Finite Group Databasebeta

← C73×#20274 #32929678

Subgroups — C73×#20274 #32929678

Order 18688.

626 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×#3397C211yesmaximal, characteristic, complemented
2C73×#3366C211yesmaximal, characteristic, complemented
3C73×#3333C211yesmaximal, characteristic, complemented
4C73×#3304C211yesmaximal, characteristic, complemented
5C73×#1717C211yesmaximal, characteristic, complemented
6C73×#1701C211yesmaximal, characteristic, complemented
7C73×#1698C211yesmaximal, characteristic, complemented
8C73×#1686C211yesmaximal, characteristic, complemented
9C73×#1677C211yesmaximal, characteristic, complemented
10C73×#1643C211yesmaximal, characteristic, complemented
11C73×#1638C211yesmaximal, characteristic, complemented
12C73×#1621C211yesmaximal, characteristic, complemented
13C73×#1621C211yesmaximal, characteristic, complemented
14C73×#1593C211yesmaximal, characteristic, complemented
15C73×#1581C211yesmaximal, characteristic, complemented
16#556×C73C2211yescharacteristic
17#554×C73C2211yescharacteristic
18#550×C73C2211yescharacteristic
19#550×C73C2211yescharacteristic
20#496×C73—21no—
21#493×C73C2211yescharacteristic
22#492×C73C2211yescharacteristic
23#490×C73—21no—
24#487×C73C2211yescharacteristic
25#486×C73C2211yescharacteristic
26#486×C73C2211yescharacteristic
27#486×C73C2211yescharacteristic
28#482×C73—21no—
29#480×C73—21no—
30#478×C73—21no—
31#477×C73C2211yescharacteristic
32#476×C73C2211yescharacteristic
33#475×C73C2211yescharacteristic
34#468×C73—21no—
35#465×C73—21no—
36#463×C73—21no—
37#461×C73C2211yescharacteristic
38#460×C73—21no—
39#460×C73C2211yescharacteristic
40#460×C73C2211yescharacteristic
41#459×C73—21no—
42#459×C73C2211yescharacteristic
43#459×C73C2211yescharacteristic
44#452×C73—21no—
45#452×C73—21no—
46#446×C73C2211yescharacteristic
47#446×C73C2211yescharacteristic
48#442×C73—21no—
49#440×C73—21no—
50C4×Q16×C73C2211yescharacteristic
51C4×D8×C73C2211yescharacteristic
52#436×C73C2211yescharacteristic
53C8×D4×C73C2211yescharacteristic
54#417×C73—21no—
55#416×C73—21no—
56#335×C73C2211yescharacteristic
57#334×C73C2211yescharacteristic
58#333×C73C2211yescharacteristic
59#332×C73C2211yescharacteristic
60#331×C73C2211yescharacteristic
61#331×C73C2211yescharacteristic
62Q8⋊C8×C73C2211yescharacteristic
63Q8⋊C8×C73C2211yescharacteristic
64D4⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×#41×C73—21no—
68C2×#41×C73—21no—
69C2×Q16×C73D411yescharacteristic
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×D8×C73—21no—
77C2×D8×C73—41no—
78C2×D8×C73D411yescharacteristic
79C2×M16×C73—21no—
80C22×C8×C73—21no—
81C4⋊Q8×C73C2311yescharacteristic
82C4⋊Q8×C73C2311yescharacteristic
83#127×C73—21no—
84#127×C73—21no—
85#127×C73C2311yescharacteristic
86#127×C73C2311yescharacteristic
87#126×C73—41no—
88#125×C73—21no—
89#124×C73—21no—
90C22⋊Q8×C73—21no—
91C22⋊Q8×C73—21no—
92C22⋊Q8×C73—41no—
93#121×C73—21no—
94#121×C73—21no—
95#121×C73—41no—
96#121×C73—41no—
97C4×Q8×C73—21no—
98C4×Q8×C73C2311yescharacteristic
99C4×Q8×C73C2311yescharacteristic
100C4×D4×C73—21no—
101C4×D4×C73—21no—
102C4×D4×C73—21no—
103C4×D4×C73C2311yescharacteristic
104C4×D4×C73C2311yescharacteristic
105#117×C73—21no—
106C2×C4⋊C4×C73—21no—
107#107×C73—21no—
108#107×C73D411yescharacteristic
109#107×C73D411yescharacteristic
110#106×C73—21no—
