Finite Group Databasebeta

← #11863962

Subgroups — #11863962

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×D3×D12C211yesmaximal, characteristic, complemented
2C3×#5524C211yesmaximal, characteristic, complemented
3C2×#63825C211yesmaximal, characteristic, complemented
4C2×#63823C211yesmaximal, characteristic, complemented
5#10592700C211yesmaximal, characteristic, complemented
6C3×#5001C211yesmaximal, characteristic, complemented
7#10591069C211yesmaximal, characteristic, complemented
8#10590596C214yesmaximal, complemented
9#10590595C214yesmaximal, complemented
10#82927—31nomaximal
11#78926—31nomaximal
12C23×D32—21no—
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic, complemented
15C22×C3×D12C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×#626—21no—
18C2×D3×D12—24no—
19C2×D3×D12—24no—
20C2×D3×D12—22no—
21C2×D3×D12C2214yes—
22C32×#117C2211yescharacteristic, complemented
23C2×#3748C2211yescharacteristic, complemented
24C2×C3×#208C2211yescharacteristic, complemented
25C3×#897C2212yescomplemented
26C3×#895C2212yescomplemented
27C3×#886—21no—
28C3×#882—21no—
29C3×C4×D12—22no—
30C2×#3717C2212yescomplemented
31C2×#3715C2212yescomplemented
32#63825—24no—
33C2×#3714C2212yescomplemented
34#63823—24no—
35C2×#3713C2212yescomplemented
36#63636C2214yescomplemented
37C3×#809C2214yescomplemented
38(C2×D3)⋊(C3⋊C8)C2214yescomplemented
39C22×D3×D4—31no—
40C23×D12—31no—
41C3×#525—31no—
42C2×#949—31no—
43C2×#949—31no—
44C2×#932—31no—
45C2×#908—31no—
46#5524D311yescharacteristic, complemented
47C3×#418—31no—
48#5207—31no—
49#5126—31no—
50#5046—34no—
51#5036—34no—
52#5001—31no—
53#5001—31no—
54#5001—61no—
55#5001D311yescharacteristic, complemented
56#4776—34no—
57#4773—34no—
58C23×C3⋊D3—21no—
59C23×C3×D3—21no—
60C23×C3×D3D411yescharacteristic
61C22×D32—28no—
62C22×D32—24no—
63C22×D32—48no—
64C22×C32×C4C2311yescharacteristic
65C2×C4⋊(C3⋊D3)—21no—
66C2×C4⋊(C3⋊D3)—22no—
67C2×C4⋊(C3⋊D3)D414yescomplemented
68C2×C4⋊(C3⋊D3)C2312yes—
69C2×C3×#67—21no—
70C22×C3×Dic3D411yescharacteristic
71C3×#235—22no—
72C3×#235—22no—
73C2×C3×D12—21no—
74C2×C3×D12—22no—
75C2×C3×D12—22no—
76C2×C3×D12D414yescomplemented
77C2×C3×D12C2312yes—
78C2×C3×D12C2311yescharacteristic, complemented
79C2×C3×C4×D3—22no—
80C2×C3×C4×D3—22no—
81C2×C3×C4×D3—21no—
82C2×C3×C4×D3D412yes—
83C2×C3×C4×D3C2312yes—
84C2×C3×Dic6C2311yescharacteristic, complemented
85C2×#626—28no—
86C2×#626—24no—
87D3×D12—216no—
88D3×D12—28no—
89D3×D12—28no—
90C32×C4⋊C4C2312yescomplemented
91C32×C22⋊C4—21no—
92C32×C42—21no—
93#3748—22no—
94C2×C3⋊(C3⋊C8)C2312yescomplemented
95C3×(C2×D3)⋊C4—22no—
96C3×(C2×D3)⋊C4—22no—
97C3×C4⋊Dic3—22no—
98C3×#208—22no—
99C2×C3×C3⋊C8C2312yescomplemented
100#3717—24no—
101#3715—24no—
102#3714—24no—
103#3713—24no—
104#3003—91noSylow
105C24×D3—61no—
106C24×D3—61no—
107C2×C3×#41—31no—
108C22×C3×D4—31no—
109C23×C3×C4—31no—
