Finite Group Databasebeta

← C7×#18100 #13195316

Subgroups — C7×#18100 #13195316

Order 1792.

1256 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3459C211yesmaximal, characteristic, complemented
2C7×#3002C212yesmaximal, complemented
3C7×#2388C211yesmaximal, characteristic, complemented
4C7×#1603C212yesmaximal, complemented
5C7×#1602C211yesmaximal, characteristic, complemented
6C7×#1601C211yesmaximal, characteristic, complemented
7C7×#1597C212yesmaximal, complemented
8C7×#1596C211yesmaximal, characteristic, complemented
9C7×#1595C211yesmaximal, characteristic, complemented
10C7×#1501C212yesmaximal, complemented
11C7×#1459C211yesmaximal, characteristic, complemented
12C22×C7×#41C2211yescharacteristic, complemented
13C2×C7×#135—22no—
14C7×#543C2211yescharacteristic
15C7×#539—22no—
16C7×#539C2212yes—
17C7×#538—22no—
18C7×#538—21no—
19C7×#534—21no—
20C7×#534C2211yescharacteristic
21C7×#529—22no—
22C7×#529—21no—
23C7×#525—22no—
24C7×#525C2212yes—
25C2×C4×C7×D4—21no—
26C2×C4×C7×D4—21no—
27C2×C4×C7×D4C2211yescharacteristic
28C7×#452—22no—
29C7×#451C2212yescomplemented
30C7×#450C2212yescomplemented
31C7×#449—22no—
32C7×#448C2212yes—
33C7×#447C2212yes—
34C7×#416—22no—
35C2×C7×C22⋊C8C2212yescomplemented
36C7×#395C2211yescharacteristic, complemented
37C7×#394—21no—
38C7×#394C2211yescharacteristic, complemented
39C7×#393C2211yescharacteristic
40C7×#392—21no—
41C7×#392C2211yescharacteristic
42C4×C7×C22⋊C4—21no—
43C4×C7×C22⋊C4C2211yescharacteristic, complemented
44C7×#328C2212yescomplemented
45C7×#328C2212yescomplemented
46C7×#327C2212yes—
47C7×#327C2212yes—
48C7×#324C2212yescomplemented
49C7×#323C2211yescharacteristic
50C7×#323C2211yescharacteristic
51#18100C711yesmaximal, characteristic, direct product factor, Sylow
52C2×C7×#41—22no—
53C2×C7×#41—22no—
54C2×C7×#41—44no—
55C2×C7×#41D412yescomplemented
56C22×C7×Q8C2311yescharacteristic
57C22×C7×D4—21no—
58C22×C7×D4—21no—
59C22×C7×D4—21no—
60C22×C7×D4D411yescharacteristic
61C22×C7×D4C2311yescharacteristic
62C23×C4×C7—21no—
63C23×C4×C7—21no—
64C23×C4×C7D411yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C7×#135—48no—
67C2×C7×Q16—22no—
68C2×C7×SD16—22no—
69C2×C7×SD16—22no—
70C2×C7×D8—22no—
71C22×C7×C8—22no—
72C7×#126—22no—
73C7×#126—22no—
74C7×#126—22no—
75C7×#125—21no—
76C7×#125—22no—
77C7×#124—22no—
78C7×#124—21no—
79C7×#123—22no—
80C7×#123—22no—
81C7×#123—22no—
82C7×#123—22no—
83C7×#123—22no—
84C7×#123—22no—
85C7×C22⋊Q8—22no—
86C7×C22⋊Q8—22no—
87C7×C22⋊Q8—21no—
88C7×C22⋊Q8—22no—
89C7×C22⋊Q8D412yescomplemented
90C7×C22⋊Q8C2312yes—
91C7×#121—22no—
92C7×#121—22no—
93C7×#121—22no—
94C7×#121—21no—
95C7×#121D412yescomplemented
96C7×#121C2312yes—
97C7×#120—22no—
98C7×#120—22no—
99C7×#120—22no—
100C4×C7×Q8—21no—
101C4×C7×D4—22no—
102C4×C7×D4—22no—
103C4×C7×D4—21no—
104C4×C7×D4—22no—
105C4×C7×D4—22no—
106C4×C7×D4—22no—
107C4×C7×D4—22no—
108C4×C7×D4—22no—
109C4×C7×D4—44no—
110C7×#117—22no—
111C7×#117D412yescomplemented
112C2×C7×C4⋊C4—21no—
113C2×C7×C4⋊C4—21no—
114C2×C7×C4⋊C4C2311yescharacteristic
115C2×C7×C22⋊C4—21no—
