Finite Group Databasebeta

← C7×#24405 #13201621

Subgroups — C7×#24405 #13201621

Order 1792.

1698 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3484C211yesmaximal, characteristic
2C2×C7×#458C211yesmaximal, characteristic, complemented
3C22×C7×#99C211yesmaximal, characteristic, complemented
4C7×#2412C212yesmaximal, complemented
5C7×#2405C211yesmaximal, characteristic, complemented
6C7×#2044C212yesmaximal, complemented
7C7×#2022C212yesmaximal, complemented
8C7×#1898C212yesmaximal, complemented
9C7×#1890C211yesmaximal, characteristic, complemented
10C7×#1867C211yesmaximal, characteristic, complemented
11C7×#1790C211yesmaximal, characteristic, complemented
12C2×C7×H(5,𝔽2)C2211yescharacteristic
13C23×C7×D4C2211yescharacteristic
14C7×#546—22no—
15C7×#546—22no—
16C7×D42—22no—
17C7×D42—22no—
18C7×#535—21no—
19C7×#534—21no—
20C7×#534C2212yes—
21C7×#525—21no—
22C2×C7×#123C2211yescharacteristic
23C2×C7×#123C2212yescomplemented
24C2×C7×#123C2211yescharacteristic, complemented
25C2×C7×#120—21no—
26C2×C7×#120C2212yes—
27C7×#518C2211yescharacteristic
28C22×C7×C22⋊C4C2211yescharacteristic, complemented
29C22×C7×C22⋊C4C2212yescomplemented
30C7×#458—24no—
31C2×C7×#99—24no—
32C2×C7×#99C2211yescharacteristic
33C2×C7×#99C2211yescharacteristic
34C2×C7×#99C2212yescomplemented
35C2×C7×#99C2212yescomplemented
36C2×C7×#99C2212yescomplemented
37C7×#397—22no—
38C7×#394—21no—
39C7×#394—21no—
40C7×#394—22no—
41C7×#386—22no—
42C7×#386C2211yescharacteristic
43C7×#386C2211yescharacteristic, complemented
44C7×#386C2212yescomplemented
45C7×#385—21no—
46C7×#385C2212yescomplemented
47C7×#381C2212yescomplemented
48C7×#380—22no—
49C7×#379—21no—
50C7×#379C2211yescharacteristic, complemented
51C7×#342C2212yescomplemented
52C7×#342C2212yescomplemented
53#24405C711yesmaximal, characteristic, direct product factor, Sylow
54C25×C7D411yescharacteristic
55C25×C7C2311yescharacteristic
56C7×H(5,𝔽2)—22no—
57C7×H(5,𝔽2)—22no—
58C7×H(5,𝔽2)—42no—
59C2×C7×#41—21no—
60C2×C7×#41—22no—
61C22×C7×D4—22no—
62C22×C7×D4—22no—
63C22×C7×D4—21no—
64C22×C7×D4—22no—
65C22×C7×D4—21no—
66C22×C7×D4—21no—
67C22×C7×D4—22no—
68C22×C7×D4—22no—
69C22×C7×D4—42no—
70C22×C7×D4D411yescharacteristic
71C22×C7×D4D411yescharacteristic
72C22×C7×D4D412yes—
73C22×C7×D4D412yes—
74C22×C7×D4C2311yescharacteristic
75C22×C7×D4C2312yes—
76C22×C7×D4C2311yescharacteristic
77C23×C4×C7—22no—
78C23×C4×C7D411yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C7×#127—22no—
82C7×#124—22no—
83C7×#123—22no—
84C7×#123—22no—
85C7×#123—22no—
86C7×#123—22no—
87C7×#123—22no—
88C7×#123—24no—
89C7×#123—42no—
90C7×#123—42no—
91C7×C22⋊Q8—21no—
92C7×C22⋊Q8—21no—
93C7×#121—21no—
94C7×#121—21no—
95C7×#121—22no—
96C7×#121—22no—
97C7×#121—22no—
