Finite Group Databasebeta

← #11898262

Subgroups — #11898262

Order 1152.

1076 conjugacy classes of subgroups.

The subgroup lattice has 633 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596024C211yesmaximal, characteristic, complemented
2#10593906C211yesmaximal, characteristic, complemented
3C3×#5015C211yesmaximal, characteristic, complemented
4C3×C4×#213C211yesmaximal, characteristic, complemented
5#10591484C212yesmaximal, complemented
6#10591433C212yesmaximal, complemented
7#10590551C212yesmaximal, complemented
8#10590459C212yesmaximal, complemented
9#10590350C211yesmaximal, characteristic, complemented
10#10590349C211yesmaximal, characteristic, complemented
11#10590254C211yesmaximal, characteristic, complemented
12#80324—31nomaximal
13#79578—31nomaximal
14C2×#3828—21no—
15C2×#3795—21no—
16C32×C4×D4C2211yescharacteristic
17#64149C2212yes—
18#64139—21no—
19#64102C2212yes—
20#64093—22no—
21#64083C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C2×C3×#213C2211yescharacteristic
24C2×C3×#213C2212yes—
25C3×#874C2211yescharacteristic
26C3×C4×D12C2211yescharacteristic
27#63914C2212yes—
28#63908—21no—
29#63898C2212yes—
30#63885—22no—
31C2×#3714C2212yes—
32C2×#3714C2212yes—
33C2×#3714C2212yes—
34C3×#832C2211yescharacteristic
35C3×#809C2211yescharacteristic
36C3×#809C2212yes—
37C3×#807C2211yescharacteristic
38C3×C4⋊(C3⋊C8)C2211yescharacteristic
39C3×C4×C3⋊C8C2211yescharacteristic
40#63572C2212yes—
41#63564C2212yes—
42#63553C2212yes—
43#5718—31no—
44#5553—31no—
45#5553—31no—
46#5553—31no—
47#5553—61no—
48C3×#459—31no—
49C3×C4×D8—31no—
50#5151—32no—
51#5151—32no—
52#5150—32no—
53#5073—31no—
54#5015—31no—
55#5015D311yescharacteristic, complemented
56C4×#213D311yescharacteristic, complemented
57#4872—32no—
58#4843—31no—
59#4830—31no—
60#4786—32no—
61#4786—32no—
62#4786—32no—
63#4756—32no—
64#4695—31no—
65C8×Dic6—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×#638—22no—
69C2×#638—22no—
70#3828—44no—
71C2×C4⋊(C3⋊D3)—21no—
72C2×C4⋊(C3⋊D3)—21no—
73C2×C4⋊(C3⋊D3)C2312yes—
74C2×C4×C3⋊D3—22no—
75C2×#634D411yescharacteristic
76C2×C3×D12—21no—
77C2×C3×D12—21no—
78C2×C3×D12C2312yes—
79C2×C3×D12C2311yescharacteristic
80C2×C3×C4×D3—21no—
81C2×#625—22no—
82C2×#625—22no—
83C2×D3×Dic3—22no—
84#3795—44no—
85C32×C4⋊C4C2311yescharacteristic
86C32×C22⋊C4—21no—
87C32×C42C2311yescharacteristic
88#3752—22no—
89C4⋊(C3⋊Dic3)D411yescharacteristic
90#3750D412yes—
91C4×C3⋊Dic3C2312yes—
92C3×#213—22no—
93C3×#213—42no—
94C3×(C2×D3)⋊C4—21no—
95C3×C4⋊Dic3C2311yescharacteristic
96C2×C3×C3⋊C8C2312yes—
97C2×C3×C3⋊C8C2311yescharacteristic
98C2×C3×C3⋊C8C2311yescharacteristic
