Finite Group Databasebeta

← #11887054

Subgroups — #11887054

Order 1152.

1058 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D122C211yesmaximal, characteristic, complemented
2#10593896C211yesmaximal, characteristic, complemented
3#10592542C211yesmaximal, characteristic, complemented
4C3×#4846C211yesmaximal, characteristic, complemented
5C3×#4834C211yesmaximal, characteristic, complemented
6#10590947C212yesmaximal, complemented
7D3×#821C212yesmaximal, complemented
8#10590832C212yesmaximal, complemented
9#10590679C212yesmaximal, complemented
10C4×#3714C211yesmaximal, characteristic, complemented
11#10590281C211yesmaximal, characteristic, complemented
12#80980—31nomaximal
13#79438—31nomaximal
14C2×D3×D12—21no—
15C2×D3×D12C2212yes—
16C2×#3796—21no—
17C2×#3745C2212yescomplemented
18#64083C2211yescharacteristic
19C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
20C2×C3×D3×C8C2212yescomplemented
21C3×C4×D12C2211yescharacteristic
22C3×C4×D12C2211yescharacteristic
23C3×#869C2211yescharacteristic, complemented
24#63923—22no—
25#63909—21no—
26#63909C2212yes—
27#63909C2212yescomplemented
28#63890—22no—
29D3×C4⋊Dic3C2212yescomplemented
30#63871—21no—
31C2×#3714C2211yescharacteristic
32C32×C4⋊C8C2211yescharacteristic, complemented
33#63648C2212yescomplemented
34C3×#821C2212yes—
35C3×(C2×D3)⋊C8C2212yescomplemented
36C3×#818C2212yescomplemented
37C3×C4×C3⋊C8C2211yescharacteristic, complemented
38#63575C2211yescharacteristic, complemented
39#63564C2212yescomplemented
40#63564C2212yescomplemented
41#63564C2211yescharacteristic, complemented
42#63563C2211yescharacteristic
43#5726—31no—
44#5555—31no—
45D4×D12—31no—
46D4×D12—31no—
47C3×#474—31no—
48C3×C8×D4—31no—
49#5115—32no—
50C2×#821—32no—
51#5088—31no—
52C4×#213—31no—
53#4883—32no—
54#4882—32no—
55#4846D311yescharacteristic, complemented
56#4843—31no—
57#4843—31no—
58#4843—61no—
59#4834D311yescharacteristic, complemented
60#4773—32no—
61D3×#102—32no—
62#4736—32no—
63#4732—32no—
64#4694—31no—
65C4×D24—31no—
66C22×D32—22no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)C2312yes—
70C2×C4⋊(C3⋊D3)C2311yescharacteristic
71C2×C4×C3⋊D3—21no—
72C2×C3×D12D411yescharacteristic
73C2×C3×D12C2311yescharacteristic
74C2×C3×C4×D3—21no—
75C2×C3×C4×D3C2312yes—
76C2×C3×Dic6—21no—
77C2×#626—22no—
78C2×#626—22no—
79C2×#626—22no—
80C2×D3×Dic3—22no—
81D3×D12—24no—
82D3×D12—42no—
83D3×D12—44no—
84#3796—44no—
85C2×C32×C8C2312yes—
86C32×C42C2311yescharacteristic
87#3752—21no—
88C4⋊(C3⋊Dic3)C2311yescharacteristic
89#3745—42no—
90C3×(C2×D3)⋊C4—21no—
91C3×(C2×D3)⋊C4D412yes—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3D411yescharacteristic
