Finite Group Databasebeta

← C7×#15113 #13192329

Subgroups — C7×#15113 #13192329

Order 1792.

2062 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#117C211yesmaximal, characteristic, complemented
2C2×C7×#388C212yesmaximal, complemented
3C2×C7×#386C211yesmaximal, characteristic
4C7×#1444C211yesmaximal, characteristic, complemented
5C7×#1442C211yesmaximal, characteristic, complemented
6C7×#1439C212yesmaximal, complemented
7C7×#1439C211yesmaximal, characteristic, complemented
8C7×#1439C211yesmaximal, characteristic, complemented
9C7×#1438C212yesmaximal
10C7×#1434C212yesmaximal, complemented
11C7×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C7×D4C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C2×C7×#117—24no—
15C2×C7×#117—28no—
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2212yes—
19C22×C7×C22⋊C4C2212yes—
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2212yes—
23C22×C7×C22⋊C4C2212yes—
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2212yes—
26C22×C42×C7C2212yes—
27C7×#388—28no—
28C7×#386—24no—
29C2×C7×#95C2211yescharacteristic
30C2×C7×#95C2211yescharacteristic
31C2×C7×#95C2212yes—
32C2×C7×#95C2212yes—
33C2×C7×#95C2211yescharacteristic
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2212yes—
36C2×C7×#95C2212yes—
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39#15113C711yesmaximal, characteristic, direct product factor, Sylow
40C25×C7C2311yescharacteristic
41C25×C7C2311yescharacteristic
42C22×C7×D4—22no—
43C22×C7×D4—22no—
44C22×C7×D4—24no—
45C22×C7×D4—22no—
46C22×C7×D4—42no—
47C23×C4×C7—24no—
48C23×C4×C7—24no—
49C23×C4×C7—22no—
50C23×C4×C7—22no—
51C23×C4×C7D414yes—
52C23×C4×C7C2312yes—
53C23×C4×C7C2311yescharacteristic
54C23×C4×C7C2311yescharacteristic
55C23×C4×C7C2312yes—
56C23×C4×C7C2312yes—
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2312yes—
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C7×#117—232no—
62C2×C7×C4⋊C4—24no—
63C2×C7×C4⋊C4—24no—
64C2×C7×C4⋊C4—22no—
65C2×C7×C4⋊C4—22no—
66C2×C7×C4⋊C4—24no—
67C2×C7×C4⋊C4—42no—
68C2×C7×C4⋊C4—42no—
69C2×C7×C22⋊C4—24no—
70C2×C7×C22⋊C4—24no—
71C2×C7×C22⋊C4—24no—
72C2×C7×C22⋊C4—24no—
73C2×C7×C22⋊C4—24no—
74C2×C7×C22⋊C4—24no—
75C2×C7×C22⋊C4—22no—
76C2×C7×C22⋊C4—24no—
77C2×C7×C22⋊C4—22no—
78C2×C7×C22⋊C4—22no—
79C2×C7×C22⋊C4—24no—
80C2×C7×C22⋊C4—24no—
81C2×C7×C22⋊C4—24no—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4—42no—
85C2×C7×C22⋊C4—42no—
86C2×C7×C22⋊C4—42no—
87C2×C7×C22⋊C4—42no—
88C2×C42×C7—24no—
89C2×C42×C7—24no—
90C2×C42×C7D418yescomplemented
91C7×#95—22no—
92C7×#95—22no—
93C7×#95—24no—
94C7×#95—24no—
95C7×#95—22no—
96C7×#95—24no—
97C7×#95—24no—
98C7×#95—22no—
99C7×#95—42no—
100C7×#95—42no—
101C22×#117C2×C711yescharacteristic, complemented
102C2×#388C2×C712yescomplemented
103C2×#386C2×C711yescharacteristic
104#1444C2×C711yescharacteristic, complemented
