Finite Group Databasebeta

← C7×#24027 #13201243

Subgroups — C7×#24027 #13201243

Order 1792.

1348 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3488C211yesmaximal, characteristic
2C7×#3092C211yesmaximal, characteristic, complemented
3C2×C7×#417C211yesmaximal, characteristic, complemented
4C7×#2504C211yesmaximal, characteristic, complemented
5C7×#2040C212yesmaximal, complemented
6C7×#2037C212yesmaximal, complemented
7C7×#1900C211yesmaximal, characteristic, complemented
8C7×#1871C211yesmaximal, characteristic, complemented
9C7×#1860C212yesmaximal, complemented
10C7×#1792C212yesmaximal, complemented
11C7×#1789C211yesmaximal, characteristic, complemented
12C2×C7×H(5,𝔽2)C2211yescharacteristic
13C22×C7×#41C2211yescharacteristic
14C22×C7×M16C2211yescharacteristic, complemented
15C7×#550—21no—
16C7×#548—21no—
17C7×#546—21no—
18C7×#546—22no—
19C7×D42—22no—
20C7×D42—21no—
21C7×#537—21no—
22C7×#537C2211yescharacteristic
23C7×#535—21no—
24C7×#535C2211yescharacteristic
25C7×#525—21no—
26C7×#525C2211yescharacteristic
27C2×C7×#121—21no—
28C2×C7×#121C2211yescharacteristic
29C7×#520C2211yescharacteristic
30C22×C7×C4⋊C4C2211yescharacteristic, complemented
31C7×#484—21no—
32C7×#483—21no—
33C7×#481—21no—
34C7×#480—21no—
35C7×#428C2212yescomplemented
36C2×C7×#104C2212yes—
37C2×C7×#104C2212yescomplemented
38C2×C7×#104C2212yescomplemented
39C7×#417—21no—
40C7×#417—21no—
41C7×#417C2212yes—
42C7×#417C2212yescomplemented
43C7×#417C2212yescomplemented
44C2×C7×#103—21no—
45C2×C7×#102—21no—
46C2×C7×#100C2212yescomplemented
47C7×#407C2211yescharacteristic, complemented
48C7×#397—22no—
49C7×#390C2212yescomplemented
50C7×#386—22no—
51C7×#382C2212yescomplemented
52C4×C7×C22⋊C4C2211yescharacteristic, complemented
53C7×#343C2212yescomplemented
54C7×#339C2212yescomplemented
55#24027C711yesmaximal, characteristic, direct product factor, Sylow
56C7×H(5,𝔽2)—24no—
57C7×H(5,𝔽2)—42no—
58C2×C7×#41—21no—
59C2×C7×#41—21no—
60C2×C7×#41—21no—
61C2×C7×#41—21no—
62C2×C7×#41—24no—
63C2×C7×#41—42no—
64C2×C7×#41D411yescharacteristic
65C2×C7×#41D411yescharacteristic
66C2×C7×#41C2311yescharacteristic
67C2×C7×#41C2311yescharacteristic
68C2×C7×#41C2311yescharacteristic
69C22×C7×Q8D411yescharacteristic
70C22×C7×D4—21no—
71C22×C7×D4—22no—
72C22×C7×D4—22no—
73C22×C7×D4—21no—
74C22×C7×D4—21no—
75C22×C7×D4D411yescharacteristic
76C22×C7×D4D412yes—
77C22×C7×D4C2311yescharacteristic
78C23×C4×C7—21no—
79C23×C4×C7—21no—
80C23×C4×C7C2311yescharacteristic
81C2×C7×M16—21no—
82C2×C7×M16—42no—
83C2×C7×M16C2312yes—
84C2×C7×M16C2312yes—
85C22×C7×C8—21no—
86C7×#127—22no—
87C7×#127—21no—
88C7×#124—22no—
89C7×#124—21no—
90C7×#123—22no—
91C7×#123—21no—
92C7×C22⋊Q8—22no—
93C7×C22⋊Q8—21no—
94C7×C22⋊Q8—21no—
95C7×C22⋊Q8D411yescharacteristic
96C7×C22⋊Q8D411yescharacteristic
97C7×#121—22no—
98C7×#121—22no—
99C7×#121—22no—
100C7×#121—22no—
101C7×#121—22no—
