Finite Group Databasebeta

← C7×#16501 #13193717

Subgroups — C7×#16501 #13193717

Order 1792.

2310 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#121C211yesmaximal, characteristic
2C2×C7×#398C211yesmaximal, characteristic, complemented
3C2×C7×#394C212yesmaximal, complemented
4C2×C7×#394C211yesmaximal, characteristic, complemented
5C2×C7×#385C211yesmaximal, characteristic, complemented
6C7×#1445C211yesmaximal, characteristic, complemented
7C7×#1439C212yesmaximal, complemented
8C7×#1439C212yesmaximal, complemented
9C7×#1438C212yesmaximal, complemented
10C7×#1438C211yesmaximal, characteristic, complemented
11C7×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C7×D4C2212yes—
13C23×C7×D4C2211yescharacteristic
14C24×C4×C7C2211yescharacteristic
15C2×C7×#121—24no—
16C2×C7×#121—24no—
17C2×C7×#121—24no—
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2212yes—
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2212yes—
23C22×C7×C22⋊C4C2212yes—
24C22×C7×C22⋊C4C2212yes—
25C22×C7×C22⋊C4C2212yes—
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2212yes—
29C22×C7×C22⋊C4C2212yes—
30C7×#398—24no—
31C7×#394—24no—
32C7×#394—28no—
33C7×#385—24no—
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2212yes—
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2211yescharacteristic
38C2×C7×#95C2211yescharacteristic
39C2×C7×#95C2212yes—
40C2×C7×#95C2212yes—
41C2×C7×#95C2212yes—
42#16501C711yesmaximal, characteristic, direct product factor, Sylow
43C25×C7C2312yes—
44C25×C7C2311yescharacteristic
45C22×C7×D4—24no—
46C22×C7×D4—24no—
47C22×C7×D4—24no—
48C22×C7×D4—24no—
49C22×C7×D4—24no—
50C22×C7×D4—22no—
51C22×C7×D4—22no—
52C22×C7×D4—42no—
53C22×C7×D4—42no—
54C22×C7×D4—42no—
55C22×C7×D4—42no—
56C22×C7×D4D414yes—
57C23×C4×C7—22no—
58C23×C4×C7—22no—
59C23×C4×C7—42no—
60C23×C4×C7—42no—
61C23×C4×C7D414yes—
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2312yes—
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2312yes—
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2312yes—
70C23×C4×C7C2311yescharacteristic
71C7×#121—232no—
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4—22no—
74C2×C7×C4⋊C4—22no—
75C2×C7×C4⋊C4—22no—
76C2×C7×C4⋊C4—24no—
77C2×C7×C4⋊C4—22no—
78C2×C7×C4⋊C4—24no—
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—42no—
81C2×C7×C4⋊C4—42no—
82C2×C7×C4⋊C4D414yes—
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4—24no—
85C2×C7×C22⋊C4—22no—
86C2×C7×C22⋊C4—24no—
87C2×C7×C22⋊C4—24no—
88C2×C7×C22⋊C4—22no—
89C2×C7×C22⋊C4—24no—
90C2×C7×C22⋊C4—24no—
91C2×C7×C22⋊C4—24no—
92C2×C7×C22⋊C4—24no—
93C2×C7×C22⋊C4—24no—
94C2×C7×C22⋊C4—24no—
95C2×C7×C22⋊C4—24no—
96C2×C7×C22⋊C4—24no—
97C2×C7×C22⋊C4—42no—
98C2×C7×C22⋊C4—42no—
99C2×C7×C22⋊C4—42no—
100C2×C7×C22⋊C4—42no—
101C2×C7×C22⋊C4—42no—
102C2×C7×C22⋊C4—42no—
103C2×C7×C22⋊C4—42no—
104C2×C7×C22⋊C4—42no—
105C2×C7×C22⋊C4D414yescomplemented
