Finite Group Databasebeta

← #11887151

Subgroups — #11887151

Order 1152.

1038 conjugacy classes of subgroups.

The subgroup lattice has 605 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596201C211yesmaximal, characteristic, complemented
2#10594004C211yesmaximal, characteristic
3C3×#5088C211yesmaximal, characteristic, complemented
4C3×#5084C211yesmaximal, characteristic, complemented
5#10590597C212yesmaximal, complemented
6#10590593C212yesmaximal, complemented
7#10590511C212yesmaximal, complemented
8#10590507C212yesmaximal, complemented
9#10590377C211yesmaximal, characteristic, complemented
10C4×#3716C211yesmaximal, characteristic, complemented
11#10590327C211yesmaximal, characteristic, complemented
12#81577—31nomaximal
13#81075—31nomaximal
14C2×#3802C2212yes—
15C2×D3×D12—21no—
16C32×C4⋊Q8C2211yescharacteristic, complemented
17#64155—22no—
18#64106C2212yescomplemented
19#64102—21no—
20C4⋊C4×C3⋊D3C2212yescomplemented
21#64099—21no—
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C4×#634C2211yescharacteristic, complemented
24C3×#874C2211yescharacteristic
25C3×C4×D12C2211yescharacteristic
26#63922—22no—
27#63916C2212yes—
28#63908—21no—
29C2×#3716C2211yescharacteristic
30C2×#3716C2212yescomplemented
31C2×#3710C2212yescomplemented
32C3×#809C2212yes—
33C3×#809C2212yescomplemented
34C3×#809C2212yescomplemented
35C3×#808C2212yescomplemented
36C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
37C3×C4×C3⋊C8C2211yescharacteristic, complemented
38#63573C2211yescharacteristic, complemented
39#63567C2211yescharacteristic, complemented
40#63563C2211yescharacteristic
41#63563C2212yescomplemented
42#63557C2212yescomplemented
43#5730—31no—
44#5730—31no—
45#5730—61no—
46#5717—31no—
47D4×D12—31no—
48C3×#486—31no—
49C3×#476—31no—
50#5088D311yescharacteristic, complemented
51#5084D311yescharacteristic, complemented
52#5075—31no—
53C4×#214—31no—
54#4864—32no—
55#4863—32no—
56#4848—31no—
57#4834—31no—
58#4778—32no—
59#4777—32no—
60#4776—32no—
61#4776—32no—
62D3×#102—32no—
63D3×#102—32no—
64C4×#204—31no—
65C8×D12—31no—
66C22×D32—22no—
67C2×C32×Q8—21no—
68C2×C4⋊(C3⋊D3)D411yescharacteristic
69C2×C4×C3⋊D3—22no—
70C2×C4×C3⋊D3C2312yes—
71C2×#634C2311yescharacteristic
72C2×C3×D12—21no—
73C2×C3×D12—21no—
74C2×C3×D12C2312yes—
75C2×C3×D12C2311yescharacteristic
76C2×C3×C4×D3—21no—
77C2×#626—22no—
78C2×#625—22no—
79#3802—24no—
80#3802—42no—
81D3×D12—44no—
82C32×C4⋊C4—21no—
83C32×C4⋊C4C2312yes—
84C32×C42C2311yescharacteristic
85#3752—22no—
86#3752D412yes—
87C4⋊(C3⋊Dic3)—22no—
88C4⋊(C3⋊Dic3)D411yescharacteristic
89C4⋊(C3⋊Dic3)C2311yescharacteristic
90#3750—21no—
91#3750—22no—
92C4×C3⋊Dic3—21no—
93C3×(C2×D3)⋊C4—21no—
