Finite Group Databasebeta

← #11787550

Subgroups — #11787550

Order 1152.

935 conjugacy classes of subgroups.

The subgroup lattice has 639 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×D12C211yesmaximal, characteristic, complemented
2C22×#3713C211yesmaximal, characteristic
3C3×#4939C211yesmaximal, characteristic, complemented
4C2×#63562C211yesmaximal, characteristic, complemented
5C2×#63562C211yesmaximal, characteristic, complemented
6#10589390C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#71613—31nomaximal
9#69657—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×C3×C4×D3—21no—
13C2×C32×C42C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×(C2×D3)⋊C4—21no—
18C2×C3×(C2×D3)⋊C4—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C3×C4×D12—22no—
22C3×C4×D12—22no—
23C2×#3713—22no—
24C2×#3713—22no—
25C2×#3713C414yescomplemented
26#63562—22no—
27#63562—22no—
28C2×C3×C4×D4—31no—
29C22×#213—31no—
30C22×#213—31no—
31C2×C4×D12D311yescharacteristic, complemented
32C3×#390—31no—
33C2×#832—31no—
34C2×#832—31no—
35C2×#809—31no—
36C2×#809—31no—
37#4939D311yescharacteristic, complemented
38#4529—31no—
39#4529—31no—
40#4524—31no—
41#4524—31no—
42#4524—61no—
43C23×C3×D3—21no—
44C23×C3×D3—21no—
45C22×C32×C4D411yescharacteristic
46C22×C32×C4D411yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12C2×C412yes—
59C2×C3×D12C2×C412yescomplemented
60C2×C3×D12D412yes—
61C2×C3×D12D412yes—
62C2×C3×C4×D3—24no—
63C2×C3×C4×D3—42no—
64C2×C3×C4×D3—42no—
65C32×C42—21no—
66C32×C42—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)—21no—
72C2×C3⋊(C3⋊C8)C2×C412yescomplemented
73C3×(C2×D3)⋊C4—24no—
74C3×(C2×D3)⋊C4—42no—
75C3×(C2×D3)⋊C4—42no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3—21no—
79C3×C4⋊Dic3D412yes—
80#3713—28no—
81#1879—91noSylow
82C22×C3×D4—31no—
83C22×C3×D4—31no—
84C23×C3×C4—61no—
85C22×D12C2×D311yescharacteristic
86C22×D12C2×D311yescharacteristic
87C22×C4×D3—21no—
88C3×C4×D4—62no—
89C3×C4×D4—62no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C4⋊C4—31no—
92C2×C3×C22⋊C4—61no—
93C2×C3×C22⋊C4—61no—
94C2×C3×C22⋊C4—61no—
95C2×C3×C42—21no—
96C2×C3×C42C2×D311yescharacteristic
97C2×C3×C42C2×D311yescharacteristic
98C2×#213—34no—
99C2×#213—34no—
100C2×#213—62no—
101C2×#213—62no—
102C2×#213—62no—
103C2×#213—62no—
104C2×(C2×D3)⋊C4—21no—
105C2×(C2×D3)⋊C4—21no—
106C2×(C2×D3)⋊C4—21no—
107C2×C4⋊Dic3C2×D311yescharacteristic
108C2×C4⋊Dic3C2×D311yescharacteristic
109C22×C3⋊C8—31no—
110C22×C3⋊C8—31no—
111C22×C3⋊C8—31no—
112C22×C3⋊C8—31no—
113C22×C3⋊C8—61no—
114C22×C3⋊C8—61no—
115C4×D12—22no—
116C4×D12—22no—
117#832—62no—
118#832—62no—
119#809—62no—
120#809—62no—
121C23×C32C2×D411yescharacteristic
122C22×C3×D3—22no—
123C22×C3×D3—22no—
124C22×C3×D3—22no—
