Finite Group Databasebeta

← C73×#19991 #32929395

Subgroups — C73×#19991 #32929395

Order 18688.

640 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3358C211yesmaximal, characteristic, complemented
2C73×#3305C211yesmaximal, characteristic, complemented
3C73×#3303C211yesmaximal, characteristic, complemented
4C73×#3298C211yesmaximal, characteristic, complemented
5C73×#1711C211yesmaximal, characteristic, complemented
6C73×#1684C211yesmaximal, characteristic, complemented
7C73×#1681C211yesmaximal, characteristic, complemented
8C73×#1679C211yesmaximal, characteristic, complemented
9C73×#1677C211yesmaximal, characteristic, complemented
10C73×#1646C211yesmaximal, characteristic, complemented
11C73×#1642C211yesmaximal, characteristic, complemented
12C73×#1637C211yesmaximal, characteristic, complemented
13C73×#1625C211yesmaximal, characteristic, complemented
14C8×SD16×C73C211yesmaximal, characteristic, complemented
15C8×D8×C73C211yesmaximal, characteristic, complemented
16#555×C73C2211yescharacteristic
17#550×C73C2211yescharacteristic
18D4×Q8×C73C2211yescharacteristic
19#547×C73C2211yescharacteristic
20#487×C73C2211yescharacteristic
21#487×C73C2211yescharacteristic
22#487×C73C2211yescharacteristic
23#486×C73—21no—
24#486×C73C2211yescharacteristic
25#486×C73C2211yescharacteristic
26#486×C73C2211yescharacteristic
27#485×C73—21no—
28#483×C73—21no—
29#482×C73—21no—
30#477×C73C2211yescharacteristic
31#476×C73C2211yescharacteristic
32#475×C73C2211yescharacteristic
33#474×C73—21no—
34#474×C73C2211yescharacteristic
35#466×C73—21no—
36#465×C73—21no—
37#465×C73—21no—
38#461×C73C2211yescharacteristic
39#461×C73C2211yescharacteristic
40#459×C73—21no—
41#459×C73C2211yescharacteristic
42#459×C73C2211yescharacteristic
43#449×C73—21no—
44#449×C73—21no—
45#448×C73—21no—
46C8×Q8×C73C2211yescharacteristic
47C4×SD16×C73C2211yescharacteristic
48C4×D8×C73—21no—
49C4×D8×C73C2211yescharacteristic
50C8×D4×C73C2211yescharacteristic
51C8×D4×C73C2211yescharacteristic
52C8×D4×C73C2211yescharacteristic
53#416×C73—21no—
54#416×C73—21no—
55C2×#103×C73—21no—
56#335×C73C2211yescharacteristic
57#334×C73C2211yescharacteristic
58#333×C73C2211yescharacteristic
59#332×C73C2211yescharacteristic
60#332×C73C2211yescharacteristic
61#331×C73C2211yescharacteristic
62Q8⋊C8×C73C2211yescharacteristic
63D4⋊C8×C73C2211yescharacteristic
64D4⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66C82×C73C2211yescharacteristic
67C2×#41×C73—21no—
68C2×#41×C73—21no—
69C22×Q8×C73—21no—
70C2×SD16×C73—21no—
71C2×SD16×C73—21no—
72C2×SD16×C73D411yescharacteristic
73C2×D8×C73—21no—
74C2×D8×C73—21no—
75C2×D8×C73D411yescharacteristic
76C22×C8×C73—21no—
77C22×C8×C73—21no—
78C22×C8×C73—21no—
79C4⋊Q8×C73—21no—
80C4⋊Q8×C73C2311yescharacteristic
81C4⋊Q8×C73C2311yescharacteristic
82C4⋊Q8×C73C2311yescharacteristic
83#127×C73—21no—
84#127×C73C2311yescharacteristic
85#124×C73—41no—
86#123×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#121×C73—41no—
95C4×Q8×C73C2311yescharacteristic
96C4×D4×C73—21no—
97C4×D4×C73—21no—
98C4×D4×C73C2311yescharacteristic
99C4×D4×C73C2311yescharacteristic
100C4×D4×C73C2311yescharacteristic
