Finite Group Databasebeta

← C73×#19947 #32929351

Subgroups — C73×#19947 #32929351

Order 18688.

658 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3399C211yesmaximal, characteristic, complemented
2C73×#3394C211yesmaximal, characteristic, complemented
3C73×#3353C211yesmaximal, characteristic, complemented
4C73×#3284C211yesmaximal, characteristic, complemented
5C73×#1706C211yesmaximal, characteristic, complemented
6C73×#1694C211yesmaximal, characteristic, complemented
7C73×#1687C211yesmaximal, characteristic, complemented
8C73×#1666C211yesmaximal, characteristic, complemented
9C73×#1665C211yesmaximal, characteristic, complemented
10C73×#1641C211yesmaximal, characteristic, complemented
11C73×#1640C211yesmaximal, characteristic, complemented
12C73×#1628C211yesmaximal, characteristic, complemented
13C73×#1625C211yesmaximal, characteristic, complemented
14C73×#1590C211yesmaximal, characteristic, complemented
15C8×SD16×C73C211yesmaximal, characteristic, complemented
16C2×#135×C73—21no—
17#559×C73C2211yescharacteristic
18#556×C73C2211yescharacteristic
19#550×C73C2211yescharacteristic
20#547×C73C2211yescharacteristic
21#500×C73C2211yescharacteristic
22#496×C73—21no—
23#495×C73—21no—
24#493×C73C2211yescharacteristic
25#492×C73C2211yescharacteristic
26#492×C73C2211yescharacteristic
27#486×C73C2211yescharacteristic
28#486×C73C2211yescharacteristic
29#484×C73—21no—
30#482×C73—21no—
31#475×C73C2211yescharacteristic
32#474×C73C2211yescharacteristic
33#468×C73—21no—
34#465×C73—21no—
35#464×C73—21no—
36#463×C73—21no—
37#463×C73—21no—
38#462×C73C2211yescharacteristic
39#462×C73C2211yescharacteristic
40#460×C73C2211yescharacteristic
41#459×C73—21no—
42#459×C73C2211yescharacteristic
43#459×C73C2211yescharacteristic
44#459×C73C2211yescharacteristic
45#452×C73—21no—
46#449×C73—21no—
47#446×C73C2211yescharacteristic
48C8×Q8×C73C2211yescharacteristic
49#442×C73—21no—
50C4×SD16×C73—21no—
51C4×SD16×C73C2211yescharacteristic
52C4×SD16×C73C2211yescharacteristic
53#436×C73C2211yescharacteristic
54C8×D4×C73C2211yescharacteristic
55#428×C73—21no—
56#334×C73C2211yescharacteristic
57#334×C73C2211yescharacteristic
58#332×C73C2211yescharacteristic
59#332×C73C2211yescharacteristic
60#331×C73C2211yescharacteristic
61#331×C73C2211yescharacteristic
62Q8⋊C8×C73C2211yescharacteristic
63Q8⋊C8×C73C2211yescharacteristic
64D4⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66C82×C73C2211yescharacteristic
67C2×#41×C73—21no—
68C2×#41×C73—21no—
69#135×C73—44no—
70C2×Q16×C73—21no—
71C2×Q16×C73—21no—
72C2×SD16×C73—21no—
73C2×SD16×C73—21no—
74C2×SD16×C73—21no—
75C2×SD16×C73—21no—
76C2×SD16×C73—21no—
77C2×SD16×C73D411yescharacteristic
78C2×SD16×C73D411yescharacteristic
79C2×D8×C73—21no—
80C2×D8×C73—21no—
81C2×D8×C73—21no—
82C2×D8×C73—21no—
83C2×D8×C73—21no—
84C2×M16×C73—21no—
85C22×C8×C73—21no—
86C4⋊Q8×C73C2311yescharacteristic
87C4⋊Q8×C73C2311yescharacteristic
88#127×C73—21no—
89#127×C73C2311yescharacteristic
90#127×C73C2311yescharacteristic
