Finite Group Databasebeta

← #11864083

Subgroups — #11864083

Order 1152.

1961 conjugacy classes of subgroups.

The subgroup lattice has 665 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3832C211yesmaximal, characteristic, complemented
2C2×C3×#942C211yesmaximal, characteristic, complemented
3#10595034C211yesmaximal, characteristic, complemented
4C2×#63825C211yesmaximal, characteristic, complemented
5C3×#5225C211yesmaximal, characteristic, complemented
6#10591602C214yesmaximal, complemented
7#10591593C214yesmaximal, complemented
8#10591096C211yesmaximal, characteristic, complemented
9#10591074C211yesmaximal, characteristic, complemented
10#83980—31nomaximal
11#78959—31nomaximal
12C22×C32×Q8C2211yescharacteristic
13C2×#3832—24no—
14C2×#3832—24no—
15C2×#3832—22no—
16C2×#3832C2214yes—
17C22×C4⋊(C3⋊D3)—21no—
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4×C3⋊D3—21no—
20C22×C4×C3⋊D3C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic
22C2×C3×#216C2212yescomplemented
23C3×#942—24no—
24C2×C3×#215C2212yescomplemented
25C3×#926C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28#63981—21no—
29#63962—21no—
30#63916C2212yescomplemented
31C4×#626—22no—
32#63871C2212yescomplemented
33C2×#3717C2212yescomplemented
34#63825—24no—
35C2×#3714C2212yescomplemented
36C3×#835C2214yescomplemented
37#63564C2214yescomplemented
38#63557C2214yescomplemented
39C22×#239—31no—
40C22×#239—31no—
41C22×#239—61no—
42C2×C3×#137—31no—
43#5828—31no—
44C2×#949—31no—
45C2×#942D311yescharacteristic, complemented
46C2×#908—31no—
47#5524—31no—
48C3×#419—31no—
49#5225D311yescharacteristic, complemented
50#5187—34no—
51#5172—34no—
52#5131—31no—
53#5126—31no—
54#5126—31no—
55#5001—31no—
56#4810—34no—
57#4808—34no—
58C23×C3⋊D3—21no—
59C23×C3⋊D3D411yescharacteristic
60C2×C32×Q8—22no—
61C2×C32×Q8—21no—
62C2×C32×Q8D414yescomplemented
63C2×C32×Q8C2312yes—
64C22×C32×C4—21no—
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3D411yescharacteristic
67#3832—216no—
68#3832—28no—
69#3832—28no—
70C2×C4⋊(C3⋊D3)—28no—
71C2×C4⋊(C3⋊D3)—24no—
72C2×C4⋊(C3⋊D3)—21no—
73C2×C4⋊(C3⋊D3)—22no—
74C2×C4⋊(C3⋊D3)D414yescomplemented
75C2×C4⋊(C3⋊D3)C2312yes—
76C2×C4×C3⋊D3—28no—
77C2×C4×C3⋊D3—22no—
78C2×C4×C3⋊D3—22no—
79C2×C4×C3⋊D3—24no—
80C2×C4×C3⋊D3D412yes—
81C2×C4×C3⋊D3C2312yes—
82C2×C3×#67—21no—
83C3×#235—22no—
84C3×#235—22no—
85C2×C3×D12C2311yescharacteristic
86C2×C3×C4×D3—21no—
87C2×C3×Dic6C2311yescharacteristic
88C2×#626—22no—
89C3×#217—21no—
90C3×#216—24no—
91C3×#215—24no—
92C3×C4⋊Dic3C2312yes—
93C3×C4×Dic3—21no—
94C3×#208—22no—
95C3×#208—22no—
96C2×C3×C3⋊C8C2312yes—
97C2×C3×C3⋊C8C2312yes—
98Dic3⋊Dic3—22no—
99#3722—22no—
100(C2×D3)⋊Dic3—22no—
101#3717—24no—
102#3714—24no—
103#3005—91noSylow
104C2×C3×#41—31no—
105C22×C3×Q8—21no—
106C22×C3×Q8C2×D311yescharacteristic
