Finite Group Databasebeta

← C7×#33560 #13210776

Subgroups — C7×#33560 #13210776

Order 1792.

1132 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3551C211yesmaximal, characteristic, complemented
2C7×#3028C211yesmaximal, characteristic, complemented
3C7×#3027C211yesmaximal, characteristic, complemented
4C7×#3018C211yesmaximal, characteristic, complemented
5C7×#2200C214yesmaximal, complemented
6C7×#2197C214yesmaximal, complemented
7C7×#2126C211yesmaximal, characteristic, complemented
8C7×#2123C211yesmaximal, characteristic, complemented
9C7×#2122C211yesmaximal, characteristic, complemented
10C7×#585C2211yescharacteristic
11C7×#575—21no—
12C7×#563—21no—
13C7×#560C2212yescomplemented
14C7×#555—21no—
15C7×#553—21no—
16C7×#552—21no—
17C7×#551C2212yescomplemented
18C7×#548—21no—
19C7×#546—21no—
20C7×#540—22no—
21C7×#538—22no—
22C7×#537—21no—
23C7×#536—21no—
24C7×#536C2211yescharacteristic
25C7×#535—21no—
26C7×#535C2211yescharacteristic
27C7×#532C2211yescharacteristic
28C7×#529—21no—
29C7×#458—22no—
30C7×#458C2214yes—
31C7×B(4,𝔽2)—22no—
32C7×B(4,𝔽2)C2214yes—
33C7×#456—21no—
34C7×#455C2212yes—
35C7×#454—21no—
36C7×#453C2212yes—
37C2×C7×#104—21no—
38C7×#413C2211yescharacteristic
39C7×#410—21no—
40C7×#410—21no—
41C7×#410C2211yescharacteristic
42C7×#410C2211yescharacteristic
43C7×#354C2212yescomplemented
44C7×#353C2212yescomplemented
45C7×#352C2214yescomplemented
46C7×AΣL(1,𝔽16)C2214yescomplemented
47#33560C711yesmaximal, 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×#41D411yescharacteristic, complemented
60C2×C7×#41C2311yescharacteristic
61C22×C7×Q8D411yescharacteristic, complemented
62C22×C7×D4D411yescharacteristic
63C7×#137—22no—
64C7×#137—41no—
65C7×AGL(1,ℤ/8)—22no—
66C7×AGL(1,ℤ/8)—41no—
67C7×#135—42no—
68C2×C7×M16—21no—
69C7×C4⋊Q8—21no—
70C7×C4⋊Q8—41no—
71C7×C4⋊Q8D411yescharacteristic, complemented
72C7×#127—21no—
73C7×#127—41no—
74C7×#127C2311yescharacteristic
75C7×#126—22no—
76C7×#126—22no—
77C7×#126—22no—
78C7×#125—21no—
79C7×#125—22no—
80C7×#124—21no—
81C7×#124—22no—
82C7×#124—21no—
83C7×#124—21no—
84C7×#124—41no—
85C7×#124—41no—
86C7×#124D411yescharacteristic, complemented
87C7×#124C2311yescharacteristic
88C7×#123—22no—
89C7×#123—22no—
90C7×#123—22no—
91C7×#123—22no—
92C7×#123—24no—
93C7×#123D412yescomplemented
94C7×#123C2312yes—
95C7×C22⋊Q8—21no—
96C7×C22⋊Q8—22no—
97C7×C22⋊Q8—22no—
98C7×C22⋊Q8—21no—
99C7×C22⋊Q8—21no—
100C7×C22⋊Q8—42no—
101C7×#121—22no—
102C7×#121—22no—
103C7×#121—21no—
104C7×#121—22no—
105C7×#121—21no—
106C7×#121—21no—
107C7×#121—22no—
108C7×#121—21no—
109C7×#121—21no—
110C7×#121—22no—
111C7×#121—22no—
112C7×#121—42no—
113C7×#120—22no—
114C7×#120—24no—
115C7×#120D412yes—
116C7×#120C2312yes—
117C4×C7×Q8—21no—
118C4×C7×D4—22no—
119C4×C7×D4—21no—
120C4×C7×D4—22no—
121C4×C7×D4—21no—
122C4×C7×D4—21no—
123C4×C7×D4—22no—
