Finite Group Databasebeta

← #2383×D73 #33248641

Subgroups — #2383×D73 #33248641

Order 18688.

2502 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#126×D73C211yesmaximal, characteristic
2#22613124C211yesmaximal, characteristic, complemented
3#22613123C211yesmaximal, characteristic, complemented
4#22613122C213yesmaximal, complemented
5#22613121C213yesmaximal, complemented
6#22613120C211yesmaximal, characteristic, complemented
7#22613119C213yesmaximal, complemented
8#22613118C213yesmaximal, complemented
9#389×D73C213yesmaximal, complemented
10#388×D73C213yesmaximal
11#387×D73C213yesmaximal, complemented
12#385×D73C213yesmaximal
13#384×D73C211yesmaximal, characteristic, complemented
14#383×D73C211yesmaximal, characteristic, complemented
15C73×#2383C211yesmaximal, characteristic, complemented
16C23×C4×D73C2211yescharacteristic
17C2×#14556586C2213yes—
18C2×#14556585C2211yescharacteristic
19C2×#14556584C2213yes—
20#126×D73C4116yescomplemented
21C2×C4⋊C4×D73C2213yes—
22C2×C4⋊C4×D73C2213yes—
23C2×C4⋊C4×D73C2213yes—
24C2×C4⋊C4×D73C2213yes—
25C2×C22⋊C4×D73C2213yes—
26C2×C22⋊C4×D73C2213yes—
27C2×C42×D73C2213yes—
28C2×C42×D73C2211yescharacteristic
29#17988486C2213yescomplemented
30#17988485C2213yescomplemented
31#17988484C2213yescomplemented
32#17988484C2213yescomplemented
33#17988483C2213yescomplemented
34#17988482C2213yescomplemented
35#17988482C2213yescomplemented
36#17988481C2213yes—
37#17988480C2213yes—
38#17988479C2213yes—
39#17988478C2213yes—
40#17988477C2213yes—
41#17988476C2213yes—
42#17988475C2213yes—
43#17988474C2213yescomplemented
44#17988473C2213yescomplemented
45#17988472C2213yescomplemented
46#17988471C2213yescomplemented
47#17988470C2213yescomplemented
48#17988469C2213yescomplemented
49#17988468C2213yescomplemented
50#17988462C2213yes—
51#17988461C2213yes—
52#17988461C2213yes—
53#17988460C2213yes—
54#17988459C2213yes—
55#17988458C2213yes—
56#17988458C2213yes—
57#17988457C2211yescharacteristic, complemented
58#17988456C2213yescomplemented
59#17988456C2213yescomplemented
60#17988455C2211yescharacteristic, complemented
61#17988454C2213yescomplemented
62#17988454C2213yescomplemented
63#95×D73C2213yes—
64#95×D73C2213yes—
65#95×D73C2213yes—
66#95×D73C2213yes—
67C2×#126×C73C2211yescharacteristic
68#389×C73C2213yescomplemented
69#388×C73C2213yes—
70#387×C73C2213yescomplemented
71#385×C73C2213yes—
72#384×C73C2211yescharacteristic, complemented
73#383×C73C2211yescharacteristic, complemented
74C24×D73C2311yescharacteristic
75C23×Dic73C2311yescharacteristic
76C22×C4×D73—46no—
77C22×C4×D73C2311yescharacteristic
78C22×C4×D73C2311yescharacteristic
79C22×C4×D73C2313yes—
80C22×C4×D73C2313yes—
81C22×C4×D73C2313yes—
82C22×C4×D73C2313yes—
83C22×C4×D73C2311yescharacteristic
84C22×C4×D73C2311yescharacteristic
85#14556586C2×C4124yescomplemented
86#14556585C2×C418yescomplemented
87#14556584C2×C4124yescomplemented
88C2×C4⋊Dic73C2313yes—
89C2×C4⋊Dic73C2313yes—
90C2×C4⋊Dic73C2313yes—
91C2×C4⋊Dic73C2313yes—
