Finite Group Databasebeta

← C73×#19941 #32929345

Subgroups — C73×#19941 #32929345

Order 18688.

560 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×#3375C211yesmaximal, characteristic
2C73×#3374C211yesmaximal, characteristic, complemented
3C73×#3365C211yesmaximal, characteristic
4C73×#3363C211yesmaximal, characteristic, complemented
5C73×#1711C211yesmaximal, characteristic
6C73×#1700C211yesmaximal, characteristic, complemented
7C73×#1698C211yesmaximal, characteristic
8C73×#1684C211yesmaximal, characteristic, complemented
9C73×#1682C211yesmaximal, characteristic
10C73×#1645C211yesmaximal, characteristic, complemented
11C73×#1640C211yesmaximal, characteristic
12C73×#1636C211yesmaximal, characteristic, complemented
13C73×#1626C211yesmaximal, characteristic
14C73×#1591C211yesmaximal, characteristic, complemented
15C8×Q16×C73C211yesmaximal, characteristic, complemented
16#559×C73C2211yescharacteristic
17Q82×C73C2211yescharacteristic
18#557×C73C2211yescharacteristic
19#557×C73C2211yescharacteristic
20#491×C73—21no—
21#489×C73—21no—
22#488×C73—21no—
23#487×C73—21no—
24#487×C73C2211yescharacteristic
25#487×C73C2211yescharacteristic
26#487×C73C2211yescharacteristic
27#486×C73C2211yescharacteristic
28#486×C73C2211yescharacteristic
29#486×C73C2211yescharacteristic
30#479×C73—21no—
31#478×C73—21no—
32#477×C73—21no—
33#477×C73C2211yescharacteristic
34#477×C73C2211yescharacteristic
35#475×C73C2211yescharacteristic
36#475×C73C2211yescharacteristic
37#474×C73—21no—
38#464×C73—21no—
39#464×C73—21no—
40#462×C73—21no—
41#462×C73—21no—
42#462×C73C2211yescharacteristic
43#462×C73C2211yescharacteristic
44#460×C73C2211yescharacteristic
45#460×C73C2211yescharacteristic
46#446×C73C2211yescharacteristic
47#446×C73C2211yescharacteristic
48C8×Q8×C73C2211yescharacteristic
49C8×Q8×C73C2211yescharacteristic
50#441×C73—21no—
51#440×C73—21no—
52C4×Q16×C73—21no—
53C4×Q16×C73C2211yescharacteristic
54C4×Q16×C73C2211yescharacteristic
55C4×SD16×C73—21no—
56#335×C73C2211yescharacteristic
57#335×C73C2211yescharacteristic
58#333×C73C2211yescharacteristic
59#332×C73C2211yescharacteristic
60#332×C73C2211yescharacteristic
61#331×C73C2211yescharacteristic
62Q8⋊C8×C73C2211yescharacteristic
63Q8⋊C8×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65Q8⋊C8×C73C2211yescharacteristic
66C82×C73C2211yescharacteristic
67C2×Q16×C73—21no—
68C2×Q16×C73—21no—
69C2×Q16×C73D411yescharacteristic
70C2×Q16×C73D411yescharacteristic
71C2×SD16×C73—21no—
72C2×SD16×C73—21no—
73C4⋊Q8×C73—21no—
74C4⋊Q8×C73—21no—
75C4⋊Q8×C73—21no—
76C4⋊Q8×C73—21no—
77C4⋊Q8×C73—41no—
78C4⋊Q8×C73C2311yescharacteristic
79C4⋊Q8×C73C2311yescharacteristic
80C4⋊Q8×C73C2311yescharacteristic
81#127×C73C2311yescharacteristic
82#125×C73—21no—
83#125×C73—21no—
84#125×C73—41no—
85#125×C73—41no—
86#124×C73—21no—
87#124×C73—21no—
88#123×C73—41no—
89C4×Q8×C73—21no—
90C4×Q8×C73—21no—
91C4×Q8×C73—21no—
92C4×Q8×C73—21no—
93C4×Q8×C73—21no—
94C4×Q8×C73—21no—
95C4×Q8×C73C2311yescharacteristic
96C4×Q8×C73C2311yescharacteristic
97C4×Q8×C73C2311yescharacteristic