124C7×#117—22no—
125C7×#117—22no—
126C7×#117—21no—
127C7×#117—21no—
128C7×#117D411yescharacteristic
129C7×#117D411yescharacteristic, complemented
130C2×C7×C4⋊C4—21no—
131C2×C7×C22⋊C4—22no—
132C2×C42×C7D411yescharacteristic, complemented
133C7×#104—22no—
134C7×#104—22no—
135C7×#101—21no—
136C7×#100C2312yes—
137C7×#99—21no—
138C7×#99—21no—
139C7×#99—24no—
140C7×#99—24no—
141C7×#99C2312yes—
142C7×#99C2312yes—
143#3551C2×C711yescharacteristic, complemented
144#3028C2×C711yescharacteristic, complemented
145#3027C2×C711yescharacteristic, complemented
146#3018C2×C711yescharacteristic, complemented
147#2200C2×C714yescomplemented
148#2197C2×C714yescomplemented
149#2126C2×C711yescharacteristic, complemented
150#2123C2×C711yescharacteristic, complemented
151#2122C2×C711yescharacteristic, complemented
152C24×C7C2×D412yes—
153C7×#41—22no—
154C7×#41—22no—
155C7×#41—41no—
156C7×#41—41no—
157C7×#41—42no—
158C7×#41—41no—
159C7×#41—41no—
160C7×#41—41no—
161C7×#41—41no—
162C7×#41—41no—
163C7×#41—42no—
164C7×#41—42no—
165C7×#41—41no—
166C7×#41—41no—
167C7×#41—42no—
168C7×#41—41no—
169C7×#41—41no—
170C7×#41—41no—
171C7×#41—81no—
172C7×#41—81no—
173C2×C7×Q8—21no—
174C2×C7×Q8—21no—
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×Q8C2×D411yescharacteristic
183C2×C7×D4—21no—
184C2×C7×D4—21no—
185C2×C7×D4—21no—
186C2×C7×D4—22no—
187C2×C7×D4—22no—
188C2×C7×D4—22no—
189C2×C7×D4—22no—
190C2×C7×D4—22no—
191C2×C7×D4—21no—
192C2×C7×D4—21no—
193C2×C7×D4—22no—
194C2×C7×D4—21no—
195C2×C7×D4—21no—
196C2×C7×D4—21no—
197C2×C7×D4—41no—
198C2×C7×D4—41no—
199C2×C7×D4—42no—
200C2×C7×D4—42no—
201C2×C7×D4—42no—
202C2×C7×D4—41no—
203C2×C7×D4—44no—
204C2×C7×D4C2×D411yescharacteristic
205C2×C7×D4C2×D411yescharacteristic
206C2×C7×D4C2×D411yescharacteristic
207C2×C7×D4C2411yescharacteristic
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7—22no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—41no—
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2×D411yescharacteristic
219C22×C4×C7C2×D412yes—
220C7×Q16—42no—
221C7×SD16—42no—
222C7×SD16—42no—
223C7×D8—42no—
224C7×M16—22no—
225C7×M16—41no—
226C2×C7×C8—41no—
227C7×C4⋊C4—22no—
228C7×C4⋊C4—22no—
229C7×C4⋊C4—22no—
230C7×C4⋊C4—22no—
231C7×C4⋊C4—22no—
232C7×C4⋊C4—22no—
233C7×C4⋊C4—21no—
234C7×C4⋊C4—21no—
235C7×C4⋊C4—21no—
236C7×C4⋊C4—21no—
237C7×C4⋊C4—22no—
238C7×C4⋊C4—41no—
239C7×C4⋊C4—41no—
240C7×C4⋊C4—44no—
241C7×C22⋊C4—22no—
242C7×C22⋊C4—22no—
243C7×C22⋊C4—22no—
244C7×C22⋊C4—22no—
245C7×C22⋊C4—22no—
246C7×C22⋊C4—22no—
247C7×C22⋊C4—21no—
248C7×C22⋊C4—22no—
249C7×C22⋊C4—21no—
250C7×C22⋊C4—21no—
251C7×C22⋊C4—21no—
252C7×C22⋊C4—22no—
253C7×C22⋊C4—22no—
254C7×C22⋊C4—22no—
255C7×C22⋊C4—22no—
256C7×C22⋊C4—44no—
257C7×C22⋊C4—44no—
258C7×C22⋊C4C2×D412yes—
259C7×C22⋊C4C2×D412yes—
260C42×C7—22no—
261C42×C7—21no—
262C42×C7—21no—
