Finite Group Databasebeta

← #11878675

Subgroups — #11878675

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
1C2×#63911C211yesmaximal, characteristic, complemented
2#10594910C211yesmaximal, characteristic, complemented
3#10592431C211yesmaximal, characteristic, complemented
4C3×#4732C211yesmaximal, characteristic, complemented
5C3×#4718C211yesmaximal, characteristic, complemented
6#10591168C211yesmaximal, characteristic, complemented
7#10591162C211yesmaximal, characteristic, complemented
8#10590880C212yesmaximal, complemented
9#10590878C212yesmaximal, complemented
10#10590765C212yesmaximal, complemented
11#10590753C212yesmaximal, complemented
12#79994—31nomaximal
13#79303—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×#626—21no—
17C22×#626—21no—
18C2×#3804—21no—
19#64139C2211yescharacteristic
20C2×#3745C2212yescomplemented
21C3×#930C2211yescharacteristic
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×D24C2212yescomplemented
24#63978—21no—
25#63918C2211yescharacteristic, complemented
26#63911—21no—
27#63911—21no—
28#63911C2212yes—
29#63911C2212yes—
30#63911C2211yescharacteristic, complemented
31#63894C2211yescharacteristic, complemented
32Dic3×D12C2211yescharacteristic, complemented
33#63880—21no—
34#63852—21no—
35C2×#3714C2212yescomplemented
36C2×#3714C2212yescomplemented
37C32×C22⋊C8C2211yescharacteristic
38#63648C2212yescomplemented
39C3×#830C2211yescharacteristic
40C3×#821C2212yescomplemented
41C3×Dic3⋊C8C2212yescomplemented
42C3×C8×Dic3C2212yescomplemented
43#63564C2212yescomplemented
44#63563C2212yescomplemented
45C2×#940—31no—
46#5596—31no—
47#5477—31no—
48C2×#874—31no—
49C3×#447—31no—
50C3×#431—31no—
51#5217—31no—
52#5151—32no—
53#5150—32no—
54#5036—31no—
55#4843—32no—
56#4843—32no—
57#4786—32no—
58#4760—32no—
59#4732—31no—
60#4732—31no—
61#4732—31no—
62#4732—31no—
63#4732—61no—
64#4732D311yescharacteristic, complemented
65#4718D311yescharacteristic, complemented
66#4695—32no—
67#4694—32no—
68C23×C3⋊D3—21no—
69C23×C3×D3—21no—
70C22×C32×C4C2311yescharacteristic
71C2×#638—21no—
72C2×C4⋊(C3⋊D3)—21no—
73C2×C4⋊(C3⋊D3)—42no—
74C2×C4⋊(C3⋊D3)C2312yes—
75C2×C4⋊(C3⋊D3)C2311yescharacteristic
76C2×C3×#67—21no—
77C22×C3×Dic3D411yescharacteristic
78C22×C3×Dic3D411yescharacteristic
79C2×C3×D12—21no—
80C2×C3×D12—42no—
81C2×C3×D12C2311yescharacteristic
82C2×C3×D12C2312yes—
83C2×#627—21no—
84C2×#626—21no—
85C2×#626—22no—
86C2×#626—22no—
87C2×#626—22no—
88C2×#626—22no—
89C2×#626—21no—
90C2×#626—44no—
91C2×#626—44no—
92C2×#624—21no—
93#3804—44no—
94C2×D3×Dic3—21no—
95C2×C32×C8C2312yes—
96#3752—21no—
97C4⋊(C3⋊Dic3)C2311yescharacteristic
98#3745—42no—
99C3×(C2×D3)⋊C4—21no—
100C3×C4⋊Dic3C2311yescharacteristic
101C3×C4×Dic3D411yescharacteristic
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3C2311yescharacteristic
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