99(C2×D3)⋊Dic3—22no—
100#3714—24no—
101#3714—42no—
102#3714—42no—
103#3391—91noSylow
104C2×#237—61no—
105C2×#235—61no—
106C2×#235—61no—
107C2×#235—61no—
108C2×#235—62no—
109C2×C3×D8—31no—
110C2×C3×D8—32no—
111C3×#127—31no—
112C3×C4×D4—21no—
113C3×C4×D4—31no—
114C3×C4×D4C2×D311yescharacteristic
115C3×C4×D4C2×D311yescharacteristic
116#940—32no—
117#940—32no—
118#940—32no—
119#940—32no—
120#940—62no—
121#939—62no—
122#938—61no—
123D4×Dic3—32no—
124C2×#213—32no—
125C2×#213—32no—
126C2×#213—32no—
127C2×#213C2×D311yescharacteristic
128C2×#213C2×D312yes—
129#930—61no—
130#930—61no—
131#930—61no—
132#930—62no—
133C2×D24—32no—
134C2×D24—32no—
135C2×D24—32no—
136#893—32no—
137#893—32no—
138#893—32no—
139#893—62no—
140#884—62no—
141#884—62no—
142#884—62no—
143#884—64no—
144#874—31no—
145#874—31no—
146#874—61no—
147#874C2×D311yescharacteristic
148C4×D12C2×D311yescharacteristic
149C4×Dic6—31no—
150C4×Dic6—31no—
151C4×Dic6—61no—
152C3×#107—31no—
153C3×C4⋊C8—31no—
154C3×#102—31no—
155C3×#102—32no—
156C3×#102—31no—
157C3×C4×C8—31no—
158#832C2×D311yescharacteristic
159#821—32no—
160Dic3⋊C8—32no—
161Dic3⋊C8—32no—
162C8×Dic3—32no—
163C8×Dic3—32no—
164#809—32no—
165#809C2×D312yes—
166#809C2×D311yescharacteristic
167#807C2×D311yescharacteristic
168C4⋊(C3⋊C8)C2×D311yescharacteristic
169C4×C3⋊C8C2×D311yescharacteristic
170C23×C32—21no—
171C22×C3⋊D3—22no—
172C22×C3×D3—22no—
173C22×C3×D3—21no—
174C32×D4—21no—
175C32×D4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—42no—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2411yescharacteristic
181#638—44no—
182#638—82no—
183C2×C3⋊Dic3C2×D412yes—
184C2×C3⋊Dic3C2×D412yes—
185C4⋊(C3⋊D3)—22no—
186C4⋊(C3⋊D3)—22no—
187C4⋊(C3⋊D3)—42no—
188C4⋊(C3⋊D3)—81no—
189C4×C3⋊D3—44no—
190#634D814yescomplemented
191C2×C3×Dic3—21no—
192C3×D12—22no—
193C3×D12—21no—
194C3×D12—21no—
195C3×D12—22no—
196C3×D12—42no—
197C3×D12—81no—
198C3×C4×D3—42no—
199#625—44no—
200#625—82no—
201D3×Dic3—44no—
202C3×C3⋊C8—21no—
203C3×C3⋊C8—22no—
204C3×C3⋊C8#4112yescomplemented
205#550—91no—
206#550—91no—
207#493—91no—
208#493—92no—
209#459—31no—
210#459—92no—
211#459—92no—
212#459—91no—
213C8×Q8—91no—
214C4×D8—31no—
215C4×D8—92no—
216C2×C3×D4—21no—
217C2×C3×D4—32no—
218C2×C3×D4—31no—
219C2×C3×D4—61no—
220C2×C3×D4—61no—
221C2×C3×D4C22×D311yescharacteristic
222C2×C3×D4C22×D311yescharacteristic
223C22×C3×C4—22no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—61no—
227C2×#67—62no—
228C2×#67—62no—
229C2×#67—62no—
230C2×#67—62no—
231C2×#67—62no—
232C2×#67—62no—
233C2×#67—62no—
234C2×#67—62no—
235C2×#67—64no—
236C2×#67—64no—
237C22×Dic3—62no—
238#237—124no—