91#126×C73—41no—
92#124×C73—21no—
93#124×C73—21no—
94#124×C73—21no—
95#123×C73—41no—
96#123×C73—41no—
97C22⋊Q8×C73—21no—
98C22⋊Q8×C73—21no—
99#121×C73—21no—
100#121×C73—21no—
101#121×C73—41no—
102C4×Q8×C73—21no—
103C4×Q8×C73C2311yescharacteristic
104C4×Q8×C73C2311yescharacteristic
105C4×D4×C73—21no—
106C4×D4×C73—21no—
107C4×D4×C73—21no—
108C4×D4×C73C2311yescharacteristic
109C4×D4×C73C2311yescharacteristic
110#117×C73—21no—
111C2×C4⋊C4×C73—21no—
112#107×C73—21no—
113#107×C73—21no—
114#107×C73—21no—
115#106×C73—21no—
116#106×C73D411yescharacteristic
117#106×C73D411yescharacteristic
118C4⋊C8×C73—21no—
119C4⋊C8×C73—21no—
120C4⋊C8×C73C2311yescharacteristic
121C4⋊C8×C73C2311yescharacteristic
122C4⋊C8×C73C2311yescharacteristic
123C4⋊C8×C73C2311yescharacteristic
124#103×C73—21no—
125#103×C73—21no—
126#103×C73—21no—
127#103×C73D411yescharacteristic
128#103×C73D411yescharacteristic
129#102×C73—21no—
130#102×C73—21no—
131#102×C73—21no—
132#102×C73—21no—
133#102×C73—21no—
134#102×C73—41no—
135#102×C73—41no—
136#102×C73D411yescharacteristic
137#102×C73D411yescharacteristic
138C22⋊C8×C73—21no—
139C22⋊C8×C73—21no—
140#97×C73—21no—
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C4×C8×C73C2311yescharacteristic
145#41×C73—42no—
146#41×C73—42no—
147#41×C73—81no—
148#41×C73—81no—
149C2×Q8×C73—21no—
150C2×Q8×C73—21no—
151C2×Q8×C73C2×D411yescharacteristic
152C2×Q8×C73C2×D411yescharacteristic
153C2×D4×C73—21no—
154C2×D4×C73—21no—
155C2×D4×C73—21no—
156C2×D4×C73—21no—
157C2×D4×C73—21no—
158C2×D4×C73—21no—
159C2×D4×C73—41no—
160C2×D4×C73—41no—
161C2×D4×C73—41no—
162C2×D4×C73C2×D411yescharacteristic
163C2×D4×C73C2×D411yescharacteristic
164C22×C4×C73—21no—
165C22×C4×C73—21no—
166C22×C4×C73—41no—
167C22×C4×C73—41no—
168C22×C4×C73—41no—
169Q16×C73—42no—
170Q16×C73—81no—
171SD16×C73—22no—
172SD16×C73—22no—
173SD16×C73—42no—
174SD16×C73—42no—
175SD16×C73—81no—
176SD16×C73—81no—
177SD16×C73—81no—
178D8×C73—42no—
179D8×C73—42no—
180D8×C73—81no—
181D8×C73—81no—
182D8×C73—81no—
183M16×C73—42no—
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73—21no—
187C2×C8×C73—21no—
188C2×C8×C73—21no—
189C2×C8×C73—42no—
190C2×C8×C73C2×D411yescharacteristic
191C2×C8×C73C2×D411yescharacteristic
192C2×C8×C73C2×D411yescharacteristic
193C2×C8×C73C2×D411yescharacteristic
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—21no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73—21no—
200C4⋊C4×C73—41no—
201C4⋊C4×C73—41no—
202C4⋊C4×C73C2×D411yescharacteristic
203C4⋊C4×C73C2×D411yescharacteristic
204C4⋊C4×C73C2×D411yescharacteristic
205C4⋊C4×C73C2×D411yescharacteristic
206C22⋊C4×C73—21no—
207C22⋊C4×C73—21no—
208C22⋊C4×C73—41no—
209C22⋊C4×C73—41no—
210C22⋊C4×C73—41no—
211C22⋊C4×C73—41no—
212C22⋊C4×C73—41no—
213C22⋊C4×C73—41no—
214C22⋊C4×C73—41no—
215C42×C73—21no—
216C42×C73—21no—
217C42×C73—41no—
218C42×C73C2411yescharacteristic
219C23×C73—21no—
220C23×C73—21no—
221C23×C73—41no—
222C23×C73—41no—
223Q8×C73—21no—
224Q8×C73—21no—
225Q8×C73—21no—
