Finite Group Databasebeta

← #11860309

Subgroups — #11860309

Order 1152.

1245 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64141C211yesmaximal, characteristic
2C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
3#10594954C211yesmaximal, characteristic, complemented
4C3×#5215C211yesmaximal, characteristic, complemented
5#10591405C212yesmaximal, complemented
6#10591404C212yesmaximal, complemented
7#10591401C212yesmaximal, complemented
8#10591400C212yesmaximal, complemented
9#10591139C211yesmaximal, characteristic, complemented
10#10591106C211yesmaximal, characteristic, complemented
11Dic3×#208C211yesmaximal, characteristic, complemented
12C4×#932—31nomaximal
13#78914—31nomaximal
14C22×C32×D4C2211yescharacteristic
15C2×#3828C2211yescharacteristic
16C23×C3×Dic3—21no—
17C2×#3754C2212yes—
18#64141C418yescomplemented
19C2×#3753C2212yes—
20C2×#3748C2211yescharacteristic
21C2×C3×#217—21no—
22C3×D4×Dic3—21no—
23C3×D4×Dic3—21no—
24C3×D4×Dic3C2212yes—
25C3×D4×Dic3C2212yes—
26C3×#926C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×#208C2211yescharacteristic
30#63952—21no—
31#63952—21no—
32#63894C2211yescharacteristic, complemented
33#63894C2211yescharacteristic, complemented
34C4×#624—21no—
35#63874—21no—
36#63844C2211yescharacteristic, complemented
37#63844C2211yescharacteristic, complemented
38C3×#832C2212yes—
39C3×#832C2212yes—
40#63576C2212yescomplemented
41#63574C2212yescomplemented
42#63567C2212yescomplemented
43#63564C2212yescomplemented
44#63554C2212yescomplemented
45Dic3×C3⋊C8C2212yescomplemented
46C2×C3×C4×D4—31no—
47C2×D4×Dic3D311yescharacteristic, complemented
48C2×#932—31no—
49C2×#932—31no—
50C2×#932—61no—
51#5522—31no—
52C4×#235—31no—
53C3×#418—31no—
54#5215D311yescharacteristic, complemented
55#5133—31no—
56Dic3×M16—31no—
57#5018—32no—
58C4×#214—32no—
59#5014—32no—
60C4×#213—32no—
61#4995—31no—
62#4966—31no—
63#4964—31no—
64C4×#208—31no—
65#4785—32no—
66#4758—32no—
67#4757—32no—
68#4756—32no—
69C24×C32—21no—
70C2×C32×D4—21no—
71C2×C32×D4—22no—
72C2×C32×D4C2×C414yescomplemented
73C2×C32×D4C2312yes—
74C22×C32×C4C2311yescharacteristic
75C2×#638—21no—
76#3828—22no—
77#3828C2×C414yescomplemented
78C2×C4⋊(C3⋊D3)C2311yescharacteristic
79C2×C4×C3⋊D3—21no—
80C2×#634C2311yescharacteristic
81C22×C3×Dic3—21no—
82C22×C3×Dic3—22no—
83C22×C3×Dic3—22no—
84C22×C3×Dic3—44no—
85C22×C3×Dic3D411yescharacteristic
86C22×C3×Dic3D411yescharacteristic
87C2×#624—21no—
88C2×#624—21no—
89#3754C2×C418yescomplemented
90#3753C2×C418yescomplemented
91#3748C2×C414yescomplemented
