Finite Group Databasebeta

← C73×#19539 #32928943

Subgroups — C73×#19539 #32928943

Order 18688.

564 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3239C211yesmaximal, characteristic
2C73×#3233C211yesmaximal, characteristic
3C73×#3209C211yesmaximal, characteristic, complemented
4C73×#2993C211yesmaximal, characteristic
5C73×#1704C211yesmaximal, characteristic, complemented
6C73×#1703C211yesmaximal, characteristic, complemented
7C73×#1690C211yesmaximal, characteristic, complemented
8C73×#1689C211yesmaximal, characteristic, complemented
9C73×#1684C211yesmaximal, characteristic, complemented
10C73×#1683C211yesmaximal, characteristic, complemented
11C73×#1670C211yesmaximal, characteristic, complemented
12C73×#1669C211yesmaximal, characteristic, complemented
13C73×#1572C211yesmaximal, characteristic, complemented
14C73×#1559C211yesmaximal, characteristic, complemented
15C73×#1546C211yesmaximal, characteristic, complemented
16#533×C73C2211yescharacteristic
17C2×C4⋊Q8×C73C2211yescharacteristic
18#529×C73C2211yescharacteristic
19#501×C73—21no—
20#499×C73—21no—
21#494×C73C2211yescharacteristic
22#494×C73C2211yescharacteristic
23#489×C73—21no—
24#488×C73—21no—
25#487×C73C2211yescharacteristic
26#487×C73C2211yescharacteristic
27#485×C73—21no—
28#484×C73—21no—
29#482×C73—21no—
30#481×C73—21no—
31#477×C73C2211yescharacteristic
32#476×C73C2211yescharacteristic
33#475×C73C2211yescharacteristic
34#475×C73C2211yescharacteristic
35#475×C73C2211yescharacteristic
36#474×C73C2211yescharacteristic
37#474×C73C2211yescharacteristic
38#474×C73C2211yescharacteristic
39#462×C73—21no—
40#462×C73—21no—
41#451×C73—21no—
42#451×C73—21no—
43#446×C73C2211yescharacteristic
44C8×Q8×C73C2211yescharacteristic
45#436×C73—21no—
46#436×C73C2211yescharacteristic
47#435×C73—21no—
48C8×D4×C73C2211yescharacteristic
49#433×C73—21no—
50#432×C73C2211yescharacteristic
51#431×C73C2211yescharacteristic
52#431×C73C2211yescharacteristic
53#424×C73—21no—
54#423×C73C2211yescharacteristic
55#335×C73C2211yescharacteristic
56#335×C73C2211yescharacteristic
57#334×C73C2211yescharacteristic
58#334×C73C2211yescharacteristic
59#333×C73C2211yescharacteristic
60#333×C73C2211yescharacteristic
61#332×C73C2211yescharacteristic
62#332×C73C2211yescharacteristic
63#332×C73C2211yescharacteristic
64#332×C73C2211yescharacteristic
65#332×C73C2211yescharacteristic
66#332×C73C2211yescharacteristic
67C22×Q8×C73—21no—
68C2×Q16×C73—21no—
69C2×Q16×C73—21no—
70C2×Q16×C73—21no—
71C2×Q16×C73—21no—
72C2×M16×C73—21no—
73C2×M16×C73—21no—
74C22×C8×C73—21no—
75C4⋊Q8×C73—21no—
76C4⋊Q8×C73—21no—
77C4⋊Q8×C73—21no—
78C4⋊Q8×C73C2311yescharacteristic
79C4⋊Q8×C73C2311yescharacteristic
80C4⋊Q8×C73C2311yescharacteristic
81C4⋊Q8×C73C2311yescharacteristic
82#126×C73—21no—
83#125×C73—21no—
84#125×C73D411yescharacteristic
85#124×C73D411yescharacteristic
86#123×C73—21no—
87C22⋊Q8×C73—21no—
88C22⋊Q8×C73—21no—
89C22⋊Q8×C73D411yescharacteristic
90#121×C73D411yescharacteristic
91C4×Q8×C73—21no—
92C4×Q8×C73—21no—
93C4×Q8×C73C2311yescharacteristic
94C4×D4×C73—21no—
95C4×D4×C73C2311yescharacteristic
96#117×C73—21no—
97#117×C73—21no—
98C2×C4⋊C4×C73—21no—
99C2×C4⋊C4×C73—21no—
100C2×C42×C73C2311yescharacteristic
101#107×C73—21no—
102#107×C73—21no—
103#107×C73—21no—
104#107×C73—21no—
105#106×C73—21no—
106#106×C73—21no—
107#106×C73—21no—
108#106×C73—21no—
