Finite Group Databasebeta

← C73×#19951 #32929355

Subgroups — C73×#19951 #32929355

Order 18688.

574 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3400C211yesmaximal, characteristic, complemented
2C73×#3364C211yesmaximal, characteristic, complemented
3C73×#3361C211yesmaximal, characteristic
4C73×#3356C211yesmaximal, characteristic, complemented
5C73×#1708C211yesmaximal, characteristic, complemented
6C73×#1692C211yesmaximal, characteristic, complemented
7C73×#1685C211yesmaximal, characteristic
8C73×#1680C211yesmaximal, characteristic, complemented
9C73×#1678C211yesmaximal, characteristic, complemented
10C73×#1644C211yesmaximal, characteristic, complemented
11C73×#1640C211yesmaximal, characteristic, complemented
12C73×#1636C211yesmaximal, characteristic, complemented
13C73×#1628C211yesmaximal, characteristic
14C73×#1590C211yesmaximal, characteristic, complemented
15C8×Q16×C73C211yesmaximal, characteristic, complemented
16#559×C73C2211yescharacteristic
17#557×C73C2211yescharacteristic
18#556×C73C2211yescharacteristic
19#554×C73C2211yescharacteristic
20#498×C73C2211yescharacteristic
21#497×C73—21no—
22#492×C73C2211yescharacteristic
23#488×C73—21no—
24#488×C73—21no—
25#487×C73C2211yescharacteristic
26#487×C73C2211yescharacteristic
27#486×C73C2211yescharacteristic
28#486×C73C2211yescharacteristic
29#485×C73—21no—
30#483×C73—21no—
31#479×C73—21no—
32#478×C73—21no—
33#477×C73C2211yescharacteristic
34#477×C73C2211yescharacteristic
35#475×C73C2211yescharacteristic
36#474×C73C2211yescharacteristic
37#470×C73—21no—
38#464×C73—21no—
39#464×C73—21no—
40#463×C73—21no—
41#462×C73C2211yescharacteristic
42#462×C73C2211yescharacteristic
43#461×C73—21no—
44#460×C73C2211yescharacteristic
45#459×C73C2211yescharacteristic
46#446×C73C2211yescharacteristic
47C8×Q8×C73C2211yescharacteristic
48C8×Q8×C73C2211yescharacteristic
49#440×C73—21no—
50C4×Q16×C73—21no—
51C4×Q16×C73C2211yescharacteristic
52C4×SD16×C73C2211yescharacteristic
53C4×D8×C73—21no—
54#436×C73C2211yescharacteristic
55#428×C73—21no—
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
66C82×C73C2211yescharacteristic
67C2×Q16×C73—21no—
68C2×Q16×C73—21no—
69C2×Q16×C73D411yescharacteristic
70C2×SD16×C73—21no—
71C2×SD16×C73—21no—
72C2×SD16×C73—21no—
73C2×SD16×C73D411yescharacteristic
74C2×D8×C73—21no—
75C2×M16×C73—21no—
76C4⋊Q8×C73—21no—
77C4⋊Q8×C73C2311yescharacteristic
78C4⋊Q8×C73C2311yescharacteristic
79C4⋊Q8×C73C2311yescharacteristic
80#127×C73C2311yescharacteristic
81#126×C73—41no—
82#125×C73—21no—
83#125×C73—21no—
84#125×C73—41no—
85#124×C73—21no—
86#124×C73—21no—
87#124×C73—21no—
88#123×C73—41no—
89C22⋊Q8×C73—21no—
90C22⋊Q8×C73—21no—
91C22⋊Q8×C73—41no—
92C4×Q8×C73—21no—
93C4×Q8×C73—21no—
94C4×Q8×C73—21no—
95C4×Q8×C73C2311yescharacteristic
96C4×Q8×C73C2311yescharacteristic
97C4×Q8×C73C2311yescharacteristic
98C4×D4×C73—21no—
99C4×D4×C73—21no—
100C4×D4×C73—21no—
101C4×D4×C73C2311yescharacteristic
102#117×C73—21no—
103C2×C4⋊C4×C73—21no—
104#107×C73—21no—
105#107×C73—21no—
106#107×C73—21no—
107#107×C73D411yescharacteristic
108#106×C73—21no—
109#106×C73—21no—
110#106×C73—21no—
111#106×C73D411yescharacteristic
112C4⋊C8×C73—21no—
