Finite Group Databasebeta

← #11887031

Subgroups — #11887031

Order 1152.

1134 conjugacy classes of subgroups.

The subgroup lattice has 635 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596026C211yesmaximal, characteristic, complemented
2C3×D4×D12C211yesmaximal, characteristic, complemented
3C3×D4×C3⋊C8C211yesmaximal, characteristic, complemented
4#10591164C212yesmaximal, complemented
5#10591162C212yesmaximal, complemented
6#10591094C212yesmaximal, complemented
7C2×#63563C212yesmaximal, complemented
8#10590355C211yesmaximal, characteristic, complemented
9C4×#3714C211yesmaximal, characteristic, complemented
10#10590273C211yesmaximal, characteristic, complemented
11#10590272C211yesmaximal, characteristic, complemented
12#83482—31nomaximal
13#79438—31nomaximal
14C2×#3830—21no—
15C2×C3×D3×D4—21no—
16C22×C3×D12C2212yes—
17C32×C4×D4C2211yescharacteristic
18#64139C2212yescomplemented
19C2×C4⋊(C3⋊Dic3)C2212yescomplemented
20#64106—21no—
21#64095—22no—
22C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
23#64078C2211yescharacteristic, complemented
24C3×#930C2212yes—
25C22×C3×C3⋊C8C2212yescomplemented
26C3×#895—21no—
27C3×#882—22no—
28C3×#874C2211yescharacteristic
29C3×C4×D12C2211yescharacteristic
30C2×#3714C2211yescharacteristic
31C2×#3714C2212yescomplemented
32C3×#830C2212yescomplemented
33C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
34C3×C4×C3⋊C8C2211yescharacteristic, complemented
35#63575C2212yescomplemented
36#63575C2211yescharacteristic, complemented
37#63564C2211yescharacteristic, complemented
38#63563C2212yes—
39#63563C2211yescharacteristic
40#63563C2212yescomplemented
41#63563C2212yescomplemented
42#63563C2212yescomplemented
43C3×D42—31no—
44#5555—31no—
45#5555—31no—
46#5555—61no—
47D4×D12D311yescharacteristic, complemented
48C3×C8×D4—31no—
49#5217—32no—
50C2×#832—32no—
51#5115—32no—
52C2×#821—32no—
53#5072—31no—
54#5070—31no—
55#5038—32no—
56#5033—32no—
57C4×#213—31no—
58D4×C3⋊C8D311yescharacteristic, complemented
59#5007—31no—
60#4846—31no—
61#4843—31no—
62#4736—32no—
63#4732—32no—
64#4694—31no—
65C4×D24—31no—
66C23×C3×D3—22no—
67C2×C32×D4D411yescharacteristic
68C22×C32×C4C2312yes—
69C2×#638—22no—
70C22×C3⋊Dic3—22no—
71#3830—44no—
72C2×C4⋊(C3⋊D3)C2311yescharacteristic
73C2×C4×C3⋊D3—21no—
74C2×#634—21no—
75C2×C3×#67—22no—
76C3×D3×D4—44no—
77C2×C3×D12—24no—
78C2×C3×D12—22no—
79C2×C3×D12—21no—
80C2×C3×D12—21no—
81C2×C3×D12—42no—
82C2×C3×D12C2312yes—
83C2×C3×D12C2311yescharacteristic
84C2×C3×C4×D3—21no—
85C32×C4⋊C4D411yescharacteristic
86C32×C22⋊C4D412yes—
87C32×C42C2311yescharacteristic
88#3752—21no—
89#3752—22no—
90C4⋊(C3⋊Dic3)—21no—
91C4⋊(C3⋊Dic3)—22no—
92C4⋊(C3⋊Dic3)C2312yes—
93C4⋊(C3⋊Dic3)C2311yescharacteristic
94C3×(C2×D3)⋊C4—21no—
95C3×(C2×D3)⋊C4—22no—
96C3×C4⋊Dic3C2311yescharacteristic
97C2×C3×C3⋊C8—42no—
98C2×C3×C3⋊C8C2311yescharacteristic
