Finite Group Databasebeta

← #11870425

Subgroups — #11870425

Order 1152.

1083 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5596C211yesmaximal, characteristic, complemented
2C2×#63894C211yesmaximal, characteristic, complemented
3#10592735C211yesmaximal, characteristic, complemented
4C3×#5033C211yesmaximal, characteristic, complemented
5#10591429C212yesmaximal, complemented
6#10591400C212yesmaximal, complemented
7#10591168C211yesmaximal, characteristic, complemented
8#10591089C211yesmaximal, characteristic, complemented
9#10591053C211yesmaximal, characteristic, complemented
10#10590464C212yesmaximal, complemented
11#10590456C212yesmaximal, complemented
12#83298—31nomaximal
13#81268—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C2×C3×#237—21no—
16C22×#624—21no—
17C32×#121C2211yescharacteristic
18C2×#3753C2212yes—
19C3×#940C2211yescharacteristic, complemented
20C3×#939—21no—
21C3×D4×Dic3C2211yescharacteristic, complemented
22C3×#930C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C3×#893C2211yescharacteristic, complemented
26C3×#888C2211yescharacteristic, complemented
27C3×#885—21no—
28C3×#67⋊C4—21no—
29C2×#3722—21no—
30#63894—21no—
31#63894—21no—
32#63894C2212yes—
33#63894C2212yes—
34C2×#3714C2212yes—
35#63657C2211yescharacteristic
36#63636C2212yes—
37C3×#832C2212yescomplemented
38C3×#830C2211yescharacteristic
39C3×#807C2212yescomplemented
40#63576C2212yescomplemented
41Dic3⋊(C3⋊C8)C2212yescomplemented
42#63564C2212yes—
43#63562C2212yescomplemented
44Dic3×C3⋊C8C2212yescomplemented
45C3×#532—31no—
46#5596D311yescharacteristic, complemented
47C2×#893—31no—
48C2×C4×D12—31no—
49C3×#480—31no—
50#5087—32no—
51#5072—32no—
52#5036—31no—
53#5036—31no—
54#5036—31no—
55#5036—61no—
56#5033—31no—
57#5033D311yescharacteristic, complemented
58C4×#213—32no—
59C4×#213—32no—
60#4967—31no—
61#4925—31no—
62#4890—32no—
63#4872—32no—
64#4786—32no—
65#4756—32no—
66#4732—31no—
67#4718—31no—
68C23×C3⋊D3—21no—
69C2×C32×D4—21no—
70C2×C32×D4C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C2×C4⋊(C3⋊D3)—21no—
73C2×C4⋊(C3⋊D3)—24no—
74C2×C4⋊(C3⋊D3)C2312yes—
75C2×C3×#67—21no—
76C2×C3×#67—21no—
77C2×C3×#67—21no—
78C22×C3×Dic3—21no—
79C22×C3×Dic3—21no—
80C22×C3×Dic3D411yescharacteristic
81C22×C3×Dic3D411yescharacteristic
82C3×#237—44no—
83C2×C3×D12C2311yescharacteristic
84C2×C3×C4×D3—21no—
85C2×C3×Dic6—21no—
86C2×#624—22no—
87C2×#624—22no—
88C2×#624—44no—
89C32×C4⋊C4C2311yescharacteristic
90C32×C22⋊C4—21no—
91#3753—24no—
92C2×C3⋊(C3⋊C8)C2312yes—
93C3×#217—21no—
94C3×(C2×D3)⋊C4—21no—
95C3×(C2×D3)⋊C4—21no—
96C3×C4⋊Dic3—21no—
97C3×C4⋊Dic3C2311yescharacteristic
98C3×C4⋊Dic3C2312yes—
99C3×Dic3⋊C4—21no—
100C3×C4×Dic3D411yescharacteristic
101C3×C4×Dic3D411yescharacteristic
102C3×C4×Dic3C2311yescharacteristic
103C3×C4×Dic3C2311yescharacteristic
104C2×C3×C3⋊C8C2312yes—
105#3722—22no—
106#3722—22no—
