Finite Group Databasebeta

← #11887052

Subgroups — #11887052

Order 1152.

1042 conjugacy classes of subgroups.

The subgroup lattice has 613 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594004C211yesmaximal, characteristic, complemented
2#10593895C211yesmaximal, characteristic, complemented
3#10592545C211yesmaximal, characteristic, complemented
4C3×#4843C211yesmaximal, characteristic, complemented
5C3×#4834C211yesmaximal, characteristic, complemented
6#10590944C212yesmaximal, complemented
7D3×#821C212yesmaximal, complemented
8#10590831C212yesmaximal, complemented
9#10590680C212yesmaximal, complemented
10C4×#3714C211yesmaximal, characteristic, complemented
11#10590273C211yesmaximal, characteristic, complemented
12#80352—31nomaximal
13#79438—31nomaximal
14C2×#3802—21no—
15C2×D3×D12C2212yes—
16C2×#3795—21no—
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18#64078C2211yescharacteristic, complemented
19C2×C3×D24C2212yescomplemented
20C2×C3×D3×C8C2212yescomplemented
21C3×#874C2211yescharacteristic
22C3×C4×D12C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic, complemented
24#63922—22no—
25#63916—21no—
26#63908C2212yes—
27#63908C2212yescomplemented
28#63891—22no—
29D3×C4⋊Dic3C2212yescomplemented
30#63857—21no—
31C2×#3714C2211yescharacteristic
32C32×C4⋊C8C2211yescharacteristic, complemented
33#63648C2212yes—
34#63645C2212yescomplemented
35C3×#821C2212yescomplemented
36C3×(C2×D3)⋊C8C2212yescomplemented
37C3×C4×C3⋊C8C2211yescharacteristic, complemented
38#63575C2211yescharacteristic, complemented
39#63564C2211yescharacteristic
40#63563C2212yescomplemented
41#63563C2212yescomplemented
42#63563C2211yescharacteristic, complemented
43#5717—31no—
44#5555—31no—
45#5551—31no—
46D4×D12—31no—
47C3×#459—31no—
48C3×C8×D4—31no—
49#5157—32no—
50#5156—32no—
51#5115—32no—
52C2×#821—32no—
53#5070—31no—
54C4×#213—31no—
55#4846—31no—
56#4846—31no—
57#4846—61no—
58#4843D311yescharacteristic, complemented
59#4834D311yescharacteristic, complemented
60#4774—32no—
61D3×#102—32no—
62#4736—32no—
63#4732—32no—
64#4694—31no—
65C4×D24—31no—
66C22×D32—22no—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×#634—21no—
70C2×C3×D12—21no—
71C2×C3×D12—21no—
72C2×C3×D12D411yescharacteristic
73C2×C3×D12C2311yescharacteristic
74C2×C3×D12C2312yes—
75C2×C3×C4×D3—21no—
76C2×C3×C4×D3C2312yes—
77C2×#626—22no—
78C2×#625—22no—
79C2×#625—22no—
80C2×D3×Dic3—22no—
81#3802—44no—
82D3×D12—24no—
83D3×D12—42no—
84#3795—44no—
85C2×C32×C8C2312yes—
86C32×C42C2311yescharacteristic
87#3752—21no—
88C4⋊(C3⋊Dic3)—21no—
89C4⋊(C3⋊Dic3)C2312yes—
90C4⋊(C3⋊Dic3)C2311yescharacteristic
91C3×(C2×D3)⋊C4—21no—
92C3×(C2×D3)⋊C4D412yes—
93C3×C4⋊Dic3D411yescharacteristic
94C3×C4⋊Dic3C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2311yescharacteristic
