Finite Group Databasebeta

← #11887162

Subgroups — #11887162

Order 1152.

983 conjugacy classes of subgroups.

The subgroup lattice has 589 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5717C211yesmaximal, characteristic
2#10593960C211yesmaximal, characteristic, complemented
3#10592769C211yesmaximal, characteristic, complemented
4C3×#5075C211yesmaximal, characteristic, complemented
5#10591499C212yesmaximal, complemented
6#10591458C212yesmaximal, complemented
7#10591415C212yesmaximal, complemented
8D3×#832C212yesmaximal, complemented
9C4×#3715C211yesmaximal, characteristic, complemented
10#10590329C211yesmaximal, characteristic, complemented
11#10590268C211yesmaximal, characteristic, complemented
12#83483—31nomaximal
13#80395—31nomaximal
14C2×C3×D3×D4—21no—
15C2×C3×D3×D4C2212yes—
16C32×#127C2211yescharacteristic
17#64078C2211yescharacteristic, complemented
18C3×#938—21no—
19C3×#938C2212yes—
20C3×#937—22no—
21C2×C3×#214C2212yescomplemented
22C3×C4×D12C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic, complemented
25#63896—22no—
26Dic3×D12—21no—
27D3×C4⋊Dic3C2212yescomplemented
28#63869—21no—
29#63856C2212yescomplemented
30C2×#3715C2211yescharacteristic
31C2×D3×C3⋊C8C2212yescomplemented
32#63659C2212yescomplemented
33#63659C2212yescomplemented
34C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
35C3×#832C2212yescomplemented
36C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
37#63574C2211yescharacteristic, complemented
38#63573C2212yescomplemented
39#63565C2211yescharacteristic, complemented
40#63563C2212yes—
41#63562C2211yescharacteristic
42(C2×D3)⋊(C3⋊C8)C2212yescomplemented
43C3×D42—31no—
44#5717D311yescharacteristic
45#5579—31no—
46#5543—31no—
47C3×#460—31no—
48#5218—32no—
49C2×#832—32no—
50#5171—32no—
51#5169—32no—
52#5075D311yescharacteristic, complemented
53#5070—31no—
54#5070—31no—
55#5070—61no—
56#5041—32no—
57#5034—32no—
58C4×#215—31no—
59C4×#214—31no—
60D4×C3⋊C8—31no—
61#5008—31no—
62#4842—31no—
63#4834—31no—
64#4777—32no—
65D3×#102—32no—
66C23×C3×D3—22no—
67C2×C32×D4—21no—
68C2×C32×D4—21no—
69C2×C32×D4C2312yes—
70C2×#634—21no—
71C2×C3×#67—22no—
72C2×C3×#67—22no—
73C3×D3×D4—24no—
74C3×D3×D4—42no—
75C3×D3×D4—44no—
76C2×C3×D12D411yescharacteristic
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3C2312yes—
80C2×C3×Dic6C2311yescharacteristic
81C2×D3×Dic3—22no—
82C32×C42C2311yescharacteristic
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)C2312yes—
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C3×#217—22no—
88C3×#214—42no—
89C3×(C2×D3)⋊C4—21no—
90C3×(C2×D3)⋊C4D412yes—
91C3×C4⋊Dic3D411yescharacteristic