107#3714—24no—
108#3100—91noSylow
109C2×C3×#41—61no—
110C2×#237—21no—
111C22×D12—31no—
112C22×D12—31no—
113C22×D12—61no—
114C22×C4×D3—61no—
115C22×C4×D3—61no—
116C3×C4⋊Q8—31no—
117C3×#127—31no—
118C3×#124—61no—
119C3×#121—21no—
120C3×#121—31no—
121C3×#121—61no—
122C3×#121C2×D311yescharacteristic
123C3×#121C2×D311yescharacteristic
124C3×C4×D4—31no—
125C3×C4×D4—31no—
126C3×C4×D4—61no—
127C2×C3×C4⋊C4—31no—
128C2×C3×C42—31no—
129#940C2×D311yescharacteristic, complemented
130#939—21no—
131D4×Dic3C2×D311yescharacteristic, complemented
132C2×#213—32no—
133C2×#213—32no—
134C2×#213—32no—
135C2×#213—62no—
136#930C2×D311yescharacteristic
137C2×(C2×D3)⋊C4—61no—
138C2×(C2×D3)⋊C4—61no—
139C2×C4⋊Dic3C2×D311yescharacteristic
140C2×C4×Dic3C2×D311yescharacteristic
141C2×D24—32no—
142#893—32no—
143#893—32no—
144#893—61no—
145#893—61no—
146#893C2×D311yescharacteristic, complemented
147#888C2×D311yescharacteristic, complemented
148#885—21no—
149#67⋊C4—21no—
150C4×D12—32no—
151C4×D12—32no—
152C4×D12—61no—
153C4×D12—61no—
154C3×#107—32no—
155C3×#102—32no—
156C3×C22⋊C8—31no—
157#832—32no—
158#832C2×D312yescomplemented
159#830—31no—
160#830—31no—
161#830—61no—
162#830C2×D311yescharacteristic
163#821—32no—
164Dic3⋊C8—32no—
165C8×Dic3—32no—
166#809—32no—
167#809—32no—
168#809—32no—
169#809—32no—
170#809—62no—
171#807—32no—
172#807—32no—
173#807C2×D312yescomplemented
174C4⋊(C3⋊C8)—32no—
175C4×C3⋊C8—32no—
176C23×C32—21no—
177C23×C32C2×D411yescharacteristic
178C22×C3⋊D3—24no—
179C22×C3⋊D3—22no—
180C22×C3⋊D3—42no—
181C22×C3⋊D3—42no—
182C22×C3×D3—21no—
183C32×D4—22no—
184C32×D4—42no—
185C2×C32×C4—22no—
186C2×C32×C4—21no—
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2411yescharacteristic
189C4⋊(C3⋊D3)—24no—
190C4⋊(C3⋊D3)—22no—
191C4⋊(C3⋊D3)#4114yescomplemented
192C3×#67—42no—
193C3×#67—42no—
194C3×#67—42no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—41no—
198C2×C3×Dic3—42no—
199C2×C3×Dic3—42no—
200C2×C3×Dic3D814yescomplemented
201C2×C3×Dic3C2×D411yescharacteristic
202C2×C3×Dic3C2×D411yescharacteristic
203C2×C3×Dic3C2×D411yescharacteristic
204C2×C3×Dic3C2×D411yescharacteristic
205C3×D12—22no—
206C3×C4×D3—42no—
207C3×Dic6—42no—
208#624—44no—
209#624—44no—
210C3⋊(C3⋊C8)—22no—
211C3×C3⋊C8—22no—
212#532—31no—
213C2×C4×D4—91no—
214#480—31no—
215#480—91no—
216#474—92no—
217#459—92no—
218#447—91no—
219#447—91no—
220C4×D8—92no—
221C4×D8—92no—
222#431—91no—
223C23×D3—61no—
224C23×D3—61no—
225C23×D3—121no—
226C3×#41—124no—
227C2×C3×Q8—61no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—31no—
232C2×C3×D4—41no—
233C2×C3×D4—61no—
234C2×C3×D4—61no—
235C2×C3×D4—61no—
236C2×C3×D4C22×D311yescharacteristic
237C2×C3×D4C22×D311yescharacteristic
238C22×C3×C4—21no—
239C22×C3×C4—31no—
240C22×C3×C4—31no—
241C22×C3×C4—61no—
242C22×C3×C4—61no—
243C22×C3×C4—61no—
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C22×D311yescharacteristic