98C7×#121—22no—
99C7×#121—22no—
100C7×#121—22no—
101C7×#120—22no—
102C7×#120—22no—
103C7×#120—22no—
104C7×#120—22no—
105C7×#120—22no—
106C7×#120—22no—
107C7×#120—22no—
108C7×#120—22no—
109C7×#120—22no—
110C4×C7×D4—22no—
111C4×C7×D4—22no—
112C4×C7×D4—22no—
113C4×C7×D4—22no—
114C7×#117—21no—
115C2×C7×C4⋊C4—22no—
116C2×C7×C4⋊C4—21no—
117C2×C7×C4⋊C4—21no—
118C2×C7×C4⋊C4—22no—
119C2×C7×C22⋊C4—21no—
120C2×C7×C22⋊C4—21no—
121C2×C7×C22⋊C4—21no—
122C2×C7×C22⋊C4—24no—
123C2×C7×C22⋊C4—21no—
124C2×C7×C22⋊C4—22no—
125C2×C7×C22⋊C4—21no—
126C2×C7×C22⋊C4—22no—
127C2×C7×C22⋊C4—22no—
128C2×C7×C22⋊C4—21no—
129C2×C7×C22⋊C4—21no—
130C2×C7×C22⋊C4—21no—
131C2×C7×C22⋊C4—22no—
132C2×C7×C22⋊C4—21no—
133C2×C7×C22⋊C4—21no—
134C2×C7×C22⋊C4—21no—
135C2×C7×C22⋊C4—22no—
136C2×C7×C22⋊C4—42no—
137C2×C7×C22⋊C4D412yes—
138C2×C7×C22⋊C4D412yes—
139C2×C7×C22⋊C4C2311yescharacteristic
140C2×C7×C22⋊C4C2311yescharacteristic
141C2×C7×C22⋊C4C2312yes—
142C2×C7×C22⋊C4C2312yes—
143C2×C7×C22⋊C4C2312yes—
144C7×#99—22no—
145C7×#99—24no—
146C7×#99—24no—
147C7×#99—42no—
148C7×#99D414yescomplemented
149C7×#95—22no—
150C7×#95—22no—
151C7×#95—22no—
152C7×#95—21no—
153C7×#95—21no—
154C7×#95—22no—
155#3484C2×C711yescharacteristic
156C2×#458C2×C711yescharacteristic, complemented
157C22×#99C2×C711yescharacteristic, complemented
158#2412C2×C712yescomplemented
159#2405C2×C711yescharacteristic, complemented
160#2044C2×C712yescomplemented
161#2022C2×C712yescomplemented
162#1898C2×C712yescomplemented
163#1890C2×C711yescharacteristic, complemented
164#1867C2×C711yescharacteristic, complemented
165#1790C2×C711yescharacteristic, complemented
166C24×C7—21no—
167C24×C7—21no—
168C24×C7—22no—
169C24×C7—21no—
170C24×C7—21no—
171C24×C7—21no—
172C24×C7—22no—
173C24×C7—41no—
174C24×C7—42no—
175C24×C7—42no—
176C24×C7—81no—
177C24×C7—81no—
178C24×C7C2×D411yescharacteristic
179C24×C7C2×D412yes—
180C24×C7C2×D411yescharacteristic
181C24×C7C2×D412yes—
182C24×C7C2×D412yes—
183C24×C7C2×D411yescharacteristic
184C24×C7C2×D411yescharacteristic
185C24×C7C2411yescharacteristic
186C7×#41—44no—
187C7×#41—44no—
188C7×#41—42no—
189C7×#41—42no—
190C2×C7×Q8—21no—
191C2×C7×D4—22no—
192C2×C7×D4—22no—
193C2×C7×D4—22no—
194C2×C7×D4—21no—
195C2×C7×D4—22no—
196C2×C7×D4—22no—
197C2×C7×D4—22no—
198C2×C7×D4—22no—
199C2×C7×D4—22no—
200C2×C7×D4—21no—
201C2×C7×D4—22no—
202C2×C7×D4—22no—
203C2×C7×D4—22no—
204C2×C7×D4—22no—
205C2×C7×D4—21no—
206C2×C7×D4—22no—
207C2×C7×D4—22no—
208C2×C7×D4—22no—
209C2×C7×D4—22no—
210C2×C7×D4—22no—
211C2×C7×D4—22no—
212C2×C7×D4—22no—
213C2×C7×D4—22no—
214C2×C7×D4—22no—
215C2×C7×D4—41no—
216C2×C7×D4—41no—
217C2×C7×D4—44no—
218C2×C7×D4—44no—
219C2×C7×D4—44no—
220C2×C7×D4—44no—
221C2×C7×D4—44no—
222C2×C7×D4—44no—
