Finite Group Databasebeta

← C73×#20086 #32929490

Subgroups — C73×#20086 #32929490

Order 18688.

622 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3386C211yesmaximal, characteristic, complemented
2C73×#3363C211yesmaximal, characteristic, complemented
3C73×#3362C211yesmaximal, characteristic
4C73×#3278C211yesmaximal, characteristic
5C73×#1719C211yesmaximal, characteristic, complemented
6C73×#1703C211yesmaximal, characteristic, complemented
7C73×#1698C211yesmaximal, characteristic, complemented
8C73×#1674C211yesmaximal, characteristic, complemented
9C73×#1666C211yesmaximal, characteristic, complemented
10C73×#1645C211yesmaximal, characteristic, complemented
11C73×#1641C211yesmaximal, characteristic
12C73×#1637C211yesmaximal, characteristic, complemented
13C73×#1626C211yesmaximal, characteristic, complemented
14C73×#1588C211yesmaximal, characteristic, complemented
15C73×#1587C211yesmaximal, characteristic, complemented
16C2×#137×C73—21no—
17Q82×C73C2211yescharacteristic
18#557×C73C2211yescharacteristic
19#550×C73C2211yescharacteristic
20D4×Q8×C73C2211yescharacteristic
21#501×C73—21no—
22#500×C73C2211yescharacteristic
23#492×C73C2211yescharacteristic
24#487×C73—21no—
25#487×C73C2211yescharacteristic
26#487×C73C2211yescharacteristic
27#486×C73—21no—
28#486×C73C2211yescharacteristic
29#486×C73C2211yescharacteristic
30#478×C73—21no—
31#477×C73—21no—
32#477×C73—21no—
33#477×C73C2211yescharacteristic
34#476×C73—21no—
35#476×C73C2211yescharacteristic
36#475×C73C2211yescharacteristic
37#474×C73C2211yescharacteristic
38#468×C73—21no—
39#462×C73—21no—
40#462×C73C2211yescharacteristic
41#462×C73C2211yescharacteristic
42#460×C73—21no—
43#460×C73C2211yescharacteristic
44#460×C73C2211yescharacteristic
45#452×C73—21no—
46#448×C73—21no—
47#446×C73C2211yescharacteristic
48C8×Q8×C73C2211yescharacteristic
49C8×Q8×C73C2211yescharacteristic
50#440×C73—21no—
51C4×Q16×C73—21no—
52C4×Q16×C73C2211yescharacteristic
53C4×SD16×C73—21no—
54C4×SD16×C73C2211yescharacteristic
55#436×C73C2211yescharacteristic
56#335×C73C2211yescharacteristic
57#334×C73C2211yescharacteristic
58#333×C73C2211yescharacteristic
59#332×C73C2211yescharacteristic
60#332×C73C2211yescharacteristic
61#331×C73C2211yescharacteristic
62Q8⋊C8×C73C2211yescharacteristic
63Q8⋊C8×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×#41×C73—21no—
68C22×Q8×C73—21no—
69#137×C73—44no—
70C2×Q16×C73—21no—
71C2×Q16×C73—21no—
72C2×Q16×C73D411yescharacteristic
73C2×SD16×C73—21no—
74C2×SD16×C73—21no—
75C2×SD16×C73—21no—
76C2×SD16×C73—21no—
77C2×SD16×C73D411yescharacteristic
78C2×M16×C73—21no—
79C4⋊Q8×C73—21no—
80C4⋊Q8×C73—21no—
81C4⋊Q8×C73—21no—
82C4⋊Q8×C73—21no—
83C4⋊Q8×C73—41no—
84C4⋊Q8×C73C2311yescharacteristic
85C4⋊Q8×C73C2311yescharacteristic
86C4⋊Q8×C73C2311yescharacteristic
87#127×C73—21no—
88#127×C73C2311yescharacteristic
89#125×C73—21no—
90#125×C73—41no—
91C22⋊Q8×C73—21no—
92C22⋊Q8×C73—41no—
93#121×C73—21no—
94#121×C73—41no—
95C4×Q8×C73—21no—
96C4×Q8×C73—21no—
97C4×Q8×C73—21no—
98C4×Q8×C73—21no—
99C4×Q8×C73C2311yescharacteristic
100C4×Q8×C73C2311yescharacteristic
101C4×Q8×C73C2311yescharacteristic
102C4×D4×C73—21no—
103C4×D4×C73—21no—
104C4×D4×C73C2311yescharacteristic
105#107×C73—21no—
106#107×C73—21no—
107#107×C73—21no—
108#107×C73—21no—
109#107×C73D411yescharacteristic
110#106×C73—21no—
111#106×C73—21no—
112#106×C73D411yescharacteristic
