Finite Group Databasebeta

← C73×#19992 #32929396

Subgroups — C73×#19992 #32929396

Order 18688.

622 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3360C211yesmaximal, characteristic, complemented
2C73×#3358C211yesmaximal, characteristic
3C73×#3304C211yesmaximal, characteristic, complemented
4C73×#3299C211yesmaximal, characteristic, complemented
5C73×#1708C211yesmaximal, characteristic, complemented
6C73×#1684C211yesmaximal, characteristic, complemented
7C73×#1683C211yesmaximal, characteristic, complemented
8C73×#1682C211yesmaximal, characteristic, complemented
9C73×#1681C211yesmaximal, characteristic, complemented
10C73×#1652C211yesmaximal, characteristic, complemented
11C73×#1651C211yesmaximal, characteristic, complemented
12C73×#1631C211yesmaximal, characteristic, complemented
13C73×#1622C211yesmaximal, characteristic, complemented
14C8×Q16×C73C211yesmaximal, characteristic, complemented
15C8×D8×C73C211yesmaximal, characteristic, complemented
16#556×C73C2211yescharacteristic
17#554×C73C2211yescharacteristic
18#550×C73C2211yescharacteristic
19D4×Q8×C73C2211yescharacteristic
20#498×C73C2211yescharacteristic
21#492×C73C2211yescharacteristic
22#488×C73—21no—
23#487×C73C2211yescharacteristic
24#487×C73C2211yescharacteristic
25#486×C73—21no—
26#486×C73C2211yescharacteristic
27#486×C73C2211yescharacteristic
28#484×C73—21no—
29#482×C73—21no—
30#479×C73—21no—
31#477×C73C2211yescharacteristic
32#476×C73C2211yescharacteristic
33#475×C73C2211yescharacteristic
34#474×C73—21no—
35#474×C73C2211yescharacteristic
36#467×C73—21no—
37#465×C73—21no—
38#463×C73—21no—
39#462×C73C2211yescharacteristic
40#461×C73C2211yescharacteristic
41#460×C73C2211yescharacteristic
42#459×C73—21no—
43#459×C73C2211yescharacteristic
44#452×C73—21no—
45#451×C73—21no—
46C8×Q8×C73C2211yescharacteristic
47C8×Q8×C73C2211yescharacteristic
48C4×Q16×C73C2211yescharacteristic
49C4×SD16×C73—21no—
50C4×D8×C73—21no—
51C4×D8×C73C2211yescharacteristic
52C8×D4×C73C2211yescharacteristic
53C8×D4×C73C2211yescharacteristic
54#416×C73—21no—
55C2×#103×C73—21no—
56#335×C73C2211yescharacteristic
57#335×C73C2211yescharacteristic
58#333×C73C2211yescharacteristic
59#332×C73C2211yescharacteristic
60#332×C73C2211yescharacteristic
61#331×C73C2211yescharacteristic
62Q8⋊C8×C73C2211yescharacteristic
63Q8⋊C8×C73C2211yescharacteristic
64D4⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66C82×C73C2211yescharacteristic
67C2×#41×C73—21no—
68C22×Q8×C73—21no—
69C2×Q16×C73—21no—
70C2×Q16×C73D411yescharacteristic
71C2×SD16×C73—21no—
72C2×SD16×C73—21no—
73C2×SD16×C73—41no—
74C2×D8×C73—21no—
75C2×D8×C73D411yescharacteristic
76C22×C8×C73—21no—
77C22×C8×C73—21no—
78C4⋊Q8×C73—21no—
79C4⋊Q8×C73C2311yescharacteristic
80C4⋊Q8×C73C2311yescharacteristic
81C4⋊Q8×C73C2311yescharacteristic
82#127×C73—21no—
83#127×C73C2311yescharacteristic
84#126×C73—41no—
85#125×C73—21no—
86#124×C73—21no—
87C22⋊Q8×C73—21no—
88C22⋊Q8×C73—21no—
89C22⋊Q8×C73—21no—
90C22⋊Q8×C73—41no—
91C22⋊Q8×C73—41no—
92#121×C73—21no—
93#121×C73—41no—
94C4×Q8×C73—21no—
95C4×Q8×C73C2311yescharacteristic
96C4×Q8×C73C2311yescharacteristic
97C4×D4×C73—21no—
98C4×D4×C73—21no—
99C4×D4×C73—21no—
100C4×D4×C73C2311yescharacteristic
101C4×D4×C73C2311yescharacteristic
102#117×C73—21no—
103C2×C4⋊C4×C73—21no—
104#107×C73—21no—
105#107×C73—21no—
106#107×C73D411yescharacteristic
107#107×C73D411yescharacteristic
108#106×C73—21no—
109#106×C73—21no—
110#106×C73—41no—
111C4⋊C8×C73—21no—
