Finite Group Databasebeta

← #11878857

Subgroups — #11878857

Order 1152.

1070 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5622C211yesmaximal, characteristic, complemented
2C2×#63911C211yesmaximal, characteristic
3#10592745C211yesmaximal, characteristic, complemented
4C3×#5046C211yesmaximal, characteristic, complemented
5#10591618C212yesmaximal, complemented
6#10591617C212yesmaximal, complemented
7#10591183C211yesmaximal, characteristic, complemented
8#10591169C211yesmaximal, characteristic, complemented
9#10591053C211yesmaximal, characteristic, complemented
10#10590549C212yesmaximal, complemented
11#10590548C212yesmaximal, complemented
12#83355—31nomaximal
13#80138—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×#626—21no—
17C22×#626—21no—
18C32×C22⋊Q8C2211yescharacteristic
19C2×#3755C2212yescomplemented
20C3×Q8×Dic3C2211yescharacteristic, complemented
21C3×#944C2211yescharacteristic, complemented
22C2×C3×#215C2212yescomplemented
23C3×#924C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C3×#889—21no—
26C3×#888C2211yescharacteristic, complemented
27C3×#887—21no—
28C3×#887C2211yescharacteristic, complemented
29C3×#878—21no—
30C3×#877—21no—
31#63911—21no—
32#63911—21no—
33#63911C2212yes—
34#63911C2212yes—
35C2×#3717C2212yescomplemented
36C2×#3715C2212yescomplemented
37#63657C2211yescharacteristic
38#63636C2212yescomplemented
39C3×#830C2211yescharacteristic
40C3×#809C2212yescomplemented
41Dic3⋊(C3⋊C8)C2212yescomplemented
42#63564C2212yescomplemented
43#63562C2212yescomplemented
44Dic3×C3⋊C8C2212yescomplemented
45C3×#533—31no—
46C2×#940—31no—
47#5622D311yescharacteristic, complemented
48C2×#874—31no—
49C3×#450—31no—
50#5218—31no—
51#5175—32no—
52#5163—32no—
53#5088—32no—
54#5085—32no—
55#5046—31no—
56#5046—31no—
57#5046—31no—
58#5046—31no—
59#5046—61no—
60#5046D311yescharacteristic, complemented
61#5027—32no—
62#5027—32no—
63#4925—31no—
64#4762—32no—
65#4760—32no—
66#4731—31no—
67#4718—31no—
68C23×C3⋊D3—21no—
69C23×C3×D3—21no—
70C2×C32×Q8C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C2×C4⋊(C3⋊D3)—21no—
73C2×C4⋊(C3⋊D3)—42no—
74C2×C4⋊(C3⋊D3)C2312yes—
75C22×C3×Dic3D411yescharacteristic
76C22×C3×Dic3D411yescharacteristic
77C2×C3×D12—21no—
78C2×C3×D12—42no—
79C2×C3×D12C2312yes—
80C2×C3×Dic6—21no—
81C2×C3×Dic6C2311yescharacteristic
82C2×#626—22no—
83C2×#626—22no—
84C2×#626—22no—
85C2×#626—22no—
86C2×#626—44no—
87C2×#626—44no—
88C32×C4⋊C4—21no—
89C32×C4⋊C4C2311yescharacteristic
90C32×C22⋊C4—21no—
91#3755—42no—
92C2×C3⋊(C3⋊C8)C2312yes—
93C3×#217—21no—
94C3×#215—42no—
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3C2311yescharacteristic
97C3×Dic3⋊C4—21no—
98C3×Dic3⋊C4—21no—
99C3×Dic3⋊C4—21no—
100C3×Dic3⋊C4—21no—
101C3×Dic3⋊C4—21no—
102C3×C4×Dic3—21no—
103C3×C4×Dic3—21no—
104C3×C4×Dic3D411yescharacteristic
105C3×C4×Dic3D411yescharacteristic