107C22×C3×Q8C2×D311yescharacteristic
108C2×#239—34no—
109C2×#239—34no—
110C2×#239—64no—
111C2×#239—62no—
112C2×#239—62no—
113C2×#239—64no—
114C2×#239—64no—
115C2×#239—64no—
116C2×#239—68no—
117C2×#239—68no—
118C2×#239—64no—
119C2×#239—64no—
120C2×#235C2×D311yescharacteristic
121C22×D12—31no—
122C22×D12—31no—
123C22×D12—61no—
124C22×D12—61no—
125C22×D12—61no—
126C22×D12—62no—
127C22×C4×D3—31no—
128C22×C4×D3—31no—
129C22×C4×D3—61no—
130C22×C4×D3—61no—
131C22×C4×D3—61no—
132C22×C4×D3—62no—
133C3×#137—64no—
134C2×C3×Q16—32no—
135C2×C3×SD16—32no—
136C2×C3×M16—31no—
137C2×C3×M16—31no—
138C3×#117—31no—
139#949—64no—
140#946—32no—
141C2×#216C2×D312yescomplemented
142#942—24no—
143C2×#215—32no—
144C2×#215C2×D312yescomplemented
145#938—32no—
146#937—61no—
147#935—61no—
148C2×#213—32no—
149C4×#67—62no—
150#926C2×D311yescharacteristic
151C2×#208C2×D311yescharacteristic
152C2×#208C2×D311yescharacteristic
153#908—64no—
154C2×D24—32no—
155C2×#204—32no—
156#897—32no—
157#895—32no—
158#886—61no—
159#882—61no—
160C4×D12—62no—
161C3×#103—34no—
162#835C2×D314yescomplemented
163#821—34no—
164(C2×D3)⋊C8—34no—
165(C2×D3)⋊C8—34no—
166#809—34no—
167C23×C32C2×D411yescharacteristic
168C22×C3⋊D3—24no—
169C22×C3⋊D3—22no—
170C22×C3⋊D3—22no—
171C22×C3⋊D3—42no—
172C22×C3⋊D3—44no—
173C22×C3⋊D3C2×D412yes—
174C22×C3×D3—21no—
175C32×Q8—24no—
176C32×Q8—22no—
177C32×Q8C2×D414yes—
178C2×C32×C4—24no—
179C2×C32×C4—22no—
180C2×C32×C4C2×D412yes—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D412yes—
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3C2×D412yes—
186C4⋊(C3⋊D3)—216no—
187C4⋊(C3⋊D3)—24no—
188C4⋊(C3⋊D3)—22no—
189C4⋊(C3⋊D3)C2×D414yes—
190C4×C3⋊D3—216no—
191C4×C3⋊D3—24no—
192C4×C3⋊D3—22no—
193C4×C3⋊D3—22no—
194C3×#67—42no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—21no—
197C3×D12—21no—
198C3×D12—21no—
199C3×C4×D3—42no—
200C3×Dic6—21no—
201C3×Dic6—21no—
202#626—44no—
203C3×C3⋊C8—22no—
204C3×C3⋊C8—22no—
205C22×#41—91no—
206C2×#137—31no—
207C2×AGL(1,ℤ/8)—91no—
208#525—91no—
209#452—94no—
210#449—94no—
211#419—31no—
212#418—91no—
213#407—91no—
214C23×D3—31no—
215C23×D3—31no—
216C23×D3—61no—
217C23×D3—62no—
218C23×D3—61no—
219C23×D3—61no—
220C3×#41—62no—
221C3×#41—62no—
222C2×C3×Q8—22no—
223C2×C3×Q8—24no—
224C2×C3×Q8—22no—
225C2×C3×Q8—22no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—24no—
229C2×C3×Q8—22no—
230C2×C3×Q8—31no—
231C2×C3×Q8D1214yescomplemented
232C2×C3×Q8#6714yescomplemented
233C2×C3×Q8C22×D312yes—
234C2×C3×Q8C22×D312yes—
235C2×C3×D4—31no—
236C2×C3×D4—61no—
237C22×C3×C4—22no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—61no—
242C22×C3×C4C22×D311yescharacteristic
243C22×C3×C4C22×D311yescharacteristic
244C2×#67—21no—
245C2×#67—62no—
246C22×Dic3—31no—
247C22×Dic3—31no—
248C22×Dic3—61no—
249#239—68no—
250#239—68no—
