Finite Group Databasebeta

← C7×#24026 #13201242

Subgroups — C7×#24026 #13201242

Order 1792.

1404 conjugacy classes of subgroups.

The subgroup lattice has 820 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×#2501C211yesmaximal, characteristic, complemented
5C7×#2039C212yesmaximal, complemented
6C7×#2037C212yesmaximal, complemented
7C7×#1900C211yesmaximal, characteristic, complemented
8C7×#1871C211yesmaximal, characteristic, complemented
9C7×#1859C212yesmaximal, 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×#123—22no—
28C2×C7×#121—21no—
29C2×C7×#121C2211yescharacteristic
30C7×#520C2211yescharacteristic
31C22×C7×C4⋊C4C2211yescharacteristic, complemented
32C7×#484—21no—
33C7×#483—21no—
34C7×#481—21no—
35C7×#480—21no—
36C7×#428C2212yescomplemented
37C2×C7×#104C2212yes—
38C2×C7×#104C2212yescomplemented
39C2×C7×#104C2212yescomplemented
40C7×#417—21no—
41C7×#417—21no—
42C7×#417C2212yes—
43C7×#417C2212yescomplemented
44C7×#417C2212yescomplemented
45C2×C7×#103—21no—
46C2×C7×#102—21no—
47C2×C7×#100C2212yescomplemented
48C7×#407C2211yescharacteristic, complemented
49C7×#399—22no—
50C7×#390C2212yescomplemented
51C7×#384C2212yescomplemented
52C4×C7×C22⋊C4C2211yescharacteristic, complemented
53C7×#343C2212yescomplemented
54C7×#339C2212yescomplemented
55#24026C711yesmaximal, 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×#123—48no—
93C7×C22⋊Q8—22no—
94C7×C22⋊Q8—21no—
95C7×C22⋊Q8—21no—
96C7×C22⋊Q8D411yescharacteristic
97C7×C22⋊Q8D411yescharacteristic
98C7×#121—22no—
99C7×#121—22no—
100C7×#121—22no—
101C7×#121—22no—
102C7×#121—22no—
103C7×#121—21no—
104C7×#121—21no—
105C7×#121—21no—
106C7×#121—21no—
107C7×#121—21no—
108C7×#121—21no—
109C7×#121—22no—
110C7×#121—21no—
111C7×#121—21no—
112C7×#121D411yescharacteristic
113C7×#121D411yescharacteristic
114C7×#120—22no—
115C7×#120—22no—
116C7×#120—22no—
117C7×#120—21no—
118C7×#120—22no—
119C4×C7×Q8—21no—
120C4×C7×D4—22no—
121C4×C7×D4—22no—
122C4×C7×D4—21no—
123C4×C7×D4—22no—
124C4×C7×D4—21no—
125C4×C7×D4—21no—
126C7×#117—21no—
127C7×#117C2311yescharacteristic
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⋊C4—21no—
134C2×C7×C4⋊C4—24no—
135C2×C7×C4⋊C4C2312yes—
136C2×C7×C4⋊C4C2311yescharacteristic
137C2×C7×C22⋊C4—22no—
138C2×C7×C22⋊C4—21no—
139C2×C7×C22⋊C4—24no—
140C2×C7×C22⋊C4D412yes—
141C2×C42×C7C2312yes—
142C7×#107—22no—
143C7×#106—22no—
144C7×#104—24no—
145C7×#104—42no—
146C7×#104—42no—
147C7×#103—22no—
148C7×#103—22no—
149C7×#103—22no—
150C7×#102—22no—
151C7×#102—22no—
152C7×#102—22no—
153C7×#100—42no—
154C7×C22⋊C8—21no—
155C7×C22⋊C8—21no—
156C7×#95—21no—
157#3488C2×C711yescharacteristic
158#3092C2×C711yescharacteristic, complemented
