Finite Group Databasebeta

← #11878678

Subgroups — #11878678

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
1D3×#874C211yesmaximal, characteristic, complemented
2#10593968C211yesmaximal, characteristic, complemented
3#10592542C211yesmaximal, characteristic, complemented
4C3×#4843C211yesmaximal, characteristic, complemented
5C3×#4833C211yesmaximal, characteristic, complemented
6#10590947C212yesmaximal, complemented
7#10590944C212yesmaximal, complemented
8#10590880C212yesmaximal, complemented
9#10590878C212yesmaximal, complemented
10#10590355C211yesmaximal, characteristic, complemented
11#10590349C211yesmaximal, characteristic, complemented
12#80336—31nomaximal
13#79303—31nomaximal
14C2×D3×D12—21no—
15C2×D3×D12—21no—
16C2×D3×D12C2212yes—
17C2×#3798—21no—
18C2×#3745C2212yescomplemented
19#64083C2211yescharacteristic
20C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
21C2×C3×D24C2212yescomplemented
22C3×#874C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic, complemented
24C3×C42×D3C2211yescharacteristic
25#63918C2211yescharacteristic, complemented
26#63911—21no—
27#63911—21no—
28#63911C2212yes—
29#63911C2211yescharacteristic, complemented
30#63909C2211yescharacteristic
31#63908C2211yescharacteristic
32#63906—21no—
33C4×#626—21no—
34#63852—21no—
35C2×#3714C2212yescomplemented
36C2×#3714C2212yescomplemented
37C32×C4⋊C8C2211yescharacteristic, complemented
38#63648C2212yescomplemented
39C3×#821C2212yescomplemented
40C3×(C2×D3)⋊C8C2212yes—
41C3×C8×Dic3C2212yescomplemented
42C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
43#63564C2212yescomplemented
44#63563C2212yescomplemented
45D3×#127—31no—
46#5548—31no—
47#5477—31no—
48C2×#874—31no—
49C3×#459—31no—
50C3×#431—31no—
51#5156—32no—
52#5151—32no—
53#5072—31no—
54#5015—31no—
55#4843—31no—
56#4843—31no—
57#4843—31no—
58#4843—31no—
59#4843—61no—
60#4843D311yescharacteristic, complemented
61#4833D311yescharacteristic, complemented
62#4773—32no—
63#4760—32no—
64#4732—32no—
65#4732—32no—
66#4695—32no—
67#4694—32no—
68C22×D32—22no—
69C2×C4⋊(C3⋊D3)—21no—
70C2×C4⋊(C3⋊D3)—21no—
71C2×C4⋊(C3⋊D3)C2312yes—
72C2×C4⋊(C3⋊D3)C2311yescharacteristic
73C2×C4×C3⋊D3—21no—
74C2×C3×D12—21no—
75C2×C3×D12—21no—
76C2×C3×D12C2311yescharacteristic
77C2×C3×D12C2312yes—
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3D411yescharacteristic
80C2×C3×C4×D3D411yescharacteristic
81C2×C3×C4×D3C2311yescharacteristic
82C2×#627—21no—
83C2×#626—21no—
84C2×#626—21no—
85C2×#626—22no—
86C2×#626—22no—
87C2×#626—22no—
88C2×#626—21no—
89C2×#625—21no—
90D3×D12—42no—
91D3×D12—42no—
92D3×D12—44no—
93D3×D12—44no—
94#3798—44no—
95C2×C32×C8C2312yes—
96C32×C42C2311yescharacteristic
97#3752—21no—
98C4⋊(C3⋊Dic3)C2311yescharacteristic
99#3745—42no—
100C3×(C2×D3)⋊C4—21no—
101C3×C4⋊Dic3C2311yescharacteristic
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3D411yescharacteristic
