Finite Group Databasebeta

← C7×#18458 #13195674

Subgroups — C7×#18458 #13195674

Order 1792.

1036 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3558C211yesmaximal, characteristic, complemented
2C7×#3213C211yesmaximal, characteristic, complemented
3C7×#3211C211yesmaximal, characteristic, complemented
4C7×#2819C211yesmaximal, characteristic, complemented
5C7×#1606C212yesmaximal, complemented
6C7×#1601C212yesmaximal, complemented
7C7×#1600C212yesmaximal, complemented
8C7×#1595C212yesmaximal, complemented
9C7×#1517C211yesmaximal, characteristic, complemented
10C7×#1512C211yesmaximal, 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×#124C2211yescharacteristic, complemented
28C7×#496—21no—
29C7×#495—21no—
30C7×#489—21no—
31C7×#488—21no—
32C7×#464—21no—
33C7×#463—21no—
34C7×#463—22no—
35C7×#451C2211yescharacteristic, complemented
36C7×#450C2211yescharacteristic, complemented
37C7×#448C2211yescharacteristic
38C7×#448C2212yescomplemented
39C7×#447C2211yescharacteristic
40C7×#447C2212yescomplemented
41C7×#432C2211yescharacteristic, complemented
42C7×#431C2211yescharacteristic, complemented
43C7×#394—22no—
44C7×#393—21no—
45C7×#393C2212yescomplemented
46C7×#392—21no—
47C7×#392C2212yescomplemented
48C7×#382C2211yescharacteristic, complemented
49C7×#328C2212yescomplemented
50C7×#327C2212yes—
51C7×#327C2212yescomplemented
52C7×#327C2212yescomplemented
53C7×#323C2212yescomplemented
54C7×#323C2212yescomplemented
55#18458C711yesmaximal, characteristic, direct product factor, Sylow
56C2×C7×#41—21no—
57C2×C7×#41—21no—
58C22×C7×Q8D411yescharacteristic
59C22×C7×Q8C2311yescharacteristic
60C22×C7×D4—21no—
61C22×C7×D4—22no—
62C22×C7×D4—22no—
63C22×C7×D4D411yescharacteristic
64C22×C7×D4C2311yescharacteristic
65C2×C7×Q16—21no—
66C2×C7×SD16—21no—
67C2×C7×SD16—21no—
68C2×C7×SD16—22no—
69C2×C7×D8—21no—
70C2×C7×D8—22no—
71C7×C4⋊Q8D411yescharacteristic, complemented
72C7×#127—21no—
73C7×#127D411yescharacteristic, complemented
74C7×#126—22no—
75C7×#126—21no—
76C7×#125D411yescharacteristic, complemented
77C7×#124—21no—
78C7×#124—22no—
79C7×#124—22no—
80C7×#124—22no—
81C7×#124—21no—
82C7×#124—21no—
83C7×#124—21no—
84C7×#124—21no—
85C7×#124—21no—
86C7×#124—21no—
87C7×#124—21no—
88C7×#124—21no—
89C7×#124—21no—
90C7×#124D411yescharacteristic, complemented
91C7×#123—22no—
92C7×#123—21no—
93C7×#123—22no—
94C7×#123—22no—
95C7×#123—22no—
96C7×C22⋊Q8—22no—
97C7×C22⋊Q8—21no—
98C7×C22⋊Q8—22no—
99C7×C22⋊Q8C2311yescharacteristic
100C7×#121—22no—
101C7×#121—22no—
102C7×#121—22no—
103C7×#121—21no—
104C7×#121—22no—
105C7×#121—21no—
106C7×#121—22no—
107C7×#121C2311yescharacteristic
108C7×#121C2312yes—
109C7×#120—22no—
110C7×#120—22no—
111C7×#120—22no—
112C7×#120—22no—
113C7×#120—22no—
114C4×C7×Q8—21no—
115C4×C7×Q8D411yescharacteristic, complemented
116C4×C7×D4—22no—
117C4×C7×D4—21no—
118C4×C7×D4—21no—
119C4×C7×D4—22no—
120C4×C7×D4—21no—
121C4×C7×D4D411yescharacteristic, complemented
122C4×C7×D4D412yescomplemented
123C7×#117—21no—
124C2×C7×C4⋊C4—21no—
125C2×C7×C22⋊C4—22no—
126C2×C7×C22⋊C4—21no—
127C2×C7×C22⋊C4—21no—
128C2×C7×C22⋊C4—22no—