106C3×C4×Dic3C2311yescharacteristic
107C3×C4×Dic3C2311yescharacteristic
108C2×C3×C3⋊C8C2312yes—
109#3717—42no—
110#3715—42no—
111#3208—91noSylow
112C22×C3×D4—31no—
113C22×#67—61no—
114C22×#67—61no—
115C22×D12—31no—
116C22×D12—31no—
117C22×D12—61no—
118C22×D12—61no—
119C22×D12—61no—
120C22×D12C2×D311yescharacteristic
121C2×C3×SD16—32no—
122C3×C4⋊Q8—31no—
123C3×C4⋊Q8—31no—
124C3×#125—61no—
125C3×C22⋊Q8—21no—
126C3×C22⋊Q8—31no—
127C3×C22⋊Q8—61no—
128C3×C22⋊Q8C2×D311yescharacteristic
129C3×C22⋊Q8C2×D311yescharacteristic
130C3×C4×Q8—31no—
131C3×C4×Q8—31no—
132C3×C4×Q8—61no—
133C3×#117—61no—
134C2×C3×C42—31no—
135Q8×Dic3C2×D311yescharacteristic, complemented
136#944C2×D311yescharacteristic, complemented
137C2×#215—32no—
138C2×#215—32no—
139C2×#215—32no—
140C2×#215—32no—
141C2×#215—62no—
142C2×#215C2×D312yescomplemented
143#940—32no—
144#940—32no—
145#940—61no—
146#940—61no—
147C2×#214—32no—
148#924C2×D311yescharacteristic
149C2×C4×Dic3C2×D311yescharacteristic
150C2×#204—32no—
151#889—21no—
152#888C2×D311yescharacteristic, complemented
153#887—21no—
154#887C2×D311yescharacteristic, complemented
155#878—21no—
156#877—21no—
157#874—32no—
158#874—32no—
159#874—61no—
160#874—61no—
161C3×#102—32no—
162C3×C22⋊C8—31no—
163#832—32no—
164#830—31no—
165#830—31no—
166#830—61no—
167#830C2×D311yescharacteristic
168#821—32no—
169Dic3⋊C8—32no—
170C8×Dic3—32no—
171#809—32no—
172#809—32no—
173#809—32no—
174#809—32no—
175#809—62no—
176#809C2×D312yescomplemented
177C4⋊(C3⋊C8)—32no—
178C4×C3⋊C8—32no—
179C23×C32C2×D411yescharacteristic
180C22×C3⋊D3—22no—
181C22×C3⋊D3—42no—
182C22×C3⋊D3—42no—
183C22×C3⋊D3—42no—
184C22×C3×D3—22no—
185C22×C3×D3—42no—
186C22×C3×D3—42no—
187C22×C3×D3—42no—
188C32×Q8—22no—
189C2×C32×C4—22no—
190C2×C32×C4—21no—
191C2×C32×C4—21no—
192C2×C32×C4C2×D411yescharacteristic
193C2×C32×C4C2411yescharacteristic
194C4⋊(C3⋊D3)—22no—
195C4⋊(C3⋊D3)—22no—
196C4⋊(C3⋊D3)—42no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3SD1614yescomplemented
201C2×C3×Dic3C2×D411yescharacteristic
202C2×C3×Dic3C2×D411yescharacteristic
203C2×C3×Dic3C2×D411yescharacteristic
204C2×C3×Dic3C2×D411yescharacteristic
205C3×D12—22no—
206C3×D12—22no—
207C3×D12—42no—
208C3×Dic6—22no—
209C3×Dic6—42no—
210#626—44no—
211#626—44no—
212#626—44no—
213#626—44no—
214C3⋊(C3⋊C8)—22no—
215C3×C3⋊C8—22no—
216#533—31no—
217C2×#127—91no—
218#492—92no—
219#486—92no—
220#460—92no—
221#460—92no—
222#450—31no—
223#450—91no—
224#450—91no—
225#450—91no—
226#431—91no—
227C24×C3—61no—
228C23×D3—21no—
229C23×D3—61no—
230C23×D3—61no—
231C23×D3—121no—
232C2×C3×Q8—21no—
233C2×C3×Q8—31no—
234C2×C3×Q8—61no—
235C2×C3×Q8C22×D311yescharacteristic
236C2×C3×Q8C22×D311yescharacteristic
237C2×C3×D4—32no—
238C2×C3×D4—61no—
239C2×C3×D4—122no—
240C22×C3×C4—21no—
241C22×C3×C4—31no—
242C22×C3×C4—31no—
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C2×#67—62no—
