Finite Group Databasebeta

← C73×#19841 #32929245

Subgroups — C73×#19841 #32929245

Order 18688.

610 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3396C211yesmaximal, characteristic, complemented
2C73×#3373C211yesmaximal, characteristic, complemented
3C73×#3361C211yesmaximal, characteristic, complemented
4C73×#3299C211yesmaximal, characteristic, complemented
5C73×#1717C211yesmaximal, characteristic, complemented
6C73×#1698C211yesmaximal, characteristic, complemented
7C73×#1684C211yesmaximal, characteristic, complemented
8C73×#1682C211yesmaximal, characteristic, complemented
9C73×#1667C211yesmaximal, characteristic
10C73×#1640C211yesmaximal, characteristic, complemented
11C73×#1630C211yesmaximal, characteristic, complemented
12C73×#1627C211yesmaximal, characteristic, complemented
13C73×#1622C211yesmaximal, characteristic, complemented
14C73×#1584C211yesmaximal, characteristic, complemented
15C73×SD16⋊C8C211yesmaximal, characteristic, complemented
16#559×C73C2211yescharacteristic
17#559×C73C2211yescharacteristic
18#554×C73C2211yescharacteristic
19D4×Q8×C73C2211yescharacteristic
20#495×C73—21no—
21#493×C73C2211yescharacteristic
22#492×C73C2211yescharacteristic
23#489×C73—21no—
24#488×C73—21no—
25#487×C73C2211yescharacteristic
26#486×C73C2211yescharacteristic
27#486×C73C2211yescharacteristic
28#486×C73C2211yescharacteristic
29#484×C73—21no—
30#478×C73—21no—
31#477×C73C2211yescharacteristic
32#477×C73C2211yescharacteristic
33#476×C73—21no—
34#475×C73C2211yescharacteristic
35#467×C73—21no—
36#463×C73—21no—
37#463×C73—21no—
38#463×C73—21no—
39#463×C73—21no—
40#462×C73C2211yescharacteristic
41#460×C73C2211yescharacteristic
42#460×C73C2211yescharacteristic
43#459×C73C2211yescharacteristic
44#459×C73C2211yescharacteristic
45#451×C73—21no—
46#446×C73C2211yescharacteristic
47C8×Q8×C73C2211yescharacteristic
48C8×Q8×C73C2211yescharacteristic
49#442×C73—21no—
50C4×Q16×C73C2211yescharacteristic
51C4×SD16×C73C2211yescharacteristic
52C4×D8×C73—21no—
53C4×D8×C73—21no—
54C8×D4×C73C2211yescharacteristic
55C2×#103×C73—21no—
56#335×C73C2211yescharacteristic
57#335×C73C2211yescharacteristic
58#333×C73C2211yescharacteristic
59#332×C73C2211yescharacteristic
60#331×C73C2211yescharacteristic
61#331×C73C2211yescharacteristic
62Q8⋊C8×C73C2211yescharacteristic
63Q8⋊C8×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C22×Q8×C73—21no—
68C2×Q16×C73—21no—
69C2×Q16×C73D411yescharacteristic
70C2×SD16×C73—21no—
71C2×SD16×C73—21no—
72C2×SD16×C73—41no—
73C2×SD16×C73D411yescharacteristic
74C2×D8×C73—21no—
75C2×D8×C73—21no—
76C2×D8×C73—21no—
77C2×D8×C73—21no—
78C22×C8×C73—21no—
79C4⋊Q8×C73—21no—
80C4⋊Q8×C73C2311yescharacteristic
81C4⋊Q8×C73C2311yescharacteristic
82#127×C73C2311yescharacteristic
83#127×C73C2311yescharacteristic
84#125×C73—21no—
85#124×C73—21no—
86#124×C73—21no—
87#124×C73—21no—
88#124×C73—21no—
89#123×C73—41no—
90#123×C73—41no—
91C22⋊Q8×C73—21no—
92C22⋊Q8×C73—21no—
93C22⋊Q8×C73—41no—
94C22⋊Q8×C73—41no—
95C4×Q8×C73C2311yescharacteristic
96C4×Q8×C73C2311yescharacteristic
97C4×Q8×C73C2311yescharacteristic
98C4×D4×C73—21no—
99C4×D4×C73—21no—
100C4×D4×C73—21no—
101C4×D4×C73—21no—
102C4×D4×C73—21no—
103C4×D4×C73—21no—
104C4×D4×C73C2311yescharacteristic
105C2×C4⋊C4×C73—21no—
106#107×C73—21no—
107#107×C73—21no—
108#107×C73D411yescharacteristic
