Finite Group Databasebeta

← #11792445

Subgroups — #11792445

Order 1152.

1121 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#940C211yesmaximal, characteristic, complemented
2C22×C3×#213C211yesmaximal, characteristic, complemented
3C22×#3713C211yesmaximal, characteristic, complemented
4C2×#63659C211yesmaximal, characteristic, complemented
5#10591318C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#72044—31nomaximal
9#71767—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×C3×#67—22no—
12C22×C3×D12C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×#940—22no—
17C3×#940—22no—
18C2×C3×#213—22no—
19C2×C3×#213—22no—
20C2×C3×#213—22no—
21C2×C3×C4×Dic3C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×(C2×D3)⋊Dic3—22no—
24C2×#3713—22no—
25C2×#3713—22no—
26C2×#3713—22no—
27#63659—22no—
28#63563—22no—
29C22×C3×D8—31no—
30C2×C3×#127—31no—
31C2×#940D311yescharacteristic, complemented
32C22×#213—31no—
33C22×#213—31no—
34C22×#213D311yescharacteristic, complemented
35#5221—31no—
36C2×#832—31no—
37C2×#832—31no—
38C2×#832—31no—
39C2×#832—61no—
40C2×#821—31no—
41#4939—31no—
42#4550—31no—
43#4524—31no—
44C24×C32—21no—
45C23×C3×D3—21no—
46C23×C3×D3—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4—21no—
50C2×C32×D4—21no—
51C2×C32×D4—21no—
52C2×C32×D4D412yes—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3—21no—
55C2×C3×#67—28no—
56C2×C3×#67—44no—
57C2×C3×#67—44no—
58C22×C3×Dic3D412yes—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12—21no—
62C2×C3×D12—21no—
63C2×C3×D12—21no—
64C2×C3×D12—21no—
65C2×C3×D12—21no—
66C2×C3×D12—21no—
67C2×C3×D12—21no—
68C2×C3×D12—21no—
69C2×C3×D12D412yes—
70C2×C3×D12D412yescomplemented
71C4⋊(C3⋊Dic3)—21no—
72C4⋊(C3⋊Dic3)—21no—
73C2×C3⋊(C3⋊C8)—21no—
74C2×C3⋊(C3⋊C8)—21no—
75C2×C3⋊(C3⋊C8)D412yescomplemented
76C3×#213—28no—
77C3×C4×Dic3—21no—
78C3×C4×Dic3—21no—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8—21no—
81C2×C3×C3⋊C8D412yescomplemented
82(C2×D3)⋊Dic3—44no—
83#3713—28no—
84#2011—91noSylow
85C22×C3×D4—21no—
86C22×C3×D4—31no—
87C22×C3×D4—31no—
88C22×C3×D4—62no—
89C22×C3×D4C2×D311yescharacteristic
90C22×C3×D4C2×D311yescharacteristic
91C22×#67—22no—
92C22×D12C2×D311yescharacteristic
93C22×D12C2×D311yescharacteristic
94C2×C3×D8—62no—
95C2×C3×D8—62no—
96C2×C3×D8—62no—
97C22×C3×C8—31no—
98C3×#127—62no—
99C3×#127—62no—
100C2×C3×C42—31no—
101C2×#217—62no—
102#940—22no—
103#940—22no—
104C2×#213—22no—
105C2×#213—22no—
106C2×#213—22no—
107C2×#213—62no—
108C2×#213—62no—
109C2×#213—62no—
110C2×#213—62no—
111C2×#213—62no—
112C2×#213—62no—
113C2×(C2×D3)⋊C4—62no—
114C2×C4⋊Dic3—31no—