92C3×C4⋊Dic3C2311yescharacteristic
93C3×C4⋊Dic3C2311yescharacteristic
94C3×Dic3⋊C4—21no—
95C3×C4×Dic3—21no—
96C2×C3×C3⋊C8C2312yes—
97#3724—22no—
98Dic3⋊Dic3—22no—
99(C2×D3)⋊Dic3—22no—
100#3715—22no—
101D3×C3⋊C8—42no—
102#3295—91noSylow
103C22×C3×D4—32no—
104C22×C3×D4—61no—
105C2×D3×D4—21no—
106C2×D3×D4C2×D312yes—
107C2×C3×SD16—32no—
108C3×#127—21no—
109C3×#127C2×D311yescharacteristic
110C3×#127C2×D311yescharacteristic
111C3×#121—32no—
112C3×#121—61no—
113C3×#120—62no—
114C3×C4×Q8—31no—
115C3×C4×D4—31no—
116C3×C4×D4—31no—
117#946—32no—
118C2×#215—31no—
119#938—21no—
120#938C2×D312yes—
121#937—22no—
122D4×Dic3—61no—
123C2×#214—31no—
124C2×#214C2×D312yescomplemented
125C2×C4⋊Dic3—32no—
126#924—32no—
127C22×C3⋊C8—32no—
128C2×D3×C8—32no—
129#896—62no—
130D3×C4⋊C4—32no—
131#890—61no—
132#878—62no—
133C4×D12—61no—
134C4×D12C2×D311yescharacteristic
135C4×D12C2×D311yescharacteristic
136#870—61no—
137#869—31no—
138#869—31no—
139#869—61no—
140C4×Dic6C2×D311yescharacteristic, complemented
141C3×C4⋊C8—31no—
142C3×#102—32no—
143#835—31no—
144#832—32no—
145#832—32no—
146#832—32no—
147#832—32no—
148#832—31no—
149#832—32no—
150#832—62no—
151#832—62no—
152#832C2×D312yescomplemented
153#830—32no—
154#821—32no—
155(C2×D3)⋊C8—32no—
156#817—32no—
157#810—31no—
158#809—31no—
159#808—31no—
160#808—31no—
161#808—32no—
162C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
163C4×C3⋊C8—31no—
164C4×C3⋊C8—31no—
165C4×C3⋊C8—61no—
166C23×C32—22no—
167C22×C3×D3—21no—
168C22×C3×D3—44no—
169C22×C3×D3—44no—
170C22×C3×D3—82no—
171C22×C3×D3C2×D412yes—
172C32×D4—22no—
173C32×D4—22no—
174C32×D4—42no—
175C32×D4—81no—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2411yescharacteristic
179C2×C3⋊Dic3—22no—
180#634—81no—
181C3×#67—44no—
182C3×#67—44no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3C2×D412yes—
187C3×D12—21no—
188C3×D12SD1614yescomplemented
189C3×D12#4112yes—
190C3×C4×D3—22no—
191C3×C4×D3—22no—
192C3×C4×D3—42no—
193C3×Dic6—21no—
194C3×Dic6—21no—
195D3×Dic3—82no—
196C3⋊(C3⋊C8)—21no—
197C3⋊(C3⋊C8)—21no—
198C3×C3⋊C8—22no—
199#554—91no—
200D42—31no—
201#486—91no—
202#481—92no—
203#476—91no—
204#465—92no—
205#460—31no—
206#450—92no—
207C4×SD16—91no—
208C8×D4—91no—
209C2×#102—92no—
210C24×C3—62no—
211C23×D3—22no—
212C2×C3×Q8—31no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—22no—
218C2×C3×D4—31no—
219C2×C3×D4—31no—
220C2×C3×D4—41no—
221C2×C3×D4—41no—
222C2×C3×D4—62no—
223C2×C3×D4—64no—
224C2×C3×D4—62no—
225C2×C3×D4—122no—
226C2×C3×D4—124no—
227C2×C3×D4C22×D312yes—
228C2×C3×D4C22×D312yes—
229C22×C3×C4—32no—
230C22×C3×C4—61no—
231C2×#67—22no—
232C2×#67—22no—
233C22×Dic3—62no—
