Finite Group Databasebeta

← C73×#19963 #32929367

Subgroups — C73×#19963 #32929367

Order 18688.

608 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3399C211yesmaximal, characteristic
2C73×#3398C211yesmaximal, characteristic, complemented
3C73×#3365C211yesmaximal, characteristic, complemented
4C73×#3304C211yesmaximal, characteristic, complemented
5C73×#1709C211yesmaximal, characteristic, complemented
6C73×#1690C211yesmaximal, characteristic, complemented
7C73×#1688C211yesmaximal, characteristic, complemented
8C73×#1682C211yesmaximal, characteristic, complemented
9C73×#1681C211yesmaximal, characteristic, complemented
10C73×#1642C211yesmaximal, characteristic, complemented
11C73×#1640C211yesmaximal, characteristic, complemented
12C73×#1628C211yesmaximal, characteristic, complemented
13C73×#1626C211yesmaximal, characteristic, complemented
14C73×#1591C211yesmaximal, characteristic, complemented
15C8×SD16×C73C211yesmaximal, characteristic, complemented
16#559×C73C2211yescharacteristic
17#557×C73C2211yescharacteristic
18#556×C73C2211yescharacteristic
19#550×C73C2211yescharacteristic
20#497×C73—21no—
21#496×C73—21no—
22#494×C73C2211yescharacteristic
23#493×C73C2211yescharacteristic
24#488×C73—21no—
25#486×C73C2211yescharacteristic
26#486×C73C2211yescharacteristic
27#486×C73C2211yescharacteristic
28#486×C73C2211yescharacteristic
29#482×C73—21no—
30#478×C73—21no—
31#475×C73C2211yescharacteristic
32#475×C73C2211yescharacteristic
33#465×C73—21no—
34#464×C73—21no—
35#464×C73—21no—
36#463×C73—21no—
37#462×C73—21no—
38#462×C73C2211yescharacteristic
39#461×C73C2211yescharacteristic
40#460×C73C2211yescharacteristic
41#460×C73C2211yescharacteristic
42#460×C73C2211yescharacteristic
43#459×C73—21no—
44#459×C73C2211yescharacteristic
45#452×C73—21no—
46#446×C73C2211yescharacteristic
47#446×C73C2211yescharacteristic
48C8×Q8×C73C2211yescharacteristic
49#442×C73—21no—
50#441×C73—21no—
51C4×Q16×C73C2211yescharacteristic
52C4×SD16×C73—21no—
53C4×SD16×C73C2211yescharacteristic
54C8×D4×C73C2211yescharacteristic
55#416×C73—21no—
56#335×C73C2211yescharacteristic
57#334×C73C2211yescharacteristic
58#332×C73C2211yescharacteristic
59#332×C73C2211yescharacteristic
60#331×C73C2211yescharacteristic
61#331×C73C2211yescharacteristic
62Q8⋊C8×C73C2211yescharacteristic
63Q8⋊C8×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66C82×C73C2211yescharacteristic
67C2×#41×C73—21no—
68C2×Q16×C73—21no—
69C2×Q16×C73—21no—
70C2×Q16×C73—21no—
71C2×Q16×C73D411yescharacteristic
72C2×SD16×C73—21no—
73C2×SD16×C73—21no—
74C2×SD16×C73—21no—
75C2×SD16×C73—21no—
76C2×SD16×C73D411yescharacteristic
77C2×D8×C73—21no—
78C2×D8×C73—21no—
79C2×D8×C73—21no—
80C22×C8×C73—21no—
81C4⋊Q8×C73—21no—
82C4⋊Q8×C73C2311yescharacteristic
83C4⋊Q8×C73C2311yescharacteristic
84#127×C73—21no—
85#127×C73C2311yescharacteristic
86#127×C73C2311yescharacteristic
87#126×C73—41no—
88#125×C73—21no—
89#125×C73—41no—
90#124×C73—21no—
91#124×C73—21no—
92#124×C73—21no—
93#123×C73—41no—
94C22⋊Q8×C73—21no—
95#121×C73—21no—
96#121×C73—41no—
97C4×Q8×C73—21no—
98C4×Q8×C73—21no—
99C4×Q8×C73—21no—
100C4×Q8×C73C2311yescharacteristic
101C4×Q8×C73C2311yescharacteristic
102C4×Q8×C73C2311yescharacteristic
103C4×D4×C73—21no—
104C4×D4×C73—21no—
105C4×D4×C73—21no—
106C4×D4×C73C2311yescharacteristic
107#117×C73—21no—
108#107×C73D411yescharacteristic
109#106×C73—21no—
110#106×C73—21no—
111#106×C73D411yescharacteristic
112C4⋊C8×C73—21no—
113C4⋊C8×C73—21no—
114C4⋊C8×C73—21no—
