Finite Group Databasebeta

← #11887030

Subgroups — #11887030

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
1C3×D4×D12C211yesmaximal, characteristic, complemented
2#10593896C211yesmaximal, characteristic, complemented
3C4×#3753C211yesmaximal, characteristic, complemented
4C3×#5007C211yesmaximal, characteristic, complemented
5#10591448C212yesmaximal, complemented
6D3×#832C212yesmaximal, complemented
7#10590576C212yesmaximal, complemented
8#10590438C212yesmaximal, complemented
9#10590355C211yesmaximal, characteristic, complemented
10#10590329C211yesmaximal, characteristic, complemented
11#10590277C211yesmaximal, characteristic, complemented
12#83482—31nomaximal
13#80980—31nomaximal
14C2×C3×D3×D4C2212yes—
15C22×C3×D12—21no—
16C2×#3796—21no—
17C32×C4×D4C2211yescharacteristic
18C2×#3753C2211yescharacteristic
19C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
20C3×#930—21no—
21C3×#895C2212yes—
22C3×#882—22no—
23C3×#874C2211yescharacteristic
24C3×C4×D12C2211yescharacteristic
25C3×#869C2211yescharacteristic, complemented
26#63909C2212yescomplemented
27#63890—22no—
28D3×C4⋊Dic3C2212yescomplemented
29#63871—21no—
30C2×#3714C2212yescomplemented
31C2×D3×C3⋊C8C2212yescomplemented
32#63659C2211yescharacteristic
33#63636C2211yescharacteristic, complemented
34#63634C2211yescharacteristic, complemented
35C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
36C3×#832C2212yes—
37C3×#807C2212yescomplemented
38C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
39#63563C2212yescomplemented
40#63562C2212yescomplemented
41#63562C2212yescomplemented
42(C2×D3)⋊(C3⋊C8)C2212yescomplemented
43C3×D42—31no—
44#5726—31no—
45#5555—31no—
46D4×D12D311yescharacteristic, complemented
47C3×#474—31no—
48#5217—32no—
49C2×#832—32no—
50#5088—31no—
51#5072—31no—
52#5070—31no—
53#5038—32no—
54#5033—32no—
55C4×#213—31no—
56C4×#213—31no—
57C4×#213—61no—
58D4×C3⋊C8—31no—
59#5007D311yescharacteristic, complemented
60#4883—32no—
61#4882—32no—
62#4843—31no—
63#4834—31no—
64#4773—32no—
65D3×#102—32no—
66C23×C3×D3—22no—
67C2×C32×D4C2311yescharacteristic
68C22×C32×C4—21no—
69C2×C4⋊(C3⋊D3)C2311yescharacteristic
70C2×C4×C3⋊D3—21no—
71C2×C3×#67—22no—
72C3×D3×D4—24no—
73C3×D3×D4—42no—
74C2×C3×D12—22no—
75C2×C3×D12—21no—
76C2×C3×D12—21no—
77C2×C3×D12—44no—
78C2×C3×D12D411yescharacteristic
79C2×C3×D12C2312yes—
80C2×C3×C4×D3C2312yes—
81C2×C3×Dic6—21no—
82C2×#626—22no—
83C2×D3×Dic3—22no—
84#3796—44no—
85C32×C4⋊C4C2311yescharacteristic
86C32×C22⋊C4—21no—
87C32×C42C2311yescharacteristic
88#3753—22no—
89#3752—21no—
90C4⋊(C3⋊Dic3)C2311yescharacteristic
91C2×C3⋊(C3⋊C8)C2311yescharacteristic
92C2×C3⋊(C3⋊C8)C2311yescharacteristic
93C3×(C2×D3)⋊C4—22no—
94C3×(C2×D3)⋊C4D412yes—
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3D411yescharacteristic
