Finite Group Databasebeta

← C7×#18451 #13195667

Subgroups — C7×#18451 #13195667

Order 1792.

1038 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3537C211yesmaximal, characteristic
2C7×#3196C211yesmaximal, characteristic, complemented
3C7×#3187C211yesmaximal, characteristic, complemented
4C7×#2816C211yesmaximal, characteristic, complemented
5C7×#1618C212yesmaximal, complemented
6C7×#1613C212yesmaximal, complemented
7C7×#1606C212yesmaximal, complemented
8C7×#1601C212yesmaximal, 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×C22⋊Q8C2211yescharacteristic, complemented
26C2×C7×#121C2211yescharacteristic
27C2×C7×#121C2211yescharacteristic
28C7×#485—21no—
29C7×#484C2211yescharacteristic, complemented
30C7×#483—21no—
31C7×#481C2212yescomplemented
32C7×#481C2211yescharacteristic, complemented
33C7×#470—21no—
34C7×#468—21no—
35C7×#465—22no—
36C7×#452—21no—
37C7×#451C2211yescharacteristic, complemented
38C7×#450—21no—
39C7×#448C2212yescomplemented
40C7×#448C2211yescharacteristic, complemented
41C7×#407C2211yescharacteristic, complemented
42C2×C7×C22⋊C8C2211yescharacteristic, complemented
43C7×#399C2212yescomplemented
44C7×#398—21no—
45C7×#394—21no—
46C7×#394—22no—
47C7×#393C2212yescomplemented
48C7×#381C2211yescharacteristic, complemented
49C7×#328C2212yescomplemented
50C7×#327C2212yescomplemented
51C7×#327C2212yescomplemented
52C7×#327C2212yescomplemented
53C7×#323C2212yescomplemented
54C7×#323C2212yescomplemented
55#18451C711yesmaximal, characteristic, direct product factor, Sylow
56C2×C7×#41D411yescharacteristic
57C22×C7×Q8C2311yescharacteristic
58C22×C7×D4—22no—
59C22×C7×D4—21no—
60C22×C7×D4—21no—
61C22×C7×D4—22no—
62C22×C7×D4D412yes—
63C22×C7×D4D411yescharacteristic
64C22×C7×D4D411yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C2×C7×Q16—21no—
67C2×C7×SD16—21no—
68C2×C7×SD16—22no—
69C2×C7×M16—21no—
70C22×C7×C8—21no—
71C7×#127—22no—
72C7×#127—21no—
73C7×#126—22no—
74C7×#126—22no—
75C7×#125—21no—
76C7×#124—22no—
77C7×#123—22no—
78C7×#123—21no—
79C7×#123—22no—
80C7×#123—22no—
81C7×#123—22no—
82C7×C22⋊Q8—21no—
83C7×C22⋊Q8—21no—
84C7×C22⋊Q8—21no—
85C7×C22⋊Q8—21no—
86C7×C22⋊Q8D411yescharacteristic
87C7×C22⋊Q8C2311yescharacteristic
88C7×#121—22no—
89C7×#121—21no—
90C7×#121—21no—
91C7×#121—22no—
92C7×#121—22no—
93C7×#121—22no—
94C7×#121—22no—
95C7×#121—21no—
96C7×#121—21no—
97C7×#121—21no—
98C7×#121—21no—
99C7×#121—21no—
100C7×#121—21no—
101C7×#121—22no—
102C7×#121D411yescharacteristic
103C7×#121D412yes—
104C7×#121C2312yes—
105C7×#121C2311yescharacteristic
106C7×#120—22no—
107C7×#120—22no—
108C7×#120—22no—
109C7×#120—21no—
110C7×#120—22no—
111C7×#120—22no—
112C7×#120—22no—
113C4×C7×D4—22no—
114C4×C7×D4—21no—
115C4×C7×D4—21no—
116C4×C7×D4—21no—
117C4×C7×D4—21no—
118C4×C7×D4—22no—
119C7×#117—21no—
120C7×#117D411yescharacteristic
121C2×C7×C4⋊C4—21no—
122C2×C7×C4⋊C4—22no—
123C2×C7×C4⋊C4D411yescharacteristic
124C2×C7×C4⋊C4D411yescharacteristic
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—21no—
133C7×#106—21no—
