Finite Group Databasebeta

← #11878668

Subgroups — #11878668

Order 1152.

1163 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5596C211yesmaximal, characteristic, complemented
2C2×#63911C211yesmaximal, characteristic, complemented
3#10592735C211yesmaximal, characteristic, complemented
4C3×#5036C211yesmaximal, characteristic, complemented
5#10591482C212yesmaximal, complemented
6#10591481C212yesmaximal, complemented
7#10591168C211yesmaximal, characteristic, complemented
8#10591160C211yesmaximal, characteristic, complemented
9#10591053C211yesmaximal, characteristic, complemented
10#10590548C212yesmaximal, complemented
11#10590547C212yesmaximal, complemented
12#83302—31nomaximal
13#79994—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C2×C3×#237—21no—
16C22×C3×D12C2211yescharacteristic
17C22×#626—21no—
18C22×#626—21no—
19C32×#121C2211yescharacteristic
20C2×#3753C2212yescomplemented
21C3×#940C2211yescharacteristic, complemented
22C3×#939—21no—
23C3×D4×Dic3C2211yescharacteristic, complemented
24C2×C3×#213C2212yescomplemented
25C3×#930C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C3×#893C2211yescharacteristic, complemented
28C3×#888C2211yescharacteristic, complemented
29C3×#885—21no—
30C3×#67⋊C4—21no—
31#63911—21no—
32#63911—21no—
33#63911C2212yes—
34#63911C2212yes—
35C2×#3714C2212yescomplemented
36C2×#3713C2212yescomplemented
37#63657C2211yescharacteristic
38#63636C2212yescomplemented
39C3×#830C2211yescharacteristic
40C3×#809C2212yescomplemented
41Dic3⋊(C3⋊C8)C2212yescomplemented
42#63564C2212yescomplemented
43#63562C2212yescomplemented
44Dic3×C3⋊C8C2212yescomplemented
45C3×#532—31no—
46C2×#940—31no—
47#5596D311yescharacteristic, complemented
48C2×#874—31no—
49C3×#447—31no—
50#5217—31no—
51#5151—32no—
52#5150—32no—
53#5088—32no—
54#5073—32no—
55#5036—31no—
56#5036—31no—
57#5036—31no—
58#5036—31no—
59#5036—61no—
60#5036D311yescharacteristic, complemented
61#5015—32no—
62#5015—32no—
63#4925—31no—
64#4786—32no—
65#4760—32no—
66#4732—31no—
67#4718—31no—
68C23×C3⋊D3—21no—
69C23×C3×D3—21no—
70C2×C32×D4—21no—
71C2×C32×D4C2311yescharacteristic
72C22×C32×C4C2311yescharacteristic
73C2×C4⋊(C3⋊D3)—21no—
74C2×C4⋊(C3⋊D3)—42no—
75C2×C4⋊(C3⋊D3)C2312yes—
76C2×C3×#67—21no—
77C2×C3×#67—21no—
78C2×C3×#67—21no—
79C22×C3×Dic3—21no—
80C22×C3×Dic3D411yescharacteristic
81C22×C3×Dic3D411yescharacteristic
82C3×#237—44no—
83C2×C3×D12—21no—
84C2×C3×D12—42no—
85C2×C3×D12C2311yescharacteristic
86C2×C3×D12C2312yes—
87C2×C3×C4×D3—21no—
88C2×C3×Dic6—21no—
89C2×#626—22no—
90C2×#626—22no—
91C2×#626—22no—
92C2×#626—22no—
93C2×#626—44no—
