Finite Group Databasebeta

← C7×#18787 #13196003

Subgroups — C7×#18787 #13196003

Order 1792.

1206 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×D4×#41C211yesmaximal, characteristic
2C7×#3206C211yesmaximal, characteristic, complemented
3C7×#3079C211yesmaximal, characteristic, complemented
4C2×C7×#476C211yesmaximal, characteristic, complemented
5C7×#1637C212yesmaximal, complemented
6C7×#1635C212yesmaximal, complemented
7C7×#1631C212yesmaximal, complemented
8C7×#1629C212yesmaximal, complemented
9C7×#1547C211yesmaximal, characteristic, complemented
10C7×#1486C211yesmaximal, characteristic, complemented
11C7×#1477C211yesmaximal, characteristic, complemented
12C22×C7×#41—21no—
13C7×#550C2211yescharacteristic
14C7×D4×Q8C2211yescharacteristic
15C7×#548—21no—
16C7×#547—21no—
17C7×#547C2211yescharacteristic
18C7×#546—22no—
19C7×#546—21no—
20C7×D42—21no—
21C7×D42C2211yescharacteristic
22C7×#532—21no—
23C7×#532C2211yescharacteristic
24C2×C7×C4⋊Q8C2211yescharacteristic, complemented
25C7×#525—22no—
26C7×#525—21no—
27C4×C7×#41C2211yescharacteristic
28C2×C4×C7×D4—21no—
29C2×C4×C7×D4C2211yescharacteristic
30C7×#492C2212yescomplemented
31C7×#487C2212yescomplemented
32C7×#477C2212yescomplemented
33C7×#476—21no—
34C7×#476—21no—
35C7×#476C2212yes—
36C7×#476C2212yescomplemented
37C7×#476C2212yescomplemented
38C7×#475—21no—
39C7×#474—21no—
40C7×#461—22no—
41C7×#448—22no—
42C7×#431C2211yescharacteristic, complemented
43C7×#428—21no—
44C2×C7×#106—21no—
45C7×#423C2211yescharacteristic, complemented
46C2×C7×C4⋊C8C2211yescharacteristic, complemented
47C7×#417—21no—
48C2×C7×#102—21no—
49C7×#332C2212yescomplemented
50C7×#331C2212yescomplemented
51C7×Q8⋊C8C2212yescomplemented
52C7×D4⋊C8C2212yes—
53C7×D4⋊C8C2212yescomplemented
54C7×D4⋊C8C2212yescomplemented
55#18787C711yesmaximal, characteristic, direct product factor, Sylow
56C2×C7×#41—22no—
57C2×C7×#41—22no—
58C2×C7×#41—21no—
59C2×C7×#41—21no—
60C2×C7×#41—21no—
61C2×C7×#41—44no—
62C2×C7×#41—44no—
63C2×C7×#41D411yescharacteristic
64C22×C7×Q8—21no—
65C22×C7×Q8—21no—
66C22×C7×D4—22no—
67C22×C7×D4—21no—
68C22×C7×D4—21no—
69C22×C7×D4D411yescharacteristic
70C23×C4×C7—22no—
71C23×C4×C7—21no—
72C2×C7×SD16—24no—
73C2×C7×M16—21no—
74C22×C7×C8—21no—
75C7×C4⋊Q8—21no—
76C7×C4⋊Q8—21no—
77C7×C4⋊Q8—21no—
78C7×C4⋊Q8—21no—
79C7×C4⋊Q8C2312yes—
80C7×C4⋊Q8C2311yescharacteristic
81C7×#127—21no—
82C7×#127C2311yescharacteristic
83C7×#124—22no—
84C7×#124—21no—
85C7×#123—22no—
86C7×#123—22no—
87C7×#123—22no—
88C7×C22⋊Q8—22no—
89C7×C22⋊Q8—21no—
90C7×C22⋊Q8—22no—
91C7×C22⋊Q8—21no—
92C7×#121—22no—
93C7×#121—22no—
94C7×#121—22no—
95C7×#121—21no—
96C7×#121—21no—
97C7×#121—21no—
98C7×#121—21no—
99C7×#121—21no—
100C7×#121D412yes—
101C7×#120—22no—
102C7×#120—22no—
