Finite Group Databasebeta

← C7×#14505 #13191721

Subgroups — C7×#14505 #13191721

Order 1792.

2070 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#123C211yesmaximal, characteristic
2C2×C7×#390C211yesmaximal, characteristic
3C2×C7×#386C211yesmaximal, characteristic
4C7×#1441C212yesmaximal, complemented
5C7×#1440C212yesmaximal, complemented
6C7×#1440C212yesmaximal, complemented
7C7×#1436C212yesmaximal, complemented
8C7×C22⋊#95C212yesmaximal, complemented
9C7×C22⋊#95C212yesmaximal, complemented
10C23×C7×D4C2211yescharacteristic
11C24×C4×C7C2211yescharacteristic
12C24×C4×C7C2211yescharacteristic
13C2×C7×#123—24no—
14C2×C7×#123—24no—
15C2×C7×#123C418yescomplemented
16C22×C7×C4⋊C4C2212yes—
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2212yes—
19C22×C7×C22⋊C4C2212yes—
20C22×C7×C22⋊C4C2212yes—
21C22×C7×C22⋊C4C2212yes—
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C42×C7C2211yescharacteristic
25C7×#390—24no—
26C7×#386—24no—
27C2×C7×#95C2212yes—
28C2×C7×#95C2212yes—
29C2×C7×#95C2212yes—
30C2×C7×#95C2212yes—
31C2×C7×#95C2212yes—
32C2×C7×#95C2212yes—
33C2×C7×#95C2212yes—
34C2×C7×#95C2212yes—
35C2×C7×#95C2212yes—
36#14505C711yesmaximal, characteristic, direct product factor, Sylow
37C25×C7C2311yescharacteristic
38C25×C7C2311yescharacteristic
39C22×C7×D4—41no—
40C22×C7×D4—41no—
41C22×C7×D4—41no—
42C22×C7×D4—41no—
43C22×C7×D4C2×C414yes—
44C22×C7×D4D414yes—
45C22×C7×D4D414yes—
46C23×C4×C7—22no—
47C23×C4×C7—22no—
48C23×C4×C7—22no—
49C23×C4×C7—24no—
50C23×C4×C7—41no—
51C23×C4×C7—41no—
52C23×C4×C7—41no—
53C23×C4×C7—41no—
54C23×C4×C7—41no—
55C23×C4×C7—41no—
56C23×C4×C7—42no—
57C23×C4×C7C2×C414yescomplemented
58C23×C4×C7C2312yes—
59C23×C4×C7C2312yes—
60C23×C4×C7C2312yes—
61C23×C4×C7C2312yes—
62C23×C4×C7C2312yes—
63C23×C4×C7C2312yes—
64C23×C4×C7C2311yescharacteristic
65C7×#123—232no—
66C2×C7×C4⋊C4—24no—
67C2×C7×C4⋊C4—24no—
68C2×C7×C4⋊C4—22no—
69C2×C7×C4⋊C4—41no—
70C2×C7×C4⋊C4—41no—
71C2×C7×C4⋊C4C2×C418yescomplemented
72C2×C7×C22⋊C4—24no—
73C2×C7×C22⋊C4—24no—
74C2×C7×C22⋊C4—22no—
75C2×C7×C22⋊C4—22no—
76C2×C7×C22⋊C4—24no—
77C2×C7×C22⋊C4—22no—
78C2×C7×C22⋊C4—24no—
79C2×C7×C22⋊C4—24no—
80C2×C7×C22⋊C4—24no—
81C2×C7×C22⋊C4—24no—
82C2×C7×C22⋊C4—24no—
83C2×C7×C22⋊C4—42no—
84C2×C7×C22⋊C4—42no—
85C2×C7×C22⋊C4—42no—
86C2×C7×C22⋊C4—41no—
87C2×C7×C22⋊C4—41no—
88C2×C7×C22⋊C4C2×C418yes—
89C2×C7×C22⋊C4C2×C414yescomplemented
90C2×C42×C7—22no—
91C2×C42×C7—41no—
92C2×C42×C7—41no—
93C7×#95—24no—
94C7×#95—24no—
95C7×#95—24no—
96C7×#95—42no—
97C7×#95—42no—
98C7×#95—42no—
99C7×#95—42no—
100C7×#95—42no—
101C7×#95—42no—
102C22×#123C2×C711yescharacteristic
103C2×#390C2×C711yescharacteristic
104C2×#386C2×C711yescharacteristic