94C3×C4⋊Dic3C2312yes—
95C3×C4⋊Dic3C2311yescharacteristic
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98C3×D3×C8—42no—
99Dic3⋊Dic3—22no—
100#3722—22no—
101#3722—22no—
102#3714—22no—
103#3294—91noSylow
104C2×#239—61no—
105C2×#237—61no—
106C2×D3×D4—32no—
107C2×D3×D4—61no—
108C22×D12—32no—
109C22×D12—61no—
110C22×C3×C8—32no—
111C3×C4⋊Q8—31no—
112C3×C4×D4—31no—
113C3×C4×D4—31no—
114#946—61no—
115C2×#213—31no—
116#930—32no—
117#930—32no—
118#930—61no—
119C2×C4⋊Dic3—32no—
120C2×D24—31no—
121C2×D24—32no—
122C2×D24—32no—
123C2×D24—62no—
124C2×D3×C8C2×D312yescomplemented
125#897—61no—
126#895—32no—
127#895—32no—
128#895—61no—
129#894—62no—
130D3×C4⋊C4—32no—
131#886—62no—
132#882—62no—
133#882—62no—
134#874—31no—
135#874—31no—
136#874—61no—
137C4×D12—31no—
138C4×D12—31no—
139C4×D12—61no—
140C4×D12C2×D311yescharacteristic
141C4×D12C2×D311yescharacteristic
142#869C2×D311yescharacteristic, complemented
143C3×#107—32no—
144C3×C4⋊C8—21no—
145C3×C4⋊C8C2×D311yescharacteristic, complemented
146C3×C4⋊C8C2×D311yescharacteristic, complemented
147C3×#102—32no—
148C3×C22⋊C8—32no—
149C3×C4×C8—31no—
150#832—31no—
151#821—31no—
152#821—32no—
153#821—32no—
154#821—31no—
155#821—32no—
156#821—32no—
157#821—62no—
158#821C2×D312yes—
159(C2×D3)⋊C8C2×D312yescomplemented
160#818—31no—
161#818C2×D312yescomplemented
162#809—32no—
163#809—31no—
164#809—32no—
165#807—31no—
166C4×C3⋊C8C2×D311yescharacteristic, complemented
167C22×C3⋊D3—22no—
168C22×C3⋊D3—21no—
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—
178C4⋊(C3⋊D3)—21no—
179C4⋊(C3⋊D3)—21no—
180C4⋊(C3⋊D3)—22no—
181C4⋊(C3⋊D3)—22no—
182C4⋊(C3⋊D3)—42no—
183C4⋊(C3⋊D3)—81no—
184C4×C3⋊D3—42no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3C2×D412yes—
188C3×D12—21no—
189C3×D12D814yescomplemented
190C3×D12#4112yescomplemented
191C3×C4×D3—22no—
192C3×C4×D3—22no—
193C3×C4×D3—42no—
194C3×Dic6—42no—
195#626—44no—
196#626—44no—
197#626—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—31no—
207#466—92no—
208#459—91no—
209#447—92no—
210C4×D8—91no—
211C8×D4—31no—
212C2×#102—92no—
213C23×D3—62no—
214C23×D3—62no—
215C2×C3×Q8—61no—
216C2×C3×D4—31no—
217C2×C3×D4—31no—
218C22×C3×C4—32no—
219C22×C3×C4—61no—
220C2×#67—62no—
221C2×#67—62no—
222C2×#67—62no—
223C22×Dic3—62no—
224#239—124no—
225#237—124no—
226D3×D4—64no—
227D3×D4—122no—
228D3×D4—124no—
229C2×D12—32no—
230C2×D12—31no—
231C2×D12—32no—
232C2×D12—31no—
233C2×D12—61no—
234C2×D12—62no—
235C2×D12—64no—
236C2×D12—62no—
237C2×D12—62no—
238C2×D12—62no—
239C2×D12—61no—
240C2×D12—61no—
241C2×D12—61no—
242C2×D12—61no—
243C2×D12—121no—
244C2×D12—121no—
245C2×D12—122no—
246C2×D12—124no—
