C7—21no—
136C24×C7—22no—
137C24×C7—21no—
138C24×C7—21no—
139C24×C7—42no—
140C24×C7—42no—
141C24×C7—41no—
142C24×C7—42no—
143C24×C7—42no—
144C24×C7C2×D411yescharacteristic
145C24×C7C2×D412yes—
146C24×C7C2×D412yes—
147C24×C7C2×D411yescharacteristic
148C24×C7C2×D412yes—
149C24×C7C2×D411yescharacteristic
150C24×C7C2×D411yescharacteristic
151C24×C7C2411yescharacteristic
152C7×#41—48no—
153C7×#41—42no—
154C7×#41—42no—
155C2×C7×Q8—21no—
156C2×C7×D4—22no—
157C2×C7×D4—22no—
158C2×C7×D4—22no—
159C2×C7×D4—21no—
160C2×C7×D4—22no—
161C2×C7×D4—22no—
162C2×C7×D4—22no—
163C2×C7×D4—22no—
164C2×C7×D4—22no—
165C2×C7×D4—22no—
166C2×C7×D4—22no—
167C2×C7×D4—22no—
168C2×C7×D4—22no—
169C2×C7×D4—24no—
170C2×C7×D4—22no—
171C2×C7×D4—24no—
172C2×C7×D4—22no—
173C2×C7×D4—22no—
174C2×C7×D4—22no—
175C2×C7×D4—22no—
176C2×C7×D4—22no—
177C2×C7×D4—41no—
178C2×C7×D4—41no—
179C2×C7×D4—48no—
180C2×C7×D4—48no—
181C2×C7×D4—48no—
182C2×C7×D4—42no—
183C2×C7×D4—42no—
184C2×C7×D4—44no—
185C2×C7×D4—44no—
186C2×C7×D4—82no—
187C2×C7×D4—82no—
188C2×C7×D4#4114yes—
189C22×C4×C7—21no—
190C22×C4×C7—24no—
191C22×C4×C7—22no—
192C22×C4×C7—28no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—22no—
196C22×C4×C7—24no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—22no—
200C22×C4×C7—24no—
201C22×C4×C7—22no—
202C22×C4×C7—44no—
203C22×C4×C7—41no—
204C22×C4×C7—44no—
205C22×C4×C7—48no—
206C22×C4×C7—42no—
207C22×C4×C7—44no—
208C22×C4×C7—42no—
209C22×C4×C7—41no—
210C22×C4×C7—41no—
211C22×C4×C7—42no—
212C22×C4×C7—42no—
213C22×C4×C7—42no—
214C22×C4×C7C2×D412yes—
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2×D412yes—
218C22×C4×C7C2×D412yes—
219C7×C4⋊C4—21no—
220C7×C4⋊C4—21no—
221C7×C4⋊C4—22no—
222C7×C4⋊C4—22no—
223C7×C4⋊C4—48no—
224C7×C22⋊C4—22no—
225C7×C22⋊C4—22no—
226C7×C22⋊C4—22no—
227C7×C22⋊C4—22no—
228C7×C22⋊C4—22no—
229C7×C22⋊C4—22no—
230C7×C22⋊C4—22no—
231C7×C22⋊C4—22no—
232C7×C22⋊C4—22no—
233C7×C22⋊C4—22no—
234C7×C22⋊C4—22no—
235C7×C22⋊C4—24no—
236C7×C22⋊C4—24no—
237C7×C22⋊C4—24no—
238C7×C22⋊C4—44no—
239C7×C22⋊C4—44no—
240C7×C22⋊C4—48no—
241C7×C22⋊C4—44no—
242C7×C22⋊C4—42no—
243C7×C22⋊C4—44no—
244C42×C7—22no—
245C2×H(5,𝔽2)C22×C711yescharacteristic
246C23×D4C22×C711yescharacteristic
247C24×C4C22×C711yescharacteristic, complemented
248#546—22no—
249#546—22no—
250D42—22no—
251D42—22no—
252#535—21no—
253#534—21no—
254#534C22×C712yes—
255#525—21no—
256C2×#123—22no—
257C2×#120—21no—
258C2×#120C22×C712yes—
259#518C22×C711yescharacteristic
260C22×C22⋊C4—21no—
261C22×C22⋊C4C22×C711yescharacteristic, complemented
262C2×#99C22×C712yes—
263C2×#99C22×C714yescomplemented
264C2×#99C22×C712yescomplemented
265#386—22no—
266#386—21no—
267#386—21no—
268#386C22×C712yes—
269#386C22×C714yescomplemented
270#386C22×C712yescomplemented
271#385—22no—
272#385C22×C714yescomplemented
273#381—22no—
274#379C22×C712yescomplemented
275C2×#95—21no—
276#342C22×C714yescomplemented
277C23×C7—21no—
278C23×C7—21no—
279C23×C7—22no—
280C23×C7—22no—
281C23×C7—21no—
282C23×C7—21no—
283C23×C7—21no—
284C23×C7—24no—
285C23×C7—24no—
