Finite Group Databasebeta

← C73×#19248 #32928652

Subgroups — C73×#19248 #32928652

Order 18688.

624 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3247C211yesmaximal, characteristic, complemented
2C73×#3212C211yesmaximal, characteristic, complemented
3C73×#3184C211yesmaximal, characteristic, complemented
4C73×#2969C211yesmaximal, characteristic, complemented
5C73×#1701C211yesmaximal, characteristic, complemented
6C73×#1697C211yesmaximal, characteristic, complemented
7C73×#1692C211yesmaximal, characteristic, complemented
8C73×#1688C211yesmaximal, characteristic, complemented
9C73×#1682C211yesmaximal, characteristic, complemented
10C73×#1678C211yesmaximal, characteristic, complemented
11C73×#1671C211yesmaximal, characteristic, complemented
12C73×#1667C211yesmaximal, characteristic, complemented
13C73×#1565C211yesmaximal, characteristic, complemented
14C73×#1543C211yesmaximal, characteristic, complemented
15C73×#1540C211yesmaximal, characteristic, complemented
16#532×C73C2211yescharacteristic
17#532×C73C2211yescharacteristic
18#529×C73C2211yescharacteristic
19#498×C73C2211yescharacteristic
20#495×C73—21no—
21#493×C73C2211yescharacteristic
22#488×C73—21no—
23#486×C73C2211yescharacteristic
24#486×C73C2211yescharacteristic
25#478×C73—21no—
26#477×C73C2211yescharacteristic
27#476×C73C2211yescharacteristic
28#469×C73—21no—
29#469×C73—21no—
30#466×C73—21no—
31#465×C73—21no—
32#463×C73—21no—
33#462×C73C2211yescharacteristic
34#461×C73C2211yescharacteristic
35#460×C73C2211yescharacteristic
36#460×C73C2211yescharacteristic
37#459×C73C2211yescharacteristic
38#459×C73C2211yescharacteristic
39#452×C73—21no—
40#449×C73—21no—
41#446×C73C2211yescharacteristic
42C8×Q8×C73C2211yescharacteristic
43#442×C73—21no—
44#442×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#333×C73C2211yescharacteristic
60#333×C73C2211yescharacteristic
61#332×C73C2211yescharacteristic
62#332×C73C2211yescharacteristic
63#331×C73C2211yescharacteristic
64#331×C73C2211yescharacteristic
65#331×C73C2211yescharacteristic
66#331×C73C2211yescharacteristic
67C2×#41×C73—21no—
68C2×#41×C73—21no—
69C2×Q16×C73—21no—
70C2×SD16×C73—21no—
71C2×SD16×C73—21no—
72C2×SD16×C73—21no—
73C2×D8×C73—21no—
74C2×D8×C73—21no—
75C2×D8×C73—21no—
76C2×D8×C73—21no—
77C2×M16×C73—21no—
78C2×M16×C73D411yescharacteristic
79C2×M16×C73D411yescharacteristic
80C22×C8×C73—21no—
81C22×C8×C73—21no—
82C4⋊Q8×C73C2311yescharacteristic
83C4⋊Q8×C73C2311yescharacteristic
84#127×C73C2311yescharacteristic
85#127×C73C2311yescharacteristic
86#126×C73—21no—
87#125×C73D411yescharacteristic
88#124×C73—21no—
89#124×C73—21no—
90#124×C73D411yescharacteristic
91#123×C73—21no—
92C22⋊Q8×C73D411yescharacteristic
93#121×C73—21no—
94#121×C73—21no—
95#121×C73—21no—
96#121×C73—21no—
97#121×C73D411yescharacteristic
98C4×Q8×C73C2311yescharacteristic
99C4×D4×C73—21no—
100C4×D4×C73—21no—
101C4×D4×C73—21no—
102C4×D4×C73—21no—
103C4×D4×C73—21no—
104C4×D4×C73C2311yescharacteristic
105#117×C73—21no—
106C2×C42×C73C2311yescharacteristic
107#107×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×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#102×C73—21no—
124#102×C73—21no—
125#102×C73—21no—
126#102×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—
146#41×C73—82no—
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—21no—
155C2×D4×C73—21no—
156C2×D4×C73—21no—
