Finite Group Databasebeta

← #11885757

Subgroups — #11885757

Order 1152.

1409 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3745C211yesmaximal, characteristic, complemented
2#10595074C212yesmaximal, complemented
3C2×D3×D24C211yesmaximal, characteristic, complemented
4C3×#5115C211yesmaximal, characteristic, complemented
5C3×C8×#67C211yesmaximal, characteristic, complemented
6#10591168C212yesmaximal, complemented
7#10590947C212yesmaximal, complemented
8#10590880C211yesmaximal, characteristic, complemented
9#10590832C211yesmaximal, characteristic, complemented
10#10590765C212yesmaximal, complemented
11#10590763C211yesmaximal, characteristic, complemented
12#80729—31nomaximal
13D4×D24—31nomaximal
14C22×C4⋊(C3⋊D3)C2212yescomplemented
15C2×#3811—22no—
16C2×D3×D12C2212yescomplemented
17C22×C32×C8C2211yescharacteristic, complemented
18C2×#3745—24no—
19C2×#3745C2211yescharacteristic
20C2×#3745C2212yescomplemented
21C2×#3745C2211yescharacteristic, complemented
22C3×#930C2212yescomplemented
23C3×C4×#67C2211yescharacteristic
24C2×C3×D24C2211yescharacteristic, complemented
25C2×C3×D3×C8C2211yescharacteristic, complemented
26#63981—22no—
27#63923—22no—
28#63911C2212yescomplemented
29#63910—22no—
30#63909C2212yescomplemented
31#63894C2212yescomplemented
32C2×#3714C2212yescomplemented
33C2×#3714C2212yescomplemented
34D3×D24—24no—
35C3×#830C2211yescharacteristic, complemented
36C3×#821C2212yescomplemented
37C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
38C3×#818C2211yescharacteristic, complemented
39C3×Dic3⋊C8C2211yescharacteristic, complemented
40C3×C8×Dic3C2211yescharacteristic, complemented
41#63564C2212yescomplemented
42#63564C2212yescomplemented
43C2×D3×D8—31no—
44C22×D24—31no—
45C22×D24—31no—
46C22×D24—31no—
47C22×D24—61no—
48#5609—32no—
49D4×D12—32no—
50C3×#466—31no—
51C3×C8×D4—31no—
52#5151—31no—
53#5115—31no—
54#5115D311yescharacteristic, complemented
55C8×#67D311yescharacteristic, complemented
56#5036—32no—
57#4883—31no—
58#4872—31no—
59#4843—32no—
60#4786—32no—
61#4773—32no—
62#4732—32no—
63#4732—32no—
64#4695—31no—
65C4×D24—31no—
66C23×C3⋊D3—22no—
67C22×D32—22no—
68C22×C32×C4C2311yescharacteristic
69C2×C4⋊(C3⋊D3)—24no—
70C2×C4⋊(C3⋊D3)—22no—
71C2×C4⋊(C3⋊D3)—42no—
72C2×C4⋊(C3⋊D3)C2312yes—
73C2×C4⋊(C3⋊D3)C2312yes—
74C2×C3×#67—22no—
75C2×C3×#67D411yescharacteristic
76C2×C3×D12C2312yes—
77C2×C3×C4×D3C2311yescharacteristic
78#3811—48no—
79C2×#626—22no—
80C2×#626—22no—
81C2×#626—22no—
82C2×#626—22no—
83C2×#624—22no—
84D3×D12—24no—
85D3×D12—42no—
86C2×C32×C8—22no—
87C2×C32×C8C2311yescharacteristic
88C2×C32×C8C2311yescharacteristic
89#3745—24no—