113C22×C3×D4—31no—
114C22×#67—61no—
115C22×#67—61no—
116C2×#237—61no—
117C2×#235—61no—
118C22×D12—31no—
119C22×D12—31no—
120C22×D12—61no—
121C22×D12—61no—
122C22×D12—61no—
123C22×D12C2×D311yescharacteristic
124C2×C3×D8—32no—
125C3×#121—31no—
126C2×C3×C42—31no—
127#940—32no—
128#940—31no—
129#940—32no—
130#940—61no—
131#940—61no—
132#939—61no—
133D4×Dic3—31no—
134C2×#213—32no—
135C2×#213—32no—
136#930—31no—
137#930—31no—
138#930—61no—
139#930—61no—
140#930C2×D311yescharacteristic
141C2×C4×Dic3C2×D311yescharacteristic
142C2×D24—32no—
143C2×D24—32no—
144C2×D24—32no—
145C2×D24—32no—
146C2×D24—62no—
147C2×D24C2×D312yescomplemented
148#893—31no—
149#888—31no—
150#885—61no—
151#67⋊C4—61no—
152#875—61no—
153#874—32no—
154#874—31no—
155#874—32no—
156#874—61no—
157#874—61no—
158C4×D12—31no—
159C4×D12—31no—
160C4×D12—61no—
161#869—31no—
162C3×C4⋊C8—32no—
163C3×#102—32no—
164C3×C22⋊C8—21no—
165C3×C22⋊C8—31no—
166C3×C22⋊C8C2×D311yescharacteristic
167C3×C22⋊C8C2×D311yescharacteristic
168C3×C4×C8—32no—
169#832—32no—
170#830C2×D311yescharacteristic
171#821—32no—
172#821—32no—
173#821—32no—
174#821—32no—
175#821—62no—
176#821C2×D312yescomplemented
177Dic3⋊C8C2×D312yescomplemented
178C8×Dic3C2×D312yescomplemented
179#809—32no—
180C23×C32C2×D411yescharacteristic
181C22×C3⋊D3—22no—
182C22×C3⋊D3—21no—
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—
191C2×C32×C4—22no—
192C2×C32×C4C2×D411yescharacteristic
193C2×C32×C4C2411yescharacteristic
194#638—42no—
195C2×C3⋊Dic3—21no—
196C4⋊(C3⋊D3)—22no—
197C4⋊(C3⋊D3)—22no—
198C4⋊(C3⋊D3)—22no—
199C4⋊(C3⋊D3)—42no—
200C3×#67—42no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3D814yescomplemented
204C2×C3×Dic3C2×D411yescharacteristic
205C2×C3×Dic3C2×D411yescharacteristic
206C2×C3×Dic3C2×D411yescharacteristic
207C2×C3×Dic3C2×D411yescharacteristic
208C3×D12—22no—
209C3×D12—22no—
210C3×D12—22no—
211C3×D12—42no—
212#627—42no—
213#626—44no—
214#626—42no—
215#626—44no—
216#626—44no—
217#626—42no—
218#626—44no—
219#624—42no—
220D3×Dic3—42no—
221C32×C8—22no—
222C3×C3⋊C8—22no—
223#532—91no—
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—31no—
234C24×C3—61no—
235C23×D3—21no—
236C23×D3—61no—
237C23×D3—61no—
238C23×D3—121no—
239C2×C3×D4—32no—
240C2×C3×D4—31no—
241C2×C3×D4—61no—
242C2×C3×D4—61no—
243C2×C3×D4—122no—
244C22×C3×C4—21no—
245C22×C3×C4—31no—
246C22×C3×C4—31no—
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C2×#67—21no—
250C2×#67—61no—
251C2×#67—61no—
252C2×#67—61no—
253C2×#67—61no—
254C2×#67—62no—
255C2×#67—62no—
256C2×#67—62no—
257C2×#67—62no—
258C2×#67—121no—
259C2×#67—124no—
260C2×#67—124no—
261C22×Dic3—61no—
262C22×Dic3D1211yescharacteristic
263C22×Dic3D1211yescharacteristic
264#237—124no—
265#235—124no—
266C2×D12—21no—
267C2×D12—32no—
268C2×D12—32no—
269C2×D12—31no—
270C2×D12—31no—
