Finite Group Databasebeta

← #11878865

Subgroups — #11878865

Order 1152.

1040 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5578C211yesmaximal, characteristic, complemented
2D3×#874C211yesmaximal, characteristic
3#10592726C211yesmaximal, characteristic, complemented
4C3×#5027C211yesmaximal, characteristic, complemented
5#10591651C212yesmaximal, complemented
6#10591618C212yesmaximal, complemented
7#10590596C212yesmaximal, complemented
8#10590548C212yesmaximal, complemented
9#10590367C211yesmaximal, characteristic, complemented
10#10590364C211yesmaximal, characteristic, complemented
11#10590248C211yesmaximal, characteristic, complemented
12#83355—31nomaximal
13#80387—31nomaximal
14C2×D3×D12—21no—
15C2×D3×D12—21no—
16C2×D3×D12C2212yes—
17C32×C4×Q8C2211yescharacteristic, complemented
18C2×#3755C2212yescomplemented
19#64083C2211yescharacteristic
20C3×#946C2211yescharacteristic
21C3×#944C2211yescharacteristic, complemented
22C2×C3×#215C2212yescomplemented
23C3×#897C2211yescharacteristic
24C3×#896—21no—
25C3×#889—21no—
26C3×#888C2211yescharacteristic, complemented
27C3×#874C2211yescharacteristic
28C3×#872—21no—
29C3×C42×D3C2211yescharacteristic
30C3×C4×Dic6—21no—
31C3×C4×Dic6C2211yescharacteristic, complemented
32#63911—21no—
33#63911—21no—
34#63911C2212yes—
35C2×#3717C2212yescomplemented
36C2×#3715C2212yescomplemented
37#63636C2212yescomplemented
38C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
39C3×#809C2212yescomplemented
40C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
41#63564C2212yescomplemented
42#63562C2212yescomplemented
43(C2×D3)⋊(C3⋊C8)C2212yes—
44Dic3×C3⋊C8C2212yescomplemented
45C3×#533—31no—
46D3×#127—31no—
47#5578D311yescharacteristic, complemented
48C2×#874—31no—
49C3×#460—31no—
50#5175—32no—
51#5169—32no—
52#5088—32no—
53#5085—32no—
54#5075—31no—
55#5046—32no—
56#5046—32no—
57#5027—31no—
58#5027—31no—
59#5027—31no—
60#5027—31no—
61#5027—61no—
62#5027D311yescharacteristic, complemented
63#4925—31no—
64#4848—31no—
65#4833—31no—
66#4776—32no—
67#4760—32no—
68C22×D32—22no—
69C2×C32×Q8C2311yescharacteristic
70C2×C4⋊(C3⋊D3)—21no—
71C2×C4⋊(C3⋊D3)—21no—
72C2×C4⋊(C3⋊D3)C2312yes—
73C2×C3×D12—21no—
74C2×C3×D12—21no—
75C2×C3×D12C2312yes—
76C2×C3×C4×D3D411yescharacteristic
77C2×C3×C4×D3D411yescharacteristic
78C2×C3×C4×D3C2311yescharacteristic
79C2×C3×Dic6—21no—
80C2×C3×Dic6C2311yescharacteristic
81C2×#626—22no—
82C2×#626—22no—
83C2×#626—22no—
84D3×D12—42no—
85D3×D12—42no—
86D3×D12—44no—
87D3×D12—44no—
88C32×C4⋊C4—21no—
89C32×C4⋊C4C2311yescharacteristic
90C32×C42—21no—
91C32×C42C2311yescharacteristic
92#3755—42no—
93C2×C3⋊(C3⋊C8)C2312yes—
94C3×#215—42no—
95C3×(C2×D3)⋊C4—21no—
96C3×(C2×D3)⋊C4—21no—
97C3×C4⋊Dic3—21no—
98C3×C4⋊Dic3C2311yescharacteristic
99C3×Dic3⋊C4—21no—
100C3×Dic3⋊C4—21no—
101C3×Dic3⋊C4—21no—
102C3×Dic3⋊C4—21no—
103C3×Dic3⋊C4—21no—
104C3×C4×Dic3—21no—
105C3×C4×Dic3D411yescharacteristic
106C3×C4×Dic3D411yescharacteristic
