Finite Group Databasebeta

← C73×#20000 #32929404

Subgroups — C73×#20000 #32929404

Order 18688.

592 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3365C211yesmaximal, characteristic, complemented
2C73×#3361C211yesmaximal, characteristic
3C73×#3359C211yesmaximal, characteristic, complemented
4C73×#3299C211yesmaximal, characteristic, complemented
5C73×#1711C211yesmaximal, characteristic, complemented
6C73×#1684C211yesmaximal, characteristic, complemented
7C73×#1681C211yesmaximal, characteristic
8C73×#1680C211yesmaximal, characteristic, complemented
9C73×#1678C211yesmaximal, characteristic, complemented
10C73×#1643C211yesmaximal, characteristic, complemented
11C73×#1640C211yesmaximal, characteristic, complemented
12C73×#1636C211yesmaximal, characteristic, complemented
13C73×#1627C211yesmaximal, characteristic
14C8×Q16×C73C211yesmaximal, characteristic, complemented
15C8×SD16×C73C211yesmaximal, characteristic, complemented
16#559×C73C2211yescharacteristic
17#557×C73C2211yescharacteristic
18#554×C73C2211yescharacteristic
19D4×Q8×C73C2211yescharacteristic
20#488×C73—21no—
21#488×C73—21no—
22#487×C73—21no—
23#487×C73C2211yescharacteristic
24#487×C73C2211yescharacteristic
25#487×C73C2211yescharacteristic
26#486×C73C2211yescharacteristic
27#486×C73C2211yescharacteristic
28#486×C73C2211yescharacteristic
29#484×C73—21no—
30#478×C73—21no—
31#478×C73—21no—
32#477×C73C2211yescharacteristic
33#477×C73C2211yescharacteristic
34#475×C73—21no—
35#475×C73C2211yescharacteristic
36#475×C73C2211yescharacteristic
37#467×C73—21no—
38#464×C73—21no—
39#463×C73—21no—
40#462×C73C2211yescharacteristic
41#461×C73—21no—
42#461×C73C2211yescharacteristic
43#460×C73C2211yescharacteristic
44#459×C73C2211yescharacteristic
45#451×C73—21no—
46C8×Q8×C73C2211yescharacteristic
47C8×Q8×C73C2211yescharacteristic
48C8×Q8×C73C2211yescharacteristic
49C4×Q16×C73C2211yescharacteristic
50C4×SD16×C73—21no—
51C4×SD16×C73—21no—
52C4×SD16×C73C2211yescharacteristic
53C4×D8×C73—21no—
54C8×D4×C73C2211yescharacteristic
55C2×#103×C73—21no—
56#335×C73C2211yescharacteristic
57#334×C73C2211yescharacteristic
58#333×C73C2211yescharacteristic
59#332×C73C2211yescharacteristic
60#332×C73C2211yescharacteristic
61#331×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×C73D411yescharacteristic
70C2×SD16×C73—21no—
71C2×SD16×C73—21no—
72C2×SD16×C73D411yescharacteristic
73C2×D8×C73—21no—
74C22×C8×C73—21no—
75C4⋊Q8×C73—21no—
76C4⋊Q8×C73—21no—
77C4⋊Q8×C73C2311yescharacteristic
78C4⋊Q8×C73C2311yescharacteristic
79C4⋊Q8×C73C2311yescharacteristic
80#127×C73C2311yescharacteristic
81#125×C73—21no—
82#125×C73—21no—
83#125×C73—41no—
84#124×C73—21no—
85#124×C73—21no—
86#123×C73—41no—
87C22⋊Q8×C73—21no—
88C22⋊Q8×C73—21no—
89C22⋊Q8×C73—41no—
90C22⋊Q8×C73—41no—
91C4×Q8×C73—21no—
92C4×Q8×C73—21no—
93C4×Q8×C73C2311yescharacteristic
94C4×Q8×C73C2311yescharacteristic
95C4×Q8×C73C2311yescharacteristic
96C4×D4×C73—21no—
97C4×D4×C73—21no—
98C4×D4×C73—21no—
99C4×D4×C73—21no—
100C4×D4×C73C2311yescharacteristic
101C2×C4⋊C4×C73—21no—
102#107×C73—21no—
103#107×C73—21no—
104#107×C73D411yescharacteristic
105#106×C73—21no—
106#106×C73—21no—
107#106×C73D411yescharacteristic
108C4⋊C8×C73—21no—
109C4⋊C8×C73—21no—
110C4⋊C8×C73—21no—