234D3×D4—24no—
235D3×D4—42no—
236D3×D4—44no—
237C2×D12#6711yescharacteristic
238C2×D12C22×D311yescharacteristic
239C2×C4×D3—21no—
240C2×C4×D3—62no—
241C2×C4×D3C22×D312yes—
242C2×Dic6—61no—
243C2×Dic6—61no—
244C2×Dic6—121no—
245C2×Dic6C22×D311yescharacteristic
246C3×SD16—122no—
247C2×C3×C8—32no—
248C3×C4⋊C4—31no—
249C3×C4⋊C4—31no—
250C3×C4⋊C4—31no—
251C3×C4⋊C4—61no—
252C3×C22⋊C4—32no—
253C3×C22⋊C4—62no—
254C3×C22⋊C4—61no—
255C3×C42—21no—
256C3×C42—61no—
257C3×C42C22×D311yescharacteristic
258C3×C42C22×D311yescharacteristic
259#217—22no—
260#217—62no—
261#215—62no—
262#214—42no—
263#214—62no—
264(C2×D3)⋊C4—21no—
265(C2×D3)⋊C4—62no—
266(C2×D3)⋊C4#6712yes—
267C4⋊Dic3—32no—
268C4⋊Dic3—32no—
269C4⋊Dic3—62no—
270C4⋊Dic3—62no—
271C4⋊Dic3—61no—
272C4⋊Dic3—61no—
273C4⋊Dic3—121no—
274C4⋊Dic3#6711yescharacteristic
275C4⋊Dic3C22×D311yescharacteristic
276C4⋊Dic3C22×D311yescharacteristic
277Dic3⋊C4—21no—
278Dic3⋊C4—62no—
279Dic3⋊C4—62no—
280Dic3⋊C4—62no—
281C4×Dic3—21no—
282C2×C3⋊C8—31no—
283C2×C3⋊C8—31no—
284C2×C3⋊C8—31no—
285C2×C3⋊C8—31no—
286C2×C3⋊C8—61no—
287C2×C3⋊C8—61no—
288C2×C3⋊C8—122no—
289C2×C3⋊C8C22×D312yes—
290D3×C8—122no—
291C22×C32—42no—
292C22×C32—42no—
293C22×C32—42no—
294C22×C32C22×D411yescharacteristic
295C2×C3×D3—22no—
296C2×C3×D3—22no—
297C2×C3×D3—22no—
298C2×C3×D3—41no—
299C2×C3×D3—41no—
300C2×C3×D3—88no—
301C2×C3×D3C2×SD1614yes—
302C32×C4—21no—
303C32×C4C2×SD1612yes—
304C32×C4C2×#4111yescharacteristic
305C32×C4H(5,𝔽2)11yescharacteristic
306C3⋊Dic3—42no—
307C3×Dic3—22no—
308C3×Dic3—41no—
309C3×Dic3—41no—
310C3×Dic3—41no—
311C22×D4—32no—
312C22×D4—61no—
313C2×SD16—32no—
314C2×SD16—91no—
315C22×C8—92no—
316C4⋊Q8—91no—
317#127D3211yescharacteristic
318#125—181no—
319C22⋊Q8—92no—
320C22⋊Q8—182no—
321#121—32no—
322#121—61no—
323#120—62no—
324C4×Q8—31no—
325C4×D4—31no—
326C4×D4—31no—
327C4×D4—181no—
328C2×C4⋊C4—92no—
329#106—91no—
330#106—92no—
331C4⋊C8—31no—
332#103—91no—
333#102—32no—
334#102—91no—
335#102—92no—
336#102—92no—
337#102—92no—
338C22⋊C8—92no—
339C4×C8—91no—
340C23×C3—22no—
341C23×C3—22no—
342C23×C3—32no—
343C23×C3—42no—
344C23×C3—61no—
345C23×C3—124no—
346C23×C3—124no—
347C23×C3—242no—
348C22×D3—21no—
349C22×D3—44no—
350C22×D3—44no—
351C22×D3—82no—
352C22×D3C2×#6712yes—
353C3×Q8—61no—
354C3×Q8—61no—
355C3×D4—22no—
356C3×D4—22no—
357C3×D4—22no—
358C3×D4—22no—
359C3×D4—34no—
360C3×D4—32no—
361C3×D4—42no—
362C3×D4—42no—
363C3×D4—42no—
364C3×D4—42no—
365C3×D4—61no—
366C3×D4—82no—
367C3×D4—81no—
368C3×D4—81no—
369C3×D4—82no—
370C3×D4—124no—
371C3×D4—124no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—32no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—61no—