105#1442C2×C711yescharacteristic, complemented
106#1439C2×C712yescomplemented
107#1439C2×C711yescharacteristic, complemented
108#1439C2×C711yescharacteristic, complemented
109#1438C2×C712yes—
110#1434C2×C712yescomplemented
111C22⋊#95C2×C711yescharacteristic, complemented
112C24×C7—22no—
113C24×C7—22no—
114C24×C7—21no—
115C24×C7—21no—
116C24×C7—21no—
117C24×C7—21no—
118C24×C7—21no—
119C24×C7—22no—
120C24×C7—21no—
121C24×C7—22no—
122C24×C7—21no—
123C24×C7—22no—
124C24×C7—21no—
125C24×C7—21no—
126C24×C7—21no—
127C24×C7—22no—
128C24×C7—21no—
129C24×C7—22no—
130C24×C7—21no—
131C24×C7C2×D412yes—
132C24×C7#4112yes—
133C24×C7#4114yes—
134C24×C7C2411yescharacteristic
135C2×C7×D4—28no—
136C2×C7×D4—48no—
137C2×C7×D4—48no—
138C2×C7×D4—44no—
139C2×C7×D4—44no—
140C22×C4×C7—216no—
141C22×C4×C7—216no—
142C22×C4×C7—28no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
145C22×C4×C7—21no—
146C22×C4×C7—21no—
147C22×C4×C7—22no—
148C22×C4×C7—28no—
149C22×C4×C7—28no—
150C22×C4×C7—21no—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—22no—
154C22×C4×C7—22no—
155C22×C4×C7—22no—
156C22×C4×C7—22no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7—22no—
163C22×C4×C7—21no—
164C22×C4×C7—22no—
165C22×C4×C7—22no—
166C22×C4×C7—22no—
167C22×C4×C7—22no—
168C22×C4×C7—22no—
169C22×C4×C7—22no—
170C22×C4×C7—22no—
171C22×C4×C7—22no—
172C22×C4×C7—22no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—22no—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
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×C7C2×D414yes—
190C22×C4×C7C2×D414yes—
191C22×C4×C7C2×D412yes—
192C22×C4×C7C2×D414yes—
193C22×C4×C7C2×D412yes—
194C22×C4×C7#4112yes—
195C22×C4×C7#4114yes—
196C22×C4×C7#4112yes—
197C22×C4×C7#4112yes—
198C7×C4⋊C4—28no—
199C7×C4⋊C4—28no—
200C7×C4⋊C4—48no—
201C7×C22⋊C4—216no—
202C7×C22⋊C4—216no—
203C7×C22⋊C4—48no—
204C7×C22⋊C4—48no—
205C7×C22⋊C4—44no—
206C7×C22⋊C4—44no—
207C7×C22⋊C4—44no—
208C42×C7—216no—
209C23×D4C22×C711yescharacteristic
210C24×C4C22×C711yescharacteristic
211C2×#117—24no—
212C2×#117—28no—
213C22×C4⋊C4C22×C711yescharacteristic
214C22×C4⋊C4C22×C711yescharacteristic
215C22×C4⋊C4C22×C712yes—
216C22×C22⋊C4C22×C712yes—
217C22×C22⋊C4C22×C712yes—
218C22×C22⋊C4C22×C711yescharacteristic
219C22×C22⋊C4C22×C711yescharacteristic
220C22×C22⋊C4C22×C712yes—
221C22×C22⋊C4C22×C712yes—
222C22×C22⋊C4C22×C711yescharacteristic
223C22×C42C22×C712yes—
224#388—28no—
225#386—24no—
226C2×#95C22×C712yes—
227C2×#95C22×C711yescharacteristic
228C2×#95C22×C711yescharacteristic
229C2×#95C22×C711yescharacteristic
230C2×#95C22×C712yes—
231C2×#95C22×C712yes—
232C2×#95C22×C712yes—
233C2×#95C22×C711yescharacteristic
234C2×#95C22×C712yes—
235C2×#95C22×C712yes—
236C23×C7—22no—
237C23×C7—22no—
238C23×C7—24no—
239C23×C7—24no—
240C23×C7—22no—
241C23×C7—22no—
242C23×C7—22no—
243C23×C7—22no—
244C23×C7—24no—
245C23×C7—24no—
