Finite Group Databasebeta

← #11863955

Subgroups — #11863955

Order 1152.

2083 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×D4C211yesmaximal, characteristic, complemented
2C2×C3×#932C211yesmaximal, characteristic, complemented
3#10595022C211yesmaximal, characteristic, complemented
4C2×#63823C211yesmaximal, characteristic, complemented
5#10592914C211yesmaximal, characteristic, complemented
6#10591458C214yesmaximal, complemented
7#10591447C214yesmaximal, complemented
8#10591086C211yesmaximal, characteristic, complemented
9#10591069C211yesmaximal, characteristic, complemented
10#84038—31nomaximal
11#83944—31nomaximal
12C24×C3×D3—21no—
13C22×C32×D4C2211yescharacteristic
14C22×C3×#67—21no—
15C2×C3×D3×D4—24no—
16C2×C3×D3×D4—24no—
17C2×C3×D3×D4—22no—
18C2×C3×D3×D4C2214yes—
19C2×C3×#235C2211yescharacteristic, complemented
20C22×C3×D12C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22#64135C2211yescharacteristic, complemented
23C2×#3748C2211yescharacteristic, complemented
24C2×C3×#214C2212yescomplemented
25C3×#932—24no—
26C2×C3×#213C2212yescomplemented
27C2×C3×#208C2211yescharacteristic, complemented
28#63976—21no—
29#63961—21no—
30#63908C2212yescomplemented
31C4×#625—22no—
32#63856C2212yescomplemented
33C2×#3715C2212yescomplemented
34#63823—24no—
35C2×#3713C2212yescomplemented
36#63659C2214yescomplemented
37#63563C2214yescomplemented
38(C2×D3)⋊(C3⋊C8)C2214yescomplemented
39C23×C3×D4—31no—
40C22×D3×D4D311yescharacteristic, complemented
41C2×C3×AGL(1,ℤ/8)—31no—
42#5828—31no—
43C2×#949—31no—
44C2×#932—31no—
45C2×#932D311yescharacteristic, complemented
46#5791—31no—
47#5218—34no—
48#5217—34no—
49#5215—31no—
50#5215—31no—
51#5215—31no—
52#5215—61no—
53#5207—31no—
54#5169—34no—
55#5156—34no—
56#5131—31no—
57#5126—31no—
58C24×C32—21no—
59C23×C3×D3—28no—
60C23×C3×D3—21no—
61C23×C3×D3—24no—
62C23×C3×D3—48no—
63C23×C3×D3D411yescharacteristic
64C2×C32×D4—21no—
65C2×C32×D4—22no—
66C2×C32×D4D414yescomplemented
67C2×C32×D4C2312yes—
68C22×C32×C4C2311yescharacteristic
69C2×C3×#67—28no—
70C2×C3×#67—21no—
71C2×C3×#67—24no—
72C22×C3×Dic3D411yescharacteristic
73C3×D3×D4—216no—
74C3×D3×D4—28no—
75C3×D3×D4—28no—
76C3×#235—22no—
77C3×#235—22no—
78C2×C3×D12—21no—
79C2×C3×D12—22no—
80C2×C3×D12D414yescomplemented
81C2×C3×D12C2312yes—
82C2×C3×D12C2311yescharacteristic, complemented
83C2×C3×C4×D3—22no—
84C2×C3×C4×D3—22no—
85C2×C3×C4×D3—21no—
86C2×C3×C4×D3D412yes—
87C2×C3×C4×D3C2312yes—
88C2×C3×Dic6C2311yescharacteristic, complemented
89C2×#625—22no—
90#3757—21no—
91C4⋊(C3⋊Dic3)C2312yescomplemented
92C4×C3⋊Dic3—21no—
93#3748—22no—
94C2×C3⋊(C3⋊C8)C2312yescomplemented
95C3×#214—24no—
96C3×#213—24no—
97C3×#208—22no—
98C2×C3×C3⋊C8C2312yescomplemented
99#3724—22no—
100(C2×D3)⋊Dic3—22no—
101(C2×D3)⋊Dic3—22no—
102#3715—24no—
103#3713—24no—
104#3003—91noSylow
105C25×C3—61no—
106C24×D3—21no—
107C2×C3×#41—31no—
108C22×C3×D4—21no—
109C22×C3×D4—34no—
110C22×C3×D4—31no—
