Finite Group Databasebeta

← C73×#19252 #32928656

Subgroups — C73×#19252 #32928656

Order 18688.

602 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3248C211yesmaximal, characteristic, complemented
2C73×#3212C211yesmaximal, characteristic
3C73×#3182C211yesmaximal, characteristic, complemented
4C73×#2969C211yesmaximal, characteristic, complemented
5C73×#1702C211yesmaximal, characteristic, complemented
6C73×#1700C211yesmaximal, characteristic, complemented
7C73×#1693C211yesmaximal, characteristic, complemented
8C73×#1685C211yesmaximal, characteristic, complemented
9C73×#1681C211yesmaximal, characteristic, complemented
10C73×#1679C211yesmaximal, characteristic, complemented
11C73×#1674C211yesmaximal, characteristic, complemented
12C73×#1666C211yesmaximal, characteristic, complemented
13C73×#1565C211yesmaximal, characteristic, complemented
14C73×#1544C211yesmaximal, characteristic, complemented
15C73×#1540C211yesmaximal, characteristic, complemented
16#533×C73C2211yescharacteristic
17#532×C73C2211yescharacteristic
18#529×C73C2211yescharacteristic
19#500×C73C2211yescharacteristic
20#495×C73—21no—
21#492×C73C2211yescharacteristic
22#488×C73—21no—
23#487×C73C2211yescharacteristic
24#486×C73C2211yescharacteristic
25#479×C73—21no—
26#475×C73C2211yescharacteristic
27#474×C73C2211yescharacteristic
28#468×C73—21no—
29#468×C73—21no—
30#467×C73—21no—
31#465×C73—21no—
32#464×C73—21no—
33#462×C73C2211yescharacteristic
34#462×C73C2211yescharacteristic
35#461×C73C2211yescharacteristic
36#461×C73C2211yescharacteristic
37#460×C73C2211yescharacteristic
38#459×C73C2211yescharacteristic
39#452×C73—21no—
40#449×C73—21no—
41#446×C73C2211yescharacteristic
42C8×Q8×C73C2211yescharacteristic
43#440×C73—21no—
44#440×C73—21no—
45#436×C73—21no—
46#436×C73C2211yescharacteristic
47#435×C73—21no—
48C8×D4×C73C2211yescharacteristic
49#433×C73—21no—
50#431×C73C2211yescharacteristic
51#431×C73C2211yescharacteristic
52C2×C4⋊C8×C73C2211yescharacteristic
53#405×C73—21no—
54C4×M16×C73C2211yescharacteristic
55#335×C73C2211yescharacteristic
56#335×C73C2211yescharacteristic
57#334×C73C2211yescharacteristic
58#334×C73C2211yescharacteristic
59#332×C73C2211yescharacteristic
60#332×C73C2211yescharacteristic
61#332×C73C2211yescharacteristic
62#332×C73C2211yescharacteristic
63#332×C73C2211yescharacteristic
64#332×C73C2211yescharacteristic
65#331×C73C2211yescharacteristic
66#331×C73C2211yescharacteristic
67C2×#41×C73—21no—
68C2×Q16×C73—21no—
69C2×Q16×C73—21no—
70C2×SD16×C73—21no—
71C2×SD16×C73—21no—
72C2×SD16×C73—21no—
73C2×SD16×C73—21no—
74C2×SD16×C73—21no—
75C2×D8×C73—21no—
76C2×M16×C73—21no—
77C2×M16×C73D411yescharacteristic
78C2×M16×C73D411yescharacteristic
79C22×C8×C73—21no—
80C22×C8×C73—21no—
81C4⋊Q8×C73C2311yescharacteristic
82C4⋊Q8×C73C2311yescharacteristic
83C4⋊Q8×C73C2311yescharacteristic
84#127×C73C2311yescharacteristic
85#126×C73—21no—
86#125×C73—21no—
87#125×C73D411yescharacteristic
88#124×C73—21no—
89#124×C73D411yescharacteristic
90#123×C73—21no—
91C22⋊Q8×C73—21no—
92C22⋊Q8×C73—21no—
93C22⋊Q8×C73D411yescharacteristic
94#121×C73—21no—
95#121×C73—21no—
96#121×C73D411yescharacteristic
97C4×Q8×C73—21no—
98C4×Q8×C73—21no—
99C4×Q8×C73C2311yescharacteristic
100C4×D4×C73—21no—
101C4×D4×C73—21no—
102C4×D4×C73—21no—
103C4×D4×C73C2311yescharacteristic
104#117×C73—21no—
105#117×C73—21no—
106C2×C42×C73C2311yescharacteristic
107#107×C73—21no—
108#107×C73—21no—
109#107×C73—21no—
110#106×C73—21no—
111C4⋊C8×C73—21no—
