Finite Group Databasebeta

← #11787447

Subgroups — #11787447

Order 1152.

885 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#215C211yesmaximal, characteristic
2C2×Dic3×D12C211yesmaximal, characteristic
3C2×#63662C211yesmaximal, characteristic, complemented
4C3×#5229C211yesmaximal, characteristic, complemented
5C2×#63562C211yesmaximal, characteristic
6#10589164C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#72047—31nomaximal
9#69687—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×D3×Dic3—21no—
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×#215—22no—
16C2×C3×#215—22no—
17C2×C3×#215C414yescomplemented
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×(C2×D3)⋊Dic3—21no—
22Dic3×D12—22no—
23Dic3×D12—22no—
24#63662—22no—
25C3×C3⋊#95—21no—
26C3×C3⋊#95—21no—
27#63562—22no—
28C22×C3×SD16—31no—
29C22×#215D311yescharacteristic
30C2×D4×Dic3—31no—
31C2×C4×D12—31no—
32C3×#391—31no—
33#5229D311yescharacteristic, complemented
34C2×#835—31no—
35C2×#835—31no—
36C2×#835—61no—
37C2×#832—31no—
38C2×#809—31no—
39#4551—31no—
40#4550—31no—
41#4529—31no—
42#4524—31no—
43C23×C3×D3—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8—21no—
48C2×C32×Q8—21no—
49C2×C32×Q8C2×C412yescomplemented
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C22×C3×Dic3D411yescharacteristic
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12C2×C412yes—
60C2×C3×D12D412yes—
61C2×C3×D12D412yes—
62C2×D3×Dic3—24no—
63C2×D3×Dic3—42no—
64C2×D3×Dic3—42no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)D412yes—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C3×#215—28no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C3×C4×Dic3—21no—
74C3×C4×Dic3—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8C2×C412yescomplemented
78(C2×D3)⋊Dic3—24no—
79#1877—91noSylow
80C22×C3×Q8—21no—
81C22×C3×Q8C2×D311yescharacteristic
82C22×C3×Q8C2×D311yescharacteristic
83C22×C3×D4—31no—
84C23×Dic3—61no—
85C22×D12C2×D311yescharacteristic
86C22×C4×D3—61no—
87C2×C3×SD16—34no—
88C2×C3×SD16—62no—
89C2×C3×SD16—62no—
90C22×C3×C8—31no—
91C2×C3×C4⋊C4—31no—
92C2×C3×C42—31no—
93C2×#217—61no—
94C2×#215—22no—
95C2×#215—22no—
96C2×#215Dic314yescomplemented
97D4×Dic3—62no—
98D4×Dic3—62no—
99C2×(C2×D3)⋊C4—61no—
100C2×C4⋊Dic3—31no—
101C2×C4⋊Dic3—31no—
102C2×C4⋊Dic3—61no—
103C2×C4⋊Dic3C2×D311yescharacteristic
104C2×C4×Dic3C2×D311yescharacteristic
105C22×C3⋊C8—31no—
106C22×C3⋊C8—31no—
107C22×C3⋊C8—61no—
108C22×C3⋊C8C2×D311yescharacteristic
109C4×D12—62no—
110C4×D12—62no—
111C3×#95—61no—
112C3×#95—61no—
113#835—62no—
114#835—62no—
115#835—64no—
116#832—62no—
117C3⋊#95—21no—
118C3⋊#95—21no—
119#809—62no—
120C23×C32C2×D411yescharacteristic
121C22×C3×D3—22no—
122C22×C3×D3—22no—
123C22×C3×D3—22no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C32×Q8—22no—
129C32×Q8—22no—
130C32×Q8—41no—
131C32×Q8—41no—
132C2×C32×C4—22no—
133C2×C32×C4—41no—
134C2×C32×C4—41no—
135C2×C32×C4C22×C411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4#4111yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—41no—
143C2×C3⋊Dic3—41no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3SD1612yescomplemented
153C3×D12—22no—
154C3×D12—22no—