159C2×#417C2×C711yescharacteristic, complemented
160#2501C2×C711yescharacteristic, complemented
161#2039C2×C712yescomplemented
162#2037C2×C712yescomplemented
163#1900C2×C711yescharacteristic, complemented
164#1871C2×C711yescharacteristic, complemented
165#1859C2×C712yescomplemented
166#1792C2×C712yescomplemented
167#1789C2×C711yescharacteristic, complemented
168C24×C7—22no—
169C24×C7—21no—
170C24×C7C2×D411yescharacteristic
171C24×C7C2×D412yes—
172C7×#41—22no—
173C7×#41—22no—
174C7×#41—22no—
175C7×#41—22no—
176C7×#41—22no—
177C7×#41—22no—
178C7×#41—22no—
179C7×#41—44no—
180C7×#41—41no—
181C7×#41—41no—
182C7×#41—44no—
183C7×#41—44no—
184C7×#41—42no—
185C7×#41—42no—
186C7×#41#4114yes—
187C2×C7×Q8—21no—
188C2×C7×Q8—22no—
189C2×C7×Q8—41no—
190C2×C7×Q8C2×D411yescharacteristic
191C2×C7×Q8C2×D411yescharacteristic
192C2×C7×Q8C2×D411yescharacteristic
193C2×C7×D4—21no—
194C2×C7×D4—22no—
195C2×C7×D4—22no—
196C2×C7×D4—22no—
197C2×C7×D4—22no—
198C2×C7×D4—21no—
199C2×C7×D4—21no—
200C2×C7×D4—21no—
201C2×C7×D4—21no—
202C2×C7×D4—21no—
203C2×C7×D4—22no—
204C2×C7×D4—22no—
205C2×C7×D4—22no—
206C2×C7×D4—21no—
207C2×C7×D4—22no—
208C2×C7×D4—21no—
209C2×C7×D4—21no—
210C2×C7×D4—21no—
211C2×C7×D4—22no—
212C2×C7×D4—22no—
213C2×C7×D4—41no—
214C2×C7×D4—44no—
215C2×C7×D4—44no—
216C2×C7×D4—48no—
217C2×C7×D4—42no—
218C2×C7×D4—42no—
219C2×C7×D4—44no—
220C2×C7×D4—84no—
221C2×C7×D4C2×D411yescharacteristic
222C2×C7×D4C2×D411yescharacteristic
223C2×C7×D4C2×D411yescharacteristic
224C22×C4×C7—21no—
225C22×C4×C7—22no—
226C22×C4×C7—22no—
227C22×C4×C7—22no—
228C22×C4×C7—21no—
229C22×C4×C7—22no—
230C22×C4×C7—22no—
231C22×C4×C7—21no—
232C22×C4×C7—21no—
233C22×C4×C7—21no—
234C22×C4×C7—21no—
235C22×C4×C7—22no—
236C22×C4×C7—44no—
237C22×C4×C7—44no—
238C22×C4×C7—41no—
239C22×C4×C7—41no—
240C22×C4×C7C2×D411yescharacteristic
241C22×C4×C7C2×D411yescharacteristic
242C22×C4×C7C2×D411yescharacteristic
243C22×C4×C7C2×D411yescharacteristic
244C22×C4×C7C2×D411yescharacteristic
245C22×C4×C7C2×D412yes—
246C22×C4×C7C2411yescharacteristic
247C7×M16—22no—
248C7×M16—22no—
249C7×M16—22no—
250C7×M16—22no—
251C7×M16—42no—
252C2×C7×C8—22no—
253C2×C7×C8—22no—
254C2×C7×C8—42no—
255C7×C4⋊C4—22no—
256C7×C4⋊C4—22no—
257C7×C4⋊C4—21no—
258C7×C4⋊C4—21no—
259C7×C4⋊C4—21no—
260C7×C4⋊C4—21no—
261C7×C4⋊C4—22no—
262C7×C4⋊C4—22no—
263C7×C4⋊C4—48no—
264C7×C4⋊C4—41no—
265C7×C4⋊C4—41no—
266C7×C4⋊C4C2×D411yescharacteristic
267C7×C4⋊C4C2×D411yescharacteristic
268C7×C22⋊C4—22no—
269C7×C22⋊C4—22no—
270C7×C22⋊C4—24no—
271C7×C22⋊C4—22no—
272C7×C22⋊C4—22no—
273C7×C22⋊C4—22no—
274C7×C22⋊C4—21no—
275C7×C22⋊C4—21no—
276C7×C22⋊C4—21no—
277C7×C22⋊C4—21no—
278C7×C22⋊C4—22no—