109C4⋊C8×C73—21no—
110C4⋊C8×C73—21no—
111C4⋊C8×C73—21no—
112C4⋊C8×C73D411yescharacteristic
113C4⋊C8×C73D411yescharacteristic
114C4⋊C8×C73C2311yescharacteristic
115C4⋊C8×C73C2311yescharacteristic
116C4⋊C8×C73C2311yescharacteristic
117C4⋊C8×C73C2311yescharacteristic
118C4⋊C8×C73C2311yescharacteristic
119C4⋊C8×C73C2311yescharacteristic
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—21no—
127#103×C73—21no—
128#102×C73—21no—
129#102×C73—21no—
130#102×C73—21no—
131#102×C73—21no—
132C22⋊C8×C73—21no—
133C22⋊C8×C73—21no—
134C22⋊C8×C73—21no—
135C22⋊C8×C73—21no—
136C22⋊C8×C73D411yescharacteristic
137C22⋊C8×C73D411yescharacteristic
138#97×C73—21no—
139#97×C73—21no—
140C4×C8×C73—21no—
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C2×Q8×C73—21no—
145C2×Q8×C73—21no—
146C2×Q8×C73—21no—
147C2×Q8×C73—21no—
148C2×Q8×C73—41no—
149C2×Q8×C73—81no—
150C2×Q8×C73—81no—
151C2×Q8×C73C2×D411yescharacteristic
152C2×D4×C73—21no—
153C2×D4×C73C2×D411yescharacteristic
154C22×C4×C73—21no—
155C22×C4×C73—41no—
156C22×C4×C73C2×D411yescharacteristic
157C22×C4×C73C2×D411yescharacteristic
158C22×C4×C73#4111yescharacteristic
159Q16×C73—81no—
160Q16×C73—81no—
161Q16×C73—81no—
162Q16×C73—81no—
163M16×C73—81no—
164M16×C73—81no—
165C2×C8×C73—21no—
166C2×C8×C73—21no—
167C2×C8×C73—21no—
168C2×C8×C73—21no—
169C2×C8×C73—21no—
170C2×C8×C73—21no—
171C2×C8×C73—81no—
172C2×C8×C73C2×D411yescharacteristic
173C2×C8×C73C2×D411yescharacteristic
174C2×C8×C73C2×D411yescharacteristic
175C2×C8×C73C2×D411yescharacteristic
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—21no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—21no—
188C4⋊C4×C73—41no—
189C4⋊C4×C73—41no—
190C4⋊C4×C73—41no—
191C4⋊C4×C73—41no—
192C4⋊C4×C73C2×D411yescharacteristic
193C4⋊C4×C73C2×D411yescharacteristic
194C22⋊C4×C73—21no—
195C22⋊C4×C73—21no—
196C22⋊C4×C73—21no—
197C22⋊C4×C73—21no—
198C22⋊C4×C73—21no—
199C22⋊C4×C73—41no—
200C42×C73—21no—
201C42×C73—41no—
202C42×C73C2×D411yescharacteristic
203C42×C73C2×D411yescharacteristic
204C42×C73#4111yescharacteristic
205C42×C73C2411yescharacteristic
206C23×C73—21no—
207C23×C73#12111yescharacteristic
208Q8×C73—21no—
209Q8×C73—21no—
210Q8×C73—41no—
211Q8×C73—41no—
212Q8×C73—41no—
213Q8×C73—41no—
214Q8×C73—41no—
215Q8×C73—41no—
216Q8×C73—81no—
217Q8×C73—82no—
218D4×C73—21no—
219D4×C73—21no—
220D4×C73—81no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—41no—
229C2×C4×C73—41no—
230C2×C4×C73—41no—
231C2×C4×C73—41no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73—82no—
236C2×C4×C73#12111yescharacteristic
237C2×C4×C73#12111yescharacteristic
238C2×C4×C73#12111yescharacteristic
239C2×C4×C73C22×D411yescharacteristic
240C2×C4×C73C22×D411yescharacteristic
241C2×C4×C73C2×#4111yescharacteristic
242C8×C73—21no—
243C8×C73—21no—
244C8×C73—21no—
245C8×C73—21no—
246C8×C73—41no—
247C8×C73—41no—
248C8×C73—41no—
249C8×C73—41no—
250C8×C73—41no—
251C8×C73—41no—
252C22×C73—21no—
253C22×C73—21no—
254C22×C73—21no—
255C22×C73—41no—
256C22×C73—41no—
257C22×C73—41no—
258C22×C73C2×#12111yescharacteristic
259C4×C73—21no—
260C4×C73—21no—
261C4×C73—21no—
262C4×C73—21no—
263C4×C73—41no—
264C4×C73—41no—
265C4×C73—41no—
266C4×C73—81no—
267C4×C73—81no—
268C4×C73—81no—
269C4×C73—81no—
270C4×C73#57611yescharacteristic
271C4×C73#57711yescharacteristic
272C4×C73#57811yescharacteristic
273C4×C73#57811yescharacteristic