246C2×#67—62no—
247C2×#67—62no—
248C2×#67—62no—
249C2×#67—124no—
250C2×#67—124no—
251C22×Dic3#6711yescharacteristic
252C22×Dic3#6711yescharacteristic
253C2×D12—21no—
254C2×D12—32no—
255C2×D12—32no—
256C2×D12—42no—
257C2×D12—62no—
258C2×D12—62no—
259C2×D12—62no—
260C2×D12—62no—
261C2×D12—62no—
262C2×D12—61no—
263C2×D12—61no—
264C2×D12—121no—
265C2×D12—122no—
266C2×D12—122no—
267C2×D12—124no—
268C2×D12—124no—
269C2×D12—124no—
270C2×D12C22×D312yes—
271C2×Dic6—21no—
272C2×Dic6C22×D311yescharacteristic
273C3×SD16—122no—
274C2×C3×C8—32no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—31no—
279C3×C4⋊C4—41no—
280C3×C4⋊C4—61no—
281C3×C4⋊C4—61no—
282C3×C4⋊C4—61no—
283C3×C4⋊C4—61no—
284C3×C4⋊C4—61no—
285C3×C4⋊C4—61no—
286C3×C4⋊C4C22×D311yescharacteristic
287C3×C4⋊C4C22×D311yescharacteristic
288C3×C22⋊C4—21no—
289C3×C22⋊C4—21no—
290C3×C22⋊C4—41no—
291C3×C22⋊C4—61no—
292C3×C42—31no—
293C3×C42—31no—
294C3×C42—31no—
295C3×C42—31no—
296C3×C42—61no—
297C3×C42—61no—
298#217—21no—
299#215—42no—
300#215—122no—
301#215—122no—
302#215—122no—
303#215—122no—
304#215—124no—
305#214—122no—
306C4⋊Dic3—21no—
307C4⋊Dic3C22×D311yescharacteristic
308Dic3⋊C4—21no—
309Dic3⋊C4—21no—
310Dic3⋊C4—21no—
311Dic3⋊C4—21no—
312Dic3⋊C4—21no—
313C4×Dic3—21no—
314C4×Dic3—21no—
315C4×Dic3#6711yescharacteristic
316C4×Dic3#6711yescharacteristic
317C4×Dic3C22×D311yescharacteristic
318C4×Dic3C22×D311yescharacteristic
319C2×C3⋊C8—32no—
320C2×C3⋊C8—32no—
321C2×C3⋊C8—62no—
322C2×C3⋊C8C22×D312yes—
323#204—122no—
324C22×C32—21no—
325C22×C32—21no—
326C22×C32C2×SD1612yes—
327C22×C32C22×D411yescharacteristic
328C2×C3⋊D3—42no—
329C2×C3⋊D3—42no—
330C2×C3⋊D3—42no—
331C2×C3⋊D3—84no—
332C2×C3×D3—42no—
333C2×C3×D3—42no—
334C2×C3×D3—42no—
335C2×C3×D3—84no—
336C32×C4—21no—
337C32×C4—41no—
338C32×C4—41no—
339C32×C4H(5,𝔽2)12yes—
340C3×Dic3—21no—
341C3×Dic3—41no—
342C3×Dic3—41no—
343C3×Dic3C2×SD1612yes—
344C3×Dic3C2×SD1612yes—
345C3×Dic3AGL(1,ℤ/8)12yes—
346C22×D4—31no—
347C22×D4—91no—
348C22×D4—181no—
349C22×D4—181no—
350C2×SD16—32no—
351C2×SD16—92no—
352C2×SD16—92no—
353C2×SD16—92no—
354C4⋊Q8—31no—
355C4⋊Q8—31no—
356#127—92no—
357#127—92no—
358#127—181no—
359#127—181no—
360#125—61no—
361C22⋊Q8—31no—
362C22⋊Q8—61no—
363C22⋊Q8D3211yescharacteristic
364C4×Q8—31no—
365C4×Q8—31no—
366C4×Q8—61no—
367#117—61no—
368C2×C42—31no—
369C4⋊C8—92no—
370#102—32no—
371#102—92no—
372#102—92no—
373#102—92no—
374C22⋊C8—31no—
375C22⋊C8—91no—
376C4×C8—92no—
377C23×C3—21no—
378C23×C3—62no—
379C23×C3—122no—
380C23×C3—122no—
381C23×C3—122no—
382C23×C3D3×D411yescharacteristic
383C23×C3C2×#6711yescharacteristic
384C22×D3—22no—
385C22×D3—42no—
386C22×D3—42no—
387C22×D3—42no—
388C22×D3—62no—
389C22×D3—62no—
390C22×D3—122no—
391C22×D3—122no—
392C22×D3—122no—
393C22×D3—122no—
394C22×D3—122no—
395C22×D3—124no—
396C22×D3—122no—
397C22×D3—122no—