115C4⋊C8×C73C2311yescharacteristic
116C4⋊C8×C73C2311yescharacteristic
117C4⋊C8×C73C2311yescharacteristic
118C4⋊C8×C73C2311yescharacteristic
119#103×C73—21no—
120#103×C73—21no—
121#103×C73—21no—
122#103×C73—21no—
123#103×C73D411yescharacteristic
124#103×C73D411yescharacteristic
125#103×C73D411yescharacteristic
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×C73—41no—
136#102×C73D411yescharacteristic
137C22⋊C8×C73—21no—
138#97×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—81no—
146C2×Q8×C73—21no—
147C2×Q8×C73—21no—
148C2×Q8×C73C2×D411yescharacteristic
149C2×Q8×C73C2×D411yescharacteristic
150C2×Q8×C73C2×D411yescharacteristic
151C2×D4×C73—21no—
152C2×D4×C73—21no—
153C2×D4×C73—21no—
154C2×D4×C73—21no—
155C2×D4×C73—21no—
156C2×D4×C73—21no—
157C2×D4×C73—41no—
158C2×D4×C73—41no—
159C2×D4×C73C2×D411yescharacteristic
160C22×C4×C73—21no—
161C22×C4×C73—41no—
162C22×C4×C73—41no—
163Q16×C73—41no—
164Q16×C73—42no—
165Q16×C73—81no—
166Q16×C73—81no—
167SD16×C73—22no—
168SD16×C73—42no—
169SD16×C73—81no—
170SD16×C73—81no—
171SD16×C73—81no—
172D8×C73—42no—
173D8×C73—81no—
174D8×C73—81no—
175C2×C8×C73—21no—
176C2×C8×C73—21no—
177C2×C8×C73—21no—
178C2×C8×C73—21no—
179C2×C8×C73—21no—
180C2×C8×C73—81no—
181C2×C8×C73C2×D411yescharacteristic
182C2×C8×C73C2×D411yescharacteristic
183C2×C8×C73C2×D411yescharacteristic
184C2×C8×C73C2×D411yescharacteristic
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—21no—
192C4⋊C4×C73—41no—
193C4⋊C4×C73—41no—
194C4⋊C4×C73—41no—
195C4⋊C4×C73—41no—
196C4⋊C4×C73C2×D411yescharacteristic
197C4⋊C4×C73C2×D411yescharacteristic
198C4⋊C4×C73C2×D411yescharacteristic
199C4⋊C4×C73C2×D411yescharacteristic
200C22⋊C4×C73—21no—
201C22⋊C4×C73—41no—
202C22⋊C4×C73—41no—
203C22⋊C4×C73—41no—
204C22⋊C4×C73—41no—
205C22⋊C4×C73—41no—
206C22⋊C4×C73—41no—
207C42×C73—21no—
208C42×C73—21no—
209C42×C73—21no—
210C42×C73—41no—
211C42×C73—41no—
212C42×C73C2411yescharacteristic
213C23×C73—21no—
214C23×C73—41no—
215C23×C73—41no—
216Q8×C73—21no—
217Q8×C73—21no—
218Q8×C73—21no—
219Q8×C73—21no—
220Q8×C73—21no—
221Q8×C73—21no—
222Q8×C73—41no—
223Q8×C73—41no—
224Q8×C73—41no—
225Q8×C73—41no—
226D4×C73—21no—
227D4×C73—21no—
228D4×C73—41no—
229D4×C73—41no—
230D4×C73—41no—
231D4×C73—41no—
232D4×C73—41no—
233D4×C73—41no—
234D4×C73—41no—
235D4×C73—41no—
236D4×C73—81no—
237D4×C73—81no—
238D4×C73—82no—
239D4×C73—161no—
240C2×C4×C73—21no—
241C2×C4×C73—21no—
242C2×C4×C73—21no—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—21no—
246C2×C4×C73—21no—
247C2×C4×C73—41no—
248C2×C4×C73—41no—
249C2×C4×C73—41no—
250C2×C4×C73—41no—
251C2×C4×C73—82no—
252C2×C4×C73—161no—
253C2×C4×C73C22×D411yescharacteristic
254C2×C4×C73C22×D411yescharacteristic
255C2×C4×C73H(5,𝔽2)11yescharacteristic
256C8×C73—21no—
257C8×C73—21no—
258C8×C73—21no—
259C8×C73—41no—
260C8×C73—41no—
261C8×C73—41no—
262C8×C73—41no—
263C8×C73—41no—
264C8×C73#13512yes—
265C22×C73—41no—
266C22×C73—41no—
267C22×C73—41no—
268C22×C73—81no—
269C22×C73—81no—
270C22×C73—81no—
271C22×C73—81no—
272C22×C73—81no—
273C22×C73—81no—
274C22×C73D4211yescharacteristic
275C4×C73—21no—
276C4×C73—41no—
277C4×C73—41no—
278C4×C73—41no—
279C4×C73—41no—
280C4×C73—41no—
281C4×C73—41no—
282C4×C73—41no—
283C4×C73—81no—
284C4×C73—81no—
285C4×C73C2×#13511yescharacteristic
286C4×C73#57511yescharacteristic
287C4×C73#57611yescharacteristic
288C4×C73#57711yescharacteristic
289#19963C7311yesmaximal, characteristic, direct product factor, Sylow
290C2×C73—81no—
291C2×C73—161no—
292C2×C73—161no—
