Finite Group Databasebeta

← C73×#19550 #32928954

Subgroups — C73×#19550 #32928954

Order 18688.

556 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3252C211yesmaximal, characteristic
2C73×#3248C211yesmaximal, characteristic
3C73×#3231C211yesmaximal, characteristic, complemented
4C73×#2993C211yesmaximal, characteristic
5C73×#1700C211yesmaximal, characteristic, complemented
6C73×#1699C211yesmaximal, characteristic, complemented
7C73×#1692C211yesmaximal, characteristic, complemented
8C73×#1691C211yesmaximal, characteristic, complemented
9C73×#1684C211yesmaximal, characteristic, complemented
10C73×#1683C211yesmaximal, characteristic, complemented
11C73×#1674C211yesmaximal, characteristic, complemented
12C73×#1673C211yesmaximal, characteristic, complemented
13C73×#1571C211yesmaximal, characteristic, complemented
14C73×#1561C211yesmaximal, characteristic, complemented
15C73×#1550C211yesmaximal, characteristic, complemented
16#533×C73C2211yescharacteristic
17#533×C73C2211yescharacteristic
18#529×C73C2211yescharacteristic
19#500×C73C2211yescharacteristic
20#498×C73C2211yescharacteristic
21#487×C73C2211yescharacteristic
22#487×C73C2211yescharacteristic
23#485×C73—21no—
24#485×C73—21no—
25#479×C73—21no—
26#479×C73—21no—
27#479×C73—21no—
28#479×C73—21no—
29#477×C73C2211yescharacteristic
30#476×C73C2211yescharacteristic
31#475×C73C2211yescharacteristic
32#474×C73C2211yescharacteristic
33#470×C73—21no—
34#468×C73—21no—
35#467×C73—21no—
36#465×C73—21no—
37#464×C73—21no—
38#464×C73—21no—
39#462×C73C2211yescharacteristic
40#462×C73C2211yescharacteristic
41#461×C73C2211yescharacteristic
42#461×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#431×C73C2211yescharacteristic
51#424×C73—21no—
52#423×C73C2211yescharacteristic
53#423×C73C2211yescharacteristic
54C2×C4⋊C8×C73C2211yescharacteristic
55#335×C73C2211yescharacteristic
56#335×C73C2211yescharacteristic
57#335×C73C2211yescharacteristic
58#335×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
67C2×Q16×C73—21no—
68C2×Q16×C73—21no—
69C2×SD16×C73—21no—
70C2×SD16×C73—21no—
71C2×M16×C73—21no—
72C2×M16×C73—21no—
73C2×M16×C73—21no—
74C22×C8×C73—21no—
75C22×C8×C73—21no—
76C4⋊Q8×C73C2311yescharacteristic
77C4⋊Q8×C73C2311yescharacteristic
78C4⋊Q8×C73C2311yescharacteristic
79C4⋊Q8×C73C2311yescharacteristic
80#126×C73—21no—
81#125×C73—21no—
82#125×C73—21no—
83#125×C73D411yescharacteristic
84#124×C73D411yescharacteristic
85#123×C73—21no—
86C22⋊Q8×C73—21no—
87C22⋊Q8×C73—21no—
88C22⋊Q8×C73—21no—
89C22⋊Q8×C73—21no—
90C22⋊Q8×C73D411yescharacteristic
91#121×C73D411yescharacteristic
92C4×Q8×C73—21no—
93C4×Q8×C73—21no—
94C4×Q8×C73—21no—
95C4×Q8×C73—21no—
96C4×Q8×C73C2311yescharacteristic
97C4×D4×C73—21no—
98C4×D4×C73C2311yescharacteristic
99#117×C73—21no—
100#117×C73—21no—
101#117×C73—21no—
102C2×C42×C73C2311yescharacteristic
103#107×C73—21no—
104#107×C73—21no—
105#107×C73—21no—
106#107×C73—21no—
107#106×C73—21no—
108#106×C73—21no—
109#106×C73—21no—
110#106×C73—21no—
111C4⋊C8×C73—21no—
112C4⋊C8×C73—21no—
113C4⋊C8×C73—21no—
114C4⋊C8×C73—21no—
115C4⋊C8×C73—21no—
