Finite Group Databasebeta

← #11792447

Subgroups — #11792447

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
1C22×C3×D24C211yesmaximal, characteristic, complemented
2C2×#63911C211yesmaximal, characteristic, complemented
3C22×#3714C211yesmaximal, characteristic, complemented
4C2×#63648C211yesmaximal, characteristic, complemented
5#10591318C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic, complemented
7C3×#4550C211yesmaximal, characteristic, complemented
8#72044—31nomaximal
9#68674—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×#626—22no—
14C22×C32×C8C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×C3×D24—22no—
19C2×C3×D24—22no—
20C2×C3×D24—22no—
21C2×(C2×D3)⋊Dic3—22no—
22#63911—22no—
23#63911—22no—
24C2×#3714—22no—
25C2×#3714—22no—
26C2×#3714—22no—
27#63648—22no—
28#63563—22no—
29C22×C3×D8—31no—
30C2×#940—31no—
31C22×#213—31no—
32C22×D24—31no—
33C22×D24D311yescharacteristic, complemented
34C2×#874—31no—
35#5221—31no—
36C2×#832—31no—
37C2×#821—31no—
38C2×#821—31no—
39C2×#821—31no—
40C2×#821—61no—
41#4939—31no—
42C3×#336—31no—
43#4550D311yescharacteristic, complemented
44C23×C3⋊D3—21no—
45C23×C3×D3—21no—
46C23×C3×D3—21no—
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)D412yes—
55C22×C3×Dic3D412yes—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
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×D12D412yes—
67C2×C3×D12D412yescomplemented
68C2×#626—28no—
69C2×#626—44no—
70C2×#626—44no—
71C2×C32×C8—21no—
72C2×C32×C8—21no—
73C2×C32×C8D412yescomplemented
74C4⋊(C3⋊Dic3)—21no—
75C4⋊(C3⋊Dic3)—21no—
76C3×C4×Dic3—21no—
77C3×C4×Dic3—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8D412yescomplemented
81C3×D24—28no—
82(C2×D3)⋊Dic3—44no—
83#3714—28no—
84#2011—91noSylow
85C22×C3×D4—31no—
86C22×C3×D4—31no—
87C22×#67—62no—
88C22×D12—31no—
89C22×D12—31no—
90C22×D12—61no—
91C22×D12—62no—
92C22×D12C2×D311yescharacteristic
93C22×D12C2×D311yescharacteristic
94C2×C3×D8—62no—
95C2×C3×D8—62no—
96C2×C3×D8—62no—
97C22×C3×C8—21no—
98C22×C3×C8—31no—
99C22×C3×C8C2×D311yescharacteristic
100C22×C3×C8C2×D311yescharacteristic
101C2×C3×C42—31no—
102C2×#217—62no—
103#940—62no—
104#940—62no—
105C2×#213—62no—
106C2×#213—62no—
107C2×#213—62no—
108C2×(C2×D3)⋊C4—62no—
109C2×C4⋊Dic3—31no—
110C2×C4⋊Dic3—31no—
111C2×C4⋊Dic3—61no—
112C2×C4×Dic3C2×D311yescharacteristic
113C22×C3⋊C8C2×D311yescharacteristic
114C2×D24—22no—
115C2×D24—22no—
116C2×D24—22no—
117C2×D24—62no—
118C2×D24—62no—
119C2×D24—62no—
120#874—62no—
121#874—62no—
122#832—62no—
123#821—64no—
124#821—62no—
125#821—62no—
126#821—62no—
127C23×C32C2×D411yescharacteristic
128C22×C3⋊D3—22no—
129C22×C3⋊D3—41no—
130C22×C3⋊D3—41no—
131C22×C3⋊D3—42no—
132C22×C3⋊D3—42no—
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—
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4#4111yescharacteristic
149C2×C3⋊Dic3—41no—
150C2×C3⋊Dic3—42no—
151C4⋊(C3⋊D3)—22no—
152C4⋊(C3⋊D3)—22no—
153C4⋊(C3⋊D3)—41no—
154C4⋊(C3⋊D3)—41no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3D814yescomplemented
158C3×D12—22no—
159C3×D12—22no—
160C3×D12—22no—
161C3×D12—22no—