97C3×D24—42no—
98C3×D3×C8—42no—
99Dic3⋊Dic3—22no—
100(C2×D3)⋊Dic3—22no—
101(C2×D3)⋊Dic3—22no—
102#3714—22no—
103#3294—91noSylow
104C2×#237—61no—
105C2×D3×D4—32no—
106C2×D3×D4—61no—
107C2×D3×D4—61no—
108C2×#235—61no—
109C22×D12—32no—
110C2×C3×D8—32no—
111C22×C3×C8—32no—
112C3×#127—31no—
113C3×C4×D4—31no—
114C3×C4×D4—31no—
115#938—32no—
116#938—32no—
117#938—61no—
118#937—62no—
119C2×#213—31no—
120#930—32no—
121#930—32no—
122C2×C4⋊Dic3—32no—
123#924—61no—
124C2×D24—31no—
125C2×D24C2×D312yescomplemented
126C2×D3×C8C2×D312yescomplemented
127#897—61no—
128#895—61no—
129D3×C4⋊C4—32no—
130#886—62no—
131#883—62no—
132#882—62no—
133#874C2×D311yescharacteristic
134C4×D12—31no—
135C4×D12—31no—
136C4×D12—61no—
137C4×D12C2×D311yescharacteristic
138C4×D12C2×D311yescharacteristic, complemented
139#869—31no—
140#869—31no—
141#869—61no—
142C3×C4⋊C8—21no—
143C3×C4⋊C8C2×D311yescharacteristic, complemented
144C3×C4⋊C8C2×D311yescharacteristic, complemented
145C3×#102—32no—
146C3×C22⋊C8—32no—
147C3×C4×C8—31no—
148#832—32no—
149#832—31no—
150#832—32no—
151#821—31no—
152#821—32no—
153#821—32no—
154#821—32no—
155#821—32no—
156#821—31no—
157#821—62no—
158#821C2×D312yescomplemented
159(C2×D3)⋊C8C2×D312yescomplemented
160#818—32no—
161#818—32no—
162#818—31no—
163#818—62no—
164#809—31no—
165#807—31no—
166C4×C3⋊C8C2×D311yescharacteristic, complemented
167C22×C3⋊D3—21no—
168C22×C3×D3—22no—
169C22×C3×D3—21no—
170C22×C3×D3C2×D412yes—
171C2×D32—44no—
172C2×D32—44no—
173C2×D32—82no—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2411yescharacteristic
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—22no—
179C4⋊(C3⋊D3)—21no—
180C4⋊(C3⋊D3)#4112yescomplemented
181C4×C3⋊D3—42no—
182#634—42no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3C2×D412yes—
185C3×D12—21no—
186C3×D12—22no—
187C3×D12—21no—
188C3×D12—22no—
189C3×D12—42no—
190C3×D12—81no—
191C3×D12D814yescomplemented
192C3×C4×D3—22no—
193C3×C4×D3—22no—
194C3×C4×D3—42no—
195#626—44no—
196#625—44no—
197#625—44no—
198D3×Dic3—44no—
199C32×C8—22no—
200C3×C3⋊C8—21no—
201C3×C3⋊C8—21no—
202#547—91no—
203D42—91no—
204#486—91no—
205#480—92no—
206#474—91no—
207#466—92no—
208#459—31no—
209#447—92no—
210C4×D8—91no—
211C8×D4—31no—
212C2×#102—92no—
213C23×D3—62no—
214C23×D3—62no—
215C2×C3×D4—31no—
216C2×C3×D4—32no—
217C2×C3×D4—31no—
218C2×C3×D4—61no—
219C2×C3×D4—61no—
220C22×C3×C4—32no—
221C22×C3×C4—61no—
222C2×#67—62no—
223C2×#67—62no—
224C2×#67—62no—
225C2×#67—62no—
226C2×#67—62no—
227C22×Dic3—62no—
228#237—124no—
229D3×D4—64no—
230D3×D4—122no—
231D3×D4—124no—
232D3×D4—124no—
233#235—124no—
234C2×D12—21no—
235C2×D12—21no—
236C2×D12—31no—
237C2×D12—31no—
238C2×D12—61no—
239C2×D12—64no—
240C2×D12—62no—
241C2×D12—122no—