239#235—124no—
240#235—124no—
241#235—124no—
242#235—128no—
243C2×D12—21no—
244C2×D12—21no—
245C2×D12—32no—
246C2×D12—32no—
247C2×D12—62no—
248C2×D12—62no—
249C2×D12—61no—
250C2×D12—61no—
251C2×D12—62no—
252C2×D12—61no—
253C2×D12—61no—
254C2×D12C22×D311yescharacteristic
255C2×D12C22×D312yes—
256C2×C4×D3—21no—
257C2×C4×D3—62no—
258C2×C4×D3—62no—
259C2×C4×D3—62no—
260C2×C4×D3—64no—
261C2×Dic6—31no—
262C2×Dic6—31no—
263C2×Dic6—61no—
264C3×D8—62no—
265C3×D8—122no—
266C2×C3×C8—31no—
267C2×C3×C8—32no—
268C2×C3×C8—31no—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—31no—
271C3×C4⋊C4C22×D311yescharacteristic
272C3×C4⋊C4C22×D311yescharacteristic
273C3×C22⋊C4—22no—
274C3×C22⋊C4—21no—
275C3×C22⋊C4—21no—
276C3×C22⋊C4—61no—
277C3×C42—21no—
278C3×C42C22×D311yescharacteristic
279C3×C42C22×D311yescharacteristic
280#217—62no—
281#213—22no—
282#213—42no—
283#213—64no—
284#213—122no—
285#213—122no—
286(C2×D3)⋊C4—21no—
287(C2×D3)⋊C4—62no—
288(C2×D3)⋊C4—62no—
289(C2×D3)⋊C4—62no—
290(C2×D3)⋊C4—64no—
291C4⋊Dic3—31no—
292C4⋊Dic3—31no—
293C4⋊Dic3—61no—
294C4⋊Dic3C22×D311yescharacteristic
295Dic3⋊C4—32no—
296Dic3⋊C4—32no—
297Dic3⋊C4—62no—
298C4×Dic3—32no—
299C4×Dic3—32no—
300C4×Dic3—62no—
301C2×C3⋊C8C22×D311yescharacteristic
302C2×C3⋊C8C22×D312yes—
303C2×C3⋊C8C22×D311yescharacteristic
304D24—64no—
305D24—122no—
306D24—122no—
307C22×C32—41no—
308C22×C32—41no—
309C22×C32—41no—
310C22×C32C22×D411yescharacteristic
311C2×C3⋊D3—42no—
312C2×C3⋊D3—42no—
313C2×C3⋊D3—42no—
314C2×C3×D3—41no—
315C2×C3×D3—42no—
316C2×C3×D3—42no—
317C2×C3×D3—41no—
318C2×C3×D3—41no—
319C2×C3×D3—42no—
320C32×C4—21no—
321C32×C4—41no—
322C32×C4C2×D812yes—
323C32×C4C2×#4111yescharacteristic
324C32×C4H(5,𝔽2)11yescharacteristic
325C3⋊Dic3—22no—
326C3⋊Dic3C2×D814yes—
327C3×Dic3—41no—
328C2×#41—181no—
329C2×#41—181no—
330C2×D8—31no—
331C2×D8—32no—
332C2×D8—92no—
333C2×D8—92no—
334C2×D8—92no—
335#127—31no—
336#127—92no—
337#127—92no—
338#127—91no—
339#121—182no—
340#121—182no—
341#121—181no—
342#121—181no—
343C4×Q8—91no—
344C4×D4—31no—
345C4×D4—92no—
346C4×D4—92no—
347C4×D4D3211yescharacteristic
348#107—31no—
349C4⋊C8—31no—
350C4⋊C8—92no—
351#102—31no—
352#102—31no—
353#102—32no—
354#102—92no—
355C4×C8—31no—
356C4×C8—92no—
357C23×C3—22no—
358C23×C3—21no—
359C23×C3—21no—
360C23×C3—62no—
361C23×C3—61no—
362C22×D3—21no—
363C22×D3—22no—
364C22×D3—64no—
365C22×D3—62no—
366C22×D3—62no—
367C3×D4—21no—
368C3×D4—21no—
369C3×D4—21no—
370C3×D4—21no—
371C3×D4—41no—
372C3×D4—41no—
373C3×D4—62no—
374C3×D4—61no—
375C3×D4—61no—
376C3×D4—62no—
377C3×D4—122no—
378C3×D4—241no—
379C2×C3×C4—22no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—44no—