111C22×C3×D4—62no—
112C22×C3×D4—61no—
113C22×C3×D4—64no—
114C22×C3×D4—64no—
115C22×C3×D4C2×D311yescharacteristic
116C22×C3×D4C2×D311yescharacteristic
117C23×C3×C4—31no—
118C22×#67—21no—
119C2×D3×D4—24no—
120C2×D3×D4—24no—
121C2×D3×D4—22no—
122C2×D3×D4C2×D314yes—
123C2×#235C2×D311yescharacteristic, complemented
124C22×D12C2×D311yescharacteristic
125C22×C4×D3C2×D311yescharacteristic
126C3×AGL(1,ℤ/8)—64no—
127C2×C3×SD16—32no—
128C2×C3×D8—32no—
129C2×C3×M16—31no—
130#953—61no—
131#949—64no—
132#946—32no—
133C2×#215—32no—
134#938—32no—
135#937—61no—
136#935—61no—
137C2×#214—32no—
138C2×#214C2×D312yescomplemented
139#932—24no—
140#932—64no—
141C2×#213—32no—
142C2×#213—32no—
143C2×#213C2×D312yescomplemented
144#930—32no—
145#929—61no—
146C4×#67—62no—
147C4×#67—62no—
148#926—31no—
149#926—31no—
150#926—61no—
151#924—32no—
152C2×#208—31no—
153C2×#208—31no—
154C2×#208—61no—
155C2×#208C2×D311yescharacteristic, complemented
156#832—34no—
157#832—34no—
158#832—34no—
159#832—64no—
160#830—34no—
161#821—34no—
162(C2×D3)⋊C8—34no—
163C23×C32—24no—
164C23×C32—22no—
165C23×C32—44no—
166C23×C32C2×D411yescharacteristic
167C22×C3×D3—22no—
168C22×C3×D3—24no—
169C22×C3×D3—216no—
170C22×C3×D3—24no—
171C22×C3×D3—22no—
172C22×C3×D3—21no—
173C22×C3×D3—432no—
174C22×C3×D3—48no—
175C22×C3×D3—44no—
176C22×C3×D3—48no—
177C22×C3×D3C2×D412yes—
178C32×D4—24no—
179C32×D4—22no—
180C32×D4C2×D414yes—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D412yes—
183C2×C32×C4C2×D412yes—
184C2×C32×C4C2411yescharacteristic
185C2×C3⋊Dic3—22no—
186C3×#67—216no—
187C3×#67—42no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3C2×D412yes—
191C3×D12—24no—
192C3×D12—22no—
193C3×D12—21no—
194C3×D12—21no—
195C3×D12C2×D414yes—
196C3×C4×D3—24no—
197C3×C4×D3—22no—
198C3×C4×D3—22no—
199C3×C4×D3—42no—
200C3×Dic6—21no—
201C3×Dic6—21no—
202#625—44no—
203C3⋊(C3⋊C8)—22no—
204C3×C3⋊C8—22no—
205C23×D4—31no—
206C2×AGL(1,ℤ/8)—31no—
207C2×AGL(1,ℤ/8)—91no—
208#525—91no—
209#450—94no—
210#447—94no—
211#418—91no—
212#418—91no—
213#407—91no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3—31no—
217C24×C3—41no—
218C24×C3—64no—
219C24×C3—68no—
220C24×C3—61no—
221C24×C3—128no—
222C23×D3—28no—
223C23×D3—21no—
224C23×D3—24no—
225C23×D3—48no—
226C23×D3#6711yescharacteristic
227C3×#41—62no—
228C3×#41—62no—
229C2×C3×Q8—31no—
230C2×C3×D4—21no—
231C2×C3×D4—22no—
232C2×C3×D4—21no—
233C2×C3×D4—22no—
234C2×C3×D4—24no—
235C2×C3×D4—22no—
236C2×C3×D4—34no—
237C2×C3×D4—32no—
238C2×C3×D4—31no—
239C2×C3×D4—42no—
240C2×C3×D4—41no—
241C2×C3×D4—64no—
242C2×C3×D4—68no—
243C2×C3×D4—616no—
244C2×C3×D4—68no—
245C2×C3×D4—68no—
246C2×C3×D4—61no—
247C2×C3×D4—61no—
248C2×C3×D4—62no—
249C2×C3×D4#6714yescomplemented
250C2×C3×D4#6714yescomplemented
251C2×C3×D4C22×D312yes—
252C2×C3×D4C22×D312yes—
253C22×C3×C4—21no—
254C22×C3×C4—31no—
255C22×C3×C4—32no—
256C22×C3×C4—32no—
257C22×C3×C4—62no—
258C22×C3×C4—62no—
259C22×C3×C4—61no—