110C22×#67—61no—
111C2×D3×D4—34no—
112C2×D3×D4—64no—
113C2×D3×D4—64no—
114C2×D3×D4—62no—
115C2×#235C2×D311yescharacteristic, complemented
116C22×D12—31no—
117C22×D12—31no—
118C22×D12—34no—
119C22×D12—61no—
120C22×D12—64no—
121C22×D12—62no—
122C22×D12—61no—
123C22×D12—64no—
124C22×D12C2×D311yescharacteristic
125C22×C4×D3C2×D311yescharacteristic
126C2×C3×M16—31no—
127C3×#123—61no—
128C3×C22⋊Q8—32no—
129C3×#121—32no—
130C3×#120—61no—
131C3×C4×D4—62no—
132C3×#117—21no—
133C3×#117C2×D311yescharacteristic, complemented
134C3×#117C2×D311yescharacteristic, complemented
135#949—64no—
136#949—64no—
137C2×#215—32no—
138C2×#215—32no—
139C2×#214—32no—
140#932—64no—
141C2×#213—32no—
142C2×#213—32no—
143C2×#213—32no—
144C2×#208—31no—
145C2×#208—31no—
146C2×#208—61no—
147C2×#208C2×D311yescharacteristic, complemented
148#908—64no—
149C2×D24—32no—
150C2×#204—32no—
151#897C2×D312yescomplemented
152#895C2×D312yescomplemented
153#886—21no—
154#882—21no—
155C4×D12—22no—
156C3×#102—34no—
157#830—34no—
158(C2×D3)⋊C8—34no—
159#809—34no—
160#809—34no—
161#809—64no—
162#809C2×D314yescomplemented
163C23×C32C2×D411yescharacteristic
164C22×C3⋊D3—24no—
165C22×C3⋊D3—22no—
166C22×C3⋊D3—44no—
167C22×C3×D3—22no—
168C22×C3×D3—24no—
169C22×C3×D3—24no—
170C22×C3×D3—22no—
171C22×C3×D3—21no—
172C22×C3×D3—44no—
173C22×C3×D3C2×D412yes—
174C2×D32—216no—
175C2×D32—432no—
176C2×D32—48no—
177C2×D32—48no—
178C2×C32×C4—22no—
179C2×C32×C4C2×D412yes—
180C2×C32×C4C2×D412yes—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2411yescharacteristic
183C4⋊(C3⋊D3)—24no—
184C4⋊(C3⋊D3)—22no—
185C4⋊(C3⋊D3)C2×D414yes—
186C3×#67—42no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3C2×D412yes—
190C3×D12—24no—
191C3×D12—22no—
192C3×D12—21no—
193C3×D12—21no—
194C3×D12—44no—
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#626—216no—
203C3⋊(C3⋊C8)—22no—
204C3×C3⋊C8—22no—
205C23×D4—91no—
206C2×AGL(1,ℤ/8)—91no—
207C2×AGL(1,ℤ/8)—91no—
208#525—31no—
209#450—94no—
210#447—94no—
211#418—31no—
212#418—91no—
213#407—91no—
214C24×C3—31no—
215C24×C3—61no—
216C23×D3—21no—
217C23×D3—64no—
218C23×D3—68no—
219C23×D3—68no—
220C23×D3—61no—
221C23×D3—61no—
222C23×D3—64no—
223C23×D3—121no—
224C23×D3—128no—
225C23×D3—128no—
226C23×D3#6711yescharacteristic
227C3×#41—62no—
228C3×#41—62no—
229C2×C3×Q8—31no—
230C2×C3×D4—34no—
231C2×C3×D4—32no—
232C2×C3×D4—31no—
233C2×C3×D4—62no—
234C2×C3×D4—61no—
235C2×C3×D4—62no—
236C2×C3×D4—61no—
237C22×C3×C4—21no—
238C22×C3×C4—31no—
239C22×C3×C4—32no—
240C22×C3×C4—32no—
241C22×C3×C4—62no—
242C22×C3×C4—62no—
243C22×C3×C4—61no—
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C22×D311yescharacteristic
246C2×#67—21no—
247C2×#67—68no—
248C2×#67—64no—
249C22×Dic3#6711yescharacteristic
250D3×D4—68no—
251D3×D4—68no—
252D3×D4—616no—
253#235—22no—
254#235—22no—
255C2×D12—22no—
256C2×D12—21no—
257C2×D12—22no—
258C2×D12—34no—
