Finite Group Databasebeta

← #11787359

Subgroups — #11787359

Order 1152.

881 conjugacy classes of subgroups.

The subgroup lattice has 633 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#895C211yesmaximal, characteristic
2C2×#63841C211yesmaximal, characteristic, complemented
3C2×#63563C211yesmaximal, characteristic, complemented
4C2×#63562C211yesmaximal, characteristic, complemented
5C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#10589395C211yesmaximal, characteristic, complemented
7C3×#4529C211yesmaximal, characteristic, complemented
8#71678—31nomaximal
9#68881—31nomaximal
10C22×C3×D12—21no—
11C22×C3×D12C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C3×#895—22no—
20C3×#895C414yescomplemented
21C2×(C2×D3)⋊Dic3—21no—
22C2×Dic32—21no—
23#63841—22no—
24#63841—22no—
25#63563—22no—
26#63562—22no—
27(C2×D3)⋊(C3⋊C8)—22no—
28C2×C3×#121—31no—
29C2×#926—31no—
30C2×#895D311yescharacteristic
31C2×#892—31no—
32C2×#832—31no—
33C2×#832—31no—
34C2×#830—31no—
35C2×#821—31no—
36C2×(C2×D3)⋊C8—31no—
37C2×#809—31no—
38C3×#340—31no—
39#4529—31no—
40#4529—31no—
41#4529—61no—
42#4529D311yescharacteristic, complemented
43C23×C3×D3—21no—
44C23×C3×D3D411yescharacteristic
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—24no—
55C2×C3×D12—21no—
56C2×C3×D12—42no—
57C2×C3×D12—42no—
58C2×C3×D12C2×C412yes—
59C2×C3×C4×D3—21no—
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3—21no—
62C2×C3×C4×D3—21no—
63C2×C3×C4×D3C2×C412yes—
64C2×C3×C4×D3D412yes—
65C32×C4⋊C4—21no—
66C32×C4⋊C4C2×C412yes—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)D412yescomplemented
69C2×C3⋊(C3⋊C8)—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)—21no—
72C3×(C2×D3)⋊C4—24no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3D412yescomplemented
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78(C2×D3)⋊Dic3—24no—
79Dic32—24no—
80#1875—91noSylow
81C22×C3×D4—31no—
82C22×C3×D4—61no—
83C23×C3×C4—31no—
84C22×D12—21no—
85C22×D12C2×D311yescharacteristic
86C22×C4×D3C2×D311yescharacteristic
87C22×C3×C8—31no—
88C3×#121—34no—
89C3×#121—62no—
90C2×C3×C4⋊C4—21no—
91C2×C3×C4⋊C4—31no—
92C2×C3×C4⋊C4C2×D311yescharacteristic
93C2×C3×C4⋊C4C2×D311yescharacteristic
94C2×C3×C22⋊C4—61no—
95C2×#217—61no—
96C2×(C2×D3)⋊C4—21no—
97C2×(C2×D3)⋊C4—61no—
98#926—62no—
99#926—62no—
100C2×C4⋊Dic3—31no—
101C2×C4⋊Dic3—31no—
102C2×C4⋊Dic3—61no—
103C2×C4⋊Dic3C2×D311yescharacteristic
104C2×C4×Dic3—61no—
105C2×C4×Dic3—61no—
106C22×C3⋊C8—31no—
107C22×C3⋊C8—31no—
108C22×C3⋊C8—61no—
109C22×C3⋊C8C2×D311yescharacteristic
110#895—22no—
111#895Dic314yescomplemented
112#892—62no—
113#892—62no—
114#832—62no—
115#832—62no—
116#830—62no—
117#821—62no—
118(C2×D3)⋊C8—62no—
119#809—62no—
120C23×C32C2×D411yescharacteristic
121C22×C3×D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3—21no—
124C22×C3×D3—21no—
125C22×C3×D3—21no—
126C22×C3×D3—21no—
127C22×C3×D3—22no—
128C22×C3×D3—41no—
129C22×C3×D3—41no—
130C22×C3×D3—41no—
131C22×C3×D3—41no—
132C22×C3×D3—41no—
133C22×C3×D3—41no—
134C22×C3×D3C22⋊C412yes—
135C2×C32×C4—22no—
136C2×C32×C4—41no—
137C2×C32×C4—41no—
138C2×C32×C4C22×C411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—41no—
146C2×C3⋊Dic3—41no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3C22⋊C412yes—
153C3×D12—22no—
154C3×D12—22no—
155C3×D12—48no—
156C3×D12—41no—
157C3×D12—41no—
158C3×C4×D3—22no—
159C3×C4×D3—22no—