260C22×C3×C4C22×D311yescharacteristic
261C22×C3×C4C22×D311yescharacteristic
262C2×#67—28no—
263C2×#67—21no—
264C2×#67—24no—
265C2×#67—62no—
266C2×#67—62no—
267C22×Dic3#6711yescharacteristic
268D3×D4—216no—
269D3×D4—28no—
270D3×D4—28no—
271#235—22no—
272#235—22no—
273C2×D12—22no—
274C2×D12—21no—
275C2×D12#6714yescomplemented
276C2×D12C22×D312yes—
277C2×D12C22×D311yescharacteristic, complemented
278C2×C4×D3—22no—
279C2×C4×D3—22no—
280C2×C4×D3—21no—
281C2×C4×D3#6712yes—
282C2×C4×D3C22×D312yes—
283C2×Dic6C22×D311yescharacteristic, complemented
284C3×SD16—64no—
285C3×D8—64no—
286C3×M16—62no—
287C2×C3×C8—32no—
288#217—62no—
289#217—61no—
290#217—61no—
291#217—62no—
292#217—121no—
293#215—64no—
294#214—24no—
295#214—64no—
296#213—24no—
297#213—64no—
298#213—64no—
299(C2×D3)⋊C4—62no—
300(C2×D3)⋊C4—62no—
301C4⋊Dic3—32no—
302C4⋊Dic3—32no—
303C4⋊Dic3—62no—
304Dic3⋊C4—62no—
305Dic3⋊C4—62no—
306C4×Dic3—61no—
307C4×Dic3—61no—
308C4×Dic3—121no—
309#208—22no—
310#208—62no—
311#208—62no—
312#208—122no—
313C2×C3⋊C8—32no—
314C2×C3⋊C8—32no—
315C2×C3⋊C8—62no—
316C2×C3⋊C8C22×D312yescomplemented
317C22×C32—22no—
318C22×C32—24no—
319C22×C32—48no—
320C22×C32—44no—
321C22×C32#12012yes—
322C22×C32C22×D411yescharacteristic
323C2×C3×D3—28no—
324C2×C3×D3—22no—
325C2×C3×D3—22no—
326C2×C3×D3—24no—
327C2×C3×D3—432no—
328C2×C3×D3—48no—
329C2×C3×D3—44no—
330C2×C3×D3—41no—
331C2×C3×D3—42no—
332C2×C3×D3AGL(1,ℤ/8)14yescomplemented
333C32×C4#12012yes—
334C32×C4C22×D411yescharacteristic
335C32×C4C22×D411yescharacteristic
336C3⋊Dic3—42no—
337C3×Dic3—22no—
338C3×Dic3—41no—
339C25—61no—
340C2×#41—31no—
341C22×D4—34no—
342C22×D4—31no—
343C22×D4—62no—
344C22×D4—61no—
345C22×D4—64no—
346C22×D4—64no—
347C22×D4D3211yescharacteristic
348C23×C4—31no—
349AGL(1,ℤ/8)—64no—
350AGL(1,ℤ/8)—184no—
351C2×SD16—32no—
352C2×SD16—92no—
353C2×D8—32no—
354C2×D8—92no—
355C2×M16—31no—
356C2×M16—91no—
357#123—181no—
358C22⋊Q8—92no—
359#121—92no—
360#120—181no—
361C4×D4—182no—
362#117—91no—
363#102—94no—
364#102—94no—
365C22⋊C8—94no—
366C23×C3—24no—
367C23×C3—24no—
368C23×C3—22no—
369C23×C3—22no—
370C23×C3—21no—
371C23×C3—32no—
372C23×C3—42no—
373C23×C3—44no—
374C23×C3—44no—
375C23×C3—44no—
376C23×C3—64no—
377C23×C3—616no—
378C23×C3—62no—
379C23×C3—64no—
380C23×C3—62no—
381C23×C3—61no—
382C23×C3—84no—
383C23×C3—124no—
384C23×C3—128no—
385C23×C3—1232no—
386C23×C3—128no—
387C23×C3D3×D411yescharacteristic
388C23×C3C2×#6711yescharacteristic
389C22×D3—22no—
390C22×D3—24no—
391C22×D3—216no—
392C22×D3—24no—
393C22×D3—22no—
394C22×D3—21no—
395C22×D3—432no—
396C22×D3—48no—
397C22×D3—44no—
398C22×D3—48no—
399C22×D3C2×#6712yes—
400C3×Q8—61no—
401C3×Q8—61no—
402C3×D4—24no—
403C3×D4—24no—
404C3×D4—22no—
405C3×D4—22no—
406C3×D4—24no—
407C3×D4—34no—
408C3×D4—42no—
409C3×D4—44no—
410C3×D4—616no—
411C3×D4—64no—
412C3×D4—62no—
413C3×D4—61no—
414C3×D4—61no—
415C3×D4—122no—
416C3×D4C2×#6714yes—
417C3×D4C2×#6714yes—
