Finite Group Databasebeta

← C73×#19920 #32929324

Subgroups — C73×#19920 #32929324

Order 18688.

572 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3374C211yesmaximal, characteristic, complemented
2C73×#3364C211yesmaximal, characteristic
3C73×#3359C211yesmaximal, characteristic
4C73×#3328C211yesmaximal, characteristic
5C73×#1710C211yesmaximal, characteristic, complemented
6C73×#1700C211yesmaximal, characteristic, complemented
7C73×#1699C211yesmaximal, characteristic
8C73×#1680C211yesmaximal, characteristic, complemented
9C73×#1680C211yesmaximal, characteristic, complemented
10C73×#1650C211yesmaximal, characteristic
11C73×#1649C211yesmaximal, characteristic
12C73×#1648C211yesmaximal, characteristic, complemented
13C73×#1648C211yesmaximal, characteristic, complemented
14C73×#1590C211yesmaximal, characteristic
15C8×Q16×C73C211yesmaximal, characteristic, complemented
16#557×C73C2211yescharacteristic
17#557×C73C2211yescharacteristic
18#556×C73C2211yescharacteristic
19D4×Q8×C73C2211yescharacteristic
20#500×C73C2211yescharacteristic
21#500×C73C2211yescharacteristic
22#491×C73—21no—
23#488×C73—21no—
24#487×C73—21no—
25#487×C73C2211yescharacteristic
26#487×C73C2211yescharacteristic
27#487×C73C2211yescharacteristic
28#487×C73C2211yescharacteristic
29#485×C73—21no—
30#479×C73—21no—
31#479×C73—21no—
32#475×C73—21no—
33#475×C73C2211yescharacteristic
34#475×C73C2211yescharacteristic
35#475×C73C2211yescharacteristic
36#474×C73C2211yescharacteristic
37#470×C73—21no—
38#464×C73—21no—
39#462×C73—21no—
40#462×C73C2211yescharacteristic
41#462×C73C2211yescharacteristic
42#462×C73C2211yescharacteristic
43#461×C73—21no—
44#461×C73C2211yescharacteristic
45#451×C73—21no—
46#446×C73C2211yescharacteristic
47C8×Q8×C73C2211yescharacteristic
48C8×Q8×C73C2211yescharacteristic
49#441×C73—21no—
50C4×Q16×C73—21no—
51C4×Q16×C73C2211yescharacteristic
52C4×SD16×C73—21no—
53C4×SD16×C73C2211yescharacteristic
54#436×C73C2211yescharacteristic
55#419×C73—21no—
56#335×C73C2211yescharacteristic
57#334×C73C2211yescharacteristic
58#332×C73C2211yescharacteristic
59#332×C73C2211yescharacteristic
60#332×C73C2211yescharacteristic
61#332×C73C2211yescharacteristic
62Q8⋊C8×C73C2211yescharacteristic
63Q8⋊C8×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66C82×C73C2211yescharacteristic
67C22×Q8×C73—21no—
68C2×Q16×C73—21no—
69C2×Q16×C73—21no—
70C2×Q16×C73—21no—
71C2×Q16×C73D411yescharacteristic
72C2×SD16×C73—21no—
73C2×SD16×C73D411yescharacteristic
74C2×M16×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—41no—
83#125×C73—21no—
84#125×C73—21no—
85#125×C73—41no—
86#125×C73—41no—
87#124×C73—21no—
88C22⋊Q8×C73—21no—
89C22⋊Q8×C73—21no—
90C22⋊Q8×C73—41no—
91C4×Q8×C73—21no—
92C4×Q8×C73—21no—
93C4×Q8×C73—21no—
94C4×Q8×C73—21no—
95C4×Q8×C73—21no—
96C4×Q8×C73C2311yescharacteristic
97C4×Q8×C73C2311yescharacteristic
98C4×Q8×C73C2311yescharacteristic
99C4×D4×C73—21no—
100C4×D4×C73C2311yescharacteristic
101#117×C73—21no—
102#107×C73—21no—
103#107×C73—41no—
104#107×C73—41no—
105#107×C73D411yescharacteristic