242C2×D12D1211yescharacteristic
243C2×D12C22×D312yes—
244C2×D12C22×D311yescharacteristic
245C2×C4×D3—21no—
246C2×C4×D3—62no—
247C2×C4×D3—61no—
248C2×C4×D3—61no—
249C2×C4×D3—121no—
250C2×C4×D3C22×D312yes—
251C2×Dic6—61no—
252C2×Dic6—61no—
253C2×Dic6—121no—
254C3×D8—122no—
255C2×C3×C8—22no—
256C2×C3×C8—31no—
257C2×C3×C8—31no—
258C2×C3×C8—122no—
259C2×C3×C8C22×D312yes—
260C2×C3×C8C22×D312yes—
261C3×C4⋊C4—31no—
262C3×C4⋊C4—31no—
263C3×C22⋊C4—32no—
264C3×C22⋊C4—61no—
265C3×C42—21no—
266C3×C42C22×D311yescharacteristic
267C3×C42C22×D311yescharacteristic
268#217—62no—
269#217—62no—
270#213—62no—
271(C2×D3)⋊C4—21no—
272(C2×D3)⋊C4—62no—
273(C2×D3)⋊C4—62no—
274(C2×D3)⋊C4—61no—
275(C2×D3)⋊C4—61no—
276(C2×D3)⋊C4—121no—
277(C2×D3)⋊C4D1212yes—
278C4⋊Dic3—31no—
279C4⋊Dic3—31no—
280C4⋊Dic3—32no—
281C4⋊Dic3—32no—
282C4⋊Dic3—61no—
283C4⋊Dic3—62no—
284C4⋊Dic3—62no—
285C4⋊Dic3—61no—
286C4⋊Dic3—61no—
287C4⋊Dic3—121no—
288C4⋊Dic3D1211yescharacteristic
289C4⋊Dic3C22×D311yescharacteristic
290Dic3⋊C4—62no—
291C2×C3⋊C8C22×D311yescharacteristic
292C2×C3⋊C8C22×D311yescharacteristic
293D24—42no—
294D24—62no—
295D3×C8—42no—
296C22×C32C22×D411yescharacteristic
297C2×C3⋊D3—22no—
298C2×C3⋊D3—41no—
299C2×C3⋊D3—41no—
300C2×C3×D3—22no—
301C2×C3×D3—22no—
302C2×C3×D3—42no—
303C2×C3×D3—41no—
304C2×C3×D3—41no—
305C2×C3×D3—42no—
306C2×C3×D3—42no—
307C2×C3×D3—41no—
308C2×C3×D3C2×D814yes—
309D32—88no—
310C32×C4—21no—
311C32×C4C2×D812yes—
312C32×C4C2×#4111yescharacteristic
313C32×C4H(5,𝔽2)11yescharacteristic
314C3⋊Dic3—42no—
315C3⋊Dic3—41no—
316C3×Dic3—22no—
317C3×Dic3—41no—
318C2×#41—181no—
319C22×D4—92no—
320C22×D4—181no—
321C2×D8—32no—
322C2×D8—91no—
323C22×C8—32no—
324C4⋊Q8—91no—
325#127—31no—
326#123—182no—
327C22⋊Q8—181no—
328#121—92no—
329#121—92no—
330#121—181no—
331#120—182no—
332C4×D4—31no—
333C4×D4—31no—
334C4×D4—91no—
335C2×C4⋊C4—92no—
336#107—91no—
337#107—92no—
338C4⋊C8D3211yescharacteristic, complemented
339#102—32no—
340#102—91no—
341#102—92no—
342#102—91no—
343#102—92no—
344#102—92no—
345C22⋊C8—32no—
346C4×C8—31no—
347C23×C3—32no—
348C23×C3—61no—
349C23×C3—62no—
350C22×D3—21no—
351C22×D3—22no—
352C22×D3—61no—
353C22×D3—61no—
354C22×D3—121no—
355C22×D3—124no—
356C22×D3—124no—
357C22×D3—124no—
358C22×D3—124no—
359C22×D3—242no—
360C22×D3—242no—
361C22×D3C2×D1212yes—
362C3×D4—34no—
363C3×D4—61no—
364C3×D4—62no—
365C3×D4—61no—
366C3×D4—62no—
367C3×D4—122no—
368C3×D4—241no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—32no—
373C2×C3×C4—62no—
374C2×C3×C4—62no—
375C2×C3×C4—61no—
376C2×C3×C4—122no—
377C2×C3×C4C2×D1211yescharacteristic
378C2×C3×C4C2×D1211yescharacteristic
379C2×C3×C4D3×D411yescharacteristic
380C2×C3×C4D3×D411yescharacteristic
381C2×C3×C4C23×D311yescharacteristic
382C2×C3×C4C23×D311yescharacteristic
