Finite Group Databasebeta

← C73×#19547 #32928951

Subgroups — C73×#19547 #32928951

Order 18688.

552 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3238C211yesmaximal, characteristic
2C73×#3233C211yesmaximal, characteristic
3C73×#3230C211yesmaximal, characteristic, complemented
4C73×#2993C211yesmaximal, characteristic
5C73×#1704C211yesmaximal, characteristic, complemented
6C73×#1703C211yesmaximal, characteristic, complemented
7C73×#1696C211yesmaximal, characteristic, complemented
8C73×#1695C211yesmaximal, characteristic, complemented
9C73×#1684C211yesmaximal, characteristic, complemented
10C73×#1683C211yesmaximal, characteristic, complemented
11C73×#1676C211yesmaximal, characteristic, complemented
12C73×#1675C211yesmaximal, characteristic, complemented
13C73×#1572C211yesmaximal, characteristic, complemented
14C73×#1559C211yesmaximal, characteristic, complemented
15C73×#1548C211yesmaximal, characteristic, complemented
16#533×C73C2211yescharacteristic
17C2×C4⋊Q8×C73C2211yescharacteristic
18#529×C73C2211yescharacteristic
19#501×C73—21no—
20#500×C73C2211yescharacteristic
21#500×C73C2211yescharacteristic
22#499×C73—21no—
23#489×C73—21no—
24#488×C73—21no—
25#487×C73C2211yescharacteristic
26#487×C73C2211yescharacteristic
27#485×C73—21no—
28#484×C73—21no—
29#484×C73—21no—
30#483×C73—21no—
31#482×C73—21no—
32#480×C73—21no—
33#477×C73—21no—
34#477×C73—21no—
35#477×C73C2211yescharacteristic
36#477×C73C2211yescharacteristic
37#477×C73C2211yescharacteristic
38#476×C73C2211yescharacteristic
39#476×C73C2211yescharacteristic
40#476×C73C2211yescharacteristic
41#475×C73C2211yescharacteristic
42#474×C73C2211yescharacteristic
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#333×C73C2211yescharacteristic
62#333×C73C2211yescharacteristic
63#333×C73C2211yescharacteristic
64#333×C73C2211yescharacteristic
65#332×C73C2211yescharacteristic
66#332×C73C2211yescharacteristic
67C22×Q8×C73—21no—
68C2×M16×C73—21no—
69C2×M16×C73—21no—
70C22×C8×C73—21no—
71C4⋊Q8×C73—21no—
72C4⋊Q8×C73—21no—
73C4⋊Q8×C73—21no—
74C4⋊Q8×C73C2311yescharacteristic
75C4⋊Q8×C73C2311yescharacteristic
76C4⋊Q8×C73C2311yescharacteristic
77C4⋊Q8×C73C2311yescharacteristic
78#126×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×C73D411yescharacteristic
86#121×C73D411yescharacteristic
87C4×Q8×C73—21no—
88C4×Q8×C73—21no—
89C4×Q8×C73C2311yescharacteristic
90C4×D4×C73—21no—
91C4×D4×C73C2311yescharacteristic
92#117×C73—21no—
93#117×C73—21no—
94C2×C4⋊C4×C73—21no—
95C2×C4⋊C4×C73—21no—
96C2×C42×C73C2311yescharacteristic
97#107×C73—21no—
98#107×C73—21no—
99#107×C73—21no—
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—
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—82no—
150C2×Q8×C73C2×D411yescharacteristic
151C2×D4×C73—21no—
152C2×D4×C73C2×D411yescharacteristic
153C22×C4×C73—21no—
154C22×C4×C73—41no—
155C22×C4×C73C2×D411yescharacteristic
156C22×C4×C73C2×D411yescharacteristic
157C22×C4×C73#4111yescharacteristic
158M16×C73—81no—
159M16×C73—81no—
160C2×C8×C73—21no—
161C2×C8×C73—21no—
162C2×C8×C73—21no—
163C2×C8×C73—21no—
164C2×C8×C73—21no—
165C2×C8×C73—21no—
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—
195C42×C73—21no—
196C42×C73—41no—
197C42×C73C2×D411yescharacteristic
198C42×C73C2×D411yescharacteristic
199C42×C73#4111yescharacteristic
200C42×C73C2411yescharacteristic
201C23×C73—21no—
202C23×C73#12111yescharacteristic
203Q8×C73—21no—
204Q8×C73—21no—
205Q8×C73—41no—
206Q8×C73—41no—
207Q8×C73—81no—
208Q8×C73—81no—
209Q8×C73—81no—
210Q8×C73—82no—
211D4×C73—21no—
212D4×C73—21no—
213D4×C73—81no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—41no—
222C2×C4×C73—41no—
223C2×C4×C73—41no—
224C2×C4×C73—41no—
225C2×C4×C73—41no—
226C2×C4×C73—41no—
227C2×C4×C73—41no—
228C2×C4×C73—82no—
229C2×C4×C73#12111yescharacteristic
230C2×C4×C73#12111yescharacteristic
231C2×C4×C73#12111yescharacteristic
