Finite Group Databasebeta

← C7×#24404 #13201620

Subgroups — C7×#24404 #13201620

Order 1792.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3484C211yesmaximal, characteristic, complemented
2C2×C7×B(4,𝔽2)C211yesmaximal, characteristic, complemented
3C22×C7×#99C211yesmaximal, characteristic, complemented
4C7×#2410C212yesmaximal, complemented
5C7×#2403C211yesmaximal, characteristic, complemented
6C7×#2044C212yesmaximal, complemented
7C7×#2021C212yesmaximal, complemented
8C7×#1898C212yesmaximal, complemented
9C7×#1889C211yesmaximal, characteristic, complemented
10C7×#1867C211yesmaximal, characteristic, complemented
11C7×#1790C211yesmaximal, characteristic, complemented
12C2×C7×H(5,𝔽2)C2211yescharacteristic
13C23×C7×D4C2211yescharacteristic
14C23×C7×D4C2211yescharacteristic, complemented
15C7×#546—22no—
16C7×#546—22no—
17C7×D42—22no—
18C7×D42—22no—
19C7×#535—21no—
20C7×#534—21no—
21C7×#534C2212yes—
22C7×#525—21no—
23C2×C7×#121—22no—
24C2×C7×#120—21no—
25C2×C7×#120—21no—
26C2×C7×#120C2211yescharacteristic
27C2×C7×#120C2212yes—
28C2×C7×#120C2212yescomplemented
29C2×C7×#120C2211yescharacteristic, complemented
30C7×#518C2211yescharacteristic
31C22×C7×C22⋊C4C2212yescomplemented
32C7×B(4,𝔽2)—24no—
33C2×C7×#99—24no—
34C2×C7×#99C2211yescharacteristic
35C2×C7×#99C2211yescharacteristic
36C2×C7×#99C2212yescomplemented
37C2×C7×#99C2212yescomplemented
38C2×C7×#99C2212yescomplemented
39C7×#394—22no—
40C7×#392—21no—
41C7×#392—21no—
42C7×#392—22no—
43C7×#386—21no—
44C7×#386—22no—
45C7×#386C2211yescharacteristic
46C7×#386C2211yescharacteristic, complemented
47C7×#386C2212yescomplemented
48C7×#385C2212yescomplemented
49C7×#379C2212yescomplemented
50C7×#379C2211yescharacteristic, complemented
51C7×#342C2212yescomplemented
52C7×#342C2212yescomplemented
53#24404C711yesmaximal, characteristic, direct product factor, Sylow
54C25×C7D411yescharacteristic, complemented
55C25×C7C2311yescharacteristic
56C25×C7C2311yescharacteristic
57C7×H(5,𝔽2)—22no—
58C7×H(5,𝔽2)—22no—
59C7×H(5,𝔽2)—42no—
60C2×C7×#41—21no—
61C2×C7×#41—22no—
62C22×C7×D4—22no—
63C22×C7×D4—22no—
64C22×C7×D4—21no—
65C22×C7×D4—22no—
66C22×C7×D4—21no—
67C22×C7×D4—22no—
68C22×C7×D4—21no—
69C22×C7×D4—21no—
70C22×C7×D4—22no—
71C22×C7×D4—22no—
72C22×C7×D4—21no—
73C22×C7×D4—22no—
74C22×C7×D4—21no—
75C22×C7×D4—21no—
76C22×C7×D4—22no—
77C22×C7×D4—44no—
78C22×C7×D4—42no—
79C22×C7×D4D411yescharacteristic, complemented
80C22×C7×D4D411yescharacteristic, complemented
81C22×C7×D4D412yescomplemented
82C22×C7×D4D412yescomplemented
83C22×C7×D4C2311yescharacteristic
84C22×C7×D4C2312yes—
85C22×C7×D4C2311yescharacteristic
86C23×C4×C7—22no—
87C23×C4×C7D411yescharacteristic, complemented
88C23×C4×C7C2311yescharacteristic
89C7×#127—22no—
90C7×#124—22no—
91C7×#123—22no—
