Finite Group Databasebeta

← C73×#19735 #32929139

Subgroups — C73×#19735 #32929139

Order 18688.

780 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3228C211yesmaximal, characteristic, complemented
2C73×#3210C211yesmaximal, characteristic, complemented
3C73×#3208C211yesmaximal, characteristic, complemented
4C73×#3207C211yesmaximal, characteristic, complemented
5C73×#3205C211yesmaximal, characteristic, complemented
6C73×#3205C211yesmaximal, characteristic, complemented
7C73×#1721C211yesmaximal, characteristic, complemented
8C73×#1721C211yesmaximal, characteristic, complemented
9C73×#1720C211yesmaximal, characteristic, complemented
10C73×#1719C211yesmaximal, characteristic, complemented
11C73×#1717C211yesmaximal, characteristic, complemented
12C73×#1715C211yesmaximal, characteristic, complemented
13C73×#1709C211yesmaximal, characteristic, complemented
14C73×#1706C211yesmaximal, characteristic, complemented
15C73×#1454C211yesmaximal, characteristic, complemented
16#533×C73C2211yescharacteristic
17#532×C73C2211yescharacteristic
18#532×C73C2211yescharacteristic
19C2×#127×C73C2211yescharacteristic
20#500×C73C2211yescharacteristic, complemented
21#498×C73C2211yescharacteristic, complemented
22#494×C73C2211yescharacteristic, complemented
23#493×C73C2211yescharacteristic
24#493×C73C2211yescharacteristic
25#493×C73C2211yescharacteristic
26#493×C73C2211yescharacteristic
27#493×C73C2211yescharacteristic, complemented
28#492×C73C2211yescharacteristic
29#492×C73C2211yescharacteristic
30#492×C73C2211yescharacteristic, complemented
31#492×C73C2211yescharacteristic, complemented
32#487×C73C2211yescharacteristic, complemented
33#487×C73C2211yescharacteristic, complemented
34#486×C73C2211yescharacteristic
35#486×C73C2211yescharacteristic
36#486×C73C2211yescharacteristic
37#486×C73C2211yescharacteristic
38#486×C73C2211yescharacteristic
39#486×C73C2211yescharacteristic
40#486×C73C2211yescharacteristic, complemented
41#486×C73C2211yescharacteristic, complemented
42#486×C73C2211yescharacteristic, complemented
43#486×C73C2211yescharacteristic, complemented
44#482×C73—22no—
45#478×C73—22no—
46#464×C73—22no—
47#463×C73—22no—
48#460×C73—22no—
49#459×C73—22no—
50#459×C73—22no—
51#452×C73—22no—
52#450×C73—22no—
53#449×C73—22no—
54#447×C73—22no—
55#447×C73—22no—
56#431×C73C2211yescharacteristic
57#431×C73C2211yescharacteristic
58#431×C73C2211yescharacteristic
59#322×C73C2211yescharacteristic, complemented
60#322×C73C2211yescharacteristic, complemented
61#322×C73C2211yescharacteristic, complemented
62C82×C73C2211yescharacteristic, complemented
63C2×#41×C73—21no—
64C2×#41×C73—21no—
65C22×D4×C73—21no—
66C22×D4×C73—21no—
67C22×D4×C73—21no—
68C2×Q16×C73—22no—
69C2×SD16×C73—22no—
70C2×SD16×C73—22no—
71C2×SD16×C73—22no—
72C2×SD16×C73—22no—
73C2×D8×C73—22no—
74C2×D8×C73—22no—
75C2×D8×C73—22no—
76C2×D8×C73—22no—
77C2×D8×C73—22no—
78C4⋊Q8×C73C2311yescharacteristic
79C4⋊Q8×C73C2311yescharacteristic
80C4⋊Q8×C73C2311yescharacteristic
81C4⋊Q8×C73C2311yescharacteristic