246C23×C7—24no—
247C23×C7—24no—
248C23×C7—24no—
249C23×C7—22no—
250C23×C7—24no—
251C23×C7—22no—
252C23×C7—22no—
253C23×C7—42no—
254C23×C7—42no—
255C23×C7—42no—
256C23×C7—42no—
257C23×C7—41no—
258C23×C7—41no—
259C23×C7—42no—
260C23×C7—42no—
261C23×C7—41no—
262C23×C7—41no—
263C23×C7—41no—
264C23×C7—41no—
265C23×C7—41no—
266C23×C7—42no—
267C23×C7—42no—
268C23×C7—42no—
269C23×C7—41no—
270C23×C7—42no—
271C23×C7—41no—
272C23×C7—42no—
273C23×C7—41no—
274C23×C7—42no—
275C23×C7—42no—
276C23×C7—42no—
277C23×C7—42no—
278C23×C7—42no—
279C23×C7—41no—
280C23×C7—41no—
281C23×C7#12314yes—
282C23×C7C22×D411yescharacteristic
283C23×C7C22×D412yes—
284C23×C7C2×#4112yes—
285C23×C7C2×#4111yescharacteristic
286C23×C7C2×#4111yescharacteristic
287C23×C7C2×#4111yescharacteristic
288C23×C7C2×#4111yescharacteristic
289C23×C7C2×#4112yes—
290C23×C7H(5,𝔽2)11yescharacteristic
291C23×C7H(5,𝔽2)12yes—
292C23×C72−1+411yescharacteristic
293C7×D4—416no—
294C2×C4×C7—232no—
295C2×C4×C7—22no—
296C2×C4×C7—22no—
297C2×C4×C7—22no—
298C2×C4×C7—22no—
299C2×C4×C7—24no—
300C2×C4×C7—24no—
301C2×C4×C7—24no—
302C2×C4×C7—24no—
303C2×C4×C7—24no—
304C2×C4×C7—24no—
305C2×C4×C7—24no—
306C2×C4×C7—24no—
307C2×C4×C7—22no—
308C2×C4×C7—24no—
309C2×C4×C7—24no—
310C2×C4×C7—24no—
311C2×C4×C7—24no—
312C2×C4×C7—24no—
313C2×C4×C7—24no—
314C2×C4×C7—41no—
315C2×C4×C7—42no—
316C2×C4×C7—42no—
317C2×C4×C7—42no—
318C2×C4×C7—42no—
319C2×C4×C7—42no—
320C2×C4×C7—42no—
321C2×C4×C7—42no—
322C2×C4×C7—42no—
323C2×C4×C7—41no—
324C2×C4×C7—42no—
325C2×C4×C7—42no—
326C2×C4×C7—42no—
327C2×C4×C7—42no—
328C2×C4×C7—42no—
329C2×C4×C7—41no—
330C2×C4×C7—41no—
331C2×C4×C7—42no—
332C2×C4×C7—42no—
333C2×C4×C7—41no—
334C2×C4×C7—42no—
335C2×C4×C7—41no—
336C2×C4×C7—41no—
337C2×C4×C7—42no—
338C2×C4×C7—42no—
339C2×C4×C7—41no—
340C2×C4×C7—42no—
341C2×C4×C7—42no—
342C2×C4×C7—42no—
343C2×C4×C7—42no—
344C2×C4×C7—42no—
345C2×C4×C7—42no—
346C2×C4×C7#12014yes—
347C2×C4×C7#12314yes—
348C25C23×C711yescharacteristic
349C25C23×C711yescharacteristic
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—24no—
353C22×D4—22no—
354C22×D4—42no—
355C23×C4—24no—
356C23×C4—24no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4C7×D414yes—
360C23×C4C23×C711yescharacteristic
361C23×C4C23×C712yes—
362C23×C4C23×C711yescharacteristic
363C23×C4C23×C712yes—
364C23×C4C23×C712yes—
365C23×C4C23×C712yes—
366C23×C4C23×C711yescharacteristic
367C23×C4C23×C711yescharacteristic
368C23×C4C23×C711yescharacteristic
369#117—232no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—42no—
376C2×C4⋊C4—42no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42C7×D418yescomplemented
399#95—22no—
400#95—22no—
401#95—24no—
402#95—24no—
403#95—22no—
404#95—24no—
405#95—24no—
406#95—22no—
407#95—42no—
408#95—42no—
409C22×C7—24no—
410C22×C7—24no—
411C22×C7—24no—
412C22×C7—44no—
413C22×C7—44no—
414C22×C7—44no—
