Finite Group Databasebeta

← C73×#20035 #32929439

Subgroups — C73×#20035 #32929439

Order 18688.

654 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3358C211yesmaximal, characteristic, complemented
2C73×#3354C211yesmaximal, characteristic, complemented
3C73×#3305C211yesmaximal, characteristic, complemented
4C73×#3276C211yesmaximal, characteristic, complemented
5C73×#1720C211yesmaximal, characteristic, complemented
6C73×#1701C211yesmaximal, characteristic, complemented
7C73×#1697C211yesmaximal, characteristic, complemented
8C73×#1672C211yesmaximal, characteristic, complemented
9C73×#1669C211yesmaximal, characteristic, complemented
10C73×#1646C211yesmaximal, characteristic, complemented
11C73×#1641C211yesmaximal, characteristic, complemented
12C73×#1637C211yesmaximal, characteristic, complemented
13C73×#1625C211yesmaximal, characteristic, complemented
14C73×#1588C211yesmaximal, characteristic, complemented
15C73×#1586C211yesmaximal, characteristic, complemented
16C2×#137×C73—21no—
17#555×C73C2211yescharacteristic
18#550×C73C2211yescharacteristic
19D4×Q8×C73C2211yescharacteristic
20#547×C73C2211yescharacteristic
21#498×C73C2211yescharacteristic
22#494×C73C2211yescharacteristic
23#487×C73C2211yescharacteristic
24#486×C73—21no—
25#486×C73C2211yescharacteristic
26#486×C73C2211yescharacteristic
27#486×C73C2211yescharacteristic
28#482×C73—21no—
29#482×C73—21no—
30#481×C73—21no—
31#477×C73C2211yescharacteristic
32#476×C73C2211yescharacteristic
33#474×C73—21no—
34#474×C73C2211yescharacteristic
35#474×C73C2211yescharacteristic
36#470×C73—21no—
37#469×C73—21no—
38#466×C73—21no—
39#462×C73C2211yescharacteristic
40#461×C73C2211yescharacteristic
41#459×C73—21no—
42#459×C73C2211yescharacteristic
43#459×C73C2211yescharacteristic
44#452×C73—21no—
45#451×C73—21no—
46#449×C73—21no—
47C8×Q8×C73C2211yescharacteristic
48C4×SD16×C73C2211yescharacteristic
49C4×D8×C73—21no—
50C4×D8×C73C2211yescharacteristic
51#436×C73C2211yescharacteristic
52#436×C73C2211yescharacteristic
53C8×D4×C73C2211yescharacteristic
54#428×C73—21no—
55#416×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
66#322×C73C2211yescharacteristic
67C2×#41×C73—21no—
68C2×#41×C73—21no—
69C22×Q8×C73—21no—
70#137×C73—44no—
71C2×Q16×C73—21no—
72C2×Q16×C73—21no—
73C2×Q16×C73—21no—
74C2×SD16×C73—21no—
75C2×SD16×C73D411yescharacteristic
76C2×D8×C73—21no—
77C2×D8×C73—21no—
78C2×D8×C73D411yescharacteristic
79C2×M16×C73—21no—
80C2×M16×C73—21no—
81C22×C8×C73—21no—
82C4⋊Q8×C73—21no—
83C4⋊Q8×C73C2311yescharacteristic
84C4⋊Q8×C73C2311yescharacteristic
85C4⋊Q8×C73C2311yescharacteristic
86#127×C73—21no—
87#127×C73C2311yescharacteristic
88#124×C73—41no—
89#123×C73—41no—
90C22⋊Q8×C73—21no—
91C22⋊Q8×C73—21no—
92C22⋊Q8×C73—41no—
93#121×C73—21no—
94#121×C73—21no—
95#121×C73—21no—
96#121×C73—21no—
97#121×C73—41no—
98C4×Q8×C73C2311yescharacteristic
99C4×D4×C73—21no—
100C4×D4×C73—21no—
101C4×D4×C73C2311yescharacteristic
102C4×D4×C73C2311yescharacteristic
103C4×D4×C73C2311yescharacteristic
104#117×C73—21no—
105#117×C73—21no—
106C2×C4⋊C4×C73—21no—
107#107×C73—21no—
108#107×C73—21no—
109#107×C73—21no—
110#107×C73D411yescharacteristic
111#106×C73—21no—
112#106×C73—21no—
113#106×C73—21no—
114#106×C73D411yescharacteristic
115C4⋊C8×C73—21no—
