Finite Group Databasebeta

← C7×#24407 #13201623

Subgroups — C7×#24407 #13201623

Order 1792.

1476 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3485C211yesmaximal, characteristic
2C2×C7×#458C211yesmaximal, characteristic, complemented
3C2×C7×#410C211yesmaximal, characteristic, complemented
4C7×#2413C212yesmaximal, complemented
5C7×#2406C211yesmaximal, characteristic, complemented
6C7×#2044C212yesmaximal, complemented
7C7×#2022C212yesmaximal, complemented
8C7×#1899C212yesmaximal, complemented
9C7×#1890C211yesmaximal, characteristic, complemented
10C7×#1867C211yesmaximal, characteristic, complemented
11C7×#1790C211yesmaximal, characteristic, complemented
12C2×C7×H(5,𝔽2)C2211yescharacteristic
13C22×C7×#41C2211yescharacteristic
14C7×#547—22no—
15C7×#547—22no—
16C7×#546—22no—
17C7×#546—22no—
18C7×#536—21no—
19C7×#534—21no—
20C7×#534C2212yes—
21C7×#525—21no—
22C2×C7×#123—21no—
23C2×C7×#123C2211yescharacteristic
24C2×C7×#123C2212yes—
25C2×C7×#123C2212yes—
26C2×C7×#123C2211yescharacteristic, complemented
27C7×#518C2211yescharacteristic
28C2×C7×#117C2212yescomplemented
29C22×C7×C4⋊C4C2211yescharacteristic, complemented
30C7×#458—24no—
31C7×#410—24no—
32C2×C7×#99C2212yes—
33C2×C7×#99C2211yescharacteristic
34C2×C7×#99C2212yes—
35C2×C7×#99C2211yescharacteristic
36C2×C7×#99C2212yescomplemented
37C7×#398—22no—
38C7×#396—22no—
39C7×#395—21no—
40C7×#394—21no—
41C7×#389—22no—
42C7×#388—22no—
43C7×#386C2211yescharacteristic
44C7×#386C2212yes—
45C7×#386C2211yescharacteristic, complemented
46C7×#385—21no—
47C7×#385—21no—
48C7×#385C2212yescomplemented
49C7×#381C2212yescomplemented
50C7×#381C2211yescharacteristic, complemented
51C7×#342C2212yescomplemented
52C7×#342C2212yescomplemented
53#24407C711yesmaximal, characteristic, direct product factor, Sylow
54C7×H(5,𝔽2)—22no—
55C7×H(5,𝔽2)—22no—
56C7×H(5,𝔽2)—42no—
57C2×C7×#41—22no—
58C2×C7×#41—22no—
59C2×C7×#41—22no—
60C2×C7×#41—22no—
61C2×C7×#41—21no—
62C2×C7×#41—22no—
63C2×C7×#41—42no—
64C22×C7×Q8D411yescharacteristic
65C22×C7×D4—21no—
66C22×C7×D4—22no—
67C22×C7×D4D411yescharacteristic
68C22×C7×D4C2311yescharacteristic
69C22×C7×D4C2312yes—
70C22×C7×D4C2311yescharacteristic
71C23×C4×C7D411yescharacteristic
72C23×C4×C7D411yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C7×C4⋊Q8—22no—
77C7×#124—22no—
78C7×#123—22no—
79C7×#123—22no—
80C7×#123—22no—
81C7×#123—22no—
82C7×#123—22no—
83C7×#123—22no—
84C7×#123—22no—
85C7×#123—22no—
86C7×#123—22no—
87C7×#123—22no—
88C7×#123—22no—
89C7×#123—24no—
90C7×#123—42no—
91C7×#123—42no—
92C7×C22⋊Q8—21no—
93C7×C22⋊Q8—21no—
94C7×C22⋊Q8—22no—
95C7×C22⋊Q8—22no—
96C7×#121—21no—
97C7×#121—21no—
98C7×#121—22no—
99C7×#121—22no—
100C7×#121—22no—
101C7×#121—22no—