90#3745—22no—
91#3745D414yescomplemented
92C3×#217D411yescharacteristic
93C3×(C2×D3)⋊C4—22no—
94C3×(C2×D3)⋊C4D411yescharacteristic
95C3×C4⋊Dic3C2312yes—
96C3×Dic3⋊C4D411yescharacteristic
97C3×C4×Dic3C2311yescharacteristic
98C2×C3×C3⋊C8C2311yescharacteristic
99C2×C3×C3⋊C8C2311yescharacteristic
100C3×D24—22no—
101C3×D3×C8—22no—
102#3722—22no—
103#3722—22no—
104#3714—24no—
105#3714—42no—
106D4×D8—91noSylow
107C2×D3×D4—32no—
108C2×D3×D4—62no—
109C2×D3×D4—62no—
110C22×D12—32no—
111C22×D12—32no—
112C22×D12—32no—
113C22×D12—62no—
114C2×C3×D8—31no—
115C22×C3×C8—21no—
116C22×C3×C8—31no—
117C22×C3×C8C2×D311yescharacteristic, complemented
118C22×C3×C8C2×D311yescharacteristic, complemented
119C3×#121—32no—
120C3×C4×D4—31no—
121#940—32no—
122#937—62no—
123C2×#213—32no—
124C2×#213—32no—
125#930—32no—
126#930C2×D312yescomplemented
127C4×#67C2×D311yescharacteristic
128D3×D8—64no—
129C2×D24—31no—
130C2×D24—31no—
131C2×D24—32no—
132C2×D24—31no—
133C2×D24—31no—
134C2×D24—32no—
135C2×D24—32no—
136C2×D24—32no—
137C2×D24—61no—
138C2×D24—62no—
139C2×D24—61no—
140C2×D24—64no—
141C2×D24—64no—
142C2×D24—64no—
143C2×D24—68no—
144C2×D24C2×D311yescharacteristic, complemented
145C2×D3×C8C2×D311yescharacteristic, complemented
146#895—32no—
147#895—62no—
148#893—32no—
149#884—62no—
150#882—62no—
151#882—62no—
152#882—62no—
153#874—32no—
154C4×D12—32no—
155C3×#107—31no—
156C3×C4⋊C8—31no—
157C3×#102—32no—
158C3×C22⋊C8—31no—
159C3×C22⋊C8—31no—
160C3×C4×C8—31no—
161#830C2×D311yescharacteristic, complemented
162#821—32no—
163#821—32no—
164#821C2×D312yescomplemented
165(C2×D3)⋊C8C2×D311yescharacteristic, complemented
166#818C2×D311yescharacteristic, complemented
167Dic3⋊C8C2×D311yescharacteristic, complemented
168C8×Dic3C2×D311yescharacteristic, complemented
169#809—32no—
170#809—32no—
171C23×C32C2×D411yescharacteristic
172C22×C3⋊D3—22no—
173C22×C3⋊D3—22no—
174C22×C3⋊D3—44no—
175C22×C3⋊D3—44no—
176C22×C3⋊D3—82no—
177C22×C3×D3—22no—
178C22×C3×D3C2×D411yescharacteristic
179C2×D32—44no—
180C2×D32—44no—
181C2×D32—82no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2411yescharacteristic
186C4⋊(C3⋊D3)—22no—
187C4⋊(C3⋊D3)—22no—
188C4⋊(C3⋊D3)—22no—
189C4⋊(C3⋊D3)—44no—
190C4⋊(C3⋊D3)C2×D414yescomplemented
191C3×#67—44no—
192C3×#67D814yescomplemented
193C2×C3×Dic3—22no—
194C2×C3×Dic3C2×D411yescharacteristic
195C2×C3×Dic3C2×D411yescharacteristic
196C2×C3×Dic3C2×D411yescharacteristic
197C3×D12—22no—
198C3×D12—22no—
199C3×C4×D3—21no—
200C3×C4×D3—21no—
201#626—44no—
202#626—44no—
203#626—44no—
204#626—82no—
205#624—44no—
206C32×C8—21no—
207C32×C8C2×D412yescomplemented
208C3×C3⋊C8—21no—
209C3×C3⋊C8—21no—