109#106×C73—21no—
110#106×C73D411yescharacteristic
111C4⋊C8×C73—21no—
112C4⋊C8×C73—21no—
113C4⋊C8×C73—21no—
114C4⋊C8×C73C2311yescharacteristic
115C4⋊C8×C73C2311yescharacteristic
116C4⋊C8×C73C2311yescharacteristic
117C4⋊C8×C73C2311yescharacteristic
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×C73D411yescharacteristic
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—21no—
135#102×C73—41no—
136#102×C73D411yescharacteristic
137C22⋊C8×C73—21no—
138#97×C73—21no—
139C4×C8×C73—21no—
140C4×C8×C73—21no—
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C2×Q8×C73—21no—
145C2×Q8×C73—21no—
146C2×Q8×C73—41no—
147C2×Q8×C73—42no—
148C2×Q8×C73—81no—
149C2×Q8×C73C2×D411yescharacteristic
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×C73C2×D411yescharacteristic
159C22×C4×C73—21no—
160C22×C4×C73—41no—
161C22×C4×C73—41no—
162C22×C4×C73—41no—
163C22×C4×C73—41no—
164Q16×C73—41no—
165Q16×C73—81no—
166SD16×C73—22no—
167SD16×C73—81no—
168SD16×C73—81no—
169SD16×C73—82no—
170D8×C73—42no—
171D8×C73—42no—
172D8×C73—42no—
173D8×C73—81no—
174C2×C8×C73—21no—
175C2×C8×C73—21no—
176C2×C8×C73—21no—
177C2×C8×C73—21no—
178C2×C8×C73—21no—
179C2×C8×C73—81no—
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—41no—
192C4⋊C4×C73—41no—
193C4⋊C4×C73—41no—
194C4⋊C4×C73C2×D411yescharacteristic
195C4⋊C4×C73C2×D411yescharacteristic
196C4⋊C4×C73C2×D411yescharacteristic
197C4⋊C4×C73C2×D411yescharacteristic
198C22⋊C4×C73—21no—
199C22⋊C4×C73—41no—
200C22⋊C4×C73—41no—
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×C73C2411yescharacteristic
211C23×C73—21no—
212C23×C73—41no—
213C23×C73—41no—
214Q8×C73—21no—
215Q8×C73—21no—
216Q8×C73—21no—
217Q8×C73—21no—
218Q8×C73—21no—
219Q8×C73—21no—
220Q8×C73—41no—
221Q8×C73—41no—
222Q8×C73—81no—
223Q8×C73—82no—
224D4×C73—21no—
225D4×C73—41no—
226D4×C73—41no—
227D4×C73—41no—
228D4×C73—41no—
229D4×C73—41no—
230D4×C73—41no—
231D4×C73—41no—
232D4×C73—41no—
233D4×C73—81no—
234D4×C73—81no—
235D4×C73#13512yes—
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—82no—
248C2×C4×C73—161no—
249C2×C4×C73—161no—
250C2×C4×C73—161no—
251C2×C4×C73C22×D411yescharacteristic
252C2×C4×C73C22×D411yescharacteristic
253C2×C4×C73H(5,𝔽2)11yescharacteristic
254C8×C73—21no—
255C8×C73—21no—
256C8×C73—21no—
257C8×C73—21no—
258C8×C73—41no—
259C8×C73—41no—
260C8×C73—41no—
261C8×C73—41no—
262C8×C73—41no—
263C22×C73—22no—
264C22×C73—41no—
265C22×C73—41no—
266C22×C73—81no—
267C22×C73—81no—
268C22×C73—81no—
269C22×C73—81no—
270C22×C73—81no—
271C22×C73—81no—
272C22×C73D4211yescharacteristic
273C4×C73—21no—
274C4×C73—41no—
275C4×C73—41no—
276C4×C73—41no—
277C4×C73—41no—
278C4×C73—41no—
279C4×C73—41no—
280C4×C73—41no—
281C4×C73—81no—
282C4×C73—81no—
283C4×C73C2×#13511yescharacteristic
284C4×C73#57511yescharacteristic
285C4×C73#57611yescharacteristic
286C4×C73#57811yescharacteristic
287#19841C7311yesmaximal, characteristic, direct product factor, Sylow
288C2×C73—42no—
289C2×C73—161no—
290C2×C73—161no—
291C2×C73#326811yescharacteristic
292C2×C73#328511yescharacteristic
293C2×C73#328811yescharacteristic
294#3396C2×C7311yescharacteristic, complemented
295#3373C2×C7311yescharacteristic, complemented
296#3361C2×C7311yescharacteristic, complemented
297#3299C2×C7311yescharacteristic, complemented
298#1717C2×C7311yescharacteristic, complemented