102C7×#121—21no—
103C7×#121—21no—
104C7×#121—21no—
105C7×#121—21no—
106C7×#121—21no—
107C7×#121—21no—
108C7×#121—22no—
109C7×#121—21no—
110C7×#121—21no—
111C7×#121D411yescharacteristic
112C7×#121D411yescharacteristic
113C7×#120—22no—
114C7×#120—22no—
115C7×#120—22no—
116C7×#120—21no—
117C7×#120—22no—
118C4×C7×Q8—21no—
119C4×C7×D4—22no—
120C4×C7×D4—22no—
121C4×C7×D4—21no—
122C4×C7×D4—22no—
123C4×C7×D4—21no—
124C4×C7×D4—21no—
125C7×#117—21no—
126C7×#117C2311yescharacteristic
127C2×C7×C4⋊C4—21no—
128C2×C7×C4⋊C4—21no—
129C2×C7×C4⋊C4—21no—
130C2×C7×C4⋊C4—21no—
131C2×C7×C4⋊C4—21no—
132C2×C7×C4⋊C4—21no—
133C2×C7×C4⋊C4C2312yes—
134C2×C7×C4⋊C4C2311yescharacteristic
135C2×C7×C22⋊C4—22no—
136C2×C7×C22⋊C4—21no—
137C2×C7×C22⋊C4—24no—
138C2×C7×C22⋊C4D412yes—
139C2×C42×C7C2312yes—
140C7×#107—22no—
141C7×#106—22no—
142C7×#104—24no—
143C7×#104—42no—
144C7×#104—42no—
145C7×#103—22no—
146C7×#103—22no—
147C7×#103—22no—
148C7×#102—22no—
149C7×#102—22no—
150C7×#102—22no—
151C7×#100—42no—
152C7×C22⋊C8—21no—
153C7×C22⋊C8—21no—
154C7×#95—21no—
155C7×#95—24no—
156#3488C2×C711yescharacteristic
157#3092C2×C711yescharacteristic, complemented
158C2×#417C2×C711yescharacteristic, complemented
159#2504C2×C711yescharacteristic, complemented
160#2040C2×C712yescomplemented
161#2037C2×C712yescomplemented
162#1900C2×C711yescharacteristic, complemented
163#1871C2×C711yescharacteristic, complemented
164#1860C2×C712yescomplemented
165#1792C2×C712yescomplemented
166#1789C2×C711yescharacteristic, complemented
167C24×C7—22no—
168C24×C7—21no—
169C24×C7C2×D411yescharacteristic
170C24×C7C2×D412yes—
171C7×#41—22no—
172C7×#41—22no—
173C7×#41—22no—
174C7×#41—22no—
175C7×#41—22no—
176C7×#41—22no—
177C7×#41—22no—
178C7×#41—44no—
179C7×#41—41no—
180C7×#41—41no—
181C7×#41—44no—
182C7×#41—44no—
183C7×#41—42no—
184C7×#41—42no—
185C7×#41#4114yes—
186C2×C7×Q8—21no—
187C2×C7×Q8—22no—
188C2×C7×Q8—41no—
189C2×C7×Q8C2×D411yescharacteristic
190C2×C7×Q8C2×D411yescharacteristic
191C2×C7×Q8C2×D411yescharacteristic
192C2×C7×D4—21no—
193C2×C7×D4—22no—
194C2×C7×D4—22no—
195C2×C7×D4—22no—
196C2×C7×D4—22no—
197C2×C7×D4—21no—
198C2×C7×D4—21no—
199C2×C7×D4—21no—
200C2×C7×D4—21no—
201C2×C7×D4—21no—
202C2×C7×D4—22no—
203C2×C7×D4—22no—
204C2×C7×D4—22no—
205C2×C7×D4—21no—
206C2×C7×D4—22no—
207C2×C7×D4—21no—
208C2×C7×D4—21no—
209C2×C7×D4—21no—
210C2×C7×D4—22no—
211C2×C7×D4—22no—
212C2×C7×D4—41no—
213C2×C7×D4—44no—
214C2×C7×D4—44no—
215C2×C7×D4—48no—
216C2×C7×D4—42no—
217C2×C7×D4—42no—
218C2×C7×D4—44no—
219C2×C7×D4—84no—
220C2×C7×D4C2×D411yescharacteristic
221C2×C7×D4C2×D411yescharacteristic
222C2×C7×D4C2×D411yescharacteristic
223C22×C4×C7—21no—
224C22×C4×C7—22no—
225C22×C4×C7—22no—
226C22×C4×C7—22no—
227C22×C4×C7—21no—
228C22×C4×C7—22no—
229C22×C4×C7—21no—
230C22×C4×C7—21no—
231C22×C4×C7—21no—
232C22×C4×C7—21no—
233C22×C4×C7—22no—
234C22×C4×C7—22no—
