Finite Group Databasebeta

← C73×#18832 #32928236

Subgroups — C73×#18832 #32928236

Order 18688.

928 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×#3511C211yesmaximal, characteristic, complemented
2C73×#3226C211yesmaximal, characteristic, complemented
3C73×#3214C211yesmaximal, characteristic, complemented
4C73×#3115C211yesmaximal, characteristic, complemented
5C73×#1650C212yesmaximal, complemented
6C73×#1647C212yesmaximal, complemented
7C73×#1628C212yesmaximal, complemented
8C73×#1625C212yesmaximal, complemented
9C73×#1556C211yesmaximal, characteristic, complemented
10C73×#1496C211yesmaximal, characteristic, complemented
11C73×#1488C211yesmaximal, characteristic, complemented
12#556×C73C2212yes—
13#555×C73—21no—
14#554×C73—21no—
15#553×C73—22no—
16#548×C73—22no—
17#547×C73C2212yes—
18#542×C73—22no—
19#537×C73—21no—
20#533×C73—21no—
21#532×C73—21no—
22#532×C73C2211yescharacteristic
23#532×C73C2211yescharacteristic
24C2×C4⋊Q8×C73C2211yescharacteristic
25#520×C73—21no—
26C4×#41×C73C2211yescharacteristic
27#500×C73C2212yes—
28#496×C73—21no—
29#489×C73—21no—
30#486×C73C2212yes—
31#482×C73—21no—
32#480×C73—22no—
33#475×C73C2211yescharacteristic
34#474×C73—22no—
35#474×C73C2211yescharacteristic
36#461×C73C2212yes—
37#460×C73C2211yescharacteristic
38#459×C73C2212yes—
39#459×C73C2211yescharacteristic
40#449×C73—21no—
41#449×C73—22no—
42#442×C73—21no—
43#440×C73—21no—
44#432×C73C2211yescharacteristic
45#432×C73C2211yescharacteristic
46#431×C73C2211yescharacteristic
47#332×C73C2212yes—
48#332×C73C2212yes—
49Q8⋊C8×C73C2212yes—
50D4⋊C8×C73C2212yes—
51D4⋊C8×C73C2212yes—
52D4⋊C8×C73C2212yes—
53C2×#41×C73—22no—
54C2×#41×C73—21no—
55C2×#41×C73—21no—
56C2×#41×C73D411yescharacteristic
57C22×Q8×C73—21no—
58C2×SD16×C73—21no—
59C2×SD16×C73—22no—
60C2×D8×C73—21no—
61C2×D8×C73—22no—
62C4⋊Q8×C73—21no—
63C4⋊Q8×C73—21no—
64C4⋊Q8×C73D412yes—
65C4⋊Q8×C73D411yescharacteristic
66C4⋊Q8×C73C2311yescharacteristic
67C4⋊Q8×C73C2312yes—
68#127×C73D411yescharacteristic
69#127×C73C2311yescharacteristic
70#126×C73—24no—
71#125×C73—22no—
72#124×C73—24no—
73#124×C73—22no—
74#124×C73—21no—
75#124×C73—21no—
76#123×C73—24no—
77C22⋊Q8×C73—22no—
78C22⋊Q8×C73—24no—
79C22⋊Q8×C73—22no—
80C22⋊Q8×C73—22no—
81#121×C73—22no—
82#121×C73—22no—
83#121×C73—24no—
84#121×C73—22no—
85#121×C73—21no—
86#121×C73—21no—
87#121×C73—21no—
88#121×C73D412yes—
89C4×Q8×C73—22no—
90C4×Q8×C73—22no—
91C4×Q8×C73D411yescharacteristic
92C4×Q8×C73C2311yescharacteristic
93C4×D4×C73—22no—
94C4×D4×C73—24no—
95C4×D4×C73—22no—
96C4×D4×C73—21no—
97C4×D4×C73—21no—
98C4×D4×C73—21no—
99C4×D4×C73—21no—
100C4×D4×C73—21no—
101C4×D4×C73D411yescharacteristic
102C4×D4×C73C2312yes—
103C4×D4×C73C2311yescharacteristic
104#117×C73—22no—
105#117×C73—22no—
106#117×C73—21no—
107#117×C73D411yescharacteristic
108C2×C4⋊C4×C73—21no—
109C2×C4⋊C4×C73—22no—
110C2×C4⋊C4×C73D412yes—
111C2×C42×C73—21no—
112C2×C42×C73C2311yescharacteristic
113#107×C73—21no—
114#107×C73—24no—
115#106×C73—21no—
116C4⋊C8×C73—21no—
117C4⋊C8×C73C2312yes—
118C4⋊C8×C73C2311yescharacteristic
119C4⋊C8×C73C2311yescharacteristic
120#103×C73—21no—
121#103×C73—22no—
122#102×C73—21no—
123#102×C73—21no—
124#102×C73—21no—
125#102×C73—22no—
126#102×C73—24no—
127C22⋊C8×C73—21no—
128C22⋊C8×C73—21no—
129C22⋊C8×C73—21no—