111#106×C73—21no—
112C4⋊C8×C73—21no—
113C4⋊C8×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#103×C73—41no—
122#103×C73D411yescharacteristic
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—21no—
134#102×C73—21no—
135#102×C73D411yescharacteristic
136#102×C73D411yescharacteristic
137C22⋊C8×C73—21no—
138C22⋊C8×C73—21no—
139#97×C73—21no—
140#97×C73—21no—
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#41×C73—42no—
145#41×C73—42no—
146#41×C73—81no—
147#41×C73—81no—
148C2×Q8×C73—21no—
149C2×Q8×C73—21no—
150C2×Q8×C73C2×D411yescharacteristic
151C2×Q8×C73C2×D411yescharacteristic
152C2×D4×C73—21no—
153C2×D4×C73—21no—
154C2×D4×C73—21no—
155C2×D4×C73—21no—
156C2×D4×C73—21no—
157C2×D4×C73—21no—
158C2×D4×C73—41no—
159C2×D4×C73—41no—
160C2×D4×C73—41no—
161C2×D4×C73—41no—
162C2×D4×C73C2×D411yescharacteristic
163C2×D4×C73C2×D411yescharacteristic
164C22×C4×C73—21no—
165C22×C4×C73—21no—
166C22×C4×C73—41no—
167C22×C4×C73—41no—
168C22×C4×C73—41no—
169Q16×C73—41no—
170SD16×C73—42no—
171SD16×C73—81no—
172SD16×C73—81no—
173SD16×C73—81no—
174SD16×C73—81no—
175D8×C73—41no—
176D8×C73—42no—
177D8×C73—81no—
178D8×C73—82no—
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×C73—41no—
198C4⋊C4×C73—41no—
199C4⋊C4×C73C2×D411yescharacteristic
200C4⋊C4×C73C2×D411yescharacteristic
201C4⋊C4×C73C2×D411yescharacteristic
202C4⋊C4×C73C2×D411yescharacteristic
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—
210C42×C73—21no—
211C42×C73—21no—
212C42×C73—41no—
213C42×C73C2411yescharacteristic
214C23×C73—21no—
215C23×C73—21no—
216C23×C73—41no—
217C23×C73—41no—
218Q8×C73—21no—
219Q8×C73—21no—
220Q8×C73—21no—
221Q8×C73—21no—
222Q8×C73—41no—
223Q8×C73—41no—
224Q8×C73—81no—
225D4×C73—21no—
226D4×C73—21no—
227D4×C73—21no—
228D4×C73—21no—
229D4×C73—41no—
230D4×C73—41no—
231D4×C73—41no—
232D4×C73—41no—
233D4×C73—41no—
234D4×C73—41no—
235D4×C73—41no—
236D4×C73—41no—
237D4×C73—81no—
238D4×C73—81no—
239D4×C73—82no—
240D4×C73—82no—
241D4×C73—161no—
242D4×C73—161no—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—21no—
246C2×C4×C73—21no—
247C2×C4×C73—21no—
248C2×C4×C73—21no—
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—82no—
256C2×C4×C73—82no—
257C2×C4×C73—161no—
258C2×C4×C73C22×D411yescharacteristic
259C2×C4×C73C22×D411yescharacteristic
260C2×C4×C73H(5,𝔽2)11yescharacteristic
261C8×C73—21no—
262C8×C73—21no—
263C8×C73—21no—
264C8×C73—21no—
265C8×C73—41no—
266C8×C73—41no—
267C8×C73—41no—
268C8×C73—41no—
269C8×C73—41no—
270C22×C73—41no—
271C22×C73—41no—
272C22×C73—41no—
273C22×C73—41no—
274C22×C73—41no—
275C22×C73—41no—
276C22×C73—81no—
277C22×C73—81no—
278C22×C73—81no—
279C22×C73—81no—
280C22×C73—81no—
281C22×C73—81no—
282C22×C73D4211yescharacteristic
283C4×C73—21no—
284C4×C73—41no—
285C4×C73—41no—
286C4×C73—41no—
287C4×C73—41no—
288C4×C73—41no—
289C4×C73—41no—
290C4×C73—81no—
291C4×C73—81no—
292C4×C73#57511yescharacteristic
293C4×C73#57511yescharacteristic
294C4×C73#57611yescharacteristic
295C4×C73#57711yescharacteristic
296#20274C7311yesmaximal, characteristic, direct product factor, Sylow
297C2×C73—81no—
298C2×C73—81no—
299C2×C73—161no—
300C2×C73—161no—
301C2×C73#327111yescharacteristic
302C2×C73#327311yescharacteristic
303C2×C73#328811yescharacteristic
304#3397C2×C7311yescharacteristic, complemented
305#3366C2×C7311yescharacteristic, complemented