415C22×C7—44no—
416C22×C7—42no—
417C22×C7—42no—
418C22×C7—42no—
419C22×C7—42no—
420C22×C7—44no—
421C22×C7—44no—
422C22×C7—42no—
423C22×C7—42no—
424C22×C7—42no—
425C22×C7—81no—
426C22×C7—82no—
427C22×C7—82no—
428C22×C7—81no—
429C22×C7—81no—
430C22×C7—81no—
431C22×C7C2×#12011yescharacteristic
432C22×C7C2×#12311yescharacteristic
433C22×C7C2×#12311yescharacteristic
434C22×C7#52512yes—
435C22×C7#52512yes—
436C22×C7#52512yes—
437C22×C7#52511yescharacteristic
438C22×C7#53212yes—
439C22×C7#53211yescharacteristic
440C22×C7#53512yes—
441C22×C7#53511yescharacteristic
442C22×C7#53712yes—
443C22×C7#53711yescharacteristic
444C22×C7#55112yes—
445C22×C7#55112yes—
446C22×C7#55112yes—
447C22×C7#55212yes—
448C22×C7#55211yescharacteristic
449C22×C7#55311yescharacteristic
450C22×C7#55312yes—
451C22×C7#55512yes—
452C22×C7#55511yescharacteristic
453C22×C7#55611yescharacteristic
454C4×C7—24no—
455C4×C7—24no—
456C4×C7—44no—
457C4×C7—44no—
458C4×C7—44no—
459C4×C7—42no—
460C4×C7—82no—
461C4×C7—81no—
462C4×C7—81no—
463C24—22no—
464C24—22no—
465C24—21no—
466C24—21no—
467C24—21no—
468C24—21no—
469C24—21no—
470C24—22no—
471C24—21no—
472C24—22no—
473C24—21no—
474C24—22no—
475C24—21no—
476C24—21no—
477C24—21no—
478C24—22no—
479C24—21no—
480C24—22no—
481C24—21no—
482C24C2×C7×D412yes—
483C24C7×#4112yes—
484C24C7×#4114yes—
485C24C24×C711yescharacteristic
486C2×D4—28no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—44no—
490C2×D4—44no—
491C22×C4—216no—
492C22×C4—216no—
493C22×C4—28no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—28no—
500C22×C4—28no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4C2×C7×D414yes—
541C22×C4C2×C7×D414yes—
542C22×C4C2×C7×D412yes—
543C22×C4C2×C7×D414yes—
544C22×C4C2×C7×D412yes—
545C22×C4C7×#4112yes—
546C22×C4C7×#4114yes—
547C22×C4C7×#4112yes—
548C22×C4C7×#4112yes—
549C4⋊C4—28no—
550C4⋊C4—28no—
551C4⋊C4—48no—
552C22⋊C4—216no—
553C22⋊C4—216no—
554C22⋊C4—48no—
555C22⋊C4—48no—
556C22⋊C4—44no—
557C22⋊C4—44no—
558C22⋊C4—44no—
559C42—216no—
560C2×C7—44no—
561C2×C7—82no—
562C2×C7#238811yescharacteristic
563C2×C7#248211yescharacteristic
564C2×C7#248511yescharacteristic
565C2×C7#249811yescharacteristic
566C2×C7#250011yescharacteristic
567C2×C7#259812yes—
568C2×C7#260112yes—
569C2×C7#260912yes—
570C2×C7#261012yes—
571C2×C7#261511yescharacteristic
572C2×C7#284911yescharacteristic
573C23—22no—
574C23—22no—
575C23—24no—
576C23—24no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—22no—
587C23—24no—
588C23—22no—
589C23—22no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—41no—
595C23—41no—
596C23—42no—
597C23—41no—
598C23—42no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—42no—
604C23—42no—
605C23—41no—
606C23—42no—
607C23—42no—
608C23—41no—
609C23—41no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—41no—
616C23—42no—
617C23—41no—
618C23C7×#12314yes—