157C2×D4×C73—41no—
158C2×D4×C73—41no—
159C2×D4×C73C2×D411yescharacteristic
160C22×C4×C73—21no—
161C22×C4×C73—41no—
162C22×C4×C73—41no—
163C22×C4×C73C2×D411yescharacteristic
164C22×C4×C73C2×D411yescharacteristic
165C22×C4×C73#4111yescharacteristic
166Q16×C73—81no—
167SD16×C73—81no—
168SD16×C73—81no—
169SD16×C73—81no—
170D8×C73—42no—
171D8×C73—42no—
172D8×C73—81no—
173D8×C73—81no—
174M16×C73—22no—
175M16×C73—41no—
176M16×C73—42no—
177C2×C8×C73—21no—
178C2×C8×C73—21no—
179C2×C8×C73—21no—
180C2×C8×C73—21no—
181C2×C8×C73—21no—
182C2×C8×C73—21no—
183C2×C8×C73—42no—
184C2×C8×C73—81no—
185C2×C8×C73C2×D411yescharacteristic
186C2×C8×C73C2×D411yescharacteristic
187C2×C8×C73C2×D411yescharacteristic
188C2×C8×C73C2×D411yescharacteristic
189C4⋊C4×C73—21no—
190C4⋊C4×C73—21no—
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73C2×D411yescharacteristic
198C4⋊C4×C73C2×D411yescharacteristic
199C22⋊C4×C73—21no—
200C22⋊C4×C73—21no—
201C22⋊C4×C73—21no—
202C22⋊C4×C73—21no—
203C22⋊C4×C73—21no—
204C22⋊C4×C73—41no—
205C22⋊C4×C73—41no—
206C22⋊C4×C73—41no—
207C22⋊C4×C73—41no—
208C42×C73—21no—
209C42×C73C2×D411yescharacteristic
210C42×C73C2×D411yescharacteristic
211C42×C73#4111yescharacteristic
212C42×C73C2411yescharacteristic
213C23×C73—21no—
214C23×C73—41no—
215C23×C73—41no—
216C23×C73#12111yescharacteristic
217Q8×C73—21no—
218Q8×C73—21no—
219Q8×C73—41no—
220Q8×C73—41no—
221Q8×C73—81no—
222D4×C73—21no—
223D4×C73—21no—
224D4×C73—41no—
225D4×C73—41no—
226D4×C73—41no—
227D4×C73—41no—
228D4×C73—41no—
229D4×C73—41no—
230D4×C73—41no—
231D4×C73—41no—
232D4×C73—81no—
233D4×C73—81no—
234D4×C73—81no—
235D4×C73—82no—
236D4×C73—82no—
237C2×C4×C73—21no—
238C2×C4×C73—21no—
239C2×C4×C73—21no—
240C2×C4×C73—21no—
241C2×C4×C73—21no—
242C2×C4×C73—21no—
243C2×C4×C73—21no—
244C2×C4×C73—41no—
245C2×C4×C73—41no—
246C2×C4×C73—41no—
247C2×C4×C73—41no—
248C2×C4×C73—41no—
249C2×C4×C73—82no—
250C2×C4×C73—82no—
251C2×C4×C73#12111yescharacteristic
252C2×C4×C73#12111yescharacteristic
253C2×C4×C73#12111yescharacteristic
254C2×C4×C73C22×D411yescharacteristic
255C2×C4×C73C22×D411yescharacteristic
256C2×C4×C73C2×#4111yescharacteristic
257C8×C73—21no—
258C8×C73—21no—
259C8×C73—21no—
260C8×C73—41no—
261C8×C73—41no—
262C8×C73—41no—
263C8×C73—41no—
264C8×C73—41no—
265C8×C73—41no—
266C8×C73#13512yes—
267C22×C73—21no—
268C22×C73—21no—
269C22×C73—21no—
270C22×C73—41no—
271C22×C73—41no—
272C22×C73—41no—
273C22×C73—81no—
274C22×C73—81no—
275C22×C73—81no—
276C22×C73—81no—
277C22×C73—81no—
278C22×C73—81no—
279C22×C73C2×#12111yescharacteristic
280C4×C73—21no—
281C4×C73—21no—
282C4×C73—21no—
283C4×C73—21no—
284C4×C73—41no—
285C4×C73—41no—
286C4×C73—41no—
287C4×C73—81no—
288C4×C73—81no—
289C4×C73C2×#13511yescharacteristic
290C4×C73#57511yescharacteristic
291C4×C73#57611yescharacteristic
292C4×C73#57711yescharacteristic
293#19248C7311yesmaximal, characteristic, direct product factor, Sylow
294C2×C73—41no—
295C2×C73—81no—
296C2×C73—161no—
297C2×C73—161no—
298C2×C73#303511yescharacteristic
299C2×C73#306211yescharacteristic
300C2×C73#306811yescharacteristic
301#3247C2×C7311yescharacteristic, complemented
302#3212C2×C7311yescharacteristic, complemented
303#3184C2×C7311yescharacteristic, complemented
304#2969C2×C7311yescharacteristic, complemented
305#1701C2×C7311yescharacteristic, complemented
306#1697C2×C7311yescharacteristic, complemented
