Finite Group Databasebeta

← C7×#18272 #13195488

Subgroups — C7×#18272 #13195488

Order 1792.

1122 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×#3558C211yesmaximal, characteristic, complemented
2C7×#3109C211yesmaximal, characteristic, complemented
3C7×#3105C211yesmaximal, characteristic, complemented
4C7×#2540C211yesmaximal, characteristic, complemented
5C7×#1618C212yesmaximal, complemented
6C7×#1613C212yesmaximal, complemented
7C7×#1600C212yesmaximal, complemented
8C7×#1595C212yesmaximal, complemented
9C7×#1509C211yesmaximal, characteristic, complemented
10C7×#1502C211yesmaximal, characteristic, complemented
11C7×#1469C211yesmaximal, characteristic, complemented
12C7×#562—21no—
13C7×H(3,𝔽4)—21no—
14C7×#559—21no—
15C7×#548—21no—
16C7×#546—21no—
17C7×#546—22no—
18C7×D42—21no—
19C7×#542—21no—
20C7×#538—22no—
21C7×#538C2212yes—
22C7×#535—21no—
23C7×#534C2212yes—
24C7×#532C2211yescharacteristic
25C7×#529C2211yescharacteristic
26C2×C7×#124C2211yescharacteristic
27C2×C7×C22⋊Q8—21no—
28C2×C7×#121—21no—
29C2×C4×C7×D4C2211yescharacteristic, complemented
30C7×#484C2211yescharacteristic, complemented
31C7×#481C2211yescharacteristic
32C7×#481C2212yescomplemented
33C7×#478—21no—
34C7×#476—21no—
35C7×#463—21no—
36C7×#459—21no—
37C7×#450C2211yescharacteristic, complemented
38C7×#447C2211yescharacteristic
39C7×#447C2212yescomplemented
40C7×#442—22no—
41C4×C7×SD16—21no—
42C4×C7×D8—21no—
43C7×#432C2211yescharacteristic, complemented
44C7×#431C2211yescharacteristic, complemented
45C7×#399C2212yescomplemented
46C7×#392C2212yescomplemented
47C7×#390—22no—
48C4×C7×C4⋊C4C2211yescharacteristic, complemented
49C7×#328C2212yescomplemented
50C7×#327C2212yes—
51C7×#327C2212yescomplemented
52C7×#327C2212yescomplemented
53C7×#323C2212yescomplemented
54C7×#323C2212yescomplemented
55#18272C711yesmaximal, characteristic, direct product factor, Sylow
56C2×C7×#41—21no—
57C2×C7×#41—21no—
58C22×C7×Q8D411yescharacteristic
59C22×C7×D4—21no—
60C22×C7×D4—22no—
61C22×C7×D4—22no—
62C22×C7×D4D411yescharacteristic
63C22×C7×D4C2311yescharacteristic
64C23×C4×C7—21no—
65C2×C7×SD16—21no—
66C2×C7×D8—21no—
67C2×C7×D8—22no—
68C7×C4⋊Q8D411yescharacteristic, complemented
69C7×#127—21no—
70C7×#127D411yescharacteristic, complemented
71C7×#126—22no—
72C7×#126—21no—
73C7×#125D411yescharacteristic, complemented
74C7×#124—21no—
75C7×#124—22no—
76C7×#124—22no—
77C7×#124—22no—
78C7×#124—21no—
79C7×#124—21no—
80C7×#124—21no—
81C7×#124—21no—
82C7×#124—21no—
83C7×#124D411yescharacteristic, complemented
84C7×#123—22no—
85C7×#123—21no—
86C7×#123—22no—
87C7×#123—22no—
88C7×#123—22no—
89C7×C22⋊Q8—22no—
90C7×C22⋊Q8—21no—
91C7×C22⋊Q8—22no—
92C7×C22⋊Q8—44no—
93C7×C22⋊Q8C2311yescharacteristic
94C7×#121—22no—
95C7×#121—22no—
