Finite Group Databasebeta

← #11887049

Subgroups — #11887049

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
1C3×#5726C211yesmaximal, characteristic, complemented
2#10594004C211yesmaximal, characteristic, complemented
3#10592786C211yesmaximal, characteristic, complemented
4C3×#5088C211yesmaximal, characteristic, complemented
5#10590595C212yesmaximal, complemented
6D3×#809C212yesmaximal, complemented
7#10590499C212yesmaximal, complemented
8#10590498C212yesmaximal, complemented
9#10590347C211yesmaximal, characteristic, complemented
10C4×#3714C211yesmaximal, characteristic, complemented
11C3⋊C8×D12C211yesmaximal, characteristic, complemented
12#83525—31nomaximal
13#81576—31nomaximal
14C2×C3×#239—21no—
15C2×#3802—21no—
16C2×D3×D12C2212yes—
17C32×C4⋊Q8C2211yescharacteristic, complemented
18C4×C4⋊(C3⋊D3)C2211yescharacteristic
19C3×#946—21no—
20C3×#895C2212yescomplemented
21C3×#894—22no—
22C3×D3×C4⋊C4C2212yescomplemented
23C3×#874C2211yescharacteristic
24C3×C4×D12C2211yescharacteristic
25C3×C4×D12C2211yescharacteristic, complemented
26#63922—22no—
27#63916—21no—
28#63908C2212yes—
29C2×#3714C2211yescharacteristic
30C2×#3713C2212yescomplemented
31C2×D3×C3⋊C8C2212yescomplemented
32#63636C2212yes—
33#63634C2212yescomplemented
34C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
35C3×#809C2212yescomplemented
36C3×#809C2212yescomplemented
37C3×C4×C3⋊C8C2211yescharacteristic, complemented
38#63575C2211yescharacteristic, complemented
39#63564C2211yescharacteristic
40#63563C2211yescharacteristic, complemented
41#63562C2212yescomplemented
42(C2×D3)⋊(C3⋊C8)C2212yescomplemented
43C3×#547—31no—
44#5726D311yescharacteristic, complemented
45#5717—31no—
46D4×D12—31no—
47C3×#486—31no—
48#5088D311yescharacteristic, complemented
49#5087—31no—
50#5087—31no—
51#5087—61no—
52#5072—31no—
53#5038—32no—
54#5036—32no—
55#5015—31no—
56C4×#213—31no—
57D4×C3⋊C8—31no—
58#4967—32no—
59C2×#809—32no—
60#4775—32no—
61#4774—32no—
62#4773—32no—
63D3×#102—32no—
64C4×D24—31no—
65C8×D12—31no—
66C22×D32—22no—
67C2×C32×Q8—21no—
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×C4×C3⋊D3—21no—
70C3×#239—44no—
71C2×C3×D12—22no—
72C2×C3×D12—21no—
73C2×C3×D12—21no—
74C2×C3×D12D411yescharacteristic
75C2×C3×D12C2311yescharacteristic
76C2×C3×D12C2312yes—
77C2×C3×C4×D3—22no—
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3C2312yes—
80C2×#626—22no—
81C2×#625—22no—
82#3802—44no—
83D3×D12—24no—
84D3×D12—42no—
85C32×C4⋊C4—21no—
86C32×C4⋊C4C2312yes—
87C32×C42C2311yescharacteristic
88#3752—21no—
89C4⋊(C3⋊Dic3)C2311yescharacteristic
90C2×C3⋊(C3⋊C8)C2312yes—
91C3×(C2×D3)⋊C4—21no—
92C3×(C2×D3)⋊C4—22no—
93C3×(C2×D3)⋊C4D412yes—
94C3×C4⋊Dic3D411yescharacteristic
95C3×C4⋊Dic3C2311yescharacteristic
96C3×Dic3⋊C4—22no—
97C2×C3×C3⋊C8C2311yescharacteristic
98C2×C3×C3⋊C8C2311yescharacteristic
99(C2×D3)⋊Dic3—22no—
100#3714—22no—
101#3713—42no—
102D3×C3⋊C8—42no—
103#3294—91noSylow
104C2×C3×#41—61no—
105C2×#239—21no—
106C2×D3×D4—32no—
107C2×D3×D4—61no—
108C2×D3×D4—61no—
109C22×D12—32no—
110C3×C4⋊Q8—21no—
111C3×C4⋊Q8C2×D311yescharacteristic, complemented
112C3×C4⋊Q8C2×D311yescharacteristic, complemented
113C3×#127—31no—
114C3×#123—62no—
115C3×C22⋊Q8—61no—
116C3×#121—32no—
117C3×C4×D4—31no—
118C3×C4×D4—31no—
119C2×C3×C4⋊C4—32no—