246C2×#67—21no—
247C2×#67—21no—
248C2×#67—21no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251C22×Dic3#6711yescharacteristic
252C22×Dic3#6711yescharacteristic
253#237—44no—
254C2×D12—32no—
255C2×D12—32no—
256C2×D12—62no—
257C2×D12—64no—
258C2×D12—64no—
259C2×D12—61no—
260C2×D12—61no—
261C2×D12—124no—
262C2×D12—121no—
263C2×D12C22×D311yescharacteristic
264C2×C4×D3—21no—
265C2×C4×D3—62no—
266C2×C4×D3—62no—
267C2×C4×D3—62no—
268C2×C4×D3—62no—
269C2×C4×D3—124no—
270C2×C4×D3—124no—
271C2×Dic6—21no—
272C2×C3×C8—32no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—31no—
275C3×C4⋊C4—32no—
276C3×C4⋊C4—61no—
277C3×C4⋊C4—61no—
278C3×C4⋊C4C22×D311yescharacteristic
279C3×C4⋊C4C22×D311yescharacteristic
280C3×C22⋊C4—21no—
281C3×C22⋊C4—21no—
282C3×C22⋊C4—41no—
283C3×C22⋊C4—61no—
284C3×C22⋊C4—61no—
285C3×C22⋊C4—61no—
286C3×C42—31no—
287C3×C42—31no—
288C3×C42—31no—
289C3×C42—31no—
290#217—21no—
291#213—64no—
292#213—64no—
293#213—64no—
294#213—124no—
295(C2×D3)⋊C4—21no—
296(C2×D3)⋊C4—21no—
297(C2×D3)⋊C4—62no—
298(C2×D3)⋊C4—62no—
299(C2×D3)⋊C4—62no—
300(C2×D3)⋊C4—62no—
301C4⋊Dic3—21no—
302C4⋊Dic3C22×D311yescharacteristic
303C4⋊Dic3C22×D312yes—
304Dic3⋊C4—21no—
305C4×Dic3#6711yescharacteristic
306C4×Dic3#6711yescharacteristic
307C4×Dic3C22×D311yescharacteristic
308C4×Dic3C22×D311yescharacteristic
309C2×C3⋊C8—32no—
310C2×C3⋊C8—32no—
311C2×C3⋊C8—62no—
312C2×C3⋊C8C22×D312yes—
313D24—64no—
314C22×C32—21no—
315C22×C32—21no—
316C22×C32—41no—
317C22×C32—41no—
318C22×C32—41no—
319C22×C32C2×D812yes—
320C22×C32C22×D411yescharacteristic
321C2×C3⋊D3—24no—
322C2×C3⋊D3—48no—
323C2×C3⋊D3—42no—
324C2×C3⋊D3—42no—
325C2×C3×D3—41no—
326C2×C3×D3—41no—
327C2×C3×D3—41no—
328C32×C4—21no—
329C32×C4—41no—
330C32×C4C2×#4112yes—
331C3×Dic3—21no—
332C3×Dic3—21no—
333C3×Dic3—42no—
334C3×Dic3—41no—
335C3×Dic3C2×D812yes—
336C3×Dic3C2×D812yes—
337C2×#41—61no—
338C22×D4—91no—
339C23×C4—181no—
340C2×D8—92no—
341C2×D8—92no—
342C4⋊Q8—31no—
343#127—31no—
344#124—61no—
345#121—31no—
346#121—61no—
347#121D3211yescharacteristic
348C4×D4—31no—
349C4×D4—31no—
350C4×D4—61no—
351C4×D4—92no—
352C4×D4—92no—
353C4×D4—181no—
354C4×D4—181no—
355C2×C4⋊C4—31no—
356C2×C22⋊C4—181no—
357C2×C42—31no—
358#107—32no—
359#107—92no—
360C4⋊C8—92no—
361#102—32no—
362#102—92no—
363#102—92no—
364#102—92no—
365C22⋊C8—31no—
366C22⋊C8—91no—
367C4×C8—92no—
368C23×C3—21no—
369C23×C3—21no—
370C23×C3—21no—
371C23×C3—41no—
372C23×C3—61no—
373C23×C3D3×D411yescharacteristic
374C23×C3C2×#6711yescharacteristic
375C22×D3—21no—
376C22×D3—64no—
377C22×D3—64no—
378C22×D3—62no—
379C22×D3—62no—
380C22×D3—122no—
381C22×D3—124no—
382C22×D3—122no—
383C22×D3—122no—
384C22×D3—122no—
385C22×D3—122no—
386C22×D3—242no—
387C22×D3—242no—
388C3×Q8—122no—
389C3×D4—22no—
390C3×D4—22no—
391C3×D4—42no—
392C3×D4—42no—
393C3×D4—42no—
394C3×D4—62no—
395C3×D4—82no—
396C3×D4—122no—
