Finite Group Databasebeta

← C73×#20239 #32929643

Subgroups — C73×#20239 #32929643

Order 18688.

648 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3354C211yesmaximal, characteristic, complemented
2C73×#3325C211yesmaximal, characteristic, complemented
3C73×#3325C211yesmaximal, characteristic, complemented
4C73×#3303C211yesmaximal, characteristic, complemented
5C73×#1720C211yesmaximal, characteristic, complemented
6C73×#1703C211yesmaximal, characteristic, complemented
7C73×#1697C211yesmaximal, characteristic, complemented
8C73×#1691C211yesmaximal, characteristic, complemented
9C73×#1677C211yesmaximal, characteristic, complemented
10C73×#1639C211yesmaximal, characteristic, complemented
11C73×#1634C211yesmaximal, characteristic, complemented
12C73×#1634C211yesmaximal, characteristic, complemented
13C73×#1625C211yesmaximal, characteristic, complemented
14C73×#1594C211yesmaximal, characteristic, complemented
15C73×#1581C211yesmaximal, characteristic, complemented
16#555×C73C2211yescharacteristic
17#555×C73C2211yescharacteristic
18#547×C73C2211yescharacteristic, complemented
19D42×C73C2211yescharacteristic
20#498×C73C2211yescharacteristic, complemented
21#494×C73C2211yescharacteristic, complemented
22#487×C73C2211yescharacteristic, complemented
23#486×C73C2211yescharacteristic
24#486×C73C2211yescharacteristic
25#486×C73C2211yescharacteristic
26#485×C73—21no—
27#482×C73—21no—
28#482×C73—21no—
29#482×C73—21no—
30#481×C73—21no—
31#476×C73C2211yescharacteristic
32#476×C73C2211yescharacteristic
33#476×C73C2211yescharacteristic, complemented
34#476×C73C2211yescharacteristic, complemented
35#474×C73C2211yescharacteristic
36#469×C73—21no—
37#469×C73—21no—
38#469×C73—21no—
39#465×C73—21no—
40#461×C73C2211yescharacteristic
41#459×C73C2211yescharacteristic
42#459×C73C2211yescharacteristic
43#449×C73—21no—
44#447×C73—21no—
45#447×C73—21no—
46C4×D8×C73C2211yescharacteristic
47C4×D8×C73C2211yescharacteristic
48#436×C73C2211yescharacteristic
49#436×C73C2211yescharacteristic
50#436×C73C2211yescharacteristic, complemented
51C8×D4×C73C2211yescharacteristic, complemented
52#428×C73—21no—
53#418×C73—21no—
54#418×C73—21no—
55#416×C73—21no—
56#335×C73C2211yescharacteristic, complemented
57#334×C73C2211yescharacteristic, complemented
58#333×C73C2211yescharacteristic, complemented
59#333×C73C2211yescharacteristic, complemented
60#332×C73C2211yescharacteristic, complemented
61#331×C73C2211yescharacteristic
62D4⋊C8×C73C2211yescharacteristic
63D4⋊C8×C73C2211yescharacteristic
64D4⋊C8×C73C2211yescharacteristic, complemented
65D4⋊C8×C73C2211yescharacteristic, complemented
66#322×C73C2211yescharacteristic, complemented
67C2×#41×C73—21no—
68C22×D4×C73—21no—
69C22×D4×C73—21no—
70C2×Q16×C73—41no—
71C2×SD16×C73—21no—
72C2×D8×C73—21no—
73C2×D8×C73—21no—
74C2×D8×C73D411yescharacteristic
75C2×D8×C73D411yescharacteristic
76C2×M16×C73—21no—
77C2×M16×C73—21no—
78C2×M16×C73—21no—
79C22×C8×C73—21no—
80C4⋊Q8×C73C2311yescharacteristic
81C4⋊Q8×C73C2311yescharacteristic
82C4⋊Q8×C73C2311yescharacteristic
83#127×C73C2311yescharacteristic
84#124×C73—41no—
85#124×C73—41no—