92C7×#123—22no—
93C7×#123—22no—
94C7×C22⋊Q8—21no—
95C7×C22⋊Q8—21no—
96C7×#121—21no—
97C7×#121—21no—
98C7×#121—22no—
99C7×#121—22no—
100C7×#121—22no—
101C7×#121—22no—
102C7×#121—22no—
103C7×#121—22no—
104C7×#121—48no—
105C7×#120—22no—
106C7×#120—22no—
107C7×#120—22no—
108C7×#120—22no—
109C7×#120—22no—
110C7×#120—22no—
111C7×#120—22no—
112C7×#120—22no—
113C7×#120—22no—
114C7×#120—22no—
115C7×#120—22no—
116C7×#120—24no—
117C7×#120—42no—
118C7×#120—42no—
119C7×#120—44no—
120C4×C7×D4—22no—
121C4×C7×D4—22no—
122C4×C7×D4—22no—
123C4×C7×D4—22no—
124C7×#117—21no—
125C2×C7×C4⋊C4—22no—
126C2×C7×C22⋊C4—21no—
127C2×C7×C22⋊C4—21no—
128C2×C7×C22⋊C4—21no—
129C2×C7×C22⋊C4—24no—
130C2×C7×C22⋊C4—22no—
131C2×C7×C22⋊C4—21no—
132C2×C7×C22⋊C4—21no—
133C2×C7×C22⋊C4—21no—
134C2×C7×C22⋊C4—22no—
135C2×C7×C22⋊C4—22no—
136C2×C7×C22⋊C4—21no—
137C2×C7×C22⋊C4—21no—
138C2×C7×C22⋊C4—22no—
139C2×C7×C22⋊C4—21no—
140C2×C7×C22⋊C4—22no—
141C2×C7×C22⋊C4—42no—
142C2×C7×C22⋊C4D412yescomplemented
143C2×C7×C22⋊C4D412yescomplemented
144C2×C7×C22⋊C4C2311yescharacteristic
145C2×C7×C22⋊C4C2311yescharacteristic
146C2×C7×C22⋊C4C2312yes—
147C2×C7×C22⋊C4C2312yes—
148C2×C7×C22⋊C4C2312yes—
149C7×#99—22no—
150C7×#99—24no—
151C7×#99—24no—
152C7×#99—42no—
153C7×#99D414yescomplemented
154C7×#95—22no—
155C7×#95—21no—
156C7×#95—21no—
157C7×#95—22no—
158#3484C2×C711yescharacteristic, complemented
159C2×B(4,𝔽2)C2×C711yescharacteristic, complemented
160C22×#99C2×C711yescharacteristic, complemented
161#2410C2×C712yescomplemented
162#2403C2×C711yescharacteristic, complemented
163#2044C2×C712yescomplemented
164#2021C2×C712yescomplemented
165#1898C2×C712yescomplemented
166#1889C2×C711yescharacteristic, complemented
167#1867C2×C711yescharacteristic, complemented
168#1790C2×C711yescharacteristic, complemented
169C24×C7—21no—
170C24×C7—21no—
171C24×C7—22no—
172C24×C7—21no—
173C24×C7—22no—
174C24×C7—21no—
175C24×C7—21no—
176C24×C7—21no—
177C24×C7—22no—
178C24×C7—21no—
179C24×C7—21no—
180C24×C7—22no—
181C24×C7—41no—
182C24×C7—42no—
183C24×C7—42no—
184C24×C7—42no—
185C24×C7—81no—
186C24×C7—81no—
187C24×C7—81no—
188C24×C7C2×D411yescharacteristic
189C24×C7C2×D412yes—
190C24×C7C2×D411yescharacteristic
191C24×C7C2×D412yes—
192C24×C7C2×D412yes—
193C24×C7C2×D411yescharacteristic
194C24×C7C2×D411yescharacteristic
195C24×C7C2411yescharacteristic
196C7×#41—44no—
197C7×#41—44no—
198C7×#41—42no—
199C7×#41—42no—
200C2×C7×Q8—21no—
201C2×C7×D4—22no—
202C2×C7×D4—22no—
203C2×C7×D4—22no—
204C2×C7×D4—24no—
205C2×C7×D4—21no—
206C2×C7×D4—28no—
207C2×C7×D4—22no—
208C2×C7×D4—22no—
209C2×C7×D4—22no—
210C2×C7×D4—22no—
211C2×C7×D4—22no—
212C2×C7×D4—21no—
213C2×C7×D4—22no—
214C2×C7×D4—22no—
215C2×C7×D4—22no—
216C2×C7×D4—22no—
217C2×C7×D4—21no—
218C2×C7×D4—22no—