120#946—21no—
121#938—32no—
122#938—61no—
123#937—62no—
124C2×#213—32no—
125C2×#213—32no—
126C2×#213—31no—
127#930—32no—
128C22×C3⋊C8—32no—
129C2×D24—31no—
130C2×D3×C8—32no—
131#895—61no—
132#895C2×D312yescomplemented
133#894—22no—
134D3×C4⋊C4C2×D312yescomplemented
135#882—62no—
136#874C2×D311yescharacteristic
137C4×D12—31no—
138C4×D12—31no—
139C4×D12—61no—
140C4×D12C2×D311yescharacteristic
141C4×D12C2×D311yescharacteristic, complemented
142C3×#102—32no—
143C3×#102—32no—
144C3×C4×C8—31no—
145#832—32no—
146#832—31no—
147#830—32no—
148#821—31no—
149#821—31no—
150(C2×D3)⋊C8—32no—
151#818—31no—
152#809—32no—
153#809—32no—
154#809—32no—
155#809—31no—
156#809—62no—
157#809C2×D312yescomplemented
158#809C2×D312yescomplemented
159#807—32no—
160#807—32no—
161#807—31no—
162#807—62no—
163C4⋊(C3⋊C8)—31no—
164C4⋊(C3⋊C8)—31no—
165C4⋊(C3⋊C8)—61no—
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—
174C32×Q8—42no—
175C2×C32×C4—22no—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2411yescharacteristic
179C2×C3⋊Dic3—21no—
180C4⋊(C3⋊D3)—21no—
181C4⋊(C3⋊D3)#4112yescomplemented
182C4×C3⋊D3—42no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3C2×D412yes—
185C3×D12—21no—
186C3×D12—22no—
187C3×D12—21no—
188C3×D12—22no—
189C3×D12—44no—
190C3×D12—42no—
191C3×D12—81no—
192C3×D12D814yescomplemented
193C3×C4×D3—22no—
194C3×C4×D3—22no—
195C3×C4×D3—44no—
196C3×C4×D3—42no—
197#626—44no—
198#625—44no—
199C3⋊(C3⋊C8)—22no—
200C3×C3⋊C8—21no—
201C3×C3⋊C8—21no—
202#547—31no—
203D42—91no—
204#486—31no—
205#480—92no—
206#474—91no—
207#466—92no—
208#459—91no—
209#447—92no—
210C4×D8—91no—
211C8×D4—91no—
212C2×#102—92no—
213C23×D3—62no—
214C23×D3—62no—
215C3×#41—124no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—41no—
219C2×C3×D4—31no—
220C2×C3×D4—32no—
221C2×C3×D4—31no—
222C2×C3×D4—62no—
223C2×C3×D4—61no—
224C2×C3×D4—61no—
225C22×C3×C4—32no—
226C22×C3×C4—62no—
227C22×C3×C4—61no—
228C2×#67—62no—
229C2×#67—62no—
230C2×#67—62no—
231#239—44no—
232D3×D4—64no—
233D3×D4—122no—
234D3×D4—124no—
235D3×D4—124no—
236C2×D12—22no—
237C2×D12—21no—
238C2×D12—21no—
239C2×D12—31no—
240C2×D12—31no—
241C2×D12—61no—
242C2×D12—64no—
243C2×D12—62no—
244C2×D12—122no—
245C2×D12#6711yescharacteristic
246C2×D12C22×D312yes—
247C2×D12C22×D311yescharacteristic
248C2×C4×D3—22no—
249C2×C4×D3—21no—
250C2×C4×D3—61no—
251C2×C4×D3—61no—
252C2×C4×D3—121no—
253C2×C4×D3C22×D312yes—
254C2×C3×C8—31no—
255C2×C3×C8—31no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—21no—
258C3×C4⋊C4—22no—
259C3×C4⋊C4—31no—
260C3×C4⋊C4—31no—
261C3×C4⋊C4—41no—
262C3×C4⋊C4—62no—
263C3×C4⋊C4C22×D312yes—
264C3×C4⋊C4C22×D312yes—
265C3×C22⋊C4—32no—
266C3×C22⋊C4—62no—
267C3×C22⋊C4—61no—
268C3×C42—21no—
269C3×C42C22×D311yescharacteristic
270C3×C42C22×D311yescharacteristic
271#217—62no—
272#213—62no—
273#213—122no—
274#213—122no—
275(C2×D3)⋊C4—21no—
276(C2×D3)⋊C4—22no—
277(C2×D3)⋊C4—62no—
278(C2×D3)⋊C4—61no—
279(C2×D3)⋊C4—61no—
280(C2×D3)⋊C4—121no—
281(C2×D3)⋊C4#6712yes—
282C4⋊Dic3—31no—
283C4⋊Dic3—31no—
284C4⋊Dic3—61no—
285C4⋊Dic3#6711yescharacteristic
286C4⋊Dic3C22×D311yescharacteristic
287Dic3⋊C4—22no—
288C2×C3⋊C8—32no—
289C2×C3⋊C8—32no—
290C2×C3⋊C8—62no—
291C2×C3⋊C8—122no—
292C2×C3⋊C8C22×D311yescharacteristic
293C2×C3⋊C8C22×D311yescharacteristic