271C2×D12—42no—
272C2×D12—62no—
273C2×D12—61no—
274C2×D12—61no—
275C2×D12—62no—
276C2×D12—62no—
277C2×D12—62no—
278C2×D12—62no—
279C2×D12—61no—
280C2×D12—61no—
281C2×D12—61no—
282C2×D12—121no—
283C2×D12—122no—
284C2×D12—122no—
285C2×D12—124no—
286C2×D12—124no—
287C2×D12—124no—
288C2×D12C22×D312yes—
289C2×D12C22×D311yescharacteristic
290C2×C4×D3—61no—
291C2×C4×D3—61no—
292C2×C4×D3—61no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C3×D8—122no—
296C2×C3×C8—22no—
297C2×C3×C8—32no—
298C2×C3×C8C22×D312yes—
299C2×C3×C8C22×D312yes—
300C3×C4⋊C4—31no—
301C3×C22⋊C4—61no—
302C3×C42—31no—
303C3×C42—31no—
304C3×C42—31no—
305C3×C42—31no—
306#217—61no—
307#213—122no—
308#213—122no—
309(C2×D3)⋊C4—21no—
310(C2×D3)⋊C4—61no—
311(C2×D3)⋊C4—61no—
312(C2×D3)⋊C4—61no—
313(C2×D3)⋊C4—61no—
314(C2×D3)⋊C4—61no—
315(C2×D3)⋊C4—121no—
316C4⋊Dic3—31no—
317C4⋊Dic3—31no—
318C4⋊Dic3—61no—
319C4⋊Dic3—61no—
320C4⋊Dic3C22×D311yescharacteristic
321Dic3⋊C4—61no—
322C4×Dic3D1211yescharacteristic
323C4×Dic3D1211yescharacteristic
324C4×Dic3C22×D311yescharacteristic
325C4×Dic3C22×D311yescharacteristic
326C2×C3⋊C8C22×D312yes—
327D24—42no—
328D24—122no—
329D24—122no—
330D24—124no—
331D24—122no—
332D24—122no—
333C22×C32—21no—
334C22×C32—21no—
335C22×C32C2×D812yes—
336C22×C32C22×D411yescharacteristic
337C2×C3⋊D3—42no—
338C2×C3⋊D3—41no—
339C2×C3⋊D3—41no—
340C2×C3⋊D3—42no—
341C2×C3⋊D3—42no—
342C2×C3⋊D3—41no—
343C2×C3⋊D3—84no—
344C2×C3×D3—42no—
345C2×C3×D3—41no—
346C2×C3×D3—41no—
347C2×C3×D3—42no—
348C2×C3×D3—42no—
349C2×C3×D3—41no—
350C2×C3×D3—84no—
351C32×C4—21no—
352C32×C4H(5,𝔽2)12yes—
353C3⋊Dic3—41no—
354C3×Dic3—21no—
355C3×Dic3—41no—
356C3×Dic3C2×D812yes—
357C3×Dic3C2×D812yes—
358C3×Dic3AGL(1,ℤ/8)12yes—
359C2×#41—181no—
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—91no—
369#127—92no—
370#127—92no—
371#127—91no—
372#127—181no—
373#127—181no—
374#124—181no—
375#121—31no—
376#121—91no—
377#121—181no—
378C4×D4—91no—
379C4×D4—91no—
380C4×D4—181no—
381C2×C42—31no—
382C4⋊C8—32no—
383#102—32no—
384#102—92no—
385#102—92no—
386#102—92no—
387C22⋊C8—31no—
388C22⋊C8D3211yescharacteristic
389C4×C8—32no—
390C23×C3—21no—
391C23×C3—61no—
392C23×C3—62no—
393C23×C3—122no—
394C23×C3—122no—
395C23×C3—122no—
396C23×C3C2×D1211yescharacteristic
397C23×C3D3×D411yescharacteristic
398C22×D3—21no—
399C22×D3—22no—
400C22×D3—42no—
401C22×D3—42no—
402C22×D3—42no—
403C22×D3—61no—
404C22×D3—62no—
405C22×D3—61no—
406C22×D3—62no—
407C22×D3—122no—
408C22×D3—121no—
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×D4—62no—
419C3×D4—62no—
420C3×D4—62no—
421C3×D4—122no—
422C3×D4—122no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—34no—
428C2×C3×C4—31no—
429C2×C3×C4—31no—
430C2×C3×C4—31no—
431C2×C3×C4—31no—
432C2×C3×C4—42no—
433C2×C3×C4—62no—
434C2×C3×C4—61no—
435C2×C3×C4C2×D1211yescharacteristic
436C2×C3×C4D3×D411yescharacteristic