105#1441C2×C712yescomplemented
106#1440C2×C712yescomplemented
107#1440C2×C712yescomplemented
108#1436C2×C712yescomplemented
109C22⋊#95C2×C712yescomplemented
110C22⋊#95C2×C712yescomplemented
111C24×C7—22no—
112C24×C7—22no—
113C24×C7—22no—
114C24×C7—22no—
115C24×C7—22no—
116C24×C7—22no—
117C24×C7—21no—
118C24×C7—21no—
119C24×C7—21no—
120C24×C7—21no—
121C24×C7—21no—
122C24×C7—21no—
123C24×C7—21no—
124C24×C7—21no—
125C24×C7—22no—
126C24×C7—22no—
127C24×C7C22×C412yes—
128C24×C7C22×C412yes—
129C24×C7C2×D412yes—
130C24×C7C2×D412yes—
131C24×C7C2×D412yes—
132C24×C7C2×D412yes—
133C24×C7C2411yescharacteristic
134C2×C7×D4—44no—
135C2×C7×D4—44no—
136C2×C7×D4—44no—
137C2×C7×D4—44no—
138C2×C7×D4—44no—
139C2×C7×D4—44no—
140C2×C7×D4C22⋊C4116yes—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7—21no—
145C22×C4×C7—28no—
146C22×C4×C7—22no—
147C22×C4×C7—22no—
148C22×C4×C7—22no—
149C22×C4×C7—22no—
150C22×C4×C7—22no—
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—22no—
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—22no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
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—44no—
185C22×C4×C7—44no—
186C22×C4×C7—44no—
187C22×C4×C7—48no—
188C22×C4×C7—48no—
189C22×C4×C7—44no—
190C22×C4×C7—44no—
191C22×C4×C7—44no—
192C22×C4×C7—44no—
193C22×C4×C7—44no—
194C22×C4×C7—44no—
195C22×C4×C7C22×C414yes—
196C22×C4×C7C22×C414yes—
197C22×C4×C7C22×C412yes—
198C22×C4×C7C2×D412yes—
199C22×C4×C7C2×D412yes—
200C22×C4×C7#4114yes—
201C22×C4×C7#4114yes—
202C7×C4⋊C4—216no—
203C7×C4⋊C4—44no—
204C7×C22⋊C4—216no—
205C7×C22⋊C4—28no—
206C7×C22⋊C4—48no—
207C7×C22⋊C4—48no—
208C7×C22⋊C4—48no—
209C7×C22⋊C4—44no—
210C42×C7—44no—
211C23×D4C22×C711yescharacteristic
212C24×C4C22×C711yescharacteristic
213C24×C4C22×C711yescharacteristic
214C2×#123—24no—
215C2×#123—24no—
216C2×#123C4×C718yescomplemented
217C22×C4⋊C4C22×C712yes—
218C22×C4⋊C4C22×C711yescharacteristic
219C22×C22⋊C4C22×C712yes—
220C22×C22⋊C4C22×C712yes—
221C22×C22⋊C4C22×C712yes—
222C22×C22⋊C4C22×C712yes—
223C22×C22⋊C4C22×C711yescharacteristic
224C22×C22⋊C4C22×C711yescharacteristic
225C22×C42C22×C711yescharacteristic
226#390—24no—
227#386—24no—
228C2×#95C22×C712yes—
229C2×#95C22×C712yes—
230C2×#95C22×C712yes—
231C2×#95C22×C712yes—
232C2×#95C22×C712yes—
233C2×#95C22×C712yes—
234C2×#95C22×C712yes—
235C2×#95C22×C712yes—
236C2×#95C22×C712yes—
237C23×C7—24no—
238C23×C7—24no—
239C23×C7—22no—
240C23×C7—22no—
241C23×C7—22no—
242C23×C7—22no—
243C23×C7—24no—
244C23×C7—24no—
245C23×C7—22no—
246C23×C7—22no—
247C23×C7—22no—
248C23×C7—22no—
249C23×C7—22no—
250C23×C7—22no—
251C23×C7—22no—
252C23×C7—22no—
253C23×C7—24no—
254C23×C7—24no—