294D24—62no—
295D3×C8—122no—
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—42no—
305C2×C3×D3—41no—
306C2×C3×D3—42no—
307C2×C3×D3—41no—
308C2×C3×D3C2×D814yes—
309D32—88no—
310C32×C4—21no—
311C32×C4—42no—
312C32×C4C2×D812yes—
313C32×C4C2×#4111yescharacteristic
314C32×C4H(5,𝔽2)11yescharacteristic
315C3⋊Dic3—41no—
316C3×Dic3—22no—
317C3×Dic3—41no—
318C2×#41—61no—
319C22×D4—92no—
320C22×D4—181no—
321C2×D8—91no—
322C2×D8—92no—
323C22×C8—92no—
324C4⋊Q8D3211yescharacteristic, complemented
325#127—31no—
326#123—62no—
327C22⋊Q8—61no—
328#121—32no—
329#121—92no—
330#121—181no—
331#120—182no—
332C4×D4—31no—
333C4×D4—31no—
334C4×D4—91no—
335C2×C4⋊C4—32no—
336#107—91no—
337#107—92no—
338C4⋊C8—91no—
339#102—32no—
340#102—32no—
341#102—91no—
342#102—92no—
343#102—91no—
344#102—92no—
345C22⋊C8—92no—
346C4×C8—31no—
347C23×C3—32no—
348C23×C3—61no—
349C23×C3—62no—
350C22×D3—22no—
351C22×D3—21no—
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×#6712yes—
362C3×Q8—42no—
363C3×Q8—42no—
364C3×Q8—82no—
365C3×D4—34no—
366C3×D4—61no—
367C3×D4—62no—
368C3×D4—61no—
369C3×D4—62no—
370C3×D4—124no—
371C3×D4—122no—
372C3×D4—241no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—32no—
379C2×C3×C4—42no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4—61no—
383C2×C3×C4—124no—
384C2×C3×C4—122no—
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4D3×D411yescharacteristic
387C2×C3×C4C2×#6711yescharacteristic
388C2×C3×C4C2×#6711yescharacteristic
389C2×C3×C4C23×D311yescharacteristic
390C2×C3×C4C23×D311yescharacteristic
391#67—124no—
392#67—124no—
393#67—124no—
394C2×Dic3—21no—
395C2×Dic3—61no—
396C2×Dic3—61no—
397C2×Dic3—121no—
398C2×Dic3C2×#6712yes—
399D12—21no—
400D12—22no—
401D12—21no—
402D12—22no—
403D12—32no—
404D12—32no—
405D12—44no—
406D12—42no—
407D12—62no—
408D12—61no—
409D12—61no—
410D12—81no—
411D12—121no—
412D12—124no—
413D12#21314yescomplemented
414C4×D3—22no—
415C4×D3—22no—
416C4×D3—44no—
417C4×D3—42no—
418C4×D3—122no—
419C4×D3—122no—
420C4×D3—242no—
421C3×C8—61no—
422C3×C8—61no—
423C3⋊C8—21no—
424C3⋊C8—21no—
425C3⋊C8—62no—
426C3⋊C8—62no—
427C3⋊C8—122no—
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—124no—
437C2×Q8—21no—
438C2×D4—32no—
439C2×D4—31no—
440C2×D4—31no—
441C2×D4—62no—
442C2×D4—61no—
443C2×D4—61no—
444C2×D4—91no—
445C2×D4—182no—
446C2×D4—184no—
447C2×D4—182no—
448C2×D4—362no—
449C2×D4—364no—
450C22×C4—32no—
451C22×C4—62no—
452C22×C4—61no—
453C22×C4—181no—
454D8—182no—
455D8—362no—
456C2×C8—31no—
457C2×C8—31no—
458C2×C8—92no—
459C2×C8—362no—
460C4⋊C4—21no—
461C4⋊C4—31no—
462C4⋊C4—31no—
463C4⋊C4—62no—
464C4⋊C4—91no—
465C4⋊C4C2×D3212yes—
466C22⋊C4—32no—
467C22⋊C4—62no—
468C22⋊C4—61no—
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—121no—
478C22×C3—121no—
479C22×C3—122no—
480C22×C3—122no—
481C22×C3—122no—
482C22×C3C2×D3×D411yescharacteristic
483C22×C3C22×#6711yescharacteristic
484C2×D3—22no—
485C2×D3—22no—
486C2×D3—42no—
487C2×D3—42no—
488C2×D3—42no—
489C2×D3—41no—
490C2×D3—41no—
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×#21314yes—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—22no—
509C3×C4—41no—
510C3×C4—42no—
511C3×C4—42no—
512C3×C4—62no—
513C3×C4—82no—
514C3×C4—121no—
515C3×C4D3×D812yes—
516C3×C4C2×#21312yes—
517C3×C4D3×#4111yescharacteristic