101#117×C73—21no—
102#117×C73—21no—
103C2×C4⋊C4×C73—21no—
104#107×C73—21no—
105#107×C73—21no—
106#107×C73D411yescharacteristic
107#106×C73—21no—
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—21no—
123#103×C73—41no—
124#103×C73D411yescharacteristic
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—
140C4×C8×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×C73—21no—
151C2×Q8×C73—41no—
152C2×Q8×C73—42no—
153C2×Q8×C73—81no—
154C2×Q8×C73C2×D411yescharacteristic
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
164C2×D4×C73C2×D411yescharacteristic
165C22×C4×C73—21no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—41no—
169C22×C4×C73—41no—
170C22×C4×C73—41no—
171SD16×C73—22no—
172SD16×C73—81no—
173SD16×C73—81no—
174D8×C73—22no—
175D8×C73—42no—
176D8×C73—81no—
177C2×C8×C73—21no—
178C2×C8×C73—21no—
179C2×C8×C73—21no—
180C2×C8×C73—21no—
181C2×C8×C73—21no—
182C2×C8×C73—81no—
183C2×C8×C73—81no—
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—41no—
197C4⋊C4×C73—41no—
198C4⋊C4×C73C2×D411yescharacteristic
199C4⋊C4×C73C2×D411yescharacteristic
200C4⋊C4×C73C2×D411yescharacteristic
201C4⋊C4×C73C2×D411yescharacteristic
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—
210C42×C73—21no—
211C42×C73—41no—
212C42×C73C2411yescharacteristic
213C23×C73—21no—
214C23×C73—21no—
215C23×C73—21no—
216C23×C73—41no—
217Q8×C73—21no—
218Q8×C73—41no—
219Q8×C73—41no—
220Q8×C73—41no—
221Q8×C73—41no—
222Q8×C73—82no—
223Q8×C73—81no—
224Q8×C73#13512yes—
225D4×C73—21no—
226D4×C73—21no—
227D4×C73—21no—
228D4×C73—21no—
229D4×C73—21no—
230D4×C73—41no—
231D4×C73—41no—
232D4×C73—41no—
233D4×C73—41no—
234D4×C73—82no—
235D4×C73—81no—
236D4×C73—82no—
237D4×C73—161no—
238D4×C73—161no—
239D4×C73#13512yes—
240C2×C4×C73—21no—
241C2×C4×C73—21no—
242C2×C4×C73—21no—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—41no—
246C2×C4×C73—41no—
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—82no—
255C2×C4×C73—82no—
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—22no—
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×C73D4211yescharacteristic
282C4×C73—22no—
283C4×C73—21no—
284C4×C73—41no—
285C4×C73—41no—
286C4×C73—41no—
287C4×C73—41no—
288C4×C73—81no—
289C4×C73—81no—
290C4×C73—81no—
291C4×C73C2×#13511yescharacteristic
292C4×C73C2×#13511yescharacteristic
293C4×C73#57611yescharacteristic
294C4×C73#57711yescharacteristic
295#19991C7311yesmaximal, characteristic, direct product factor, Sylow
296C2×C73—42no—
297C2×C73—81no—
298C2×C73—81no—
299C2×C73—161no—
300C2×C73#328011yescharacteristic
301C2×C73#328211yescharacteristic
302C2×C73#329011yescharacteristic
303#3358C2×C7311yescharacteristic, complemented
304#3305C2×C7311yescharacteristic, complemented
305#3303C2×C7311yescharacteristic, complemented
306#3298C2×C7311yescharacteristic, complemented
307#1711C2×C7311yescharacteristic, complemented
308#1684C2×C7311yescharacteristic, complemented
309#1681C2×C7311yescharacteristic, complemented
310#1679C2×C7311yescharacteristic, complemented
311#1677C2×C7311yescharacteristic, complemented
312#1646C2×C7311yescharacteristic, complemented
313#1642C2×C7311yescharacteristic, complemented
