Finite Group Databasebeta

← C7×#15950 #13193166

Subgroups — C7×#15950 #13193166

Order 1792.

2678 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#123C211yesmaximal, characteristic, complemented
2C22×C7×#121C211yesmaximal, characteristic
3C2×C7×#386C211yesmaximal, characteristic, complemented
4C2×C7×#385C211yesmaximal, characteristic, complemented
5C2×C7×#385C212yesmaximal, complemented
6C7×#1441C212yesmaximal, complemented
7C7×#1440C211yesmaximal, characteristic, complemented
8C7×#1439C212yesmaximal, complemented
9C7×#1438C212yesmaximal, complemented
10C7×#1438C211yesmaximal, characteristic, complemented
11C7×#1438C211yesmaximal, characteristic, complemented
12C23×C7×D4C2211yescharacteristic
13C23×C7×D4C2211yescharacteristic
14C23×C7×D4C2211yescharacteristic
15C24×C4×C7C2211yescharacteristic
16C24×C4×C7C2211yescharacteristic
17C2×C7×#123—24no—
18C2×C7×#123—28no—
19C2×C7×#121—24no—
20C2×C7×#121—24no—
21C2×C7×#121—24no—
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2212yes—
24C22×C7×C4⋊C4C2212yes—
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2212yes—
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2211yescharacteristic
29C22×C7×C22⋊C4C2212yes—
30C22×C7×C22⋊C4C2212yes—
31C22×C7×C22⋊C4C2211yescharacteristic
32C22×C7×C22⋊C4C2211yescharacteristic
33C22×C7×C22⋊C4C2212yes—
34C7×#386—24no—
35C7×#385—28no—
36C7×#385—24no—
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39C2×C7×#95C2212yes—
40C2×C7×#95C2212yes—
41C2×C7×#95C2212yes—
42C2×C7×#95C2212yes—
43#15950C711yesmaximal, characteristic, direct product factor, Sylow
44C25×C7C2311yescharacteristic
45C25×C7C2311yescharacteristic
46C25×C7C2311yescharacteristic
47C22×C7×D4—22no—
48C22×C7×D4—22no—
49C22×C7×D4—22no—
50C22×C7×D4—22no—
51C22×C7×D4—22no—
52C22×C7×D4—22no—
53C22×C7×D4—24no—
54C22×C7×D4—24no—
55C22×C7×D4—22no—
56C22×C7×D4—24no—
57C22×C7×D4—42no—
58C22×C7×D4—42no—
59C22×C7×D4—42no—
60C22×C7×D4D414yes—
61C22×C7×D4D414yes—
62C23×C4×C7—22no—
63C23×C4×C7—22no—
64C23×C4×C7—22no—
65C23×C4×C7—22no—
66C23×C4×C7—24no—
67C23×C4×C7—22no—
68C23×C4×C7—22no—
69C23×C4×C7—24no—
70C23×C4×C7—42no—
71C23×C4×C7—42no—
72C23×C4×C7C2312yes—
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2312yes—
76C23×C4×C7C2312yes—
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2312yes—
79C23×C4×C7C2311yescharacteristic
80C7×#123—232no—
81C7×#121—232no—
82C2×C7×C4⋊C4—22no—
83C2×C7×C4⋊C4—22no—
84C2×C7×C4⋊C4—22no—
85C2×C7×C4⋊C4—24no—
86C2×C7×C4⋊C4—24no—
87C2×C7×C4⋊C4—24no—
88C2×C7×C4⋊C4—24no—
89C2×C7×C4⋊C4—42no—
90C2×C7×C4⋊C4D418yescomplemented
91C2×C7×C22⋊C4—22no—
92C2×C7×C22⋊C4—22no—
93C2×C7×C22⋊C4—22no—
94C2×C7×C22⋊C4—22no—
95C2×C7×C22⋊C4—22no—
96C2×C7×C22⋊C4—24no—
97C2×C7×C22⋊C4—24no—
98C2×C7×C22⋊C4—24no—
99C2×C7×C22⋊C4—22no—
100C2×C7×C22⋊C4—22no—
101C2×C7×C22⋊C4—24no—
102C2×C7×C22⋊C4—24no—
103C2×C7×C22⋊C4—24no—
104C2×C7×C22⋊C4—24no—
105C2×C7×C22⋊C4—24no—
106C2×C7×C22⋊C4—24no—
107C2×C7×C22⋊C4—22no—
108C2×C7×C22⋊C4—24no—
109C2×C7×C22⋊C4—24no—
110C2×C7×C22⋊C4—42no—