251#239—616no—
252#239—632no—
253#239—616no—
254#239—616no—
255#239—616no—
256#239—68no—
257#239—68no—
258#235—22no—
259#235—22no—
260C2×D12—34no—
261C2×D12—34no—
262C2×D12—32no—
263C2×D12—32no—
264C2×D12—64no—
265C2×D12—62no—
266C2×D12—64no—
267C2×D12—64no—
268C2×D12—68no—
269C2×D12—616no—
270C2×D12—68no—
271C2×D12—68no—
272C2×D12—64no—
273C2×D12—62no—
274C2×D12—62no—
275C2×D12—61no—
276C2×D12—61no—
277C2×D12—62no—
278C2×D12—62no—
279C2×D12C22×D311yescharacteristic
280C2×C4×D3—21no—
281C2×C4×D3—32no—
282C2×C4×D3—32no—
283C2×C4×D3—32no—
284C2×C4×D3—32no—
285C2×C4×D3—62no—
286C2×C4×D3—62no—
287C2×C4×D3—64no—
288C2×C4×D3—64no—
289C2×C4×D3—68no—
290C2×C4×D3—616no—
291C2×C4×D3—68no—
292C2×C4×D3—68no—
293C2×C4×D3—64no—
294C2×C4×D3—64no—
295C2×C4×D3—62no—
296C2×C4×D3—62no—
297C2×C4×D3—62no—
298C2×C4×D3—62no—
299C2×Dic6C22×D311yescharacteristic
300C3×Q16—64no—
301C3×SD16—64no—
302C3×M16—62no—
303C3×M16—62no—
304C2×C3×C8—32no—
305C2×C3×C8—32no—
306C3×C4⋊C4—32no—
307C3×C22⋊C4—61no—
308C3×C42—61no—
309#217—21no—
310#217—62no—
311#216—24no—
312#215—24no—
313#215—64no—
314#213—64no—
315(C2×D3)⋊C4—62no—
316(C2×D3)⋊C4—62no—
317(C2×D3)⋊C4—62no—
318C4⋊Dic3—62no—
319C4⋊Dic3C22×D312yes—
320Dic3⋊C4—62no—
321C4×Dic3—21no—
322#208—22no—
323#208—22no—
324C2×C3⋊C8C22×D312yes—
325C2×C3⋊C8C22×D312yes—
326D24—64no—
327#204—64no—
328C22×C32—22no—
329C22×C32#12012yes—
330C22×C32C22×D411yescharacteristic
331C2×C3⋊D3—22no—
332C2×C3⋊D3—24no—
333C2×C3⋊D3—22no—
334C2×C3⋊D3—22no—
335C2×C3⋊D3—44no—
336C2×C3⋊D3—48no—
337C2×C3⋊D3—44no—
338C2×C3×D3—41no—
339C2×C3×D3—42no—
340C32×C4—24no—
341C32×C4#12012yes—
342C32×C4C22×D411yescharacteristic
343C32×C4C22×D411yescharacteristic
344C3⋊Dic3—22no—
345C3×Dic3—41no—
346C3×Dic3—42no—
347C2×#41—31no—
348C2×#41—94no—
349C2×#41—182no—
350C2×#41—184no—
351C2×#41—184no—
352C22×Q8D3211yescharacteristic
353C22×D4—91no—
354C22×D4—181no—
355C23×C4—91no—
356C23×C4—181no—
357#137—64no—
358AGL(1,ℤ/8)—184no—
359C2×Q16—32no—
360C2×SD16—32no—
361C2×SD16—92no—
362C2×D8—92no—
363C2×M16—31no—
364C2×M16—31no—
365#123—181no—
366C22⋊Q8—92no—
367#121—92no—
368#120—181no—
369C4×D4—182no—
370#117—31no—
371#103—34no—
372#102—94no—
373C22⋊C8—94no—
374C23×C3—21no—
375C23×C3—61no—
376C23×C3D3×D411yescharacteristic
377C23×C3D3×D411yescharacteristic
378C22×D3—21no—
379C22×D3—32no—
380C22×D3—32no—
381C22×D3—62no—
382C22×D3—64no—
383C22×D3—68no—
384C22×D3—64no—
385C22×D3—64no—
386C22×D3—62no—
387C22×D3—64no—
388C22×D3—62no—
389C22×D3—62no—
390C22×D3—62no—
391C22×D3—122no—
392C22×D3—122no—
393C22×D3—124no—
394C22×D3—128no—
395C22×D3—124no—
396C22×D3—124no—
397C3×Q8—24no—
398C3×Q8—28no—
399C3×Q8—24no—
400C3×Q8—24no—
401C3×Q8—22no—
402C3×Q8—22no—
403C3×Q8—24no—
404C3×Q8—61no—
405C3×Q8—61no—
406C3×Q8C2×D1214yes—
407C3×Q8C2×#6714yes—
408C3×D4—61no—
409C3×D4—61no—