94C2×#626—44no—
95C32×C4⋊C4C2311yescharacteristic
96C32×C22⋊C4—21no—
97#3753—42no—
98C2×C3⋊(C3⋊C8)C2312yes—
99C3×#217—21no—
100C3×#213—42no—
101C3×(C2×D3)⋊C4—21no—
102C3×(C2×D3)⋊C4—21no—
103C3×C4⋊Dic3C2311yescharacteristic
104C3×Dic3⋊C4—21no—
105C3×C4×Dic3D411yescharacteristic
106C3×C4×Dic3D411yescharacteristic
107C3×C4×Dic3C2311yescharacteristic
108C3×C4×Dic3C2311yescharacteristic
109C2×C3×C3⋊C8C2312yes—
110#3714—42no—
111#3713—42no—
112#3205—91noSylow
113C2×C3×#41—61no—
114C22×C3×D4—31no—
115C22×#67—61no—
116C22×#67—61no—
117C2×#237—21no—
118C22×D12—31no—
119C22×D12—31no—
120C22×D12—61no—
121C22×D12—61no—
122C22×D12—61no—
123C22×D12C2×D311yescharacteristic
124C2×C3×D8—32no—
125C3×C4⋊Q8—31no—
126C3×#127—31no—
127C3×#124—61no—
128C3×#121—21no—
129C3×#121—31no—
130C3×#121—61no—
131C3×#121C2×D311yescharacteristic
132C3×#121C2×D311yescharacteristic
133C3×C4×D4—31no—
134C3×C4×D4—31no—
135C3×C4×D4—61no—
136C2×C3×C42—31no—
137#940—32no—
138#940—32no—
139#940—61no—
140#940—61no—
141#940C2×D311yescharacteristic, complemented
142#939—21no—
143D4×Dic3C2×D311yescharacteristic, complemented
144C2×#213—32no—
145C2×#213—32no—
146C2×#213—32no—
147C2×#213—32no—
148C2×#213—32no—
149C2×#213—62no—
150C2×#213C2×D312yescomplemented
151#930C2×D311yescharacteristic
152C2×C4×Dic3C2×D311yescharacteristic
153C2×D24—32no—
154#893C2×D311yescharacteristic, complemented
155#888C2×D311yescharacteristic, complemented
156#885—21no—
157#67⋊C4—21no—
158#874—32no—
159#874—32no—
160#874—61no—
161#874—61no—
162C3×#102—32no—
163C3×C22⋊C8—31no—
164#832—32no—
165#830—31no—
166#830—31no—
167#830—61no—
168#830C2×D311yescharacteristic
169#821—32no—
170Dic3⋊C8—32no—
171C8×Dic3—32no—
172#809—32no—
173#809—32no—
174#809—32no—
175#809—32no—
176#809—62no—
177#809C2×D312yescomplemented
178C4⋊(C3⋊C8)—32no—
179C4×C3⋊C8—32no—
180C23×C32—21no—
181C23×C32C2×D411yescharacteristic
182C22×C3⋊D3—22no—
183C22×C3⋊D3—42no—
184C22×C3⋊D3—42no—
185C22×C3⋊D3—42no—
186C22×C3×D3—22no—
187C22×C3×D3—21no—
188C22×C3×D3—42no—
189C22×C3×D3—42no—
190C22×C3×D3—42no—
191C32×D4—22no—
192C32×D4—42no—
193C2×C32×C4—22no—
194C2×C32×C4—21no—
195C2×C32×C4C2×D411yescharacteristic
196C2×C32×C4C2411yescharacteristic
197C4⋊(C3⋊D3)—22no—
198C4⋊(C3⋊D3)—22no—
199C4⋊(C3⋊D3)—42no—
200C3×#67—42no—
201C3×#67—42no—
202C3×#67—42no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—21no—
205C2×C3×Dic3—42no—
206C2×C3×Dic3D814yescomplemented
207C2×C3×Dic3C2×D411yescharacteristic
208C2×C3×Dic3C2×D411yescharacteristic
209C2×C3×Dic3C2×D411yescharacteristic
210C2×C3×Dic3C2×D411yescharacteristic
211C3×D12—22no—