162C3×D12—41no—
163C3×D12—41no—
164C3×D12—41no—
165C3×D12—41no—
166#626—416no—
167C32×C8—22no—
168C3×C3⋊C8—22no—
169C22×D8—31no—
170C22×D8—91no—
171C2×#127—91no—
172C2×#102—91no—
173C2×#102—91no—
174#390—91no—
175#336—31no—
176C24×C3—61no—
177C24×C3—61no—
178C23×D3—21no—
179C23×D3—21no—
180C23×D3—61no—
181C23×D3—61no—
182C23×D3—121no—
183C2×C3×D4—32no—
184C2×C3×D4—32no—
185C2×C3×D4—61no—
186C2×C3×D4—61no—
187C2×C3×D4—61no—
188C2×C3×D4—61no—
189C2×C3×D4—61no—
190C2×C3×D4—61no—
191C2×C3×D4—61no—
192C2×C3×D4—61no—
193C2×C3×D4—61no—
194C2×C3×D4—61no—
195C22×C3×C4—21no—
196C22×C3×C4—32no—
197C22×C3×C4C22×D311yescharacteristic
198C22×C3×C4C22×D311yescharacteristic
199C2×#67—68no—
200C2×#67—124no—
201C2×#67—124no—
202C22×Dic3—61no—
203C22×Dic3—61no—
204C22×Dic3—121no—
205C22×Dic3D1212yes—
206C2×D12—21no—
207C2×D12—21no—
208C2×D12—21no—
209C2×D12—21no—
210C2×D12—21no—
211C2×D12—21no—
212C2×D12—21no—
213C2×D12—21no—
214C2×D12—21no—
215C2×D12—21no—
216C2×D12—32no—
217C2×D12—32no—
218C2×D12—62no—
219C2×D12—62no—
220C2×D12—62no—
221C2×D12—61no—
222C2×D12—61no—
223C2×D12—61no—
224C2×D12—61no—
225C2×D12—61no—
226C2×D12—61no—
227C2×D12—61no—
228C2×D12—61no—
229C2×D12—68no—
230C2×D12—61no—
231C2×D12—61no—
232C2×D12—121no—
233C2×D12—121no—
234C2×D12—121no—
235C2×D12—124no—
236C2×D12—124no—
237C2×D12#6712yes—
238C2×D12#6712yescomplemented
239C3×D8—68no—
240C2×C3×C8—21no—
241C2×C3×C8—21no—
242C2×C3×C8—21no—
243C2×C3×C8—21no—
244C2×C3×C8—22no—
245C2×C3×C8—32no—
246C2×C3×C8—41no—
247C2×C3×C8—41no—
248C2×C3×C8—61no—
249C2×C3×C8—61no—
250C2×C3×C8D1212yescomplemented
251C2×C3×C8#6712yescomplemented
252C3×C42—61no—
253C3×C42—61no—
254#217—124no—
255#213—68no—
256(C2×D3)⋊C4—124no—
257C4⋊Dic3—62no—
258C4⋊Dic3—61no—
259C4⋊Dic3—61no—
260C4⋊Dic3—61no—
261C4⋊Dic3—61no—
262C4⋊Dic3—121no—
263C4×Dic3—21no—
264C4×Dic3—21no—
265C2×C3⋊C8—21no—
266C2×C3⋊C8—21no—
267C2×C3⋊C8D1212yescomplemented
268D24—28no—
269D24—68no—
270C22×C32#12011yescharacteristic
271C22×C32#12111yescharacteristic
272C22×C32#12711yescharacteristic
273C22×C32C2×D812yes—
274C22×C32AGL(1,ℤ/8)12yes—
275C2×C3⋊D3—42no—
276C2×C3⋊D3—44no—
277C2×C3⋊D3—82no—
278C2×C3⋊D3—81no—
279C2×C3⋊D3—81no—
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—91no—
299C22×D4—182no—
300C2×D8—62no—
301C2×D8—62no—
302C2×D8—62no—
303C2×D8—182no—
304C2×D8—182no—
305C2×D8—182no—
306C22×C8—31no—
307C22×C8D3211yescharacteristic
308#127—182no—
309#127—182no—
310C2×C4⋊C4—91no—
311C2×C22⋊C4—182no—
312C2×C42—31no—
313#102—182no—
314#102—182no—
315C23×C3—21no—
316C23×C3—62no—
317C23×C3—62no—
318C23×C3—121no—
319C23×C3—121no—
320C23×C3—121no—
321C23×C3—121no—
322C23×C3—122no—
323C23×C3—122no—
324C23×C3—122no—
325C23×C3—122no—
326C23×C3C2×D1211yescharacteristic
327C23×C3D3×D411yescharacteristic
328C22×D3—22no—
329C22×D3—22no—
330C22×D3—42no—
331C22×D3—42no—
332C22×D3—42no—
333C22×D3—42no—
334C22×D3—41no—
335C22×D3—41no—
336C22×D3—41no—
337C22×D3—41no—
338C22×D3—62no—
339C22×D3—62no—
340C22×D3—122no—
341C22×D3—122no—
342C22×D3—122no—
343C22×D3—121no—
344C22×D3—121no—
345C22×D3—122no—
346C22×D3—122no—
347C22×D3—122no—