160C3×C4×D3—22no—
161C3×C4×D3—22no—
162C3⋊(C3⋊C8)—41no—
163C3×C3⋊C8—41no—
164C2×#121—31no—
165C2×#117—91no—
166C2×#102—91no—
167C2×#102—91no—
168C2×C22⋊C8—91no—
169#340—31no—
170#340—91no—
171C24×C3—31no—
172C24×C3—61no—
173C23×D3—21no—
174C23×D3#6711yescharacteristic
175C2×C3×D4—32no—
176C2×C3×D4—64no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C2×C3×D4—61no—
180C2×C3×D4—61no—
181C2×C3×D4—61no—
182C2×C3×D4—122no—
183C2×C3×D4—122no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—31no—
188C22×C3×C4—32no—
189C22×C3×C4—32no—
190C22×C3×C4—41no—
191C22×C3×C4—61no—
192C22×C3×C4—61no—
193C22×C3×C4—61no—
194C22×C3×C4—61no—
195C22×C3×C4—61no—
196C22×C3×C4C22×D311yescharacteristic
197C22×C3×C4C22×D311yescharacteristic
198C22×Dic3—21no—
199C22×Dic3—61no—
200C22×Dic3—61no—
201C22×Dic3—121no—
202C22×Dic3#6711yescharacteristic
203C2×D12—21no—
204C2×D12—21no—
205C2×D12—21no—
206C2×D12—21no—
207C2×D12—24no—
208C2×D12—21no—
209C2×D12—42no—
210C2×D12—42no—
211C2×D12C2×Dic312yes—
212C2×C4×D3—21no—
213C2×C4×D3—21no—
214C2×C4×D3—21no—
215C2×C4×D3—21no—
216C2×C4×D3C2×Dic312yes—
217C2×C4×D3#6712yes—
218C2×C3×C8—61no—
219C2×C3×C8—61no—
220C2×C3×C8—61no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—22no—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—41no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4C4×D312yes—
228C3×C4⋊C4C2×Dic312yes—
229C3×C22⋊C4—64no—
230#217—64no—
231(C2×D3)⋊C4—24no—
232(C2×D3)⋊C4—64no—
233C4⋊Dic3—21no—
234C4⋊Dic3—32no—
235C4⋊Dic3—32no—
236C4⋊Dic3—62no—
237C4⋊Dic3—61no—
238C4⋊Dic3—61no—
239C4⋊Dic3—121no—
240C4⋊Dic3D1212yescomplemented
241C4×Dic3—64no—
242C4×Dic3—64no—
243C2×C3⋊C8—21no—
244C2×C3⋊C8—21no—
245C2×C3⋊C8—21no—
246C2×C3⋊C8—62no—
247C2×C3⋊C8—61no—
248C2×C3⋊C8—61no—
249C2×C3⋊C8—61no—
250C2×C3⋊C8—61no—
251C2×C3⋊C8—61no—
252C2×C3⋊C8—61no—
253C2×C3⋊C8—121no—
254C2×C3⋊C8—121no—
255C22×C32C2×C22⋊C411yescharacteristic
256C22×C32#12011yescharacteristic
257C22×C32#12311yescharacteristic
258C22×C32#13511yescharacteristic
259C22×C32#13511yescharacteristic
260C22×C32AGL(1,ℤ/8)11yescharacteristic
261C22×C32AGL(1,ℤ/8)11yescharacteristic
262C2×C3×D3—22no—
263C2×C3×D3—22no—
264C2×C3×D3—22no—
265C2×C3×D3—41no—
266C2×C3×D3—41no—
267C2×C3×D3—41no—
268C2×C3×D3—41no—
269C2×C3×D3—42no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C2×C3×D3—81no—
273C2×C3×D3—81no—
274C2×C3×D3—81no—
275C2×C3×D3—81no—
276C32×C4—42no—
277C32×C4C4×D411yescharacteristic
278C32×C4C4×D411yescharacteristic
279C32×C4#12111yescharacteristic
280C32×C4#12111yescharacteristic
281C3⋊Dic3—42no—
282C3×Dic3—22no—
283C3×Dic3—42no—
284C22×D4—31no—
285C22×D4—61no—
286C23×C4—31no—
287C22×C8—31no—
288C22×C8—91no—
289#121—34no—
290#121—62no—
291#117—182no—
292#117—182no—
293C2×C4⋊C4—31no—
294C2×C4⋊C4—91no—
295C2×C4⋊C4D3211yescharacteristic
296C2×C22⋊C4—61no—
297C2×C22⋊C4—181no—
298C2×C42—181no—
299#102—182no—
300#102—182no—
301C22⋊C8—182no—
302C23×C3—21no—
303C23×C3—32no—
304C23×C3—61no—
305C23×C3—61no—
306C23×C3—61no—
307C23×C3—61no—
308C23×C3—61no—
309C23×C3—61no—
310C23×C3—62no—
311C23×C3—121no—
312C23×C3—121no—
313C23×C3—121no—
314C23×C3—121no—
315C23×C3—121no—
316C23×C3—121no—
317C23×C3D3×D411yescharacteristic
318C23×C3C2×#6711yescharacteristic
319C22×D3—21no—
320C22×D3—21no—
321C22×D3—21no—
322C22×D3—21no—
323C22×D3—21no—
324C22×D3—21no—
325C22×D3—22no—
326C22×D3—41no—