223C2×C7×D4—42no—
224C2×C7×D4—42no—
225C2×C7×D4—44no—
226C2×C7×D4—82no—
227C2×C7×D4—82no—
228C2×C7×D4—82no—
229C2×C7×D4C2×D412yes—
230C2×C7×D4#4112yes—
231C22×C4×C7—21no—
232C22×C4×C7—22no—
233C22×C4×C7—21no—
234C22×C4×C7—21no—
235C22×C4×C7—22no—
236C22×C4×C7—21no—
237C22×C4×C7—21no—
238C22×C4×C7—22no—
239C22×C4×C7—22no—
240C22×C4×C7—21no—
241C22×C4×C7—22no—
242C22×C4×C7—22no—
243C22×C4×C7—21no—
244C22×C4×C7—21no—
245C22×C4×C7—21no—
246C22×C4×C7—21no—
247C22×C4×C7—21no—
248C22×C4×C7—22no—
249C22×C4×C7—41no—
250C22×C4×C7—44no—
251C22×C4×C7—44no—
252C22×C4×C7—81no—
253C22×C4×C7—82no—
254C22×C4×C7C2×D412yes—
255C22×C4×C7C2×D411yescharacteristic
256C22×C4×C7C2×D411yescharacteristic
257C22×C4×C7C2×D412yes—
258C22×C4×C7C2×D412yes—
259C7×C4⋊C4—21no—
260C7×C4⋊C4—21no—
261C7×C4⋊C4—22no—
262C7×C4⋊C4—22no—
263C7×C4⋊C4—44no—
264C7×C4⋊C4—42no—
265C7×C4⋊C4—42no—
266C7×C4⋊C4—82no—
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—22no—
274C7×C22⋊C4—22no—
275C7×C22⋊C4—22no—
276C7×C22⋊C4—22no—
277C7×C22⋊C4—22no—
278C7×C22⋊C4—22no—
279C7×C22⋊C4—22no—
280C7×C22⋊C4—21no—
281C7×C22⋊C4—21no—
282C7×C22⋊C4—22no—
283C7×C22⋊C4—22no—
284C7×C22⋊C4—44no—
285C7×C22⋊C4—44no—
286C7×C22⋊C4—42no—
287C7×C22⋊C4—42no—
288C7×C22⋊C4—41no—
289C7×C22⋊C4—42no—
290C7×C22⋊C4—41no—
291C7×C22⋊C4—42no—
292C7×C22⋊C4—81no—
293C7×C22⋊C4—81no—
294C7×C22⋊C4—81no—
295C7×C22⋊C4—82no—
296C7×C22⋊C4C2×D414yescomplemented
297C42×C7—22no—
298C2×H(5,𝔽2)C22×C711yescharacteristic
299C23×D4C22×C711yescharacteristic
300#546—22no—
301#546—22no—
302D42—22no—
303D42—22no—
304#535—21no—
305#534—21no—
306#534C22×C712yes—
307#525—21no—
308C2×#123C22×C711yescharacteristic
309C2×#123C22×C712yescomplemented
310C2×#123C22×C711yescharacteristic, complemented
311C2×#120—21no—
312C2×#120C22×C712yes—
313#518C22×C711yescharacteristic
314C22×C22⋊C4C22×C711yescharacteristic, complemented
315C22×C22⋊C4C22×C712yescomplemented
316#458—24no—
317C2×#99—24no—
318C2×#99C22×C711yescharacteristic
319C2×#99C22×C711yescharacteristic
320C2×#99C22×C712yescomplemented
321C2×#99C22×C712yescomplemented
322C2×#99C22×C712yescomplemented
323#397—22no—
324#394—21no—
325#394—21no—
326#394—22no—
327#386—22no—
328#386C22×C711yescharacteristic
329#386C22×C711yescharacteristic, complemented
330#386C22×C712yescomplemented
331#385—21no—
332#385C22×C712yescomplemented
333#381C22×C712yescomplemented
334#380—22no—
335#379—21no—
336#379C22×C711yescharacteristic, complemented
337#342C22×C712yescomplemented
338#342C22×C712yescomplemented
339C23×C7—21no—
340C23×C7—21no—
341C23×C7—21no—
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—22no—
345C23×C7—24no—
346C23×C7—21no—
347C23×C7—21no—
348C23×C7—21no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—21no—