279C7×C22⋊C4—22no—
280C7×C22⋊C4—21no—
281C7×C22⋊C4—48no—
282C42×C7—22no—
283C42×C7—21no—
284C42×C7—22no—
285C42×C7—22no—
286C2×H(5,𝔽2)C22×C711yescharacteristic
287C22×#41C22×C711yescharacteristic
288C22×M16C22×C711yescharacteristic, complemented
289#550—21no—
290#548—21no—
291#546—21no—
292#546—22no—
293D42—22no—
294D42—21no—
295#537—21no—
296#537C22×C711yescharacteristic
297#535—21no—
298#535C22×C711yescharacteristic
299#525—21no—
300#525C22×C711yescharacteristic
301C2×#123—22no—
302C2×#121—21no—
303C2×#121C22×C711yescharacteristic
304#520C22×C711yescharacteristic
305C22×C4⋊C4C22×C711yescharacteristic, complemented
306#484—21no—
307#483—21no—
308#481—21no—
309#480—21no—
310#428C22×C712yescomplemented
311C2×#104C22×C712yes—
312C2×#104C22×C712yescomplemented
313C2×#104C22×C712yescomplemented
314#417—21no—
315#417—21no—
316#417C22×C712yes—
317#417C22×C712yescomplemented
318#417C22×C712yescomplemented
319C2×#103—21no—
320C2×#102—21no—
321C2×#100C22×C712yescomplemented
322#407C22×C711yescharacteristic, complemented
323#399—22no—
324#390C22×C712yescomplemented
325#384C22×C712yescomplemented
326C4×C22⋊C4C22×C711yescharacteristic, complemented
327#343C22×C712yescomplemented
328#339C22×C712yescomplemented
329C23×C7—21no—
330C23×C7—22no—
331C23×C7—22no—
332C23×C7—22no—
333C23×C7—21no—
334C23×C7—21no—
335C23×C7—24no—
336C23×C7—41no—
337C23×C7—42no—
338C23×C7—44no—
339C23×C7—42no—
340C23×C7—42no—
341C23×C7—42no—
342C23×C7—81no—
343C23×C7—82no—
344C23×C7—82no—
345C23×C7#12011yescharacteristic
346C23×C7#12011yescharacteristic
347C23×C7C22×D411yescharacteristic
348C7×Q8—21no—
349C7×Q8—21no—
350C7×Q8—21no—
351C7×Q8—22no—
352C7×Q8—42no—
353C7×Q8#12312yescomplemented
354C7×D4—24no—
355C7×D4—21no—
356C7×D4—21no—
357C7×D4—21no—
358C7×D4—22no—
359C7×D4—42no—
360C7×D4—42no—
361C7×D4—44no—
362C7×D4—42no—
363C7×D4—44no—
364C7×D4—42no—
365C7×D4—42no—
366C7×D4—44no—
367C7×D4—42no—
368C7×D4—41no—
369C7×D4—41no—
370C7×D4—42no—
371C7×D4—81no—
372C7×D4—82no—
373C7×D4—82no—
374C7×D4—82no—
375C7×D4—82no—
376C7×D4#12312yescomplemented
377C2×C4×C7—21no—
378C2×C4×C7—22no—
379C2×C4×C7—21no—
380C2×C4×C7—21no—
381C2×C4×C7—21no—
382C2×C4×C7—21no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—24no—
386C2×C4×C7—24no—
387C2×C4×C7—21no—
388C2×C4×C7—22no—
389C2×C4×C7—21no—
390C2×C4×C7—21no—
391C2×C4×C7—21no—
392C2×C4×C7—42no—
393C2×C4×C7—42no—
394C2×C4×C7—42no—
395C2×C4×C7—44no—
396C2×C4×C7—42no—
397C2×C4×C7—42no—
398C2×C4×C7—41no—
399C2×C4×C7—41no—
400C2×C4×C7—42no—
401C2×C4×C7—42no—
402C2×C4×C7—44no—
403C2×C4×C7—42no—
404C2×C4×C7—82no—
405C2×C4×C7—82no—
406C2×C4×C7—82no—
407C2×C4×C7#12011yescharacteristic