125C22×C3×D3—22no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
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×D3—41no—
135C22×C3×D3—41no—
136C2×C32×C4—21no—
137C2×C32×C4—21no—
138C2×C32×C4—21no—
139C2×C32×C4—21no—
140C2×C32×C4—21no—
141C2×C32×C4D812yescomplemented
142C2×C32×C4C22×C411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4#4111yescharacteristic
147C2×C32×C4#4111yescharacteristic
148C2×C3×Dic3—22no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C3×D12—22no—
155C3×D12—22no—
156C3×D12—22no—
157C3×D12—22no—
158C3×D12—22no—
159C3×D12—41no—
160C3×D12—41no—
161C3×D12C22⋊C414yescomplemented
162C3×C4×D3—48no—
163C3⋊(C3⋊C8)—22no—
164C3⋊(C3⋊C8)—41no—
165C22×D8—91no—
166C2×C4×D4—31no—
167C2×#102—91no—
168C2×#102—91no—
169#390—31no—
170#340—91no—
171#336—91no—
172C24×C3—61no—
173C24×C3—61no—
174C23×D3—21no—
175C23×D3—21no—
176C2×C3×D4—32no—
177C2×C3×D4—32no—
178C2×C3×D4—32no—
179C2×C3×D4—32no—
180C2×C3×D4—61no—
181C2×C3×D4—61no—
182C2×C3×D4—61no—
183C2×C3×D4—61no—
184C2×C3×D4—61no—
185C2×C3×D4—61no—
186C2×C3×D4—61no—
187C2×C3×D4—61no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—64no—
192C22×C3×C4—61no—
193C22×C3×C4—61no—
194C22×C3×C4—122no—
195C22×C3×C4—122no—
196C22×C3×C4#6711yescharacteristic
197C22×C3×C4#6711yescharacteristic
198C22×C3×C4#6711yescharacteristic
199C22×C3×C4#6711yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×Dic3—21no—
203C22×Dic3—21no—
204C2×D12—21no—
205C2×D12—21no—
206C2×D12—21no—
207C2×D12—21no—
208C2×D12—21no—
209C2×D12—21no—
210C2×D12—21no—
211C2×D12—21no—
212C2×D12C4×D312yes—
213C2×D12C4×D312yescomplemented
214C2×D12D1212yes—
215C2×D12#6712yes—
216C2×C4×D3—24no—
217C2×C4×D3—42no—
218C2×C4×D3—42no—
219C3×C4⋊C4—32no—
220C3×C4⋊C4—61no—
221C3×C4⋊C4—61no—
222C3×C4⋊C4—61no—
223C3×C22⋊C4—64no—
224C3×C22⋊C4—122no—
225C3×C22⋊C4—122no—
226C3×C42—21no—
227C3×C42—21no—
228C3×C42—21no—
229C3×C42—21no—
230C3×C42—41no—
231C3×C42—41no—
232#213—68no—
233#213—68no—
234(C2×D3)⋊C4—24no—
235(C2×D3)⋊C4—42no—
236(C2×D3)⋊C4—42no—
237C4⋊Dic3—21no—
238C4⋊Dic3—21no—
239C4⋊Dic3—21no—
240C4⋊Dic3#6712yes—
241C2×C3⋊C8—32no—
242C2×C3⋊C8—32no—
243C2×C3⋊C8—62no—
244C2×C3⋊C8—61no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8—61no—
247C2×C3⋊C8—61no—
248C2×C3⋊C8—62no—
249C2×C3⋊C8—61no—
250C2×C3⋊C8—61no—
251C2×C3⋊C8—61no—
252C2×C3⋊C8—61no—
253C2×C3⋊C8—61no—
254C2×C3⋊C8—61no—
255C2×C3⋊C8—121no—
256C2×C3⋊C8—121no—
257C2×C3⋊C8—121no—
258C2×C3⋊C8—121no—
259C22×C32C4×D411yescharacteristic
260C22×C32#12011yescharacteristic
261C22×C32#12111yescharacteristic
262C22×C32C2×D811yescharacteristic
263C22×C32#13511yescharacteristic
264C22×C32AGL(1,ℤ/8)11yescharacteristic
265C22×C32AGL(1,ℤ/8)11yescharacteristic
266C2×C3×D3—24no—
267C2×C3×D3—42no—
268C2×C3×D3—42no—
