Finite Group Databasebeta

← C7×#23996 #13201212

Subgroups — C7×#23996 #13201212

Order 1792.

1396 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3490C211yesmaximal, characteristic, complemented
2C7×#3026C211yesmaximal, characteristic, complemented
3C2×C7×B(4,𝔽2)C211yesmaximal, characteristic, complemented
4C7×#2883C211yesmaximal, characteristic, complemented
5C7×#2032C212yesmaximal, complemented
6C7×#2021C212yesmaximal, complemented
7C7×#1913C211yesmaximal, characteristic, complemented
8C7×#1913C212yesmaximal, complemented
9C7×#1898C212yesmaximal, complemented
10C7×#1889C211yesmaximal, characteristic, complemented
11C7×#1828C211yesmaximal, characteristic, complemented
12C2×C7×H(5,𝔽2)C2211yescharacteristic
13C7×#551—22no—
14C7×#551—22no—
15C7×#546—22no—
16C7×#546—22no—
17C7×#543C2211yescharacteristic, complemented
18C7×#538—22no—
19C7×#534C2212yes—
20C7×#534C2211yescharacteristic
21C7×#525—22no—
22C2×C7×#120C2212yes—
23C2×C7×#120C2211yescharacteristic
24C2×C7×#120C2211yescharacteristic, complemented
25C7×#518C2211yescharacteristic
26C7×#518C2211yescharacteristic
27C7×#518C2211yescharacteristic, complemented
28C22×C7×C22⋊C4C2211yescharacteristic, complemented
29C7×#458—22no—
30C7×B(4,𝔽2)—22no—
31C7×B(4,𝔽2)—22no—
32C7×B(4,𝔽2)—22no—
33C7×#410—22no—
34C2×C7×#99—22no—
35C2×C7×#99C2212yes—
36C2×C7×#99C2212yes—
37C2×C7×#99C2212yes—
38C2×C7×#99C2211yescharacteristic
39C2×C7×#99C2211yescharacteristic
40C2×C7×#99C2212yes—
41C2×C7×#99C2212yescomplemented
42C7×#379C2212yescomplemented
43C7×#342C2212yescomplemented
44C7×#342C2212yescomplemented
45C7×#342C2212yescomplemented
46C7×#342C2212yescomplemented
47#23996C711yesmaximal, characteristic, direct product factor, Sylow
48C25×C7C2311yescharacteristic
49C7×H(5,𝔽2)—22no—
50C7×H(5,𝔽2)—22no—
51C7×H(5,𝔽2)—42no—
52C2×C7×#41—22no—
53C2×C7×#41—21no—
54C2×C7×#41—22no—
55C22×C7×D4—21no—
56C22×C7×D4—22no—
57C22×C7×D4—21no—
58C22×C7×D4—21no—
59C22×C7×D4—22no—
60C22×C7×D4C2311yescharacteristic
61C22×C7×D4C2311yescharacteristic
62C22×C7×D4C2312yes—
63C23×C4×C7—21no—
64C7×#126—22no—
65C7×#126—22no—
66C7×#124—22no—
67C7×#124—22no—
68C7×#123—22no—
69C7×#123—22no—
70C7×#123—22no—
71C7×#123—22no—
72C7×#123—21no—
73C7×#123—22no—
74C7×#123—22no—
75C7×#123D412yescomplemented
76C7×C22⋊Q8—22no—
77C7×C22⋊Q8—22no—
78C7×C22⋊Q8—22no—
79C7×C22⋊Q8—22no—
80C7×#121—22no—
81C7×#121—22no—
82C7×#121—22no—
83C7×#121—22no—
84C7×#121—42no—
85C7×#120—21no—
86C7×#120—21no—
87C7×#120—21no—
88C7×#120—22no—
89C7×#120—22no—
90C7×#120—22no—
91C7×#120—22no—
92C7×#120—22no—
93C7×#120—22no—
94C7×#120—42no—
95C7×#120D412yescomplemented
96C7×#120D412yescomplemented