96C7×#121—22no—
97C7×#121—21no—
98C7×#121—22no—
99C7×#121—21no—
100C7×#121—22no—
101C7×#121—44no—
102C7×#121C2311yescharacteristic
103C7×#121C2312yes—
104C7×#120—22no—
105C7×#120—22no—
106C7×#120—22no—
107C7×#120—22no—
108C7×#120—22no—
109C4×C7×Q8—21no—
110C4×C7×Q8D411yescharacteristic, complemented
111C4×C7×D4—22no—
112C4×C7×D4—21no—
113C4×C7×D4—21no—
114C4×C7×D4—22no—
115C4×C7×D4—21no—
116C4×C7×D4—21no—
117C4×C7×D4—21no—
118C4×C7×D4—21no—
119C4×C7×D4—21no—
120C4×C7×D4D411yescharacteristic, complemented
121C4×C7×D4D412yescomplemented
122C7×#117—21no—
123C2×C7×C4⋊C4—21no—
124C2×C7×C4⋊C4—22no—
125C2×C7×C4⋊C4C2311yescharacteristic
126C2×C7×C22⋊C4—22no—
127C2×C7×C22⋊C4—22no—
128C2×C7×C22⋊C4—21no—
129C2×C7×C22⋊C4—22no—
130C2×C7×C22⋊C4D412yes—
131C2×C7×C22⋊C4C2312yes—
132C2×C42×C7—21no—
133C2×C42×C7C2311yescharacteristic
134C7×#107—21no—
135C7×#106—22no—
136C7×#106—21no—
137C7×C4⋊C8—21no—
138C7×C4⋊C8—21no—
139C7×#103—21no—
140C7×#102—21no—
141C7×#102—22no—
142C7×#102—22no—
143C7×#102—21no—
144C7×#102—21no—
145C7×C22⋊C8C2311yescharacteristic
146C7×C22⋊C8C2312yes—
147C7×C22⋊C8C2311yescharacteristic
148C7×#97—21no—
149C4×C7×C8—21no—
150C7×#95C2312yes—
151#3558C2×C711yescharacteristic, complemented
152#3109C2×C711yescharacteristic, complemented
153#3105C2×C711yescharacteristic, complemented
154#2540C2×C711yescharacteristic, complemented
155#1618C2×C712yescomplemented
156#1613C2×C712yescomplemented
157#1600C2×C712yescomplemented
158#1595C2×C712yescomplemented
159#1509C2×C711yescharacteristic, complemented
160#1502C2×C711yescharacteristic, complemented
161#1469C2×C711yescharacteristic, complemented
162C24×C7—22no—
163C24×C7—21no—
164C24×C7C2×D412yes—
165C7×#41—81no—
166C7×#41—81no—
167C7×#41—82no—
168C2×C7×Q8—21no—
169C2×C7×Q8—21no—
170C2×C7×Q8—21no—
171C2×C7×Q8—42no—
172C2×C7×Q8C2×D411yescharacteristic
173C2×C7×D4—22no—
174C2×C7×D4—21no—
175C2×C7×D4—22no—
176C2×C7×D4—22no—
177C2×C7×D4—22no—
178C2×C7×D4—22no—
179C2×C7×D4—22no—
180C2×C7×D4—21no—
181C2×C7×D4—21no—
182C2×C7×D4—21no—
183C2×C7×D4—21no—
184C2×C7×D4—21no—
185C2×C7×D4—21no—
186C2×C7×D4—42no—
187C2×C7×D4—44no—
188C2×C7×D4—42no—
189C2×C7×D4—44no—
190C2×C7×D4—82no—
191C2×C7×D4—82no—
192C2×C7×D4—82no—
193C2×C7×D4—82no—
194C2×C7×D4C2×D411yescharacteristic
195C2×C7×D4C2×D412yes—
196C22×C4×C7—22no—
197C22×C4×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7—21no—
200C22×C4×C7—22no—
201C22×C4×C7—21no—
202C22×C4×C7—42no—
203C22×C4×C7—42no—
204C22×C4×C7—41no—
205C22×C4×C7—41no—
206C22×C4×C7C2×D411yescharacteristic
207C22×C4×C7C2×D411yescharacteristic
208C22×C4×C7C2×D412yes—
209C22×C4×C7C2411yescharacteristic
210C7×SD16—42no—
211C7×D8—44no—
212C7×D8—42no—
213C2×C7×C8—21no—
214C2×C7×C8—21no—
215C2×C7×C8—22no—
216C7×C4⋊C4—24no—