103C7×#120—22no—
104C4×C7×Q8D411yescharacteristic
105C4×C7×Q8C2311yescharacteristic
106C4×C7×D4—22no—
107C4×C7×D4—22no—
108C4×C7×D4—22no—
109C4×C7×D4—21no—
110C4×C7×D4—21no—
111C4×C7×D4—21no—
112C4×C7×D4—21no—
113C4×C7×D4—21no—
114C4×C7×D4—21no—
115C4×C7×D4—21no—
116C4×C7×D4D411yescharacteristic
117C4×C7×D4D411yescharacteristic
118C4×C7×D4D411yescharacteristic
119C4×C7×D4D412yes—
120C4×C7×D4C2311yescharacteristic
121C4×C7×D4C2311yescharacteristic
122C4×C7×D4C2311yescharacteristic
123C7×#117—21no—
124C7×#117D411yescharacteristic
125C2×C7×C4⋊C4—21no—
126C2×C7×C4⋊C4—21no—
127C2×C7×C4⋊C4—21no—
128C2×C7×C4⋊C4D411yescharacteristic
129C2×C7×C22⋊C4—22no—
130C2×C7×C22⋊C4—21no—
131C2×C42×C7—21no—
132C2×C42×C7C2311yescharacteristic
133C7×#107—22no—
134C7×#106—22no—
135C7×#106—22no—
136C7×#106—22no—
137C7×C4⋊C8—21no—
138C7×C4⋊C8—21no—
139C7×C4⋊C8—21no—
140C7×C4⋊C8C2312yes—
141C7×C4⋊C8C2312yes—
142C7×#103—22no—
143C7×#103—24no—
144C7×#102—22no—
145C7×#102—22no—
146C7×#102—22no—
147C7×C22⋊C8—21no—
148C4×C7×C8C2312yes—
149D4×#41C2×C711yescharacteristic
150#3206C2×C711yescharacteristic, complemented
151#3079C2×C711yescharacteristic, complemented
152C2×#476C2×C711yescharacteristic, complemented
153#1637C2×C712yescomplemented
154#1635C2×C712yescomplemented
155#1631C2×C712yescomplemented
156#1629C2×C712yescomplemented
157#1547C2×C711yescharacteristic, complemented
158#1486C2×C711yescharacteristic, complemented
159#1477C2×C711yescharacteristic, complemented
160C24×C7—22no—
161C24×C7—21no—
162C7×#41—22no—
163C7×#41—48no—
164C7×#41—48no—
165C7×#41—42no—
166C7×#41—42no—
167C7×#41—42no—
168C7×#41—42no—
169C7×#41—42no—
170C7×#41—42no—
171C7×#41SD1614yescomplemented
172C2×C7×Q8—22no—
173C2×C7×Q8—21no—
174C2×C7×Q8—22no—
175C2×C7×Q8—42no—
176C2×C7×Q8—42no—
177C2×C7×Q8—41no—
178C2×C7×Q8—82no—
179C2×C7×Q8C2×D411yescharacteristic
180C2×C7×D4—21no—
181C2×C7×D4—22no—
182C2×C7×D4—22no—
183C2×C7×D4—22no—
184C2×C7×D4—22no—
185C2×C7×D4—22no—
186C2×C7×D4—22no—
187C2×C7×D4—22no—
188C2×C7×D4—21no—
189C2×C7×D4—21no—
190C2×C7×D4—21no—
191C2×C7×D4—41no—
192C2×C7×D4—42no—
193C2×C7×D4—48no—
194C2×C7×D4—42no—
195C2×C7×D4—42no—
196C2×C7×D4—42no—
197C2×C7×D4C2×D411yescharacteristic
198C2×C7×D4C2×D411yescharacteristic
199C2×C7×D4C2×D411yescharacteristic
200C2×C7×D4C2×D412yes—
201C22×C4×C7—21no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—22no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—48no—
214C22×C4×C7—42no—
215C22×C4×C7—42no—
216C22×C4×C7—41no—
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2×D411yescharacteristic
219C22×C4×C7C2×D411yescharacteristic
220C7×SD16—84no—
221C7×M16—42no—
222C2×C7×C8—22no—
223C2×C7×C8—22no—
224C2×C7×C8—22no—
225C2×C7×C8—42no—
226C7×C4⋊C4—22no—