437C2×C3×C4C23×D311yescharacteristic
438C2×C3×C4C23×D311yescharacteristic
439#67—42no—
440#67—124no—
441#67—122no—
442#67—122no—
443#67—122no—
444#67—124no—
445#67—124no—
446#67—122no—
447#67—124no—
448#67—242no—
449C2×Dic3—22no—
450C2×Dic3—21no—
451C2×Dic3—61no—
452C2×Dic3—61no—
453C2×Dic3—121no—
454C2×Dic3—122no—
455C2×Dic3D2414yescomplemented
456C2×Dic3C2×D1211yescharacteristic
457C2×Dic3C2×D1211yescharacteristic
458C2×Dic3C2×D1211yescharacteristic
459C2×Dic3C2×D1211yescharacteristic
460D12—22no—
461D12—22no—
462D12—22no—
463D12—42no—
464D12—64no—
465D12—62no—
466D12—62no—
467D12—62no—
468D12—62no—
469D12—62no—
470D12—62no—
471D12—122no—
472D12—122no—
473D12—122no—
474D12—122no—
475D12—122no—
476D12—124no—
477D12—124no—
478D12—124no—
479D12—122no—
480D12—124no—
481D12—124no—
482C4×D3—122no—
483C4×D3—122no—
484C4×D3—122no—
485Dic6—122no—
486Dic6—122no—
487C3×C8—22no—
488C3×C8—22no—
489C3×C8—42no—
490C3×C8—62no—
491C3⋊C8—22no—
492C2×C32—22no—
493C2×C32#53511yescharacteristic
494C2×C32C22×D811yescharacteristic
495C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
496C3⋊D3—82no—
497C3⋊D3—81no—
498C3×D3—81no—
499C3×D3—82no—
500C24—61no—
501C24—181no—
502#41—364no—
503C2×Q8—181no—
504C2×D4—32no—
505C2×D4—31no—
506C2×D4—61no—
507C2×D4—61no—
508C2×D4—92no—
509C2×D4—91no—
510C2×D4—122no—
511C2×D4—181no—
512C2×D4—181no—
513C2×D4—182no—
514C2×D4—182no—
515C2×D4—182no—
516C2×D4—182no—
517C2×D4—181no—
518C2×D4—181no—
519C2×D4—362no—
520C2×D4—364no—
521C2×D4—364no—
522C22×C4—31no—
523C22×C4—31no—
524C22×C4—181no—
525C22×C4—181no—
526C22×C4C2×D3211yescharacteristic
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—
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—121no—
553C22×C3—122no—
554C22×C3—122no—
555C22×C3—121no—
556C22×C3—122no—
557C22×C3—121no—
558C22×C3—244no—
559C22×C3C2×D2412yes—
560C22×C3D3×D812yes—
561C22×C3C22×D1211yescharacteristic
562C22×C3C2×D3×D411yescharacteristic
563C2×D3—41no—
564C2×D3—42no—
565C2×D3—42no—
566C2×D3—41no—
567C2×D3—42no—
568C2×D3—41no—
569C2×D3—84no—
570C2×D3—124no—
571C2×D3—121no—
572C2×D3—122no—
573C2×D3—122no—
574C2×D3—121no—
575C2×D3—121no—
576C2×D3—122no—
577C2×D3—122no—
578C2×D3—121no—
579C2×D3—122no—
580C2×D3—121no—
581C2×D3—122no—
582C2×D3—121no—
583C2×D3—242no—
584C2×D3—242no—
585C2×D3—241no—
586C2×D3—241no—
587C2×D3—241no—
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—61no—
599C3×C4—121no—
600C3×C4#100412yes—
601C3×C4#100912yes—
602Dic3—21no—
603Dic3—41no—
604Dic3—121no—
605Dic3—121no—
606Dic3—241no—
607Dic3C2×D2412yes—
608Dic3C2×D2412yes—
609Dic3#90812yes—
610C32#320511yescharacteristic, complemented, Sylow
611C23—61no—
612C23—62no—
613C23—122no—
614C23—122no—
615C23—122no—
616C23—181no—
617C23—182no—
618C23—362no—
619C23—362no—
620C23—362no—
621C23D3×D1211yescharacteristic
622Q8—362no—