269C2×C3×D3—42no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C2×C3×D3—42no—
273C2×C3×D3—42no—
274C2×C3×D3—42no—
275C2×C3×D3—42no—
276C2×C3×D3—81no—
277C2×C3×D3—81no—
278C2×C3×D3—81no—
279C2×C3×D3—81no—
280C32×C4—22no—
281C32×C4—41no—
282C32×C4C2×C22⋊C411yescharacteristic
283C32×C4C4×D411yescharacteristic
284C32×C4#12111yescharacteristic
285C32×C4#12311yescharacteristic
286C3×Dic3—42no—
287C3×Dic3—81no—
288C22×D4—31no—
289C22×D4—31no—
290C23×C4—61no—
291C2×D8—94no—
292C2×D8—182no—
293C2×D8—182no—
294C22×C8—91no—
295C22×C8—91no—
296C4×D4—62no—
297C4×D4—62no—
298C2×C4⋊C4—31no—
299C2×C4⋊C4—31no—
300C2×C22⋊C4—61no—
301C2×C22⋊C4—61no—
302C2×C22⋊C4—61no—
303C2×C42D3211yescharacteristic
304#102—182no—
305#102—182no—
306C23×C3—21no—
307C23×C3—62no—
308C23×C3—62no—
309C23×C3—62no—
310C23×C3—62no—
311C23×C3—121no—
312C23×C3—121no—
313C23×C3—121no—
314C23×C3—121no—
315C23×C3—121no—
316C23×C3—121no—
317C23×C3—121no—
318C23×C3—121no—
319C23×C3—121no—
320C23×C3—121no—
321C23×C3C2×#6711yescharacteristic
322C23×C3C2×#6711yescharacteristic
323C22×D3—22no—
324C22×D3—22no—
325C22×D3—22no—
326C22×D3—22no—
327C22×D3—41no—
328C22×D3—41no—
329C22×D3—41no—
330C22×D3—41no—
331C22×D3—41no—
332C22×D3—41no—
333C22×D3—41no—
334C22×D3—41no—
335C22×D3—41no—
336C22×D3—41no—
337C3×D4—34no—
338C3×D4—62no—
339C3×D4—62no—
340C3×D4—62no—
341C3×D4—62no—
342C3×D4—62no—
343C3×D4—121no—
344C3×D4—121no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—22no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—22no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—41no—
364C2×C3×C4—41no—
365C2×C3×C4—41no—
366C2×C3×C4—41no—
367C2×C3×C4—62no—
368C2×C3×C4—128no—
369C2×C3×C4—121no—
370C2×C3×C4—121no—
371C2×C3×C4—121no—
372C2×C3×C4—121no—
373C2×C3×C4—121no—
374C2×C3×C4#21312yescomplemented
375C2×C3×C4#21312yescomplemented
376C2×C3×C4C2×C4×D311yescharacteristic
377C2×C3×C4C2×C4×D311yescharacteristic
378C2×C3×C4C2×D1211yescharacteristic
379C2×C3×C4#23511yescharacteristic
380C2×C3×C4#23511yescharacteristic
381C2×C3×C4#23511yescharacteristic
382C2×C3×C4D3×D411yescharacteristic
383C2×C3×C4D3×D411yescharacteristic
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4#23711yescharacteristic
386C2×C3×C4C2×#6711yescharacteristic
387C2×C3×C4C2×#6711yescharacteristic
388C2×Dic3—22no—
389C2×Dic3—41no—
390C2×Dic3—41no—
391C2×Dic3—41no—
392C2×Dic3—41no—
393C2×Dic3—41no—
394D12—22no—
395D12—22no—
396D12—22no—
397D12—22no—
398D12—22no—
399D12—41no—
400D12—41no—
401D12(C2×D3)⋊C414yescomplemented
402C4×D3—48no—
403C3⋊C8—62no—
404C3⋊C8—62no—
405C3⋊C8—122no—
406C3⋊C8—122no—
407C3⋊C8—121no—
408C3⋊C8—121no—
409C2×C32#38611yescharacteristic
410C2×C32C4×D811yescharacteristic
411C2×C32#44211yescharacteristic
