Finite Group Databasebeta

← #11792444

Subgroups — #11792444

Order 1152.

1269 conjugacy classes of subgroups.

The subgroup lattice has 661 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64149C211yesmaximal, characteristic, complemented
2C22×C3×#213C211yesmaximal, characteristic, complemented
3C22×#3714C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5#10591323C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic, complemented
7#10589156C211yesmaximal, characteristic, complemented
8#72044—31nomaximal
9#70209—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×#638—22no—
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14#64149—22no—
15#64149—22no—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C3×#213—22no—
18C2×C3×#213—22no—
19C2×C3×#213—22no—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×(C2×D3)⋊Dic3—22no—
24C2×#3714—22no—
25C2×#3714—22no—
26C2×#3714—22no—
27C3×#832—22no—
28#63564—22no—
29C22×C3×D8—31no—
30C2×#940—31no—
31C2×#940—31no—
32C2×#940—61no—
33C22×#213—31no—
34C22×#213D311yescharacteristic, complemented
35C22×D24—31no—
36C2×C3×#102—31no—
37#5221—31no—
38C2×#832D311yescharacteristic, complemented
39C2×#821—31no—
40#4988—31no—
41C2×#809—31no—
42#4550—31no—
43#4550—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
54C2×#638—28no—
55C2×#638—44no—
56C2×#638—44no—
57C22×C3⋊Dic3D412yes—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)—21no—
63C2×C4⋊(C3⋊D3)D412yes—
64C22×C3×Dic3—21no—
65C2×C3×D12—21no—
66C2×C3×D12—21no—
67C2×C3×D12—21no—
68C2×C3×D12—21no—
69C2×C3×D12—21no—
70C2×C3×D12D412yescomplemented
71C4×C3⋊Dic3—21no—
72C4×C3⋊Dic3—21no—
73C3×#213—28no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8D412yescomplemented
81C2×C3×C3⋊C8D412yescomplemented
82(C2×D3)⋊Dic3—44no—
83#3714—28no—
84#2011—91noSylow
85C22×C3×D4—21no—
86C22×C3×D4—31no—
87C22×C3×D4C2×D311yescharacteristic
88C22×C3×D4C2×D311yescharacteristic
89C22×#67—62no—
90C22×#67—62no—
91C22×#67—64no—
92C22×D12—31no—
93C22×D12—31no—
94C22×D12—61no—
95C22×D12C2×D311yescharacteristic
96C2×C3×D8—62no—
97C2×C3×D8—62no—
98C2×C3×D8—62no—
99C22×C3×C8—31no—
100C22×C3×C8—31no—
101C2×C3×C4⋊C4—31no—
102C2×#217—62no—
103#940—62no—
104#940—62no—
105#940—64no—
106#940—64no—
107#940—62no—
108#940—62no—
109C2×#213—22no—
110C2×#213—22no—
111C2×#213—22no—
112C2×#213—62no—
113C2×#213—62no—
114C2×#213—62no—
115C2×(C2×D3)⋊C4—62no—
116C2×C4⋊Dic3C2×D311yescharacteristic
117C2×C4×Dic3—31no—
118C2×C4×Dic3—31no—
119C2×C4×Dic3—61no—
120C22×C3⋊C8C2×D311yescharacteristic
121C22×C3⋊C8C2×D311yescharacteristic
122C2×D24—62no—
123C2×D24—62no—
124C2×D24—62no—
125C3×#102—62no—