94C3×C4⋊Dic3C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2312yes—
97C2×C3×C3⋊C8C2311yescharacteristic
98(C2×D3)⋊Dic3—22no—
99#3716—22no—
100#3716—42no—
101#3710—42no—
102#3295—91noSylow
103C2×D3×D4—32no—
104C2×D3×D4—32no—
105C2×D3×D4—61no—
106C22×D12—61no—
107C3×C4⋊Q8—21no—
108C3×C4⋊Q8C2×D311yescharacteristic, complemented
109C3×C4⋊Q8C2×D311yescharacteristic, complemented
110C3×#127—31no—
111C3×C4×D4—31no—
112#946—62no—
113#946—62no—
114#946—64no—
115#938—32no—
116#938—61no—
117#937—62no—
118C2×#214—31no—
119C2×#214—32no—
120#930—61no—
121C2×#204—31no—
122C2×#204—32no—
123C2×D3×C8—32no—
124C2×D3×C8—32no—
125#897—32no—
126#897—32no—
127#897—62no—
128#895—32no—
129#893—61no—
130#893—61no—
131#893—62no—
132D3×C4⋊C4—32no—
133D3×C4⋊C4—32no—
134D3×C4⋊C4—62no—
135#890—61no—
136#890—61no—
137#890—62no—
138#882—62no—
139#874C2×D311yescharacteristic
140C4×D12—31no—
141C4×D12—31no—
142C4×D12—61no—
143C4×D12C2×D311yescharacteristic
144C4×Dic6—31no—
145C4×Dic6—31no—
146C4×Dic6—61no—
147C3×#106—32no—
148C3×C4⋊C8—31no—
149C3×#102—32no—
150C3×#102—32no—
151C3×#102—32no—
152C3×C4×C8—31no—
153#832—31no—
154#832—32no—
155#821—31no—
156#821—32no—
157(C2×D3)⋊C8—32no—
158(C2×D3)⋊C8—32no—
159#817—31no—
160#816—31no—
161#810—31no—
162#809C2×D312yes—
163#809C2×D312yescomplemented
164#809C2×D312yescomplemented
165#808—31no—
166#808C2×D312yescomplemented
167C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
168C4×C3⋊C8C2×D311yescharacteristic, complemented
169C22×C3⋊D3C2×D412yes—
170C22×C3×D3—21no—
171C22×C3×D3—22no—
172C2×D32—44no—
173C2×D32—44no—
174C2×D32—82no—
175C32×Q8—81no—
176C2×C32×C4—22no—
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2411yescharacteristic
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3C2×D412yes—
183C4⋊(C3⋊D3)SD1614yescomplemented
184C4×C3⋊D3—22no—
185C4×C3⋊D3—22no—
186C4×C3⋊D3—82no—
187#634—21no—
188#634—21no—
189C2×C3×Dic3—21no—
190C3×D12—22no—
191C3×D12—21no—
192C3×D12—22no—
193C3×D12—42no—
194C3×D12—81no—
195C3×D12#4112yes—
196C3×C4×D3—42no—
197#626—44no—
198#625—44no—
199C3×C3⋊C8—21no—
200C3×C3⋊C8—21no—
201C3×C3⋊C8—22no—
202#554—91no—
203D42—91no—
204#486—31no—
205#481—92no—
206#476—31no—
207#465—92no—
208#460—91no—
209#450—92no—
210C4×SD16—91no—
211C8×D4—91no—
212C2×#102—92no—
213C23×D3—62no—
214C23×D3—62no—
215C2×C3×Q8—22no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×D4—31no—
219C2×C3×D4—32no—
220C2×C3×D4—61no—
221C2×C3×D4—61no—
222C22×C3×C4—61no—
223C2×#67—62no—
224C2×#67—62no—
225C2×#67—62no—
226D3×D4—64no—
227D3×D4—64no—
228D3×D4—124no—
229D3×D4—122no—
230D3×D4—122no—
231C2×D12—21no—
232C2×D12—21no—
233C2×D12—31no—
234C2×D12—31no—
235C2×D12—61no—
236C2×D12—62no—
237C2×D12—124no—