307#1692C2×C7311yescharacteristic, complemented
308#1688C2×C7311yescharacteristic, complemented
309#1682C2×C7311yescharacteristic, complemented
310#1678C2×C7311yescharacteristic, complemented
311#1671C2×C7311yescharacteristic, complemented
312#1667C2×C7311yescharacteristic, complemented
313#1565C2×C7311yescharacteristic, complemented
314#1543C2×C7311yescharacteristic, complemented
315#1540C2×C7311yescharacteristic, complemented
316C73#1924811yescharacteristic, direct product factor, Sylow
317#532C22×C7311yescharacteristic
318#532C22×C7311yescharacteristic
319#529C22×C7311yescharacteristic
320#498C22×C7311yescharacteristic
321#495—21no—
322#493C22×C7311yescharacteristic
323#488—21no—
324#486C22×C7311yescharacteristic
325#486C22×C7311yescharacteristic
326#478—21no—
327#477C22×C7311yescharacteristic
328#476C22×C7311yescharacteristic
329#469—21no—
330#469—21no—
331#466—21no—
332#465—21no—
333#463—21no—
334#462C22×C7311yescharacteristic
335#461C22×C7311yescharacteristic
336#460C22×C7311yescharacteristic
337#460C22×C7311yescharacteristic
338#459C22×C7311yescharacteristic
339#459C22×C7311yescharacteristic
340#452—21no—
341#449—21no—
342#446C22×C7311yescharacteristic
343C8×Q8C22×C7311yescharacteristic
344#442—21no—
345#442—21no—
346#436—21no—
347#436C22×C7311yescharacteristic
348#435—21no—
349C8×D4C22×C7311yescharacteristic
350#433—21no—
351#431C22×C7311yescharacteristic
352#431C22×C7311yescharacteristic
353C2×C4⋊C8C22×C7311yescharacteristic
354#405—21no—
355C4×M16C22×C7311yescharacteristic
356#335C22×C7311yescharacteristic
357#335C22×C7311yescharacteristic
358#334C22×C7311yescharacteristic
359#334C22×C7311yescharacteristic
360#333C22×C7311yescharacteristic
361#333C22×C7311yescharacteristic
362#332C22×C7311yescharacteristic
363#332C22×C7311yescharacteristic
364#331C22×C7311yescharacteristic
365#331C22×C7311yescharacteristic
366#331C22×C7311yescharacteristic
367#331C22×C7311yescharacteristic
368C2×#41—21no—
369C2×#41—21no—
370C2×Q16—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16—21no—
374C2×D8—21no—
375C2×D8—21no—
376C2×D8—21no—
377C2×D8—21no—
378C2×M16—21no—
379C2×M16D4×C7311yescharacteristic
380C2×M16D4×C7311yescharacteristic
381C22×C8—21no—
382C22×C8—21no—
383C4⋊Q8C23×C7311yescharacteristic
384C4⋊Q8C23×C7311yescharacteristic
385#127C23×C7311yescharacteristic
386#127C23×C7311yescharacteristic
387#126—21no—
388#125D4×C7311yescharacteristic
389#124—21no—
390#124—21no—
391#124D4×C7311yescharacteristic
392#123—21no—
393C22⋊Q8D4×C7311yescharacteristic
394#121—21no—
395#121—21no—
396#121—21no—
397#121—21no—
398#121D4×C7311yescharacteristic
399C4×Q8C23×C7311yescharacteristic
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4C23×C7311yescharacteristic
406#117—21no—
407C2×C42C23×C7311yescharacteristic
408#107—21no—
409#106—21no—
410#106—21no—
411#106—21no—
412C4⋊C8—21no—
413C4⋊C8—21no—
414C4⋊C8—21no—
415C4⋊C8C23×C7311yescharacteristic
416C4⋊C8C23×C7311yescharacteristic
417C4⋊C8C23×C7311yescharacteristic
418C4⋊C8C23×C7311yescharacteristic
419C4⋊C8C23×C7311yescharacteristic
420C4⋊C8C23×C7311yescharacteristic
421#103—21no—
422#103—21no—
423#103—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433C22⋊C8—21no—
434C22⋊C8—21no—
435C22⋊C8—21no—
436C22⋊C8—21no—
437#97—21no—
438#97D4×C7311yescharacteristic
439#97D4×C7311yescharacteristic
440C4×C8—21no—
441C4×C8—21no—
442C4×C8—21no—
