Finite Group Databasebeta

← C7×#18788 #13196004

Subgroups — C7×#18788 #13196004

Order 1792.

1032 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×Q8×#41C211yesmaximal, characteristic, complemented
2C7×#3208C211yesmaximal, characteristic, complemented
3C7×#3038C211yesmaximal, characteristic
4C2×C7×#460C211yesmaximal, characteristic, complemented
5C7×#1627C212yesmaximal, complemented
6C7×#1626C212yesmaximal, complemented
7C7×#1623C212yesmaximal, complemented
8C7×#1622C212yesmaximal, complemented
9C7×#1550C211yesmaximal, characteristic, complemented
10C7×#1487C211yesmaximal, characteristic, complemented
11C7×#1477C211yesmaximal, characteristic, complemented
12C2×C7×AGL(1,ℤ/8)—21no—
13C22×C7×SD16—21no—
14C7×Q82C2211yescharacteristic, complemented
15C7×#557—21no—
16C7×#557C2211yescharacteristic, complemented
17C7×#554—22no—
18C7×#554—21no—
19C7×#554—21no—
20C7×#554C2211yescharacteristic, complemented
21C7×D4×Q8—21no—
22C7×D4×Q8C2211yescharacteristic, complemented
23C7×#533—22no—
24C7×#533—21no—
25C7×#533—21no—
26C7×#533C2211yescharacteristic
27C2×C7×#127C2211yescharacteristic
28C4×C7×#41—21no—
29C4×C7×#41C2211yescharacteristic
30C2×C4×C7×Q8—21no—
31C2×C4×C7×Q8C2211yescharacteristic
32C7×#492C2212yes—
33C7×#486C2212yes—
34C7×#460—22no—
35C7×#460—21no—
36C7×#460—21no—
37C7×#460—21no—
38C7×#460C2212yes—
39C7×#460C2212yes—
40C7×#460C2212yes—
41C7×#459—21no—
42C7×#459C2212yes—
43C7×#450—22no—
44C7×#431C2211yescharacteristic
45C7×#423C2211yescharacteristic
46C2×C7×C4⋊C8C2211yescharacteristic
47C7×#418—21no—
48C2×C7×#102—21no—
49C7×#333C2212yescomplemented
50C7×#332C2212yescomplemented
51C7×Q8⋊C8C2212yescomplemented
52C7×Q8⋊C8C2212yescomplemented
53C7×Q8⋊C8C2212yescomplemented
54C7×D4⋊C8C2212yescomplemented
55#18788C711yesmaximal, characteristic, direct product factor, Sylow
56C2×C7×#41D411yescharacteristic
57C22×C7×Q8—21no—
58C22×C7×Q8D411yescharacteristic
59C22×C7×D4—21no—
60C22×C7×D4—21no—
61C22×C7×D4—21no—
62C7×AGL(1,ℤ/8)—44no—
63C2×C7×SD16—22no—
64C2×C7×SD16—22no—
65C2×C7×SD16—22no—
66C2×C7×SD16—24no—
67C2×C7×SD16—44no—
68C2×C7×D8—22no—
69C2×C7×M16—21no—
70C22×C7×C8—21no—
71C7×C4⋊Q8—22no—
72C7×C4⋊Q8—21no—
73C7×C4⋊Q8—22no—
74C7×C4⋊Q8—21no—
75C7×C4⋊Q8—21no—
76C7×C4⋊Q8—21no—
77C7×C4⋊Q8C2311yescharacteristic
78C7×C4⋊Q8C2311yescharacteristic
79C7×#127—21no—
80C7×#127—21no—
81C7×#127—21no—
82C7×#127C2312yes—
83C7×#125—22no—
84C7×#125—22no—
85C7×#125—22no—
86C7×#125—21no—
87C7×#125—21no—
88C7×#125—21no—
89C7×C22⋊Q8—22no—
90C7×C22⋊Q8—22no—
91C7×C22⋊Q8—22no—
92C7×C22⋊Q8—22no—
93C7×C22⋊Q8—22no—
94C7×C22⋊Q8—21no—
95C7×C22⋊Q8—22no—
96C7×C22⋊Q8—21no—