259C2×D12—34no—
260C2×D12—32no—
261C2×D12—32no—
262C2×D12—62no—
263C2×D12—64no—
264C2×D12—68no—
265C2×D12—616no—
266C2×D12—64no—
267C2×D12—68no—
268C2×D12—62no—
269C2×D12—61no—
270C2×D12—62no—
271C2×D12—61no—
272C2×D12—68no—
273C2×D12—122no—
274C2×D12—121no—
275C2×D12D1214yescomplemented
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×M16—62no—
285C2×C3×C8—32no—
286C3×C4⋊C4—22no—
287C3×C4⋊C4—62no—
288C3×C4⋊C4C22×D312yescomplemented
289C3×C4⋊C4C22×D312yescomplemented
290C3×C22⋊C4—21no—
291C3×C22⋊C4—21no—
292C3×C22⋊C4—41no—
293C3×C22⋊C4—62no—
294C3×C22⋊C4—62no—
295C3×C42—21no—
296C3×C42—21no—
297C3×C42—41no—
298#215—64no—
299#215—64no—
300#214—64no—
301#213—64no—
302#213—64no—
303#213—64no—
304(C2×D3)⋊C4—22no—
305(C2×D3)⋊C4—22no—
306C4⋊Dic3—22no—
307#208—22no—
308#208—62no—
309#208—62no—
310#208—122no—
311C2×C3⋊C8—32no—
312C2×C3⋊C8—32no—
313C2×C3⋊C8—62no—
314C2×C3⋊C8C22×D312yescomplemented
315D24—64no—
316#204—64no—
317C22×C32—22no—
318C22×C32#12012yes—
319C22×C32C22×D411yescharacteristic
320C2×C3⋊D3—24no—
321C2×C3⋊D3—48no—
322C2×C3⋊D3—44no—
323C2×C3×D3—28no—
324C2×C3×D3—22no—
325C2×C3×D3—22no—
326C2×C3×D3—24no—
327C2×C3×D3—48no—
328C2×C3×D3—44no—
329C2×C3×D3—41no—
330C2×C3×D3—42no—
331C2×C3×D3AGL(1,ℤ/8)14yescomplemented
332D32—432no—
333C32×C4—42no—
334C32×C4#12012yes—
335C32×C4C22×D411yescharacteristic
336C32×C4C22×D411yescharacteristic
337C3×Dic3—22no—
338C3×Dic3—41no—
339C25—181no—
340C2×#41—31no—
341C22×D4—31no—
342C22×D4—94no—
343C22×D4—91no—
344C22×D4—182no—
345C22×D4—181no—
346C22×D4—184no—
347C22×D4—184no—
348C23×C4—31no—
349AGL(1,ℤ/8)—184no—
350AGL(1,ℤ/8)—184no—
351C2×SD16—92no—
352C2×SD16—92no—
353C2×D8—92no—
354C2×D8—92no—
355C2×M16—31no—
356C2×M16—91no—
357#123—61no—
358C22⋊Q8—32no—
359#121—32no—
360#120—61no—
361C4×D4—62no—
362#117D3211yescharacteristic, complemented
363#102—34no—
364#102—94no—
365C22⋊C8—94no—
366C23×C3—21no—
367C23×C3—32no—
368C23×C3—64no—
369C23×C3—62no—
370C23×C3—64no—
371C23×C3—62no—
372C23×C3—61no—
373C23×C3—124no—
374C23×C3D3×D411yescharacteristic
375C23×C3C2×#6711yescharacteristic
376C22×D3—22no—
377C22×D3—24no—
378C22×D3—24no—
379C22×D3—22no—
380C22×D3—21no—
381C22×D3—44no—
382C22×D3—616no—
383C22×D3—616no—
384C22×D3—64no—
385C22×D3—64no—
386C22×D3—62no—
387C22×D3—62no—
388C22×D3—122no—
389C22×D3—124no—
390C22×D3—1232no—
391C22×D3—128no—
392C22×D3—128no—
393C22×D3—1232no—
394C22×D3—128no—
395C22×D3—124no—
396C22×D3—124no—
397C22×D3—128no—
398C22×D3—244no—
399C22×D3C2×#6712yes—
400C3×Q8—61no—
401C3×Q8—61no—
402C3×D4—34no—
403C3×D4—64no—
404C3×D4—61no—
405C3×D4—62no—
406C3×D4—61no—
407C3×D4—124no—
408C3×D4—122no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—21no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—21no—
415C2×C3×C4—32no—
416C2×C3×C4—42no—
417C2×C3×C4—62no—
418C2×C3×C4—64no—
419C2×C3×C4—62no—
420C2×C3×C4—62no—
