Finite Group Databasebeta

← C7×#24406 #13201622

Subgroups — C7×#24406 #13201622

Order 1792.

1620 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3485C211yesmaximal, characteristic, complemented
2C2×C7×B(4,𝔽2)C211yesmaximal, characteristic, complemented
3C2×C7×#410C211yesmaximal, characteristic, complemented
4C7×#2411C212yesmaximal, complemented
5C7×#2404C211yesmaximal, characteristic, complemented
6C7×#2044C212yesmaximal, complemented
7C7×#2021C212yesmaximal, complemented
8C7×#1899C212yesmaximal, complemented
9C7×#1889C211yesmaximal, 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×#123C2212yes—
24C2×C7×#120C2211yescharacteristic
25C2×C7×#120C2212yes—
26C2×C7×#120C2211yescharacteristic, complemented
27C7×#518C2211yescharacteristic
28C2×C7×#117C2212yescomplemented
29C22×C7×C22⋊C4C2211yescharacteristic, complemented
30C7×B(4,𝔽2)—24no—
31C7×#410—24no—
32C2×C7×#99C2212yes—
33C2×C7×#99C2211yescharacteristic
34C2×C7×#99C2212yes—
35C2×C7×#99C2211yescharacteristic
36C2×C7×#99C2212yescomplemented
37C7×#396—22no—
38C7×#394—22no—
39C7×#393—21no—
40C7×#392—21no—
41C7×#390—22no—
42C7×#388—22no—
43C7×#386—21no—
44C7×#386—21no—
45C7×#386C2211yescharacteristic
46C7×#386C2212yes—
47C7×#386C2211yescharacteristic, complemented
48C7×#385C2212yescomplemented
49C7×#381C2211yescharacteristic, complemented
50C7×#379C2212yescomplemented
51C7×#342C2212yescomplemented
52C7×#342C2212yescomplemented
53#24406C711yesmaximal, characteristic, direct product factor, Sylow
54C25×C7C2311yescharacteristic
55C7×H(5,𝔽2)—22no—
56C7×H(5,𝔽2)—22no—
57C7×H(5,𝔽2)—42no—
58C2×C7×#41—22no—
59C2×C7×#41—22no—
60C2×C7×#41—22no—
61C2×C7×#41—22no—
62C2×C7×#41—21no—
63C2×C7×#41—22no—
64C2×C7×#41—42no—
65C22×C7×Q8D411yescharacteristic, complemented
66C22×C7×D4—21no—
67C22×C7×D4—22no—
68C22×C7×D4—21no—
69C22×C7×D4—22no—
70C22×C7×D4—21no—
71C22×C7×D4D411yescharacteristic, complemented
72C22×C7×D4C2311yescharacteristic
73C22×C7×D4C2312yes—
74C22×C7×D4C2311yescharacteristic
75C23×C4×C7D411yescharacteristic, complemented
76C23×C4×C7D411yescharacteristic, complemented
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C7×C4⋊Q8—22no—
80C7×#124—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—22no—
90C7×C22⋊Q8—21no—
91C7×C22⋊Q8—21no—
92C7×C22⋊Q8—22no—
93C7×C22⋊Q8—22no—
94C7×#121—21no—
95C7×#121—21no—
96C7×#121—22no—
97C7×#121—22no—
98C7×#121—22no—
99C7×#121—22no—
100C7×#120—22no—
101C7×#120—22no—
102C7×#120—22no—
103C7×#120—22no—
104C7×#120—22no—
105C7×#120—24no—
106C7×#120—42no—
107C7×#120—42no—
108C4×C7×D4—22no—
109C4×C7×D4—22no—
110C4×C7×D4—22no—
111C4×C7×D4—22no—
112C7×#117—21no—
113C7×#117—24no—
114C7×#117—42no—
115C2×C7×C4⋊C4—21no—
116C2×C7×C4⋊C4—21no—
117C2×C7×C4⋊C4—22no—
118C2×C7×C4⋊C4—22no—
119C2×C7×C4⋊C4D412yescomplemented
120C2×C7×C4⋊C4D412yescomplemented
121C2×C7×C22⋊C4—21no—
122C2×C7×C22⋊C4—21no—
123C2×C7×C22⋊C4—21no—
124C2×C7×C22⋊C4—21no—
125C2×C7×C22⋊C4—22no—
126C2×C7×C22⋊C4—21no—
127C2×C7×C22⋊C4—22no—
128C2×C7×C22⋊C4—22no—
129C2×C7×C22⋊C4—21no—