226Q8×C73—21no—
227Q8×C73—41no—
228Q8×C73—41no—
229Q8×C73—41no—
230Q8×C73—41no—
231D4×C73—21no—
232D4×C73—21no—
233D4×C73—21no—
234D4×C73—21no—
235D4×C73—41no—
236D4×C73—41no—
237D4×C73—41no—
238D4×C73—41no—
239D4×C73—41no—
240D4×C73—41no—
241D4×C73—41no—
242D4×C73—41no—
243D4×C73—81no—
244D4×C73—81no—
245D4×C73—82no—
246D4×C73—82no—
247D4×C73—161no—
248C2×C4×C73—21no—
249C2×C4×C73—21no—
250C2×C4×C73—21no—
251C2×C4×C73—21no—
252C2×C4×C73—21no—
253C2×C4×C73—21no—
254C2×C4×C73—41no—
255C2×C4×C73—41no—
256C2×C4×C73—41no—
257C2×C4×C73—41no—
258C2×C4×C73—41no—
259C2×C4×C73—41no—
260C2×C4×C73—82no—
261C2×C4×C73—82no—
262C2×C4×C73—161no—
263C2×C4×C73C22×D411yescharacteristic
264C2×C4×C73C22×D411yescharacteristic
265C2×C4×C73H(5,𝔽2)11yescharacteristic
266C8×C73—21no—
267C8×C73—21no—
268C8×C73—41no—
269C8×C73—41no—
270C8×C73—41no—
271C8×C73—41no—
272C8×C73—41no—
273C8×C73#13512yescomplemented
274C8×C73AGL(1,ℤ/8)12yes—
275C22×C73—41no—
276C22×C73—41no—
277C22×C73—41no—
278C22×C73—41no—
279C22×C73—41no—
280C22×C73—41no—
281C22×C73—81no—
282C22×C73—81no—
283C22×C73—81no—
284C22×C73—81no—
285C22×C73—81no—
286C22×C73—81no—
287C22×C73D4211yescharacteristic
288C4×C73—21no—
289C4×C73—41no—
290C4×C73—41no—
291C4×C73—41no—
292C4×C73—41no—
293C4×C73—41no—
294C4×C73—41no—
295C4×C73—81no—
296C4×C73—81no—
297C4×C73C2×#13511yescharacteristic
298C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C73#57611yescharacteristic
300C4×C73#57711yescharacteristic
301#19947C7311yesmaximal, characteristic, direct product factor, Sylow
302C2×C73—81no—
303C2×C73—81no—
304C2×C73—161no—
305C2×C73—161no—
306C2×C73#327411yescharacteristic
307C2×C73#328411yescharacteristic
308C2×C73#329011yescharacteristic
309#3399C2×C7311yescharacteristic, complemented
310#3394C2×C7311yescharacteristic, complemented
311#3353C2×C7311yescharacteristic, complemented
312#3284C2×C7311yescharacteristic, complemented
313#1706C2×C7311yescharacteristic, complemented
314#1694C2×C7311yescharacteristic, complemented
315#1687C2×C7311yescharacteristic, complemented
316#1666C2×C7311yescharacteristic, complemented
317#1665C2×C7311yescharacteristic, complemented
318#1641C2×C7311yescharacteristic, complemented
319#1640C2×C7311yescharacteristic, complemented
320#1628C2×C7311yescharacteristic, complemented
321#1625C2×C7311yescharacteristic, complemented
322#1590C2×C7311yescharacteristic, complemented
323C8×SD16C2×C7311yescharacteristic, complemented
324C73#1994711yescharacteristic, direct product factor, Sylow
325C2×#135—21no—
326#559C22×C7311yescharacteristic
327#556C22×C7311yescharacteristic
328#550C22×C7311yescharacteristic
329#547C22×C7311yescharacteristic
330#500C22×C7311yescharacteristic
331#496—21no—
332#495—21no—
333#493C22×C7311yescharacteristic
334#492C22×C7311yescharacteristic
335#492C22×C7311yescharacteristic
336#486C22×C7311yescharacteristic
337#486C22×C7311yescharacteristic
338#484—21no—
339#482—21no—
340#475C22×C7311yescharacteristic
341#474C22×C7311yescharacteristic