112C4⋊C8×C73—21no—
113C4⋊C8×C73—21no—
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#102×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—
136#97×C73—21no—
137#97×C73D411yescharacteristic
138#97×C73D411yescharacteristic
139C4×C8×C73—21no—
140C4×C8×C73—21no—
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#41×C73—81no—
145#41×C73—81no—
146C2×Q8×C73—21no—
147C2×Q8×C73—21no—
148C2×Q8×C73—21no—
149C2×Q8×C73C2×D411yescharacteristic
150C2×D4×C73—21no—
151C2×D4×C73—21no—
152C2×D4×C73—21no—
153C2×D4×C73—21no—
154C2×D4×C73—41no—
155C2×D4×C73C2×D411yescharacteristic
156C22×C4×C73—21no—
157C22×C4×C73—41no—
158C22×C4×C73C2×D411yescharacteristic
159C22×C4×C73C2×D411yescharacteristic
160C22×C4×C73#4111yescharacteristic
161Q16×C73—81no—
162Q16×C73—81no—
163SD16×C73—42no—
164SD16×C73—42no—
165SD16×C73—81no—
166SD16×C73—81no—
167SD16×C73—81no—
168D8×C73—81no—
169M16×C73—22no—
170M16×C73—41no—
171M16×C73—42no—
172C2×C8×C73—21no—
173C2×C8×C73—21no—
174C2×C8×C73—21no—
175C2×C8×C73—21no—
176C2×C8×C73—21no—
177C2×C8×C73—21no—
178C2×C8×C73—42no—
179C2×C8×C73—81no—
180C2×C8×C73C2×D411yescharacteristic
181C2×C8×C73C2×D411yescharacteristic
182C2×C8×C73C2×D411yescharacteristic
183C2×C8×C73C2×D411yescharacteristic
184C4⋊C4×C73—21no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—21no—
188C4⋊C4×C73—21no—
189C4⋊C4×C73—21no—
190C4⋊C4×C73—21no—
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—41no—
195C4⋊C4×C73—41no—
196C4⋊C4×C73C2×D411yescharacteristic
197C4⋊C4×C73C2×D411yescharacteristic
198C22⋊C4×C73—21no—
199C22⋊C4×C73—21no—
200C22⋊C4×C73—21no—
201C22⋊C4×C73—21no—
202C22⋊C4×C73—21no—
203C22⋊C4×C73—41no—
204C22⋊C4×C73—41no—
205C22⋊C4×C73—41no—
206C42×C73—21no—
207C42×C73—41no—
208C42×C73C2×D411yescharacteristic
209C42×C73C2×D411yescharacteristic
210C42×C73#4111yescharacteristic
211C42×C73C2411yescharacteristic
212C23×C73—21no—
213C23×C73—41no—
214C23×C73#12111yescharacteristic
215Q8×C73—21no—
216Q8×C73—21no—
217Q8×C73—41no—
218Q8×C73—41no—
219Q8×C73—41no—
220Q8×C73—41no—
221Q8×C73—41no—
222Q8×C73—41no—
223D4×C73—21no—
224D4×C73—21no—
225D4×C73—41no—
226D4×C73—41no—
227D4×C73—41no—
228D4×C73—41no—
229D4×C73—81no—
230D4×C73—81no—
231D4×C73—82no—
232C2×C4×C73—21no—
233C2×C4×C73—21no—
234C2×C4×C73—21no—
235C2×C4×C73—21no—
236C2×C4×C73—21no—
237C2×C4×C73—21no—
238C2×C4×C73—21no—
239C2×C4×C73—41no—
240C2×C4×C73—41no—
241C2×C4×C73—41no—
242C2×C4×C73—41no—
243C2×C4×C73—41no—
244C2×C4×C73—41no—
245C2×C4×C73—82no—
246C2×C4×C73#12111yescharacteristic
247C2×C4×C73#12111yescharacteristic
248C2×C4×C73#12111yescharacteristic
249C2×C4×C73C22×D411yescharacteristic
250C2×C4×C73C22×D411yescharacteristic
251C2×C4×C73C2×#4111yescharacteristic
252C8×C73—21no—
253C8×C73—21no—
254C8×C73—21no—
255C8×C73—41no—
256C8×C73—41no—
257C8×C73—41no—
258C8×C73—41no—
259C8×C73—41no—
260C8×C73—41no—
261C8×C73#13512yes—
262C22×C73—21no—
263C22×C73—21no—
264C22×C73—21no—
265C22×C73—41no—
266C22×C73—41no—
267C22×C73—41no—
268C22×C73—81no—
269C22×C73—81no—
270C22×C73—81no—
271C22×C73C2×#12111yescharacteristic
272C4×C73—21no—
273C4×C73—21no—
274C4×C73—21no—
275C4×C73—21no—
276C4×C73—41no—
277C4×C73—41no—
278C4×C73—41no—
279C4×C73—81no—
280C4×C73—81no—
281C4×C73—81no—
282C4×C73C2×#13511yescharacteristic
283C4×C73#57511yescharacteristic
284C4×C73#57611yescharacteristic
285C4×C73#57711yescharacteristic
286#19252C7311yesmaximal, characteristic, direct product factor, Sylow
287C2×C73—41no—
288C2×C73—81no—
289C2×C73—161no—