97C7×#120D412yescomplemented
98C4×C7×D4—22no—
99C4×C7×D4—22no—
100C4×C7×D4—22no—
101C4×C7×D4—22no—
102C4×C7×D4—22no—
103C4×C7×D4—22no—
104C4×C7×D4—42no—
105C7×#117—22no—
106C7×#117—21no—
107C7×#117—21no—
108C7×#117D412yescomplemented
109C2×C7×C22⋊C4—21no—
110C2×C7×C22⋊C4—21no—
111C2×C7×C22⋊C4—21no—
112C2×C7×C22⋊C4—21no—
113C2×C7×C22⋊C4—22no—
114C2×C7×C22⋊C4—22no—
115C2×C7×C22⋊C4—21no—
116C2×C7×C22⋊C4—22no—
117C2×C7×C22⋊C4—42no—
118C2×C7×C22⋊C4D412yescomplemented
119C2×C7×C22⋊C4C2312yes—
120C2×C7×C22⋊C4C2312yes—
121C2×C7×C22⋊C4C2312yes—
122C2×C7×C22⋊C4C2311yescharacteristic
123C2×C7×C22⋊C4C2311yescharacteristic
124C2×C7×C22⋊C4C2311yescharacteristic
125C2×C7×C22⋊C4C2311yescharacteristic
126C7×#99—22no—
127C7×#99—22no—
128C7×#99—24no—
129C7×#99—24no—
130C7×#99—24no—
131C7×#99—24no—
132C7×#99—42no—
133#3490C2×C711yescharacteristic, complemented
134#3026C2×C711yescharacteristic, complemented
135C2×B(4,𝔽2)C2×C711yescharacteristic, complemented
136#2883C2×C711yescharacteristic, complemented
137#2032C2×C712yescomplemented
138#2021C2×C712yescomplemented
139#1913C2×C711yescharacteristic, complemented
140#1913C2×C712yescomplemented
141#1898C2×C712yescomplemented
142#1889C2×C711yescharacteristic, complemented
143#1828C2×C711yescharacteristic, complemented
144C24×C7—21no—
145C24×C7—21no—
146C24×C7—21no—
147C24×C7—22no—
148C24×C7—22no—
149C24×C7—82no—
150C24×C7C2×D411yescharacteristic
151C24×C7C2×D411yescharacteristic
152C24×C7C2×D411yescharacteristic
153C24×C7C2×D411yescharacteristic
154C24×C7#4112yescomplemented
155C24×C7C2411yescharacteristic
156C7×#41—44no—
157C7×#41—44no—
158C7×#41—42no—
159C7×#41—42no—
160C7×#41—84no—
161C2×C7×Q8—21no—
162C2×C7×Q8—22no—
163C2×C7×D4—22no—
164C2×C7×D4—22no—
165C2×C7×D4—22no—
166C2×C7×D4—21no—
167C2×C7×D4—22no—
168C2×C7×D4—22no—
169C2×C7×D4—22no—
170C2×C7×D4—22no—
171C2×C7×D4—22no—
172C2×C7×D4—21no—
173C2×C7×D4—21no—
174C2×C7×D4—22no—
175C2×C7×D4—22no—
176C2×C7×D4—22no—
177C2×C7×D4—22no—
178C2×C7×D4—22no—
179C2×C7×D4—22no—
180C2×C7×D4—22no—
181C2×C7×D4—22no—
182C2×C7×D4—44no—
183C2×C7×D4—44no—
184C2×C7×D4—42no—
185C2×C7×D4—42no—
186C2×C7×D4—42no—
187C2×C7×D4—42no—
188C2×C7×D4—42no—
189C2×C7×D4—82no—
190C2×C7×D4—82no—
191C2×C7×D4—84no—
192C2×C7×D4C2×D412yes—
193C2×C7×D4C2×D412yes—
194C22×C4×C7—22no—
195C22×C4×C7—22no—
196C22×C4×C7—21no—
197C22×C4×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—41no—
208C22×C4×C7—82no—
209C22×C4×C7C2×D411yescharacteristic
210C22×C4×C7C2×D411yescharacteristic
211C22×C4×C7#4112yescomplemented
212C7×C4⋊C4—22no—
213C7×C4⋊C4—22no—
214C7×C4⋊C4—22no—
215C7×C4⋊C4—22no—
216C7×C4⋊C4—22no—
217C7×C4⋊C4—22no—
218C7×C4⋊C4—42no—