379C2×C3×C4—61no—
380C2×C3×C4—61no—
381C2×C3×C4—122no—
382C2×C3×C4D3×D411yescharacteristic
383C2×C3×C4D3×D411yescharacteristic
384C2×C3×C4C2×#6711yescharacteristic
385C2×C3×C4C2×#6711yescharacteristic
386C2×C3×C4C23×D311yescharacteristic
387C2×C3×C4C23×D311yescharacteristic
388#67—44no—
389#67—44no—
390C2×Dic3—21no—
391C2×Dic3—21no—
392C2×Dic3—21no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—122no—
396C2×Dic3—242no—
397C2×Dic3C2×#6712yes—
398D12—21no—
399D12#21414yescomplemented
400D12#23712yes—
401C4×D3—22no—
402C4×D3—22no—
403C4×D3—42no—
404C4×D3—242no—
405Dic6—21no—
406Dic6—21no—
407Dic6—241no—
408Dic6—241no—
409Dic6—242no—
410C3×C8—62no—
411C3⋊C8—22no—
412C3⋊C8—61no—
413C3⋊C8—61no—
414C3⋊C8—61no—
415C3⋊C8—61no—
416C3⋊C8—121no—
417C3⋊C8—121no—
418C2×C32—82no—
419C2×C32#54611yescharacteristic
420C2×C32C22×SD1611yescharacteristic
421C2×C32#57611yescharacteristic
422C3×D3—24no—
423C3×D3—42no—
424C24—62no—
425C2×Q8—31no—
426C2×Q8—181no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—31no—
430C2×D4—31no—
431C2×D4—62no—
432C2×D4—64no—
433C2×D4—62no—
434C2×D4—122no—
435C2×D4—124no—
436C2×D4C2×D3212yes—
437C22×C4—32no—
438C22×C4—61no—
439C22×C4—182no—
440SD16—122no—
441SD16—182no—
442C2×C8—32no—
443C2×C8—91no—
444C2×C8—91no—
445C2×C8—362no—
446C4⋊C4—31no—
447C4⋊C4—31no—
448C4⋊C4—31no—
449C4⋊C4—61no—
450C4⋊C4—92no—
451C4⋊C4—182no—
452C4⋊C4—182no—
453C4⋊C4—181no—
454C22⋊C4—32no—
455C22⋊C4—62no—
456C22⋊C4—61no—
457C22⋊C4—182no—
458C42—61no—
459C42C2×D3211yescharacteristic
460C22×C3—21no—
461C22×C3—34no—
462C22×C3—42no—
463C22×C3—42no—
464C22×C3—42no—
465C22×C3—42no—
466C22×C3—42no—
467C22×C3—42no—
468C22×C3—62no—
469C22×C3—62no—
470C22×C3—62no—
471C22×C3—82no—
472C22×C3—82no—
473C22×C3—82no—
474C22×C3—121no—
475C22×C3—121no—
476C22×C3—248no—
477C22×C3C2×D3×D411yescharacteristic
478C22×C3C22×#6711yescharacteristic
479C2×D3—22no—
480C2×D3—22no—
481C2×D3—22no—
482C2×D3—41no—
483C2×D3—41no—
484C2×D3—88no—
485C2×D3C2×#21414yes—
486C3×C4—22no—
487C3×C4—21no—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—21no—
491C3×C4—22no—
492C3×C4—62no—
493C3×C4—121no—
494C3×C4—121no—
495C3×C4—121no—
496C3×C4D3×SD1612yes—
497C3×C4C2×#21412yes—
498C3×C4C2×#23711yescharacteristic
499C3×C4#100411yescharacteristic
500C3×C4#100411yescharacteristic
501C3×C4D3×#4111yescharacteristic
502Dic3—22no—
503Dic3—41no—
504Dic3—41no—
505Dic3—41no—
506Dic3—122no—
507Dic3—122no—
508Dic3—242no—
509C32#329511yescharacteristic, complemented, Sylow
510C23—22no—
511C23—32no—
512C23—61no—
513C23—124no—
514C23—124no—
515C23—242no—
516Q8—61no—
517Q8—61no—