97C7×C22⋊Q8—21no—
98C7×C22⋊Q8—22no—
99C7×C22⋊Q8D412yes—
100C4×C7×Q8—22no—
101C4×C7×Q8—22no—
102C4×C7×Q8—22no—
103C4×C7×Q8—21no—
104C4×C7×Q8—21no—
105C4×C7×Q8—21no—
106C4×C7×Q8—21no—
107C4×C7×Q8—21no—
108C4×C7×Q8—21no—
109C4×C7×Q8—21no—
110C4×C7×Q8D411yescharacteristic
111C4×C7×Q8D411yescharacteristic
112C4×C7×Q8D411yescharacteristic
113C4×C7×Q8D412yes—
114C4×C7×Q8C2311yescharacteristic
115C4×C7×Q8C2311yescharacteristic
116C4×C7×Q8C2311yescharacteristic
117C4×C7×D4—22no—
118C4×C7×D4—22no—
119C4×C7×D4—21no—
120C4×C7×D4—21no—
121C4×C7×D4—21no—
122C4×C7×D4—21no—
123C4×C7×D4D411yescharacteristic
124C4×C7×D4C2311yescharacteristic
125C7×#117—22no—
126C7×#117—21no—
127C7×#117—21no—
128C7×#117D411yescharacteristic
129C2×C7×C4⋊C4—22no—
130C2×C7×C4⋊C4—21no—
131C2×C7×C4⋊C4—21no—
132C2×C7×C4⋊C4D411yescharacteristic
133C2×C42×C7—22no—
134C2×C42×C7—21no—
135C2×C42×C7—21no—
136C2×C42×C7C2311yescharacteristic
137C7×C4⋊C8—21no—
138C7×C4⋊C8—21no—
139C7×C4⋊C8—21no—
140C7×C4⋊C8C2312yes—
141C7×C4⋊C8C2312yes—
142C7×#102—24no—
143C7×#102—22no—
144C7×#102—22no—
145C7×#102—22no—
146C7×#102—22no—
147C7×C22⋊C8—21no—
148C4×C7×C8C2312yes—
149Q8×#41C2×C711yescharacteristic, complemented
150#3208C2×C711yescharacteristic, complemented
151#3038C2×C711yescharacteristic
152C2×#460C2×C711yescharacteristic, complemented
153#1627C2×C712yescomplemented
154#1626C2×C712yescomplemented
155#1623C2×C712yescomplemented
156#1622C2×C712yescomplemented
157#1550C2×C711yescharacteristic, complemented
158#1487C2×C711yescharacteristic, complemented
159#1477C2×C711yescharacteristic, complemented
160C24×C7—41no—
161C7×#41—22no—
162C7×#41SD1614yescomplemented
163C2×C7×Q8—22no—
164C2×C7×Q8—22no—
165C2×C7×Q8—21no—
166C2×C7×Q8—21no—
167C2×C7×Q8—22no—
168C2×C7×Q8—41no—
169C2×C7×Q8—42no—
170C2×C7×Q8—42no—
171C2×C7×Q8C2×D411yescharacteristic
172C2×C7×Q8C2×D411yescharacteristic
173C2×C7×Q8C2×D411yescharacteristic
174C2×C7×Q8C2×D412yes—
175C2×C7×D4—21no—
176C2×C7×D4—22no—
177C2×C7×D4—22no—
178C2×C7×D4—22no—
179C2×C7×D4—42no—
180C2×C7×D4—42no—
181C2×C7×D4—41no—
182C2×C7×D4—41no—
183C2×C7×D4—41no—
184C2×C7×D4—42no—
185C2×C7×D4—42no—
186C2×C7×D4—82no—
187C2×C7×D4C2×D411yescharacteristic
188C22×C4×C7—21no—
189C22×C4×C7—22no—
190C22×C4×C7—21no—
191C22×C4×C7—22no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7C2×D411yescharacteristic
196C22×C4×C7C2×D411yescharacteristic
197C22×C4×C7C2×D411yescharacteristic
198C7×SD16—44no—
199C7×SD16—44no—
200C7×SD16—44no—
201C7×SD16—84no—
202C7×D8—44no—
203C7×M16—42no—
204C2×C7×C8—22no—
205C2×C7×C8—22no—
206C2×C7×C8—22no—
207C2×C7×C8—42no—
208C7×C4⋊C4—22no—
209C7×C4⋊C4—22no—