104C3×C4×Dic3C2311yescharacteristic
105C2×C3×C3⋊C8C2312yes—
106C3×D24—42no—
107Dic3⋊Dic3—21no—
108#3722—21no—
109(C2×D3)⋊Dic3—21no—
110#3714—42no—
111#3714—42no—
112#3205—91noSylow
113C2×D3×D4—32no—
114C2×D3×D4—61no—
115C2×D3×D4—61no—
116C2×#235—61no—
117C2×#235—61no—
118C22×D12—32no—
119C22×D12—61no—
120C22×D12—61no—
121C2×C3×D8—32no—
122C3×#127—31no—
123C3×C4×D4—31no—
124C2×C3×C42—31no—
125#940—31no—
126#940—32no—
127#940—61no—
128#940—61no—
129#938—31no—
130C2×#213—32no—
131C2×#213—32no—
132#930—31no—
133#930—31no—
134#930—61no—
135C4×#67—61no—
136C2×D24—32no—
137C2×D24—32no—
138C2×D24—32no—
139C2×D24—32no—
140C2×D24—62no—
141C2×D24C2×D312yescomplemented
142#895—31no—
143#888—31no—
144#885—61no—
145#884—61no—
146#875—61no—
147#874—32no—
148#874—31no—
149#874—31no—
150#874—31no—
151#874—61no—
152#874—61no—
153#874—61no—
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—21no—
163C3×C4⋊C8—31no—
164C3×C4⋊C8C2×D311yescharacteristic, complemented
165C3×C4⋊C8C2×D311yescharacteristic, complemented
166C3×#102—32no—
167C3×C22⋊C8—32no—
168C3×C4×C8—32no—
169#832—32no—
170#821—32no—
171#821—32no—
172#821—32no—
173#821—32no—
174#821—62no—
175#821C2×D312yescomplemented
176(C2×D3)⋊C8C2×D312yes—
177C8×Dic3C2×D312yescomplemented
178#809—32no—
179C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
180C22×C3⋊D3—22no—
181C22×C3⋊D3—21no—
182C22×C3×D3—22no—
183C22×C3×D3—21no—
184C22×C3×D3C2×D411yescharacteristic
185C2×D32—44no—
186C2×D32—44no—
187C2×D32—44no—
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2411yescharacteristic
191C2×C3⋊Dic3—21no—
192C4⋊(C3⋊D3)—21no—
193C4⋊(C3⋊D3)—21no—
194C4⋊(C3⋊D3)—22no—
195C4⋊(C3⋊D3)—22no—
196C4⋊(C3⋊D3)—42no—
197C4⋊(C3⋊D3)—42no—
198C4×C3⋊D3—42no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3C2×D411yescharacteristic
201C2×C3×Dic3C2×D411yescharacteristic
202C2×C3×Dic3C2×D411yescharacteristic
203C3×D12—21no—
204C3×D12—22no—
205C3×D12—21no—
206C3×D12—22no—
207C3×D12—42no—
208C3×D12—42no—
209C3×C4×D3—21no—
210C3×C4×D3—21no—
211C3×C4×D3—22no—
212C3×C4×D3—42no—
213C3×C4×D3D814yescomplemented
214#627—42no—
215#626—44no—
216#626—42no—
217#626—42no—
218#626—44no—
219#626—44no—
220#626—42no—
221#625—42no—
222C32×C8—22no—
223C3×C3⋊C8—22no—
224#532—91no—
225C2×#127—91no—
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—31no—
235C23×D3—62no—
236C23×D3—62no—
237C2×C3×D4—32no—
238C2×C3×D4—31no—
239C2×C3×D4—61no—
240C2×C3×D4—61no—
241C22×C3×C4—31no—
242C22×C3×C4—31no—
243C22×C3×C4—31no—
244C22×C3×C4—61no—
245C2×#67—61no—
246C2×#67—61no—
247C2×#67—61no—
248C2×#67—61no—
249C2×#67—61no—
250C2×#67—62no—
251C2×#67—62no—
252C2×#67—62no—
253D3×D4—122no—
254D3×D4—122no—
255D3×D4—124no—
256D3×D4—124no—
257#235—124no—
258#235—124no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12—32no—
262C2×D12—32no—
263C2×D12—31no—
264C2×D12—31no—
265C2×D12—61no—
266C2×D12—62no—
267C2×D12—61no—
