Finite Group Databasebeta

← C73×#19916 #32929320

Subgroups — C73×#19916 #32929320

Order 18688.

610 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×#3373C211yesmaximal, characteristic, complemented
2C73×#3361C211yesmaximal, characteristic, complemented
3C73×#3331C211yesmaximal, characteristic, complemented
4C73×#3298C211yesmaximal, characteristic, complemented
5C73×#1711C211yesmaximal, characteristic, complemented
6C73×#1704C211yesmaximal, characteristic, complemented
7C73×#1701C211yesmaximal, characteristic, complemented
8C73×#1680C211yesmaximal, characteristic, complemented
9C73×#1677C211yesmaximal, characteristic, complemented
10C73×#1643C211yesmaximal, characteristic, complemented
11C73×#1640C211yesmaximal, characteristic, complemented
12C73×#1637C211yesmaximal, characteristic, complemented
13C73×#1625C211yesmaximal, characteristic
14C73×#1590C211yesmaximal, characteristic, complemented
15C8×SD16×C73C211yesmaximal, characteristic, complemented
16#559×C73C2211yescharacteristic
17#554×C73C2211yescharacteristic
18D4×Q8×C73C2211yescharacteristic
19#547×C73C2211yescharacteristic
20#489×C73—21no—
21#488×C73—21no—
22#487×C73C2211yescharacteristic
23#487×C73C2211yescharacteristic
24#487×C73C2211yescharacteristic
25#486×C73C2211yescharacteristic
26#486×C73C2211yescharacteristic
27#486×C73C2211yescharacteristic
28#483×C73—21no—
29#483×C73—21no—
30#478×C73—21no—
31#477×C73C2211yescharacteristic
32#476×C73—21no—
33#476×C73C2211yescharacteristic
34#475×C73C2211yescharacteristic
35#475×C73C2211yescharacteristic
36#470×C73—21no—
37#465×C73—21no—
38#463×C73—21no—
39#463×C73—21no—
40#462×C73C2211yescharacteristic
41#461×C73C2211yescharacteristic
42#459×C73C2211yescharacteristic
43#459×C73C2211yescharacteristic
44#452×C73—21no—
45#448×C73—21no—
46#446×C73C2211yescharacteristic
47C8×Q8×C73C2211yescharacteristic
48#442×C73—21no—
49C4×SD16×C73C2211yescharacteristic
50C4×SD16×C73C2211yescharacteristic
51C4×D8×C73—21no—
52#436×C73C2211yescharacteristic
53C8×D4×C73C2211yescharacteristic
54#417×C73—21no—
55C2×#103×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—
68C22×Q8×C73—21no—
69C2×Q16×C73—21no—
70C2×SD16×C73—21no—
71C2×SD16×C73D411yescharacteristic
72C2×SD16×C73D411yescharacteristic
73C2×D8×C73—21no—
74C2×D8×C73—21no—
75C2×M16×C73—21no—
76C22×C8×C73—21no—
77C4⋊Q8×C73—21no—
78C4⋊Q8×C73C2311yescharacteristic
79C4⋊Q8×C73C2311yescharacteristic
80C4⋊Q8×C73C2311yescharacteristic
81#127×C73C2311yescharacteristic
82#125×C73—21no—
83#124×C73—21no—
84#124×C73—21no—
85#123×C73—41no—
86#123×C73—41no—
87C22⋊Q8×C73—21no—
88C22⋊Q8×C73—21no—
89C22⋊Q8×C73—21no—
90C22⋊Q8×C73—41no—
91C22⋊Q8×C73—41no—
92#121×C73—21no—
93C4×Q8×C73C2311yescharacteristic
94C4×Q8×C73C2311yescharacteristic
95C4×D4×C73—21no—
96C4×D4×C73—21no—
97C4×D4×C73—21no—
98C4×D4×C73—21no—
99C4×D4×C73C2311yescharacteristic
100C4×D4×C73C2311yescharacteristic
101C2×C4⋊C4×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—21no—
123#103×C73—21no—
124#103×C73—41no—
125#103×C73D411yescharacteristic
126#103×C73D411yescharacteristic
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—81no—
146C2×Q8×C73—21no—
147C2×Q8×C73—21no—
148C2×Q8×C73—21no—
149C2×Q8×C73—41no—
150C2×Q8×C73—42no—
151C2×Q8×C73—81no—
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×C73C2×D411yescharacteristic
159C2×D4×C73C2×D411yescharacteristic
160C22×C4×C73—21no—
161C22×C4×C73—21no—