210C7×C4⋊C4—22no—
211C7×C4⋊C4—22no—
212C7×C4⋊C4—22no—
213C7×C4⋊C4—22no—
214C7×C4⋊C4—22no—
215C7×C4⋊C4—22no—
216C7×C4⋊C4—21no—
217C7×C4⋊C4—22no—
218C7×C4⋊C4—21no—
219C7×C4⋊C4—21no—
220C7×C4⋊C4—21no—
221C7×C4⋊C4—22no—
222C7×C4⋊C4—21no—
223C7×C4⋊C4—21no—
224C7×C4⋊C4—21no—
225C7×C4⋊C4—21no—
226C7×C4⋊C4—21no—
227C7×C4⋊C4—21no—
228C7×C4⋊C4C2×D411yescharacteristic
229C7×C4⋊C4C2×D411yescharacteristic
230C7×C4⋊C4C2×D411yescharacteristic
231C7×C4⋊C4C2×D411yescharacteristic
232C7×C4⋊C4C2×D412yes—
233C7×C22⋊C4—22no—
234C7×C22⋊C4—22no—
235C7×C22⋊C4—22no—
236C7×C22⋊C4—21no—
237C7×C22⋊C4—21no—
238C7×C22⋊C4—21no—
239C42×C7—22no—
240C42×C7—22no—
241C42×C7—21no—
242C42×C7—22no—
243C42×C7—21no—
244C42×C7—21no—
245C42×C7—21no—
246C42×C7—21no—
247C42×C7—21no—
248C42×C7—21no—
249C42×C7C2×D411yescharacteristic
250C42×C7C2×D411yescharacteristic
251C42×C7C2×D411yescharacteristic
252C42×C7C2411yescharacteristic
253C2×AGL(1,ℤ/8)—21no—
254C22×SD16—21no—
255Q82C22×C711yescharacteristic, complemented
256#557—21no—
257#557C22×C711yescharacteristic, complemented
258#554—22no—
259#554—21no—
260#554—21no—
261#554C22×C711yescharacteristic, complemented
262D4×Q8—21no—
263D4×Q8C22×C711yescharacteristic, complemented
264#533—22no—
265#533—21no—
266#533—21no—
267#533C22×C711yescharacteristic
268C2×#127C22×C711yescharacteristic
269C4×#41—21no—
270C4×#41C22×C711yescharacteristic
271C2×C4×Q8—21no—
272C2×C4×Q8C22×C711yescharacteristic
273#492C22×C712yes—
274#486C22×C712yes—
275#460—22no—
276#460—21no—
277#460—21no—
278#460—21no—
279#460C22×C712yes—
280#460C22×C712yes—
281#460C22×C712yes—
282#459—21no—
283#459C22×C712yes—
284#450—22no—
285#431C22×C711yescharacteristic
286#423C22×C711yescharacteristic
287C2×C4⋊C8C22×C711yescharacteristic
288#418—21no—
289C2×#102—21no—
290#333C22×C712yescomplemented
291#332C22×C712yescomplemented
292Q8⋊C8C22×C712yescomplemented
293Q8⋊C8C22×C712yescomplemented
294Q8⋊C8C22×C712yescomplemented
295D4⋊C8C22×C712yescomplemented
296C23×C7—21no—
297C23×C7—42no—
298C23×C7—82no—
299C23×C7—82no—
300C23×C7—82no—
301C23×C7#12011yescharacteristic
302C7×Q8—21no—
303C7×Q8—21no—
304C7×Q8—21no—
305C7×Q8—21no—
306C7×Q8—42no—
307C7×Q8—42no—
308C7×Q8—44no—
309C7×Q8—41no—
310C7×Q8—41no—
311C7×Q8—82no—
312C7×Q8C2×SD1612yescomplemented
313C7×Q8AGL(1,ℤ/8)12yescomplemented
314C7×D4—24no—
315C7×D4—21no—
316C7×D4—44no—
317C7×D4—42no—
318C7×D4—42no—
319C7×D4—42no—
320C7×D4—42no—
321C7×D4—82no—
322C7×D4—82no—
323C7×D4—82no—
324C7×D4C2×SD1612yescomplemented
325C2×C4×C7—21no—
326C2×C4×C7—21no—
327C2×C4×C7—21no—
328C2×C4×C7—21no—
329C2×C4×C7—24no—
330C2×C4×C7—21no—