111C2×C7×C22⋊C4—42no—
112C2×C7×C22⋊C4—42no—
113C2×C7×C22⋊C4—42no—
114C2×C7×C22⋊C4D414yes—
115C7×#95—24no—
116C7×#95—24no—
117C7×#95—24no—
118C7×#95—24no—
119C7×#95—42no—
120C7×#95—42no—
121C22×#123C2×C711yescharacteristic, complemented
122C22×#121C2×C711yescharacteristic
123C2×#386C2×C711yescharacteristic, complemented
124C2×#385C2×C712yescomplemented
125C2×#385C2×C711yescharacteristic, complemented
126#1441C2×C712yescomplemented
127#1440C2×C711yescharacteristic, complemented
128#1439C2×C712yescomplemented
129#1438C2×C712yescomplemented
130#1438C2×C711yescharacteristic, complemented
131#1438C2×C711yescharacteristic, complemented
132C24×C7—22no—
133C24×C7—22no—
134C24×C7—21no—
135C24×C7—21no—
136C24×C7—22no—
137C24×C7—22no—
138C24×C7—22no—
139C24×C7—22no—
140C24×C7—22no—
141C24×C7—22no—
142C24×C7—22no—
143C24×C7—22no—
144C24×C7—22no—
145C24×C7—22no—
146C24×C7—21no—
147C24×C7—21no—
148C24×C7—22no—
149C24×C7—22no—
150C24×C7—22no—
151C24×C7—22no—
152C24×C7—22no—
153C24×C7C2×D412yes—
154C24×C7C2×D412yes—
155C24×C7C2×D412yes—
156C24×C7C2×D412yes—
157C24×C7C2×D412yes—
158C24×C7#4114yes—
159C24×C7C2411yescharacteristic
160C2×C7×D4—28no—
161C2×C7×D4—28no—
162C2×C7×D4—28no—
163C2×C7×D4—28no—
164C2×C7×D4—28no—
165C2×C7×D4—44no—
166C2×C7×D4—44no—
167C2×C7×D4—48no—
168C2×C7×D4—48no—
169C2×C7×D4—48no—
170C2×C7×D4—48no—
171C2×C7×D4—48no—
172C2×C7×D4—48no—
173C2×C7×D4—44no—
174C2×C7×D4—44no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—22no—
178C22×C4×C7—28no—
179C22×C4×C7—28no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—22no—
184C22×C4×C7—22no—
185C22×C4×C7—22no—
186C22×C4×C7—22no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—22no—
196C22×C4×C7—22no—
197C22×C4×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—48no—
218C22×C4×C7—48no—
219C22×C4×C7—48no—
220C22×C4×C7—48no—
221C22×C4×C7—44no—
222C22×C4×C7—44no—
223C22×C4×C7—44no—
224C22×C4×C7—44no—
225C22×C4×C7C2×D412yes—
226C22×C4×C7C2×D412yes—
227C22×C4×C7C2×D414yes—
228C22×C4×C7C2×D414yes—
229C22×C4×C7C2×D412yes—
230C22×C4×C7C2×D414yes—
231C22×C4×C7C2×D412yes—
232C22×C4×C7#4114yes—
233C7×C4⋊C4—28no—
234C7×C4⋊C4—216no—
235C7×C4⋊C4—48no—
236C7×C22⋊C4—216no—
237C7×C22⋊C4—28no—
238C7×C22⋊C4—28no—
239C7×C22⋊C4—28no—
240C7×C22⋊C4—216no—
241C7×C22⋊C4—28no—
242C7×C22⋊C4—48no—
243C7×C22⋊C4—48no—
244C7×C22⋊C4—44no—
245C23×D4C22×C711yescharacteristic
246C23×D4C22×C711yescharacteristic
247C23×D4C22×C711yescharacteristic
248C24×C4C22×C711yescharacteristic
249C24×C4C22×C711yescharacteristic
250C2×#123—24no—
251C2×#123—28no—
252C2×#121—24no—
253C2×#121—24no—
254C2×#121—24no—
255C22×C4⋊C4C22×C711yescharacteristic
256C22×C4⋊C4C22×C712yes—
257C22×C4⋊C4C22×C712yes—
258C22×C22⋊C4C22×C711yescharacteristic
259C22×C22⋊C4C22×C712yes—
260C22×C22⋊C4C22×C711yescharacteristic
261C22×C22⋊C4C22×C711yescharacteristic
262C22×C22⋊C4C22×C712yes—
263C22×C22⋊C4C22×C712yes—
264C22×C22⋊C4C22×C711yescharacteristic
265C22×C22⋊C4C22×C712yes—
266C22×C22⋊C4C22×C711yescharacteristic
267#386—24no—
