Finite Group Databasebeta

← C73×#19585 #32928989

Subgroups — C73×#19585 #32928989

Order 18688.

550 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3252C211yesmaximal, characteristic
2C73×#3233C211yesmaximal, characteristic
3C73×#3231C211yesmaximal, characteristic, complemented
4C73×#2994C211yesmaximal, characteristic
5C73×#1704C211yesmaximal, characteristic, complemented
6C73×#1699C211yesmaximal, characteristic, complemented
7C73×#1695C211yesmaximal, characteristic, complemented
8C73×#1692C211yesmaximal, characteristic, complemented
9C73×#1683C211yesmaximal, characteristic, complemented
10C73×#1680C211yesmaximal, characteristic, complemented
11C73×#1676C211yesmaximal, characteristic, complemented
12C73×#1671C211yesmaximal, characteristic, complemented
13C73×#1574C211yesmaximal, characteristic, complemented
14C73×#1550C211yesmaximal, characteristic, complemented
15C73×#1542C211yesmaximal, characteristic, complemented
16#533×C73C2211yescharacteristic
17#533×C73C2211yescharacteristic
18#529×C73C2211yescharacteristic
19#500×C73C2211yescharacteristic
20#499×C73—21no—
21#498×C73C2211yescharacteristic
22#488×C73—21no—
23#487×C73C2211yescharacteristic
24#487×C73C2211yescharacteristic
25#485×C73—21no—
26#485×C73—21no—
27#485×C73—21no—
28#482×C73—21no—
29#479×C73—21no—
30#479×C73—21no—
31#479×C73—21no—
32#477×C73C2211yescharacteristic
33#477×C73C2211yescharacteristic
34#476×C73C2211yescharacteristic
35#476×C73C2211yescharacteristic
36#475×C73C2211yescharacteristic
37#474×C73C2211yescharacteristic
38#470×C73—21no—
39#468×C73—21no—
40#464×C73—21no—
41#462×C73C2211yescharacteristic
42#461×C73C2211yescharacteristic
43#446×C73C2211yescharacteristic
44C8×Q8×C73C2211yescharacteristic
45#436×C73C2211yescharacteristic
46#435×C73—21no—
47C8×D4×C73—21no—
48C8×D4×C73C2211yescharacteristic
49#433×C73—21no—
50#431×C73C2211yescharacteristic
51#431×C73C2211yescharacteristic
52#424×C73—21no—
53#423×C73C2211yescharacteristic
54C2×C4⋊C8×C73C2211yescharacteristic
55#335×C73C2211yescharacteristic
56#335×C73C2211yescharacteristic
57#334×C73C2211yescharacteristic
58#334×C73C2211yescharacteristic
59#333×C73C2211yescharacteristic
60#333×C73C2211yescharacteristic
61#333×C73C2211yescharacteristic
62#333×C73C2211yescharacteristic
63#332×C73C2211yescharacteristic
64#332×C73C2211yescharacteristic
65#332×C73C2211yescharacteristic
66#332×C73C2211yescharacteristic
67C2×Q16×C73—21no—
68C2×SD16×C73—21no—
69C2×M16×C73—21no—
70C2×M16×C73—21no—
71C22×C8×C73—21no—
72C22×C8×C73—21no—
73C4⋊Q8×C73C2311yescharacteristic
74C4⋊Q8×C73C2311yescharacteristic
75C4⋊Q8×C73C2311yescharacteristic
76C4⋊Q8×C73C2311yescharacteristic
77#126×C73—21no—
78#125×C73—21no—
79#125×C73—21no—
80#125×C73D411yescharacteristic
81#124×C73D411yescharacteristic
82#123×C73—21no—
83C22⋊Q8×C73—21no—
84C22⋊Q8×C73—21no—
85C22⋊Q8×C73—21no—
86C22⋊Q8×C73—21no—
87C22⋊Q8×C73D411yescharacteristic
88#121×C73D411yescharacteristic
89C4×Q8×C73—21no—
90C4×Q8×C73—21no—
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—
98#117×C73—21no—
99C2×C42×C73C2311yescharacteristic
100#107×C73—21no—
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—
109#106×C73—21no—
110C4⋊C8×C73—21no—
111C4⋊C8×C73—21no—
112C4⋊C8×C73—21no—
113C4⋊C8×C73—21no—
114C4⋊C8×C73D411yescharacteristic