102C7×#120—22no—
103C7×#120—22no—
104C7×#120—22no—
105C4×C7×D4—22no—
106C4×C7×D4—22no—
107C4×C7×D4—22no—
108C4×C7×D4—22no—
109C7×#117—21no—
110C7×#117—24no—
111C7×#117—42no—
112C2×C7×C4⋊C4—21no—
113C2×C7×C4⋊C4—21no—
114C2×C7×C4⋊C4—21no—
115C2×C7×C4⋊C4—22no—
116C2×C7×C4⋊C4—21no—
117C2×C7×C4⋊C4—22no—
118C2×C7×C4⋊C4—22no—
119C2×C7×C4⋊C4—21no—
120C2×C7×C4⋊C4—21no—
121C2×C7×C4⋊C4—22no—
122C2×C7×C4⋊C4—22no—
123C2×C7×C4⋊C4D412yes—
124C2×C7×C4⋊C4D412yes—
125C2×C7×C22⋊C4—21no—
126C2×C7×C22⋊C4—21no—
127C2×C7×C22⋊C4—21no—
128C2×C7×C22⋊C4—21no—
129C2×C7×C22⋊C4—21no—
130C2×C7×C22⋊C4—21no—
131C2×C7×C22⋊C4—21no—
132C2×C7×C22⋊C4—22no—
133C2×C7×C22⋊C4—22no—
134C2×C7×C22⋊C4D412yes—
135C2×C7×C22⋊C4D412yes—
136C2×C7×C22⋊C4C2311yescharacteristic
137C2×C7×C22⋊C4C2311yescharacteristic
138C2×C7×C22⋊C4C2312yes—
139C2×C7×C22⋊C4C2312yes—
140C2×C7×C22⋊C4C2312yes—
141C2×C42×C7—22no—
142C7×#99—22no—
143C7×#99—24no—
144C7×#99—24no—
145C7×#99—42no—
146C7×#99D414yescomplemented
147C7×#95—21no—
148C7×#95—22no—
149C7×#95—22no—
150C7×#95—21no—
151C7×#95—21no—
152C7×#95—21no—
153C7×#95—22no—
154C7×#95—22no—
155#3485C2×C711yescharacteristic
156C2×#458C2×C711yescharacteristic, complemented
157C2×#410C2×C711yescharacteristic, complemented
158#2413C2×C712yescomplemented
159#2406C2×C711yescharacteristic, complemented
160#2044C2×C712yescomplemented
161#2022C2×C712yescomplemented
162#1899C2×C712yescomplemented
163#1890C2×C711yescharacteristic, complemented
164#1867C2×C711yescharacteristic, complemented
165#1790C2×C711yescharacteristic, complemented
166C24×C7—21no—
167C24×C7C2×D412yes—
168C24×C7C2×D411yescharacteristic
169C24×C7C2×D411yescharacteristic
170C24×C7C2411yescharacteristic
171C7×#41—44no—
172C7×#41—44no—
173C7×#41—44no—
174C7×#41—44no—
175C7×#41—44no—
176C7×#41—44no—
177C7×#41—42no—
178C7×#41—42no—
179C2×C7×Q8—21no—
180C2×C7×Q8—22no—
181C2×C7×Q8—22no—
182C2×C7×Q8—41no—
183C2×C7×D4—22no—
184C2×C7×D4—22no—
185C2×C7×D4—22no—
186C2×C7×D4—21no—
187C2×C7×D4—22no—
188C2×C7×D4—21no—
189C2×C7×D4—22no—
190C2×C7×D4—22no—
191C2×C7×D4—22no—
192C2×C7×D4—22no—
193C2×C7×D4—21no—
194C2×C7×D4—22no—
195C2×C7×D4—22no—
196C2×C7×D4—22no—
197C2×C7×D4—22no—
198C2×C7×D4—22no—
199C2×C7×D4—22no—
200C2×C7×D4—22no—
201C2×C7×D4—41no—
202C2×C7×D4—44no—
203C2×C7×D4—44no—
204C2×C7×D4—42no—
205C2×C7×D4—42no—
206C2×C7×D4C2×D412yes—
207C2×C7×D4#4112yes—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—22no—
211C22×C4×C7—21no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—21no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7—21no—
220C22×C4×C7—21no—
221C22×C4×C7—21no—
222C22×C4×C7—21no—
223C22×C4×C7—22no—
224C22×C4×C7—22no—
225C22×C4×C7—21no—
226C22×C4×C7—21no—
227C22×C4×C7—22no—
228C22×C4×C7—21no—