134C7×#106—22no—
135C7×#103—21no—
136C7×#103—21no—
137C7×#103—21no—
138C7×#103—22no—
139C7×#102—21no—
140C7×#102—22no—
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
150#3196C2×C711yescharacteristic, complemented
151#3187C2×C711yescharacteristic, complemented
152#2816C2×C711yescharacteristic, complemented
153#1618C2×C712yescomplemented
154#1613C2×C712yescomplemented
155#1606C2×C712yescomplemented
156#1601C2×C712yescomplemented
157#1516C2×C711yescharacteristic, complemented
158#1510C2×C711yescharacteristic, complemented
159#1471C2×C711yescharacteristic, complemented
160C24×C7—22no—
161C24×C7—21no—
162C24×C7C2×D412yes—
163C24×C7C2×D411yescharacteristic
164C7×#41—81no—
165C2×C7×Q8—21no—
166C2×C7×Q8—21no—
167C2×C7×Q8—81no—
168C2×C7×Q8C2×D411yescharacteristic
169C2×C7×D4—22no—
170C2×C7×D4—21no—
171C2×C7×D4—21no—
172C2×C7×D4—22no—
173C2×C7×D4—22no—
174C2×C7×D4—22no—
175C2×C7×D4—22no—
176C2×C7×D4—22no—
177C2×C7×D4—22no—
178C2×C7×D4—21no—
179C2×C7×D4—22no—
180C2×C7×D4—22no—
181C2×C7×D4—21no—
182C2×C7×D4—21no—
183C2×C7×D4—21no—
184C2×C7×D4—81no—
185C2×C7×D4—82no—
186C2×C7×D4—81no—
187C2×C7×D4—82no—
188C2×C7×D4—82no—
189C2×C7×D4—84no—
190C2×C7×D4—84no—
191C2×C7×D4C2×D411yescharacteristic
192C2×C7×D4C2×D412yes—
193C22×C4×C7—22no—
194C22×C4×C7—22no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—22no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—81no—
201C22×C4×C7C2×D412yes—
202C22×C4×C7C2×D411yescharacteristic
203C22×C4×C7C2×D411yescharacteristic
204C22×C4×C7C2×D411yescharacteristic
205C22×C4×C7C2×D411yescharacteristic
206C22×C4×C7C2×D411yescharacteristic
207C22×C4×C7C2411yescharacteristic
208C7×Q16—81no—
209C7×SD16—82no—
210C7×SD16—81no—
211C7×M16—81no—
212C2×C7×C8—22no—
213C2×C7×C8—21no—
214C2×C7×C8—21no—
215C2×C7×C8—81no—
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—21no—
224C7×C4⋊C4—21no—
225C7×C4⋊C4—41no—
226C7×C4⋊C4—41no—
227C7×C4⋊C4—82no—
228C7×C4⋊C4C2×D412yes—
229C7×C4⋊C4C2×D411yescharacteristic
230C7×C4⋊C4C2×D411yescharacteristic
231C7×C22⋊C4—22no—
232C7×C22⋊C4—22no—
233C7×C22⋊C4—22no—
234C7×C22⋊C4—22no—
235C7×C22⋊C4—22no—
236C7×C22⋊C4—21no—
237C7×C22⋊C4—21no—
238C7×C22⋊C4—21no—
239C7×C22⋊C4—22no—
240C7×C22⋊C4—21no—
241C7×C22⋊C4—22no—
242C7×C22⋊C4—22no—
243C7×C22⋊C4—22no—
244C7×C22⋊C4—21no—
245C7×C22⋊C4—41no—
246C7×C22⋊C4—41no—
247C7×C22⋊C4—81no—
248C7×C22⋊C4—82no—
249C7×C22⋊C4—82no—
250C42×C7—22no—
251C42×C7—21no—
252#560—22no—
253#553—21no—
254#553—21no—
255D42—22no—
256D42—21no—
257D42—21no—
258#540—21no—
259#538—21no—
260#538C22×C712yes—
261#535—21no—
262#534—21no—
263#534C22×C712yes—
264#525C22×C711yescharacteristic
265C2×C22⋊Q8C22×C711yescharacteristic, complemented
266C2×#121C22×C711yescharacteristic
267C2×#121C22×C711yescharacteristic
268#485—21no—
269#484C22×C711yescharacteristic, complemented
270#483—21no—
271#481C22×C711yescharacteristic, complemented
272#481C22×C712yescomplemented
273#470—21no—
274#468—21no—
275#465—22no—
276#452—21no—
277#451C22×C711yescharacteristic, complemented
278#450—21no—