92C2×#11924007C2313yes—
93C2×#11924007C2313yes—
94C2×#11924007C2313yes—
95C2×#11924007C2313yes—
96C2×#11924007C2313yes—
97C2×#11924007C2313yes—
98C2×#11924007C2313yes—
99C2×#11924007C2313yes—
100C4⋊C4×D73—46no—
101C4⋊C4×D73—46no—
102C4⋊C4×D73—46no—
103C4⋊C4×D73C2×C4124yescomplemented
104C2×C22⋊Dic73C2313yes—
105C2×C22⋊Dic73C2313yes—
106C2×#11924005C2313yes—
107C2×#11924005C2313yes—
108C2×#11924005C2313yes—
109C2×#11924005C2313yes—
110C22⋊C4×D73—46no—
111C22⋊C4×D73C2×C4124yes—
112C2×C4×Dic73C2313yes—
113C2×C4×Dic73C2313yes—
114C2×C4×Dic73C2313yes—
115C2×C4×Dic73C2313yes—
116C42×D73—46no—
117C42×D73C2×C418yescomplemented
118#14556498C2313yes—
119#14556498C2313yes—
120#14556498C2313yes—
121#14556498C2313yes—
122#14556498C2313yes—
123#14556498C2313yes—
124#14556498C2313yes—
125#14556498C2313yes—
126#14556498C2313yes—
127#14556498C2313yes—
128#14556498C2313yes—
129#14556498C2313yes—
130C23×C4×C73C2311yescharacteristic
131#126×C73C2×C418yescomplemented
132C2×C4⋊C4×C73C2313yes—
133C2×C4⋊C4×C73C2313yes—
134C2×C4⋊C4×C73C2313yes—
135C2×C4⋊C4×C73C2313yes—
136C2×C22⋊C4×C73C2313yes—
137C2×C22⋊C4×C73C2313yes—
138C2×C42×C73C2313yes—
139C2×C42×C73C2311yescharacteristic
140#95×C73C2313yes—
141#95×C73C2313yes—
142#95×C73C2313yes—
143#95×C73C2313yes—
144C23×D73—26no—
145C23×D73—26no—
146C23×D73C22×C414yes—
147C23×D73C2411yescharacteristic
148C23×D73C2411yescharacteristic
149C22×Dic73—43no—
150C22×Dic73C2413yes—
151C22×Dic73C2411yescharacteristic
152C22×Dic73C2411yescharacteristic
153C22×Dic73C2413yes—
154C22×Dic73C2413yes—
155C22×Dic73C2413yes—
156C2×C4×D73—26no—
157C2×C4×D73—26no—
158C2×C4×D73—26no—
159C2×C4×D73—26no—
160C2×C4×D73—26no—
161C2×C4×D73—26no—
162C2×C4×D73—26no—
163C2×C4×D73—26no—
164C2×C4×D73—26no—
165C2×C4×D73—26no—
166C2×C4×D73—212no—
167C2×C4×D73—43no—
168C2×C4×D73—43no—
169C2×C4×D73—416no—
170C2×C4×D73C22×C4112yes—
171C2×C4×D73C22×C4112yes—
172C4⋊Dic73—43no—
173C4⋊Dic73—43no—
174C4⋊Dic73—43no—
175C4⋊Dic73C22×C4112yescomplemented
176#11924007—43no—
177#11924007—43no—
178#11924007—43no—
179#11924007—43no—
180#11924007—43no—
181#11924007—43no—
182#11924007C22×C4112yescomplemented
183#11924007C22×C4112yescomplemented
184C22⋊Dic73—43no—
185C22⋊Dic73C22×C4112yes—
186#11924005—43no—
187#11924005—43no—
188#11924005C22×C4112yes—
189#11924005C22×C4112yes—
190C4×Dic73—43no—
191C4×Dic73—43no—
192C4×Dic73—43no—
193C4×Dic73C22×C4112yescomplemented
194C24×C73C2411yescharacteristic
195C22×C4×C73—43no—
196C22×C4×C73C2413yes—
197C22×C4×C73C2411yescharacteristic
198C22×C4×C73C2411yescharacteristic
199C22×C4×C73C2413yes—
200C22×C4×C73C2413yes—
201C22×C4×C73C2413yes—
202C4⋊C4×C73—43no—
203C4⋊C4×C73—43no—
204C4⋊C4×C73—43no—
205C4⋊C4×C73C22×C4112yescomplemented
206C22⋊C4×C73—43no—
207C22⋊C4×C73C22×C4112yes—
208C42×C73—43no—
209C42×C73C22×C414yescomplemented
210C23×C73—23no—
211C23×C73—23no—
212C23×C73C23×C412yes—
213C23×C73C2511yescharacteristic
214C22×D73—23no—
215C22×D73—23no—
216C22×D73—224no—
217C22×D73—44no—