348C22×D3—122no—
349C22×D3—121no—
350C22×D3—121no—
351C22×D3—242no—
352C22×D3—242no—
353C3×D4—62no—
354C3×D4—62no—
355C3×D4—62no—
356C3×D4—62no—
357C3×D4—121no—
358C3×D4—121no—
359C3×D4—121no—
360C3×D4—121no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—34no—
368C2×C3×C4—62no—
369C2×C3×C4—62no—
370C2×C3×C4C2×D1211yescharacteristic
371C2×C3×C4C2×D1211yescharacteristic
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4D3×D411yescharacteristic
374C2×C3×C4D3×D411yescharacteristic
375C2×C3×C4D3×D411yescharacteristic
376C2×C3×C4D3×D411yescharacteristic
377C2×C3×C4#23711yescharacteristic
378C2×C3×C4#23911yescharacteristic
379C2×C3×C4C2×#6711yescharacteristic
380C2×C3×C4C2×#6711yescharacteristic
381C2×C3×C4C2×#6711yescharacteristic
382#67—1216no—
383C2×Dic3—22no—
384C2×Dic3—22no—
385C2×Dic3—122no—
386C2×Dic3—121no—
387C2×Dic3—122no—
388C2×Dic3—122no—
389C2×Dic3—121no—
390C2×Dic3—242no—
391C2×Dic3D2414yescomplemented
392D12—22no—
393D12—22no—
394D12—22no—
395D12—22no—
396D12—41no—
397D12—41no—
398D12—41no—
399D12—41no—
400D12—64no—
401D12—62no—
402D12—62no—
403D12—62no—
404D12—62no—
405D12—122no—
406D12—122no—
407D12—122no—
408D12—1216no—
409D12—121no—
410D12—121no—
411D12—121no—
412D12—121no—
413C3×C8—22no—
414C3×C8—22no—
415C3×C8—42no—
416C3×C8—62no—
417C3⋊C8—22no—
418C2×C32#39211yescharacteristic
419C2×C32#44712yes—
420C2×C32#45912yes—
421C2×C32#49311yescharacteristic
422C2×C32#49611yescharacteristic
423C3⋊D3—82no—
424C3×D3—82no—
425C3×D3—82no—
426C24—61no—
427C24—61no—
428C24—181no—
429C2×D4—32no—
430C2×D4—32no—
431C2×D4—61no—
432C2×D4—61no—
433C2×D4—61no—
434C2×D4—61no—
435C2×D4—61no—
436C2×D4—61no—
437C2×D4—61no—
438C2×D4—61no—
439C2×D4—61no—
440C2×D4—61no—
441C2×D4—92no—
442C2×D4—188no—
443C2×D4—181no—
444C2×D4—181no—
445C2×D4—181no—
446C2×D4—181no—
447C2×D4—181no—
448C2×D4—364no—
449C2×D4—364no—
450C22×C4—32no—
451C22×C4—181no—
452C22×C4C2×D3211yescharacteristic
453D8—68no—
454D8—188no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—32no—
458C2×C8—61no—
459C2×C8—61no—
460C2×C8#62612yescomplemented
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—122no—
472C22×C3—122no—
473C22×C3—124no—
474C22×C3—124no—
475C22×C3—241no—
476C22×C3—241no—
477C22×C3—241no—
478C22×C3—241no—
479C22×C3—242no—
480C22×C3—242no—
481C22×C3#87411yescharacteristic
482C22×C3#88211yescharacteristic
483C22×C3#89511yescharacteristic
484C22×C3C2×D2412yes—
485C22×C3#90812yes—
486C22×C3D3×D812yes—
487C22×C3#91112yes—
488C22×C3#93711yescharacteristic
489C22×C3#93911yescharacteristic
490C22×C3#94011yescharacteristic
491C2×D3—44no—
492C2×D3—44no—
493C2×D3—42no—
494C2×D3—42no—
495C2×D3—82no—
496C2×D3—81no—
497C2×D3—81no—
498C2×D3—81no—
499C2×D3—81no—
500C2×D3—82no—
501C2×D3—124no—
502C2×D3—124no—
503C2×D3—122no—
504C2×D3—122no—
505C2×D3—124no—
506C2×D3—244no—
507C2×D3—244no—
508C2×D3—242no—
509C2×D3—242no—
510C2×D3—242no—
511C2×D3—241no—
512C2×D3—241no—
513C2×D3—241no—
514C2×D3—241no—
515C2×D3—242no—
516C3×C4—21no—
517C3×C4—21no—
518C3×C4—21no—
519C3×C4—21no—
520C3×C4—64no—
521C3×C4#88211yescharacteristic
522C3×C4#88211yescharacteristic
