Finite Group Databasebeta

← C7×#24142 #13201358

Subgroups — C7×#24142 #13201358

Order 1792.

1292 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3505C211yesmaximal, characteristic, complemented
2C7×#2626C211yesmaximal, characteristic, complemented
3C7×#2617C211yesmaximal, characteristic, complemented
4C7×#2321C211yesmaximal, characteristic, complemented
5C7×#2044C212yesmaximal, complemented
6C7×#2021C212yesmaximal, complemented
7C7×#1996C211yesmaximal, characteristic, complemented
8C7×#1964C211yesmaximal, characteristic, complemented
9C7×#1889C212yesmaximal, complemented
10C7×#1867C212yesmaximal, complemented
11C7×#1799C211yesmaximal, characteristic, complemented
12C7×#553—22no—
13C7×#553—21no—
14C7×#552—21no—
15C7×#551—22no—
16C7×#548—21no—
17C7×#546—21no—
18C7×#539—21no—
19C7×#538—21no—
20C7×#534C2212yes—
21C7×#529—21no—
22C7×#525—21no—
23C2×C7×C22⋊Q8C2211yescharacteristic
24C2×C7×#121C2211yescharacteristic
25C2×C7×#120C2211yescharacteristic
26C2×C7×#120C2212yes—
27C7×#518C2212yes—
28C2×C4×C7×D4C2211yescharacteristic
29C22×C7×C22⋊C4C2211yescharacteristic
30C2×C7×#99C2212yes—
31C2×C7×#99C2212yes—
32C2×C7×#99C2212yes—
33C7×#399—21no—
34C7×#397—21no—
35C7×#396—22no—
36C7×#394—22no—
37C7×#393—21no—
38C7×#392—21no—
39C7×#390—21no—
40C7×#388—21no—
41C7×#388—21no—
42C7×#386—21no—
43C7×#386C2211yescharacteristic
44C7×#386C2212yes—
45C7×#385C2212yes—
46C7×#385C2211yescharacteristic
47C7×#380C2211yescharacteristic
48C7×#380C2211yescharacteristic
49C7×#379C2212yes—
50C7×#379C2211yescharacteristic
51C4×C7×C22⋊C4C2211yescharacteristic
52C7×#342C2212yes—
53C7×#342C2212yes—
54C7×#342C2212yes—
55#24142C711yesmaximal, characteristic, direct product factor, Sylow
56C25×C7C2311yescharacteristic
57C2×C7×#41—21no—
58C22×C7×Q8D411yescharacteristic, complemented
59C22×C7×D4—21no—
60C22×C7×D4—22no—
61C22×C7×D4D411yescharacteristic, complemented
62C22×C7×D4C2311yescharacteristic
63C22×C7×D4C2312yes—
64C23×C4×C7D411yescharacteristic, complemented
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C7×#126—22no—
68C7×#126—22no—
69C7×#126—22no—
70C7×#125—21no—
71C7×#125—22no—
72C7×#124—21no—
73C7×#124—22no—
74C7×#123—22no—
75C7×#123—22no—
76C7×#123—22no—
77C7×#123—22no—
78C7×#123—22no—
79C7×C22⋊Q8—21no—
80C7×C22⋊Q8—22no—
81C7×C22⋊Q8—21no—
82C7×C22⋊Q8—21no—
83C7×C22⋊Q8—21no—
84C7×C22⋊Q8—21no—
85C7×#121—21no—
86C7×#121—22no—
87C7×#121—21no—
88C7×#121—21no—
89C7×#121—21no—
90C7×#121—21no—
91C7×#121—22no—
92C7×#121—22no—
93C7×#120—22no—
94C7×#120—22no—
95C7×#120—22no—
96C7×#120—22no—
97C7×#120—24no—
98C7×#120—42no—
99C4×C7×Q8—21no—
100C4×C7×D4—22no—
101C4×C7×D4—21no—
102C4×C7×D4—21no—
103C4×C7×D4—21no—
104C4×C7×D4—21no—
105C4×C7×D4—21no—
106C4×C7×D4—22no—
107C4×C7×D4—22no—
108C4×C7×D4—22no—
109C4×C7×D4—22no—
110C7×#117—21no—
111C7×#117—22no—
112C7×#117—22no—
113C2×C7×C4⋊C4—21no—
114C2×C7×C4⋊C4—21no—
115C2×C7×C4⋊C4—21no—
116C2×C7×C4⋊C4—22no—
117C2×C7×C4⋊C4D411yescharacteristic, complemented