99C2×C3×C3⋊C8C2312yes—
100C2×C3×C3⋊C8C2311yescharacteristic
101#3714—22no—
102#3714—42no—
103#3294—91noSylow
104C22×C3×D4—32no—
105C22×C3×D4—61no—
106C2×#237—62no—
107C2×#237—61no—
108C2×#237—61no—
109C2×D3×D4—21no—
110C22×D12C2×D312yes—
111C22×C3×C8—32no—
112C3×#127—31no—
113C3×#121—32no—
114C3×#121—61no—
115C3×#120—62no—
116C3×C4×D4—21no—
117C3×C4×D4—31no—
118C3×C4×D4C2×D311yescharacteristic
119C3×C4×D4C2×D311yescharacteristic
120C2×#213—31no—
121C2×#213—32no—
122#930—32no—
123#930—32no—
124#930—62no—
125#930C2×D312yes—
126C2×C4⋊Dic3—32no—
127C2×C4⋊Dic3—32no—
128C2×C4⋊Dic3—62no—
129C22×C3⋊C8C2×D312yescomplemented
130C2×D24—31no—
131C2×D24—32no—
132#897—62no—
133#897—61no—
134#897—61no—
135#895—21no—
136#886—64no—
137#886—62no—
138#886—62no—
139#882—22no—
140#874C2×D311yescharacteristic
141C4×D12—31no—
142C4×D12—31no—
143C4×D12—61no—
144C4×D12C2×D311yescharacteristic
145#869—31no—
146#869—31no—
147#869—61no—
148C3×C4⋊C8—31no—
149C3×C22⋊C8—32no—
150C3×C4×C8—31no—
151#832—31no—
152#832—32no—
153#832—32no—
154#832—32no—
155#832—32no—
156#830C2×D312yescomplemented
157#821—31no—
158#821—32no—
159#821—32no—
160#821—32no—
161#821—32no—
162#821—31no—
163#818—31no—
164#818—32no—
165#809—31no—
166#807—32no—
167#807—31no—
168C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
169C4×C3⋊C8C2×D311yescharacteristic, complemented
170C23×C32C2×D412yes—
171C22×C3⋊D3—21no—
172C22×C3×D3—21no—
173C22×C3×D3—22no—
174C22×C3×D3—44no—
175C22×C3×D3—44no—
176C22×C3×D3—82no—
177C32×D4D814yescomplemented
178C2×C32×C4—22no—
179C2×C32×C4—22no—
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D412yes—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184#638—44no—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—44no—
188C4⋊(C3⋊D3)—21no—
189C4⋊(C3⋊D3)—21no—
190C4×C3⋊D3—42no—
191#634—42no—
192C3×#67—44no—
193C2×C3×Dic3—21no—
194C3×D12—22no—
195C3×D12—21no—
196C3×D12—22no—
197C3×D12—44no—
198C3×D12—42no—
199C3×D12—81no—
200C3×D12#4112yescomplemented
201C3×C4×D3—42no—
202C3×C3⋊C8—21no—
203C3×C3⋊C8—22no—
204C3×C3⋊C8—21no—
205#547—91no—
206D42—31no—
207#486—91no—
208#480—92no—
209#474—91no—
210#466—92no—
211#459—91no—
212#447—92no—
213C4×D8—91no—
214C8×D4—31no—
215C2×#102—92no—
216C24×C3—62no—
217C23×D3—22no—
218C2×C3×D4—21no—
219C2×C3×D4—31no—
220C2×C3×D4—32no—
221C2×C3×D4—64no—
222C2×C3×D4—62no—
223C2×C3×D4—62no—
224C2×C3×D4—61no—
225C2×C3×D4—61no—
226C2×C3×D4—122no—
227C2×C3×D4—124no—
228C2×C3×D4D1211yescharacteristic
229C2×C3×D4#6711yescharacteristic
230C22×C3×C4—22no—
231C22×C3×C4—61no—
232C22×C3×C4C22×D312yes—
233C22×C3×C4C22×D312yes—
234C2×#67—22no—
235C2×#67—64no—
236C2×#67—62no—
237C2×#67—62no—
238C22×Dic3—64no—
239C22×Dic3—62no—
240C22×Dic3—62no—
241#237—128no—
242#237—124no—
243#237—124no—
244D3×D4—44no—
245C2×D12—24no—
246C2×D12—21no—
247C2×D12—22no—
248C2×D12—21no—