235C22×C4×C7—44no—
236C22×C4×C7—41no—
237C22×C4×C7—41no—
238C22×C4×C7—82no—
239C22×C4×C7C2×D411yescharacteristic
240C22×C4×C7C2×D411yescharacteristic
241C22×C4×C7C2×D411yescharacteristic
242C22×C4×C7C2×D411yescharacteristic
243C22×C4×C7C2×D411yescharacteristic
244C22×C4×C7C2×D412yes—
245C22×C4×C7C2411yescharacteristic
246C7×M16—22no—
247C7×M16—22no—
248C7×M16—22no—
249C7×M16—22no—
250C7×M16—42no—
251C2×C7×C8—22no—
252C2×C7×C8—22no—
253C2×C7×C8—42no—
254C7×C4⋊C4—22no—
255C7×C4⋊C4—22no—
256C7×C4⋊C4—21no—
257C7×C4⋊C4—21no—
258C7×C4⋊C4—21no—
259C7×C4⋊C4—21no—
260C7×C4⋊C4—22no—
261C7×C4⋊C4—22no—
262C7×C4⋊C4—41no—
263C7×C4⋊C4—41no—
264C7×C4⋊C4C2×D411yescharacteristic
265C7×C4⋊C4C2×D411yescharacteristic
266C7×C22⋊C4—22no—
267C7×C22⋊C4—22no—
268C7×C22⋊C4—22no—
269C7×C22⋊C4—22no—
270C7×C22⋊C4—22no—
271C7×C22⋊C4—21no—
272C7×C22⋊C4—21no—
273C7×C22⋊C4—21no—
274C7×C22⋊C4—21no—
275C7×C22⋊C4—22no—
276C7×C22⋊C4—22no—
277C7×C22⋊C4—21no—
278C7×C22⋊C4—42no—
279C7×C22⋊C4—84no—
280C42×C7—22no—
281C42×C7—21no—
282C42×C7—22no—
283C42×C7—22no—
284C2×H(5,𝔽2)C22×C711yescharacteristic
285C22×#41C22×C711yescharacteristic
286C22×M16C22×C711yescharacteristic, complemented
287#550—21no—
288#548—21no—
289#546—21no—
290#546—22no—
291D42—22no—
292D42—21no—
293#537—21no—
294#537C22×C711yescharacteristic
295#535—21no—
296#535C22×C711yescharacteristic
297#525—21no—
298#525C22×C711yescharacteristic
299C2×#121—21no—
300C2×#121C22×C711yescharacteristic
301#520C22×C711yescharacteristic
302C22×C4⋊C4C22×C711yescharacteristic, complemented
303#484—21no—
304#483—21no—
305#481—21no—
306#480—21no—
307#428C22×C712yescomplemented
308C2×#104C22×C712yes—
309C2×#104C22×C712yescomplemented
310C2×#104C22×C712yescomplemented
311#417—21no—
312#417—21no—
313#417C22×C712yes—
314#417C22×C712yescomplemented
315#417C22×C712yescomplemented
316C2×#103—21no—
317C2×#102—21no—
318C2×#100C22×C712yescomplemented
319#407C22×C711yescharacteristic, complemented
320#397—22no—
321#390C22×C712yescomplemented
322#386—22no—
323#382C22×C712yescomplemented
324C4×C22⋊C4C22×C711yescharacteristic, complemented
325#343C22×C712yescomplemented
326#339C22×C712yescomplemented
327C23×C7—21no—
328C23×C7—22no—
329C23×C7—22no—
330C23×C7—22no—
331C23×C7—21no—
332C23×C7—21no—
333C23×C7—24no—
334C23×C7—41no—
335C23×C7—42no—
336C23×C7—44no—
337C23×C7—42no—
338C23×C7—42no—
339C23×C7—42no—
340C23×C7—81no—
341C23×C7—82no—
342C23×C7—82no—
343C23×C7#12011yescharacteristic
344C23×C7#12011yescharacteristic
345C23×C7C22×D411yescharacteristic
346C7×Q8—21no—
347C7×Q8—21no—
348C7×Q8—21no—
349C7×Q8—22no—
350C7×Q8—42no—
351C7×Q8#12312yes—
352C7×D4—24no—
353C7×D4—21no—
354C7×D4—21no—
355C7×D4—21no—
356C7×D4—22no—
357C7×D4—42no—
358C7×D4—42no—
359C7×D4—44no—
360C7×D4—42no—
361C7×D4—44no—
362C7×D4—42no—
363C7×D4—42no—
364C7×D4—44no—
365C7×D4—42no—
366C7×D4—41no—
367C7×D4—41no—
368C7×D4—42no—
