Finite Group Databasebeta

← #11878665

Subgroups — #11878665

Order 1152.

1134 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#127C211yesmaximal, characteristic, complemented
2#10593968C211yesmaximal, characteristic, complemented
3#10592771C211yesmaximal, characteristic, complemented
4C3×#5072C211yesmaximal, characteristic, complemented
5#10591487C212yesmaximal, complemented
6#10591482C212yesmaximal, complemented
7#10591448C212yesmaximal, complemented
8#10591447C212yesmaximal, complemented
9#10590355C211yesmaximal, characteristic, complemented
10#10590347C211yesmaximal, characteristic, complemented
11#10590248C211yesmaximal, characteristic, complemented
12#83166—31nomaximal
13#80336—31nomaximal
14C2×C3×D3×D4—21no—
15C2×C3×D3×D4—21no—
16C2×C3×D3×D4C2212yes—
17C2×#3798—21no—
18C32×#127C2211yescharacteristic
19C2×#3753C2212yescomplemented
20C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
21C3×#940—21no—
22C3×#940—21no—
23C3×#940C2212yes—
24C2×C3×#213C2212yescomplemented
25C3×#874C2211yescharacteristic
26C3×C4×D12C2211yescharacteristic, complemented
27C3×C42×D3C2211yescharacteristic
28#63918C2211yescharacteristic, complemented
29#63911C2211yescharacteristic, complemented
30#63909C2211yescharacteristic
31#63908C2211yescharacteristic
32#63906—21no—
33C4×#626—21no—
34#63852—21no—
35C2×#3714C2212yescomplemented
36C2×#3713C2212yescomplemented
37#63659C2212yescomplemented
38C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
39C3×#832C2212yescomplemented
40C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
41#63563C2212yescomplemented
42#63562C2212yescomplemented
43(C2×D3)⋊(C3⋊C8)C2212yes—
44Dic3×C3⋊C8C2212yescomplemented
45C2×C3×#127—31no—
46D3×#127D311yescharacteristic, complemented
47#5548—31no—
48#5477—31no—
49C3×#459—31no—
50#5217—32no—
51#5217—32no—
52#5156—32no—
53#5151—32no—
54#5073—32no—
55#5072—31no—
56#5072—31no—
57#5072—31no—
58#5072—31no—
59#5072—61no—
60#5072D311yescharacteristic, complemented
61#5070—32no—
62#5015—31no—
63#4925—31no—
64#4843—31no—
65#4833—31no—
66#4773—32no—
67#4760—32no—
68C23×C3×D3—22no—
69C2×C32×D4—21no—
70C2×C32×D4—21no—
71C2×C32×D4C2312yes—
72C2×C4⋊(C3⋊D3)C2311yescharacteristic
73C2×C4×C3⋊D3—21no—
74C2×C3×#67—22no—
75C2×C3×#67—22no—
76C2×C3×#67—22no—
77C3×D3×D4—42no—
78C3×D3×D4—42no—
79C3×D3×D4—44no—
80C3×D3×D4—44no—
81C2×C3×D12—21no—
82C2×C3×D12—21no—
83C2×C3×D12C2311yescharacteristic
84C2×C3×D12C2312yes—
85C2×C3×C4×D3—21no—
86C2×C3×C4×D3D411yescharacteristic
87C2×C3×C4×D3D411yescharacteristic
88C2×C3×C4×D3C2311yescharacteristic
89C2×#627—21no—
90C2×#626—21no—
91C2×#626—21no—
92C2×#626—21no—
93C2×#625—21no—
94#3798—44no—
95C32×C42C2311yescharacteristic
96#3753—42no—
97#3752—21no—
98C4⋊(C3⋊Dic3)C2311yescharacteristic
99C2×C3⋊(C3⋊C8)C2312yes—
100C3×#213—42no—
101C3×(C2×D3)⋊C4—21no—
102C3×C4⋊Dic3C2311yescharacteristic
103C3×C4×Dic3D411yescharacteristic
104C3×C4×Dic3D411yescharacteristic
105C3×C4×Dic3C2311yescharacteristic
106C2×C3×C3⋊C8C2312yes—
107Dic3⋊Dic3—21no—
108#3722—21no—
109(C2×D3)⋊Dic3—21no—
110#3714—42no—
111#3713—42no—
112#3205—91noSylow