92C2×C3⋊(C3⋊C8)C2312yes—
93C3×#217—21no—
94C3×#217—22no—
95C3×#217—22no—
96C3×C4⋊Dic3—21no—
97C3×C4⋊Dic3C2312yes—
98C3×C4⋊Dic3C2311yescharacteristic
99C3×C4⋊Dic3C2311yescharacteristic
100C3×C4×Dic3—21no—
101C3×C4×Dic3D411yescharacteristic
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3C2311yescharacteristic
104C3×C4×Dic3C2311yescharacteristic
105C3×#208—22no—
106C2×C3×C3⋊C8C2312yes—
107#3724—21no—
108#3724—21no—
109#3722—21no—
110#3722—21no—
111Dic32—21no—
112Dic32—21no—
113C4×AGL(1,ℤ/8)—91noSylow
114C22×C3×D4—21no—
115C22×C3×D4C2×D311yescharacteristic
116C22×C3×D4C2×D311yescharacteristic
117C23×C3×C4—61no—
118C23×Dic3—21no—
119C2×#235—31no—
120C2×#235—31no—
121C2×#235—61no—
122C2×C3×M16—31no—
123C3×C4×D4—32no—
124C3×C4×D4—32no—
125C3×C4×D4—61no—
126C3×C4×D4—61no—
127C3×#117—31no—
128C2×C3×C4⋊C4—31no—
129C2×C3×C22⋊C4—61no—
130C2×C3×C42—31no—
131C2×#217—21no—
132D4×Dic3—21no—
133D4×Dic3—21no—
134D4×Dic3C2×D312yes—
135D4×Dic3C2×D312yes—
136C2×#214—32no—
137C2×#214—32no—
138C2×#214—62no—
139#932—38no—
140#932—38no—
141#932—68no—
142C2×#213—32no—
143C2×#213—32no—
144C2×#213—62no—
145C4×#67—61no—
146C4×#67—61no—
147#926C2×D311yescharacteristic
148C2×C4⋊Dic3C2×D311yescharacteristic
149C2×C4×Dic3C2×D311yescharacteristic
150C2×#208—31no—
151C2×#208—31no—
152C2×#208—61no—
153C2×#208C2×D311yescharacteristic
154#893—31no—
155#893—31no—
156#887—31no—
157#887—31no—
158#67⋊C4—61no—
159#67⋊C4—61no—
160C4×D12—31no—
161C4×D12—31no—
162#872—61no—
163#872—61no—
164C42×D3—61no—
165C42×D3—61no—
166C4×Dic6—31no—
167C4×Dic6—31no—
168C3×#102—32no—
169C3×#102—32no—
170#832C2×D312yes—
171#832C2×D312yes—
172#821—32no—
173#816—32no—
174#815—32no—
175C8×Dic3—32no—
176#810—32no—
177#809—32no—
178#808—32no—
179#808—32no—
180#807—32no—
181#807—32no—
182#803—32no—
183C4×C3⋊C8—32no—
184C23×C32—24no—
185C23×C32—22no—
186C23×C32—42no—
187C23×C32—42no—
188C23×C32C2×D411yescharacteristic
189C22×C3⋊D3—21no—
190C32×D4—24no—
191C32×D4—22no—
192C32×D4C22×C414yes—
193C2×C32×C4C22×C412yes—
194C2×C32×C4C2×D411yescharacteristic
195C2×C32×C4#4112yes—
196C2×C32×C4C2411yescharacteristic
197#638—24no—
198C2×C3⋊Dic3—21no—
199C4⋊(C3⋊D3)—21no—
200C4⋊(C3⋊D3)C22×C412yescomplemented
201C4×C3⋊D3—24no—
202#634—21no—
203#634C22×C412yescomplemented
204C2×C3×Dic3—22no—
205C2×C3×Dic3—21no—
206C2×C3×Dic3—21no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—41no—
209C2×C3×Dic3—44no—
210C2×C3×Dic3—42no—
211C2×C3×Dic3—44no—
212C2×C3×Dic3C2×D411yescharacteristic
213C2×C3×Dic3C2×D411yescharacteristic
214C2×C3×Dic3C2×D411yescharacteristic