97C3×C4⋊Dic3C2312yes—
98C2×C3×C3⋊C8C2312yes—
99Dic3⋊Dic3—22no—
100#3722—22no—
101#3714—42no—
102D3×C3⋊C8—42no—
103#3294—91noSylow
104C22×C3×D4—32no—
105C22×C3×D4—61no—
106C2×#239—61no—
107C2×#237—61no—
108C2×D3×D4C2×D312yes—
109C22×D12—21no—
110C3×C4⋊Q8—31no—
111C3×#127—31no—
112C3×#121—32no—
113C3×#121—61no—
114C3×#120—62no—
115C3×C4×D4—21no—
116C3×C4×D4—31no—
117C3×C4×D4C2×D311yescharacteristic
118C3×C4×D4C2×D311yescharacteristic
119#946—61no—
120C2×#213—31no—
121C2×#213—31no—
122C2×#213—32no—
123C2×#213—61no—
124#930—21no—
125#930—32no—
126C2×C4⋊Dic3—32no—
127C22×C3⋊C8—32no—
128C2×D24—32no—
129C2×D3×C8—32no—
130#897—61no—
131#895—32no—
132#895C2×D312yes—
133#894—62no—
134D3×C4⋊C4—32no—
135#886—62no—
136#882—22no—
137#874C2×D311yescharacteristic
138C4×D12—31no—
139C4×D12—31no—
140C4×D12—61no—
141C4×D12C2×D311yescharacteristic
142#869C2×D311yescharacteristic, complemented
143C3×#107—32no—
144C3×C4⋊C8—31no—
145C3×#102—32no—
146#832—31no—
147#832—31no—
148#832—32no—
149#832—32no—
150#832—32no—
151#832—61no—
152#832C2×D312yes—
153#830—32no—
154#821—32no—
155(C2×D3)⋊C8—32no—
156#809—32no—
157#809—32no—
158#809—31no—
159#809—31no—
160#809—61no—
161#807—31no—
162#807—31no—
163#807—61no—
164#807C2×D312yescomplemented
165C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
166C4×C3⋊C8—31no—
167C4×C3⋊C8—31no—
168C4×C3⋊C8—61no—
169C23×C32—21no—
170C22×C3⋊D3—21no—
171C22×C3×D3—22no—
172C22×C3×D3—44no—
173C22×C3×D3—44no—
174C22×C3×D3—82no—
175C22×C3×D3C2×D412yes—
176C32×D4—21no—
177C32×D4#4112yescomplemented
178C2×C32×C4—21no—
179C2×C32×C4—42no—
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2411yescharacteristic
183C2×C3⋊Dic3—21no—
184C4⋊(C3⋊D3)—21no—
185C4⋊(C3⋊D3)—21no—
186C4×C3⋊D3—42no—
187C3×#67—44no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3C2×D412yes—
190C3×D12—22no—
191C3×D12—22no—
192C3×D12—44no—
193C3×D12—42no—
194C3×D12—81no—
195C3×D12D814yescomplemented
196C3×C4×D3—22no—
197C3×C4×D3—22no—
198C3×Dic6—42no—
199#626—44no—
200D3×Dic3—44no—
201C3⋊(C3⋊C8)—21no—
202C3⋊(C3⋊C8)—21no—
203C3×C3⋊C8—22no—
204#547—91no—
205D42—31no—
206#486—91no—
207#480—92no—
208#474—31no—
209#466—92no—
210#459—91no—
211#447—92no—
212C4×D8—91no—
213C8×D4—91no—
214C2×#102—92no—
215C24×C3—62no—
216C23×D3—22no—
217C2×C3×Q8—61no—
218C2×C3×D4—21no—
219C2×C3×D4—31no—
220C2×C3×D4—32no—
221C2×C3×D4—62no—
222C2×C3×D4—62no—
223C2×C3×D4—64no—
224C2×C3×D4—61no—
225C2×C3×D4—61no—
226C2×C3×D4—124no—
227C2×C3×D4—122no—
228C2×C3×D4C22×D311yescharacteristic
229C2×C3×D4C22×D311yescharacteristic
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—32no—
233C22×C3×C4—41no—
234C2×#67—22no—
235C2×#67—62no—
236C22×Dic3—62no—
237#239—124no—
238#237—124no—
239D3×D4—24no—
240D3×D4—42no—
241C2×D12—22no—
242C2×D12—21no—