116C2×C7×C22⋊C4—21no—
117C2×C7×C22⋊C4—21no—
118C2×C7×C22⋊C4—21no—
119C2×C7×C22⋊C4—21no—
120C2×C7×C22⋊C4—21no—
121C2×C7×C22⋊C4—21no—
122C2×C7×C22⋊C4D411yescharacteristic
123C2×C7×C22⋊C4C2311yescharacteristic
124C2×C42×C7—21no—
125C2×C42×C7—21no—
126C2×C42×C7D411yescharacteristic
127C7×#103—22no—
128C7×#103—22no—
129C7×#102—22no—
130C7×#102—22no—
131C7×C22⋊C8—22no—
132C7×C22⋊C8C2312yes—
133C7×C22⋊C8C2312yes—
134C7×#95—21no—
135C7×#95—21no—
136C7×#95C2311yescharacteristic
137C7×#95C2311yescharacteristic
138#3459C2×C711yescharacteristic, complemented
139#3002C2×C712yescomplemented
140#2388C2×C711yescharacteristic, complemented
141#1603C2×C712yescomplemented
142#1602C2×C711yescharacteristic, complemented
143#1601C2×C711yescharacteristic, complemented
144#1597C2×C712yescomplemented
145#1596C2×C711yescharacteristic, complemented
146#1595C2×C711yescharacteristic, complemented
147#1501C2×C712yescomplemented
148#1459C2×C711yescharacteristic, complemented
149C24×C7—21no—
150C24×C7—21no—
151C24×C7C2×D411yescharacteristic
152C24×C7C2×D411yescharacteristic
153C7×#41—28no—
154C7×#41—44no—
155C7×#41—44no—
156C7×#41—44no—
157C7×#41—44no—
158C2×C7×Q8—21no—
159C2×C7×Q8—22no—
160C2×C7×Q8—42no—
161C2×C7×Q8C2×D412yes—
162C2×C7×D4—22no—
163C2×C7×D4—22no—
164C2×C7×D4—22no—
165C2×C7×D4—22no—
166C2×C7×D4—21no—
167C2×C7×D4—22no—
168C2×C7×D4—22no—
169C2×C7×D4—22no—
170C2×C7×D4—41no—
171C2×C7×D4—42no—
172C2×C7×D4—42no—
173C2×C7×D4—42no—
174C2×C7×D4—42no—
175C2×C7×D4—42no—
176C2×C7×D4—42no—
177C2×C7×D4—42no—
178C2×C7×D4—42no—
179C2×C7×D4—42no—
180C2×C7×D4C2×D412yes—
181C22×C4×C7—21no—
182C22×C4×C7—24no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—22no—
188C22×C4×C7—21no—
189C22×C4×C7—22no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—42no—
193C22×C4×C7—42no—
194C22×C4×C7—42no—
195C22×C4×C7—41no—
196C22×C4×C7—41no—
197C22×C4×C7—82no—
198C22×C4×C7C2×D411yescharacteristic
199C22×C4×C7C2×D411yescharacteristic
200C22×C4×C7C2×D412yes—
201C22×C4×C7C2×D411yescharacteristic
202C22×C4×C7C2×D411yescharacteristic
203C22×C4×C7C2×D412yes—
204C22×C4×C7C2411yescharacteristic
205C7×Q16—44no—
206C7×SD16—44no—
207C7×SD16—44no—
208C7×D8—44no—
209C2×C7×C8—22no—
210C2×C7×C8—22no—
211C2×C7×C8—44no—
212C7×C4⋊C4—22no—
213C7×C4⋊C4—22no—
214C7×C4⋊C4—22no—
215C7×C4⋊C4—21no—
216C7×C4⋊C4—21no—
217C7×C4⋊C4—22no—
218C7×C4⋊C4—22no—
219C7×C4⋊C4—22no—
220C7×C4⋊C4—22no—
221C7×C4⋊C4—42no—
222C7×C4⋊C4C2×D412yes—
223C7×C4⋊C4C2×D412yes—
224C7×C22⋊C4—22no—
225C7×C22⋊C4—22no—
226C7×C22⋊C4—22no—
227C7×C22⋊C4—22no—
228C7×C22⋊C4—22no—
229C7×C22⋊C4—22no—
230C7×C22⋊C4—22no—
231C7×C22⋊C4—22no—
232C7×C22⋊C4—22no—
233C7×C22⋊C4—22no—
234C7×C22⋊C4—22no—
235C7×C22⋊C4—22no—
236C7×C22⋊C4—42no—
237C7×C22⋊C4—42no—
238C7×C22⋊C4—42no—
239C7×C22⋊C4—42no—
240C7×C22⋊C4—42no—
241C42×C7—22no—
242C42×C7—21no—
243C42×C7—22no—
244C42×C7—21no—
245C42×C7—42no—
246C22×#41C22×C711yescharacteristic, complemented
247C2×#135—22no—
248#543C22×C711yescharacteristic
249#539—22no—
250#539C22×C712yes—
251#538—22no—
252#538—21no—
253#534—21no—