286C23×C7—24no—
287C23×C7—24no—
288C23×C7—21no—
289C23×C7—21no—
290C23×C7—22no—
291C23×C7—21no—
292C23×C7—21no—
293C23×C7—24no—
294C23×C7—42no—
295C23×C7—41no—
296C23×C7—41no—
297C23×C7—42no—
298C23×C7—41no—
299C23×C7—41no—
300C23×C7—42no—
301C23×C7—42no—
302C23×C7—48no—
303C23×C7—48no—
304C23×C7—41no—
305C23×C7—41no—
306C23×C7—41no—
307C23×C7—41no—
308C23×C7—48no—
309C23×C7—42no—
310C23×C7—42no—
311C23×C7—42no—
312C23×C7—42no—
313C23×C7—42no—
314C23×C7—81no—
315C23×C7—81no—
316C23×C7—84no—
317C23×C7—81no—
318C23×C7—81no—
319C23×C7#12012yes—
320C23×C7#12011yescharacteristic
321C23×C7#12011yescharacteristic
322C23×C7#12312yescomplemented
323C23×C7C22×D411yescharacteristic
324C23×C7C22×D412yes—
325C23×C7C2×#4112yes—
326C23×C7H(5,𝔽2)12yes—
327C7×Q8—42no—
328C7×D4—28no—
329C7×D4—44no—
330C7×D4—42no—
331C7×D4—44no—
332C7×D4—44no—
333C7×D4—42no—
334C7×D4—42no—
335C7×D4—44no—
336C7×D4—44no—
337C7×D4—44no—
338C7×D4—44no—
339C7×D4—82no—
340C7×D4—82no—
341C7×D4—82no—
342C7×D4—82no—
343C2×C4×C7—21no—
344C2×C4×C7—21no—
345C2×C4×C7—24no—
346C2×C4×C7—28no—
347C2×C4×C7—22no—
348C2×C4×C7—22no—
349C2×C4×C7—22no—
350C2×C4×C7—21no—
351C2×C4×C7—21no—
352C2×C4×C7—21no—
353C2×C4×C7—24no—
354C2×C4×C7—42no—
355C2×C4×C7—42no—
356C2×C4×C7—44no—
357C2×C4×C7—44no—
358C2×C4×C7—42no—
359C2×C4×C7—44no—
360C2×C4×C7—48no—
361C2×C4×C7—42no—
362C2×C4×C7—42no—
363C2×C4×C7—44no—
364C2×C4×C7—42no—
365C2×C4×C7—42no—
366C2×C4×C7—44no—
367C2×C4×C7—42no—
368C2×C4×C7—44no—
369C2×C4×C7—42no—
370C2×C4×C7—42no—
371C2×C4×C7—44no—
372C2×C4×C7—81no—
373C2×C4×C7—81no—
374C2×C4×C7—84no—
375C2×C4×C7#12312yescomplemented
376C25C7×D411yescharacteristic
377C25C23×C711yescharacteristic
378H(5,𝔽2)—24no—
379H(5,𝔽2)—42no—
380C2×#41—21no—
381C2×#41—22no—
382C22×D4—21no—
383C22×D4—22no—
384C22×D4—22no—
385C22×D4—22no—
386C22×D4—21no—
387C22×D4—21no—
388C22×D4—24no—
389C22×D4—42no—
390C22×D4C7×D411yescharacteristic
391C22×D4C7×D411yescharacteristic
392C22×D4C7×D412yes—
393C22×D4C7×D412yes—
394C22×D4C23×C712yes—
395C22×D4C23×C711yescharacteristic
396C22×D4C23×C711yescharacteristic
397C23×C4—21no—
398C23×C4—22no—
399C23×C4—21no—
400C23×C4—22no—
401C23×C4—21no—
402C23×C4—44no—
403C23×C4C7×D411yescharacteristic
404C23×C4C23×C712yes—
405#127—22no—
406#124—22no—
407#123—22no—
408#123—22no—
409#123—22no—
410#123—48no—
411C22⋊Q8—21no—
412C22⋊Q8—21no—
413#121—21no—
414#121—21no—
415#121—22no—
416#121—22no—
417#121—22no—
418#121—22no—
419#121—22no—
420#121—22no—
421#120—22no—
422#120—22no—
423#120—22no—
424#120—22no—
425#120—22no—
426#120—22no—
427#120—22no—
428#120—22no—
429#120—22no—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—22no—
433C4×D4—22no—
434#117—21no—
435C2×C4⋊C4—24no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—42no—
446C2×C22⋊C4—44no—
447C2×C22⋊C4C7×D412yes—
448C2×C22⋊C4C7×D412yes—
449C2×C22⋊C4C23×C712yes—
450C2×C22⋊C4C23×C714yes—
451C2×C22⋊C4C23×C712yes—
452#99—24no—
453#99—42no—
454#99—44no—
455#95—22no—
456#95—22no—
457#95—24no—
458#95—24no—
459C22×C7—24no—
460C22×C7—24no—
461C22×C7—21no—
