Finite Group Databasebeta

← C73×#19923 #32929327

Subgroups — C73×#19923 #32929327

Order 18688.

608 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3369C211yesmaximal, characteristic, complemented
2C73×#3362C211yesmaximal, characteristic, complemented
3C73×#3332C211yesmaximal, characteristic
4C73×#3302C211yesmaximal, characteristic, complemented
5C73×#1711C211yesmaximal, characteristic, complemented
6C73×#1703C211yesmaximal, characteristic, complemented
7C73×#1702C211yesmaximal, characteristic, complemented
8C73×#1680C211yesmaximal, characteristic, complemented
9C73×#1677C211yesmaximal, characteristic, complemented
10C73×#1645C211yesmaximal, characteristic, complemented
11C73×#1641C211yesmaximal, characteristic, complemented
12C73×#1635C211yesmaximal, characteristic, complemented
13C73×#1628C211yesmaximal, characteristic, complemented
14C73×#1590C211yesmaximal, characteristic, complemented
15C8×SD16×C73C211yesmaximal, characteristic, complemented
16Q82×C73C2211yescharacteristic
17#556×C73C2211yescharacteristic
18#550×C73C2211yescharacteristic
19#547×C73C2211yescharacteristic
20#489×C73—21no—
21#487×C73C2211yescharacteristic
22#487×C73C2211yescharacteristic
23#487×C73C2211yescharacteristic
24#486×C73—21no—
25#486×C73C2211yescharacteristic
26#486×C73C2211yescharacteristic
27#486×C73C2211yescharacteristic
28#485×C73—21no—
29#481×C73—21no—
30#476×C73—21no—
31#476×C73C2211yescharacteristic
32#476×C73C2211yescharacteristic
33#475×C73—21no—
34#475×C73C2211yescharacteristic
35#474×C73C2211yescharacteristic
36#469×C73—21no—
37#467×C73—21no—
38#464×C73—21no—
39#462×C73C2211yescharacteristic
40#462×C73C2211yescharacteristic
41#460×C73—21no—
42#460×C73C2211yescharacteristic
43#459×C73C2211yescharacteristic
44#452×C73—21no—
45#449×C73—21no—
46#446×C73C2211yescharacteristic
47C8×Q8×C73C2211yescharacteristic
48#441×C73—21no—
49C4×SD16×C73—21no—
50C4×SD16×C73C2211yescharacteristic
51C4×SD16×C73C2211yescharacteristic
52#436×C73C2211yescharacteristic
53C8×D4×C73C2211yescharacteristic
54#417×C73—21no—
55#416×C73—21no—
56#334×C73C2211yescharacteristic
57#334×C73C2211yescharacteristic
58#333×C73C2211yescharacteristic
59#332×C73C2211yescharacteristic
60#332×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—
69C2×Q16×C73—21no—
70C2×Q16×C73—21no—
71C2×SD16×C73—21no—
72C2×SD16×C73D411yescharacteristic
73C2×SD16×C73D411yescharacteristic
74C2×D8×C73—21no—
75C2×M16×C73—21no—
76C22×C8×C73—21no—
77C4⋊Q8×C73—21no—
78C4⋊Q8×C73—21no—
79C4⋊Q8×C73—41no—
80C4⋊Q8×C73C2311yescharacteristic
81C4⋊Q8×C73C2311yescharacteristic
82C4⋊Q8×C73C2311yescharacteristic
83#127×C73—21no—
84#127×C73C2311yescharacteristic
85#126×C73—41no—
86#124×C73—21no—
87#123×C73—41no—
88C22⋊Q8×C73—21no—
89C22⋊Q8×C73—21no—
90#121×C73—21no—
91#121×C73—21no—
92#121×C73—41no—
93C4×Q8×C73—21no—
94C4×Q8×C73—21no—
95C4×Q8×C73—21no—
96C4×Q8×C73C2311yescharacteristic
97C4×Q8×C73C2311yescharacteristic
98C4×D4×C73—21no—
99C4×D4×C73C2311yescharacteristic
100C4×D4×C73C2311yescharacteristic
101#117×C73—21no—
102C2×C4⋊C4×C73—21no—
103#107×C73—21no—
104#106×C73—21no—
105#106×C73—21no—
106#106×C73—21no—
107#106×C73D411yescharacteristic
108#106×C73D411yescharacteristic
109C4⋊C8×C73—21no—
110C4⋊C8×C73—21no—
111C4⋊C8×C73C2311yescharacteristic
112C4⋊C8×C73C2311yescharacteristic
113C4⋊C8×C73C2311yescharacteristic
114C4⋊C8×C73C2311yescharacteristic
115#103×C73—21no—
116#103×C73—21no—
117#103×C73—21no—
118#103×C73—21no—
119#103×C73—21no—