619C23C22×C7×D411yescharacteristic
620C23C22×C7×D412yes—
621C23C2×C7×#4112yes—
622C23C2×C7×#4111yescharacteristic
623C23C2×C7×#4111yescharacteristic
624C23C2×C7×#4111yescharacteristic
625C23C2×C7×#4111yescharacteristic
626C23C2×C7×#4112yes—
627C23C7×H(5,𝔽2)12yes—
628C23C7×H(5,𝔽2)11yescharacteristic
629C23C7×2−1+411yescharacteristic
630D4—416no—
631C2×C4—232no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—22no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—41no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—42no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4C7×#12014yes—
684C2×C4C7×#12314yes—
685C7#1511311yescharacteristic, direct product factor, Sylow
686C22—24no—
687C22—24no—
688C22—24no—
689C22—42no—
690C22—42no—
691C22—42no—
692C22—44no—
693C22—44no—
694C22—44no—
695C22—44no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—44no—
701C22—44no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—82no—
706C22—82no—
707C22—81no—
708C22C2×C7×#12011yescharacteristic
709C22C2×C7×#12311yescharacteristic
710C22C2×C7×#12311yescharacteristic
711C22C7×#52511yescharacteristic
712C22C7×#52512yes—
713C22C7×#52512yes—
714C22C7×#52512yes—
715C22C7×#53211yescharacteristic
716C22C7×#53212yes—
717C22C7×#53511yescharacteristic
718C22C7×#53512yes—
719C22C7×#53711yescharacteristic
720C22C7×#53712yes—
721C22C7×#55112yes—
722C22C7×#55112yes—
723C22C7×#55112yes—
724C22C7×#55211yescharacteristic
725C22C7×#55212yes—
726C22C7×#55311yescharacteristic
727C22C7×#55312yes—
728C22C7×#55511yescharacteristic
729C22C7×#55512yes—
730C22C7×#55611yescharacteristic
731C4—24no—
732C4—24no—
733C4—44no—
734C4—42no—
735C4—44no—
736C4—44no—
737C4—81no—
738C4—82no—
739C4—81no—
740C2—44no—
741C2—82no—
742C2C7×#238811yescharacteristic
743C2C7×#248211yescharacteristic
744C2C7×#248511yescharacteristic
745C2C7×#249811yescharacteristic
746C2C7×#250011yescharacteristic
747C2C7×#259812yes—
748C2C7×#260112yes—
749C2C7×#260912yes—
750C2C7×#261012yes—
751C2C7×#261511yescharacteristic
752C2C7×#284911yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC23×C7×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C7×#117C2semidirect
2. C2×C7×#388C2semidirect
4. C7×#1444C2semidirect
5. C7×#1442C2semidirect
6. C7×#1439C2semidirect
7. C7×#1439C2semidirect
8. C7×#1439C2semidirect
10. C7×#1434C2semidirect
11. C7×C22⋊#95C2semidirect
39. #15113C7direct (N × H)
90. C2×C42×C7D4semidirect
101. C22×#117C2×C7semidirect
102. C2×#388C2×C7semidirect
104. #1444C2×C7semidirect
105. #1442C2×C7semidirect
106. #1439C2×C7semidirect
107. #1439C2×C7semidirect
108. #1439C2×C7semidirect
110. #1434C2×C7semidirect
111. C22⋊#95C2×C7semidirect
398. C2×C42C7×D4semidirect
685. C7#15113direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1172
C2×C7×#3882
C2×C7×#3862
C7×#14442
C7×#14422
C7×#14392
C7×#14382
C7×#14342
C7×C22⋊#952
#151137