210C22×D8—91no—
211C22×D8—91no—
212D42—92no—
213#493—91no—
214#466—31no—
215#466—91no—
216#459—92no—
217#447—92no—
218#447—92no—
219C4×D8—91no—
220C8×D4—31no—
221C23×D3—62no—
222C23×D3—62no—
223C23×D3—62no—
224C23×D3—62no—
225C23×D3—122no—
226C2×C3×D4—31no—
227C2×C3×D4—32no—
228C2×C3×D4—62no—
229C22×C3×C4—21no—
230C22×C3×C4—31no—
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C2×#67—22no—
234C2×#67—62no—
235C2×#67—62no—
236C2×#67—62no—
237C2×#67—62no—
238C2×#67D1211yescharacteristic
239D3×D4—64no—
240D3×D4—122no—
241D3×D4—128no—
242D3×D4—128no—
243C2×D12—32no—
244C2×D12—32no—
245C2×D12—32no—
246C2×D12—32no—
247C2×D12—62no—
248C2×D12—62no—
249C2×D12—64no—
250C2×D12—64no—
251C2×D12—64no—
252C2×D12—68no—
253C2×D12—62no—
254C2×D12—62no—
255C2×D12—62no—
256C2×D12—62no—
257C2×D12—62no—
258C2×D12—62no—
259C2×D12—122no—
260C2×D12—122no—
261C2×D12—122no—
262C2×D12—122no—
263C2×D12—124no—
264C2×D12C22×D312yes—
265C2×C4×D3—62no—
266C2×C4×D3—62no—
267C2×C4×D3C22×D311yescharacteristic
268C3×D8—62no—
269C2×C3×C8—24no—
270C2×C3×C8—22no—
271C2×C3×C8—22no—
272C2×C3×C8—21no—
273C2×C3×C8—21no—
274C2×C3×C8—31no—
275C2×C3×C8—31no—
276C2×C3×C8—62no—
277C2×C3×C8C22×D311yescharacteristic
278C2×C3×C8C22×D311yescharacteristic
279C2×C3×C8C22×D311yescharacteristic
280C2×C3×C8C22×D311yescharacteristic
281C3×C4⋊C4—31no—
282C3×C4⋊C4—32no—
283C3×C22⋊C4—31no—
284C3×C22⋊C4—31no—
285C3×C22⋊C4—62no—
286C3×C42—31no—
287#217D1211yescharacteristic
288#213—64no—
289#213—122no—
290(C2×D3)⋊C4—22no—
291(C2×D3)⋊C4—62no—
292(C2×D3)⋊C4—62no—
293(C2×D3)⋊C4—62no—
294(C2×D3)⋊C4—62no—
295(C2×D3)⋊C4D1211yescharacteristic
296C4⋊Dic3C22×D312yes—
297Dic3⋊C4D1211yescharacteristic
298C4×Dic3C22×D311yescharacteristic
299C2×C3⋊C8C22×D311yescharacteristic
300C2×C3⋊C8C22×D311yescharacteristic
301D24—22no—
302D24—34no—
303D24—34no—
304D24—64no—
305D24—64no—
306D24—64no—
307D24—68no—
308D24—64no—
309D24—64no—
310D24—62no—
311D24—62no—
312D24—122no—
313D3×C8—22no—
314C22×C32—21no—
315C22×C32—21no—
316C22×C32C2×D812yescomplemented
317C22×C32C22×D411yescharacteristic
318C2×C3⋊D3—24no—
319C2×C3⋊D3—42no—
320C2×C3⋊D3—42no—
321C2×C3⋊D3—42no—
322C2×C3⋊D3—42no—
323C2×C3⋊D3—42no—
324C2×C3⋊D3—88no—
325C2×C3×D3—21no—
326C2×C3×D3—21no—
327C2×C3×D3—42no—
328C2×C3×D3—42no—
329C2×C3×D3—42no—
330C2×C3×D3C2×D812yescomplemented
331D32—88no—
332C32×C4—21no—
333C32×C4C22×D411yescharacteristic
334C32×C4H(5,𝔽2)11yescharacteristic
335C3×Dic3—21no—
336C3×Dic3—21no—
337C3×Dic3—42no—
338C3×Dic3C2×D812yescomplemented
339C22×D4—92no—
340C22×D4—92no—
341C22×D4—182no—
342C2×D8—31no—
343C2×D8—92no—
344C2×D8—92no—
345C2×D8—91no—
346C2×D8—92no—