342#468—21no—
343#465—21no—
344#464—21no—
345#463—21no—
346#463—21no—
347#462C22×C7311yescharacteristic
348#462C22×C7311yescharacteristic
349#460C22×C7311yescharacteristic
350#459—21no—
351#459C22×C7311yescharacteristic
352#459C22×C7311yescharacteristic
353#459C22×C7311yescharacteristic
354#452—21no—
355#449—21no—
356#446C22×C7311yescharacteristic
357C8×Q8C22×C7311yescharacteristic
358#442—21no—
359C4×SD16—21no—
360C4×SD16C22×C7311yescharacteristic
361C4×SD16C22×C7311yescharacteristic
362#436C22×C7311yescharacteristic
363C8×D4C22×C7311yescharacteristic
364#428—21no—
365#334C22×C7311yescharacteristic
366#334C22×C7311yescharacteristic
367#332C22×C7311yescharacteristic
368#332C22×C7311yescharacteristic
369#331C22×C7311yescharacteristic
370#331C22×C7311yescharacteristic
371Q8⋊C8C22×C7311yescharacteristic
372Q8⋊C8C22×C7311yescharacteristic
373D4⋊C8C22×C7311yescharacteristic
374D4⋊C8C22×C7311yescharacteristic
375C82C22×C7311yescharacteristic
376C2×#41—21no—
377C2×#41—21no—
378#135—44no—
379C2×Q16—21no—
380C2×Q16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16—21no—
384C2×SD16—21no—
385C2×SD16—21no—
386C2×SD16D4×C7311yescharacteristic
387C2×SD16D4×C7311yescharacteristic
388C2×D8—21no—
389C2×D8—21no—
390C2×D8—21no—
391C2×D8—21no—
392C2×D8—21no—
393C2×M16—21no—
394C22×C8—21no—
395C4⋊Q8C23×C7311yescharacteristic
396C4⋊Q8C23×C7311yescharacteristic
397#127—21no—
398#127C23×C7311yescharacteristic
399#127C23×C7311yescharacteristic
400#126—41no—
401#124—21no—
402#124—21no—
403#124—21no—
404#123—41no—
405#123—41no—
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408#121—21no—
409#121—21no—
410#121—41no—
411C4×Q8—21no—
412C4×Q8C23×C7311yescharacteristic
413C4×Q8C23×C7311yescharacteristic
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4C23×C7311yescharacteristic
418C4×D4C23×C7311yescharacteristic
419#117—21no—
420C2×C4⋊C4—21no—
421#107—21no—
422#107—21no—
423#107—21no—
424#106—21no—
425#106D4×C7311yescharacteristic
426#106D4×C7311yescharacteristic
427C4⋊C8—21no—
428C4⋊C8—21no—
429C4⋊C8C23×C7311yescharacteristic
430C4⋊C8C23×C7311yescharacteristic
431C4⋊C8C23×C7311yescharacteristic
432C4⋊C8C23×C7311yescharacteristic
433#103—21no—
434#103—21no—
435#103—21no—
436#103D4×C7311yescharacteristic
437#103D4×C7311yescharacteristic
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—41no—
444#102—41no—
445#102D4×C7311yescharacteristic
446#102D4×C7311yescharacteristic
447C22⋊C8—21no—
448C22⋊C8—21no—
449#97—21no—
450C4×C8—21no—
451C4×C8C23×C7311yescharacteristic
452C4×C8C23×C7311yescharacteristic
453C4×C8C23×C7311yescharacteristic
454#41—42no—
455#41—42no—
456#41—81no—
457#41—81no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8C2×D4×C7311yescharacteristic
461C2×Q8C2×D4×C7311yescharacteristic
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4C2×D4×C7311yescharacteristic
472C2×D4C2×D4×C7311yescharacteristic
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478Q16—42no—
479Q16—81no—
480SD16—22no—