274#19539C7311yesmaximal, characteristic, direct product factor, Sylow
275C2×C73—41no—
276C2×C73—81no—
277C2×C73#304511yescharacteristic
278C2×C73#305911yescharacteristic
279C2×C73#306911yescharacteristic
280#3239C2×C7311yescharacteristic
281#3233C2×C7311yescharacteristic
282#3209C2×C7311yescharacteristic, complemented
283#2993C2×C7311yescharacteristic
284#1704C2×C7311yescharacteristic, complemented
285#1703C2×C7311yescharacteristic, complemented
286#1690C2×C7311yescharacteristic, complemented
287#1689C2×C7311yescharacteristic, complemented
288#1684C2×C7311yescharacteristic, complemented
289#1683C2×C7311yescharacteristic, complemented
290#1670C2×C7311yescharacteristic, complemented
291#1669C2×C7311yescharacteristic, complemented
292#1572C2×C7311yescharacteristic, complemented
293#1559C2×C7311yescharacteristic, complemented
294#1546C2×C7311yescharacteristic, complemented
295C73#1953911yescharacteristic, direct product factor, Sylow
296#533C22×C7311yescharacteristic
297C2×C4⋊Q8C22×C7311yescharacteristic
298#529C22×C7311yescharacteristic
299#501—21no—
300#499—21no—
301#494C22×C7311yescharacteristic
302#494C22×C7311yescharacteristic
303#489—21no—
304#488—21no—
305#487C22×C7311yescharacteristic
306#487C22×C7311yescharacteristic
307#485—21no—
308#484—21no—
309#482—21no—
310#481—21no—
311#477C22×C7311yescharacteristic
312#476C22×C7311yescharacteristic
313#475C22×C7311yescharacteristic
314#475C22×C7311yescharacteristic
315#475C22×C7311yescharacteristic
316#474C22×C7311yescharacteristic
317#474C22×C7311yescharacteristic
318#474C22×C7311yescharacteristic
319#462—21no—
320#462—21no—
321#451—21no—
322#451—21no—
323#446C22×C7311yescharacteristic
324C8×Q8C22×C7311yescharacteristic
325#436—21no—
326#436C22×C7311yescharacteristic
327#435—21no—
328C8×D4C22×C7311yescharacteristic
329#433—21no—
330#432C22×C7311yescharacteristic
331#431C22×C7311yescharacteristic
332#431C22×C7311yescharacteristic
333#424—21no—
334#423C22×C7311yescharacteristic
335#335C22×C7311yescharacteristic
336#335C22×C7311yescharacteristic
337#334C22×C7311yescharacteristic
338#334C22×C7311yescharacteristic
339#333C22×C7311yescharacteristic
340#333C22×C7311yescharacteristic
341#332C22×C7311yescharacteristic
342#332C22×C7311yescharacteristic
343#332C22×C7311yescharacteristic
344#332C22×C7311yescharacteristic
345#332C22×C7311yescharacteristic
346#332C22×C7311yescharacteristic
347C22×Q8—21no—
348C2×Q16—21no—
349C2×Q16—21no—
350C2×Q16—21no—
351C2×Q16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C22×C8—21no—
355C4⋊Q8—21no—
356C4⋊Q8—21no—
357C4⋊Q8—21no—
358C4⋊Q8C23×C7311yescharacteristic
359C4⋊Q8C23×C7311yescharacteristic
360C4⋊Q8C23×C7311yescharacteristic
361C4⋊Q8C23×C7311yescharacteristic
362#126—21no—
363#125—21no—
364#125D4×C7311yescharacteristic
365#124D4×C7311yescharacteristic
366#123—21no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8D4×C7311yescharacteristic
370#121D4×C7311yescharacteristic
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8C23×C7311yescharacteristic
374C4×D4—21no—
375C4×D4C23×C7311yescharacteristic
376#117—21no—
377#117—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C42C23×C7311yescharacteristic
381#107—21no—
382#107—21no—
383#107—21no—
384#107—21no—
385#106—21no—
386#106—21no—
387#106—21no—
388#106—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8D4×C7311yescharacteristic