219C2×C7×D4—22no—
220C2×C7×D4—22no—
221C2×C7×D4—22no—
222C2×C7×D4—22no—
223C2×C7×D4—22no—
224C2×C7×D4—22no—
225C2×C7×D4—22no—
226C2×C7×D4—22no—
227C2×C7×D4—41no—
228C2×C7×D4—41no—
229C2×C7×D4—42no—
230C2×C7×D4—44no—
231C2×C7×D4—44no—
232C2×C7×D4—44no—
233C2×C7×D4—44no—
234C2×C7×D4—44no—
235C2×C7×D4—44no—
236C2×C7×D4—44no—
237C2×C7×D4—44no—
238C2×C7×D4—44no—
239C2×C7×D4—42no—
240C2×C7×D4—42no—
241C2×C7×D4—44no—
242C2×C7×D4—42no—
243C2×C7×D4—41no—
244C2×C7×D4—42no—
245C2×C7×D4—41no—
246C2×C7×D4—42no—
247C2×C7×D4—44no—
248C2×C7×D4—42no—
249C2×C7×D4—42no—
250C2×C7×D4—42no—
251C2×C7×D4—44no—
252C2×C7×D4—42no—
253C2×C7×D4—82no—
254C2×C7×D4—82no—
255C2×C7×D4—81no—
256C2×C7×D4—81no—
257C2×C7×D4—82no—
258C2×C7×D4—82no—
259C2×C7×D4C2×D412yes—
260C2×C7×D4#4112yes—
261C22×C4×C7—21no—
262C22×C4×C7—22no—
263C22×C4×C7—21no—
264C22×C4×C7—21no—
265C22×C4×C7—21no—
266C22×C4×C7—22no—
267C22×C4×C7—22no—
268C22×C4×C7—21no—
269C22×C4×C7—21no—
270C22×C4×C7—22no—
271C22×C4×C7—22no—
272C22×C4×C7—21no—
273C22×C4×C7—21no—
274C22×C4×C7—42no—
275C22×C4×C7—41no—
276C22×C4×C7—44no—
277C22×C4×C7—44no—
278C22×C4×C7—82no—
279C22×C4×C7C2×D412yes—
280C22×C4×C7C2×D411yescharacteristic
281C22×C4×C7C2×D411yescharacteristic
282C22×C4×C7C2×D412yes—
283C22×C4×C7C2×D412yes—
284C7×C4⋊C4—21no—
285C7×C4⋊C4—21no—
286C7×C4⋊C4—22no—
287C7×C4⋊C4—22no—
288C7×C4⋊C4—44no—
289C7×C22⋊C4—22no—
290C7×C22⋊C4—22no—
291C7×C22⋊C4—22no—
292C7×C22⋊C4—22no—
293C7×C22⋊C4—22no—
294C7×C22⋊C4—22no—
295C7×C22⋊C4—22no—
296C7×C22⋊C4—22no—
297C7×C22⋊C4—22no—
298C7×C22⋊C4—22no—
299C7×C22⋊C4—22no—
300C7×C22⋊C4—22no—
301C7×C22⋊C4—22no—
302C7×C22⋊C4—21no—
303C7×C22⋊C4—21no—
304C7×C22⋊C4—22no—
305C7×C22⋊C4—22no—
306C7×C22⋊C4—44no—
307C7×C22⋊C4—44no—
308C7×C22⋊C4—42no—
309C7×C22⋊C4—42no—
310C7×C22⋊C4—42no—
311C7×C22⋊C4—44no—
312C7×C22⋊C4—42no—
313C7×C22⋊C4—44no—
314C7×C22⋊C4—42no—
315C7×C22⋊C4—82no—
316C7×C22⋊C4—81no—
317C7×C22⋊C4C2×D414yescomplemented
318C42×C7—22no—
319C2×H(5,𝔽2)C22×C711yescharacteristic
320C23×D4C22×C711yescharacteristic
321C23×D4C22×C711yescharacteristic, complemented
322#546—22no—
323#546—22no—
324D42—22no—
325D42—22no—
326#535—21no—
327#534—21no—
328#534C22×C712yes—
329#525—21no—
330C2×#121—22no—
331C2×#120—21no—
332C2×#120—21no—
333C2×#120C22×C711yescharacteristic
334C2×#120C22×C712yes—
335C2×#120C22×C712yescomplemented
336C2×#120C22×C711yescharacteristic, complemented
337#518C22×C711yescharacteristic
338C22×C22⋊C4C22×C712yescomplemented
339B(4,𝔽2)—24no—
340C2×#99—24no—
341C2×#99C22×C711yescharacteristic
342C2×#99C22×C711yescharacteristic
343C2×#99C22×C712yescomplemented
344C2×#99C22×C712yescomplemented
345C2×#99C22×C712yescomplemented
346#394—22no—
347#392—21no—
348#392—21no—
349#392—22no—
350#386—21no—
351#386—22no—
