Finite Group Databasebeta

← #11887058

Subgroups — #11887058

Order 1152.

1055 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594004C211yesmaximal, characteristic, complemented
2#10593896C211yesmaximal, characteristic, complemented
3C4×#3745C211yesmaximal, characteristic, complemented
4C3×#4694C211yesmaximal, characteristic, complemented
5C3×C8×D12C211yesmaximal, characteristic, complemented
6#10590947C212yesmaximal, complemented
7D3×#821C212yesmaximal, complemented
8#10590826C212yesmaximal, complemented
9#10590680C212yesmaximal, complemented
10#10590355C211yesmaximal, characteristic, complemented
11#10590313C211yesmaximal, characteristic, complemented
12#81576—31nomaximal
13#79438—31nomaximal
14C2×#3802—21no—
15C2×D3×D12C2212yes—
16C2×#3796—21no—
17C2×#3745C2211yescharacteristic
18C4×C4⋊(C3⋊D3)C2211yescharacteristic
19C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
20C2×C3×D3×C8C2212yescomplemented
21C3×#874C2211yescharacteristic
22C3×C4×D12C2211yescharacteristic
23C3×#869C2211yescharacteristic, complemented
24#63922—22no—
25#63916—21no—
26#63909C2212yescomplemented
27#63908C2212yes—
28#63890—22no—
29D3×C4⋊Dic3C2212yescomplemented
30#63871—21no—
31C2×#3714C2212yescomplemented
32C32×C4×C8C2211yescharacteristic, complemented
33#63648C2211yescharacteristic
34#63648C2211yescharacteristic, complemented
35#63645C2211yescharacteristic, complemented
36C3×#821C2212yescomplemented
37C3×#821C2212yescomplemented
38C3×(C2×D3)⋊C8C2212yescomplemented
39C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
40#63575C2212yescomplemented
41#63564C2212yes—
42#63563C2212yescomplemented
43#5726—31no—
44#5717—31no—
45#5555—31no—
46D4×D12—31no—
47C3×#486—31no—
48C3×C8×D4—31no—
49#5115—32no—
50C2×#821—32no—
51#5087—31no—
52#5072—31no—
53#4846—31no—
54#4843—31no—
55#4775—32no—
56#4774—32no—
57#4773—32no—
58D3×#102—32no—
59#4736—32no—
60#4732—32no—
61#4694D311yescharacteristic, complemented
62C4×D24—31no—
63C4×D24—31no—
64C4×D24—61no—
65C8×D12D311yescharacteristic, complemented
66C22×D32—22no—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×C4×C3⋊D3—21no—
70C2×C4×C3⋊D3—21no—
71C2×C3×D12—21no—
72C2×C3×D12—21no—
73C2×C3×D12D411yescharacteristic
74C2×C3×D12C2312yes—
75C2×C3×C4×D3C2312yes—
76C2×C3×Dic6—21no—
77C2×#626—22no—
78C2×#626—22no—
79C2×#625—22no—
80C2×D3×Dic3—22no—
81#3802—44no—
82D3×D12—24no—
83D3×D12—42no—
84#3796—44no—
85C2×C32×C8C2311yescharacteristic
86C2×C32×C8C2311yescharacteristic
87C32×C42C2311yescharacteristic
88#3752—21no—
89#3752—21no—
90C4⋊(C3⋊Dic3)C2311yescharacteristic
91C4⋊(C3⋊Dic3)C2311yescharacteristic
92#3745—22no—
93C3×(C2×D3)⋊C4D412yes—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3D411yescharacteristic
96C3×C4⋊Dic3C2312yes—
97C2×C3×C3⋊C8C2312yes—
98C3×D3×C8—42no—