347C2×D8—91no—
348C2×D8—184no—
349C2×D8—184no—
350C22×C8—31no—
351C22×C8D3211yescharacteristic, complemented
352#127—92no—
353#121—32no—
354#121—92no—
355#121—182no—
356#120—182no—
357#120—182no—
358C4×D4—31no—
359C4×D4—92no—
360#107—31no—
361C4⋊C8—31no—
362#102—32no—
363#102—92no—
364#102—92no—
365C22⋊C8—31no—
366C22⋊C8—31no—
367C4×C8—31no—
368C23×C3—21no—
369C23×C3—31no—
370C23×C3—62no—
371C23×C3C2×D1211yescharacteristic
372C23×C3D3×D411yescharacteristic
373C22×D3—22no—
374C22×D3—62no—
375C22×D3—62no—
376C22×D3—62no—
377C22×D3—62no—
378C22×D3—122no—
379C22×D3—122no—
380C22×D3—124no—
381C22×D3—124no—
382C22×D3—124no—
383C22×D3—124no—
384C22×D3—124no—
385C22×D3—128no—
386C22×D3—124no—
387C22×D3—124no—
388C22×D3—124no—
389C22×D3—244no—
390C22×D3—242no—
391C22×D3—242no—
392C22×D3—242no—
393C22×D3—242no—
394C22×D3—244no—
395C22×D3C2×D1211yescharacteristic
396C3×D4—34no—
397C3×D4—62no—
398C3×D4—62no—
399C3×D4—124no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—31no—
409C2×C3×C4—31no—
410C2×C3×C4—31no—
411C2×C3×C4—61no—
412C2×C3×C4—61no—
413C2×C3×C4—62no—
414C2×C3×C4C2×D1211yescharacteristic
415C2×C3×C4D3×D411yescharacteristic
416C2×C3×C4C23×D311yescharacteristic
417C2×C3×C4C23×D311yescharacteristic
418#67—44no—
419#67—124no—
420#67—124no—
421#67—124no—
422#67—242no—
423#67D2414yescomplemented
424C2×Dic3—22no—
425C2×Dic3C2×D1211yescharacteristic
426C2×Dic3C2×D1211yescharacteristic
427C2×Dic3C2×D1211yescharacteristic
428D12—22no—
429D12—22no—
430D12—34no—
431D12—34no—
432D12—64no—
433D12—64no—
434D12—62no—
435D12—62no—
436D12—62no—
437D12—62no—
438D12—62no—
439D12—62no—
440D12—122no—
441D12—122no—
442D12—124no—
443D12—124no—
444D12—128no—
445D12—124no—
446D12—124no—
447D12—124no—
448D12—242no—
449C4×D3—21no—
450C4×D3—21no—
451C4×D3—124no—
452C4×D3—124no—
453C3×C8—22no—
454C3×C8—21no—
455C3×C8—21no—
456C3×C8—22no—
457C3×C8—61no—
458C3×C8—61no—
459C3×C8D3×D412yescomplemented
460C3×C8D3×D412yescomplemented
461C3⋊C8—21no—
462C3⋊C8—21no—
463C2×C32—22no—
464C2×C32D4211yescharacteristic
465C2×C32C22×D811yescharacteristic
466C2×C32#57611yescharacteristic
467C3⋊D3—44no—
468C3⋊D3—82no—
469C3×D3—22no—
470C3×D3—82no—
471C24—182no—
472C24—182no—
473C2×D4—31no—
474C2×D4—32no—
475C2×D4—62no—
476C2×D4—92no—
477C2×D4—92no—
478C2×D4—184no—
479C2×D4—182no—
480C2×D4—182no—
481C2×D4—182no—
482C2×D4—184no—
483C2×D4—182no—
484C2×D4—182no—
485C2×D4—362no—
486C2×D4—362no—
487C2×D4—368no—
488C22×C4—31no—
489C22×C4—182no—
490C22×C4C2×D3211yescharacteristic
491D8—62no—
492D8—94no—
493D8—184no—
494D8—184no—
495D8—182no—
496D8—362no—
497C2×C8—22no—
498C2×C8—31no—
499C2×C8—31no—
