Finite Group Databasebeta

← C7×#33556 #13210772

Subgroups — C7×#33556 #13210772

Order 1792.

1134 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3540C211yesmaximal, characteristic, complemented
2C7×#3028C211yesmaximal, characteristic, complemented
3C7×#3025C211yesmaximal, characteristic, complemented
4C7×#3021C211yesmaximal, characteristic, complemented
5C7×#2200C214yesmaximal, complemented
6C7×#2198C214yesmaximal, complemented
7C7×#2128C211yesmaximal, characteristic, complemented
8C7×#2123C211yesmaximal, characteristic, complemented
9C7×#2120C211yesmaximal, characteristic, complemented
10C7×#585C2211yescharacteristic
11C2×C7×AGL(1,ℤ/8)—21no—
12C7×H(3,𝔽4)—21no—
13C7×#560C2212yescomplemented
14C7×#559C2212yescomplemented
15C7×#556—21no—
16C7×#555—21no—
17C7×#551—21no—
18C7×#548—21no—
19C7×#546—21no—
20C7×#542—22no—
21C7×#542—21no—
22C7×#538—22no—
23C7×#536—21no—
24C7×#536C2211yescharacteristic
25C7×#535C2211yescharacteristic
26C7×#525—21no—
27C7×#525—21no—
28C7×#525C2211yescharacteristic
29C7×#458—21no—
30C7×#458—22no—
31C7×#458C2212yescomplemented
32C7×#458C2214yescomplemented
33C7×B(4,𝔽2)—21no—
34C7×B(4,𝔽2)C2212yescomplemented
35C7×#454—22no—
36C7×#453C2214yes—
37C7×#421—21no—
38C7×#413C2211yescharacteristic
39C7×#410—21no—
40C7×#410—21no—
41C7×#410C2211yescharacteristic
42C7×#410C2211yescharacteristic
43C7×#353C2214yescomplemented
44C7×#352C2212yescomplemented
45C7×#352C2214yescomplemented
46C7×AΣL(1,𝔽16)C2212yescomplemented
47#33556C711yesmaximal, characteristic, direct product factor, Sylow
48C7×2−1+4—21no—
49C7×2−1+4—41no—
50C7×H(5,𝔽2)—21no—
51C7×H(5,𝔽2)—21no—
52C7×H(5,𝔽2)—41no—
53C7×H(5,𝔽2)C2312yes—
54C2×C7×#41—21no—
55C2×C7×#41—21no—
56C2×C7×#41—21no—
57C2×C7×#41—21no—
58C2×C7×#41—42no—
59C2×C7×#41C2311yescharacteristic
60C22×C7×Q8D411yescharacteristic, complemented
61C22×C7×D4D411yescharacteristic, complemented
62C23×C4×C7D411yescharacteristic
63C7×AGL(1,ℤ/8)—24no—
64C7×AGL(1,ℤ/8)—42no—
65C2×C7×SD16—41no—
66C2×C7×D8—41no—
67C2×C7×M16—21no—
68C7×C4⋊Q8—21no—
69C7×C4⋊Q8—21no—
70C7×C4⋊Q8—41no—
71C7×#127C2312yes—
72C7×#126—22no—
73C7×#126—22no—
74C7×#126—22no—
75C7×#124—22no—
76C7×#124—21no—
77C7×#124—22no—
78C7×#124—22no—
79C7×#124—21no—
80C7×#124—22no—
81C7×#124—22no—
82C7×#124—41no—
83C7×#124D412yescomplemented
84C7×#123—22no—
85C7×#123—22no—
86C7×#123—22no—
87C7×#123—22no—
88C7×#123—24no—
89C7×#123D411yescharacteristic
90C7×#123D412yescomplemented
91C7×#123C2311yescharacteristic
92C7×#123C2312yes—
93C7×C22⋊Q8—21no—
94C7×C22⋊Q8—22no—
95C7×C22⋊Q8—22no—
96C7×C22⋊Q8—21no—
97C7×C22⋊Q8—21no—
98C7×C22⋊Q8—21no—