217C7×C4⋊C4—22no—
218C7×C4⋊C4—22no—
219C7×C4⋊C4—21no—
220C7×C4⋊C4—21no—
221C7×C4⋊C4—21no—
222C7×C4⋊C4—21no—
223C7×C4⋊C4—21no—
224C7×C4⋊C4—21no—
225C7×C4⋊C4—21no—
226C7×C4⋊C4—44no—
227C7×C4⋊C4C2×D412yes—
228C7×C4⋊C4C2×D411yescharacteristic
229C7×C4⋊C4C2×D411yescharacteristic
230C7×C22⋊C4—22no—
231C7×C22⋊C4—22no—
232C7×C22⋊C4—22no—
233C7×C22⋊C4—22no—
234C7×C22⋊C4—22no—
235C7×C22⋊C4—21no—
236C7×C22⋊C4—21no—
237C7×C22⋊C4—22no—
238C7×C22⋊C4—22no—
239C7×C22⋊C4—21no—
240C7×C22⋊C4—21no—
241C7×C22⋊C4—22no—
242C7×C22⋊C4—22no—
243C7×C22⋊C4—22no—
244C7×C22⋊C4—21no—
245C7×C22⋊C4—22no—
246C7×C22⋊C4—44no—
247C7×C22⋊C4—44no—
248C7×C22⋊C4—41no—
249C7×C22⋊C4—41no—
250C42×C7—22no—
251C42×C7—21no—
252C42×C7—81no—
253C42×C7C2×D411yescharacteristic
254C42×C7C2×D411yescharacteristic
255C42×C7C2×D411yescharacteristic
256C42×C7C2×D411yescharacteristic
257#562—21no—
258H(3,𝔽4)—21no—
259#559—21no—
260#548—21no—
261#546—21no—
262#546—22no—
263D42—21no—
264#542—21no—
265#538—22no—
266#538C22×C712yes—
267#535—21no—
268#534C22×C712yes—
269#532C22×C711yescharacteristic
270#529C22×C711yescharacteristic
271C2×#124C22×C711yescharacteristic
272C2×C22⋊Q8—21no—
273C2×#121—21no—
274C2×C4×D4C22×C711yescharacteristic, complemented
275#484C22×C711yescharacteristic, complemented
276#481C22×C711yescharacteristic
277#481C22×C712yescomplemented
278#478—21no—
279#476—21no—
280#463—21no—
281#459—21no—
282#450C22×C711yescharacteristic, complemented
283#447C22×C711yescharacteristic
284#447C22×C712yescomplemented
285#442—22no—
286C4×SD16—21no—
287C4×D8—21no—
288#432C22×C711yescharacteristic, complemented
289#431C22×C711yescharacteristic, complemented
290#399C22×C712yescomplemented
291#392C22×C712yescomplemented
292#390—22no—
293C4×C4⋊C4C22×C711yescharacteristic, complemented
294#328C22×C712yescomplemented
295#327C22×C712yes—
296#327C22×C712yescomplemented
297#327C22×C712yescomplemented
298#323C22×C712yescomplemented
299#323C22×C712yescomplemented
300C23×C7—22no—
301C23×C7—22no—
302C23×C7—21no—
303C23×C7—22no—
304C23×C7—22no—
305C23×C7—22no—
306C23×C7—41no—
307C23×C7—41no—
308C23×C7—41no—
309C23×C7—42no—
310C23×C7—42no—
311C23×C7—41no—
312C23×C7—41no—
313C23×C7—41no—
314C23×C7—82no—
315C23×C7—82no—
316C23×C7—82no—
317C23×C7C22×D411yescharacteristic
318C7×Q8—41no—
319C7×Q8—42no—
320C7×Q8—81no—
321C7×Q8—81no—
322C7×D4—22no—
323C7×D4—22no—
324C7×D4—42no—
325C7×D4—41no—
326C7×D4—41no—
327C7×D4—41no—
328C7×D4—41no—
329C7×D4—42no—
330C7×D4—41no—
331C7×D4—42no—
332C7×D4—42no—
333C7×D4—42no—
334C7×D4—81no—
335C7×D4—81no—
336C7×D4—82no—
337C7×D4—82no—
338C7×D4—82no—
339C7×D4—82no—
340C7×D4—82no—
341C7×D4—88no—
342C2×C4×C7—21no—
343C2×C4×C7—21no—
344C2×C4×C7—22no—
345C2×C4×C7—24no—
346C2×C4×C7—21no—
347C2×C4×C7—22no—
348C2×C4×C7—22no—