410C3×D4—122no—
411C2×C3×C4—24no—
412C2×C3×C4—28no—
413C2×C3×C4—24no—
414C2×C3×C4—24no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—21no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—21no—
421C2×C3×C4—61no—
422C2×C3×C4—62no—
423C2×C3×C4—122no—
424C2×C3×C4C2×D1212yes—
425C2×C3×C4D3×D411yescharacteristic
426C2×C3×C4D3×D412yes—
427C2×C3×C4D3×D411yescharacteristic
428C2×C3×C4D3×D412yes—
429C2×C3×C4C2×#6712yes—
430C2×C3×C4C23×D311yescharacteristic
431C2×C3×C4C23×D311yescharacteristic
432#67—42no—
433#67—124no—
434C2×Dic3—22no—
435C2×Dic3—21no—
436C2×Dic3—32no—
437C2×Dic3—32no—
438C2×Dic3—62no—
439C2×Dic3—64no—
440C2×Dic3—62no—
441C2×Dic3—62no—
442D12—21no—
443D12—21no—
444D12—34no—
445D12—34no—
446D12—64no—
447D12—632no—
448D12—616no—
449D12—616no—
450D12—64no—
451D12—68no—
452D12—64no—
453D12—64no—
454D12—62no—
455D12—62no—
456D12—124no—
457C4×D3—42no—
458C4×D3—632no—
459C4×D3—616no—
460C4×D3—616no—
461C4×D3—64no—
462C4×D3—64no—
463C4×D3—68no—
464C4×D3—64no—
465C4×D3—64no—
466C4×D3—62no—
467C4×D3—62no—
468C4×D3—62no—
469C4×D3—62no—
470Dic6—21no—
471Dic6—21no—
472C3×C8—62no—
473C3×C8—62no—
474C3⋊C8—22no—
475C3⋊C8—22no—
476C2×C32—22no—
477C2×C32C2×#12011yescharacteristic
478C2×C32#57512yes—
479C3⋊D3—42no—
480C3⋊D3—44no—
481C3×D3—81no—
482C24—91no—
483C24—181no—
484#41—62no—
485#41—62no—
486#41—188no—
487#41—1816no—
488#41—188no—
489C2×Q8—21no—
490C2×Q8—22no—
491C2×Q8—31no—
492C2×Q8#62614yescomplemented
493C2×Q8C2×D3212yes—
494C2×D4—31no—
495C2×D4—61no—
496C2×D4—92no—
497C2×D4—94no—
498C2×D4—184no—
499C2×D4—188no—
500C2×D4—182no—
501C2×D4—182no—
502C2×D4—181no—
503C22×C4—21no—
504C22×C4—61no—
505C22×C4—91no—
506C22×C4—92no—
507C22×C4—92no—
508C22×C4—184no—
509C22×C4—188no—
510C22×C4—182no—
511C22×C4—182no—
512C22×C4C2×D3211yescharacteristic
513Q16—64no—
514SD16—64no—
515SD16—184no—
516D8—184no—
517M16—62no—
518M16—62no—
519C2×C8—32no—
520C2×C8—32no—
521C4⋊C4—32no—
522C4⋊C4—182no—
523C22⋊C4—61no—
524C22⋊C4—182no—
525C22⋊C4—182no—
526C42—61no—
527C22×C3—24no—
528C22×C3—22no—
529C22×C3—22no—
530C22×C3—21no—
531C22×C3—22no—
532C22×C3—121no—
533C22×C3—122no—
534C22×C3#88212yes—
535C22×C3#93712yes—
536C22×C3C2×D3×D411yescharacteristic
537C22×C3C2×D3×D411yescharacteristic
538C2×D3—42no—
539C2×D3—41no—
540C2×D3—68no—
541C2×D3—64no—
542C2×D3—64no—
543C2×D3—62no—
544C2×D3—62no—
545C2×D3—62no—
546C2×D3—62no—
547C2×D3—62no—
548C2×D3—64no—
549C2×D3—62no—
550C2×D3—122no—
551C2×D3—122no—
552C2×D3—128no—
553C2×D3—1216no—
554C2×D3—124no—
555C2×D3—128no—
556C2×D3—124no—
557C2×D3—128no—
558C2×D3—128no—
559C2×D3—124no—
560C2×D3—124no—
561C3×C4—28no—
562C3×C4—24no—
563C3×C4—24no—
564C3×C4—21no—
565C3×C4—21no—
566C3×C4—22no—
567C3×C4—121no—
568C3×C4—122no—
569C3×C4#88212yes—
570C3×C4#93712yes—
571C3×C4C22×D1211yescharacteristic