314#1637C2×C7311yescharacteristic, complemented
315#1625C2×C7311yescharacteristic, complemented
316C8×SD16C2×C7311yescharacteristic, complemented
317C8×D8C2×C7311yescharacteristic, complemented
318C73#1999111yescharacteristic, direct product factor, Sylow
319#555C22×C7311yescharacteristic
320#550C22×C7311yescharacteristic
321D4×Q8C22×C7311yescharacteristic
322#547C22×C7311yescharacteristic
323#487C22×C7311yescharacteristic
324#487C22×C7311yescharacteristic
325#487C22×C7311yescharacteristic
326#486—21no—
327#486C22×C7311yescharacteristic
328#486C22×C7311yescharacteristic
329#486C22×C7311yescharacteristic
330#485—21no—
331#483—21no—
332#482—21no—
333#477C22×C7311yescharacteristic
334#476C22×C7311yescharacteristic
335#475C22×C7311yescharacteristic
336#474—21no—
337#474C22×C7311yescharacteristic
338#466—21no—
339#465—21no—
340#465—21no—
341#461C22×C7311yescharacteristic
342#461C22×C7311yescharacteristic
343#459—21no—
344#459C22×C7311yescharacteristic
345#459C22×C7311yescharacteristic
346#449—21no—
347#449—21no—
348#448—21no—
349C8×Q8C22×C7311yescharacteristic
350C4×SD16C22×C7311yescharacteristic
351C4×D8—21no—
352C4×D8C22×C7311yescharacteristic
353C8×D4C22×C7311yescharacteristic
354C8×D4C22×C7311yescharacteristic
355C8×D4C22×C7311yescharacteristic
356#416—21no—
357#416—21no—
358C2×#103—21no—
359#335C22×C7311yescharacteristic
360#334C22×C7311yescharacteristic
361#333C22×C7311yescharacteristic
362#332C22×C7311yescharacteristic
363#332C22×C7311yescharacteristic
364#331C22×C7311yescharacteristic
365Q8⋊C8C22×C7311yescharacteristic
366D4⋊C8C22×C7311yescharacteristic
367D4⋊C8C22×C7311yescharacteristic
368D4⋊C8C22×C7311yescharacteristic
369C82C22×C7311yescharacteristic
370C2×#41—21no—
371C2×#41—21no—
372C22×Q8—21no—
373C2×SD16—21no—
374C2×SD16—21no—
375C2×SD16D4×C7311yescharacteristic
376C2×D8—21no—
377C2×D8—21no—
378C2×D8D4×C7311yescharacteristic
379C22×C8—21no—
380C22×C8—21no—
381C22×C8—21no—
382C4⋊Q8—21no—
383C4⋊Q8C23×C7311yescharacteristic
384C4⋊Q8C23×C7311yescharacteristic
385C4⋊Q8C23×C7311yescharacteristic
386#127—21no—
387#127C23×C7311yescharacteristic
388#124—41no—
389#123—41no—
390C22⋊Q8—21no—
391C22⋊Q8—21no—
392C22⋊Q8—41no—
393#121—21no—
394#121—21no—
395#121—21no—
396#121—21no—
397#121—41no—
398C4×Q8C23×C7311yescharacteristic
399C4×D4—21no—
400C4×D4—21no—
401C4×D4C23×C7311yescharacteristic
402C4×D4C23×C7311yescharacteristic
403C4×D4C23×C7311yescharacteristic
404#117—21no—
405#117—21no—
406C2×C4⋊C4—21no—
407#107—21no—
408#107—21no—
409#107D4×C7311yescharacteristic
410#106—21no—
411#106—21no—
412#106D4×C7311yescharacteristic
413C4⋊C8—21no—
414C4⋊C8C23×C7311yescharacteristic
415C4⋊C8C23×C7311yescharacteristic
416C4⋊C8C23×C7311yescharacteristic
417C4⋊C8C23×C7311yescharacteristic
418#103—21no—
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—41no—
437#102D4×C7311yescharacteristic
438#102D4×C7311yescharacteristic
439#102D4×C7311yescharacteristic
440C22⋊C8—21no—
441C22⋊C8—21no—
442C22⋊C8—21no—
443C4×C8—21no—
444C4×C8C23×C7311yescharacteristic
445C4×C8C23×C7311yescharacteristic
446C4×C8C23×C7311yescharacteristic
447#41—42no—
448#41—42no—