331C2×C4×C7—21no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—21no—
335C2×C4×C7—21no—
336C2×C4×C7—21no—
337C2×C4×C7—41no—
338C2×C4×C7—42no—
339C2×C4×C7—44no—
340C2×C4×C7—41no—
341C2×C4×C7—41no—
342C2×C4×C7—81no—
343C2×C4×C7—81no—
344C2×C4×C7—82no—
345C2×C4×C7#12011yescharacteristic
346C2×C4×C7#12011yescharacteristic
347C2×C4×C7#12011yescharacteristic
348C2×C4×C7C2×SD1612yes—
349C2×C4×C7#13712yes—
350C2×C4×C7C22×D411yescharacteristic
351C2×C4×C7C22×D411yescharacteristic
352C2×C4×C7C22×D411yescharacteristic
353C7×C8—42no—
354C7×C8—42no—
355C7×C8—42no—
356C2×#41C7×D411yescharacteristic
357C22×Q8—21no—
358C22×Q8C7×D411yescharacteristic
359C22×D4—21no—
360C22×D4—21no—
361C22×D4—21no—
362AGL(1,ℤ/8)—44no—
363C2×SD16—22no—
364C2×SD16—22no—
365C2×SD16—22no—
366C2×SD16—24no—
367C2×SD16—44no—
368C2×D8—22no—
369C2×M16—21no—
370C22×C8—21no—
371C4⋊Q8—22no—
372C4⋊Q8—21no—
373C4⋊Q8—22no—
374C4⋊Q8—21no—
375C4⋊Q8—21no—
376C4⋊Q8—21no—
377C4⋊Q8C23×C711yescharacteristic
378C4⋊Q8C23×C711yescharacteristic
379#127—21no—
380#127—21no—
381#127—21no—
382#127C23×C712yes—
383#125—22no—
384#125—22no—
385#125—22no—
386#125—21no—
387#125—21no—
388#125—21no—
389C22⋊Q8—22no—
390C22⋊Q8—22no—
391C22⋊Q8—22no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8—21no—
395C22⋊Q8—22no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—22no—
399C22⋊Q8C7×D412yes—
400C4×Q8—22no—
401C4×Q8—22no—
402C4×Q8—22no—
403C4×Q8—21no—
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8—21no—
407C4×Q8—21no—
408C4×Q8—21no—
409C4×Q8—21no—
410C4×Q8C7×D411yescharacteristic
411C4×Q8C7×D411yescharacteristic
412C4×Q8C7×D411yescharacteristic
413C4×Q8C7×D412yes—
414C4×Q8C23×C711yescharacteristic
415C4×Q8C23×C711yescharacteristic
416C4×Q8C23×C711yescharacteristic
417C4×D4—22no—
418C4×D4—22no—
419C4×D4—21no—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4C7×D411yescharacteristic
424C4×D4C23×C711yescharacteristic
425#117—22no—
426#117—21no—
427#117—21no—
428#117C7×D411yescharacteristic
429C2×C4⋊C4—22no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4C7×D411yescharacteristic
433C2×C42—22no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42C23×C711yescharacteristic
437C4⋊C8—21no—
438C4⋊C8—21no—
439C4⋊C8—21no—
440C4⋊C8C23×C712yes—
441C4⋊C8C23×C712yes—
442#102—22no—
443#102—22no—
444#102—22no—
445#102—22no—
446#102—24no—
447C22⋊C8—21no—
448C4×C8C23×C712yes—
449C22×C7—21no—
450C22×C7—21no—
451C22×C7—22no—
452C22×C7—41no—
453C22×C7—41no—
454C22×C7—82no—
455C22×C7—82no—
456C22×C7—82no—
457C22×C7—164no—
458C22×C7#44812yes—
459C22×C7C2×#12011yescharacteristic
460C4×C7—22no—
461C4×C7—21no—
462C4×C7—22no—
463C4×C7—21no—
464C4×C7—21no—