523C3×C4#89511yescharacteristic
524C3×C4#89511yescharacteristic
525C3×C4#93711yescharacteristic
526C3×C4#93811yescharacteristic
527C3×C4#93911yescharacteristic
528C3×C4#95311yescharacteristic
529Dic3—24no—
530Dic3—242no—
531Dic3—241no—
532Dic3—241no—
533C32#201111yescharacteristic, complemented, Sylow
534C23—62no—
535C23—62no—
536C23—122no—
537C23—122no—
538C23—122no—
539C23—122no—
540C23—121no—
541C23—121no—
542C23—121no—
543C23—121no—
544C23—182no—
545C23—362no—
546C23—362no—
547C23—361no—
548C23—361no—
549C23D3×D1211yescharacteristic
550D4—62no—
551D4—62no—
552D4—62no—
553D4—62no—
554D4—121no—
555D4—121no—
556D4—121no—
557D4—121no—
558D4—182no—
559D4—182no—
560D4—3616no—
561D4—361no—
562D4—361no—
563C2×C4—34no—
564C2×C4—62no—
565C2×C4—62no—
566C2×C4—362no—
567C2×C4—361no—
568C2×C4#379611yescharacteristic
569C2×C4D3×D1211yescharacteristic
570C2×C4#380211yescharacteristic
571C2×C4C2×#62611yescharacteristic
572C2×C4D3×#6711yescharacteristic
573C2×C4D3×#6711yescharacteristic
574C8—22no—
575C8—62no—
576C2×C3—22no—
577C2×C3—21no—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—22no—
581C2×C3—242no—
582C2×C3—242no—
583C2×C3#467111yescharacteristic
584C2×C3#469511yescharacteristic
585C2×C3#471211yescharacteristic
586C2×C3#473212yes—
587C2×C3#484312yes—
588C2×C3#515012yes—
589C2×C3#515111yescharacteristic
590C2×C3#515411yescharacteristic
591C2×C3#515612yes—
592C2×C3#522311yescharacteristic
593D3—82no—
594D3—82no—
595D3—244no—
596D3—242no—
597D3—242no—
598C22—124no—
599C22—122no—
600C22—122no—
601C22—124no—
602C22—242no—
603C22—241no—
604C22—241no—
605C22—241no—
606C22—241no—
607C22—242no—
608C22—362no—
609C22—364no—
610C22—722no—
611C22—721no—
612C22—721no—
613C22D3×D2412yes—
614C22#6379512yes—
615C22#6388611yescharacteristic
616C22#6391111yescharacteristic
617C22#6392211yescharacteristic
618C4—64no—
619C4—721no—
620C4#6388611yescharacteristic
621C4#6391611yescharacteristic
622C4#6392211yescharacteristic
623C4#6397711yescharacteristic
624C3—21no—
625C3#6867411yescharacteristic, complemented
626C3#7204411yescharacteristic, complemented
627C2—242no—
628C2—242no—
629C2—722no—
630C2#1059075312yes—
631C2#1059088011yescharacteristic
632C2#1059088311yescharacteristic
633C2#1059094412yes—
634C2#1059139111yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
hypercenterC22×C8D32
hypocenterC32#2011
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C3×D24C2semidirect
2. C2×#63911C2semidirect
3. C22×#3714C2semidirect
4. C2×#63648C2semidirect
5. #10591318C2semidirect
6. C2×#63563C2semidirect
7. C3×#4550C2semidirect
33. C22×D24D3semidirect
43. #4550D3semidirect
67. C2×C3×D12D4semidirect
73. C2×C32×C8D4semidirect
80. C2×C3×C3⋊C8D4semidirect
157. C2×C3×Dic3D8semidirect
238. C2×D12#67semidirect
250. C2×C3×C8D12semidirect
251. C2×C3×C8#67semidirect
267. C2×C3⋊C8D12semidirect
391. C2×Dic3D24semidirect
460. C2×C8#626semidirect
533. C32#2011semidirect
625. C3#68674semidirect
626. C3#72044semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D242
C2×#639112
C22×#37142
C2×#636482
#105913182
C2×#635632
C3×#45502
#720443
#686743