118C2×C7×C4⋊C4D411yescharacteristic, complemented
119C2×C7×C4⋊C4D412yescomplemented
120C2×C7×C4⋊C4D411yescharacteristic, complemented
121C2×C7×C22⋊C4—22no—
122C2×C7×C22⋊C4—21no—
123C2×C7×C22⋊C4—21no—
124C2×C7×C22⋊C4—21no—
125C2×C7×C22⋊C4—21no—
126C2×C7×C22⋊C4—21no—
127C2×C7×C22⋊C4—21no—
128C2×C7×C22⋊C4—21no—
129C2×C7×C22⋊C4—22no—
130C2×C7×C22⋊C4—21no—
131C2×C7×C22⋊C4—22no—
132C2×C7×C22⋊C4—21no—
133C2×C7×C22⋊C4—21no—
134C2×C7×C22⋊C4—22no—
135C2×C7×C22⋊C4—22no—
136C2×C7×C22⋊C4D411yescharacteristic, complemented
137C2×C7×C22⋊C4D412yescomplemented
138C2×C7×C22⋊C4C2312yes—
139C2×C7×C22⋊C4C2311yescharacteristic
140C2×C7×C22⋊C4C2312yes—
141C2×C7×C22⋊C4C2311yescharacteristic
142C2×C7×C22⋊C4C2312yes—
143C2×C7×C22⋊C4C2311yescharacteristic
144C2×C42×C7—21no—
145C2×C42×C7D411yescharacteristic, complemented
146C7×#99—24no—
147C7×#99—42no—
148C7×#99—42no—
149C7×#95—21no—
150C7×#95—21no—
151C7×#95—21no—
152C7×#95—21no—
153C7×#95—22no—
154C7×#95—21no—
155C7×#95—22no—
156#3505C2×C711yescharacteristic, complemented
157#2626C2×C711yescharacteristic, complemented
158#2617C2×C711yescharacteristic, complemented
159#2321C2×C711yescharacteristic, complemented
160#2044C2×C712yescomplemented
161#2021C2×C712yescomplemented
162#1996C2×C711yescharacteristic, complemented
163#1964C2×C711yescharacteristic, complemented
164#1889C2×C712yescomplemented
165#1867C2×C712yescomplemented
166#1799C2×C711yescharacteristic, complemented
167C24×C7—21no—
168C24×C7—21no—
169C24×C7—21no—
170C24×C7—21no—
171C24×C7—21no—
172C24×C7—21no—
173C24×C7—81no—
174C24×C7—81no—
175C24×C7C2×D412yes—
176C24×C7C2×D411yescharacteristic
177C24×C7#4112yescomplemented
178C24×C7C2411yescharacteristic
179C7×#41—82no—
180C2×C7×Q8—21no—
181C2×C7×Q8—21no—
182C2×C7×Q8—81no—
183C2×C7×D4—21no—
184C2×C7×D4—22no—
185C2×C7×D4—21no—
186C2×C7×D4—22no—
187C2×C7×D4—22no—
188C2×C7×D4—21no—
189C2×C7×D4—21no—
190C2×C7×D4—22no—
191C2×C7×D4—21no—
192C2×C7×D4—22no—
193C2×C7×D4—21no—
194C2×C7×D4—22no—
195C2×C7×D4—22no—
196C2×C7×D4—22no—
197C2×C7×D4—24no—
198C2×C7×D4—21no—
199C2×C7×D4—21no—
200C2×C7×D4—44no—
201C2×C7×D4—81no—
202C2×C7×D4—81no—
203C2×C7×D4—81no—
204C2×C7×D4—82no—
205C2×C7×D4—82no—
206C22×C4×C7—21no—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—21no—
217C22×C4×C7—81no—
218C22×C4×C7—81no—
219C22×C4×C7—81no—
220C22×C4×C7C2×D411yescharacteristic
221C22×C4×C7C2×D412yes—
222C22×C4×C7C2×D411yescharacteristic
223C22×C4×C7C2×D412yes—
224C22×C4×C7C2×D411yescharacteristic
225C22×C4×C7C2×D412yes—
226C22×C4×C7C2×D411yescharacteristic
227C22×C4×C7C2×D411yescharacteristic
228C22×C4×C7C2×D411yescharacteristic
229C22×C4×C7C2×D411yescharacteristic
230C22×C4×C7C2×D411yescharacteristic
231C22×C4×C7C2×D411yescharacteristic
232C7×C4⋊C4—22no—
233C7×C4⋊C4—22no—
234C7×C4⋊C4—22no—
235C7×C4⋊C4—22no—
236C7×C4⋊C4—21no—
237C7×C4⋊C4—22no—
238C7×C4⋊C4—21no—
239C7×C4⋊C4—21no—
240C7×C4⋊C4—21no—
241C7×C4⋊C4—21no—
242C7×C4⋊C4—22no—
243C7×C4⋊C4—21no—
244C7×C4⋊C4—81no—
245C7×C4⋊C4—81no—
246C7×C4⋊C4—81no—
