Finite Group Databasebeta

← C73×#20139 #32929543

Subgroups — C73×#20139 #32929543

Order 18688.

628 conjugacy classes of subgroups.

The subgroup lattice has 612 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×#3332C211yesmaximal, characteristic, complemented
4C73×#3302C211yesmaximal, characteristic, complemented
5C73×#1717C211yesmaximal, characteristic, complemented
6C73×#1700C211yesmaximal, characteristic, complemented
7C73×#1685C211yesmaximal, characteristic, complemented
8C73×#1682C211yesmaximal, characteristic, complemented
9C73×#1667C211yesmaximal, characteristic, complemented
10C73×#1641C211yesmaximal, characteristic, complemented
11C73×#1640C211yesmaximal, characteristic, complemented
12C73×#1628C211yesmaximal, characteristic, complemented
13C73×#1625C211yesmaximal, characteristic, complemented
14C73×#1588C211yesmaximal, characteristic, complemented
15C73×#1585C211yesmaximal, characteristic, complemented
16#559×C73C2211yescharacteristic
17#556×C73C2211yescharacteristic
18#550×C73C2211yescharacteristic
19#547×C73C2211yescharacteristic
20#496×C73—21no—
21#495×C73—21no—
22#493×C73C2211yescharacteristic
23#492×C73C2211yescharacteristic
24#487×C73C2211yescharacteristic
25#486×C73C2211yescharacteristic
26#486×C73C2211yescharacteristic
27#486×C73C2211yescharacteristic
28#485×C73—21no—
29#481×C73—21no—
30#475×C73C2211yescharacteristic
31#474×C73C2211yescharacteristic
32#469×C73—21no—
33#467×C73—21no—
34#464×C73—21no—
35#463×C73—21no—
36#463×C73—21no—
37#462×C73C2211yescharacteristic
38#462×C73C2211yescharacteristic
39#460×C73C2211yescharacteristic
40#459×C73—21no—
41#459×C73C2211yescharacteristic
42#459×C73C2211yescharacteristic
43#459×C73C2211yescharacteristic
44#452×C73—21no—
45#449×C73—21no—
46#446×C73C2211yescharacteristic
47C8×Q8×C73C2211yescharacteristic
48#442×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#335×C73C2211yescharacteristic
57#335×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
66#322×C73C2211yescharacteristic
67C2×#41×C73—21no—
68C2×#41×C73—21no—
69C2×Q16×C73—21no—
70C2×Q16×C73—21no—
71C2×SD16×C73—21no—
72C2×SD16×C73—21no—
73C2×SD16×C73—21no—
74C2×SD16×C73D411yescharacteristic
75C2×SD16×C73D411yescharacteristic
76C2×D8×C73—21no—
77C2×D8×C73—21no—
78C2×D8×C73—21no—
79C2×D8×C73—21no—
80C2×D8×C73—21no—
81C2×M16×C73—21no—
82C22×C8×C73—21no—
83C4⋊Q8×C73C2311yescharacteristic
84C4⋊Q8×C73C2311yescharacteristic
85#127×C73—21no—
86#127×C73C2311yescharacteristic
87#127×C73C2311yescharacteristic
88#126×C73—41no—
89#124×C73—21no—
90#124×C73—21no—
91#124×C73—21no—
92#123×C73—41no—
93#123×C73—41no—
94C22⋊Q8×C73—21no—
95C22⋊Q8×C73—21no—
96#121×C73—21no—
97#121×C73—21no—
98#121×C73—41no—
99C4×Q8×C73—21no—
100C4×Q8×C73C2311yescharacteristic
101C4×Q8×C73C2311yescharacteristic
102C4×D4×C73—21no—
103C4×D4×C73—21no—
104C4×D4×C73—21no—
105C4×D4×C73C2311yescharacteristic
106C4×D4×C73C2311yescharacteristic
107#117×C73—21no—
108C2×C4⋊C4×C73—21no—
109#107×C73—21no—
110#106×C73—21no—
111#106×C73D411yescharacteristic
112#106×C73D411yescharacteristic
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×C73—21no—
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—41no—
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×C73C2×D411yescharacteristic
151C2×Q8×C73C2×D411yescharacteristic