215C2×C3×Dic3C2×D411yescharacteristic
216#624—42no—
217#624—42no—
218C3⋊(C3⋊C8)C22×C414yescomplemented
219C3×C3⋊C8—22no—
220C2×AGL(1,ℤ/8)—91no—
221C4×#41—91no—
222C2×C4×D4—31no—
223#442—92no—
224#440—92no—
225C4×SD16—92no—
226C4×D8—92no—
227#428—91no—
228#418—31no—
229#417—91no—
230C4×M16—91no—
231C24×C3—21no—
232C24×C3—21no—
233C24×C3—41no—
234C2×C3×D4—22no—
235C2×C3×D4—21no—
236C2×C3×D4—22no—
237C2×C3×D4—21no—
238C2×C3×D4—24no—
239C2×C3×D4—22no—
240C2×C3×D4—42no—
241C2×C3×D4—41no—
242C2×C3×D4C4×D314yescomplemented
243C2×C3×D4C4×D314yescomplemented
244C2×C3×D4C22×D312yes—
245C2×C3×D4C22×D312yes—
246C22×C3×C4—21no—
247C22×C3×C4—31no—
248C22×C3×C4—31no—
249C22×C3×C4—62no—
250C22×C3×C4—62no—
251C22×C3×C4—61no—
252C22×C3×C4—124no—
253C22×C3×C4C22×D311yescharacteristic
254C22×C3×C4C22×D311yescharacteristic
255C2×#67—61no—
256C2×#67—61no—
257C2×#67—121no—
258C22×Dic3—21no—
259C22×Dic3—22no—
260C22×Dic3—22no—
261C22×Dic3—44no—
262C22×Dic3#6711yescharacteristic
263C22×Dic3#6711yescharacteristic
264#235—34no—
265#235—34no—
266#235—64no—
267#235—62no—
268#235—62no—
269#235—122no—
270C2×D12—31no—
271C2×D12—31no—
272C2×D12—61no—
273C2×C4×D3—61no—
274C2×C4×D3—61no—
275C2×C4×D3—61no—
276C2×C4×D3—61no—
277C2×C4×D3—61no—
278C2×C4×D3—61no—
279C2×C4×D3—121no—
280C2×Dic6—31no—
281C2×Dic6—31no—
282C2×Dic6—61no—
283C3×M16—62no—
284C2×C3×C8—32no—
285C3×C4⋊C4—31no—
286C3×C4⋊C4—32no—
287C3×C4⋊C4—31no—
288C3×C4⋊C4—61no—
289C3×C22⋊C4—62no—
290C3×C22⋊C4—62no—
291C3×C22⋊C4—61no—
292C3×C42—31no—
293C3×C42—31no—
294C3×C42—31no—
295C3×C42—31no—
296C3×C42—61no—
297#217—21no—
298#217—22no—
299#217—22no—
300#214—38no—
301#214—38no—
302#214—68no—
303#213—38no—
304#213—38no—
305#213—68no—
306(C2×D3)⋊C4—61no—
307(C2×D3)⋊C4—61no—
308(C2×D3)⋊C4—61no—
309(C2×D3)⋊C4—61no—
310C4⋊Dic3—21no—
311C4⋊Dic3C22×D311yescharacteristic
312C4⋊Dic3C22×D312yes—
313C4⋊Dic3C22×D311yescharacteristic
314Dic3⋊C4—61no—
315Dic3⋊C4—61no—
316Dic3⋊C4—61no—
317Dic3⋊C4—61no—
318C4×Dic3—21no—
319C4×Dic3—61no—
320C4×Dic3—61no—
321C4×Dic3—61no—
322C4×Dic3—61no—
323C4×Dic3#6711yescharacteristic
324C4×Dic3#6711yescharacteristic
325C4×Dic3C22×D311yescharacteristic
326C4×Dic3C22×D311yescharacteristic
327#208—22no—
328#208—34no—
329#208—34no—
330#208—64no—
331C2×C3⋊C8—32no—
332C2×C3⋊C8—32no—
333C2×C3⋊C8—62no—
334C2×C3⋊C8C22×D312yes—
335C22×C32—21no—
336C22×C32—21no—
337C22×C32—24no—
338C22×C32—48no—
339C22×C32—42no—
340C22×C32—42no—
341C22×C32C4×D412yes—
342C22×C32C22×D411yescharacteristic
343C2×C3⋊D3—22no—
344C2×C3⋊D3—41no—
345C2×C3⋊D3—41no—