106C7×#95—22no—
107C7×#95—22no—
108C7×#95—24no—
109C7×#95—22no—
110C7×#95—22no—
111C7×#95—24no—
112C7×#95—42no—
113C7×#95—42no—
114C22×#121C2×C711yescharacteristic
115C2×#398C2×C711yescharacteristic, complemented
116C2×#394C2×C711yescharacteristic, complemented
117C2×#394C2×C712yescomplemented
118C2×#385C2×C711yescharacteristic, complemented
119#1445C2×C711yescharacteristic, complemented
120#1439C2×C712yescomplemented
121#1439C2×C712yescomplemented
122#1438C2×C712yescomplemented
123#1438C2×C711yescharacteristic, complemented
124C22⋊#95C2×C711yescharacteristic, complemented
125C24×C7—21no—
126C24×C7—21no—
127C24×C7—22no—
128C24×C7—22no—
129C24×C7—22no—
130C24×C7—21no—
131C24×C7—21no—
132C24×C7—22no—
133C24×C7—22no—
134C24×C7—22no—
135C24×C7—22no—
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—22no—
147C24×C7C2×D414yes—
148C24×C7C2×D412yes—
149C24×C7C2×D412yes—
150C24×C7#4112yes—
151C24×C7C2411yescharacteristic
152C2×C7×D4—216no—
153C2×C7×D4—28no—
154C2×C7×D4—48no—
155C2×C7×D4—48no—
156C2×C7×D4—48no—
157C2×C7×D4—44no—
158C2×C7×D4—44no—
159C2×C7×D4—48no—
160C2×C7×D4—48no—
161C2×C7×D4—48no—
162C2×C7×D4—48no—
163C2×C7×D4—48no—
164C22×C4×C7—22no—
165C22×C4×C7—22no—
166C22×C4×C7—22no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—22no—
170C22×C4×C7—21no—
171C22×C4×C7—22no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—22no—
184C22×C4×C7—21no—
185C22×C4×C7—22no—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—21no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7—28no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—22no—
196C22×C4×C7—22no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—21no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—21no—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—44no—
211C22×C4×C7—44no—
212C22×C4×C7—48no—
213C22×C4×C7—48no—
214C22×C4×C7C2×D412yes—
215C22×C4×C7C2×D412yes—
216C22×C4×C7C2×D414yes—
217C22×C4×C7C2×D412yes—
218C22×C4×C7C2×D412yes—
219C22×C4×C7C2×D412yes—
220C22×C4×C7C2×D412yes—
221C22×C4×C7#4114yes—
222C7×C4⋊C4—28no—
223C7×C4⋊C4—48no—
224C7×C4⋊C4—44no—
225C7×C4⋊C4—44no—
226C7×C22⋊C4—216no—
227C7×C22⋊C4—28no—
228C7×C22⋊C4—48no—
229C7×C22⋊C4—48no—
230C7×C22⋊C4—48no—
231C7×C22⋊C4—48no—
232C7×C22⋊C4—44no—
233C7×C22⋊C4—48no—
234C23×D4C22×C712yes—
235C23×D4C22×C711yescharacteristic
236C24×C4C22×C711yescharacteristic
237C2×#121—24no—
238C2×#121—24no—
239C2×#121—24no—
240C22×C4⋊C4C22×C711yescharacteristic
241C22×C4⋊C4C22×C712yes—
242C22×C4⋊C4C22×C711yescharacteristic
243C22×C4⋊C4C22×C711yescharacteristic
244C22×C22⋊C4C22×C712yes—
245C22×C22⋊C4C22×C712yes—
246C22×C22⋊C4C22×C712yes—
247C22×C22⋊C4C22×C712yes—
248C22×C22⋊C4C22×C711yescharacteristic
249C22×C22⋊C4C22×C712yes—
250C22×C22⋊C4C22×C712yes—
251C22×C22⋊C4C22×C711yescharacteristic
252#398—24no—
253#394—24no—
254#394—28no—
255#385—24no—
256C2×#95C22×C711yescharacteristic