126#832—22no—
127#821—62no—
128#809—62no—
129C23×C32—22no—
130C23×C32—41no—
131C23×C32—41no—
132C23×C32—42no—
133C23×C32—42no—
134C23×C32C2×D411yescharacteristic
135C22×C3⋊D3—22no—
136C22×C3⋊D3—41no—
137C22×C3⋊D3—41no—
138C22×C3⋊D3—42no—
139C22×C3⋊D3—42no—
140C22×C3×D3—22no—
141C22×C3×D3—41no—
142C22×C3×D3—41no—
143C22×C3×D3—42no—
144C22×C3×D3—42no—
145C32×D4—22no—
146C32×D4—22no—
147C32×D4—41no—
148C32×D4—41no—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4#4111yescharacteristic
155#638—416no—
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3D814yescomplemented
159C4⋊(C3⋊D3)—22no—
160C4⋊(C3⋊D3)—22no—
161C4⋊(C3⋊D3)—41no—
162C4⋊(C3⋊D3)—41no—
163C2×C3×Dic3—41no—
164C2×C3×Dic3—42no—
165C3×D12—22no—
166C3×D12—22no—
167C3×D12—41no—
168C3×D12—41no—
169C3×C3⋊C8—22no—
170C3×C3⋊C8—22no—
171C22×D8—31no—
172C22×D8—91no—
173C2×#127—91no—
174C2×#102—31no—
175C2×#102—91no—
176#390—91no—
177#336—91no—
178C24×C3—22no—
179C24×C3—21no—
180C24×C3—21no—
181C24×C3—61no—
182C23×D3—21no—
183C23×D3—62no—
184C23×D3—61no—
185C23×D3—61no—
186C2×C3×D4—22no—
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—21no—
196C2×C3×D4—21no—
197C2×C3×D4—22no—
198C2×C3×D4—32no—
199C2×C3×D4—41no—
200C2×C3×D4—41no—
201C2×C3×D4—41no—
202C2×C3×D4—41no—
203C2×C3×D4—61no—
204C2×C3×D4—61no—
205C2×C3×D4—61no—
206C2×C3×D4—61no—
207C2×C3×D4—61no—
208C2×C3×D4D1212yes—
209C2×C3×D4#6712yes—
210C22×C3×C4—21no—
211C22×C3×C4—61no—
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C2×#67—616no—
215C2×#67—68no—
216C2×#67—68no—
217C2×#67—124no—
218C2×#67—124no—
219C2×#67—128no—
220C2×#67—128no—
221C2×#67—124no—
222C2×#67—124no—
223C22×Dic3—21no—
224C22×Dic3—32no—
225C22×Dic3—32no—
226C22×Dic3—62no—
227C2×D12—21no—
228C2×D12—21no—
229C2×D12—21no—
230C2×D12—21no—
231C2×D12—21no—
232C2×D12—32no—
233C2×D12—32no—
234C2×D12—62no—
235C2×D12—61no—
236C2×D12—61no—
237C2×D12—61no—
238C2×D12—61no—
239C2×D12—61no—
240C2×D12—61no—
241C2×D12—61no—
242C2×D12—61no—
243C2×D12—62no—
244C2×D12—61no—
245C2×D12—61no—
246C2×D12—121no—
247C2×D12—121no—
248C2×D12—121no—
249C2×D12—121no—
250C2×D12#6712yescomplemented
251C3×D8—68no—
252C2×C3×C8—32no—
253C2×C3×C8—32no—
254C2×C3×C8—61no—
255C2×C3×C8—61no—
256C2×C3×C8—61no—
257C2×C3×C8—61no—
258C3×C4⋊C4—61no—
259C3×C4⋊C4—61no—
260#217—124no—
261#213—28no—
262#213—68no—
263(C2×D3)⋊C4—124no—
264C4⋊Dic3—21no—
265C4⋊Dic3—21no—
266C4×Dic3—62no—
267C4×Dic3—62no—
268C4×Dic3—61no—
269C4×Dic3—61no—
270C4×Dic3—61no—
271C4×Dic3—61no—
272C2×C3⋊C8—21no—
273C2×C3⋊C8—21no—
274C2×C3⋊C8—21no—
275C2×C3⋊C8—21no—
276C2×C3⋊C8#6712yescomplemented
277C2×C3⋊C8#6712yescomplemented
278D24—68no—