462C22×C7—21no—
463C22×C7—22no—
464C22×C7—21no—
465C22×C7—21no—
466C22×C7—22no—
467C22×C7—21no—
468C22×C7—21no—
469C22×C7—22no—
470C22×C7—22no—
471C22×C7—22no—
472C22×C7—22no—
473C22×C7—42no—
474C22×C7—42no—
475C22×C7—48no—
476C22×C7—48no—
477C22×C7—42no—
478C22×C7—42no—
479C22×C7—42no—
480C22×C7—42no—
481C22×C7—41no—
482C22×C7—41no—
483C22×C7—42no—
484C22×C7—41no—
485C22×C7—42no—
486C22×C7—41no—
487C22×C7—42no—
488C22×C7—41no—
489C22×C7—81no—
490C22×C7—84no—
491C22×C7—84no—
492C22×C7—84no—
493C22×C7—81no—
494C22×C7—162no—
495C22×C7B(4,𝔽2)12yes—
496C22×C7#45812yes—
497C22×C7C2×#12011yescharacteristic
498C22×C7C2×#12311yescharacteristic
499C22×C7#53411yescharacteristic
500C22×C7#54614yes—
501C4×C7—22no—
502C4×C7—41no—
503C4×C7—42no—
504C4×C7—44no—
505C4×C7—42no—
506C4×C7—42no—
507C4×C7—84no—
508C4×C7—82no—
509C24—22no—
510C24—22no—
511C24—21no—
512C24—22no—
513C24—21no—
514C24—21no—
515C24—42no—
516C24—42no—
517C24—41no—
518C24—42no—
519C24—42no—
520C24C2×C7×D411yescharacteristic
521C24C2×C7×D412yes—
522C24C2×C7×D412yes—
523C24C2×C7×D411yescharacteristic
524C24C2×C7×D412yes—
525C24C2×C7×D411yescharacteristic
526C24C2×C7×D411yescharacteristic
527C24C24×C711yescharacteristic
528#41—48no—
529#41—42no—
530#41—42no—
531C2×Q8—21no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—21no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—24no—
546C2×D4—22no—
547C2×D4—24no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—41no—
554C2×D4—41no—
555C2×D4—48no—
556C2×D4—48no—
557C2×D4—48no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—44no—
561C2×D4—44no—
562C2×D4—82no—
563C2×D4—82no—
564C2×D4C7×#4114yes—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—28no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—44no—
579C22×C4—41no—
580C22×C4—44no—
581C22×C4—48no—
582C22×C4—42no—
583C22×C4—44no—
584C22×C4—42no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4C2×C7×D412yes—
591C22×C4C2×C7×D411yescharacteristic
592C22×C4C2×C7×D411yescharacteristic
593C22×C4C2×C7×D412yes—
594C22×C4C2×C7×D412yes—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—48no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—24no—
612C22⋊C4—24no—
613C22⋊C4—24no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—48no—
617C22⋊C4—42no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C42—22no—
621C2×C7—21no—
622C2×C7—24no—
623C2×C7—21no—
624C2×C7—22no—
625C2×C7—22no—
626C2×C7—42no—
627C2×C7—42no—
628C2×C7—81no—
629C2×C7—82no—
630C2×C7#240511yescharacteristic
631C2×C7C2×B(4,𝔽2)11yescharacteristic
632C2×C7C2×#45811yescharacteristic
633C23—21no—
634C23—21no—
635C23—22no—
636C23—22no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—21no—
645C23—21no—
646C23—22no—
647C23—21no—
648C23—21no—
649C23—24no—
650C23—42no—
651C23—41no—
652C23—41no—
653C23—42no—
654C23—41no—
655C23—41no—
656C23—42no—
657C23—42no—
658C23—48no—
659C23—48no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—48no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—81no—
671C23—81no—
672C23—84no—