418C2×C3×C4—21no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—21no—
422C2×C3×C4—32no—
423C2×C3×C4—62no—
424C2×C3×C4—64no—
425C2×C3×C4—62no—
426C2×C3×C4—62no—
427C2×C3×C4—61no—
428C2×C3×C4—122no—
429C2×C3×C4D3×D411yescharacteristic
430C2×C3×C4D3×D412yes—
431C2×C3×C4C2×#6712yes—
432C2×C3×C4C2×#6712yes—
433C2×C3×C4C2×#6711yescharacteristic
434C2×C3×C4C2×#6712yes—
435C2×C3×C4C23×D311yescharacteristic
436C2×C3×C4C23×D311yescharacteristic
437#67—216no—
438#67—42no—
439#67—124no—
440#67—124no—
441C2×Dic3—22no—
442C2×Dic3—21no—
443C2×Dic3—62no—
444C2×Dic3—62no—
445C2×Dic3—122no—
446C2×Dic3C2×#6712yes—
447D12—24no—
448D12—21no—
449D12—22no—
450D12—21no—
451D12C2×#6714yes—
452C4×D3—24no—
453C4×D3—22no—
454C4×D3—22no—
455C4×D3—42no—
456Dic6—21no—
457Dic6—21no—
458C3×C8—62no—
459C3⋊C8—22no—
460C3⋊C8—62no—
461C3⋊C8—62no—
462C3⋊C8—122no—
463C2×C32—22no—
464C2×C32—44no—
465C2×C32C2×#12011yescharacteristic
466C2×C32C2×AGL(1,ℤ/8)12yes—
467C3×D3—24no—
468C3×D3—44no—
469C3×D3—81no—
470C24—21no—
471C24—31no—
472C24—64no—
473C24—68no—
474C24—61no—
475C24—128no—
476#41—62no—
477#41—62no—
478C2×Q8—31no—
479C2×D4—22no—
480C2×D4—21no—
481C2×D4—32no—
482C2×D4—31no—
483C2×D4—34no—
484C2×D4—64no—
485C2×D4—68no—
486C2×D4—616no—
487C2×D4—68no—
488C2×D4—68no—
489C2×D4—61no—
490C2×D4—62no—
491C2×D4—61no—
492C2×D4—182no—
493C2×D4#62514yescomplemented
494C2×D4C2×D3212yes—
495C22×C4—31no—
496C22×C4—32no—
497C22×C4—32no—
498C22×C4—62no—
499C22×C4—62no—
500C22×C4—61no—
501C22×C4C2×D3211yescharacteristic
502SD16—64no—
503SD16—184no—
504D8—64no—
505D8—184no—
506M16—62no—
507M16—182no—
508C2×C8—32no—
509C2×C8—92no—
510C4⋊C4—92no—
511C4⋊C4—182no—
512C22⋊C4—182no—
513C22⋊C4—182no—
514C22⋊C4—181no—
515C42—181no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—24no—
519C22×C3—24no—
520C22×C3—21no—
521C22×C3—22no—
522C22×C3—34no—
523C22×C3—42no—
524C22×C3—44no—
525C22×C3—48no—
526C22×C3—48no—
527C22×C3—44no—
528C22×C3—44no—
529C22×C3—68no—
530C22×C3—62no—
531C22×C3—62no—
532C22×C3—64no—
533C22×C3—84no—
534C22×C3—88no—
535C22×C3—128no—
536C22×C3—1232no—
537C22×C3—124no—
538C22×C3—122no—
539C22×C3—121no—
540C22×C3#93712yes—
541C22×C3#95312yes—
542C22×C3C2×D3×D411yescharacteristic
543C22×C3C22×#6711yescharacteristic
544C2×D3—28no—
545C2×D3—22no—
546C2×D3—22no—
547C2×D3—24no—
548C2×D3—432no—
549C2×D3—48no—
550C2×D3—44no—
551C2×D3—42no—
552C2×D3—41no—
553C2×D3#93214yescomplemented
554C3×C4—21no—
555C3×C4—21no—
556C3×C4—22no—
557C3×C4—62no—
558C3×C4—121no—
559C3×C4#93712yes—
560C3×C4#95312yes—
561C3×C4C2×D3×D411yescharacteristic
562C3×C4C22×#6711yescharacteristic
563C3×C4C22×#6711yescharacteristic
564C3×C4C22×#6711yescharacteristic
565Dic3—22no—
566Dic3—41no—
567Dic3—122no—
568Dic3—122no—
569Dic3—242no—
570C32#300311yescharacteristic, complemented, Sylow
571C23—22no—
572C23—24no—
573C23—32no—
574C23—44no—
575C23—64no—
576C23—616no—
577C23—62no—
578C23—62no—
579C23—64no—
580C23—61no—
581C23—124no—
