Finite Group Databasebeta

← C7×#24141 #13201357

Subgroups — C7×#24141 #13201357

Order 1792.

1200 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3505C211yesmaximal, characteristic
2C7×#2855C211yesmaximal, characteristic, complemented
3C7×#2854C211yesmaximal, characteristic, complemented
4C4×C7×#123C211yesmaximal, characteristic, complemented
5C7×#2044C212yesmaximal, complemented
6C7×#2022C212yesmaximal, complemented
7C7×#1996C211yesmaximal, characteristic, complemented
8C7×#1964C211yesmaximal, characteristic, complemented
9C7×#1890C212yesmaximal, complemented
10C7×#1867C212yesmaximal, complemented
11C7×#1799C211yesmaximal, characteristic, complemented
12C7×#553—22no—
13C7×#553—21no—
14C7×#552—21no—
15C7×#551—22no—
16C7×#548—21no—
17C7×#546—21no—
18C7×#539—21no—
19C7×#538—21no—
20C7×#534C2212yes—
21C7×#529—21no—
22C7×#525—21no—
23C2×C7×#123C2211yescharacteristic
24C2×C7×#123C2212yes—
25C2×C7×C22⋊Q8C2211yescharacteristic
26C2×C7×#121C2211yescharacteristic
27C7×#518C2212yes—
28C2×C4×C7×D4C2211yescharacteristic
29C22×C42×C7C2211yescharacteristic
30C2×C7×#99C2212yes—
31C2×C7×#99C2212yes—
32C2×C7×#99C2212yes—
33C7×#391—21no—
34C7×#390—21no—
35C7×#389—21no—
36C7×#389—21no—
37C7×#388—21no—
38C7×#388—22no—
39C7×#387—21no—
40C7×#387—22no—
41C7×#386C2211yescharacteristic
42C7×#386C2212yes—
43C7×#385C2212yes—
44C7×#385C2211yescharacteristic
45C7×#381C2212yes—
46C7×#381C2211yescharacteristic
47C7×#380C2211yescharacteristic
48C7×#380C2211yescharacteristic
49C4×C7×C4⋊C4—21no—
50C4×C7×C22⋊C4—21no—
51C4×C7×C22⋊C4C2211yescharacteristic
52C7×#342C2212yes—
53C7×#342C2212yes—
54C7×#342C2212yes—
55#24141C711yesmaximal, characteristic, direct product factor, Sylow
56C2×C7×#41—21no—
57C22×C7×Q8D411yescharacteristic
58C22×C7×D4D411yescharacteristic
59C22×C7×D4C2311yescharacteristic
60C22×C7×D4C2312yes—
61C23×C4×C7D411yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C7×#126—22no—
66C7×#126—22no—
67C7×#126—22no—
68C7×#125—21no—
69C7×#125—22no—
70C7×#124—21no—
71C7×#124—22no—
72C7×#123—22no—
73C7×#123—22no—
74C7×#123—22no—
75C7×#123—22no—
76C7×#123—22no—
77C7×#123—22no—
78C7×#123—22no—
79C7×#123—24no—
80C7×#123—42no—
81C7×C22⋊Q8—21no—
82C7×C22⋊Q8—22no—
83C7×C22⋊Q8—21no—
84C7×C22⋊Q8—21no—
85C7×C22⋊Q8—21no—
86C7×C22⋊Q8—21no—
87C7×#121—21no—
88C7×#121—22no—
89C7×#121—21no—
90C7×#121—21no—
91C7×#121—21no—
92C7×#121—21no—
93C7×#121—22no—
94C7×#121—22no—
95C7×#120—22no—
96C7×#120—22no—
97C4×C7×Q8—21no—
98C4×C7×D4—22no—
99C4×C7×D4—21no—
100C4×C7×D4—21no—
101C4×C7×D4—21no—
102C4×C7×D4—21no—
103C4×C7×D4—21no—
104C4×C7×D4—22no—
105C4×C7×D4—22no—
106C4×C7×D4—22no—
107C4×C7×D4—22no—
108C7×#117—21no—
109C7×#117—22no—
110C7×#117—22no—
111C2×C7×C4⋊C4—21no—
112C2×C7×C4⋊C4—21no—
113C2×C7×C4⋊C4—21no—
114C2×C7×C4⋊C4—21no—
115C2×C7×C4⋊C4—22no—
116C2×C7×C4⋊C4—22no—
117C2×C7×C4⋊C4D411yescharacteristic
118C2×C7×C4⋊C4D411yescharacteristic
119C2×C7×C4⋊C4D412yes—
120C2×C7×C4⋊C4D411yescharacteristic
121C2×C7×C22⋊C4—21no—
122C2×C7×C22⋊C4—22no—
123C2×C7×C22⋊C4—21no—
124C2×C7×C22⋊C4—22no—
125C2×C7×C22⋊C4—22no—
126C2×C7×C22⋊C4D411yescharacteristic
127C2×C7×C22⋊C4D412yes—