229C22×C4×C7—21no—
230C22×C4×C7—21no—
231C22×C4×C7—22no—
232C22×C4×C7—42no—
233C22×C4×C7—41no—
234C22×C4×C7—41no—
235C22×C4×C7C2×D412yes—
236C22×C4×C7C2×D411yescharacteristic
237C22×C4×C7C2×D411yescharacteristic
238C22×C4×C7C2×D411yescharacteristic
239C22×C4×C7C2×D412yes—
240C22×C4×C7C2×D412yes—
241C22×C4×C7C2×D411yescharacteristic
242C22×C4×C7C2×D412yes—
243C22×C4×C7C2×D412yes—
244C7×C4⋊C4—22no—
245C7×C4⋊C4—22no—
246C7×C4⋊C4—21no—
247C7×C4⋊C4—21no—
248C7×C4⋊C4—22no—
249C7×C4⋊C4—22no—
250C7×C4⋊C4—22no—
251C7×C4⋊C4—22no—
252C7×C4⋊C4—44no—
253C7×C4⋊C4—44no—
254C7×C4⋊C4—44no—
255C7×C4⋊C4—42no—
256C7×C4⋊C4—41no—
257C7×C4⋊C4—41no—
258C7×C4⋊C4—42no—
259C7×C4⋊C4—42no—
260C7×C22⋊C4—22no—
261C7×C22⋊C4—22no—
262C7×C22⋊C4—22no—
263C7×C22⋊C4—22no—
264C7×C22⋊C4—22no—
265C7×C22⋊C4—22no—
266C7×C22⋊C4—22no—
267C7×C22⋊C4—22no—
268C7×C22⋊C4—22no—
269C7×C22⋊C4—22no—
270C7×C22⋊C4—22no—
271C7×C22⋊C4—22no—
272C7×C22⋊C4—22no—
273C7×C22⋊C4—21no—
274C7×C22⋊C4—21no—
275C7×C22⋊C4—22no—
276C7×C22⋊C4—22no—
277C7×C22⋊C4—44no—
278C7×C22⋊C4—42no—
279C7×C22⋊C4—42no—
280C7×C22⋊C4—44no—
281C7×C22⋊C4—42no—
282C7×C22⋊C4—42no—
283C7×C22⋊C4C2×D414yes—
284C42×C7—22no—
285C42×C7—44no—
286C2×H(5,𝔽2)C22×C711yescharacteristic
287C22×#41C22×C711yescharacteristic
288#547—22no—
289#547—22no—
290#546—22no—
291#546—22no—
292#536—21no—
293#534—21no—
294#534C22×C712yes—
295#525—21no—
296C2×#123—21no—
297C2×#123C22×C711yescharacteristic
298C2×#123C22×C712yes—
299C2×#123C22×C712yes—
300C2×#123C22×C711yescharacteristic, complemented
301#518C22×C711yescharacteristic
302C2×#117C22×C712yescomplemented
303C22×C4⋊C4C22×C711yescharacteristic, complemented
304#458—24no—
305#410—24no—
306C2×#99C22×C711yescharacteristic
307C2×#99C22×C712yes—
308C2×#99C22×C712yes—
309C2×#99C22×C711yescharacteristic
310C2×#99C22×C712yescomplemented
311#398—22no—
312#396—22no—
313#395—21no—
314#394—21no—
315#389—22no—
316#388—22no—
317#386C22×C711yescharacteristic
318#386C22×C712yes—
319#386C22×C711yescharacteristic, complemented
320#385—21no—
321#385—21no—
322#385C22×C712yescomplemented
323#381C22×C712yescomplemented
324#381C22×C711yescharacteristic, complemented
325#342C22×C712yescomplemented
326#342C22×C712yescomplemented
327C23×C7—21no—
328C23×C7—21no—
329C23×C7—22no—
330C23×C7—21no—
331C23×C7—21no—
332C23×C7—21no—
333C23×C7—22no—
334C23×C7—22no—
335C23×C7—41no—
336C23×C7—41no—
337C23×C7—41no—
338C23×C7—41no—
339C23×C7—41no—
340C23×C7—41no—
341C23×C7—42no—
342C23×C7—42no—
343C23×C7—42no—
344C23×C7—81no—
345C23×C7—81no—
346C23×C7#12112yes—
347C23×C7C22×D411yescharacteristic
348C23×C7C22×D412yes—
349C23×C7C22×D411yescharacteristic
350C23×C7C2×#4111yescharacteristic
351C23×C7H(5,𝔽2)12yes—
352C7×Q8—44no—