268#385—28no—
269#385—24no—
270C2×#95C22×C712yes—
271C2×#95C22×C712yes—
272C2×#95C22×C712yes—
273C2×#95C22×C712yes—
274C2×#95C22×C712yes—
275C2×#95C22×C712yes—
276C23×C7—22no—
277C23×C7—22no—
278C23×C7—22no—
279C23×C7—22no—
280C23×C7—24no—
281C23×C7—22no—
282C23×C7—22no—
283C23×C7—22no—
284C23×C7—22no—
285C23×C7—24no—
286C23×C7—24no—
287C23×C7—24no—
288C23×C7—24no—
289C23×C7—24no—
290C23×C7—24no—
291C23×C7—24no—
292C23×C7—24no—
293C23×C7—24no—
294C23×C7—24no—
295C23×C7—24no—
296C23×C7—24no—
297C23×C7—24no—
298C23×C7—22no—
299C23×C7—22no—
300C23×C7—22no—
301C23×C7—24no—
302C23×C7—24no—
303C23×C7—41no—
304C23×C7—41no—
305C23×C7—42no—
306C23×C7—41no—
307C23×C7—41no—
308C23×C7—42no—
309C23×C7—42no—
310C23×C7—42no—
311C23×C7—42no—
312C23×C7—42no—
313C23×C7—42no—
314C23×C7—42no—
315C23×C7—42no—
316C23×C7—42no—
317C23×C7—42no—
318C23×C7—42no—
319C23×C7—42no—
320C23×C7—42no—
321C23×C7—41no—
322C23×C7—41no—
323C23×C7—42no—
324C23×C7—41no—
325C23×C7—41no—
326C23×C7—42no—
327C23×C7—42no—
328C23×C7—42no—
329C23×C7—42no—
330C23×C7—42no—
331C23×C7—42no—
332C23×C7—42no—
333C23×C7—42no—
334C23×C7—42no—
335C23×C7—42no—
336C23×C7—42no—
337C23×C7#12014yes—
338C23×C7#12314yescomplemented
339C23×C7C22×D411yescharacteristic
340C23×C7C22×D411yescharacteristic
341C23×C7C22×D411yescharacteristic
342C23×C7C22×D412yes—
343C23×C7C2×#4112yes—
344C23×C7C2×#4112yes—
345C23×C7H(5,𝔽2)12yes—
346C23×C7H(5,𝔽2)12yes—
347C23×C72−1+412yes—
348C7×D4—416no—
349C7×D4—416no—
350C7×D4—416no—
351C2×C4×C7—22no—
352C2×C4×C7—22no—
353C2×C4×C7—24no—
354C2×C4×C7—24no—
355C2×C4×C7—24no—
356C2×C4×C7—22no—
357C2×C4×C7—24no—
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—22no—
361C2×C4×C7—24no—
362C2×C4×C7—24no—
363C2×C4×C7—24no—
364C2×C4×C7—22no—
365C2×C4×C7—24no—
366C2×C4×C7—24no—
367C2×C4×C7—24no—
368C2×C4×C7—24no—
369C2×C4×C7—24no—
370C2×C4×C7—24no—
371C2×C4×C7—416no—
372C2×C4×C7—416no—
373C2×C4×C7—42no—
374C2×C4×C7—41no—
375C2×C4×C7—41no—
376C2×C4×C7—41no—
377C2×C4×C7—42no—
378C2×C4×C7—41no—
379C2×C4×C7—42no—
380C2×C4×C7—42no—
381C2×C4×C7—42no—
382C2×C4×C7—42no—
383C2×C4×C7—42no—
384C2×C4×C7—42no—
385C2×C4×C7—42no—
386C2×C4×C7—42no—
387C2×C4×C7—42no—
388C2×C4×C7—42no—
389C2×C4×C7—42no—
390C2×C4×C7—42no—
391C2×C4×C7—42no—
392C2×C4×C7—42no—
393C2×C4×C7—42no—
394C2×C4×C7—42no—
395C2×C4×C7—42no—
396C2×C4×C7—42no—
397C2×C4×C7—42no—
398C2×C4×C7—42no—
399C2×C4×C7—42no—
400C2×C4×C7#12014yes—
401C25C23×C711yescharacteristic
402C25C23×C711yescharacteristic
403C25C23×C711yescharacteristic
404C22×D4—22no—
405C22×D4—22no—
406C22×D4—22no—
407C22×D4—22no—
408C22×D4—22no—
409C22×D4—22no—
410C22×D4—24no—
411C22×D4—24no—
412C22×D4—22no—
413C22×D4—24no—
414C22×D4—42no—
415C22×D4—42no—
416C22×D4—42no—
417C22×D4C7×D414yes—
418C22×D4C7×D414yes—
419C23×C4—22no—
420C23×C4—22no—
421C23×C4—22no—
422C23×C4—22no—
423C23×C4—24no—
424C23×C4—22no—
425C23×C4—22no—
426C23×C4—24no—
427C23×C4—42no—
428C23×C4—42no—
429C23×C4C23×C712yes—
430C23×C4C23×C712yes—
431C23×C4C23×C712yes—