249C2×D12—31no—
250C2×D12—31no—
251C2×D12—42no—
252C2×D12—61no—
253C2×D12C22×D312yes—
254C2×D12C22×D311yescharacteristic
255C2×C4×D3—21no—
256C2×C4×D3—62no—
257C2×C4×D3—61no—
258C2×C4×D3—61no—
259C2×Dic6—62no—
260C2×Dic6—61no—
261C2×Dic6—61no—
262C2×C3×C8—31no—
263C2×C3×C8—32no—
264C2×C3×C8—31no—
265C2×C3×C8—122no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—31no—
268C3×C4⋊C4D1211yescharacteristic
269C3×C4⋊C4#6711yescharacteristic
270C3×C22⋊C4—22no—
271C3×C22⋊C4—61no—
272C3×C22⋊C4—62no—
273C3×C22⋊C4D1212yes—
274C3×C22⋊C4#6712yes—
275C3×C42—21no—
276C3×C42C22×D311yescharacteristic
277C3×C42C22×D311yescharacteristic
278#213—62no—
279#213—122no—
280(C2×D3)⋊C4—21no—
281(C2×D3)⋊C4—22no—
282(C2×D3)⋊C4—62no—
283(C2×D3)⋊C4—64no—
284(C2×D3)⋊C4—61no—
285(C2×D3)⋊C4—62no—
286(C2×D3)⋊C4—61no—
287(C2×D3)⋊C4—62no—
288C4⋊Dic3—32no—
289C4⋊Dic3—31no—
290C4⋊Dic3—32no—
291C4⋊Dic3—31no—
292C4⋊Dic3—62no—
293C4⋊Dic3—61no—
294C4⋊Dic3—62no—
295C4⋊Dic3—64no—
296C4⋊Dic3—61no—
297C4⋊Dic3—62no—
298C4⋊Dic3—61no—
299C4⋊Dic3—62no—
300C4⋊Dic3C22×D311yescharacteristic
301C2×C3⋊C8—42no—
302C2×C3⋊C8C22×D311yescharacteristic
303C2×C3⋊C8C22×D311yescharacteristic
304C2×C3⋊C8C22×D312yes—
305D24—62no—
306D24—122no—
307C22×C32—22no—
308C22×C32—22no—
309C22×C32C2×D814yes—
310C22×C32C22×D411yescharacteristic
311C2×C3⋊D3—41no—
312C2×C3⋊D3—41no—
313C2×C3⋊D3—41no—
314C2×C3×D3—22no—
315C2×C3×D3—41no—
316C2×C3×D3—41no—
317C2×C3×D3—42no—
318C2×C3×D3—42no—
319C2×C3×D3—42no—
320C2×C3×D3—88no—
321C32×C4—22no—
322C32×C4—21no—
323C32×C4C2×D812yes—
324C32×C4C2×#4111yescharacteristic
325C32×C4H(5,𝔽2)11yescharacteristic
326C3⋊Dic3—42no—
327C3⋊Dic3—41no—
328C3×Dic3—41no—
329C2×#41—181no—
330C22×D4—32no—
331C22×D4—61no—
332C2×D8—91no—
333C2×D8—92no—
334C22×C8—32no—
335C4⋊Q8—91no—
336#127—31no—
337#123—182no—
338C22⋊Q8—181no—
339#121—32no—
340#121—61no—
341#121—92no—
342#120—62no—
343C4×D4—31no—
344C4×D4—91no—
345C4×D4D3211yescharacteristic
346C2×C4⋊C4—92no—
347#107—91no—
348#107—92no—
349C4⋊C8—31no—
350#102—91no—
351#102—91no—
352#102—92no—
353#102—92no—
354#102—92no—
355#102—92no—
356C22⋊C8—32no—
357C4×C8—31no—
358C23×C3—22no—
359C23×C3—61no—
360C23×C3—62no—
361C23×C3—124no—
362C23×C3—124no—
363C23×C3—242no—
364C23×C3C2×D1212yes—
365C23×C3C2×#6712yes—
366C22×D3—21no—
367C22×D3—22no—
368C22×D3—44no—
369C22×D3—44no—
370C22×D3—62no—
371C22×D3—61no—
372C22×D3—61no—
373C22×D3—82no—
374C3×D4—24no—
375C3×D4—32no—
376C3×D4—61no—
377C3×D4—62no—
378C3×D4—62no—
379C3×D4—124no—
380C3×D4—124no—
381C3×D4—122no—
382C3×D4—241no—
383C3×D4D2414yescomplemented
384C3×D4#21314yescomplemented
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—22no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4—61no—
396C2×C3×C4—122no—
397C2×C3×C4C2×D1211yescharacteristic
398C2×C3×C4C2×D1212yes—
399C2×C3×C4C2×D1211yescharacteristic
