Finite Group Databasebeta

← C73×#20287 #32929691

Subgroups — C73×#20287 #32929691

Order 18688.

634 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3367C211yesmaximal, characteristic, complemented
2C73×#3329C211yesmaximal, characteristic, complemented
3C73×#3325C211yesmaximal, characteristic
4C73×#3324C211yesmaximal, characteristic, complemented
5C73×#1711C211yesmaximal, characteristic, complemented
6C73×#1703C211yesmaximal, characteristic, complemented
7C73×#1701C211yesmaximal, characteristic, complemented
8C73×#1699C211yesmaximal, characteristic, complemented
9C73×#1698C211yesmaximal, characteristic, complemented
10C73×#1646C211yesmaximal, characteristic, complemented
11C73×#1639C211yesmaximal, characteristic, complemented
12C73×#1638C211yesmaximal, characteristic, complemented
13C73×#1627C211yesmaximal, characteristic, complemented
14C73×#1590C211yesmaximal, characteristic, complemented
15C73×#1589C211yesmaximal, characteristic, complemented
16#556×C73C2211yescharacteristic
17#555×C73C2211yescharacteristic
18D4×Q8×C73C2211yescharacteristic, complemented
19D42×C73C2211yescharacteristic
20#489×C73—21no—
21#487×C73C2211yescharacteristic, complemented
22#487×C73C2211yescharacteristic, complemented
23#487×C73C2211yescharacteristic, complemented
24#486×C73C2211yescharacteristic
25#486×C73C2211yescharacteristic
26#486×C73C2211yescharacteristic
27#485×C73—21no—
28#482×C73—21no—
29#482×C73—21no—
30#477×C73—21no—
31#477×C73C2211yescharacteristic, complemented
32#476×C73C2211yescharacteristic
33#474×C73C2211yescharacteristic
34#474×C73C2211yescharacteristic
35#469×C73—21no—
36#468×C73—21no—
37#468×C73—21no—
38#463×C73—21no—
39#461×C73C2211yescharacteristic
40#461×C73C2211yescharacteristic, complemented
41#460×C73C2211yescharacteristic
42#459×C73C2211yescharacteristic
43#450×C73—21no—
44#448×C73—21no—
45#447×C73—21no—
46#446×C73C2211yescharacteristic, complemented
47#440×C73—21no—
48C4×SD16×C73C2211yescharacteristic
49C4×D8×C73C2211yescharacteristic
50#436×C73C2211yescharacteristic
51#436×C73C2211yescharacteristic
52#436×C73C2211yescharacteristic, complemented
53#419×C73—21no—
54#418×C73—21no—
55#418×C73—21no—
56#335×C73C2211yescharacteristic, complemented
57#334×C73C2211yescharacteristic, complemented
58#333×C73C2211yescharacteristic, complemented
59#332×C73C2211yescharacteristic, complemented
60#332×C73C2211yescharacteristic, complemented
61#331×C73C2211yescharacteristic
62Q8⋊C8×C73C2211yescharacteristic, complemented
63D4⋊C8×C73C2211yescharacteristic
64D4⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic, complemented
66C82×C73C2211yescharacteristic, complemented
67C22×Q8×C73—21no—
68C22×D4×C73—21no—
69C22×D4×C73—21no—
70C2×SD16×C73—21no—
71C2×SD16×C73—21no—
72C2×SD16×C73—21no—
73C2×SD16×C73D411yescharacteristic
74C2×D8×C73—21no—
75C2×D8×C73D411yescharacteristic
76C2×M16×C73—21no—
77C2×M16×C73—21no—
78C2×M16×C73—21no—
79C4⋊Q8×C73—21no—
80C4⋊Q8×C73C2311yescharacteristic
81C4⋊Q8×C73C2311yescharacteristic
82C4⋊Q8×C73C2311yescharacteristic