155C3×D12—22no—
156C3×D12C22⋊C414yes—
157D3×Dic3—48no—
158C3⋊(C3⋊C8)—41no—
159C3×C3⋊C8—22no—
160C22×SD16—31no—
161C2×C4×D4—91no—
162C2×#103—91no—
163C2×#102—91no—
164#391—31no—
165#340—91no—
166#336—91no—
167C24×C3—61no—
168C23×D3—21no—
169C2×C3×Q8—21no—
170C2×C3×Q8—21no—
171C2×C3×Q8—22no—
172C2×C3×Q8—22no—
173C2×C3×Q8—21no—
174C2×C3×Q8—21no—
175C2×C3×Q8—21no—
176C2×C3×Q8—21no—
177C2×C3×Q8—21no—
178C2×C3×Q8—21no—
179C2×C3×Q8—21no—
180C2×C3×Q8—21no—
181C2×C3×Q8—22no—
182C2×C3×Q8—41no—
183C2×C3×Q8—41no—
184C2×C3×Q8—41no—
185C2×C3×Q8C4×D312yescomplemented
186C2×C3×Q8C2×Dic312yescomplemented
187C2×C3×D4—32no—
188C2×C3×D4—32no—
189C2×C3×D4—32no—
190C2×C3×D4—61no—
191C2×C3×D4—61no—
192C2×C3×D4—61no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—31no—
197C22×C3×C4—31no—
198C22×C3×C4—41no—
199C22×C3×C4—61no—
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×Dic3—21no—
203C22×Dic3—64no—
204C22×Dic3—61no—
205C22×Dic3—61no—
206C22×Dic3—121no—
207C22×Dic3—122no—
208C22×Dic3—122no—
209C22×Dic3#6711yescharacteristic
210C22×Dic3#6711yescharacteristic
211C2×D12—21no—
212C2×D12—21no—
213C2×D12—21no—
214C2×D12C2×Dic312yes—
215C2×D12#6712yes—
216C2×D12#6712yes—
217C2×C4×D3—64no—
218C2×C4×D3—122no—
219C2×C4×D3—122no—
220C3×SD16—68no—
221C2×C3×C8—32no—
222C2×C3×C8—61no—
223C2×C3×C8—61no—
224C3×C4⋊C4—61no—
225C3×C4⋊C4—61no—
226C3×C42—61no—
227C3×C42—61no—
228#217—64no—
229#215—28no—
230(C2×D3)⋊C4—64no—
231C4⋊Dic3—21no—
232C4⋊Dic3—21no—
233C4⋊Dic3—32no—
234C4⋊Dic3—32no—
235C4⋊Dic3—62no—
236C4⋊Dic3—61no—
237C4⋊Dic3—61no—
238C4⋊Dic3—121no—
239C4×Dic3—21no—
240C4×Dic3—21no—
241C2×C3⋊C8—21no—
242C2×C3⋊C8—21no—
243C2×C3⋊C8—62no—
244C2×C3⋊C8—61no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8—61no—
247C2×C3⋊C8—61no—
248C2×C3⋊C8—61no—
249C2×C3⋊C8—61no—
250C2×C3⋊C8—121no—
251C2×C3⋊C8—121no—
252C2×C3⋊C8C2×Dic312yescomplemented
253C22×C32C4×D411yescharacteristic
254C22×C32#12011yescharacteristic
255C22×C32#12111yescharacteristic
256C22×C32C2×SD1611yescharacteristic
257C22×C32#13511yescharacteristic
258C22×C32AGL(1,ℤ/8)11yescharacteristic
259C22×C32#13711yescharacteristic
260C2×C3×D3—24no—
261C2×C3×D3—42no—
262C2×C3×D3—42no—
263C2×C3×D3—42no—
264C2×C3×D3—42no—
265C2×C3×D3—42no—
266C2×C3×D3—42no—
267C32×C4—42no—
268C32×C4C2×C22⋊C411yescharacteristic
269C32×C4C4×D411yescharacteristic
270C32×C4#12111yescharacteristic
271C32×C4#12311yescharacteristic
272C3⋊Dic3—42no—
273C3×Dic3—22no—
274C3×Dic3—41no—
275C3×Dic3—81no—
276C22×Q8D3211yescharacteristic
277C22×D4—31no—
278C23×C4—181no—
279C2×SD16—34no—
280C2×SD16—62no—
281C2×SD16—62no—
282C22×C8—31no—
283C22×C8—91no—
284C4×D4—182no—
285C4×D4—182no—
286C2×C4⋊C4—31no—
287C2×C4⋊C4—91no—
288C2×C22⋊C4—181no—
289C2×C42—31no—
290#103—182no—
291#102—182no—
292#95—61no—
293#95—61no—
294C23×C3—21no—
295C23×C3—62no—
296C23×C3—62no—
297C23×C3—62no—
298C23×C3—121no—
299C23×C3—121no—
300C23×C3—121no—
301C23×C3—121no—
302C23×C3D3×D411yescharacteristic
303C23×C3C2×#6711yescharacteristic
304C22×D3—22no—
305C22×D3—22no—
306C22×D3—22no—
307C22×D3—41no—
308C22×D3—41no—
309C22×D3—41no—
310C22×D3—41no—
311C3×Q8—24no—
312C3×Q8—22no—
313C3×Q8—22no—
314C3×Q8—22no—
315C3×Q8—22no—