352#386C22×C711yescharacteristic
353#386C22×C711yescharacteristic, complemented
354#386C22×C712yescomplemented
355#385C22×C712yescomplemented
356#379C22×C712yescomplemented
357#379C22×C711yescharacteristic, complemented
358#342C22×C712yescomplemented
359#342C22×C712yescomplemented
360C23×C7—21no—
361C23×C7—21no—
362C23×C7—21no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—24no—
367C23×C7—21no—
368C23×C7—21no—
369C23×C7—21no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—24no—
373C23×C7—22no—
374C23×C7—21no—
375C23×C7—22no—
376C23×C7—21no—
377C23×C7—21no—
378C23×C7—22no—
379C23×C7—22no—
380C23×C7—41no—
381C23×C7—42no—
382C23×C7—41no—
383C23×C7—41no—
384C23×C7—41no—
385C23×C7—42no—
386C23×C7—41no—
387C23×C7—42no—
388C23×C7—42no—
389C23×C7—42no—
390C23×C7—41no—
391C23×C7—41no—
392C23×C7—41no—
393C23×C7—41no—
394C23×C7—42no—
395C23×C7—42no—
396C23×C7—41no—
397C23×C7—42no—
398C23×C7—41no—
399C23×C7—41no—
400C23×C7—42no—
401C23×C7—42no—
402C23×C7—42no—
403C23×C7—42no—
404C23×C7—41no—
405C23×C7—41no—
406C23×C7—41no—
407C23×C7—42no—
408C23×C7—42no—
409C23×C7—42no—
410C23×C7—81no—
411C23×C7—81no—
412C23×C7—82no—
413C23×C7—82no—
414C23×C7—82no—
415C23×C7—82no—
416C23×C7—84no—
417C23×C7—84no—
418C23×C7—81no—
419C23×C7—81no—
420C23×C7—84no—
421C23×C7—84no—
422C23×C7#12011yescharacteristic
423C23×C7#12012yes—
424C23×C7#12011yescharacteristic
425C23×C7#12112yescomplemented
426C23×C7C22×D411yescharacteristic
427C23×C7C22×D412yes—
428C23×C7C22×D411yescharacteristic
429C23×C7C2×#4111yescharacteristic
430C23×C7H(5,𝔽2)12yes—
431C7×Q8—42no—
432C7×D4—24no—
433C7×D4—24no—
434C7×D4—44no—
435C7×D4—42no—
436C7×D4—44no—
437C7×D4—48no—
438C7×D4—44no—
439C7×D4—44no—
440C7×D4—44no—
441C7×D4—42no—
442C7×D4—42no—
443C7×D4—42no—
444C7×D4—42no—
445C7×D4—42no—
446C7×D4—42no—
447C7×D4—44no—
448C7×D4—44no—
449C7×D4—82no—
450C7×D4—82no—
451C7×D4—82no—
452C7×D4—82no—
453C7×D4—88no—
454C7×D4—84no—
455C7×D4—84no—
456C2×C4×C7—21no—
457C2×C4×C7—21no—
458C2×C4×C7—22no—
459C2×C4×C7—24no—
460C2×C4×C7—22no—
461C2×C4×C7—22no—
462C2×C4×C7—22no—
463C2×C4×C7—21no—
464C2×C4×C7—21no—
465C2×C4×C7—21no—
466C2×C4×C7—24no—
467C2×C4×C7—22no—
468C2×C4×C7—22no—
469C2×C4×C7—42no—
470C2×C4×C7—42no—
471C2×C4×C7—44no—
472C2×C4×C7—42no—
473C2×C4×C7—42no—
474C2×C4×C7—41no—
475C2×C4×C7—42no—
476C2×C4×C7—42no—
477C2×C4×C7—41no—
478C2×C4×C7—42no—
479C2×C4×C7—42no—
480C2×C4×C7—42no—
481C2×C4×C7—41no—
482C2×C4×C7—41no—
483C2×C4×C7—42no—
484C2×C4×C7—41no—
485C2×C4×C7—41no—
486C2×C4×C7—41no—
487C2×C4×C7—41no—
488C2×C4×C7—42no—
489C2×C4×C7—81no—
490C2×C4×C7—81no—
491C2×C4×C7—88no—
492C2×C4×C7#12112yescomplemented
493C25C7×D411yescharacteristic, complemented
494C25C23×C711yescharacteristic
495C25C23×C711yescharacteristic
496H(5,𝔽2)—22no—