129C2×C7×C22⋊C4—22no—
130C2×C7×C22⋊C4D412yes—
131C2×C7×C22⋊C4C2312yes—
132C2×C42×C7C2311yescharacteristic
133C7×C4⋊C8—21no—
134C7×C4⋊C8—21no—
135C7×#103—21no—
136C7×#103—21no—
137C7×#103—22no—
138C7×#102—21no—
139C7×#102—21no—
140C7×#102—22no—
141C7×C22⋊C8C2312yes—
142C7×C22⋊C8C2311yescharacteristic
143C7×C22⋊C8C2311yescharacteristic
144C7×#97—21no—
145C4×C7×C8—21no—
146C7×#95—21no—
147C7×#95—22no—
148C7×#95C2312yes—
149#3558C2×C711yescharacteristic, complemented
150#3213C2×C711yescharacteristic, complemented
151#3211C2×C711yescharacteristic, complemented
152#2819C2×C711yescharacteristic, complemented
153#1606C2×C712yescomplemented
154#1601C2×C712yescomplemented
155#1600C2×C712yescomplemented
156#1595C2×C712yescomplemented
157#1517C2×C711yescharacteristic, complemented
158#1512C2×C711yescharacteristic, complemented
159#1469C2×C711yescharacteristic, complemented
160C24×C7—22no—
161C24×C7—21no—
162C24×C7C2×D412yes—
163C7×#41—81no—
164C7×#41—81no—
165C7×#41—82no—
166C2×C7×Q8—21no—
167C2×C7×Q8—21no—
168C2×C7×Q8—21no—
169C2×C7×Q8—21no—
170C2×C7×Q8—21no—
171C2×C7×Q8—81no—
172C2×C7×Q8—81no—
173C2×C7×Q8C2×D411yescharacteristic
174C2×C7×D4—22no—
175C2×C7×D4—21no—
176C2×C7×D4—22no—
177C2×C7×D4—22no—
178C2×C7×D4—22no—
179C2×C7×D4—22no—
180C2×C7×D4—22no—
181C2×C7×D4—21no—
182C2×C7×D4—21no—
183C2×C7×D4—21no—
184C2×C7×D4—21no—
185C2×C7×D4—21no—
186C2×C7×D4—21no—
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×D4C2×D411yescharacteristic
196C2×C7×D4C2×D412yes—
197C22×C4×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7—21no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—21no—
203C22×C4×C7C2×D411yescharacteristic
204C22×C4×C7C2×D412yes—
205C22×C4×C7C2×D411yescharacteristic
206C22×C4×C7C2411yescharacteristic
207C7×Q16—81no—
208C7×SD16—82no—
209C7×SD16—81no—
210C7×SD16—81no—
211C7×D8—82no—
212C7×D8—81no—
213C2×C7×C8—21no—
214C2×C7×C8—21no—
215C2×C7×C8—22no—
216C7×C4⋊C4—22no—
217C7×C4⋊C4—22no—
218C7×C4⋊C4—21no—
219C7×C4⋊C4—21no—
220C7×C4⋊C4—21no—
221C7×C4⋊C4—21no—
222C7×C4⋊C4—21no—
223C7×C4⋊C4—81no—
224C7×C4⋊C4C2×D412yes—
225C7×C4⋊C4C2×D411yescharacteristic
226C7×C4⋊C4C2×D411yescharacteristic
227C7×C22⋊C4—22no—
228C7×C22⋊C4—22no—
229C7×C22⋊C4—22no—
230C7×C22⋊C4—22no—
231C7×C22⋊C4—22no—
232C7×C22⋊C4—21no—
233C7×C22⋊C4—21no—
234C7×C22⋊C4—22no—
235C7×C22⋊C4—22no—
236C7×C22⋊C4—21no—
237C7×C22⋊C4—21no—
238C7×C22⋊C4—22no—
239C7×C22⋊C4—22no—
240C7×C22⋊C4—22no—
241C7×C22⋊C4—21no—
242C7×C22⋊C4—22no—
243C7×C22⋊C4—41no—
244C7×C22⋊C4—41no—
245C7×C22⋊C4—41no—
246C7×C22⋊C4—41no—
247C7×C22⋊C4—82no—
248C7×C22⋊C4—82no—
249C42×C7—22no—
250C42×C7—21no—
251C42×C7C2×D411yescharacteristic
252C42×C7C2×D411yescharacteristic
253C42×C7C2×D411yescharacteristic
254C42×C7C2×D411yescharacteristic
255#562—21no—
256H(3,𝔽4)—21no—
257#559—21no—
258#548—21no—
259#546—21no—
260#546—22no—
261D42—21no—
262#542—21no—
263#538—22no—
264#538C22×C712yes—
265#535—21no—
266#534C22×C712yes—
267#532C22×C711yescharacteristic
268#529C22×C711yescharacteristic
269C2×#124C22×C711yescharacteristic
270C2×#124C22×C711yescharacteristic, complemented
271#496—21no—
272#495—21no—