398C22×D3—242no—
399C22×D3—242no—
400C3×Q8—22no—
401C3×Q8—22no—
402C3×Q8—42no—
403C3×Q8—62no—
404C3×Q8—122no—
405C3×D4—62no—
406C3×D4—62no—
407C3×D4—122no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—34no—
417C2×C3×C4—31no—
418C2×C3×C4—31no—
419C2×C3×C4—31no—
420C2×C3×C4—31no—
421C2×C3×C4—42no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—62no—
425C2×C3×C4—61no—
426C2×C3×C4—61no—
427C2×C3×C4D3×D411yescharacteristic
428C2×C3×C4C2×#6711yescharacteristic
429C2×C3×C4C23×D311yescharacteristic
430C2×C3×C4C23×D311yescharacteristic
431#67—124no—
432#67—124no—
433#67—124no—
434#67—124no—
435C2×Dic3—22no—
436C2×Dic3—21no—
437C2×Dic3—21no—
438C2×Dic3#21514yescomplemented
439C2×Dic3C2×#6711yescharacteristic
440C2×Dic3C2×#6711yescharacteristic
441C2×Dic3C2×#6711yescharacteristic
442C2×Dic3C2×#6711yescharacteristic
443D12—22no—
444D12—22no—
445D12—42no—
446D12—64no—
447D12—62no—
448D12—62no—
449D12—62no—
450D12—62no—
451D12—122no—
452D12—122no—
453D12—122no—
454D12—124no—
455D12—124no—
456D12—124no—
457D12—124no—
458D12—124no—
459Dic6—22no—
460Dic6—42no—
461C3×C8—62no—
462C3⋊C8—22no—
463C3⋊C8—62no—
464C3⋊C8—62no—
465C3⋊C8—122no—
466C2×C32—22no—
467C2×C32#53511yescharacteristic
468C2×C32C22×SD1611yescharacteristic
469C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
470C3⋊D3—82no—
471C3×D3—82no—
472C24—61no—
473C24—181no—
474C2×Q8—31no—
475C2×Q8—61no—
476C2×Q8C2×D3211yescharacteristic
477C2×D4—32no—
478C2×D4—61no—
479C2×D4—92no—
480C2×D4—122no—
481C2×D4—182no—
482C2×D4—182no—
483C2×D4—182no—
484C2×D4—182no—
485C2×D4—181no—
486C2×D4—362no—
487C2×D4—364no—
488C2×D4—364no—
489C22×C4—31no—
490C22×C4—31no—
491C22×C4C2×D3211yescharacteristic
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—21no—
508C22⋊C4—61no—
509C42—31no—
510C42—31no—
511C42—31no—
512C42—31no—
513C42—61no—
514C42—61no—
515C22×C3—21no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—21no—
520C22×C3—22no—
521C22×C3—41no—
522C22×C3—41no—
523C22×C3—122no—
524C22×C3—122no—
525C22×C3—122no—
526C22×C3—244no—
527C22×C3D3×SD1612yes—
528C22×C3C2×#21512yes—
529C22×C3C2×D3×D411yescharacteristic
530C22×C3C22×#6711yescharacteristic
531C2×D3—42no—
532C2×D3—42no—
533C2×D3—42no—
534C2×D3—84no—
535C2×D3—124no—
536C2×D3—122no—
537C2×D3—122no—
538C2×D3—122no—
539C2×D3—122no—
540C2×D3—122no—
541C2×D3—122no—
542C2×D3—242no—
543C2×D3—242no—
544C2×D3—244no—
545C2×D3—244no—
546C2×D3—248no—
547C3×C4—21no—
548C3×C4—21no—
549C3×C4—22no—
550C3×C4—32no—
551C3×C4—32no—
552C3×C4—32no—
553C3×C4—41no—
554C3×C4—41no—
555C3×C4—41no—
556C3×C4—41no—
557C3×C4—41no—
558C3×C4—61no—
559C3×C4—81no—
560C3×C4—81no—
561C3×C4—121no—
562C3×C4—121no—
563C3×C4#100412yes—
564C3×C4#100912yes—
565Dic3—21no—
566Dic3—41no—
567Dic3—41no—
568Dic3C2×#21512yes—
569Dic3C2×#21512yes—
570Dic3#94912yes—
571C32#320811yescharacteristic, complemented, Sylow