162C22×C4×C73—41no—
163C22×C4×C73—41no—
164C22×C4×C73—41no—
165C22×C4×C73—41no—
166Q16×C73—81no—
167SD16×C73—22no—
168SD16×C73—41no—
169SD16×C73—81no—
170D8×C73—42no—
171D8×C73—42no—
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—
205C22⋊C4×C73—41no—
206C22⋊C4×C73—41no—
207C42×C73—21no—
208C42×C73—21no—
209C42×C73C2411yescharacteristic
210C23×C73—21no—
211C23×C73—21no—
212C23×C73—41no—
213Q8×C73—21no—
214Q8×C73—21no—
215Q8×C73—21no—
216Q8×C73—21no—
217Q8×C73—41no—
218Q8×C73—41no—
219Q8×C73—41no—
220Q8×C73—41no—
221Q8×C73—81no—
222Q8×C73—82no—
223D4×C73—21no—
224D4×C73—21no—
225D4×C73—21no—
226D4×C73—41no—
227D4×C73—41no—
228D4×C73—41no—
229D4×C73—41no—
230D4×C73—81no—
231D4×C73—82no—
232D4×C73#13512yes—
233C2×C4×C73—21no—
234C2×C4×C73—21no—
235C2×C4×C73—21no—
236C2×C4×C73—21no—
237C2×C4×C73—21no—
238C2×C4×C73—21no—
239C2×C4×C73—41no—
240C2×C4×C73—41no—
241C2×C4×C73—41no—
242C2×C4×C73—41no—
243C2×C4×C73—41no—
244C2×C4×C73—41no—
245C2×C4×C73—41no—
246C2×C4×C73—82no—
247C2×C4×C73—82no—
248C2×C4×C73—161no—
249C2×C4×C73—161no—
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—22no—
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—21no—
273C4×C73—41no—
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#19916C7311yesmaximal, characteristic, direct product factor, Sylow
287C2×C73—42no—
288C2×C73—81no—
289C2×C73—161no—
290C2×C73#327511yescharacteristic
291C2×C73#328211yescharacteristic
292C2×C73#329011yescharacteristic
293#3373C2×C7311yescharacteristic, complemented
294#3361C2×C7311yescharacteristic, complemented
295#3331C2×C7311yescharacteristic, complemented
296#3298C2×C7311yescharacteristic, complemented
297#1711C2×C7311yescharacteristic, complemented
298#1704C2×C7311yescharacteristic, complemented
299#1701C2×C7311yescharacteristic, complemented
300#1680C2×C7311yescharacteristic, complemented
301#1677C2×C7311yescharacteristic, complemented
302#1643C2×C7311yescharacteristic, complemented
303#1640C2×C7311yescharacteristic, complemented
304#1637C2×C7311yescharacteristic, complemented
305#1625C2×C7311yescharacteristic
306#1590C2×C7311yescharacteristic, complemented
307C8×SD16C2×C7311yescharacteristic, complemented
308C73#1991611yescharacteristic, direct product factor, Sylow
309#559C22×C7311yescharacteristic
310#554C22×C7311yescharacteristic
311D4×Q8C22×C7311yescharacteristic
312#547C22×C7311yescharacteristic
313#489—21no—
314#488—21no—
315#487C22×C7311yescharacteristic
316#487C22×C7311yescharacteristic
317#487C22×C7311yescharacteristic
318#486C22×C7311yescharacteristic
319#486C22×C7311yescharacteristic
320#486C22×C7311yescharacteristic
321#483—21no—
322#483—21no—
323#478—21no—
324#477C22×C7311yescharacteristic
325#476—21no—
326#476C22×C7311yescharacteristic
327#475C22×C7311yescharacteristic
328#475C22×C7311yescharacteristic
329#470—21no—
330#465—21no—
331#463—21no—
332#463—21no—
333#462C22×C7311yescharacteristic
334#461C22×C7311yescharacteristic
335#459C22×C7311yescharacteristic
336#459C22×C7311yescharacteristic
337#452—21no—
338#448—21no—
339#446C22×C7311yescharacteristic
340C8×Q8C22×C7311yescharacteristic
341#442—21no—
342C4×SD16C22×C7311yescharacteristic
343C4×SD16C22×C7311yescharacteristic
344C4×D8—21no—
345#436C22×C7311yescharacteristic
346C8×D4C22×C7311yescharacteristic
347#417—21no—
348C2×#103—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—
361C22×Q8—21no—