518C3×C4D3×#4111yescharacteristic
519C3×C4#100911yescharacteristic
520C3×C4#100911yescharacteristic
521Dic3—22no—
522Dic3—41no—
523Dic3—121no—
524Dic3—121no—
525Dic3—241no—
526C32#329411yescharacteristic, complemented, Sylow
527C23—32no—
528C23—61no—
529C23—62no—
530C23—181no—
531C23—364no—
532C23—364no—
533C23—722no—
534Q8—42no—
535D4—34no—
536D4—61no—
537D4—62no—
538D4—61no—
539D4—62no—
540D4—92no—
541D4—124no—
542D4—122no—
543D4—181no—
544D4—241no—
545D4—364no—
546D4—364no—
547C2×C4—22no—
548C2×C4—32no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—61no—
552C2×C4—124no—
553C2×C4—122no—
554C2×C4—181no—
555C2×C4—362no—
556C2×C4D3×#6711yescharacteristic
557C2×C4D3×#6711yescharacteristic
558C2×C4C22×D3211yescharacteristic
559C8—61no—
560C8—61no—
561C8—182no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—64no—
566C2×C3—242no—
567C2×C3—241no—
568C2×C3#567611yescharacteristic
569C2×C3C2×D3×D811yescharacteristic
570C2×C3#576211yescharacteristic
571C2×C3C22×#21311yescharacteristic
572C2×C3#582911yescharacteristic
573C2×C3#583711yescharacteristic
574D3—24no—
575D3—81no—
576D3—82no—
577D3—122no—
578D3—122no—
579D3—242no—
580C22—34no—
581C22—62no—
582C22—62no—
583C22—121no—
584C22—122no—
585C22—122no—
586C22—121no—
587C22—122no—
588C22—121no—
589C22—182no—
590C22—361no—
591C22—361no—
592C22—728no—
593C22C2×D3×#6711yescharacteristic
594C4—21no—
595C4—42no—
596C4—62no—
597C4—121no—
598C4—361no—
599C4D3×#21312yes—
600C4#6431911yescharacteristic
601C4#6432011yescharacteristic
602C3—21no—
603C3#8157611yescharacteristic, complemented
604C3#8352511yescharacteristic, complemented
605C2—64no—
606C2—242no—
607C2—241no—
608C2—362no—
609C2C2×D3×#21311yescharacteristic
610C2#1059531811yescharacteristic
611C2#1059542811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
hypercenterC4⋊Q8D32
hypocenterC32#3294
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. C3×#5726C2semidirect
2. #10594004C2semidirect
3. #10592786C2semidirect
4. C3×#5088C2semidirect
5. #10590595C2semidirect
6. D3×#809C2semidirect
7. #10590499C2semidirect
8. #10590498C2semidirect
9. #10590347C2semidirect
10. C4×#3714C2semidirect
11. C3⋊C8×D12C2semidirect
17. C32×C4⋊Q8C22semidirect
20. C3×#895C22semidirect
22. C3×D3×C4⋊C4C22semidirect
25. C3×C4×D12C22semidirect
30. C2×#3713C22semidirect
31. C2×D3×C3⋊C8C22semidirect
33. #63634C22semidirect
34. C4⋊(C3⋊(C3⋊C8))C22semidirect
35. C3×#809C22semidirect
36. C3×#809C22semidirect
37. C3×C4×C3⋊C8C22semidirect
38. #63575C22semidirect
40. #63563C22semidirect
41. #63562C22semidirect
42. (C2×D3)⋊(C3⋊C8)C22semidirect
44. #5726D3semidirect
48. #5088D3semidirect
111. C3×C4⋊Q8C2×D3semidirect
112. C3×C4⋊Q8C2×D3semidirect
132. #895C2×D3semidirect
134. D3×C4⋊C4C2×D3semidirect
141. C4×D12C2×D3semidirect
157. #809C2×D3semidirect
158. #809C2×D3semidirect
166. C4×C3⋊C8C2×D3semidirect
181. C4⋊(C3⋊D3)#41semidirect
192. C3×D12D8semidirect
324. C4⋊Q8D32semidirect
413. D12#213semidirect
526. C32#3294semidirect
603. C3#81576semidirect
604. C3#83525semidirect

Maximal subgroups

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

subgroupindex
C3×#57262
#105940042
#105927862
C3×#50882
#105905952
D3×#8092
#105904992
#105904982
#105903472
C4×#37142
C3⋊C8×D122
#835253
#815763