107C3×C4×Dic3C2311yescharacteristic
108C2×C3×C3⋊C8C2312yes—
109#3717—42no—
110#3715—42no—
111#3208—91noSylow
112C2×D3×D4—32no—
113C2×D3×D4—61no—
114C2×D3×D4—61no—
115C22×D12—32no—
116C22×D12—61no—
117C22×D12—61no—
118C2×C3×SD16—32no—
119C3×C4⋊Q8—31no—
120C3×C4⋊Q8—31no—
121C3×#127—31no—
122C3×#125—61no—
123C3×C22⋊Q8—31no—
124C3×C22⋊Q8—31no—
125C3×C22⋊Q8—61no—
126C3×C4×Q8—21no—
127C3×C4×Q8—31no—
128C3×C4×Q8—61no—
129C3×C4×Q8C2×D311yescharacteristic, complemented
130C3×C4×Q8C2×D311yescharacteristic, complemented
131C3×#117—61no—
132C2×C3×C42—31no—
133#946C2×D311yescharacteristic
134#944C2×D311yescharacteristic, complemented
135C2×#215—32no—
136C2×#215—32no—
137C2×#215—32no—
138C2×#215—32no—
139C2×#215—62no—
140C2×#215C2×D312yescomplemented
141#940—32no—
142#940—61no—
143#940—61no—
144C2×#214—32no—
145C2×#204—32no—
146#897C2×D311yescharacteristic
147#896—21no—
148#889—21no—
149#888C2×D311yescharacteristic, complemented
150#874—32no—
151#874—31no—
152#874—31no—
153#874—61no—
154#874—61no—
155#874—61no—
156#874C2×D311yescharacteristic
157#872—21no—
158C42×D3C2×D311yescharacteristic
159C4×Dic6—21no—
160C4×Dic6C2×D311yescharacteristic, complemented
161C3×C4⋊C8—31no—
162C3×#102—32no—
163#832—32no—
164#830—32no—
165#821—32no—
166(C2×D3)⋊C8—32no—
167C8×Dic3—32no—
168#809—32no—
169#809—32no—
170#809—32no—
171#809—32no—
172#809—62no—
173#809C2×D312yescomplemented
174C4⋊(C3⋊C8)—31no—
175C4⋊(C3⋊C8)—31no—
176C4⋊(C3⋊C8)—61no—
177C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
178C4×C3⋊C8—32no—
179C22×C3⋊D3—22no—
180C22×C3×D3—22no—
181C22×C3×D3C2×D411yescharacteristic
182C2×D32—44no—
183C2×D32—44no—
184C2×D32—44no—
185C32×Q8—21no—
186C32×Q8—21no—
187C2×C32×C4—21no—
188C2×C32×C4—21no—
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2411yescharacteristic
192C4⋊(C3⋊D3)—22no—
193C4⋊(C3⋊D3)—22no—
194C4⋊(C3⋊D3)—42no—
195C4⋊(C3⋊D3)—42no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3C2×D411yescharacteristic
199C2×C3×Dic3C2×D411yescharacteristic
200C2×C3×Dic3C2×D411yescharacteristic
201C3×D12—22no—
202C3×D12—22no—
203C3×D12—42no—
204C3×D12—42no—
205C3×C4×D3—21no—
206C3×C4×D3—21no—
207C3×C4×D3—22no—
208C3×C4×D3SD1614yescomplemented
209C3×Dic6—21no—
210C3×Dic6—21no—
211C3×Dic6—42no—
212#626—44no—
213#626—44no—
214#626—44no—
215C3⋊(C3⋊C8)—22no—
216C3×C3⋊C8—22no—
217#533—31no—
218C2×#127—91no—
219#492—92no—
220#486—92no—
221#460—31no—
222#460—91no—
223#460—91no—
224#460—91no—
225#450—92no—
226#450—92no—
227#431—91no—
228C23×D3—62no—
229C23×D3—62no—
230C2×C3×Q8—21no—
231C2×C3×Q8—31no—
232C2×C3×Q8—61no—
233C2×C3×Q8C22×D311yescharacteristic
234C2×C3×Q8C22×D311yescharacteristic
235C2×C3×D4—32no—
236C2×C3×D4—61no—
237C2×C3×D4—61no—
238C22×C3×C4—31no—
239C22×C3×C4—31no—
240C22×C3×C4—31no—
241C2×#67—62no—
242C2×#67—62no—
243C2×#67—62no—
244D3×D4—122no—
245D3×D4—122no—
246D3×D4—124no—
247D3×D4—124no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—32no—
251C2×D12—32no—
252C2×D12—62no—
253C2×D12—62no—