219C7×C4⋊C4—41no—
220C7×C22⋊C4—22no—
221C7×C22⋊C4—22no—
222C7×C22⋊C4—22no—
223C7×C22⋊C4—22no—
224C7×C22⋊C4—22no—
225C7×C22⋊C4—22no—
226C7×C22⋊C4—22no—
227C7×C22⋊C4—21no—
228C7×C22⋊C4—21no—
229C7×C22⋊C4—21no—
230C7×C22⋊C4—21no—
231C7×C22⋊C4—22no—
232C7×C22⋊C4—22no—
233C7×C22⋊C4—22no—
234C7×C22⋊C4—22no—
235C7×C22⋊C4—22no—
236C7×C22⋊C4—22no—
237C7×C22⋊C4—22no—
238C7×C22⋊C4—22no—
239C7×C22⋊C4—22no—
240C7×C22⋊C4—42no—
241C7×C22⋊C4—42no—
242C7×C22⋊C4—42no—
243C7×C22⋊C4—42no—
244C7×C22⋊C4—41no—
245C7×C22⋊C4—84no—
246C7×C22⋊C4C2×D412yes—
247C7×C22⋊C4C2×D412yes—
248C7×C22⋊C4C2×D412yes—
249C7×C22⋊C4C2×D412yes—
250C42×C7—22no—
251C42×C7—22no—
252C42×C7—41no—
253C2×H(5,𝔽2)C22×C711yescharacteristic
254#551—22no—
255#551—22no—
256#546—22no—
257#546—22no—
258#543C22×C711yescharacteristic, complemented
259#538—22no—
260#534C22×C712yes—
261#534C22×C711yescharacteristic
262#525—22no—
263C2×#120C22×C712yes—
264C2×#120C22×C711yescharacteristic
265C2×#120C22×C711yescharacteristic, complemented
266#518C22×C711yescharacteristic
267#518C22×C711yescharacteristic
268#518C22×C711yescharacteristic, complemented
269C22×C22⋊C4C22×C711yescharacteristic, complemented
270#458—22no—
271B(4,𝔽2)—22no—
272B(4,𝔽2)—22no—
273B(4,𝔽2)—22no—
274#410—22no—
275C2×#99—22no—
276C2×#99C22×C711yescharacteristic
277C2×#99C22×C711yescharacteristic
278C2×#99C22×C712yes—
279C2×#99C22×C712yes—
280C2×#99C22×C712yes—
281C2×#99C22×C712yes—
282C2×#99C22×C712yescomplemented
283#379C22×C712yescomplemented
284#342C22×C712yescomplemented
285#342C22×C712yescomplemented
286#342C22×C712yescomplemented
287#342C22×C712yescomplemented
288C23×C7—21no—
289C23×C7—22no—
290C23×C7—21no—
291C23×C7—21no—
292C23×C7—21no—
293C23×C7—21no—
294C23×C7—22no—
295C23×C7—22no—
296C23×C7—22no—
297C23×C7—22no—
298C23×C7—22no—
299C23×C7—42no—
300C23×C7—44no—
301C23×C7—42no—
302C23×C7—42no—
303C23×C7—44no—
304C23×C7—42no—
305C23×C7—41no—
306C23×C7—41no—
307C23×C7—42no—
308C23×C7—81no—
309C23×C7—81no—
310C23×C7—81no—
311C23×C7—81no—
312C23×C7—82no—
313C23×C7—81no—
314C23×C7—81no—
315C23×C7—82no—
316C23×C7—82no—
317C23×C7—161no—
318C23×C7#12012yes—
319C23×C7C22×D411yescharacteristic
320C23×C7C22×D411yescharacteristic
321C23×C7C22×D411yescharacteristic
322C23×C7C2×#4112yes—
323C23×C7H(5,𝔽2)12yes—
324C7×Q8—42no—
325C7×Q8—82no—
326C7×D4—24no—
327C7×D4—24no—
328C7×D4—42no—
329C7×D4—44no—
330C7×D4—44no—
331C7×D4—44no—
332C7×D4—42no—
333C7×D4—41no—
334C7×D4—41no—
335C7×D4—42no—
336C7×D4—42no—
337C7×D4—42no—
338C7×D4—42no—
339C7×D4—82no—
340C7×D4—82no—
341C7×D4—82no—
342C7×D4—84no—
343C7×D4—84no—
344C7×D4—162no—
345C2×C4×C7—21no—
346C2×C4×C7—21no—
347C2×C4×C7—21no—