369C7×D4—81no—
370C7×D4—82no—
371C7×D4—82no—
372C7×D4—82no—
373C7×D4—82no—
374C7×D4#12312yes—
375C2×C4×C7—21no—
376C2×C4×C7—22no—
377C2×C4×C7—21no—
378C2×C4×C7—21no—
379C2×C4×C7—21no—
380C2×C4×C7—21no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—24no—
384C2×C4×C7—21no—
385C2×C4×C7—22no—
386C2×C4×C7—21no—
387C2×C4×C7—21no—
388C2×C4×C7—21no—
389C2×C4×C7—42no—
390C2×C4×C7—42no—
391C2×C4×C7—42no—
392C2×C4×C7—44no—
393C2×C4×C7—41no—
394C2×C4×C7—41no—
395C2×C4×C7—42no—
396C2×C4×C7—42no—
397C2×C4×C7—42no—
398C2×C4×C7—42no—
399C2×C4×C7—44no—
400C2×C4×C7—42no—
401C2×C4×C7—42no—
402C2×C4×C7—82no—
403C2×C4×C7—82no—
404C2×C4×C7—82no—
405C2×C4×C7#12011yescharacteristic
406C2×C4×C7#12011yescharacteristic
407C2×C4×C7C22×D411yescharacteristic
408C2×C4×C7C22×D411yescharacteristic
409C2×C4×C7C2×#4112yes—
410C2×C4×C7H(5,𝔽2)12yes—
411C7×C8—42no—
412C7×C8—42no—
413H(5,𝔽2)—24no—
414H(5,𝔽2)—42no—
415C2×#41—21no—
416C2×#41—21no—
417C2×#41—21no—
418C2×#41—21no—
419C2×#41—24no—
420C2×#41—42no—
421C2×#41C7×D411yescharacteristic
422C2×#41C7×D411yescharacteristic
423C2×#41C23×C711yescharacteristic
424C2×#41C23×C711yescharacteristic
425C2×#41C23×C711yescharacteristic
426C22×Q8C7×D411yescharacteristic
427C22×D4—21no—
428C22×D4—22no—
429C22×D4—22no—
430C22×D4—21no—
431C22×D4—21no—
432C22×D4C7×D411yescharacteristic
433C22×D4C7×D412yes—
434C22×D4C23×C711yescharacteristic
435C23×C4—21no—
436C23×C4—21no—
437C23×C4C23×C711yescharacteristic
438C2×M16—21no—
439C2×M16—42no—
440C2×M16C23×C712yes—
441C2×M16C23×C712yes—
442C22×C8—21no—
443#127—22no—
444#127—21no—
445#124—22no—
446#124—21no—
447#123—22no—
448#123—21no—
449C22⋊Q8—22no—
450C22⋊Q8—21no—
451C22⋊Q8—21no—
452C22⋊Q8C7×D411yescharacteristic
453C22⋊Q8C7×D411yescharacteristic
454#121—22no—
455#121—22no—
456#121—22no—
457#121—22no—
458#121—22no—
459#121—21no—
460#121—21no—
461#121—21no—
462#121—21no—
463#121—21no—
464#121—21no—
465#121—22no—
466#121—21no—
467#121—21no—
468#121C7×D411yescharacteristic
469#121C7×D411yescharacteristic
470#120—22no—
471#120—22no—
472#120—22no—
473#120—21no—
474#120—22no—
475C4×Q8—21no—
476C4×D4—22no—
477C4×D4—22no—
478C4×D4—21no—
479C4×D4—22no—
480C4×D4—21no—
481C4×D4—21no—
482#117—21no—
483#117C23×C711yescharacteristic
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4C23×C712yes—
491C2×C4⋊C4C23×C711yescharacteristic
492C2×C22⋊C4—22no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4C7×D412yes—
496C2×C42C23×C712yes—
497#107—22no—
498#106—22no—
499#104—24no—
500#104—42no—
501#104—42no—
502#103—22no—
503#103—22no—
504#103—22no—
505#102—22no—
506#102—22no—
507#102—22no—
508#100—42no—
509C22⋊C8—21no—
510C22⋊C8—21no—
511#95—21no—
512#95—24no—
513C22×C7—21no—
514C22×C7—21no—
515C22×C7—21no—
516C22×C7—21no—
517C22×C7—21no—
518C22×C7—22no—
519C22×C7—21no—
520C22×C7—21no—
521C22×C7—44no—
522C22×C7—41no—
523C22×C7—41no—