254C2×D12—62no—
255C2×D12—62no—
256C2×D12—61no—
257C2×D12—61no—
258C2×D12—61no—
259C2×D12—61no—
260C2×D12—121no—
261C2×D12—121no—
262C2×D12—122no—
263C2×D12—122no—
264C2×D12—124no—
265C2×D12—124no—
266C2×D12C22×D312yes—
267C2×C4×D3#6711yescharacteristic
268C2×C4×D3#6711yescharacteristic
269C2×C4×D3C22×D311yescharacteristic
270C2×Dic6—21no—
271C2×Dic6C22×D311yescharacteristic
272C3×SD16—122no—
273C2×C3×C8—32no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—31no—
278C3×C4⋊C4—41no—
279C3×C4⋊C4—61no—
280C3×C4⋊C4—61no—
281C3×C4⋊C4—61no—
282C3×C4⋊C4—61no—
283C3×C4⋊C4—61no—
284C3×C4⋊C4—61no—
285C3×C4⋊C4C22×D311yescharacteristic
286C3×C4⋊C4C22×D311yescharacteristic
287C3×C22⋊C4—61no—
288C3×C22⋊C4—61no—
289C3×C42—21no—
290C3×C42—21no—
291C3×C42—21no—
292C3×C42—31no—
293C3×C42—31no—
294C3×C42—31no—
295C3×C42—41no—
296C3×C42—61no—
297C3×C42C22×D311yescharacteristic
298C3×C42C22×D311yescharacteristic
299#215—42no—
300#215—122no—
301#215—122no—
302#215—122no—
303#215—122no—
304#215—124no—
305#214—122no—
306(C2×D3)⋊C4—21no—
307(C2×D3)⋊C4—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3C22×D311yescharacteristic
310Dic3⋊C4—21no—
311Dic3⋊C4—21no—
312Dic3⋊C4—21no—
313Dic3⋊C4—21no—
314Dic3⋊C4—21no—
315C4×Dic3—21no—
316C4×Dic3#6711yescharacteristic
317C4×Dic3#6711yescharacteristic
318C4×Dic3C22×D311yescharacteristic
319C2×C3⋊C8—32no—
320C2×C3⋊C8—32no—
321C2×C3⋊C8—62no—
322C2×C3⋊C8C22×D312yes—
323#204—122no—
324C22×C32C22×D411yescharacteristic
325C2×C3⋊D3—42no—
326C2×C3⋊D3—42no—
327C2×C3⋊D3—42no—
328C2×C3×D3—21no—
329C2×C3×D3—21no—
330C2×C3×D3—42no—
331C2×C3×D3—42no—
332C2×C3×D3—42no—
333C2×C3×D3C2×SD1612yes—
334D32—88no—
335C32×C4—21no—
336C32×C4—41no—
337C32×C4—41no—
338C32×C4C2×SD1612yes—
339C32×C4H(5,𝔽2)11yescharacteristic
340C32×C4H(5,𝔽2)11yescharacteristic
341C3×Dic3—21no—
342C3×Dic3—41no—
343C3×Dic3—41no—
344C3×Dic3C2×SD1612yes—
345C3×Dic3AGL(1,ℤ/8)12yes—
346C22×D4—92no—
347C22×D4—181no—
348C22×D4—181no—
349C2×SD16—32no—
350C2×SD16—92no—
351C2×SD16—92no—
352C2×SD16—92no—
353C4⋊Q8—31no—
354C4⋊Q8—31no—
355#127—31no—
356#127—92no—
357#127—91no—
358#127—181no—
359#127—181no—
360#125—61no—
361C22⋊Q8—31no—
362C22⋊Q8—31no—
363C22⋊Q8—61no—
364C4×Q8—31no—
365C4×Q8—61no—
366C4×Q8D3211yescharacteristic, complemented
367#117—61no—
368C2×C42—31no—
369C4⋊C8—31no—
370C4⋊C8—91no—
371#102—32no—
372#102—92no—
373#102—92no—
374#102—92no—
375C22⋊C8—92no—
376C4×C8—92no—
377C23×C3—31no—
378C23×C3—62no—
379C22×D3—22no—
380C22×D3—62no—
381C22×D3—62no—
382C22×D3—122no—
383C22×D3—124no—
384C22×D3—124no—
385C22×D3—124no—
386C22×D3—124no—
387C22×D3—124no—
388C22×D3—124no—
389C22×D3C2×#6711yescharacteristic
390C3×Q8—22no—
391C3×Q8—21no—
392C3×Q8—21no—
393C3×Q8—21no—
394C3×Q8—21no—
395C3×Q8—41no—
396C3×Q8—61no—
397C3×Q8—61no—
398C3×Q8—122no—
399C3×D4—62no—
400C3×D4—62no—
401C3×D4—122no—
402C3×D4—122no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—31no—
411C2×C3×C4—31no—
412C2×C3×C4—34no—
413C2×C3×C4—31no—