247C7×C4⋊C4—82no—
248C7×C22⋊C4—22no—
249C7×C22⋊C4—22no—
250C7×C22⋊C4—24no—
251C7×C22⋊C4—22no—
252C7×C22⋊C4—22no—
253C7×C22⋊C4—22no—
254C7×C22⋊C4—22no—
255C7×C22⋊C4—21no—
256C7×C22⋊C4—22no—
257C7×C22⋊C4—21no—
258C7×C22⋊C4—22no—
259C7×C22⋊C4—21no—
260C7×C22⋊C4—22no—
261C7×C22⋊C4—21no—
262C7×C22⋊C4—21no—
263C7×C22⋊C4—22no—
264C7×C22⋊C4—22no—
265C7×C22⋊C4—22no—
266C7×C22⋊C4—21no—
267C7×C22⋊C4—22no—
268C7×C22⋊C4—22no—
269C7×C22⋊C4—21no—
270C7×C22⋊C4—44no—
271C7×C22⋊C4—41no—
272C7×C22⋊C4—41no—
273C7×C22⋊C4—41no—
274C7×C22⋊C4—41no—
275C7×C22⋊C4—81no—
276C7×C22⋊C4—82no—
277C7×C22⋊C4—81no—
278C7×C22⋊C4—82no—
279C7×C22⋊C4—81no—
280C7×C22⋊C4—82no—
281C7×C22⋊C4#4112yescomplemented
282C42×C7—22no—
283C42×C7—22no—
284C42×C7—21no—
285C42×C7—21no—
286C42×C7—81no—
287#553—22no—
288#553—21no—
289#552—21no—
290#551—22no—
291#548—21no—
292#546—21no—
293#539—21no—
294#538—21no—
295#534C22×C712yes—
296#529—21no—
297#525—21no—
298C2×C22⋊Q8C22×C711yescharacteristic
299C2×#121C22×C711yescharacteristic
300C2×#120C22×C711yescharacteristic
301C2×#120C22×C712yes—
302#518C22×C712yes—
303C2×C4×D4C22×C711yescharacteristic
304C22×C22⋊C4C22×C711yescharacteristic
305C2×#99C22×C712yes—
306C2×#99C22×C712yes—
307C2×#99C22×C712yes—
308#399—21no—
309#397—21no—
310#396—22no—
311#394—22no—
312#393—21no—
313#392—21no—
314#390—21no—
315#388—21no—
316#388—21no—
317#386—21no—
318#386C22×C711yescharacteristic
319#386C22×C712yes—
320#385C22×C711yescharacteristic
321#385C22×C712yes—
322#380C22×C711yescharacteristic
323#380C22×C711yescharacteristic
324#379C22×C711yescharacteristic
325#379C22×C712yes—
326C4×C22⋊C4C22×C711yescharacteristic
327#342C22×C712yes—
328#342C22×C712yes—
329#342C22×C712yes—
330C23×C7—21no—
331C23×C7—22no—
332C23×C7—22no—
333C23×C7—21no—
334C23×C7—22no—
335C23×C7—22no—
336C23×C7—21no—
337C23×C7—22no—
338C23×C7—22no—
339C23×C7—41no—
340C23×C7—41no—
341C23×C7—41no—
342C23×C7—41no—
343C23×C7—42no—
344C23×C7—41no—
345C23×C7—42no—
346C23×C7—41no—
347C23×C7—41no—
348C23×C7—42no—
349C23×C7—41no—
350C23×C7—42no—
351C23×C7—42no—
352C23×C7—42no—
353C23×C7—41no—
354C23×C7—41no—
355C23×C7—41no—
356C23×C7—41no—
357C23×C7—82no—
358C23×C7—82no—
359C23×C7—82no—
360C23×C7—82no—
361C23×C7C22×D411yescharacteristic
362C23×C7C22×D411yescharacteristic
363C23×C7C22×D411yescharacteristic
364C23×C7C2×#4111yescharacteristic
365C23×C7C2×#4111yescharacteristic
366C23×C7H(5,𝔽2)11yescharacteristic
367C23×C72−1+411yescharacteristic
368C7×Q8—42no—
369C7×Q8—81no—
370C7×D4—42no—
371C7×D4—42no—
372C7×D4—42no—
373C7×D4—41no—
374C7×D4—41no—
375C7×D4—41no—
376C7×D4—42no—
377C7×D4—42no—
378C7×D4—41no—
379C7×D4—81no—
380C7×D4—82no—
381C7×D4—84no—
382C7×D4—82no—
383C7×D4—88no—
384C2×C4×C7—21no—
385C2×C4×C7—22no—
386C2×C4×C7—21no—
387C2×C4×C7—21no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—21no—
391C2×C4×C7—22no—
392C2×C4×C7—21no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—41no—
396C2×C4×C7—41no—
397C2×C4×C7—41no—
398C2×C4×C7—41no—