268C2×D12—62no—
269C2×D12—62no—
270C2×D12—61no—
271C2×D12—62no—
272C2×D12—61no—
273C2×D12—61no—
274C2×D12—61no—
275C2×D12—61no—
276C2×D12—61no—
277C2×D12—121no—
278C2×D12—121no—
279C2×D12—122no—
280C2×D12—122no—
281C2×D12—124no—
282C2×D12—124no—
283C2×D12C22×D312yes—
284C2×D12C22×D311yescharacteristic
285C2×C4×D3—21no—
286C2×C4×D3—61no—
287C2×C4×D3—61no—
288C2×C4×D3—121no—
289C2×C4×D3D1211yescharacteristic
290C2×C4×D3D1211yescharacteristic
291C2×C4×D3C22×D311yescharacteristic
292C2×Dic6—61no—
293C2×Dic6—61no—
294C3×D8—122no—
295C2×C3×C8—22no—
296C2×C3×C8—32no—
297C2×C3×C8C22×D312yes—
298C2×C3×C8C22×D312yes—
299C3×C4⋊C4—31no—
300C3×C22⋊C4—61no—
301C3×C42—21no—
302C3×C42—31no—
303C3×C42—31no—
304C3×C42—31no—
305C3×C42C22×D311yescharacteristic
306C3×C42C22×D311yescharacteristic
307#217—61no—
308#213—122no—
309#213—122no—
310(C2×D3)⋊C4—21no—
311(C2×D3)⋊C4—61no—
312(C2×D3)⋊C4—61no—
313(C2×D3)⋊C4—61no—
314(C2×D3)⋊C4—61no—
315(C2×D3)⋊C4—61no—
316(C2×D3)⋊C4—121no—
317C4⋊Dic3—31no—
318C4⋊Dic3—31no—
319C4⋊Dic3—61no—
320C4⋊Dic3—61no—
321C4⋊Dic3C22×D311yescharacteristic
322Dic3⋊C4—61no—
323C4×Dic3D1211yescharacteristic
324C4×Dic3D1211yescharacteristic
325C4×Dic3C22×D311yescharacteristic
326C2×C3⋊C8C22×D312yes—
327D24—42no—
328D24—122no—
329D24—122no—
330D24—124no—
331D24—122no—
332D24—122no—
333C22×C32C22×D411yescharacteristic
334C2×C3⋊D3—41no—
335C2×C3⋊D3—42no—
336C2×C3⋊D3—41no—
337C2×C3⋊D3—42no—
338C2×C3⋊D3—42no—
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—42no—
347C2×C3×D3—41no—
348C2×C3×D3C2×D812yes—
349D32—88no—
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—92no—
361C22×D4—181no—
362C22×D4—181no—
363C2×D8—32no—
364C2×D8—92no—
365C2×D8—92no—
366C2×D8—92no—
367C4⋊Q8—91no—
368#127—31no—
369#127—92no—
370#127—91no—
371#127—91no—
372#127—181no—
373#127—181no—
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⋊C8D3211yescharacteristic, complemented
384#102—32no—
385#102—92no—
386#102—92no—
387#102—92no—
388C22⋊C8—32no—
389C4×C8—32no—
390C23×C3—31no—
391C23×C3—61no—
392C23×C3—62no—
393C22×D3—21no—
394C22×D3—22no—
395C22×D3—61no—
396C22×D3—62no—
397C22×D3—61no—
398C22×D3—62no—
399C22×D3—121no—
400C22×D3—122no—
401C22×D3—124no—
402C22×D3—124no—
403C22×D3—124no—
404C22×D3—124no—
405C22×D3—124no—
406C22×D3—124no—
407C22×D3C2×D1211yescharacteristic
408C3×D4—61no—
409C3×D4—62no—
410C3×D4—61no—
411C3×D4—62no—
412C3×D4—122no—
413C3×D4—122no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—31no—
418C2×C3×C4—31no—
419C2×C3×C4—34no—
420C2×C3×C4—31no—
421C2×C3×C4—62no—
422C2×C3×C4—61no—
423C2×C3×C4—61no—
424C2×C3×C4—61no—
425C2×C3×C4—122no—
426C2×C3×C4C2×D1211yescharacteristic
427C2×C3×C4C2×D1211yescharacteristic
428C2×C3×C4D3×D411yescharacteristic
429C2×C3×C4D3×D411yescharacteristic
430C2×C3×C4C23×D311yescharacteristic
431C2×C3×C4C23×D311yescharacteristic
432#67—124no—
433#67—122no—
434#67—122no—