116C4⋊C8×C73D411yescharacteristic
117C4⋊C8×C73D411yescharacteristic
118C4⋊C8×C73C2311yescharacteristic
119C4⋊C8×C73C2311yescharacteristic
120C4⋊C8×C73C2311yescharacteristic
121C4⋊C8×C73C2311yescharacteristic
122C4⋊C8×C73C2311yescharacteristic
123C4⋊C8×C73C2311yescharacteristic
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#103×C73—21no—
132#103×C73—21no—
133#103×C73—21no—
134#102×C73—21no—
135#102×C73—21no—
136C22⋊C8×C73—21no—
137C22⋊C8×C73—21no—
138C22⋊C8×C73D411yescharacteristic
139C22⋊C8×C73D411yescharacteristic
140#97×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—
156Q16×C73—81no—
157SD16×C73—81no—
158SD16×C73—81no—
159M16×C73—81no—
160M16×C73—81no—
161M16×C73—81no—
162C2×C8×C73—21no—
163C2×C8×C73—21no—
164C2×C8×C73—21no—
165C2×C8×C73—21no—
166C2×C8×C73—21no—
167C2×C8×C73—21no—
168C2×C8×C73—81no—
169C2×C8×C73—81no—
170C2×C8×C73C2×D411yescharacteristic
171C2×C8×C73C2×D411yescharacteristic
172C2×C8×C73C2×D411yescharacteristic
173C2×C8×C73C2×D411yescharacteristic
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—21no—
184C4⋊C4×C73—21no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—41no—
187C4⋊C4×C73—41no—
188C4⋊C4×C73—41no—
189C4⋊C4×C73—41no—
190C4⋊C4×C73C2×D411yescharacteristic
191C4⋊C4×C73C2×D411yescharacteristic
192C22⋊C4×C73—21no—
193C22⋊C4×C73—21no—
194C22⋊C4×C73—21no—
195C22⋊C4×C73—21no—
196C22⋊C4×C73—21no—
197C22⋊C4×C73—41no—
198C22⋊C4×C73—41no—
199C42×C73—21no—
200C42×C73—41no—
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—
217D4×C73—21no—
218D4×C73—21no—
219D4×C73—81no—
220C2×C4×C73—21no—
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—41no—
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#12111yescharacteristic
235C2×C4×C73#12111yescharacteristic
236C2×C4×C73#12111yescharacteristic
237C2×C4×C73C22×D411yescharacteristic
238C2×C4×C73C22×D411yescharacteristic
239C2×C4×C73C2×#4111yescharacteristic
240C8×C73—21no—
241C8×C73—21no—
242C8×C73—21no—
243C8×C73—21no—
244C8×C73—41no—
245C8×C73—41no—
246C8×C73—41no—
247C8×C73—41no—
248C8×C73—41no—
249C8×C73—41no—
250C22×C73—21no—
251C22×C73—21no—
252C22×C73—21no—
253C22×C73—41no—
254C22×C73—41no—
255C22×C73—41no—
256C22×C73C2×#12111yescharacteristic
257C4×C73—21no—
258C4×C73—21no—
259C4×C73—21no—
260C4×C73—21no—
261C4×C73—41no—
262C4×C73—41no—
263C4×C73—41no—
264C4×C73—81no—
265C4×C73—81no—
266C4×C73—81no—
267C4×C73—81no—
268C4×C73#57611yescharacteristic
269C4×C73#57711yescharacteristic
270C4×C73#57811yescharacteristic
271C4×C73#57811yescharacteristic
272#19550C7311yesmaximal, characteristic, direct product factor, Sylow
273C2×C73—41no—
274C2×C73—81no—
275C2×C73#304611yescharacteristic
276C2×C73#306111yescharacteristic
277C2×C73#306911yescharacteristic
278#3252C2×C7311yescharacteristic
279#3248C2×C7311yescharacteristic
280#3231C2×C7311yescharacteristic, complemented
281#2993C2×C7311yescharacteristic
282#1700C2×C7311yescharacteristic, complemented
283#1699C2×C7311yescharacteristic, complemented
284#1692C2×C7311yescharacteristic, complemented
285#1691C2×C7311yescharacteristic, complemented