414C2×C3×C4—41no—
415C2×C3×C4—41no—
416C2×C3×C4—62no—
417C2×C3×C4—61no—
418C2×C3×C4—61no—
419C2×C3×C4—61no—
420C2×C3×C4—61no—
421C2×C3×C4D3×D411yescharacteristic
422C2×C3×C4D3×D411yescharacteristic
423C2×C3×C4C2×#6711yescharacteristic
424C2×C3×C4C2×#6711yescharacteristic
425C2×C3×C4C23×D311yescharacteristic
426C2×C3×C4C23×D311yescharacteristic
427#67—124no—
428#67—124no—
429#67—124no—
430C2×Dic3—21no—
431C2×Dic3—21no—
432C2×Dic3C2×#6711yescharacteristic
433C2×Dic3C2×#6711yescharacteristic
434C2×Dic3C2×#6711yescharacteristic
435D12—22no—
436D12—22no—
437D12—42no—
438D12—42no—
439D12—62no—
440D12—62no—
441D12—62no—
442D12—62no—
443D12—122no—
444D12—122no—
445D12—122no—
446D12—122no—
447D12—124no—
448D12—124no—
449D12—124no—
450D12—122no—
451D12—122no—
452D12—242no—
453D12—242no—
454C4×D3—21no—
455C4×D3—21no—
456C4×D3—22no—
457C4×D3#21514yescomplemented
458Dic6—21no—
459Dic6—21no—
460Dic6—42no—
461C3×C8—62no—
462C3⋊C8—22no—
463C3⋊C8—62no—
464C3⋊C8—62no—
465C3⋊C8—122no—
466C2×C32#53511yescharacteristic
467C2×C32C22×SD1611yescharacteristic
468C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
469C3⋊D3—82no—
470C3×D3—22no—
471C3×D3—82no—
472C24—182no—
473C2×Q8—31no—
474C2×Q8—61no—
475C2×Q8C2×D3211yescharacteristic
476C2×D4—32no—
477C2×D4—61no—
478C2×D4—61no—
479C2×D4—92no—
480C2×D4—182no—
481C2×D4—182no—
482C2×D4—182no—
483C2×D4—181no—
484C2×D4—181no—
485C2×D4—364no—
486C2×D4—362no—
487C2×D4—362no—
488C2×D4—364no—
489C22×C4—31no—
490C22×C4—31no—
491C22×C4—31no—
492SD16—122no—
493SD16—362no—
494SD16—362no—
495SD16—362no—
496C2×C8—32no—
497C2×C8—92no—
498C4⋊C4—21no—
499C4⋊C4—31no—
500C4⋊C4—61no—
501C4⋊C4—61no—
502C4⋊C4—61no—
503C4⋊C4—61no—
504C4⋊C4—61no—
505C4⋊C4—61no—
506C4⋊C4C2×D3211yescharacteristic
507C22⋊C4—61no—
508C22⋊C4—61no—
509C42—21no—
510C42—31no—
511C42—31no—
512C42—31no—
513C42—61no—
514C42C2×D3211yescharacteristic
515C22×C3—21no—
516C22×C3—32no—
517C22×C3—61no—
518C22×C3—61no—
519C22×C3—122no—
520C22×C3—122no—
521C22×C3—122no—
522C22×C3C2×D3×D411yescharacteristic
523C22×C3C22×#6711yescharacteristic
524C2×D3—21no—
525C2×D3—21no—
526C2×D3—42no—
527C2×D3—42no—
528C2×D3—42no—
529C2×D3—122no—
530C2×D3—122no—
531C2×D3—122no—
532C2×D3—122no—
533C2×D3—122no—
534C2×D3—122no—
535C2×D3—242no—
536C2×D3—242no—
537C2×D3—242no—
538C2×D3—248no—
539C2×D3—248no—
540C2×D3C2×#21512yes—
541C3×C4—21no—
542C3×C4—21no—
543C3×C4—21no—
544C3×C4—21no—
545C3×C4—22no—
546C3×C4—32no—
547C3×C4—32no—
548C3×C4—41no—
549C3×C4—42no—
550C3×C4—41no—
551C3×C4—41no—
552C3×C4—41no—
553C3×C4—41no—
554C3×C4—61no—
555C3×C4—81no—
556C3×C4—121no—
557C3×C4—121no—
558C3×C4D3×SD1612yes—
559C3×C4C2×#21512yes—
560C3×C4#100411yescharacteristic
561C3×C4#100911yescharacteristic
562C3×C4#100911yescharacteristic
563C3×C4#100911yescharacteristic
564Dic3—21no—
565Dic3—41no—
566Dic3—41no—
567Dic3C2×#21512yes—
568Dic3#94912yes—
569C32#320811yescharacteristic, complemented, Sylow
570C23—31no—
571C23—62no—
572C23—182no—