212C3×D12—22no—
213C3×D12—22no—
214C3×D12—42no—
215C3×C4×D3—42no—
216C3×Dic6—42no—
217#626—44no—
218#626—44no—
219#626—44no—
220#626—44no—
221C3⋊(C3⋊C8)—22no—
222C3×C3⋊C8—22no—
223#532—31no—
224C2×#127—91no—
225#493—92no—
226#486—92no—
227#459—92no—
228#459—92no—
229#447—31no—
230#447—91no—
231#447—91no—
232#447—91no—
233#431—91no—
234C24×C3—61no—
235C23×D3—21no—
236C23×D3—61no—
237C23×D3—61no—
238C23×D3—121no—
239C3×#41—124no—
240C2×C3×Q8—61no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—32no—
245C2×C3×D4—31no—
246C2×C3×D4—41no—
247C2×C3×D4—61no—
248C2×C3×D4—61no—
249C2×C3×D4—61no—
250C2×C3×D4—61no—
251C2×C3×D4—122no—
252C2×C3×D4C22×D311yescharacteristic
253C2×C3×D4C22×D311yescharacteristic
254C22×C3×C4—21no—
255C22×C3×C4—31no—
256C22×C3×C4—31no—
257C22×C3×C4—61no—
258C22×C3×C4—61no—
259C22×C3×C4C22×D311yescharacteristic
260C22×C3×C4C22×D311yescharacteristic
261C2×#67—21no—
262C2×#67—21no—
263C2×#67—21no—
264C2×#67—62no—
265C2×#67—62no—
266C2×#67—62no—
267C2×#67—62no—
268C2×#67—124no—
269C2×#67—124no—
270C22×Dic3—21no—
271C22×Dic3#6711yescharacteristic
272C22×Dic3#6711yescharacteristic
273#237—44no—
274C2×D12—21no—
275C2×D12—32no—
276C2×D12—32no—
277C2×D12—42no—
278C2×D12—62no—
279C2×D12—62no—
280C2×D12—62no—
281C2×D12—62no—
282C2×D12—62no—
283C2×D12—61no—
284C2×D12—61no—
285C2×D12—121no—
286C2×D12—122no—
287C2×D12—122no—
288C2×D12—124no—
289C2×D12—124no—
290C2×D12—124no—
291C2×D12C22×D312yes—
292C2×D12C22×D311yescharacteristic
293C2×C4×D3—21no—
294C2×Dic6—21no—
295C3×D8—122no—
296C2×C3×C8—32no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—31no—
299C3×C4⋊C4—61no—
300C3×C4⋊C4C22×D311yescharacteristic
301C3×C4⋊C4C22×D311yescharacteristic
302C3×C22⋊C4—21no—
303C3×C22⋊C4—21no—
304C3×C22⋊C4—41no—
305C3×C22⋊C4—61no—
306C3×C22⋊C4—61no—
307C3×C22⋊C4—61no—
308C3×C42—31no—
309C3×C42—31no—
310C3×C42—31no—
311C3×C42—31no—
312#217—21no—
313#213—42no—
314#213—122no—
315#213—122no—
316#213—122no—
317#213—122no—
318#213—122no—
319#213—124no—
320(C2×D3)⋊C4—21no—
321(C2×D3)⋊C4—21no—
322C4⋊Dic3C22×D311yescharacteristic
323Dic3⋊C4—21no—
324C4×Dic3#6711yescharacteristic
325C4×Dic3#6711yescharacteristic
326C4×Dic3C22×D311yescharacteristic
327C4×Dic3C22×D311yescharacteristic
328C2×C3⋊C8—32no—
329C2×C3⋊C8—32no—
330C2×C3⋊C8—62no—
331C2×C3⋊C8C22×D312yes—
332D24—122no—
333C22×C32—21no—
334C22×C32—21no—
335C22×C32—41no—
336C22×C32—41no—
337C22×C32—41no—
338C22×C32C2×D812yes—
339C22×C32C22×D411yescharacteristic
340C2×C3⋊D3—42no—
341C2×C3⋊D3—42no—
342C2×C3⋊D3—42no—
343C2×C3⋊D3—84no—
344C2×C3×D3—42no—
345C2×C3×D3—41no—