232C2×C4×C73C22×D411yescharacteristic
233C2×C4×C73C22×D411yescharacteristic
234C2×C4×C73C2×#4111yescharacteristic
235C8×C73—21no—
236C8×C73—21no—
237C8×C73—21no—
238C8×C73—21no—
239C8×C73—41no—
240C8×C73—41no—
241C8×C73—41no—
242C8×C73—41no—
243C8×C73—41no—
244C8×C73—41no—
245C22×C73—21no—
246C22×C73—21no—
247C22×C73—21no—
248C22×C73—41no—
249C22×C73—41no—
250C22×C73—41no—
251C22×C73C2×#12111yescharacteristic
252C4×C73—21no—
253C4×C73—21no—
254C4×C73—21no—
255C4×C73—21no—
256C4×C73—41no—
257C4×C73—41no—
258C4×C73—41no—
259C4×C73—81no—
260C4×C73—81no—
261C4×C73—81no—
262C4×C73—81no—
263C4×C73#57711yescharacteristic
264C4×C73#57811yescharacteristic
265C4×C73#57811yescharacteristic
266C4×C73#57811yescharacteristic
267#19547C7311yesmaximal, characteristic, direct product factor, Sylow
268C2×C73—41no—
269C2×C73—81no—
270C2×C73#304611yescharacteristic
271C2×C73#305911yescharacteristic
272C2×C73#306811yescharacteristic
273#3238C2×C7311yescharacteristic
274#3233C2×C7311yescharacteristic
275#3230C2×C7311yescharacteristic, complemented
276#2993C2×C7311yescharacteristic
277#1704C2×C7311yescharacteristic, complemented
278#1703C2×C7311yescharacteristic, complemented
279#1696C2×C7311yescharacteristic, complemented
280#1695C2×C7311yescharacteristic, complemented
281#1684C2×C7311yescharacteristic, complemented
282#1683C2×C7311yescharacteristic, complemented
283#1676C2×C7311yescharacteristic, complemented
284#1675C2×C7311yescharacteristic, complemented
285#1572C2×C7311yescharacteristic, complemented
286#1559C2×C7311yescharacteristic, complemented
287#1548C2×C7311yescharacteristic, complemented
288C73#1954711yescharacteristic, direct product factor, Sylow
289#533C22×C7311yescharacteristic
290C2×C4⋊Q8C22×C7311yescharacteristic
291#529C22×C7311yescharacteristic
292#501—21no—
293#500C22×C7311yescharacteristic
294#500C22×C7311yescharacteristic
295#499—21no—
296#489—21no—
297#488—21no—
298#487C22×C7311yescharacteristic
299#487C22×C7311yescharacteristic
300#485—21no—
301#484—21no—
302#484—21no—
303#483—21no—
304#482—21no—
305#480—21no—
306#477—21no—
307#477—21no—
308#477C22×C7311yescharacteristic
309#477C22×C7311yescharacteristic
310#477C22×C7311yescharacteristic
311#476C22×C7311yescharacteristic
312#476C22×C7311yescharacteristic
313#476C22×C7311yescharacteristic
314#475C22×C7311yescharacteristic
315#474C22×C7311yescharacteristic
316#446C22×C7311yescharacteristic
317C8×Q8C22×C7311yescharacteristic
318#436—21no—
319#436C22×C7311yescharacteristic
320#435—21no—
321C8×D4C22×C7311yescharacteristic
322#433—21no—
323#432C22×C7311yescharacteristic
324#431C22×C7311yescharacteristic
325#431C22×C7311yescharacteristic
326#424—21no—
327#423C22×C7311yescharacteristic
328#335C22×C7311yescharacteristic
329#335C22×C7311yescharacteristic
330#334C22×C7311yescharacteristic
331#334C22×C7311yescharacteristic
332#333C22×C7311yescharacteristic
333#333C22×C7311yescharacteristic
334#333C22×C7311yescharacteristic
335#333C22×C7311yescharacteristic
336#333C22×C7311yescharacteristic
337#333C22×C7311yescharacteristic
338#332C22×C7311yescharacteristic
339#332C22×C7311yescharacteristic
340C22×Q8—21no—
341C2×M16—21no—
342C2×M16—21no—
343C22×C8—21no—
344C4⋊Q8—21no—
345C4⋊Q8—21no—
346C4⋊Q8—21no—
347C4⋊Q8C23×C7311yescharacteristic
348C4⋊Q8C23×C7311yescharacteristic
349C4⋊Q8C23×C7311yescharacteristic
350C4⋊Q8C23×C7311yescharacteristic
351#126—21no—
352#125—21no—
353#125D4×C7311yescharacteristic
354#124D4×C7311yescharacteristic
355#123—21no—
356C22⋊Q8—21no—
357C22⋊Q8—21no—
358C22⋊Q8D4×C7311yescharacteristic
359#121D4×C7311yescharacteristic
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8C23×C7311yescharacteristic
363C4×D4—21no—
364C4×D4C23×C7311yescharacteristic
365#117—21no—
366#117—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C42C23×C7311yescharacteristic
370#107—21no—
371#107—21no—
372#107—21no—