128C2×C7×C22⋊C4C2312yes—
129C2×C7×C22⋊C4C2311yescharacteristic
130C2×C7×C22⋊C4C2312yes—
131C2×C7×C22⋊C4C2311yescharacteristic
132C2×C7×C22⋊C4C2312yes—
133C2×C7×C22⋊C4C2311yescharacteristic
134C2×C42×C7—21no—
135C2×C42×C7—21no—
136C2×C42×C7—21no—
137C2×C42×C7—21no—
138C2×C42×C7—21no—
139C2×C42×C7—21no—
140C2×C42×C7—21no—
141C2×C42×C7D411yescharacteristic
142C7×#99—24no—
143C7×#99—42no—
144C7×#99—42no—
145C7×#95—21no—
146C7×#95—21no—
147C7×#95—21no—
148C7×#95—21no—
149C7×#95—21no—
150C7×#95—21no—
151C7×#95—21no—
152C7×#95—22no—
153C7×#95—22no—
154C7×#95—22no—
155C7×#95—22no—
156#3505C2×C711yescharacteristic
157#2855C2×C711yescharacteristic, complemented
158#2854C2×C711yescharacteristic, complemented
159C4×#123C2×C711yescharacteristic, complemented
160#2044C2×C712yescomplemented
161#2022C2×C712yescomplemented
162#1996C2×C711yescharacteristic, complemented
163#1964C2×C711yescharacteristic, complemented
164#1890C2×C712yescomplemented
165#1867C2×C712yescomplemented
166#1799C2×C711yescharacteristic, complemented
167C24×C7C2×D412yes—
168C24×C7C2×D411yescharacteristic
169C24×C7C2411yescharacteristic
170C7×#41—82no—
171C2×C7×Q8—21no—
172C2×C7×Q8—21no—
173C2×C7×Q8—42no—
174C2×C7×D4—21no—
175C2×C7×D4—22no—
176C2×C7×D4—21no—
177C2×C7×D4—22no—
178C2×C7×D4—22no—
179C2×C7×D4—21no—
180C2×C7×D4—21no—
181C2×C7×D4—22no—
182C2×C7×D4—21no—
183C2×C7×D4—22no—
184C2×C7×D4—21no—
185C2×C7×D4—22no—
186C2×C7×D4—22no—
187C2×C7×D4—22no—
188C2×C7×D4—21no—
189C2×C7×D4—21no—
190C2×C7×D4—42no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—21no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—42no—
209C22×C4×C7—42no—
210C22×C4×C7—42no—
211C22×C4×C7C2×D411yescharacteristic
212C22×C4×C7C2×D412yes—
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2×D412yes—
218C22×C4×C7C2×D411yescharacteristic
219C22×C4×C7C2×D412yes—
220C22×C4×C7C2×D411yescharacteristic
221C22×C4×C7C2×D411yescharacteristic
222C22×C4×C7C2×D411yescharacteristic
223C22×C4×C7#4112yescomplemented
224C7×C4⋊C4—24no—
225C7×C4⋊C4—22no—
226C7×C4⋊C4—22no—
227C7×C4⋊C4—22no—
228C7×C4⋊C4—22no—
229C7×C4⋊C4—21no—
230C7×C4⋊C4—22no—
231C7×C4⋊C4—21no—
232C7×C4⋊C4—21no—
233C7×C4⋊C4—21no—
234C7×C4⋊C4—21no—
235C7×C4⋊C4—22no—
236C7×C4⋊C4—21no—
237C7×C4⋊C4—44no—
238C7×C4⋊C4—42no—
239C7×C4⋊C4—42no—
240C7×C4⋊C4—42no—
241C7×C4⋊C4—44no—
242C7×C22⋊C4—22no—
243C7×C22⋊C4—22no—
244C7×C22⋊C4—24no—
245C7×C22⋊C4—22no—
246C7×C22⋊C4—22no—
247C7×C22⋊C4—22no—
248C7×C22⋊C4—22no—
249C7×C22⋊C4—21no—
250C7×C22⋊C4—22no—
251C7×C22⋊C4—21no—
252C7×C22⋊C4—22no—
253C7×C22⋊C4—21no—
254C7×C22⋊C4—22no—
255C7×C22⋊C4—21no—
256C7×C22⋊C4—21no—
257C7×C22⋊C4—22no—
258C7×C22⋊C4—22no—
259C7×C22⋊C4—22no—
260C7×C22⋊C4—21no—
261C7×C22⋊C4—22no—
262C7×C22⋊C4—22no—
263C7×C22⋊C4—21no—
264C7×C22⋊C4—44no—
265C7×C22⋊C4—44no—
266C7×C22⋊C4—42no—
267C7×C22⋊C4#4112yescomplemented
268C42×C7—22no—
269C42×C7—22no—
270C42×C7—21no—
271C42×C7—21no—
272C42×C7—42no—
273C42×C7—41no—
274C42×C7—41no—
275C42×C7—41no—
276C42×C7—41no—
277#553—22no—
278#553—21no—
279#552—21no—
280#551—22no—
281#548—21no—
282#546—21no—
283#539—21no—
284#538—21no—