86#123×C73—41no—
87C22⋊Q8×C73—21no—
88#121×C73—21no—
89#121×C73—21no—
90#121×C73—21no—
91#121×C73—21no—
92#121×C73—21no—
93#121×C73—21no—
94#121×C73—21no—
95#120×C73—41no—
96C4×D4×C73C2311yescharacteristic
97C4×D4×C73C2311yescharacteristic
98C4×D4×C73C2311yescharacteristic
99C4×D4×C73C2311yescharacteristic
100#117×C73—21no—
101#117×C73—21no—
102#117×C73—21no—
103#117×C73—21no—
104C2×C4⋊C4×C73—21no—
105#107×C73—21no—
106#107×C73D411yescharacteristic
107#107×C73D411yescharacteristic
108#106×C73—21no—
109#106×C73—21no—
110#106×C73—21no—
111#106×C73—21no—
112#106×C73—21no—
113#106×C73—21no—
114C4⋊C8×C73C2311yescharacteristic
115C4⋊C8×C73C2311yescharacteristic
116C4⋊C8×C73C2311yescharacteristic
117C4⋊C8×C73C2311yescharacteristic
118#103×C73—21no—
119#103×C73—21no—
120#103×C73—21no—
121#102×C73—21no—
122#102×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—
132#102×C73—41no—
133#102×C73D411yescharacteristic
134#102×C73D411yescharacteristic
135#102×C73D411yescharacteristic
136#102×C73D411yescharacteristic
137C22⋊C8×C73—21no—
138C22⋊C8×C73—21no—
139C22⋊C8×C73—21no—
140C22⋊C8×C73—21no—
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C24×C73—41no—
145#41×C73—42no—
146#41×C73—81no—
147C2×Q8×C73—21no—
148C2×Q8×C73—21no—
149C2×Q8×C73—21no—
150C2×D4×C73—21no—
151C2×D4×C73—21no—
152C2×D4×C73—21no—
153C2×D4×C73—41no—
154C2×D4×C73—41no—
155C2×D4×C73—42no—
156C2×D4×C73—42no—
157C2×D4×C73—41no—
158C2×D4×C73—41no—
159C2×D4×C73—41no—
160C2×D4×C73—81no—
161C2×D4×C73—81no—
162C2×D4×C73C2×D411yescharacteristic
163C2×D4×C73C2×D411yescharacteristic
164C2×D4×C73C2×D411yescharacteristic
165C2×D4×C73C2×D411yescharacteristic
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73—41no—
171Q16×C73—82no—
172SD16×C73—81no—
173D8×C73—41no—
174D8×C73—41no—
175D8×C73—81no—
176D8×C73—81no—
177M16×C73—42no—
178M16×C73—81no—
179M16×C73—81no—
180C2×C8×C73—21no—
181C2×C8×C73—21no—
182C2×C8×C73—21no—
183C2×C8×C73—21no—
184C2×C8×C73—21no—
185C2×C8×C73—81no—
186C2×C8×C73C2×D411yescharacteristic
187C2×C8×C73C2×D411yescharacteristic
188C2×C8×C73C2×D411yescharacteristic
189C2×C8×C73C2×D411yescharacteristic
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—41no—
197C4⋊C4×C73C2×D411yescharacteristic
198C4⋊C4×C73C2×D411yescharacteristic
199C4⋊C4×C73C2×D411yescharacteristic
200C4⋊C4×C73C2×D411yescharacteristic
201C22⋊C4×C73—21no—
202C22⋊C4×C73—21no—
203C22⋊C4×C73—21no—
204C22⋊C4×C73—21no—
205C22⋊C4×C73—41no—
206C22⋊C4×C73—41no—
207C22⋊C4×C73—41no—
208C22⋊C4×C73—41no—
209C22⋊C4×C73—41no—
210C22⋊C4×C73—41no—
211C42×C73—41no—
212C42×C73—41no—
213C42×C73C2411yescharacteristic
214C23×C73—21no—
215C23×C73—21no—
216C23×C73—21no—
217C23×C73—21no—
218C23×C73—41no—
219C23×C73—82no—
220C23×C73—82no—
221C23×C73—161no—
222Q8×C73—41no—
223Q8×C73—41no—
224Q8×C73—81no—
225Q8×C73—81no—
226D4×C73—21no—
227D4×C73—21no—
228D4×C73—21no—
229D4×C73—21no—
230D4×C73—21no—
231D4×C73—21no—
232D4×C73—21no—
233D4×C73—21no—
234D4×C73—41no—
235D4×C73—41no—
236D4×C73—41no—
237D4×C73—41no—
238D4×C73—81no—
239D4×C73—82no—
240D4×C73—82no—
241D4×C73—82no—
242D4×C73—161no—
243D4×C73—161no—
244C2×C4×C73—21no—