254#534C22×C711yescharacteristic
255#529—22no—
256#529—21no—
257#525—22no—
258#525C22×C712yes—
259C2×C4×D4—21no—
260C2×C4×D4—21no—
261C2×C4×D4C22×C711yescharacteristic
262#452—22no—
263#451C22×C712yescomplemented
264#450C22×C712yescomplemented
265#449—22no—
266#448C22×C712yes—
267#447C22×C712yes—
268#416—22no—
269C2×C22⋊C8C22×C712yescomplemented
270#395C22×C711yescharacteristic, complemented
271#394—21no—
272#394C22×C711yescharacteristic, complemented
273#393C22×C711yescharacteristic
274#392—21no—
275#392C22×C711yescharacteristic
276C4×C22⋊C4—21no—
277C4×C22⋊C4C22×C711yescharacteristic, complemented
278#328C22×C712yescomplemented
279#328C22×C712yescomplemented
280#327C22×C712yes—
281#327C22×C712yes—
282#324C22×C712yescomplemented
283#323C22×C711yescharacteristic
284#323C22×C711yescharacteristic
285C23×C7—21no—
286C23×C7—21no—
287C23×C7—21no—
288C23×C7—21no—
289C23×C7—22no—
290C23×C7—22no—
291C23×C7—41no—
292C23×C7—41no—
293C23×C7—41no—
294C23×C7—41no—
295C23×C7—41no—
296C23×C7—41no—
297C23×C7—41no—
298C23×C7—42no—
299C23×C7—41no—
300C23×C7—41no—
301C23×C7—41no—
302C23×C7—81no—
303C23×C7—81no—
304C23×C7#12012yes—
305C23×C7#13512yescomplemented
306C23×C7C22×D411yescharacteristic
307C7×Q8—24no—
308C7×Q8—42no—
309C7×Q8—42no—
310C7×Q8—81no—
311C7×D4—24no—
312C7×D4—42no—
313C7×D4—42no—
314C7×D4—44no—
315C7×D4—44no—
316C7×D4—48no—
317C7×D4—48no—
318C7×D4—42no—
319C7×D4—42no—
320C7×D4—82no—
321C7×D4—82no—
322C7×D4—81no—
323C2×C4×C7—22no—
324C2×C4×C7—24no—
325C2×C4×C7—22no—
326C2×C4×C7—22no—
327C2×C4×C7—21no—
328C2×C4×C7—22no—
329C2×C4×C7—21no—
330C2×C4×C7—22no—
331C2×C4×C7—21no—
332C2×C4×C7—22no—
333C2×C4×C7—21no—
334C2×C4×C7—21no—
335C2×C4×C7—42no—
336C2×C4×C7—41no—
337C2×C4×C7—44no—
338C2×C4×C7—41no—
339C2×C4×C7—41no—
340C2×C4×C7—42no—
341C2×C4×C7—41no—
342C2×C4×C7—41no—
343C2×C4×C7—44no—
344C2×C4×C7—42no—
345C2×C4×C7—44no—
346C2×C4×C7—41no—
347C2×C4×C7—41no—
348C2×C4×C7—41no—
349C2×C4×C7—41no—
350C2×C4×C7—41no—
351C2×C4×C7—81no—
352C2×C4×C7—81no—
353C2×C4×C7—82no—
354C2×C4×C7—81no—
355C2×C4×C7#12011yescharacteristic
356C2×C4×C7#12011yescharacteristic
357C2×C4×C7C22×D412yes—
358C7×C8—42no—
359C7×C8—42no—
360C2×#41—22no—
361C2×#41—22no—
362C2×#41—44no—
363C2×#41C7×D412yescomplemented
364C22×Q8C23×C711yescharacteristic
365C22×D4—21no—
366C22×D4—21no—
367C22×D4—21no—
368C22×D4C7×D411yescharacteristic
369C22×D4C23×C711yescharacteristic
370C23×C4—21no—
371C23×C4—21no—
372C23×C4C7×D411yescharacteristic
373C23×C4C23×C711yescharacteristic
374#135—48no—
375C2×Q16—22no—
376C2×SD16—22no—
377C2×SD16—22no—
378C2×D8—22no—
379C22×C8—22no—
380#126—22no—
381#126—22no—
382#126—22no—
383#125—21no—
384#125—22no—
385#124—22no—
386#124—21no—
387#123—22no—
388#123—22no—
389#123—22no—
390#123—22no—
391#123—22no—
392#123—22no—
393C22⋊Q8—22no—
394C22⋊Q8—22no—
395C22⋊Q8—21no—
396C22⋊Q8—22no—
397C22⋊Q8C7×D412yescomplemented
398C22⋊Q8C23×C712yes—
399#121—22no—
400#121—22no—
401#121—22no—
402#121—21no—
403#121C7×D412yescomplemented
404#121C23×C712yes—
405#120—22no—
406#120—22no—
407#120—22no—
408C4×Q8—21no—