449#41—81no—
450#41—81no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—41no—
455C2×Q8—42no—
456C2×Q8—81no—
457C2×Q8C2×D4×C7311yescharacteristic
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4C2×D4×C7311yescharacteristic
466C2×D4C2×D4×C7311yescharacteristic
467C2×D4C2×D4×C7311yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474SD16—22no—
475SD16—81no—
476SD16—81no—
477D8—22no—
478D8—42no—
479D8—81no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—81no—
486C2×C8—81no—
487C2×C8—81no—
488C2×C8C2×D4×C7311yescharacteristic
489C2×C8C2×D4×C7311yescharacteristic
490C2×C8C2×D4×C7311yescharacteristic
491C2×C8C2×D4×C7311yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4C2×D4×C7311yescharacteristic
502C4⋊C4C2×D4×C7311yescharacteristic
503C4⋊C4C2×D4×C7311yescharacteristic
504C4⋊C4C2×D4×C7311yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C42—21no—
514C42—41no—
515C42C24×C7311yescharacteristic
516C23—21no—
517C23—21no—
518C23—21no—
519C23—41no—
520Q8—21no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524Q8—41no—
525Q8—82no—
526Q8—81no—
527Q8#135×C7312yes—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—82no—
538D4—81no—
539D4—82no—
540D4—161no—
541D4—161no—
542D4#135×C7312yes—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—82no—
558C2×C4—82no—
559C2×C4—82no—
560C2×C4C22×D4×C7311yescharacteristic
561C2×C4C22×D4×C7311yescharacteristic
562C2×C4H(5,𝔽2)×C7311yescharacteristic
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8—41no—
571C8—41no—
572C22—22no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22D42×C7311yescharacteristic
585C4—22no—
586C4—21no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—81no—
592C4—81no—
593C4—81no—
594C4C2×#135×C7311yescharacteristic
595C4C2×#135×C7311yescharacteristic
596C4#576×C7311yescharacteristic
597C4#577×C7311yescharacteristic
598C2—42no—
599C2—81no—
600C2—81no—
601C2—161no—
602C2C73×#328011yescharacteristic
603C2C73×#328211yescharacteristic
604C2C73×#329011yescharacteristic
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×#3358C2semidirect
2. C73×#3305C2semidirect
3. C73×#3303C2semidirect
4. C73×#3298C2semidirect
5. C73×#1711C2semidirect
6. C73×#1684C2semidirect
7. C73×#1681C2semidirect
8. C73×#1679C2semidirect
9. C73×#1677C2semidirect
10. C73×#1646C2semidirect
11. C73×#1642C2semidirect
12. C73×#1637C2semidirect
13. C73×#1625C2semidirect
14. C8×SD16×C73C2semidirect
15. C8×D8×C73C2semidirect
295. #19991C73direct (N × H)
303. #3358C2×C73semidirect
304. #3305C2×C73semidirect
305. #3303C2×C73semidirect
306. #3298C2×C73semidirect
307. #1711C2×C73semidirect
308. #1684C2×C73semidirect
309. #1681C2×C73semidirect
310. #1679C2×C73semidirect
311. #1677C2×C73semidirect
312. #1646C2×C73semidirect
313. #1642C2×C73semidirect
314. #1637C2×C73semidirect
315. #1625C2×C73semidirect
316. C8×SD16C2×C73semidirect
317. C8×D8C2×C73semidirect
318. C73#19991direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#33582
C73×#33052
C73×#33032
C73×#32982
C73×#17112
C73×#16842
C73×#16812
C73×#16792
C73×#16772
C73×#16462
C73×#16422
C73×#16372
C73×#16252
C8×SD16×C732
C8×D8×C732
#1999173