106#106×C73—21no—
107#106×C73—21no—
108#106×C73—21no—
109#106×C73D411yescharacteristic
110C4⋊C8×C73—21no—
111C4⋊C8×C73—21no—
112C4⋊C8×C73—21no—
113C4⋊C8×C73C2311yescharacteristic
114C4⋊C8×C73C2311yescharacteristic
115C4⋊C8×C73C2311yescharacteristic
116C4⋊C8×C73C2311yescharacteristic
117#103×C73—21no—
118#103×C73—21no—
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—21no—
127#103×C73—21no—
128#103×C73—21no—
129#103×C73—21no—
130#103×C73—21no—
131#103×C73—21no—
132#103×C73D411yescharacteristic
133#103×C73D411yescharacteristic
134#103×C73D411yescharacteristic
135#102×C73—21no—
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×C73—21no—
148C2×Q8×C73—41no—
149C2×Q8×C73—42no—
150C2×Q8×C73—81no—
151C2×Q8×C73C2×D411yescharacteristic
152C2×Q8×C73C2×D411yescharacteristic
153C2×Q8×C73C2×D411yescharacteristic
154C2×D4×C73C2×D411yescharacteristic
155C22×C4×C73—21no—
156C22×C4×C73—41no—
157Q16×C73—22no—
158Q16×C73—42no—
159Q16×C73—42no—
160Q16×C73—81no—
161SD16×C73—41no—
162SD16×C73—42no—
163M16×C73—81no—
164C2×C8×C73—21no—
165C2×C8×C73—21no—
166C2×C8×C73—21no—
167C2×C8×C73—21no—
168C2×C8×C73—21no—
169C2×C8×C73C2×D411yescharacteristic
170C2×C8×C73C2×D411yescharacteristic
171C2×C8×C73C2×D411yescharacteristic
172C2×C8×C73C2×D411yescharacteristic
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—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×C73—41no—
191C4⋊C4×C73—41no—
192C4⋊C4×C73C2×D411yescharacteristic
193C4⋊C4×C73C2×D411yescharacteristic
194C4⋊C4×C73C2×D411yescharacteristic
195C4⋊C4×C73C2×D411yescharacteristic
196C22⋊C4×C73—21no—
197C22⋊C4×C73—41no—
198C22⋊C4×C73—41no—
199C22⋊C4×C73—41no—
200C42×C73—21no—
201C42×C73—21no—
202C42×C73—21no—
203C42×C73—41no—
204C42×C73—41no—
205C42×C73—41no—
206C42×C73C2411yescharacteristic
207C23×C73—21no—
208Q8×C73—21no—
209Q8×C73—21no—
210Q8×C73—21no—
211Q8×C73—21no—
212Q8×C73—21no—
213Q8×C73—41no—
214Q8×C73—41no—
215Q8×C73—41no—
216Q8×C73—41no—
217Q8×C73—41no—
218Q8×C73—41no—
219Q8×C73—41no—
220Q8×C73—41no—
221Q8×C73—82no—
222Q8×C73#13512yes—
223D4×C73—21no—
224D4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73—82no—
239C2×C4×C73C22×D411yescharacteristic
240C2×C4×C73C22×D411yescharacteristic
241C2×C4×C73H(5,𝔽2)11yescharacteristic
242C8×C73—22no—
243C8×C73—21no—
244C8×C73—21no—
245C8×C73—21no—
246C8×C73—21no—
247C8×C73—41no—
248C8×C73—41no—
249C8×C73—41no—
250C8×C73—41no—
251C22×C73—41no—
252C22×C73—41no—
253C22×C73—41no—
254C22×C73D4211yescharacteristic
255C4×C73—22no—
256C4×C73—21no—
257C4×C73—41no—
258C4×C73—41no—
259C4×C73—41no—
260C4×C73—41no—
261C4×C73—41no—
262C4×C73—41no—
263C4×C73—81no—
264C4×C73—81no—
265C4×C73—81no—
266C4×C73—81no—
267C4×C73C2×#13511yescharacteristic
268C4×C73#57511yescharacteristic
269C4×C73#57711yescharacteristic
270C4×C73#57811yescharacteristic
271#19920C7311yesmaximal, characteristic, direct product factor, Sylow
272C2×C73—81no—
273C2×C73#327711yescharacteristic
274C2×C73#328211yescharacteristic
275C2×C73#329311yescharacteristic
276#3374C2×C7311yescharacteristic, complemented