353C7×Q8—42no—
354C7×D4—24no—
355C7×D4—24no—
356C7×D4—44no—
357C7×D4—42no—
358C7×D4—44no—
359C7×D4—42no—
360C7×D4—42no—
361C7×D4—42no—
362C7×D4—42no—
363C7×D4—42no—
364C7×D4—42no—
365C7×D4—82no—
366C7×D4—82no—
367C2×C4×C7—21no—
368C2×C4×C7—21no—
369C2×C4×C7—21no—
370C2×C4×C7—21no—
371C2×C4×C7—21no—
372C2×C4×C7—21no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—24no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—21no—
382C2×C4×C7—22no—
383C2×C4×C7—21no—
384C2×C4×C7—21no—
385C2×C4×C7—24no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—42no—
389C2×C4×C7—42no—
390C2×C4×C7—42no—
391C2×C4×C7—42no—
392C2×C4×C7—44no—
393C2×C4×C7—42no—
394C2×C4×C7—42no—
395C2×C4×C7—42no—
396C2×C4×C7—41no—
397C2×C4×C7—42no—
398C2×C4×C7—41no—
399C2×C4×C7—42no—
400C2×C4×C7—42no—
401C2×C4×C7—42no—
402C2×C4×C7—41no—
403C2×C4×C7—41no—
404C2×C4×C7—42no—
405C2×C4×C7—41no—
406C2×C4×C7—41no—
407C2×C4×C7—41no—
408C2×C4×C7—41no—
409C2×C4×C7—41no—
410C2×C4×C7—41no—
411C2×C4×C7—41no—
412C2×C4×C7—42no—
413C2×C4×C7—42no—
414C2×C4×C7—42no—
415C2×C4×C7—81no—
416C2×C4×C7—81no—
417C2×C4×C7#12011yescharacteristic
418C2×C4×C7#12011yescharacteristic
419C2×C4×C7#12012yes—
420C2×C4×C7#12112yes—
421H(5,𝔽2)—22no—
422H(5,𝔽2)—22no—
423H(5,𝔽2)—42no—
424C2×#41—22no—
425C2×#41—22no—
426C2×#41—21no—
427C2×#41—22no—
428C2×#41—22no—
429C2×#41—22no—
430C2×#41—42no—
431C22×Q8C7×D411yescharacteristic
432C22×D4—21no—
433C22×D4—22no—
434C22×D4C7×D411yescharacteristic
435C22×D4C23×C712yes—
436C22×D4C23×C711yescharacteristic
437C22×D4C23×C711yescharacteristic
438C23×C4C7×D411yescharacteristic
439C23×C4C7×D411yescharacteristic
440C23×C4C23×C711yescharacteristic
441C23×C4C23×C711yescharacteristic
442C23×C4C23×C711yescharacteristic
443C4⋊Q8—22no—
444#124—22no—
445#123—22no—
446#123—22no—
447#123—22no—
448#123—22no—
449#123—22no—
450#123—22no—
451#123—22no—
452#123—22no—
453#123—22no—
454#123—22no—
455#123—22no—
456#123—24no—
457#123—42no—
458#123—42no—
459C22⋊Q8—21no—
460C22⋊Q8—21no—
461C22⋊Q8—22no—
462C22⋊Q8—22no—
463#121—21no—
464#121—21no—
465#121—22no—
466#121—22no—
467#121—22no—
468#121—22no—
469#120—22no—
470#120—22no—
471#120—22no—
472C4×D4—22no—
473C4×D4—22no—
474C4×D4—22no—
475C4×D4—22no—
476#117—21no—
477#117—24no—
478#117—42no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4C7×D412yes—
491C2×C4⋊C4C7×D412yes—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4C7×D412yes—
502C2×C22⋊C4C7×D412yes—
503C2×C22⋊C4C23×C712yes—
504C2×C22⋊C4C23×C711yescharacteristic
505C2×C22⋊C4C23×C711yescharacteristic
506C2×C22⋊C4C23×C712yes—
507C2×C22⋊C4C23×C712yes—
508C2×C42—22no—
509#99—22no—
510#99—24no—
511#99—24no—
512#99—42no—
513#99C7×D414yescomplemented
514#95—21no—
515#95—22no—