113C4⋊C8×C73—21no—
114C4⋊C8×C73—21no—
115C4⋊C8×C73—21no—
116C4⋊C8×C73C2311yescharacteristic
117C4⋊C8×C73C2311yescharacteristic
118C4⋊C8×C73C2311yescharacteristic
119C4⋊C8×C73C2311yescharacteristic
120#103×C73—21no—
121#103×C73—21no—
122#103×C73—21no—
123#103×C73—21no—
124#103×C73—21no—
125#103×C73—21no—
126#103×C73—41no—
127#103×C73D411yescharacteristic
128#103×C73D411yescharacteristic
129#103×C73D411yescharacteristic
130#102×C73—21no—
131#102×C73—21no—
132#102×C73—21no—
133#102×C73—21no—
134#102×C73—21no—
135#102×C73—21no—
136#102×C73—41no—
137#102×C73D411yescharacteristic
138C22⋊C8×C73—21no—
139#97×C73—21no—
140C4×C8×C73—21no—
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C4×C8×C73C2311yescharacteristic
145#41×C73—42no—
146#41×C73—81no—
147C2×Q8×C73—21no—
148C2×Q8×C73—21no—
149C2×Q8×C73—21no—
150C2×Q8×C73—41no—
151C2×Q8×C73—41no—
152C2×Q8×C73—42no—
153C2×Q8×C73—81no—
154C2×Q8×C73C2×D411yescharacteristic
155C2×Q8×C73C2×D411yescharacteristic
156C2×Q8×C73C2×D411yescharacteristic
157C2×D4×C73—21no—
158C2×D4×C73—21no—
159C2×D4×C73—21no—
160C2×D4×C73—41no—
161C2×D4×C73—41no—
162C2×D4×C73C2×D411yescharacteristic
163C22×C4×C73—21no—
164C22×C4×C73—41no—
165C22×C4×C73—41no—
166Q16×C73—22no—
167Q16×C73—42no—
168Q16×C73—42no—
169SD16×C73—22no—
170SD16×C73—42no—
171SD16×C73—42no—
172SD16×C73—42no—
173SD16×C73—81no—
174M16×C73—42no—
175C2×C8×C73—21no—
176C2×C8×C73—21no—
177C2×C8×C73—21no—
178C2×C8×C73—21no—
179C2×C8×C73—21no—
180C2×C8×C73C2×D411yescharacteristic
181C2×C8×C73C2×D411yescharacteristic
182C2×C8×C73C2×D411yescharacteristic
183C2×C8×C73C2×D411yescharacteristic
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—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—41no—
194C4⋊C4×C73—41no—
195C4⋊C4×C73—41no—
196C4⋊C4×C73—41no—
197C4⋊C4×C73—41no—
198C4⋊C4×C73—41no—
199C4⋊C4×C73C2×D411yescharacteristic
200C4⋊C4×C73C2×D411yescharacteristic
201C4⋊C4×C73C2×D411yescharacteristic
202C4⋊C4×C73C2×D411yescharacteristic
203C22⋊C4×C73—21no—
204C22⋊C4×C73—41no—
205C22⋊C4×C73—41no—
206C42×C73—21no—
207C42×C73—21no—
208C42×C73—21no—
209C42×C73—41no—
210C42×C73—41no—
211C42×C73C2411yescharacteristic
212C23×C73—21no—
213C23×C73—41no—
214Q8×C73—21no—
215Q8×C73—21no—
216Q8×C73—21no—
217Q8×C73—21no—
218Q8×C73—41no—
219Q8×C73—41no—
220Q8×C73—41no—
221Q8×C73—41no—
222Q8×C73—81no—
223Q8×C73—82no—
224Q8×C73—161no—
225Q8×C73AGL(1,ℤ/8)12yes—
226Q8×C73#13712yescomplemented
227D4×C73—21no—
228D4×C73—21no—
229D4×C73—41no—
230D4×C73—41no—
231D4×C73—41no—
232D4×C73—41no—
233D4×C73—82no—
234D4×C73—81no—
235D4×C73—161no—
236C2×C4×C73—21no—
237C2×C4×C73—21no—
238C2×C4×C73—21no—
239C2×C4×C73—21no—
240C2×C4×C73—21no—
241C2×C4×C73—21no—
242C2×C4×C73—21no—
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—81no—
266C22×C73—81no—
267C22×C73—81no—
268C22×C73D4211yescharacteristic
269C4×C73—22no—
270C4×C73—22no—
271C4×C73—21no—
272C4×C73—41no—
273C4×C73—41no—
274C4×C73—41no—
275C4×C73—41no—
276C4×C73—41no—
277C4×C73—81no—
278C4×C73—81no—
279C4×C73—81no—
280C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
281C4×C73C2×#13711yescharacteristic
282C4×C73#57711yescharacteristic
283C4×C73#57811yescharacteristic
284#20086C7311yesmaximal, characteristic, direct product factor, Sylow
285C2×C73—81no—
286C2×C73—161no—
287C2×C73#326511yescharacteristic
288C2×C73#327011yescharacteristic
289C2×C73#329011yescharacteristic