316C3×Q8—42no—
317C3×Q8—42no—
318C3×Q8—42no—
319C3×Q8—41no—
320C3×Q8—41no—
321C3×Q8—41no—
322C3×Q8—41no—
323C3×D4—34no—
324C3×D4—62no—
325C3×D4—62no—
326C3×D4—62no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—32no—
336C2×C3×C4—42no—
337C2×C3×C4—42no—
338C2×C3×C4—42no—
339C2×C3×C4—41no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—41no—
343C2×C3×C4—61no—
344C2×C3×C4—61no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—61no—
348C2×C3×C4—121no—
349C2×C3×C4—121no—
350C2×C3×C4—121no—
351C2×C3×C4C2×C4×D311yescharacteristic
352C2×C3×C4#23511yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4#23711yescharacteristic
358C2×C3×C4#23711yescharacteristic
359C2×C3×C4#23711yescharacteristic
360C2×C3×C4C22×Dic311yescharacteristic
361C2×C3×C4C2×#6711yescharacteristic
362C2×C3×C4C2×#6711yescharacteristic
363C2×Dic3—21no—
364C2×Dic3—21no—
365C2×Dic3—21no—
366C2×Dic3—21no—
367C2×Dic3—21no—
368C2×Dic3—41no—
369C2×Dic3—41no—
370C2×Dic3—41no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—122no—
374C2×Dic3—128no—
375C2×Dic3—121no—
376C2×Dic3—121no—
377C2×Dic3—121no—
378C2×Dic3—121no—
379C2×Dic3—241no—
380C2×Dic3—241no—
381C2×Dic3#21512yescomplemented
382D12—22no—
383D12—22no—
384D12—22no—
385D12#21714yes—
386C4×D3—128no—
387C3×C8—62no—
388C3⋊C8—22no—
389C3⋊C8—122no—
390C3⋊C8—121no—
391C3⋊C8—121no—
392C2×C32#38611yescharacteristic
393C2×C32C4×SD1611yescharacteristic
394C2×C32#44011yescharacteristic
395C2×C32#45011yescharacteristic
396C2×C32#45211yescharacteristic
397C2×C32#46111yescharacteristic
398C2×C32#46311yescharacteristic
399C3×D3—44no—
400C24—61no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8D3×Dic312yescomplemented
407C2×D4—32no—
408C2×D4—32no—
409C2×D4—32no—
410C2×D4—61no—
411C2×D4—61no—
412C2×D4—61no—
413C22×C4—21no—
414C22×C4—31no—
415C22×C4—31no—
416C22×C4—61no—
417C22×C4—184no—
418C22×C4—181no—
419C22×C4—362no—
420C22×C4—362no—
421C22×C4C2×D3211yescharacteristic
422SD16—68no—
423C2×C8—32no—
424C2×C8—61no—
425C2×C8—61no—
426C2×C8—181no—
427C2×C8—181no—
428C2×C8—181no—
429C4⋊C4—61no—
430C4⋊C4—61no—
431C4⋊C4—92no—
432C4⋊C4—181no—
433C22⋊C4—184no—
434C42—61no—
435C42—61no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—64no—
444C22×C3—122no—
445C22×C3—122no—
446C22×C3—122no—
447C22×C3—122no—
448C22×C3—122no—
449C22×C3—122no—
450C22×C3D3×SD1611yescharacteristic
451C22×C3#91411yescharacteristic
452C22×C3#91511yescharacteristic
453C22×C3#91611yescharacteristic
454C22×C3C4×#6711yescharacteristic
455C22×C3D4×Dic311yescharacteristic
456C22×C3#93711yescharacteristic
457C22×C3#93711yescharacteristic
458C22×C3#93811yescharacteristic
459C22×C3#93911yescharacteristic
460C22×C3C2×#21511yescharacteristic
461C22×C3#94211yescharacteristic
462C22×C3#94911yescharacteristic
463C22×C3#95011yescharacteristic
464C2×D3—24no—
465C2×D3—42no—
466C2×D3—42no—
467C2×D3—42no—
468C2×D3—42no—
469C2×D3—42no—
470C2×D3—42no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—44no—
476C3×C4—42no—
477C3×C4—42no—
478C3×C4—62no—
479C3×C4—121no—
480C3×C4—241no—
481C3×C4D3×C22⋊C411yescharacteristic
482C3×C4#67⋊C411yescharacteristic
483C3×C4#88311yescharacteristic
484C3×C4#88411yescharacteristic