286#1684C2×C7311yescharacteristic, complemented
287#1683C2×C7311yescharacteristic, complemented
288#1674C2×C7311yescharacteristic, complemented
289#1673C2×C7311yescharacteristic, complemented
290#1571C2×C7311yescharacteristic, complemented
291#1561C2×C7311yescharacteristic, complemented
292#1550C2×C7311yescharacteristic, complemented
293C73#1955011yescharacteristic, direct product factor, Sylow
294#533C22×C7311yescharacteristic
295#533C22×C7311yescharacteristic
296#529C22×C7311yescharacteristic
297#500C22×C7311yescharacteristic
298#498C22×C7311yescharacteristic
299#487C22×C7311yescharacteristic
300#487C22×C7311yescharacteristic
301#485—21no—
302#485—21no—
303#479—21no—
304#479—21no—
305#479—21no—
306#479—21no—
307#477C22×C7311yescharacteristic
308#476C22×C7311yescharacteristic
309#475C22×C7311yescharacteristic
310#474C22×C7311yescharacteristic
311#470—21no—
312#468—21no—
313#467—21no—
314#465—21no—
315#464—21no—
316#464—21no—
317#462C22×C7311yescharacteristic
318#462C22×C7311yescharacteristic
319#461C22×C7311yescharacteristic
320#461C22×C7311yescharacteristic
321#446C22×C7311yescharacteristic
322C8×Q8C22×C7311yescharacteristic
323#436—21no—
324#436C22×C7311yescharacteristic
325#435—21no—
326C8×D4C22×C7311yescharacteristic
327#433—21no—
328#431C22×C7311yescharacteristic
329#424—21no—
330#423C22×C7311yescharacteristic
331#423C22×C7311yescharacteristic
332C2×C4⋊C8C22×C7311yescharacteristic
333#335C22×C7311yescharacteristic
334#335C22×C7311yescharacteristic
335#335C22×C7311yescharacteristic
336#335C22×C7311yescharacteristic
337#333C22×C7311yescharacteristic
338#333C22×C7311yescharacteristic
339#332C22×C7311yescharacteristic
340#332C22×C7311yescharacteristic
341#332C22×C7311yescharacteristic
342#332C22×C7311yescharacteristic
343#332C22×C7311yescharacteristic
344#332C22×C7311yescharacteristic
345C2×Q16—21no—
346C2×Q16—21no—
347C2×SD16—21no—
348C2×SD16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C22×C8—21no—
353C22×C8—21no—
354C4⋊Q8C23×C7311yescharacteristic
355C4⋊Q8C23×C7311yescharacteristic
356C4⋊Q8C23×C7311yescharacteristic
357C4⋊Q8C23×C7311yescharacteristic
358#126—21no—
359#125—21no—
360#125—21no—
361#125D4×C7311yescharacteristic
362#124D4×C7311yescharacteristic
363#123—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8D4×C7311yescharacteristic
369#121D4×C7311yescharacteristic
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8C23×C7311yescharacteristic
375C4×D4—21no—
376C4×D4C23×C7311yescharacteristic
377#117—21no—
378#117—21no—
379#117—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⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8D4×C7311yescharacteristic
395C4⋊C8D4×C7311yescharacteristic
396C4⋊C8C23×C7311yescharacteristic
397C4⋊C8C23×C7311yescharacteristic
398C4⋊C8C23×C7311yescharacteristic
399C4⋊C8C23×C7311yescharacteristic
400C4⋊C8C23×C7311yescharacteristic
401C4⋊C8C23×C7311yescharacteristic
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#102—21no—
413#102—21no—
414C22⋊C8—21no—
415C22⋊C8—21no—
416C22⋊C8D4×C7311yescharacteristic
417C22⋊C8D4×C7311yescharacteristic
418#97—21no—