115C2×C4⋊Dic3—31no—
116C2×C4⋊Dic3—61no—
117C2×C4×Dic3C2×D311yescharacteristic
118C22×C3⋊C8—31no—
119C22×C3⋊C8—31no—
120C22×C3⋊C8—61no—
121C22×C3⋊C8C2×D311yescharacteristic
122#832—62no—
123#832—62no—
124#832—64no—
125#832—62no—
126#821—62no—
127C23×C32—22no—
128C23×C32—41no—
129C23×C32—41no—
130C23×C32—42no—
131C23×C32—42no—
132C23×C32C2×D411yescharacteristic
133C22×C3×D3—22no—
134C22×C3×D3—22no—
135C22×C3×D3—41no—
136C22×C3×D3—41no—
137C22×C3×D3—41no—
138C22×C3×D3—41no—
139C22×C3×D3—42no—
140C22×C3×D3—42no—
141C22×C3×D3—42no—
142C22×C3×D3—42no—
143C32×D4—22no—
144C32×D4—22no—
145C32×D4—41no—
146C32×D4—41no—
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4#4111yescharacteristic
153C2×C3⋊Dic3—41no—
154C2×C3⋊Dic3—42no—
155C3×#67—416no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3D814yescomplemented
159C3×D12—22no—
160C3×D12—22no—
161C3×D12—22no—
162C3×D12—22no—
163C3×D12—41no—
164C3×D12—41no—
165C3×D12—41no—
166C3×D12—41no—
167C3⋊(C3⋊C8)—22no—
168C3×C3⋊C8—22no—
169C22×D8—31no—
170C22×D8—91no—
171C2×#127—31no—
172C2×#102—91no—
173C2×#102—91no—
174#390—91no—
175#336—91no—
176C24×C3—21no—
177C24×C3—21no—
178C24×C3—41no—
179C24×C3—61no—
180C24×C3—61no—
181C23×D3—21no—
182C23×D3—21no—
183C2×C3×D4—22no—
184C2×C3×D4—22no—
185C2×C3×D4—21no—
186C2×C3×D4—21no—
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4—21no—
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—22no—
196C2×C3×D4—32no—
197C2×C3×D4—32no—
198C2×C3×D4—41no—
199C2×C3×D4—41no—
200C2×C3×D4—41no—
201C2×C3×D4—68no—
202C2×C3×D4—61no—
203C2×C3×D4—61no—
204C2×C3×D4—61no—
205C2×C3×D4—61no—
206C2×C3×D4—61no—
207C2×C3×D4—61no—
208C2×C3×D4—61no—
209C2×C3×D4—61no—
210C2×C3×D4—61no—
211C2×C3×D4—61no—
212C2×C3×D4—124no—
213C2×C3×D4—124no—
214C2×C3×D4#6712yes—
215C2×C3×D4#6712yes—
216C22×C3×C4—21no—
217C22×C3×C4—32no—
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C2×#67—28no—
221C2×#67—44no—
222C2×#67—44no—
223C22×Dic3—61no—
224C22×Dic3—61no—
225C22×Dic3—121no—
226C22×Dic3#6712yes—
227C2×D12—21no—
228C2×D12—21no—
229C2×D12—21no—
230C2×D12—21no—
231C2×D12—21no—
232C2×D12—21no—
233C2×D12—21no—
234C2×D12—21no—
235C2×D12—21no—
236C2×D12—21no—
237C2×D12#6712yes—
238C2×D12#6712yescomplemented
239C3×D8—68no—
240C2×C3×C8—32no—
241C2×C3×C8—61no—
242C2×C3×C8—61no—
243C3×C42—61no—
244C3×C42—61no—
245#217—124no—
246#213—28no—
247#213—68no—
248#213—68no—
249(C2×D3)⋊C4—124no—
250C4⋊Dic3—62no—
251C4⋊Dic3—61no—
252C4⋊Dic3—61no—
253C4⋊Dic3—61no—
254C4⋊Dic3—61no—
255C4⋊Dic3—121no—
256C4×Dic3—21no—
257C4×Dic3—21no—
258C2×C3⋊C8—21no—
259C2×C3⋊C8—21no—
260C2×C3⋊C8—32no—
