Finite Group Databasebeta

← C7×#18450 #13195666

Subgroups — C7×#18450 #13195666

Order 1792.

1096 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3537C211yesmaximal, characteristic, complemented
2C7×#3194C211yesmaximal, characteristic, complemented
3C7×#3186C211yesmaximal, characteristic, complemented
4C7×#2815C211yesmaximal, characteristic, complemented
5C7×#1612C212yesmaximal, complemented
6C7×#1607C212yesmaximal, complemented
7C7×#1600C212yesmaximal, complemented
8C7×#1595C212yesmaximal, complemented
9C7×#1516C211yesmaximal, characteristic, complemented
10C7×#1510C211yesmaximal, characteristic, complemented
11C7×#1471C211yesmaximal, characteristic, complemented
12C7×#560—22no—
13C7×#553—21no—
14C7×#553—21no—
15C7×D42—22no—
16C7×D42—21no—
17C7×D42—21no—
18C7×#540—21no—
19C7×#538—21no—
20C7×#538C2212yes—
21C7×#535—21no—
22C7×#534—21no—
23C7×#534C2212yes—
24C7×#525C2211yescharacteristic
25C2×C7×#121C2211yescharacteristic
26C2×C7×#121C2211yescharacteristic
27C2×C7×#121C2211yescharacteristic, complemented
28C7×#483C2211yescharacteristic, complemented
29C7×#482—21no—
30C7×#480—21no—
31C7×#480C2212yescomplemented
32C7×#480C2211yescharacteristic, complemented
33C7×#469—21no—
34C7×#468—21no—
35C7×#466—22no—
36C7×#450C2211yescharacteristic, complemented
37C7×#449—21no—
38C7×#447—21no—
39C7×#447C2212yescomplemented
40C7×#447C2211yescharacteristic, complemented
41C7×#407C2211yescharacteristic, complemented
42C2×C7×C22⋊C8C2211yescharacteristic, complemented
43C7×#397—21no—
44C7×#397C2212yescomplemented
45C7×#392—21no—
46C7×#392—22no—
47C7×#392C2212yescomplemented
48C7×#381C2211yescharacteristic, complemented
49C7×#328C2212yescomplemented
50C7×#327C2212yescomplemented
51C7×#327C2212yescomplemented
52C7×#327C2212yescomplemented
53C7×#323C2212yescomplemented
54C7×#323C2212yescomplemented
55#18450C711yesmaximal, characteristic, direct product factor, Sylow
56C2×C7×#41D411yescharacteristic, complemented
57C22×C7×D4—22no—
58C22×C7×D4—21no—
59C22×C7×D4—21no—
60C22×C7×D4—22no—
61C22×C7×D4—21no—
62C22×C7×D4—22no—
63C22×C7×D4D412yes—
64C22×C7×D4D411yescharacteristic
65C22×C7×D4D411yescharacteristic, complemented
66C22×C7×D4C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C2×C7×SD16—21no—
69C2×C7×D8—22no—
70C2×C7×D8—21no—
71C2×C7×M16—21no—
72C22×C7×C8—21no—
73C7×#127—22no—
74C7×#127—21no—
75C7×#126—22no—
76C7×#126—22no—
77C7×#125—21no—
78C7×#124—22no—
79C7×#123—22no—
80C7×#123—21no—
81C7×#123—22no—
82C7×#123—22no—
83C7×#123—22no—
84C7×C22⋊Q8D411yescharacteristic, complemented
85C7×C22⋊Q8C2311yescharacteristic
86C7×#121—22no—
87C7×#121—21no—
88C7×#121—21no—
89C7×#121—22no—
90C7×#121—22no—
91C7×#121—22no—
92C7×#121—22no—
93C7×#121—21no—
94C7×#121—21no—
95C7×#121—21no—
96C7×#121—21no—
97C7×#121—21no—
98C7×#121—21no—
99C7×#121—22no—