409C4×D4—22no—
410C4×D4—22no—
411C4×D4—21no—
412C4×D4—22no—
413C4×D4—22no—
414C4×D4—22no—
415C4×D4—22no—
416C4×D4—22no—
417C4×D4—44no—
418#117—22no—
419#117C7×D412yescomplemented
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4C23×C711yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4C7×D411yescharacteristic
431C2×C22⋊C4C23×C711yescharacteristic
432C2×C42—21no—
433C2×C42—21no—
434C2×C42C7×D411yescharacteristic
435#103—22no—
436#103—22no—
437#102—22no—
438#102—22no—
439C22⋊C8—22no—
440C22⋊C8C23×C712yes—
441C22⋊C8C23×C712yes—
442#95—21no—
443#95—21no—
444#95C23×C711yescharacteristic
445#95C23×C711yescharacteristic
446C22×C7—21no—
447C22×C7—21no—
448C22×C7—22no—
449C22×C7—22no—
450C22×C7—22no—
451C22×C7—22no—
452C22×C7—42no—
453C22×C7—42no—
454C22×C7—42no—
455C22×C7—41no—
456C22×C7—41no—
457C22×C7—42no—
458C22×C7—42no—
459C22×C7—42no—
460C22×C7—42no—
461C22×C7—81no—
462C22×C7—81no—
463C22×C7—81no—
464C22×C7—81no—
465C22×C7—81no—
466C22×C7—84no—
467C22×C7—81no—
468C22×C7—81no—
469C22×C7C2×#12011yescharacteristic
470C22×C7C2×#13511yescharacteristic
471C22×C7#57511yescharacteristic
472C4×C7—22no—
473C4×C7—21no—
474C4×C7—42no—
475C4×C7—41no—
476C4×C7—42no—
477C4×C7—41no—
478C4×C7—42no—
479C4×C7—42no—
480C4×C7—41no—
481C4×C7—42no—
482C4×C7—81no—
483C4×C7B(4,𝔽2)12yes—
484C24—21no—
485C24—21no—
486C24C2×C7×D411yescharacteristic
487C24C2×C7×D411yescharacteristic
488#41—28no—
489#41—44no—
490#41—44no—
491#41—44no—
492#41—44no—
493C2×Q8—21no—
494C2×Q8—22no—
495C2×Q8—42no—
496C2×Q8C2×C7×D412yes—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—21no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—41no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4C2×C7×D412yes—
516C22×C4—21no—
517C22×C4—24no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—82no—
533C22×C4C2×C7×D411yescharacteristic
534C22×C4C2×C7×D411yescharacteristic
535C22×C4C2×C7×D412yes—
536C22×C4C2×C7×D411yescharacteristic
537C22×C4C2×C7×D411yescharacteristic
538C22×C4C2×C7×D412yes—
539C22×C4C24×C711yescharacteristic
540Q16—44no—
541SD16—44no—
542SD16—44no—
543D8—44no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—44no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—42no—
557C4⋊C4C2×C7×D412yes—
558C4⋊C4C2×C7×D412yes—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C42—22no—
577C42—22no—
578C42—21no—
579C42—21no—
580C42—42no—
581C2×C7—21no—
582C2×C7—21no—
583C2×C7—42no—
584C2×C7—42no—
585C2×C7—82no—
586C2×C7—82no—
587C2×C7#300211yescharacteristic
588C2×C7#301811yescharacteristic
589C2×C7C2×B(4,𝔽2)11yescharacteristic
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—22no—
595C23—22no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—42no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—81no—
608C23—81no—
609C23C7×#12012yes—
610C23C7×#13512yescomplemented
611C23C22×C7×D411yescharacteristic
612Q8—24no—
613Q8—42no—
614Q8—42no—
615Q8—81no—
616D4—24no—
617D4—42no—
618D4—42no—
619D4—44no—
620D4—44no—
621D4—48no—
622D4—48no—
623D4—42no—
624D4—42no—
625D4—82no—
626D4—82no—