99Dic3⋊Dic3—22no—
100#3722—22no—
101(C2×D3)⋊Dic3—22no—
102#3714—42no—
103#3294—91noSylow
104C2×#239—61no—
105C2×#237—61no—
106C2×D3×D4—32no—
107C2×D3×D4—61no—
108C2×D3×D4—61no—
109C22×D12—32no—
110C22×C3×C8—32no—
111C3×C4⋊Q8—31no—
112C3×#127—31no—
113C3×C4×D4—31no—
114#946—61no—
115#938—32no—
116#938—61no—
117#937—62no—
118C2×#213—32no—
119#930—32no—
120#930—32no—
121C2×C4⋊Dic3—32no—
122C2×D24—31no—
123C2×D24—31no—
124C2×D24—32no—
125C2×D24—61no—
126C2×D3×C8C2×D312yescomplemented
127#897—61no—
128#895—32no—
129#895—61no—
130#894—62no—
131D3×C4⋊C4—32no—
132#886—62no—
133#882—62no—
134#874C2×D311yescharacteristic
135C4×D12—31no—
136C4×D12—31no—
137C4×D12—31no—
138C4×D12—31no—
139C4×D12—61no—
140C4×D12—61no—
141C4×D12C2×D311yescharacteristic
142#869C2×D311yescharacteristic, complemented
143C3×C4⋊C8—31no—
144C3×#102—32no—
145C3×#102—32no—
146C3×C22⋊C8—32no—
147C3×C4×C8—21no—
148C3×C4×C8C2×D311yescharacteristic, complemented
149C3×C4×C8C2×D311yescharacteristic, complemented
150#832—32no—
151#821—32no—
152#821—31no—
153#821—31no—
154#821—31no—
155#821—31no—
156#821—32no—
157#821—61no—
158#821—61no—
159#821C2×D312yescomplemented
160#821C2×D312yescomplemented
161(C2×D3)⋊C8C2×D312yescomplemented
162#818—31no—
163#818—31no—
164#818—32no—
165#818—61no—
166#809—32no—
167#807—32no—
168C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
169C22×C3⋊D3—21no—
170C22×C3⋊D3—21no—
171C22×C3×D3—22no—
172C22×C3×D3C2×D412yes—
173C2×D32—44no—
174C2×D32—44no—
175C2×D32—82no—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2411yescharacteristic
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3—21no—
181C4⋊(C3⋊D3)—21no—
182C4⋊(C3⋊D3)—21no—
183C4⋊(C3⋊D3)—21no—
184C4⋊(C3⋊D3)#4112yescomplemented
185C4×C3⋊D3—42no—
186C4×C3⋊D3—42no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3C2×D412yes—
189C3×D12—22no—
190C3×D12—22no—
191C3×D12—42no—
192C3×D12—81no—
193C3×D12D814yescomplemented
194C3×C4×D3—22no—
195C3×C4×D3—22no—
196C3×Dic6—42no—
197#626—44no—
198#626—44no—
199#625—44no—
200D3×Dic3—44no—
201C32×C8—21no—
202C32×C8—21no—
203C3×C3⋊C8—22no—
204#547—91no—
205D42—91no—
206#486—31no—
207#480—92no—
208#474—91no—
209#466—92no—
210#459—91no—
211#447—92no—
212C4×D8—91no—
213C8×D4—31no—
214C2×#102—92no—
215C23×D3—62no—
216C23×D3—62no—
217C2×C3×Q8—61no—
218C2×C3×D4—31no—
219C2×C3×D4—32no—
220C2×C3×D4—61no—
221C2×C3×D4—61no—
222C22×C3×C4—32no—
223C2×#67—62no—
224C2×#67—62no—
225C2×#67—62no—
226C2×#67—62no—
227C22×Dic3—62no—
228#239—124no—
229#237—124no—
230D3×D4—64no—
231D3×D4—122no—
232D3×D4—124no—
233D3×D4—124no—
234C2×D12—21no—
235C2×D12—21no—
236C2×D12—31no—
237C2×D12—31no—
238C2×D12—31no—
239C2×D12—31no—
240C2×D12—61no—
241C2×D12—61no—
242C2×D12—64no—
243C2×D12—62no—
244C2×D12—62no—
245C2×D12—122no—
246C2×D12D1211yescharacteristic