100C7×#121—21no—
101C7×#121—21no—
102C7×#121—21no—
103C7×#121—21no—
104C7×#121D412yescomplemented
105C7×#121D411yescharacteristic, complemented
106C7×#121C2312yes—
107C7×#121C2311yescharacteristic
108C7×#120—22no—
109C7×#120—22no—
110C7×#120—22no—
111C7×#120—21no—
112C7×#120—22no—
113C7×#120—22no—
114C7×#120—22no—
115C4×C7×D4—22no—
116C4×C7×D4—21no—
117C4×C7×D4—21no—
118C4×C7×D4—21no—
119C4×C7×D4—21no—
120C4×C7×D4—22no—
121C7×#117—21no—
122C7×#117D411yescharacteristic, complemented
123C2×C7×C4⋊C4D411yescharacteristic
124C2×C7×C4⋊C4D411yescharacteristic, complemented
125C2×C7×C4⋊C4C2311yescharacteristic
126C2×C7×C22⋊C4—21no—
127C2×C7×C22⋊C4—21no—
128C2×C7×C22⋊C4—21no—
129C2×C7×C22⋊C4—22no—
130C2×C7×C22⋊C4—22no—
131C2×C7×C22⋊C4C2312yes—
132C7×#107—22no—
133C7×#107—21no—
134C7×#106—21no—
135C7×#103—21no—
136C7×#102—22no—
137C7×#102—21no—
138C7×#102—22no—
139C7×#102—21no—
140C7×#102—21no—
141C7×C22⋊C8—21no—
142C7×C22⋊C8—21no—
143C7×C22⋊C8C2311yescharacteristic
144C7×C22⋊C8C2312yes—
145C7×C22⋊C8C2311yescharacteristic
146C7×#95—21no—
147C7×#95—22no—
148C7×#95C2312yes—
149#3537C2×C711yescharacteristic, complemented
150#3194C2×C711yescharacteristic, complemented
151#3186C2×C711yescharacteristic, complemented
152#2815C2×C711yescharacteristic, complemented
153#1612C2×C712yescomplemented
154#1607C2×C712yescomplemented
155#1600C2×C712yescomplemented
156#1595C2×C712yescomplemented
157#1516C2×C711yescharacteristic, complemented
158#1510C2×C711yescharacteristic, complemented
159#1471C2×C711yescharacteristic, complemented
160C24×C7—22no—
161C24×C7—21no—
162C24×C7—21no—
163C24×C7C2×D412yes—
164C24×C7C2×D411yescharacteristic
165C7×#41—81no—
166C2×C7×Q8C2×D411yescharacteristic
167C2×C7×D4—22no—
168C2×C7×D4—21no—
169C2×C7×D4—21no—
170C2×C7×D4—22no—
171C2×C7×D4—22no—
172C2×C7×D4—22no—
173C2×C7×D4—22no—
174C2×C7×D4—22no—
175C2×C7×D4—22no—
176C2×C7×D4—21no—
177C2×C7×D4—22no—
178C2×C7×D4—22no—
179C2×C7×D4—21no—
180C2×C7×D4—21no—
181C2×C7×D4—21no—
182C2×C7×D4—21no—
183C2×C7×D4—21no—
184C2×C7×D4—41no—
185C2×C7×D4—41no—
186C2×C7×D4—81no—
187C2×C7×D4—81no—
188C2×C7×D4—82no—
189C2×C7×D4—81no—
190C2×C7×D4—82no—
191C2×C7×D4—82no—
192C2×C7×D4—82no—
193C2×C7×D4—82no—
194C2×C7×D4—82no—
195C2×C7×D4—82no—
196C2×C7×D4—82no—
197C2×C7×D4—82no—
198C2×C7×D4—84no—
199C2×C7×D4C2×D411yescharacteristic
200C2×C7×D4C2×D412yes—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—22no—
206C22×C4×C7—21no—
207C22×C4×C7—81no—
208C22×C4×C7C2×D412yes—
209C22×C4×C7C2×D411yescharacteristic
210C22×C4×C7C2×D411yescharacteristic
211C22×C4×C7C2×D411yescharacteristic
212C22×C4×C7C2×D411yescharacteristic
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2411yescharacteristic
215C7×SD16—81no—
216C7×D8—82no—
217C7×D8—81no—
218C7×M16—81no—
219C2×C7×C8—22no—
220C2×C7×C8—21no—
