Finite Group Databasebeta

← C7×#16557 #13193773

Subgroups — C7×#16557 #13193773

Order 1792.

2226 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#121C211yesmaximal, characteristic
2C2×C7×#400C211yesmaximal, characteristic, complemented
3C2×C7×#394C211yesmaximal, characteristic, complemented
4C2×C7×#385C211yesmaximal, characteristic, complemented
5C7×#1445C211yesmaximal, characteristic, complemented
6C7×#1440C212yesmaximal, complemented
7C7×#1439C212yesmaximal, complemented
8C7×#1438C212yesmaximal, 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⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2212yes—
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2212yes—
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2212yes—
26C22×C7×C22⋊C4C2212yes—
27C22×C7×C22⋊C4C2212yes—
28C22×C7×C22⋊C4C2212yes—
29C7×#400—24no—
30C7×#394—24no—
31C7×#385—24no—
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2212yes—
34C2×C7×#95C2212yes—
35C2×C7×#95C2211yescharacteristic
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2211yescharacteristic
38C2×C7×#95C2212yes—
39C2×C7×#95C2212yes—
40C2×C7×#95C2212yes—
41#16557C711yesmaximal, characteristic, direct product factor, Sylow
42C25×C7C2312yes—
43C25×C7C2311yescharacteristic
44C22×C7×D4—24no—
45C22×C7×D4—24no—
46C22×C7×D4—24no—
47C22×C7×D4—24no—
48C22×C7×D4—24no—
49C22×C7×D4—22no—
50C22×C7×D4—22no—
51C22×C7×D4—42no—
52C22×C7×D4—42no—
53C22×C7×D4—42no—
54C22×C7×D4—42no—
55C22×C7×D4D414yes—
56C23×C4×C7—22no—
57C23×C4×C7—22no—
58C23×C4×C7—42no—
59C23×C4×C7—42no—
60C23×C4×C7D414yes—
61C23×C4×C7C2312yes—
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2312yes—
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2312yes—
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C7×#121—232no—
71C2×C7×C4⋊C4—22no—
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4—22no—
74C2×C7×C4⋊C4—22no—
75C2×C7×C4⋊C4—22no—
76C2×C7×C4⋊C4—22no—
77C2×C7×C4⋊C4—42no—
78C2×C7×C4⋊C4D414yes—
79C2×C7×C22⋊C4—22no—
80C2×C7×C22⋊C4—24no—
81C2×C7×C22⋊C4—24no—
82C2×C7×C22⋊C4—24no—
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4—22no—
85C2×C7×C22⋊C4—22no—
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—42no—
92C2×C7×C22⋊C4—42no—
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⋊C4—42no—
102C7×#95—22no—
103C7×#95—22no—
104C7×#95—22no—
105C7×#95—24no—
106C7×#95—22no—
107C7×#95—24no—
108C7×#95—42no—
109C7×#95—42no—
110C7×#95—42no—
111C22×#121C2×C711yescharacteristic
112C2×#400C2×C711yescharacteristic, complemented
113C2×#394C2×C711yescharacteristic, complemented
114C2×#385C2×C711yescharacteristic, complemented
115#1445C2×C711yescharacteristic, complemented
116#1440C2×C712yescomplemented
117#1439C2×C712yescomplemented
118#1438C2×C712yescomplemented
119#1438C2×C712yescomplemented
120#1438C2×C711yescharacteristic, complemented
121C22⋊#95C2×C711yescharacteristic, complemented
122C24×C7—21no—
123C24×C7—21no—
124C24×C7—21no—
125C24×C7—21no—
126C24×C7—21no—
127C24×C7—22no—
128C24×C7—22no—
129C24×C7—22no—
130C24×C7—21no—
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×C7C2×D414yes—
146C24×C7C2×D412yes—
147C24×C7#4114yes—
148C24×C7C2411yescharacteristic
149C2×C7×D4—216no—
150C2×C7×D4—28no—
151C2×C7×D4—48no—
152C2×C7×D4—48no—
153C2×C7×D4—48no—
154C2×C7×D4—44no—
155C2×C7×D4—44no—
156C2×C7×D4—48no—