299#1698C2×C7311yescharacteristic, complemented
300#1684C2×C7311yescharacteristic, complemented
301#1682C2×C7311yescharacteristic, complemented
302#1667C2×C7311yescharacteristic
303#1640C2×C7311yescharacteristic, complemented
304#1630C2×C7311yescharacteristic, complemented
305#1627C2×C7311yescharacteristic, complemented
306#1622C2×C7311yescharacteristic, complemented
307#1584C2×C7311yescharacteristic, complemented
308SD16⋊C8C2×C7311yescharacteristic, complemented
309C73#1984111yescharacteristic, direct product factor, Sylow
310#559C22×C7311yescharacteristic
311#559C22×C7311yescharacteristic
312#554C22×C7311yescharacteristic
313D4×Q8C22×C7311yescharacteristic
314#495—21no—
315#493C22×C7311yescharacteristic
316#492C22×C7311yescharacteristic
317#489—21no—
318#488—21no—
319#487C22×C7311yescharacteristic
320#486C22×C7311yescharacteristic
321#486C22×C7311yescharacteristic
322#486C22×C7311yescharacteristic
323#484—21no—
324#478—21no—
325#477C22×C7311yescharacteristic
326#477C22×C7311yescharacteristic
327#476—21no—
328#475C22×C7311yescharacteristic
329#467—21no—
330#463—21no—
331#463—21no—
332#463—21no—
333#463—21no—
334#462C22×C7311yescharacteristic
335#460C22×C7311yescharacteristic
336#460C22×C7311yescharacteristic
337#459C22×C7311yescharacteristic
338#459C22×C7311yescharacteristic
339#451—21no—
340#446C22×C7311yescharacteristic
341C8×Q8C22×C7311yescharacteristic
342C8×Q8C22×C7311yescharacteristic
343#442—21no—
344C4×Q16C22×C7311yescharacteristic
345C4×SD16C22×C7311yescharacteristic
346C4×D8—21no—
347C4×D8—21no—
348C8×D4C22×C7311yescharacteristic
349C2×#103—21no—
350#335C22×C7311yescharacteristic
351#335C22×C7311yescharacteristic
352#333C22×C7311yescharacteristic
353#332C22×C7311yescharacteristic
354#331C22×C7311yescharacteristic
355#331C22×C7311yescharacteristic
356Q8⋊C8C22×C7311yescharacteristic
357Q8⋊C8C22×C7311yescharacteristic
358Q8⋊C8C22×C7311yescharacteristic
359D4⋊C8C22×C7311yescharacteristic
360#322C22×C7311yescharacteristic
361C22×Q8—21no—
362C2×Q16—21no—
363C2×Q16D4×C7311yescharacteristic
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—41no—
367C2×SD16D4×C7311yescharacteristic
368C2×D8—21no—
369C2×D8—21no—
370C2×D8—21no—
371C2×D8—21no—
372C22×C8—21no—
373C4⋊Q8—21no—
374C4⋊Q8C23×C7311yescharacteristic
375C4⋊Q8C23×C7311yescharacteristic
376#127C23×C7311yescharacteristic
377#127C23×C7311yescharacteristic
378#125—21no—
379#124—21no—
380#124—21no—
381#124—21no—
382#124—21no—
383#123—41no—
384#123—41no—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387C22⋊Q8—41no—
388C22⋊Q8—41no—
389C4×Q8C23×C7311yescharacteristic
390C4×Q8C23×C7311yescharacteristic
391C4×Q8C23×C7311yescharacteristic
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4C23×C7311yescharacteristic
399C2×C4⋊C4—21no—
400#107—21no—
401#107—21no—
402#107D4×C7311yescharacteristic
403#106—21no—
404#106D4×C7311yescharacteristic
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8—21no—
408C4⋊C8C23×C7311yescharacteristic
409C4⋊C8C23×C7311yescharacteristic
410C4⋊C8C23×C7311yescharacteristic
411C4⋊C8C23×C7311yescharacteristic
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103D4×C7311yescharacteristic
419#103D4×C7311yescharacteristic
420#103D4×C7311yescharacteristic
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—41no—