261C2×C3⋊C8—32no—
262C2×C3⋊C8—62no—
263C2×C3⋊C8—61no—
264C2×C3⋊C8—61no—
265C2×C3⋊C8—61no—
266C2×C3⋊C8—61no—
267C2×C3⋊C8—121no—
268C2×C3⋊C8—121no—
269C2×C3⋊C8#6712yescomplemented
270C22×C32—42no—
271C22×C32—44no—
272C22×C32—82no—
273C22×C32—81no—
274C22×C32—81no—
275C22×C32#12011yescharacteristic
276C22×C32#12111yescharacteristic
277C22×C32#12711yescharacteristic
278C22×C32C2×D812yes—
279C22×C32AGL(1,ℤ/8)12yes—
280C2×C3×D3—42no—
281C2×C3×D3—42no—
282C2×C3×D3—44no—
283C2×C3×D3—44no—
284C2×C3×D3—82no—
285C2×C3×D3—82no—
286C2×C3×D3—81no—
287C2×C3×D3—81no—
288C2×C3×D3—81no—
289C2×C3×D3—81no—
290C32×C4#12011yescharacteristic
291C32×C4#12011yescharacteristic
292C32×C4#12111yescharacteristic
293C32×C4#12111yescharacteristic
294C3⋊Dic3—81no—
295C3×Dic3—24no—
296C22×D4—31no—
297C22×D4—31no—
298C22×D4—62no—
299C22×D4D3211yescharacteristic
300C2×D8—62no—
301C2×D8—62no—
302C2×D8—62no—
303C2×D8—182no—
304C2×D8—182no—
305C2×D8—182no—
306C22×C8—31no—
307C22×C8—91no—
308#127—62no—
309#127—62no—
310C2×C4⋊C4—91no—
311C2×C22⋊C4—182no—
312C2×C42—31no—
313#102—182no—
314#102—182no—
315C23×C3—22no—
316C23×C3—22no—
317C23×C3—21no—
318C23×C3—42no—
319C23×C3—42no—
320C23×C3—42no—
321C23×C3—42no—
322C23×C3—42no—
323C23×C3—42no—
324C23×C3—42no—
325C23×C3—41no—
326C23×C3—41no—
327C23×C3—41no—
328C23×C3—41no—
329C23×C3—62no—
330C23×C3—62no—
331C23×C3—82no—
332C23×C3—82no—
333C23×C3—122no—
334C23×C3—122no—
335C23×C3—122no—
336C23×C3—122no—
337C23×C3—121no—
338C23×C3—121no—
339C23×C3—121no—
340C23×C3—121no—
341C23×C3D3×D411yescharacteristic
342C23×C3C2×#6711yescharacteristic
343C22×D3—22no—
344C22×D3—22no—
345C22×D3—42no—
346C22×D3—42no—
347C22×D3—42no—
348C22×D3—42no—
349C22×D3—41no—
350C22×D3—41no—
351C22×D3—41no—
352C22×D3—41no—
353C3×D4—24no—
354C3×D4—22no—
355C3×D4—22no—
356C3×D4—22no—
357C3×D4—22no—
358C3×D4—42no—
359C3×D4—42no—
360C3×D4—42no—
361C3×D4—41no—
362C3×D4—41no—
363C3×D4—41no—
364C3×D4—41no—
365C3×D4—62no—
366C3×D4—62no—
367C3×D4—62no—
368C3×D4—62no—
369C3×D4—1216no—
370C3×D4—121no—
371C3×D4—121no—
372C3×D4—121no—
373C3×D4—121no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—34no—
381C2×C3×C4—62no—
382C2×C3×C4—62no—
383C2×C3×C4D3×D411yescharacteristic
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4D3×D411yescharacteristic
387C2×C3×C4D3×D411yescharacteristic
388C2×C3×C4#23711yescharacteristic
389C2×C3×C4#23711yescharacteristic
390C2×C3×C4C2×#6711yescharacteristic
391C2×C3×C4C2×#6711yescharacteristic
392C2×C3×C4C2×#6711yescharacteristic
393C2×C3×C4C2×#6711yescharacteristic
394C2×C3×C4C2×#6711yescharacteristic