285#534C22×C712yes—
286#529—21no—
287#525—21no—
288C2×#123C22×C711yescharacteristic
289C2×#123C22×C712yes—
290C2×C22⋊Q8C22×C711yescharacteristic
291C2×#121C22×C711yescharacteristic
292#518C22×C712yes—
293C2×C4×D4C22×C711yescharacteristic
294C22×C42C22×C711yescharacteristic
295C2×#99C22×C712yes—
296C2×#99C22×C712yes—
297C2×#99C22×C712yes—
298#391—21no—
299#390—21no—
300#389—21no—
301#389—21no—
302#388—22no—
303#388—21no—
304#387—22no—
305#387—21no—
306#386C22×C712yes—
307#386C22×C711yescharacteristic
308#385C22×C712yes—
309#385C22×C711yescharacteristic
310#381C22×C712yes—
311#381C22×C711yescharacteristic
312#380C22×C711yescharacteristic
313#380C22×C711yescharacteristic
314C4×C4⋊C4—21no—
315C4×C22⋊C4—21no—
316C4×C22⋊C4C22×C711yescharacteristic
317#342C22×C712yes—
318#342C22×C712yes—
319#342C22×C712yes—
320C23×C7—21no—
321C23×C7—22no—
322C23×C7—21no—
323C23×C7—21no—
324C23×C7—22no—
325C23×C7—22no—
326C23×C7—41no—
327C23×C7—41no—
328C23×C7—41no—
329C23×C7—41no—
330C23×C7—42no—
331C23×C7—42no—
332C23×C7C22×D411yescharacteristic
333C23×C7C22×D411yescharacteristic
334C23×C7C22×D411yescharacteristic
335C23×C7C2×#4111yescharacteristic
336C23×C7C2×#4111yescharacteristic
337C23×C7H(5,𝔽2)11yescharacteristic
338C23×C72−1+411yescharacteristic
339C7×Q8—42no—
340C7×Q8—81no—
341C7×D4—42no—
342C7×D4—42no—
343C7×D4—41no—
344C7×D4—41no—
345C7×D4—41no—
346C7×D4—42no—
347C7×D4—42no—
348C7×D4—41no—
349C7×D4—42no—
350C7×D4—81no—
351C7×D4—82no—
352C7×D4—82no—
353C2×C4×C7—22no—
354C2×C4×C7—22no—
355C2×C4×C7—22no—
356C2×C4×C7—22no—
357C2×C4×C7—22no—
358C2×C4×C7—22no—
359C2×C4×C7—21no—
360C2×C4×C7—22no—
361C2×C4×C7—21no—
362C2×C4×C7—21no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—21no—
368C2×C4×C7—21no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—41no—
374C2×C4×C7—41no—
375C2×C4×C7—41no—
376C2×C4×C7—41no—
377C2×C4×C7—41no—
378C2×C4×C7—41no—
379C2×C4×C7—41no—
380C2×C4×C7—41no—
381C2×C4×C7—41no—
382C2×C4×C7—41no—
383C2×C4×C7—41no—
384C2×C4×C7—41no—
385C2×C4×C7—41no—
386C2×C4×C7—42no—
387C2×C4×C7—41no—
388C2×C4×C7—42no—
389C2×C4×C7—41no—
390C2×C4×C7—42no—
391C2×C4×C7—41no—
392C2×C4×C7—41no—
393C2×C4×C7—42no—
394C2×C4×C7—42no—
395C2×C4×C7—42no—
396C2×C4×C7—42no—
397C2×C4×C7—41no—
398C2×C4×C7—42no—
399C2×C4×C7—42no—
400C2×C4×C7—81no—
401C2×C4×C7—82no—
402C2×C4×C7—82no—
403C2×C4×C7#12011yescharacteristic
404C2×C4×C7#12011yescharacteristic
405C2×C4×C7#12011yescharacteristic
406C2×C4×C7#12011yescharacteristic
407C2×#41—21no—
408C22×Q8C7×D411yescharacteristic
409C22×D4C7×D411yescharacteristic
410C22×D4C23×C711yescharacteristic
411C22×D4C23×C712yes—
412C23×C4C7×D411yescharacteristic
413C23×C4C23×C711yescharacteristic
414C23×C4C23×C711yescharacteristic
415C23×C4C23×C711yescharacteristic
416#126—22no—
417#126—22no—
418#126—22no—
419#125—21no—
420#125—22no—
421#124—21no—
422#124—22no—
423#123—22no—
424#123—22no—
425#123—22no—
426#123—22no—
427#123—22no—
428#123—22no—
429#123—22no—
430#123—24no—
431#123—42no—
432C22⋊Q8—21no—
433C22⋊Q8—22no—
434C22⋊Q8—21no—
435C22⋊Q8—21no—
436C22⋊Q8—21no—
437C22⋊Q8—21no—
438#121—21no—
439#121—22no—
440#121—21no—