115C4⋊C8×C73D411yescharacteristic
116C4⋊C8×C73C2311yescharacteristic
117C4⋊C8×C73C2311yescharacteristic
118C4⋊C8×C73C2311yescharacteristic
119C4⋊C8×C73C2311yescharacteristic
120C4⋊C8×C73C2311yescharacteristic
121C4⋊C8×C73C2311yescharacteristic
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#103×C73—21no—
129#103×C73—21no—
130#103×C73—21no—
131#102×C73—21no—
132#102×C73—21no—
133#102×C73—21no—
134C22⋊C8×C73—21no—
135C22⋊C8×C73—21no—
136C22⋊C8×C73—21no—
137C22⋊C8×C73D411yescharacteristic
138C22⋊C8×C73D411yescharacteristic
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×C73C2×D411yescharacteristic
149C2×D4×C73—21no—
150C2×D4×C73C2×D411yescharacteristic
151C22×C4×C73—21no—
152C22×C4×C73C2×D411yescharacteristic
153C22×C4×C73C2×D411yescharacteristic
154C22×C4×C73#4111yescharacteristic
155Q16×C73—81no—
156SD16×C73—81no—
157M16×C73—81no—
158M16×C73—81no—
159C2×C8×C73—21no—
160C2×C8×C73—21no—
161C2×C8×C73—21no—
162C2×C8×C73—21no—
163C2×C8×C73—21no—
164C2×C8×C73—21no—
165C2×C8×C73—81no—
166C2×C8×C73—81no—
167C2×C8×C73C2×D411yescharacteristic
168C2×C8×C73C2×D411yescharacteristic
169C2×C8×C73C2×D411yescharacteristic
170C2×C8×C73C2×D411yescharacteristic
171C4⋊C4×C73—21no—
172C4⋊C4×C73—21no—
173C4⋊C4×C73—21no—
174C4⋊C4×C73—21no—
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—41no—
184C4⋊C4×C73—41no—
185C4⋊C4×C73—41no—
186C4⋊C4×C73—41no—
187C4⋊C4×C73C2×D411yescharacteristic
188C4⋊C4×C73C2×D411yescharacteristic
189C22⋊C4×C73—21no—
190C22⋊C4×C73—21no—
191C22⋊C4×C73—21no—
192C22⋊C4×C73—21no—
193C22⋊C4×C73—21no—
194C22⋊C4×C73—41no—
195C22⋊C4×C73—41no—
196C42×C73—21no—
197C42×C73—41no—
198C42×C73—41no—
199C42×C73C2×D411yescharacteristic
200C42×C73C2×D411yescharacteristic
201C42×C73#4111yescharacteristic
202C42×C73C2411yescharacteristic
203C23×C73—21no—
204C23×C73#12111yescharacteristic
205Q8×C73—21no—
206Q8×C73—21no—
207Q8×C73—41no—
208Q8×C73—41no—
209Q8×C73—41no—
210Q8×C73—41no—
211Q8×C73—81no—
212Q8×C73—81no—
213D4×C73—21no—
214D4×C73—21no—
215D4×C73—42no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—41no—
224C2×C4×C73—41no—
225C2×C4×C73—41no—
226C2×C4×C73—41no—
227C2×C4×C73—41no—
228C2×C4×C73—41no—
229C2×C4×C73—41no—
230C2×C4×C73#12111yescharacteristic
231C2×C4×C73#12111yescharacteristic
232C2×C4×C73#12111yescharacteristic
233C2×C4×C73C22×D411yescharacteristic
234C2×C4×C73C22×D411yescharacteristic
235C2×C4×C73C2×#4111yescharacteristic
236C8×C73—21no—
237C8×C73—21no—
238C8×C73—21no—
239C8×C73—21no—
240C8×C73—41no—
241C8×C73—41no—
242C8×C73—41no—
243C8×C73—41no—
244C8×C73—41no—
245C8×C73—41no—
246C22×C73—21no—
247C22×C73—21no—
248C22×C73—21no—
249C22×C73—41no—
250C22×C73—41no—
251C22×C73—41no—
252C22×C73C2×#12111yescharacteristic
253C4×C73—21no—
254C4×C73—21no—
255C4×C73—21no—
256C4×C73—21no—
257C4×C73—41no—
258C4×C73—41no—
259C4×C73—41no—
260C4×C73—81no—
261C4×C73—81no—
262C4×C73—81no—
263C4×C73—81no—
264C4×C73#57711yescharacteristic
265C4×C73#57711yescharacteristic
266C4×C73#57811yescharacteristic
267C4×C73#57811yescharacteristic
268#19585C7311yesmaximal, characteristic, direct product factor, Sylow
269C2×C73—41no—
270C2×C73—81no—
271C2×C73#304611yescharacteristic
272C2×C73#306311yescharacteristic
273C2×C73#306711yescharacteristic