113C22×C3×D4—32no—
114C22×C3×D4—61no—
115C22×C3×D4—61no—
116C2×D3×D4—21no—
117C2×D3×D4—21no—
118C2×D3×D4C2×D312yes—
119C2×#235—61no—
120C2×#235—61no—
121C2×C3×D8—32no—
122C3×#127—21no—
123C3×#127—32no—
124C3×#127—31no—
125C3×#127—61no—
126C3×#127—61no—
127C3×#127C2×D311yescharacteristic
128C3×#127C2×D311yescharacteristic
129C3×C4×D4—31no—
130C2×C3×C42—31no—
131#940—21no—
132#940—21no—
133#940—31no—
134#940C2×D312yes—
135#938—31no—
136C2×#213—32no—
137C2×#213—32no—
138C2×#213—32no—
139C2×#213—32no—
140C2×#213—32no—
141C2×#213—62no—
142C2×#213C2×D312yescomplemented
143#930—31no—
144#930—31no—
145#930—61no—
146C4×#67—61no—
147C2×D24—32no—
148#895—31no—
149#888—31no—
150#885—61no—
151#884—61no—
152#875—61no—
153#874—31no—
154#874C2×D311yescharacteristic
155C4×D12—31no—
156C4×D12—31no—
157C4×D12—61no—
158C4×D12—61no—
159C4×D12C2×D311yescharacteristic, complemented
160C42×D3C2×D311yescharacteristic
161#869—31no—
162C3×C4⋊C8—31no—
163C3×#102—32no—
164#832—32no—
165#832—32no—
166#832—32no—
167#832—32no—
168#832—62no—
169#832C2×D312yescomplemented
170#830—32no—
171#821—32no—
172(C2×D3)⋊C8—32no—
173C8×Dic3—32no—
174#809—32no—
175C4⋊(C3⋊C8)—31no—
176C4⋊(C3⋊C8)—31no—
177C4⋊(C3⋊C8)—61no—
178C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
179C4×C3⋊C8—32no—
180C23×C32—22no—
181C22×C3⋊D3—21no—
182C22×C3×D3—22no—
183C22×C3×D3—21no—
184C22×C3×D3—44no—
185C22×C3×D3—44no—
186C22×C3×D3—44no—
187C22×C3×D3C2×D411yescharacteristic
188C32×D4—22no—
189C32×D4—22no—
190C32×D4—42no—
191C32×D4—42no—
192C2×C32×C4C2×D411yescharacteristic
193C2×C32×C4C2×D411yescharacteristic
194C2×C32×C4C2411yescharacteristic
195C2×C3⋊Dic3—21no—
196C4⋊(C3⋊D3)—21no—
197C4⋊(C3⋊D3)—21no—
198C4×C3⋊D3—42no—
199C3×#67—44no—
200C3×#67—44no—
201C3×#67—44no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3C2×D411yescharacteristic
204C2×C3×Dic3C2×D411yescharacteristic
205C2×C3×Dic3C2×D411yescharacteristic
206C3×D12—21no—
207C3×D12—22no—
208C3×D12—22no—
209C3×D12—21no—
210C3×D12—42no—
211C3×D12—42no—
212C3×C4×D3—21no—
213C3×C4×D3—21no—
214C3×C4×D3—22no—
215C3×C4×D3—42no—
216C3×C4×D3D814yescomplemented
217#627—42no—
218#626—42no—
219#626—42no—
220#626—42no—
221#625—42no—
222C3⋊(C3⋊C8)—22no—
223C3×C3⋊C8—22no—
224#532—91no—
225C2×#127—31no—
226#493—92no—
227#486—92no—
228#459—31no—
229#459—91no—
230#459—91no—
231#459—91no—
232#447—92no—
233#447—92no—
234#431—91no—
235C24×C3—62no—
236C23×D3—22no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—22no—
242C2×C3×D4—32no—
243C2×C3×D4—31no—
244C2×C3×D4—41no—
245C2×C3×D4—41no—
246C2×C3×D4—62no—
247C2×C3×D4—62no—
248C2×C3×D4—62no—
249C2×C3×D4—61no—
250C2×C3×D4—61no—
251C2×C3×D4—124no—
252C2×C3×D4—122no—
253C2×C3×D4—122no—
254C2×C3×D4—124no—
255C2×C3×D4C22×D312yes—
256C2×C3×D4C22×D312yes—
257C22×C3×C4—31no—
258C22×C3×C4—31no—
259C22×C3×C4—31no—
260C22×C3×C4—61no—
261C2×#67—22no—
262C2×#67—22no—
263C2×#67—22no—
264C2×#67—61no—
265C2×#67—61no—
266C2×#67—61no—
267C2×#67—61no—
268C2×#67—61no—
269D3×D4—42no—
270D3×D4—42no—
271D3×D4—44no—
272D3×D4—44no—
273#235—124no—