290#3386C2×C7311yescharacteristic, complemented
291#3363C2×C7311yescharacteristic, complemented
292#3362C2×C7311yescharacteristic
293#3278C2×C7311yescharacteristic
294#1719C2×C7311yescharacteristic, complemented
295#1703C2×C7311yescharacteristic, complemented
296#1698C2×C7311yescharacteristic, complemented
297#1674C2×C7311yescharacteristic, complemented
298#1666C2×C7311yescharacteristic, complemented
299#1645C2×C7311yescharacteristic, complemented
300#1641C2×C7311yescharacteristic
301#1637C2×C7311yescharacteristic, complemented
302#1626C2×C7311yescharacteristic, complemented
303#1588C2×C7311yescharacteristic, complemented
304#1587C2×C7311yescharacteristic, complemented
305C73#2008611yescharacteristic, direct product factor, Sylow
306C2×#137—21no—
307Q82C22×C7311yescharacteristic
308#557C22×C7311yescharacteristic
309#550C22×C7311yescharacteristic
310D4×Q8C22×C7311yescharacteristic
311#501—21no—
312#500C22×C7311yescharacteristic
313#492C22×C7311yescharacteristic
314#487—21no—
315#487C22×C7311yescharacteristic
316#487C22×C7311yescharacteristic
317#486—21no—
318#486C22×C7311yescharacteristic
319#486C22×C7311yescharacteristic
320#478—21no—
321#477—21no—
322#477—21no—
323#477C22×C7311yescharacteristic
324#476—21no—
325#476C22×C7311yescharacteristic
326#475C22×C7311yescharacteristic
327#474C22×C7311yescharacteristic
328#468—21no—
329#462—21no—
330#462C22×C7311yescharacteristic
331#462C22×C7311yescharacteristic
332#460—21no—
333#460C22×C7311yescharacteristic
334#460C22×C7311yescharacteristic
335#452—21no—
336#448—21no—
337#446C22×C7311yescharacteristic
338C8×Q8C22×C7311yescharacteristic
339C8×Q8C22×C7311yescharacteristic
340#440—21no—
341C4×Q16—21no—
342C4×Q16C22×C7311yescharacteristic
343C4×SD16—21no—
344C4×SD16C22×C7311yescharacteristic
345#436C22×C7311yescharacteristic
346#335C22×C7311yescharacteristic
347#334C22×C7311yescharacteristic
348#333C22×C7311yescharacteristic
349#332C22×C7311yescharacteristic
350#332C22×C7311yescharacteristic
351#331C22×C7311yescharacteristic
352Q8⋊C8C22×C7311yescharacteristic
353Q8⋊C8C22×C7311yescharacteristic
354Q8⋊C8C22×C7311yescharacteristic
355D4⋊C8C22×C7311yescharacteristic
356#322C22×C7311yescharacteristic
357C2×#41—21no—
358C22×Q8—21no—
359#137—44no—
360C2×Q16—21no—
361C2×Q16—21no—
362C2×Q16D4×C7311yescharacteristic
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16D4×C7311yescharacteristic
368C2×M16—21no—
369C4⋊Q8—21no—
370C4⋊Q8—21no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8—41no—
374C4⋊Q8C23×C7311yescharacteristic
375C4⋊Q8C23×C7311yescharacteristic
376C4⋊Q8C23×C7311yescharacteristic
377#127—21no—
378#127C23×C7311yescharacteristic
379#125—21no—
380#125—41no—
381C22⋊Q8—21no—
382C22⋊Q8—41no—
383#121—21no—
384#121—41no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8C23×C7311yescharacteristic
390C4×Q8C23×C7311yescharacteristic
391C4×Q8C23×C7311yescharacteristic
392C4×D4—21no—
393C4×D4—21no—
394C4×D4C23×C7311yescharacteristic
395#107—21no—
396#107—21no—
397#107—21no—
398#107—21no—
399#107D4×C7311yescharacteristic
400#106—21no—
401#106—21no—
402#106D4×C7311yescharacteristic
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8C23×C7311yescharacteristic
407C4⋊C8C23×C7311yescharacteristic
408C4⋊C8C23×C7311yescharacteristic
409C4⋊C8C23×C7311yescharacteristic
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—41no—
417#103D4×C7311yescharacteristic