120#103×C73—21no—
121#103×C73—21no—
122#103×C73—41no—
123#103×C73D411yescharacteristic
124#103×C73D411yescharacteristic
125#102×C73—21no—
126#102×C73—21no—
127#102×C73—21no—
128#102×C73—21no—
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×C73D411yescharacteristic
136#102×C73D411yescharacteristic
137C22⋊C8×C73—21no—
138C22⋊C8×C73—21no—
139#97×C73—21no—
140C4×C8×C73—21no—
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#41×C73—42no—
145#41×C73—42no—
146#41×C73—81no—
147#41×C73—81no—
148C2×Q8×C73—21no—
149C2×Q8×C73—21no—
150C2×Q8×C73—21no—
151C2×Q8×C73—41no—
152C2×Q8×C73C2×D411yescharacteristic
153C2×Q8×C73C2×D411yescharacteristic
154C2×D4×C73—21no—
155C2×D4×C73—21no—
156C2×D4×C73—21no—
157C2×D4×C73—41no—
158C2×D4×C73—41no—
159C2×D4×C73—41no—
160C2×D4×C73C2×D411yescharacteristic
161C2×D4×C73C2×D411yescharacteristic
162C22×C4×C73—21no—
163C22×C4×C73—21no—
164C22×C4×C73—41no—
165C22×C4×C73—41no—
166Q16×C73—42no—
167Q16×C73—81no—
168SD16×C73—22no—
169SD16×C73—41no—
170SD16×C73—42no—
171D8×C73—81no—
172M16×C73—81no—
173C2×C8×C73—21no—
174C2×C8×C73—21no—
175C2×C8×C73—21no—
176C2×C8×C73—21no—
177C2×C8×C73—21no—
178C2×C8×C73—81no—
179C2×C8×C73C2×D411yescharacteristic
180C2×C8×C73C2×D411yescharacteristic
181C2×C8×C73C2×D411yescharacteristic
182C2×C8×C73C2×D411yescharacteristic
183C4⋊C4×C73—21no—
184C4⋊C4×C73—21no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—21no—
188C4⋊C4×C73—21no—
189C4⋊C4×C73—21no—
190C4⋊C4×C73—21no—
191C4⋊C4×C73—41no—
192C4⋊C4×C73—41no—
193C4⋊C4×C73—41no—
194C4⋊C4×C73—41no—
195C4⋊C4×C73C2×D411yescharacteristic
196C4⋊C4×C73C2×D411yescharacteristic
197C4⋊C4×C73C2×D411yescharacteristic
198C4⋊C4×C73C2×D411yescharacteristic
199C22⋊C4×C73—21no—
200C22⋊C4×C73—21no—
201C22⋊C4×C73—41no—
202C22⋊C4×C73—41no—
203C22⋊C4×C73—41no—
204C22⋊C4×C73—41no—
205C42×C73—21no—
206C42×C73—21no—
207C42×C73—41no—
208C42×C73—41no—
209C42×C73C2411yescharacteristic
210C23×C73—21no—
211C23×C73—21no—
212C23×C73—41no—
213Q8×C73—21no—
214Q8×C73—21no—
215Q8×C73—21no—
216Q8×C73—41no—
217Q8×C73—41no—
218Q8×C73—41no—
219Q8×C73—41no—
220Q8×C73—81no—
221Q8×C73—161no—
222Q8×C73#13512yes—
223D4×C73—21no—
224D4×C73—21no—
225D4×C73—21no—
226D4×C73—21no—
227D4×C73—41no—
228D4×C73—41no—
229D4×C73—41no—
230D4×C73—41no—
231D4×C73—82no—
232D4×C73—81no—
233D4×C73—82no—
234D4×C73—161no—
235C2×C4×C73—21no—
236C2×C4×C73—21no—
237C2×C4×C73—21no—
238C2×C4×C73—21no—
239C2×C4×C73—21no—
240C2×C4×C73—21no—
241C2×C4×C73—41no—
242C2×C4×C73—41no—
243C2×C4×C73—41no—
244C2×C4×C73—41no—
245C2×C4×C73—41no—
246C2×C4×C73—41no—
247C2×C4×C73—41no—
248C2×C4×C73—82no—
249C2×C4×C73—82no—
250C2×C4×C73C22×D411yescharacteristic
251C2×C4×C73C22×D411yescharacteristic
252C2×C4×C73H(5,𝔽2)11yescharacteristic
253C8×C73—21no—
254C8×C73—21no—
255C8×C73—21no—
256C8×C73—21no—
257C8×C73—41no—
258C8×C73—41no—
259C8×C73—41no—
260C8×C73—41no—
261C8×C73—41no—
262C22×C73—41no—
263C22×C73—41no—
264C22×C73—41no—
265C22×C73—41no—
266C22×C73—41no—
267C22×C73—41no—
268C22×C73—81no—
269C22×C73—81no—
270C22×C73—81no—
271C22×C73D4211yescharacteristic
272C4×C73—22no—
273C4×C73—21no—
274C4×C73—41no—
275C4×C73—41no—
276C4×C73—41no—
277C4×C73—41no—
278C4×C73—41no—
279C4×C73—81no—
280C4×C73—81no—
281C4×C73—81no—
282C4×C73C2×#13511yescharacteristic
283C4×C73#57511yescharacteristic
284C4×C73#57711yescharacteristic
285C4×C73#57711yescharacteristic
286#19923C7311yesmaximal, characteristic, direct product factor, Sylow
287C2×C73—81no—
288C2×C73—81no—