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⋊C4D412yescomplemented
137C2×C7×C22⋊C4D412yescomplemented
138C2×C7×C22⋊C4C2311yescharacteristic
139C2×C7×C22⋊C4C2311yescharacteristic
140C2×C7×C22⋊C4C2312yes—
141C2×C7×C22⋊C4C2312yes—
142C2×C7×C22⋊C4C2312yes—
143C2×C42×C7—22no—
144C7×#99—22no—
145C7×#99—24no—
146C7×#99—24no—
147C7×#99—42no—
148C7×#99D414yescomplemented
149C7×#95—21no—
150C7×#95—21no—
151C7×#95—22no—
152C7×#95—21no—
153C7×#95—21no—
154C7×#95—22no—
155#3485C2×C711yescharacteristic, complemented
156C2×B(4,𝔽2)C2×C711yescharacteristic, complemented
157C2×#410C2×C711yescharacteristic, complemented
158#2411C2×C712yescomplemented
159#2404C2×C711yescharacteristic, complemented
160#2044C2×C712yescomplemented
161#2021C2×C712yescomplemented
162#1899C2×C712yescomplemented
163#1889C2×C711yescharacteristic, complemented
164#1867C2×C711yescharacteristic, complemented
165#1790C2×C711yescharacteristic, complemented
166C24×C7—21no—
167C24×C7—22no—
168C24×C7—21no—
169C24×C7—21no—
170C24×C7—21no—
171C24×C7—22no—
172C24×C7—42no—
173C24×C7—81no—
174C24×C7C2×D412yes—
175C24×C7C2×D411yescharacteristic
176C24×C7C2×D411yescharacteristic
177C24×C7C2411yescharacteristic
178C7×#41—44no—
179C7×#41—44no—
180C7×#41—44no—
181C7×#41—44no—
182C7×#41—44no—
183C7×#41—44no—
184C7×#41—42no—
185C7×#41—42no—
186C2×C7×Q8—21no—
187C2×C7×Q8—22no—
188C2×C7×Q8—22no—
189C2×C7×Q8—41no—
190C2×C7×D4—22no—
191C2×C7×D4—22no—
192C2×C7×D4—22no—
193C2×C7×D4—21no—
194C2×C7×D4—22no—
195C2×C7×D4—21no—
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—22no—
206C2×C7×D4—22no—
207C2×C7×D4—22no—
208C2×C7×D4—41no—
209C2×C7×D4—44no—
210C2×C7×D4—44no—
211C2×C7×D4—44no—
212C2×C7×D4—42no—
213C2×C7×D4—42no—
214C2×C7×D4—42no—
215C2×C7×D4—44no—
216C2×C7×D4—42no—
217C2×C7×D4—42no—
218C2×C7×D4—42no—
219C2×C7×D4—82no—
220C2×C7×D4—81no—
221C2×C7×D4—81no—
222C2×C7×D4C2×D412yes—
223C2×C7×D4#4112yes—
224C22×C4×C7—21no—
225C22×C4×C7—21no—
226C22×C4×C7—22no—
227C22×C4×C7—21no—
228C22×C4×C7—22no—
229C22×C4×C7—22no—
230C22×C4×C7—22no—
231C22×C4×C7—21no—
232C22×C4×C7—21no—
233C22×C4×C7—21no—
234C22×C4×C7—21no—
235C22×C4×C7—21no—
236C22×C4×C7—21no—
237C22×C4×C7—22no—
238C22×C4×C7—21no—
239C22×C4×C7—21no—
240C22×C4×C7—21no—
241C22×C4×C7—22no—
242C22×C4×C7—22no—
243C22×C4×C7—41no—
244C22×C4×C7—41no—
245C22×C4×C7—81no—
246C22×C4×C7C2×D412yes—
247C22×C4×C7C2×D411yescharacteristic
248C22×C4×C7C2×D411yescharacteristic
249C22×C4×C7C2×D411yescharacteristic
250C22×C4×C7C2×D412yes—
251C22×C4×C7C2×D412yes—
252C22×C4×C7C2×D411yescharacteristic
253C22×C4×C7C2×D412yes—
254C22×C4×C7C2×D412yes—
255C7×C4⋊C4—22no—
256C7×C4⋊C4—22no—
257C7×C4⋊C4—21no—
258C7×C4⋊C4—21no—
259C7×C4⋊C4—22no—
260C7×C4⋊C4—22no—
261C7×C4⋊C4—22no—
262C7×C4⋊C4—22no—
263C7×C4⋊C4—44no—
264C7×C4⋊C4—82no—
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—22no—
274C7×C22⋊C4—22no—
275C7×C22⋊C4—22no—
276C7×C22⋊C4—22no—
277C7×C22⋊C4—22no—
278C7×C22⋊C4—21no—
279C7×C22⋊C4—21no—
280C7×C22⋊C4—22no—
281C7×C22⋊C4—22no—