112C4⋊C8×C73—21no—
113C4⋊C8×C73C2311yescharacteristic
114C4⋊C8×C73C2311yescharacteristic
115C4⋊C8×C73C2311yescharacteristic
116C4⋊C8×C73C2311yescharacteristic
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—21no—
124#103×C73—21no—
125#103×C73D411yescharacteristic
126#103×C73D411yescharacteristic
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—
139C4×C8×C73—21no—
140C4×C8×C73—21no—
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#41×C73—42no—
145#41×C73—81no—
146C2×Q8×C73—21no—
147C2×Q8×C73—21no—
148C2×Q8×C73—21no—
149C2×Q8×C73—41no—
150C2×Q8×C73—42no—
151C2×Q8×C73—81no—
152C2×Q8×C73C2×D411yescharacteristic
153C2×Q8×C73C2×D411yescharacteristic
154C2×D4×C73—21no—
155C2×D4×C73—21no—
156C2×D4×C73—21no—
157C2×D4×C73—41no—
158C2×D4×C73—41no—
159C2×D4×C73C2×D411yescharacteristic
160C2×D4×C73C2×D411yescharacteristic
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—41no—
164C22×C4×C73—41no—
165C22×C4×C73—41no—
166Q16×C73—22no—
167Q16×C73—81no—
168SD16×C73—42no—
169SD16×C73—82no—
170SD16×C73—81no—
171D8×C73—22no—
172D8×C73—42no—
173C2×C8×C73—21no—
174C2×C8×C73—21no—
175C2×C8×C73—21no—
176C2×C8×C73—21no—
177C2×C8×C73—21no—
178C2×C8×C73—81no—
179C2×C8×C73—81no—
180C2×C8×C73C2×D411yescharacteristic
181C2×C8×C73C2×D411yescharacteristic
182C2×C8×C73C2×D411yescharacteristic
183C2×C8×C73C2×D411yescharacteristic
184C4⋊C4×C73—21no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—21no—
188C4⋊C4×C73—21no—
189C4⋊C4×C73—21no—
190C4⋊C4×C73—21no—
191C4⋊C4×C73—21no—
192C4⋊C4×C73—41no—
193C4⋊C4×C73—41no—
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—41no—
203C22⋊C4×C73—41no—
204C22⋊C4×C73—41no—
205C22⋊C4×C73—41no—
206C22⋊C4×C73—41no—
207C42×C73—21no—
208C42×C73—21no—
209C42×C73—41no—
210C42×C73C2411yescharacteristic
211C23×C73—21no—
212C23×C73—21no—
213C23×C73—41no—
214Q8×C73—21no—
215Q8×C73—21no—
216Q8×C73—21no—
217Q8×C73—41no—
218Q8×C73—41no—
219Q8×C73—41no—
220Q8×C73—41no—
221Q8×C73—82no—
222Q8×C73—81no—
223Q8×C73#13512yes—
224D4×C73—21no—
225D4×C73—21no—
226D4×C73—21no—
227D4×C73—41no—
228D4×C73—41no—
229D4×C73—41no—
230D4×C73—41no—
231D4×C73—82no—
232D4×C73—81no—
233D4×C73—161no—
234D4×C73#13512yes—
235C2×C4×C73—21no—
236C2×C4×C73—21no—
237C2×C4×C73—21no—
238C2×C4×C73—21no—
239C2×C4×C73—21no—
240C2×C4×C73—21no—
241C2×C4×C73—41no—
242C2×C4×C73—41no—
243C2×C4×C73—41no—
244C2×C4×C73—41no—
245C2×C4×C73—41no—
246C2×C4×C73—41no—
247C2×C4×C73—41no—
248C2×C4×C73—82no—
249C2×C4×C73—82no—
250C2×C4×C73—161no—
251C2×C4×C73C22×D411yescharacteristic
252C2×C4×C73C22×D411yescharacteristic
253C2×C4×C73H(5,𝔽2)11yescharacteristic
254C8×C73—22no—
255C8×C73—21no—
256C8×C73—21no—
257C8×C73—21no—
258C8×C73—21no—
259C8×C73—41no—
260C8×C73—41no—
261C8×C73—41no—
262C8×C73—41no—
263C22×C73—22no—
264C22×C73—41no—
265C22×C73—41no—
266C22×C73—41no—
267C22×C73—41no—
268C22×C73—41no—
269C22×C73—81no—
270C22×C73—81no—
271C22×C73—81no—
272C22×C73D4211yescharacteristic
273C4×C73—22no—
274C4×C73—21no—
275C4×C73—41no—
276C4×C73—41no—
277C4×C73—41no—
278C4×C73—41no—
279C4×C73—41no—
280C4×C73—81no—
281C4×C73—81no—
282C4×C73—81no—
283C4×C73C2×#13511yescharacteristic
284C4×C73C2×#13511yescharacteristic
285C4×C73#57611yescharacteristic
286C4×C73#57811yescharacteristic
287#19992C7311yesmaximal, characteristic, direct product factor, Sylow
288C2×C73—42no—
289C2×C73—81no—
290C2×C73—161no—
291C2×C73#328011yescharacteristic
292C2×C73#328511yescharacteristic
293C2×C73#329111yescharacteristic