348C2×C4×C7—22no—
349C2×C4×C7—22no—
350C2×C4×C7—22no—
351C2×C4×C7—22no—
352C2×C4×C7—22no—
353C2×C4×C7—22no—
354C2×C4×C7—22no—
355C2×C4×C7—22no—
356C2×C4×C7—44no—
357C2×C4×C7—44no—
358C2×C4×C7—42no—
359C2×C4×C7—42no—
360C2×C4×C7—42no—
361C2×C4×C7—42no—
362C2×C4×C7—81no—
363C2×C4×C7—82no—
364C2×C4×C7—81no—
365C2×C4×C7—81no—
366C2×C4×C7—81no—
367C2×C4×C7—82no—
368C2×C4×C7—82no—
369C2×C4×C7—82no—
370C2×C4×C7—82no—
371C2×C4×C7—82no—
372C2×C4×C7—161no—
373C2×C4×C7#12012yes—
374C25C23×C711yescharacteristic
375H(5,𝔽2)—22no—
376H(5,𝔽2)—22no—
377H(5,𝔽2)—42no—
378C2×#41—22no—
379C2×#41—21no—
380C2×#41—22no—
381C22×D4—21no—
382C22×D4—22no—
383C22×D4—21no—
384C22×D4—21no—
385C22×D4—22no—
386C22×D4C23×C711yescharacteristic
387C22×D4C23×C711yescharacteristic
388C22×D4C23×C712yes—
389C23×C4—21no—
390#126—22no—
391#126—22no—
392#124—22no—
393#124—22no—
394#123—22no—
395#123—22no—
396#123—22no—
397#123—22no—
398#123—21no—
399#123—22no—
400#123—22no—
401#123C7×D412yescomplemented
402C22⋊Q8—22no—
403C22⋊Q8—22no—
404C22⋊Q8—22no—
405C22⋊Q8—22no—
406#121—22no—
407#121—22no—
408#121—22no—
409#121—22no—
410#121—42no—
411#120—21no—
412#120—21no—
413#120—21no—
414#120—22no—
415#120—22no—
416#120—22no—
417#120—22no—
418#120—22no—
419#120—22no—
420#120—42no—
421#120C7×D412yescomplemented
422#120C7×D412yescomplemented
423#120C7×D412yescomplemented
424C4×D4—22no—
425C4×D4—22no—
426C4×D4—22no—
427C4×D4—22no—
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—42no—
431#117—22no—
432#117—21no—
433#117—21no—
434#117C7×D412yescomplemented
435C2×C22⋊C4—21no—
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—42no—
444C2×C22⋊C4C7×D412yescomplemented
445C2×C22⋊C4C23×C712yes—
446C2×C22⋊C4C23×C712yes—
447C2×C22⋊C4C23×C712yes—
448C2×C22⋊C4C23×C711yescharacteristic
449C2×C22⋊C4C23×C711yescharacteristic
450C2×C22⋊C4C23×C711yescharacteristic
451C2×C22⋊C4C23×C711yescharacteristic
452#99—22no—
453#99—22no—
454#99—24no—
455#99—24no—
456#99—24no—
457#99—24no—
458#99—42no—
459C22×C7—22no—
460C22×C7—24no—
461C22×C7—22no—
462C22×C7—41no—
463C22×C7—42no—
464C22×C7—41no—
465C22×C7—41no—
466C22×C7—42no—
467C22×C7—42no—
468C22×C7—41no—
469C22×C7—42no—
470C22×C7—42no—
471C22×C7—41no—
472C22×C7—41no—
473C22×C7—42no—
474C22×C7—42no—
475C22×C7—41no—
476C22×C7—42no—
477C22×C7—41no—
478C22×C7—41no—
479C22×C7—81no—
480C22×C7—81no—
481C22×C7—82no—
482C22×C7—84no—
483C22×C7—82no—
484C22×C7—82no—
485C22×C7—82no—
486C22×C7—82no—
487C22×C7—82no—
488C22×C7—162no—
489C22×C7C2×#12011yescharacteristic
490C22×C7#52511yescharacteristic
491C22×C7#53511yescharacteristic
492C22×C7#54612yes—
493C22×C7#54612yes—
494C4×C7—22no—
495C4×C7—42no—