257C2×#95C22×C712yes—
258C2×#95C22×C711yescharacteristic
259C2×#95C22×C712yes—
260C2×#95C22×C711yescharacteristic
261C2×#95C22×C711yescharacteristic
262C2×#95C22×C712yes—
263C2×#95C22×C712yes—
264C23×C7—22no—
265C23×C7—22no—
266C23×C7—22no—
267C23×C7—22no—
268C23×C7—22no—
269C23×C7—22no—
270C23×C7—24no—
271C23×C7—24no—
272C23×C7—22no—
273C23×C7—22no—
274C23×C7—24no—
275C23×C7—22no—
276C23×C7—22no—
277C23×C7—24no—
278C23×C7—24no—
279C23×C7—24no—
280C23×C7—24no—
281C23×C7—24no—
282C23×C7—24no—
283C23×C7—24no—
284C23×C7—24no—
285C23×C7—42no—
286C23×C7—42no—
287C23×C7—42no—
288C23×C7—42no—
289C23×C7—42no—
290C23×C7—42no—
291C23×C7—42no—
292C23×C7—42no—
293C23×C7—42no—
294C23×C7—42no—
295C23×C7—42no—
296C23×C7—42no—
297C23×C7—42no—
298C23×C7—42no—
299C23×C7—42no—
300C23×C7—42no—
301C23×C7—42no—
302C23×C7—42no—
303C23×C7—42no—
304C23×C7—42no—
305C23×C7—42no—
306C23×C7—42no—
307C23×C7—42no—
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#12114yes—
322C23×C7C22×D411yescharacteristic
323C23×C7C22×D411yescharacteristic
324C23×C7C22×D411yescharacteristic
325C23×C7C22×D411yescharacteristic
326C23×C7C2×#4111yescharacteristic
327C23×C7C2×#4112yes—
328C23×C7H(5,𝔽2)12yes—
329C23×C7H(5,𝔽2)12yes—
330C23×C7H(5,𝔽2)11yescharacteristic
331C23×C7H(5,𝔽2)11yescharacteristic
332C23×C72−1+412yes—
333C7×D4—416no—
334C7×D4—432no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—24no—
338C2×C4×C7—24no—
339C2×C4×C7—22no—
340C2×C4×C7—24no—
341C2×C4×C7—22no—
342C2×C4×C7—22no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—24no—
346C2×C4×C7—22no—
347C2×C4×C7—22no—
348C2×C4×C7—24no—
349C2×C4×C7—24no—
350C2×C4×C7—24no—
351C2×C4×C7—24no—
352C2×C4×C7—24no—
353C2×C4×C7—416no—
354C2×C4×C7—41no—
355C2×C4×C7—42no—
356C2×C4×C7—41no—
357C2×C4×C7—41no—
358C2×C4×C7—42no—
359C2×C4×C7—41no—
360C2×C4×C7—42no—
361C2×C4×C7—42no—
362C2×C4×C7—42no—
363C2×C4×C7—42no—
364C2×C4×C7—42no—
365C2×C4×C7—42no—
366C2×C4×C7—41no—
367C2×C4×C7—41no—
368C2×C4×C7—42no—
369C2×C4×C7—42no—
370C2×C4×C7—42no—
371C2×C4×C7—41no—
372C2×C4×C7—41no—
373C2×C4×C7—41no—
374C2×C4×C7—42no—
375C2×C4×C7—41no—
376C2×C4×C7—42no—
377C2×C4×C7—41no—
378C2×C4×C7—42no—
379C2×C4×C7—41no—
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#12014yes—
389C25C23×C712yes—
390C25C23×C711yescharacteristic
391C22×D4—24no—
392C22×D4—24no—
393C22×D4—24no—
394C22×D4—24no—
395C22×D4—24no—
396C22×D4—22no—
397C22×D4—22no—
398C22×D4—42no—
399C22×D4—42no—
400C22×D4—42no—
401C22×D4—42no—
402C22×D4C7×D414yes—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4C7×D414yes—
408C23×C4C23×C711yescharacteristic
409C23×C4C23×C711yescharacteristic
410C23×C4C23×C712yes—
411C23×C4C23×C711yescharacteristic
412C23×C4C23×C711yescharacteristic
413C23×C4C23×C711yescharacteristic
414C23×C4C23×C712yes—
415C23×C4C23×C712yes—
416C23×C4C23×C711yescharacteristic
417#121—232no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—42no—