346C2×C3×D3—42no—
347C2×C3×D3—41no—
348C2×C3×D3—42no—
349C2×C3×D3—41no—
350C2×C3×D3—84no—
351C32×C4—21no—
352C32×C4—41no—
353C32×C4H(5,𝔽2)12yes—
354C3×Dic3—21no—
355C3×Dic3—41no—
356C3×Dic3C2×D812yes—
357C3×Dic3C2×D812yes—
358C3×Dic3AGL(1,ℤ/8)12yes—
359C2×#41—61no—
360C22×D4—31no—
361C22×D4—91no—
362C22×D4—181no—
363C22×D4—181no—
364C2×D8—32no—
365C2×D8—92no—
366C2×D8—92no—
367C2×D8—92no—
368C4⋊Q8—31no—
369#127—31no—
370#127—92no—
371#127—92no—
372#127—181no—
373#127—181no—
374#124—61no—
375#121—31no—
376#121—61no—
377#121D3211yescharacteristic
378C4×D4—31no—
379C4×D4—31no—
380C4×D4—61no—
381C2×C42—31no—
382C4⋊C8—92no—
383#102—32no—
384#102—92no—
385#102—92no—
386#102—92no—
387C22⋊C8—31no—
388C22⋊C8—91no—
389C4×C8—92no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—21no—
393C23×C3—41no—
394C23×C3—61no—
395C23×C3—62no—
396C23×C3—122no—
397C23×C3—122no—
398C23×C3—122no—
399C23×C3D3×D411yescharacteristic
400C23×C3C2×#6711yescharacteristic
401C22×D3—22no—
402C22×D3—21no—
403C22×D3—42no—
404C22×D3—42no—
405C22×D3—42no—
406C22×D3—62no—
407C22×D3—62no—
408C22×D3—122no—
409C22×D3—122no—
410C22×D3—122no—
411C22×D3—122no—
412C22×D3—122no—
413C22×D3—124no—
414C22×D3—122no—
415C22×D3—122no—
416C22×D3—242no—
417C22×D3—242no—
418C3×Q8—122no—
419C3×D4—22no—
420C3×D4—22no—
421C3×D4—42no—
422C3×D4—42no—
423C3×D4—42no—
424C3×D4—62no—
425C3×D4—62no—
426C3×D4—62no—
427C3×D4—82no—
428C3×D4—122no—
429C3×D4—122no—
430C3×D4—122no—
431C3×D4—122no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—34no—
439C2×C3×C4—31no—
440C2×C3×C4—31no—
441C2×C3×C4—31no—
442C2×C3×C4—31no—
443C2×C3×C4—42no—
444C2×C3×C4—41no—
445C2×C3×C4—62no—
446C2×C3×C4—61no—
447C2×C3×C4—122no—
448C2×C3×C4—122no—
449C2×C3×C4D3×D411yescharacteristic
450C2×C3×C4C2×#6711yescharacteristic
451C2×C3×C4C23×D311yescharacteristic
452C2×C3×C4C23×D311yescharacteristic
453#67—42no—
454#67—42no—
455#67—42no—
456#67—124no—
457#67—124no—
458#67—124no—
459#67—124no—
460C2×Dic3—22no—
461C2×Dic3—21no—
462C2×Dic3—42no—
463C2×Dic3#21314yescomplemented
464C2×Dic3C2×#6711yescharacteristic
465C2×Dic3C2×#6711yescharacteristic
466C2×Dic3C2×#6711yescharacteristic
467C2×Dic3C2×#6711yescharacteristic
468D12—22no—
469D12—22no—
470D12—22no—
471D12—42no—
472D12—64no—
473D12—62no—
474D12—62no—
475D12—62no—
476D12—62no—
477D12—122no—
478D12—122no—
479D12—122no—
480D12—124no—
481D12—124no—
482D12—124no—
483D12—124no—
484D12—124no—
485C4×D3—42no—
486Dic6—42no—
487C3×C8—62no—
488C3⋊C8—22no—
489C3⋊C8—62no—
490C3⋊C8—62no—
491C3⋊C8—122no—
492C2×C32—22no—
493C2×C32—81no—
494C2×C32#53511yescharacteristic