496C4×C7—42no—
497C4×C7—42no—
498C4×C7—42no—
499C4×C7—42no—
500C4×C7—41no—
501C4×C7—82no—
502C4×C7—82no—
503C4×C7—82no—
504C24—21no—
505C24—21no—
506C24—21no—
507C24—22no—
508C24—22no—
509C24—82no—
510C24C2×C7×D411yescharacteristic
511C24C2×C7×D411yescharacteristic
512C24C2×C7×D411yescharacteristic
513C24C2×C7×D411yescharacteristic
514C24C7×#4112yescomplemented
515C24C24×C711yescharacteristic
516#41—44no—
517#41—44no—
518#41—42no—
519#41—42no—
520#41—84no—
521C2×Q8—21no—
522C2×Q8—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—21no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—82no—
550C2×D4—82no—
551C2×D4—84no—
552C2×D4C2×C7×D412yes—
553C2×D4C2×C7×D412yes—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—41no—
568C22×C4—82no—
569C22×C4C2×C7×D411yescharacteristic
570C22×C4C2×C7×D411yescharacteristic
571C22×C4C7×#4112yescomplemented
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—42no—
579C4⋊C4—41no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—21no—
588C22⋊C4—21no—
589C22⋊C4—21no—
590C22⋊C4—21no—
591C22⋊C4—22no—
592C22⋊C4—22no—
593C22⋊C4—22no—
594C22⋊C4—22no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—41no—
605C22⋊C4—84no—
606C22⋊C4C2×C7×D412yes—
607C22⋊C4C2×C7×D412yes—
608C22⋊C4C2×C7×D412yes—
609C22⋊C4C2×C7×D412yes—
610C42—22no—
611C42—22no—
612C42—41no—
613C2×C7—21no—
614C2×C7—21no—
615C2×C7—22no—
616C2×C7—22no—
617C2×C7—21no—
618C2×C7—42no—
619C2×C7—42no—
620C2×C7—81no—
621C2×C7—81no—
622C2×C7—82no—
623C2×C7#240411yescharacteristic
624C23—21no—
625C23—22no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—42no—
636C23—44no—
637C23—42no—
638C23—42no—
639C23—44no—
640C23—42no—
641C23—41no—
642C23—41no—
643C23—42no—
644C23—81no—
645C23—81no—
646C23—81no—
647C23—81no—
648C23—82no—
649C23—81no—
650C23—81no—
651C23—82no—
652C23—82no—
653C23—161no—
654C23C7×#12012yes—
655C23C22×C7×D411yescharacteristic
656C23C22×C7×D411yescharacteristic
657C23C22×C7×D411yescharacteristic
658C23C2×C7×#4112yes—
659C23C7×H(5,𝔽2)12yes—
660Q8—42no—
661Q8—82no—
662D4—24no—
663D4—24no—
664D4—42no—
665D4—44no—
666D4—44no—
667D4—44no—
668D4—42no—
669D4—41no—
670D4—41no—
671D4—42no—
672D4—42no—
673D4—42no—
674D4—42no—
675D4—82no—
676D4—82no—
677D4—82no—
678D4—84no—
679D4—84no—
680D4—162no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—81no—
699C2×C4—82no—
700C2×C4—81no—
701C2×C4—81no—
702C2×C4—81no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4—82no—
707C2×C4—82no—
708C2×C4—161no—
709C2×C4C7×#12012yes—
710C7#2399611yescharacteristic, direct product factor, Sylow
711C22—22no—
712C22—24no—
713C22—22no—
714C22—41no—
715C22—42no—