247C2×D12D1211yescharacteristic
248C2×D12C22×D311yescharacteristic
249C2×C4×D3—21no—
250C2×C4×D3—62no—
251C2×C4×D3—61no—
252C2×C4×D3—61no—
253C2×C4×D3—121no—
254C2×C4×D3C22×D312yes—
255C2×Dic6—21no—
256C2×C3×C8—22no—
257C2×C3×C8—31no—
258C2×C3×C8—31no—
259C2×C3×C8—122no—
260C2×C3×C8C22×D312yes—
261C2×C3×C8C22×D312yes—
262C3×C4⋊C4—31no—
263C3×C4⋊C4—31no—
264C3×C4⋊C4—32no—
265C3×C4⋊C4—61no—
266C3×C22⋊C4—32no—
267C3×C22⋊C4—61no—
268C3×C42—21no—
269C3×C42C22×D311yescharacteristic
270C3×C42C22×D311yescharacteristic
271#213—62no—
272(C2×D3)⋊C4—21no—
273(C2×D3)⋊C4—62no—
274(C2×D3)⋊C4—62no—
275(C2×D3)⋊C4—61no—
276(C2×D3)⋊C4—61no—
277(C2×D3)⋊C4—62no—
278(C2×D3)⋊C4—62no—
279(C2×D3)⋊C4—121no—
280(C2×D3)⋊C4D1212yes—
281C4⋊Dic3—21no—
282C4⋊Dic3—31no—
283C4⋊Dic3—31no—
284C4⋊Dic3—61no—
285C4⋊Dic3—62no—
286C4⋊Dic3D1211yescharacteristic
287C4⋊Dic3C22×D311yescharacteristic
288C4⋊Dic3C22×D312yes—
289Dic3⋊C4—62no—
290C2×C3⋊C8C22×D311yescharacteristic
291C2×C3⋊C8C22×D311yescharacteristic
292D24—62no—
293D24—122no—
294D24—122no—
295D24—124no—
296D3×C8—42no—
297C22×C32C22×D411yescharacteristic
298C2×C3⋊D3—41no—
299C2×C3⋊D3—42no—
300C2×C3⋊D3—41no—
301C2×C3⋊D3—42no—
302C2×C3⋊D3—42no—
303C2×C3⋊D3—41no—
304C2×C3×D3—22no—
305C2×C3×D3—22no—
306C2×C3×D3—22no—
307C2×C3×D3—41no—
308C2×C3×D3—41no—
309C2×C3×D3C2×D814yes—
310D32—88no—
311C32×C4—21no—
312C32×C4C2×D812yes—
313C32×C4C2×#4111yescharacteristic
314C32×C4H(5,𝔽2)11yescharacteristic
315C3⋊Dic3—41no—
316C3×Dic3—22no—
317C3×Dic3—42no—
318C3×Dic3—41no—
319C2×#41—181no—
320C22×D4—92no—
321C22×D4—181no—
322C2×D8—91no—
323C2×D8—92no—
324C22×C8—32no—
325C4⋊Q8—31no—
326#127—91no—
327#123—182no—
328C22⋊Q8—181no—
329#121—92no—
330#121—92no—
331#121—181no—
332#120—182no—
333C4×D4—31no—
334C4×D4—31no—
335C4×D4—91no—
336C2×C4⋊C4—92no—
337#107—32no—
338#107—91no—
339C4⋊C8D3211yescharacteristic, complemented
340#102—32no—
341#102—92no—
342#102—91no—
343#102—92no—
344#102—91no—
345#102—92no—
346C22⋊C8—32no—
347C4×C8—31no—
348C23×C3—32no—
349C23×C3—61no—
350C22×D3—21no—
351C22×D3—61no—
352C22×D3—62no—
353C22×D3—61no—
354C22×D3—62no—
355C22×D3—121no—
356C22×D3—122no—
357C22×D3—124no—
358C22×D3—124no—
359C22×D3—124no—
360C22×D3—124no—
361C22×D3—242no—
362C22×D3—242no—
363C22×D3C2×D1212yes—
364C3×Q8—122no—
365C3×D4—34no—
366C3×D4—32no—
367C3×D4—61no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—32no—
372C2×C3×C4—62no—
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—
386C2×Dic3—22no—
387C2×Dic3—21no—
388C2×Dic3—61no—
389C2×Dic3—61no—
390C2×Dic3—121no—
391C2×Dic3—124no—
392C2×Dic3C2×D1212yes—
393D12—21no—
394D12—62no—
395D12—61no—
396D12—62no—
397D12—61no—