352C23×C7—22no—
353C23×C7—21no—
354C23×C7—21no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—42no—
358C23×C7—41no—
359C23×C7—41no—
360C23×C7—41no—
361C23×C7—41no—
362C23×C7—42no—
363C23×C7—42no—
364C23×C7—41no—
365C23×C7—42no—
366C23×C7—42no—
367C23×C7—41no—
368C23×C7—41no—
369C23×C7—41no—
370C23×C7—41no—
371C23×C7—42no—
372C23×C7—42no—
373C23×C7—42no—
374C23×C7—42no—
375C23×C7—42no—
376C23×C7—81no—
377C23×C7—81no—
378C23×C7—82no—
379C23×C7—82no—
380C23×C7—84no—
381C23×C7—81no—
382C23×C7—81no—
383C23×C7—84no—
384C23×C7—84no—
385C23×C7#12011yescharacteristic
386C23×C7#12012yes—
387C23×C7#12011yescharacteristic
388C23×C7#12112yes—
389C23×C7C22×D411yescharacteristic
390C23×C7C22×D412yes—
391C23×C7C22×D411yescharacteristic
392C23×C7C2×#4111yescharacteristic
393C23×C7H(5,𝔽2)12yes—
394C7×Q8—42no—
395C7×D4—24no—
396C7×D4—24no—
397C7×D4—44no—
398C7×D4—42no—
399C7×D4—44no—
400C7×D4—44no—
401C7×D4—44no—
402C7×D4—42no—
403C7×D4—42no—
404C7×D4—42no—
405C7×D4—42no—
406C7×D4—42no—
407C7×D4—42no—
408C7×D4—44no—
409C7×D4—82no—
410C7×D4—82no—
411C7×D4—82no—
412C7×D4—82no—
413C2×C4×C7—21no—
414C2×C4×C7—21no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—21no—
419C2×C4×C7—21no—
420C2×C4×C7—21no—
421C2×C4×C7—24no—
422C2×C4×C7—22no—
423C2×C4×C7—22no—
424C2×C4×C7—42no—
425C2×C4×C7—42no—
426C2×C4×C7—44no—
427C2×C4×C7—42no—
428C2×C4×C7—42no—
429C2×C4×C7—42no—
430C2×C4×C7—42no—
431C2×C4×C7—42no—
432C2×C4×C7—41no—
433C2×C4×C7—41no—
434C2×C4×C7—41no—
435C2×C4×C7—41no—
436C2×C4×C7—42no—
437C2×C4×C7—42no—
438C2×C4×C7—41no—
439C2×C4×C7—41no—
440C2×C4×C7—42no—
441C2×C4×C7—42no—
442C2×C4×C7—41no—
443C2×C4×C7—41no—
444C2×C4×C7—41no—
445C2×C4×C7—41no—
446C2×C4×C7—41no—
447C2×C4×C7—41no—
448C2×C4×C7—42no—
449C2×C4×C7—42no—
450C2×C4×C7—42no—
451C2×C4×C7—81no—
452C2×C4×C7—81no—
453C2×C4×C7—88no—
454C2×C4×C7#12112yes—
455C25C7×D411yescharacteristic
456C25C23×C711yescharacteristic
457H(5,𝔽2)—22no—
458H(5,𝔽2)—22no—
459H(5,𝔽2)—42no—
460C2×#41—21no—
461C2×#41—22no—
462C22×D4—21no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4—22no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—42no—
471C22×D4C7×D411yescharacteristic
472C22×D4C7×D411yescharacteristic
473C22×D4C7×D412yes—
474C22×D4C7×D412yes—
475C22×D4C23×C712yes—
476C22×D4C23×C711yescharacteristic
477C22×D4C23×C711yescharacteristic
478C23×C4—22no—
479C23×C4C7×D411yescharacteristic
480C23×C4C23×C711yescharacteristic
481C23×C4C23×C711yescharacteristic
482#127—22no—
483#124—22no—
484#123—22no—
485#123—22no—
486#123—22no—
487#123—22no—
488#123—22no—
489#123—24no—
490#123—42no—
491#123—42no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494#121—21no—
495#121—21no—