623D4—62no—
624D4—62no—
625D4—62no—
626D4—122no—
627D4—122no—
628D4—182no—
629D4—182no—
630D4—182no—
631D4—362no—
632D4—364no—
633D4—364no—
634D4—364no—
635D4—362no—
636D4—362no—
637D4—364no—
638D4—362no—
639C2×C4—22no—
640C2×C4—31no—
641C2×C4—31no—
642C2×C4—31no—
643C2×C4—34no—
644C2×C4—31no—
645C2×C4—62no—
646C2×C4—61no—
647C2×C4—181no—
648C2×C4—362no—
649C2×C4—362no—
650C2×C4D3×D1211yescharacteristic
651C2×C4C22×D3211yescharacteristic
652C8—22no—
653C8—62no—
654C2×C3—22no—
655C2×C3—22no—
656C2×C3—21no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—42no—
660C2×C3—242no—
661C2×C3—241no—
662C2×C3#552511yescharacteristic
663C2×C3#559211yescharacteristic
664C2×C3C22×D2411yescharacteristic
665C2×C3C2×#90811yescharacteristic
666C2×C3C2×D3×D811yescharacteristic
667C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
668D3—82no—
669D3—81no—
670D3—244no—
671D3—242no—
672D3—241no—
673D3—242no—
674D3—241no—
675D3—481no—
676C22—21no—
677C22—21no—
678C22—122no—
679C22—121no—
680C22—121no—
681C22—122no—
682C22—122no—
683C22—121no—
684C22—244no—
685C22—362no—
686C22—361no—
687C22—361no—
688C22—362no—
689C22—362no—
690C22—361no—
691C22—724no—
692C22D3×D2412yes—
693C22C2×D3×D1211yescharacteristic
694C4—21no—
695C4—32no—
696C4—32no—
697C4—32no—
698C4—61no—
699C4—121no—
700C4—361no—
701C4#6431412yes—
702C3—21no—
703C3#7930311yescharacteristic, complemented
704C3#7999411yescharacteristic, complemented
705C2—22no—
706C2—242no—
707C2—241no—
708C2—722no—
709C2—721no—
710C2#1059408011yescharacteristic
711C2C2×D3×D2411yescharacteristic
712C2D3×#90811yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3205
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#63911C2semidirect
2. #10594910C2semidirect
3. #10592431C2semidirect
4. C3×#4732C2semidirect
5. C3×#4718C2semidirect
6. #10591168C2semidirect
7. #10591162C2semidirect
8. #10590880C2semidirect
9. #10590878C2semidirect
10. #10590765C2semidirect
11. #10590753C2semidirect
20. C2×#3745C22semidirect
23. C2×C3×D24C22semidirect
25. #63918C22semidirect
30. #63911C22semidirect
31. #63894C22semidirect
32. Dic3×D12C22semidirect
35. C2×#3714C22semidirect
36. C2×#3714C22semidirect
38. #63648C22semidirect
40. C3×#821C22semidirect
41. C3×Dic3⋊C8C22semidirect
42. C3×C8×Dic3C22semidirect
43. #63564C22semidirect
44. #63563C22semidirect
64. #4732D3semidirect
65. #4718D3semidirect
147. C2×D24C2×D3semidirect
176. #821C2×D3semidirect
177. Dic3⋊C8C2×D3semidirect
178. C8×Dic3C2×D3semidirect
203. C2×C3×Dic3D8semidirect
455. C2×Dic3D24semidirect
610. C32#3205semidirect
703. C3#79303semidirect
704. C3#79994semidirect

Maximal subgroups

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

subgroupindex
C2×#639112
#105949102
#105924312
C3×#47322
C3×#47182
#105911682
#105911622
#105908802
#105908782
#105907652
#105907532
#799943
#793033