435#67—122no—
436#67—122no—
437#67—124no—
438#67—124no—
439#67—122no—
440C2×Dic3—21no—
441C2×Dic3—61no—
442C2×Dic3—61no—
443C2×Dic3—121no—
444C2×Dic3C2×D1211yescharacteristic
445C2×Dic3C2×D1211yescharacteristic
446C2×Dic3C2×D1211yescharacteristic
447D12—21no—
448D12—22no—
449D12—21no—
450D12—22no—
451D12—42no—
452D12—42no—
453D12—62no—
454D12—61no—
455D12—62no—
456D12—61no—
457D12—61no—
458D12—62no—
459D12—62no—
460D12—61no—
461D12—62no—
462D12—121no—
463D12—122no—
464D12—122no—
465D12—122no—
466D12—122no—
467D12—122no—
468D12—124no—
469D12—124no—
470D12—122no—
471D12—124no—
472D12—122no—
473D12—122no—
474D12—122no—
475D12—242no—
476D12—242no—
477C4×D3—21no—
478C4×D3—21no—
479C4×D3—22no—
480C4×D3—42no—
481C4×D3—122no—
482C4×D3—122no—
483C4×D3—242no—
484C4×D3D2414yescomplemented
485Dic6—122no—
486Dic6—122no—
487C3×C8—22no—
488C3×C8—22no—
489C3×C8—42no—
490C3×C8—62no—
491C3⋊C8—22no—
492C2×C32#53511yescharacteristic
493C2×C32C22×D811yescharacteristic
494C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
495C3⋊D3—81no—
496C3⋊D3—82no—
497C3×D3—22no—
498C3×D3—82no—
499C3×D3—81no—
500C24—182no—
501#41—364no—
502C2×Q8—181no—
503C2×D4—32no—
504C2×D4—31no—
505C2×D4—61no—
506C2×D4—61no—
507C2×D4—92no—
508C2×D4—91no—
509C2×D4—181no—
510C2×D4—181no—
511C2×D4—182no—
512C2×D4—182no—
513C2×D4—182no—
514C2×D4—181no—
515C2×D4—181no—
516C2×D4—181no—
517C2×D4—181no—
518C2×D4—364no—
519C2×D4—362no—
520C2×D4—362no—
521C2×D4—364no—
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×C8C2×D3212yes—
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—61no—
547C22×C3—61no—
548C22×C3—121no—
549C22×C3—122no—
550C22×C3—122no—
551C22×C3—121no—
552C22×C3—122no—
553C22×C3—121no—
554C22×C3C22×D1211yescharacteristic
555C22×C3C2×D3×D411yescharacteristic
556C2×D3—21no—
557C2×D3—21no—
558C2×D3—41no—
559C2×D3—42no—
560C2×D3—42no—
561C2×D3—41no—
562C2×D3—42no—
563C2×D3—41no—
564C2×D3—122no—
565C2×D3—121no—
566C2×D3—122no—
567C2×D3—122no—
568C2×D3—121no—
569C2×D3—121no—
570C2×D3—122no—
571C2×D3—122no—
572C2×D3—121no—
573C2×D3—122no—
574C2×D3—121no—
575C2×D3—122no—
576C2×D3—121no—
577C2×D3—241no—
578C2×D3—241no—
579C2×D3—242no—
580C2×D3—242no—
581C2×D3—242no—
582C2×D3—248no—
583C2×D3—248no—
584C2×D3C2×D2412yes—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—22no—
588C3×C4—21no—
589C3×C4—21no—
590C3×C4—32no—
591C3×C4—32no—
592C3×C4—41no—
593C3×C4—61no—
594C3×C4—121no—
595C3×C4C2×D2412yes—
596C3×C4D3×D812yes—
597C3×C4#100411yescharacteristic
598C3×C4#100911yescharacteristic
599C3×C4#100911yescharacteristic
600C3×C4#100911yescharacteristic
601Dic3—21no—
602Dic3—41no—
603Dic3—121no—
604Dic3—121no—
605Dic3—241no—
606Dic3C2×D2412yes—
607Dic3#90812yes—
608C32#320511yescharacteristic, complemented, Sylow
609C23—31no—
610C23—61no—
611C23—62no—
612C23—181no—
613C23—182no—
614C23—364no—
615C23—364no—
616C23—364no—
617Q8—362no—