524C22×C7—41no—
525C22×C7—41no—
526C22×C7—42no—
527C22×C7—42no—
528C22×C7—41no—
529C22×C7—41no—
530C22×C7—41no—
531C22×C7—42no—
532C22×C7—41no—
533C22×C7—84no—
534C22×C7—84no—
535C22×C7—164no—
536C22×C7#45512yes—
537C22×C7C2×#12011yescharacteristic
538C22×C7#54612yes—
539C4×C7—21no—
540C4×C7—21no—
541C4×C7—22no—
542C4×C7—41no—
543C4×C7—41no—
544C4×C7—42no—
545C4×C7—41no—
546C4×C7—41no—
547C4×C7—82no—
548C4×C7—82no—
549C4×C7C2×#12311yescharacteristic
550C4×C7#53411yescharacteristic
551C4×C7#54612yes—
552C24—22no—
553C24—21no—
554C24C2×C7×D411yescharacteristic
555C24C2×C7×D412yes—
556#41—22no—
557#41—22no—
558#41—22no—
559#41—22no—
560#41—22no—
561#41—22no—
562#41—22no—
563#41—44no—
564#41—41no—
565#41—41no—
566#41—44no—
567#41—44no—
568#41—42no—
569#41—42no—
570#41C7×#4114yes—
571C2×Q8—21no—
572C2×Q8—22no—
573C2×Q8—41no—
574C2×Q8C2×C7×D411yescharacteristic
575C2×Q8C2×C7×D411yescharacteristic
576C2×Q8C2×C7×D411yescharacteristic
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—21no—
591C2×D4—22no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—41no—
598C2×D4—44no—
599C2×D4—44no—
600C2×D4—48no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—44no—
604C2×D4—84no—
605C2×D4C2×C7×D411yescharacteristic
606C2×D4C2×C7×D411yescharacteristic
607C2×D4C2×C7×D411yescharacteristic
608C22×C4—21no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—44no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—82no—
624C22×C4C2×C7×D411yescharacteristic
625C22×C4C2×C7×D411yescharacteristic
626C22×C4C2×C7×D411yescharacteristic
627C22×C4C2×C7×D411yescharacteristic
628C22×C4C2×C7×D411yescharacteristic
629C22×C4C2×C7×D412yes—
630C22×C4C24×C711yescharacteristic
631M16—22no—
632M16—22no—
633M16—22no—
634M16—22no—
635M16—42no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—42no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—41no—
648C4⋊C4—41no—
649C4⋊C4C2×C7×D411yescharacteristic
650C4⋊C4C2×C7×D411yescharacteristic
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—21no—
663C22⋊C4—42no—
664C22⋊C4—84no—
665C42—22no—
666C42—21no—
667C42—22no—
668C42—22no—
669C2×C7—22no—
670C2×C7—22no—
671C2×C7—41no—
672C2×C7—42no—
673C2×C7—81no—
674C2×C7—82no—
675C2×C7—81no—
676C2×C7#240511yescharacteristic
677C2×C7C2×#45511yescharacteristic
678C2×C7#302111yescharacteristic
679C23—21no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—21no—
684C23—21no—
685C23—24no—
686C23—41no—
687C23—42no—
688C23—44no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—81no—
693C23—82no—
694C23—82no—
695C23C7×#12011yescharacteristic
696C23C7×#12011yescharacteristic
697C23C22×C7×D411yescharacteristic
698Q8—21no—
699Q8—21no—
700Q8—21no—
701Q8—22no—
702Q8—42no—
703Q8C7×#12312yes—
704D4—24no—
705D4—21no—
706D4—21no—
707D4—21no—
708D4—22no—
709D4—42no—
710D4—42no—
711D4—44no—
712D4—42no—
713D4—44no—
714D4—42no—
715D4—42no—