327C22×D3—41no—
328C22×D3—41no—
329C22×D3—41no—
330C22×D3—41no—
331C22×D3—41no—
332C22×D3#21712yes—
333C3×D4—62no—
334C3×D4—62no—
335C3×D4—128no—
336C3×D4—121no—
337C3×D4—121no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—32no—
347C2×C3×C4—42no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—41no—
351C2×C3×C4—41no—
352C2×C3×C4—61no—
353C2×C3×C4—61no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—81no—
360C2×C3×C4—81no—
361C2×C3×C4—121no—
362C2×C3×C4—121no—
363C2×C3×C4C2×C4×D311yescharacteristic
364C2×C3×C4C2×D1211yescharacteristic
365C2×C3×C4#23511yescharacteristic
366C2×C3×C4D3×D411yescharacteristic
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4#23711yescharacteristic
371C2×C3×C4#23711yescharacteristic
372C2×C3×C4#23911yescharacteristic
373C2×C3×C4C22×Dic311yescharacteristic
374C2×C3×C4C2×#6711yescharacteristic
375C2×Dic3—21no—
376C2×Dic3—21no—
377C2×Dic3—22no—
378C2×Dic3—41no—
379C2×Dic3—41no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—122no—
383C2×Dic3—121no—
384C2×Dic3—121no—
385C2×Dic3—121no—
386C2×Dic3—121no—
387C2×Dic3—241no—
388C2×Dic3—241no—
389C2×Dic3#21712yes—
390D12—22no—
391D12—22no—
392D12—48no—
393D12—41no—
394D12—41no—
395C4×D3—22no—
396C4×D3—22no—
397C4×D3—22no—
398C4×D3—22no—
399C3×C8—121no—
400C3⋊C8—41no—
401C3⋊C8—122no—
402C3⋊C8—121no—
403C3⋊C8—121no—
404C2×C32#38611yescharacteristic
405C2×C32#41611yescharacteristic
406C2×C32#41811yescharacteristic
407C2×C32#44911yescharacteristic
408C2×C32#44911yescharacteristic
409C2×C32#48211yescharacteristic
410C2×C32#48211yescharacteristic
411C3×D3—42no—
412C3×D3—82no—
413C24—31no—
414C24—61no—
415C2×D4—32no—
416C2×D4—64no—
417C2×D4—61no—
418C2×D4—61no—
419C2×D4—61no—
420C2×D4—61no—
421C2×D4—61no—
422C2×D4—122no—
423C2×D4—122no—
424C22×C4—21no—
425C22×C4—31no—
426C22×C4—32no—
427C22×C4—32no—
428C22×C4—61no—
429C22×C4—61no—
430C22×C4—61no—
431C22×C4—61no—
432C22×C4—61no—
433C22×C4—181no—
434C22×C4C2×D3211yescharacteristic
435C2×C8—61no—
436C2×C8—61no—
437C2×C8—61no—
438C2×C8—181no—
439C2×C8—181no—
440C2×C8—181no—
441C4⋊C4—21no—
442C4⋊C4—32no—
443C4⋊C4—61no—
444C4⋊C4—92no—
445C4⋊C4—181no—
446C4⋊C4D3×Dic312yes—
447C22⋊C4—64no—
448C22⋊C4—184no—
449C42—184no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—62no—
458C22×C3—62no—
459C22×C3—62no—
460C22×C3—121no—
461C22×C3—121no—
462C22×C3—121no—
463C22×C3—121no—
464C22×C3—122no—
465C22×C3—122no—
466C22×C3—122no—
467C22×C3—241no—
468C22×C3—241no—
469C22×C3—241no—
470C22×C3—241no—
471C22×C3D3×C22⋊C411yescharacteristic
472C22×C3#88211yescharacteristic
473C22×C3#89411yescharacteristic
474C22×C3#91111yescharacteristic
475C22×C3#91411yescharacteristic
476C22×C3#91611yescharacteristic
477C22×C3#91911yescharacteristic
478C22×C3#93211yescharacteristic
479C22×C3#93211yescharacteristic
480C22×C3#93511yescharacteristic
481C22×C3#93711yescharacteristic
482C22×C3#95011yescharacteristic
483C22×C3#95011yescharacteristic
484C22×C3C2×#21711yescharacteristic
485C2×D3—22no—
486C2×D3—22no—
487C2×D3—22no—
488C2×D3—41no—
489C2×D3—41no—
490C2×D3—41no—
491C2×D3—41no—
492C2×D3—42no—
493C2×D3—42no—
494C2×D3—42no—
495C2×D3—81no—
496C2×D3—81no—
497C2×D3—81no—
498C2×D3—81no—
499C3×C4—21no—
500C3×C4—21no—
501C3×C4—21no—
502C3×C4—21no—
503C3×C4—42no—
504C3×C4—42no—
505C3×C4—62no—
506C3×C4—82no—
507C3×C4—122no—
508C3×C4C4×D1211yescharacteristic