243C2×D12—21no—
244C2×D12—31no—
245C2×D12—31no—
246C2×D12—44no—
247C2×D12—61no—
248C2×D12—62no—
249C2×D12#6711yescharacteristic
250C2×D12C22×D312yes—
251C2×C4×D3—62no—
252C2×C4×D3—61no—
253C2×C4×D3—61no—
254C2×C4×D3—121no—
255C2×C4×D3C22×D312yes—
256C2×Dic6—21no—
257C2×C3×C8—32no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—31no—
260C3×C4⋊C4—32no—
261C3×C4⋊C4—61no—
262C3×C4⋊C4C22×D311yescharacteristic
263C3×C4⋊C4C22×D311yescharacteristic
264C3×C22⋊C4—21no—
265C3×C22⋊C4—21no—
266C3×C22⋊C4—32no—
267C3×C22⋊C4—41no—
268C3×C22⋊C4—62no—
269C3×C42—21no—
270C3×C42C22×D311yescharacteristic
271C3×C42C22×D311yescharacteristic
272#213—64no—
273#213—62no—
274#213—62no—
275#213—122no—
276(C2×D3)⋊C4—22no—
277(C2×D3)⋊C4—62no—
278(C2×D3)⋊C4—61no—
279(C2×D3)⋊C4—61no—
280(C2×D3)⋊C4—62no—
281(C2×D3)⋊C4—121no—
282(C2×D3)⋊C4#6712yes—
283C4⋊Dic3—21no—
284C4⋊Dic3—31no—
285C4⋊Dic3—31no—
286C4⋊Dic3—61no—
287C4⋊Dic3—62no—
288C4⋊Dic3#6711yescharacteristic
289C4⋊Dic3C22×D312yes—
290Dic3⋊C4—62no—
291C2×C3⋊C8—31no—
292C2×C3⋊C8—31no—
293C2×C3⋊C8—31no—
294C2×C3⋊C8—31no—
295C2×C3⋊C8—61no—
296C2×C3⋊C8—61no—
297C2×C3⋊C8—122no—
298C2×C3⋊C8C22×D312yes—
299D24—122no—
300D3×C8—122no—
301C22×C32—22no—
302C22×C32—41no—
303C22×C32—41no—
304C22×C32C22×D411yescharacteristic
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×D3—88no—
314C2×C3×D3C2×D814yes—
315C32×C4—21no—
316C32×C4—41no—
317C32×C4C2×D812yes—
318C32×C4C2×#4111yescharacteristic
319C32×C4H(5,𝔽2)11yescharacteristic
320C3⋊Dic3—41no—
321C3×Dic3—22no—
322C3×Dic3—42no—
323C2×#41—181no—
324C22×D4—32no—
325C22×D4—61no—
326C2×D8—92no—
327C2×D8—91no—
328C22×C8—92no—
329C4⋊Q8—31no—
330#127—31no—
331#123—182no—
332C22⋊Q8—181no—
333#121—32no—
334#121—61no—
335#121—92no—
336#120—62no—
337C4×D4—31no—
338C4×D4—91no—
339C4×D4D3211yescharacteristic
340C2×C4⋊C4—92no—
341#107—32no—
342#107—91no—
343C4⋊C8—31no—
344#102—32no—
345#102—92no—
346#102—92no—
347#102—92no—
348#102—91no—
349#102—91no—
350C22⋊C8—92no—
351C4×C8—91no—
352C23×C3—21no—
353C23×C3—21no—
354C23×C3—32no—
355C23×C3—41no—
356C23×C3—62no—
357C23×C3—124no—
358C23×C3—124no—
359C23×C3—242no—
360C22×D3—22no—
361C22×D3—44no—
362C22×D3—44no—
363C22×D3—61no—
364C22×D3—61no—
365C22×D3—82no—
366C22×D3—121no—
367C22×D3C2×#6712yes—
368C3×Q8—122no—
369C3×D4—21no—
370C3×D4—21no—
371C3×D4—22no—
372C3×D4—34no—
373C3×D4—41no—
374C3×D4—62no—
375C3×D4—62no—
376C3×D4—124no—
377C3×D4—124no—
378C3×D4—122no—
379C3×D4—241no—
380C3×D4#23712yescomplemented
381C3×D4#23912yescomplemented
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—32no—
388C2×C3×C4—41no—
389C2×C3×C4—42no—
390C2×C3×C4—42no—
391C2×C3×C4—62no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4—82no—
395C2×C3×C4D3×D411yescharacteristic
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4C2×#6711yescharacteristic