238C2×D12C22×D312yes—
239C2×D12C22×D311yescharacteristic
240C2×C4×D3—21no—
241C2×C4×D3—32no—
242C2×C4×D3—32no—
243C2×C4×D3—62no—
244C2×C4×D3—62no—
245C2×C4×D3—62no—
246C2×C4×D3—64no—
247C2×Dic6—31no—
248C2×Dic6—31no—
249C2×Dic6—61no—
250C2×C3×C8—31no—
251C2×C3×C8—31no—
252C2×C3×C8—32no—
253C3×C4⋊C4—22no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—21no—
256C3×C4⋊C4—22no—
257C3×C4⋊C4—31no—
258C3×C4⋊C4C22×D312yes—
259C3×C4⋊C4C22×D312yes—
260C3×C22⋊C4—61no—
261C3×C42—21no—
262C3×C42C22×D311yescharacteristic
263C3×C42C22×D311yescharacteristic
264#217—62no—
265#214—62no—
266#214—122no—
267(C2×D3)⋊C4—21no—
268(C2×D3)⋊C4—32no—
269(C2×D3)⋊C4—32no—
270(C2×D3)⋊C4—62no—
271(C2×D3)⋊C4—62no—
272(C2×D3)⋊C4—62no—
273(C2×D3)⋊C4—62no—
274(C2×D3)⋊C4—64no—
275C4⋊Dic3—31no—
276C4⋊Dic3—31no—
277C4⋊Dic3—31no—
278C4⋊Dic3—31no—
279C4⋊Dic3—61no—
280C4⋊Dic3—61no—
281C4⋊Dic3—62no—
282C4⋊Dic3—62no—
283C4⋊Dic3—64no—
284C4⋊Dic3C22×D311yescharacteristic
285Dic3⋊C4—62no—
286Dic3⋊C4—62no—
287Dic3⋊C4—62no—
288Dic3⋊C4—64no—
289Dic3⋊C4—61no—
290Dic3⋊C4—61no—
291C4×Dic3—62no—
292C4×Dic3—61no—
293C4×Dic3—61no—
294C2×C3⋊C8C22×D311yescharacteristic
295C2×C3⋊C8C22×D311yescharacteristic
296C2×C3⋊C8C22×D312yes—
297#204—62no—
298#204—122no—
299D3×C8—122no—
300D3×C8—122no—
301C22×C32C22×D411yescharacteristic
302C2×C3⋊D3—22no—
303C2×C3⋊D3—22no—
304C2×C3⋊D3C2×SD1614yes—
305C2×C3×D3—22no—
306C2×C3×D3—41no—
307C2×C3×D3—41no—
308C2×C3×D3—42no—
309C2×C3×D3—42no—
310C2×C3×D3—42no—
311D32—88no—
312C32×C4—21no—
313C32×C4—42no—
314C32×C4C2×SD1612yes—
315C32×C4C2×#4111yescharacteristic
316C32×C4H(5,𝔽2)11yescharacteristic
317C3⋊Dic3—22no—
318C3⋊Dic3—41no—
319C3⋊Dic3—41no—
320C3×Dic3—41no—
321C22×D4—92no—
322C22×D4—181no—
323C2×SD16—91no—
324C2×SD16—92no—
325C22×C8—92no—
326C4⋊Q8D3211yescharacteristic, complemented
327#127—31no—
328#125—181no—
329C22⋊Q8—92no—
330C22⋊Q8—182no—
331#121—92no—
332#121—181no—
333#120—182no—
334C4×Q8—91no—
335C4×D4—31no—
336C4×D4—91no—
337C4×D4—181no—
338C2×C4⋊C4—92no—
339#106—32no—
340#106—91no—
341C4⋊C8—31no—
342#103—91no—
343#102—32no—
344#102—32no—
345#102—32no—
346#102—91no—
347#102—92no—
348C22⋊C8—92no—
349C4×C8—31no—
350C23×C3—61no—
351C23×C3—62no—
352C22×D3—21no—
353C22×D3—22no—
354C22×D3—32no—
355C22×D3—32no—
356C22×D3—62no—
357C22×D3—124no—
358C22×D3—124no—
359C22×D3—124no—
360C22×D3—124no—
361C22×D3—242no—
362C22×D3—242no—
363C3×Q8—81no—
364C3×Q8—81no—
365C3×Q8—82no—
366C3×D4—32no—
367C3×D4—62no—
368C3×D4—61no—
369C3×D4—62no—
370C3×D4—122no—
371C3×D4—241no—
372C2×C3×C4—24no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—61no—
379C2×C3×C4—122no—
380C2×C3×C4D3×D411yescharacteristic
381C2×C3×C4D3×D411yescharacteristic