282C7×C22⋊C4—44no—
283C7×C22⋊C4—42no—
284C7×C22⋊C4—44no—
285C7×C22⋊C4—41no—
286C7×C22⋊C4—41no—
287C7×C22⋊C4—42no—
288C7×C22⋊C4—42no—
289C7×C22⋊C4—82no—
290C7×C22⋊C4—82no—
291C7×C22⋊C4—81no—
292C7×C22⋊C4—81no—
293C7×C22⋊C4C2×D414yes—
294C42×C7—22no—
295C42×C7—44no—
296C2×H(5,𝔽2)C22×C711yescharacteristic
297C22×#41C22×C711yescharacteristic
298#547—22no—
299#547—22no—
300#546—22no—
301#546—22no—
302#536—21no—
303#534—21no—
304#534C22×C712yes—
305#525—21no—
306C2×#123—21no—
307C2×#123C22×C712yes—
308C2×#120C22×C711yescharacteristic
309C2×#120C22×C712yes—
310C2×#120C22×C711yescharacteristic, complemented
311#518C22×C711yescharacteristic
312C2×#117C22×C712yescomplemented
313C22×C22⋊C4C22×C711yescharacteristic, complemented
314B(4,𝔽2)—24no—
315#410—24no—
316C2×#99C22×C711yescharacteristic
317C2×#99C22×C712yes—
318C2×#99C22×C712yes—
319C2×#99C22×C711yescharacteristic
320C2×#99C22×C712yescomplemented
321#396—22no—
322#394—22no—
323#393—21no—
324#392—21no—
325#390—22no—
326#388—22no—
327#386—21no—
328#386—21no—
329#386C22×C711yescharacteristic
330#386C22×C712yes—
331#386C22×C711yescharacteristic, complemented
332#385C22×C712yescomplemented
333#381C22×C711yescharacteristic, complemented
334#379C22×C712yescomplemented
335#342C22×C712yescomplemented
336#342C22×C712yescomplemented
337C23×C7—21no—
338C23×C7—21no—
339C23×C7—24no—
340C23×C7—22no—
341C23×C7—22no—
342C23×C7—21no—
343C23×C7—21no—
344C23×C7—21no—
345C23×C7—22no—
346C23×C7—22no—
347C23×C7—41no—
348C23×C7—41no—
349C23×C7—41no—
350C23×C7—41no—
351C23×C7—41no—
352C23×C7—41no—
353C23×C7—42no—
354C23×C7—42no—
355C23×C7—41no—
356C23×C7—41no—
357C23×C7—42no—
358C23×C7—41no—
359C23×C7—42no—
360C23×C7—42no—
361C23×C7—42no—
362C23×C7—41no—
363C23×C7—41no—
364C23×C7—41no—
365C23×C7—42no—
366C23×C7—42no—
367C23×C7—82no—
368C23×C7—82no—
369C23×C7—84no—
370C23×C7—81no—
371C23×C7—81no—
372C23×C7#12112yes—
373C23×C7C22×D411yescharacteristic
374C23×C7C22×D412yes—
375C23×C7C22×D411yescharacteristic
376C23×C7C2×#4111yescharacteristic
377C23×C7H(5,𝔽2)12yes—
378C7×Q8—44no—
379C7×Q8—42no—
380C7×D4—24no—
381C7×D4—24no—
382C7×D4—44no—
383C7×D4—42no—
384C7×D4—44no—
385C7×D4—42no—
386C7×D4—42no—
387C7×D4—42no—
388C7×D4—42no—
389C7×D4—42no—
390C7×D4—42no—
391C7×D4—82no—
392C7×D4—82no—
393C7×D4—88no—
394C7×D4—84no—
395C7×D4—84no—
396C2×C4×C7—21no—
397C2×C4×C7—21no—
398C2×C4×C7—21no—
399C2×C4×C7—21no—
400C2×C4×C7—21no—
401C2×C4×C7—21no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—21no—
409C2×C4×C7—22no—
410C2×C4×C7—21no—
411C2×C4×C7—21no—
412C2×C4×C7—24no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—42no—
416C2×C4×C7—42no—
417C2×C4×C7—42no—
418C2×C4×C7—42no—
419C2×C4×C7—44no—
420C2×C4×C7—42no—
421C2×C4×C7—42no—
422C2×C4×C7—42no—
423C2×C4×C7—42no—
424C2×C4×C7—42no—
425C2×C4×C7—42no—
426C2×C4×C7—42no—
427C2×C4×C7—42no—
428C2×C4×C7—41no—
429C2×C4×C7—41no—
430C2×C4×C7—41no—
431C2×C4×C7—41no—
432C2×C4×C7—42no—
433C2×C4×C7—41no—
434C2×C4×C7—41no—
435C2×C4×C7—41no—
436C2×C4×C7—41no—
437C2×C4×C7—41no—