497H(5,𝔽2)—22no—
498H(5,𝔽2)—42no—
499C2×#41—21no—
500C2×#41—22no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—22no—
504C22×D4—22no—
505C22×D4—22no—
506C22×D4—22no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—22no—
510C22×D4—22no—
511C22×D4—21no—
512C22×D4—22no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—22no—
516C22×D4—44no—
517C22×D4—42no—
518C22×D4C7×D411yescharacteristic, complemented
519C22×D4C7×D411yescharacteristic, complemented
520C22×D4C7×D412yescomplemented
521C22×D4C7×D412yescomplemented
522C22×D4C23×C712yes—
523C22×D4C23×C711yescharacteristic
524C22×D4C23×C711yescharacteristic
525C23×C4—22no—
526C23×C4C7×D411yescharacteristic, complemented
527C23×C4C23×C711yescharacteristic
528#127—22no—
529#124—22no—
530#123—22no—
531#123—22no—
532#123—22no—
533C22⋊Q8—21no—
534C22⋊Q8—21no—
535#121—21no—
536#121—21no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121—22no—
541#121—22no—
542#121—22no—
543#121—48no—
544#120—22no—
545#120—22no—
546#120—22no—
547#120—22no—
548#120—22no—
549#120—22no—
550#120—22no—
551#120—22no—
552#120—22no—
553#120—22no—
554#120—22no—
555#120—24no—
556#120—42no—
557#120—42no—
558#120—44no—
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—22no—
562C4×D4—22no—
563#117—21no—
564C2×C4⋊C4—22no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—22no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—42no—
581C2×C22⋊C4C7×D412yescomplemented
582C2×C22⋊C4C7×D412yescomplemented
583C2×C22⋊C4C23×C712yes—
584C2×C22⋊C4C23×C711yescharacteristic
585C2×C22⋊C4C23×C711yescharacteristic
586C2×C22⋊C4C23×C712yes—
587C2×C22⋊C4C23×C712yes—
588#99—22no—
589#99—24no—
590#99—24no—
591#99—42no—
592#99C7×D414yescomplemented
593#95—22no—
594#95—21no—
595#95—21no—
596#95—22no—
597C22×C7—21no—
598C22×C7—22no—
599C22×C7—21no—
600C22×C7—22no—
601C22×C7—21no—
602C22×C7—21no—
603C22×C7—21no—
604C22×C7—22no—
605C22×C7—22no—
606C22×C7—22no—
607C22×C7—21no—
608C22×C7—21no—
609C22×C7—22no—
610C22×C7—41no—
611C22×C7—41no—
612C22×C7—42no—
613C22×C7—44no—
614C22×C7—44no—
615C22×C7—42no—
616C22×C7—42no—
617C22×C7—42no—
618C22×C7—44no—
619C22×C7—42no—
620C22×C7—42no—
621C22×C7—42no—
622C22×C7—44no—
623C22×C7—41no—
624C22×C7—41no—
625C22×C7—42no—
626C22×C7—41no—
627C22×C7—42no—
628C22×C7—42no—
629C22×C7—41no—
630C22×C7—42no—
631C22×C7—41no—
632C22×C7—82no—
633C22×C7—81no—
634C22×C7—81no—
635C22×C7—81no—
636C22×C7—82no—
637C22×C7—84no—
638C22×C7—82no—
639C22×C7—82no—
640C22×C7—81no—
641C22×C7—82no—
642C22×C7—81no—
643C22×C7—81no—
644C22×C7—82no—
645C22×C7—84no—
646C22×C7—81no—
647C22×C7—81no—
648C22×C7—162no—
649C22×C7B(4,𝔽2)12yescomplemented
650C22×C7C2×#12011yescharacteristic
651C22×C7C2×#12111yescharacteristic
652C22×C7#53411yescharacteristic
653C22×C7D4212yes—