306#3333C2×C7311yescharacteristic, complemented
307#3304C2×C7311yescharacteristic, complemented
308#1717C2×C7311yescharacteristic, complemented
309#1701C2×C7311yescharacteristic, complemented
310#1698C2×C7311yescharacteristic, complemented
311#1686C2×C7311yescharacteristic, complemented
312#1677C2×C7311yescharacteristic, complemented
313#1643C2×C7311yescharacteristic, complemented
314#1638C2×C7311yescharacteristic, complemented
315#1621C2×C7311yescharacteristic, complemented
316#1621C2×C7311yescharacteristic, complemented
317#1593C2×C7311yescharacteristic, complemented
318#1581C2×C7311yescharacteristic, complemented
319C73#2027411yescharacteristic, direct product factor, Sylow
320#556C22×C7311yescharacteristic
321#554C22×C7311yescharacteristic
322#550C22×C7311yescharacteristic
323#550C22×C7311yescharacteristic
324#496—21no—
325#493C22×C7311yescharacteristic
326#492C22×C7311yescharacteristic
327#490—21no—
328#487C22×C7311yescharacteristic
329#486C22×C7311yescharacteristic
330#486C22×C7311yescharacteristic
331#486C22×C7311yescharacteristic
332#482—21no—
333#480—21no—
334#478—21no—
335#477C22×C7311yescharacteristic
336#476C22×C7311yescharacteristic
337#475C22×C7311yescharacteristic
338#468—21no—
339#465—21no—
340#463—21no—
341#461C22×C7311yescharacteristic
342#460—21no—
343#460C22×C7311yescharacteristic
344#460C22×C7311yescharacteristic
345#459—21no—
346#459C22×C7311yescharacteristic
347#459C22×C7311yescharacteristic
348#452—21no—
349#452—21no—
350#446C22×C7311yescharacteristic
351#446C22×C7311yescharacteristic
352#442—21no—
353#440—21no—
354C4×Q16C22×C7311yescharacteristic
355C4×D8C22×C7311yescharacteristic
356#436C22×C7311yescharacteristic
357C8×D4C22×C7311yescharacteristic
358#417—21no—
359#416—21no—
360#335C22×C7311yescharacteristic
361#334C22×C7311yescharacteristic
362#333C22×C7311yescharacteristic
363#332C22×C7311yescharacteristic
364#331C22×C7311yescharacteristic
365#331C22×C7311yescharacteristic
366Q8⋊C8C22×C7311yescharacteristic
367Q8⋊C8C22×C7311yescharacteristic
368D4⋊C8C22×C7311yescharacteristic
369D4⋊C8C22×C7311yescharacteristic
370#322C22×C7311yescharacteristic
371C2×#41—21no—
372C2×#41—21no—
373C2×Q16D4×C7311yescharacteristic
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×D8—21no—
380C2×D8—21no—
381C2×D8—41no—
382C2×D8D4×C7311yescharacteristic
383C2×M16—21no—
384C22×C8—21no—
385C4⋊Q8C23×C7311yescharacteristic
386C4⋊Q8C23×C7311yescharacteristic
387#127—21no—
388#127—21no—
389#127C23×C7311yescharacteristic
390#127C23×C7311yescharacteristic
391#126—41no—
392#125—21no—
393#124—21no—
394C22⋊Q8—21no—
395C22⋊Q8—21no—
396C22⋊Q8—41no—
397#121—21no—
398#121—21no—
399#121—41no—
400#121—41no—
401C4×Q8—21no—
402C4×Q8C23×C7311yescharacteristic
403C4×Q8C23×C7311yescharacteristic
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4C23×C7311yescharacteristic
408C4×D4C23×C7311yescharacteristic
409#117—21no—
410C2×C4⋊C4—21no—
411#107—21no—
412#107D4×C7311yescharacteristic
413#107D4×C7311yescharacteristic
414#106—21no—
415#106—21no—
416C4⋊C8—21no—
417C4⋊C8—21no—
418C4⋊C8C23×C7311yescharacteristic
419C4⋊C8C23×C7311yescharacteristic
420C4⋊C8C23×C7311yescharacteristic
421C4⋊C8C23×C7311yescharacteristic
422#103—21no—
423#103—21no—
424#103—21no—
425#103—41no—
426#103D4×C7311yescharacteristic
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—21no—