83#127×C73C2311yescharacteristic
84#126×C73—41no—
85#124×C73—21no—
86#124×C73—41no—
87C22⋊Q8×C73—21no—
88C22⋊Q8×C73—21no—
89C22⋊Q8×C73—41no—
90#121×C73—21no—
91#121×C73—21no—
92#121×C73—21no—
93#121×C73—21no—
94#120×C73—41no—
95C4×Q8×C73—21no—
96C4×Q8×C73C2311yescharacteristic
97C4×D4×C73—21no—
98C4×D4×C73C2311yescharacteristic
99C4×D4×C73C2311yescharacteristic
100C4×D4×C73C2311yescharacteristic
101#117×C73—21no—
102#117×C73—21no—
103#117×C73—21no—
104#107×C73—21no—
105#107×C73—21no—
106#107×C73—21no—
107#107×C73D411yescharacteristic
108#106×C73—21no—
109#106×C73D411yescharacteristic
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—41no—
123#103×C73D411yescharacteristic
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—21no—
133#102×C73—41no—
134#102×C73D411yescharacteristic
135#102×C73D411yescharacteristic
136#102×C73D411yescharacteristic
137C22⋊C8×C73—21no—
138C22⋊C8×C73—21no—
139C22⋊C8×C73—21no—
140#97×C73—21no—
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C24×C73—41no—
145C2×Q8×C73—21no—
146C2×Q8×C73—21no—
147C2×Q8×C73—21no—
148C2×Q8×C73—41no—
149C2×Q8×C73—42no—
150C2×Q8×C73—81no—
151C2×Q8×C73C2×D411yescharacteristic
152C2×D4×C73—21no—
153C2×D4×C73—21no—
154C2×D4×C73—21no—
155C2×D4×C73—41no—
156C2×D4×C73—41no—
157C2×D4×C73—42no—
158C2×D4×C73—42no—
159C2×D4×C73—41no—
160C2×D4×C73—81no—
161C2×D4×C73—81no—
162C2×D4×C73C2×D411yescharacteristic
163C2×D4×C73C2×D411yescharacteristic
164C2×D4×C73C2×D411yescharacteristic
165C22×C4×C73—21no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—41no—
169SD16×C73—41no—
170SD16×C73—42no—
171SD16×C73—81no—
172SD16×C73—81no—
173D8×C73—41no—
174D8×C73—81no—
175M16×C73—81no—
176M16×C73—81no—
177M16×C73—81no—
178C2×C8×C73—21no—
179C2×C8×C73—21no—
180C2×C8×C73—21no—
181C2×C8×C73—21no—
182C2×C8×C73—21no—
183C2×C8×C73C2×D411yescharacteristic
184C2×C8×C73C2×D411yescharacteristic
185C2×C8×C73C2×D411yescharacteristic
186C2×C8×C73C2×D411yescharacteristic
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
198C4⋊C4×C73C2×D411yescharacteristic
199C4⋊C4×C73C2×D411yescharacteristic
200C22⋊C4×C73—21no—
201C22⋊C4×C73—21no—
202C22⋊C4×C73—21no—
203C22⋊C4×C73—41no—
204C22⋊C4×C73—41no—
205C22⋊C4×C73—41no—
206C22⋊C4×C73—41no—
207C22⋊C4×C73—41no—
208C22⋊C4×C73—41no—
209C42×C73—21no—
210C42×C73—41no—
211C42×C73—41no—
212C42×C73C2411yescharacteristic
213C23×C73—21no—
214C23×C73—21no—
215C23×C73—21no—
216C23×C73—41no—
217C23×C73—82no—
218C23×C73—82no—
219C23×C73—161no—
220Q8×C73—21no—
221Q8×C73—21no—
222Q8×C73—41no—
223Q8×C73—41no—
224Q8×C73—41no—
225Q8×C73—41no—
226Q8×C73—81no—
227Q8×C73—82no—
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—161no—
242C2×C4×C73—21no—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—21no—
246C2×C4×C73—21no—
247C2×C4×C73—41no—
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—82no—
257C2×C4×C73C22×D411yescharacteristic
258C2×C4×C73C22×D411yescharacteristic
259C2×C4×C73H(5,𝔽2)11yescharacteristic
260C8×C73—21no—
261C8×C73—21no—
262C8×C73—21no—