289C2×C73—161no—
290C2×C73#327511yescharacteristic
291C2×C73#328211yescharacteristic
292C2×C73#329011yescharacteristic
293#3369C2×C7311yescharacteristic, complemented
294#3362C2×C7311yescharacteristic, complemented
295#3332C2×C7311yescharacteristic
296#3302C2×C7311yescharacteristic, complemented
297#1711C2×C7311yescharacteristic, complemented
298#1703C2×C7311yescharacteristic, complemented
299#1702C2×C7311yescharacteristic, complemented
300#1680C2×C7311yescharacteristic, complemented
301#1677C2×C7311yescharacteristic, complemented
302#1645C2×C7311yescharacteristic, complemented
303#1641C2×C7311yescharacteristic, complemented
304#1635C2×C7311yescharacteristic, complemented
305#1628C2×C7311yescharacteristic, complemented
306#1590C2×C7311yescharacteristic, complemented
307C8×SD16C2×C7311yescharacteristic, complemented
308C73#1992311yescharacteristic, direct product factor, Sylow
309Q82C22×C7311yescharacteristic
310#556C22×C7311yescharacteristic
311#550C22×C7311yescharacteristic
312#547C22×C7311yescharacteristic
313#489—21no—
314#487C22×C7311yescharacteristic
315#487C22×C7311yescharacteristic
316#487C22×C7311yescharacteristic
317#486—21no—
318#486C22×C7311yescharacteristic
319#486C22×C7311yescharacteristic
320#486C22×C7311yescharacteristic
321#485—21no—
322#481—21no—
323#476—21no—
324#476C22×C7311yescharacteristic
325#476C22×C7311yescharacteristic
326#475—21no—
327#475C22×C7311yescharacteristic
328#474C22×C7311yescharacteristic
329#469—21no—
330#467—21no—
331#464—21no—
332#462C22×C7311yescharacteristic
333#462C22×C7311yescharacteristic
334#460—21no—
335#460C22×C7311yescharacteristic
336#459C22×C7311yescharacteristic
337#452—21no—
338#449—21no—
339#446C22×C7311yescharacteristic
340C8×Q8C22×C7311yescharacteristic
341#441—21no—
342C4×SD16—21no—
343C4×SD16C22×C7311yescharacteristic
344C4×SD16C22×C7311yescharacteristic
345#436C22×C7311yescharacteristic
346C8×D4C22×C7311yescharacteristic
347#417—21no—
348#416—21no—
349#334C22×C7311yescharacteristic
350#334C22×C7311yescharacteristic
351#333C22×C7311yescharacteristic
352#332C22×C7311yescharacteristic
353#332C22×C7311yescharacteristic
354#331C22×C7311yescharacteristic
355Q8⋊C8C22×C7311yescharacteristic
356Q8⋊C8C22×C7311yescharacteristic
357D4⋊C8C22×C7311yescharacteristic
358D4⋊C8C22×C7311yescharacteristic
359C82C22×C7311yescharacteristic
360C2×#41—21no—
361C2×#41—21no—
362C2×Q16—21no—
363C2×Q16—21no—
364C2×SD16—21no—
365C2×SD16D4×C7311yescharacteristic
366C2×SD16D4×C7311yescharacteristic
367C2×D8—21no—
368C2×M16—21no—
369C22×C8—21no—
370C4⋊Q8—21no—
371C4⋊Q8—21no—
372C4⋊Q8—41no—
373C4⋊Q8C23×C7311yescharacteristic
374C4⋊Q8C23×C7311yescharacteristic
375C4⋊Q8C23×C7311yescharacteristic
376#127—21no—
377#127C23×C7311yescharacteristic
378#126—41no—
379#124—21no—
380#123—41no—
381C22⋊Q8—21no—
382C22⋊Q8—21no—
383#121—21no—
384#121—21no—
385#121—41no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8C23×C7311yescharacteristic
390C4×Q8C23×C7311yescharacteristic
391C4×D4—21no—
392C4×D4C23×C7311yescharacteristic
393C4×D4C23×C7311yescharacteristic
394#117—21no—
395C2×C4⋊C4—21no—
396#107—21no—
397#106—21no—
398#106—21no—
399#106—21no—
400#106D4×C7311yescharacteristic
401#106D4×C7311yescharacteristic
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8C23×C7311yescharacteristic
405C4⋊C8C23×C7311yescharacteristic
406C4⋊C8C23×C7311yescharacteristic
407C4⋊C8C23×C7311yescharacteristic
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—41no—
