Finite Group Databasebeta

← #11792441

Subgroups — #11792441

Order 1152.

1189 conjugacy classes of subgroups.

The subgroup lattice has 655 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3753C211yesmaximal, characteristic, complemented
2C22×C3×#213C211yesmaximal, characteristic, complemented
3C2×#63911C211yesmaximal, characteristic, complemented
4C3×#5221C211yesmaximal, characteristic, complemented
5C2×#63564C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#72044—31nomaximal
9#69658—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×#626—22no—
14C2×#3753—22no—
15C2×#3753—22no—
16C2×#3753—22no—
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×#217—22no—
19C2×C3×#213—22no—
20C2×C3×#213—22no—
21C2×C3×#213—22no—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25#63911—22no—
26#63911—22no—
27#63564—22no—
28#63562—22no—
29C22×C3×D8—31no—
30C2×#940—31no—
31C22×#213—31no—
32C22×#213—31no—
33C22×#213—61no—
34C22×#213D311yescharacteristic, complemented
35C2×#874—31no—
36C3×#390—31no—
37#5221D311yescharacteristic, complemented
38C2×#832—31no—
39C2×#821—31no—
40C2×#809—31no—
41C2×#809—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×D4D412yescomplemented
53C22×C32×C4C2311yescharacteristic
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)D412yes—
60C22×C3×Dic3—21no—
61C22×C3×Dic3D412yes—
62C2×C3×D12—21no—
63C2×C3×D12—21no—
64C2×C3×D12—21no—
65C2×C3×D12—21no—
66C2×C3×D12—21no—
67C2×C3×D12D412yes—
68C2×#626—28no—
69C2×#626—44no—
70C2×#626—44no—
71#3753—28no—
72C2×C3⋊(C3⋊C8)—21no—
73C2×C3⋊(C3⋊C8)—21no—
74C2×C3⋊(C3⋊C8)D412yescomplemented
75C3×#217—44no—
76C3×#213—28no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3—21no—
79C3×C4×Dic3—21no—
80C3×C4×Dic3—21no—
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8—21no—
83C2×C3×C3⋊C8D412yescomplemented
84#2011—91noSylow
85C22×C3×D4—21no—
86C22×C3×D4—31no—
87C22×C3×D4C2×D311yescharacteristic
88C22×C3×D4C2×D311yescharacteristic
89C22×#67—62no—
90C22×D12—31no—
91C22×D12—31no—
92C22×D12—61no—
93C22×D12—62no—
94C22×D12C2×D311yescharacteristic
95C2×C3×D8—62no—
96C2×C3×D8—62no—
97C2×C3×D8—62no—
98C22×C3×C8—31no—
99C2×C3×C4⋊C4—31no—
100C2×C3×C22⋊C4—62no—
101C2×C3×C42—31no—
102C2×#217—22no—
103#940—62no—
104#940—62no—
105C2×#213—22no—
106C2×#213—22no—
107C2×#213—22no—
108C2×#213—62no—
109C2×#213—62no—
110C2×#213—62no—
111C2×#213—62no—
112C2×#213—64no—
113C2×#213—64no—
114C2×#213—64no—
115C2×#213—62no—
116C2×#213—62no—
117C2×C4⋊Dic3C2×D311yescharacteristic
118C2×C4×Dic3C2×D311yescharacteristic
119C22×C3⋊C8—31no—
120C22×C3⋊C8—31no—
121C22×C3⋊C8—61no—
122C22×C3⋊C8C2×D311yescharacteristic
123#874—62no—
124#874—62no—
125#832—62no—
126#821—62no—
127#809—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
155C4⋊(C3⋊D3)—22no—
156C4⋊(C3⋊D3)—22no—
157C4⋊(C3⋊D3)—41no—
158C4⋊(C3⋊D3)—41no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—41no—
162C2×C3×Dic3—42no—
163C2×C3×Dic3D814yescomplemented
164C3×D12—22no—
165C3×D12—22no—
166C3×D12—41no—
167C3×D12—41no—
168#626—416no—
169C3⋊(C3⋊C8)—22no—
170C3×C3⋊C8—22no—
171C22×D8—31no—
172C22×D8—91no—
173C2×#127—91no—
174C2×#102—91no—
175C2×#102—91no—