273#489—21no—
274#488—21no—
275#464—21no—
276#463—21no—
277#463—22no—
278#451C22×C711yescharacteristic, complemented
279#450C22×C711yescharacteristic, complemented
280#448C22×C711yescharacteristic
281#448C22×C712yescomplemented
282#447C22×C711yescharacteristic
283#447C22×C712yescomplemented
284#432C22×C711yescharacteristic, complemented
285#431C22×C711yescharacteristic, complemented
286#394—22no—
287#393—21no—
288#393C22×C712yescomplemented
289#392—21no—
290#392C22×C712yescomplemented
291#382C22×C711yescharacteristic, complemented
292#328C22×C712yescomplemented
293#327C22×C712yes—
294#327C22×C712yescomplemented
295#327C22×C712yescomplemented
296#323C22×C712yescomplemented
297#323C22×C712yescomplemented
298C23×C7—22no—
299C23×C7—21no—
300C23×C7—22no—
301C23×C7—22no—
302C23×C7—22no—
303C23×C7—42no—
304C23×C7—42no—
305C23×C7—42no—
306C23×C7—42no—
307C23×C7—41no—
308C23×C7—41no—
309C23×C7—41no—
310C23×C7—82no—
311C23×C7—82no—
312C23×C7—82no—
313C23×C7C22×D411yescharacteristic
314C7×Q8—41no—
315C7×Q8—42no—
316C7×Q8—42no—
317C7×Q8—41no—
318C7×Q8—41no—
319C7×Q8—81no—
320C7×Q8—81no—
321C7×D4—42no—
322C7×D4—41no—
323C7×D4—42no—
324C7×D4—42no—
325C7×D4—42no—
326C7×D4—41no—
327C7×D4—41no—
328C7×D4—41no—
329C7×D4—42no—
330C7×D4—41no—
331C7×D4—42no—
332C7×D4—81no—
333C7×D4—81no—
334C7×D4—82no—
335C7×D4—82no—
336C7×D4—82no—
337C7×D4—82no—
338C7×D4—82no—
339C7×D4—88no—
340C2×C4×C7—21no—
341C2×C4×C7—21no—
342C2×C4×C7—21no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—21no—
346C2×C4×C7—21no—
347C2×C4×C7—41no—
348C2×C4×C7—41no—
349C2×C4×C7—42no—
350C2×C4×C7—42no—
351C2×C4×C7—42no—
352C2×C4×C7—42no—
353C2×C4×C7—42no—
354C2×C4×C7—41no—
355C2×C4×C7—42no—
356C2×C4×C7—82no—
357C2×C4×C7—82no—
358C2×C4×C7—82no—
359C2×C4×C7#12011yescharacteristic
360C2×C4×C7#12011yescharacteristic
361C2×C4×C7#12011yescharacteristic
362C2×C4×C7#12011yescharacteristic
363C2×C4×C7C22×D411yescharacteristic
364C2×C4×C7C22×D411yescharacteristic
365C7×C8—42no—
366C7×C8—41no—
367C7×C8—41no—
368C2×#41—21no—
369C2×#41—21no—
370C22×Q8C7×D411yescharacteristic
371C22×Q8C23×C711yescharacteristic
372C22×D4—21no—
373C22×D4—22no—
374C22×D4—22no—
375C22×D4C7×D411yescharacteristic
376C22×D4C23×C711yescharacteristic
377C2×Q16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—22no—
381C2×D8—21no—
382C2×D8—22no—
383C4⋊Q8C7×D411yescharacteristic, complemented
384#127—21no—
385#127C7×D411yescharacteristic, complemented
386#126—22no—
387#126—21no—
388#125C7×D411yescharacteristic, complemented
389#124—21no—
390#124—22no—
391#124—22no—
392#124—22no—
393#124—21no—
394#124—21no—
395#124—21no—
396#124—21no—
397#124—21no—
398#124—21no—
399#124—21no—
400#124—21no—
401#124—21no—
402#124C7×D411yescharacteristic, complemented
403#123—22no—
404#123—21no—
405#123—22no—
406#123—22no—
407#123—22no—
408C22⋊Q8—22no—
409C22⋊Q8—21no—
410C22⋊Q8—22no—
411C22⋊Q8C23×C711yescharacteristic
412#121—22no—
413#121—22no—
414#121—22no—
415#121—21no—
416#121—22no—
417#121—21no—
418#121—22no—
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×D4C7×D411yescharacteristic, complemented
434C4×D4C7×D412yescomplemented