346C32×C4C4×D412yes—
347C32×C4C23×C411yescharacteristic
348C32×C4C2×#4111yescharacteristic
349C3⋊Dic3—22no—
350C3×Dic3—21no—
351C3×Dic3—21no—
352C3×Dic3—21no—
353C3×Dic3—41no—
354C3×Dic3—42no—
355C3×Dic3—41no—
356C3×Dic3AGL(1,ℤ/8)12yescomplemented
357C2×#41—91no—
358C22×D4D3211yescharacteristic
359C23×C4—61no—
360AGL(1,ℤ/8)—98no—
361C2×SD16—92no—
362C2×D8—92no—
363C2×M16—31no—
364C2×M16—91no—
365C4×Q8—91no—
366C4×Q8—91no—
367C4×D4—32no—
368C4×D4—32no—
369C4×D4—61no—
370C4×D4—61no—
371C4×D4—91no—
372C4×D4—91no—
373C4×D4—181no—
374C4×D4—181no—
375#117—31no—
376#117—181no—
377C2×C4⋊C4—31no—
378C2×C22⋊C4—61no—
379C2×C42—31no—
380C2×C42—181no—
381#107—92no—
382#106—92no—
383#103—92no—
384#102—32no—
385#102—32no—
386#102—92no—
387#97—92no—
388C4×C8—92no—
389C23×C3—24no—
390C23×C3—24no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—21no—
394C23×C3—42no—
395C23×C3—44no—
396C23×C3—42no—
397C23×C3—42no—
398C23×C3—42no—
399C23×C3—42no—
400C23×C3—82no—
401C23×C3—82no—
402C23×C3D3×D411yescharacteristic
403C23×C3C2×#6711yescharacteristic
404C22×D3—61no—
405C22×D3—61no—
406C22×D3—121no—
407C3×D4—24no—
408C3×D4—24no—
409C3×D4—22no—
410C3×D4—22no—
411C3×D4—24no—
412C3×D4—42no—
413C3×D4—44no—
414C3×D4C2×C4×D314yes—
415C3×D4C2×C4×D314yes—
416C2×C3×C4—21no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—21no—
420C2×C3×C4—31no—
421C2×C3×C4—31no—
422C2×C3×C4—31no—
423C2×C3×C4—31no—
424C2×C3×C4—62no—
425C2×C3×C4—62no—
426C2×C3×C4—61no—
427C2×C3×C4—61no—
428C2×C3×C4—124no—
429C2×C3×C4—121no—
430C2×C3×C4—124no—
431C2×C3×C4—122no—
432C2×C3×C4C2×C4×D312yes—
433C2×C3×C4C2×C4×D312yes—
434C2×C3×C4#23512yes—
435C2×C3×C4D3×D411yescharacteristic
436C2×C3×C4#23712yes—
437C2×C3×C4C2×#6711yescharacteristic
438C2×C3×C4C23×D311yescharacteristic
439C2×C3×C4C23×D311yescharacteristic
440#67—64no—
441#67—64no—
442#67—124no—
443C2×Dic3—22no—
444C2×Dic3—21no—
445C2×Dic3—21no—
446C2×Dic3—22no—
447C2×Dic3—41no—
448C2×Dic3—44no—
449C2×Dic3—42no—
450C2×Dic3—44no—
451C2×Dic3—61no—
452C2×Dic3—61no—
453C2×Dic3—121no—
454C2×Dic3C2×#6711yescharacteristic
455C2×Dic3C2×#6711yescharacteristic
456C2×Dic3C2×#6711yescharacteristic
457C2×Dic3C2×#6711yescharacteristic
458D12—32no—
459D12—32no—
460D12—62no—
461D12—61no—
462D12—61no—
463D12—121no—
464C4×D3—64no—
465C4×D3—64no—
466C4×D3—124no—
467C4×D3—122no—
468C4×D3—122no—
469C4×D3—122no—
470C4×D3—122no—
471Dic6—32no—
472Dic6—32no—
473Dic6—62no—
474Dic6—61no—
475Dic6—61no—
476Dic6—121no—
477C3×C8—62no—
478C3⋊C8—22no—
479C3⋊C8—34no—
480C3⋊C8—34no—
481C3⋊C8—64no—