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#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—21no—
134#102×C73—41no—
135#102×C73D411yescharacteristic
136#102×C73D411yescharacteristic
137#102×C73D411yescharacteristic
138C22⋊C8×C73—21no—
139C22⋊C8×C73—21no—
140C22⋊C8×C73—21no—
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C4×C8×C73C2311yescharacteristic
145#41×C73—42no—
146#41×C73—42no—
147#41×C73—81no—
148#41×C73—81no—
149C2×Q8×C73—21no—
150C2×Q8×C73—21no—
151C2×Q8×C73—21no—
152C2×Q8×C73—41no—
153C2×Q8×C73—42no—
154C2×Q8×C73—81no—
155C2×Q8×C73C2×D411yescharacteristic
156C2×D4×C73—21no—
157C2×D4×C73—21no—
158C2×D4×C73—21no—
159C2×D4×C73—41no—
160C2×D4×C73—41no—
161C2×D4×C73—41no—
162C2×D4×C73—41no—
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—41no—
170C22×C4×C73—41no—
171C22×C4×C73—41no—
172Q16×C73—42no—
173Q16×C73—42no—
174Q16×C73—81no—
175SD16×C73—22no—
176SD16×C73—42no—
177D8×C73—41no—
178D8×C73—42no—
179D8×C73—81no—
180M16×C73—42no—
181M16×C73—42no—
182C2×C8×C73—21no—
183C2×C8×C73—21no—
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73—21no—
187C2×C8×C73—81no—
188C2×C8×C73C2×D411yescharacteristic
189C2×C8×C73C2×D411yescharacteristic
190C2×C8×C73C2×D411yescharacteristic
191C2×C8×C73C2×D411yescharacteristic
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—21no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73—41no—
200C4⋊C4×C73—41no—
201C4⋊C4×C73C2×D411yescharacteristic
202C4⋊C4×C73C2×D411yescharacteristic
203C4⋊C4×C73C2×D411yescharacteristic
204C4⋊C4×C73C2×D411yescharacteristic
205C22⋊C4×C73—21no—
206C22⋊C4×C73—21no—
207C22⋊C4×C73—21no—
208C22⋊C4×C73—41no—
209C22⋊C4×C73—41no—
210C22⋊C4×C73—41no—
211C22⋊C4×C73—41no—
212C22⋊C4×C73—41no—
213C42×C73—21no—
214C42×C73—41no—
215C42×C73C2411yescharacteristic
216C23×C73—21no—
217C23×C73—21no—
218C23×C73—21no—
219C23×C73—41no—
220Q8×C73—21no—
221Q8×C73—41no—
222Q8×C73—41no—
223Q8×C73—41no—
224Q8×C73—41no—
225Q8×C73—82no—
226Q8×C73—81no—
227Q8×C73AGL(1,ℤ/8)12yes—
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—82no—
239D4×C73—81no—
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—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—82no—
258C2×C4×C73—82no—
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—81no—
282C22×C73—81no—
283C22×C73—81no—
284C22×C73D4211yescharacteristic
285C4×C73—22no—
286C4×C73—21no—
287C4×C73—41no—
288C4×C73—41no—
289C4×C73—41no—
290C4×C73—41no—
291C4×C73—81no—
292C4×C73—81no—
293C4×C73—81no—
294C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
295C4×C73#57511yescharacteristic
296C4×C73#57611yescharacteristic
297C4×C73#57811yescharacteristic
298#20035C7311yesmaximal, characteristic, direct product factor, Sylow
299C2×C73—81no—
300C2×C73—81no—
301C2×C73—81no—
302C2×C73—161no—
303C2×C73#326411yescharacteristic
304C2×C73#326911yescharacteristic
305C2×C73#329011yescharacteristic
306#3358C2×C7311yescharacteristic, complemented
307#3354C2×C7311yescharacteristic, complemented
308#3305C2×C7311yescharacteristic, complemented
309#3276C2×C7311yescharacteristic, complemented
310#1720C2×C7311yescharacteristic, complemented
311#1701C2×C7311yescharacteristic, complemented
312#1697C2×C7311yescharacteristic, complemented
313#1672C2×C7311yescharacteristic, complemented