416#103D4×C7311yescharacteristic
417#103D4×C7311yescharacteristic
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—41no—
428#102D4×C7311yescharacteristic
429#102D4×C7311yescharacteristic
430C22⋊C8—21no—
431C22⋊C8—21no—
432#97—21no—
433C4×C8—21no—
434C4×C8C23×C7311yescharacteristic
435C4×C8C23×C7311yescharacteristic
436C4×C8C23×C7311yescharacteristic
437#41—42no—
438#41—42no—
439#41—81no—
440#41—81no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—41no—
445C2×Q8C2×D4×C7311yescharacteristic
446C2×Q8C2×D4×C7311yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4C2×D4×C7311yescharacteristic
454C2×D4C2×D4×C7311yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—41no—
458C22×C4—41no—
459Q16—42no—
460Q16—81no—
461SD16—22no—
462SD16—41no—
463SD16—42no—
464D8—81no—
465M16—81no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—81no—
472C2×C8C2×D4×C7311yescharacteristic
473C2×C8C2×D4×C7311yescharacteristic
474C2×C8C2×D4×C7311yescharacteristic
475C2×C8C2×D4×C7311yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4C2×D4×C7311yescharacteristic
489C4⋊C4C2×D4×C7311yescharacteristic
490C4⋊C4C2×D4×C7311yescharacteristic
491C4⋊C4C2×D4×C7311yescharacteristic
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C42—21no—
499C42—21no—
500C42—41no—
501C42—41no—
502C42C24×C7311yescharacteristic
503C23—21no—
504C23—21no—
505C23—41no—
506Q8—21no—
507Q8—21no—
508Q8—21no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—81no—
514Q8—161no—
515Q8#135×C7312yes—
516D4—21no—
517D4—21no—
518D4—21no—
519D4—21no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—82no—
525D4—81no—
526D4—82no—
527D4—161no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4C22×D4×C7311yescharacteristic
544C2×C4C22×D4×C7311yescharacteristic
545C2×C4H(5,𝔽2)×C7311yescharacteristic
546C8—21no—
547C8—21no—
548C8—21no—
549C8—21no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22D42×C7311yescharacteristic
565C4—22no—
566C4—21no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4C2×#135×C7311yescharacteristic
576C4#575×C7311yescharacteristic
577C4#577×C7311yescharacteristic
578C4#577×C7311yescharacteristic
579C2—81no—
580C2—81no—
581C2—161no—
582C2C73×#327511yescharacteristic
583C2C73×#328211yescharacteristic
584C2C73×#329011yescharacteristic
subgroupG/H
center, socleC22×C73D42
commutator, Frattini, cosocleC42C24×C73
prime radicalC73×#3332C2
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×#3369C2semidirect
2. C73×#3362C2semidirect
4. C73×#3302C2semidirect
5. C73×#1711C2semidirect
6. C73×#1703C2semidirect
7. C73×#1702C2semidirect
8. C73×#1680C2semidirect
9. C73×#1677C2semidirect
10. C73×#1645C2semidirect
11. C73×#1641C2semidirect
12. C73×#1635C2semidirect
13. C73×#1628C2semidirect
14. C73×#1590C2semidirect
15. C8×SD16×C73C2semidirect
286. #19923C73direct (N × H)
293. #3369C2×C73semidirect
294. #3362C2×C73semidirect
296. #3302C2×C73semidirect
297. #1711C2×C73semidirect
298. #1703C2×C73semidirect
299. #1702C2×C73semidirect
300. #1680C2×C73semidirect
301. #1677C2×C73semidirect
302. #1645C2×C73semidirect
303. #1641C2×C73semidirect
304. #1635C2×C73semidirect
305. #1628C2×C73semidirect
306. #1590C2×C73semidirect
307. C8×SD16C2×C73semidirect
308. C73#19923direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#33692
C73×#33622
C73×#33322
C73×#33022
C73×#17112
C73×#17032
C73×#17022
C73×#16802
C73×#16772
C73×#16452
C73×#16412
C73×#16352
C73×#16282
C73×#15902
C8×SD16×C732
#1992373