716D4—44no—
717D4—42no—
718D4—41no—
719D4—41no—
720D4—42no—
721D4—81no—
722D4—82no—
723D4—82no—
724D4—82no—
725D4—82no—
726D4C7×#12312yes—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—82no—
755C2×C4—82no—
756C2×C4—82no—
757C2×C4C7×#12011yescharacteristic
758C2×C4C7×#12011yescharacteristic
759C2×C4C22×C7×D411yescharacteristic
760C2×C4C22×C7×D411yescharacteristic
761C2×C4C2×C7×#4112yes—
762C2×C4C7×H(5,𝔽2)12yes—
763C8—42no—
764C8—42no—
765C7#2402711yescharacteristic, direct product factor, Sylow
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—22no—
772C22—21no—
773C22—21no—
774C22—44no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—42no—
780C22—42no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—42no—
785C22—41no—
786C22—84no—
787C22—84no—
788C22—164no—
789C22C7×#45512yes—
790C22C2×C7×#12011yescharacteristic
791C22C7×#54612yes—
792C4—21no—
793C4—21no—
794C4—22no—
795C4—41no—
796C4—41no—
797C4—42no—
798C4—41no—
799C4—41no—
800C4—82no—
801C4—82no—
802C4C2×C7×#12311yescharacteristic
803C4C7×#53411yescharacteristic
804C4C7×#54612yes—
805C2—22no—
806C2—22no—
807C2—41no—
808C2—42no—
809C2—81no—
810C2—82no—
811C2—81no—
812C2C7×#240511yescharacteristic
813C2C2×C7×#45511yescharacteristic
814C2C7×#302111yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC7×#3488C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C7×#3092C2semidirect
3. C2×C7×#417C2semidirect
4. C7×#2504C2semidirect
5. C7×#2040C2semidirect
6. C7×#2037C2semidirect
7. C7×#1900C2semidirect
8. C7×#1871C2semidirect
9. C7×#1860C2semidirect
10. C7×#1792C2semidirect
11. C7×#1789C2semidirect
14. C22×C7×M16C22semidirect
30. C22×C7×C4⋊C4C22semidirect
35. C7×#428C22semidirect
37. C2×C7×#104C22semidirect
38. C2×C7×#104C22semidirect
42. C7×#417C22semidirect
43. C7×#417C22semidirect
46. C2×C7×#100C22semidirect
47. C7×#407C22semidirect
49. C7×#390C22semidirect
51. C7×#382C22semidirect
52. C4×C7×C22⋊C4C22semidirect
53. C7×#343C22semidirect
54. C7×#339C22semidirect
55. #24027C7direct (N × H)
157. #3092C2×C7semidirect
158. C2×#417C2×C7semidirect
159. #2504C2×C7semidirect
160. #2040C2×C7semidirect
161. #2037C2×C7semidirect
162. #1900C2×C7semidirect
163. #1871C2×C7semidirect
164. #1860C2×C7semidirect
165. #1792C2×C7semidirect
166. #1789C2×C7semidirect
286. C22×M16C22×C7semidirect
302. C22×C4⋊C4C22×C7semidirect
307. #428C22×C7semidirect
309. C2×#104C22×C7semidirect
310. C2×#104C22×C7semidirect
314. #417C22×C7semidirect
315. #417C22×C7semidirect
318. C2×#100C22×C7semidirect
319. #407C22×C7semidirect
321. #390C22×C7semidirect
323. #382C22×C7semidirect
324. C4×C22⋊C4C22×C7semidirect
325. #343C22×C7semidirect
326. #339C22×C7semidirect
765. C7#24027direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#34882
C7×#30922
C2×C7×#4172
C7×#25042
C7×#20402
C7×#20372
C7×#19002
C7×#18712
C7×#18602
C7×#17922
C7×#17892
#240277