382C2×C3×C4D3×D411yescharacteristic
383C2×C3×C4D3×D411yescharacteristic
384C2×C3×C4C23×D311yescharacteristic
385C2×C3×C4C23×D311yescharacteristic
386#67—124no—
387#67—124no—
388#67—124no—
389C2×Dic3—21no—
390C2×Dic3—32no—
391C2×Dic3—32no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—61no—
396C2×Dic3—61no—
397C2×Dic3—61no—
398C2×Dic3—61no—
399D12—22no—
400D12—21no—
401D12—22no—
402D12—34no—
403D12—34no—
404D12—42no—
405D12—64no—
406D12—81no—
407D12—124no—
408D12#23912yes—
409C4×D3—42no—
410C4×D3—62no—
411C4×D3—62no—
412C4×D3—62no—
413C4×D3—62no—
414C4×D3—122no—
415C4×D3—122no—
416C4×D3—242no—
417C4×D3—242no—
418C4×D3—244no—
419Dic6—61no—
420Dic6—61no—
421Dic6—61no—
422Dic6—61no—
423Dic6—121no—
424Dic6—121no—
425C3×C8—61no—
426C3×C8—61no—
427C3×C8—62no—
428C3⋊C8—21no—
429C3⋊C8—21no—
430C3⋊C8—22no—
431C2×C32#54611yescharacteristic
432C2×C32C22×SD1611yescharacteristic
433C2×C32#57611yescharacteristic
434C3⋊D3—24no—
435C3×D3—42no—
436C3×D3—82no—
437C24—182no—
438C2×Q8—21no—
439C2×Q8—91no—
440C2×D4—31no—
441C2×D4—32no—
442C2×D4—61no—
443C2×D4—61no—
444C2×D4—91no—
445C2×D4—182no—
446C2×D4—182no—
447C2×D4—184no—
448C2×D4—364no—
449C2×D4—362no—
450C22×C4—61no—
451C22×C4—92no—
452C22×C4—182no—
453SD16—182no—
454SD16—362no—
455C2×C8—31no—
456C2×C8—31no—
457C2×C8—32no—
458C2×C8—362no—
459C4⋊C4—21no—
460C4⋊C4—31no—
461C4⋊C4—91no—
462C4⋊C4—91no—
463C4⋊C4—182no—
464C4⋊C4—182no—
465C4⋊C4—181no—
466C4⋊C4C2×D3212yes—
467C22⋊C4—61no—
468C22⋊C4—92no—
469C22⋊C4—182no—
470C22⋊C4—182no—
471C42—181no—
472C42C2×D3211yescharacteristic
473C22×C3—21no—
474C22×C3—62no—
475C22×C3—121no—
476C22×C3—121no—
477C22×C3—122no—
478C22×C3—122no—
479C22×C3—122no—
480C22×C3C2×D3×D411yescharacteristic
481C22×C3C2×D3×D411yescharacteristic
482C2×D3—22no—
483C2×D3—34no—
484C2×D3—34no—
485C2×D3—41no—
486C2×D3—41no—
487C2×D3—42no—
488C2×D3—42no—
489C2×D3—42no—
490C2×D3—64no—
491C2×D3—62no—
492C2×D3—62no—
493C2×D3—62no—
494C2×D3—62no—
495C2×D3—122no—
496C2×D3—122no—
497C2×D3—248no—
498C2×D3—248no—
499C3×C4—21no—
500C3×C4—21no—
501C3×C4—21no—
502C3×C4—21no—
503C3×C4—22no—
504C3×C4—41no—
505C3×C4—44no—
506C3×C4—42no—
507C3×C4—42no—
508C3×C4—121no—
509C3×C4D3×SD1612yes—
510C3×C4D3×SD1612yes—
511C3×C4C2×#23911yescharacteristic
512C3×C4D3×#4111yescharacteristic
513C3×C4#100911yescharacteristic
514C3×C4#100911yescharacteristic
515Dic3—41no—
516Dic3—62no—
517Dic3—62no—
518Dic3—122no—
519Dic3—122no—
520Dic3—122no—
521Dic3—121no—
522Dic3—121no—
523Dic3—121no—
524Dic3—121no—
525C32#329511yescharacteristic, complemented, Sylow
526C23—61no—
527C23—62no—
528C23—92no—
529C23—364no—
530C23—364no—
531C23—722no—
532Q8—81no—
533Q8—181no—
534Q8—181no—
535D4—32no—