294#3360C2×C7311yescharacteristic, complemented
295#3358C2×C7311yescharacteristic
296#3304C2×C7311yescharacteristic, complemented
297#3299C2×C7311yescharacteristic, complemented
298#1708C2×C7311yescharacteristic, complemented
299#1684C2×C7311yescharacteristic, complemented
300#1683C2×C7311yescharacteristic, complemented
301#1682C2×C7311yescharacteristic, complemented
302#1681C2×C7311yescharacteristic, complemented
303#1652C2×C7311yescharacteristic, complemented
304#1651C2×C7311yescharacteristic, complemented
305#1631C2×C7311yescharacteristic, complemented
306#1622C2×C7311yescharacteristic, complemented
307C8×Q16C2×C7311yescharacteristic, complemented
308C8×D8C2×C7311yescharacteristic, complemented
309C73#1999211yescharacteristic, direct product factor, Sylow
310#556C22×C7311yescharacteristic
311#554C22×C7311yescharacteristic
312#550C22×C7311yescharacteristic
313D4×Q8C22×C7311yescharacteristic
314#498C22×C7311yescharacteristic
315#492C22×C7311yescharacteristic
316#488—21no—
317#487C22×C7311yescharacteristic
318#487C22×C7311yescharacteristic
319#486—21no—
320#486C22×C7311yescharacteristic
321#486C22×C7311yescharacteristic
322#484—21no—
323#482—21no—
324#479—21no—
325#477C22×C7311yescharacteristic
326#476C22×C7311yescharacteristic
327#475C22×C7311yescharacteristic
328#474—21no—
329#474C22×C7311yescharacteristic
330#467—21no—
331#465—21no—
332#463—21no—
333#462C22×C7311yescharacteristic
334#461C22×C7311yescharacteristic
335#460C22×C7311yescharacteristic
336#459—21no—
337#459C22×C7311yescharacteristic
338#452—21no—
339#451—21no—
340C8×Q8C22×C7311yescharacteristic
341C8×Q8C22×C7311yescharacteristic
342C4×Q16C22×C7311yescharacteristic
343C4×SD16—21no—
344C4×D8—21no—
345C4×D8C22×C7311yescharacteristic
346C8×D4C22×C7311yescharacteristic
347C8×D4C22×C7311yescharacteristic
348#416—21no—
349C2×#103—21no—
350#335C22×C7311yescharacteristic
351#335C22×C7311yescharacteristic
352#333C22×C7311yescharacteristic
353#332C22×C7311yescharacteristic
354#332C22×C7311yescharacteristic
355#331C22×C7311yescharacteristic
356Q8⋊C8C22×C7311yescharacteristic
357Q8⋊C8C22×C7311yescharacteristic
358D4⋊C8C22×C7311yescharacteristic
359D4⋊C8C22×C7311yescharacteristic
360C82C22×C7311yescharacteristic
361C2×#41—21no—
362C22×Q8—21no—
363C2×Q16—21no—
364C2×Q16D4×C7311yescharacteristic
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—41no—
368C2×D8—21no—
369C2×D8D4×C7311yescharacteristic
370C22×C8—21no—
371C22×C8—21no—
372C4⋊Q8—21no—
373C4⋊Q8C23×C7311yescharacteristic
374C4⋊Q8C23×C7311yescharacteristic
375C4⋊Q8C23×C7311yescharacteristic
376#127—21no—
377#127C23×C7311yescharacteristic
378#126—41no—
379#125—21no—
380#124—21no—
381C22⋊Q8—21no—
382C22⋊Q8—21no—
383C22⋊Q8—21no—
384C22⋊Q8—41no—
385C22⋊Q8—41no—
386#121—21no—
387#121—41no—
388C4×Q8—21no—
389C4×Q8C23×C7311yescharacteristic
390C4×Q8C23×C7311yescharacteristic
391C4×D4—21no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4C23×C7311yescharacteristic
395C4×D4C23×C7311yescharacteristic
396#117—21no—
397C2×C4⋊C4—21no—
398#107—21no—
399#107—21no—
400#107D4×C7311yescharacteristic
401#107D4×C7311yescharacteristic
402#106—21no—
403#106—21no—
404#106—41no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8C23×C7311yescharacteristic
408C4⋊C8C23×C7311yescharacteristic
409C4⋊C8C23×C7311yescharacteristic
410C4⋊C8C23×C7311yescharacteristic
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103D4×C7311yescharacteristic
420#103D4×C7311yescharacteristic