373#107—21no—
374#107—21no—
375#107—21no—
376#107—21no—
377#107—21no—
378#106—21no—
379#106—21no—
380#106—21no—
381#106—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8D4×C7311yescharacteristic
386C4⋊C8D4×C7311yescharacteristic
387C4⋊C8C23×C7311yescharacteristic
388C4⋊C8C23×C7311yescharacteristic
389C4⋊C8C23×C7311yescharacteristic
390C4⋊C8C23×C7311yescharacteristic
391C4⋊C8C23×C7311yescharacteristic
392C4⋊C8C23×C7311yescharacteristic
393#103—21no—
394#103—21no—
395#103—21no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#102—21no—
402#102—21no—
403#102—21no—
404#102—21no—
405C22⋊C8—21no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8D4×C7311yescharacteristic
410C22⋊C8D4×C7311yescharacteristic
411#97—21no—
412#97—21no—
413C4×C8—21no—
414C4×C8—21no—
415C4×C8C23×C7311yescharacteristic
416C4×C8C23×C7311yescharacteristic
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—41no—
422C2×Q8—82no—
423C2×Q8C2×D4×C7311yescharacteristic
424C2×D4—21no—
425C2×D4C2×D4×C7311yescharacteristic
426C22×C4—21no—
427C22×C4—41no—
428C22×C4C2×D4×C7311yescharacteristic
429C22×C4C2×D4×C7311yescharacteristic
430C22×C4#41×C7311yescharacteristic
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×C8C2×D4×C7311yescharacteristic
441C2×C8C2×D4×C7311yescharacteristic
442C2×C8C2×D4×C7311yescharacteristic
443C2×C8C2×D4×C7311yescharacteristic
444C4⋊C4—21no—
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—41no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4C2×D4×C7311yescharacteristic
461C4⋊C4C2×D4×C7311yescharacteristic
462C22⋊C4—21no—
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—41no—
468C42—21no—
469C42—41no—
470C42C2×D4×C7311yescharacteristic
471C42C2×D4×C7311yescharacteristic
472C42#41×C7311yescharacteristic
473C42C24×C7311yescharacteristic
474C23—21no—
475C23#121×C7311yescharacteristic
476Q8—21no—
477Q8—21no—
478Q8—41no—
479Q8—41no—
480Q8—81no—
481Q8—81no—
482Q8—81no—
483Q8—82no—
484D4—21no—
485D4—21no—
486D4—81no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—82no—
502C2×C4#121×C7311yescharacteristic
503C2×C4#121×C7311yescharacteristic
504C2×C4#121×C7311yescharacteristic
505C2×C4C22×D4×C7311yescharacteristic
506C2×C4C22×D4×C7311yescharacteristic
507C2×C4C2×#41×C7311yescharacteristic
508C8—21no—
509C8—21no—
510C8—21no—
511C8—21no—
512C8—41no—
513C8—41no—
514C8—41no—
515C8—41no—
516C8—41no—
517C8—41no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—41no—
522C22—41no—
523C22—41no—
524C22C2×#121×C7311yescharacteristic
525C4—21no—
526C4—21no—
527C4—21no—
528C4—21no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—81no—
533C4—81no—
534C4—81no—
535C4—81no—
536C4#577×C7311yescharacteristic
537C4#578×C7311yescharacteristic
538C4#578×C7311yescharacteristic
539C4#578×C7311yescharacteristic
540C2—41no—
541C2—81no—
542C2C73×#304611yescharacteristic
543C2C73×#305911yescharacteristic
544C2C73×#306811yescharacteristic
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×#3230C2semidirect
5. C73×#1704C2semidirect
6. C73×#1703C2semidirect
7. C73×#1696C2semidirect
8. C73×#1695C2semidirect
9. C73×#1684C2semidirect
10. C73×#1683C2semidirect
11. C73×#1676C2semidirect
12. C73×#1675C2semidirect
13. C73×#1572C2semidirect
14. C73×#1559C2semidirect
15. C73×#1548C2semidirect
267. #19547C73direct (N × H)
275. #3230C2×C73semidirect
277. #1704C2×C73semidirect
278. #1703C2×C73semidirect
279. #1696C2×C73semidirect
280. #1695C2×C73semidirect
281. #1684C2×C73semidirect
282. #1683C2×C73semidirect
283. #1676C2×C73semidirect
284. #1675C2×C73semidirect
285. #1572C2×C73semidirect
286. #1559C2×C73semidirect
287. #1548C2×C73semidirect
288. C73#19547direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#32382
C73×#32332
C73×#32302
C73×#29932
C73×#17042
C73×#17032
C73×#16962
C73×#16952
C73×#16842
C73×#16832
C73×#16762
C73×#16752
C73×#15722
C73×#15592
C73×#15482
#1954773