263C8×C73—21no—
264C8×C73—41no—
265C8×C73—41no—
266C8×C73—41no—
267C8×C73—41no—
268C8×C73—41no—
269C22×C73—41no—
270C22×C73—41no—
271C22×C73—41no—
272C22×C73—41no—
273C22×C73—41no—
274C22×C73—41no—
275C22×C73—41no—
276C22×C73—41no—
277C22×C73—41no—
278C22×C73—81no—
279C22×C73—81no—
280C22×C73—81no—
281C22×C73—164no—
282C22×C73D4211yescharacteristic
283C4×C73—21no—
284C4×C73—41no—
285C4×C73—41no—
286C4×C73—41no—
287C4×C73—41no—
288C4×C73—41no—
289C4×C73—81no—
290C4×C73—81no—
291C4×C73—81no—
292C4×C73#57511yescharacteristic
293C4×C73#57511yescharacteristic
294C4×C73#57611yescharacteristic
295C4×C73#57711yescharacteristic
296#20287C7311yesmaximal, characteristic, direct product factor, Sylow
297C2×C73—81no—
298C2×C73—81no—
299C2×C73—81no—
300C2×C73—161no—
301C2×C73#327311yescharacteristic
302C2×C73#327511yescharacteristic
303C2×C73#329011yescharacteristic
304#3367C2×C7311yescharacteristic, complemented
305#3329C2×C7311yescharacteristic, complemented
306#3325C2×C7311yescharacteristic
307#3324C2×C7311yescharacteristic, complemented
308#1711C2×C7311yescharacteristic, complemented
309#1703C2×C7311yescharacteristic, complemented
310#1701C2×C7311yescharacteristic, complemented
311#1699C2×C7311yescharacteristic, complemented
312#1698C2×C7311yescharacteristic, complemented
313#1646C2×C7311yescharacteristic, complemented
314#1639C2×C7311yescharacteristic, complemented
315#1638C2×C7311yescharacteristic, complemented
316#1627C2×C7311yescharacteristic, complemented
317#1590C2×C7311yescharacteristic, complemented
318#1589C2×C7311yescharacteristic, complemented
319C73#2028711yescharacteristic, direct product factor, Sylow
320#556C22×C7311yescharacteristic
321#555C22×C7311yescharacteristic
322D4×Q8C22×C7311yescharacteristic, complemented
323D42C22×C7311yescharacteristic
324#489—21no—
325#487C22×C7311yescharacteristic, complemented
326#487C22×C7311yescharacteristic, complemented
327#487C22×C7311yescharacteristic, complemented
328#486C22×C7311yescharacteristic
329#486C22×C7311yescharacteristic
330#486C22×C7311yescharacteristic
331#485—21no—
332#482—21no—
333#482—21no—
334#477—21no—
335#477C22×C7311yescharacteristic, complemented
336#476C22×C7311yescharacteristic
337#474C22×C7311yescharacteristic
338#474C22×C7311yescharacteristic
339#469—21no—
340#468—21no—
341#468—21no—
342#463—21no—
343#461C22×C7311yescharacteristic
344#461C22×C7311yescharacteristic, complemented
345#460C22×C7311yescharacteristic
346#459C22×C7311yescharacteristic
347#450—21no—
348#448—21no—
349#447—21no—
350#446C22×C7311yescharacteristic, complemented
351#440—21no—
352C4×SD16C22×C7311yescharacteristic
353C4×D8C22×C7311yescharacteristic
354#436C22×C7311yescharacteristic
355#436C22×C7311yescharacteristic
356#436C22×C7311yescharacteristic, complemented
357#419—21no—
358#418—21no—
359#418—21no—
360#335C22×C7311yescharacteristic, complemented
361#334C22×C7311yescharacteristic, complemented
362#333C22×C7311yescharacteristic, complemented
363#332C22×C7311yescharacteristic, complemented