218C22×D73—412no—
219C22×D73C23×C412yes—
220C22×D73C23×C412yes—
221C22×D73H(5,𝔽2)16yes—
222C22×D732−1+416yes—
223C2×C4×C73—23no—
224C2×C4×C73—23no—
225C2×C4×C73—23no—
226C2×C4×C73—23no—
227C2×C4×C73—23no—
228C2×C4×C73—23no—
229C2×C4×C73—23no—
230C2×C4×C73—23no—
231C2×C4×C73—23no—
232C2×C4×C73—23no—
233C2×C4×C73—26no—
234C2×C4×C73—44no—
235C2×C4×C73C23×C416yes—
236C2×C4×C73C23×C416yes—
237C2×Dic73—23no—
238C2×Dic73—23no—
239C2×Dic73—23no—
240C2×Dic73—23no—
241C2×Dic73—23no—
242C2×Dic73—23no—
243C2×Dic73—23no—
244C2×Dic73—23no—
245C2×Dic73—23no—
246C2×Dic73—23no—
247C2×Dic73—26no—
248C2×Dic73—44no—
249C2×Dic73C23×C416yes—
250C2×Dic73C23×C416yes—
251C4×D73—224no—
252C4×D73—224no—
253C4×D73—44no—
254C4×D73—44no—
255C4×D73—412no—
256C4×D73—44no—
257C4×D73—44no—
258C4×D73—412no—
259C22×C73—26no—
260C22×C73—41no—
261C22×C73—43no—
262C22×C73C24×C411yescharacteristic
263C22×C73C2×H(5,𝔽2)13yes—
264C22×C73C2×2−1+413yes—
265C2×D73—26no—
266C2×D73—41no—
267C2×D73—43no—
268C2×D73—416no—
269C2×D73#520112yes—
270C2×D73#56014yes—
271C2×D73#563112yes—
272C4×C73—26no—
273C4×C73—26no—
274C4×C73—41no—
275C4×C73—41no—
276C4×C73—43no—
277C4×C73—43no—
278Dic73—26no—
279Dic73—26no—
280Dic73—41no—
281Dic73—41no—
282Dic73—43no—
283Dic73—43no—
284C2×#2383—731nomaximal, Sylow
285C2×C73—42no—
286C2×C73C2×#52013yes—
287C2×C73C2×#56011yescharacteristic
288C2×C73C2×#56313yes—
289D73—42no—
290D73#238318yesdirect product factor
291C22×#126—731no—
292#2383—733no—
293#2383—733no—
294#2383—733no—
295#2383—733no—
296#2383—731no—
297#2383—731no—
298#2383—731no—
299#2383D7311yescharacteristic, direct product factor
300C2×#389—733no—
301C2×#388—733no—
302C2×#387—733no—
303C2×#385—733no—
304C2×#384—731no—
305C2×#383—731no—
306C73C2×#238311yescharacteristic, complemented, Sylow
307C24×C4—731no—
308C2×#126—7316no—
309C2×#126—733no—
310C2×#126—733no—
311C2×#126—731no—
312C2×#126C2×D7311yescharacteristic
313C22×C4⋊C4—733no—
314C22×C4⋊C4—733no—
315C22×C4⋊C4—733no—
316C22×C4⋊C4—733no—
317C22×C22⋊C4—733no—
318C22×C22⋊C4—733no—
319C22×C42—733no—
320C22×C42—731no—
321#389—733no—
322#389—733no—
323#389—733no—
324#389—733no—
325#389—733no—
326#389—733no—
327#389—733no—
328#389C2×D7313yescomplemented
329#388—733no—
330#388—733no—
331#388—733no—
332#388—733no—
333#388—733no—
334#388—733no—
335#388—733no—
336#388C2×D7313yes—
337#387—733no—
338#387—733no—
339#387—733no—
340#387—733no—
341#387—733no—
342#387—733no—
343#387—733no—
344#387C2×D7313yescomplemented
345#385—733no—
346#385—733no—
347#385—733no—
348#385—733no—
349#385—733no—
350#385—733no—
351#385—733no—
352#385C2×D7313yes—
353#384—733no—
354#384—733no—
355#384—731no—
356#384C2×D7311yescharacteristic, complemented
357#383—731no—
358#383—733no—
359#383—733no—
360#383C2×D7311yescharacteristic, complemented
361C2×#95—733no—
362C2×#95—733no—
363C2×#95—733no—
364C2×#95—733no—
365C25—731no—
366C23×C4—2926no—
367C23×C4—731no—
368C23×C4—731no—
369C23×C4—731no—
370C23×C4—733no—
371C23×C4—733no—