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×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—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—21no—
147C2×Q8×C73C2×D411yescharacteristic
148C2×Q8×C73C2×D411yescharacteristic
149C2×Q8×C73C2×D411yescharacteristic
150C2×D4×C73—21no—
151C2×D4×C73—21no—
152C2×D4×C73—21no—
153C2×D4×C73C2×D411yescharacteristic
154C22×C4×C73—21no—
155C22×C4×C73—41no—
156C22×C4×C73—41no—
157Q16×C73—22no—
158Q16×C73—42no—
159Q16×C73—81no—
160SD16×C73—41no—
161SD16×C73—42no—
162SD16×C73—81no—
163SD16×C73—81no—
164D8×C73—42no—
165M16×C73—42no—
166C2×C8×C73—21no—
167C2×C8×C73—21no—
168C2×C8×C73—21no—
169C2×C8×C73—21no—
170C2×C8×C73—21no—
171C2×C8×C73C2×D411yescharacteristic
172C2×C8×C73C2×D411yescharacteristic
173C2×C8×C73C2×D411yescharacteristic
174C2×C8×C73C2×D411yescharacteristic
175C4⋊C4×C73—21no—
176C4⋊C4×C73—21no—
177C4⋊C4×C73—21no—
178C4⋊C4×C73—21no—
179C4⋊C4×C73—21no—
180C4⋊C4×C73—21no—
181C4⋊C4×C73—21no—
182C4⋊C4×C73—21no—
183C4⋊C4×C73—21no—
184C4⋊C4×C73—41no—
185C4⋊C4×C73—41no—
186C4⋊C4×C73—41no—
187C4⋊C4×C73—41no—
188C4⋊C4×C73—41no—
189C4⋊C4×C73—41no—
190C4⋊C4×C73C2×D411yescharacteristic
191C4⋊C4×C73C2×D411yescharacteristic
192C4⋊C4×C73C2×D411yescharacteristic
193C4⋊C4×C73C2×D411yescharacteristic
194C22⋊C4×C73—21no—
195C22⋊C4×C73—41no—
196C22⋊C4×C73—41no—
197C22⋊C4×C73—41no—
198C22⋊C4×C73—41no—
199C22⋊C4×C73—41no—
200C22⋊C4×C73—41no—
201C42×C73—21no—
202C42×C73—21no—
203C42×C73—21no—
204C42×C73—41no—
205C42×C73—41no—
206C42×C73C2411yescharacteristic
207C23×C73—21no—
208C23×C73—41no—
209Q8×C73—21no—
210Q8×C73—21no—
211Q8×C73—21no—
212Q8×C73—21no—
213Q8×C73—21no—
214Q8×C73—21no—
215Q8×C73—41no—
216Q8×C73—41no—
217Q8×C73—41no—
218Q8×C73—41no—
219Q8×C73—81no—
220D4×C73—21no—
221D4×C73—21no—
222D4×C73—41no—
223D4×C73—41no—
224D4×C73—41no—
225D4×C73—41no—
226D4×C73—81no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—21no—
233C2×C4×C73—21no—
234C2×C4×C73—41no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73—41no—
239C2×C4×C73—161no—
240C2×C4×C73—161no—
241C2×C4×C73C22×D411yescharacteristic
242C2×C4×C73C22×D411yescharacteristic
243C2×C4×C73H(5,𝔽2)11yescharacteristic
244C8×C73—21no—
245C8×C73—21no—
246C8×C73—21no—
247C8×C73—41no—
248C8×C73—41no—
249C8×C73—41no—
250C8×C73—41no—
251C8×C73—41no—
252C8×C73#13512yes—
253C22×C73—41no—
254C22×C73—41no—
255C22×C73—41no—
256C22×C73—81no—
257C22×C73—81no—
258C22×C73—81no—
259C22×C73D4211yescharacteristic
260C4×C73—21no—
261C4×C73—41no—
262C4×C73—41no—
263C4×C73—41no—
264C4×C73—41no—
265C4×C73—41no—
266C4×C73—41no—
267C4×C73—41no—
268C4×C73—81no—
269C4×C73—81no—
270C4×C73—81no—
271C4×C73C2×#13511yescharacteristic
272C4×C73#57511yescharacteristic
273C4×C73#57711yescharacteristic
274C4×C73#57811yescharacteristic
275#19951C7311yesmaximal, characteristic, direct product factor, Sylow
276C2×C73—81no—
277C2×C73—161no—
278C2×C73#327711yescharacteristic
279C2×C73#328411yescharacteristic
280C2×C73#329011yescharacteristic
281#3400C2×C7311yescharacteristic, complemented
282#3364C2×C7311yescharacteristic, complemented
283#3361C2×C7311yescharacteristic
284#3356C2×C7311yescharacteristic, complemented