274#3252C2×C7311yescharacteristic
275#3233C2×C7311yescharacteristic
276#3231C2×C7311yescharacteristic, complemented
277#2994C2×C7311yescharacteristic
278#1704C2×C7311yescharacteristic, complemented
279#1699C2×C7311yescharacteristic, complemented
280#1695C2×C7311yescharacteristic, complemented
281#1692C2×C7311yescharacteristic, complemented
282#1683C2×C7311yescharacteristic, complemented
283#1680C2×C7311yescharacteristic, complemented
284#1676C2×C7311yescharacteristic, complemented
285#1671C2×C7311yescharacteristic, complemented
286#1574C2×C7311yescharacteristic, complemented
287#1550C2×C7311yescharacteristic, complemented
288#1542C2×C7311yescharacteristic, complemented
289C73#1958511yescharacteristic, direct product factor, Sylow
290#533C22×C7311yescharacteristic
291#533C22×C7311yescharacteristic
292#529C22×C7311yescharacteristic
293#500C22×C7311yescharacteristic
294#499—21no—
295#498C22×C7311yescharacteristic
296#488—21no—
297#487C22×C7311yescharacteristic
298#487C22×C7311yescharacteristic
299#485—21no—
300#485—21no—
301#485—21no—
302#482—21no—
303#479—21no—
304#479—21no—
305#479—21no—
306#477C22×C7311yescharacteristic
307#477C22×C7311yescharacteristic
308#476C22×C7311yescharacteristic
309#476C22×C7311yescharacteristic
310#475C22×C7311yescharacteristic
311#474C22×C7311yescharacteristic
312#470—21no—
313#468—21no—
314#464—21no—
315#462C22×C7311yescharacteristic
316#461C22×C7311yescharacteristic
317#446C22×C7311yescharacteristic
318C8×Q8C22×C7311yescharacteristic
319#436C22×C7311yescharacteristic
320#435—21no—
321C8×D4—21no—
322C8×D4C22×C7311yescharacteristic
323#433—21no—
324#431C22×C7311yescharacteristic
325#431C22×C7311yescharacteristic
326#424—21no—
327#423C22×C7311yescharacteristic
328C2×C4⋊C8C22×C7311yescharacteristic
329#335C22×C7311yescharacteristic
330#335C22×C7311yescharacteristic
331#334C22×C7311yescharacteristic
332#334C22×C7311yescharacteristic
333#333C22×C7311yescharacteristic
334#333C22×C7311yescharacteristic
335#333C22×C7311yescharacteristic
336#333C22×C7311yescharacteristic
337#332C22×C7311yescharacteristic
338#332C22×C7311yescharacteristic
339#332C22×C7311yescharacteristic
340#332C22×C7311yescharacteristic
341C2×Q16—21no—
342C2×SD16—21no—
343C2×M16—21no—
344C2×M16—21no—
345C22×C8—21no—
346C22×C8—21no—
347C4⋊Q8C23×C7311yescharacteristic
348C4⋊Q8C23×C7311yescharacteristic
349C4⋊Q8C23×C7311yescharacteristic
350C4⋊Q8C23×C7311yescharacteristic
351#126—21no—
352#125—21no—
353#125—21no—
354#125D4×C7311yescharacteristic
355#124D4×C7311yescharacteristic
356#123—21no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8D4×C7311yescharacteristic
362#121D4×C7311yescharacteristic
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8C23×C7311yescharacteristic
368C4×D4—21no—
369C4×D4C23×C7311yescharacteristic
370#117—21no—
371#117—21no—
372#117—21no—
373C2×C42C23×C7311yescharacteristic
374#107—21no—
375#107—21no—
376#107—21no—
377#107—21no—
378#107—21no—
379#106—21no—
380#106—21no—
381#106—21no—
382#106—21no—
383#106—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8D4×C7311yescharacteristic
389C4⋊C8D4×C7311yescharacteristic
390C4⋊C8C23×C7311yescharacteristic
391C4⋊C8C23×C7311yescharacteristic
392C4⋊C8C23×C7311yescharacteristic
393C4⋊C8C23×C7311yescharacteristic