372C23×C4—733no—
373C23×C4—733no—
374C23×C4—731no—
375C23×C4—731no—
376C23×C4C22×D7311yescharacteristic
377#126—7324no—
378#126—7324no—
379#126—738no—
380#126C4×D7318yescomplemented
381C2×C4⋊C4—2926no—
382C2×C4⋊C4—2926no—
383C2×C4⋊C4—2926no—
384C2×C4⋊C4—733no—
385C2×C4⋊C4—733no—
386C2×C4⋊C4—733no—
387C2×C4⋊C4—733no—
388C2×C4⋊C4—733no—
389C2×C4⋊C4—733no—
390C2×C4⋊C4—733no—
391C2×C4⋊C4—733no—
392C2×C4⋊C4—733no—
393C2×C4⋊C4—733no—
394C2×C4⋊C4—733no—
395C2×C4⋊C4—733no—
396C2×C4⋊C4—7324no—
397C2×C4⋊C4C22×D7313yes—
398C2×C4⋊C4C22×D7313yes—
399C2×C4⋊C4C22×D7313yes—
400C2×C4⋊C4C22×D7313yes—
401C2×C22⋊C4—2926no—
402C2×C22⋊C4—733no—
403C2×C22⋊C4—733no—
404C2×C22⋊C4—733no—
405C2×C22⋊C4—733no—
406C2×C22⋊C4—733no—
407C2×C22⋊C4—733no—
408C2×C22⋊C4—7324no—
409C2×C22⋊C4C22×D7313yes—
410C2×C22⋊C4C22×D7313yes—
411C2×C42—2926no—
412C2×C42—733no—
413C2×C42—733no—
414C2×C42—733no—
415C2×C42—733no—
416C2×C42—738no—
417C2×C42C22×D7313yes—
418C2×C42C22×D7311yescharacteristic
419#95—733no—
420#95—733no—
421#95—733no—
422#95—733no—
423#95—733no—
424#95—733no—
425#95—733no—
426#95—733no—
427#95—733no—
428#95—733no—
429#95—733no—
430#95—733no—
431#95C22×D7313yes—
432#95C22×D7313yes—
433#95C22×D7313yes—
434#95C22×D7313yes—
435C24—731no—
436C24—734no—
437C24—731no—
438C24—1466no—
439C24—1466no—
440C24C23×D7311yescharacteristic
441C22×C4—43no—
442C22×C4—2923no—
443C22×C4—2923no—
444C22×C4—29216no—
445C22×C4—2923no—
446C22×C4—733no—
447C22×C4—733no—
448C22×C4—7312no—
449C22×C4—7312no—
450C22×C4—733no—
451C22×C4—731no—
452C22×C4—731no—
453C22×C4—733no—
454C22×C4—1466no—
455C22×C4—1466no—
456C22×C4—1466no—
457C22×C4—1466no—
458C22×C4—1466no—
459C22×C4—1466no—
460C22×C4—14612no—
461C22×C4—1466no—
462C22×C4—1466no—
463C22×C4—1466no—
464C22×C4—1466no—
465C22×C4C23×D7313yes—
466C22×C4C23×D7311yescharacteristic
467C22×C4C23×D7311yescharacteristic
468C22×C4C23×D7313yes—
469C22×C4C23×D7313yes—
470C22×C4C23×D7313yes—
471C4⋊C4—43no—
472C4⋊C4—43no—
473C4⋊C4—43no—
474C4⋊C4—2923no—
475C4⋊C4—2923no—
476C4⋊C4—2923no—
477C4⋊C4—2923no—
478C4⋊C4—2923no—
479C4⋊C4—2923no—
480C4⋊C4—2923no—
481C4⋊C4—2923no—
482C4⋊C4—2923no—
483C4⋊C4—7312no—
484C4⋊C4—7312no—
485C4⋊C4—7312no—
486C4⋊C4C2×C4×D73112yescomplemented
487C22⋊C4—43no—
488C22⋊C4—2923no—
489C22⋊C4—2923no—
490C22⋊C4—2923no—
491C22⋊C4—7312no—
492C22⋊C4—7312no—
493C22⋊C4—7312no—
494C22⋊C4C2×C4×D73112yes—
495C42—43no—
496C42—2923no—
497C42—2923no—
498C42—2923no—
499C42—7312no—
500C42C2×C4×D7314yescomplemented
501C23—23no—
502C23—23no—
503C23—2924no—
504C23—29212no—
505C23—732no—
506C23—736no—
507C23—736no—
508C23—732no—
509C23—14624no—
510C23—1463no—
511C23—1463no—
512C23C22×C4×D7312yes—
513C23C24×D7311yescharacteristic
514C2×C4—23no—
515C2×C4—23no—
516C2×C4—23no—
517C2×C4—23no—
518C2×C4—23no—
519C2×C4—23no—
520C2×C4—23no—
521C2×C4—23no—
522C2×C4—23no—
523C2×C4—23no—
524C2×C4—26no—
525C2×C4—44no—
526C2×C4—2924no—
527C2×C4—2924no—
528C2×C4—2924no—
529C2×C4—2924no—
530C2×C4—29212no—