99C7×C22⋊Q8—42no—
100C7×C22⋊Q8—41no—
101C7×#121—21no—
102C7×#121—21no—
103C7×#121—22no—
104C7×#121—21no—
105C7×#121—21no—
106C7×#121—22no—
107C7×#121—22no—
108C7×#121—41no—
109C7×#120—22no—
110C7×#120—22no—
111C7×#120—21no—
112C7×#120—21no—
113C7×#120—22no—
114C7×#120D411yescharacteristic
115C7×#120C2311yescharacteristic
116C4×C7×Q8—21no—
117C4×C7×Q8—22no—
118C4×C7×D4—22no—
119C4×C7×D4—21no—
120C4×C7×D4—22no—
121C4×C7×D4—21no—
122C4×C7×D4—21no—
123C4×C7×D4—22no—
124C4×C7×D4—42no—
125C7×#117—21no—
126C7×#117—22no—
127C7×#117—21no—
128C7×#117—21no—
129C7×#117D411yescharacteristic
130C7×#117D411yescharacteristic, complemented
131C7×#117D411yescharacteristic, complemented
132C2×C7×C22⋊C4—22no—
133C7×#104—24no—
134C7×#101—21no—
135C7×#100C2312yes—
136C7×#99—21no—
137C7×#99—21no—
138C7×#99—22no—
139C7×#99—22no—
140C7×#99—24no—
141C7×#99C2312yes—
142C7×#99C2312yes—
143#3540C2×C711yescharacteristic, complemented
144#3028C2×C711yescharacteristic, complemented
145#3025C2×C711yescharacteristic, complemented
146#3021C2×C711yescharacteristic, complemented
147#2200C2×C714yescomplemented
148#2198C2×C714yescomplemented
149#2128C2×C711yescharacteristic, complemented
150#2123C2×C711yescharacteristic, complemented
151#2120C2×C711yescharacteristic, complemented
152C24×C7—21no—
153C24×C7C2×D411yescharacteristic
154C7×#41—22no—
155C7×#41—22no—
156C7×#41—41no—
157C7×#41—41no—
158C7×#41—42no—
159C7×#41—41no—
160C7×#41—41no—
161C7×#41—41no—
162C7×#41—41no—
163C7×#41—41no—
164C7×#41—42no—
165C7×#41—42no—
166C7×#41—42no—
167C7×#41—41no—
168C7×#41—41no—
169C7×#41—41no—
170C7×#41—81no—
171C7×#41—81no—
172C2×C7×Q8—21no—
173C2×C7×Q8—21no—
174C2×C7×Q8—22no—
175C2×C7×Q8—21no—
176C2×C7×Q8—21no—
177C2×C7×Q8—21no—
178C2×C7×Q8—41no—
179C2×C7×Q8—41no—
180C2×C7×Q8—42no—
181C2×C7×Q8C2×D411yescharacteristic
182C2×C7×D4—21no—
183C2×C7×D4—21no—
184C2×C7×D4—21no—
185C2×C7×D4—22no—
186C2×C7×D4—22no—
187C2×C7×D4—22no—
188C2×C7×D4—22no—
189C2×C7×D4—21no—
190C2×C7×D4—22no—
191C2×C7×D4—22no—
192C2×C7×D4—21no—
193C2×C7×D4—21no—
194C2×C7×D4—41no—
195C2×C7×D4—41no—
196C2×C7×D4—42no—
197C2×C7×D4—42no—
198C2×C7×D4—42no—
199C2×C7×D4—41no—
200C2×C7×D4—42no—
201C2×C7×D4C2×D411yescharacteristic
202C2×C7×D4C2×D411yescharacteristic
203C2×C7×D4C2×D412yes—
204C2×C7×D4C2411yescharacteristic
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—41no—
212C22×C4×C7—41no—
213C22×C4×C7—41no—
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2×D412yes—
219C7×SD16—44no—
220C7×D8—44no—
221C7×M16—22no—
222C7×M16—41no—
223C2×C7×C8—41no—
224C7×C4⋊C4—22no—
225C7×C4⋊C4—22no—
226C7×C4⋊C4—22no—