279C22×C32—42no—
280C22×C32—44no—
281C22×C32—82no—
282C22×C32—81no—
283C22×C32—81no—
284C22×C32#12011yescharacteristic
285C22×C32#12111yescharacteristic
286C22×C32#12711yescharacteristic
287C22×C32C2×D812yes—
288C22×C32AGL(1,ℤ/8)12yes—
289C2×C3⋊D3—42no—
290C2×C3⋊D3—44no—
291C2×C3⋊D3—82no—
292C2×C3⋊D3—81no—
293C2×C3⋊D3—81no—
294C2×C3×D3—42no—
295C2×C3×D3—44no—
296C2×C3×D3—82no—
297C2×C3×D3—81no—
298C2×C3×D3—81no—
299C32×C4#12011yescharacteristic
300C32×C4#12011yescharacteristic
301C32×C4#12111yescharacteristic
302C32×C4#12111yescharacteristic
303C3⋊Dic3—24no—
304C3×Dic3—81no—
305C22×D4—31no—
306C22×D4—91no—
307C22×D4—182no—
308C22×D4D3211yescharacteristic
309C2×D8—62no—
310C2×D8—62no—
311C2×D8—62no—
312C2×D8—182no—
313C2×D8—182no—
314C2×D8—182no—
315C22×C8—31no—
316C22×C8—31no—
317#127—182no—
318#127—182no—
319C2×C4⋊C4—31no—
320C2×C22⋊C4—182no—
321C2×C42—91no—
322#102—62no—
323#102—182no—
324C23×C3—24no—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3—21no—
328C23×C3—44no—
329C23×C3—44no—
330C23×C3—42no—
331C23×C3—42no—
332C23×C3—41no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3—42no—
336C23×C3—42no—
337C23×C3—41no—
338C23×C3—41no—
339C23×C3—41no—
340C23×C3—62no—
341C23×C3—121no—
342C23×C3—122no—
343C23×C3—122no—
344C23×C3—121no—
345C23×C3D3×D411yescharacteristic
346C23×C3D3×D411yescharacteristic
347C22×D3—22no—
348C22×D3—42no—
349C22×D3—42no—
350C22×D3—41no—
351C22×D3—41no—
352C22×D3—64no—
353C22×D3—62no—
354C22×D3—62no—
355C22×D3—122no—
356C22×D3—122no—
357C22×D3—124no—
358C22×D3—124no—
359C22×D3—121no—
360C22×D3—122no—
361C22×D3—122no—
362C22×D3—122no—
363C22×D3—122no—
364C22×D3—121no—
365C22×D3—121no—
366C22×D3—121no—
367C3×D4—22no—
368C3×D4—22no—
369C3×D4—22no—
370C3×D4—22no—
371C3×D4—42no—
372C3×D4—42no—
373C3×D4—42no—
374C3×D4—42no—
375C3×D4—41no—
376C3×D4—41no—
377C3×D4—41no—
378C3×D4—41no—
379C3×D4—62no—
380C3×D4—62no—
381C3×D4—121no—
382C3×D4—121no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—122no—
390C2×C3×C4—121no—
391C2×C3×C4C2×D1211yescharacteristic
392C2×C3×C4#23511yescharacteristic
393C2×C3×C4D3×D411yescharacteristic
394C2×C3×C4D3×D411yescharacteristic
395C2×C3×C4D3×D411yescharacteristic
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4#23711yescharacteristic
399C2×C3×C4C2×#6711yescharacteristic
400C2×C3×C4C2×#6711yescharacteristic
401C2×C3×C4C2×#6711yescharacteristic
402C2×C3×C4C2×#6711yescharacteristic
403#67—1232no—
404#67—1216no—
405#67—1216no—
406C2×Dic3—34no—
407C2×Dic3—34no—
408C2×Dic3—42no—
409C2×Dic3—41no—
410C2×Dic3—64no—
411C2×Dic3—64no—
412C2×Dic3—64no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416C2×Dic3—62no—