279#448C22×C711yescharacteristic, complemented
280#448C22×C712yescomplemented
281#407C22×C711yescharacteristic, complemented
282C2×C22⋊C8C22×C711yescharacteristic, complemented
283#399C22×C712yescomplemented
284#398—21no—
285#394—21no—
286#394—22no—
287#393C22×C712yescomplemented
288#381C22×C711yescharacteristic, complemented
289#328C22×C712yescomplemented
290#327C22×C712yescomplemented
291#327C22×C712yescomplemented
292#327C22×C712yescomplemented
293#323C22×C712yescomplemented
294#323C22×C712yescomplemented
295C23×C7—22no—
296C23×C7—22no—
297C23×C7—22no—
298C23×C7—21no—
299C23×C7—24no—
300C23×C7—41no—
301C23×C7—41no—
302C23×C7—42no—
303C23×C7—42no—
304C23×C7—42no—
305C23×C7—81no—
306C23×C7—81no—
307C23×C7—82no—
308C23×C7—82no—
309C23×C7—82no—
310C23×C7#12011yescharacteristic
311C23×C7#12011yescharacteristic
312C23×C7C22×D411yescharacteristic
313C7×Q8—41no—
314C7×Q8—42no—
315C7×Q8—41no—
316C7×Q8—41no—
317C7×D4—42no—
318C7×D4—41no—
319C7×D4—42no—
320C7×D4—42no—
321C7×D4—44no—
322C7×D4—42no—
323C7×D4—44no—
324C7×D4—42no—
325C7×D4—81no—
326C7×D4—82no—
327C7×D4—82no—
328C7×D4—81no—
329C7×D4—82no—
330C7×D4—82no—
331C7×D4—82no—
332C7×D4—82no—
333C7×D4—82no—
334C2×C4×C7—21no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—21no—
338C2×C4×C7—21no—
339C2×C4×C7—41no—
340C2×C4×C7—41no—
341C2×C4×C7—41no—
342C2×C4×C7—41no—
343C2×C4×C7—41no—
344C2×C4×C7—41no—
345C2×C4×C7—42no—
346C2×C4×C7—42no—
347C2×C4×C7—42no—
348C2×C4×C7—41no—
349C2×C4×C7—42no—
350C2×C4×C7—42no—
351C2×C4×C7—41no—
352C2×C4×C7—41no—
353C2×C4×C7—41no—
354C2×C4×C7—42no—
355C2×C4×C7—81no—
356C2×C4×C7—82no—
357C2×C4×C7—82no—
358C2×C4×C7#12011yescharacteristic
359C2×C4×C7#12011yescharacteristic
360C2×C4×C7C22×D411yescharacteristic
361C2×C4×C7C22×D411yescharacteristic
362C7×C8—42no—
363C7×C8—41no—
364C7×C8—41no—
365C2×#41C7×D411yescharacteristic
366C22×Q8C23×C711yescharacteristic
367C22×D4—22no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—22no—
371C22×D4C7×D412yes—
372C22×D4C7×D411yescharacteristic
373C22×D4C7×D411yescharacteristic
374C23×C4C23×C711yescharacteristic
375C2×Q16—21no—
376C2×SD16—22no—
377C2×SD16—21no—
378C2×M16—21no—
379C22×C8—21no—
380#127—22no—
381#127—21no—
382#126—22no—
383#126—22no—
384#125—21no—
385#124—22no—
386#123—22no—
387#123—21no—
388#123—22no—
389#123—22no—
390#123—22no—
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393C22⋊Q8—21no—
394C22⋊Q8—21no—
395C22⋊Q8C7×D411yescharacteristic
396C22⋊Q8C23×C711yescharacteristic
397#121—22no—
398#121—21no—
399#121—21no—
400#121—22no—
401#121—22no—
402#121—22no—
403#121—22no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—21no—
408#121—21no—
409#121—21no—
410#121—22no—
411#121C7×D412yes—
412#121C7×D411yescharacteristic
413#121C23×C712yes—
414#121C23×C711yescharacteristic
415#120—22no—
416#120—22no—
417#120—22no—
418#120—21no—
419#120—22no—
420#120—22no—
421#120—22no—
422C4×D4—22no—
423C4×D4—21no—
424C4×D4—21no—
425C4×D4—21no—
426C4×D4—21no—
427C4×D4—22no—
428#117—21no—
429#117C7×D411yescharacteristic