277#3364C2×C7311yescharacteristic
278#3359C2×C7311yescharacteristic
279#3328C2×C7311yescharacteristic
280#1710C2×C7311yescharacteristic, complemented
281#1700C2×C7311yescharacteristic, complemented
282#1699C2×C7311yescharacteristic
283#1680C2×C7311yescharacteristic, complemented
284#1680C2×C7311yescharacteristic, complemented
285#1650C2×C7311yescharacteristic
286#1649C2×C7311yescharacteristic
287#1648C2×C7311yescharacteristic, complemented
288#1648C2×C7311yescharacteristic, complemented
289#1590C2×C7311yescharacteristic
290C8×Q16C2×C7311yescharacteristic, complemented
291C73#1992011yescharacteristic, direct product factor, Sylow
292#557C22×C7311yescharacteristic
293#557C22×C7311yescharacteristic
294#556C22×C7311yescharacteristic
295D4×Q8C22×C7311yescharacteristic
296#500C22×C7311yescharacteristic
297#500C22×C7311yescharacteristic
298#491—21no—
299#488—21no—
300#487—21no—
301#487C22×C7311yescharacteristic
302#487C22×C7311yescharacteristic
303#487C22×C7311yescharacteristic
304#487C22×C7311yescharacteristic
305#485—21no—
306#479—21no—
307#479—21no—
308#475—21no—
309#475C22×C7311yescharacteristic
310#475C22×C7311yescharacteristic
311#475C22×C7311yescharacteristic
312#474C22×C7311yescharacteristic
313#470—21no—
314#464—21no—
315#462—21no—
316#462C22×C7311yescharacteristic
317#462C22×C7311yescharacteristic
318#462C22×C7311yescharacteristic
319#461—21no—
320#461C22×C7311yescharacteristic
321#451—21no—
322#446C22×C7311yescharacteristic
323C8×Q8C22×C7311yescharacteristic
324C8×Q8C22×C7311yescharacteristic
325#441—21no—
326C4×Q16—21no—
327C4×Q16C22×C7311yescharacteristic
328C4×SD16—21no—
329C4×SD16C22×C7311yescharacteristic
330#436C22×C7311yescharacteristic
331#419—21no—
332#335C22×C7311yescharacteristic
333#334C22×C7311yescharacteristic
334#332C22×C7311yescharacteristic
335#332C22×C7311yescharacteristic
336#332C22×C7311yescharacteristic
337#332C22×C7311yescharacteristic
338Q8⋊C8C22×C7311yescharacteristic
339Q8⋊C8C22×C7311yescharacteristic
340Q8⋊C8C22×C7311yescharacteristic
341D4⋊C8C22×C7311yescharacteristic
342C82C22×C7311yescharacteristic
343C22×Q8—21no—
344C2×Q16—21no—
345C2×Q16—21no—
346C2×Q16—21no—
347C2×Q16D4×C7311yescharacteristic
348C2×SD16—21no—
349C2×SD16D4×C7311yescharacteristic
350C2×M16—21no—
351C4⋊Q8—21no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8C23×C7311yescharacteristic
355C4⋊Q8C23×C7311yescharacteristic
356C4⋊Q8C23×C7311yescharacteristic
357C4⋊Q8C23×C7311yescharacteristic
358#126—41no—
359#125—21no—
360#125—21no—
361#125—41no—
362#125—41no—
363#124—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—41no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8C23×C7311yescharacteristic
373C4×Q8C23×C7311yescharacteristic
374C4×Q8C23×C7311yescharacteristic
375C4×D4—21no—
376C4×D4C23×C7311yescharacteristic
377#117—21no—
378#107—21no—
379#107—41no—
380#107—41no—
381#107D4×C7311yescharacteristic
382#106—21no—
383#106—21no—
384#106—21no—
385#106D4×C7311yescharacteristic
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8—21no—
