Finite Group Databasebeta

← C7×#15909 #13193125

Subgroups — C7×#15909 #13193125

Order 1792.

2150 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#126C211yesmaximal, characteristic, complemented
2C2×C7×#394C211yesmaximal, characteristic, complemented
3C2×C7×#392C211yesmaximal, characteristic
4C2×C7×#390C211yesmaximal, characteristic, complemented
5C7×#1445C211yesmaximal, characteristic, complemented
6C7×#1439C212yesmaximal, complemented
7C7×#1438C212yesmaximal, complemented
8C7×#1438C212yesmaximal, complemented
9C7×#1437C212yesmaximal, complemented
10C7×#1437C211yesmaximal, characteristic, complemented
11C7×#1436C211yesmaximal, characteristic, complemented
12C23×C7×D4C2211yescharacteristic
13C23×C7×D4C2212yes—
14C2×C7×#126—24no—
15C2×C7×#126—24no—
16C2×C7×#126—24no—
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2212yes—
23C22×C7×C22⋊C4C2212yes—
24C22×C7×C22⋊C4C2212yes—
25C22×C7×C22⋊C4C2212yes—
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2212yes—
28C22×C7×C22⋊C4C2212yes—
29C22×C42×C7C2211yescharacteristic
30C22×C42×C7C2211yescharacteristic
31C7×#394—24no—
32C7×#392—24no—
33C7×#390—24no—
34C2×C7×#95C2212yes—
35C2×C7×#95C2211yescharacteristic
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39C2×C7×#95C2212yes—
40C2×C7×#95C2212yes—
41#15909C711yesmaximal, characteristic, direct product factor, Sylow
42C25×C7C2311yescharacteristic
43C25×C7C2312yes—
44C22×C7×D4—24no—
45C22×C7×D4—24no—
46C22×C7×D4—24no—
47C22×C7×D4—22no—
48C22×C7×D4—22no—
49C22×C7×D4—22no—
50C22×C7×D4—24no—
51C22×C7×D4—42no—
52C22×C7×D4—42no—
53C22×C7×D4—42no—
54C22×C7×D4—42no—
55C22×C7×D4—42no—
56C23×C4×C7C2312yes—
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2312yes—
63C23×C4×C7C2312yes—
64C23×C4×C7C2311yescharacteristic
65C7×#126—232no—
66C2×C7×C4⋊C4—22no—
67C2×C7×C4⋊C4—22no—
68C2×C7×C4⋊C4—22no—
69C2×C7×C4⋊C4—22no—
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4—22no—
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4D414yescomplemented
74C2×C7×C4⋊C4D414yescomplemented
75C2×C7×C22⋊C4—22no—
76C2×C7×C22⋊C4—22no—
77C2×C7×C22⋊C4—22no—
78C2×C7×C22⋊C4—22no—
79C2×C7×C22⋊C4—22no—
80C2×C7×C22⋊C4—22no—
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—24no—
84C2×C7×C22⋊C4—24no—
85C2×C7×C22⋊C4—24no—
86C2×C7×C22⋊C4—24no—
87C2×C7×C22⋊C4—24no—
88C2×C7×C22⋊C4—24no—
89C2×C7×C22⋊C4—24no—
90C2×C7×C22⋊C4—24no—
91C2×C7×C22⋊C4—24no—
92C2×C7×C22⋊C4—24no—
93C2×C7×C22⋊C4—42no—
94C2×C7×C22⋊C4—42no—
95C2×C7×C22⋊C4—42no—
96C2×C7×C22⋊C4—42no—
97C2×C7×C22⋊C4—42no—
98C2×C7×C22⋊C4—42no—
99C2×C7×C22⋊C4—42no—
100C2×C7×C22⋊C4—42no—
101C2×C7×C22⋊C4D414yes—
102C2×C42×C7—22no—
103C2×C42×C7—22no—
104C2×C42×C7—22no—
105C2×C42×C7—22no—
106C2×C42×C7—42no—
107C7×#95—22no—
108C7×#95—22no—
109C7×#95—24no—
110C7×#95—42no—
111C7×#95—42no—
112C7×#95—42no—
113C7×#95—42no—
114C22×#126C2×C711yescharacteristic, complemented
115C2×#394C2×C711yescharacteristic, complemented
116C2×#392C2×C711yescharacteristic
117C2×#390C2×C711yescharacteristic, complemented
118#1445C2×C711yescharacteristic, complemented
119#1439C2×C712yescomplemented
120#1438C2×C712yescomplemented
121#1438C2×C712yescomplemented
122#1437C2×C712yescomplemented
123#1437C2×C711yescharacteristic, complemented
124#1436C2×C711yescharacteristic, complemented