255C23×C7—24no—
256C23×C7—24no—
257C23×C7—24no—
258C23×C7—24no—
259C23×C7—24no—
260C23×C7—24no—
261C23×C7—42no—
262C23×C7—42no—
263C23×C7—42no—
264C23×C7—42no—
265C23×C7—42no—
266C23×C7—42no—
267C23×C7—42no—
268C23×C7—42no—
269C23×C7—41no—
270C23×C7—41no—
271C23×C7—42no—
272C23×C7—42no—
273C23×C7—41no—
274C23×C7—41no—
275C23×C7—41no—
276C23×C7—41no—
277C23×C7—42no—
278C23×C7—42no—
279C23×C7—41no—
280C23×C7—41no—
281C23×C7C2×C22⋊C414yes—
282C23×C7C2×C22⋊C414yes—
283C23×C7C23×C411yescharacteristic
284C23×C7C22×D411yescharacteristic
285C23×C7C22×D411yescharacteristic
286C23×C7C2×#4112yes—
287C23×C7C2×#4112yes—
288C23×C7H(5,𝔽2)11yescharacteristic
289C23×C7H(5,𝔽2)11yescharacteristic
290C23×C7H(5,𝔽2)11yescharacteristic
291C23×C7H(5,𝔽2)11yescharacteristic
292C23×C7H(5,𝔽2)12yes—
293C23×C72−1+412yes—
294C7×D4—416no—
295C2×C4×C7—22no—
296C2×C4×C7—22no—
297C2×C4×C7—22no—
298C2×C4×C7—22no—
299C2×C4×C7—22no—
300C2×C4×C7—22no—
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—24no—
308C2×C4×C7—24no—
309C2×C4×C7—24no—
310C2×C4×C7—24no—
311C2×C4×C7—24no—
312C2×C4×C7—24no—
313C2×C4×C7—416no—
314C2×C4×C7—416no—
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—42no—
324C2×C4×C7—42no—
325C2×C4×C7—42no—
326C2×C4×C7—42no—
327C2×C4×C7—42no—
328C2×C4×C7—42no—
329C2×C4×C7—42no—
330C2×C4×C7—42no—
331C2×C4×C7—42no—
332C2×C4×C7—42no—
333C2×C4×C7—42no—
334C2×C4×C7—42no—
335C2×C4×C7—42no—
336C2×C4×C7—42no—
337C2×C4×C7—42no—
338C2×C4×C7—42no—
339C2×C4×C7—42no—
340C2×C4×C7—42no—
341C2×C4×C7—42no—
342C2×C4×C7—42no—
343C2×C4×C7—42no—
344C2×C4×C7—42no—
345C2×C4×C7C2×C22⋊C414yes—
346C25C23×C711yescharacteristic
347C25C23×C711yescharacteristic
348C22×D4—41no—
349C22×D4—41no—
350C22×D4—41no—
351C22×D4—41no—
352C22×D4C2×C4×C714yes—
353C22×D4C7×D414yes—
354C22×D4C7×D414yes—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—24no—
359C23×C4—41no—
360C23×C4—41no—
361C23×C4—41no—
362C23×C4—41no—
363C23×C4—41no—
364C23×C4—41no—
365C23×C4—42no—
366C23×C4C2×C4×C714yescomplemented
367C23×C4C23×C712yes—
368C23×C4C23×C712yes—
369C23×C4C23×C712yes—
370C23×C4C23×C712yes—
371C23×C4C23×C712yes—
372C23×C4C23×C712yes—
373C23×C4C23×C711yescharacteristic
374#123—232no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—41no—
379C2×C4⋊C4—41no—
380C2×C4⋊C4C2×C4×C718yescomplemented
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—41no—
396C2×C22⋊C4—41no—
397C2×C22⋊C4C2×C4×C718yes—
398C2×C22⋊C4C2×C4×C714yescomplemented
399C2×C42—22no—
400C2×C42—41no—
401C2×C42—41no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—42no—
411C22×C7—24no—
412C22×C7—24no—
413C22×C7—28no—
414C22×C7—28no—
415C22×C7—44no—
416C22×C7—44no—
417C22×C7—42no—