438#102—21no—
439#102D4×C7311yescharacteristic
440#102D4×C7311yescharacteristic
441C22⋊C8—21no—
442C22⋊C8—21no—
443#97—21no—
444#97—21no—
445C4×C8C23×C7311yescharacteristic
446C4×C8C23×C7311yescharacteristic
447C4×C8C23×C7311yescharacteristic
448#41—42no—
449#41—42no—
450#41—81no—
451#41—81no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8C2×D4×C7311yescharacteristic
455C2×Q8C2×D4×C7311yescharacteristic
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4C2×D4×C7311yescharacteristic
467C2×D4C2×D4×C7311yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473Q16—41no—
474SD16—42no—
475SD16—81no—
476SD16—81no—
477SD16—81no—
478SD16—81no—
479D8—41no—
480D8—42no—
481D8—81no—
482D8—82no—
483M16—81no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—81no—
490C2×C8C2×D4×C7311yescharacteristic
491C2×C8C2×D4×C7311yescharacteristic
492C2×C8C2×D4×C7311yescharacteristic
493C2×C8C2×D4×C7311yescharacteristic
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4C2×D4×C7311yescharacteristic
504C4⋊C4C2×D4×C7311yescharacteristic
505C4⋊C4C2×D4×C7311yescharacteristic
506C4⋊C4C2×D4×C7311yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C42—21no—
515C42—21no—
516C42—41no—
517C42C24×C7311yescharacteristic
518C23—21no—
519C23—21no—
520C23—41no—
521C23—41no—
522Q8—21no—
523Q8—21no—
524Q8—21no—
525Q8—21no—
526Q8—41no—
527Q8—41no—
528Q8—81no—
529D4—21no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—81no—
542D4—81no—
543D4—82no—
544D4—82no—
545D4—161no—
546D4—161no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4—161no—
562C2×C4C22×D4×C7311yescharacteristic
563C2×C4C22×D4×C7311yescharacteristic
564C2×C4H(5,𝔽2)×C7311yescharacteristic
565C8—21no—
566C8—21no—
567C8—21no—
568C8—21no—
569C8—41no—
570C8—41no—
571C8—41no—
572C8—41no—
573C8—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22D42×C7311yescharacteristic
587C4—21no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—81no—
595C4—81no—
596C4#575×C7311yescharacteristic
597C4#575×C7311yescharacteristic
598C4#576×C7311yescharacteristic
599C4#577×C7311yescharacteristic
600C2—81no—
601C2—81no—
602C2—161no—
603C2—161no—
604C2C73×#327111yescharacteristic
605C2C73×#327311yescharacteristic
606C2C73×#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×#3397C2semidirect
2. C73×#3366C2semidirect
3. C73×#3333C2semidirect
4. C73×#3304C2semidirect
5. C73×#1717C2semidirect
6. C73×#1701C2semidirect
7. C73×#1698C2semidirect
8. C73×#1686C2semidirect
9. C73×#1677C2semidirect
10. C73×#1643C2semidirect
11. C73×#1638C2semidirect
12. C73×#1621C2semidirect
13. C73×#1621C2semidirect
14. C73×#1593C2semidirect
15. C73×#1581C2semidirect
296. #20274C73direct (N × H)
304. #3397C2×C73semidirect
305. #3366C2×C73semidirect
306. #3333C2×C73semidirect
307. #3304C2×C73semidirect
308. #1717C2×C73semidirect
309. #1701C2×C73semidirect
310. #1698C2×C73semidirect
311. #1686C2×C73semidirect
312. #1677C2×C73semidirect
313. #1643C2×C73semidirect
314. #1638C2×C73semidirect
315. #1621C2×C73semidirect
316. #1621C2×C73semidirect
317. #1593C2×C73semidirect
318. #1581C2×C73semidirect
319. C73#20274direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#33972
C73×#33662
C73×#33332
C73×#33042
C73×#17172
C73×#17012
C73×#16982
C73×#16862
C73×#16772
C73×#16432
C73×#16382
C73×#16212
C73×#15932
C73×#15812
#2027473