227C7×C4⋊C4—21no—
228C7×C4⋊C4—21no—
229C7×C4⋊C4—22no—
230C7×C4⋊C4—21no—
231C7×C4⋊C4—21no—
232C7×C4⋊C4—21no—
233C7×C4⋊C4—22no—
234C7×C4⋊C4—41no—
235C7×C4⋊C4—41no—
236C7×C4⋊C4—42no—
237C7×C4⋊C4—44no—
238C7×C22⋊C4—22no—
239C7×C22⋊C4—22no—
240C7×C22⋊C4—22no—
241C7×C22⋊C4—22no—
242C7×C22⋊C4—22no—
243C7×C22⋊C4—22no—
244C7×C22⋊C4—21no—
245C7×C22⋊C4—22no—
246C7×C22⋊C4—21no—
247C7×C22⋊C4—21no—
248C7×C22⋊C4—22no—
249C7×C22⋊C4—22no—
250C7×C22⋊C4—22no—
251C7×C22⋊C4—21no—
252C7×C22⋊C4—21no—
253C7×C22⋊C4—22no—
254C7×C22⋊C4—22no—
255C7×C22⋊C4—42no—
256C7×C22⋊C4—42no—
257C7×C22⋊C4—44no—
258C7×C22⋊C4C2×D411yescharacteristic
259C7×C22⋊C4C2×D411yescharacteristic
260C7×C22⋊C4C2×D412yes—
261C42×C7—22no—
262C42×C7—22no—
263C42×C7—21no—
264C42×C7—21no—
265C42×C7—41no—
266C42×C7—41no—
267C42×C7C2×D412yes—
268#585C22×C711yescharacteristic
269C2×AGL(1,ℤ/8)—21no—
270H(3,𝔽4)—21no—
271#560C22×C712yescomplemented
272#559C22×C712yescomplemented
273#556—21no—
274#555—21no—
275#551—21no—
276#548—21no—
277#546—21no—
278#542—22no—
279#542—21no—
280#538—22no—
281#536—21no—
282#536C22×C711yescharacteristic
283#535C22×C711yescharacteristic
284#525—21no—
285#525—21no—
286#525C22×C711yescharacteristic
287#458—21no—
288#458—22no—
289#458C22×C712yescomplemented
290#458C22×C714yescomplemented
291B(4,𝔽2)—21no—
292B(4,𝔽2)C22×C712yescomplemented
293#454—22no—
294#453C22×C714yes—
295#421—21no—
296#413C22×C711yescharacteristic
297#410—21no—
298#410—21no—
299#410C22×C711yescharacteristic
300#410C22×C711yescharacteristic
301#353C22×C714yescomplemented
302#352C22×C712yescomplemented
303#352C22×C714yescomplemented
304AΣL(1,𝔽16)C22×C712yescomplemented
305C23×C7—22no—
306C23×C7—22no—
307C23×C7—21no—
308C23×C7—22no—
309C23×C7—41no—
310C23×C7—41no—
311C23×C7—81no—
312C23×C7—81no—
313C23×C7—82no—
314C23×C7#12011yescharacteristic
315C23×C7C22×D411yescharacteristic
316C23×C7C22×D411yescharacteristic
317C7×Q8—22no—
318C7×Q8—41no—
319C7×Q8—41no—
320C7×Q8—41no—
321C7×Q8—41no—
322C7×Q8—41no—
323C7×Q8—41no—
324C7×Q8—81no—
325C7×Q8—82no—
326C7×D4—22no—
327C7×D4—41no—
328C7×D4—41no—
329C7×D4—41no—
330C7×D4—42no—
331C7×D4—41no—
332C7×D4—41no—
333C7×D4—42no—
334C7×D4—42no—
335C7×D4—42no—
336C7×D4—42no—
337C7×D4—41no—
338C7×D4—41no—
339C7×D4—41no—
340C7×D4—81no—
341C7×D4—82no—
342C7×D4—82no—
343C7×D4—82no—
344C7×D4—81no—
345C7×D4—82no—
346C7×D4—84no—
347C2×C4×C7—21no—
348C2×C4×C7—21no—
349C2×C4×C7—21no—
350C2×C4×C7—21no—
351C2×C4×C7—21no—
352C2×C4×C7—21no—
353C2×C4×C7—22no—
354C2×C4×C7—22no—
355C2×C4×C7—21no—
356C2×C4×C7—22no—
357C2×C4×C7—22no—
358C2×C4×C7—21no—
359C2×C4×C7—22no—
360C2×C4×C7—21no—