418C22×C7—42no—
419C22×C7—42no—
420C22×C7—42no—
421C22×C7—42no—
422C22×C7—42no—
423C22×C7—44no—
424C22×C7—44no—
425C22×C7—44no—
426C22×C7—44no—
427C22×C7—42no—
428C22×C7—42no—
429C22×C7—42no—
430C22×C7—42no—
431C22×C7—42no—
432C22×C7—42no—
433C22×C7C22×C22⋊C411yescharacteristic
434C22×C7C4×#4112yes—
435C22×C7#51811yescharacteristic
436C22×C7#51811yescharacteristic
437C22×C7#52012yes—
438C22×C7#53411yescharacteristic
439C22×C7#53411yescharacteristic
440C22×C7#53411yescharacteristic
441C22×C7#53411yescharacteristic
442C22×C7#53812yes—
443C22×C7#53912yes—
444C22×C7#54012yes—
445C22×C7#54212yes—
446C22×C7#54612yes—
447C22×C7#54612yes—
448C22×C7#54712yes—
449C22×C7#54712yes—
450C22×C7#55111yescharacteristic
451C22×C7#55312yes—
452C22×C7#55911yescharacteristic
453C22×C7#56011yescharacteristic
454C22×C7#56212yes—
455C22×C7#56311yescharacteristic
456C4×C7—24no—
457C4×C7—44no—
458C4×C7—44no—
459C4×C7—44no—
460C4×C7—44no—
461C4×C7—82no—
462C4×C7—82no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—21no—
470C24—21no—
471C24—21no—
472C24—21no—
473C24—21no—
474C24—21no—
475C24—21no—
476C24—21no—
477C24—22no—
478C24—22no—
479C24C22×C4×C712yes—
480C24C22×C4×C712yes—
481C24C2×C7×D412yes—
482C24C2×C7×D412yes—
483C24C2×C7×D412yes—
484C24C2×C7×D412yes—
485C24C24×C711yescharacteristic
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4C7×C22⋊C4116yes—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—28no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
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—22no—
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—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4C22×C4×C714yes—
548C22×C4C22×C4×C714yes—
549C22×C4C22×C4×C712yes—
550C22×C4C2×C7×D412yes—
551C22×C4C2×C7×D412yes—
552C22×C4C7×#4114yes—
553C22×C4C7×#4114yes—
554C4⋊C4—216no—
555C4⋊C4—44no—
556C22⋊C4—216no—
557C22⋊C4—28no—
558C22⋊C4—48no—
559C22⋊C4—48no—
560C22⋊C4—48no—
561C22⋊C4—44no—
562C42—44no—
563C2×C7—44no—
564C2×C7—44no—
565C2×C7#230811yescharacteristic
566C2×C7#233512yes—
567C2×C7#233912yes—
568C2×C7#237411yescharacteristic
569C2×C7#237611yescharacteristic
570C2×C7#269711yescharacteristic
571C2×C7#270112yes—
572C2×C7#270812yes—
573C2×C7#270911yescharacteristic
574C2×C7#271711yescharacteristic
575C2×C7#272411yescharacteristic
576C23—24no—
577C23—24no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—24no—
583C23—24no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—41no—
609C23—41no—
610C23—42no—
611C23—42no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—42no—
617C23—42no—
618C23—41no—
619C23—41no—
620C23C2×C7×C22⋊C414yes—
621C23C2×C7×C22⋊C414yes—