386C2×C3×C4—42no—
387C2×C3×C4—42no—
388C2×C3×C4—61no—
389C2×C3×C4—122no—
390C2×C3×C4D3×D411yescharacteristic
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4D3×D411yescharacteristic
394C2×C3×C4C23×D311yescharacteristic
395C2×C3×C4C23×D311yescharacteristic
396#67—124no—
397#67—124no—
398#67—124no—
399#67—124no—
400#67—128no—
401#67—242no—
402#67—242no—
403#67—242no—
404#67—242no—
405#67—244no—
406C2×Dic3—21no—
407C2×Dic3—32no—
408C2×Dic3—32no—
409C2×Dic3—32no—
410C2×Dic3—32no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—124no—
414D12—21no—
415D12—22no—
416D12—22no—
417D12—21no—
418D12—42no—
419D12—62no—
420D12—62no—
421D12—62no—
422D12—62no—
423D12—81no—
424D12—122no—
425D12—122no—
426D12—124no—
427D12—122no—
428D12—122no—
429D12—241no—
430D12—241no—
431D12—242no—
432C4×D3—42no—
433C4×D3—124no—
434C4×D3—124no—
435C4×D3—124no—
436C4×D3—128no—
437Dic6—34no—
438Dic6—34no—
439Dic6—64no—
440C3×C8—32no—
441C3×C8—61no—
442C3×C8—62no—
443C3⋊C8—22no—
444C3⋊C8—21no—
445C3⋊C8#23512yescomplemented
446C2×C32—81no—
447C2×C32#55011yescharacteristic
448C2×C32C22×D811yescharacteristic
449C2×C32#57611yescharacteristic
450C3⋊D3—82no—
451C3×D3—82no—
452C3×D3—81no—
453#41—364no—
454#41—364no—
455C2×Q8—91no—
456C2×D4—31no—
457C2×D4—32no—
458C2×D4—61no—
459C2×D4—61no—
460C2×D4—92no—
461C2×D4—182no—
462C2×D4—182no—
463C2×D4—182no—
464C2×D4—182no—
465C2×D4—181no—
466C2×D4—181no—
467C2×D4C2×D3211yescharacteristic
468C22×C4—21no—
469C22×C4—61no—
470C22×C4—182no—
471C22×C4—182no—
472D8—62no—
473D8—122no—
474D8—184no—
475D8—362no—
476D8—362no—
477C2×C8—31no—
478C2×C8—31no—
479C2×C8—32no—
480C4⋊C4—31no—
481C4⋊C4—92no—
482C4⋊C4—91no—
483C4⋊C4C2×D3211yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—61no—
486C22⋊C4—182no—
487C22⋊C4—182no—
488C42—92no—
489C42C2×D3211yescharacteristic
490C22×C3—21no—
491C22×C3—42no—
492C22×C3—42no—
493C22×C3—42no—
494C22×C3—41no—
495C22×C3—41no—
496C22×C3—41no—
497C22×C3—41no—
498C22×C3—41no—
499C22×C3—41no—
500C22×C3—122no—
501C22×C3—121no—
502C22×C3—122no—
503C22×C3—121no—
504C22×C3—122no—
505C22×C3—121no—
506C22×C3C2×D3×D411yescharacteristic
507C22×C3C2×D3×D411yescharacteristic
508C2×D3—41no—
509C2×D3—42no—
510C2×D3—41no—
511C2×D3—42no—
512C2×D3—41no—
513C2×D3—42no—
514C2×D3—124no—
515C2×D3—124no—
516C2×D3—124no—
517C2×D3—122no—
518C2×D3—122no—
519C2×D3—122no—
520C2×D3—122no—
521C2×D3—122no—
522C2×D3—122no—
523C3×C4—21no—
524C3×C4—21no—
525C3×C4—21no—
526C3×C4—21no—
527C3×C4—22no—
528C3×C4—41no—
529C3×C4—42no—
530C3×C4—41no—
531C3×C4—41no—
532C3×C4—121no—
533C3×C4D3×D812yes—
534C3×C4D3×D812yes—