82#127×C73—21no—
83#127×C73—21no—
84#127×C73—21no—
85#127×C73C2311yescharacteristic
86#127×C73C2311yescharacteristic
87#127×C73C2311yescharacteristic
88#127×C73C2311yescharacteristic
89#125×C73—21no—
90#124×C73—21no—
91#124×C73—21no—
92C22⋊Q8×C73—21no—
93C22⋊Q8×C73—21no—
94#121×C73—21no—
95#121×C73—21no—
96#121×C73—21no—
97#121×C73—21no—
98C4×Q8×C73—21no—
99C4×Q8×C73—21no—
100C4×D4×C73—21no—
101C4×D4×C73—21no—
102C4×D4×C73—21no—
103C4×D4×C73—21no—
104#117×C73—21no—
105C2×C42×C73C2311yescharacteristic
106#107×C73—22no—
107#106×C73—22no—
108C4⋊C8×C73D412yes—
109C4⋊C8×C73D412yes—
110C4⋊C8×C73D412yes—
111#103×C73—22no—
112#103×C73—22no—
113#102×C73—22no—
114#102×C73—22no—
115#102×C73—22no—
116#102×C73—22no—
117#102×C73—22no—
118#102×C73—22no—
119#102×C73—22no—
120#102×C73—22no—
121#102×C73—22no—
122#102×C73—22no—
123C22⋊C8×C73D412yes—
124C22⋊C8×C73D412yes—
125C22⋊C8×C73D412yes—
126C4×C8×C73C2311yescharacteristic
127C4×C8×C73C2311yescharacteristic
128C4×C8×C73C2311yescharacteristic
129C4×C8×C73C2311yescharacteristic
130C4×C8×C73C2311yescharacteristic
131C4×C8×C73C2311yescharacteristic
132C24×C73—41no—
133#41×C73—82no—
134#41×C73—82no—
135C2×Q8×C73—21no—
136C2×Q8×C73—21no—
137C2×Q8×C73—21no—
138C2×Q8×C73—21no—
139C2×D4×C73—21no—
140C2×D4×C73—21no—
141C2×D4×C73—21no—
142C2×D4×C73—21no—
143C2×D4×C73—21no—
144C2×D4×C73—21no—
145C2×D4×C73—21no—
146C2×D4×C73—21no—
147C2×D4×C73—21no—
148C2×D4×C73—21no—
149C2×D4×C73—21no—
150C2×D4×C73—21no—
151C2×D4×C73—41no—
152C2×D4×C73—41no—
153C2×D4×C73—41no—
154C2×D4×C73—41no—
155C2×D4×C73—41no—
156C2×D4×C73—82no—
157C2×D4×C73—82no—
158C2×D4×C73—82no—
159C22×C4×C73—41no—
160C22×C4×C73—41no—
161C22×C4×C73C2×D411yescharacteristic
162C22×C4×C73C2×D411yescharacteristic
163C22×C4×C73C2×D411yescharacteristic
164Q16×C73—82no—
165SD16×C73—82no—
166SD16×C73—82no—
167SD16×C73—82no—
168SD16×C73—82no—
169D8×C73—82no—
170D8×C73—82no—
171D8×C73—82no—
172D8×C73—82no—
173D8×C73—82no—
174C2×C8×C73C2×D412yes—
175C2×C8×C73C2×D412yes—
176C2×C8×C73C2×D412yes—
177C2×C8×C73C2×D412yes—
178C2×C8×C73C2×D412yes—
179C2×C8×C73C2×D412yes—
180C4⋊C4×C73—21no—
181C4⋊C4×C73—21no—
182C4⋊C4×C73—21no—
183C4⋊C4×C73—21no—
184C4⋊C4×C73—21no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—21no—
188C4⋊C4×C73—41no—
189C4⋊C4×C73—41no—
190C22⋊C4×C73—41no—
191C22⋊C4×C73—41no—
192C22⋊C4×C73—41no—
193C22⋊C4×C73—41no—
194C22⋊C4×C73—41no—
195C42×C73—41no—
196C42×C73C2×D411yescharacteristic
197C42×C73C2×D411yescharacteristic
198C42×C73C2×D411yescharacteristic
199C42×C73C2411yescharacteristic
200C23×C73—41no—
201C23×C73—41no—
202C23×C73—41no—
203C23×C73—41no—
204C23×C73—82no—
205C23×C73—82no—
206C23×C73—82no—
207C23×C73#12711yescharacteristic
208Q8×C73—42no—
209Q8×C73—42no—
210Q8×C73—42no—
211Q8×C73—42no—
212D4×C73—42no—
213D4×C73—42no—
214D4×C73—42no—
215D4×C73—42no—
216D4×C73—42no—
217D4×C73—42no—
218D4×C73—42no—
219D4×C73—42no—
220D4×C73—42no—
221D4×C73—42no—
222D4×C73—42no—
223D4×C73—42no—
224D4×C73—82no—
225D4×C73—82no—