274#235—124no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12—31no—
278C2×D12—31no—
279C2×D12—61no—
280C2×D12—61no—
281C2×D12—61no—
282C2×D12—61no—
283C2×D12C22×D312yes—
284C2×D12C22×D311yescharacteristic
285C2×C4×D3—21no—
286C2×C4×D3—61no—
287C2×C4×D3—61no—
288C2×C4×D3—121no—
289C2×C4×D3#6711yescharacteristic
290C2×C4×D3#6711yescharacteristic
291C2×C4×D3C22×D311yescharacteristic
292C2×Dic6—61no—
293C2×Dic6—61no—
294C3×D8—122no—
295C2×C3×C8—32no—
296C3×C4⋊C4—31no—
297C3×C22⋊C4—61no—
298C3×C42—21no—
299C3×C42—31no—
300C3×C42—31no—
301C3×C42—31no—
302C3×C42C22×D311yescharacteristic
303C3×C42C22×D311yescharacteristic
304#217—61no—
305#213—42no—
306#213—122no—
307#213—122no—
308#213—122no—
309#213—122no—
310#213—122no—
311#213—124no—
312(C2×D3)⋊C4—21no—
313(C2×D3)⋊C4—61no—
314(C2×D3)⋊C4—61no—
315(C2×D3)⋊C4—61no—
316(C2×D3)⋊C4—61no—
317(C2×D3)⋊C4—61no—
318(C2×D3)⋊C4—121no—
319C4⋊Dic3—31no—
320C4⋊Dic3—31no—
321C4⋊Dic3—61no—
322C4⋊Dic3—61no—
323C4⋊Dic3C22×D311yescharacteristic
324Dic3⋊C4—61no—
325C4×Dic3#6711yescharacteristic
326C4×Dic3#6711yescharacteristic
327C4×Dic3C22×D311yescharacteristic
328C2×C3⋊C8—32no—
329C2×C3⋊C8—32no—
330C2×C3⋊C8—62no—
331C2×C3⋊C8C22×D312yes—
332D24—122no—
333C22×C32—42no—
334C22×C32—42no—
335C22×C32—42no—
336C22×C32C22×D411yescharacteristic
337C2×C3⋊D3—41no—
338C2×C3⋊D3—41no—
339C2×C3⋊D3—41no—
340C2×C3×D3—21no—
341C2×C3×D3—21no—
342C2×C3×D3—42no—
343C2×C3×D3—41no—
344C2×C3×D3—41no—
345C2×C3×D3—42no—
346C2×C3×D3—41no—
347C2×C3×D3—42no—
348C2×C3×D3—88no—
349C2×C3×D3C2×D812yes—
350C32×C4—21no—
351C32×C4C2×D812yes—
352C32×C4H(5,𝔽2)11yescharacteristic
353C32×C4H(5,𝔽2)11yescharacteristic
354C3⋊Dic3—41no—
355C3×Dic3—21no—
356C3×Dic3—41no—
357C3×Dic3C2×D812yes—
358C3×Dic3AGL(1,ℤ/8)12yes—
359C2×#41—181no—
360C22×D4—32no—
361C22×D4—61no—
362C22×D4—61no—
363C2×D8—32no—
364C2×D8—92no—
365C2×D8—92no—
366C2×D8—92no—
367C4⋊Q8—91no—
368#127—32no—
369#127—31no—
370#127—61no—
371#127—61no—
372#127—91no—
373#127D3211yescharacteristic
374#124—181no—
375#121—91no—
376#121—91no—
377#121—181no—
378C4×D4—31no—
379C4×D4—91no—
380C4×D4—181no—
381C2×C42—31no—
382C4⋊C8—31no—
383C4⋊C8—91no—
384#102—32no—
385#102—92no—
386#102—92no—
387#102—92no—
388C22⋊C8—92no—
389C4×C8—92no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—31no—
393C23×C3—42no—
394C23×C3—62no—
395C23×C3—61no—
396C23×C3—124no—
397C23×C3—124no—
398C23×C3—124no—
399C22×D3—21no—
400C22×D3—22no—
401C22×D3—44no—
402C22×D3—44no—
403C22×D3—44no—
404C22×D3—61no—
405C22×D3—61no—
406C22×D3—121no—
407C22×D3C2×#6711yescharacteristic
408C3×D4—22no—
409C3×D4—22no—
410C3×D4—22no—
411C3×D4—22no—
412C3×D4—42no—
413C3×D4—42no—
414C3×D4—42no—
415C3×D4—42no—
416C3×D4—42no—
417C3×D4—42no—
418C3×D4—61no—
419C3×D4—62no—
420C3×D4—61no—
421C3×D4—62no—
422C3×D4—82no—
423C3×D4—82no—
424C3×D4—122no—
425C3×D4—124no—
426C3×D4—124no—
427C3×D4—124no—
428C3×D4—122no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—31no—
433C2×C3×C4—31no—
434C2×C3×C4—34no—
435C2×C3×C4—31no—
436C2×C3×C4—62no—
437C2×C3×C4—61no—
438C2×C3×C4—61no—
439C2×C3×C4—61no—
440C2×C3×C4—122no—