495C2×C32C22×D811yescharacteristic
496C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
497C3⋊D3—82no—
498C3×D3—81no—
499C3×D3—82no—
500C24—61no—
501C24—181no—
502#41—124no—
503C2×Q8—61no—
504C2×D4—21no—
505C2×D4—32no—
506C2×D4—31no—
507C2×D4—61no—
508C2×D4—61no—
509C2×D4—61no—
510C2×D4—61no—
511C2×D4—92no—
512C2×D4—122no—
513C2×D4—182no—
514C2×D4—182no—
515C2×D4—182no—
516C2×D4—182no—
517C2×D4—181no—
518C2×D4—362no—
519C2×D4—364no—
520C2×D4—364no—
521C2×D4C2×D3211yescharacteristic
522C22×C4—31no—
523C22×C4—31no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4C2×D3211yescharacteristic
527D8—122no—
528D8—362no—
529D8—362no—
530D8—362no—
531C2×C8—32no—
532C2×C8—92no—
533C4⋊C4—31no—
534C4⋊C4—61no—
535C4⋊C4C2×D3211yescharacteristic
536C22⋊C4—21no—
537C22⋊C4—61no—
538C22⋊C4—61no—
539C22⋊C4—61no—
540C42—31no—
541C42—31no—
542C42—31no—
543C42—31no—
544C22×C3—21no—
545C22×C3—21no—
546C22×C3—21no—
547C22×C3—21no—
548C22×C3—21no—
549C22×C3—22no—
550C22×C3—41no—
551C22×C3—41no—
552C22×C3—41no—
553C22×C3—41no—
554C22×C3—41no—
555C22×C3—41no—
556C22×C3—41no—
557C22×C3—41no—
558C22×C3—81no—
559C22×C3—81no—
560C22×C3—81no—
561C22×C3—121no—
562C22×C3—121no—
563C22×C3—122no—
564C22×C3—122no—
565C22×C3—122no—
566C22×C3—121no—
567C22×C3—244no—
568C22×C3D3×D812yes—
569C22×C3C2×#21312yes—
570C22×C3C2×D3×D411yescharacteristic
571C22×C3C22×#6711yescharacteristic
572C2×D3—42no—
573C2×D3—42no—
574C2×D3—41no—
575C2×D3—41no—
576C2×D3—41no—
577C2×D3—42no—
578C2×D3—84no—
579C2×D3—124no—
580C2×D3—122no—
581C2×D3—122no—
582C2×D3—122no—
583C2×D3—122no—
584C2×D3—122no—
585C2×D3—122no—
586C2×D3—242no—
587C2×D3—242no—
588C2×D3—244no—
589C2×D3—244no—
590C2×D3—248no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—22no—
594C3×C4—32no—
595C3×C4—32no—
596C3×C4—32no—
597C3×C4—41no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4—61no—
601C3×C4—81no—
602C3×C4—121no—
603C3×C4#100412yes—
604C3×C4#100912yes—
605Dic3—21no—
606Dic3—41no—
607Dic3C2×#21312yes—
608Dic3C2×#21312yes—
609Dic3#94912yes—
610C32#320511yescharacteristic, complemented, Sylow
611C23—21no—
612C23—61no—
613C23—62no—
614C23—122no—
615C23—122no—
616C23—122no—
617C23—182no—
618C23—362no—
619C23—362no—
620C23—362no—
621C23D3×#6711yescharacteristic
622Q8—122no—
623D4—22no—
624D4—42no—
625D4—62no—
626D4—62no—
627D4—62no—
628D4—122no—
629D4—122no—
630D4—122no—
631D4—122no—
632D4—182no—
633D4—182no—
634D4—362no—
635D4—364no—
636D4—364no—
637D4—364no—
638D4—364no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—31no—
642C2×C4—31no—
643C2×C4—31no—
644C2×C4—34no—
645C2×C4—31no—