397C3×D4—122no—
398C3×D4—122no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—34no—
406C2×C3×C4—31no—
407C2×C3×C4—31no—
408C2×C3×C4—31no—
409C2×C3×C4—31no—
410C2×C3×C4—42no—
411C2×C3×C4—41no—
412C2×C3×C4—61no—
413C2×C3×C4—62no—
414C2×C3×C4—122no—
415C2×C3×C4—122no—
416C2×C3×C4—121no—
417C2×C3×C4—122no—
418C2×C3×C4D3×D411yescharacteristic
419C2×C3×C4C2×#6711yescharacteristic
420C2×C3×C4C23×D311yescharacteristic
421C2×C3×C4C23×D311yescharacteristic
422#67—42no—
423#67—42no—
424#67—42no—
425C2×Dic3—22no—
426C2×Dic3—21no—
427C2×Dic3—41no—
428C2×Dic3—42no—
429C2×Dic3—42no—
430C2×Dic3#21314yescomplemented
431C2×Dic3C2×#6711yescharacteristic
432C2×Dic3C2×#6711yescharacteristic
433C2×Dic3C2×#6711yescharacteristic
434C2×Dic3C2×#6711yescharacteristic
435D12—22no—
436D12—34no—
437D12—34no—
438D12—64no—
439D12—64no—
440D12—64no—
441D12—62no—
442D12—62no—
443D12—122no—
444D12—124no—
445C4×D3—42no—
446C4×D3—124no—
447C4×D3—124no—
448C4×D3—124no—
449C4×D3—124no—
450Dic6—42no—
451C3×C8—62no—
452C3⋊C8—22no—
453C3⋊C8—62no—
454C3⋊C8—62no—
455C3⋊C8—122no—
456C2×C32—22no—
457C2×C32—81no—
458C2×C32#52511yescharacteristic
459C2×C32C22×D811yescharacteristic
460C2×C32#57511yescharacteristic
461C3⋊D3—44no—
462C3×D3—81no—
463C24—181no—
464#41—124no—
465C2×Q8—61no—
466C2×D4—21no—
467C2×D4—31no—
468C2×D4—61no—
469C2×D4—61no—
470C2×D4—61no—
471C2×D4—92no—
472C2×D4—184no—
473C2×D4—181no—
474C2×D4C2×D3211yescharacteristic
475C22×C4—31no—
476C22×C4—31no—
477C22×C4—61no—
478C22×C4—61no—
479C22×C4—61no—
480C22×C4—182no—
481C22×C4—182no—
482C22×C4—364no—
483C22×C4C2×D3211yescharacteristic
484D8—184no—
485D8—184no—
486C2×C8—32no—
487C2×C8—92no—
488C4⋊C4—32no—
489C4⋊C4—31no—
490C4⋊C4—61no—
491C4⋊C4—61no—
492C4⋊C4C2×D3211yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—61no—
495C22⋊C4—61no—
496C22⋊C4—61no—
497C22⋊C4—182no—
498C22⋊C4—182no—
499C42—31no—
500C42—31no—
501C42—31no—
502C42—31no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—22no—
509C22×C3—41no—
510C22×C3—41no—
511C22×C3—41no—
512C22×C3—41no—
513C22×C3—41no—
514C22×C3—41no—
515C22×C3—41no—
516C22×C3—41no—
517C22×C3—81no—
518C22×C3—81no—
519C22×C3—81no—
520C22×C3—121no—
521C22×C3—121no—
522C22×C3—121no—
523C22×C3D3×D812yes—
524C22×C3C2×#21312yes—
525C22×C3C2×D3×D411yescharacteristic
526C22×C3C22×#6711yescharacteristic
527C2×D3—41no—
528C2×D3—41no—
529C2×D3—41no—
530C2×D3—64no—
531C2×D3—64no—
532C2×D3—124no—
533C2×D3—128no—
534C2×D3—128no—
535C2×D3—122no—
536C2×D3—122no—
537C2×D3—122no—
538C2×D3—122no—
539C2×D3—242no—
540C2×D3—242no—
541C2×D3—248no—
542C3×C4—21no—
543C3×C4—21no—
544C3×C4—22no—
545C3×C4—32no—
546C3×C4—32no—
547C3×C4—41no—
548C3×C4—41no—
549C3×C4—41no—
550C3×C4—61no—
551C3×C4—61no—
552C3×C4—81no—
553C3×C4—121no—
554C3×C4—122no—
555C3×C4D3×#4112yes—
556C3×C4D3×#4112yes—
557Dic3—21no—
558Dic3—21no—
559Dic3—42no—
560Dic3—41no—