399C2×C4×C7—41no—
400C2×C4×C7—41no—
401C2×C4×C7—42no—
402C2×C4×C7—41no—
403C2×C4×C7—41no—
404C2×C4×C7—41no—
405C2×C4×C7—42no—
406C2×C4×C7—41no—
407C2×C4×C7—42no—
408C2×C4×C7—41no—
409C2×C4×C7—41no—
410C2×C4×C7—42no—
411C2×C4×C7—42no—
412C2×C4×C7—41no—
413C2×C4×C7—42no—
414C2×C4×C7—42no—
415C2×C4×C7—42no—
416C2×C4×C7—41no—
417C2×C4×C7—42no—
418C2×C4×C7—41no—
419C2×C4×C7—41no—
420C2×C4×C7—42no—
421C2×C4×C7—42no—
422C2×C4×C7—81no—
423C2×C4×C7—82no—
424C2×C4×C7—82no—
425C2×C4×C7#12011yescharacteristic
426C2×C4×C7#12011yescharacteristic
427C2×C4×C7#12011yescharacteristic
428C2×C4×C7#12011yescharacteristic
429C25C23×C711yescharacteristic
430C2×#41—21no—
431C22×Q8C7×D411yescharacteristic, complemented
432C22×D4—21no—
433C22×D4—22no—
434C22×D4C7×D411yescharacteristic, complemented
435C22×D4C23×C711yescharacteristic
436C22×D4C23×C712yes—
437C23×C4C7×D411yescharacteristic, complemented
438C23×C4C23×C711yescharacteristic
439C23×C4C23×C711yescharacteristic
440#126—22no—
441#126—22no—
442#126—22no—
443#125—21no—
444#125—22no—
445#124—21no—
446#124—22no—
447#123—22no—
448#123—22no—
449#123—22no—
450#123—22no—
451#123—22no—
452C22⋊Q8—21no—
453C22⋊Q8—22no—
454C22⋊Q8—21no—
455C22⋊Q8—21no—
456C22⋊Q8—21no—
457C22⋊Q8—21no—
458#121—21no—
459#121—22no—
460#121—21no—
461#121—21no—
462#121—21no—
463#121—21no—
464#121—22no—
465#121—22no—
466#120—22no—
467#120—22no—
468#120—22no—
469#120—22no—
470#120—24no—
471#120—42no—
472C4×Q8—21no—
473C4×D4—22no—
474C4×D4—21no—
475C4×D4—21no—
476C4×D4—21no—
477C4×D4—21no—
478C4×D4—21no—
479C4×D4—22no—
480C4×D4—22no—
481C4×D4—22no—
482C4×D4—22no—
483#117—21no—
484#117—22no—
485#117—22no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4C7×D411yescharacteristic, complemented
491C2×C4⋊C4C7×D411yescharacteristic, complemented
492C2×C4⋊C4C7×D412yescomplemented
493C2×C4⋊C4C7×D411yescharacteristic, complemented
494C2×C22⋊C4—22no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4C7×D411yescharacteristic, complemented
510C2×C22⋊C4C7×D412yescomplemented
511C2×C22⋊C4C23×C712yes—
512C2×C22⋊C4C23×C711yescharacteristic
513C2×C22⋊C4C23×C712yes—
514C2×C22⋊C4C23×C711yescharacteristic
515C2×C22⋊C4C23×C712yes—
516C2×C22⋊C4C23×C711yescharacteristic
517C2×C42—21no—
518C2×C42C7×D411yescharacteristic, complemented
519#99—24no—
520#99—42no—
521#99—42no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—22no—
527#95—21no—
528#95—22no—
529C22×C7—21no—
530C22×C7—21no—
531C22×C7—21no—
532C22×C7—21no—
533C22×C7—21no—
534C22×C7—21no—
535C22×C7—41no—
536C22×C7—41no—
537C22×C7—41no—
538C22×C7—41no—
539C22×C7—42no—
540C22×C7—42no—
541C22×C7—44no—
542C22×C7—42no—
543C22×C7—44no—
544C22×C7—41no—
545C22×C7—42no—
546C22×C7—42no—
547C22×C7—41no—
548C22×C7—42no—
549C22×C7—42no—
550C22×C7—41no—
551C22×C7—82no—
552C22×C7—81no—
553C22×C7—82no—
554C22×C7—82no—
555C22×C7—81no—
556C22×C7—81no—
557C22×C7—82no—
558C22×C7—81no—
559C22×C7—81no—
560C22×C7C2×#12011yescharacteristic
561C22×C7#52511yescharacteristic