432C23×C4C23×C711yescharacteristic
433C23×C4C23×C711yescharacteristic
434C23×C4C23×C711yescharacteristic
435C23×C4C23×C712yes—
436C23×C4C23×C711yescharacteristic
437#123—232no—
438#121—232no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4C7×D418yescomplemented
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—42no—
468C2×C22⋊C4—42no—
469C2×C22⋊C4—42no—
470C2×C22⋊C4—42no—
471C2×C22⋊C4C7×D414yes—
472#95—24no—
473#95—24no—
474#95—24no—
475#95—24no—
476#95—42no—
477#95—42no—
478C22×C7—24no—
479C22×C7—24no—
480C22×C7—24no—
481C22×C7—24no—
482C22×C7—28no—
483C22×C7—42no—
484C22×C7—42no—
485C22×C7—44no—
486C22×C7—44no—
487C22×C7—44no—
488C22×C7—44no—
489C22×C7—44no—
490C22×C7—44no—
491C22×C7—44no—
492C22×C7—44no—
493C22×C7—44no—
494C22×C7—44no—
495C22×C7—44no—
496C22×C7—42no—
497C22×C7—42no—
498C22×C7—42no—
499C22×C7—44no—
500C22×C7—44no—
501C22×C7—82no—
502C22×C7—82no—
503C22×C7—82no—
504C22×C7—82no—
505C22×C7C2×#12011yescharacteristic
506C22×C7C2×#12011yescharacteristic
507C22×C7C2×#12311yescharacteristic
508C22×C7#52511yescharacteristic
509C22×C7#52512yes—
510C22×C7#53411yescharacteristic
511C22×C7#53411yescharacteristic
512C22×C7#53611yescharacteristic
513C22×C7#53712yes—
514C22×C7#53812yes—
515C22×C7#53912yes—
516C22×C7D4212yes—
517C22×C7D4212yes—
518C22×C7#54612yes—
519C22×C7#54612yes—
520C22×C7#54712yes—
521C22×C7#54712yes—
522C22×C7#54812yes—
523C22×C7#55012yes—
524C22×C7#55312yes—
525C22×C7#56212yes—
526C4×C7—24no—
527C4×C7—42no—
528C4×C7—44no—
529C4×C7—42no—
530C4×C7—42no—
531C4×C7—44no—
532C4×C7—44no—
533C4×C7—82no—
534C24—22no—
535C24—22no—
536C24—21no—
537C24—21no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—21no—
549C24—21no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24C2×C7×D412yes—
556C24C2×C7×D412yes—
557C24C2×C7×D412yes—
558C24C2×C7×D412yes—
559C24C2×C7×D412yes—
560C24C7×#4114yes—
561C24C24×C711yescharacteristic
562C2×D4—28no—
563C2×D4—28no—
564C2×D4—28no—
565C2×D4—28no—
566C2×D4—28no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—48no—
570C2×D4—48no—
571C2×D4—48no—
572C2×D4—48no—
573C2×D4—48no—
574C2×D4—48no—
575C2×D4—44no—
576C2×D4—44no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—28no—
581C22×C4—28no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—48no—
620C22×C4—48no—
621C22×C4—48no—
622C22×C4—48no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4C2×C7×D412yes—
628C22×C4C2×C7×D412yes—
629C22×C4C2×C7×D414yes—
630C22×C4C2×C7×D414yes—
631C22×C4C2×C7×D412yes—
632C22×C4C2×C7×D414yes—
633C22×C4C2×C7×D412yes—
634C22×C4C7×#4114yes—
635C4⋊C4—28no—
636C4⋊C4—216no—
637C4⋊C4—48no—
638C22⋊C4—28no—
639C22⋊C4—28no—
640C22⋊C4—216no—
641C22⋊C4—216no—
642C22⋊C4—28no—
643C22⋊C4—28no—
644C22⋊C4—48no—
645C22⋊C4—48no—
646C22⋊C4—44no—
647C2×C7—44no—
648C2×C7—44no—
649C2×C7—82no—
650C2×C7#240311yescharacteristic
651C2×C7#240511yescharacteristic
652C2×C7#240611yescharacteristic
653C2×C7#240712yes—
654C2×C7#244312yes—
655C2×C7#245612yes—
656C2×C7#268112yes—
657C2×C7#268212yes—