349C2×C4×C7—21no—
350C2×C4×C7—21no—
351C2×C4×C7—41no—
352C2×C4×C7—42no—
353C2×C4×C7—42no—
354C2×C4×C7—42no—
355C2×C4×C7—42no—
356C2×C4×C7—41no—
357C2×C4×C7—41no—
358C2×C4×C7—41no—
359C2×C4×C7—82no—
360C2×C4×C7—82no—
361C2×C4×C7—82no—
362C2×C4×C7—82no—
363C2×C4×C7—82no—
364C2×C4×C7#12011yescharacteristic
365C2×C4×C7#12011yescharacteristic
366C2×C4×C7#12011yescharacteristic
367C2×C4×C7#12011yescharacteristic
368C2×C4×C7C22×D411yescharacteristic
369C2×C4×C7C22×D411yescharacteristic
370C7×C8—42no—
371C7×C8—41no—
372C7×C8—41no—
373C2×#41—21no—
374C2×#41—21no—
375C22×Q8C7×D411yescharacteristic
376C22×D4—21no—
377C22×D4—22no—
378C22×D4—22no—
379C22×D4C7×D411yescharacteristic
380C22×D4C23×C711yescharacteristic
381C23×C4—21no—
382C2×SD16—21no—
383C2×D8—21no—
384C2×D8—22no—
385C4⋊Q8C7×D411yescharacteristic, complemented
386#127—21no—
387#127C7×D411yescharacteristic, complemented
388#126—22no—
389#126—21no—
390#125C7×D411yescharacteristic, complemented
391#124—21no—
392#124—22no—
393#124—22no—
394#124—22no—
395#124—21no—
396#124—21no—
397#124—21no—
398#124—21no—
399#124—21no—
400#124C7×D411yescharacteristic, complemented
401#123—22no—
402#123—21no—
403#123—22no—
404#123—22no—
405#123—22no—
406C22⋊Q8—22no—
407C22⋊Q8—21no—
408C22⋊Q8—22no—
409C22⋊Q8—44no—
410C22⋊Q8C23×C711yescharacteristic
411#121—22no—
412#121—22no—
413#121—22no—
414#121—21no—
415#121—22no—
416#121—21no—
417#121—22no—
418#121—44no—
419#121C23×C711yescharacteristic
420#121C23×C712yes—
421#120—22no—
422#120—22no—
423#120—22no—
424#120—22no—
425#120—22no—
426C4×Q8—21no—
427C4×Q8C7×D411yescharacteristic, complemented
428C4×D4—22no—
429C4×D4—21no—
430C4×D4—21no—
431C4×D4—22no—
432C4×D4—21no—
433C4×D4—21no—
434C4×D4—21no—
435C4×D4—21no—
436C4×D4—21no—
437C4×D4C7×D411yescharacteristic, complemented
438C4×D4C7×D412yescomplemented
439#117—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4C23×C711yescharacteristic
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4C7×D412yes—
448C2×C22⋊C4C23×C712yes—
449C2×C42—21no—
450C2×C42C23×C711yescharacteristic
451#107—21no—
452#106—21no—
453#106—22no—
454C4⋊C8—21no—
455C4⋊C8—21no—
456#103—21no—
457#102—21no—
458#102—22no—
459#102—21no—
460#102—21no—
461#102—22no—
462C22⋊C8C23×C712yes—
463C22⋊C8C23×C711yescharacteristic
464C22⋊C8C23×C711yescharacteristic
465#97—21no—
466C4×C8—21no—
467#95C23×C712yes—
468C22×C7—21no—
469C22×C7—21no—
470C22×C7—42no—
471C22×C7—42no—
472C22×C7—42no—
473C22×C7—42no—
474C22×C7—41no—
475C22×C7—41no—
476C22×C7—42no—
477C22×C7—42no—
478C22×C7—42no—
479C22×C7—42no—
480C22×C7—41no—
481C22×C7—42no—
482C22×C7—82no—
483C22×C7—82no—
484C22×C7—81no—
485C22×C7—81no—
486C22×C7—81no—
487C22×C7—81no—
488C22×C7—164no—
489C22×C7C2×#12011yescharacteristic