245C2×C4×C73—21no—
246C2×C4×C73—21no—
247C2×C4×C73—21no—
248C2×C4×C73—41no—
249C2×C4×C73—41no—
250C2×C4×C73—41no—
251C2×C4×C73—41no—
252C2×C4×C73—41no—
253C2×C4×C73—41no—
254C2×C4×C73—41no—
255C2×C4×C73—41no—
256C2×C4×C73—41no—
257C2×C4×C73—41no—
258C2×C4×C73—41no—
259C2×C4×C73—82no—
260C2×C4×C73C22×D411yescharacteristic
261C2×C4×C73C22×D411yescharacteristic
262C2×C4×C73H(5,𝔽2)11yescharacteristic
263C8×C73—21no—
264C8×C73—21no—
265C8×C73—21no—
266C8×C73—21no—
267C8×C73—41no—
268C8×C73—41no—
269C8×C73—41no—
270C8×C73—41no—
271C8×C73—41no—
272C22×C73—41no—
273C22×C73—41no—
274C22×C73—41no—
275C22×C73—41no—
276C22×C73—41no—
277C22×C73—41no—
278C22×C73—41no—
279C22×C73—41no—
280C22×C73—41no—
281C22×C73—41no—
282C22×C73—41no—
283C22×C73—41no—
284C22×C73—81no—
285C22×C73—81no—
286C22×C73—81no—
287C22×C73—164no—
288C22×C73D4211yescharacteristic
289C4×C73—21no—
290C4×C73—41no—
291C4×C73—41no—
292C4×C73—41no—
293C4×C73—41no—
294C4×C73—81no—
295C4×C73—81no—
296C4×C73—81no—
297C4×C73#57511yescharacteristic
298C4×C73#57511yescharacteristic
299C4×C73#57611yescharacteristic
300C4×C73#57711yescharacteristic
301#20239C7311yesmaximal, characteristic, direct product factor, Sylow
302C2×C73—81no—
303C2×C73—81no—
304C2×C73—81no—
305C2×C73—81no—
306C2×C73—161no—
307C2×C73#326711yescharacteristic
308C2×C73#327311yescharacteristic
309C2×C73#328811yescharacteristic
310#3354C2×C7311yescharacteristic, complemented
311#3325C2×C7311yescharacteristic, complemented
312#3325C2×C7311yescharacteristic, complemented
313#3303C2×C7311yescharacteristic, complemented
314#1720C2×C7311yescharacteristic, complemented
315#1703C2×C7311yescharacteristic, complemented
316#1697C2×C7311yescharacteristic, complemented
317#1691C2×C7311yescharacteristic, complemented
318#1677C2×C7311yescharacteristic, complemented
319#1639C2×C7311yescharacteristic, complemented
320#1634C2×C7311yescharacteristic, complemented
321#1634C2×C7311yescharacteristic, complemented
322#1625C2×C7311yescharacteristic, complemented
323#1594C2×C7311yescharacteristic, complemented
324#1581C2×C7311yescharacteristic, complemented
325C73#2023911yescharacteristic, direct product factor, Sylow
326#555C22×C7311yescharacteristic
327#555C22×C7311yescharacteristic
328#547C22×C7311yescharacteristic, complemented
329D42C22×C7311yescharacteristic
330#498C22×C7311yescharacteristic, complemented
331#494C22×C7311yescharacteristic, complemented
332#487C22×C7311yescharacteristic, complemented
333#486C22×C7311yescharacteristic
334#486C22×C7311yescharacteristic
335#486C22×C7311yescharacteristic
336#485—21no—
337#482—21no—
338#482—21no—
339#482—21no—
340#481—21no—
341#476C22×C7311yescharacteristic
342#476C22×C7311yescharacteristic
343#476C22×C7311yescharacteristic, complemented
344#476C22×C7311yescharacteristic, complemented
345#474C22×C7311yescharacteristic
346#469—21no—
347#469—21no—
348#469—21no—
349#465—21no—
350#461C22×C7311yescharacteristic
351#459C22×C7311yescharacteristic
352#459C22×C7311yescharacteristic
353#449—21no—
354#447—21no—
355#447—21no—
356C4×D8C22×C7311yescharacteristic
357C4×D8C22×C7311yescharacteristic