176#390—31no—
177#336—91no—
178C24×C3—21no—
179C24×C3—21no—
180C24×C3—41no—
181C24×C3—61no—
182C23×D3—21no—
183C23×D3—61no—
184C23×D3—61no—
185C23×D3—121no—
186C2×C3×D4—22no—
187C2×C3×D4—22no—
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—21no—
198C2×C3×D4—22no—
199C2×C3×D4—32no—
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×D4D1212yescomplemented
209C2×C3×D4#6712yescomplemented
210C22×C3×C4—21no—
211C22×C3×C4—32no—
212C22×C3×C4—61no—
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C2×#67—68no—
216C2×#67—124no—
217C2×#67—124no—
218C22×Dic3—21no—
219C22×Dic3#6712yes—
220C2×D12—21no—
221C2×D12—21no—
222C2×D12—21no—
223C2×D12—21no—
224C2×D12—21no—
225C2×D12—32no—
226C2×D12—32no—
227C2×D12—62no—
228C2×D12—62no—
229C2×D12—62no—
230C2×D12—61no—
231C2×D12—61no—
232C2×D12—61no—
233C2×D12—61no—
234C2×D12—61no—
235C2×D12—61no—
236C2×D12—61no—
237C2×D12—61no—
238C2×D12—68no—
239C2×D12—61no—
240C2×D12—61no—
241C2×D12—121no—
242C2×D12—121no—
243C2×D12—121no—
244C2×D12—124no—
245C2×D12—124no—
246C2×D12#6712yes—
247C3×D8—68no—
248C2×C3×C8—32no—
249C2×C3×C8—61no—
250C2×C3×C8—61no—
251C3×C4⋊C4—61no—
252C3×C4⋊C4—61no—
253C3×C22⋊C4—124no—
254C3×C42—61no—
255C3×C42—61no—
256#217—44no—
257#213—28no—
258#213—616no—
259#213—68no—
260#213—68no—
261C4⋊Dic3—21no—
262C4⋊Dic3—21no—
263C4×Dic3—21no—
264C4×Dic3—21no—
265C2×C3⋊C8—21no—
266C2×C3⋊C8—21no—
267C2×C3⋊C8—32no—
268C2×C3⋊C8—32no—
269C2×C3⋊C8—62no—
270C2×C3⋊C8—62no—
271C2×C3⋊C8—62no—
272C2×C3⋊C8—61no—
273C2×C3⋊C8—61no—
274C2×C3⋊C8—61no—
275C2×C3⋊C8—61no—
276C2×C3⋊C8#6712yescomplemented
277C22×C32—42no—
278C22×C32—44no—
279C22×C32—82no—
280C22×C32—81no—
281C22×C32—81no—
282C22×C32#12011yescharacteristic
283C22×C32#12111yescharacteristic
284C22×C32#12711yescharacteristic
285C22×C32C2×D812yes—
286C22×C32AGL(1,ℤ/8)12yes—
287C2×C3⋊D3—42no—
288C2×C3⋊D3—44no—
289C2×C3⋊D3—82no—
290C2×C3⋊D3—81no—
291C2×C3⋊D3—81no—
292C2×C3×D3—42no—
293C2×C3×D3—44no—
294C2×C3×D3—82no—
295C2×C3×D3—81no—
296C2×C3×D3—81no—
297C32×C4#12011yescharacteristic
298C32×C4#12011yescharacteristic
299C32×C4#12111yescharacteristic
300C32×C4#12111yescharacteristic
301C3×Dic3—24no—
302C3×Dic3—81no—
303C22×D4—31no—
304C22×D4—91no—
305C22×D4—182no—
306C22×D4D3211yescharacteristic
307C2×D8—62no—
308C2×D8—62no—
309C2×D8—62no—
310C2×D8—182no—
311C2×D8—182no—
312C2×D8—182no—
313C22×C8—31no—
314C22×C8—91no—
315#127—182no—
316#127—182no—
317C2×C4⋊C4—31no—
318C2×C22⋊C4—62no—
319C2×C42—31no—
320#102—182no—
321#102—182no—
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—21no—
325C23×C3—42no—
326C23×C3—42no—
327C23×C3—42no—
328C23×C3—42no—
329C23×C3—42no—
330C23×C3—42no—
331C23×C3—41no—
332C23×C3—41no—
333C23×C3—41no—
334C23×C3—41no—
335C23×C3—42no—
336C23×C3—62no—
337C23×C3—82no—
338C23×C3—82no—
339C23×C3—121no—
340C23×C3—122no—
341C23×C3—121no—
342C23×C3—122no—
343C23×C3D3×D411yescharacteristic
344C23×C3C2×#6711yescharacteristic
345C22×D3—22no—
346C22×D3—42no—
347C22×D3—42no—
348C22×D3—41no—
349C22×D3—41no—
350C22×D3—62no—
351C22×D3—62no—
352C22×D3—122no—
353C22×D3—122no—
354C22×D3—122no—
355C22×D3—122no—
356C22×D3—122no—
357C22×D3—121no—
358C22×D3—122no—