398D12—62no—
399D12—61no—
400D12—62no—
401D12—61no—
402D12—62no—
403D12—121no—
404D12—122no—
405D12—122no—
406D12—124no—
407D12—124no—
408D12—124no—
409D12—122no—
410D12—122no—
411D12—242no—
412D12—241no—
413D12—241no—
414D12—242no—
415D12D2414yescomplemented
416D12#23912yescomplemented
417C4×D3—22no—
418C4×D3—22no—
419C4×D3—42no—
420C4×D3—124no—
421C4×D3—122no—
422C4×D3—122no—
423C4×D3—242no—
424Dic6—42no—
425C3×C8—22no—
426C3×C8—22no—
427C3×C8—42no—
428C3×C8—61no—
429C3×C8—61no—
430C3⋊C8—21no—
431C3⋊C8—21no—
432C2×C32#54611yescharacteristic
433C2×C32C22×D811yescharacteristic
434C2×C32#57711yescharacteristic
435C3⋊D3—81no—
436C3⋊D3—82no—
437C3×D3—24no—
438C3×D3—42no—
439C24—182no—
440#41—364no—
441C2×Q8—61no—
442C2×D4—31no—
443C2×D4—31no—
444C2×D4—92no—
445C2×D4—91no—
446C2×D4—182no—
447C2×D4—184no—
448C2×D4—182no—
449C2×D4—182no—
450C2×D4—181no—
451C2×D4—181no—
452C2×D4—362no—
453C2×D4—364no—
454C22×C4—32no—
455C22×C4—61no—
456C22×C4—182no—
457C22×C4—181no—
458D8—182no—
459D8—362no—
460C2×C8—31no—
461C2×C8—31no—
462C2×C8—122no—
463C2×C8C2×D3212yes—
464C4⋊C4—31no—
465C4⋊C4—32no—
466C4⋊C4—31no—
467C4⋊C4—61no—
468C4⋊C4—91no—
469C4⋊C4—182no—
470C22⋊C4—32no—
471C22⋊C4—61no—
472C22⋊C4—182no—
473C22⋊C4—182no—
474C22⋊C4—181no—
475C42C2×D3211yescharacteristic
476C22×C3—21no—
477C22×C3—34no—
478C22×C3—62no—
479C22×C3—62no—
480C22×C3—62no—
481C22×C3—121no—
482C22×C3—121no—
483C22×C3C22×D1211yescharacteristic
484C22×C3C2×D3×D411yescharacteristic
485C2×D3—22no—
486C2×D3—22no—
487C2×D3—22no—
488C2×D3—41no—
489C2×D3—41no—
490C2×D3—122no—
491C2×D3—121no—
492C2×D3—122no—
493C2×D3—122no—
494C2×D3—121no—
495C2×D3—121no—
496C2×D3—122no—
497C2×D3—122no—
498C2×D3—121no—
499C2×D3—122no—
500C2×D3—121no—
501C2×D3—122no—
502C2×D3—121no—
503C2×D3—241no—
504C2×D3—241no—
505C2×D3—242no—
506C2×D3—242no—
507C2×D3—242no—
508C2×D3—248no—
509C2×D3—248no—
510C2×D3C2×D2414yes—
511C3×C4—21no—
512C3×C4—21no—
513C3×C4—22no—
514C3×C4—21no—
515C3×C4—21no—
516C3×C4—41no—
517C3×C4—62no—
518C3×C4—122no—
519C3×C4—121no—
520C3×C4C2×D2412yes—
521C3×C4D3×D812yes—
522C3×C4#100411yescharacteristic
523C3×C4C2×#23911yescharacteristic
524C3×C4D3×#4111yescharacteristic
525C3×C4#100911yescharacteristic
526Dic3—22no—
527Dic3—42no—
528Dic3—41no—
529Dic3—121no—
530Dic3—121no—
531Dic3—241no—
532C32#329411yescharacteristic, complemented, Sylow
533C23—32no—
534C23—61no—
535C23—181no—
536C23—182no—
537C23—364no—
538C23—364no—
539C23—722no—
540Q8—122no—
541D4—34no—
542D4—32no—
543D4—61no—
544D4—181no—
545D4—182no—
546D4—181no—
547D4—182no—
548D4—364no—
549D4—364no—
550D4—364no—
551D4—362no—
552D4—721no—