152C2×D4×C73—21no—
153C2×D4×C73—21no—
154C2×D4×C73—21no—
155C2×D4×C73—21no—
156C2×D4×C73—21no—
157C2×D4×C73—21no—
158C2×D4×C73—41no—
159C2×D4×C73—41no—
160C2×D4×C73—41no—
161C2×D4×C73C2×D411yescharacteristic
162C2×D4×C73C2×D411yescharacteristic
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73—41no—
166C22×C4×C73—41no—
167C22×C4×C73—41no—
168Q16×C73—81no—
169Q16×C73—81no—
170SD16×C73—41no—
171SD16×C73—41no—
172SD16×C73—42no—
173SD16×C73—81no—
174SD16×C73—81no—
175D8×C73—42no—
176D8×C73—81no—
177D8×C73—81no—
178D8×C73—81no—
179D8×C73—81no—
180M16×C73—81no—
181C2×C8×C73—21no—
182C2×C8×C73—21no—
183C2×C8×C73—21no—
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73—81no—
187C2×C8×C73C2×D411yescharacteristic
188C2×C8×C73C2×D411yescharacteristic
189C2×C8×C73C2×D411yescharacteristic
190C2×C8×C73C2×D411yescharacteristic
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
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—21no—
205C22⋊C4×C73—41no—
206C22⋊C4×C73—41no—
207C22⋊C4×C73—41no—
208C22⋊C4×C73—41no—
209C22⋊C4×C73—41no—
210C22⋊C4×C73—41no—
211C22⋊C4×C73—41no—
212C42×C73—21no—
213C42×C73—21no—
214C42×C73—41no—
215C42×C73C2411yescharacteristic
216C23×C73—21no—
217C23×C73—21no—
218C23×C73—41no—
219C23×C73—41no—
220Q8×C73—21no—
221Q8×C73—21no—
222Q8×C73—21no—
223Q8×C73—21no—
224Q8×C73—41no—
225Q8×C73—41no—
226Q8×C73—41no—
227Q8×C73—41no—
228D4×C73—21no—
229D4×C73—21no—
230D4×C73—21no—
231D4×C73—21no—
232D4×C73—41no—
233D4×C73—41no—
234D4×C73—41no—
235D4×C73—41no—
236D4×C73—41no—
237D4×C73—41no—
238D4×C73—41no—
239D4×C73—41no—
240D4×C73—81no—
241D4×C73—81no—
242D4×C73—82no—
243D4×C73—82no—
244D4×C73—161no—
245C2×C4×C73—21no—
246C2×C4×C73—21no—
247C2×C4×C73—21no—
248C2×C4×C73—21no—
249C2×C4×C73—21no—
250C2×C4×C73—21no—
251C2×C4×C73—41no—
252C2×C4×C73—41no—
253C2×C4×C73—41no—
254C2×C4×C73—41no—
255C2×C4×C73—41no—
256C2×C4×C73—41no—
257C2×C4×C73—82no—
258C2×C4×C73—82no—
259C2×C4×C73—161no—
260C2×C4×C73C22×D411yescharacteristic
261C2×C4×C73C22×D411yescharacteristic
262C2×C4×C73H(5,𝔽2)11yescharacteristic
263C8×C73—21no—
264C8×C73—21no—
265C8×C73—21no—
266C8×C73—21no—
267C8×C73—41no—
268C8×C73—41no—
269C8×C73—41no—
270C8×C73—41no—
271C8×C73—41no—
272C22×C73—41no—
273C22×C73—41no—
274C22×C73—41no—
275C22×C73—41no—
276C22×C73—41no—
277C22×C73—41no—
278C22×C73—81no—
279C22×C73—81no—
280C22×C73—81no—
281C22×C73—81no—
282C22×C73—81no—
283C22×C73—81no—
284C22×C73D4211yescharacteristic
285C4×C73—21no—
286C4×C73—41no—
287C4×C73—41no—
288C4×C73—41no—
289C4×C73—41no—
290C4×C73—41no—
291C4×C73—41no—
292C4×C73—81no—
293C4×C73—81no—
294C4×C73#57511yescharacteristic
295C4×C73#57511yescharacteristic
296C4×C73#57611yescharacteristic
297C4×C73#57611yescharacteristic
298#20139C7311yesmaximal, characteristic, direct product factor, Sylow
299C2×C73—81no—
300C2×C73—81no—
301C2×C73—161no—
302C2×C73—161no—
303C2×C73#326811yescharacteristic
304C2×C73#326811yescharacteristic
305C2×C73#329011yescharacteristic
306#3399C2×C7311yescharacteristic, complemented
307#3394C2×C7311yescharacteristic, complemented
308#3332C2×C7311yescharacteristic, complemented
309#3302C2×C7311yescharacteristic, complemented
310#1717C2×C7311yescharacteristic, complemented
311#1700C2×C7311yescharacteristic, complemented
312#1685C2×C7311yescharacteristic, complemented