500C2×C8—62no—
501C2×C8C2×D3211yescharacteristic
502C2×C8C2×D3211yescharacteristic
503C4⋊C4—31no—
504C4⋊C4—32no—
505C22⋊C4—31no—
506C22⋊C4—31no—
507C22⋊C4—62no—
508C22⋊C4—182no—
509C22⋊C4—182no—
510C42—31no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—21no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—22no—
519C22×C3—32no—
520C22×C3—61no—
521C22×C3—61no—
522C22×C3—122no—
523C22×C3—122no—
524C22×C3—122no—
525C22×C3C2×D2412yescomplemented
526C22×C3D3×D812yescomplemented
527C22×C3C22×D1211yescharacteristic
528C22×C3C2×D3×D411yescharacteristic
529C2×D3—21no—
530C2×D3—21no—
531C2×D3—42no—
532C2×D3—42no—
533C2×D3—42no—
534C2×D3—64no—
535C2×D3—64no—
536C2×D3—124no—
537C2×D3—122no—
538C2×D3—122no—
539C2×D3—122no—
540C2×D3—122no—
541C2×D3—124no—
542C2×D3—122no—
543C2×D3—122no—
544C2×D3—122no—
545C2×D3—122no—
546C2×D3—122no—
547C2×D3—122no—
548C2×D3—242no—
549C2×D3—242no—
550C2×D3—242no—
551C2×D3—242no—
552C2×D3—248no—
553C2×D3—248no—
554C2×D3—248no—
555C2×D3—248no—
556C2×D3—2416no—
557C2×D3C2×D2412yescomplemented
558C3×C4—22no—
559C3×C4—21no—
560C3×C4—21no—
561C3×C4—21no—
562C3×C4—21no—
563C3×C4—32no—
564C3×C4—61no—
565C3×C4—61no—
566C3×C4—122no—
567C3×C4C2×D3×D411yescharacteristic
568C3×C4C2×D3×D411yescharacteristic
569C3×C4#100911yescharacteristic
570C3×C4#100911yescharacteristic
571Dic3—21no—
572Dic3—21no—
573Dic3—42no—
574Dic3C2×D2412yescomplemented
575C32D4×D811yescharacteristic, complemented, Sylow
576C23—31no—
577C23—62no—
578C23—182no—
579C23—182no—
580C23—364no—
581C23—364no—
582C23—364no—
583C23—364no—
584C23—722no—
585C23—722no—
586C23D3×D1211yescharacteristic
587D4—34no—
588D4—62no—
589D4—62no—
590D4—94no—
591D4—124no—
592D4—182no—
593D4—182no—
594D4—182no—
595D4—364no—
596D4—364no—
597D4—364no—
598D4—364no—
599D4—722no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—31no—
603C2×C4—31no—
604C2×C4—31no—
605C2×C4—61no—
606C2×C4—61no—
607C2×C4—62no—
608C2×C4—364no—
609C2×C4D3×D1211yescharacteristic
610C2×C4C22×D3211yescharacteristic
611C8—21no—
612C8—61no—
613C8—61no—
614C8#381112yescomplemented
615C2×C3—24no—
616C2×C3—22no—
617C2×C3—22no—
618C2×C3—21no—
619C2×C3—21no—
620C2×C3—21no—
621C2×C3—62no—
622C2×C3—242no—
623C2×C3D4×D1211yescharacteristic
624C2×C3#560911yescharacteristic
625C2×C3C22×D2411yescharacteristic
626C2×C3#575211yescharacteristic
627C2×C3C2×D3×D811yescharacteristic
628C2×C3#576911yescharacteristic
629D3—22no—
630D3—82no—
631D3—124no—
632D3—124no—
633D3—244no—
634D3—244no—
635D3—242no—
636D3—242no—
637C22—21no—
638C22—21no—
639C22—32no—
640C22—61no—
641C22—61no—
642C22—122no—
643C22—122no—
644C22—122no—
645C22—184no—