654C22×C7#54612yes—
655C4×C7—22no—
656C4×C7—44no—
657C4×C7—41no—
658C4×C7—42no—
659C4×C7—42no—
660C4×C7—42no—
661C4×C7—42no—
662C4×C7—82no—
663C4×C7—81no—
664C4×C7—81no—
665C24—21no—
666C24—21no—
667C24—22no—
668C24—21no—
669C24—22no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—22no—
674C24—21no—
675C24—21no—
676C24—22no—
677C24—41no—
678C24—42no—
679C24—42no—
680C24—42no—
681C24—81no—
682C24—81no—
683C24—81no—
684C24C2×C7×D411yescharacteristic
685C24C2×C7×D412yes—
686C24C2×C7×D411yescharacteristic
687C24C2×C7×D412yes—
688C24C2×C7×D412yes—
689C24C2×C7×D411yescharacteristic
690C24C2×C7×D411yescharacteristic
691C24C24×C711yescharacteristic
692#41—44no—
693#41—44no—
694#41—42no—
695#41—42no—
696C2×Q8—21no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—22no—
700C2×D4—24no—
701C2×D4—21no—
702C2×D4—28no—
703C2×D4—22no—
704C2×D4—22no—
705C2×D4—22no—
706C2×D4—22no—
707C2×D4—22no—
708C2×D4—21no—
709C2×D4—22no—
710C2×D4—22no—
711C2×D4—22no—
712C2×D4—22no—
713C2×D4—21no—
714C2×D4—22no—
715C2×D4—22no—
716C2×D4—22no—
717C2×D4—22no—
718C2×D4—22no—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—41no—
724C2×D4—41no—
725C2×D4—42no—
726C2×D4—44no—
727C2×D4—44no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—42no—
736C2×D4—42no—
737C2×D4—44no—
738C2×D4—42no—
739C2×D4—41no—
740C2×D4—42no—
741C2×D4—41no—
742C2×D4—42no—
743C2×D4—44no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—44no—
748C2×D4—42no—
749C2×D4—82no—
750C2×D4—82no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—82no—
754C2×D4—82no—
755C2×D4C2×C7×D412yes—
756C2×D4C7×#4112yes—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—42no—
771C22×C4—41no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—82no—
775C22×C4C2×C7×D412yes—
776C22×C4C2×C7×D411yescharacteristic
777C22×C4C2×C7×D411yescharacteristic
778C22×C4C2×C7×D412yes—
779C22×C4C2×C7×D412yes—
780C4⋊C4—21no—
781C4⋊C4—21no—
782C4⋊C4—22no—
783C4⋊C4—22no—
784C4⋊C4—44no—
785C22⋊C4—22no—
786C22⋊C4—22no—
787C22⋊C4—22no—
788C22⋊C4—22no—
789C22⋊C4—22no—
790C22⋊C4—22no—
791C22⋊C4—22no—
792C22⋊C4—22no—
793C22⋊C4—22no—
794C22⋊C4—22no—
795C22⋊C4—22no—
796C22⋊C4—22no—
797C22⋊C4—22no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—44no—
803C22⋊C4—44no—
804C22⋊C4—42no—
805C22⋊C4—42no—
806C22⋊C4—42no—
807C22⋊C4—44no—
808C22⋊C4—42no—
809C22⋊C4—44no—
810C22⋊C4—42no—
811C22⋊C4—82no—
812C22⋊C4—81no—
813C22⋊C4C2×C7×D414yescomplemented
814C42—22no—
815C2×C7—22no—
816C2×C7—21no—
817C2×C7—21no—
818C2×C7—22no—
819C2×C7—22no—
820C2×C7—42no—
821C2×C7—41no—
822C2×C7—42no—
823C2×C7—82no—
824C2×C7—81no—
825C2×C7—82no—
826C2×C7#241011yescharacteristic
827C2×C7C2×B(4,𝔽2)11yescharacteristic
828C2×C7#302611yescharacteristic
829C23—21no—
830C23—21no—