285#1708C2×C7311yescharacteristic, complemented
286#1692C2×C7311yescharacteristic, complemented
287#1685C2×C7311yescharacteristic
288#1680C2×C7311yescharacteristic, complemented
289#1678C2×C7311yescharacteristic, complemented
290#1644C2×C7311yescharacteristic, complemented
291#1640C2×C7311yescharacteristic, complemented
292#1636C2×C7311yescharacteristic, complemented
293#1628C2×C7311yescharacteristic
294#1590C2×C7311yescharacteristic, complemented
295C8×Q16C2×C7311yescharacteristic, complemented
296C73#1995111yescharacteristic, direct product factor, Sylow
297#559C22×C7311yescharacteristic
298#557C22×C7311yescharacteristic
299#556C22×C7311yescharacteristic
300#554C22×C7311yescharacteristic
301#498C22×C7311yescharacteristic
302#497—21no—
303#492C22×C7311yescharacteristic
304#488—21no—
305#488—21no—
306#487C22×C7311yescharacteristic
307#487C22×C7311yescharacteristic
308#486C22×C7311yescharacteristic
309#486C22×C7311yescharacteristic
310#485—21no—
311#483—21no—
312#479—21no—
313#478—21no—
314#477C22×C7311yescharacteristic
315#477C22×C7311yescharacteristic
316#475C22×C7311yescharacteristic
317#474C22×C7311yescharacteristic
318#470—21no—
319#464—21no—
320#464—21no—
321#463—21no—
322#462C22×C7311yescharacteristic
323#462C22×C7311yescharacteristic
324#461—21no—
325#460C22×C7311yescharacteristic
326#459C22×C7311yescharacteristic
327#446C22×C7311yescharacteristic
328C8×Q8C22×C7311yescharacteristic
329C8×Q8C22×C7311yescharacteristic
330#440—21no—
331C4×Q16—21no—
332C4×Q16C22×C7311yescharacteristic
333C4×SD16C22×C7311yescharacteristic
334C4×D8—21no—
335#436C22×C7311yescharacteristic
336#428—21no—
337#335C22×C7311yescharacteristic
338#334C22×C7311yescharacteristic
339#333C22×C7311yescharacteristic
340#332C22×C7311yescharacteristic
341#332C22×C7311yescharacteristic
342#331C22×C7311yescharacteristic
343Q8⋊C8C22×C7311yescharacteristic
344Q8⋊C8C22×C7311yescharacteristic
345Q8⋊C8C22×C7311yescharacteristic
346D4⋊C8C22×C7311yescharacteristic
347C82C22×C7311yescharacteristic
348C2×Q16—21no—
349C2×Q16—21no—
350C2×Q16D4×C7311yescharacteristic
351C2×SD16—21no—
352C2×SD16—21no—
353C2×SD16—21no—
354C2×SD16D4×C7311yescharacteristic
355C2×D8—21no—
356C2×M16—21no—
357C4⋊Q8—21no—
358C4⋊Q8C23×C7311yescharacteristic
359C4⋊Q8C23×C7311yescharacteristic
360C4⋊Q8C23×C7311yescharacteristic
361#127C23×C7311yescharacteristic
362#126—41no—
363#125—21no—
364#125—21no—
365#125—41no—
366#124—21no—
367#124—21no—
368#124—21no—
369#123—41no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372C22⋊Q8—41no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8C23×C7311yescharacteristic
377C4×Q8C23×C7311yescharacteristic
378C4×Q8C23×C7311yescharacteristic
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4C23×C7311yescharacteristic
383#117—21no—
384C2×C4⋊C4—21no—
385#107—21no—
386#107—21no—
387#107—21no—
388#107D4×C7311yescharacteristic
389#106—21no—
390#106—21no—
391#106—21no—
392#106D4×C7311yescharacteristic
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8C23×C7311yescharacteristic
397C4⋊C8C23×C7311yescharacteristic
398C4⋊C8C23×C7311yescharacteristic
399C4⋊C8C23×C7311yescharacteristic