247C2×D12C22×D312yes—
248C2×C4×D3—62no—
249C2×C4×D3—61no—
250C2×C4×D3—61no—
251C2×C4×D3—61no—
252C2×C4×D3—61no—
253C2×C4×D3—121no—
254C2×C4×D3—121no—
255C2×C4×D3C22×D312yes—
256C2×Dic6—21no—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—32no—
260C2×C3×C8—122no—
261C2×C3×C8C22×D311yescharacteristic
262C2×C3×C8C22×D311yescharacteristic
263C2×C3×C8C22×D311yescharacteristic
264C2×C3×C8C22×D311yescharacteristic
265C3×C4⋊C4—31no—
266C3×C4⋊C4—32no—
267C3×C4⋊C4—61no—
268C3×C22⋊C4—32no—
269C3×C42—21no—
270C3×C42C22×D311yescharacteristic
271C3×C42C22×D311yescharacteristic
272#217—62no—
273#213—122no—
274(C2×D3)⋊C4—62no—
275(C2×D3)⋊C4—62no—
276(C2×D3)⋊C4—61no—
277(C2×D3)⋊C4—61no—
278(C2×D3)⋊C4—61no—
279(C2×D3)⋊C4—61no—
280(C2×D3)⋊C4—62no—
281(C2×D3)⋊C4—121no—
282(C2×D3)⋊C4—121no—
283(C2×D3)⋊C4D1212yes—
284C4⋊Dic3—21no—
285C4⋊Dic3—31no—
286C4⋊Dic3—31no—
287C4⋊Dic3—31no—
288C4⋊Dic3—31no—
289C4⋊Dic3—61no—
290C4⋊Dic3—61no—
291C4⋊Dic3—62no—
292C4⋊Dic3D1211yescharacteristic
293C4⋊Dic3C22×D312yes—
294Dic3⋊C4—62no—
295C2×C3⋊C8C22×D312yes—
296D24—62no—
297D24—62no—
298D24—64no—
299D24—122no—
300D3×C8—42no—
301C22×C32C22×D411yescharacteristic
302C2×C3⋊D3—22no—
303C2×C3⋊D3—41no—
304C2×C3⋊D3—41no—
305C2×C3⋊D3—41no—
306C2×C3⋊D3—41no—
307C2×C3⋊D3—41no—
308C2×C3×D3—22no—
309C2×C3×D3—22no—
310C2×C3×D3—42no—
311C2×C3×D3—42no—
312C2×C3×D3—42no—
313C2×C3×D3C2×D814yes—
314D32—88no—
315C32×C4—21no—
316C32×C4C2×D812yes—
317C32×C4C2×#4111yescharacteristic
318C32×C4H(5,𝔽2)11yescharacteristic
319C3⋊Dic3—41no—
320C3⋊Dic3—41no—
321C3×Dic3—22no—
322C3×Dic3—42no—
323C2×#41—181no—
324C22×D4—92no—
325C22×D4—181no—
326C2×D8—92no—
327C2×D8—91no—
328C22×C8—32no—
329C4⋊Q8—31no—
330#127—31no—
331#123—182no—
332C22⋊Q8—181no—
333#121—92no—
334#121—92no—
335#121—181no—
336#120—182no—
337C4×D4—31no—
338C4×D4—91no—
339C4×D4—91no—
340C2×C4⋊C4—92no—
341#107—92no—
342#107—91no—
343C4⋊C8—31no—
344#102—32no—
345#102—32no—
346#102—92no—
347#102—92no—
348#102—91no—
349#102—91no—
350C22⋊C8—32no—
351C4×C8D3211yescharacteristic, complemented
352C23×C3—32no—
353C23×C3—62no—
354C22×D3—22no—
355C22×D3—61no—
356C22×D3—61no—
357C22×D3—61no—
358C22×D3—61no—
359C22×D3—121no—
360C22×D3—121no—
361C22×D3—124no—
362C22×D3—124no—
363C22×D3—124no—
364C22×D3—124no—
365C22×D3—242no—
366C22×D3—242no—
367C22×D3C2×D1212yes—
368C3×Q8—122no—
369C3×D4—34no—
370C3×D4—62no—
371C3×D4—62no—
372C3×D4—122no—
373C3×D4—241no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—32no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4C2×D1211yescharacteristic
382C2×C3×C4C2×D1211yescharacteristic
383C2×C3×C4D3×D411yescharacteristic
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4C23×D311yescharacteristic
386C2×C3×C4C23×D311yescharacteristic
387#67—124no—