441C2×C3×C4D3×D411yescharacteristic
442C2×C3×C4D3×D411yescharacteristic
443C2×C3×C4C2×#6711yescharacteristic
444C2×C3×C4C2×#6711yescharacteristic
445C2×C3×C4C23×D311yescharacteristic
446C2×C3×C4C23×D311yescharacteristic
447#67—44no—
448#67—44no—
449#67—44no—
450#67—122no—
451#67—122no—
452#67—122no—
453#67—122no—
454#67—122no—
455C2×Dic3—21no—
456C2×Dic3—61no—
457C2×Dic3—61no—
458C2×Dic3—121no—
459C2×Dic3C2×#6711yescharacteristic
460C2×Dic3C2×#6711yescharacteristic
461C2×Dic3C2×#6711yescharacteristic
462D12—22no—
463D12—21no—
464D12—22no—
465D12—21no—
466D12—42no—
467D12—42no—
468D12—62no—
469D12—61no—
470D12—61no—
471D12—61no—
472D12—61no—
473D12—121no—
474D12—122no—
475D12—122no—
476D12—122no—
477C4×D3—21no—
478C4×D3—21no—
479C4×D3—22no—
480C4×D3—42no—
481C4×D3—122no—
482C4×D3—122no—
483C4×D3—242no—
484C4×D3#21314yescomplemented
485Dic6—122no—
486Dic6—122no—
487C3×C8—62no—
488C3⋊C8—22no—
489C3⋊C8—62no—
490C3⋊C8—62no—
491C3⋊C8—122no—
492C2×C32—82no—
493C2×C32#53511yescharacteristic
494C2×C32C22×D811yescharacteristic
495C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
496C3⋊D3—81no—
497C3×D3—22no—
498C3×D3—81no—
499C3×D3—82no—
500C24—62no—
501#41—364no—
502C2×Q8—181no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—32no—
506C2×D4—31no—
507C2×D4—62no—
508C2×D4—62no—
509C2×D4—62no—
510C2×D4—61no—
511C2×D4—61no—
512C2×D4—91no—
513C2×D4—124no—
514C2×D4—122no—
515C2×D4—122no—
516C2×D4—124no—
517C2×D4—181no—
518C2×D4—181no—
519C2×D4—181no—
520C2×D4—181no—
521C2×D4C2×D3212yes—
522C22×C4—31no—
523C22×C4—31no—
524C22×C4—31no—
525C22×C4—61no—
526C22×C4—181no—
527D8—122no—
528D8—362no—
529D8—362no—
530D8—362no—
531C2×C8—32no—
532C2×C8—92no—
533C4⋊C4—31no—
534C4⋊C4—91no—
535C4⋊C4—181no—
536C22⋊C4—61no—
537C22⋊C4—181no—
538C22⋊C4—181no—
539C22⋊C4—181no—
540C42—31no—
541C42—31no—
542C42—31no—
543C42C2×D3211yescharacteristic
544C22×C3—21no—
545C22×C3—32no—
546C22×C3—42no—
547C22×C3—42no—
548C22×C3—42no—
549C22×C3—42no—
550C22×C3—42no—
551C22×C3—42no—
552C22×C3—61no—
553C22×C3—61no—
554C22×C3—82no—
555C22×C3—82no—
556C22×C3—82no—
557C22×C3—122no—
558C22×C3—122no—
559C22×C3—121no—
560C22×C3—121no—
561C22×C3—121no—
562C22×C3—122no—
563C22×C3—248no—
564C22×C3C2×D3×D411yescharacteristic
565C22×C3C22×#6711yescharacteristic
566C2×D3—21no—
567C2×D3—21no—
568C2×D3—41no—
569C2×D3—41no—
570C2×D3—42no—
571C2×D3—42no—
572C2×D3—42no—
573C2×D3—41no—
574C2×D3—88no—
575C2×D3—122no—
576C2×D3—121no—
577C2×D3—121no—
578C2×D3—121no—
579C2×D3—121no—
580C2×D3—121no—
581C2×D3—121no—
582C2×D3—241no—
583C2×D3—241no—
584C2×D3C2×#21312yes—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—21no—
588C3×C4—21no—
589C3×C4—22no—
590C3×C4—32no—
591C3×C4—32no—
592C3×C4—41no—
593C3×C4—61no—
594C3×C4—121no—
595C3×C4D3×D812yes—
596C3×C4C2×#21312yes—
597C3×C4#100411yescharacteristic
598C3×C4#100411yescharacteristic
599C3×C4#100411yescharacteristic
600C3×C4#100911yescharacteristic
601Dic3—21no—
602Dic3—41no—
603Dic3—121no—
604Dic3—121no—
605Dic3—241no—
606Dic3C2×#21312yes—
607Dic3#93212yes—
608C32#320511yescharacteristic, complemented, Sylow