465C4×C7—41no—
466C4×C7—42no—
467C4×C7—41no—
468C4×C7—41no—
469C4×C7—42no—
470C4×C7—41no—
471C4×C7—41no—
472C4×C7#44812yes—
473C4×C7C22×SD1611yescharacteristic
474C4×C7C2×AGL(1,ℤ/8)11yescharacteristic
475C4×C7C2×#13711yescharacteristic
476C4×C7#57511yescharacteristic
477C24—41no—
478#41—22no—
479#41C7×SD1614yescomplemented
480C2×Q8—22no—
481C2×Q8—22no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—22no—
485C2×Q8—41no—
486C2×Q8—42no—
487C2×Q8—42no—
488C2×Q8C2×C7×D411yescharacteristic
489C2×Q8C2×C7×D411yescharacteristic
490C2×Q8C2×C7×D411yescharacteristic
491C2×Q8C2×C7×D412yes—
492C2×D4—21no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—41no—
499C2×D4—41no—
500C2×D4—41no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—82no—
504C2×D4C2×C7×D411yescharacteristic
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4C2×C7×D411yescharacteristic
513C22×C4C2×C7×D411yescharacteristic
514C22×C4C2×C7×D411yescharacteristic
515SD16—44no—
516SD16—44no—
517SD16—44no—
518SD16—84no—
519D8—44no—
520M16—42no—
521C2×C8—22no—
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—42no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—21no—
534C4⋊C4—22no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—22no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4C2×C7×D411yescharacteristic
546C4⋊C4C2×C7×D411yescharacteristic
547C4⋊C4C2×C7×D411yescharacteristic
548C4⋊C4C2×C7×D411yescharacteristic
549C4⋊C4C2×C7×D412yes—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—21no—
554C22⋊C4—21no—
555C22⋊C4—21no—
556C42—22no—
557C42—22no—
558C42—21no—
559C42—22no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42C2×C7×D411yescharacteristic
567C42C2×C7×D411yescharacteristic
568C42C2×C7×D411yescharacteristic
569C42C24×C711yescharacteristic
570C2×C7—22no—
571C2×C7—42no—
572C2×C7—162no—
573C2×C7C2×#44811yescharacteristic
574C2×C7#300611yescharacteristic
575C2×C7#302111yescharacteristic
576C23—21no—
577C23—42no—
578C23—82no—
579C23—82no—
580C23—82no—
581C23C7×#12011yescharacteristic
582Q8—21no—
583Q8—21no—
584Q8—21no—
585Q8—21no—
586Q8—42no—
587Q8—42no—
588Q8—44no—
589Q8—41no—
590Q8—41no—
591Q8—82no—
592Q8C2×C7×SD1612yescomplemented
593Q8C7×AGL(1,ℤ/8)12yescomplemented
594D4—24no—
595D4—21no—
596D4—44no—
597D4—42no—
598D4—42no—
599D4—42no—
600D4—42no—
601D4—82no—
602D4—82no—
603D4—82no—
604D4C2×C7×SD1612yescomplemented
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—24no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—44no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—81no—
623C2×C4—81no—
624C2×C4—82no—
625C2×C4C7×#12011yescharacteristic