572C23—62no—
573C23—122no—
574C23—122no—
575C23—122no—
576C23—182no—
577C23—362no—
578C23—362no—
579C23—362no—
580C23D3×#6711yescharacteristic
581Q8—22no—
582Q8—62no—
583Q8—122no—
584D4—62no—
585D4—62no—
586D4—122no—
587D4—182no—
588D4—182no—
589D4—362no—
590D4—364no—
591D4—364no—
592D4—364no—
593D4—364no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—31no—
598C2×C4—31no—
599C2×C4—31no—
600C2×C4—34no—
601C2×C4—31no—
602C2×C4—62no—
603C2×C4—61no—
604C2×C4—61no—
605C2×C4D3×#6711yescharacteristic
606C2×C4C22×D3211yescharacteristic
607C8—62no—
608C8—182no—
609C2×C3—22no—
610C2×C3—22no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—42no—
615C2×C3—242no—
616C2×C3#559211yescharacteristic
617C2×C3C2×D3×SD1611yescharacteristic
618C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
619C2×C3C22×#21511yescharacteristic
620C2×C3C2×#94911yescharacteristic
621C2×C3#583011yescharacteristic
622D3—82no—
623D3—244no—
624D3—242no—
625D3—242no—
626C22—21no—
627C22—21no—
628C22—122no—
629C22—122no—
630C22—122no—
631C22—244no—
632C22—362no—
633C22—362no—
634C22—362no—
635C22—724no—
636C22D3×#21512yes—
637C22C2×D3×#6711yescharacteristic
638C4—21no—
639C4—32no—
640C4—32no—
641C4—32no—
642C4—41no—
643C4—41no—
644C4—61no—
645C4—121no—
646C4—121no—
647C4#6431412yes—
648C3—21no—
649C3#8013811yescharacteristic, complemented
650C3#8335511yescharacteristic, complemented
651C2—22no—
652C2—242no—
653C2—722no—
654C2#1059523811yescharacteristic
655C2C2×D3×#21511yescharacteristic
656C2D3×#94911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#63911C2
hypercenterC22⋊Q8D32
hypocenterC32#3208
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. C3×#5622C2semidirect
3. #10592745C2semidirect
4. C3×#5046C2semidirect
5. #10591618C2semidirect
6. #10591617C2semidirect
7. #10591183C2semidirect
8. #10591169C2semidirect
9. #10591053C2semidirect
10. #10590549C2semidirect
11. #10590548C2semidirect
19. C2×#3755C22semidirect
20. C3×Q8×Dic3C22semidirect
21. C3×#944C22semidirect
22. C2×C3×#215C22semidirect
26. C3×#888C22semidirect
28. C3×#887C22semidirect
35. C2×#3717C22semidirect
36. C2×#3715C22semidirect
38. #63636C22semidirect
40. C3×#809C22semidirect
41. Dic3⋊(C3⋊C8)C22semidirect
42. #63564C22semidirect
43. #63562C22semidirect
44. Dic3×C3⋊C8C22semidirect
47. #5622D3semidirect
60. #5046D3semidirect
135. Q8×Dic3C2×D3semidirect
136. #944C2×D3semidirect
142. C2×#215C2×D3semidirect
152. #888C2×D3semidirect
154. #887C2×D3semidirect
176. #809C2×D3semidirect
200. C2×C3×Dic3SD16semidirect
438. C2×Dic3#215semidirect
571. C32#3208semidirect
649. C3#80138semidirect
650. C3#83355semidirect

Maximal subgroups

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

subgroupindex
C3×#56222
C2×#639112
#105927452
C3×#50462
#105916182
#105916172
#105911832
#105911692
#105910532
#105905492
#105905482
#833553
#801383