417D12—22no—
418D12—22no—
419D12—41no—
420D12—41no—
421D12—62no—
422D12—62no—
423D12—62no—
424D12—62no—
425D12—122no—
426D12—122no—
427D12—122no—
428D12—122no—
429D12—121no—
430D12—121no—
431D12—121no—
432D12—121no—
433C3×C8—62no—
434C3×C8—62no—
435C3⋊C8—22no—
436C3⋊C8—22no—
437C2×C32—82no—
438C2×C32#39211yescharacteristic
439C2×C32#44712yes—
440C2×C32#45912yes—
441C2×C32#49311yescharacteristic
442C2×C32#49611yescharacteristic
443C3⋊D3—82no—
444C3×D3—82no—
445C24—21no—
446C24—61no—
447C24—181no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—32no—
454C2×D4—61no—
455C2×D4—61no—
456C2×D4—61no—
457C2×D4—61no—
458C2×D4—61no—
459C2×D4—92no—
460C2×D4—188no—
461C2×D4—181no—
462C2×D4—181no—
463C2×D4—181no—
464C2×D4—181no—
465C2×D4—181no—
466C2×D4—364no—
467C2×D4—364no—
468C2×D4#62612yes—
469C22×C4—61no—
470C22×C4—92no—
471C22×C4C2×D3211yescharacteristic
472D8—68no—
473D8—188no—
474C2×C8—32no—
475C2×C8—32no—
476C2×C8—61no—
477C2×C8—61no—
478C2×C8—61no—
479C2×C8—61no—
480C4⋊C4—61no—
481C4⋊C4—61no—
482C22⋊C4—364no—
483C42—181no—
484C42—181no—
485C22×C3—22no—
486C22×C3—22no—
487C22×C3—21no—
488C22×C3—21no—
489C22×C3—21no—
490C22×C3—48no—
491C22×C3—44no—
492C22×C3—44no—
493C22×C3—42no—
494C22×C3—42no—
495C22×C3—44no—
496C22×C3—84no—
497C22×C3—82no—
498C22×C3—82no—
499C22×C3—82no—
500C22×C3—81no—
501C22×C3—81no—
502C22×C3—81no—
503C22×C3—81no—
504C22×C3—82no—
505C22×C3—122no—
506C22×C3—124no—
507C22×C3—241no—
508C22×C3—241no—
509C22×C3—242no—
510C22×C3#88211yescharacteristic
511C22×C3#88411yescharacteristic
512C22×C3D3×D812yes—
513C22×C3D3×D812yes—
514C22×C3#91112yes—
515C22×C3#91412yes—
516C22×C3#93711yescharacteristic
517C22×C3#93911yescharacteristic
518C22×C3#94011yescharacteristic
519C22×C3#94011yescharacteristic
520C2×D3—44no—
521C2×D3—42no—
522C2×D3—81no—
523C2×D3—81no—
524C2×D3—82no—
525C2×D3—124no—
526C2×D3—128no—
527C2×D3—124no—
528C2×D3—122no—
529C2×D3—122no—
530C2×D3—124no—
531C2×D3—244no—
532C2×D3—242no—
533C2×D3—242no—
534C2×D3—242no—
535C2×D3—241no—
536C2×D3—241no—
537C2×D3—241no—
538C2×D3—241no—
539C2×D3—242no—
540C3×C4—21no—
541C3×C4—21no—
542C3×C4—21no—
543C3×C4—21no—
544C3×C4—241no—
545C3×C4#88211yescharacteristic
546C3×C4#88411yescharacteristic
547C3×C4#93011yescharacteristic
548C3×C4#93711yescharacteristic
549C3×C4#93711yescharacteristic
550C3×C4#93811yescharacteristic
551C3×C4#93911yescharacteristic
552C3×C4#95311yescharacteristic
553Dic3—68no—
554Dic3—64no—
555Dic3—64no—
556Dic3—81no—
557C32#201111yescharacteristic, complemented, Sylow
558C23—22no—
559C23—42no—
560C23—42no—
561C23—41no—
562C23—41no—
563C23—62no—
564C23—122no—