130#97×C73—21no—
131#97×C73—21no—
132C4×C8×C73C2312yes—
133#41×C73—41no—
134#41×C73—41no—
135#41×C73—42no—
136#41×C73—42no—
137#41×C73—82no—
138#41×C73—82no—
139#41×C73—82no—
140C2×Q8×C73—21no—
141C2×Q8×C73—22no—
142C2×Q8×C73—22no—
143C2×Q8×C73—21no—
144C2×Q8×C73—82no—
145C2×Q8×C73C2×D411yescharacteristic
146C2×D4×C73—21no—
147C2×D4×C73—22no—
148C2×D4×C73—24no—
149C2×D4×C73—21no—
150C2×D4×C73—21no—
151C2×D4×C73—21no—
152C2×D4×C73—21no—
153C2×D4×C73—21no—
154C2×D4×C73—41no—
155C2×D4×C73C2×D411yescharacteristic
156C2×D4×C73C2×D412yes—
157C22×C4×C73—24no—
158C22×C4×C73—22no—
159C22×C4×C73—21no—
160C22×C4×C73—21no—
161C22×C4×C73—21no—
162C22×C4×C73—22no—
163C22×C4×C73—41no—
164C22×C4×C73C2×D411yescharacteristic
165C22×C4×C73C2×D411yescharacteristic
166C22×C4×C73C2×D411yescharacteristic
167SD16×C73—42no—
168SD16×C73—82no—
169D8×C73—42no—
170D8×C73—82no—
171C2×C8×C73—22no—
172C2×C8×C73—21no—
173C2×C8×C73—21no—
174C2×C8×C73—22no—
175C4⋊C4×C73—24no—
176C4⋊C4×C73—24no—
177C4⋊C4×C73—22no—
178C4⋊C4×C73—22no—
179C4⋊C4×C73—21no—
180C4⋊C4×C73—21no—
181C4⋊C4×C73—22no—
182C4⋊C4×C73—21no—
183C4⋊C4×C73—21no—
184C4⋊C4×C73—21no—
185C4⋊C4×C73C2×D412yes—
186C4⋊C4×C73C2×D411yescharacteristic
187C4⋊C4×C73C2×D411yescharacteristic
188C4⋊C4×C73C2×D414yes—
189C22⋊C4×C73—24no—
190C22⋊C4×C73—24no—
191C22⋊C4×C73—24no—
192C22⋊C4×C73—21no—
193C22⋊C4×C73—21no—
194C22⋊C4×C73—22no—
195C22⋊C4×C73—21no—
196C22⋊C4×C73—22no—
197C22⋊C4×C73—41no—
198C22⋊C4×C73—41no—
199C42×C73—24no—
200C42×C73—21no—
201C42×C73—21no—
202C42×C73—21no—
203C42×C73C2×D411yescharacteristic
204C42×C73C2×D411yescharacteristic
205C42×C73C2×D411yescharacteristic
206C42×C73C2411yescharacteristic
207C23×C73—21no—
208C23×C73—22no—
209C23×C73—41no—
210C23×C73#12011yescharacteristic
211Q8×C73—21no—
212Q8×C73—21no—
213Q8×C73—42no—
214Q8×C73—42no—
215Q8×C73—42no—
216Q8×C73—42no—
217Q8×C73—82no—
218D4×C73—21no—
219D4×C73—21no—
220D4×C73—22no—
221D4×C73—22no—
222D4×C73—42no—
223D4×C73—42no—
224D4×C73—42no—
225D4×C73—42no—
226D4×C73—44no—
227D4×C73—41no—
228D4×C73—41no—
229D4×C73—42no—
230D4×C73—84no—
231D4×C73—82no—
232C2×C4×C73—21no—
233C2×C4×C73—21no—
234C2×C4×C73—22no—
235C2×C4×C73—21no—
236C2×C4×C73—21no—
237C2×C4×C73—22no—
238C2×C4×C73—21no—
239C2×C4×C73—24no—
240C2×C4×C73—41no—
241C2×C4×C73—42no—
242C2×C4×C73—42no—
243C2×C4×C73—42no—
244C2×C4×C73—42no—
245C2×C4×C73—42no—
246C2×C4×C73—41no—
247C2×C4×C73—82no—
248C2×C4×C73—82no—
249C2×C4×C73—84no—
250C2×C4×C73#12011yescharacteristic
251C2×C4×C73#12011yescharacteristic
252C2×C4×C73#12011yescharacteristic
253C2×C4×C73C22×D411yescharacteristic
254C2×C4×C73C22×D411yescharacteristic
255C2×C4×C73C22×D411yescharacteristic
256C8×C73—42no—
257C8×C73—41no—
258C8×C73—41no—
259C8×C73—42no—
260C22×C73—21no—
261C22×C73—21no—
262C22×C73—21no—
263C22×C73—41no—
264C22×C73—42no—
265C22×C73—41no—
266C22×C73—42no—
267C22×C73—41no—
268C22×C73—42no—
269C22×C73—81no—
270C22×C73—81no—
271C22×C73—81no—
272C22×C73C2×#12011yescharacteristic
273C4×C73—21no—
274C4×C73—21no—
275C4×C73—21no—
276C4×C73—21no—
277C4×C73—41no—
278C4×C73—42no—
279C4×C73—41no—
280C4×C73—44no—
281C4×C73—41no—
282C4×C73—81no—
283C4×C73#57511yescharacteristic
284C4×C73#57511yescharacteristic
285C4×C73#57612yes—
286#18832C7311yesmaximal, characteristic, direct product factor, Sylow