573C23—364no—
574C23—364no—
575C23—364no—
576Q8—21no—
577Q8—21no—
578Q8—61no—
579Q8—61no—
580Q8—122no—
581D4—62no—
582D4—62no—
583D4—122no—
584D4—122no—
585D4—182no—
586D4—182no—
587D4—362no—
588D4—364no—
589D4—364no—
590D4—364no—
591D4—362no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—31no—
595C2×C4—31no—
596C2×C4—34no—
597C2×C4—31no—
598C2×C4—62no—
599C2×C4—61no—
600C2×C4—61no—
601C2×C4—61no—
602C2×C4—61no—
603C2×C4D3×#6711yescharacteristic
604C2×C4D3×#6711yescharacteristic
605C2×C4C22×D3211yescharacteristic
606C8—62no—
607C8—182no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—62no—
612C2×C3—242no—
613C2×C3#560711yescharacteristic
614C2×C3C2×D3×SD1611yescharacteristic
615C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
616C2×C3C22×#21511yescharacteristic
617C2×C3C2×#94911yescharacteristic
618C2×C3#583011yescharacteristic
619D3—22no—
620D3—82no—
621D3—242no—
622D3—242no—
623D3—482no—
624C22—32no—
625C22—61no—
626C22—61no—
627C22—122no—
628C22—122no—
629C22—122no—
630C22—362no—
631C22—362no—
632C22—362no—
633C22—728no—
634C22C2×D3×#6711yescharacteristic
635C4—21no—
636C4—32no—
637C4—32no—
638C4—41no—
639C4—41no—
640C4—61no—
641C4—121no—
642C4—121no—
643C4D3×#21512yes—
644C4#6430711yescharacteristic
645C4#6430811yescharacteristic
646C3—21no—
647C3#8038711yescharacteristic, complemented
648C3#8335511yescharacteristic, complemented
649C2—62no—
650C2—242no—
651C2—722no—
652C2#1059506411yescharacteristic
653C2C2×D3×#21511yescharacteristic
654C2D3×#94911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalD3×#874C2
hypercenterC4×Q8D32
hypocenterC32#3208
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5578C2semidirect
3. #10592726C2semidirect
4. C3×#5027C2semidirect
5. #10591651C2semidirect
6. #10591618C2semidirect
7. #10590596C2semidirect
8. #10590548C2semidirect
9. #10590367C2semidirect
10. #10590364C2semidirect
11. #10590248C2semidirect
17. C32×C4×Q8C22semidirect
18. C2×#3755C22semidirect
21. C3×#944C22semidirect
22. C2×C3×#215C22semidirect
26. C3×#888C22semidirect
31. C3×C4×Dic6C22semidirect
35. C2×#3717C22semidirect
36. C2×#3715C22semidirect
37. #63636C22semidirect
38. C4⋊(C3⋊(C3⋊C8))C22semidirect
39. C3×#809C22semidirect
40. C3×C4⋊(C3⋊C8)C22semidirect
41. #63564C22semidirect
42. #63562C22semidirect
44. Dic3×C3⋊C8C22semidirect
47. #5578D3semidirect
62. #5027D3semidirect
129. C3×C4×Q8C2×D3semidirect
130. C3×C4×Q8C2×D3semidirect
134. #944C2×D3semidirect
140. C2×#215C2×D3semidirect
149. #888C2×D3semidirect
160. C4×Dic6C2×D3semidirect
173. #809C2×D3semidirect
177. C4⋊(C3⋊C8)C2×D3semidirect
208. C3×C4×D3SD16semidirect
366. C4×Q8D32semidirect
457. C4×D3#215semidirect
569. C32#3208semidirect
647. C3#80387semidirect
648. C3#83355semidirect

Maximal subgroups

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

subgroupindex
C3×#55782
D3×#8742
#105927262
C3×#50272
#105916512
#105916182
#105905962
#105905482
#105903672
#105903642
#105902482
#833553
#803873