553C2×C4—32no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4—61no—
557C2×C4—62no—
558C2×C4—122no—
559C2×C4—181no—
560C2×C4—364no—
561C2×C4—362no—
562C2×C4D3×D1211yescharacteristic
563C2×C4D3×D1211yescharacteristic
564C2×C4C22×D3211yescharacteristic
565C8—22no—
566C8—61no—
567C8—61no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—64no—
572C2×C3—122no—
573C2×C3#555411yescharacteristic
574C2×C3#563011yescharacteristic
575C2×C3C22×D2411yescharacteristic
576C2×C3#575111yescharacteristic
577C2×C3C2×D3×D811yescharacteristic
578C2×C3#577811yescharacteristic
579D3—24no—
580D3—42no—
581D3—242no—
582D3—242no—
583D3—241no—
584D3—242no—
585D3—241no—
586D3—482no—
587C22—34no—
588C22—62no—
589C22—62no—
590C22—62no—
591C22—121no—
592C22—121no—
593C22—362no—
594C22—361no—
595C22—361no—
596C22—362no—
597C22—362no—
598C22—361no—
599C22—728no—
600C22C2×D3×D1211yescharacteristic
601C4—21no—
602C4—62no—
603C4—121no—
604C4—122no—
605C4—361no—
606C4D3×D2412yes—
607C4#6431411yescharacteristic
608C4D3×#23911yescharacteristic
609C3—21no—
610C3#7943811yescharacteristic, complemented
611C3#8098011yescharacteristic, complemented
612C2—64no—
613C2—122no—
614C2—722no—
615C2—721no—
616C2#1059462911yescharacteristic
617C2C2×D3×D2411yescharacteristic
618C2#1059471511yescharacteristic
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. D122C2semidirect
2. #10593896C2semidirect
3. #10592542C2semidirect
4. C3×#4846C2semidirect
5. C3×#4834C2semidirect
6. #10590947C2semidirect
7. D3×#821C2semidirect
8. #10590832C2semidirect
9. #10590679C2semidirect
10. C4×#3714C2semidirect
11. #10590281C2semidirect
17. C2×#3745C22semidirect
19. C4×C4⋊(C3⋊D3)C22semidirect
20. C2×C3×D3×C8C22semidirect
23. C3×#869C22semidirect
27. #63909C22semidirect
29. D3×C4⋊Dic3C22semidirect
32. C32×C4⋊C8C22semidirect
33. #63648C22semidirect
35. C3×(C2×D3)⋊C8C22semidirect
36. C3×#818C22semidirect
37. C3×C4×C3⋊C8C22semidirect
38. #63575C22semidirect
39. #63564C22semidirect
40. #63564C22semidirect
41. #63564C22semidirect
55. #4846D3semidirect
59. #4834D3semidirect
124. C2×D3×C8C2×D3semidirect
142. #869C2×D3semidirect
145. C3×C4⋊C8C2×D3semidirect
146. C3×C4⋊C8C2×D3semidirect
159. (C2×D3)⋊C8C2×D3semidirect
161. #818C2×D3semidirect
166. C4×C3⋊C8C2×D3semidirect
189. C3×D12D8semidirect
190. C3×D12#41semidirect
339. C4⋊C8D32semidirect
415. D12D24semidirect
416. D12#239semidirect
532. C32#3294semidirect
610. C3#79438semidirect
611. C3#80980semidirect

Maximal subgroups

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

subgroupindex
D1222
#105938962
#105925422
C3×#48462
C3×#48342
#105909472
D3×#8212
#105908322
#105906792
C4×#37142
#105902812
#809803
#794383