398C2×C3×C4C2×#6711yescharacteristic
399C2×C3×C4C23×D311yescharacteristic
400C2×C3×C4C23×D311yescharacteristic
401#67—44no—
402#67—124no—
403C2×Dic3—22no—
404C2×Dic3—61no—
405C2×Dic3—61no—
406C2×Dic3—121no—
407C2×Dic3—124no—
408C2×Dic3C2×#6712yes—
409D12—22no—
410D12—22no—
411D12—44no—
412D12—42no—
413D12—62no—
414D12—61no—
415D12—61no—
416D12—61no—
417D12—61no—
418D12—81no—
419D12—121no—
420D12—124no—
421D12#21314yescomplemented
422C4×D3—22no—
423C4×D3—22no—
424C4×D3—124no—
425C4×D3—122no—
426C4×D3—122no—
427C4×D3—242no—
428Dic6—42no—
429C3×C8—62no—
430C3⋊C8—22no—
431C3⋊C8—62no—
432C3⋊C8—61no—
433C3⋊C8—61no—
434C3⋊C8—61no—
435C3⋊C8—61no—
436C3⋊C8—121no—
437C2×C32—42no—
438C2×C32#54611yescharacteristic
439C2×C32C22×D811yescharacteristic
440C2×C32#57711yescharacteristic
441C3⋊D3—81no—
442C3×D3—24no—
443C3×D3—82no—
444C24—62no—
445#41—364no—
446C2×Q8—61no—
447C2×D4—32no—
448C2×D4—31no—
449C2×D4—62no—
450C2×D4—62no—
451C2×D4—64no—
452C2×D4—61no—
453C2×D4—61no—
454C2×D4—91no—
455C2×D4—124no—
456C2×D4—122no—
457C2×D4—182no—
458C2×D4C2×D3211yescharacteristic
459C22×C4—21no—
460C22×C4—32no—
461C22×C4—182no—
462C22×C4—181no—
463D8—182no—
464D8—362no—
465C2×C8—32no—
466C2×C8—91no—
467C2×C8—91no—
468C2×C8—362no—
469C4⋊C4—31no—
470C4⋊C4—32no—
471C4⋊C4—61no—
472C4⋊C4—91no—
473C4⋊C4—182no—
474C4⋊C4C2×D3211yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—32no—
477C22⋊C4—62no—
478C22⋊C4—182no—
479C22⋊C4—181no—
480C42C2×D3211yescharacteristic
481C22×C3—22no—
482C22×C3—22no—
483C22×C3—21no—
484C22×C3—34no—
485C22×C3—42no—
486C22×C3—41no—
487C22×C3—41no—
488C22×C3—41no—
489C22×C3—41no—
490C22×C3—62no—
491C22×C3—62no—
492C22×C3—81no—
493C22×C3—81no—
494C22×C3—122no—
495C22×C3—122no—
496C22×C3—122no—
497C22×C3—248no—
498C22×C3C2×D3×D411yescharacteristic
499C22×C3C22×#6711yescharacteristic
500C2×D3—22no—
501C2×D3—22no—
502C2×D3—42no—
503C2×D3—42no—
504C2×D3—42no—
505C2×D3—88no—
506C2×D3—122no—
507C2×D3—121no—
508C2×D3—121no—
509C2×D3—121no—
510C2×D3—121no—
511C2×D3—121no—
512C2×D3—121no—
513C2×D3—241no—
514C2×D3—241no—
515C2×D3C2×#21314yes—
516C3×C4—21no—
517C3×C4—21no—
518C3×C4—21no—
519C3×C4—21no—
520C3×C4—22no—
521C3×C4—41no—
522C3×C4—41no—
523C3×C4—41no—
524C3×C4—62no—
525C3×C4—81no—
526C3×C4—122no—
527C3×C4D3×D812yes—
528C3×C4C2×#21312yes—
529C3×C4C2×#23711yescharacteristic
530C3×C4#100411yescharacteristic
531C3×C4C2×#23911yescharacteristic
532C3×C4#100911yescharacteristic
533Dic3—22no—
534Dic3—42no—
535Dic3—121no—
536Dic3—121no—
537Dic3—241no—
538C32#329411yescharacteristic, complemented, Sylow
539C23—21no—
540C23—32no—
541C23—62no—
542C23—124no—
543C23—124no—
544C23—181no—
545C23—242no—
546Q8—122no—
547D4—21no—
548D4—34no—
549D4—62no—
550D4—62no—
551D4—124no—
552D4—124no—