221C2×C7×C8—21no—
222C2×C7×C8—81no—
223C7×C4⋊C4—22no—
224C7×C4⋊C4—22no—
225C7×C4⋊C4—21no—
226C7×C4⋊C4—21no—
227C7×C4⋊C4—21no—
228C7×C4⋊C4—21no—
229C7×C4⋊C4—21no—
230C7×C4⋊C4—21no—
231C7×C4⋊C4—21no—
232C7×C4⋊C4C2×D411yescharacteristic
233C7×C4⋊C4C2×D412yes—
234C7×C4⋊C4C2×D411yescharacteristic
235C7×C22⋊C4—22no—
236C7×C22⋊C4—22no—
237C7×C22⋊C4—22no—
238C7×C22⋊C4—22no—
239C7×C22⋊C4—22no—
240C7×C22⋊C4—21no—
241C7×C22⋊C4—21no—
242C7×C22⋊C4—21no—
243C7×C22⋊C4—22no—
244C7×C22⋊C4—21no—
245C7×C22⋊C4—22no—
246C7×C22⋊C4—22no—
247C7×C22⋊C4—22no—
248C7×C22⋊C4—21no—
249C7×C22⋊C4—41no—
250C7×C22⋊C4—41no—
251C7×C22⋊C4—82no—
252C7×C22⋊C4—82no—
253C7×C22⋊C4—81no—
254C42×C7—22no—
255C42×C7—21no—
256#560—22no—
257#553—21no—
258#553—21no—
259D42—22no—
260D42—21no—
261D42—21no—
262#540—21no—
263#538—21no—
264#538C22×C712yes—
265#535—21no—
266#534—21no—
267#534C22×C712yes—
268#525C22×C711yescharacteristic
269C2×#121C22×C711yescharacteristic
270C2×#121C22×C711yescharacteristic
271C2×#121C22×C711yescharacteristic, complemented
272#483C22×C711yescharacteristic, complemented
273#482—21no—
274#480—21no—
275#480C22×C711yescharacteristic, complemented
276#480C22×C712yescomplemented
277#469—21no—
278#468—21no—
279#466—22no—
280#450C22×C711yescharacteristic, complemented
281#449—21no—
282#447—21no—
283#447C22×C711yescharacteristic, complemented
284#447C22×C712yescomplemented
285#407C22×C711yescharacteristic, complemented
286C2×C22⋊C8C22×C711yescharacteristic, complemented
287#397—21no—
288#397C22×C712yescomplemented
289#392—21no—
290#392—22no—
291#392C22×C712yescomplemented
292#381C22×C711yescharacteristic, complemented
293#328C22×C712yescomplemented
294#327C22×C712yescomplemented
295#327C22×C712yescomplemented
296#327C22×C712yescomplemented
297#323C22×C712yescomplemented
298#323C22×C712yescomplemented
299C23×C7—22no—
300C23×C7—22no—
301C23×C7—22no—
302C23×C7—21no—
303C23×C7—22no—
304C23×C7—22no—
305C23×C7—41no—
306C23×C7—41no—
307C23×C7—42no—
308C23×C7—42no—
309C23×C7—42no—
310C23×C7—41no—
311C23×C7—41no—
312C23×C7—42no—
313C23×C7—41no—
314C23×C7—42no—
315C23×C7—81no—
316C23×C7—81no—
317C23×C7—82no—
318C23×C7—82no—
319C23×C7—82no—
320C23×C7#12011yescharacteristic
321C23×C7#12011yescharacteristic
322C23×C7C22×D411yescharacteristic
323C7×Q8—41no—
324C7×D4—42no—
325C7×D4—41no—
326C7×D4—42no—
327C7×D4—42no—
328C7×D4—42no—
329C7×D4—41no—
330C7×D4—41no—
331C7×D4—44no—
332C7×D4—42no—
333C7×D4—42no—
334C7×D4—42no—
335C7×D4—42no—
336C7×D4—81no—
337C7×D4—82no—
338C7×D4—82no—
339C7×D4—81no—
340C7×D4—82no—
341C7×D4—82no—
342C7×D4—82no—
343C7×D4—82no—
344C7×D4—82no—
345C7×D4—82no—
346C7×D4—82no—
347C7×D4—88no—
348C2×C4×C7—21no—
349C2×C4×C7—22no—
350C2×C4×C7—22no—
351C2×C4×C7—21no—
352C2×C4×C7—21no—
353C2×C4×C7—41no—
354C2×C4×C7—41no—
355C2×C4×C7—41no—
356C2×C4×C7—41no—