227C7×C4⋊C4—22no—
228C7×C4⋊C4—21no—
229C7×C4⋊C4—21no—
230C7×C4⋊C4—21no—
231C7×C4⋊C4—21no—
232C7×C4⋊C4—22no—
233C7×C4⋊C4—22no—
234C7×C4⋊C4—41no—
235C7×C4⋊C4—41no—
236C7×C4⋊C4C2×D412yes—
237C7×C4⋊C4C2×D411yescharacteristic
238C7×C4⋊C4C2×D411yescharacteristic
239C7×C4⋊C4C2×D411yescharacteristic
240C7×C4⋊C4C2×D411yescharacteristic
241C7×C22⋊C4—22no—
242C7×C22⋊C4—22no—
243C7×C22⋊C4—22no—
244C7×C22⋊C4—22no—
245C7×C22⋊C4—21no—
246C7×C22⋊C4—21no—
247C7×C22⋊C4—22no—
248C7×C22⋊C4—21no—
249C7×C22⋊C4—21no—
250C7×C22⋊C4—22no—
251C7×C22⋊C4—21no—
252C7×C22⋊C4—21no—
253C7×C22⋊C4—21no—
254C42×C7—21no—
255C42×C7—21no—
256C42×C7—21no—
257C42×C7C2×D411yescharacteristic
258C42×C7C2×D411yescharacteristic
259C42×C7C2×D411yescharacteristic
260C42×C7C2411yescharacteristic
261C22×#41—21no—
262#550C22×C711yescharacteristic
263D4×Q8C22×C711yescharacteristic
264#548—21no—
265#547—21no—
266#547C22×C711yescharacteristic
267#546—22no—
268#546—21no—
269D42—21no—
270D42C22×C711yescharacteristic
271#532—21no—
272#532C22×C711yescharacteristic
273C2×C4⋊Q8C22×C711yescharacteristic, complemented
274#525—22no—
275#525—21no—
276C4×#41C22×C711yescharacteristic
277C2×C4×D4—21no—
278C2×C4×D4C22×C711yescharacteristic
279#492C22×C712yescomplemented
280#487C22×C712yescomplemented
281#477C22×C712yescomplemented
282#476—21no—
283#476—21no—
284#476C22×C712yes—
285#476C22×C712yescomplemented
286#476C22×C712yescomplemented
287#475—21no—
288#474—21no—
289#461—22no—
290#448—22no—
291#431C22×C711yescharacteristic, complemented
292#428—21no—
293C2×#106—21no—
294#423C22×C711yescharacteristic, complemented
295C2×C4⋊C8C22×C711yescharacteristic, complemented
296#417—21no—
297C2×#102—21no—
298#332C22×C712yescomplemented
299#331C22×C712yescomplemented
300Q8⋊C8C22×C712yescomplemented
301D4⋊C8C22×C712yes—
302D4⋊C8C22×C712yescomplemented
303D4⋊C8C22×C712yescomplemented
304C23×C7—21no—
305C23×C7—21no—
306C23×C7—21no—
307C23×C7—22no—
308C23×C7—42no—
309C23×C7—44no—
310C23×C7—44no—
311C23×C7—42no—
312C23×C7—81no—
313C23×C7—82no—
314C23×C7#12011yescharacteristic
315C7×Q8—21no—
316C7×Q8—44no—
317C7×Q8—44no—
318C7×Q8—41no—
319C7×Q8—41no—
320C7×Q8—82no—
321C7×Q8C2×SD1612yes—
322C7×D4—24no—
323C7×D4—21no—
324C7×D4—21no—
325C7×D4—21no—
326C7×D4—21no—
327C7×D4—42no—
328C7×D4—42no—
329C7×D4—44no—
330C7×D4—44no—
331C7×D4—44no—
332C7×D4—44no—
333C7×D4—44no—
334C7×D4—41no—
335C7×D4—41no—
336C7×D4—41no—
337C7×D4—41no—
338C7×D4—82no—
339C7×D4C2×SD1612yes—
340C7×D4#13712yes—
341C2×C4×C7—21no—
342C2×C4×C7—21no—
343C2×C4×C7—21no—
344C2×C4×C7—24no—
345C2×C4×C7—21no—
346C2×C4×C7—21no—
347C2×C4×C7—21no—
348C2×C4×C7—22no—
349C2×C4×C7—21no—
350C2×C4×C7—41no—
351C2×C4×C7—44no—
352C2×C4×C7—44no—
353C2×C4×C7—44no—
354C2×C4×C7—42no—
355C2×C4×C7—41no—