572C3×C4C2×D3×D411yescharacteristic
573C3×C4C2×D3×D411yescharacteristic
574C3×C4C22×#6711yescharacteristic
575Dic3—42no—
576Dic3—41no—
577Dic3—64no—
578Dic3—62no—
579Dic3—62no—
580C32#300511yescharacteristic, complemented, Sylow
581C23—61no—
582C23—92no—
583C23—182no—
584C23—184no—
585C23—182no—
586C23—362no—
587C23—364no—
588C23#381111yescharacteristic
589Q8—22no—
590Q8—24no—
591Q8—61no—
592Q8—61no—
593Q8C2×#62614yes—
594D4—61no—
595D4—61no—
596D4—94no—
597D4—122no—
598D4—1816no—
599D4—182no—
600D4—184no—
601D4—364no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—62no—
605C2×C4—61no—
606C2×C4—92no—
607C2×C4—122no—
608C2×C4—1816no—
609C2×C4—182no—
610C2×C4—182no—
611C2×C4—182no—
612C2×C4—184no—
613C2×C4C2×#62612yes—
614C2×C4#381112yes—
615C2×C4#381111yescharacteristic
616C2×C4C22×D3211yescharacteristic
617C8—62no—
618C8—62no—
619C2×C3—24no—
620C2×C3—22no—
621C2×C3—22no—
622C2×C3—21no—
623C2×C3—22no—
624C2×C3—241no—
625C2×C3C2×#88211yescharacteristic
626C2×C3#577712yes—
627C2×C3#577712yes—
628C2×C3C2×#93711yescharacteristic
629D3—81no—
630D3—124no—
631D3—128no—
632D3—122no—
633D3—124no—
634D3—122no—
635D3—124no—
636C22—22no—
637C22—121no—
638C22—122no—
639C22—184no—
640C22—182no—
641C22—182no—
642C22—182no—
643C22—364no—
644C22—368no—
645C22—364no—
646C22#6398112yes—
647C22C2×#381111yescharacteristic
648C4—24no—
649C4—121no—
650C4—122no—
651C4—182no—
652C4#6398112yes—
653C4C22×#62611yescharacteristic
654C4C2×#381111yescharacteristic
655C3—21no—
656C3#7895911yescharacteristic, complemented
657C3#8398011yescharacteristic, complemented
658C2—22no—
659C2—241no—
660C2—362no—
661C2—364no—
662C2#1059532312yes—
663C2C2×#6398111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
hypercenterC22×Q8D32
hypocenterC32#3005
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#3832C2semidirect
2. C2×C3×#942C2semidirect
3. #10595034C2semidirect
4. C2×#63825C2semidirect
5. C3×#5225C2semidirect
6. #10591602C2semidirect
7. #10591593C2semidirect
8. #10591096C2semidirect
9. #10591074C2semidirect
22. C2×C3×#216C22semidirect
24. C2×C3×#215C22semidirect
30. #63916C22semidirect
32. #63871C22semidirect
33. C2×#3717C22semidirect
35. C2×#3714C22semidirect
36. C3×#835C22semidirect
37. #63564C22semidirect
38. #63557C22semidirect
45. C2×#942D3semidirect
49. #5225D3semidirect
62. C2×C32×Q8D4semidirect
74. C2×C4⋊(C3⋊D3)D4semidirect
141. C2×#216C2×D3semidirect
144. C2×#215C2×D3semidirect
162. #835C2×D3semidirect
231. C2×C3×Q8D12semidirect
232. C2×C3×Q8#67semidirect
492. C2×Q8#626semidirect
580. C32#3005semidirect
656. C3#78959semidirect
657. C3#83980semidirect

Maximal subgroups

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

subgroupindex
C22×#38322
C2×C3×#9422
#105950342
C2×#638252
C3×#52252
#105916022
#105915932
#105910962
#105910742
#839803
#789593