111C4⋊C8×C73C2311yescharacteristic
112C4⋊C8×C73C2311yescharacteristic
113C4⋊C8×C73C2311yescharacteristic
114C4⋊C8×C73C2311yescharacteristic
115#103×C73—21no—
116#103×C73—21no—
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—41no—
126#103×C73D411yescharacteristic
127#103×C73D411yescharacteristic
128#103×C73D411yescharacteristic
129#102×C73—21no—
130#102×C73—21no—
131#102×C73—21no—
132#102×C73—21no—
133#102×C73—21no—
134#102×C73—21no—
135#102×C73—41no—
136#102×C73D411yescharacteristic
137C22⋊C8×C73—21no—
138C4×C8×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—41no—
148C2×Q8×C73—42no—
149C2×Q8×C73—81no—
150C2×Q8×C73C2×D411yescharacteristic
151C2×Q8×C73C2×D411yescharacteristic
152C2×Q8×C73C2×D411yescharacteristic
153C2×D4×C73—21no—
154C2×D4×C73—21no—
155C2×D4×C73—21no—
156C2×D4×C73C2×D411yescharacteristic
157C22×C4×C73—21no—
158C22×C4×C73—41no—
159C22×C4×C73—41no—
160C22×C4×C73—41no—
161Q16×C73—22no—
162Q16×C73—81no—
163SD16×C73—22no—
164SD16×C73—42no—
165SD16×C73—42no—
166D8×C73—42no—
167C2×C8×C73—21no—
168C2×C8×C73—21no—
169C2×C8×C73—21no—
170C2×C8×C73—21no—
171C2×C8×C73—21no—
172C2×C8×C73—81no—
173C2×C8×C73C2×D411yescharacteristic
174C2×C8×C73C2×D411yescharacteristic
175C2×C8×C73C2×D411yescharacteristic
176C2×C8×C73C2×D411yescharacteristic
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×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—
200C22⋊C4×C73—41no—
201C22⋊C4×C73—41no—
202C42×C73—21no—
203C42×C73—21no—
204C42×C73—21no—
205C42×C73—41no—
206C42×C73C2411yescharacteristic
207C23×C73—21no—
208C23×C73—41no—
209Q8×C73—21no—
210Q8×C73—21no—
211Q8×C73—21no—
212Q8×C73—21no—
213Q8×C73—21no—
214Q8×C73—41no—
215Q8×C73—41no—
216Q8×C73—41no—
217Q8×C73—41no—
218Q8×C73—82no—
219Q8×C73—81no—
220Q8×C73#13512yes—
221D4×C73—21no—
222D4×C73—41no—
223D4×C73—41no—
224D4×C73—41no—
225D4×C73—41no—
226D4×C73—81no—
227D4×C73#13512yes—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—21no—
233C2×C4×C73—21no—
234C2×C4×C73—21no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73—41no—
239C2×C4×C73—41no—
240C2×C4×C73—82no—
241C2×C4×C73—161no—
242C2×C4×C73—161no—
243C2×C4×C73C22×D411yescharacteristic
244C2×C4×C73C22×D411yescharacteristic
245C2×C4×C73H(5,𝔽2)11yescharacteristic
246C8×C73—21no—
247C8×C73—21no—
248C8×C73—21no—
249C8×C73—21no—
250C8×C73—41no—
251C8×C73—41no—
252C8×C73—41no—
253C8×C73—41no—
254C8×C73—41no—
255C22×C73—22no—
256C22×C73—41no—
257C22×C73—41no—
258C22×C73—81no—
259C22×C73—81no—
260C22×C73—81no—
261C22×C73D4211yescharacteristic
262C4×C73—22no—
263C4×C73—21no—
264C4×C73—41no—
265C4×C73—41no—
266C4×C73—41no—
267C4×C73—41no—
268C4×C73—41no—
269C4×C73—41no—
270C4×C73—81no—
271C4×C73—81no—
272C4×C73—81no—
273C4×C73C2×#13511yescharacteristic
274C4×C73C2×#13511yescharacteristic
275C4×C73#57711yescharacteristic
276C4×C73#57811yescharacteristic
277#20000C7311yesmaximal, characteristic, direct product factor, Sylow
278C2×C73—42no—
279C2×C73—161no—
280C2×C73#328211yescharacteristic
281C2×C73#328511yescharacteristic
282C2×C73#329011yescharacteristic
283#3365C2×C7311yescharacteristic, complemented
284#3361C2×C7311yescharacteristic
285#3359C2×C7311yescharacteristic, complemented
286#3299C2×C7311yescharacteristic, complemented
287#1711C2×C7311yescharacteristic, complemented