395#67—416no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—122no—
399C2×Dic3—122no—
400C2×Dic3—122no—
401C2×Dic3—121no—
402C2×Dic3—121no—
403C2×Dic3—242no—
404C2×Dic3#21314yescomplemented
405D12—22no—
406D12—22no—
407D12—22no—
408D12—22no—
409D12—41no—
410D12—41no—
411D12—41no—
412D12—41no—
413C3×C8—62no—
414C3⋊C8—22no—
415C3⋊C8—62no—
416C3⋊C8—62no—
417C3⋊C8—122no—
418C2×C32—82no—
419C2×C32#39211yescharacteristic
420C2×C32#44712yes—
421C2×C32#45912yes—
422C2×C32#49311yescharacteristic
423C2×C32#49611yescharacteristic
424C3×D3—82no—
425C3×D3—82no—
426C24—21no—
427C24—61no—
428C24—61no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—32no—
435C2×D4—32no—
436C2×D4—68no—
437C2×D4—61no—
438C2×D4—61no—
439C2×D4—61no—
440C2×D4—61no—
441C2×D4—61no—
442C2×D4—61no—
443C2×D4—61no—
444C2×D4—61no—
445C2×D4—61no—
446C2×D4—61no—
447C2×D4—124no—
448C2×D4—124no—
449C2×D4#62512yes—
450C22×C4—32no—
451C22×C4—181no—
452C22×C4C2×D3211yescharacteristic
453D8—68no—
454D8—188no—
455C2×C8—32no—
456C2×C8—61no—
457C2×C8—61no—
458C2×C8—92no—
459C2×C8—181no—
460C2×C8—181no—
461C4⋊C4—181no—
462C4⋊C4—181no—
463C22⋊C4—364no—
464C42—61no—
465C42—61no—
466C22×C3—22no—
467C22×C3—22no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—44no—
472C22×C3—44no—
473C22×C3—44no—
474C22×C3—42no—
475C22×C3—42no—
476C22×C3—84no—
477C22×C3—84no—
478C22×C3—82no—
479C22×C3—82no—
480C22×C3—82no—
481C22×C3—81no—
482C22×C3—81no—
483C22×C3—82no—
484C22×C3—81no—
485C22×C3—81no—
486C22×C3—124no—
487C22×C3—122no—
488C22×C3—122no—
489C22×C3—124no—
490C22×C3—242no—
491C22×C3—241no—
492C22×C3—241no—
493C22×C3—242no—
494C22×C3—241no—
495C22×C3—241no—
496C22×C3D3×D812yes—
497C22×C3#91112yes—
498C22×C3C2×#21312yes—
499C22×C3#93212yes—
500C22×C3#93711yescharacteristic
501C22×C3#93811yescharacteristic
502C22×C3#93911yescharacteristic
503C22×C3#94011yescharacteristic
504C22×C3#94011yescharacteristic
505C22×C3#95311yescharacteristic
506C2×D3—44no—
507C2×D3—44no—
508C2×D3—42no—
509C2×D3—42no—
510C2×D3—81no—
511C2×D3—81no—
512C2×D3—82no—
513C2×D3—82no—
514C2×D3—81no—
515C2×D3—81no—
516C3×C4—21no—
517C3×C4—21no—
518C3×C4—21no—
519C3×C4—21no—
520C3×C4—64no—
521C3×C4#93711yescharacteristic
522C3×C4#93711yescharacteristic
523C3×C4#93711yescharacteristic
524C3×C4#93811yescharacteristic
525C3×C4#93911yescharacteristic
526C3×C4#93911yescharacteristic
527C3×C4#93911yescharacteristic
528C3×C4#95311yescharacteristic
529Dic3—24no—
530Dic3—242no—
531Dic3—241no—
532Dic3—241no—
533C32#201111yescharacteristic, complemented, Sylow
534C23—22no—
535C23—42no—
536C23—42no—
537C23—41no—
538C23—41no—
539C23—62no—