226D4×C73—82no—
227D4×C73—82no—
228D4×C73—82no—
229C2×C4×C73—22no—
230C2×C4×C73—22no—
231C2×C4×C73—22no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73—41no—
236C2×C4×C73—82no—
237C2×C4×C73—82no—
238C2×C4×C73#12711yescharacteristic
239C2×C4×C73#12711yescharacteristic
240C2×C4×C73#12711yescharacteristic
241C2×C4×C73C22×D411yescharacteristic
242C2×C4×C73C22×D411yescharacteristic
243C2×C4×C73C22×D411yescharacteristic
244C8×C73—22no—
245C8×C73—22no—
246C8×C73—22no—
247C8×C73—22no—
248C8×C73—22no—
249C8×C73—22no—
250C22×C73—21no—
251C22×C73—21no—
252C22×C73—21no—
253C22×C73—81no—
254C22×C73—81no—
255C22×C73—81no—
256C22×C73—81no—
257C22×C73—81no—
258C22×C73—81no—
259C22×C73—81no—
260C22×C73—81no—
261C22×C73—81no—
262C22×C73—81no—
263C22×C73—81no—
264C22×C73—81no—
265C22×C73—164no—
266C22×C73C2×#12711yescharacteristic
267C4×C73—21no—
268C4×C73—21no—
269C4×C73—21no—
270C4×C73—81no—
271C4×C73—81no—
272C4×C73—81no—
273C4×C73—81no—
274C4×C73#57612yes—
275C4×C73#57612yes—
276C4×C73#57712yes—
277#19735C7311yesmaximal, characteristic, direct product factor, Sylow
278C2×C73—41no—
279C2×C73—161no—
280C2×C73—161no—
281C2×C73—161no—
282C2×C73—161no—
283C2×C73#315411yescharacteristic
284C2×C73#315511yescharacteristic
285C2×C73#315511yescharacteristic
286#3228C2×C7311yescharacteristic, complemented
287#3210C2×C7311yescharacteristic, complemented
288#3208C2×C7311yescharacteristic, complemented
289#3207C2×C7311yescharacteristic, complemented
290#3205C2×C7311yescharacteristic, complemented
291#3205C2×C7311yescharacteristic, complemented
292#1721C2×C7311yescharacteristic, complemented
293#1721C2×C7311yescharacteristic, complemented
294#1720C2×C7311yescharacteristic, complemented
295#1719C2×C7311yescharacteristic, complemented
296#1717C2×C7311yescharacteristic, complemented
297#1715C2×C7311yescharacteristic, complemented
298#1709C2×C7311yescharacteristic, complemented
299#1706C2×C7311yescharacteristic, complemented
300#1454C2×C7311yescharacteristic, complemented
301C73#1973511yescharacteristic, direct product factor, Sylow
302#533C22×C7311yescharacteristic
303#532C22×C7311yescharacteristic
304#532C22×C7311yescharacteristic
305C2×#127C22×C7311yescharacteristic
306#500C22×C7311yescharacteristic, complemented
307#498C22×C7311yescharacteristic, complemented
308#494C22×C7311yescharacteristic, complemented
309#493C22×C7311yescharacteristic
310#493C22×C7311yescharacteristic
311#493C22×C7311yescharacteristic
312#493C22×C7311yescharacteristic
313#493C22×C7311yescharacteristic, complemented
314#492C22×C7311yescharacteristic
315#492C22×C7311yescharacteristic
316#492C22×C7311yescharacteristic, complemented
317#492C22×C7311yescharacteristic, complemented
318#487C22×C7311yescharacteristic, complemented
319#487C22×C7311yescharacteristic, complemented
320#486C22×C7311yescharacteristic
321#486C22×C7311yescharacteristic
322#486C22×C7311yescharacteristic
323#486C22×C7311yescharacteristic
324#486C22×C7311yescharacteristic
325#486C22×C7311yescharacteristic