125C24×C7—21no—
126C24×C7—21no—
127C24×C7—22no—
128C24×C7—22no—
129C24×C7—22no—
130C24×C7—22no—
131C24×C7—22no—
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×D412yes—
148C24×C7#4114yes—
149C24×C7C2411yescharacteristic
150C2×C7×D4—28no—
151C2×C7×D4—48no—
152C2×C7×D4—48no—
153C2×C7×D4—48no—
154C2×C7×D4—48no—
155C2×C7×D4—44no—
156C2×C7×D4—48no—
157C2×C7×D4—48no—
158C2×C7×D4—48no—
159C2×C7×D4—48no—
160C2×C7×D4—48no—
161C2×C7×D4—44no—
162C22×C4×C7—22no—
163C22×C4×C7—22no—
164C22×C4×C7—22no—
165C22×C4×C7—22no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
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—22no—
188C22×C4×C7—22no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—22no—
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×C7C2×D412yes—
204C22×C4×C7C2×D412yes—
205C22×C4×C7C2×D412yes—
206C22×C4×C7C2×D412yes—
207C22×C4×C7C2×D412yes—
208C22×C4×C7C2×D412yes—
209C22×C4×C7C2×D412yes—
210C22×C4×C7C2×D412yes—
211C22×C4×C7#4114yes—
212C22×C4×C7#4114yes—
213C7×C4⋊C4—28no—
214C7×C4⋊C4—28no—
215C7×C4⋊C4—28no—
216C7×C22⋊C4—28no—
217C7×C22⋊C4—28no—
218C7×C22⋊C4—28no—
219C7×C22⋊C4—48no—
220C7×C22⋊C4—48no—
221C7×C22⋊C4—48no—
222C7×C22⋊C4—48no—
223C7×C22⋊C4—48no—
224C7×C22⋊C4—48no—
225C42×C7—28no—
226C42×C7—44no—
227C23×D4C22×C711yescharacteristic
228C23×D4C22×C712yes—
229C2×#126—24no—
230C2×#126—24no—
231C2×#126—24no—
232C22×C4⋊C4C22×C711yescharacteristic
233C22×C4⋊C4C22×C711yescharacteristic
234C22×C4⋊C4C22×C711yescharacteristic
235C22×C22⋊C4C22×C711yescharacteristic
236C22×C22⋊C4C22×C711yescharacteristic
237C22×C22⋊C4C22×C712yes—
238C22×C22⋊C4C22×C712yes—
239C22×C22⋊C4C22×C712yes—
240C22×C22⋊C4C22×C712yes—
241C22×C22⋊C4C22×C711yescharacteristic
242C22×C22⋊C4C22×C712yes—
243C22×C22⋊C4C22×C712yes—
244C22×C42C22×C711yescharacteristic
245C22×C42C22×C711yescharacteristic
246#394—24no—
247#392—24no—
248#390—24no—
249C2×#95C22×C711yescharacteristic
250C2×#95C22×C711yescharacteristic
251C2×#95C22×C712yes—
252C2×#95C22×C712yes—
253C2×#95C22×C712yes—
254C2×#95C22×C712yes—
255C2×#95C22×C712yes—
256C23×C7—22no—
257C23×C7—24no—
258C23×C7—24no—
259C23×C7—22no—
260C23×C7—22no—
261C23×C7—24no—
262C23×C7—24no—
263C23×C7—24no—
264C23×C7—24no—
265C23×C7—24no—
266C23×C7—24no—
267C23×C7—24no—
268C23×C7—42no—
269C23×C7—41no—
270C23×C7—42no—
271C23×C7—42no—
272C23×C7—41no—
273C23×C7—42no—
274C23×C7—42no—
275C23×C7—42no—
276C23×C7—42no—
277C23×C7—42no—
278C23×C7—41no—
279C23×C7—41no—
280C23×C7—42no—
281C23×C7—42no—
282C23×C7—42no—
283C23×C7—42no—
284C23×C7—42no—
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×C7C22×D411yescharacteristic
313C23×C7C22×D411yescharacteristic
314C23×C7C22×D411yescharacteristic
315C23×C7C2×#4112yes—
316C23×C7C2×#4112yes—
317C23×C7C2×#4112yes—
318C23×C7H(5,𝔽2)12yes—
319C23×C7H(5,𝔽2)12yes—
320C23×C7H(5,𝔽2)12yes—
321C7×D4—416no—
322C7×D4—432no—
323C2×C4×C7—22no—
324C2×C4×C7—22no—
325C2×C4×C7—24no—
326C2×C4×C7—24no—
327C2×C4×C7—22no—
328C2×C4×C7—22no—
329C2×C4×C7—22no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—24no—
335C2×C4×C7—24no—
336C2×C4×C7—24no—
337C2×C4×C7—24no—
338C2×C4×C7—24no—
339C2×C4×C7—24no—
340C2×C4×C7—24no—
341C2×C4×C7—24no—
342C2×C4×C7—24no—
343C2×C4×C7—24no—
344C2×C4×C7—41no—
345C2×C4×C7—41no—
346C2×C4×C7—41no—
347C2×C4×C7—41no—