627D4—81no—
628C2×C4—22no—
629C2×C4—24no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—21no—
635C2×C4—22no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—42no—
641C2×C4—41no—
642C2×C4—44no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—42no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—44no—
649C2×C4—42no—
650C2×C4—44no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—81no—
657C2×C4—81no—
658C2×C4—82no—
659C2×C4—81no—
660C2×C4C7×#12011yescharacteristic
661C2×C4C7×#12011yescharacteristic
662C2×C4C22×C7×D412yes—
663C8—42no—
664C8—42no—
665C7#1810011yescharacteristic, direct product factor, Sylow
666C22—21no—
667C22—21no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—41no—
676C22—41no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—84no—
687C22—81no—
688C22—81no—
689C22C2×C7×#12011yescharacteristic
690C22C2×C7×#13511yescharacteristic
691C22C7×#57511yescharacteristic
692C4—22no—
693C4—21no—
694C4—42no—
695C4—41no—
696C4—42no—
697C4—41no—
698C4—42no—
699C4—42no—
700C4—41no—
701C4—42no—
702C4—81no—
703C4C7×B(4,𝔽2)12yes—
704C2—21no—
705C2—21no—
706C2—42no—
707C2—42no—
708C2—82no—
709C2—82no—
710C2C7×#300211yescharacteristic
711C2C7×#301811yescharacteristic
712C2C2×C7×B(4,𝔽2)11yescharacteristic
subgroupG/H
centerC2×C4×C7#120
commutator, Frattini, cosocleC22×C4C24×C7
socleC22×C7C2×#120
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C7 ◁ C23×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C7×#3459C2semidirect
2. C7×#3002C2semidirect
3. C7×#2388C2semidirect
4. C7×#1603C2semidirect
5. C7×#1602C2semidirect
6. C7×#1601C2semidirect
7. C7×#1597C2semidirect
8. C7×#1596C2semidirect
9. C7×#1595C2semidirect
10. C7×#1501C2semidirect
11. C7×#1459C2semidirect
12. C22×C7×#41C22semidirect
29. C7×#451C22semidirect
30. C7×#450C22semidirect
35. C2×C7×C22⋊C8C22semidirect
36. C7×#395C22semidirect
38. C7×#394C22semidirect
43. C4×C7×C22⋊C4C22semidirect
44. C7×#328C22semidirect
45. C7×#328C22semidirect
48. C7×#324C22semidirect
51. #18100C7direct (N × H)
55. C2×C7×#41D4semidirect
89. C7×C22⋊Q8D4semidirect
95. C7×#121D4semidirect
111. C7×#117D4semidirect
138. #3459C2×C7semidirect
139. #3002C2×C7semidirect
140. #2388C2×C7semidirect
141. #1603C2×C7semidirect
142. #1602C2×C7semidirect
143. #1601C2×C7semidirect
144. #1597C2×C7semidirect
145. #1596C2×C7semidirect
146. #1595C2×C7semidirect
147. #1501C2×C7semidirect
148. #1459C2×C7semidirect
246. C22×#41C22×C7semidirect
263. #451C22×C7semidirect
264. #450C22×C7semidirect
269. C2×C22⋊C8C22×C7semidirect
270. #395C22×C7semidirect
272. #394C22×C7semidirect
277. C4×C22⋊C4C22×C7semidirect
278. #328C22×C7semidirect
279. #328C22×C7semidirect
282. #324C22×C7semidirect
305. C23×C7#135semidirect
363. C2×#41C7×D4semidirect
397. C22⋊Q8C7×D4semidirect
403. #121C7×D4semidirect
419. #117C7×D4semidirect
610. C23C7×#135semidirect
665. C7#18100direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#34592
C7×#30022
C7×#23882
C7×#16032
C7×#16022
C7×#16012
C7×#15972
C7×#15962
C7×#15952
C7×#15012
C7×#14592
#181007