356C2×C4×C7—41no—
357C2×C4×C7—41no—
358C2×C4×C7—41no—
359C2×C4×C7—41no—
360C2×C4×C7—41no—
361C2×C4×C7—42no—
362C2×C4×C7—44no—
363C2×C4×C7—42no—
364C2×C4×C7—42no—
365C2×C4×C7—81no—
366C2×C4×C7—82no—
367C2×C4×C7#12011yescharacteristic
368C2×C4×C7#12011yescharacteristic
369C2×C4×C7#12011yescharacteristic
370C2×C4×C7C2×SD1612yes—
371C2×C4×C7AGL(1,ℤ/8)12yes—
372C2×C4×C7C22×D411yescharacteristic
373C2×C4×C7C22×D411yescharacteristic
374C2×C4×C7C22×D411yescharacteristic
375C7×C8—42no—
376C7×C8—42no—
377C7×C8—42no—
378C2×#41—22no—
379C2×#41—22no—
380C2×#41—21no—
381C2×#41—21no—
382C2×#41—21no—
383C2×#41—44no—
384C2×#41—44no—
385C2×#41C7×D411yescharacteristic
386C22×Q8—21no—
387C22×Q8—21no—
388C22×D4—22no—
389C22×D4—21no—
390C22×D4—21no—
391C22×D4C7×D411yescharacteristic
392C23×C4—22no—
393C23×C4—21no—
394C2×SD16—24no—
395C2×M16—21no—
396C22×C8—21no—
397C4⋊Q8—21no—
398C4⋊Q8—21no—
399C4⋊Q8—21no—
400C4⋊Q8—21no—
401C4⋊Q8C23×C712yes—
402C4⋊Q8C23×C711yescharacteristic
403#127—21no—
404#127C23×C711yescharacteristic
405#124—22no—
406#124—21no—
407#123—22no—
408#123—22no—
409#123—22no—
410C22⋊Q8—22no—
411C22⋊Q8—21no—
412C22⋊Q8—22no—
413C22⋊Q8—21no—
414#121—22no—
415#121—22no—
416#121—22no—
417#121—21no—
418#121—21no—
419#121—21no—
420#121—21no—
421#121—21no—
422#121C7×D412yes—
423#120—22no—
424#120—22no—
425#120—22no—
426C4×Q8C7×D411yescharacteristic
427C4×Q8C23×C711yescharacteristic
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—22no—
431C4×D4—21no—
432C4×D4—21no—
433C4×D4—21no—
434C4×D4—21no—
435C4×D4—21no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4C7×D411yescharacteristic
439C4×D4C7×D411yescharacteristic
440C4×D4C7×D411yescharacteristic
441C4×D4C7×D412yes—
442C4×D4C23×C711yescharacteristic
443C4×D4C23×C711yescharacteristic
444C4×D4C23×C711yescharacteristic
445#117—21no—
446#117C7×D411yescharacteristic
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4C7×D411yescharacteristic
451C2×C22⋊C4—22no—
452C2×C22⋊C4—21no—
453C2×C42—21no—
454C2×C42C23×C711yescharacteristic
455#107—22no—
456#106—22no—
457#106—22no—
458#106—22no—
459C4⋊C8—21no—
460C4⋊C8—21no—
461C4⋊C8—21no—
462C4⋊C8C23×C712yes—
463C4⋊C8C23×C712yes—
464#103—22no—
465#103—24no—
466#102—22no—
467#102—22no—
468#102—22no—
469C22⋊C8—21no—
470C4×C8C23×C712yes—
471C22×C7—21no—
472C22×C7—21no—
473C22×C7—22no—
474C22×C7—22no—
475C22×C7—41no—
476C22×C7—41no—
477C22×C7—41no—
478C22×C7—41no—
479C22×C7—42no—
480C22×C7—41no—
481C22×C7—41no—
482C22×C7—42no—
483C22×C7—42no—
484C22×C7—41no—
485C22×C7—84no—
486C22×C7—88no—
487C22×C7#45012yes—
488C22×C7C2×#12011yescharacteristic
489C4×C7—22no—
490C4×C7—21no—
491C4×C7—21no—
492C4×C7—21no—
493C4×C7—41no—
494C4×C7—42no—
495C4×C7—41no—
496C4×C7—41no—
497C4×C7—41no—