383#67—124no—
384#67—124no—
385#67—124no—
386#67—124no—
387#67—124no—
388C2×Dic3—21no—
389C2×Dic3—62no—
390C2×Dic3—61no—
391C2×Dic3—62no—
392C2×Dic3—61no—
393C2×Dic3—122no—
394C2×Dic3—121no—
395C2×Dic3—124no—
396C2×Dic3C2×D1212yes—
397D12—21no—
398D12—22no—
399D12—21no—
400D12—22no—
401D12—32no—
402D12—32no—
403D12—42no—
404D12—62no—
405D12—61no—
406D12—61no—
407D12—81no—
408D12—121no—
409D12—124no—
410D12D2414yescomplemented
411C4×D3—22no—
412C4×D3—22no—
413C4×D3—42no—
414C4×D3—124no—
415C4×D3—122no—
416C4×D3—122no—
417C4×D3—242no—
418Dic6—122no—
419Dic6—122no—
420Dic6—242no—
421C3×C8—22no—
422C3×C8—22no—
423C3×C8—42no—
424C3×C8—61no—
425C3×C8—61no—
426C3⋊C8—21no—
427C3⋊C8—21no—
428C2×C32#54611yescharacteristic
429C2×C32C22×D811yescharacteristic
430C2×C32#57711yescharacteristic
431C3⋊D3—42no—
432C3×D3—24no—
433C3×D3—82no—
434C3×D3—81no—
435C24—182no—
436#41—364no—
437C2×Q8—181no—
438C2×D4—32no—
439C2×D4—31no—
440C2×D4—31no—
441C2×D4—61no—
442C2×D4—61no—
443C2×D4—91no—
444C2×D4—182no—
445C2×D4—184no—
446C2×D4—182no—
447C2×D4—182no—
448C2×D4—362no—
449C2×D4—364no—
450C22×C4—32no—
451C22×C4—61no—
452C22×C4—182no—
453C22×C4—181no—
454D8—122no—
455D8—182no—
456C2×C8—31no—
457C2×C8—31no—
458C2×C8—122no—
459C2×C8C2×D3212yes—
460C4⋊C4—31no—
461C4⋊C4—31no—
462C4⋊C4—92no—
463C4⋊C4—91no—
464C4⋊C4—182no—
465C4⋊C4—181no—
466C22⋊C4—32no—
467C22⋊C4—61no—
468C22⋊C4—182no—
469C22⋊C4—182no—
470C22⋊C4—181no—
471C42C2×D3211yescharacteristic
472C22×C3—21no—
473C22×C3—34no—
474C22×C3—62no—
475C22×C3—62no—
476C22×C3—121no—
477C22×C3—122no—
478C22×C3—122no—
479C22×C3—121no—
480C22×C3—122no—
481C22×C3—121no—
482C22×C3C22×D1211yescharacteristic
483C22×C3C2×D3×D411yescharacteristic
484C2×D3—22no—
485C2×D3—22no—
486C2×D3—41no—
487C2×D3—42no—
488C2×D3—42no—
489C2×D3—41no—
490C2×D3—42no—
491C2×D3—41no—
492C2×D3—62no—
493C2×D3—62no—
494C2×D3—122no—
495C2×D3—121no—
496C2×D3—121no—
497C2×D3—121no—
498C2×D3—121no—
499C2×D3—241no—
500C2×D3—241no—
501C2×D3—248no—
502C2×D3—248no—
503C2×D3C2×D2414yes—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—22no—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—41no—
510C3×C4—62no—
511C3×C4—121no—
512C3×C4C2×D2412yes—
513C3×C4D3×D812yes—
514C3×C4#100411yescharacteristic
515C3×C4#100411yescharacteristic
516C3×C4D3×#4111yescharacteristic
517C3×C4D3×#4111yescharacteristic
518Dic3—22no—
519Dic3—41no—
520Dic3—122no—
521Dic3—121no—
522Dic3—122no—
523Dic3—121no—
524Dic3—242no—
525Dic3—241no—
526C32#329411yescharacteristic, complemented, Sylow
527C23—32no—
528C23—61no—
529C23—62no—
530C23—181no—
531C23—364no—
532C23—364no—
533C23—722no—
534Q8—362no—
535D4—34no—
536D4—61no—
537D4—62no—
538D4—61no—
539D4—62no—
540D4—92no—
541D4—122no—
542D4—181no—
543D4—241no—