408C2×C4×C7#12011yescharacteristic
409C2×C4×C7C22×D411yescharacteristic
410C2×C4×C7C22×D411yescharacteristic
411C2×C4×C7C2×#4112yes—
412C2×C4×C7H(5,𝔽2)12yes—
413C7×C8—42no—
414C7×C8—42no—
415H(5,𝔽2)—24no—
416H(5,𝔽2)—42no—
417C2×#41—21no—
418C2×#41—21no—
419C2×#41—21no—
420C2×#41—21no—
421C2×#41—24no—
422C2×#41—42no—
423C2×#41C7×D411yescharacteristic
424C2×#41C7×D411yescharacteristic
425C2×#41C23×C711yescharacteristic
426C2×#41C23×C711yescharacteristic
427C2×#41C23×C711yescharacteristic
428C22×Q8C7×D411yescharacteristic
429C22×D4—21no—
430C22×D4—22no—
431C22×D4—22no—
432C22×D4—21no—
433C22×D4—21no—
434C22×D4C7×D411yescharacteristic
435C22×D4C7×D412yes—
436C22×D4C23×C711yescharacteristic
437C23×C4—21no—
438C23×C4—21no—
439C23×C4C23×C711yescharacteristic
440C2×M16—21no—
441C2×M16—42no—
442C2×M16C23×C712yes—
443C2×M16C23×C712yes—
444C22×C8—21no—
445#127—22no—
446#127—21no—
447#124—22no—
448#124—21no—
449#123—22no—
450#123—21no—
451#123—48no—
452C22⋊Q8—22no—
453C22⋊Q8—21no—
454C22⋊Q8—21no—
455C22⋊Q8C7×D411yescharacteristic
456C22⋊Q8C7×D411yescharacteristic
457#121—22no—
458#121—22no—
459#121—22no—
460#121—22no—
461#121—22no—
462#121—21no—
463#121—21no—
464#121—21no—
465#121—21no—
466#121—21no—
467#121—21no—
468#121—22no—
469#121—21no—
470#121—21no—
471#121C7×D411yescharacteristic
472#121C7×D411yescharacteristic
473#120—22no—
474#120—22no—
475#120—22no—
476#120—21no—
477#120—22no—
478C4×Q8—21no—
479C4×D4—22no—
480C4×D4—22no—
481C4×D4—21no—
482C4×D4—22no—
483C4×D4—21no—
484C4×D4—21no—
485#117—21no—
486#117C23×C711yescharacteristic
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4C23×C712yes—
495C2×C4⋊C4C23×C711yescharacteristic
496C2×C22⋊C4—22no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4C7×D412yes—
500C2×C42C23×C712yes—
501#107—22no—
502#106—22no—
503#104—24no—
504#104—42no—
505#104—42no—
506#103—22no—
507#103—22no—
508#103—22no—
509#102—22no—
510#102—22no—
511#102—22no—
512#100—42no—
513C22⋊C8—21no—
514C22⋊C8—21no—
515#95—21no—
516C22×C7—21no—
517C22×C7—21no—
518C22×C7—21no—
519C22×C7—21no—
520C22×C7—21no—
521C22×C7—22no—
522C22×C7—21no—
523C22×C7—21no—
524C22×C7—44no—
525C22×C7—41no—
526C22×C7—41no—
527C22×C7—41no—
528C22×C7—41no—
529C22×C7—42no—
530C22×C7—42no—
531C22×C7—41no—
532C22×C7—41no—
533C22×C7—41no—
534C22×C7—42no—
535C22×C7—41no—
536C22×C7—84no—
537C22×C7—84no—
538C22×C7—164no—
539C22×C7#45312yes—
540C22×C7C2×#12011yescharacteristic
541C22×C7#54612yes—
542C4×C7—21no—
543C4×C7—21no—
544C4×C7—22no—
545C4×C7—44no—
546C4×C7—41no—
547C4×C7—41no—
548C4×C7—42no—
549C4×C7—41no—
550C4×C7—41no—
551C4×C7—82no—
552C4×C7C2×#12311yescharacteristic
553C4×C7#53411yescharacteristic