716C22—41no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—41no—
721C22—42no—
722C22—42no—
723C22—41no—
724C22—41no—
725C22—42no—
726C22—42no—
727C22—41no—
728C22—42no—
729C22—41no—
730C22—41no—
731C22—81no—
732C22—81no—
733C22—82no—
734C22—84no—
735C22—82no—
736C22—82no—
737C22—82no—
738C22—82no—
739C22—82no—
740C22—162no—
741C22C2×C7×#12011yescharacteristic
742C22C7×#52511yescharacteristic
743C22C7×#53511yescharacteristic
744C22C7×#54612yes—
745C22C7×#54612yes—
746C4—22no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—41no—
753C4—82no—
754C4—82no—
755C4—82no—
756C2—21no—
757C2—21no—
758C2—22no—
759C2—22no—
760C2—21no—
761C2—42no—
762C2—42no—
763C2—81no—
764C2—81no—
765C2—82no—
766C2C7×#240411yescharacteristic
subgroupG/H
center, socleC2×C7#2404
commutator, Frattini, cosocleC24C24×C7
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C2×C7 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C7×#3490C2semidirect
2. C7×#3026C2semidirect
3. C2×C7×B(4,𝔽2)C2semidirect
4. C7×#2883C2semidirect
5. C7×#2032C2semidirect
6. C7×#2021C2semidirect
7. C7×#1913C2semidirect
8. C7×#1913C2semidirect
9. C7×#1898C2semidirect
10. C7×#1889C2semidirect
11. C7×#1828C2semidirect
17. C7×#543C22semidirect
24. C2×C7×#120C22semidirect
27. C7×#518C22semidirect
28. C22×C7×C22⋊C4C22semidirect
41. C2×C7×#99C22semidirect
42. C7×#379C22semidirect
43. C7×#342C22semidirect
44. C7×#342C22semidirect
45. C7×#342C22semidirect
46. C7×#342C22semidirect
47. #23996C7direct (N × H)
75. C7×#123D4semidirect
95. C7×#120D4semidirect
96. C7×#120D4semidirect
97. C7×#120D4semidirect
108. C7×#117D4semidirect
118. C2×C7×C22⋊C4D4semidirect
133. #3490C2×C7semidirect
134. #3026C2×C7semidirect
135. C2×B(4,𝔽2)C2×C7semidirect
136. #2883C2×C7semidirect
137. #2032C2×C7semidirect
138. #2021C2×C7semidirect
139. #1913C2×C7semidirect
140. #1913C2×C7semidirect
141. #1898C2×C7semidirect
142. #1889C2×C7semidirect
143. #1828C2×C7semidirect
154. C24×C7#41semidirect
211. C22×C4×C7#41semidirect
258. #543C22×C7semidirect
265. C2×#120C22×C7semidirect
268. #518C22×C7semidirect
269. C22×C22⋊C4C22×C7semidirect
282. C2×#99C22×C7semidirect
283. #379C22×C7semidirect
284. #342C22×C7semidirect
285. #342C22×C7semidirect
286. #342C22×C7semidirect
287. #342C22×C7semidirect
401. #123C7×D4semidirect
421. #120C7×D4semidirect
422. #120C7×D4semidirect
423. #120C7×D4semidirect
434. #117C7×D4semidirect
444. C2×C22⋊C4C7×D4semidirect
514. C24C7×#41semidirect
571. C22×C4C7×#41semidirect
710. C7#23996direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#34902
C7×#30262
C2×C7×B(4,𝔽2)2
C7×#28832
C7×#20322
C7×#20212
C7×#19132
C7×#18982
C7×#18892
C7×#18282
#239967