393C4⋊C8D4×C7311yescharacteristic
394C4⋊C8C23×C7311yescharacteristic
395C4⋊C8C23×C7311yescharacteristic
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—21no—
408#102—21no—
409#102—21no—
410#102—21no—
411#102—21no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—21no—
416C22⋊C8D4×C7311yescharacteristic
417C22⋊C8D4×C7311yescharacteristic
418#97—21no—
419#97—21no—
420C4×C8—21no—
421C4×C8—21no—
422C4×C8C23×C7311yescharacteristic
423C4×C8C23×C7311yescharacteristic
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—41no—
429C2×Q8—81no—
430C2×Q8—81no—
431C2×Q8C2×D4×C7311yescharacteristic
432C2×D4—21no—
433C2×D4C2×D4×C7311yescharacteristic
434C22×C4—21no—
435C22×C4—41no—
436C22×C4C2×D4×C7311yescharacteristic
437C22×C4C2×D4×C7311yescharacteristic
438C22×C4#41×C7311yescharacteristic
439Q16—81no—
440Q16—81no—
441Q16—81no—
442Q16—81no—
443M16—81no—
444M16—81no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—81no—
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—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4C2×D4×C7311yescharacteristic
473C4⋊C4C2×D4×C7311yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—41no—
480C42—21no—
481C42—41no—
482C42C2×D4×C7311yescharacteristic
483C42C2×D4×C7311yescharacteristic
484C42#41×C7311yescharacteristic
485C42C24×C7311yescharacteristic
486C23—21no—
487C23#121×C7311yescharacteristic
488Q8—21no—
489Q8—21no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—81no—
497Q8—82no—
498D4—21no—
499D4—21no—
500D4—81no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—82no—
516C2×C4#121×C7311yescharacteristic
517C2×C4#121×C7311yescharacteristic
518C2×C4#121×C7311yescharacteristic
519C2×C4C22×D4×C7311yescharacteristic
520C2×C4C22×D4×C7311yescharacteristic
521C2×C4C2×#41×C7311yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—41no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22C2×#121×C7311yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—81no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4#576×C7311yescharacteristic
551C4#577×C7311yescharacteristic
552C4#578×C7311yescharacteristic
553C4#578×C7311yescharacteristic
554C2—41no—
555C2—81no—
556C2C73×#304511yescharacteristic
557C2C73×#305911yescharacteristic
558C2C73×#306911yescharacteristic
subgroupG/H
center, socleC22×C73C2×#121
commutator, Frattini, cosocleC42C24×C73
prime radical#121×C73D4
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
3. C73×#3209C2semidirect
5. C73×#1704C2semidirect
6. C73×#1703C2semidirect
7. C73×#1690C2semidirect
8. C73×#1689C2semidirect
9. C73×#1684C2semidirect
10. C73×#1683C2semidirect
11. C73×#1670C2semidirect
12. C73×#1669C2semidirect
13. C73×#1572C2semidirect
14. C73×#1559C2semidirect
15. C73×#1546C2semidirect
274. #19539C73direct (N × H)
282. #3209C2×C73semidirect
284. #1704C2×C73semidirect
285. #1703C2×C73semidirect
286. #1690C2×C73semidirect
287. #1689C2×C73semidirect
288. #1684C2×C73semidirect
289. #1683C2×C73semidirect
290. #1670C2×C73semidirect
291. #1669C2×C73semidirect
292. #1572C2×C73semidirect
293. #1559C2×C73semidirect
294. #1546C2×C73semidirect
295. C73#19539direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#32392
C73×#32332
C73×#32092
C73×#29932
C73×#17042
C73×#17032
C73×#16902
C73×#16892
C73×#16842
C73×#16832
C73×#16702
C73×#16692
C73×#15722
C73×#15592
C73×#15462
#1953973