435#117—21no—
436C2×C4⋊C4—21no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4C7×D412yes—
443C2×C22⋊C4C23×C712yes—
444C2×C42C23×C711yescharacteristic
445C4⋊C8—21no—
446C4⋊C8—21no—
447#103—21no—
448#103—22no—
449#103—21no—
450#102—21no—
451#102—22no—
452#102—21no—
453C22⋊C8C23×C712yes—
454C22⋊C8C23×C711yescharacteristic
455C22⋊C8C23×C711yescharacteristic
456#97—21no—
457C4×C8—21no—
458#95—21no—
459#95—22no—
460#95C23×C712yes—
461C22×C7—21no—
462C22×C7—21no—
463C22×C7—42no—
464C22×C7—42no—
465C22×C7—41no—
466C22×C7—41no—
467C22×C7—42no—
468C22×C7—42no—
469C22×C7—42no—
470C22×C7—41no—
471C22×C7—42no—
472C22×C7—82no—
473C22×C7—82no—
474C22×C7—82no—
475C22×C7—82no—
476C22×C7—81no—
477C22×C7—81no—
478C22×C7—81no—
479C22×C7—164no—
480C22×C7C2×#12011yescharacteristic
481C22×C7#57611yescharacteristic
482C22×C7#57711yescharacteristic
483C4×C7—21no—
484C4×C7—21no—
485C4×C7—21no—
486C4×C7—21no—
487C4×C7—21no—
488C4×C7—21no—
489C4×C7—41no—
490C4×C7—42no—
491C4×C7—41no—
492C4×C7—42no—
493C4×C7—41no—
494C4×C7—82no—
495C4×C7—81no—
496C24—22no—
497C24—21no—
498C24C2×C7×D412yes—
499#41—81no—
500#41—81no—
501#41—82no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—81no—
508C2×Q8—81no—
509C2×Q8C2×C7×D411yescharacteristic
510C2×D4—22no—
511C2×D4—21no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—81no—
524C2×D4—82no—
525C2×D4—81no—
526C2×D4—82no—
527C2×D4—82no—
528C2×D4—82no—
529C2×D4—82no—
530C2×D4—82no—
531C2×D4C2×C7×D411yescharacteristic
532C2×D4C2×C7×D412yes—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4C2×C7×D411yescharacteristic
540C22×C4C2×C7×D412yes—
541C22×C4C2×C7×D411yescharacteristic
542C22×C4C24×C711yescharacteristic
543Q16—81no—
544SD16—82no—
545SD16—81no—
546SD16—81no—
547D8—82no—
548D8—81no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—22no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—81no—
560C4⋊C4C2×C7×D412yes—
561C4⋊C4C2×C7×D411yescharacteristic
562C4⋊C4C2×C7×D411yescharacteristic
563C22⋊C4—22no—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—21no—
569C22⋊C4—21no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—21no—
573C22⋊C4—21no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—21no—
578C22⋊C4—22no—
579C22⋊C4—41no—
580C22⋊C4—41no—
581C22⋊C4—41no—
582C22⋊C4—41no—
583C22⋊C4—82no—
584C22⋊C4—82no—
585C42—22no—
586C42—21no—
587C42C2×C7×D411yescharacteristic
588C42C2×C7×D411yescharacteristic
589C42C2×C7×D411yescharacteristic
590C42C2×C7×D411yescharacteristic
591C2×C7—21no—
592C2×C7—21no—
593C2×C7—82no—
594C2×C7—82no—
595C2×C7—81no—
596C2×C7—161no—
597C2×C7#301211yescharacteristic
598C2×C7#301911yescharacteristic
599C2×C7#302711yescharacteristic
600C23—22no—
601C23—21no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—82no—
613C23—82no—
614C23—82no—
615C23C22×C7×D411yescharacteristic
616Q8—41no—
617Q8—42no—
618Q8—42no—
619Q8—41no—
620Q8—41no—
621Q8—81no—
622Q8—81no—
623D4—42no—
624D4—41no—
625D4—42no—
626D4—42no—
627D4—42no—
628D4—41no—
629D4—41no—
630D4—41no—
631D4—42no—
632D4—41no—
633D4—42no—
634D4—81no—
635D4—81no—
636D4—82no—
637D4—82no—
638D4—82no—