263C42×C7—21no—
264C42×C7—41no—
265C42×C7—41no—
266C42×C7C2×D411yescharacteristic
267C42×C7C2×D411yescharacteristic
268#585C22×C711yescharacteristic
269#575—21no—
270#563—21no—
271#560C22×C712yescomplemented
272#555—21no—
273#553—21no—
274#552—21no—
275#551C22×C712yescomplemented
276#548—21no—
277#546—21no—
278#540—22no—
279#538—22no—
280#537—21no—
281#536—21no—
282#536C22×C711yescharacteristic
283#535—21no—
284#535C22×C711yescharacteristic
285#532C22×C711yescharacteristic
286#529—21no—
287#458—22no—
288#458C22×C714yes—
289B(4,𝔽2)—22no—
290B(4,𝔽2)C22×C714yes—
291#456—21no—
292#455C22×C712yes—
293#454—21no—
294#453C22×C712yes—
295C2×#104—21no—
296#413C22×C711yescharacteristic
297#410—21no—
298#410—21no—
299#410C22×C711yescharacteristic
300#410C22×C711yescharacteristic
301#354C22×C712yescomplemented
302#353C22×C712yescomplemented
303#352C22×C714yescomplemented
304AΣL(1,𝔽16)C22×C714yescomplemented
305C23×C7—22no—
306C23×C7—22no—
307C23×C7—22no—
308C23×C7—21no—
309C23×C7—41no—
310C23×C7—42no—
311C23×C7—82no—
312C23×C7#12011yescharacteristic
313C23×C7C22×D411yescharacteristic
314C23×C7C22×D411yescharacteristic
315C7×Q8—22no—
316C7×Q8—41no—
317C7×Q8—41no—
318C7×Q8—41no—
319C7×Q8—41no—
320C7×Q8—41no—
321C7×Q8—41no—
322C7×Q8—41no—
323C7×Q8—81no—
324C7×D4—22no—
325C7×D4—41no—
326C7×D4—41no—
327C7×D4—41no—
328C7×D4—41no—
329C7×D4—41no—
330C7×D4—41no—
331C7×D4—42no—
332C7×D4—42no—
333C7×D4—42no—
334C7×D4—42no—
335C7×D4—41no—
336C7×D4—41no—
337C7×D4—41no—
338C7×D4—81no—
339C7×D4—81no—
340C7×D4—82no—
341C7×D4—82no—
342C7×D4—82no—
343C7×D4—81no—
344C7×D4—81no—
345C7×D4—82no—
346C7×D4—164no—
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—21no—
358C2×C4×C7—22no—
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—42no—
369C2×C4×C7—42no—
370C2×C4×C7—42no—
371C2×C4×C7—82no—
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×#41C7×D411yescharacteristic, complemented
392C2×#41C23×C711yescharacteristic
393C22×Q8C7×D411yescharacteristic, complemented
394C22×D4C7×D411yescharacteristic
395#137—22no—
396#137—41no—
397AGL(1,ℤ/8)—22no—
398AGL(1,ℤ/8)—41no—
399#135—42no—
400C2×M16—21no—
401C4⋊Q8—21no—
402C4⋊Q8—41no—
403C4⋊Q8C7×D411yescharacteristic, complemented
404#127—21no—
405#127—41no—
406#127C23×C711yescharacteristic
407#126—22no—
408#126—22no—
409#126—22no—
410#125—21no—
411#125—22no—
412#124—21no—
413#124—22no—
414#124—21no—
415#124—21no—
416#124—41no—
417#124—41no—
418#124C7×D411yescharacteristic, complemented
419#124C23×C711yescharacteristic
420#123—22no—
421#123—22no—
422#123—22no—
423#123—22no—
424#123—24no—
425#123C7×D412yescomplemented
426#123C23×C712yes—
427C22⋊Q8—21no—
428C22⋊Q8—22no—
429C22⋊Q8—22no—
430C22⋊Q8—21no—
431C22⋊Q8—21no—
432C22⋊Q8—42no—
433#121—22no—
434#121—22no—
435#121—21no—
436#121—22no—
437#121—21no—
438#121—21no—
439#121—22no—