157C2×C7×D4—48no—
158C2×C7×D4—48no—
159C2×C7×D4—48no—
160C2×C7×D4—48no—
161C22×C4×C7—22no—
162C22×C4×C7—22no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—22no—
170C22×C4×C7—22no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
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—21no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7—21no—
183C22×C4×C7—28no—
184C22×C4×C7—22no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—22no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
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—21no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—21no—
208C22×C4×C7—44no—
209C22×C4×C7—44no—
210C22×C4×C7—48no—
211C22×C4×C7—48no—
212C22×C4×C7C2×D414yes—
213C22×C4×C7C2×D412yes—
214C22×C4×C7C2×D412yes—
215C22×C4×C7C2×D412yes—
216C22×C4×C7C2×D412yes—
217C22×C4×C7#4112yes—
218C22×C4×C7#4112yes—
219C7×C4⋊C4—28no—
220C7×C4⋊C4—44no—
221C7×C4⋊C4—44no—
222C7×C22⋊C4—28no—
223C7×C22⋊C4—216no—
224C7×C22⋊C4—48no—
225C7×C22⋊C4—48no—
226C7×C22⋊C4—44no—
227C7×C22⋊C4—48no—
228C7×C22⋊C4—48no—
229C7×C22⋊C4—48no—
230C23×D4C22×C712yes—
231C23×D4C22×C711yescharacteristic
232C24×C4C22×C711yescharacteristic
233C2×#121—24no—
234C2×#121—24no—
235C2×#121—24no—
236C22×C4⋊C4C22×C711yescharacteristic
237C22×C4⋊C4C22×C711yescharacteristic
238C22×C4⋊C4C22×C711yescharacteristic
239C22×C22⋊C4C22×C712yes—
240C22×C22⋊C4C22×C711yescharacteristic
241C22×C22⋊C4C22×C712yes—
242C22×C22⋊C4C22×C712yes—
243C22×C22⋊C4C22×C712yes—
244C22×C22⋊C4C22×C712yes—
245C22×C22⋊C4C22×C711yescharacteristic
246C22×C22⋊C4C22×C712yes—
247#400—24no—
248#394—24no—
249#385—24no—
250C2×#95C22×C711yescharacteristic
251C2×#95C22×C711yescharacteristic
252C2×#95C22×C712yes—
253C2×#95C22×C712yes—
254C2×#95C22×C711yescharacteristic
255C2×#95C22×C711yescharacteristic
256C2×#95C22×C712yes—
257C2×#95C22×C712yes—
258C2×#95C22×C712yes—
259C23×C7—22no—
260C23×C7—22no—
261C23×C7—22no—
262C23×C7—22no—
263C23×C7—22no—
264C23×C7—22no—
265C23×C7—24no—
266C23×C7—24no—
267C23×C7—24no—
268C23×C7—24no—
269C23×C7—24no—
270C23×C7—24no—
271C23×C7—24no—
272C23×C7—24no—
273C23×C7—24no—
274C23×C7—24no—
275C23×C7—24no—
276C23×C7—24no—
277C23×C7—24no—
278C23×C7—42no—
279C23×C7—42no—
280C23×C7—42no—
281C23×C7—42no—
282C23×C7—41no—
283C23×C7—41no—
284C23×C7—41no—
285C23×C7—41no—
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#12414yes—
317C23×C7C22×D411yescharacteristic
318C23×C7C22×D411yescharacteristic
319C23×C7C22×D411yescharacteristic
320C23×C7C2×#4111yescharacteristic
321C23×C7C2×#4111yescharacteristic
322C23×C7C2×#4112yes—
323C23×C7H(5,𝔽2)12yes—
324C23×C7H(5,𝔽2)12yes—
325C23×C7H(5,𝔽2)12yes—
326C23×C7H(5,𝔽2)11yescharacteristic
327C23×C72−1+411yescharacteristic
328C7×D4—416no—
329C7×D4—432no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—24no—
333C2×C4×C7—24no—
334C2×C4×C7—22no—
335C2×C4×C7—24no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—24no—
341C2×C4×C7—22no—
342C2×C4×C7—24no—
343C2×C4×C7—24no—
344C2×C4×C7—22no—
345C2×C4×C7—416no—
346C2×C4×C7—41no—
347C2×C4×C7—42no—
348C2×C4×C7—41no—
349C2×C4×C7—42no—
350C2×C4×C7—41no—
351C2×C4×C7—42no—
352C2×C4×C7—42no—
353C2×C4×C7—41no—
354C2×C4×C7—42no—
355C2×C4×C7—42no—
356C2×C4×C7—42no—
357C2×C4×C7—41no—
358C2×C4×C7—41no—
359C2×C4×C7—41no—
360C2×C4×C7—41no—
361C2×C4×C7—42no—
362C2×C4×C7—42no—