441#121—21no—
442#121—21no—
443#121—21no—
444#121—22no—
445#121—22no—
446#120—22no—
447#120—22no—
448C4×Q8—21no—
449C4×D4—22no—
450C4×D4—21no—
451C4×D4—21no—
452C4×D4—21no—
453C4×D4—21no—
454C4×D4—21no—
455C4×D4—22no—
456C4×D4—22no—
457C4×D4—22no—
458C4×D4—22no—
459#117—21no—
460#117—22no—
461#117—22no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4C7×D411yescharacteristic
469C2×C4⋊C4C7×D411yescharacteristic
470C2×C4⋊C4C7×D412yes—
471C2×C4⋊C4C7×D411yescharacteristic
472C2×C22⋊C4—22no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4C7×D411yescharacteristic
478C2×C22⋊C4C7×D412yes—
479C2×C22⋊C4C23×C712yes—
480C2×C22⋊C4C23×C711yescharacteristic
481C2×C22⋊C4C23×C712yes—
482C2×C22⋊C4C23×C711yescharacteristic
483C2×C22⋊C4C23×C712yes—
484C2×C22⋊C4C23×C711yescharacteristic
485C2×C42—21no—
486C2×C42—21no—
487C2×C42—21no—
488C2×C42—21no—
489C2×C42—21no—
490C2×C42—21no—
491C2×C42—21no—
492C2×C42C7×D411yescharacteristic
493#99—24no—
494#99—42no—
495#99—42no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—22no—
504#95—22no—
505#95—22no—
506#95—22no—
507C22×C7—21no—
508C22×C7—21no—
509C22×C7—21no—
510C22×C7—21no—
511C22×C7—21no—
512C22×C7—21no—
513C22×C7—41no—
514C22×C7—41no—
515C22×C7—41no—
516C22×C7—41no—
517C22×C7—42no—
518C22×C7—41no—
519C22×C7—42no—
520C22×C7—41no—
521C22×C7—42no—
522C22×C7—42no—
523C22×C7—41no—
524C22×C7—82no—
525C22×C7—81no—
526C22×C7—82no—
527C22×C7C2×#12011yescharacteristic
528C22×C7#52511yescharacteristic
529C22×C7#53711yescharacteristic
530C22×C7#54611yescharacteristic
531C22×C7#54711yescharacteristic
532C22×C7#54811yescharacteristic
533C22×C7#55011yescharacteristic
534C4×C7—21no—
535C4×C7—21no—
536C4×C7—21no—
537C4×C7—42no—
538C4×C7—42no—
539C4×C7—41no—
540C4×C7—42no—
541C4×C7—41no—
542C4×C7—42no—
543C4×C7—42no—
544C4×C7—41no—
545C4×C7—42no—
546C4×C7—82no—
547C4×C7—82no—
548C4×C7—81no—
549C4×C7#45812yes—
550C24C2×C7×D412yes—
551C24C2×C7×D411yescharacteristic
552C24C24×C711yescharacteristic
553#41—82no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—42no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—42no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4C2×C7×D411yescharacteristic
595C22×C4C2×C7×D412yes—
596C22×C4C2×C7×D411yescharacteristic
597C22×C4C2×C7×D411yescharacteristic
598C22×C4C2×C7×D411yescharacteristic
599C22×C4C2×C7×D411yescharacteristic
600C22×C4C2×C7×D412yes—
601C22×C4C2×C7×D411yescharacteristic
602C22×C4C2×C7×D412yes—
603C22×C4C2×C7×D411yescharacteristic
604C22×C4C2×C7×D411yescharacteristic
605C22×C4C2×C7×D411yescharacteristic
606C22×C4C7×#4112yescomplemented
607C4⋊C4—24no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—21no—
613C4⋊C4—22no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—22no—
619C4⋊C4—21no—
620C4⋊C4—44no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—44no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—24no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—21no—
633C22⋊C4—22no—
634C22⋊C4—21no—
635C22⋊C4—22no—
636C22⋊C4—21no—
637C22⋊C4—22no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—21no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—21no—