554C4×C7#54612yes—
555C24—22no—
556C24—21no—
557C24C2×C7×D411yescharacteristic
558C24C2×C7×D412yes—
559#41—22no—
560#41—22no—
561#41—22no—
562#41—22no—
563#41—22no—
564#41—22no—
565#41—22no—
566#41—44no—
567#41—41no—
568#41—41no—
569#41—44no—
570#41—44no—
571#41—42no—
572#41—42no—
573#41C7×#4114yes—
574C2×Q8—21no—
575C2×Q8—22no—
576C2×Q8—41no—
577C2×Q8C2×C7×D411yescharacteristic
578C2×Q8C2×C7×D411yescharacteristic
579C2×Q8C2×C7×D411yescharacteristic
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—21no—
594C2×D4—22no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—41no—
601C2×D4—44no—
602C2×D4—44no—
603C2×D4—48no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—44no—
607C2×D4—84no—
608C2×D4C2×C7×D411yescharacteristic
609C2×D4C2×C7×D411yescharacteristic
610C2×D4C2×C7×D411yescharacteristic
611C22×C4—21no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4C2×C7×D411yescharacteristic
628C22×C4C2×C7×D411yescharacteristic
629C22×C4C2×C7×D411yescharacteristic
630C22×C4C2×C7×D411yescharacteristic
631C22×C4C2×C7×D411yescharacteristic
632C22×C4C2×C7×D412yes—
633C22×C4C24×C711yescharacteristic
634M16—22no—
635M16—22no—
636M16—22no—
637M16—22no—
638M16—42no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—42no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—48no—
651C4⋊C4—41no—
652C4⋊C4—41no—
653C4⋊C4C2×C7×D411yescharacteristic
654C4⋊C4C2×C7×D411yescharacteristic
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—24no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—48no—
669C42—22no—
670C42—21no—
671C42—22no—
672C42—22no—
673C2×C7—22no—
674C2×C7—22no—
675C2×C7—41no—
676C2×C7—42no—
677C2×C7—81no—
678C2×C7—82no—
679C2×C7—81no—
680C2×C7#240511yescharacteristic
681C2×C7C2×#45311yescharacteristic
682C2×C7#302211yescharacteristic
683C23—21no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—21no—
688C23—21no—
689C23—24no—
690C23—41no—
691C23—42no—
692C23—44no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—81no—
697C23—82no—
698C23—82no—
699C23C7×#12011yescharacteristic
700C23C7×#12011yescharacteristic
701C23C22×C7×D411yescharacteristic
702Q8—21no—
703Q8—21no—
704Q8—21no—
705Q8—22no—
706Q8—42no—
707Q8C7×#12312yescomplemented
708D4—24no—
709D4—21no—
710D4—21no—
711D4—21no—
712D4—22no—
713D4—42no—
714D4—42no—
715D4—44no—
716D4—42no—
717D4—44no—
718D4—42no—
719D4—42no—
720D4—44no—
721D4—42no—
722D4—41no—
723D4—41no—
724D4—42no—
725D4—81no—
726D4—82no—
727D4—82no—
728D4—82no—
729D4—82no—
730D4C7×#12312yescomplemented
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—21no—
742C2×C4—22no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—44no—
757C2×C4—42no—