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—41no—
408#103D4×C7311yescharacteristic
409#103D4×C7311yescharacteristic
410#103D4×C7311yescharacteristic
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—41no—
417#102D4×C7311yescharacteristic
418C22⋊C8—21no—
419#97—21no—
420C4×C8—21no—
421C4×C8—21no—
422C4×C8C23×C7311yescharacteristic
423C4×C8C23×C7311yescharacteristic
424C4×C8C23×C7311yescharacteristic
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8C2×D4×C7311yescharacteristic
429C2×Q8C2×D4×C7311yescharacteristic
430C2×Q8C2×D4×C7311yescharacteristic
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4C2×D4×C7311yescharacteristic
435C22×C4—21no—
436C22×C4—41no—
437C22×C4—41no—
438Q16—22no—
439Q16—42no—
440Q16—81no—
441SD16—41no—
442SD16—42no—
443SD16—81no—
444SD16—81no—
445D8—42no—
446M16—42no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8C2×D4×C7311yescharacteristic
453C2×C8C2×D4×C7311yescharacteristic
454C2×C8C2×D4×C7311yescharacteristic
455C2×C8C2×D4×C7311yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4C2×D4×C7311yescharacteristic
472C4⋊C4C2×D4×C7311yescharacteristic
473C4⋊C4C2×D4×C7311yescharacteristic
474C4⋊C4C2×D4×C7311yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—41no—
486C42—41no—
487C42C24×C7311yescharacteristic
488C23—21no—
489C23—41no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—81no—
501D4—21no—
502D4—21no—
503D4—41no—
504D4—41no—
505D4—41no—
506D4—41no—
507D4—81no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—161no—
521C2×C4—161no—
522C2×C4C22×D4×C7311yescharacteristic
523C2×C4C22×D4×C7311yescharacteristic
524C2×C4H(5,𝔽2)×C7311yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8#135×C7312yes—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22D42×C7311yescharacteristic
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—81no—
550C4—81no—
551C4—81no—
552C4C2×#135×C7311yescharacteristic
553C4#575×C7311yescharacteristic
554C4#577×C7311yescharacteristic
555C4#578×C7311yescharacteristic
556C2—81no—
557C2—161no—
558C2C73×#327711yescharacteristic
559C2C73×#328411yescharacteristic
560C2C73×#329011yescharacteristic
subgroupG/H
center, socleC22×C73D42
commutator, Frattini, cosocleC42C24×C73
prime radical#459×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×#3400C2semidirect
2. C73×#3364C2semidirect
4. C73×#3356C2semidirect
5. C73×#1708C2semidirect
6. C73×#1692C2semidirect
8. C73×#1680C2semidirect
9. C73×#1678C2semidirect
10. C73×#1644C2semidirect
11. C73×#1640C2semidirect
12. C73×#1636C2semidirect
14. C73×#1590C2semidirect
15. C8×Q16×C73C2semidirect
275. #19951C73direct (N × H)
281. #3400C2×C73semidirect
282. #3364C2×C73semidirect
284. #3356C2×C73semidirect
285. #1708C2×C73semidirect
286. #1692C2×C73semidirect
288. #1680C2×C73semidirect
289. #1678C2×C73semidirect
290. #1644C2×C73semidirect
291. #1640C2×C73semidirect
292. #1636C2×C73semidirect
294. #1590C2×C73semidirect
295. C8×Q16C2×C73semidirect
296. C73#19951direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#34002
C73×#33642
C73×#33612
C73×#33562
C73×#17082
C73×#16922
C73×#16852
C73×#16802
C73×#16782
C73×#16442
C73×#16402
C73×#16362
C73×#16282
C73×#15902
C8×Q16×C732
#1995173