509C3×C4#88411yescharacteristic
510C3×C4#89311yescharacteristic
511C3×C4#89511yescharacteristic
512C3×C4D4×Dic311yescharacteristic
513C3×C4D4×Dic311yescharacteristic
514C3×C4#93911yescharacteristic
515C3×C4#93911yescharacteristic
516Dic3—22no—
517Dic3—42no—
518Dic3—122no—
519Dic3—122no—
520Dic3—242no—
521C32#187511yescharacteristic, complemented, Sylow
522C23—32no—
523C23—61no—
524C23—61no—
525C23—61no—
526C23—61no—
527C23—61no—
528C23—61no—
529C23—62no—
530C23—121no—
531C23—121no—
532C23—121no—
533C23—121no—
534C23—121no—
535C23—121no—
536C23D3×#6711yescharacteristic
537D4—62no—
538D4—62no—
539D4—128no—
540D4—121no—
541D4—121no—
542C2×C4—22no—
543C2×C4—32no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—61no—
547C2×C4—61no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—62no—
553C2×C4—121no—
554C2×C4—121no—
555C2×C4—182no—
556C2×C4—361no—
557C2×C4—361no—
558C2×C4#379511yescharacteristic
559C2×C4#379611yescharacteristic
560C2×C4D3×D1211yescharacteristic
561C2×C4#380211yescharacteristic
562C2×C4C2×D3×Dic311yescharacteristic
563C2×C4D3×#6711yescharacteristic
564C8—121no—
565C8—361no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—122no—
574C2×C3—242no—
575C2×C3#466511yescharacteristic
576C2×C3#477011yescharacteristic
577C2×C3#478111yescharacteristic
578C2×C3#480411yescharacteristic
579C2×C3#481011yescharacteristic
580C2×C3#486611yescharacteristic
581C2×C3#488511yescharacteristic
582C2×C3#503511yescharacteristic
583C2×C3#503511yescharacteristic
584C2×C3#503711yescharacteristic
585C2×C3#503711yescharacteristic
586C2×C3#521511yescharacteristic
587C2×C3#522011yescharacteristic
588C2×C3#523311yescharacteristic
589D3—42no—
590D3—82no—
591C22—62no—
592C22—62no—
593C22—62no—
594C22—121no—
595C22—121no—
596C22—121no—
597C22—121no—
598C22—122no—
599C22—122no—
600C22—122no—
601C22—241no—
602C22—241no—
603C22—241no—
604C22—241no—
605C22#6388411yescharacteristic
606C22#6392211yescharacteristic
607C22#6393211yescharacteristic
608C22#6393411yescharacteristic
609C22#6394711yescharacteristic
610C22#6394911yescharacteristic
611C22D3×#21711yescharacteristic
612C4—42no—
613C4—62no—
614C4—122no—
615C4—362no—
616C4#6388511yescharacteristic
617C4#6388611yescharacteristic
618C4Dic3×D1211yescharacteristic
619C4#6389811yescharacteristic
620C3—21no—
621C3#6888111yescharacteristic, complemented
622C3#7167811yescharacteristic, complemented
623C2—122no—
624C2—242no—
625C2#1059044611yescharacteristic
626C2#1059044911yescharacteristic
627C2#1059061311yescharacteristic
628C2#1059061511yescharacteristic
629C2#1059137611yescharacteristic
630C2#1059142111yescharacteristic
631C2#1059155611yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC2×C3×#895C2
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1875
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63841C2semidirect
3. C2×#63563C2semidirect
4. C2×#63562C2semidirect
5. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
6. #10589395C2semidirect
7. C3×#4529C2semidirect
20. C3×#895C4semidirect
42. #4529D3semidirect
68. C4⋊(C3⋊Dic3)D4semidirect
74. C3×C4⋊Dic3D4semidirect
111. #895Dic3semidirect
240. C4⋊Dic3D12semidirect
521. C32#1875semidirect
621. C3#68881semidirect
622. C3#71678semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8952
C2×#638412
C2×#635632
C2×#635622
C2×(C2×D3)⋊(C3⋊C8)2
#105893952
C3×#45292
#716783
#688813