540C23—62no—
541C23—122no—
542C23—122no—
543C23—122no—
544C23—122no—
545C23—121no—
546C23—121no—
547C23—121no—
548C23—121no—
549C23D3×#6711yescharacteristic
550D4—22no—
551D4—22no—
552D4—41no—
553D4—41no—
554D4—62no—
555D4—62no—
556D4—62no—
557D4—62no—
558D4—1216no—
559D4—121no—
560D4—121no—
561D4—121no—
562D4—121no—
563C2×C4—34no—
564C2×C4—62no—
565C2×C4—62no—
566C2×C4—362no—
567C2×C4—361no—
568C2×C4#380511yescharacteristic
569C2×C4C2×#62511yescharacteristic
570C2×C4D3×#6711yescharacteristic
571C2×C4D3×#6711yescharacteristic
572C2×C4D3×#6711yescharacteristic
573C2×C4#381111yescharacteristic
574C8—62no—
575C8—182no—
576C2×C3—22no—
577C2×C3—22no—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—84no—
582C2×C3—82no—
583C2×C3—82no—
584C2×C3—242no—
585C2×C3—242no—
586C2×C3#507212yes—
587C2×C3#507311yescharacteristic
588C2×C3#507411yescharacteristic
589C2×C3#515012yes—
590C2×C3#515111yescharacteristic
591C2×C3#515411yescharacteristic
592C2×C3#515612yes—
593C2×C3#521712yes—
594C2×C3#522311yescharacteristic
595C2×C3#522311yescharacteristic
596D3—82no—
597D3—82no—
598C22—44no—
599C22—42no—
600C22—82no—
601C22—81no—
602C22—81no—
603C22—124no—
604C22—124no—
605C22—122no—
606C22—122no—
607C22—242no—
608C22—242no—
609C22—241no—
610C22—241no—
611C22—241no—
612C22—241no—
613C22D3×#21312yes—
614C22#6393212yes—
615C22#6397011yescharacteristic
616C22#6397611yescharacteristic
617C22#6397911yescharacteristic
618C4—64no—
619C4—721no—
620C4#6397011yescharacteristic
621C4#6397611yescharacteristic
622C4#6398011yescharacteristic
623C4#6398311yescharacteristic
624C3—21no—
625C3#7176711yescharacteristic, complemented
626C3#7204411yescharacteristic, complemented
627C2—82no—
628C2—242no—
629C2—242no—
630C2#1059142812yes—
631C2#1059144712yes—
632C2#1059146911yescharacteristic
633C2#1059148211yescharacteristic
634C2#1059172311yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32#2011
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#940C2semidirect
2. C22×C3×#213C2semidirect
3. C22×#3713C2semidirect
4. C2×#63659C2semidirect
5. #10591318C2semidirect
6. C2×#63563C2semidirect
7. #10589155C2semidirect
31. C2×#940D3semidirect
34. C22×#213D3semidirect
70. C2×C3×D12D4semidirect
75. C2×C3⋊(C3⋊C8)D4semidirect
81. C2×C3×C3⋊C8D4semidirect
158. C2×C3×Dic3D8semidirect
238. C2×D12#67semidirect
269. C2×C3⋊C8#67semidirect
404. C2×Dic3#213semidirect
533. C32#2011semidirect
625. C3#71767semidirect
626. C3#72044semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9402
C22×C3×#2132
C22×#37132
C2×#636592
#105913182
C2×#635632
#105891552
#720443
#717673