358#436C22×C7311yescharacteristic
359#436C22×C7311yescharacteristic
360#436C22×C7311yescharacteristic, complemented
361C8×D4C22×C7311yescharacteristic, complemented
362#428—21no—
363#418—21no—
364#418—21no—
365#416—21no—
366#335C22×C7311yescharacteristic, complemented
367#334C22×C7311yescharacteristic, complemented
368#333C22×C7311yescharacteristic, complemented
369#333C22×C7311yescharacteristic, complemented
370#332C22×C7311yescharacteristic, complemented
371#331C22×C7311yescharacteristic
372D4⋊C8C22×C7311yescharacteristic
373D4⋊C8C22×C7311yescharacteristic
374D4⋊C8C22×C7311yescharacteristic, complemented
375D4⋊C8C22×C7311yescharacteristic, complemented
376#322C22×C7311yescharacteristic, complemented
377C2×#41—21no—
378C22×D4—21no—
379C22×D4—21no—
380C2×Q16—41no—
381C2×SD16—21no—
382C2×D8—21no—
383C2×D8—21no—
384C2×D8D4×C7311yescharacteristic
385C2×D8D4×C7311yescharacteristic
386C2×M16—21no—
387C2×M16—21no—
388C2×M16—21no—
389C22×C8—21no—
390C4⋊Q8C23×C7311yescharacteristic
391C4⋊Q8C23×C7311yescharacteristic
392C4⋊Q8C23×C7311yescharacteristic
393#127C23×C7311yescharacteristic
394#124—41no—
395#124—41no—
396#123—41no—
397C22⋊Q8—21no—
398#121—21no—
399#121—21no—
400#121—21no—
401#121—21no—
402#121—21no—
403#121—21no—
404#121—21no—
405#120—41no—
406C4×D4C23×C7311yescharacteristic
407C4×D4C23×C7311yescharacteristic
408C4×D4C23×C7311yescharacteristic
409C4×D4C23×C7311yescharacteristic
410#117—21no—
411#117—21no—
412#117—21no—
413#117—21no—
414C2×C4⋊C4—21no—
415#107—21no—
416#107D4×C7311yescharacteristic
417#107D4×C7311yescharacteristic
418#106—21no—
419#106—21no—
420#106—21no—
421#106—21no—
422#106—21no—
423#106—21no—
424C4⋊C8C23×C7311yescharacteristic
425C4⋊C8C23×C7311yescharacteristic
426C4⋊C8C23×C7311yescharacteristic
427C4⋊C8C23×C7311yescharacteristic
428#103—21no—
429#103—21no—
430#103—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—41no—
443#102D4×C7311yescharacteristic
444#102D4×C7311yescharacteristic
445#102D4×C7311yescharacteristic
446#102D4×C7311yescharacteristic
447C22⋊C8—21no—
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—21no—
451C4×C8C23×C7311yescharacteristic
452C4×C8C23×C7311yescharacteristic
453C4×C8C23×C7311yescharacteristic
454C24—41no—
455#41—42no—
456#41—81no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—81no—
471C2×D4—81no—
472C2×D4C2×D4×C7311yescharacteristic
473C2×D4C2×D4×C7311yescharacteristic
474C2×D4C2×D4×C7311yescharacteristic
475C2×D4C2×D4×C7311yescharacteristic
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—41no—
481Q16—82no—
482SD16—81no—
483D8—41no—
484D8—41no—
485D8—81no—
486D8—81no—
487M16—42no—
488M16—81no—
489M16—81no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—81no—
496C2×C8C2×D4×C7311yescharacteristic
497C2×C8C2×D4×C7311yescharacteristic
498C2×C8C2×D4×C7311yescharacteristic
499C2×C8C2×D4×C7311yescharacteristic
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—41no—
507C4⋊C4C2×D4×C7311yescharacteristic
508C4⋊C4C2×D4×C7311yescharacteristic
509C4⋊C4C2×D4×C7311yescharacteristic
510C4⋊C4C2×D4×C7311yescharacteristic
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C42—41no—