618D4—61no—
619D4—62no—
620D4—61no—
621D4—62no—
622D4—122no—
623D4—122no—
624D4—181no—
625D4—182no—
626D4—181no—
627D4—182no—
628D4—362no—
629D4—364no—
630D4—364no—
631D4—362no—
632D4—362no—
633D4—364no—
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×D1211yescharacteristic
649C2×C4D3×D1211yescharacteristic
650C2×C4C22×D3211yescharacteristic
651C8—22no—
652C8—62no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—62no—
657C2×C3—242no—
658C2×C3—241no—
659C2×C3#552511yescharacteristic
660C2×C3#560711yescharacteristic
661C2×C3C22×D2411yescharacteristic
662C2×C3C2×#90811yescharacteristic
663C2×C3C2×D3×D811yescharacteristic
664C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
665D3—22no—
666D3—82no—
667D3—81no—
668D3—242no—
669D3—242no—
670D3—241no—
671D3—242no—
672D3—241no—
673D3—482no—
674C22—32no—
675C22—61no—
676C22—61no—
677C22—122no—
678C22—121no—
679C22—121no—
680C22—122no—
681C22—122no—
682C22—121no—
683C22—362no—
684C22—361no—
685C22—361no—
686C22—362no—
687C22—362no—
688C22—361no—
689C22—728no—
690C22C2×D3×D1211yescharacteristic
691C4—21no—
692C4—32no—
693C4—32no—
694C4—61no—
695C4—121no—
696C4—361no—
697C4D3×D2412yes—
698C4#6431411yescharacteristic
699C4#6432011yescharacteristic
700C3—21no—
701C3#7930311yescharacteristic, complemented
702C3#8033611yescharacteristic, complemented
703C2—62no—
704C2—242no—
705C2—241no—
706C2—722no—
707C2—721no—
708C2#1059462811yescharacteristic
709C2C2×D3×D2411yescharacteristic
710C2D3×#90811yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3205
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. D3×#874C2semidirect
2. #10593968C2semidirect
3. #10592542C2semidirect
4. C3×#4843C2semidirect
5. C3×#4833C2semidirect
6. #10590947C2semidirect
7. #10590944C2semidirect
8. #10590880C2semidirect
9. #10590878C2semidirect
10. #10590355C2semidirect
11. #10590349C2semidirect
18. C2×#3745C22semidirect
20. C4×C4⋊(C3⋊D3)C22semidirect
21. C2×C3×D24C22semidirect
23. C3×C4×D12C22semidirect
25. #63918C22semidirect
29. #63911C22semidirect
35. C2×#3714C22semidirect
36. C2×#3714C22semidirect
37. C32×C4⋊C8C22semidirect
38. #63648C22semidirect
39. C3×#821C22semidirect
41. C3×C8×Dic3C22semidirect
42. C3×C4⋊(C3⋊C8)C22semidirect
43. #63564C22semidirect
44. #63563C22semidirect
60. #4843D3semidirect
61. #4833D3semidirect
141. C2×D24C2×D3semidirect
159. C4×D12C2×D3semidirect
164. C3×C4⋊C8C2×D3semidirect
165. C3×C4⋊C8C2×D3semidirect
175. #821C2×D3semidirect
177. C8×Dic3C2×D3semidirect
179. C4⋊(C3⋊C8)C2×D3semidirect
213. C3×C4×D3D8semidirect
383. C4⋊C8D32semidirect
484. C4×D3D24semidirect
608. C32#3205semidirect
701. C3#79303semidirect
702. C3#80336semidirect

Maximal subgroups

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

subgroupindex
D3×#8742
#105939682
#105925422
C3×#48432
C3×#48332
#105909472
#105909442
#105908802
#105908782
#105903552
#105903492
#803363
#793033