609C23—22no—
610C23—31no—
611C23—61no—
612C23—62no—
613C23—124no—
614C23—124no—
615C23—124no—
616C23—181no—
617Q8—362no—
618D4—22no—
619D4—22no—
620D4—42no—
621D4—42no—
622D4—61no—
623D4—62no—
624D4—61no—
625D4—62no—
626D4—122no—
627D4—124no—
628D4—124no—
629D4—124no—
630D4—122no—
631D4—181no—
632D4—181no—
633D4—362no—
634D4—362no—
635D4—362no—
636D4—362no—
637C2×C4—31no—
638C2×C4—31no—
639C2×C4—34no—
640C2×C4—31no—
641C2×C4—62no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—122no—
646C2×C4—181no—
647C2×C4—362no—
648C2×C4D3×#6711yescharacteristic
649C2×C4D3×#6711yescharacteristic
650C2×C4C22×D3211yescharacteristic
651C8—62no—
652C8—182no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—62no—
657C2×C3—82no—
658C2×C3—82no—
659C2×C3—162no—
660C2×C3—242no—
661C2×C3—241no—
662C2×C3#560711yescharacteristic
663C2×C3C2×D3×D811yescharacteristic
664C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
665C2×C3C22×#21311yescharacteristic
666C2×C3C2×#93211yescharacteristic
667C2×C3#580511yescharacteristic
668D3—22no—
669D3—81no—
670D3—82no—
671D3—242no—
672D3—241no—
673D3—241no—
674C22—32no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—61no—
679C22—61no—
680C22—121no—
681C22—122no—
682C22—122no—
683C22—121no—
684C22—122no—
685C22—121no—
686C22—248no—
687C22—361no—
688C22—361no—
689C22—361no—
690C22C2×D3×#6711yescharacteristic
691C4—21no—
692C4—32no—
693C4—32no—
694C4—61no—
695C4—121no—
696C4—361no—
697C4D3×#21312yes—
698C4#6431311yescharacteristic
699C4#6431411yescharacteristic
700C3—21no—
701C3#8033611yescharacteristic, complemented
702C3#8316611yescharacteristic, complemented
703C2—62no—
704C2—82no—
705C2—242no—
706C2—241no—
707C2—721no—
708C2C2×D3×#21311yescharacteristic
709C2D3×#93211yescharacteristic
710C2#1059523111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
hypercenter#127D32
hypocenterC32#3205
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C3×D3×#127C2semidirect
2. #10593968C2semidirect
3. #10592771C2semidirect
4. C3×#5072C2semidirect
5. #10591487C2semidirect
6. #10591482C2semidirect
7. #10591448C2semidirect
8. #10591447C2semidirect
9. #10590355C2semidirect
10. #10590347C2semidirect
11. #10590248C2semidirect
19. C2×#3753C22semidirect
20. C4×C4⋊(C3⋊D3)C22semidirect
24. C2×C3×#213C22semidirect
26. C3×C4×D12C22semidirect
28. #63918C22semidirect
29. #63911C22semidirect
35. C2×#3714C22semidirect
36. C2×#3713C22semidirect
37. #63659C22semidirect
38. C4⋊(C3⋊(C3⋊C8))C22semidirect
39. C3×#832C22semidirect
40. C3×C4⋊(C3⋊C8)C22semidirect
41. #63563C22semidirect
42. #63562C22semidirect
44. Dic3×C3⋊C8C22semidirect
46. D3×#127D3semidirect
60. #5072D3semidirect
142. C2×#213C2×D3semidirect
159. C4×D12C2×D3semidirect
169. #832C2×D3semidirect
178. C4⋊(C3⋊C8)C2×D3semidirect
216. C3×C4×D3D8semidirect
484. C4×D3#213semidirect
608. C32#3205semidirect
701. C3#80336semidirect
702. C3#83166semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1272
#105939682
#105927712
C3×#50722
#105914872
#105914822
#105914482
#105914472
#105903552
#105903472
#105902482
#831663
#803363