364#332C22×C7311yescharacteristic, complemented
365#331C22×C7311yescharacteristic
366Q8⋊C8C22×C7311yescharacteristic, complemented
367D4⋊C8C22×C7311yescharacteristic
368D4⋊C8C22×C7311yescharacteristic
369D4⋊C8C22×C7311yescharacteristic, complemented
370C82C22×C7311yescharacteristic, complemented
371C22×Q8—21no—
372C22×D4—21no—
373C22×D4—21no—
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16D4×C7311yescharacteristic
378C2×D8—21no—
379C2×D8D4×C7311yescharacteristic
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—21no—
383C4⋊Q8—21no—
384C4⋊Q8C23×C7311yescharacteristic
385C4⋊Q8C23×C7311yescharacteristic
386C4⋊Q8C23×C7311yescharacteristic
387#127C23×C7311yescharacteristic
388#126—41no—
389#124—21no—
390#124—41no—
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393C22⋊Q8—41no—
394#121—21no—
395#121—21no—
396#121—21no—
397#121—21no—
398#120—41no—
399C4×Q8—21no—
400C4×Q8C23×C7311yescharacteristic
401C4×D4—21no—
402C4×D4C23×C7311yescharacteristic
403C4×D4C23×C7311yescharacteristic
404C4×D4C23×C7311yescharacteristic
405#117—21no—
406#117—21no—
407#117—21no—
408#107—21no—
409#107—21no—
410#107—21no—
411#107D4×C7311yescharacteristic
412#106—21no—
413#106D4×C7311yescharacteristic
414C4⋊C8—21no—
415C4⋊C8C23×C7311yescharacteristic
416C4⋊C8C23×C7311yescharacteristic
417C4⋊C8C23×C7311yescharacteristic
418C4⋊C8C23×C7311yescharacteristic
419#103—21no—
420#103—21no—
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#103—21no—
426#103—41no—
427#103D4×C7311yescharacteristic
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—41no—
438#102D4×C7311yescharacteristic
439#102D4×C7311yescharacteristic
440#102D4×C7311yescharacteristic
441C22⋊C8—21no—
442C22⋊C8—21no—
443C22⋊C8—21no—
444#97—21no—
445C4×C8C23×C7311yescharacteristic
446C4×C8C23×C7311yescharacteristic
447C4×C8C23×C7311yescharacteristic
448C24—41no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—41no—
453C2×Q8—42no—
454C2×Q8—81no—
455C2×Q8C2×D4×C7311yescharacteristic
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—42no—
462C2×D4—42no—
463C2×D4—41no—
464C2×D4—81no—
465C2×D4—81no—
466C2×D4C2×D4×C7311yescharacteristic
467C2×D4C2×D4×C7311yescharacteristic
468C2×D4C2×D4×C7311yescharacteristic
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—41no—
473SD16—41no—
474SD16—42no—
475SD16—81no—
476SD16—81no—
477D8—41no—
478D8—81no—
479M16—81no—
480M16—81no—
481M16—81no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8C2×D4×C7311yescharacteristic
488C2×C8C2×D4×C7311yescharacteristic
489C2×C8C2×D4×C7311yescharacteristic
490C2×C8C2×D4×C7311yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4C2×D4×C7311yescharacteristic
501C4⋊C4C2×D4×C7311yescharacteristic
502C4⋊C4C2×D4×C7311yescharacteristic
503C4⋊C4C2×D4×C7311yescharacteristic
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C42—21no—
514C42—41no—
515C42—41no—
516C42C24×C7311yescharacteristic
517C23—21no—
518C23—21no—
519C23—21no—
520C23—41no—
521C23—82no—
522C23—82no—
523C23—161no—
524Q8—21no—