647C22⋊C4—44no—
648C22⋊C4—44no—
649C22⋊C4—42no—
650C22⋊C4C7×#4112yescomplemented
651C42—22no—
652C42—22no—
653C42—21no—
654C42—21no—
655C42—42no—
656C42—41no—
657C42—41no—
658C42—41no—
659C42—41no—
660C2×C7—21no—
661C2×C7—21no—
662C2×C7—21no—
663C2×C7—21no—
664C2×C7—21no—
665C2×C7—21no—
666C2×C7—81no—
667C2×C7—82no—
668C2×C7#240711yescharacteristic
669C2×C7C2×#45811yescharacteristic
670C2×C7#302511yescharacteristic
671C23—21no—
672C23—22no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—22no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—42no—
682C23—42no—
683C23C22×C7×D411yescharacteristic
684C23C22×C7×D411yescharacteristic
685C23C22×C7×D411yescharacteristic
686C23C2×C7×#4111yescharacteristic
687C23C2×C7×#4111yescharacteristic
688C23C7×H(5,𝔽2)11yescharacteristic
689C23C7×2−1+411yescharacteristic
690Q8—42no—
691Q8—81no—
692D4—42no—
693D4—42no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—42no—
698D4—42no—
699D4—41no—
700D4—42no—
701D4—81no—
702D4—82no—
703D4—82no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—81no—
752C2×C4—82no—
753C2×C4—82no—
754C2×C4C7×#12011yescharacteristic
755C2×C4C7×#12011yescharacteristic
756C2×C4C7×#12011yescharacteristic
757C2×C4C7×#12011yescharacteristic
758C7#2414111yescharacteristic, direct product factor, Sylow
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—42no—
772C22—41no—
773C22—42no—
774C22—42no—
775C22—41no—
776C22—82no—
777C22—81no—
778C22—82no—
779C22C2×C7×#12011yescharacteristic
780C22C7×#52511yescharacteristic
781C22C7×#53711yescharacteristic
782C22C7×#54611yescharacteristic
783C22C7×#54711yescharacteristic
784C22C7×#54811yescharacteristic
785C22C7×#55011yescharacteristic
786C4—21no—
787C4—21no—
788C4—21no—
789C4—42no—
790C4—42no—
791C4—41no—
792C4—42no—
793C4—41no—
794C4—42no—
795C4—42no—
796C4—41no—
797C4—42no—
798C4—82no—
799C4—82no—
800C4—81no—
801C4C7×#45812yes—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—21no—
806C2—21no—
807C2—21no—
808C2—81no—
809C2—82no—
810C2C7×#240711yescharacteristic
811C2C2×C7×#45811yescharacteristic
812C2C7×#302511yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC24C24×C7
prime radicalC7×#3505C2
LCSG ▷ C24 ▷ 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×#2855C2semidirect
3. C7×#2854C2semidirect
4. C4×C7×#123C2semidirect
5. C7×#2044C2semidirect
6. C7×#2022C2semidirect
7. C7×#1996C2semidirect
8. C7×#1964C2semidirect
9. C7×#1890C2semidirect
10. C7×#1867C2semidirect
11. C7×#1799C2semidirect
55. #24141C7direct (N × H)
157. #2855C2×C7semidirect
158. #2854C2×C7semidirect
159. C4×#123C2×C7semidirect
160. #2044C2×C7semidirect
161. #2022C2×C7semidirect
162. #1996C2×C7semidirect
163. #1964C2×C7semidirect
164. #1890C2×C7semidirect
165. #1867C2×C7semidirect
166. #1799C2×C7semidirect
223. C22×C4×C7#41semidirect
267. C7×C22⋊C4#41semidirect
606. C22×C4C7×#41semidirect
650. C22⋊C4C7×#41semidirect
758. C7#24141direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#35052
C7×#28552
C7×#28542
C4×C7×#1232
C7×#20442
C7×#20222
C7×#19962
C7×#19642
C7×#18902
C7×#18672
C7×#17992
#241417