288#1684C2×C7311yescharacteristic, complemented
289#1681C2×C7311yescharacteristic
290#1680C2×C7311yescharacteristic, complemented
291#1678C2×C7311yescharacteristic, complemented
292#1643C2×C7311yescharacteristic, complemented
293#1640C2×C7311yescharacteristic, complemented
294#1636C2×C7311yescharacteristic, complemented
295#1627C2×C7311yescharacteristic
296C8×Q16C2×C7311yescharacteristic, complemented
297C8×SD16C2×C7311yescharacteristic, complemented
298C73#2000011yescharacteristic, direct product factor, Sylow
299#559C22×C7311yescharacteristic
300#557C22×C7311yescharacteristic
301#554C22×C7311yescharacteristic
302D4×Q8C22×C7311yescharacteristic
303#488—21no—
304#488—21no—
305#487—21no—
306#487C22×C7311yescharacteristic
307#487C22×C7311yescharacteristic
308#487C22×C7311yescharacteristic
309#486C22×C7311yescharacteristic
310#486C22×C7311yescharacteristic
311#486C22×C7311yescharacteristic
312#484—21no—
313#478—21no—
314#478—21no—
315#477C22×C7311yescharacteristic
316#477C22×C7311yescharacteristic
317#475—21no—
318#475C22×C7311yescharacteristic
319#475C22×C7311yescharacteristic
320#467—21no—
321#464—21no—
322#463—21no—
323#462C22×C7311yescharacteristic
324#461—21no—
325#461C22×C7311yescharacteristic
326#460C22×C7311yescharacteristic
327#459C22×C7311yescharacteristic
328#451—21no—
329C8×Q8C22×C7311yescharacteristic
330C8×Q8C22×C7311yescharacteristic
331C8×Q8C22×C7311yescharacteristic
332C4×Q16C22×C7311yescharacteristic
333C4×SD16—21no—
334C4×SD16—21no—
335C4×SD16C22×C7311yescharacteristic
336C4×D8—21no—
337C8×D4C22×C7311yescharacteristic
338C2×#103—21no—
339#335C22×C7311yescharacteristic
340#334C22×C7311yescharacteristic
341#333C22×C7311yescharacteristic
342#332C22×C7311yescharacteristic
343#332C22×C7311yescharacteristic
344#331C22×C7311yescharacteristic
345Q8⋊C8C22×C7311yescharacteristic
346Q8⋊C8C22×C7311yescharacteristic
347Q8⋊C8C22×C7311yescharacteristic
348D4⋊C8C22×C7311yescharacteristic
349C82C22×C7311yescharacteristic
350C22×Q8—21no—
351C2×Q16—21no—
352C2×Q16D4×C7311yescharacteristic
353C2×SD16—21no—
354C2×SD16—21no—
355C2×SD16D4×C7311yescharacteristic
356C2×D8—21no—
357C22×C8—21no—
358C4⋊Q8—21no—
359C4⋊Q8—21no—
360C4⋊Q8C23×C7311yescharacteristic
361C4⋊Q8C23×C7311yescharacteristic
362C4⋊Q8C23×C7311yescharacteristic
363#127C23×C7311yescharacteristic
364#125—21no—
365#125—21no—
366#125—41no—
367#124—21no—
368#124—21no—
369#123—41no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372C22⋊Q8—41no—
373C22⋊Q8—41no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8C23×C7311yescharacteristic
377C4×Q8C23×C7311yescharacteristic
378C4×Q8C23×C7311yescharacteristic
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4C23×C7311yescharacteristic
384C2×C4⋊C4—21no—
385#107—21no—
386#107—21no—
387#107D4×C7311yescharacteristic
388#106—21no—
389#106—21no—
390#106D4×C7311yescharacteristic
391C4⋊C8—21no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8C23×C7311yescharacteristic
395C4⋊C8C23×C7311yescharacteristic
396C4⋊C8C23×C7311yescharacteristic
397C4⋊C8C23×C7311yescharacteristic
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#103—41no—
409#103D4×C7311yescharacteristic
410#103D4×C7311yescharacteristic
411#103D4×C7311yescharacteristic