388#67—124no—
389#67—124no—
390#67—124no—
391C2×Dic3—22no—
392C2×Dic3—61no—
393C2×Dic3—61no—
394C2×Dic3—61no—
395C2×Dic3—61no—
396C2×Dic3—121no—
397C2×Dic3—121no—
398C2×Dic3—124no—
399C2×Dic3C2×D1212yes—
400D12—22no—
401D12—22no—
402D12—32no—
403D12—32no—
404D12—42no—
405D12—62no—
406D12—62no—
407D12—61no—
408D12—61no—
409D12—61no—
410D12—61no—
411D12—61no—
412D12—61no—
413D12—81no—
414D12—121no—
415D12—121no—
416D12—124no—
417D12—124no—
418D12D2414yescomplemented
419C4×D3—22no—
420C4×D3—22no—
421C4×D3—124no—
422C4×D3—122no—
423C4×D3—122no—
424C4×D3—122no—
425C4×D3—122no—
426C4×D3—242no—
427C4×D3—242no—
428Dic6—42no—
429C3×C8—22no—
430C3×C8—21no—
431C3×C8—21no—
432C3×C8—21no—
433C3×C8—21no—
434C3×C8—41no—
435C3×C8—62no—
436C3⋊C8—22no—
437C2×C32#54611yescharacteristic
438C2×C32C22×D811yescharacteristic
439C2×C32#57711yescharacteristic
440C3⋊D3—42no—
441C3⋊D3—81no—
442C3×D3—24no—
443C3×D3—82no—
444C24—182no—
445#41—364no—
446C2×Q8—61no—
447C2×D4—32no—
448C2×D4—31no—
449C2×D4—61no—
450C2×D4—61no—
451C2×D4—91no—
452C2×D4—91no—
453C2×D4—182no—
454C2×D4—184no—
455C2×D4—182no—
456C2×D4—182no—
457C2×D4—362no—
458C2×D4—364no—
459C22×C4—32no—
460C22×C4—182no—
461C22×C4—181no—
462C22×C4—181no—
463D8—182no—
464D8—362no—
465C2×C8—32no—
466C2×C8—122no—
467C2×C8C2×D3211yescharacteristic
468C2×C8C2×D3211yescharacteristic
469C4⋊C4—31no—
470C4⋊C4—32no—
471C4⋊C4—61no—
472C4⋊C4—91no—
473C4⋊C4—91no—
474C4⋊C4—182no—
475C22⋊C4—32no—
476C22⋊C4—182no—
477C22⋊C4—182no—
478C22⋊C4—181no—
479C22⋊C4—181no—
480C42C2×D3211yescharacteristic
481C22×C3—21no—
482C22×C3—34no—
483C22×C3—62no—
484C22×C3—62no—
485C22×C3—122no—
486C22×C3—122no—
487C22×C3—122no—
488C22×C3C22×D1211yescharacteristic
489C22×C3C2×D3×D411yescharacteristic
490C2×D3—22no—
491C2×D3—22no—
492C2×D3—42no—
493C2×D3—42no—
494C2×D3—42no—
495C2×D3—62no—
496C2×D3—62no—
497C2×D3—122no—
498C2×D3—121no—
499C2×D3—121no—
500C2×D3—121no—
501C2×D3—121no—
502C2×D3—122no—
503C2×D3—121no—
504C2×D3—121no—
505C2×D3—121no—
506C2×D3—121no—
507C2×D3—121no—
508C2×D3—121no—
509C2×D3—241no—
510C2×D3—241no—
511C2×D3—241no—
512C2×D3—241no—
513C2×D3—248no—
514C2×D3—248no—
515C2×D3C2×D2414yes—
516C3×C4—21no—
517C3×C4—21no—
518C3×C4—22no—
519C3×C4—21no—
520C3×C4—21no—
521C3×C4—41no—
522C3×C4—62no—
523C3×C4—122no—
524C3×C4C2×D2412yes—
525C3×C4D3×D812yes—
526C3×C4#100411yescharacteristic
527C3×C4D3×#4111yescharacteristic
528C3×C4D3×#4111yescharacteristic
529C3×C4#100911yescharacteristic
530Dic3—22no—
531Dic3—42no—
532Dic3—121no—
533Dic3—121no—
534Dic3—121no—
535Dic3—121no—
536Dic3—241no—
537Dic3—241no—
538C32#329411yescharacteristic, complemented, Sylow
539C23—32no—
540C23—62no—
541C23—181no—
542C23—181no—
543C23—364no—
544C23—364no—
545C23—722no—
546Q8—122no—
547D4—34no—
548D4—62no—
549D4—62no—