430#102D4×C7311yescharacteristic
431C22⋊C8—21no—
432#97—21no—
433C4×C8—21no—
434C4×C8—21no—
435C4×C8C23×C7311yescharacteristic
436C4×C8C23×C7311yescharacteristic
437C4×C8C23×C7311yescharacteristic
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—41no—
441C2×Q8—42no—
442C2×Q8—81no—
443C2×Q8C2×D4×C7311yescharacteristic
444C2×Q8C2×D4×C7311yescharacteristic
445C2×Q8C2×D4×C7311yescharacteristic
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4C2×D4×C7311yescharacteristic
453C22×C4—21no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458Q16—41no—
459Q16—81no—
460SD16—22no—
461SD16—81no—
462SD16—81no—
463SD16—82no—
464D8—42no—
465D8—42no—
466D8—42no—
467D8—81no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—81no—
474C2×C8C2×D4×C7311yescharacteristic
475C2×C8C2×D4×C7311yescharacteristic
476C2×C8C2×D4×C7311yescharacteristic
477C2×C8C2×D4×C7311yescharacteristic
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
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—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42C24×C7311yescharacteristic
505C23—21no—
506C23—41no—
507C23—41no—
508Q8—21no—
509Q8—21no—
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—21no—
514Q8—41no—
515Q8—41no—
516Q8—81no—
517Q8—82no—
518D4—21no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—81no—
528D4—81no—
529D4#135×C7312yes—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—82no—
542C2×C4—161no—
543C2×C4—161no—
544C2×C4—161no—
545C2×C4C22×D4×C7311yescharacteristic
546C2×C4C22×D4×C7311yescharacteristic
547C2×C4H(5,𝔽2)×C7311yescharacteristic
548C8—21no—
549C8—21no—
550C8—21no—
551C8—21no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—41no—
557C22—22no—
558C22—41no—
559C22—41no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22D42×C7311yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—81no—
576C4—81no—
577C4C2×#135×C7311yescharacteristic
578C4#575×C7311yescharacteristic
579C4#576×C7311yescharacteristic
580C4#578×C7311yescharacteristic
581C2—42no—
582C2—161no—
583C2—161no—
584C2C73×#326811yescharacteristic
585C2C73×#328511yescharacteristic
586C2C73×#328811yescharacteristic
subgroupG/H
center, socleC22×C73D42
commutator, Frattini, cosocleC42C24×C73
prime radicalC73×#1667C2
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×#3396C2semidirect
2. C73×#3373C2semidirect
3. C73×#3361C2semidirect
4. C73×#3299C2semidirect
5. C73×#1717C2semidirect
6. C73×#1698C2semidirect
7. C73×#1684C2semidirect
8. C73×#1682C2semidirect
10. C73×#1640C2semidirect
11. C73×#1630C2semidirect
12. C73×#1627C2semidirect
13. C73×#1622C2semidirect
14. C73×#1584C2semidirect
15. C73×SD16⋊C8C2semidirect
287. #19841C73direct (N × H)
294. #3396C2×C73semidirect
295. #3373C2×C73semidirect
296. #3361C2×C73semidirect
297. #3299C2×C73semidirect
298. #1717C2×C73semidirect
299. #1698C2×C73semidirect
300. #1684C2×C73semidirect
301. #1682C2×C73semidirect
303. #1640C2×C73semidirect
304. #1630C2×C73semidirect
305. #1627C2×C73semidirect
306. #1622C2×C73semidirect
307. #1584C2×C73semidirect
308. SD16⋊C8C2×C73semidirect
309. C73#19841direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#33962
C73×#33732
C73×#33612
C73×#32992
C73×#17172
C73×#16982
C73×#16842
C73×#16822
C73×#16672
C73×#16402
C73×#16302
C73×#16272
C73×#16222
C73×#15842
C73×SD16⋊C82
#1984173