313#1682C2×C7311yescharacteristic, complemented
314#1667C2×C7311yescharacteristic, complemented
315#1641C2×C7311yescharacteristic, complemented
316#1640C2×C7311yescharacteristic, complemented
317#1628C2×C7311yescharacteristic, complemented
318#1625C2×C7311yescharacteristic, complemented
319#1588C2×C7311yescharacteristic, complemented
320#1585C2×C7311yescharacteristic, complemented
321C73#2013911yescharacteristic, direct product factor, Sylow
322#559C22×C7311yescharacteristic
323#556C22×C7311yescharacteristic
324#550C22×C7311yescharacteristic
325#547C22×C7311yescharacteristic
326#496—21no—
327#495—21no—
328#493C22×C7311yescharacteristic
329#492C22×C7311yescharacteristic
330#487C22×C7311yescharacteristic
331#486C22×C7311yescharacteristic
332#486C22×C7311yescharacteristic
333#486C22×C7311yescharacteristic
334#485—21no—
335#481—21no—
336#475C22×C7311yescharacteristic
337#474C22×C7311yescharacteristic
338#469—21no—
339#467—21no—
340#464—21no—
341#463—21no—
342#463—21no—
343#462C22×C7311yescharacteristic
344#462C22×C7311yescharacteristic
345#460C22×C7311yescharacteristic
346#459—21no—
347#459C22×C7311yescharacteristic
348#459C22×C7311yescharacteristic
349#459C22×C7311yescharacteristic
350#452—21no—
351#449—21no—
352#446C22×C7311yescharacteristic
353C8×Q8C22×C7311yescharacteristic
354#442—21no—
355C4×SD16—21no—
356C4×SD16C22×C7311yescharacteristic
357C4×SD16C22×C7311yescharacteristic
358#436C22×C7311yescharacteristic
359C8×D4C22×C7311yescharacteristic
360#417—21no—
361#416—21no—
362#335C22×C7311yescharacteristic
363#335C22×C7311yescharacteristic
364#332C22×C7311yescharacteristic
365#332C22×C7311yescharacteristic
366#331C22×C7311yescharacteristic
367#331C22×C7311yescharacteristic
368Q8⋊C8C22×C7311yescharacteristic
369Q8⋊C8C22×C7311yescharacteristic
370D4⋊C8C22×C7311yescharacteristic
371D4⋊C8C22×C7311yescharacteristic
372#322C22×C7311yescharacteristic
373C2×#41—21no—
374C2×#41—21no—
375C2×Q16—21no—
376C2×Q16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16D4×C7311yescharacteristic
381C2×SD16D4×C7311yescharacteristic
382C2×D8—21no—
383C2×D8—21no—
384C2×D8—21no—
385C2×D8—21no—
386C2×D8—21no—
387C2×M16—21no—
388C22×C8—21no—
389C4⋊Q8C23×C7311yescharacteristic
390C4⋊Q8C23×C7311yescharacteristic
391#127—21no—
392#127C23×C7311yescharacteristic
393#127C23×C7311yescharacteristic
394#126—41no—
395#124—21no—
396#124—21no—
397#124—21no—
398#123—41no—
399#123—41no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402#121—21no—
403#121—21no—
404#121—41no—
405C4×Q8—21no—
406C4×Q8C23×C7311yescharacteristic
407C4×Q8C23×C7311yescharacteristic
408C4×D4—21no—
409C4×D4—21no—
410C4×D4—21no—
411C4×D4C23×C7311yescharacteristic
412C4×D4C23×C7311yescharacteristic
413#117—21no—
414C2×C4⋊C4—21no—
415#107—21no—
416#106—21no—
417#106D4×C7311yescharacteristic
418#106D4×C7311yescharacteristic
419C4⋊C8—21no—
420C4⋊C8—21no—
421C4⋊C8C23×C7311yescharacteristic
422C4⋊C8C23×C7311yescharacteristic
423C4⋊C8C23×C7311yescharacteristic
424C4⋊C8C23×C7311yescharacteristic
425#103—21no—
426#103—21no—
427#103—21no—
428#103—21no—
429#103—21no—
430#103D4×C7311yescharacteristic
431#103D4×C7311yescharacteristic
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—41no—
440#102—41no—
441#102D4×C7311yescharacteristic