622C23C23×C4×C711yescharacteristic
623C23C22×C7×D411yescharacteristic
624C23C22×C7×D411yescharacteristic
625C23C2×C7×#4112yes—
626C23C2×C7×#4112yes—
627C23C7×H(5,𝔽2)11yescharacteristic
628C23C7×H(5,𝔽2)11yescharacteristic
629C23C7×H(5,𝔽2)11yescharacteristic
630C23C7×H(5,𝔽2)11yescharacteristic
631C23C7×H(5,𝔽2)12yes—
632C23C7×2−1+412yes—
633D4—416no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—416no—
653C2×C4—416no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4C2×C7×C22⋊C414yes—
685C7#1450511yescharacteristic, direct product factor, Sylow
686C22—24no—
687C22—24no—
688C22—28no—
689C22—28no—
690C22—42no—
691C22—42no—
692C22—44no—
693C22—44no—
694C22—44no—
695C22—44no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—44no—
703C22—44no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22C22×C7×C22⋊C411yescharacteristic
709C22C4×C7×#4112yes—
710C22C7×#51811yescharacteristic
711C22C7×#51811yescharacteristic
712C22C7×#52012yes—
713C22C7×#53411yescharacteristic
714C22C7×#53411yescharacteristic
715C22C7×#53411yescharacteristic
716C22C7×#53411yescharacteristic
717C22C7×#53812yes—
718C22C7×#53912yes—
719C22C7×#54012yes—
720C22C7×#54212yes—
721C22C7×#54612yes—
722C22C7×#54612yes—
723C22C7×#54712yes—
724C22C7×#54712yes—
725C22C7×#55111yescharacteristic
726C22C7×#55312yes—
727C22C7×#55911yescharacteristic
728C22C7×#56011yescharacteristic
729C22C7×#56212yes—
730C22C7×#56311yescharacteristic
731C4—24no—
732C4—44no—
733C4—44no—
734C4—44no—
735C4—44no—
736C4—82no—
737C4—82no—
738C2—44no—
739C2—44no—
740C2C7×#230811yescharacteristic
741C2C7×#233512yes—
742C2C7×#233912yes—
743C2C7×#237411yescharacteristic
744C2C7×#237611yescharacteristic
745C2C7×#269711yescharacteristic
746C2C7×#270112yes—
747C2C7×#270812yes—
748C2C7×#270911yescharacteristic
749C2C7×#271711yescharacteristic
750C2C7×#272411yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC23×C7×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
4. C7×#1441C2semidirect
5. C7×#1440C2semidirect
6. C7×#1440C2semidirect
7. C7×#1436C2semidirect
8. C7×C22⋊#95C2semidirect
9. C7×C22⋊#95C2semidirect
15. C2×C7×#123C4semidirect
36. #14505C7direct (N × H)
57. C23×C4×C7C2×C4semidirect
71. C2×C7×C4⋊C4C2×C4semidirect
89. C2×C7×C22⋊C4C2×C4semidirect
105. #1441C2×C7semidirect
106. #1440C2×C7semidirect
107. #1440C2×C7semidirect
108. #1436C2×C7semidirect
109. C22⋊#95C2×C7semidirect
110. C22⋊#95C2×C7semidirect
216. C2×#123C4×C7semidirect
366. C23×C4C2×C4×C7semidirect
380. C2×C4⋊C4C2×C4×C7semidirect
398. C2×C22⋊C4C2×C4×C7semidirect
685. C7#14505direct (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
C2×C7×#3902
C2×C7×#3862
C7×#14412
C7×#14402
C7×#14362
C7×C22⋊#952
#145057