562C22×C7#53711yescharacteristic
563C22×C7#54611yescharacteristic
564C22×C7#54711yescharacteristic
565C22×C7#54811yescharacteristic
566C22×C7#55011yescharacteristic
567C4×C7—21no—
568C4×C7—21no—
569C4×C7—21no—
570C4×C7—21no—
571C4×C7—42no—
572C4×C7—41no—
573C4×C7—42no—
574C4×C7—41no—
575C4×C7—42no—
576C4×C7—41no—
577C4×C7—42no—
578C4×C7—82no—
579C4×C7—81no—
580C4×C7—82no—
581C4×C7—81no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—21no—
586C24—21no—
587C24—21no—
588C24—81no—
589C24—81no—
590C24C2×C7×D412yes—
591C24C2×C7×D411yescharacteristic
592C24C7×#4112yescomplemented
593C24C24×C711yescharacteristic
594#41—82no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—81no—
598C2×D4—21no—
599C2×D4—22no—
600C2×D4—21no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—22no—
606C2×D4—21no—
607C2×D4—22no—
608C2×D4—21no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—44no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4—82no—
620C2×D4—82no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—21no—
632C22×C4—81no—
633C22×C4—81no—
634C22×C4—81no—
635C22×C4C2×C7×D411yescharacteristic
636C22×C4C2×C7×D412yes—
637C22×C4C2×C7×D411yescharacteristic
638C22×C4C2×C7×D412yes—
639C22×C4C2×C7×D411yescharacteristic
640C22×C4C2×C7×D412yes—
641C22×C4C2×C7×D411yescharacteristic
642C22×C4C2×C7×D411yescharacteristic
643C22×C4C2×C7×D411yescharacteristic
644C22×C4C2×C7×D411yescharacteristic
645C22×C4C2×C7×D411yescharacteristic
646C22×C4C2×C7×D411yescharacteristic
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—21no—
652C4⋊C4—22no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—81no—
660C4⋊C4—81no—
661C4⋊C4—81no—
662C4⋊C4—82no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—24no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—21no—
671C22⋊C4—22no—
672C22⋊C4—21no—
673C22⋊C4—22no—
674C22⋊C4—21no—
675C22⋊C4—22no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—21no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—21no—
685C22⋊C4—44no—
686C22⋊C4—41no—
687C22⋊C4—41no—
688C22⋊C4—41no—
689C22⋊C4—41no—
690C22⋊C4—81no—
691C22⋊C4—82no—
692C22⋊C4—81no—
693C22⋊C4—82no—
694C22⋊C4—81no—
695C22⋊C4—82no—
696C22⋊C4C7×#4112yescomplemented
697C42—22no—
698C42—22no—
699C42—21no—
700C42—21no—
701C42—81no—
702C2×C7—21no—
703C2×C7—21no—
704C2×C7—21no—
705C2×C7—21no—
706C2×C7—21no—
707C2×C7—21no—
708C2×C7—82no—
709C2×C7—81no—
710C2×C7—82no—
711C2×C7#240711yescharacteristic
712C2×C7#302611yescharacteristic
713C2×C7#302711yescharacteristic
714C23—21no—
715C23—22no—
716C23—22no—
717C23—21no—
718C23—22no—
719C23—22no—
720C23—21no—
721C23—22no—
722C23—22no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—42no—
728C23—41no—
729C23—42no—
730C23—41no—
731C23—41no—
732C23—42no—
733C23—41no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—82no—
742C23—82no—
743C23—82no—
744C23—82no—
745C23C22×C7×D411yescharacteristic
746C23C22×C7×D411yescharacteristic
747C23C22×C7×D411yescharacteristic
748C23C2×C7×#4111yescharacteristic