362C2×Q16—21no—
363C2×SD16—21no—
364C2×SD16D4×C7311yescharacteristic
365C2×SD16D4×C7311yescharacteristic
366C2×D8—21no—
367C2×D8—21no—
368C2×M16—21no—
369C22×C8—21no—
370C4⋊Q8—21no—
371C4⋊Q8C23×C7311yescharacteristic
372C4⋊Q8C23×C7311yescharacteristic
373C4⋊Q8C23×C7311yescharacteristic
374#127C23×C7311yescharacteristic
375#125—21no—
376#124—21no—
377#124—21no—
378#123—41no—
379#123—41no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382C22⋊Q8—21no—
383C22⋊Q8—41no—
384C22⋊Q8—41no—
385#121—21no—
386C4×Q8C23×C7311yescharacteristic
387C4×Q8C23×C7311yescharacteristic
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4C23×C7311yescharacteristic
393C4×D4C23×C7311yescharacteristic
394C2×C4⋊C4—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—21no—
416#103—21no—
417#103—41no—
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—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—81no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—41no—
443C2×Q8—42no—
444C2×Q8—81no—
445C2×Q8C2×D4×C7311yescharacteristic
446C2×Q8C2×D4×C7311yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4C2×D4×C7311yescharacteristic
452C2×D4C2×D4×C7311yescharacteristic
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459Q16—81no—
460SD16—22no—
461SD16—41no—
462SD16—81no—
463D8—42no—
464D8—42no—
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—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C42—21no—
501C42—21no—
502C42C24×C7311yescharacteristic
503C23—21no—
504C23—21no—
505C23—41no—
506Q8—21no—
507Q8—21no—
508Q8—21no—
509Q8—21no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—81no—
515Q8—82no—
516D4—21no—
517D4—21no—
518D4—21no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—81no—
524D4—82no—
525D4#135×C7312yes—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—82no—
540C2×C4—82no—
541C2×C4—161no—
542C2×C4—161no—
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—22no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22D42×C7311yescharacteristic
565C4—21no—
566C4—41no—
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—42no—
580C2—81no—
581C2—161no—
582C2C73×#327511yescharacteristic
583C2C73×#328211yescharacteristic
584C2C73×#329011yescharacteristic
subgroupG/H
center, socleC22×C73D42
commutator, Frattini, cosocleC42C24×C73
prime radicalC73×#1625C2
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×#3373C2semidirect
2. C73×#3361C2semidirect
3. C73×#3331C2semidirect
4. C73×#3298C2semidirect
5. C73×#1711C2semidirect
6. C73×#1704C2semidirect
7. C73×#1701C2semidirect
8. C73×#1680C2semidirect
9. C73×#1677C2semidirect
10. C73×#1643C2semidirect
11. C73×#1640C2semidirect
12. C73×#1637C2semidirect
14. C73×#1590C2semidirect
15. C8×SD16×C73C2semidirect
286. #19916C73direct (N × H)
293. #3373C2×C73semidirect
294. #3361C2×C73semidirect
295. #3331C2×C73semidirect
296. #3298C2×C73semidirect
297. #1711C2×C73semidirect
298. #1704C2×C73semidirect
299. #1701C2×C73semidirect
300. #1680C2×C73semidirect
301. #1677C2×C73semidirect
302. #1643C2×C73semidirect
303. #1640C2×C73semidirect
304. #1637C2×C73semidirect
306. #1590C2×C73semidirect
307. C8×SD16C2×C73semidirect
308. C73#19916direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#33732
C73×#33612
C73×#33312
C73×#32982
C73×#17112
C73×#17042
C73×#17012
C73×#16802
C73×#16772
C73×#16432
C73×#16402
C73×#16372
C73×#16252
C73×#15902
C8×SD16×C732
#1991673