831C23—21no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—24no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—22no—
840C23—22no—
841C23—24no—
842C23—22no—
843C23—21no—
844C23—22no—
845C23—21no—
846C23—21no—
847C23—22no—
848C23—22no—
849C23—41no—
850C23—42no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—42no—
855C23—41no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—42no—
864C23—42no—
865C23—41no—
866C23—42no—
867C23—41no—
868C23—41no—
869C23—42no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23—81no—
880C23—81no—
881C23—82no—
882C23—82no—
883C23—82no—
884C23—82no—
885C23—84no—
886C23—84no—
887C23—81no—
888C23—81no—
889C23—84no—
890C23—84no—
891C23C7×#12011yescharacteristic
892C23C7×#12012yes—
893C23C7×#12011yescharacteristic
894C23C7×#12112yescomplemented
895C23C22×C7×D411yescharacteristic
896C23C22×C7×D412yes—
897C23C22×C7×D411yescharacteristic
898C23C2×C7×#4111yescharacteristic
899C23C7×H(5,𝔽2)12yes—
900Q8—42no—
901D4—24no—
902D4—24no—
903D4—44no—
904D4—42no—
905D4—44no—
906D4—48no—
907D4—44no—
908D4—44no—
909D4—44no—
910D4—42no—
911D4—42no—
912D4—42no—
913D4—42no—
914D4—42no—
915D4—42no—
916D4—44no—
917D4—44no—
918D4—82no—
919D4—82no—
920D4—82no—
921D4—82no—
922D4—88no—
923D4—84no—
924D4—84no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—22no—
928C2×C4—24no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—24no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—44no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—41no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—41no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—42no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—42no—
958C2×C4—81no—
959C2×C4—81no—
960C2×C4—88no—
961C2×C4C7×#12112yescomplemented
962C7#2440411yescharacteristic, direct product factor, Sylow
963C22—21no—
964C22—22no—
965C22—21no—
966C22—22no—
967C22—21no—
968C22—21no—
969C22—21no—
970C22—22no—
971C22—22no—
972C22—22no—
973C22—21no—
974C22—21no—
975C22—22no—
976C22—41no—
977C22—41no—
978C22—42no—
979C22—44no—
980C22—42no—
981C22—42no—
982C22—44no—
983C22—42no—
984C22—44no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—44no—
989C22—41no—
990C22—41no—
991C22—42no—
992C22—41no—
993C22—42no—
994C22—42no—
995C22—41no—
996C22—42no—
997C22—41no—
998C22—82no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22—82no—
1003C22—84no—
1004C22—82no—
1005C22—81no—
1006C22—82no—
1007C22—82no—
1008C22—81no—
1009C22—81no—
1010C22—82no—
1011C22—84no—
1012C22—81no—
1013C22—81no—
1014C22—162no—
1015C22C7×B(4,𝔽2)12yescomplemented
1016C22C2×C7×#12011yescharacteristic
1017C22C2×C7×#12111yescharacteristic
1018C22C7×#53411yescharacteristic
1019C22C7×D4212yes—
1020C22C7×#54612yes—
1021C4—22no—
1022C4—44no—