421C2×C3×C4—61no—
422C2×C3×C4—122no—
423C2×C3×C4C2×D1212yes—
424C2×C3×C4D3×D412yes—
425C2×C3×C4D3×D412yes—
426C2×C3×C4D3×D412yes—
427C2×C3×C4D3×D411yescharacteristic
428C2×C3×C4C2×#6711yescharacteristic
429C2×C3×C4C23×D311yescharacteristic
430C2×C3×C4C23×D311yescharacteristic
431#67—42no—
432#67—616no—
433C2×Dic3—22no—
434C2×Dic3—21no—
435C2×Dic3C2×#6712yes—
436D12—24no—
437D12—22no—
438D12—21no—
439D12—21no—
440D12—34no—
441D12—34no—
442D12—44no—
443D12—64no—
444D12—616no—
445D12—64no—
446D12—64no—
447D12—62no—
448D12—62no—
449D12—122no—
450D12—124no—
451D12C2×D1214yes—
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×C32C2×#12011yescharacteristic
465C2×C32C2×AGL(1,ℤ/8)12yes—
466C3⋊D3—44no—
467C3×D3—24no—
468C3×D3—44no—
469C3×D3—81no—
470C24—31no—
471C24—61no—
472C24—184no—
473C24—188no—
474C24—181no—
475C24—368no—
476#41—62no—
477#41—62no—
478C2×Q8—31no—
479C2×D4—32no—
480C2×D4—31no—
481C2×D4—34no—
482C2×D4—62no—
483C2×D4—61no—
484C2×D4—62no—
485C2×D4—61no—
486C2×D4—92no—
487C2×D4—94no—
488C2×D4—184no—
489C2×D4—188no—
490C2×D4—188no—
491C2×D4—1816no—
492C2×D4—188no—
493C2×D4—182no—
494C2×D4—181no—
495C22×C4—31no—
496C22×C4—32no—
497C22×C4—32no—
498C22×C4—62no—
499C22×C4—62no—
500C22×C4—61no—
501C22×C4C2×D3211yescharacteristic
502SD16—184no—
503SD16—184no—
504D8—184no—
505D8—184no—
506M16—62no—
507M16—182no—
508C2×C8—32no—
509C2×C8—92no—
510C4⋊C4—62no—
511C4⋊C4C2×D3212yescomplemented
512C22⋊C4—21no—
513C22⋊C4—62no—
514C22⋊C4—62no—
515C42—21no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—21no—
519C22×C3—22no—
520C22×C3—34no—
521C22×C3—42no—
522C22×C3—68no—
523C22×C3—62no—
524C22×C3—62no—
525C22×C3—64no—
526C22×C3—128no—
527C22×C3—124no—
528C22×C3—121no—
529C22×C3—122no—
530C22×C3#88212yes—
531C22×C3#93712yes—
532C22×C3C2×D3×D411yescharacteristic
533C22×C3C22×#6711yescharacteristic
534C2×D3—28no—
535C2×D3—22no—
536C2×D3—22no—
537C2×D3—24no—
538C2×D3—48no—
539C2×D3—44no—
540C2×D3—41no—
541C2×D3—42no—
542C2×D3—64no—
543C2×D3—64no—
544C2×D3—124no—
545C2×D3—1232no—
546C2×D3—1232no—
547C2×D3—128no—
548C2×D3—128no—
549C2×D3—124no—
550C2×D3—124no—
551C2×D3—244no—
552C2×D3—248no—
553C2×D3#94914yescomplemented
554C3×C4—21no—
555C3×C4—21no—
556C3×C4—22no—
557C3×C4—42no—
558C3×C4—42no—
559C3×C4—62no—
560C3×C4—82no—
561C3×C4—121no—
562C3×C4#88212yes—
563C3×C4#93712yes—
564C3×C4C22×D1211yescharacteristic
565C3×C4C2×D3×D411yescharacteristic
566C3×C4C2×D3×D411yescharacteristic
567C3×C4C2×D3×D411yescharacteristic
568Dic3—22no—
569Dic3—41no—
570C32#300311yescharacteristic, complemented, Sylow
571C23—32no—
572C23—64no—
573C23—62no—
574C23—62no—
575C23—64no—
576C23—61no—
577C23—124no—
578C23—1816no—
579C23—182no—
580C23—184no—
581C23—364no—
582C23—368no—
583C23—3632no—
584C23—368no—
585C23D3×#6711yescharacteristic
586Q8—61no—
587Q8—61no—
588D4—34no—
589D4—61no—
590D4—62no—