626C2×C4C7×#12011yescharacteristic
627C2×C4C7×#12011yescharacteristic
628C2×C4C2×C7×SD1612yes—
629C2×C4C7×#13712yes—
630C2×C4C22×C7×D411yescharacteristic
631C2×C4C22×C7×D411yescharacteristic
632C2×C4C22×C7×D411yescharacteristic
633C8—42no—
634C8—42no—
635C8—42no—
636C7#1878811yescharacteristic, direct product factor, Sylow
637C22—21no—
638C22—21no—
639C22—22no—
640C22—41no—
641C22—41no—
642C22—82no—
643C22—82no—
644C22—82no—
645C22—164no—
646C22C7×#44812yes—
647C22C2×C7×#12011yescharacteristic
648C4—22no—
649C4—21no—
650C4—22no—
651C4—21no—
652C4—21no—
653C4—41no—
654C4—42no—
655C4—41no—
656C4—41no—
657C4—42no—
658C4—41no—
659C4—41no—
660C4C7×#44812yes—
661C4C22×C7×SD1611yescharacteristic
662C4C2×C7×AGL(1,ℤ/8)11yescharacteristic
663C4C2×C7×#13711yescharacteristic
664C4C7×#57511yescharacteristic
665C2—22no—
666C2—42no—
667C2—162no—
668C2C2×C7×#44811yescharacteristic
669C2C7×#300611yescharacteristic
670C2C7×#302111yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC42C24×C7
prime radicalC7×#3038C2
LCSG ▷ C42 ▷ 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×Q8×#41C2semidirect
2. C7×#3208C2semidirect
4. C2×C7×#460C2semidirect
5. C7×#1627C2semidirect
6. C7×#1626C2semidirect
7. C7×#1623C2semidirect
8. C7×#1622C2semidirect
9. C7×#1550C2semidirect
10. C7×#1487C2semidirect
11. C7×#1477C2semidirect
14. C7×Q82C22semidirect
16. C7×#557C22semidirect
20. C7×#554C22semidirect
22. C7×D4×Q8C22semidirect
49. C7×#333C22semidirect
50. C7×#332C22semidirect
51. C7×Q8⋊C8C22semidirect
52. C7×Q8⋊C8C22semidirect
53. C7×Q8⋊C8C22semidirect
54. C7×D4⋊C8C22semidirect
55. #18788C7direct (N × H)
149. Q8×#41C2×C7semidirect
150. #3208C2×C7semidirect
152. C2×#460C2×C7semidirect
153. #1627C2×C7semidirect
154. #1626C2×C7semidirect
155. #1623C2×C7semidirect
156. #1622C2×C7semidirect
157. #1550C2×C7semidirect
158. #1487C2×C7semidirect
159. #1477C2×C7semidirect
162. C7×#41SD16semidirect
255. Q82C22×C7semidirect
257. #557C22×C7semidirect
261. #554C22×C7semidirect
263. D4×Q8C22×C7semidirect
290. #333C22×C7semidirect
291. #332C22×C7semidirect
292. Q8⋊C8C22×C7semidirect
293. Q8⋊C8C22×C7semidirect
294. Q8⋊C8C22×C7semidirect
295. D4⋊C8C22×C7semidirect
312. C7×Q8C2×SD16semidirect
313. C7×Q8AGL(1,ℤ/8)semidirect
324. C7×D4C2×SD16semidirect
479. #41C7×SD16semidirect
592. Q8C2×C7×SD16semidirect
593. Q8C7×AGL(1,ℤ/8)semidirect
604. D4C2×C7×SD16semidirect
636. C7#18788direct (N × H)

Maximal subgroups

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

subgroupindex
C7×Q8×#412
C7×#32082
C7×#30382
C2×C7×#4602
C7×#16272
C7×#16262
C7×#16232
C7×#16222
C7×#15502
C7×#14872
C7×#14772
#187887