550D4—92no—
551D4—122no—
552D4—181no—
553D4—181no—
554D4—181no—
555D4—241no—
556D4—364no—
557D4—364no—
558D4—364no—
559C2×C4—32no—
560C2×C4—62no—
561C2×C4—62no—
562C2×C4—62no—
563C2×C4—181no—
564C2×C4—181no—
565C2×C4—364no—
566C2×C4—362no—
567C2×C4—362no—
568C2×C4D3×D1211yescharacteristic
569C2×C4D3×D1211yescharacteristic
570C2×C4C22×D3211yescharacteristic
571C8—21no—
572C8—21no—
573C8—62no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—64no—
578C2×C3—242no—
579C2×C3#555411yescharacteristic
580C2×C3#567611yescharacteristic
581C2×C3C22×D2411yescharacteristic
582C2×C3#575111yescharacteristic
583C2×C3C2×D3×D811yescharacteristic
584C2×C3#576211yescharacteristic
585D3—24no—
586D3—82no—
587D3—122no—
588D3—122no—
589D3—242no—
590D3—242no—
591D3—241no—
592D3—241no—
593C22—34no—
594C22—62no—
595C22—62no—
596C22—122no—
597C22—122no—
598C22—122no—
599C22—182no—
600C22—361no—
601C22—361no—
602C22—361no—
603C22—361no—
604C22—361no—
605C22—728no—
606C22C2×D3×D1211yescharacteristic
607C4—21no—
608C4—62no—
609C4—122no—
610C4—361no—
611C4—361no—
612C4D3×D2412yes—
613C4#6430611yescharacteristic
614C4#6430711yescharacteristic
615C3—21no—
616C3#7943811yescharacteristic, complemented
617C3#8157611yescharacteristic, complemented
618C2—64no—
619C2—242no—
620C2—362no—
621C2—721no—
622C2#1059400511yescharacteristic
623C2C2×D3×D2411yescharacteristic
624C2#1059467711yescharacteristic
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. #10593896C2semidirect
3. C4×#3745C2semidirect
4. C3×#4694C2semidirect
5. C3×C8×D12C2semidirect
6. #10590947C2semidirect
7. D3×#821C2semidirect
8. #10590826C2semidirect
9. #10590680C2semidirect
10. #10590355C2semidirect
11. #10590313C2semidirect
19. C4×C4⋊(C3⋊D3)C22semidirect
20. C2×C3×D3×C8C22semidirect
23. C3×#869C22semidirect
26. #63909C22semidirect
29. D3×C4⋊Dic3C22semidirect
31. C2×#3714C22semidirect
32. C32×C4×C8C22semidirect
34. #63648C22semidirect
35. #63645C22semidirect
36. C3×#821C22semidirect
37. C3×#821C22semidirect
38. C3×(C2×D3)⋊C8C22semidirect
39. C3×C4⋊(C3⋊C8)C22semidirect
40. #63575C22semidirect
42. #63563C22semidirect
61. #4694D3semidirect
65. C8×D12D3semidirect
126. C2×D3×C8C2×D3semidirect
142. #869C2×D3semidirect
148. C3×C4×C8C2×D3semidirect
149. C3×C4×C8C2×D3semidirect
159. #821C2×D3semidirect
160. #821C2×D3semidirect
161. (C2×D3)⋊C8C2×D3semidirect
168. C4⋊(C3⋊C8)C2×D3semidirect
184. C4⋊(C3⋊D3)#41semidirect
193. C3×D12D8semidirect
351. C4×C8D32semidirect
418. D12D24semidirect
538. C32#3294semidirect
616. C3#79438semidirect
617. C3#81576semidirect

Maximal subgroups

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

subgroupindex
#105940042
#105938962
C4×#37452
C3×#46942
C3×C8×D122
#105909472
D3×#8212
#105908262
#105906802
#105903552
#105903132
#815763
#794383