440#121—21no—
441#121—21no—
442#121—22no—
443#121—22no—
444#121—42no—
445#120—22no—
446#120—24no—
447#120C7×D412yes—
448#120C23×C712yes—
449C4×Q8—21no—
450C4×D4—22no—
451C4×D4—21no—
452C4×D4—22no—
453C4×D4—21no—
454C4×D4—21no—
455C4×D4—22no—
456#117—22no—
457#117—22no—
458#117—21no—
459#117—21no—
460#117C7×D411yescharacteristic
461#117C7×D411yescharacteristic, complemented
462C2×C4⋊C4—21no—
463C2×C22⋊C4—22no—
464C2×C42C7×D411yescharacteristic, complemented
465#104—22no—
466#104—22no—
467#101—21no—
468#100C23×C712yes—
469#99—21no—
470#99—21no—
471#99—24no—
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—41no—
482C22×C7—42no—
483C22×C7—41no—
484C22×C7—42no—
485C22×C7—42no—
486C22×C7—41no—
487C22×C7—42no—
488C22×C7—82no—
489C22×C7—84no—
490C22×C7—82no—
491C22×C7—161no—
492C22×C7C2×#12011yescharacteristic
493C4×C7—21no—
494C4×C7—21no—
495C4×C7—21no—
496C4×C7—41no—
497C4×C7—42no—
498C4×C7—42no—
499C4×C7—41no—
500C4×C7—42no—
501C4×C7—41no—
502C4×C7—42no—
503C4×C7—82no—
504C4×C7—82no—
505C4×C7B(4,𝔽2)11yescharacteristic
506C4×C7B(4,𝔽2)11yescharacteristic
507C24C2×C7×D412yes—
508#41—22no—
509#41—22no—
510#41—41no—
511#41—41no—
512#41—42no—
513#41—41no—
514#41—41no—
515#41—41no—
516#41—41no—
517#41—41no—
518#41—42no—
519#41—42no—
520#41—41no—
521#41—41no—
522#41—42no—
523#41—41no—
524#41—41no—
525#41—41no—
526#41—81no—
527#41—81no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—41no—
534C2×Q8—41no—
535C2×Q8—42no—
536C2×Q8C2×C7×D411yescharacteristic
537C2×Q8C2×C7×D411yescharacteristic
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—22no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—41no—
553C2×D4—41no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—41no—
558C2×D4—44no—
559C2×D4C2×C7×D411yescharacteristic
560C2×D4C2×C7×D411yescharacteristic
561C2×D4C2×C7×D411yescharacteristic
562C2×D4C24×C711yescharacteristic
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—41no—
571C22×C4C2×C7×D411yescharacteristic
572C22×C4C2×C7×D411yescharacteristic
573C22×C4C2×C7×D411yescharacteristic
574C22×C4C2×C7×D412yes—
575Q16—42no—
576SD16—42no—
577SD16—42no—
578D8—42no—
579M16—22no—
580M16—41no—
581C2×C8—41no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—22no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—22no—
593C4⋊C4—41no—
594C4⋊C4—41no—
595C4⋊C4—44no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—21no—
603C22⋊C4—22no—
604C22⋊C4—21no—
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4C2×C7×D412yes—
614C22⋊C4C2×C7×D412yes—
615C42—22no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—41no—
620C42—41no—
621C42C2×C7×D411yescharacteristic
622C42C2×C7×D411yescharacteristic
623C2×C7—21no—
624C2×C7—41no—
625C2×C7—41no—
626C2×C7—41no—
627C2×C7—81no—
628C2×C7—82no—
629C2×C7—82no—
630C2×C7C2×B(4,𝔽2)11yescharacteristic