522C42—41no—
523C42C24×C7311yescharacteristic
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—41no—
529C23—82no—
530C23—82no—
531C23—161no—
532Q8—41no—
533Q8—41no—
534Q8—81no—
535Q8—81no—
536D4—21no—
537D4—21no—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—81no—
549D4—82no—
550D4—82no—
551D4—82no—
552D4—161no—
553D4—161no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—82no—
570C2×C4C22×D4×C7311yescharacteristic
571C2×C4C22×D4×C7311yescharacteristic
572C2×C4H(5,𝔽2)×C7311yescharacteristic
573C8—21no—
574C8—21no—
575C8—21no—
576C8—21no—
577C8—41no—
578C8—41no—
579C8—41no—
580C8—41no—
581C8—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—164no—
598C22D42×C7311yescharacteristic
599C4—21no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4—81no—
607C4#575×C7311yescharacteristic
608C4#575×C7311yescharacteristic
609C4#576×C7311yescharacteristic
610C4#577×C7311yescharacteristic
611C2—81no—
612C2—81no—
613C2—81no—
614C2—81no—
615C2—161no—
616C2C73×#326711yescharacteristic
617C2C73×#327311yescharacteristic
618C2C73×#328811yescharacteristic
subgroupG/H
center, socleC22×C73D42
commutator, Frattini, cosocleC42C24×C73
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×#3354C2semidirect
2. C73×#3325C2semidirect
3. C73×#3325C2semidirect
4. C73×#3303C2semidirect
5. C73×#1720C2semidirect
6. C73×#1703C2semidirect
7. C73×#1697C2semidirect
8. C73×#1691C2semidirect
9. C73×#1677C2semidirect
10. C73×#1639C2semidirect
11. C73×#1634C2semidirect
12. C73×#1634C2semidirect
13. C73×#1625C2semidirect
14. C73×#1594C2semidirect
15. C73×#1581C2semidirect
18. #547×C73C22semidirect
20. #498×C73C22semidirect
21. #494×C73C22semidirect
22. #487×C73C22semidirect
33. #476×C73C22semidirect
34. #476×C73C22semidirect
50. #436×C73C22semidirect
51. C8×D4×C73C22semidirect
56. #335×C73C22semidirect
57. #334×C73C22semidirect
58. #333×C73C22semidirect
59. #333×C73C22semidirect
60. #332×C73C22semidirect
64. D4⋊C8×C73C22semidirect
65. D4⋊C8×C73C22semidirect
66. #322×C73C22semidirect
301. #20239C73direct (N × H)
310. #3354C2×C73semidirect
311. #3325C2×C73semidirect
312. #3325C2×C73semidirect
313. #3303C2×C73semidirect
314. #1720C2×C73semidirect
315. #1703C2×C73semidirect
316. #1697C2×C73semidirect
317. #1691C2×C73semidirect
318. #1677C2×C73semidirect
319. #1639C2×C73semidirect
320. #1634C2×C73semidirect
321. #1634C2×C73semidirect
322. #1625C2×C73semidirect
323. #1594C2×C73semidirect
324. #1581C2×C73semidirect
325. C73#20239direct (N × H)
328. #547C22×C73semidirect
330. #498C22×C73semidirect
331. #494C22×C73semidirect
332. #487C22×C73semidirect
343. #476C22×C73semidirect
344. #476C22×C73semidirect
360. #436C22×C73semidirect
361. C8×D4C22×C73semidirect
366. #335C22×C73semidirect
367. #334C22×C73semidirect
368. #333C22×C73semidirect
369. #333C22×C73semidirect
370. #332C22×C73semidirect
374. D4⋊C8C22×C73semidirect
375. D4⋊C8C22×C73semidirect
376. #322C22×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#33542
C73×#33252
C73×#33032
C73×#17202
C73×#17032
C73×#16972
C73×#16912
C73×#16772
C73×#16392
C73×#16342
C73×#16252
C73×#15942
C73×#15812
#2023973