442#102D4×C7311yescharacteristic
443C22⋊C8—21no—
444C22⋊C8—21no—
445#97—21no—
446C4×C8—21no—
447C4×C8C23×C7311yescharacteristic
448C4×C8C23×C7311yescharacteristic
449C4×C8C23×C7311yescharacteristic
450#41—42no—
451#41—42no—
452#41—81no—
453#41—81no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8C2×D4×C7311yescharacteristic
457C2×Q8C2×D4×C7311yescharacteristic
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4C2×D4×C7311yescharacteristic
468C2×D4C2×D4×C7311yescharacteristic
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474Q16—81no—
475Q16—81no—
476SD16—41no—
477SD16—41no—
478SD16—42no—
479SD16—81no—
480SD16—81no—
481D8—42no—
482D8—81no—
483D8—81no—
484D8—81no—
485D8—81no—
486M16—81no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—81no—
493C2×C8C2×D4×C7311yescharacteristic
494C2×C8C2×D4×C7311yescharacteristic
495C2×C8C2×D4×C7311yescharacteristic
496C2×C8C2×D4×C7311yescharacteristic
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4C2×D4×C7311yescharacteristic
506C4⋊C4C2×D4×C7311yescharacteristic
507C4⋊C4C2×D4×C7311yescharacteristic
508C4⋊C4C2×D4×C7311yescharacteristic
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C42—21no—
519C42—21no—
520C42—41no—
521C42C24×C7311yescharacteristic
522C23—21no—
523C23—21no—
524C23—41no—
525C23—41no—
526Q8—21no—
527Q8—21no—
528Q8—21no—
529Q8—21no—
530Q8—41no—
531Q8—41no—
532Q8—41no—
533Q8—41no—
534D4—21no—
535D4—21no—
536D4—21no—
537D4—21no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—81no—
547D4—81no—
548D4—82no—
549D4—82no—
550D4—161no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—82no—
564C2×C4—82no—
565C2×C4—161no—
566C2×C4C22×D4×C7311yescharacteristic
567C2×C4C22×D4×C7311yescharacteristic
568C2×C4H(5,𝔽2)×C7311yescharacteristic
569C8—21no—
570C8—21no—
571C8—21no—
572C8—21no—
573C8—41no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22D42×C7311yescharacteristic
591C4—21no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—81no—
599C4—81no—
600C4#575×C7311yescharacteristic
601C4#575×C7311yescharacteristic
602C4#576×C7311yescharacteristic
603C4#576×C7311yescharacteristic
604C2—81no—
605C2—81no—
606C2—161no—
607C2—161no—
608C2C73×#326811yescharacteristic
609C2C73×#326811yescharacteristic
610C2C73×#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×#3332C2semidirect
4. C73×#3302C2semidirect
5. C73×#1717C2semidirect
6. C73×#1700C2semidirect
7. C73×#1685C2semidirect
8. C73×#1682C2semidirect
9. C73×#1667C2semidirect
10. C73×#1641C2semidirect
11. C73×#1640C2semidirect
12. C73×#1628C2semidirect
13. C73×#1625C2semidirect
14. C73×#1588C2semidirect
15. C73×#1585C2semidirect
298. #20139C73direct (N × H)
306. #3399C2×C73semidirect
307. #3394C2×C73semidirect
308. #3332C2×C73semidirect
309. #3302C2×C73semidirect
310. #1717C2×C73semidirect
311. #1700C2×C73semidirect
312. #1685C2×C73semidirect
313. #1682C2×C73semidirect
314. #1667C2×C73semidirect
315. #1641C2×C73semidirect
316. #1640C2×C73semidirect
317. #1628C2×C73semidirect
318. #1625C2×C73semidirect
319. #1588C2×C73semidirect
320. #1585C2×C73semidirect
321. C73#20139direct (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×#33942
C73×#33322
C73×#33022
C73×#17172
C73×#17002
C73×#16852
C73×#16822
C73×#16672
C73×#16412
C73×#16402
C73×#16282
C73×#16252
C73×#15882
C73×#15852
#2013973