348C2×C4×C7—42no—
349C2×C4×C7—41no—
350C2×C4×C7—41no—
351C2×C4×C7—41no—
352C2×C4×C7—41no—
353C2×C4×C7—42no—
354C2×C4×C7—42no—
355C2×C4×C7—42no—
356C2×C4×C7—42no—
357C2×C4×C7—42no—
358C2×C4×C7—42no—
359C2×C4×C7—42no—
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—42no—
367C2×C4×C7—42no—
368C2×C4×C7—42no—
369C2×C4×C7—42no—
370C2×C4×C7—42no—
371C2×C4×C7—42no—
372C2×C4×C7—42no—
373C2×C4×C7#12014yes—
374C25C23×C711yescharacteristic
375C25C23×C712yes—
376C22×D4—24no—
377C22×D4—24no—
378C22×D4—24no—
379C22×D4—22no—
380C22×D4—22no—
381C22×D4—22no—
382C22×D4—24no—
383C22×D4—42no—
384C22×D4—42no—
385C22×D4—42no—
386C22×D4—42no—
387C22×D4—42no—
388C23×C4C23×C712yes—
389C23×C4C23×C711yescharacteristic
390C23×C4C23×C711yescharacteristic
391C23×C4C23×C711yescharacteristic
392C23×C4C23×C711yescharacteristic
393C23×C4C23×C711yescharacteristic
394C23×C4C23×C712yes—
395C23×C4C23×C712yes—
396C23×C4C23×C711yescharacteristic
397#126—232no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4C7×D414yescomplemented
406C2×C4⋊C4C7×D414yescomplemented
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—24no—
418C2×C22⋊C4—24no—
419C2×C22⋊C4—24no—
420C2×C22⋊C4—24no—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—24no—
423C2×C22⋊C4—24no—
424C2×C22⋊C4—24no—
425C2×C22⋊C4—42no—
426C2×C22⋊C4—42no—
427C2×C22⋊C4—42no—
428C2×C22⋊C4—42no—
429C2×C22⋊C4—42no—
430C2×C22⋊C4—42no—
431C2×C22⋊C4—42no—
432C2×C22⋊C4—42no—
433C2×C22⋊C4C7×D414yes—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—42no—
439#95—22no—
440#95—22no—
441#95—24no—
442#95—42no—
443#95—42no—
444#95—42no—
445#95—42no—
446C22×C7—44no—
447C22×C7—42no—
448C22×C7—44no—
449C22×C7—44no—
450C22×C7—42no—
451C22×C7—42no—
452C22×C7—44no—
453C22×C7—44no—
454C22×C7—44no—
455C22×C7—44no—
456C22×C7—44no—
457C22×C7—44no—
458C22×C7—82no—
459C22×C7—82no—
460C22×C7—82no—
461C22×C7—82no—
462C22×C7—82no—
463C22×C7—82no—
464C22×C7—82no—
465C22×C7—82no—
466C22×C7—82no—
467C22×C7—82no—
468C22×C7—82no—
469C22×C7—82no—
470C22×C7C2×#12011yescharacteristic
471C22×C7#52511yescharacteristic
472C22×C7#52912yes—
473C22×C7#53211yescharacteristic
474C22×C7#53211yescharacteristic
475C22×C7#53511yescharacteristic
476C22×C7#53511yescharacteristic
477C22×C7#53511yescharacteristic
478C22×C7#53812yes—
479C22×C7#53812yes—
480C22×C7#53812yes—
481C22×C7#54612yes—
482C22×C7#54612yes—
483C22×C7#54612yes—
484C22×C7#54612yes—
485C22×C7#55012yes—
486C22×C7#55012yes—
487C22×C7#55112yes—
488C22×C7#55312yes—
489C22×C7#55312yes—
490C22×C7#56012yes—
491C4×C7—24no—
492C4×C7—42no—
493C4×C7—44no—
494C4×C7—42no—
495C4×C7—42no—
496C4×C7—42no—
497C4×C7—42no—
498C4×C7—44no—
499C4×C7—82no—
500C24—21no—
501C24—21no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24C2×C7×D412yes—
523C24C7×#4114yes—
524C24C24×C711yescharacteristic
525C2×D4—28no—
526C2×D4—48no—
527C2×D4—48no—
528C2×D4—48no—
529C2×D4—48no—
530C2×D4—44no—
531C2×D4—48no—
532C2×D4—48no—
533C2×D4—48no—
534C2×D4—48no—
535C2×D4—48no—
536C2×D4—44no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4C2×C7×D412yes—
579C22×C4C2×C7×D412yes—
580C22×C4C2×C7×D412yes—
581C22×C4C2×C7×D412yes—
582C22×C4C2×C7×D412yes—
583C22×C4C2×C7×D412yes—
584C22×C4C2×C7×D412yes—
585C22×C4C2×C7×D412yes—
586C22×C4C7×#4114yes—
587C22×C4C7×#4114yes—
588C4⋊C4—28no—