430C2×C4⋊C4—21no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4C7×D411yescharacteristic
433C2×C4⋊C4C7×D411yescharacteristic
434C2×C4⋊C4C23×C711yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4C23×C712yes—
441#107—21no—
442#106—22no—
443#106—21no—
444#103—21no—
445#103—22no—
446#103—21no—
447#103—21no—
448#102—22no—
449#102—21no—
450C22⋊C8—21no—
451C22⋊C8—21no—
452C22⋊C8C23×C711yescharacteristic
453C22⋊C8C23×C711yescharacteristic
454C22⋊C8C23×C712yes—
455#95—21no—
456#95—22no—
457#95C23×C712yes—
458C22×C7—21no—
459C22×C7—21no—
460C22×C7—21no—
461C22×C7—21no—
462C22×C7—21no—
463C22×C7—21no—
464C22×C7—21no—
465C22×C7—21no—
466C22×C7—42no—
467C22×C7—42no—
468C22×C7—41no—
469C22×C7—42no—
470C22×C7—42no—
471C22×C7—41no—
472C22×C7—41no—
473C22×C7—42no—
474C22×C7—42no—
475C22×C7—82no—
476C22×C7—84no—
477C22×C7—162no—
478C22×C7—164no—
479C22×C7C2×#12011yescharacteristic
480C22×C7#57712yes—
481C4×C7—21no—
482C4×C7—21no—
483C4×C7—21no—
484C4×C7—21no—
485C4×C7—42no—
486C4×C7—41no—
487C4×C7—42no—
488C4×C7—41no—
489C4×C7—41no—
490C4×C7—82no—
491C4×C7—81no—
492C4×C7—81no—
493C24—22no—
494C24—21no—
495C24C2×C7×D412yes—
496C24C2×C7×D411yescharacteristic
497#41—81no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—81no—
501C2×Q8C2×C7×D411yescharacteristic
502C2×D4—22no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—21no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—81no—
518C2×D4—82no—
519C2×D4—81no—
520C2×D4—82no—
521C2×D4—82no—
522C2×D4—84no—
523C2×D4—84no—
524C2×D4C2×C7×D411yescharacteristic
525C2×D4C2×C7×D412yes—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—81no—
534C22×C4C2×C7×D412yes—
535C22×C4C2×C7×D411yescharacteristic
536C22×C4C2×C7×D411yescharacteristic
537C22×C4C2×C7×D411yescharacteristic
538C22×C4C2×C7×D411yescharacteristic
539C22×C4C2×C7×D411yescharacteristic
540C22×C4C24×C711yescharacteristic
541Q16—81no—
542SD16—82no—
543SD16—81no—
544M16—81no—
545C2×C8—22no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—81no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—41no—
559C4⋊C4—41no—
560C4⋊C4—82no—
561C4⋊C4C2×C7×D412yes—
562C4⋊C4C2×C7×D411yescharacteristic
563C4⋊C4C2×C7×D411yescharacteristic
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—21no—
570C22⋊C4—21no—
571C22⋊C4—21no—
572C22⋊C4—22no—
573C22⋊C4—21no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—21no—
578C22⋊C4—41no—
579C22⋊C4—41no—
580C22⋊C4—81no—
581C22⋊C4—82no—
582C22⋊C4—82no—
583C42—22no—
584C42—21no—
585C2×C7—22no—
586C2×C7—41no—
587C2×C7—41no—
588C2×C7—82no—
589C2×C7—82no—
590C2×C7—81no—
591C2×C7#300911yescharacteristic
592C2×C7#301911yescharacteristic
593C2×C7#302611yescharacteristic
594C23—22no—
595C23—22no—
596C23—22no—
597C23—21no—
598C23—24no—
599C23—41no—
600C23—41no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—81no—
605C23—81no—
606C23—82no—
607C23—82no—
608C23—82no—
609C23C7×#12011yescharacteristic
610C23C7×#12011yescharacteristic
611C23C22×C7×D411yescharacteristic
612Q8—41no—
613Q8—42no—