561Dic3C2×#21312yes—
562Dic3C2×#21312yes—
563C32#310011yescharacteristic, complemented, Sylow
564C23—21no—
565C23—61no—
566C23—184no—
567C23—182no—
568C23—362no—
569C23—362no—
570C23D3×#6711yescharacteristic
571Q8—122no—
572D4—22no—
573D4—42no—
574D4—62no—
575D4—94no—
576D4—122no—
577D4—122no—
578D4—122no—
579D4—184no—
580D4—182no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—31no—
584C2×C4—31no—
585C2×C4—34no—
586C2×C4—31no—
587C2×C4—31no—
588C2×C4—61no—
589C2×C4—62no—
590C2×C4—122no—
591C2×C4—122no—
592C2×C4—121no—
593C2×C4—122no—
594C2×C4—364no—
595C2×C4—364no—
596C2×C4D3×#6711yescharacteristic
597C2×C4C22×D3211yescharacteristic
598C8—62no—
599C8—182no—
600C2×C3—22no—
601C2×C3—22no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—42no—
606C2×C3—81no—
607C2×C3—81no—
608C2×C3—161no—
609C2×C3—241no—
610C2×C3#565611yescharacteristic
611C2×C3C2×D3×D811yescharacteristic
612C2×C3#577711yescharacteristic
613C2×C3C22×#21311yescharacteristic
614C2×C3#582211yescharacteristic
615C2×C3#582811yescharacteristic
616D3—81no—
617D3—124no—
618D3—124no—
619D3—244no—
620C22—21no—
621C22—21no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—121no—
626C22—121no—
627C22—121no—
628C22—184no—
629C22—368no—
630C22—362no—
631C22—362no—
632C22D3×#21312yes—
633C22C2×D3×#6711yescharacteristic
634C4—21no—
635C4—32no—
636C4—32no—
637C4—41no—
638C4—61no—
639C4—61no—
640C4—122no—
641C4—121no—
642C4#6431212yes—
643C3—21no—
644C3#8126811yescharacteristic, complemented
645C3#8329811yescharacteristic, complemented
646C2—22no—
647C2—81no—
648C2—241no—
649C2—364no—
650C2C2×D3×#21311yescharacteristic
651C2#1059515911yescharacteristic
652C2#1059547011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3100
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×#63894C2semidirect
3. #10592735C2semidirect
4. C3×#5033C2semidirect
5. #10591429C2semidirect
6. #10591400C2semidirect
7. #10591168C2semidirect
8. #10591089C2semidirect
9. #10591053C2semidirect
10. #10590464C2semidirect
11. #10590456C2semidirect
19. C3×#940C22semidirect
21. C3×D4×Dic3C22semidirect
25. C3×#893C22semidirect
26. C3×#888C22semidirect
37. C3×#832C22semidirect
39. C3×#807C22semidirect
40. #63576C22semidirect
41. Dic3⋊(C3⋊C8)C22semidirect
43. #63562C22semidirect
44. Dic3×C3⋊C8C22semidirect
46. #5596D3semidirect
57. #5033D3semidirect
129. #940C2×D3semidirect
131. D4×Dic3C2×D3semidirect
146. #893C2×D3semidirect
147. #888C2×D3semidirect
158. #832C2×D3semidirect
173. #807C2×D3semidirect
191. C4⋊(C3⋊D3)#41semidirect
200. C2×C3×Dic3D8semidirect
430. C2×Dic3#213semidirect
563. C32#3100semidirect
644. C3#81268semidirect
645. C3#83298semidirect

Maximal subgroups

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

subgroupindex
C3×#55962
C2×#638942
#105927352
C3×#50332
#105914292
#105914002
#105911682
#105910892
#105910532
#105904642
#105904562
#832983
#812683