394C4⋊C8C23×C7311yescharacteristic
395C4⋊C8C23×C7311yescharacteristic
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#102—21no—
406#102—21no—
407#102—21no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8D4×C7311yescharacteristic
412C22⋊C8D4×C7311yescharacteristic
413#97—21no—
414C4×C8—21no—
415C4×C8—21no—
416C4×C8C23×C7311yescharacteristic
417C4×C8C23×C7311yescharacteristic
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8C2×D4×C7311yescharacteristic
423C2×D4—21no—
424C2×D4C2×D4×C7311yescharacteristic
425C22×C4—21no—
426C22×C4C2×D4×C7311yescharacteristic
427C22×C4C2×D4×C7311yescharacteristic
428C22×C4#41×C7311yescharacteristic
429Q16—81no—
430SD16—81no—
431M16—81no—
432M16—81no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—81no—
440C2×C8—81no—
441C2×C8C2×D4×C7311yescharacteristic
442C2×C8C2×D4×C7311yescharacteristic
443C2×C8C2×D4×C7311yescharacteristic
444C2×C8C2×D4×C7311yescharacteristic
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4C2×D4×C7311yescharacteristic
462C4⋊C4C2×D4×C7311yescharacteristic
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—21no—
468C22⋊C4—41no—
469C22⋊C4—41no—
470C42—21no—
471C42—41no—
472C42—41no—
473C42C2×D4×C7311yescharacteristic
474C42C2×D4×C7311yescharacteristic
475C42#41×C7311yescharacteristic
476C42C24×C7311yescharacteristic
477C23—21no—
478C23#121×C7311yescharacteristic
479Q8—21no—
480Q8—21no—
481Q8—41no—
482Q8—41no—
483Q8—41no—
484Q8—41no—
485Q8—81no—
486Q8—81no—
487D4—21no—
488D4—21no—
489D4—42no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4#121×C7311yescharacteristic
505C2×C4#121×C7311yescharacteristic
506C2×C4#121×C7311yescharacteristic
507C2×C4C22×D4×C7311yescharacteristic
508C2×C4C22×D4×C7311yescharacteristic
509C2×C4C2×#41×C7311yescharacteristic
510C8—21no—
511C8—21no—
512C8—21no—
513C8—21no—
514C8—41no—
515C8—41no—
516C8—41no—
517C8—41no—
518C8—41no—
519C8—41no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22C2×#121×C7311yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—81no—
535C4—81no—
536C4—81no—
537C4—81no—
538C4#577×C7311yescharacteristic
539C4#577×C7311yescharacteristic
540C4#578×C7311yescharacteristic
541C4#578×C7311yescharacteristic
542C2—41no—
543C2—81no—
544C2C73×#304611yescharacteristic
545C2C73×#306311yescharacteristic
546C2C73×#306711yescharacteristic
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×#3231C2semidirect
5. C73×#1704C2semidirect
6. C73×#1699C2semidirect
7. C73×#1695C2semidirect
8. C73×#1692C2semidirect
9. C73×#1683C2semidirect
10. C73×#1680C2semidirect
11. C73×#1676C2semidirect
12. C73×#1671C2semidirect
13. C73×#1574C2semidirect
14. C73×#1550C2semidirect
15. C73×#1542C2semidirect
268. #19585C73direct (N × H)
276. #3231C2×C73semidirect
278. #1704C2×C73semidirect
279. #1699C2×C73semidirect
280. #1695C2×C73semidirect
281. #1692C2×C73semidirect
282. #1683C2×C73semidirect
283. #1680C2×C73semidirect
284. #1676C2×C73semidirect
285. #1671C2×C73semidirect
286. #1574C2×C73semidirect
287. #1550C2×C73semidirect
288. #1542C2×C73semidirect
289. C73#19585direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#32522
C73×#32332
C73×#32312
C73×#29942
C73×#17042
C73×#16992
C73×#16952
C73×#16922
C73×#16832
C73×#16802
C73×#16762
C73×#16712
C73×#15742
C73×#15502
C73×#15422
#1958573