418#103D4×C7311yescharacteristic
419#103D4×C7311yescharacteristic
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—41no—
427#102D4×C7311yescharacteristic
428C22⋊C8—21no—
429#97—21no—
430C4×C8—21no—
431C4×C8—21no—
432C4×C8C23×C7311yescharacteristic
433C4×C8C23×C7311yescharacteristic
434C4×C8C23×C7311yescharacteristic
435#41—42no—
436#41—81no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—41no—
441C2×Q8—41no—
442C2×Q8—42no—
443C2×Q8—81no—
444C2×Q8C2×D4×C7311yescharacteristic
445C2×Q8C2×D4×C7311yescharacteristic
446C2×Q8C2×D4×C7311yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4C2×D4×C7311yescharacteristic
453C22×C4—21no—
454C22×C4—41no—
455C22×C4—41no—
456Q16—22no—
457Q16—42no—
458Q16—42no—
459SD16—22no—
460SD16—42no—
461SD16—42no—
462SD16—42no—
463SD16—81no—
464M16—42no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8C2×D4×C7311yescharacteristic
471C2×C8C2×D4×C7311yescharacteristic
472C2×C8C2×D4×C7311yescharacteristic
473C2×C8C2×D4×C7311yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4C2×D4×C7311yescharacteristic
490C4⋊C4C2×D4×C7311yescharacteristic
491C4⋊C4C2×D4×C7311yescharacteristic
492C4⋊C4C2×D4×C7311yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—41no—
500C42—41no—
501C42C24×C7311yescharacteristic
502C23—21no—
503C23—41no—
504Q8—21no—
505Q8—21no—
506Q8—21no—
507Q8—21no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—81no—
513Q8—82no—
514Q8—161no—
515Q8AGL(1,ℤ/8)×C7312yes—
516Q8#137×C7312yescomplemented
517D4—21no—
518D4—21no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—82no—
524D4—81no—
525D4—161no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—82no—
539C2×C4—82no—
540C2×C4C22×D4×C7311yescharacteristic
541C2×C4C22×D4×C7311yescharacteristic
542C2×C4H(5,𝔽2)×C7311yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—21no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22D42×C7311yescharacteristic
559C4—22no—
560C4—22no—
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4C2×AGL(1,ℤ/8)×C7311yescharacteristic
571C4C2×#137×C7311yescharacteristic
572C4#577×C7311yescharacteristic
573C4#578×C7311yescharacteristic
574C2—81no—
575C2—161no—
576C2C73×#326511yescharacteristic
577C2C73×#327011yescharacteristic
578C2C73×#329011yescharacteristic
subgroupG/H
center, socleC22×C73D42
commutator, Frattini, cosocleC42C24×C73
prime radical#550×C73C22
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×#3386C2semidirect
2. C73×#3363C2semidirect
5. C73×#1719C2semidirect
6. C73×#1703C2semidirect
7. C73×#1698C2semidirect
8. C73×#1674C2semidirect
9. C73×#1666C2semidirect
10. C73×#1645C2semidirect
12. C73×#1637C2semidirect
13. C73×#1626C2semidirect
14. C73×#1588C2semidirect
15. C73×#1587C2semidirect
226. Q8×C73#137semidirect
284. #20086C73direct (N × H)
290. #3386C2×C73semidirect
291. #3363C2×C73semidirect
294. #1719C2×C73semidirect
295. #1703C2×C73semidirect
296. #1698C2×C73semidirect
297. #1674C2×C73semidirect
298. #1666C2×C73semidirect
299. #1645C2×C73semidirect
301. #1637C2×C73semidirect
302. #1626C2×C73semidirect
303. #1588C2×C73semidirect
304. #1587C2×C73semidirect
305. C73#20086direct (N × H)
516. Q8#137×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#33862
C73×#33632
C73×#33622
C73×#32782
C73×#17192
C73×#17032
C73×#16982
C73×#16742
C73×#16662
C73×#16452
C73×#16412
C73×#16372
C73×#16262
C73×#15882
C73×#15872
#2008673