438C2×C4×C7—42no—
439C2×C4×C7—81no—
440C2×C4×C7—81no—
441C2×C4×C7#12011yescharacteristic
442C2×C4×C7#12011yescharacteristic
443C2×C4×C7#12012yes—
444C2×C4×C7#12112yes—
445C25C23×C711yescharacteristic
446H(5,𝔽2)—22no—
447H(5,𝔽2)—22no—
448H(5,𝔽2)—42no—
449C2×#41—22no—
450C2×#41—22no—
451C2×#41—21no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—22no—
455C2×#41—42no—
456C22×Q8C7×D411yescharacteristic, complemented
457C22×D4—21no—
458C22×D4—22no—
459C22×D4—21no—
460C22×D4—22no—
461C22×D4—21no—
462C22×D4C7×D411yescharacteristic, complemented
463C22×D4C23×C712yes—
464C22×D4C23×C711yescharacteristic
465C22×D4C23×C711yescharacteristic
466C23×C4C7×D411yescharacteristic, complemented
467C23×C4C7×D411yescharacteristic, complemented
468C23×C4C23×C711yescharacteristic
469C23×C4C23×C711yescharacteristic
470C4⋊Q8—22no—
471#124—22no—
472#123—22no—
473#123—22no—
474#123—22no—
475#123—22no—
476#123—22no—
477#123—22no—
478#123—22no—
479#123—22no—
480#123—22no—
481C22⋊Q8—21no—
482C22⋊Q8—21no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485#121—21no—
486#121—21no—
487#121—22no—
488#121—22no—
489#121—22no—
490#121—22no—
491#120—22no—
492#120—22no—
493#120—22no—
494#120—22no—
495#120—22no—
496#120—24no—
497#120—42no—
498#120—42no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502C4×D4—22no—
503#117—21no—
504#117—24no—
505#117—42no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4C7×D412yescomplemented
511C2×C4⋊C4C7×D412yescomplemented
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4C7×D412yescomplemented
528C2×C22⋊C4C7×D412yescomplemented
529C2×C22⋊C4C23×C712yes—
530C2×C22⋊C4C23×C711yescharacteristic
531C2×C22⋊C4C23×C711yescharacteristic
532C2×C22⋊C4C23×C712yes—
533C2×C22⋊C4C23×C712yes—
534C2×C42—22no—
535#99—22no—
536#99—24no—
537#99—24no—
538#99—42no—
539#99C7×D414yescomplemented
540#95—21no—
541#95—21no—
542#95—22no—
543#95—21no—
544#95—21no—
545#95—22no—
546C22×C7—22no—
547C22×C7—21no—
548C22×C7—22no—
549C22×C7—21no—
550C22×C7—22no—
551C22×C7—41no—
552C22×C7—41no—
553C22×C7—42no—
554C22×C7—42no—
555C22×C7—42no—
556C22×C7—44no—
557C22×C7—42no—
558C22×C7—42no—
559C22×C7—44no—
560C22×C7—41no—
561C22×C7—41no—
562C22×C7—41no—
563C22×C7—42no—
564C22×C7—41no—
565C22×C7—42no—
566C22×C7—42no—
567C22×C7—41no—
568C22×C7—42no—
569C22×C7—81no—
570C22×C7—82no—
571C22×C7—81no—
572C22×C7—82no—
573C22×C7—82no—
574C22×C7—81no—
575C22×C7—81no—
576C22×C7—82no—
577C22×C7—81no—
578C22×C7—81no—
579C22×C7—162no—
580C22×C7C2×#12011yescharacteristic
581C22×C7C2×#12111yescharacteristic
582C22×C7#53411yescharacteristic
583C22×C7D4212yes—
584C22×C7#54612yes—
585C4×C7—21no—
586C4×C7—21no—
587C4×C7—22no—
588C4×C7—22no—
589C4×C7—44no—
590C4×C7—42no—
591C4×C7—41no—
592C4×C7—42no—
593C4×C7—42no—
594C4×C7—82no—
595C4×C7—81no—
596C4×C7—81no—
597C4×C7—81no—
598C24—21no—
599C24—22no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—22no—
604C24—42no—
605C24—81no—
606C24C2×C7×D412yes—
607C24C2×C7×D411yescharacteristic
608C24C2×C7×D411yescharacteristic