591D4—61no—
592D4—64no—
593D4—94no—
594D4—124no—
595D4—122no—
596D4—1816no—
597D4—182no—
598D4—184no—
599C2×C4—22no—
600C2×C4—32no—
601C2×C4—62no—
602C2×C4—62no—
603C2×C4—62no—
604C2×C4—64no—
605C2×C4—61no—
606C2×C4—122no—
607C2×C4D3×D1212yes—
608C2×C4#380212yes—
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—64no—
619C2×C3—124no—
620C2×C3—241no—
621C2×C3C2×#88211yescharacteristic
622C2×C3D3×AGL(1,ℤ/8)12yes—
623C2×C3C2×#93711yescharacteristic
624C2×C3C2×#94912yes—
625D3—24no—
626D3—44no—
627D3—81no—
628D3—124no—
629D3—124no—
630D3—244no—
631C22—22no—
632C22—34no—
633C22—68no—
634C22—62no—
635C22—62no—
636C22—64no—
637C22—128no—
638C22—124no—
639C22—122no—
640C22—121no—
641C22—184no—
642C22—368no—
643C22—3632no—
644C22—364no—
645C22#6392212yes—
646C22C2×D3×#6711yescharacteristic
647C4—42no—
648C4—62no—
649C4—121no—
650C4#6392212yes—
651C4C2×D3×D1211yescharacteristic
652C4C2×#380211yescharacteristic
653C3—21no—
654C3#7892611yescharacteristic, complemented
655C3#8292711yescharacteristic, complemented
656C2—22no—
657C2—64no—
658C2—124no—
659C2—241no—
660C2—364no—
661C2C2×#6392211yescharacteristic
662C2D3×#94912yes—
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
hypercenter#117D32
hypocenterC32#3003
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C22×D3×D12C2semidirect
2. C3×#5524C2semidirect
3. C2×#63825C2semidirect
4. C2×#63823C2semidirect
5. #10592700C2semidirect
6. C3×#5001C2semidirect
7. #10591069C2semidirect
8. #10590596C2semidirect
9. #10590595C2semidirect
14. C2×C3×#235C22semidirect
22. C32×#117C22semidirect
23. C2×#3748C22semidirect
24. C2×C3×#208C22semidirect
25. C3×#897C22semidirect
26. C3×#895C22semidirect
30. C2×#3717C22semidirect
31. C2×#3715C22semidirect
33. C2×#3714C22semidirect
35. C2×#3713C22semidirect
36. #63636C22semidirect
37. C3×#809C22semidirect
38. (C2×D3)⋊(C3⋊C8)C22semidirect
46. #5524D3semidirect
55. #5001D3semidirect
67. C2×C4⋊(C3⋊D3)D4semidirect
76. C2×C3×D12D4semidirect
78. C2×C3×D12C23semidirect
84. C2×C3×Dic6C23semidirect
90. C32×C4⋊C4C23semidirect
94. C2×C3⋊(C3⋊C8)C23semidirect
99. C2×C3×C3⋊C8C23semidirect
115. C2×#235C2×D3semidirect
133. C3×#117C2×D3semidirect
134. C3×#117C2×D3semidirect
147. C2×#208C2×D3semidirect
151. #897C2×D3semidirect
152. #895C2×D3semidirect
162. #809C2×D3semidirect
275. C2×D12D12semidirect
277. C2×D12C22×D3semidirect
283. C2×Dic6C22×D3semidirect
288. C3×C4⋊C4C22×D3semidirect
289. C3×C4⋊C4C22×D3semidirect
314. C2×C3⋊C8C22×D3semidirect
331. C2×C3×D3AGL(1,ℤ/8)semidirect
362. #117D32semidirect
511. C4⋊C4C2×D32semidirect
553. C2×D3#949semidirect
570. C32#3003semidirect
654. C3#78926semidirect
655. C3#82927semidirect

Maximal subgroups

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

subgroupindex
C22×D3×D122
C3×#55242
C2×#638252
C2×#638232
#105927002
C3×#50012
#105910692
#105905962
#105905952
#829273
#789263