400C2×C3×C4C2×#6711yescharacteristic
401C2×C3×C4C2×#6712yes—
402C2×C3×C4C2×#6711yescharacteristic
403C2×C3×C4C23×D311yescharacteristic
404C2×C3×C4C23×D311yescharacteristic
405#67—44no—
406#67—128no—
407#67—124no—
408#67—124no—
409C2×Dic3—21no—
410C2×Dic3—64no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—61no—
414C2×Dic3—62no—
415C2×Dic3—61no—
416C2×Dic3—128no—
417C2×Dic3—124no—
418C2×Dic3—124no—
419D12—22no—
420D12—21no—
421D12—22no—
422D12—44no—
423D12—42no—
424D12—61no—
425D12—61no—
426D12—61no—
427D12—61no—
428D12—81no—
429D12—121no—
430D12—121no—
431D12#23712yescomplemented
432C4×D3—42no—
433C4×D3—124no—
434C4×D3—122no—
435C4×D3—122no—
436Dic6—124no—
437Dic6—122no—
438Dic6—122no—
439C3×C8—61no—
440C3×C8—62no—
441C3×C8—61no—
442C3⋊C8—21no—
443C3⋊C8—22no—
444C3⋊C8—21no—
445C2×C32—24no—
446C2×C32#54611yescharacteristic
447C2×C32C22×D811yescharacteristic
448C2×C32#57711yescharacteristic
449C3⋊D3—81no—
450C3×D3—42no—
451C3×D3—82no—
452C24—62no—
453#41—364no—
454C2×Q8—181no—
455C2×D4—31no—
456C2×D4—32no—
457C2×D4—64no—
458C2×D4—62no—
459C2×D4—62no—
460C2×D4—61no—
461C2×D4—61no—
462C2×D4—91no—
463C2×D4—122no—
464C2×D4—124no—
465C2×D4—182no—
466C2×D4#62611yescharacteristic
467C22×C4—61no—
468C22×C4—182no—
469C22×C4—181no—
470C22×C4C2×D3212yes—
471D8—182no—
472D8—362no—
473C2×C8—31no—
474C2×C8—31no—
475C2×C8—32no—
476C2×C8—122no—
477C4⋊C4—31no—
478C4⋊C4—91no—
479C4⋊C4—92no—
480C4⋊C4—182no—
481C4⋊C4—181no—
482C4⋊C4#62611yescharacteristic
483C22⋊C4—61no—
484C22⋊C4—62no—
485C22⋊C4—181no—
486C22⋊C4—182no—
487C22⋊C4#62612yes—
488C42C2×D3211yescharacteristic
489C22×C3—22no—
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—22no—
493C22×C3—21no—
494C22×C3—24no—
495C22×C3—42no—
496C22×C3—42no—
497C22×C3—62no—
498C22×C3—121no—
499C22×C3—121no—
500C22×C3—122no—
501C22×C3—122no—
502C22×C3—122no—
503C22×C3—248no—
504C22×C3C2×D2414yes—
505C22×C3C2×#21314yes—
506C22×C3C22×D1211yescharacteristic
507C22×C3C22×#6711yescharacteristic
508C2×D3—22no—
509C2×D3—41no—
510C2×D3—41no—
511C2×D3—42no—
512C2×D3—42no—
513C2×D3—42no—
514C2×D3—88no—
515C2×D3—122no—
516C2×D3—122no—
517C2×D3—122no—
518C2×D3—121no—
519C2×D3—121no—
520C2×D3—121no—
521C2×D3—121no—
522C2×D3—121no—
523C2×D3—121no—
524C3×C4—21no—
525C3×C4—22no—
526C3×C4—22no—
527C3×C4—21no—
528C3×C4—21no—
529C3×C4—21no—
530C3×C4—22no—
531C3×C4—42no—
532C3×C4—41no—
533C3×C4—121no—
534C3×C4C2×D2412yes—
535C3×C4C2×#21312yes—
536C3×C4C2×#23711yescharacteristic
537C3×C4#100411yescharacteristic
538C3×C4#100411yescharacteristic
539C3×C4D3×#4111yescharacteristic
540Dic3—41no—
541Dic3—124no—
542Dic3—122no—
543Dic3—122no—
544Dic3—121no—
545Dic3—122no—
546Dic3—121no—
547C32#329411yescharacteristic, complemented, Sylow
548C23—61no—
549C23—62no—
550C23—124no—
551C23—124no—
552C23—181no—
553C23—242no—
554C23C2×#62612yes—
555Q8—362no—
556D4—32no—
557D4—62no—