609C24C24×C711yescharacteristic
610#41—44no—
611#41—44no—
612#41—44no—
613#41—44no—
614#41—44no—
615#41—44no—
616#41—42no—
617#41—42no—
618C2×Q8—21no—
619C2×Q8—22no—
620C2×Q8—22no—
621C2×Q8—41no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—21no—
626C2×D4—22no—
627C2×D4—21no—
628C2×D4—22no—
629C2×D4—22no—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—21no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—22no—
637C2×D4—22no—
638C2×D4—22no—
639C2×D4—22no—
640C2×D4—41no—
641C2×D4—44no—
642C2×D4—44no—
643C2×D4—44no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—44no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—82no—
652C2×D4—81no—
653C2×D4—81no—
654C2×D4C2×C7×D412yes—
655C2×D4C7×#4112yes—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—22no—
659C22×C4—21no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—22no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—41no—
676C22×C4—41no—
677C22×C4—81no—
678C22×C4C2×C7×D412yes—
679C22×C4C2×C7×D411yescharacteristic
680C22×C4C2×C7×D411yescharacteristic
681C22×C4C2×C7×D411yescharacteristic
682C22×C4C2×C7×D412yes—
683C22×C4C2×C7×D412yes—
684C22×C4C2×C7×D411yescharacteristic
685C22×C4C2×C7×D412yes—
686C22×C4C2×C7×D412yes—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4—22no—
695C4⋊C4—44no—
696C4⋊C4—82no—
697C22⋊C4—22no—
698C22⋊C4—22no—
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—22no—
713C22⋊C4—22no—
714C22⋊C4—44no—
715C22⋊C4—42no—
716C22⋊C4—44no—
717C22⋊C4—41no—
718C22⋊C4—41no—
719C22⋊C4—42no—
720C22⋊C4—42no—
721C22⋊C4—82no—
722C22⋊C4—82no—
723C22⋊C4—81no—
724C22⋊C4—81no—
725C22⋊C4C2×C7×D414yes—
726C42—22no—
727C42—44no—
728C2×C7—22no—
729C2×C7—21no—
730C2×C7—21no—
731C2×C7—22no—
732C2×C7—42no—
733C2×C7—82no—
734C2×C7—81no—
735C2×C7—82no—
736C2×C7#241011yescharacteristic
737C2×C7#302511yescharacteristic
738C2×C7#302711yescharacteristic
739C23—21no—
740C23—21no—
741C23—24no—
742C23—22no—
743C23—22no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—22no—
748C23—22no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—42no—
756C23—42no—
757C23—41no—
758C23—41no—
759C23—42no—
760C23—41no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—42no—
768C23—42no—
769C23—82no—
770C23—82no—
771C23—84no—
772C23—81no—
773C23—81no—
774C23C7×#12112yes—
775C23C22×C7×D411yescharacteristic
776C23C22×C7×D412yes—
777C23C22×C7×D411yescharacteristic
778C23C2×C7×#4111yescharacteristic
779C23C7×H(5,𝔽2)12yes—
780Q8—44no—
781Q8—42no—
782D4—24no—
783D4—24no—
784D4—44no—
785D4—42no—
786D4—44no—
787D4—42no—
788D4—42no—
789D4—42no—
790D4—42no—
791D4—42no—
792D4—42no—
793D4—82no—
794D4—82no—
795D4—88no—
796D4—84no—
797D4—84no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—21no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—24no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—44no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—42no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—42no—
841C2×C4—81no—