290C2×C73#303511yescharacteristic
291C2×C73#306211yescharacteristic
292C2×C73#306911yescharacteristic
293#3248C2×C7311yescharacteristic, complemented
294#3212C2×C7311yescharacteristic
295#3182C2×C7311yescharacteristic, complemented
296#2969C2×C7311yescharacteristic, complemented
297#1702C2×C7311yescharacteristic, complemented
298#1700C2×C7311yescharacteristic, complemented
299#1693C2×C7311yescharacteristic, complemented
300#1685C2×C7311yescharacteristic, complemented
301#1681C2×C7311yescharacteristic, complemented
302#1679C2×C7311yescharacteristic, complemented
303#1674C2×C7311yescharacteristic, complemented
304#1666C2×C7311yescharacteristic, complemented
305#1565C2×C7311yescharacteristic, complemented
306#1544C2×C7311yescharacteristic, complemented
307#1540C2×C7311yescharacteristic, complemented
308C73#1925211yescharacteristic, direct product factor, Sylow
309#533C22×C7311yescharacteristic
310#532C22×C7311yescharacteristic
311#529C22×C7311yescharacteristic
312#500C22×C7311yescharacteristic
313#495—21no—
314#492C22×C7311yescharacteristic
315#488—21no—
316#487C22×C7311yescharacteristic
317#486C22×C7311yescharacteristic
318#479—21no—
319#475C22×C7311yescharacteristic
320#474C22×C7311yescharacteristic
321#468—21no—
322#468—21no—
323#467—21no—
324#465—21no—
325#464—21no—
326#462C22×C7311yescharacteristic
327#462C22×C7311yescharacteristic
328#461C22×C7311yescharacteristic
329#461C22×C7311yescharacteristic
330#460C22×C7311yescharacteristic
331#459C22×C7311yescharacteristic
332#452—21no—
333#449—21no—
334#446C22×C7311yescharacteristic
335C8×Q8C22×C7311yescharacteristic
336#440—21no—
337#440—21no—
338#436—21no—
339#436C22×C7311yescharacteristic
340#435—21no—
341C8×D4C22×C7311yescharacteristic
342#433—21no—
343#431C22×C7311yescharacteristic
344#431C22×C7311yescharacteristic
345C2×C4⋊C8C22×C7311yescharacteristic
346#405—21no—
347C4×M16C22×C7311yescharacteristic
348#335C22×C7311yescharacteristic
349#335C22×C7311yescharacteristic
350#334C22×C7311yescharacteristic
351#334C22×C7311yescharacteristic
352#332C22×C7311yescharacteristic
353#332C22×C7311yescharacteristic
354#332C22×C7311yescharacteristic
355#332C22×C7311yescharacteristic
356#332C22×C7311yescharacteristic
357#332C22×C7311yescharacteristic
358#331C22×C7311yescharacteristic
359#331C22×C7311yescharacteristic
360C2×#41—21no—
361C2×Q16—21no—
362C2×Q16—21no—
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×D8—21no—
369C2×M16—21no—
370C2×M16D4×C7311yescharacteristic
371C2×M16D4×C7311yescharacteristic
372C22×C8—21no—
373C22×C8—21no—
374C4⋊Q8C23×C7311yescharacteristic
375C4⋊Q8C23×C7311yescharacteristic
376C4⋊Q8C23×C7311yescharacteristic
377#127C23×C7311yescharacteristic
378#126—21no—
379#125—21no—
380#125D4×C7311yescharacteristic
381#124—21no—
382#124D4×C7311yescharacteristic
383#123—21no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8D4×C7311yescharacteristic
387#121—21no—
388#121—21no—
389#121D4×C7311yescharacteristic
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8C23×C7311yescharacteristic
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4C23×C7311yescharacteristic
397#117—21no—
398#117—21no—
399C2×C42C23×C7311yescharacteristic
400#107—21no—
401#107—21no—
402#107—21no—
403#106—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8C23×C7311yescharacteristic
408C4⋊C8C23×C7311yescharacteristic
409C4⋊C8C23×C7311yescharacteristic
410C4⋊C8C23×C7311yescharacteristic
411C4⋊C8C23×C7311yescharacteristic
412C4⋊C8C23×C7311yescharacteristic