287C2×C73—41no—
288C2×C73—81no—
289C2×C73—82no—
290C2×C73—161no—
291C2×C73#300511yescharacteristic
292C2×C73#300811yescharacteristic
293C2×C73#302011yescharacteristic
294#3511C2×C7311yescharacteristic, complemented
295#3226C2×C7311yescharacteristic, complemented
296#3214C2×C7311yescharacteristic, complemented
297#3115C2×C7311yescharacteristic, complemented
298#1650C2×C7312yescomplemented
299#1647C2×C7312yescomplemented
300#1628C2×C7312yescomplemented
301#1625C2×C7312yescomplemented
302#1556C2×C7311yescharacteristic, complemented
303#1496C2×C7311yescharacteristic, complemented
304#1488C2×C7311yescharacteristic, complemented
305C73#1883211yescharacteristic, direct product factor, Sylow
306#556C22×C7312yes—
307#555—21no—
308#554—21no—
309#553—22no—
310#548—22no—
311#547C22×C7312yes—
312#542—22no—
313#537—21no—
314#533—21no—
315#532—21no—
316#532C22×C7311yescharacteristic
317#532C22×C7311yescharacteristic
318C2×C4⋊Q8C22×C7311yescharacteristic
319#520—21no—
320C4×#41C22×C7311yescharacteristic
321#500C22×C7312yes—
322#496—21no—
323#489—21no—
324#486C22×C7312yes—
325#482—21no—
326#480—22no—
327#475C22×C7311yescharacteristic
328#474—22no—
329#474C22×C7311yescharacteristic
330#461C22×C7312yes—
331#460C22×C7311yescharacteristic
332#459C22×C7311yescharacteristic
333#459C22×C7312yes—
334#449—21no—
335#449—22no—
336#442—21no—
337#440—21no—
338#432C22×C7311yescharacteristic
339#432C22×C7311yescharacteristic
340#431C22×C7311yescharacteristic
341#332C22×C7312yes—
342#332C22×C7312yes—
343Q8⋊C8C22×C7312yes—
344D4⋊C8C22×C7312yes—
345D4⋊C8C22×C7312yes—
346D4⋊C8C22×C7312yes—
347C2×#41—22no—
348C2×#41—21no—
349C2×#41—21no—
350C2×#41D4×C7311yescharacteristic
351C22×Q8—21no—
352C2×SD16—21no—
353C2×SD16—22no—
354C2×D8—21no—
355C2×D8—22no—
356C4⋊Q8—21no—
357C4⋊Q8—21no—
358C4⋊Q8D4×C7312yes—
359C4⋊Q8D4×C7311yescharacteristic
360C4⋊Q8C23×C7311yescharacteristic
361C4⋊Q8C23×C7312yes—
362#127D4×C7311yescharacteristic
363#127C23×C7311yescharacteristic
364#126—24no—
365#125—22no—
366#124—24no—
367#124—22no—
368#124—21no—
369#124—21no—
370#123—24no—
371C22⋊Q8—22no—
372C22⋊Q8—24no—
373C22⋊Q8—22no—
374C22⋊Q8—22no—
375#121—22no—
376#121—22no—
377#121—24no—
378#121—22no—
379#121—21no—
380#121—21no—
381#121—21no—
382#121D4×C7312yes—
383C4×Q8—22no—
384C4×Q8—22no—
385C4×Q8D4×C7311yescharacteristic
386C4×Q8C23×C7311yescharacteristic
387C4×D4—22no—
388C4×D4—24no—
389C4×D4—22no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4D4×C7311yescharacteristic
396C4×D4C23×C7311yescharacteristic
397C4×D4C23×C7312yes—
398#117—22no—
399#117—22no—
400#117—21no—
401#117D4×C7311yescharacteristic
402C2×C4⋊C4—21no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4D4×C7312yes—
405C2×C42—21no—
406C2×C42C23×C7311yescharacteristic
407#107—21no—
408#107—24no—
409#106—21no—
410C4⋊C8—21no—
411C4⋊C8C23×C7311yescharacteristic
412C4⋊C8C23×C7311yescharacteristic
413C4⋊C8C23×C7312yes—
414#103—21no—
415#103—22no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—22no—
420#102—24no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424#97—21no—
425#97—21no—
426C4×C8C23×C7312yes—
427#41—41no—
428#41—41no—
429#41—42no—
430#41—42no—
431#41—82no—
432#41—82no—
433#41—82no—
434C2×Q8—21no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—21no—
438C2×Q8—82no—