758C2×C4—82no—
759C2×C4—82no—
760C2×C4—82no—
761C2×C4C7×#12011yescharacteristic
762C2×C4C7×#12011yescharacteristic
763C2×C4C22×C7×D411yescharacteristic
764C2×C4C22×C7×D411yescharacteristic
765C2×C4C2×C7×#4112yes—
766C2×C4C7×H(5,𝔽2)12yes—
767C8—42no—
768C8—42no—
769C7#2402611yescharacteristic, direct product factor, Sylow
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—22no—
776C22—21no—
777C22—21no—
778C22—44no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—42no—
784C22—42no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—42no—
789C22—41no—
790C22—84no—
791C22—84no—
792C22—164no—
793C22C7×#45312yes—
794C22C2×C7×#12011yescharacteristic
795C22C7×#54612yes—
796C4—21no—
797C4—21no—
798C4—22no—
799C4—44no—
800C4—41no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—41no—
805C4—82no—
806C4C2×C7×#12311yescharacteristic
807C4C7×#53411yescharacteristic
808C4C7×#54612yes—
809C2—22no—
810C2—22no—
811C2—41no—
812C2—42no—
813C2—81no—
814C2—82no—
815C2—81no—
816C2C7×#240511yescharacteristic
817C2C2×C7×#45311yescharacteristic
818C2C7×#302211yescharacteristic
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×#2501C2semidirect
5. C7×#2039C2semidirect
6. C7×#2037C2semidirect
7. C7×#1900C2semidirect
8. C7×#1871C2semidirect
9. C7×#1859C2semidirect
10. C7×#1792C2semidirect
11. C7×#1789C2semidirect
14. C22×C7×M16C22semidirect
31. C22×C7×C4⋊C4C22semidirect
36. C7×#428C22semidirect
38. C2×C7×#104C22semidirect
39. C2×C7×#104C22semidirect
43. C7×#417C22semidirect
44. C7×#417C22semidirect
47. C2×C7×#100C22semidirect
48. C7×#407C22semidirect
50. C7×#390C22semidirect
51. C7×#384C22semidirect
52. C4×C7×C22⋊C4C22semidirect
53. C7×#343C22semidirect
54. C7×#339C22semidirect
55. #24026C7direct (N × H)
158. #3092C2×C7semidirect
159. C2×#417C2×C7semidirect
160. #2501C2×C7semidirect
161. #2039C2×C7semidirect
162. #2037C2×C7semidirect
163. #1900C2×C7semidirect
164. #1871C2×C7semidirect
165. #1859C2×C7semidirect
166. #1792C2×C7semidirect
167. #1789C2×C7semidirect
288. C22×M16C22×C7semidirect
305. C22×C4⋊C4C22×C7semidirect
310. #428C22×C7semidirect
312. C2×#104C22×C7semidirect
313. C2×#104C22×C7semidirect
317. #417C22×C7semidirect
318. #417C22×C7semidirect
321. C2×#100C22×C7semidirect
322. #407C22×C7semidirect
324. #390C22×C7semidirect
325. #384C22×C7semidirect
326. C4×C22⋊C4C22×C7semidirect
327. #343C22×C7semidirect
328. #339C22×C7semidirect
353. C7×Q8#123semidirect
376. C7×D4#123semidirect
707. Q8C7×#123semidirect
730. D4C7×#123semidirect
769. C7#24026direct (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×#25012
C7×#20392
C7×#20372
C7×#19002
C7×#18712
C7×#18592
C7×#17922
C7×#17892
#240267