516#95—22no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—22no—
521#95—22no—
522C22×C7—22no—
523C22×C7—21no—
524C22×C7—22no—
525C22×C7—21no—
526C22×C7—22no—
527C22×C7—41no—
528C22×C7—41no—
529C22×C7—42no—
530C22×C7—42no—
531C22×C7—42no—
532C22×C7—41no—
533C22×C7—41no—
534C22×C7—41no—
535C22×C7—42no—
536C22×C7—41no—
537C22×C7—42no—
538C22×C7—41no—
539C22×C7—42no—
540C22×C7—81no—
541C22×C7—82no—
542C22×C7—81no—
543C22×C7—82no—
544C22×C7—162no—
545C22×C7C2×#12011yescharacteristic
546C22×C7C2×#12111yescharacteristic
547C22×C7#53411yescharacteristic
548C22×C7D4212yes—
549C22×C7#54612yes—
550C4×C7—21no—
551C4×C7—21no—
552C4×C7—22no—
553C4×C7—22no—
554C4×C7—44no—
555C4×C7—42no—
556C4×C7—41no—
557C4×C7—42no—
558C4×C7—42no—
559C4×C7—42no—
560C4×C7—82no—
561C4×C7—81no—
562C4×C7—81no—
563C4×C7—81no—
564C24—21no—
565C24C2×C7×D412yes—
566C24C2×C7×D411yescharacteristic
567C24C2×C7×D411yescharacteristic
568C24C24×C711yescharacteristic
569#41—44no—
570#41—44no—
571#41—44no—
572#41—44no—
573#41—44no—
574#41—44no—
575#41—42no—
576#41—42no—
577C2×Q8—21no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—41no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—41no—
600C2×D4—44no—
601C2×D4—44no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4C2×C7×D412yes—
605C2×D4C7×#4112yes—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—22no—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—22no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—22no—
630C22×C4—42no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4C2×C7×D412yes—
634C22×C4C2×C7×D411yescharacteristic
635C22×C4C2×C7×D411yescharacteristic
636C22×C4C2×C7×D411yescharacteristic
637C22×C4C2×C7×D412yes—
638C22×C4C2×C7×D412yes—
639C22×C4C2×C7×D411yescharacteristic
640C22×C4C2×C7×D412yes—
641C22×C4C2×C7×D412yes—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—44no—
651C4⋊C4—44no—
652C4⋊C4—42no—
653C4⋊C4—44no—
654C4⋊C4—41no—
655C4⋊C4—41no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—44no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—44no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4C2×C7×D414yes—
682C42—22no—
683C42—44no—
684C2×C7—22no—
685C2×C7—21no—
686C2×C7—21no—
687C2×C7—22no—
688C2×C7—42no—
689C2×C7—81no—
690C2×C7—82no—
691C2×C7#241011yescharacteristic
692C2×C7#302511yescharacteristic
693C2×C7#302811yescharacteristic
694C23—21no—
695C23—21no—
696C23—22no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—22no—
701C23—22no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—81no—
712C23—81no—
713C23C7×#12112yes—
714C23C22×C7×D411yescharacteristic
715C23C22×C7×D412yes—
716C23C22×C7×D411yescharacteristic
717C23C2×C7×#4111yescharacteristic
718C23C7×H(5,𝔽2)12yes—