565C23—122no—
566C23—121no—
567C23—121no—
568C23—182no—
569C23—362no—
570C23—362no—
571C23—361no—
572C23—361no—
573C23#381111yescharacteristic
574D4—22no—
575D4—22no—
576D4—41no—
577D4—41no—
578D4—62no—
579D4—62no—
580D4—121no—
581D4—121no—
582D4—182no—
583D4—182no—
584D4—3616no—
585D4—361no—
586D4—361no—
587C2×C4—94no—
588C2×C4—122no—
589C2×C4—121no—
590C2×C4—182no—
591C2×C4—182no—
592C2×C4#380411yescharacteristic
593C2×C4C2×#62611yescharacteristic
594C2×C4D3×#6711yescharacteristic
595C2×C4D3×#6711yescharacteristic
596C2×C4D3×#6711yescharacteristic
597C2×C4#381111yescharacteristic
598C8—62no—
599C8—62no—
600C2×C3—22no—
601C2×C3—22no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—84no—
606C2×C3—82no—
607C2×C3—82no—
608C2×C3—242no—
609C2×C3#477312yes—
610C2×C3#478612yes—
611C2×C3#496011yescharacteristic
612C2×C3#515012yes—
613C2×C3#515111yescharacteristic
614C2×C3#515111yescharacteristic
615C2×C3#515411yescharacteristic
616C2×C3#515612yes—
617C2×C3#517611yescharacteristic
618C2×C3#522311yescharacteristic
619D3—82no—
620D3—244no—
621D3—242no—
622D3—242no—
623C22—44no—
624C22—42no—
625C22—82no—
626C22—81no—
627C22—81no—
628C22—124no—
629C22—122no—
630C22—242no—
631C22—241no—
632C22—241no—
633C22—364no—
634C22—362no—
635C22—722no—
636C22—721no—
637C22—721no—
638C22#6392612yes—
639C22#6393712yes—
640C22#6397111yescharacteristic
641C22#6397911yescharacteristic
642C22#6398111yescharacteristic
643C4—184no—
644C4—241no—
645C4#6395811yescharacteristic
646C4#6397711yescharacteristic
647C4#6397811yescharacteristic
648C4#6398311yescharacteristic
649C3—21no—
650C3#7020911yescharacteristic, complemented
651C3#7204411yescharacteristic, complemented
652C2—82no—
653C2—242no—
654C2—722no—
655C2#1059143312yes—
656C2#1059145612yes—
657C2#1059147511yescharacteristic
658C2#1059148411yescharacteristic
659C2#1059172411yescharacteristic
subgroupG/H
centerC23#3811
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×#64149C2semidirect
2. C22×C3×#213C2semidirect
3. C22×#3714C2semidirect
4. C2×C3×#832C2semidirect
5. #10591323C2semidirect
6. C2×#63564C2semidirect
7. #10589156C2semidirect
34. C22×#213D3semidirect
38. C2×#832D3semidirect
70. C2×C3×D12D4semidirect
80. C2×C3×C3⋊C8D4semidirect
81. C2×C3×C3⋊C8D4semidirect
158. C2×C3⋊Dic3D8semidirect
250. C2×D12#67semidirect
276. C2×C3⋊C8#67semidirect
277. C2×C3⋊C8#67semidirect
557. C32#2011semidirect
650. C3#70209semidirect
651. C3#72044semidirect

Maximal subgroups

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

subgroupindex
C2×#641492
C22×C3×#2132
C22×#37142
C2×C3×#8322
#105913232
C2×#635642
#105891562
#720443
#702093