443C4×C8C23×C7311yescharacteristic
444C4×C8C23×C7311yescharacteristic
445#41—81no—
446#41—81no—
447#41—82no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8C2×D4×C7311yescharacteristic
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4C2×D4×C7311yescharacteristic
461C22×C4—21no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4C2×D4×C7311yescharacteristic
465C22×C4C2×D4×C7311yescharacteristic
466C22×C4#41×C7311yescharacteristic
467Q16—81no—
468SD16—81no—
469SD16—81no—
470SD16—81no—
471D8—42no—
472D8—42no—
473D8—81no—
474D8—81no—
475M16—22no—
476M16—41no—
477M16—42no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—42no—
485C2×C8—81no—
486C2×C8C2×D4×C7311yescharacteristic
487C2×C8C2×D4×C7311yescharacteristic
488C2×C8C2×D4×C7311yescharacteristic
489C2×C8C2×D4×C7311yescharacteristic
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4C2×D4×C7311yescharacteristic
499C4⋊C4C2×D4×C7311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C42—21no—
510C42C2×D4×C7311yescharacteristic
511C42C2×D4×C7311yescharacteristic
512C42#41×C7311yescharacteristic
513C42C24×C7311yescharacteristic
514C23—21no—
515C23—41no—
516C23—41no—
517C23#121×C7311yescharacteristic
518Q8—21no—
519Q8—21no—
520Q8—41no—
521Q8—41no—
522Q8—81no—
523D4—21no—
524D4—21no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—81no—
534D4—81no—
535D4—81no—
536D4—82no—
537D4—82no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—82no—
551C2×C4—82no—
552C2×C4#121×C7311yescharacteristic
553C2×C4#121×C7311yescharacteristic
554C2×C4#121×C7311yescharacteristic
555C2×C4C22×D4×C7311yescharacteristic
556C2×C4C22×D4×C7311yescharacteristic
557C2×C4C2×#41×C7311yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8#135×C7312yes—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22C2×#121×C7311yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—81no—
589C4—81no—
590C4C2×#135×C7311yescharacteristic
591C4#575×C7311yescharacteristic
592C4#576×C7311yescharacteristic
593C4#577×C7311yescharacteristic
594C2—41no—
595C2—81no—
596C2—161no—
597C2—161no—
598C2C73×#303511yescharacteristic
599C2C73×#306211yescharacteristic
600C2C73×#306811yescharacteristic
subgroupG/H
center, socleC22×C73C2×#121
commutator, Frattini, cosocleC42C24×C73
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×#3247C2semidirect
2. C73×#3212C2semidirect
3. C73×#3184C2semidirect
4. C73×#2969C2semidirect
5. C73×#1701C2semidirect
6. C73×#1697C2semidirect
7. C73×#1692C2semidirect
8. C73×#1688C2semidirect
9. C73×#1682C2semidirect
10. C73×#1678C2semidirect
11. C73×#1671C2semidirect
12. C73×#1667C2semidirect
13. C73×#1565C2semidirect
14. C73×#1543C2semidirect
15. C73×#1540C2semidirect
293. #19248C73direct (N × H)
301. #3247C2×C73semidirect
302. #3212C2×C73semidirect
303. #3184C2×C73semidirect
304. #2969C2×C73semidirect
305. #1701C2×C73semidirect
306. #1697C2×C73semidirect
307. #1692C2×C73semidirect
308. #1688C2×C73semidirect
309. #1682C2×C73semidirect
310. #1678C2×C73semidirect
311. #1671C2×C73semidirect
312. #1667C2×C73semidirect
313. #1565C2×C73semidirect
314. #1543C2×C73semidirect
315. #1540C2×C73semidirect
316. C73#19248direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#32472
C73×#32122
C73×#31842
C73×#29692
C73×#17012
C73×#16972
C73×#16922
C73×#16882
C73×#16822
C73×#16782
C73×#16712
C73×#16672
C73×#15652
C73×#15432
C73×#15402
#1924873