498C4×C7—82no—
499C4×C7#45012yes—
500C4×C7C22×SD1611yescharacteristic
501C4×C7C2×AGL(1,ℤ/8)11yescharacteristic
502C4×C7C2×#13711yescharacteristic
503C4×C7#57511yescharacteristic
504C24—22no—
505C24—21no—
506#41—22no—
507#41—48no—
508#41—48no—
509#41—42no—
510#41—42no—
511#41—42no—
512#41—42no—
513#41—42no—
514#41—42no—
515#41C7×SD1614yescomplemented
516C2×Q8—22no—
517C2×Q8—21no—
518C2×Q8—22no—
519C2×Q8—42no—
520C2×Q8—42no—
521C2×Q8—41no—
522C2×Q8—82no—
523C2×Q8C2×C7×D411yescharacteristic
524C2×D4—21no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—41no—
536C2×D4—48no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4C2×C7×D411yescharacteristic
542C2×D4C2×C7×D411yescharacteristic
543C2×D4C2×C7×D411yescharacteristic
544C2×D4C2×C7×D412yes—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—48no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—41no—
561C22×C4C2×C7×D411yescharacteristic
562C22×C4C2×C7×D411yescharacteristic
563C22×C4C2×C7×D411yescharacteristic
564SD16—84no—
565M16—42no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—42no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—41no—
579C4⋊C4—41no—
580C4⋊C4C2×C7×D412yes—
581C4⋊C4C2×C7×D411yescharacteristic
582C4⋊C4C2×C7×D411yescharacteristic
583C4⋊C4C2×C7×D411yescharacteristic
584C4⋊C4C2×C7×D411yescharacteristic
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—21no—
590C22⋊C4—21no—
591C22⋊C4—22no—
592C22⋊C4—21no—
593C22⋊C4—21no—
594C22⋊C4—22no—
595C22⋊C4—21no—
596C22⋊C4—21no—
597C22⋊C4—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42C2×C7×D411yescharacteristic
602C42C2×C7×D411yescharacteristic
603C42C2×C7×D411yescharacteristic
604C42C24×C711yescharacteristic
605C2×C7—22no—
606C2×C7—42no—
607C2×C7—42no—
608C2×C7—81no—
609C2×C7—82no—
610C2×C7C2×#45011yescharacteristic
611C2×C7#300711yescharacteristic
612C2×C7#302111yescharacteristic
613C23—21no—
614C23—21no—
615C23—21no—
616C23—22no—
617C23—42no—
618C23—44no—
619C23—44no—
620C23—42no—
621C23—81no—
622C23—82no—
623C23C7×#12011yescharacteristic
624Q8—21no—
625Q8—44no—
626Q8—44no—
627Q8—41no—
628Q8—41no—
629Q8—82no—
630Q8C2×C7×SD1612yes—
631D4—24no—
632D4—21no—
633D4—21no—
634D4—21no—
635D4—21no—
636D4—42no—
637D4—42no—
638D4—44no—
639D4—44no—
640D4—44no—
641D4—44no—
642D4—44no—
643D4—41no—
644D4—41no—
645D4—41no—
646D4—41no—
647D4—82no—
648D4C2×C7×SD1612yes—
649D4C7×#13712yes—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—24no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—41no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—44no—
663C2×C4—42no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—44no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—81no—
675C2×C4—82no—
676C2×C4C7×#12011yescharacteristic