293C2×C73#327511yescharacteristic
294C2×C73#328711yescharacteristic
295C2×C73#329011yescharacteristic
296#3399C2×C7311yescharacteristic
297#3398C2×C7311yescharacteristic, complemented
298#3365C2×C7311yescharacteristic, complemented
299#3304C2×C7311yescharacteristic, complemented
300#1709C2×C7311yescharacteristic, complemented
301#1690C2×C7311yescharacteristic, complemented
302#1688C2×C7311yescharacteristic, complemented
303#1682C2×C7311yescharacteristic, complemented
304#1681C2×C7311yescharacteristic, complemented
305#1642C2×C7311yescharacteristic, complemented
306#1640C2×C7311yescharacteristic, complemented
307#1628C2×C7311yescharacteristic, complemented
308#1626C2×C7311yescharacteristic, complemented
309#1591C2×C7311yescharacteristic, complemented
310C8×SD16C2×C7311yescharacteristic, complemented
311C73#1996311yescharacteristic, direct product factor, Sylow
312#559C22×C7311yescharacteristic
313#557C22×C7311yescharacteristic
314#556C22×C7311yescharacteristic
315#550C22×C7311yescharacteristic
316#497—21no—
317#496—21no—
318#494C22×C7311yescharacteristic
319#493C22×C7311yescharacteristic
320#488—21no—
321#486C22×C7311yescharacteristic
322#486C22×C7311yescharacteristic
323#486C22×C7311yescharacteristic
324#486C22×C7311yescharacteristic
325#482—21no—
326#478—21no—
327#475C22×C7311yescharacteristic
328#475C22×C7311yescharacteristic
329#465—21no—
330#464—21no—
331#464—21no—
332#463—21no—
333#462—21no—
334#462C22×C7311yescharacteristic
335#461C22×C7311yescharacteristic
336#460C22×C7311yescharacteristic
337#460C22×C7311yescharacteristic
338#460C22×C7311yescharacteristic
339#459—21no—
340#459C22×C7311yescharacteristic
341#452—21no—
342#446C22×C7311yescharacteristic
343#446C22×C7311yescharacteristic
344C8×Q8C22×C7311yescharacteristic
345#442—21no—
346#441—21no—
347C4×Q16C22×C7311yescharacteristic
348C4×SD16—21no—
349C4×SD16C22×C7311yescharacteristic
350C8×D4C22×C7311yescharacteristic
351#416—21no—
352#335C22×C7311yescharacteristic
353#334C22×C7311yescharacteristic
354#332C22×C7311yescharacteristic
355#332C22×C7311yescharacteristic
356#331C22×C7311yescharacteristic
357#331C22×C7311yescharacteristic
358Q8⋊C8C22×C7311yescharacteristic
359Q8⋊C8C22×C7311yescharacteristic
360Q8⋊C8C22×C7311yescharacteristic
361D4⋊C8C22×C7311yescharacteristic
362C82C22×C7311yescharacteristic
363C2×#41—21no—
364C2×Q16—21no—
365C2×Q16—21no—
366C2×Q16—21no—
367C2×Q16D4×C7311yescharacteristic
368C2×SD16—21no—
369C2×SD16—21no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16D4×C7311yescharacteristic
373C2×D8—21no—
374C2×D8—21no—
375C2×D8—21no—
376C22×C8—21no—
377C4⋊Q8—21no—
378C4⋊Q8C23×C7311yescharacteristic
379C4⋊Q8C23×C7311yescharacteristic
380#127—21no—
381#127C23×C7311yescharacteristic
382#127C23×C7311yescharacteristic
383#126—41no—
384#125—21no—
385#125—41no—
386#124—21no—
387#124—21no—
388#124—21no—
389#123—41no—
390C22⋊Q8—21no—
391#121—21no—
392#121—41no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8C23×C7311yescharacteristic
397C4×Q8C23×C7311yescharacteristic
398C4×Q8C23×C7311yescharacteristic
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4C23×C7311yescharacteristic
403#117—21no—
404#107D4×C7311yescharacteristic
405#106—21no—
406#106—21no—
407#106D4×C7311yescharacteristic
408C4⋊C8—21no—
409C4⋊C8—21no—
410C4⋊C8—21no—
411C4⋊C8C23×C7311yescharacteristic
412C4⋊C8C23×C7311yescharacteristic
413C4⋊C8C23×C7311yescharacteristic
414C4⋊C8C23×C7311yescharacteristic
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103D4×C7311yescharacteristic