427C2×C4⋊C4—42no—
428C2×C4⋊C4C7×D414yes—
429C2×C22⋊C4—24no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—24no—
433C2×C22⋊C4—24no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—42no—
444C2×C22⋊C4—42no—
445C2×C22⋊C4—42no—
446C2×C22⋊C4—42no—
447C2×C22⋊C4—42no—
448C2×C22⋊C4—42no—
449C2×C22⋊C4—42no—
450C2×C22⋊C4—42no—
451C2×C22⋊C4C7×D414yescomplemented
452#95—22no—
453#95—22no—
454#95—24no—
455#95—22no—
456#95—22no—
457#95—24no—
458#95—42no—
459#95—42no—
460C22×C7—24no—
461C22×C7—24no—
462C22×C7—24no—
463C22×C7—42no—
464C22×C7—42no—
465C22×C7—42no—
466C22×C7—44no—
467C22×C7—44no—
468C22×C7—42no—
469C22×C7—44no—
470C22×C7—44no—
471C22×C7—44no—
472C22×C7—44no—
473C22×C7—44no—
474C22×C7—44no—
475C22×C7—44no—
476C22×C7—44no—
477C22×C7—44no—
478C22×C7—82no—
479C22×C7—82no—
480C22×C7—82no—
481C22×C7—82no—
482C22×C7—82no—
483C22×C7—82no—
484C22×C7—82no—
485C22×C7—82no—
486C22×C7C2×#12011yescharacteristic
487C22×C7C2×#12111yescharacteristic
488C22×C7#53211yescharacteristic
489C22×C7#53411yescharacteristic
490C22×C7#53411yescharacteristic
491C22×C7#53412yes—
492C22×C7#53511yescharacteristic
493C22×C7#53512yes—
494C22×C7#53611yescharacteristic
495C22×C7#53712yes—
496C22×C7#53812yes—
497C22×C7#53912yes—
498C22×C7#54012yes—
499C22×C7D4211yescharacteristic
500C22×C7D4211yescharacteristic
501C22×C7#54611yescharacteristic
502C22×C7#54611yescharacteristic
503C22×C7#54612yes—
504C22×C7#54712yes—
505C22×C7#54812yes—
506C22×C7#55312yes—
507C22×C7#56212yes—
508C22×C7#56212yes—
509C4×C7—24no—
510C4×C7—42no—
511C4×C7—42no—
512C4×C7—44no—
513C4×C7—44no—
514C4×C7—42no—
515C4×C7—81no—
516C4×C7—81no—
517C4×C7—82no—
518C24—21no—
519C24—21no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—21no—
524C24—21no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24C2×C7×D414yes—
541C24C2×C7×D412yes—
542C24C2×C7×D412yes—
543C24C7×#4112yes—
544C24C24×C711yescharacteristic
545C2×D4—216no—
546C2×D4—28no—
547C2×D4—48no—
548C2×D4—48no—
549C2×D4—48no—
550C2×D4—44no—
551C2×D4—44no—
552C2×D4—48no—
553C2×D4—48no—
554C2×D4—48no—
555C2×D4—48no—
556C2×D4—48no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—28no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4C2×C7×D412yes—
608C22×C4C2×C7×D412yes—
609C22×C4C2×C7×D414yes—
610C22×C4C2×C7×D412yes—
611C22×C4C2×C7×D412yes—
612C22×C4C2×C7×D412yes—
613C22×C4C2×C7×D412yes—
614C22×C4C7×#4114yes—
615C4⋊C4—28no—
616C4⋊C4—48no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C22⋊C4—216no—
620C22⋊C4—28no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—44no—
626C22⋊C4—48no—
627C2×C7—44no—
628C2×C7—84no—
629C2×C7#240811yescharacteristic
630C2×C7#243211yescharacteristic
631C2×C7#254311yescharacteristic
632C2×C7#261311yescharacteristic
633C2×C7#261811yescharacteristic
634C2×C7#266111yescharacteristic
635C2×C7#267112yes—
636C2×C7#267612yes—
637C2×C7#270812yes—