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—41no—
419#102D4×C7311yescharacteristic
420C22⋊C8—21no—
421C4×C8—21no—
422C4×C8—21no—
423C4×C8—21no—
424C4×C8C23×C7311yescharacteristic
425C4×C8C23×C7311yescharacteristic
426C4×C8C23×C7311yescharacteristic
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—41no—
431C2×Q8—42no—
432C2×Q8—81no—
433C2×Q8C2×D4×C7311yescharacteristic
434C2×Q8C2×D4×C7311yescharacteristic
435C2×Q8C2×D4×C7311yescharacteristic
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4C2×D4×C7311yescharacteristic
440C22×C4—21no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444Q16—22no—
445Q16—81no—
446SD16—22no—
447SD16—42no—
448SD16—42no—
449D8—42no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—81no—
456C2×C8C2×D4×C7311yescharacteristic
457C2×C8C2×D4×C7311yescharacteristic
458C2×C8C2×D4×C7311yescharacteristic
459C2×C8C2×D4×C7311yescharacteristic
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—21no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4C2×D4×C7311yescharacteristic
476C4⋊C4C2×D4×C7311yescharacteristic
477C4⋊C4C2×D4×C7311yescharacteristic
478C4⋊C4C2×D4×C7311yescharacteristic
479C22⋊C4—21no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—41no—
489C42C24×C7311yescharacteristic
490C23—21no—
491C23—41no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—82no—
502Q8—81no—
503Q8#135×C7312yes—
504D4—21no—
505D4—41no—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—81no—
510D4#135×C7312yes—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—82no—
524C2×C4—161no—
525C2×C4—161no—
526C2×C4C22×D4×C7311yescharacteristic
527C2×C4C22×D4×C7311yescharacteristic
528C2×C4H(5,𝔽2)×C7311yescharacteristic
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C22—22no—
539C22—41no—
540C22—41no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22D42×C7311yescharacteristic
545C4—22no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4C2×#135×C7311yescharacteristic
557C4C2×#135×C7311yescharacteristic
558C4#577×C7311yescharacteristic
559C4#578×C7311yescharacteristic
560C2—42no—
561C2—161no—
562C2C73×#328211yescharacteristic
563C2C73×#328511yescharacteristic
564C2C73×#329011yescharacteristic
subgroupG/H
center, socleC22×C73D42
commutator, Frattini, cosocleC42C24×C73
prime radical#459×C73C22
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×#3365C2semidirect
3. C73×#3359C2semidirect
4. C73×#3299C2semidirect
5. C73×#1711C2semidirect
6. C73×#1684C2semidirect
8. C73×#1680C2semidirect
9. C73×#1678C2semidirect
10. C73×#1643C2semidirect
11. C73×#1640C2semidirect
12. C73×#1636C2semidirect
14. C8×Q16×C73C2semidirect
15. C8×SD16×C73C2semidirect
277. #20000C73direct (N × H)
283. #3365C2×C73semidirect
285. #3359C2×C73semidirect
286. #3299C2×C73semidirect
287. #1711C2×C73semidirect
288. #1684C2×C73semidirect
290. #1680C2×C73semidirect
291. #1678C2×C73semidirect
292. #1643C2×C73semidirect
293. #1640C2×C73semidirect
294. #1636C2×C73semidirect
296. C8×Q16C2×C73semidirect
297. C8×SD16C2×C73semidirect
298. C73#20000direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#33652
C73×#33612
C73×#33592
C73×#32992
C73×#17112
C73×#16842
C73×#16812
C73×#16802
C73×#16782
C73×#16432
C73×#16402
C73×#16362
C73×#16272
C8×Q16×C732
C8×SD16×C732
#2000073