326#486C22×C7311yescharacteristic, complemented
327#486C22×C7311yescharacteristic, complemented
328#486C22×C7311yescharacteristic, complemented
329#486C22×C7311yescharacteristic, complemented
330#482—22no—
331#478—22no—
332#464—22no—
333#463—22no—
334#460—22no—
335#459—22no—
336#459—22no—
337#452—22no—
338#450—22no—
339#449—22no—
340#447—22no—
341#447—22no—
342#431C22×C7311yescharacteristic
343#431C22×C7311yescharacteristic
344#431C22×C7311yescharacteristic
345#322C22×C7311yescharacteristic, complemented
346#322C22×C7311yescharacteristic, complemented
347#322C22×C7311yescharacteristic, complemented
348C82C22×C7311yescharacteristic, complemented
349C2×#41—21no—
350C2×#41—21no—
351C22×D4—21no—
352C22×D4—21no—
353C22×D4—21no—
354C2×Q16—22no—
355C2×SD16—22no—
356C2×SD16—22no—
357C2×SD16—22no—
358C2×SD16—22no—
359C2×D8—22no—
360C2×D8—22no—
361C2×D8—22no—
362C2×D8—22no—
363C2×D8—22no—
364C4⋊Q8C23×C7311yescharacteristic
365C4⋊Q8C23×C7311yescharacteristic
366C4⋊Q8C23×C7311yescharacteristic
367C4⋊Q8C23×C7311yescharacteristic
368#127—21no—
369#127—21no—
370#127—21no—
371#127C23×C7311yescharacteristic
372#127C23×C7311yescharacteristic
373#127C23×C7311yescharacteristic
374#127C23×C7311yescharacteristic
375#125—21no—
376#124—21no—
377#124—21no—
378C22⋊Q8—21no—
379C22⋊Q8—21no—
380#121—21no—
381#121—21no—
382#121—21no—
383#121—21no—
384C4×Q8—21no—
385C4×Q8—21no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4—21no—
390#117—21no—
391C2×C42C23×C7311yescharacteristic
392#107—22no—
393#106—22no—
394C4⋊C8D4×C7312yes—
395C4⋊C8D4×C7312yes—
396C4⋊C8D4×C7312yes—
397#103—22no—
398#103—22no—
399#102—22no—
400#102—22no—
401#102—22no—
402#102—22no—
403#102—22no—
404#102—22no—
405#102—22no—
406#102—22no—
407#102—22no—
408#102—22no—
409C22⋊C8D4×C7312yes—
410C22⋊C8D4×C7312yes—
411C22⋊C8D4×C7312yes—
412C4×C8C23×C7311yescharacteristic
413C4×C8C23×C7311yescharacteristic
414C4×C8C23×C7311yescharacteristic
415C4×C8C23×C7311yescharacteristic
416C4×C8C23×C7311yescharacteristic
417C4×C8C23×C7311yescharacteristic
418C24—41no—
419#41—82no—
420#41—82no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—82no—
443C2×D4—82no—
444C2×D4—82no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4C2×D4×C7311yescharacteristic
448C22×C4C2×D4×C7311yescharacteristic
449C22×C4C2×D4×C7311yescharacteristic
450Q16—82no—
451SD16—82no—
452SD16—82no—
453SD16—82no—
454SD16—82no—
455D8—82no—
456D8—82no—
457D8—82no—
458D8—82no—
459D8—82no—
460C2×C8C2×D4×C7312yes—
461C2×C8C2×D4×C7312yes—
462C2×C8C2×D4×C7312yes—
463C2×C8C2×D4×C7312yes—
464C2×C8C2×D4×C7312yes—
465C2×C8C2×D4×C7312yes—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C42—41no—
482C42C2×D4×C7311yescharacteristic
483C42C2×D4×C7311yescharacteristic
484C42C2×D4×C7311yescharacteristic
485C42C24×C7311yescharacteristic
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—82no—
491C23—82no—
492C23—82no—
493C23#127×C7311yescharacteristic
494Q8—42no—
495Q8—42no—
496Q8—42no—
497Q8—42no—
498D4—42no—
499D4—42no—