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102D4×C7311yescharacteristic
430#102D4×C7311yescharacteristic
431C22⋊C8—21no—
432C22⋊C8—21no—
433C4×C8—21no—
434C4×C8—21no—
435C4×C8C23×C7311yescharacteristic
436C4×C8C23×C7311yescharacteristic
437C4×C8C23×C7311yescharacteristic
438#41—42no—
439#41—81no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—41no—
444C2×Q8—42no—
445C2×Q8—81no—
446C2×Q8C2×D4×C7311yescharacteristic
447C2×Q8C2×D4×C7311yescharacteristic
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4C2×D4×C7311yescharacteristic
454C2×D4C2×D4×C7311yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460Q16—22no—
461Q16—81no—
462SD16—42no—
463SD16—82no—
464SD16—81no—
465D8—22no—
466D8—42no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—81no—
473C2×C8—81no—
474C2×C8C2×D4×C7311yescharacteristic
475C2×C8C2×D4×C7311yescharacteristic
476C2×C8C2×D4×C7311yescharacteristic
477C2×C8C2×D4×C7311yescharacteristic
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4C2×D4×C7311yescharacteristic
491C4⋊C4C2×D4×C7311yescharacteristic
492C4⋊C4C2×D4×C7311yescharacteristic
493C4⋊C4C2×D4×C7311yescharacteristic
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C42—21no—
502C42—21no—
503C42—41no—
504C42C24×C7311yescharacteristic
505C23—21no—
506C23—21no—
507C23—41no—
508Q8—21no—
509Q8—21no—
510Q8—21no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—82no—
516Q8—81no—
517Q8#135×C7312yes—
518D4—21no—
519D4—21no—
520D4—21no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—82no—
526D4—81no—
527D4—161no—
528D4#135×C7312yes—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—82no—
543C2×C4—82no—
544C2×C4—161no—
545C2×C4C22×D4×C7311yescharacteristic
546C2×C4C22×D4×C7311yescharacteristic
547C2×C4H(5,𝔽2)×C7311yescharacteristic
548C8—22no—
549C8—21no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—41no—
557C22—22no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22D42×C7311yescharacteristic
567C4—22no—
568C4—21no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4C2×#135×C7311yescharacteristic
578C4C2×#135×C7311yescharacteristic
579C4#576×C7311yescharacteristic
580C4#578×C7311yescharacteristic
581C2—42no—
582C2—81no—
583C2—161no—
584C2C73×#328011yescharacteristic
585C2C73×#328511yescharacteristic
586C2C73×#329111yescharacteristic
subgroupG/H
center, socleC22×C73D42
commutator, Frattini, cosocleC42C24×C73
prime radicalC73×#3358C2
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×#3360C2semidirect
3. C73×#3304C2semidirect
4. C73×#3299C2semidirect
5. C73×#1708C2semidirect
6. C73×#1684C2semidirect
7. C73×#1683C2semidirect
8. C73×#1682C2semidirect
9. C73×#1681C2semidirect
10. C73×#1652C2semidirect
11. C73×#1651C2semidirect
12. C73×#1631C2semidirect
13. C73×#1622C2semidirect
14. C8×Q16×C73C2semidirect
15. C8×D8×C73C2semidirect
287. #19992C73direct (N × H)
294. #3360C2×C73semidirect
296. #3304C2×C73semidirect
297. #3299C2×C73semidirect
298. #1708C2×C73semidirect
299. #1684C2×C73semidirect
300. #1683C2×C73semidirect
301. #1682C2×C73semidirect
302. #1681C2×C73semidirect
303. #1652C2×C73semidirect
304. #1651C2×C73semidirect
305. #1631C2×C73semidirect
306. #1622C2×C73semidirect
307. C8×Q16C2×C73semidirect
308. C8×D8C2×C73semidirect
309. C73#19992direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#33602
C73×#33582
C73×#33042
C73×#32992
C73×#17082
C73×#16842
C73×#16832
C73×#16822
C73×#16812
C73×#16522
C73×#16512
C73×#16312
C73×#16222
C8×Q16×C732
C8×D8×C732
#1999273