536D4—62no—
537D4—61no—
538D4—62no—
539D4—94no—
540D4—122no—
541D4—241no—
542D4—364no—
543D4—364no—
544C2×C4—22no—
545C2×C4—61no—
546C2×C4—92no—
547C2×C4—122no—
548C2×C4—182no—
549C2×C4—182no—
550C2×C4—181no—
551C2×C4—181no—
552C2×C4—722no—
553C2×C4#381111yescharacteristic
554C2×C4#381111yescharacteristic
555C2×C4C22×D3211yescharacteristic
556C8—61no—
557C8—61no—
558C8—62no—
559C2×C3—21no—
560C2×C3—21no—
561C2×C3—21no—
562C2×C3—122no—
563C2×C3—242no—
564C2×C3#563011yescharacteristic
565C2×C3#567611yescharacteristic
566C2×C3#575711yescharacteristic
567C2×C3C2×D3×SD1611yescharacteristic
568C2×C3C2×D3×SD1611yescharacteristic
569C2×C3#577411yescharacteristic
570D3—42no—
571D3—64no—
572D3—64no—
573D3—82no—
574D3—124no—
575C22—62no—
576C22—94no—
577C22—121no—
578C22—121no—
579C22—122no—
580C22—122no—
581C22—122no—
582C22—182no—
583C22—182no—
584C22—728no—
585C22C2×#381111yescharacteristic
586C4—21no—
587C4—42no—
588C4—121no—
589C4—182no—
590C4—361no—
591C4—361no—
592C4#6394012yes—
593C4D3×#23911yescharacteristic
594C4#6432011yescharacteristic
595C3—21no—
596C3#8107511yescharacteristic, complemented
597C3#8157711yescharacteristic, complemented
598C2—122no—
599C2—184no—
600C2—242no—
601C2#1059510211yescharacteristic
602C2C2×#6394011yescharacteristic
603C2#1059543111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10594004C2
hypercenterC4⋊Q8D32
hypocenterC32#3295
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596201C2semidirect
3. C3×#5088C2semidirect
4. C3×#5084C2semidirect
5. #10590597C2semidirect
6. #10590593C2semidirect
7. #10590511C2semidirect
8. #10590507C2semidirect
9. #10590377C2semidirect
10. C4×#3716C2semidirect
11. #10590327C2semidirect
16. C32×C4⋊Q8C22semidirect
18. #64106C22semidirect
20. C4⋊C4×C3⋊D3C22semidirect
23. C4×#634C22semidirect
30. C2×#3716C22semidirect
31. C2×#3710C22semidirect
33. C3×#809C22semidirect
34. C3×#809C22semidirect
35. C3×#808C22semidirect
36. C3×C4⋊(C3⋊C8)C22semidirect
37. C3×C4×C3⋊C8C22semidirect
38. #63573C22semidirect
39. #63567C22semidirect
41. #63563C22semidirect
42. #63557C22semidirect
50. #5088D3semidirect
51. #5084D3semidirect
108. C3×C4⋊Q8C2×D3semidirect
109. C3×C4⋊Q8C2×D3semidirect
163. #809C2×D3semidirect
164. #809C2×D3semidirect
166. #808C2×D3semidirect
167. C4⋊(C3⋊C8)C2×D3semidirect
168. C4×C3⋊C8C2×D3semidirect
183. C4⋊(C3⋊D3)SD16semidirect
326. C4⋊Q8D32semidirect
525. C32#3295semidirect
596. C3#81075semidirect
597. C3#81577semidirect

Maximal subgroups

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

subgroupindex
#105962012
#105940042
C3×#50882
C3×#50842
#105905972
#105905932
#105905112
#105905072
#105903772
C4×#37162
#105903272
#815773
#810753