359C22×D3—121no—
360C22×D3—121no—
361C22×D3—121no—
362C22×D3—122no—
363C22×D3—242no—
364C22×D3—242no—
365C3×D4—24no—
366C3×D4—22no—
367C3×D4—22no—
368C3×D4—22no—
369C3×D4—22no—
370C3×D4—42no—
371C3×D4—42no—
372C3×D4—42no—
373C3×D4—41no—
374C3×D4—41no—
375C3×D4—41no—
376C3×D4—41no—
377C3×D4—62no—
378C3×D4—62no—
379C3×D4—121no—
380C3×D4—121no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—34no—
388C2×C3×C4—62no—
389C2×C3×C4—62no—
390C2×C3×C4—122no—
391C2×C3×C4—121no—
392C2×C3×C4C2×D1211yescharacteristic
393C2×C3×C4#23511yescharacteristic
394C2×C3×C4D3×D411yescharacteristic
395C2×C3×C4D3×D411yescharacteristic
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4D3×D411yescharacteristic
400C2×C3×C4#23711yescharacteristic
401C2×C3×C4C2×#6711yescharacteristic
402C2×C3×C4C2×#6711yescharacteristic
403C2×C3×C4C2×#6711yescharacteristic
404#67—1216no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—42no—
408C2×Dic3—41no—
409C2×Dic3#21314yescomplemented
410D12—22no—
411D12—22no—
412D12—41no—
413D12—41no—
414D12—64no—
415D12—62no—
416D12—62no—
417D12—62no—
418D12—62no—
419D12—122no—
420D12—122no—
421D12—122no—
422D12—1216no—
423D12—121no—
424D12—121no—
425D12—121no—
426D12—121no—
427C3×C8—62no—
428C3⋊C8—22no—
429C3⋊C8—64no—
430C3⋊C8—62no—
431C3⋊C8—62no—
432C2×C32—82no—
433C2×C32#39211yescharacteristic
434C2×C32#44712yes—
435C2×C32#45912yes—
436C2×C32#49311yescharacteristic
437C2×C32#49611yescharacteristic
438C3⋊D3—82no—
439C3×D3—82no—
440C24—21no—
441C24—61no—
442C24—181no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—32no—
449C2×D4—61no—
450C2×D4—61no—
451C2×D4—61no—
452C2×D4—61no—
453C2×D4—61no—
454C2×D4—92no—
455C2×D4—188no—
456C2×D4—181no—
457C2×D4—181no—
458C2×D4—181no—
459C2×D4—181no—
460C2×D4—181no—
461C2×D4—364no—
462C2×D4—364no—
463C2×D4#62612yescomplemented
464C22×C4—32no—
465C22×C4—61no—
466C22×C4C2×D3211yescharacteristic
467D8—68no—
468D8—188no—
469C2×C8—32no—
470C2×C8—61no—
471C2×C8—61no—
472C2×C8—92no—
473C2×C8—181no—
474C2×C8—181no—
475C4⋊C4—61no—
476C4⋊C4—61no—
477C22⋊C4—124no—
478C42—61no—
479C42—61no—
480C22×C3—22no—
481C22×C3—22no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—44no—
486C22×C3—44no—
487C22×C3—42no—
488C22×C3—42no—
489C22×C3—44no—
490C22×C3—84no—
491C22×C3—84no—
492C22×C3—82no—
493C22×C3—82no—
494C22×C3—81no—
495C22×C3—81no—
496C22×C3—82no—
497C22×C3—82no—
498C22×C3—81no—
499C22×C3—81no—
500C22×C3—122no—
501C22×C3—124no—
502C22×C3—242no—
503C22×C3—241no—
504C22×C3—241no—
505C22×C3D3×D812yes—
506C22×C3#91112yes—
507C22×C3#93011yescharacteristic
508C22×C3C2×#21312yes—
509C22×C3#93711yescharacteristic
510C22×C3#93711yescharacteristic
511C22×C3#93911yescharacteristic
512C22×C3#94011yescharacteristic
513C22×C3#94011yescharacteristic
514C22×C3#94912yes—
515C2×D3—44no—
516C2×D3—42no—
517C2×D3—82no—
518C2×D3—81no—
519C2×D3—81no—
520C2×D3—124no—
521C2×D3—124no—
522C2×D3—122no—
523C2×D3—122no—
524C2×D3—124no—
525C2×D3—244no—
526C2×D3—244no—
527C2×D3—242no—
528C2×D3—242no—
529C2×D3—242no—
530C2×D3—241no—
531C2×D3—241no—
532C2×D3—242no—
533C2×D3—241no—
534C2×D3—241no—
535C3×C4—21no—
536C3×C4—21no—
537C3×C4—21no—
538C3×C4—21no—