631C23—22no—
632C23—22no—
633C23—22no—
634C23—21no—
635C23—41no—
636C23—42no—
637C23—82no—
638C23C7×#12011yescharacteristic
639C23C22×C7×D411yescharacteristic
640C23C22×C7×D411yescharacteristic
641Q8—22no—
642Q8—41no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—81no—
650D4—22no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—41no—
657D4—42no—
658D4—42no—
659D4—42no—
660D4—42no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—81no—
665D4—81no—
666D4—82no—
667D4—82no—
668D4—82no—
669D4—81no—
670D4—81no—
671D4—82no—
672D4—164no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—82no—
698C2×C4—81no—
699C2×C4—82no—
700C2×C4—82no—
701C2×C4C7×#12011yescharacteristic
702C2×C4C7×#12011yescharacteristic
703C2×C4C7×#12011yescharacteristic
704C2×C4C22×C7×D411yescharacteristic
705C8—42no—
706C7#3356011yescharacteristic, direct product factor, Sylow
707C22—21no—
708C22—21no—
709C22—21no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—42no—
715C22—41no—
716C22—42no—
717C22—42no—
718C22—41no—
719C22—42no—
720C22—82no—
721C22—84no—
722C22—82no—
723C22—161no—
724C22C2×C7×#12011yescharacteristic
725C4—21no—
726C4—21no—
727C4—21no—
728C4—41no—
729C4—42no—
730C4—42no—
731C4—41no—
732C4—42no—
733C4—41no—
734C4—42no—
735C4—82no—
736C4—82no—
737C4C7×B(4,𝔽2)11yescharacteristic
738C4C7×B(4,𝔽2)11yescharacteristic
739C2—21no—
740C2—41no—
741C2—41no—
742C2—41no—
743C2—82no—
744C2—81no—
745C2—82no—
746C2C2×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×#3551C2semidirect
2. C7×#3028C2semidirect
3. C7×#3027C2semidirect
4. C7×#3018C2semidirect
5. C7×#2200C2semidirect
6. C7×#2197C2semidirect
7. C7×#2126C2semidirect
8. C7×#2123C2semidirect
9. C7×#2122C2semidirect
13. C7×#560C22semidirect
17. C7×#551C22semidirect
43. C7×#354C22semidirect
44. C7×#353C22semidirect
45. C7×#352C22semidirect
46. C7×AΣL(1,𝔽16)C22semidirect
47. #33560C7direct (N × H)
59. C2×C7×#41D4semidirect
61. C22×C7×Q8D4semidirect
71. C7×C4⋊Q8D4semidirect
86. C7×#124D4semidirect
93. C7×#123D4semidirect
129. C7×#117D4semidirect
132. C2×C42×C7D4semidirect
143. #3551C2×C7semidirect
144. #3028C2×C7semidirect
145. #3027C2×C7semidirect
146. #3018C2×C7semidirect
147. #2200C2×C7semidirect
148. #2197C2×C7semidirect
149. #2126C2×C7semidirect
150. #2123C2×C7semidirect
151. #2122C2×C7semidirect
271. #560C22×C7semidirect
275. #551C22×C7semidirect
301. #354C22×C7semidirect
302. #353C22×C7semidirect
303. #352C22×C7semidirect
304. AΣL(1,𝔽16)C22×C7semidirect
391. C2×#41C7×D4semidirect
393. C22×Q8C7×D4semidirect
403. C4⋊Q8C7×D4semidirect
418. #124C7×D4semidirect
425. #123C7×D4semidirect
461. #117C7×D4semidirect
464. C2×C42C7×D4semidirect
706. C7#33560direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#35512
C7×#30282
C7×#30272
C7×#30182
C7×#22002
C7×#21972
C7×#21262
C7×#21232
C7×#21222
#335607