363C2×C4×C7—41no—
364C2×C4×C7—41no—
365C2×C4×C7—42no—
366C2×C4×C7—42no—
367C2×C4×C7—41no—
368C2×C4×C7—41no—
369C2×C4×C7—42no—
370C2×C4×C7—42no—
371C2×C4×C7—42no—
372C2×C4×C7—42no—
373C2×C4×C7—42no—
374C2×C4×C7—42no—
375C2×C4×C7—42no—
376C2×C4×C7—42no—
377C2×C4×C7—42no—
378C2×C4×C7—42no—
379C2×C4×C7—42no—
380C2×C4×C7—42no—
381C2×C4×C7—42no—
382C2×C4×C7—42no—
383C2×C4×C7#12014yes—
384C25C23×C712yes—
385C25C23×C711yescharacteristic
386C22×D4—24no—
387C22×D4—24no—
388C22×D4—24no—
389C22×D4—24no—
390C22×D4—24no—
391C22×D4—22no—
392C22×D4—22no—
393C22×D4—42no—
394C22×D4—42no—
395C22×D4—42no—
396C22×D4—42no—
397C22×D4C7×D414yes—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4C7×D414yes—
403C23×C4C23×C711yescharacteristic
404C23×C4C23×C712yes—
405C23×C4C23×C711yescharacteristic
406C23×C4C23×C712yes—
407C23×C4C23×C711yescharacteristic
408C23×C4C23×C712yes—
409C23×C4C23×C711yescharacteristic
410C23×C4C23×C711yescharacteristic
411C23×C4C23×C711yescharacteristic
412#121—232no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—42no—
420C2×C4⋊C4C7×D414yes—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—24no—
424C2×C22⋊C4—24no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—24no—
429C2×C22⋊C4—24no—
430C2×C22⋊C4—24no—
431C2×C22⋊C4—24no—
432C2×C22⋊C4—24no—
433C2×C22⋊C4—42no—
434C2×C22⋊C4—42no—
435C2×C22⋊C4—42no—
436C2×C22⋊C4—42no—
437C2×C22⋊C4—42no—
438C2×C22⋊C4—42no—
439C2×C22⋊C4—42no—
440C2×C22⋊C4—42no—
441C2×C22⋊C4—42no—
442C2×C22⋊C4—42no—
443C2×C22⋊C4—42no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—24no—
448#95—22no—
449#95—24no—
450#95—42no—
451#95—42no—
452#95—42no—
453C22×C7—24no—
454C22×C7—24no—
455C22×C7—24no—
456C22×C7—42no—
457C22×C7—42no—
458C22×C7—42no—
459C22×C7—44no—
460C22×C7—44no—
461C22×C7—44no—
462C22×C7—44no—
463C22×C7—42no—
464C22×C7—44no—
465C22×C7—44no—
466C22×C7—44no—
467C22×C7—44no—
468C22×C7—44no—
469C22×C7—44no—
470C22×C7—44no—
471C22×C7—82no—
472C22×C7—82no—
473C22×C7—82no—
474C22×C7—82no—
475C22×C7—82no—
476C22×C7—82no—
477C22×C7—82no—
478C22×C7—82no—
479C22×C7C2×#12011yescharacteristic
480C22×C7#52511yescharacteristic
481C22×C7C2×#12411yescharacteristic
482C22×C7#53411yescharacteristic
483C22×C7#53411yescharacteristic
484C22×C7#53412yes—
485C22×C7#53512yes—
486C22×C7#53511yescharacteristic
487C22×C7#53711yescharacteristic
488C22×C7#53812yes—
489C22×C7#53812yes—
490C22×C7#53912yes—
491C22×C7#54012yes—
492C22×C7#54611yescharacteristic
493C22×C7#54612yes—
494C22×C7#54612yes—
495C22×C7#54711yescharacteristic
496C22×C7#54811yescharacteristic
497C22×C7#55011yescharacteristic
498C22×C7#55312yes—
499C22×C7#55312yes—
500C22×C7#56012yes—
501C22×C7#56212yes—
502C4×C7—24no—
503C4×C7—42no—
504C4×C7—42no—
505C4×C7—42no—
506C4×C7—44no—
507C4×C7—81no—
508C4×C7—82no—
509C4×C7—82no—
510C4×C7—81no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—21no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24C2×C7×D414yes—
535C24C2×C7×D412yes—
536C24C7×#4114yes—
537C24C24×C711yescharacteristic
538C2×D4—216no—
539C2×D4—28no—
540C2×D4—48no—
541C2×D4—48no—
542C2×D4—48no—
543C2×D4—44no—
544C2×D4—44no—
545C2×D4—48no—
546C2×D4—48no—
547C2×D4—48no—
548C2×D4—48no—
549C2×D4—48no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—28no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4C2×C7×D414yes—