558D4—61no—
559D4—62no—
560D4—124no—
561D4—124no—
562D4—122no—
563D4—181no—
564D4—181no—
565D4—241no—
566D4—364no—
567D4#371414yescomplemented
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—61no—
571C2×C4—122no—
572C2×C4—181no—
573C2×C4—182no—
574C2×C4—364no—
575C2×C4—362no—
576C2×C4C2×#62611yescharacteristic
577C2×C4C2×#62612yes—
578C2×C4C2×#62611yescharacteristic
579C2×C4C22×D3211yescharacteristic
580C8—61no—
581C8—61no—
582C8—62no—
583C2×C3—24no—
584C2×C3—24no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—44no—
589C2×C3—122no—
590C2×C3—242no—
591C2×C3#555411yescharacteristic
592C2×C3C22×D2411yescharacteristic
593C2×C3#575111yescharacteristic
594C2×C3C22×#21311yescharacteristic
595C2×C3#580611yescharacteristic
596C2×C3#583611yescharacteristic
597D3—42no—
598D3—82no—
599D3—242no—
600D3—241no—
601D3—241no—
602C22—22no—
603C22—22no—
604C22—62no—
605C22—121no—
606C22—121no—
607C22—122no—
608C22—122no—
609C22—122no—
610C22—248no—
611C22—361no—
612C22—361no—
613C22—361no—
614C22C2×#371414yes—
615C22C22×#62611yescharacteristic
616C4—21no—
617C4—22no—
618C4—121no—
619C4—361no—
620C4—362no—
621C4C2×#371412yes—
622C4D3×#23711yescharacteristic
623C4#6431311yescharacteristic
624C3—21no—
625C3#7943811yescharacteristic, complemented
626C3#8348211yescharacteristic, complemented
627C2—24no—
628C2—122no—
629C2—242no—
630C2—721no—
631C2C22×#371411yescharacteristic
632C2#1059524611yescharacteristic
633C2#1059544711yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3294
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596026C2semidirect
2. C3×D4×D12C2semidirect
3. C3×D4×C3⋊C8C2semidirect
4. #10591164C2semidirect
5. #10591162C2semidirect
6. #10591094C2semidirect
7. C2×#63563C2semidirect
8. #10590355C2semidirect
9. C4×#3714C2semidirect
10. #10590273C2semidirect
11. #10590272C2semidirect
18. #64139C22semidirect
19. C2×C4⋊(C3⋊Dic3)C22semidirect
22. C4×C4⋊(C3⋊D3)C22semidirect
23. #64078C22semidirect
25. C22×C3×C3⋊C8C22semidirect
31. C2×#3714C22semidirect
32. C3×#830C22semidirect
33. C3×C4⋊(C3⋊C8)C22semidirect
34. C3×C4×C3⋊C8C22semidirect
35. #63575C22semidirect
36. #63575C22semidirect
37. #63564C22semidirect
40. #63563C22semidirect
41. #63563C22semidirect
42. #63563C22semidirect
47. D4×D12D3semidirect
58. D4×C3⋊C8D3semidirect
129. C22×C3⋊C8C2×D3semidirect
156. #830C2×D3semidirect
168. C4⋊(C3⋊C8)C2×D3semidirect
169. C4×C3⋊C8C2×D3semidirect
177. C32×D4D8semidirect
200. C3×D12#41semidirect
383. C3×D4D24semidirect
384. C3×D4#213semidirect
431. D12#237semidirect
547. C32#3294semidirect
567. D4#3714semidirect
625. C3#79438semidirect
626. C3#83482semidirect

Maximal subgroups

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

subgroupindex
#105960262
C3×D4×D122
C3×D4×C3⋊C82
#105911642
#105911622
#105910942
C2×#635632
#105903552
C4×#37142
#105902732
#105902722
#834823
#794383