535C3×C4C2×#23511yescharacteristic
536C3×C4#100411yescharacteristic
537C3×C4D3×#4111yescharacteristic
538C3×C4#100911yescharacteristic
539Dic3—34no—
540Dic3—34no—
541Dic3—41no—
542Dic3—64no—
543Dic3—62no—
544Dic3—62no—
545Dic3—122no—
546C32#339111yescharacteristic, complemented, Sylow
547C23—21no—
548C23—61no—
549C23—62no—
550C23—182no—
551Q8—94no—
552D4—21no—
553D4—21no—
554D4—61no—
555D4—62no—
556D4—62no—
557D4—61no—
558D4—122no—
559D4—182no—
560D4—182no—
561D4—241no—
562D4—364no—
563D4—364no—
564D4—362no—
565D4—721no—
566D4—722no—
567D4—722no—
568C2×C4—21no—
569C2×C4—42no—
570C2×C4—61no—
571C2×C4—92no—
572C2×C4—92no—
573C2×C4—122no—
574C2×C4—364no—
575C2×C4—364no—
576C2×C4#381111yescharacteristic
577C2×C4#381111yescharacteristic
578C2×C4C22×D3211yescharacteristic
579C8—32no—
580C8—62no—
581C8—61no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—82no—
586C2×C3—81no—
587C2×C3—81no—
588C2×C3—241no—
589C2×C3—242no—
590C2×C3#555311yescharacteristic
591C2×C3#559911yescharacteristic
592C2×C3C2×D3×D811yescharacteristic
593C2×C3C2×D3×D811yescharacteristic
594C2×C3#576911yescharacteristic
595C2×C3#577411yescharacteristic
596D3—82no—
597D3—81no—
598D3—244no—
599D3—242no—
600D3—242no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—121no—
605C22—122no—
606C22—121no—
607C22—122no—
608C22—122no—
609C22—121no—
610C22—362no—
611C22—362no—
612C22—362no—
613C22C2×#381111yescharacteristic
614C4—21no—
615C4—41no—
616C4—94no—
617C4—121no—
618C4—182no—
619C4#6392612yes—
620C4D3×#23511yescharacteristic
621C4#6430711yescharacteristic
622C3—21no—
623C3#7957811yescharacteristic, complemented
624C3#8032411yescharacteristic, complemented
625C2—81no—
626C2—241no—
627C2—242no—
628C2—722no—
629C2#1059491911yescharacteristic
630C2C2×#6392611yescharacteristic
631C2#1059546111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3391
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596024C2semidirect
2. #10593906C2semidirect
3. C3×#5015C2semidirect
4. C3×C4×#213C2semidirect
5. #10591484C2semidirect
6. #10591433C2semidirect
7. #10590551C2semidirect
8. #10590459C2semidirect
9. #10590350C2semidirect
10. #10590349C2semidirect
11. #10590254C2semidirect
55. #5015D3semidirect
56. C4×#213D3semidirect
190. #634D8semidirect
204. C3×C3⋊C8#41semidirect
445. C3⋊C8#235semidirect
546. C32#3391semidirect
623. C3#79578semidirect
624. C3#80324semidirect

Maximal subgroups

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

subgroupindex
#105960242
#105939062
C3×#50152
C3×C4×#2132
#105914842
#105914332
#105905512
#105904592
#105903502
#105903492
#105902542
#803243
#795783