357C2×C4×C7—41no—
358C2×C4×C7—41no—
359C2×C4×C7—42no—
360C2×C4×C7—42no—
361C2×C4×C7—42no—
362C2×C4×C7—42no—
363C2×C4×C7—41no—
364C2×C4×C7—42no—
365C2×C4×C7—42no—
366C2×C4×C7—81no—
367C2×C4×C7—82no—
368C2×C4×C7—82no—
369C2×C4×C7#12011yescharacteristic
370C2×C4×C7#12011yescharacteristic
371C2×C4×C7C22×D411yescharacteristic
372C2×C4×C7C22×D411yescharacteristic
373C7×C8—42no—
374C7×C8—41no—
375C7×C8—41no—
376C2×#41C7×D411yescharacteristic, complemented
377C22×D4—22no—
378C22×D4—21no—
379C22×D4—21no—
380C22×D4—22no—
381C22×D4—21no—
382C22×D4—22no—
383C22×D4C7×D412yes—
384C22×D4C7×D411yescharacteristic
385C22×D4C7×D411yescharacteristic, complemented
386C22×D4C23×C711yescharacteristic
387C23×C4C23×C711yescharacteristic
388C2×SD16—21no—
389C2×D8—22no—
390C2×D8—21no—
391C2×M16—21no—
392C22×C8—21no—
393#127—22no—
394#127—21no—
395#126—22no—
396#126—22no—
397#125—21no—
398#124—22no—
399#123—22no—
400#123—21no—
401#123—22no—
402#123—22no—
403#123—22no—
404C22⋊Q8C7×D411yescharacteristic, complemented
405C22⋊Q8C23×C711yescharacteristic
406#121—22no—
407#121—21no—
408#121—21no—
409#121—22no—
410#121—22no—
411#121—22no—
412#121—22no—
413#121—21no—
414#121—21no—
415#121—21no—
416#121—21no—
417#121—21no—
418#121—21no—
419#121—22no—
420#121—21no—
421#121—21no—
422#121—21no—
423#121—21no—
424#121C7×D412yescomplemented
425#121C7×D411yescharacteristic, complemented
426#121C23×C712yes—
427#121C23×C711yescharacteristic
428#120—22no—
429#120—22no—
430#120—22no—
431#120—21no—
432#120—22no—
433#120—22no—
434#120—22no—
435C4×D4—22no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4—21no—
440C4×D4—22no—
441#117—21no—
442#117C7×D411yescharacteristic, complemented
443C2×C4⋊C4C7×D411yescharacteristic
444C2×C4⋊C4C7×D411yescharacteristic, complemented
445C2×C4⋊C4C23×C711yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4C23×C712yes—
452#107—22no—
453#107—21no—
454#106—21no—
455#103—21no—
456#102—22no—
457#102—21no—
458#102—22no—
459#102—21no—
460#102—21no—
461C22⋊C8—21no—
462C22⋊C8—21no—
463C22⋊C8C23×C711yescharacteristic
464C22⋊C8C23×C711yescharacteristic
465C22⋊C8C23×C712yes—
466#95—21no—
467#95—22no—
468#95C23×C712yes—
469C22×C7—21no—
470C22×C7—21no—
471C22×C7—21no—
472C22×C7—21no—
473C22×C7—21no—
474C22×C7—21no—
475C22×C7—21no—
476C22×C7—21no—
477C22×C7—42no—
478C22×C7—42no—
479C22×C7—41no—
480C22×C7—42no—
481C22×C7—42no—
482C22×C7—41no—
483C22×C7—41no—
484C22×C7—42no—
485C22×C7—42no—
486C22×C7—82no—
487C22×C7—82no—
488C22×C7—82no—
489C22×C7—82no—
490C22×C7—82no—
491C22×C7—81no—
492C22×C7—81no—
493C22×C7—81no—
494C22×C7—162no—
495C22×C7—164no—
496C22×C7C2×#12011yescharacteristic
497C22×C7#57612yes—
498C4×C7—21no—
499C4×C7—21no—
500C4×C7—21no—
501C4×C7—21no—
502C4×C7—42no—
503C4×C7—41no—
504C4×C7—42no—
505C4×C7—41no—
506C4×C7—41no—
507C4×C7—82no—