638C2×C7#271112yes—
639C2×C7#281611yescharacteristic
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—24no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—22no—
652C23—22no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23C7×#12114yes—
698C23C22×C7×D411yescharacteristic
699C23C22×C7×D411yescharacteristic
700C23C22×C7×D411yescharacteristic
701C23C22×C7×D411yescharacteristic
702C23C2×C7×#4111yescharacteristic
703C23C2×C7×#4112yes—
704C23C7×H(5,𝔽2)12yes—
705C23C7×H(5,𝔽2)12yes—
706C23C7×H(5,𝔽2)11yescharacteristic
707C23C7×H(5,𝔽2)11yescharacteristic
708C23C7×2−1+412yes—
709D4—416no—
710D4—432no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—416no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4C7×#12014yes—
765C7#1650111yescharacteristic, direct product factor, Sylow
766C22—24no—
767C22—24no—
768C22—24no—
769C22—42no—
770C22—44no—
771C22—44no—
772C22—42no—
773C22—44no—
774C22—44no—
775C22—42no—
776C22—42no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22C2×C7×#12011yescharacteristic
793C22C2×C7×#12111yescharacteristic
794C22C7×#53211yescharacteristic
795C22C7×#53411yescharacteristic
796C22C7×#53412yes—
797C22C7×#53411yescharacteristic
798C22C7×#53511yescharacteristic
799C22C7×#53512yes—
800C22C7×#53611yescharacteristic
801C22C7×#53712yes—
802C22C7×#53812yes—
803C22C7×#53912yes—
804C22C7×#54012yes—
805C22C7×D4211yescharacteristic
806C22C7×D4211yescharacteristic
807C22C7×#54611yescharacteristic
808C22C7×#54611yescharacteristic
809C22C7×#54612yes—
810C22C7×#54712yes—
811C22C7×#54812yes—
812C22C7×#55312yes—
813C22C7×#56212yes—
814C22C7×#56212yes—
815C4—24no—
816C4—44no—
817C4—42no—
818C4—44no—
819C4—42no—
820C4—42no—
821C4—81no—
822C4—82no—
823C4—81no—
824C2—44no—
825C2—84no—
826C2C7×#240811yescharacteristic
827C2C7×#243211yescharacteristic
828C2C7×#254311yescharacteristic
829C2C7×#261311yescharacteristic
830C2C7×#261811yescharacteristic
831C2C7×#266111yescharacteristic
832C2C7×#267112yes—
833C2C7×#267612yes—
834C2C7×#270812yes—
835C2C7×#271112yes—
836C2C7×#281611yescharacteristic
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
2. C2×C7×#398C2semidirect
3. C2×C7×#394C2semidirect
4. C2×C7×#394C2semidirect
5. C2×C7×#385C2semidirect
6. C7×#1445C2semidirect
7. C7×#1439C2semidirect
8. C7×#1439C2semidirect
9. C7×#1438C2semidirect
10. C7×#1438C2semidirect
11. C7×C22⋊#95C2semidirect
42. #16501C7direct (N × H)
105. C2×C7×C22⋊C4D4semidirect
115. C2×#398C2×C7semidirect
116. C2×#394C2×C7semidirect
117. C2×#394C2×C7semidirect
118. C2×#385C2×C7semidirect
119. #1445C2×C7semidirect
120. #1439C2×C7semidirect
121. #1439C2×C7semidirect
122. #1438C2×C7semidirect
123. #1438C2×C7semidirect
124. C22⋊#95C2×C7semidirect
451. C2×C22⋊C4C7×D4semidirect
765. C7#16501direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1212
C2×C7×#3982
C2×C7×#3942
C2×C7×#3852
C7×#14452
C7×#14392
C7×#14382
C7×C22⋊#952
#165017