496#121—22no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#120—22no—
503#120—22no—
504#120—22no—
505#120—22no—
506#120—22no—
507#120—22no—
508#120—22no—
509#120—22no—
510#120—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—22no—
515#117—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—22no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4C7×D412yes—
539C2×C22⋊C4C7×D412yes—
540C2×C22⋊C4C23×C712yes—
541C2×C22⋊C4C23×C711yescharacteristic
542C2×C22⋊C4C23×C711yescharacteristic
543C2×C22⋊C4C23×C712yes—
544C2×C22⋊C4C23×C712yes—
545#99—22no—
546#99—24no—
547#99—24no—
548#99—42no—
549#99C7×D414yescomplemented
550#95—22no—
551#95—22no—
552#95—22no—
553#95—21no—
554#95—21no—
555#95—22no—
556C22×C7—21no—
557C22×C7—22no—
558C22×C7—21no—
559C22×C7—22no—
560C22×C7—21no—
561C22×C7—21no—
562C22×C7—21no—
563C22×C7—22no—
564C22×C7—22no—
565C22×C7—22no—
566C22×C7—21no—
567C22×C7—21no—
568C22×C7—22no—
569C22×C7—41no—
570C22×C7—41no—
571C22×C7—42no—
572C22×C7—44no—
573C22×C7—44no—
574C22×C7—42no—
575C22×C7—42no—
576C22×C7—42no—
577C22×C7—42no—
578C22×C7—41no—
579C22×C7—41no—
580C22×C7—42no—
581C22×C7—41no—
582C22×C7—42no—
583C22×C7—41no—
584C22×C7—42no—
585C22×C7—41no—
586C22×C7—82no—
587C22×C7—81no—
588C22×C7—81no—
589C22×C7—81no—
590C22×C7—82no—
591C22×C7—84no—
592C22×C7—82no—
593C22×C7—82no—
594C22×C7—81no—
595C22×C7—84no—
596C22×C7—162no—
597C22×C7#45812yescomplemented
598C22×C7C2×#12011yescharacteristic
599C22×C7C2×#12111yescharacteristic
600C22×C7#53411yescharacteristic
601C22×C7D4212yes—
602C22×C7#54612yes—
603C4×C7—22no—
604C4×C7—44no—
605C4×C7—41no—
606C4×C7—42no—
607C4×C7—42no—
608C4×C7—42no—
609C4×C7—81no—
610C4×C7—81no—
611C4×C7—82no—
612C4×C7—81no—
613C4×C7—81no—
614C24—21no—
615C24—21no—
616C24—22no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—22no—
621C24—41no—
622C24—42no—
623C24—42no—
624C24—81no—
625C24—81no—
626C24C2×C7×D411yescharacteristic
627C24C2×C7×D412yes—
628C24C2×C7×D411yescharacteristic
629C24C2×C7×D412yes—
630C24C2×C7×D412yes—
631C24C2×C7×D411yescharacteristic
632C24C2×C7×D411yescharacteristic
633C24C24×C711yescharacteristic
634#41—44no—
635#41—44no—
636#41—42no—
637#41—42no—
638C2×Q8—21no—
639C2×D4—22no—
640C2×D4—22no—
641C2×D4—22no—
642C2×D4—21no—
643C2×D4—22no—
644C2×D4—22no—
645C2×D4—22no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—22no—
652C2×D4—22no—
653C2×D4—21no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—22no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—22no—
663C2×D4—41no—
664C2×D4—41no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—44no—
668C2×D4—44no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—44no—
674C2×D4—82no—
675C2×D4—82no—
676C2×D4—82no—
677C2×D4C2×C7×D412yes—