500D4—42no—
501D4—42no—
502D4—42no—
503D4—42no—
504D4—42no—
505D4—42no—
506D4—42no—
507D4—42no—
508D4—42no—
509D4—42no—
510D4—82no—
511D4—82no—
512D4—82no—
513D4—82no—
514D4—82no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—82no—
523C2×C4—82no—
524C2×C4#127×C7311yescharacteristic
525C2×C4#127×C7311yescharacteristic
526C2×C4#127×C7311yescharacteristic
527C2×C4C22×D4×C7311yescharacteristic
528C2×C4C22×D4×C7311yescharacteristic
529C2×C4C22×D4×C7311yescharacteristic
530C8—22no—
531C8—22no—
532C8—22no—
533C8—22no—
534C8—22no—
535C8—22no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22—81no—
551C22—164no—
552C22C2×#127×C7311yescharacteristic
553C4—21no—
554C4—21no—
555C4—21no—
556C4—81no—
557C4—81no—
558C4—81no—
559C4—81no—
560C4#576×C7312yes—
561C4#576×C7312yes—
562C4#577×C7312yes—
563C2—41no—
564C2—161no—
565C2—161no—
566C2—161no—
567C2—161no—
568C2C73×#315411yescharacteristic
569C2C73×#315511yescharacteristic
570C2C73×#315511yescharacteristic
subgroupG/H
center, socleC22×C73C2×#127
commutator, Frattini, cosocleC42C24×C73
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3228C2semidirect
2. C73×#3210C2semidirect
3. C73×#3208C2semidirect
4. C73×#3207C2semidirect
5. C73×#3205C2semidirect
6. C73×#3205C2semidirect
7. C73×#1721C2semidirect
8. C73×#1721C2semidirect
9. C73×#1720C2semidirect
10. C73×#1719C2semidirect
11. C73×#1717C2semidirect
12. C73×#1715C2semidirect
13. C73×#1709C2semidirect
14. C73×#1706C2semidirect
15. C73×#1454C2semidirect
20. #500×C73C22semidirect
21. #498×C73C22semidirect
22. #494×C73C22semidirect
27. #493×C73C22semidirect
30. #492×C73C22semidirect
31. #492×C73C22semidirect
32. #487×C73C22semidirect
33. #487×C73C22semidirect
40. #486×C73C22semidirect
41. #486×C73C22semidirect
42. #486×C73C22semidirect
43. #486×C73C22semidirect
59. #322×C73C22semidirect
60. #322×C73C22semidirect
61. #322×C73C22semidirect
62. C82×C73C22semidirect
277. #19735C73direct (N × H)
286. #3228C2×C73semidirect
287. #3210C2×C73semidirect
288. #3208C2×C73semidirect
289. #3207C2×C73semidirect
290. #3205C2×C73semidirect
291. #3205C2×C73semidirect
292. #1721C2×C73semidirect
293. #1721C2×C73semidirect
294. #1720C2×C73semidirect
295. #1719C2×C73semidirect
296. #1717C2×C73semidirect
297. #1715C2×C73semidirect
298. #1709C2×C73semidirect
299. #1706C2×C73semidirect
300. #1454C2×C73semidirect
301. C73#19735direct (N × H)
306. #500C22×C73semidirect
307. #498C22×C73semidirect
308. #494C22×C73semidirect
313. #493C22×C73semidirect
316. #492C22×C73semidirect
317. #492C22×C73semidirect
318. #487C22×C73semidirect
319. #487C22×C73semidirect
326. #486C22×C73semidirect
327. #486C22×C73semidirect
328. #486C22×C73semidirect
329. #486C22×C73semidirect
345. #322C22×C73semidirect
346. #322C22×C73semidirect
347. #322C22×C73semidirect
348. C82C22×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#32282
C73×#32102
C73×#32082
C73×#32072
C73×#32052
C73×#17212
C73×#17202
C73×#17192
C73×#17172
C73×#17152
C73×#17092
C73×#17062
C73×#14542
#1973573