419C4×C8—21no—
420C4×C8C23×C7311yescharacteristic
421C4×C8C23×C7311yescharacteristic
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8C2×D4×C7311yescharacteristic
427C2×D4—21no—
428C2×D4C2×D4×C7311yescharacteristic
429C22×C4—21no—
430C22×C4C2×D4×C7311yescharacteristic
431C22×C4C2×D4×C7311yescharacteristic
432C22×C4#41×C7311yescharacteristic
433Q16—81no—
434Q16—81no—
435SD16—81no—
436SD16—81no—
437M16—81no—
438M16—81no—
439M16—81no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—81no—
447C2×C8—81no—
448C2×C8C2×D4×C7311yescharacteristic
449C2×C8C2×D4×C7311yescharacteristic
450C2×C8C2×D4×C7311yescharacteristic
451C2×C8C2×D4×C7311yescharacteristic
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
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—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4C2×D4×C7311yescharacteristic
469C4⋊C4C2×D4×C7311yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C42—21no—
478C42—41no—
479C42—41no—
480C42C2×D4×C7311yescharacteristic
481C42C2×D4×C7311yescharacteristic
482C42#41×C7311yescharacteristic
483C42C24×C7311yescharacteristic
484C23—21no—
485C23#121×C7311yescharacteristic
486Q8—21no—
487Q8—21no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—81no—
495D4—21no—
496D4—21no—
497D4—81no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4#121×C7311yescharacteristic
513C2×C4#121×C7311yescharacteristic
514C2×C4#121×C7311yescharacteristic
515C2×C4C22×D4×C7311yescharacteristic
516C2×C4C22×D4×C7311yescharacteristic
517C2×C4C2×#41×C7311yescharacteristic
518C8—21no—
519C8—21no—
520C8—21no—
521C8—21no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—41no—
527C8—41no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22C2×#121×C7311yescharacteristic
535C4—21no—
536C4—21no—
537C4—21no—
538C4—21no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—81no—
543C4—81no—
544C4—81no—
545C4—81no—
546C4#576×C7311yescharacteristic
547C4#577×C7311yescharacteristic
548C4#578×C7311yescharacteristic
549C4#578×C7311yescharacteristic
550C2—41no—
551C2—81no—
552C2C73×#304611yescharacteristic
553C2C73×#306111yescharacteristic
554C2C73×#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×#3231C2semidirect
5. C73×#1700C2semidirect
6. C73×#1699C2semidirect
7. C73×#1692C2semidirect
8. C73×#1691C2semidirect
9. C73×#1684C2semidirect
10. C73×#1683C2semidirect
11. C73×#1674C2semidirect
12. C73×#1673C2semidirect
13. C73×#1571C2semidirect
14. C73×#1561C2semidirect
15. C73×#1550C2semidirect
272. #19550C73direct (N × H)
280. #3231C2×C73semidirect
282. #1700C2×C73semidirect
283. #1699C2×C73semidirect
284. #1692C2×C73semidirect
285. #1691C2×C73semidirect
286. #1684C2×C73semidirect
287. #1683C2×C73semidirect
288. #1674C2×C73semidirect
289. #1673C2×C73semidirect
290. #1571C2×C73semidirect
291. #1561C2×C73semidirect
292. #1550C2×C73semidirect
293. C73#19550direct (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×#32482
C73×#32312
C73×#29932
C73×#17002
C73×#16992
C73×#16922
C73×#16912
C73×#16842
C73×#16832
C73×#16742
C73×#16732
C73×#15712
C73×#15612
C73×#15502
#1955073