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429#97—21no—
430#97D4×C7311yescharacteristic
431#97D4×C7311yescharacteristic
432C4×C8—21no—
433C4×C8—21no—
434C4×C8—21no—
435C4×C8C23×C7311yescharacteristic
436C4×C8C23×C7311yescharacteristic
437#41—81no—
438#41—81no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8C2×D4×C7311yescharacteristic
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4C2×D4×C7311yescharacteristic
449C22×C4—21no—
450C22×C4—41no—
451C22×C4C2×D4×C7311yescharacteristic
452C22×C4C2×D4×C7311yescharacteristic
453C22×C4#41×C7311yescharacteristic
454Q16—81no—
455Q16—81no—
456SD16—42no—
457SD16—42no—
458SD16—81no—
459SD16—81no—
460SD16—81no—
461D8—81no—
462M16—22no—
463M16—41no—
464M16—42no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—42no—
472C2×C8—81no—
473C2×C8C2×D4×C7311yescharacteristic
474C2×C8C2×D4×C7311yescharacteristic
475C2×C8C2×D4×C7311yescharacteristic
476C2×C8C2×D4×C7311yescharacteristic
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4C2×D4×C7311yescharacteristic
490C4⋊C4C2×D4×C7311yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C42—21no—
500C42—41no—
501C42C2×D4×C7311yescharacteristic
502C42C2×D4×C7311yescharacteristic
503C42#41×C7311yescharacteristic
504C42C24×C7311yescharacteristic
505C23—21no—
506C23—41no—
507C23#121×C7311yescharacteristic
508Q8—21no—
509Q8—21no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516D4—21no—
517D4—21no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—81no—
523D4—81no—
524D4—82no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—82no—
539C2×C4#121×C7311yescharacteristic
540C2×C4#121×C7311yescharacteristic
541C2×C4#121×C7311yescharacteristic
542C2×C4C22×D4×C7311yescharacteristic
543C2×C4C22×D4×C7311yescharacteristic
544C2×C4C2×#41×C7311yescharacteristic
545C8—21no—
546C8—21no—
547C8—21no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8#135×C7312yes—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22C2×#121×C7311yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4C2×#135×C7311yescharacteristic
576C4#575×C7311yescharacteristic
577C4#576×C7311yescharacteristic
578C4#577×C7311yescharacteristic
579C2—41no—
580C2—81no—
581C2—161no—
582C2C73×#303511yescharacteristic
583C2C73×#306211yescharacteristic
584C2C73×#306911yescharacteristic
subgroupG/H
center, socleC22×C73C2×#121
commutator, Frattini, cosocleC42C24×C73
prime radicalC73×#3212C2
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
1. C73×#3248C2semidirect
3. C73×#3182C2semidirect
4. C73×#2969C2semidirect
5. C73×#1702C2semidirect
6. C73×#1700C2semidirect
7. C73×#1693C2semidirect
8. C73×#1685C2semidirect
9. C73×#1681C2semidirect
10. C73×#1679C2semidirect
11. C73×#1674C2semidirect
12. C73×#1666C2semidirect
13. C73×#1565C2semidirect
14. C73×#1544C2semidirect
15. C73×#1540C2semidirect
286. #19252C73direct (N × H)
293. #3248C2×C73semidirect
295. #3182C2×C73semidirect
296. #2969C2×C73semidirect
297. #1702C2×C73semidirect
298. #1700C2×C73semidirect
299. #1693C2×C73semidirect
300. #1685C2×C73semidirect
301. #1681C2×C73semidirect
302. #1679C2×C73semidirect
303. #1674C2×C73semidirect
304. #1666C2×C73semidirect
305. #1565C2×C73semidirect
306. #1544C2×C73semidirect
307. #1540C2×C73semidirect
308. C73#19252direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#32482
C73×#32122
C73×#31822
C73×#29692
C73×#17022
C73×#17002
C73×#16932
C73×#16852
C73×#16812
C73×#16792
C73×#16742
C73×#16662
C73×#15652
C73×#15442
C73×#15402
#1925273