481SD16—22no—
482SD16—42no—
483SD16—42no—
484SD16—81no—
485SD16—81no—
486SD16—81no—
487D8—42no—
488D8—42no—
489D8—81no—
490D8—81no—
491D8—81no—
492M16—42no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—42no—
499C2×C8C2×D4×C7311yescharacteristic
500C2×C8C2×D4×C7311yescharacteristic
501C2×C8C2×D4×C7311yescharacteristic
502C2×C8C2×D4×C7311yescharacteristic
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4C2×D4×C7311yescharacteristic
512C4⋊C4C2×D4×C7311yescharacteristic
513C4⋊C4C2×D4×C7311yescharacteristic
514C4⋊C4C2×D4×C7311yescharacteristic
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C42—21no—
525C42—21no—
526C42—41no—
527C42C24×C7311yescharacteristic
528C23—21no—
529C23—21no—
530C23—41no—
531C23—41no—
532Q8—21no—
533Q8—21no—
534Q8—21no—
535Q8—21no—
536Q8—41no—
537Q8—41no—
538Q8—41no—
539Q8—41no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—81no—
553D4—81no—
554D4—82no—
555D4—82no—
556D4—161no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—82no—
570C2×C4—82no—
571C2×C4—161no—
572C2×C4C22×D4×C7311yescharacteristic
573C2×C4C22×D4×C7311yescharacteristic
574C2×C4H(5,𝔽2)×C7311yescharacteristic
575C8—21no—
576C8—21no—
577C8—41no—
578C8—41no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8#135×C7312yescomplemented
583C8AGL(1,ℤ/8)×C7312yes—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22D42×C7311yescharacteristic
597C4—21no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4C2×#135×C7311yescharacteristic
607C4C2×AGL(1,ℤ/8)×C7311yescharacteristic
608C4#576×C7311yescharacteristic
609C4#577×C7311yescharacteristic
610C2—81no—
611C2—81no—
612C2—161no—
613C2—161no—
614C2C73×#327411yescharacteristic
615C2C73×#328411yescharacteristic
616C2C73×#329011yescharacteristic
subgroupG/H
center, socleC22×C73D42
commutator, Frattini, cosocleC42C24×C73
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3399C2semidirect
2. C73×#3394C2semidirect
3. C73×#3353C2semidirect
4. C73×#3284C2semidirect
5. C73×#1706C2semidirect
6. C73×#1694C2semidirect
7. C73×#1687C2semidirect
8. C73×#1666C2semidirect
9. C73×#1665C2semidirect
10. C73×#1641C2semidirect
11. C73×#1640C2semidirect
12. C73×#1628C2semidirect
13. C73×#1625C2semidirect
14. C73×#1590C2semidirect
15. C8×SD16×C73C2semidirect
273. C8×C73#135semidirect
301. #19947C73direct (N × H)
309. #3399C2×C73semidirect
310. #3394C2×C73semidirect
311. #3353C2×C73semidirect
312. #3284C2×C73semidirect
313. #1706C2×C73semidirect
314. #1694C2×C73semidirect
315. #1687C2×C73semidirect
316. #1666C2×C73semidirect
317. #1665C2×C73semidirect
318. #1641C2×C73semidirect
319. #1640C2×C73semidirect
320. #1628C2×C73semidirect
321. #1625C2×C73semidirect
322. #1590C2×C73semidirect
323. C8×SD16C2×C73semidirect
324. C73#19947direct (N × H)
582. C8#135×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#33992
C73×#33942
C73×#33532
C73×#32842
C73×#17062
C73×#16942
C73×#16872
C73×#16662
C73×#16652
C73×#16412
C73×#16402
C73×#16282
C73×#16252
C73×#15902
C8×SD16×C732
#1994773