678C2×D4C7×#4112yes—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—21no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—22no—
697C22×C4—41no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—81no—
701C22×C4—82no—
702C22×C4C2×C7×D412yes—
703C22×C4C2×C7×D411yescharacteristic
704C22×C4C2×C7×D411yescharacteristic
705C22×C4C2×C7×D412yes—
706C22×C4C2×C7×D412yes—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—22no—
710C4⋊C4—22no—
711C4⋊C4—44no—
712C4⋊C4—42no—
713C4⋊C4—42no—
714C4⋊C4—82no—
715C22⋊C4—22no—
716C22⋊C4—22no—
717C22⋊C4—22no—
718C22⋊C4—22no—
719C22⋊C4—22no—
720C22⋊C4—22no—
721C22⋊C4—22no—
722C22⋊C4—22no—
723C22⋊C4—22no—
724C22⋊C4—22no—
725C22⋊C4—22no—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—44no—
733C22⋊C4—44no—
734C22⋊C4—42no—
735C22⋊C4—42no—
736C22⋊C4—41no—
737C22⋊C4—42no—
738C22⋊C4—41no—
739C22⋊C4—42no—
740C22⋊C4—81no—
741C22⋊C4—81no—
742C22⋊C4—81no—
743C22⋊C4—82no—
744C22⋊C4C2×C7×D414yescomplemented
745C42—22no—
746C2×C7—22no—
747C2×C7—21no—
748C2×C7—21no—
749C2×C7—22no—
750C2×C7—22no—
751C2×C7—42no—
752C2×C7—41no—
753C2×C7—42no—
754C2×C7—81no—
755C2×C7—82no—
756C2×C7#241011yescharacteristic
757C2×C7C2×#45811yescharacteristic
758C2×C7#302611yescharacteristic
759C23—21no—
760C23—21no—
761C23—21no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—24no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—22no—
770C23—22no—
771C23—21no—
772C23—22no—
773C23—21no—
774C23—21no—
775C23—22no—
776C23—22no—
777C23—42no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—42no—
783C23—42no—
784C23—41no—
785C23—42no—
786C23—42no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—81no—
797C23—81no—
798C23—82no—
799C23—82no—
800C23—84no—
801C23—81no—
802C23—81no—
803C23—84no—
804C23—84no—
805C23C7×#12011yescharacteristic
806C23C7×#12012yes—
807C23C7×#12011yescharacteristic
808C23C7×#12112yes—
809C23C22×C7×D411yescharacteristic
810C23C22×C7×D412yes—
811C23C22×C7×D411yescharacteristic
812C23C2×C7×#4111yescharacteristic
813C23C7×H(5,𝔽2)12yes—
814Q8—42no—
815D4—24no—
816D4—24no—
817D4—44no—
818D4—42no—
819D4—44no—
820D4—44no—
821D4—44no—
822D4—42no—
823D4—42no—
824D4—42no—
825D4—42no—
826D4—42no—
827D4—42no—
828D4—44no—
829D4—82no—
830D4—82no—
831D4—82no—
832D4—82no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—24no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—44no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—81no—
872C2×C4—81no—
873C2×C4—88no—
874C2×C4C7×#12112yes—
875C7#2440511yescharacteristic, direct product factor, Sylow
876C22—21no—
877C22—22no—
878C22—21no—
879C22—22no—
880C22—21no—
881C22—21no—
882C22—21no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—21no—
887C22—21no—
888C22—22no—
889C22—41no—