490C22×C7#57611yescharacteristic
491C22×C7#57711yescharacteristic
492C4×C7—21no—
493C4×C7—21no—
494C4×C7—21no—
495C4×C7—21no—
496C4×C7—21no—
497C4×C7—44no—
498C4×C7—41no—
499C4×C7—42no—
500C4×C7—41no—
501C4×C7—42no—
502C4×C7—41no—
503C4×C7—81no—
504C4×C7#45312yes—
505C24—22no—
506C24—21no—
507C24C2×C7×D412yes—
508#41—81no—
509#41—81no—
510#41—82no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—42no—
515C2×Q8C2×C7×D411yescharacteristic
516C2×D4—22no—
517C2×D4—21no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—42no—
530C2×D4—44no—
531C2×D4—42no—
532C2×D4—44no—
533C2×D4—82no—
534C2×D4—82no—
535C2×D4—82no—
536C2×D4—82no—
537C2×D4C2×C7×D411yescharacteristic
538C2×D4C2×C7×D412yes—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4C2×C7×D411yescharacteristic
550C22×C4C2×C7×D411yescharacteristic
551C22×C4C2×C7×D412yes—
552C22×C4C24×C711yescharacteristic
553SD16—42no—
554D8—44no—
555D8—42no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—22no—
559C4⋊C4—24no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—44no—
570C4⋊C4C2×C7×D412yes—
571C4⋊C4C2×C7×D411yescharacteristic
572C4⋊C4C2×C7×D411yescharacteristic
573C22⋊C4—22no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—21no—
579C22⋊C4—21no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—21no—
583C22⋊C4—21no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—21no—
588C22⋊C4—22no—
589C22⋊C4—44no—
590C22⋊C4—44no—
591C22⋊C4—41no—
592C22⋊C4—41no—
593C42—22no—
594C42—21no—
595C42—81no—
596C42C2×C7×D411yescharacteristic
597C42C2×C7×D411yescharacteristic
598C42C2×C7×D411yescharacteristic
599C42C2×C7×D411yescharacteristic
600C2×C7—21no—
601C2×C7—21no—
602C2×C7—82no—
603C2×C7—82no—
604C2×C7—82no—
605C2×C7—81no—
606C2×C7#301211yescharacteristic
607C2×C7C2×#45311yescharacteristic
608C2×C7#302511yescharacteristic
609C23—22no—
610C23—22no—
611C23—21no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—42no—
619C23—42no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—82no—
624C23—82no—
625C23—82no—
626C23C22×C7×D411yescharacteristic
627Q8—41no—
628Q8—42no—
629Q8—81no—
630Q8—81no—
631D4—22no—
632D4—22no—
633D4—42no—
634D4—41no—
635D4—41no—
636D4—41no—
637D4—41no—
638D4—42no—
639D4—41no—
640D4—42no—
641D4—42no—
642D4—42no—
643D4—81no—
644D4—81no—
645D4—82no—
646D4—82no—
647D4—82no—
648D4—82no—
649D4—82no—
650D4—88no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—82no—
669C2×C4—82no—
670C2×C4—82no—
671C2×C4—82no—
672C2×C4—82no—
673C2×C4C7×#12011yescharacteristic
674C2×C4C7×#12011yescharacteristic
675C2×C4C7×#12011yescharacteristic
676C2×C4C7×#12011yescharacteristic
677C2×C4C22×C7×D411yescharacteristic
678C2×C4C22×C7×D411yescharacteristic
679C8—42no—
680C8—41no—
681C8—41no—
682C7#1827211yescharacteristic, direct product factor, Sylow