582C23—128no—
583C23—1232no—
584C23—128no—
585C23D3×#6711yescharacteristic
586Q8—61no—
587Q8—61no—
588D4—22no—
589D4—24no—
590D4—34no—
591D4—616no—
592D4—62no—
593D4—61no—
594D4—61no—
595D4—64no—
596D4—122no—
597D4—364no—
598D4C2×#62514yes—
599C2×C4—32no—
600C2×C4—62no—
601C2×C4—62no—
602C2×C4—62no—
603C2×C4—64no—
604C2×C4—61no—
605C2×C4—122no—
606C2×C4—182no—
607C2×C4C2×#62512yes—
608C2×C4D3×#6712yes—
609C2×C4D3×#6711yescharacteristic
610C2×C4C22×D3211yescharacteristic
611C8—62no—
612C8—182no—
613C2×C3—22no—
614C2×C3—22no—
615C2×C3—22no—
616C2×C3—21no—
617C2×C3—42no—
618C2×C3—44no—
619C2×C3—44no—
620C2×C3—64no—
621C2×C3—84no—
622C2×C3—124no—
623C2×C3—241no—
624C2×C3D3×AGL(1,ℤ/8)12yes—
625C2×C3C2×#93212yes—
626C2×C3C2×#93711yescharacteristic
627C2×C3C2×#95311yescharacteristic
628D3—24no—
629D3—44no—
630D3—81no—
631C22—22no—
632C22—24no—
633C22—34no—
634C22—48no—
635C22—44no—
636C22—68no—
637C22—62no—
638C22—62no—
639C22—64no—
640C22—128no—
641C22—1232no—
642C22—124no—
643C22—122no—
644C22—121no—
645C22#6397612yes—
646C22C2×D3×#6711yescharacteristic
647C4—62no—
648C4—121no—
649C4—362no—
650C4#6397612yes—
651C4C22×#62511yescharacteristic
652C4C2×D3×#6711yescharacteristic
653C3—21no—
654C3#8394411yescharacteristic, complemented
655C3#8403811yescharacteristic, complemented
656C2—22no—
657C2—44no—
658C2—64no—
659C2—124no—
660C2—241no—
661C2D3×#93212yes—
662C2C2×#6397611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3003
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×D4C2semidirect
2. C2×C3×#932C2semidirect
3. #10595022C2semidirect
4. C2×#63823C2semidirect
5. #10592914C2semidirect
6. #10591458C2semidirect
7. #10591447C2semidirect
8. #10591086C2semidirect
9. #10591069C2semidirect
19. C2×C3×#235C22semidirect
22. #64135C22semidirect
23. C2×#3748C22semidirect
24. C2×C3×#214C22semidirect
26. C2×C3×#213C22semidirect
27. C2×C3×#208C22semidirect
30. #63908C22semidirect
32. #63856C22semidirect
33. C2×#3715C22semidirect
35. C2×#3713C22semidirect
36. #63659C22semidirect
37. #63563C22semidirect
38. (C2×D3)⋊(C3⋊C8)C22semidirect
40. C22×D3×D4D3semidirect
45. C2×#932D3semidirect
66. C2×C32×D4D4semidirect
80. C2×C3×D12D4semidirect
82. C2×C3×D12C23semidirect
88. C2×C3×Dic6C23semidirect
91. C4⋊(C3⋊Dic3)C23semidirect
94. C2×C3⋊(C3⋊C8)C23semidirect
98. C2×C3×C3⋊C8C23semidirect
123. C2×#235C2×D3semidirect
138. C2×#214C2×D3semidirect
143. C2×#213C2×D3semidirect
155. C2×#208C2×D3semidirect
249. C2×C3×D4#67semidirect
250. C2×C3×D4#67semidirect
275. C2×D12#67semidirect
277. C2×D12C22×D3semidirect
283. C2×Dic6C22×D3semidirect
316. C2×C3⋊C8C22×D3semidirect
332. C2×C3×D3AGL(1,ℤ/8)semidirect
493. C2×D4#625semidirect
553. C2×D3#932semidirect
570. C32#3003semidirect
654. C3#83944semidirect
655. C3#84038semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×D42
C2×C3×#9322
#105950222
C2×#638232
#105929142
#105914582
#105914472
#105910862
#105910692
#840383
#839443