439C2×Q8C2×D4×C7311yescharacteristic
440C2×D4—21no—
441C2×D4—22no—
442C2×D4—24no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—41no—
449C2×D4C2×D4×C7311yescharacteristic
450C2×D4C2×D4×C7312yes—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—41no—
458C22×C4C2×D4×C7311yescharacteristic
459C22×C4C2×D4×C7311yescharacteristic
460C22×C4C2×D4×C7311yescharacteristic
461SD16—42no—
462SD16—82no—
463D8—42no—
464D8—82no—
465C2×C8—22no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—22no—
469C4⋊C4—24no—
470C4⋊C4—24no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4C2×D4×C7312yes—
480C4⋊C4C2×D4×C7311yescharacteristic
481C4⋊C4C2×D4×C7311yescharacteristic
482C4⋊C4C2×D4×C7314yes—
483C22⋊C4—24no—
484C22⋊C4—24no—
485C22⋊C4—24no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—22no—
489C22⋊C4—21no—
490C22⋊C4—22no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C42—24no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42C2×D4×C7311yescharacteristic
498C42C2×D4×C7311yescharacteristic
499C42C2×D4×C7311yescharacteristic
500C42C24×C7311yescharacteristic
501C23—21no—
502C23—22no—
503C23—41no—
504C23#120×C7311yescharacteristic
505Q8—21no—
506Q8—21no—
507Q8—42no—
508Q8—42no—
509Q8—42no—
510Q8—42no—
511Q8—82no—
512D4—21no—
513D4—21no—
514D4—22no—
515D4—22no—
516D4—42no—
517D4—42no—
518D4—42no—
519D4—42no—
520D4—44no—
521D4—41no—
522D4—41no—
523D4—42no—
524D4—84no—
525D4—82no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—24no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4—84no—
544C2×C4#120×C7311yescharacteristic
545C2×C4#120×C7311yescharacteristic
546C2×C4#120×C7311yescharacteristic
547C2×C4C22×D4×C7311yescharacteristic
548C2×C4C22×D4×C7311yescharacteristic
549C2×C4C22×D4×C7311yescharacteristic
550C8—42no—
551C8—41no—
552C8—41no—
553C8—42no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—41no—
558C22—42no—
559C22—41no—
560C22—42no—
561C22—41no—
562C22—42no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22C2×#120×C7311yescharacteristic
567C4—21no—
568C4—21no—
569C4—21no—
570C4—21no—
571C4—41no—
572C4—42no—
573C4—41no—
574C4—44no—
575C4—41no—
576C4—81no—
577C4#575×C7311yescharacteristic
578C4#575×C7311yescharacteristic
579C4#576×C7312yes—
580C2—41no—
581C2—81no—
582C2—82no—
583C2—161no—
584C2C73×#300511yescharacteristic
585C2C73×#300811yescharacteristic
586C2C73×#302011yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC42C24×C73
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C73×#3511C2semidirect
2. C73×#3226C2semidirect
3. C73×#3214C2semidirect
4. C73×#3115C2semidirect
5. C73×#1650C2semidirect
6. C73×#1647C2semidirect
7. C73×#1628C2semidirect
8. C73×#1625C2semidirect
9. C73×#1556C2semidirect
10. C73×#1496C2semidirect
11. C73×#1488C2semidirect
286. #18832C73direct (N × H)
294. #3511C2×C73semidirect
295. #3226C2×C73semidirect
296. #3214C2×C73semidirect
297. #3115C2×C73semidirect
298. #1650C2×C73semidirect
299. #1647C2×C73semidirect
300. #1628C2×C73semidirect
301. #1625C2×C73semidirect
302. #1556C2×C73semidirect
303. #1496C2×C73semidirect
304. #1488C2×C73semidirect
305. C73#18832direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#35112
C73×#32262
C73×#32142
C73×#31152
C73×#16502
C73×#16472
C73×#16282
C73×#16252
C73×#15562
C73×#14962
C73×#14882
#1883273