314#1669C2×C7311yescharacteristic, complemented
315#1646C2×C7311yescharacteristic, complemented
316#1641C2×C7311yescharacteristic, complemented
317#1637C2×C7311yescharacteristic, complemented
318#1625C2×C7311yescharacteristic, complemented
319#1588C2×C7311yescharacteristic, complemented
320#1586C2×C7311yescharacteristic, complemented
321C73#2003511yescharacteristic, direct product factor, Sylow
322C2×#137—21no—
323#555C22×C7311yescharacteristic
324#550C22×C7311yescharacteristic
325D4×Q8C22×C7311yescharacteristic
326#547C22×C7311yescharacteristic
327#498C22×C7311yescharacteristic
328#494C22×C7311yescharacteristic
329#487C22×C7311yescharacteristic
330#486—21no—
331#486C22×C7311yescharacteristic
332#486C22×C7311yescharacteristic
333#486C22×C7311yescharacteristic
334#482—21no—
335#482—21no—
336#481—21no—
337#477C22×C7311yescharacteristic
338#476C22×C7311yescharacteristic
339#474—21no—
340#474C22×C7311yescharacteristic
341#474C22×C7311yescharacteristic
342#470—21no—
343#469—21no—
344#466—21no—
345#462C22×C7311yescharacteristic
346#461C22×C7311yescharacteristic
347#459—21no—
348#459C22×C7311yescharacteristic
349#459C22×C7311yescharacteristic
350#452—21no—
351#451—21no—
352#449—21no—
353C8×Q8C22×C7311yescharacteristic
354C4×SD16C22×C7311yescharacteristic
355C4×D8—21no—
356C4×D8C22×C7311yescharacteristic
357#436C22×C7311yescharacteristic
358#436C22×C7311yescharacteristic
359C8×D4C22×C7311yescharacteristic
360#428—21no—
361#416—21no—
362#335C22×C7311yescharacteristic
363#334C22×C7311yescharacteristic
364#333C22×C7311yescharacteristic
365#332C22×C7311yescharacteristic
366#332C22×C7311yescharacteristic
367#331C22×C7311yescharacteristic
368Q8⋊C8C22×C7311yescharacteristic
369D4⋊C8C22×C7311yescharacteristic
370D4⋊C8C22×C7311yescharacteristic
371D4⋊C8C22×C7311yescharacteristic
372#322C22×C7311yescharacteristic
373C2×#41—21no—
374C2×#41—21no—
375C22×Q8—21no—
376#137—44no—
377C2×Q16—21no—
378C2×Q16—21no—
379C2×Q16—21no—
380C2×SD16—21no—
381C2×SD16D4×C7311yescharacteristic
382C2×D8—21no—
383C2×D8—21no—
384C2×D8D4×C7311yescharacteristic
385C2×M16—21no—
386C2×M16—21no—
387C22×C8—21no—
388C4⋊Q8—21no—
389C4⋊Q8C23×C7311yescharacteristic
390C4⋊Q8C23×C7311yescharacteristic
391C4⋊Q8C23×C7311yescharacteristic
392#127—21no—
393#127C23×C7311yescharacteristic
394#124—41no—
395#123—41no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—41no—
399#121—21no—
400#121—21no—
401#121—21no—
402#121—21no—
403#121—41no—
404C4×Q8C23×C7311yescharacteristic
405C4×D4—21no—
406C4×D4—21no—
407C4×D4C23×C7311yescharacteristic
408C4×D4C23×C7311yescharacteristic
409C4×D4C23×C7311yescharacteristic
410#117—21no—
411#117—21no—
412C2×C4⋊C4—21no—
413#107—21no—
414#107—21no—
415#107—21no—
416#107D4×C7311yescharacteristic
417#106—21no—
418#106—21no—
419#106—21no—
420#106D4×C7311yescharacteristic
421C4⋊C8—21no—
422C4⋊C8C23×C7311yescharacteristic
423C4⋊C8C23×C7311yescharacteristic
424C4⋊C8C23×C7311yescharacteristic
425C4⋊C8C23×C7311yescharacteristic
426#103—21no—
427#103—21no—
428#103—21no—
429#103—41no—
430#103D4×C7311yescharacteristic
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—41no—
441#102D4×C7311yescharacteristic
442#102D4×C7311yescharacteristic
443#102D4×C7311yescharacteristic
444C22⋊C8—21no—
445C22⋊C8—21no—