525Q8—21no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—81no—
531Q8—82no—
532D4—21no—
533D4—21no—
534D4—21no—
535D4—21no—
536D4—21no—
537D4—21no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—81no—
543D4—82no—
544D4—82no—
545D4—161no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—82no—
561C2×C4C22×D4×C7311yescharacteristic
562C2×C4C22×D4×C7311yescharacteristic
563C2×C4H(5,𝔽2)×C7311yescharacteristic
564C8—21no—
565C8—21no—
566C8—21no—
567C8—21no—
568C8—41no—
569C8—41no—
570C8—41no—
571C8—41no—
572C8—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—164no—
586C22D42×C7311yescharacteristic
587C4—21no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—81no—
594C4—81no—
595C4—81no—
596C4#575×C7311yescharacteristic
597C4#575×C7311yescharacteristic
598C4#576×C7311yescharacteristic
599C4#577×C7311yescharacteristic
600C2—81no—
601C2—81no—
602C2—81no—
603C2—161no—
604C2C73×#327311yescharacteristic
605C2C73×#327511yescharacteristic
606C2C73×#329011yescharacteristic
subgroupG/H
center, socleC22×C73D42
commutator, Frattini, cosocleC42C24×C73
prime radicalC73×#3325C2
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×#3367C2semidirect
2. C73×#3329C2semidirect
4. C73×#3324C2semidirect
5. C73×#1711C2semidirect
6. C73×#1703C2semidirect
7. C73×#1701C2semidirect
8. C73×#1699C2semidirect
9. C73×#1698C2semidirect
10. C73×#1646C2semidirect
11. C73×#1639C2semidirect
12. C73×#1638C2semidirect
13. C73×#1627C2semidirect
14. C73×#1590C2semidirect
15. C73×#1589C2semidirect
18. D4×Q8×C73C22semidirect
21. #487×C73C22semidirect
22. #487×C73C22semidirect
23. #487×C73C22semidirect
31. #477×C73C22semidirect
40. #461×C73C22semidirect
46. #446×C73C22semidirect
52. #436×C73C22semidirect
56. #335×C73C22semidirect
57. #334×C73C22semidirect
58. #333×C73C22semidirect
59. #332×C73C22semidirect
60. #332×C73C22semidirect
62. Q8⋊C8×C73C22semidirect
65. D4⋊C8×C73C22semidirect
66. C82×C73C22semidirect
296. #20287C73direct (N × H)
304. #3367C2×C73semidirect
305. #3329C2×C73semidirect
307. #3324C2×C73semidirect
308. #1711C2×C73semidirect
309. #1703C2×C73semidirect
310. #1701C2×C73semidirect
311. #1699C2×C73semidirect
312. #1698C2×C73semidirect
313. #1646C2×C73semidirect
314. #1639C2×C73semidirect
315. #1638C2×C73semidirect
316. #1627C2×C73semidirect
317. #1590C2×C73semidirect
318. #1589C2×C73semidirect
319. C73#20287direct (N × H)
322. D4×Q8C22×C73semidirect
325. #487C22×C73semidirect
326. #487C22×C73semidirect
327. #487C22×C73semidirect
335. #477C22×C73semidirect
344. #461C22×C73semidirect
350. #446C22×C73semidirect
356. #436C22×C73semidirect
360. #335C22×C73semidirect
361. #334C22×C73semidirect
362. #333C22×C73semidirect
363. #332C22×C73semidirect
364. #332C22×C73semidirect
366. Q8⋊C8C22×C73semidirect
369. D4⋊C8C22×C73semidirect
370. C82C22×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#33672
C73×#33292
C73×#33252
C73×#33242
C73×#17112
C73×#17032
C73×#17012
C73×#16992
C73×#16982
C73×#16462
C73×#16392
C73×#16382
C73×#16272
C73×#15902
C73×#15892
#2028773