98C4×Q8×C73C2311yescharacteristic
99C4×D4×C73—21no—
100C4×D4×C73—21no—
101#107×C73—21no—
102#107×C73—21no—
103#107×C73D411yescharacteristic
104#107×C73D411yescharacteristic
105#106×C73—21no—
106#106×C73—21no—
107C4⋊C8×C73—21no—
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#103×C73D411yescharacteristic
130#102×C73—21no—
131#102×C73—21no—
132#102×C73—21no—
133#102×C73—21no—
134#102×C73—21no—
135#102×C73—21no—
136#102×C73—41no—
137#97×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—41no—
148C2×Q8×C73C2×D411yescharacteristic
149C2×Q8×C73C2×D411yescharacteristic
150C2×Q8×C73C2×D411yescharacteristic
151C2×Q8×C73C2×D411yescharacteristic
152C2×D4×C73—21no—
153C2×D4×C73—21no—
154C2×D4×C73—21no—
155C22×C4×C73—41no—
156Q16×C73—22no—
157Q16×C73—41no—
158Q16×C73—42no—
159Q16×C73—42no—
160SD16×C73—42no—
161SD16×C73—42no—
162C2×C8×C73—21no—
163C2×C8×C73—21no—
164C2×C8×C73—21no—
165C2×C8×C73—21no—
166C2×C8×C73—21no—
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—41no—
182C4⋊C4×C73—41no—
183C4⋊C4×C73—41no—
184C4⋊C4×C73—41no—
185C4⋊C4×C73—41no—
186C4⋊C4×C73—41no—
187C4⋊C4×C73—41no—
188C4⋊C4×C73—41no—
189C4⋊C4×C73C2×D411yescharacteristic
190C4⋊C4×C73C2×D411yescharacteristic
191C4⋊C4×C73C2×D411yescharacteristic
192C4⋊C4×C73C2×D411yescharacteristic
193C22⋊C4×C73—41no—
194C22⋊C4×C73—41no—
195C22⋊C4×C73—41no—
196C42×C73—21no—
197C42×C73—21no—
198C42×C73—21no—
199C42×C73—21no—
200C42×C73—41no—
201C42×C73—41no—
202C42×C73—41no—
203C42×C73C2411yescharacteristic
204C23×C73—41no—
205Q8×C73—21no—
206Q8×C73—21no—
207Q8×C73—21no—
208Q8×C73—21no—
209Q8×C73—21no—
210Q8×C73—21no—
211Q8×C73—21no—
212Q8×C73—41no—
213Q8×C73—41no—
214Q8×C73—41no—
215Q8×C73—41no—
216Q8×C73—81no—
217Q8×C73—161no—
218Q8×C73#13512yes—
219D4×C73—41no—
220D4×C73—41no—
221D4×C73—41no—
222D4×C73—41no—
223D4×C73—81no—
224C2×C4×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—161no—
236C2×C4×C73C22×D411yescharacteristic
237C2×C4×C73C22×D411yescharacteristic
238C2×C4×C73H(5,𝔽2)11yescharacteristic
239C8×C73—21no—
240C8×C73—21no—
241C8×C73—21no—
242C8×C73—21no—
243C8×C73—41no—
244C8×C73—41no—
245C8×C73—41no—
246C8×C73—41no—
247C8×C73—41no—
248C22×C73—81no—
249C22×C73—81no—
250C22×C73—81no—
251C22×C73D4211yescharacteristic
252C4×C73—22no—
253C4×C73—21no—
254C4×C73—41no—
255C4×C73—41no—
256C4×C73—41no—
257C4×C73—41no—
258C4×C73—41no—
259C4×C73—41no—
260C4×C73—41no—
261C4×C73—81no—
262C4×C73—81no—
263C4×C73—81no—
264C4×C73C2×#13511yescharacteristic
265C4×C73#57511yescharacteristic
266C4×C73#57811yescharacteristic
267C4×C73#57811yescharacteristic
268#19941C7311yesmaximal, characteristic, direct product factor, Sylow
269C2×C73—161no—
270C2×C73#327711yescharacteristic
271C2×C73#328511yescharacteristic
272C2×C73#329011yescharacteristic
273#3375C2×C7311yescharacteristic
274#3374C2×C7311yescharacteristic, complemented
275#3365C2×C7311yescharacteristic
276#3363C2×C7311yescharacteristic, complemented
277#1711C2×C7311yescharacteristic
278#1700C2×C7311yescharacteristic, complemented
279#1698C2×C7311yescharacteristic