544D4—364no—
545D4—364no—
546D4—364no—
547C2×C4—32no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—61no—
551C2×C4—122no—
552C2×C4—181no—
553C2×C4—182no—
554C2×C4—364no—
555C2×C4—362no—
556C2×C4D3×D1211yescharacteristic
557C2×C4D3×D1211yescharacteristic
558C2×C4C22×D3211yescharacteristic
559C8—22no—
560C8—61no—
561C8—61no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—64no—
566C2×C3—242no—
567C2×C3—241no—
568C2×C3#555411yescharacteristic
569C2×C3#561211yescharacteristic
570C2×C3C22×D2411yescharacteristic
571C2×C3#575111yescharacteristic
572C2×C3C2×D3×D811yescharacteristic
573C2×C3#577511yescharacteristic
574D3—24no—
575D3—82no—
576D3—81no—
577D3—122no—
578D3—122no—
579D3—242no—
580C22—34no—
581C22—62no—
582C22—62no—
583C22—122no—
584C22—121no—
585C22—121no—
586C22—122no—
587C22—122no—
588C22—121no—
589C22—182no—
590C22—361no—
591C22—361no—
592C22—728no—
593C22C2×D3×D1211yescharacteristic
594C4—21no—
595C4—62no—
596C4—121no—
597C4—361no—
598C4—362no—
599C4D3×D2412yes—
600C4#6431311yescharacteristic
601C4#6431911yescharacteristic
602C3—21no—
603C3#7943811yescharacteristic, complemented
604C3#8035211yescharacteristic, complemented
605C2—64no—
606C2—242no—
607C2—241no—
608C2—362no—
609C2#1059463011yescharacteristic
610C2C2×D3×D2411yescharacteristic
611C2#1059471311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3294
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #10594004C2semidirect
2. #10593895C2semidirect
3. #10592545C2semidirect
4. C3×#4843C2semidirect
5. C3×#4834C2semidirect
6. #10590944C2semidirect
7. D3×#821C2semidirect
8. #10590831C2semidirect
9. #10590680C2semidirect
10. C4×#3714C2semidirect
11. #10590273C2semidirect
18. #64078C22semidirect
19. C2×C3×D24C22semidirect
20. C2×C3×D3×C8C22semidirect
23. C3×C4×D12C22semidirect
27. #63908C22semidirect
29. D3×C4⋊Dic3C22semidirect
32. C32×C4⋊C8C22semidirect
34. #63645C22semidirect
35. C3×#821C22semidirect
36. C3×(C2×D3)⋊C8C22semidirect
37. C3×C4×C3⋊C8C22semidirect
38. #63575C22semidirect
40. #63563C22semidirect
41. #63563C22semidirect
42. #63563C22semidirect
58. #4843D3semidirect
59. #4834D3semidirect
125. C2×D24C2×D3semidirect
126. C2×D3×C8C2×D3semidirect
138. C4×D12C2×D3semidirect
143. C3×C4⋊C8C2×D3semidirect
144. C3×C4⋊C8C2×D3semidirect
158. #821C2×D3semidirect
159. (C2×D3)⋊C8C2×D3semidirect
166. C4×C3⋊C8C2×D3semidirect
180. C4⋊(C3⋊D3)#41semidirect
191. C3×D12D8semidirect
338. C4⋊C8D32semidirect
410. D12D24semidirect
526. C32#3294semidirect
603. C3#79438semidirect
604. C3#80352semidirect

Maximal subgroups

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

subgroupindex
#105940042
#105938952
#105925452
C3×#48432
C3×#48342
#105909442
D3×#8212
#105908312
#105906802
C4×#37142
#105902732
#803523
#794383