646C22—362no—
647C22—362no—
648C22—362no—
649C22—362no—
650C22—362no—
651C22—728no—
652C22—728no—
653C22D3×D2412yescomplemented
654C22C2×D3×D1211yescharacteristic
655C4—21no—
656C4—32no—
657C4—61no—
658C4—61no—
659C4—122no—
660C4#6430811yescharacteristic
661C4C2×#381111yescharacteristic
662C3—21no—
663C3D4×D2411yescharacteristic, complemented
664C3#8072911yescharacteristic, complemented
665C2—22no—
666C2—62no—
667C2—242no—
668C2—364no—
669C2—722no—
670C2C2×D3×D2411yescharacteristic
671C2#1059468011yescharacteristic
672C2#1059507411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
hypercenterC22×C8D32
hypocenterC32D4×D8
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. C22×#3745C2semidirect
2. #10595074C2semidirect
3. C2×D3×D24C2semidirect
4. C3×#5115C2semidirect
5. C3×C8×#67C2semidirect
6. #10591168C2semidirect
7. #10590947C2semidirect
8. #10590880C2semidirect
9. #10590832C2semidirect
10. #10590765C2semidirect
11. #10590763C2semidirect
14. C22×C4⋊(C3⋊D3)C22semidirect
16. C2×D3×D12C22semidirect
17. C22×C32×C8C22semidirect
20. C2×#3745C22semidirect
21. C2×#3745C22semidirect
22. C3×#930C22semidirect
24. C2×C3×D24C22semidirect
25. C2×C3×D3×C8C22semidirect
28. #63911C22semidirect
30. #63909C22semidirect
31. #63894C22semidirect
32. C2×#3714C22semidirect
33. C2×#3714C22semidirect
35. C3×#830C22semidirect
36. C3×#821C22semidirect
37. C3×(C2×D3)⋊C8C22semidirect
38. C3×#818C22semidirect
39. C3×Dic3⋊C8C22semidirect
40. C3×C8×Dic3C22semidirect
41. #63564C22semidirect
42. #63564C22semidirect
54. #5115D3semidirect
55. C8×#67D3semidirect
91. #3745D4semidirect
117. C22×C3×C8C2×D3semidirect
118. C22×C3×C8C2×D3semidirect
126. #930C2×D3semidirect
144. C2×D24C2×D3semidirect
145. C2×D3×C8C2×D3semidirect
161. #830C2×D3semidirect
164. #821C2×D3semidirect
165. (C2×D3)⋊C8C2×D3semidirect
166. #818C2×D3semidirect
167. Dic3⋊C8C2×D3semidirect
168. C8×Dic3C2×D3semidirect
190. C4⋊(C3⋊D3)C2×D4semidirect
192. C3×#67D8semidirect
207. C32×C8C2×D4semidirect
316. C22×C32C2×D8semidirect
330. C2×C3×D3C2×D8semidirect
338. C3×Dic3C2×D8semidirect
351. C22×C8D32semidirect
423. #67D24semidirect
459. C3×C8D3×D4semidirect
460. C3×C8D3×D4semidirect
525. C22×C3C2×D24semidirect
526. C22×C3D3×D8semidirect
557. C2×D3C2×D24semidirect
574. Dic3C2×D24semidirect
575. C32D4×D8semidirect
614. C8#3811semidirect
653. C22D3×D24semidirect
663. C3D4×D24semidirect
664. C3#80729semidirect

Maximal subgroups

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

subgroupindex
C22×#37452
#105950742
C2×D3×D242
C3×#51152
C3×C8×#672
#105911682
#105909472
#105908802
#105908322
#105907652
#105907632
#807293
D4×D243