508C4×C7—81no—
509C24—22no—
510C24—21no—
511C24—21no—
512C24C2×C7×D412yes—
513C24C2×C7×D411yescharacteristic
514#41—81no—
515C2×Q8C2×C7×D411yescharacteristic
516C2×D4—22no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—21no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—41no—
534C2×D4—41no—
535C2×D4—81no—
536C2×D4—81no—
537C2×D4—82no—
538C2×D4—81no—
539C2×D4—82no—
540C2×D4—82no—
541C2×D4—82no—
542C2×D4—82no—
543C2×D4—82no—
544C2×D4—82no—
545C2×D4—82no—
546C2×D4—82no—
547C2×D4—84no—
548C2×D4C2×C7×D411yescharacteristic
549C2×D4C2×C7×D412yes—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—81no—
557C22×C4C2×C7×D412yes—
558C22×C4C2×C7×D411yescharacteristic
559C22×C4C2×C7×D411yescharacteristic
560C22×C4C2×C7×D411yescharacteristic
561C22×C4C2×C7×D411yescharacteristic
562C22×C4C2×C7×D411yescharacteristic
563C22×C4C24×C711yescharacteristic
564SD16—81no—
565D8—82no—
566D8—81no—
567M16—81no—
568C2×C8—22no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—81no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4C2×C7×D411yescharacteristic
582C4⋊C4C2×C7×D412yes—
583C4⋊C4C2×C7×D411yescharacteristic
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—21no—
590C22⋊C4—21no—
591C22⋊C4—21no—
592C22⋊C4—22no—
593C22⋊C4—21no—
594C22⋊C4—22no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—21no—
598C22⋊C4—41no—
599C22⋊C4—41no—
600C22⋊C4—82no—
601C22⋊C4—82no—
602C22⋊C4—81no—
603C42—22no—
604C42—21no—
605C2×C7—22no—
606C2×C7—41no—
607C2×C7—41no—
608C2×C7—82no—
609C2×C7—82no—
610C2×C7—81no—
611C2×C7—161no—
612C2×C7#300811yescharacteristic
613C2×C7#301911yescharacteristic
614C2×C7#302611yescharacteristic
615C23—22no—
616C23—22no—
617C23—22no—
618C23—21no—
619C23—22no—
620C23—22no—
621C23—41no—
622C23—41no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—41no—
627C23—41no—
628C23—42no—
629C23—41no—
630C23—42no—
631C23—81no—
632C23—81no—
633C23—82no—
634C23—82no—
635C23—82no—
636C23C7×#12011yescharacteristic
637C23C7×#12011yescharacteristic
638C23C22×C7×D411yescharacteristic
639Q8—41no—
640D4—42no—
641D4—41no—
642D4—42no—
643D4—42no—
644D4—42no—
645D4—41no—
646D4—41no—
647D4—44no—
648D4—42no—
649D4—42no—
650D4—42no—
651D4—42no—
652D4—81no—
653D4—82no—
654D4—82no—
655D4—81no—
656D4—82no—
657D4—82no—
658D4—82no—
659D4—82no—
660D4—82no—
661D4—82no—
662D4—82no—
663D4—88no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—81no—
683C2×C4—82no—
684C2×C4—82no—
685C2×C4C7×#12011yescharacteristic
686C2×C4C7×#12011yescharacteristic
687C2×C4C22×C7×D411yescharacteristic
688C2×C4C22×C7×D411yescharacteristic
689C8—42no—
690C8—41no—
691C8—41no—
692C7#1845011yescharacteristic, direct product factor, Sylow
693C22—21no—
694C22—21no—
695C22—21no—
696C22—21no—
697C22—21no—
698C22—21no—
699C22—21no—
700C22—21no—
701C22—42no—
702C22—42no—