639D4—82no—
640D4—82no—
641D4—88no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—41no—
657C2×C4—42no—
658C2×C4—82no—
659C2×C4—82no—
660C2×C4—82no—
661C2×C4C7×#12011yescharacteristic
662C2×C4C7×#12011yescharacteristic
663C2×C4C7×#12011yescharacteristic
664C2×C4C7×#12011yescharacteristic
665C2×C4C22×C7×D411yescharacteristic
666C2×C4C22×C7×D411yescharacteristic
667C8—42no—
668C8—41no—
669C8—41no—
670C7#1845811yescharacteristic, direct product factor, Sylow
671C22—21no—
672C22—21no—
673C22—42no—
674C22—42no—
675C22—41no—
676C22—41no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—41no—
681C22—42no—
682C22—82no—
683C22—82no—
684C22—82no—
685C22—82no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—164no—
690C22C2×C7×#12011yescharacteristic
691C22C7×#57611yescharacteristic
692C22C7×#57711yescharacteristic
693C4—21no—
694C4—21no—
695C4—21no—
696C4—21no—
697C4—21no—
698C4—21no—
699C4—41no—
700C4—42no—
701C4—41no—
702C4—42no—
703C4—41no—
704C4—82no—
705C4—81no—
706C2—21no—
707C2—21no—
708C2—82no—
709C2—81no—
710C2—82no—
711C2—161no—
712C2C7×#301211yescharacteristic
713C2C7×#301911yescharacteristic
714C2C7×#302711yescharacteristic
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×#3213C2semidirect
3. C7×#3211C2semidirect
4. C7×#2819C2semidirect
5. C7×#1606C2semidirect
6. C7×#1601C2semidirect
7. C7×#1600C2semidirect
8. C7×#1595C2semidirect
9. C7×#1517C2semidirect
10. C7×#1512C2semidirect
11. C7×#1469C2semidirect
27. C2×C7×#124C22semidirect
35. C7×#451C22semidirect
36. C7×#450C22semidirect
38. C7×#448C22semidirect
40. C7×#447C22semidirect
41. C7×#432C22semidirect
42. C7×#431C22semidirect
45. C7×#393C22semidirect
47. C7×#392C22semidirect
48. C7×#382C22semidirect
49. C7×#328C22semidirect
51. C7×#327C22semidirect
52. C7×#327C22semidirect
53. C7×#323C22semidirect
54. C7×#323C22semidirect
55. #18458C7direct (N × H)
71. C7×C4⋊Q8D4semidirect
73. C7×#127D4semidirect
76. C7×#125D4semidirect
90. C7×#124D4semidirect
115. C4×C7×Q8D4semidirect
121. C4×C7×D4D4semidirect
122. C4×C7×D4D4semidirect
149. #3558C2×C7semidirect
150. #3213C2×C7semidirect
151. #3211C2×C7semidirect
152. #2819C2×C7semidirect
153. #1606C2×C7semidirect
154. #1601C2×C7semidirect
155. #1600C2×C7semidirect
156. #1595C2×C7semidirect
157. #1517C2×C7semidirect
158. #1512C2×C7semidirect
159. #1469C2×C7semidirect
270. C2×#124C22×C7semidirect
278. #451C22×C7semidirect
279. #450C22×C7semidirect
281. #448C22×C7semidirect
283. #447C22×C7semidirect
284. #432C22×C7semidirect
285. #431C22×C7semidirect
288. #393C22×C7semidirect
290. #392C22×C7semidirect
291. #382C22×C7semidirect
292. #328C22×C7semidirect
294. #327C22×C7semidirect
295. #327C22×C7semidirect
296. #323C22×C7semidirect
297. #323C22×C7semidirect
383. C4⋊Q8C7×D4semidirect
385. #127C7×D4semidirect
388. #125C7×D4semidirect
402. #124C7×D4semidirect
427. C4×Q8C7×D4semidirect
433. C4×D4C7×D4semidirect
434. C4×D4C7×D4semidirect
670. C7#18458direct (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×#32132
C7×#32112
C7×#28192
C7×#16062
C7×#16012
C7×#16002
C7×#15952
C7×#15172
C7×#15122
C7×#14692
#184587