280#1684C2×C7311yescharacteristic, complemented
281#1682C2×C7311yescharacteristic
282#1645C2×C7311yescharacteristic, complemented
283#1640C2×C7311yescharacteristic
284#1636C2×C7311yescharacteristic, complemented
285#1626C2×C7311yescharacteristic
286#1591C2×C7311yescharacteristic, complemented
287C8×Q16C2×C7311yescharacteristic, complemented
288C73#1994111yescharacteristic, direct product factor, Sylow
289#559C22×C7311yescharacteristic
290Q82C22×C7311yescharacteristic
291#557C22×C7311yescharacteristic
292#557C22×C7311yescharacteristic
293#491—21no—
294#489—21no—
295#488—21no—
296#487—21no—
297#487C22×C7311yescharacteristic
298#487C22×C7311yescharacteristic
299#487C22×C7311yescharacteristic
300#486C22×C7311yescharacteristic
301#486C22×C7311yescharacteristic
302#486C22×C7311yescharacteristic
303#479—21no—
304#478—21no—
305#477—21no—
306#477C22×C7311yescharacteristic
307#477C22×C7311yescharacteristic
308#475C22×C7311yescharacteristic
309#475C22×C7311yescharacteristic
310#474—21no—
311#464—21no—
312#464—21no—
313#462—21no—
314#462—21no—
315#462C22×C7311yescharacteristic
316#462C22×C7311yescharacteristic
317#460C22×C7311yescharacteristic
318#460C22×C7311yescharacteristic
319#446C22×C7311yescharacteristic
320#446C22×C7311yescharacteristic
321C8×Q8C22×C7311yescharacteristic
322C8×Q8C22×C7311yescharacteristic
323#441—21no—
324#440—21no—
325C4×Q16—21no—
326C4×Q16C22×C7311yescharacteristic
327C4×Q16C22×C7311yescharacteristic
328C4×SD16—21no—
329#335C22×C7311yescharacteristic
330#335C22×C7311yescharacteristic
331#333C22×C7311yescharacteristic
332#332C22×C7311yescharacteristic
333#332C22×C7311yescharacteristic
334#331C22×C7311yescharacteristic
335Q8⋊C8C22×C7311yescharacteristic
336Q8⋊C8C22×C7311yescharacteristic
337Q8⋊C8C22×C7311yescharacteristic
338Q8⋊C8C22×C7311yescharacteristic
339C82C22×C7311yescharacteristic
340C2×Q16—21no—
341C2×Q16—21no—
342C2×Q16D4×C7311yescharacteristic
343C2×Q16D4×C7311yescharacteristic
344C2×SD16—21no—
345C2×SD16—21no—
346C4⋊Q8—21no—
347C4⋊Q8—21no—
348C4⋊Q8—21no—
349C4⋊Q8—21no—
350C4⋊Q8—41no—
351C4⋊Q8C23×C7311yescharacteristic
352C4⋊Q8C23×C7311yescharacteristic
353C4⋊Q8C23×C7311yescharacteristic
354#127C23×C7311yescharacteristic
355#125—21no—
356#125—21no—
357#125—41no—
358#125—41no—
359#124—21no—
360#124—21no—
361#123—41no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8C23×C7311yescharacteristic
369C4×Q8C23×C7311yescharacteristic
370C4×Q8C23×C7311yescharacteristic
371C4×Q8C23×C7311yescharacteristic
372C4×D4—21no—
373C4×D4—21no—
374#107—21no—
375#107—21no—
376#107D4×C7311yescharacteristic
377#107D4×C7311yescharacteristic
378#106—21no—
379#106—21no—
380C4⋊C8—21no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8C23×C7311yescharacteristic
385C4⋊C8C23×C7311yescharacteristic
386C4⋊C8C23×C7311yescharacteristic
387C4⋊C8C23×C7311yescharacteristic
388#103—21no—
389#103—21no—
390#103—21no—
391#103—21no—
392#103—21no—
393#103—21no—
394#103—21no—
395#103—21no—
396#103—21no—
397#103—21no—
398#103—41no—
399#103D4×C7311yescharacteristic