420#103D4×C7311yescharacteristic
421#103D4×C7311yescharacteristic
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—41no—
431#102—41no—
432#102D4×C7311yescharacteristic
433C22⋊C8—21no—
434#97—21no—
435#97—21no—
436C4×C8—21no—
437C4×C8C23×C7311yescharacteristic
438C4×C8C23×C7311yescharacteristic
439C4×C8C23×C7311yescharacteristic
440#41—42no—
441#41—81no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8C2×D4×C7311yescharacteristic
445C2×Q8C2×D4×C7311yescharacteristic
446C2×Q8C2×D4×C7311yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4C2×D4×C7311yescharacteristic
456C22×C4—21no—
457C22×C4—41no—
458C22×C4—41no—
459Q16—41no—
460Q16—42no—
461Q16—81no—
462Q16—81no—
463SD16—22no—
464SD16—42no—
465SD16—81no—
466SD16—81no—
467SD16—81no—
468D8—42no—
469D8—81no—
470D8—81no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—81no—
477C2×C8C2×D4×C7311yescharacteristic
478C2×C8C2×D4×C7311yescharacteristic
479C2×C8C2×D4×C7311yescharacteristic
480C2×C8C2×D4×C7311yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4C2×D4×C7311yescharacteristic
493C4⋊C4C2×D4×C7311yescharacteristic
494C4⋊C4C2×D4×C7311yescharacteristic
495C4⋊C4C2×D4×C7311yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—41no—
507C42—41no—
508C42C24×C7311yescharacteristic
509C23—21no—
510C23—41no—
511C23—41no—
512Q8—21no—
513Q8—21no—
514Q8—21no—
515Q8—21no—
516Q8—21no—
517Q8—21no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—41no—
522D4—21no—
523D4—21no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—81no—
533D4—81no—
534D4—82no—
535D4—161no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—82no—
548C2×C4—161no—
549C2×C4C22×D4×C7311yescharacteristic
550C2×C4C22×D4×C7311yescharacteristic
551C2×C4H(5,𝔽2)×C7311yescharacteristic
552C8—21no—
553C8—21no—
554C8—21no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8#135×C7312yes—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22D42×C7311yescharacteristic
571C4—21no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—81no—
580C4—81no—
581C4C2×#135×C7311yescharacteristic
582C4#575×C7311yescharacteristic
583C4#576×C7311yescharacteristic
584C4#577×C7311yescharacteristic
585C2—81no—
586C2—161no—
587C2—161no—
588C2C73×#327511yescharacteristic
589C2C73×#328711yescharacteristic
590C2C73×#329011yescharacteristic
subgroupG/H
center, socleC22×C73D42
commutator, Frattini, cosocleC42C24×C73
prime radicalC73×#3399C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#3398C2semidirect
3. C73×#3365C2semidirect
4. C73×#3304C2semidirect
5. C73×#1709C2semidirect
6. C73×#1690C2semidirect
7. C73×#1688C2semidirect
8. C73×#1682C2semidirect
9. C73×#1681C2semidirect
10. C73×#1642C2semidirect
11. C73×#1640C2semidirect
12. C73×#1628C2semidirect
13. C73×#1626C2semidirect
14. C73×#1591C2semidirect
15. C8×SD16×C73C2semidirect
289. #19963C73direct (N × H)
297. #3398C2×C73semidirect
298. #3365C2×C73semidirect
299. #3304C2×C73semidirect
300. #1709C2×C73semidirect
301. #1690C2×C73semidirect
302. #1688C2×C73semidirect
303. #1682C2×C73semidirect
304. #1681C2×C73semidirect
305. #1642C2×C73semidirect
306. #1640C2×C73semidirect
307. #1628C2×C73semidirect
308. #1626C2×C73semidirect
309. #1591C2×C73semidirect
310. C8×SD16C2×C73semidirect
311. C73#19963direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#33992
C73×#33982
C73×#33652
C73×#33042
C73×#17092
C73×#16902
C73×#16882
C73×#16822
C73×#16812
C73×#16422
C73×#16402
C73×#16282
C73×#16262
C73×#15912
C8×SD16×C732
#1996373