646C2×C4—62no—
647C2×C4—61no—
648C2×C4—122no—
649C2×C4—122no—
650C2×C4D3×#6711yescharacteristic
651C2×C4C22×D3211yescharacteristic
652C8—62no—
653C8—182no—
654C2×C3—22no—
655C2×C3—22no—
656C2×C3—21no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—42no—
660C2×C3—81no—
661C2×C3—81no—
662C2×C3—161no—
663C2×C3—242no—
664C2×C3—241no—
665C2×C3#559211yescharacteristic
666C2×C3C2×D3×D811yescharacteristic
667C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
668C2×C3C22×#21311yescharacteristic
669C2×C3C2×#94911yescharacteristic
670C2×C3#583011yescharacteristic
671D3—81no—
672D3—82no—
673D3—244no—
674D3—242no—
675D3—242no—
676C22—21no—
677C22—21no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—121no—
682C22—122no—
683C22—121no—
684C22—122no—
685C22—122no—
686C22—121no—
687C22—244no—
688C22—362no—
689C22—362no—
690C22—362no—
691C22—724no—
692C22D3×#21312yes—
693C22C2×D3×#6711yescharacteristic
694C4—21no—
695C4—32no—
696C4—32no—
697C4—32no—
698C4—41no—
699C4—61no—
700C4—121no—
701C4#6431412yes—
702C3—21no—
703C3#7999411yescharacteristic, complemented
704C3#8330211yescharacteristic, complemented
705C2—22no—
706C2—81no—
707C2—242no—
708C2—241no—
709C2—722no—
710C2C2×D3×#21311yescharacteristic
711C2#1059523811yescharacteristic
712C2D3×#94911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3205
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#5596C2semidirect
2. C2×#63911C2semidirect
3. #10592735C2semidirect
4. C3×#5036C2semidirect
5. #10591482C2semidirect
6. #10591481C2semidirect
7. #10591168C2semidirect
8. #10591160C2semidirect
9. #10591053C2semidirect
10. #10590548C2semidirect
11. #10590547C2semidirect
20. C2×#3753C22semidirect
21. C3×#940C22semidirect
23. C3×D4×Dic3C22semidirect
24. C2×C3×#213C22semidirect
27. C3×#893C22semidirect
28. C3×#888C22semidirect
35. C2×#3714C22semidirect
36. C2×#3713C22semidirect
38. #63636C22semidirect
40. C3×#809C22semidirect
41. Dic3⋊(C3⋊C8)C22semidirect
42. #63564C22semidirect
43. #63562C22semidirect
44. Dic3×C3⋊C8C22semidirect
47. #5596D3semidirect
60. #5036D3semidirect
141. #940C2×D3semidirect
143. D4×Dic3C2×D3semidirect
150. C2×#213C2×D3semidirect
154. #893C2×D3semidirect
155. #888C2×D3semidirect
177. #809C2×D3semidirect
206. C2×C3×Dic3D8semidirect
463. C2×Dic3#213semidirect
610. C32#3205semidirect
703. C3#79994semidirect
704. C3#83302semidirect

Maximal subgroups

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

subgroupindex
C3×#55962
C2×#639112
#105927352
C3×#50362
#105914822
#105914812
#105911682
#105911602
#105910532
#105905482
#105905472
#833023
#799943