677C2×C4C7×#12011yescharacteristic
678C2×C4C7×#12011yescharacteristic
679C2×C4C2×C7×SD1612yes—
680C2×C4C7×AGL(1,ℤ/8)12yes—
681C2×C4C22×C7×D411yescharacteristic
682C2×C4C22×C7×D411yescharacteristic
683C2×C4C22×C7×D411yescharacteristic
684C8—42no—
685C8—42no—
686C8—42no—
687C7#1878711yescharacteristic, direct product factor, Sylow
688C22—21no—
689C22—21no—
690C22—22no—
691C22—22no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—42no—
697C22—41no—
698C22—41no—
699C22—42no—
700C22—42no—
701C22—41no—
702C22—84no—
703C22—88no—
704C22C7×#45012yes—
705C22C2×C7×#12011yescharacteristic
706C4—22no—
707C4—21no—
708C4—21no—
709C4—21no—
710C4—41no—
711C4—42no—
712C4—41no—
713C4—41no—
714C4—41no—
715C4—82no—
716C4C7×#45012yes—
717C4C22×C7×SD1611yescharacteristic
718C4C2×C7×AGL(1,ℤ/8)11yescharacteristic
719C4C2×C7×#13711yescharacteristic
720C4C7×#57511yescharacteristic
721C2—22no—
722C2—42no—
723C2—42no—
724C2—81no—
725C2—82no—
726C2C2×C7×#45011yescharacteristic
727C2C7×#300711yescharacteristic
728C2C7×#302111yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC42C24×C7
prime radicalC7×D4×#41C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C7×#3206C2semidirect
3. C7×#3079C2semidirect
4. C2×C7×#476C2semidirect
5. C7×#1637C2semidirect
6. C7×#1635C2semidirect
7. C7×#1631C2semidirect
8. C7×#1629C2semidirect
9. C7×#1547C2semidirect
10. C7×#1486C2semidirect
11. C7×#1477C2semidirect
24. C2×C7×C4⋊Q8C22semidirect
30. C7×#492C22semidirect
31. C7×#487C22semidirect
32. C7×#477C22semidirect
36. C7×#476C22semidirect
37. C7×#476C22semidirect
42. C7×#431C22semidirect
45. C7×#423C22semidirect
46. C2×C7×C4⋊C8C22semidirect
49. C7×#332C22semidirect
50. C7×#331C22semidirect
51. C7×Q8⋊C8C22semidirect
53. C7×D4⋊C8C22semidirect
54. C7×D4⋊C8C22semidirect
55. #18787C7direct (N × H)
150. #3206C2×C7semidirect
151. #3079C2×C7semidirect
152. C2×#476C2×C7semidirect
153. #1637C2×C7semidirect
154. #1635C2×C7semidirect
155. #1631C2×C7semidirect
156. #1629C2×C7semidirect
157. #1547C2×C7semidirect
158. #1486C2×C7semidirect
159. #1477C2×C7semidirect
171. C7×#41SD16semidirect
273. C2×C4⋊Q8C22×C7semidirect
279. #492C22×C7semidirect
280. #487C22×C7semidirect
281. #477C22×C7semidirect
285. #476C22×C7semidirect
286. #476C22×C7semidirect
291. #431C22×C7semidirect
294. #423C22×C7semidirect
295. C2×C4⋊C8C22×C7semidirect
298. #332C22×C7semidirect
299. #331C22×C7semidirect
300. Q8⋊C8C22×C7semidirect
302. D4⋊C8C22×C7semidirect
303. D4⋊C8C22×C7semidirect
515. #41C7×SD16semidirect
687. C7#18787direct (N × H)

Maximal subgroups

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

subgroupindex
C7×D4×#412
C7×#32062
C7×#30792
C2×C7×#4762
C7×#16372
C7×#16352
C7×#16312
C7×#16292
C7×#15472
C7×#14862
C7×#14772
#187877