719Q8—44no—
720Q8—42no—
721D4—24no—
722D4—24no—
723D4—44no—
724D4—42no—
725D4—44no—
726D4—42no—
727D4—42no—
728D4—42no—
729D4—42no—
730D4—42no—
731D4—42no—
732D4—82no—
733D4—82no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—24no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—44no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4C7×#12011yescharacteristic
785C2×C4C7×#12011yescharacteristic
786C2×C4C7×#12012yes—
787C2×C4C7×#12112yes—
788C7#2440711yescharacteristic, direct product factor, Sylow
789C22—22no—
790C22—21no—
791C22—22no—
792C22—21no—
793C22—22no—
794C22—41no—
795C22—41no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—41no—
806C22—42no—
807C22—81no—
808C22—82no—
809C22—81no—
810C22—82no—
811C22—162no—
812C22C2×C7×#12011yescharacteristic
813C22C2×C7×#12111yescharacteristic
814C22C7×#53411yescharacteristic
815C22C7×D4212yes—
816C22C7×#54612yes—
817C4—21no—
818C4—21no—
819C4—22no—
820C4—22no—
821C4—44no—
822C4—42no—
823C4—41no—
824C4—42no—
825C4—42no—
826C4—42no—
827C4—82no—
828C4—81no—
829C4—81no—
830C4—81no—
831C2—22no—
832C2—21no—
833C2—21no—
834C2—22no—
835C2—42no—
836C2—81no—
837C2—82no—
838C2C7×#241011yescharacteristic
839C2C7×#302511yescharacteristic
840C2C7×#302811yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC24C24×C7
prime radicalC7×#3485C2
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
2. C2×C7×#458C2semidirect
3. C2×C7×#410C2semidirect
4. C7×#2413C2semidirect
5. C7×#2406C2semidirect
6. C7×#2044C2semidirect
7. C7×#2022C2semidirect
8. C7×#1899C2semidirect
9. C7×#1890C2semidirect
10. C7×#1867C2semidirect
11. C7×#1790C2semidirect
26. C2×C7×#123C22semidirect
28. C2×C7×#117C22semidirect
29. C22×C7×C4⋊C4C22semidirect
36. C2×C7×#99C22semidirect
45. C7×#386C22semidirect
48. C7×#385C22semidirect
49. C7×#381C22semidirect
50. C7×#381C22semidirect
51. C7×#342C22semidirect
52. C7×#342C22semidirect
53. #24407C7direct (N × H)
146. C7×#99D4semidirect
156. C2×#458C2×C7semidirect
157. C2×#410C2×C7semidirect
158. #2413C2×C7semidirect
159. #2406C2×C7semidirect
160. #2044C2×C7semidirect
161. #2022C2×C7semidirect
162. #1899C2×C7semidirect
163. #1890C2×C7semidirect
164. #1867C2×C7semidirect
165. #1790C2×C7semidirect
300. C2×#123C22×C7semidirect
302. C2×#117C22×C7semidirect
303. C22×C4⋊C4C22×C7semidirect
310. C2×#99C22×C7semidirect
319. #386C22×C7semidirect
322. #385C22×C7semidirect
323. #381C22×C7semidirect
324. #381C22×C7semidirect
325. #342C22×C7semidirect
326. #342C22×C7semidirect
513. #99C7×D4semidirect
788. C7#24407direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#34852
C2×C7×#4582
C2×C7×#4102
C7×#24132
C7×#24062
C7×#20442
C7×#20222
C7×#18992
C7×#18902
C7×#18672
C7×#17902
#244077