361C2×C4×C7—42no—
362C2×C4×C7—42no—
363C2×C4×C7—42no—
364C2×C4×C7—41no—
365C2×C4×C7—42no—
366C2×C4×C7—41no—
367C2×C4×C7—41no—
368C2×C4×C7—41no—
369C2×C4×C7—42no—
370C2×C4×C7—42no—
371C2×C4×C7—42no—
372C2×C4×C7—81no—
373C2×C4×C7—82no—
374C2×C4×C7—82no—
375C2×C4×C7#12011yescharacteristic
376C2×C4×C7#12011yescharacteristic
377C2×C4×C7#12011yescharacteristic
378C2×C4×C7C22×D411yescharacteristic
379C7×C8—42no—
3802−1+4—21no—
3812−1+4—41no—
382H(5,𝔽2)—21no—
383H(5,𝔽2)—21no—
384H(5,𝔽2)—41no—
385H(5,𝔽2)C23×C712yes—
386C2×#41—21no—
387C2×#41—21no—
388C2×#41—21no—
389C2×#41—21no—
390C2×#41—42no—
391C2×#41C23×C711yescharacteristic
392C22×Q8C7×D411yescharacteristic, complemented
393C22×D4C7×D411yescharacteristic, complemented
394C23×C4C7×D411yescharacteristic
395AGL(1,ℤ/8)—24no—
396AGL(1,ℤ/8)—42no—
397C2×SD16—41no—
398C2×D8—41no—
399C2×M16—21no—
400C4⋊Q8—21no—
401C4⋊Q8—21no—
402C4⋊Q8—41no—
403#127C23×C712yes—
404#126—22no—
405#126—22no—
406#126—22no—
407#124—22no—
408#124—21no—
409#124—22no—
410#124—22no—
411#124—21no—
412#124—22no—
413#124—22no—
414#124—41no—
415#124C7×D412yescomplemented
416#123—22no—
417#123—22no—
418#123—22no—
419#123—22no—
420#123—24no—
421#123C7×D411yescharacteristic
422#123C7×D412yescomplemented
423#123C23×C711yescharacteristic
424#123C23×C712yes—
425C22⋊Q8—21no—
426C22⋊Q8—22no—
427C22⋊Q8—22no—
428C22⋊Q8—21no—
429C22⋊Q8—21no—
430C22⋊Q8—21no—
431C22⋊Q8—42no—
432C22⋊Q8—41no—
433#121—21no—
434#121—21no—
435#121—22no—
436#121—21no—
437#121—21no—
438#121—22no—
439#121—22no—
440#121—41no—
441#120—22no—
442#120—22no—
443#120—21no—
444#120—21no—
445#120—22no—
446#120C7×D411yescharacteristic
447#120C23×C711yescharacteristic
448C4×Q8—21no—
449C4×Q8—22no—
450C4×D4—22no—
451C4×D4—21no—
452C4×D4—22no—
453C4×D4—21no—
454C4×D4—21no—
455C4×D4—22no—
456C4×D4—42no—
457#117—21no—
458#117—22no—
459#117—21no—
460#117—21no—
461#117C7×D411yescharacteristic
462#117C7×D411yescharacteristic, complemented
463#117C7×D411yescharacteristic, complemented
464C2×C22⋊C4—22no—
465#104—24no—
466#101—21no—
467#100C23×C712yes—
468#99—21no—
469#99—21no—
470#99—22no—
471#99—22no—
472#99—24no—
473#99C23×C712yes—
474#99C23×C712yes—
475C22×C7—21no—
476C22×C7—21no—
477C22×C7—21no—
478C22×C7—41no—
479C22×C7—41no—
480C22×C7—41no—
481C22×C7—42no—
482C22×C7—41no—
483C22×C7—41no—
484C22×C7—42no—
485C22×C7—42no—
486C22×C7—42no—
487C22×C7—41no—
488C22×C7—42no—
489C22×C7—82no—
490C22×C7—82no—
491C22×C7—81no—
492C22×C7—161no—
493C22×C7—162no—
494C22×C7C2×#12011yescharacteristic
495C4×C7—21no—
496C4×C7—21no—
497C4×C7—21no—
498C4×C7—41no—
499C4×C7—42no—