539C3×C4—64no—
540C3×C4—241no—
541C3×C4#88211yescharacteristic
542C3×C4#88211yescharacteristic
543C3×C4#88411yescharacteristic
544C3×C4#88411yescharacteristic
545C3×C4#93711yescharacteristic
546C3×C4#93811yescharacteristic
547C3×C4#93911yescharacteristic
548C3×C4#95311yescharacteristic
549Dic3—24no—
550Dic3—81no—
551C32#201111yescharacteristic, complemented, Sylow
552C23—22no—
553C23—42no—
554C23—42no—
555C23—41no—
556C23—41no—
557C23—62no—
558C23—122no—
559C23—122no—
560C23—121no—
561C23—121no—
562C23—182no—
563C23—362no—
564C23—362no—
565C23—361no—
566C23—361no—
567C23D3×#6711yescharacteristic
568D4—22no—
569D4—22no—
570D4—41no—
571D4—41no—
572D4—62no—
573D4—62no—
574D4—121no—
575D4—121no—
576D4—182no—
577D4—182no—
578D4—3616no—
579D4—361no—
580D4—361no—
581C2×C4—34no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4—122no—
585C2×C4—121no—
586C2×C4#380411yescharacteristic
587C2×C4C2×#62611yescharacteristic
588C2×C4D3×#6711yescharacteristic
589C2×C4D3×#6711yescharacteristic
590C2×C4#381111yescharacteristic
591C2×C4#381111yescharacteristic
592C8—62no—
593C8—182no—
594C2×C3—22no—
595C2×C3—21no—
596C2×C3—22no—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—84no—
600C2×C3—82no—
601C2×C3—82no—
602C2×C3—242no—
603C2×C3#496011yescharacteristic
604C2×C3#501512yes—
605C2×C3#503612yes—
606C2×C3#505811yescharacteristic
607C2×C3#507311yescharacteristic
608C2×C3#515012yes—
609C2×C3#515111yescharacteristic
610C2×C3#515411yescharacteristic
611C2×C3#515612yes—
612C2×C3#522311yescharacteristic
613D3—82no—
614D3—244no—
615D3—242no—
616D3—242no—
617C22—42no—
618C22—44no—
619C22—82no—
620C22—81no—
621C22—81no—
622C22—124no—
623C22—122no—
624C22—242no—
625C22—241no—
626C22—241no—
627C22—364no—
628C22—362no—
629C22—722no—
630C22—721no—
631C22—721no—
632C22D3×#21312yes—
633C22#6392512yes—
634C22#6397811yescharacteristic
635C22#6397911yescharacteristic
636C22#6398311yescharacteristic
637C4—64no—
638C4—241no—
639C4#6395811yescharacteristic
640C4#6397111yescharacteristic
641C4#6397711yescharacteristic
642C4#6398111yescharacteristic
643C3—21no—
644C3#6965811yescharacteristic, complemented
645C3#7204411yescharacteristic, complemented
646C2—82no—
647C2—242no—
648C2—722no—
649C2#1059148112yes—
650C2#1059148211yescharacteristic
651C2#1059148311yescharacteristic
652C2#1059151512yes—
653C2#1059172411yescharacteristic
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. C22×#3753C2semidirect
2. C22×C3×#213C2semidirect
3. C2×#63911C2semidirect
4. C3×#5221C2semidirect
5. C2×#63564C2semidirect
6. C2×#63562C2semidirect
7. #10589155C2semidirect
34. C22×#213D3semidirect
37. #5221D3semidirect
52. C2×C32×D4D4semidirect
74. C2×C3⋊(C3⋊C8)D4semidirect
83. C2×C3×C3⋊C8D4semidirect
163. C2×C3×Dic3D8semidirect
208. C2×C3×D4D12semidirect
209. C2×C3×D4#67semidirect
276. C2×C3⋊C8#67semidirect
409. C2×Dic3#213semidirect
463. C2×D4#626semidirect
551. C32#2011semidirect
644. C3#69658semidirect
645. C3#72044semidirect

Maximal subgroups

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

subgroupindex
C22×#37532
C22×C3×#2132
C2×#639112
C3×#52212
C2×#635642
C2×#635622
#105891552
#720443
#696583