531C2×C4—29212no—
532C2×C4—2924no—
533C2×C4—736no—
534C2×C4—736no—
535C2×C4—14624no—
536C2×C4—14624no—
537C2×C4—1463no—
538C2×C4—1463no—
539C2×C4—1463no—
540C2×C4—1463no—
541C2×C4—1463no—
542C2×C4—1463no—
543C2×C4—1466no—
544C2×C4—1463no—
545C2×C4—1463no—
546C2×C4—1463no—
547C2×C4—1463no—
548C2×C4C22×C4×D7316yes—
549C2×C4C22×C4×D7316yes—
550C22—26no—
551C22—41no—
552C22—43no—
553C22—29216no—
554C22—2921no—
555C22—2923no—
556C22—734no—
557C22—7312no—
558C22—7312no—
559C22—1466no—
560C22C23×C4×D7311yescharacteristic
561C22H(5,𝔽2)×D7313yes—
562C222−1+4×D7313yes—
563C4—26no—
564C4—26no—
565C4—41no—
566C4—41no—
567C4—43no—
568C4—43no—
569C4—2921no—
570C4—2921no—
571C4—2923no—
572C4—2923no—
573C4—1466no—
574C4—1466no—
575C2—42no—
576C2—2922no—
577C2—738no—
578C2#520×D7313yes—
579C2#560×D7311yescharacteristic
580C2#563×D7313yes—
subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
FittingC73×#2383C2
socle, cosocleC23×C73C25
prime radicalC24×D73C23
hypercenter#2383D73
hypocenterC73C2×#2383
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2383

Complements

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

NH ≅ G/Ntype
2. #22613124C2semidirect
3. #22613123C2semidirect
4. #22613122C2semidirect
5. #22613121C2semidirect
6. #22613120C2semidirect
7. #22613119C2semidirect
8. #22613118C2semidirect
9. #389×D73C2semidirect
11. #387×D73C2semidirect
13. #384×D73C2semidirect
14. #383×D73C2semidirect
15. C73×#2383C2semidirect
20. #126×D73C4semidirect
29. #17988486C22semidirect
30. #17988485C22semidirect
31. #17988484C22semidirect
32. #17988484C22semidirect
33. #17988483C22semidirect
34. #17988482C22semidirect
35. #17988482C22semidirect
43. #17988474C22semidirect
44. #17988473C22semidirect
45. #17988472C22semidirect
46. #17988471C22semidirect
47. #17988470C22semidirect
48. #17988469C22semidirect
49. #17988468C22semidirect
57. #17988457C22semidirect
58. #17988456C22semidirect
59. #17988456C22semidirect
60. #17988455C22semidirect
61. #17988454C22semidirect
62. #17988454C22semidirect
68. #389×C73C22semidirect
70. #387×C73C22semidirect
72. #384×C73C22semidirect
73. #383×C73C22semidirect
85. #14556586C2×C4semidirect
86. #14556585C2×C4semidirect
87. #14556584C2×C4semidirect
103. C4⋊C4×D73C2×C4semidirect
117. C42×D73C2×C4semidirect
131. #126×C73C2×C4semidirect
175. C4⋊Dic73C22×C4semidirect
182. #11924007C22×C4semidirect
183. #11924007C22×C4semidirect
193. C4×Dic73C22×C4semidirect
205. C4⋊C4×C73C22×C4semidirect
209. C42×C73C22×C4semidirect
290. D73#2383direct (N × H)
299. #2383D73direct (N × H)
306. C73C2×#2383semidirect
328. #389C2×D73semidirect
344. #387C2×D73semidirect
356. #384C2×D73semidirect
360. #383C2×D73semidirect
380. #126C4×D73semidirect
486. C4⋊C4C2×C4×D73semidirect
500. C42C2×C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#126×D732
#226131242
#226131232
#226131222
#226131212
#226131202
#226131192
#226131182
#389×D732
#388×D732
#387×D732
#385×D732
#384×D732
#383×D732
C73×#23832
C2×#238373