500C4×C7—42no—
501C4×C7—41no—
502C4×C7—42no—
503C4×C7—41no—
504C4×C7—42no—
505C4×C7—82no—
506C4×C7—82no—
507C4×C7B(4,𝔽2)11yescharacteristic
508C4×C7B(4,𝔽2)11yescharacteristic
509C24—21no—
510C24C2×C7×D411yescharacteristic
511#41—22no—
512#41—22no—
513#41—41no—
514#41—41no—
515#41—42no—
516#41—41no—
517#41—41no—
518#41—41no—
519#41—41no—
520#41—41no—
521#41—42no—
522#41—42no—
523#41—42no—
524#41—41no—
525#41—41no—
526#41—41no—
527#41—81no—
528#41—81no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—22no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—41no—
536C2×Q8—41no—
537C2×Q8—42no—
538C2×Q8C2×C7×D411yescharacteristic
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—21no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—41no—
552C2×D4—41no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—41no—
557C2×D4—42no—
558C2×D4C2×C7×D411yescharacteristic
559C2×D4C2×C7×D411yescharacteristic
560C2×D4C2×C7×D412yes—
561C2×D4C24×C711yescharacteristic
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4C2×C7×D411yescharacteristic
572C22×C4C2×C7×D411yescharacteristic
573C22×C4C2×C7×D411yescharacteristic
574C22×C4C2×C7×D411yescharacteristic
575C22×C4C2×C7×D412yes—
576SD16—44no—
577D8—44no—
578M16—22no—
579M16—41no—
580C2×C8—41no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—22no—
589C4⋊C4—21no—
590C4⋊C4—22no—
591C4⋊C4—41no—
592C4⋊C4—41no—
593C4⋊C4—42no—
594C4⋊C4—44no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—21no—
602C22⋊C4—22no—
603C22⋊C4—21no—
604C22⋊C4—21no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—21no—
609C22⋊C4—21no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—44no—
615C22⋊C4C2×C7×D411yescharacteristic
616C22⋊C4C2×C7×D411yescharacteristic
617C22⋊C4C2×C7×D412yes—
618C42—22no—
619C42—22no—
620C42—21no—
621C42—21no—
622C42—41no—
623C42—41no—
624C42C2×C7×D412yes—
625C2×C7—21no—
626C2×C7—41no—
627C2×C7—41no—
628C2×C7—41no—
629C2×C7—81no—
630C2×C7—82no—
631C2×C7—82no—
632C2×C7C2×B(4,𝔽2)11yescharacteristic
633C23—22no—
634C23—22no—
635C23—21no—
636C23—22no—
637C23—41no—
638C23—41no—
639C23—81no—
640C23—81no—
641C23—82no—
642C23C7×#12011yescharacteristic
643C23C22×C7×D411yescharacteristic
644C23C22×C7×D411yescharacteristic
645Q8—22no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651Q8—41no—
652Q8—81no—
653Q8—82no—
654D4—22no—
655D4—41no—
656D4—41no—
657D4—41no—
658D4—42no—
659D4—41no—
660D4—41no—
661D4—42no—
662D4—42no—
663D4—42no—
664D4—42no—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—81no—
669D4—82no—
670D4—82no—
671D4—82no—
672D4—81no—
673D4—82no—