703C22—41no—
704C22—42no—
705C22—42no—
706C22—41no—
707C22—41no—
708C22—42no—
709C22—42no—
710C22—82no—
711C22—82no—
712C22—82no—
713C22—82no—
714C22—82no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—162no—
719C22—164no—
720C22C2×C7×#12011yescharacteristic
721C22C7×#57612yes—
722C4—21no—
723C4—21no—
724C4—21no—
725C4—21no—
726C4—42no—
727C4—41no—
728C4—42no—
729C4—41no—
730C4—41no—
731C4—82no—
732C4—81no—
733C2—22no—
734C2—41no—
735C2—41no—
736C2—82no—
737C2—82no—
738C2—81no—
739C2—161no—
740C2C7×#300811yescharacteristic
741C2C7×#301911yescharacteristic
742C2C7×#302611yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC22×C4C24×C7
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C7×#3537C2semidirect
2. C7×#3194C2semidirect
3. C7×#3186C2semidirect
4. C7×#2815C2semidirect
5. C7×#1612C2semidirect
6. C7×#1607C2semidirect
7. C7×#1600C2semidirect
8. C7×#1595C2semidirect
9. C7×#1516C2semidirect
10. C7×#1510C2semidirect
11. C7×#1471C2semidirect
27. C2×C7×#121C22semidirect
28. C7×#483C22semidirect
31. C7×#480C22semidirect
32. C7×#480C22semidirect
36. C7×#450C22semidirect
39. C7×#447C22semidirect
40. C7×#447C22semidirect
41. C7×#407C22semidirect
42. C2×C7×C22⋊C8C22semidirect
44. C7×#397C22semidirect
47. C7×#392C22semidirect
48. C7×#381C22semidirect
49. C7×#328C22semidirect
50. C7×#327C22semidirect
51. C7×#327C22semidirect
52. C7×#327C22semidirect
53. C7×#323C22semidirect
54. C7×#323C22semidirect
55. #18450C7direct (N × H)
56. C2×C7×#41D4semidirect
65. C22×C7×D4D4semidirect
84. C7×C22⋊Q8D4semidirect
104. C7×#121D4semidirect
105. C7×#121D4semidirect
122. C7×#117D4semidirect
124. C2×C7×C4⋊C4D4semidirect
149. #3537C2×C7semidirect
150. #3194C2×C7semidirect
151. #3186C2×C7semidirect
152. #2815C2×C7semidirect
153. #1612C2×C7semidirect
154. #1607C2×C7semidirect
155. #1600C2×C7semidirect
156. #1595C2×C7semidirect
157. #1516C2×C7semidirect
158. #1510C2×C7semidirect
159. #1471C2×C7semidirect
271. C2×#121C22×C7semidirect
272. #483C22×C7semidirect
275. #480C22×C7semidirect
276. #480C22×C7semidirect
280. #450C22×C7semidirect
283. #447C22×C7semidirect
284. #447C22×C7semidirect
285. #407C22×C7semidirect
286. C2×C22⋊C8C22×C7semidirect
288. #397C22×C7semidirect
291. #392C22×C7semidirect
292. #381C22×C7semidirect
293. #328C22×C7semidirect
294. #327C22×C7semidirect
295. #327C22×C7semidirect
296. #327C22×C7semidirect
297. #323C22×C7semidirect
298. #323C22×C7semidirect
376. C2×#41C7×D4semidirect
385. C22×D4C7×D4semidirect
404. C22⋊Q8C7×D4semidirect
424. #121C7×D4semidirect
425. #121C7×D4semidirect
442. #117C7×D4semidirect
444. C2×C4⋊C4C7×D4semidirect
692. C7#18450direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#35372
C7×#31942
C7×#31862
C7×#28152
C7×#16122
C7×#16072
C7×#16002
C7×#15952
C7×#15162
C7×#15102
C7×#14712
#184507