842C2×C4—81no—
843C2×C4C7×#12011yescharacteristic
844C2×C4C7×#12011yescharacteristic
845C2×C4C7×#12012yes—
846C2×C4C7×#12112yes—
847C7#2440611yescharacteristic, direct product factor, Sylow
848C22—22no—
849C22—21no—
850C22—22no—
851C22—21no—
852C22—22no—
853C22—41no—
854C22—41no—
855C22—42no—
856C22—42no—
857C22—44no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—44no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—42no—
866C22—41no—
867C22—42no—
868C22—42no—
869C22—41no—
870C22—42no—
871C22—81no—
872C22—82no—
873C22—81no—
874C22—82no—
875C22—82no—
876C22—81no—
877C22—81no—
878C22—82no—
879C22—81no—
880C22—81no—
881C22—162no—
882C22C2×C7×#12011yescharacteristic
883C22C2×C7×#12111yescharacteristic
884C22C7×#53411yescharacteristic
885C22C7×D4212yes—
886C22C7×#54612yes—
887C4—21no—
888C4—21no—
889C4—22no—
890C4—22no—
891C4—44no—
892C4—42no—
893C4—41no—
894C4—42no—
895C4—42no—
896C4—81no—
897C4—81no—
898C4—82no—
899C4—81no—
900C2—22no—
901C2—21no—
902C2—21no—
903C2—22no—
904C2—42no—
905C2—82no—
906C2—81no—
907C2—82no—
908C2C7×#241011yescharacteristic
909C2C7×#302511yescharacteristic
910C2C7×#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×#3485C2semidirect
2. C2×C7×B(4,𝔽2)C2semidirect
3. C2×C7×#410C2semidirect
4. C7×#2411C2semidirect
5. C7×#2404C2semidirect
6. C7×#2044C2semidirect
7. C7×#2021C2semidirect
8. C7×#1899C2semidirect
9. C7×#1889C2semidirect
10. C7×#1867C2semidirect
11. C7×#1790C2semidirect
26. C2×C7×#120C22semidirect
28. C2×C7×#117C22semidirect
29. C22×C7×C22⋊C4C22semidirect
36. C2×C7×#99C22semidirect
47. C7×#386C22semidirect
48. C7×#385C22semidirect
49. C7×#381C22semidirect
50. C7×#379C22semidirect
51. C7×#342C22semidirect
52. C7×#342C22semidirect
53. #24406C7direct (N × H)
65. C22×C7×Q8D4semidirect
71. C22×C7×D4D4semidirect
75. C23×C4×C7D4semidirect
76. C23×C4×C7D4semidirect
119. C2×C7×C4⋊C4D4semidirect
120. C2×C7×C4⋊C4D4semidirect
136. C2×C7×C22⋊C4D4semidirect
137. C2×C7×C22⋊C4D4semidirect
148. C7×#99D4semidirect
155. #3485C2×C7semidirect
156. C2×B(4,𝔽2)C2×C7semidirect
157. C2×#410C2×C7semidirect
158. #2411C2×C7semidirect
159. #2404C2×C7semidirect
160. #2044C2×C7semidirect
161. #2021C2×C7semidirect
162. #1899C2×C7semidirect
163. #1889C2×C7semidirect
164. #1867C2×C7semidirect
165. #1790C2×C7semidirect
310. C2×#120C22×C7semidirect
312. C2×#117C22×C7semidirect
313. C22×C22⋊C4C22×C7semidirect
320. C2×#99C22×C7semidirect
331. #386C22×C7semidirect
332. #385C22×C7semidirect
333. #381C22×C7semidirect
334. #379C22×C7semidirect
335. #342C22×C7semidirect
336. #342C22×C7semidirect
456. C22×Q8C7×D4semidirect
462. C22×D4C7×D4semidirect
466. C23×C4C7×D4semidirect
467. C23×C4C7×D4semidirect
510. C2×C4⋊C4C7×D4semidirect
511. C2×C4⋊C4C7×D4semidirect
527. C2×C22⋊C4C7×D4semidirect
528. C2×C22⋊C4C7×D4semidirect
539. #99C7×D4semidirect
847. C7#24406direct (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×B(4,𝔽2)2
C2×C7×#4102
C7×#24112
C7×#24042
C7×#20442
C7×#20212
C7×#18992
C7×#18892
C7×#18672
C7×#17902
#244067