1023C4—41no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—82no—
1029C4—81no—
1030C4—81no—
1031C2—22no—
1032C2—21no—
1033C2—21no—
1034C2—22no—
1035C2—22no—
1036C2—41no—
1037C2—42no—
1038C2—42no—
1039C2—82no—
1040C2—81no—
1041C2—82no—
1042C2C7×#241011yescharacteristic
1043C2C2×C7×B(4,𝔽2)11yescharacteristic
1044C2C7×#302611yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC24C24×C7
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C25×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C7×#3484C2semidirect
2. C2×C7×B(4,𝔽2)C2semidirect
3. C22×C7×#99C2semidirect
4. C7×#2410C2semidirect
5. C7×#2403C2semidirect
6. C7×#2044C2semidirect
7. C7×#2021C2semidirect
8. C7×#1898C2semidirect
9. C7×#1889C2semidirect
10. C7×#1867C2semidirect
11. C7×#1790C2semidirect
14. C23×C7×D4C22semidirect
28. C2×C7×#120C22semidirect
29. C2×C7×#120C22semidirect
31. C22×C7×C22⋊C4C22semidirect
36. C2×C7×#99C22semidirect
37. C2×C7×#99C22semidirect
38. C2×C7×#99C22semidirect
46. C7×#386C22semidirect
47. C7×#386C22semidirect
48. C7×#385C22semidirect
49. C7×#379C22semidirect
50. C7×#379C22semidirect
51. C7×#342C22semidirect
52. C7×#342C22semidirect
53. #24404C7direct (N × H)
54. C25×C7D4semidirect
79. C22×C7×D4D4semidirect
80. C22×C7×D4D4semidirect
81. C22×C7×D4D4semidirect
82. C22×C7×D4D4semidirect
87. C23×C4×C7D4semidirect
142. C2×C7×C22⋊C4D4semidirect
143. C2×C7×C22⋊C4D4semidirect
153. C7×#99D4semidirect
158. #3484C2×C7semidirect
159. C2×B(4,𝔽2)C2×C7semidirect
160. C22×#99C2×C7semidirect
161. #2410C2×C7semidirect
162. #2403C2×C7semidirect
163. #2044C2×C7semidirect
164. #2021C2×C7semidirect
165. #1898C2×C7semidirect
166. #1889C2×C7semidirect
167. #1867C2×C7semidirect
168. #1790C2×C7semidirect
317. C7×C22⋊C4C2×D4semidirect
321. C23×D4C22×C7semidirect
335. C2×#120C22×C7semidirect
336. C2×#120C22×C7semidirect
338. C22×C22⋊C4C22×C7semidirect
343. C2×#99C22×C7semidirect
344. C2×#99C22×C7semidirect
345. C2×#99C22×C7semidirect
353. #386C22×C7semidirect
354. #386C22×C7semidirect
355. #385C22×C7semidirect
356. #379C22×C7semidirect
357. #379C22×C7semidirect
358. #342C22×C7semidirect
359. #342C22×C7semidirect
425. C23×C7#121semidirect
492. C2×C4×C7#121semidirect
493. C25C7×D4semidirect
518. C22×D4C7×D4semidirect
519. C22×D4C7×D4semidirect
520. C22×D4C7×D4semidirect
521. C22×D4C7×D4semidirect
526. C23×C4C7×D4semidirect
581. C2×C22⋊C4C7×D4semidirect
582. C2×C22⋊C4C7×D4semidirect
592. #99C7×D4semidirect
649. C22×C7B(4,𝔽2)semidirect
813. C22⋊C4C2×C7×D4semidirect
894. C23C7×#121semidirect
961. C2×C4C7×#121semidirect
962. C7#24404direct (N × H)
1015. C22C7×B(4,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C7×#34842
C2×C7×B(4,𝔽2)2
C22×C7×#992
C7×#24102
C7×#24032
C7×#20442
C7×#20212
C7×#18982
C7×#18892
C7×#18672
C7×#17902
#244047