890C22—41no—
891C22—42no—
892C22—44no—
893C22—42no—
894C22—42no—
895C22—44no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—82no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—82no—
911C22—84no—
912C22—81no—
913C22—82no—
914C22—82no—
915C22—84no—
916C22—162no—
917C22C7×#45812yescomplemented
918C22C2×C7×#12011yescharacteristic
919C22C2×C7×#12111yescharacteristic
920C22C7×#53411yescharacteristic
921C22C7×D4212yes—
922C22C7×#54612yes—
923C4—22no—
924C4—44no—
925C4—41no—
926C4—42no—
927C4—42no—
928C4—42no—
929C4—82no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4—81no—
934C2—22no—
935C2—21no—
936C2—21no—
937C2—22no—
938C2—22no—
939C2—41no—
940C2—42no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2C7×#241011yescharacteristic
945C2C2×C7×#45811yescharacteristic
946C2C7×#302611yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC24C24×C7
prime radicalC7×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C25×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#458C2semidirect
3. C22×C7×#99C2semidirect
4. C7×#2412C2semidirect
5. C7×#2405C2semidirect
6. C7×#2044C2semidirect
7. C7×#2022C2semidirect
8. C7×#1898C2semidirect
9. C7×#1890C2semidirect
10. C7×#1867C2semidirect
11. C7×#1790C2semidirect
23. C2×C7×#123C22semidirect
24. C2×C7×#123C22semidirect
28. C22×C7×C22⋊C4C22semidirect
29. C22×C7×C22⋊C4C22semidirect
34. C2×C7×#99C22semidirect
35. C2×C7×#99C22semidirect
36. C2×C7×#99C22semidirect
43. C7×#386C22semidirect
44. C7×#386C22semidirect
46. C7×#385C22semidirect
47. C7×#381C22semidirect
50. C7×#379C22semidirect
51. C7×#342C22semidirect
52. C7×#342C22semidirect
53. #24405C7direct (N × H)
148. C7×#99D4semidirect
156. C2×#458C2×C7semidirect
157. C22×#99C2×C7semidirect
158. #2412C2×C7semidirect
159. #2405C2×C7semidirect
160. #2044C2×C7semidirect
161. #2022C2×C7semidirect
162. #1898C2×C7semidirect
163. #1890C2×C7semidirect
164. #1867C2×C7semidirect
165. #1790C2×C7semidirect
296. C7×C22⋊C4C2×D4semidirect
309. C2×#123C22×C7semidirect
310. C2×#123C22×C7semidirect
314. C22×C22⋊C4C22×C7semidirect
315. C22×C22⋊C4C22×C7semidirect
320. C2×#99C22×C7semidirect
321. C2×#99C22×C7semidirect
322. C2×#99C22×C7semidirect
329. #386C22×C7semidirect
330. #386C22×C7semidirect
332. #385C22×C7semidirect
333. #381C22×C7semidirect
336. #379C22×C7semidirect
337. #342C22×C7semidirect
338. #342C22×C7semidirect
549. #99C7×D4semidirect
597. C22×C7#458semidirect
744. C22⋊C4C2×C7×D4semidirect
875. C7#24405direct (N × H)
917. C22C7×#458semidirect

Maximal subgroups

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

subgroupindex
C7×#34842
C2×C7×#4582
C22×C7×#992
C7×#24122
C7×#24052
C7×#20442
C7×#20222
C7×#18982
C7×#18902
C7×#18672
C7×#17902
#244057