518Q8—721no—
519D4—22no—
520D4—22no—
521D4—32no—
522D4—34no—
523D4—42no—
524D4—61no—
525D4—81no—
526D4—124no—
527D4—124no—
528C2×C4—32no—
529C2×C4—62no—
530C2×C4—62no—
531C2×C4—61no—
532C2×C4—61no—
533C2×C4—61no—
534C2×C4—122no—
535C2×C4—182no—
536C2×C4—722no—
537C2×C4D3×#6711yescharacteristic
538C2×C4D3×#6711yescharacteristic
539C2×C4C22×D3211yescharacteristic
540C8—62no—
541C8—181no—
542C8—181no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—64no—
547C2×C3—82no—
548C2×C3—82no—
549C2×C3—122no—
550C2×C3—162no—
551C2×C3#561211yescharacteristic
552C2×C3C2×D3×SD1611yescharacteristic
553C2×C3#577411yescharacteristic
554C2×C3C22×#21411yescharacteristic
555C2×C3#580611yescharacteristic
556C2×C3#583511yescharacteristic
557D3—24no—
558D3—42no—
559C22—34no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—62no—
564C22—62no—
565C22—62no—
566C22—121no—
567C22—121no—
568C22—248no—
569C22C2×D3×#6711yescharacteristic
570C4—21no—
571C4—62no—
572C4—121no—
573C4—121no—
574C4—121no—
575C4—362no—
576C4D3×#21412yes—
577C4D3×#23711yescharacteristic
578C4#6431311yescharacteristic
579C3—21no—
580C3#8039511yescharacteristic, complemented
581C3#8348311yescharacteristic, complemented
582C2—64no—
583C2—82no—
584C2—122no—
585C2#1059509711yescharacteristic
586C2C2×D3×#21411yescharacteristic
587C2#1059522811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
prime radicalC3×#5717C2
hypercenter#127D32
hypocenterC32#3295
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #10593960C2semidirect
3. #10592769C2semidirect
4. C3×#5075C2semidirect
5. #10591499C2semidirect
6. #10591458C2semidirect
7. #10591415C2semidirect
8. D3×#832C2semidirect
9. C4×#3715C2semidirect
10. #10590329C2semidirect
11. #10590268C2semidirect
17. #64078C22semidirect
21. C2×C3×#214C22semidirect
24. C3×C4×Dic6C22semidirect
27. D3×C4⋊Dic3C22semidirect
29. #63856C22semidirect
31. C2×D3×C3⋊C8C22semidirect
32. #63659C22semidirect
33. #63659C22semidirect
34. C4×C3⋊(C3⋊C8)C22semidirect
35. C3×#832C22semidirect
36. C3×C4⋊(C3⋊C8)C22semidirect
37. #63574C22semidirect
38. #63573C22semidirect
39. #63565C22semidirect
42. (C2×D3)⋊(C3⋊C8)C22semidirect
52. #5075D3semidirect
124. C2×#214C2×D3semidirect
140. C4×Dic6C2×D3semidirect
152. #832C2×D3semidirect
162. C4⋊(C3⋊C8)C2×D3semidirect
188. C3×D12SD16semidirect
399. D12#214semidirect
509. C32#3295semidirect
580. C3#80395semidirect
581. C3#83483semidirect

Maximal subgroups

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

subgroupindex
C3×#57172
#105939602
#105927692
C3×#50752
#105914992
#105914582
#105914152
D3×#8322
C4×#37152
#105903292
#105902682
#834833
#803953