400#103D4×C7311yescharacteristic
401#103D4×C7311yescharacteristic
402#103D4×C7311yescharacteristic
403#102—21no—
404#102—21no—
405#102—21no—
406#102—21no—
407#102—21no—
408#102—21no—
409#102—41no—
410#97—21no—
411#97—21no—
412C4×C8—21no—
413C4×C8—21no—
414C4×C8C23×C7311yescharacteristic
415C4×C8C23×C7311yescharacteristic
416C4×C8C23×C7311yescharacteristic
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—41no—
421C2×Q8C2×D4×C7311yescharacteristic
422C2×Q8C2×D4×C7311yescharacteristic
423C2×Q8C2×D4×C7311yescharacteristic
424C2×Q8C2×D4×C7311yescharacteristic
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C22×C4—41no—
429Q16—22no—
430Q16—41no—
431Q16—42no—
432Q16—42no—
433SD16—42no—
434SD16—42no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
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—41no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4C2×D4×C7311yescharacteristic
463C4⋊C4C2×D4×C7311yescharacteristic
464C4⋊C4C2×D4×C7311yescharacteristic
465C4⋊C4C2×D4×C7311yescharacteristic
466C22⋊C4—41no—
467C22⋊C4—41no—
468C22⋊C4—41no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—41no—
474C42—41no—
475C42—41no—
476C42C24×C7311yescharacteristic
477C23—41no—
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—41no—
486Q8—41no—
487Q8—41no—
488Q8—41no—
489Q8—81no—
490Q8—161no—
491Q8#135×C7312yes—
492D4—41no—
493D4—41no—
494D4—41no—
495D4—41no—
496D4—81no—
497C2×C4—21no—
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—161no—
509C2×C4C22×D4×C7311yescharacteristic
510C2×C4C22×D4×C7311yescharacteristic
511C2×C4H(5,𝔽2)×C7311yescharacteristic
512C8—21no—
513C8—21no—
514C8—21no—
515C8—21no—
516C8—41no—
517C8—41no—
518C8—41no—
519C8—41no—
520C8—41no—
521C22—81no—
522C22—81no—
523C22—81no—
524C22D42×C7311yescharacteristic
525C4—22no—
526C4—21no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—81no—
535C4—81no—
536C4—81no—
537C4C2×#135×C7311yescharacteristic
538C4#575×C7311yescharacteristic
539C4#578×C7311yescharacteristic
540C4#578×C7311yescharacteristic
541C2—161no—
542C2C73×#327711yescharacteristic
543C2C73×#328511yescharacteristic
544C2C73×#329011yescharacteristic
subgroupG/H
center, socleC22×C73D42
commutator, Frattini, cosocleC42C24×C73
prime radical#127×C73C23
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ C42×C73 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C73×#3374C2semidirect
4. C73×#3363C2semidirect
6. C73×#1700C2semidirect
8. C73×#1684C2semidirect
10. C73×#1645C2semidirect
12. C73×#1636C2semidirect
14. C73×#1591C2semidirect
15. C8×Q16×C73C2semidirect
268. #19941C73direct (N × H)
274. #3374C2×C73semidirect
276. #3363C2×C73semidirect
278. #1700C2×C73semidirect
280. #1684C2×C73semidirect
282. #1645C2×C73semidirect
284. #1636C2×C73semidirect
286. #1591C2×C73semidirect
287. C8×Q16C2×C73semidirect
288. C73#19941direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#33752
C73×#33742
C73×#33652
C73×#33632
C73×#17112
C73×#17002
C73×#16982
C73×#16842
C73×#16822
C73×#16452
C73×#16402
C73×#16362
C73×#16262
C73×#15912
C8×Q16×C732
#1994173