485C3×C4D4×Dic311yescharacteristic
486C3×C4#93511yescharacteristic
487C3×C4#93911yescharacteristic
488C3×C4C2×#21711yescharacteristic
489Dic3—22no—
490Dic3—41no—
491Dic3—81no—
492Dic3—122no—
493Dic3—122no—
494Dic3—242no—
495C32#187711yescharacteristic, complemented, Sylow
496C23—62no—
497C23—62no—
498C23—62no—
499C23—121no—
500C23—121no—
501C23—121no—
502C23—121no—
503C23D3×#6711yescharacteristic
504Q8—22no—
505Q8—22no—
506Q8—41no—
507Q8—41no—
508D4—34no—
509D4—62no—
510D4—62no—
511D4—62no—
512C2×C4—22no—
513C2×C4—32no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—61no—
517C2×C4—61no—
518C2×C4—61no—
519C2×C4—61no—
520C2×C4—61no—
521C2×C4—121no—
522C2×C4—121no—
523C2×C4—121no—
524C2×C4—182no—
525C2×C4—368no—
526C2×C4—361no—
527C2×C4—361no—
528C2×C4C2×D3×Dic311yescharacteristic
529C2×C4#380411yescharacteristic
530C2×C4#380511yescharacteristic
531C2×C4D3×#6711yescharacteristic
532C2×C4D3×#6711yescharacteristic
533C2×C4#381111yescharacteristic
534C8—62no—
535C8—361no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—124no—
544C2×C3#495611yescharacteristic
545C2×C3C4×#21511yescharacteristic
546C2×C3#502611yescharacteristic
547C2×C3#504611yescharacteristic
548C2×C3#504711yescharacteristic
549C2×C3#505711yescharacteristic
550C2×C3#508311yescharacteristic
551C2×C3Dic3×SD1611yescharacteristic
552C2×C3#516211yescharacteristic
553C2×C3#516411yescharacteristic
554C2×C3#516511yescharacteristic
555C2×C3#516911yescharacteristic
556C2×C3#517311yescharacteristic
557C2×C3#522011yescharacteristic
558D3—44no—
559C22—64no—
560C22—122no—
561C22—122no—
562C22—122no—
563C22—122no—
564C22—122no—
565C22—122no—
566C22D3×#21511yescharacteristic
567C22#6393911yescharacteristic
568C22#6394611yescharacteristic
569C22#6394711yescharacteristic
570C22#6397011yescharacteristic
571C22Dic3×#6711yescharacteristic
572C22#6398311yescharacteristic
573C4—42no—
574C4—62no—
575C4—121no—
576C4—241no—
577C4—362no—
578C4D3×#21711yescharacteristic
579C4#6396911yescharacteristic
580C4#6397111yescharacteristic
581C4#67⋊Dic311yescharacteristic
582C3—21no—
583C3#6968711yescharacteristic, complemented
584C3#7204711yescharacteristic, complemented
585C2—124no—
586C2Dic3×#21511yescharacteristic
587C2#1059156411yescharacteristic
588C2#1059156611yescharacteristic
589C2#1059156711yescharacteristic
590C2#1059165111yescharacteristic
591C2#1059165511yescharacteristic
592C2#1059172111yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC22×Q8D32
hypocenterC32#1877
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. C2×#63662C2semidirect
4. C3×#5229C2semidirect
6. #10589164C2semidirect
7. #10589155C2semidirect
17. C2×C3×#215C4semidirect
33. #5229D3semidirect
49. C2×C32×Q8C2×C4semidirect
77. C2×C3×C3⋊C8C2×C4semidirect
96. C2×#215Dic3semidirect
152. C2×C3×Dic3SD16semidirect
185. C2×C3×Q8C4×D3semidirect
186. C2×C3×Q8C2×Dic3semidirect
252. C2×C3⋊C8C2×Dic3semidirect
381. C2×Dic3#215semidirect
406. C2×Q8D3×Dic3semidirect
495. C32#1877semidirect
583. C3#69687semidirect
584. C3#72047semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2152
C2×Dic3×D122
C2×#636622
C3×#52292
C2×#635622
#105891642
#105891552
#720473
#696873