602C22×C4C2×C7×D412yes—
603C22×C4C2×C7×D412yes—
604C22×C4C2×C7×D412yes—
605C22×C4C2×C7×D412yes—
606C22×C4C7×#4112yes—
607C22×C4C7×#4112yes—
608C4⋊C4—28no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C22⋊C4—216no—
612C22⋊C4—28no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—44no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C2×C7—44no—
620C2×C7—84no—
621C2×C7#240711yescharacteristic
622C2×C7#243511yescharacteristic
623C2×C7#259111yescharacteristic
624C2×C7#261311yescharacteristic
625C2×C7#263511yescharacteristic
626C2×C7#263911yescharacteristic
627C2×C7#268812yes—
628C2×C7#270812yes—
629C2×C7#271112yes—
630C2×C7#271412yes—
631C2×C7#281311yescharacteristic
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—42no—
660C23—42no—
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—
689C23C7×#12414yes—
690C23C22×C7×D411yescharacteristic
691C23C22×C7×D411yescharacteristic
692C23C22×C7×D411yescharacteristic
693C23C2×C7×#4111yescharacteristic
694C23C2×C7×#4111yescharacteristic
695C23C2×C7×#4112yes—
696C23C7×H(5,𝔽2)12yes—
697C23C7×H(5,𝔽2)12yes—
698C23C7×H(5,𝔽2)12yes—
699C23C7×H(5,𝔽2)11yescharacteristic
700C23C7×2−1+411yescharacteristic
701D4—416no—
702D4—432no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—416no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4C7×#12014yes—
757C7#1655711yescharacteristic, direct product factor, Sylow
758C22—24no—
759C22—24no—
760C22—24no—
761C22—42no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22C2×C7×#12011yescharacteristic
785C22C7×#52511yescharacteristic
786C22C2×C7×#12411yescharacteristic
787C22C7×#53412yes—
788C22C7×#53411yescharacteristic
789C22C7×#53411yescharacteristic
790C22C7×#53511yescharacteristic
791C22C7×#53512yes—
792C22C7×#53711yescharacteristic
793C22C7×#53812yes—
794C22C7×#53812yes—
795C22C7×#53912yes—
796C22C7×#54012yes—
797C22C7×#54611yescharacteristic
798C22C7×#54612yes—
799C22C7×#54612yes—
800C22C7×#54711yescharacteristic
801C22C7×#54811yescharacteristic
802C22C7×#55011yescharacteristic
803C22C7×#55312yes—
804C22C7×#55312yes—
805C22C7×#56012yes—
806C22C7×#56212yes—
807C4—24no—
808C4—42no—
809C4—44no—
810C4—42no—
811C4—42no—
812C4—82no—
813C4—82no—
814C4—81no—
815C4—81no—
816C2—44no—
817C2—84no—
818C2C7×#240711yescharacteristic
819C2C7×#243511yescharacteristic
820C2C7×#259111yescharacteristic
821C2C7×#261311yescharacteristic
822C2C7×#263511yescharacteristic
823C2C7×#263911yescharacteristic
824C2C7×#268812yes—
825C2C7×#270812yes—
826C2C7×#271112yes—
827C2C7×#271412yes—
828C2C7×#281311yescharacteristic
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×#400C2semidirect
3. C2×C7×#394C2semidirect
4. C2×C7×#385C2semidirect
5. C7×#1445C2semidirect
6. C7×#1440C2semidirect
7. C7×#1439C2semidirect
8. C7×#1438C2semidirect
9. C7×#1438C2semidirect
10. C7×#1438C2semidirect
11. C7×C22⋊#95C2semidirect
41. #16557C7direct (N × H)
112. C2×#400C2×C7semidirect
113. C2×#394C2×C7semidirect
114. C2×#385C2×C7semidirect
115. #1445C2×C7semidirect
116. #1440C2×C7semidirect
117. #1439C2×C7semidirect
118. #1438C2×C7semidirect
119. #1438C2×C7semidirect
120. #1438C2×C7semidirect
121. C22⋊#95C2×C7semidirect
757. C7#16557direct (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×#4002
C2×C7×#3942
C2×C7×#3852
C7×#14452
C7×#14402
C7×#14392
C7×#14382
C7×C22⋊#952
#165577