412C2×C32#44711yescharacteristic
413C2×C32#44911yescharacteristic
414C2×C32#45911yescharacteristic
415C2×C32#46311yescharacteristic
416C3×D3—44no—
417C3×D3—82no—
418C24—61no—
419C24—61no—
420C2×D4—32no—
421C2×D4—32no—
422C2×D4—32no—
423C2×D4—32no—
424C2×D4—61no—
425C2×D4—61no—
426C2×D4—61no—
427C2×D4—61no—
428C2×D4—61no—
429C2×D4—61no—
430C2×D4—61no—
431C2×D4—61no—
432C22×C4—64no—
433C22×C4—61no—
434C22×C4—61no—
435C22×C4—122no—
436C22×C4—122no—
437C22×C4#62511yescharacteristic
438C22×C4#62511yescharacteristic
439C22×C4C2×D3211yescharacteristic
440D8—188no—
441C2×C8—92no—
442C2×C8—181no—
443C2×C8—181no—
444C2×C8—181no—
445C2×C8—181no—
446C2×C8—181no—
447C4⋊C4—32no—
448C4⋊C4—61no—
449C4⋊C4—61no—
450C4⋊C4—61no—
451C22⋊C4—64no—
452C22⋊C4—122no—
453C22⋊C4—122no—
454C42—21no—
455C42—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—64no—
464C22×C3—122no—
465C22×C3—122no—
466C22×C3—122no—
467C22×C3—122no—
468C22×C3—122no—
469C22×C3—122no—
470C22×C3—122no—
471C22×C3—122no—
472C22×C3—122no—
473C22×C3—241no—
474C22×C3—241no—
475C22×C3—241no—
476C22×C3—241no—
477C22×C3C4×#6711yescharacteristic
478C22×C3C4×#6711yescharacteristic
479C22×C3#93011yescharacteristic
480C22×C3C2×#21311yescharacteristic
481C22×C3C2×#21311yescharacteristic
482C22×C3#93211yescharacteristic
483C22×C3#93211yescharacteristic
484C22×C3#93711yescharacteristic
485C22×C3#93811yescharacteristic
486C22×C3#94911yescharacteristic
487C22×C3#94911yescharacteristic
488C22×C3#95011yescharacteristic
489C22×C3#95011yescharacteristic
490C22×C3#95311yescharacteristic
491C2×D3—24no—
492C2×D3—42no—
493C2×D3—42no—
494C2×D3—42no—
495C2×D3—42no—
496C2×D3—42no—
497C2×D3—42no—
498C2×D3—42no—
499C2×D3—42no—
500C2×D3—42no—
501C2×D3—81no—
502C2×D3—81no—
503C2×D3—81no—
504C2×D3—81no—
505C3×C4—22no—
506C3×C4—22no—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—21no—
511C3×C4—42no—
512C3×C4—42no—
513C3×C4—41no—
514C3×C4—41no—
515C3×C4—122no—
516C3×C4—241no—
517C3×C4D3×C22⋊C411yescharacteristic
518C3×C4#67⋊C411yescharacteristic
519C3×C4#88311yescharacteristic
520C3×C4#88411yescharacteristic
521C3×C4C2×(C2×D3)⋊C411yescharacteristic
522C3×C4C4×#6711yescharacteristic
523C3×C4#92911yescharacteristic
524C3×C4#93011yescharacteristic
525Dic3—42no—
526Dic3—81no—
527C32#187911yescharacteristic, complemented, Sylow
528C23—62no—
529C23—62no—
530C23—62no—
531C23—62no—
532C23—121no—
533C23—121no—
534C23—121no—
535C23—121no—
536C23—121no—
537C23—121no—
538C23—121no—
539C23—121no—
540C23—121no—
541C23—121no—
542C23C2×#62511yescharacteristic
543D4—34no—
544D4—62no—
545D4—62no—
546D4—62no—
547D4—62no—
548D4—62no—
549D4—121no—
550D4—121no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—62no—
557C2×C4—128no—
558C2×C4—121no—
559C2×C4—121no—
560C2×C4—121no—