589C4⋊C4—28no—
590C4⋊C4—28no—
591C22⋊C4—28no—
592C22⋊C4—28no—
593C22⋊C4—28no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—48no—
597C22⋊C4—48no—
598C22⋊C4—48no—
599C22⋊C4—48no—
600C42—28no—
601C42—44no—
602C2×C7—84no—
603C2×C7—82no—
604C2×C7#240411yescharacteristic
605C2×C7#243111yescharacteristic
606C2×C7#243111yescharacteristic
607C2×C7#246712yes—
608C2×C7#255412yes—
609C2×C7#255912yes—
610C2×C7#268512yes—
611C2×C7#271412yes—
612C2×C7#271412yes—
613C23—22no—
614C23—24no—
615C23—24no—
616C23—22no—
617C23—22no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—42no—
626C23—41no—
627C23—42no—
628C23—42no—
629C23—41no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—41no—
636C23—41no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23C22×C7×D411yescharacteristic
670C23C22×C7×D411yescharacteristic
671C23C22×C7×D411yescharacteristic
672C23C2×C7×#4112yes—
673C23C2×C7×#4112yes—
674C23C2×C7×#4112yes—
675C23C7×H(5,𝔽2)12yes—
676C23C7×H(5,𝔽2)12yes—
677C23C7×H(5,𝔽2)12yes—
678D4—416no—
679D4—432no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4C7×#12014yes—
731C7#1590911yescharacteristic, direct product factor, Sylow
732C22—44no—
733C22—42no—
734C22—44no—
735C22—44no—
736C22—42no—
737C22—42no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—82no—
745C22—82no—
746C22—82no—
747C22—82no—
748C22—82no—
749C22—82no—
750C22—82no—
751C22—82no—
752C22—82no—
753C22—82no—
754C22—82no—
755C22—82no—
756C22C2×C7×#12011yescharacteristic
757C22C7×#52511yescharacteristic
758C22C7×#52912yes—
759C22C7×#53211yescharacteristic
760C22C7×#53211yescharacteristic
761C22C7×#53511yescharacteristic
762C22C7×#53511yescharacteristic
763C22C7×#53511yescharacteristic
764C22C7×#53812yes—
765C22C7×#53812yes—
766C22C7×#53812yes—
767C22C7×#54612yes—
768C22C7×#54612yes—
769C22C7×#54612yes—
770C22C7×#54612yes—
771C22C7×#55012yes—
772C22C7×#55012yes—
773C22C7×#55112yes—
774C22C7×#55312yes—
775C22C7×#55312yes—
776C22C7×#56012yes—
777C4—24no—
778C4—42no—
779C4—44no—
780C4—42no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—44no—
785C4—82no—
786C2—84no—
787C2—82no—
788C2C7×#240411yescharacteristic
789C2C7×#243111yescharacteristic
790C2C7×#243111yescharacteristic
791C2C7×#246712yes—
792C2C7×#255412yes—
793C2C7×#255912yes—
794C2C7×#268512yes—
795C2C7×#271412yes—
796C2C7×#271412yes—
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC2×C7×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C7×#126C2semidirect
2. C2×C7×#394C2semidirect
4. C2×C7×#390C2semidirect
5. C7×#1445C2semidirect
6. C7×#1439C2semidirect
7. C7×#1438C2semidirect
8. C7×#1438C2semidirect
9. C7×#1437C2semidirect
10. C7×#1437C2semidirect
11. C7×#1436C2semidirect
41. #15909C7direct (N × H)
73. C2×C7×C4⋊C4D4semidirect
74. C2×C7×C4⋊C4D4semidirect
114. C22×#126C2×C7semidirect
115. C2×#394C2×C7semidirect
117. C2×#390C2×C7semidirect
118. #1445C2×C7semidirect
119. #1439C2×C7semidirect
120. #1438C2×C7semidirect
121. #1438C2×C7semidirect
122. #1437C2×C7semidirect
123. #1437C2×C7semidirect
124. #1436C2×C7semidirect
405. C2×C4⋊C4C7×D4semidirect
406. C2×C4⋊C4C7×D4semidirect
731. C7#15909direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1262
C2×C7×#3942
C2×C7×#3922
C2×C7×#3902
C7×#14452
C7×#14392
C7×#14382
C7×#14372
C7×#14362
#159097