482C2×C32—22no—
483C2×C32—44no—
484C2×C32C2×C4×D411yescharacteristic
485C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
486C2×C32#57511yescharacteristic
487C3⋊D3—42no—
488C24—21no—
489#41—94no—
490#41—182no—
491C2×Q8—91no—
492C2×D4—22no—
493C2×D4—21no—
494C2×D4—91no—
495C2×D4—181no—
496C2×D4#62414yescomplemented
497C2×D4C2×D3212yes—
498C22×C4—31no—
499C22×C4—31no—
500C22×C4—62no—
501C22×C4—62no—
502C22×C4—61no—
503C22×C4—124no—
504C22×C4—181no—
505C22×C4—181no—
506C22×C4—181no—
507C22×C4C2×D3211yescharacteristic
508SD16—98no—
509D8—98no—
510M16—62no—
511M16—94no—
512C2×C8—32no—
513C2×C8—92no—
514C4⋊C4—31no—
515C4⋊C4—31no—
516C4⋊C4—32no—
517C4⋊C4—61no—
518C4⋊C4—181no—
519C4⋊C4—181no—
520C22⋊C4—62no—
521C22⋊C4—62no—
522C22⋊C4—61no—
523C22⋊C4—181no—
524C22⋊C4—181no—
525C42—31no—
526C42—31no—
527C42—31no—
528C42—31no—
529C42—61no—
530C42—181no—
531C42—181no—
532C22×C3—21no—
533C22×C3—21no—
534C22×C3—21no—
535C22×C3—21no—
536C22×C3—24no—
537C22×C3—24no—
538C22×C3—21no—
539C22×C3—22no—
540C22×C3—41no—
541C22×C3—41no—
542C22×C3—44no—
543C22×C3—48no—
544C22×C3—48no—
545C22×C3—42no—
546C22×C3—42no—
547C22×C3—42no—
548C22×C3—42no—
549C22×C3—82no—
550C22×C3—82no—
551C22×C3—88no—
552C22×C3#67⋊C412yes—
553C22×C3C4×#6712yes—
554C22×C3C2×D3×D411yescharacteristic
555C22×C3C22×#6711yescharacteristic
556C2×D3—62no—
557C2×D3—62no—
558C2×D3—122no—
559C2×D3—121no—
560C2×D3—121no—
561C2×D3—121no—
562C2×D3—121no—
563C2×D3—241no—
564C2×D3—241no—
565C3×C4—21no—
566C3×C4—21no—
567C3×C4—22no—
568C3×C4—32no—
569C3×C4—61no—
570C3×C4—61no—
571C3×C4—61no—
572C3×C4—122no—
573C3×C4—121no—
574C3×C4—121no—
575C3×C4#67⋊C412yes—
576C3×C4C4×#6712yes—
577C3×C4C22×C4×D311yescharacteristic
578C3×C4C22×C4×D311yescharacteristic
579C3×C4C2×#23511yescharacteristic
580C3×C4C2×#23711yescharacteristic
581Dic3—21no—
582Dic3—21no—
583Dic3—21no—
584Dic3—41no—
585Dic3—41no—
586Dic3—42no—
587Dic3—62no—
588Dic3—62no—
589Dic3—122no—
590Dic3#93212yescomplemented
591C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
592C23—22no—
593C23—24no—
594C23—42no—
595C23—42no—
596C23—181no—
597C23D3×#6711yescharacteristic
598Q8—92no—
599Q8—181no—
600D4—22no—
601D4—24no—
602D4—92no—
603D4—184no—
604D4—181no—
605D4C2×#62414yes—
606C2×C4—31no—
607C2×C4—31no—
608C2×C4—31no—
609C2×C4—31no—
610C2×C4—62no—
611C2×C4—61no—
612C2×C4—61no—
613C2×C4—62no—
614C2×C4—124no—
615C2×C4—121no—
616C2×C4—124no—
617C2×C4—122no—
618C2×C4—181no—
619C2×C4—184no—
620C2×C4—362no—
621C2×C4—362no—
622C2×C4#380412yes—
623C2×C4C2×#62412yes—
624C2×C4D3×#6711yescharacteristic