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#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103D4×C7311yescharacteristic
409#103D4×C7311yescharacteristic
410#103D4×C7311yescharacteristic
411#102—21no—
412#102D4×C7311yescharacteristic
413C22⋊C8—21no—
414#97—21no—
415C4×C8—21no—
416C4×C8—21no—
417C4×C8C23×C7311yescharacteristic
418C4×C8C23×C7311yescharacteristic
419C4×C8C23×C7311yescharacteristic
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—41no—
425C2×Q8—42no—
426C2×Q8—81no—
427C2×Q8C2×D4×C7311yescharacteristic
428C2×Q8C2×D4×C7311yescharacteristic
429C2×Q8C2×D4×C7311yescharacteristic
430C2×D4C2×D4×C7311yescharacteristic
431C22×C4—21no—
432C22×C4—41no—
433Q16—22no—
434Q16—42no—
435Q16—42no—
436Q16—81no—
437SD16—41no—
438SD16—42no—
439M16—81no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8C2×D4×C7311yescharacteristic
446C2×C8C2×D4×C7311yescharacteristic
447C2×C8C2×D4×C7311yescharacteristic
448C2×C8C2×D4×C7311yescharacteristic
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—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4C2×D4×C7311yescharacteristic
469C4⋊C4C2×D4×C7311yescharacteristic
470C4⋊C4C2×D4×C7311yescharacteristic
471C4⋊C4C2×D4×C7311yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—41no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—41no—
480C42—41no—
481C42—41no—
482C42C24×C7311yescharacteristic
483C23—21no—
484Q8—21no—
485Q8—21no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—82no—
498Q8#135×C7312yes—
499D4—21no—
500D4—21no—
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—82no—
515C2×C4C22×D4×C7311yescharacteristic
516C2×C4C22×D4×C7311yescharacteristic
517C2×C4H(5,𝔽2)×C7311yescharacteristic
518C8—22no—
519C8—21no—
520C8—21no—
521C8—21no—
522C8—21no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22D42×C7311yescharacteristic
531C4—22no—
532C4—21no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—81no—
540C4—81no—
541C4—81no—
542C4—81no—
543C4C2×#135×C7311yescharacteristic
544C4#575×C7311yescharacteristic
545C4#577×C7311yescharacteristic
546C4#578×C7311yescharacteristic
547C2—81no—
548C2C73×#327711yescharacteristic
549C2C73×#328211yescharacteristic
550C2C73×#329311yescharacteristic
subgroupG/H
center, socleC22×C73D42
commutator, Frattini, cosocleC42C24×C73
prime radicalC2×D4×C73C2×D4
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×#3374C2semidirect
5. C73×#1710C2semidirect
6. C73×#1700C2semidirect
8. C73×#1680C2semidirect
9. C73×#1680C2semidirect
12. C73×#1648C2semidirect
13. C73×#1648C2semidirect
15. C8×Q16×C73C2semidirect
271. #19920C73direct (N × H)
276. #3374C2×C73semidirect
280. #1710C2×C73semidirect
281. #1700C2×C73semidirect
283. #1680C2×C73semidirect
284. #1680C2×C73semidirect
287. #1648C2×C73semidirect
288. #1648C2×C73semidirect
290. C8×Q16C2×C73semidirect
291. C73#19920direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#33742
C73×#33642
C73×#33592
C73×#33282
C73×#17102
C73×#17002
C73×#16992
C73×#16802
C73×#16502
C73×#16492
C73×#16482
C73×#15902
C8×Q16×C732
#1992073