614Q8—41no—
615Q8—41no—
616D4—42no—
617D4—41no—
618D4—42no—
619D4—42no—
620D4—44no—
621D4—42no—
622D4—44no—
623D4—42no—
624D4—81no—
625D4—82no—
626D4—82no—
627D4—81no—
628D4—82no—
629D4—82no—
630D4—82no—
631D4—82no—
632D4—82no—
633C2×C4—21no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—41no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—42no—
654C2×C4—81no—
655C2×C4—82no—
656C2×C4—82no—
657C2×C4C7×#12011yescharacteristic
658C2×C4C7×#12011yescharacteristic
659C2×C4C22×C7×D411yescharacteristic
660C2×C4C22×C7×D411yescharacteristic
661C8—42no—
662C8—41no—
663C8—41no—
664C7#1845111yescharacteristic, direct product factor, Sylow
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—42no—
674C22—42no—
675C22—41no—
676C22—42no—
677C22—42no—
678C22—41no—
679C22—41no—
680C22—42no—
681C22—42no—
682C22—82no—
683C22—84no—
684C22—162no—
685C22—164no—
686C22C2×C7×#12011yescharacteristic
687C22C7×#57712yes—
688C4—21no—
689C4—21no—
690C4—21no—
691C4—21no—
692C4—42no—
693C4—41no—
694C4—42no—
695C4—41no—
696C4—41no—
697C4—82no—
698C4—81no—
699C4—81no—
700C2—22no—
701C2—41no—
702C2—41no—
703C2—82no—
704C2—82no—
705C2—81no—
706C2C7×#300911yescharacteristic
707C2C7×#301911yescharacteristic
708C2C7×#302611yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC7×#3537C2
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
2. C7×#3196C2semidirect
3. C7×#3187C2semidirect
4. C7×#2816C2semidirect
5. C7×#1618C2semidirect
6. C7×#1613C2semidirect
7. C7×#1606C2semidirect
8. C7×#1601C2semidirect
9. C7×#1516C2semidirect
10. C7×#1510C2semidirect
11. C7×#1471C2semidirect
25. C2×C7×C22⋊Q8C22semidirect
29. C7×#484C22semidirect
31. C7×#481C22semidirect
32. C7×#481C22semidirect
37. C7×#451C22semidirect
39. C7×#448C22semidirect
40. C7×#448C22semidirect
41. C7×#407C22semidirect
42. C2×C7×C22⋊C8C22semidirect
43. C7×#399C22semidirect
47. C7×#393C22semidirect
48. C7×#381C22semidirect
49. C7×#328C22semidirect
50. C7×#327C22semidirect
51. C7×#327C22semidirect
52. C7×#327C22semidirect
53. C7×#323C22semidirect
54. C7×#323C22semidirect
55. #18451C7direct (N × H)
150. #3196C2×C7semidirect
151. #3187C2×C7semidirect
152. #2816C2×C7semidirect
153. #1618C2×C7semidirect
154. #1613C2×C7semidirect
155. #1606C2×C7semidirect
156. #1601C2×C7semidirect
157. #1516C2×C7semidirect
158. #1510C2×C7semidirect
159. #1471C2×C7semidirect
265. C2×C22⋊Q8C22×C7semidirect
269. #484C22×C7semidirect
271. #481C22×C7semidirect
272. #481C22×C7semidirect
277. #451C22×C7semidirect
279. #448C22×C7semidirect
280. #448C22×C7semidirect
281. #407C22×C7semidirect
282. C2×C22⋊C8C22×C7semidirect
283. #399C22×C7semidirect
287. #393C22×C7semidirect
288. #381C22×C7semidirect
289. #328C22×C7semidirect
290. #327C22×C7semidirect
291. #327C22×C7semidirect
292. #327C22×C7semidirect
293. #323C22×C7semidirect
294. #323C22×C7semidirect
664. C7#18451direct (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×#31962
C7×#31872
C7×#28162
C7×#16182
C7×#16132
C7×#16062
C7×#16012
C7×#15162
C7×#15102
C7×#14712
#184517