673C23—81no—
674C23—81no—
675C23C7×#12012yes—
676C23C7×#12011yescharacteristic
677C23C7×#12011yescharacteristic
678C23C7×#12312yescomplemented
679C23C22×C7×D411yescharacteristic
680C23C22×C7×D412yes—
681C23C2×C7×#4112yes—
682C23C7×H(5,𝔽2)12yes—
683Q8—42no—
684D4—28no—
685D4—44no—
686D4—42no—
687D4—44no—
688D4—44no—
689D4—42no—
690D4—42no—
691D4—44no—
692D4—44no—
693D4—44no—
694D4—44no—
695D4—82no—
696D4—82no—
697D4—82no—
698D4—82no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—24no—
702C2×C4—28no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—24no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—42no—
715C2×C4—44no—
716C2×C4—48no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—84no—
731C2×C4C7×#12312yescomplemented
732C7#2405611yescharacteristic, direct product factor, Sylow
733C22—24no—
734C22—24no—
735C22—21no—
736C22—21no—
737C22—22no—
738C22—21no—
739C22—21no—
740C22—22no—
741C22—21no—
742C22—21no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—42no—
748C22—42no—
749C22—48no—
750C22—48no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—41no—
756C22—41no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—81no—
764C22—84no—
765C22—84no—
766C22—81no—
767C22—84no—
768C22—162no—
769C22C7×B(4,𝔽2)12yes—
770C22C7×#45812yes—
771C22C2×C7×#12011yescharacteristic
772C22C2×C7×#12311yescharacteristic
773C22C7×#53411yescharacteristic
774C22C7×#54614yes—
775C4—22no—
776C4—41no—
777C4—42no—
778C4—44no—
779C4—42no—
780C4—42no—
781C4—82no—
782C4—84no—
783C2—21no—
784C2—24no—
785C2—21no—
786C2—22no—
787C2—22no—
788C2—42no—
789C2—42no—
790C2—81no—
791C2—82no—
792C2C7×#240511yescharacteristic
793C2C2×C7×B(4,𝔽2)11yescharacteristic
794C2C2×C7×#45811yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC24C24×C7
prime radicalC7×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C25×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C7×#2849C2semidirect
3. C2×C7×#386C2semidirect
4. C7×#2044C2semidirect
5. C7×#1898C2semidirect
6. C7×#1867C2semidirect
7. C7×#1790C2semidirect
8. C7×#1781C2semidirect
11. C24×C4×C7C22semidirect
25. C22×C7×C22⋊C4C22semidirect
27. C2×C7×#99C22semidirect
28. C2×C7×#99C22semidirect
33. C7×#386C22semidirect
34. C7×#386C22semidirect
36. C7×#385C22semidirect
38. C7×#379C22semidirect
40. C7×#342C22semidirect
41. #24056C7direct (N × H)
126. #2849C2×C7semidirect
127. C2×#386C2×C7semidirect
128. #2044C2×C7semidirect
129. #1898C2×C7semidirect
130. #1867C2×C7semidirect
131. #1790C2×C7semidirect
132. #1781C2×C7semidirect
247. C24×C4C22×C7semidirect
261. C22×C22⋊C4C22×C7semidirect
263. C2×#99C22×C7semidirect
264. C2×#99C22×C7semidirect
269. #386C22×C7semidirect
270. #386C22×C7semidirect
272. #385C22×C7semidirect
274. #379C22×C7semidirect
276. #342C22×C7semidirect
322. C23×C7#123semidirect
375. C2×C4×C7#123semidirect
678. C23C7×#123semidirect
731. C2×C4C7×#123semidirect
732. C7#24056direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#34842
C7×#28492
C2×C7×#3862
C7×#20442
C7×#18982
C7×#18672
C7×#17902
C7×#17812
#240567