658C2×C7#270812yes—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—24no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—24no—
685C23—24no—
686C23—41no—
687C23—41no—
688C23—42no—
689C23—41no—
690C23—41no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—41no—
705C23—41no—
706C23—42no—
707C23—41no—
708C23—41no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23C7×#12014yes—
721C23C7×#12314yescomplemented
722C23C22×C7×D411yescharacteristic
723C23C22×C7×D411yescharacteristic
724C23C22×C7×D411yescharacteristic
725C23C22×C7×D412yes—
726C23C2×C7×#4112yes—
727C23C2×C7×#4112yes—
728C23C7×H(5,𝔽2)12yes—
729C23C7×H(5,𝔽2)12yes—
730C23C7×2−1+412yes—
731D4—416no—
732D4—416no—
733D4—416no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—416no—
755C2×C4—416no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4C7×#12014yes—
784C7#1595011yescharacteristic, direct product factor, Sylow
785C22—24no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—28no—
790C22—42no—
791C22—42no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22—44no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—44no—
807C22—44no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22C2×C7×#12011yescharacteristic
813C22C2×C7×#12011yescharacteristic
814C22C2×C7×#12311yescharacteristic
815C22C7×#52511yescharacteristic
816C22C7×#52512yes—
817C22C7×#53411yescharacteristic
818C22C7×#53411yescharacteristic
819C22C7×#53611yescharacteristic
820C22C7×#53712yes—
821C22C7×#53812yes—
822C22C7×#53912yes—
823C22C7×D4212yes—
824C22C7×D4212yes—
825C22C7×#54612yes—
826C22C7×#54612yes—
827C22C7×#54712yes—
828C22C7×#54712yes—
829C22C7×#54812yes—
830C22C7×#55012yes—
831C22C7×#55312yes—
832C22C7×#56212yes—
833C4—24no—
834C4—42no—
835C4—44no—
836C4—42no—
837C4—42no—
838C4—44no—
839C4—44no—
840C4—82no—
841C2—44no—
842C2—44no—
843C2—82no—
844C2C7×#240311yescharacteristic
845C2C7×#240511yescharacteristic
846C2C7×#240611yescharacteristic
847C2C7×#240712yes—
848C2C7×#244312yes—
849C2C7×#245612yes—
850C2C7×#268112yes—
851C2C7×#268212yes—
852C2C7×#270812yes—
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC22×C7×#121C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C7×#123C2semidirect
3. C2×C7×#386C2semidirect
4. C2×C7×#385C2semidirect
5. C2×C7×#385C2semidirect
6. C7×#1441C2semidirect
7. C7×#1440C2semidirect
8. C7×#1439C2semidirect
9. C7×#1438C2semidirect
10. C7×#1438C2semidirect
11. C7×#1438C2semidirect
43. #15950C7direct (N × H)
90. C2×C7×C4⋊C4D4semidirect
121. C22×#123C2×C7semidirect
123. C2×#386C2×C7semidirect
124. C2×#385C2×C7semidirect
125. C2×#385C2×C7semidirect
126. #1441C2×C7semidirect
127. #1440C2×C7semidirect
128. #1439C2×C7semidirect
129. #1438C2×C7semidirect
130. #1438C2×C7semidirect
131. #1438C2×C7semidirect
338. C23×C7#123semidirect
447. C2×C4⋊C4C7×D4semidirect
721. C23C7×#123semidirect
784. C7#15950direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1232
C22×C7×#1212
C2×C7×#3862
C2×C7×#3852
C7×#14412
C7×#14402
C7×#14392
C7×#14382
#159507