553D4—122no—
554D4—181no—
555D4—181no—
556D4—241no—
557D4—364no—
558D4#379612yescomplemented
559C2×C4—21no—
560C2×C4—32no—
561C2×C4—42no—
562C2×C4—62no—
563C2×C4—62no—
564C2×C4—62no—
565C2×C4—181no—
566C2×C4—364no—
567C2×C4—362no—
568C2×C4D3×#6711yescharacteristic
569C2×C4D3×#6711yescharacteristic
570C2×C4C22×D3211yescharacteristic
571C8—62no—
572C8—181no—
573C8—181no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—42no—
578C2×C3—42no—
579C2×C3—64no—
580C2×C3—82no—
581C2×C3—242no—
582C2×C3#563011yescharacteristic
583C2×C3C2×D3×D811yescharacteristic
584C2×C3#577811yescharacteristic
585C2×C3C22×#21311yescharacteristic
586C2×C3#580611yescharacteristic
587C2×C3#583611yescharacteristic
588D3—24no—
589D3—82no—
590D3—242no—
591D3—241no—
592D3—241no—
593C22—22no—
594C22—34no—
595C22—41no—
596C22—41no—
597C22—62no—
598C22—62no—
599C22—122no—
600C22—122no—
601C22—122no—
602C22—248no—
603C22—361no—
604C22—361no—
605C22—361no—
606C22C2×D3×#6711yescharacteristic
607C4—21no—
608C4—41no—
609C4—62no—
610C4—122no—
611C4—361no—
612C4D3×#21312yes—
613C4C2×#379611yescharacteristic
614C4#6430711yescharacteristic
615C3—21no—
616C3#8098011yescharacteristic, complemented
617C3#8348211yescharacteristic, complemented
618C2—42no—
619C2—64no—
620C2—242no—
621C2—721no—
622C2#1059488911yescharacteristic
623C2C2×D3×#21311yescharacteristic
624C2#1059546411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
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 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×D4×D12C2semidirect
2. #10593896C2semidirect
3. C4×#3753C2semidirect
4. C3×#5007C2semidirect
5. #10591448C2semidirect
6. D3×#832C2semidirect
7. #10590576C2semidirect
8. #10590438C2semidirect
9. #10590355C2semidirect
10. #10590329C2semidirect
11. #10590277C2semidirect
19. C4×C4⋊(C3⋊D3)C22semidirect
25. C3×#869C22semidirect
26. #63909C22semidirect
28. D3×C4⋊Dic3C22semidirect
30. C2×#3714C22semidirect
31. C2×D3×C3⋊C8C22semidirect
33. #63636C22semidirect
34. #63634C22semidirect
35. C4×C3⋊(C3⋊C8)C22semidirect
37. C3×#807C22semidirect
38. C3×C4⋊(C3⋊C8)C22semidirect
39. #63563C22semidirect
40. #63562C22semidirect
41. #63562C22semidirect
42. (C2×D3)⋊(C3⋊C8)C22semidirect
46. D4×D12D3semidirect
59. #5007D3semidirect
142. #869C2×D3semidirect
164. #807C2×D3semidirect
165. C4⋊(C3⋊C8)C2×D3semidirect
177. C32×D4#41semidirect
195. C3×D12D8semidirect
380. C3×D4#237semidirect
381. C3×D4#239semidirect
421. D12#213semidirect
538. C32#3294semidirect
558. D4#3796semidirect
616. C3#80980semidirect
617. C3#83482semidirect

Maximal subgroups

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

subgroupindex
C3×D4×D122
#105938962
C4×#37532
C3×#50072
#105914482
D3×#8322
#105905762
#105904382
#105903552
#105903292
#105902772
#834823
#809803