561C2×C4—121no—
562C2×C4—121no—
563C2×C4#371312yescomplemented
564C2×C4#379511yescharacteristic
565C2×C4#379811yescharacteristic
566C2×C4C4×D3211yescharacteristic
567C2×C4D3×D1211yescharacteristic
568C2×C4D3×#6711yescharacteristic
569C2×C4D3×#6711yescharacteristic
570C8—182no—
571C8—361no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—21no—
578C2×C3—21no—
579C2×C3—124no—
580C2×C3—242no—
581C2×C3#495611yescharacteristic
582C2×C3C4×#21311yescharacteristic
583C2×C3C4×#21311yescharacteristic
584C2×C3#501411yescharacteristic
585C2×C3#501411yescharacteristic
586C2×C3#501511yescharacteristic
587C2×C3#501611yescharacteristic
588C2×C3#503611yescharacteristic
589C2×C3#503711yescharacteristic
590C2×C3#505711yescharacteristic
591C2×C3#507211yescharacteristic
592C2×C3#521311yescharacteristic
593C2×C3#521711yescharacteristic
594C2×C3#523811yescharacteristic
595D3—44no—
596D3—82no—
597C22—64no—
598C22—122no—
599C22—122no—
600C22—122no—
601C22—122no—
602C22—122no—
603C22—122no—
604C22—122no—
605C22—122no—
606C22—122no—
607C22—241no—
608C22—241no—
609C22—241no—
610C22—241no—
611C22C2×#371311yescharacteristic
612C22#6382211yescharacteristic
613C22#6382311yescharacteristic
614C22#6382311yescharacteristic
615C22C4×#62511yescharacteristic
616C22#6390811yescharacteristic
617C22#6397611yescharacteristic
618C4—22no—
619C4—41no—
620C4—122no—
621C4—241no—
622C4#6387911yescharacteristic
623C4#6390511yescharacteristic
624C4#6390611yescharacteristic
625C4D3×(C2×D3)⋊C411yescharacteristic
626C3—21no—
627C3#6965711yescharacteristic, complemented
628C3#7161311yescharacteristic, complemented
629C2—124no—
630C2—242no—
631C2C4×#371311yescharacteristic
632C2#1059034411yescharacteristic
633C2#1059034711yescharacteristic
634C2#1059034811yescharacteristic
635C2#1059116011yescharacteristic
636C2#1059116111yescharacteristic
637C2#1059138111yescharacteristic
subgroupG/H
centerC23C2×#625
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×#3713C2
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1879
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×D12C2semidirect
3. C3×#4939C2semidirect
4. C2×#63562C2semidirect
5. C2×#63562C2semidirect
6. #10589390C2semidirect
7. #10589163C2semidirect
25. C2×#3713C4semidirect
31. C2×C4×D12D3semidirect
37. #4939D3semidirect
59. C2×C3×D12C2×C4semidirect
72. C2×C3⋊(C3⋊C8)C2×C4semidirect
141. C2×C32×C4D8semidirect
161. C3×D12C22⋊C4semidirect
213. C2×D12C4×D3semidirect
374. C2×C3×C4#213semidirect
375. C2×C3×C4#213semidirect
401. D12(C2×D3)⋊C4semidirect
527. C32#1879semidirect
563. C2×C4#3713semidirect
627. C3#69657semidirect
628. C3#71613semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D122
C22×#37132
C3×#49392
C2×#635622
#105893902
#105891632
#716133
#696573