674D4—84no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—81no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4C7×#12011yescharacteristic
704C2×C4C7×#12011yescharacteristic
705C2×C4C7×#12011yescharacteristic
706C2×C4C22×C7×D411yescharacteristic
707C8—42no—
708C7#3355611yescharacteristic, direct product factor, Sylow
709C22—21no—
710C22—21no—
711C22—21no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—42no—
716C22—41no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—41no—
722C22—42no—
723C22—82no—
724C22—82no—
725C22—81no—
726C22—161no—
727C22—162no—
728C22C2×C7×#12011yescharacteristic
729C4—21no—
730C4—21no—
731C4—21no—
732C4—41no—
733C4—42no—
734C4—42no—
735C4—41no—
736C4—42no—
737C4—41no—
738C4—42no—
739C4—82no—
740C4—82no—
741C4C7×B(4,𝔽2)11yescharacteristic
742C4C7×B(4,𝔽2)11yescharacteristic
743C2—21no—
744C2—41no—
745C2—41no—
746C2—41no—
747C2—81no—
748C2—82no—
749C2—82no—
750C2C2×C7×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C7C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C7
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C7 ◁ C2×C4×C7 ◁ C2×C7×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C7×#3540C2semidirect
2. C7×#3028C2semidirect
3. C7×#3025C2semidirect
4. C7×#3021C2semidirect
5. C7×#2200C2semidirect
6. C7×#2198C2semidirect
7. C7×#2128C2semidirect
8. C7×#2123C2semidirect
9. C7×#2120C2semidirect
13. C7×#560C22semidirect
14. C7×#559C22semidirect
31. C7×#458C22semidirect
32. C7×#458C22semidirect
34. C7×B(4,𝔽2)C22semidirect
43. C7×#353C22semidirect
44. C7×#352C22semidirect
45. C7×#352C22semidirect
46. C7×AΣL(1,𝔽16)C22semidirect
47. #33556C7direct (N × H)
60. C22×C7×Q8D4semidirect
61. C22×C7×D4D4semidirect
83. C7×#124D4semidirect
90. C7×#123D4semidirect
130. C7×#117D4semidirect
131. C7×#117D4semidirect
143. #3540C2×C7semidirect
144. #3028C2×C7semidirect
145. #3025C2×C7semidirect
146. #3021C2×C7semidirect
147. #2200C2×C7semidirect
148. #2198C2×C7semidirect
149. #2128C2×C7semidirect
150. #2123C2×C7semidirect
151. #2120C2×C7semidirect
271. #560C22×C7semidirect
272. #559C22×C7semidirect
289. #458C22×C7semidirect
290. #458C22×C7semidirect
292. B(4,𝔽2)C22×C7semidirect
301. #353C22×C7semidirect
302. #352C22×C7semidirect
303. #352C22×C7semidirect
304. AΣL(1,𝔽16)C22×C7semidirect
392. C22×Q8C7×D4semidirect
393. C22×D4C7×D4semidirect
415. #124C7×D4semidirect
422. #123C7×D4semidirect
462. #117C7×D4semidirect
463. #117C7×D4semidirect
708. C7#33556direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#35402
C7×#30282
C7×#30252
C7×#30212
C7×#22002
C7×#21982
C7×#21282
C7×#21232
C7×#21202
#335567