683C22—21no—
684C22—21no—
685C22—42no—
686C22—42no—
687C22—42no—
688C22—42no—
689C22—41no—
690C22—41no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—41no—
696C22—42no—
697C22—82no—
698C22—82no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22—164no—
704C22C2×C7×#12011yescharacteristic
705C22C7×#57611yescharacteristic
706C22C7×#57711yescharacteristic
707C4—21no—
708C4—21no—
709C4—21no—
710C4—21no—
711C4—21no—
712C4—44no—
713C4—41no—
714C4—42no—
715C4—41no—
716C4—42no—
717C4—41no—
718C4—81no—
719C4C7×#45312yes—
720C2—21no—
721C2—21no—
722C2—82no—
723C2—82no—
724C2—81no—
725C2—82no—
726C2C7×#301211yescharacteristic
727C2C2×C7×#45311yescharacteristic
728C2C7×#302511yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC22×C4C24×C7
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C7×#3558C2semidirect
2. C7×#3109C2semidirect
3. C7×#3105C2semidirect
4. C7×#2540C2semidirect
5. C7×#1618C2semidirect
6. C7×#1613C2semidirect
7. C7×#1600C2semidirect
8. C7×#1595C2semidirect
9. C7×#1509C2semidirect
10. C7×#1502C2semidirect
11. C7×#1469C2semidirect
29. C2×C4×C7×D4C22semidirect
30. C7×#484C22semidirect
32. C7×#481C22semidirect
37. C7×#450C22semidirect
39. C7×#447C22semidirect
43. C7×#432C22semidirect
44. C7×#431C22semidirect
45. C7×#399C22semidirect
46. C7×#392C22semidirect
48. C4×C7×C4⋊C4C22semidirect
49. C7×#328C22semidirect
51. C7×#327C22semidirect
52. C7×#327C22semidirect
53. C7×#323C22semidirect
54. C7×#323C22semidirect
55. #18272C7direct (N × H)
68. C7×C4⋊Q8D4semidirect
70. C7×#127D4semidirect
73. C7×#125D4semidirect
83. C7×#124D4semidirect
110. C4×C7×Q8D4semidirect
120. C4×C7×D4D4semidirect
121. C4×C7×D4D4semidirect
151. #3558C2×C7semidirect
152. #3109C2×C7semidirect
153. #3105C2×C7semidirect
154. #2540C2×C7semidirect
155. #1618C2×C7semidirect
156. #1613C2×C7semidirect
157. #1600C2×C7semidirect
158. #1595C2×C7semidirect
159. #1509C2×C7semidirect
160. #1502C2×C7semidirect
161. #1469C2×C7semidirect
274. C2×C4×D4C22×C7semidirect
275. #484C22×C7semidirect
277. #481C22×C7semidirect
282. #450C22×C7semidirect
284. #447C22×C7semidirect
288. #432C22×C7semidirect
289. #431C22×C7semidirect
290. #399C22×C7semidirect
291. #392C22×C7semidirect
293. C4×C4⋊C4C22×C7semidirect
294. #328C22×C7semidirect
296. #327C22×C7semidirect
297. #327C22×C7semidirect
298. #323C22×C7semidirect
299. #323C22×C7semidirect
385. C4⋊Q8C7×D4semidirect
387. #127C7×D4semidirect
390. #125C7×D4semidirect
400. #124C7×D4semidirect
427. C4×Q8C7×D4semidirect
437. C4×D4C7×D4semidirect
438. C4×D4C7×D4semidirect
682. C7#18272direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#35582
C7×#31092
C7×#31052
C7×#25402
C7×#16182
C7×#16132
C7×#16002
C7×#15952
C7×#15092
C7×#15022
C7×#14692
#182727