446C22⋊C8—21no—
447C4×C8—21no—
448C4×C8C23×C7311yescharacteristic
449C4×C8C23×C7311yescharacteristic
450C4×C8C23×C7311yescharacteristic
451#41—42no—
452#41—42no—
453#41—81no—
454#41—81no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—41no—
459C2×Q8—42no—
460C2×Q8—81no—
461C2×Q8C2×D4×C7311yescharacteristic
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4C2×D4×C7311yescharacteristic
470C2×D4C2×D4×C7311yescharacteristic
471C2×D4C2×D4×C7311yescharacteristic
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478Q16—42no—
479Q16—42no—
480Q16—81no—
481SD16—22no—
482SD16—42no—
483D8—41no—
484D8—42no—
485D8—81no—
486M16—42no—
487M16—42no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—81no—
494C2×C8C2×D4×C7311yescharacteristic
495C2×C8C2×D4×C7311yescharacteristic
496C2×C8C2×D4×C7311yescharacteristic
497C2×C8C2×D4×C7311yescharacteristic
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—41no—
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—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C42—21no—
520C42—41no—
521C42C24×C7311yescharacteristic
522C23—21no—
523C23—21no—
524C23—21no—
525C23—41no—
526Q8—21no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—41no—
531Q8—82no—
532Q8—81no—
533Q8AGL(1,ℤ/8)×C7312yes—
534D4—21no—
535D4—21no—
536D4—21no—
537D4—21no—
538D4—21no—
539D4—21no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—82no—
545D4—81no—
546D4—82no—
547D4—161no—
548D4—161no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—82no—
564C2×C4—82no—
565C2×C4—82no—
566C2×C4C22×D4×C7311yescharacteristic
567C2×C4C22×D4×C7311yescharacteristic
568C2×C4H(5,𝔽2)×C7311yescharacteristic
569C8—21no—
570C8—21no—
571C8—21no—
572C8—21no—
573C8—41no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22D42×C7311yescharacteristic
591C4—22no—
592C4—21no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—81no—
598C4—81no—
599C4—81no—
600C4C2×AGL(1,ℤ/8)×C7311yescharacteristic
601C4#575×C7311yescharacteristic
602C4#576×C7311yescharacteristic
603C4#578×C7311yescharacteristic
604C2—81no—
605C2—81no—
606C2—81no—
607C2—161no—
608C2C73×#326411yescharacteristic
609C2C73×#326911yescharacteristic
610C2C73×#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×#3354C2semidirect
3. C73×#3305C2semidirect
4. C73×#3276C2semidirect
5. C73×#1720C2semidirect
6. C73×#1701C2semidirect
7. C73×#1697C2semidirect
8. C73×#1672C2semidirect
9. C73×#1669C2semidirect
10. C73×#1646C2semidirect
11. C73×#1641C2semidirect
12. C73×#1637C2semidirect
13. C73×#1625C2semidirect
14. C73×#1588C2semidirect
15. C73×#1586C2semidirect
298. #20035C73direct (N × H)
306. #3358C2×C73semidirect
307. #3354C2×C73semidirect
308. #3305C2×C73semidirect
309. #3276C2×C73semidirect
310. #1720C2×C73semidirect
311. #1701C2×C73semidirect
312. #1697C2×C73semidirect
313. #1672C2×C73semidirect
314. #1669C2×C73semidirect
315. #1646C2×C73semidirect
316. #1641C2×C73semidirect
317. #1637C2×C73semidirect
318. #1625C2×C73semidirect
319. #1588C2×C73semidirect
320. #1586C2×C73semidirect
321. C73#20035direct (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×#33542
C73×#33052
C73×#32762
C73×#17202
C73×#17012
C73×#16972
C73×#16722
C73×#16692
C73×#16462
C73×#16412
C73×#16372
C73×#16252
C73×#15882
C73×#15862
#2003573