749C23C2×C7×#4111yescharacteristic
750C23C7×H(5,𝔽2)11yescharacteristic
751C23C7×2−1+411yescharacteristic
752Q8—42no—
753Q8—81no—
754D4—42no—
755D4—42no—
756D4—42no—
757D4—41no—
758D4—41no—
759D4—41no—
760D4—42no—
761D4—42no—
762D4—41no—
763D4—81no—
764D4—82no—
765D4—84no—
766D4—82no—
767D4—88no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—81no—
807C2×C4—82no—
808C2×C4—82no—
809C2×C4C7×#12011yescharacteristic
810C2×C4C7×#12011yescharacteristic
811C2×C4C7×#12011yescharacteristic
812C2×C4C7×#12011yescharacteristic
813C7#2414211yescharacteristic, direct product factor, Sylow
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—41no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—41no—
836C22—82no—
837C22—81no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C2×C7×#12011yescharacteristic
846C22C7×#52511yescharacteristic
847C22C7×#53711yescharacteristic
848C22C7×#54611yescharacteristic
849C22C7×#54711yescharacteristic
850C22C7×#54811yescharacteristic
851C22C7×#55011yescharacteristic
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—42no—
857C4—41no—
858C4—42no—
859C4—41no—
860C4—42no—
861C4—41no—
862C4—42no—
863C4—82no—
864C4—82no—
865C4—81no—
866C4—81no—
867C2—21no—
868C2—21no—
869C2—21no—
870C2—21no—
871C2—21no—
872C2—21no—
873C2—82no—
874C2—81no—
875C2—82no—
876C2C7×#240711yescharacteristic
877C2C7×#302611yescharacteristic
878C2C7×#302711yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC24C24×C7
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C7×#3505C2semidirect
2. C7×#2626C2semidirect
3. C7×#2617C2semidirect
4. C7×#2321C2semidirect
5. C7×#2044C2semidirect
6. C7×#2021C2semidirect
7. C7×#1996C2semidirect
8. C7×#1964C2semidirect
9. C7×#1889C2semidirect
10. C7×#1867C2semidirect
11. C7×#1799C2semidirect
55. #24142C7direct (N × H)
58. C22×C7×Q8D4semidirect
61. C22×C7×D4D4semidirect
64. C23×C4×C7D4semidirect
117. C2×C7×C4⋊C4D4semidirect
118. C2×C7×C4⋊C4D4semidirect
119. C2×C7×C4⋊C4D4semidirect
120. C2×C7×C4⋊C4D4semidirect
136. C2×C7×C22⋊C4D4semidirect
137. C2×C7×C22⋊C4D4semidirect
145. C2×C42×C7D4semidirect
156. #3505C2×C7semidirect
157. #2626C2×C7semidirect
158. #2617C2×C7semidirect
159. #2321C2×C7semidirect
160. #2044C2×C7semidirect
161. #2021C2×C7semidirect
162. #1996C2×C7semidirect
163. #1964C2×C7semidirect
164. #1889C2×C7semidirect
165. #1867C2×C7semidirect
166. #1799C2×C7semidirect
177. C24×C7#41semidirect
281. C7×C22⋊C4#41semidirect
431. C22×Q8C7×D4semidirect
434. C22×D4C7×D4semidirect
437. C23×C4C7×D4semidirect
490. C2×C4⋊C4C7×D4semidirect
491. C2×C4⋊C4C7×D4semidirect
492. C2×C4⋊C4C7×D4semidirect
493. C2×C4⋊C4C7×D4semidirect
509. C2×C22⋊C4C7×D4semidirect
510. C2×C22⋊C4C7×D4semidirect
518. C2×C42C7×D4semidirect
592. C24C7×#41semidirect
696. C22⋊C4C7×#41semidirect
813. C7#24142direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#35052
C7×#26262
C7×#26172
C7×#23212
C7×#20442
C7×#20212
C7×#19962
C7×#19642
C7×#18892
C7×#18672
C7×#17992
#241427