625C2×C4C22×D3211yescharacteristic
626C8—62no—
627C8—94no—
628C2×C3—22no—
629C2×C3—22no—
630C2×C3—21no—
631C2×C3—21no—
632C2×C3—21no—
633C2×C3—42no—
634C2×C3—44no—
635C2×C3—44no—
636C2×C3—84no—
637C2×C3C2×#67⋊C411yescharacteristic
638C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
639C2×C3#577311yescharacteristic
640C2×C3C2×C4×#6711yescharacteristic
641C2×C3C2×#93211yescharacteristic
642C2×C3#582211yescharacteristic
643D3—122no—
644D3—122no—
645D3—242no—
646C22—21no—
647C22—21no—
648C22—24no—
649C22—48no—
650C22—42no—
651C22—42no—
652C22—182no—
653C22—361no—
654C22—361no—
655C22#6395212yes—
656C22C2×D3×#6711yescharacteristic
657C4—32no—
658C4—61no—
659C4—61no—
660C4—61no—
661C4—122no—
662C4—121no—
663C4—121no—
664C4—182no—
665C4#6395212yes—
666C4C2×#380411yescharacteristic
667C4C22×#62411yescharacteristic
668C3—21no—
669C3#7891411yescharacteristic, complemented
670C3C4×#93211yescharacteristic, complemented
671C2—22no—
672C2—44no—
673C2—362no—
674C2D3×#93211yescharacteristic
675C2#1059509511yescharacteristic
676C2C2×#6395211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalC2×#64141C2
cosocleC2×C32×C4C24
hypercenterC22×D4D32
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ 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
2. C2×C3×D4×Dic3C2semidirect
3. #10594954C2semidirect
4. C3×#5215C2semidirect
5. #10591405C2semidirect
6. #10591404C2semidirect
7. #10591401C2semidirect
8. #10591400C2semidirect
9. #10591139C2semidirect
10. #10591106C2semidirect
11. Dic3×#208C2semidirect
18. #64141C4semidirect
32. #63894C22semidirect
33. #63894C22semidirect
36. #63844C22semidirect
37. #63844C22semidirect
40. #63576C22semidirect
41. #63574C22semidirect
42. #63567C22semidirect
43. #63564C22semidirect
44. #63554C22semidirect
45. Dic3×C3⋊C8C22semidirect
47. C2×D4×Dic3D3semidirect
54. #5215D3semidirect
72. C2×C32×D4C2×C4semidirect
77. #3828C2×C4semidirect
89. #3754C2×C4semidirect
90. #3753C2×C4semidirect
91. #3748C2×C4semidirect
200. C4⋊(C3⋊D3)C22×C4semidirect
203. #634C22×C4semidirect
218. C3⋊(C3⋊C8)C22×C4semidirect
242. C2×C3×D4C4×D3semidirect
243. C2×C3×D4C4×D3semidirect
356. C3×Dic3AGL(1,ℤ/8)semidirect
496. C2×D4#624semidirect
590. Dic3#932semidirect
591. C32C4×AGL(1,ℤ/8)semidirect
669. C3#78914semidirect
670. C3C4×#932semidirect

Maximal subgroups

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

subgroupindex
C2×#641412
C2×C3×D4×Dic32
#105949542
C3×#52152
#105914052
#105914042
#105914012
#105914002
#105911392
#105911062
Dic3×#2082
C4×#9323
#789143