Finite Group Databasebeta

← #11787449

Subgroups — #11787449

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 603 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#215C211yesmaximal, characteristic
2C2×#63898C211yesmaximal, characteristic
3#10592928C211yesmaximal, characteristic, complemented
4C2×C3×#835C211yesmaximal, characteristic, complemented
5C2×#63563C211yesmaximal, characteristic
6#10589164C211yesmaximal, characteristic, complemented
7#10589156C211yesmaximal, characteristic, complemented
8#72047—31nomaximal
9#70276—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×D3×Dic3—21no—
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C3×#215—22no—
16C2×C3×#215—22no—
17C2×C3×#215C414yescomplemented
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×(C2×D3)⋊Dic3—21no—
22#63898—22no—
23#63898—22no—
24#63658—21no—
25#63658—21no—
26C3×#835—22no—
27#63563—22no—
28C22×C3×SD16—31no—
29C22×#215D311yescharacteristic
30C2×D4×Dic3—31no—
31C2×#893—31no—
32C2×C3×#103—31no—
33#5229—31no—
34#5229—31no—
35#5229—61no—
36C2×#835D311yescharacteristic, complemented
37C2×#832—31no—
38C2×#821—31no—
39#4551—31no—
40#4550—31no—
41#4550—31no—
42#4529—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⋊Dic3D411yescharacteristic
54C22×C3⋊Dic3D411yescharacteristic
55C22×C3×Dic3—21no—
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)—21no—
67C4×C3⋊Dic3—21no—
68C4×C3⋊Dic3—21no—
69C3×#215—28no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3D412yes—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—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—
91C22×C3×C8—31no—
92C2×C3×C4⋊C4—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×Dic3—31no—
105C2×C4×Dic3—31no—
106C2×C4×Dic3—61no—
107C22×C3⋊C8C2×D311yescharacteristic
108C22×C3⋊C8C2×D311yescharacteristic
109#893—62no—
110#893—62no—
111C3×#103—62no—
112#835—22no—
113#832—62no—
114C3⋊#95—61no—
115C3⋊#95—61no—
116C3⋊#95—61no—
117C3⋊#95—61no—
118C3⋊#95—62no—
119C3⋊#95—62no—
120#821—62no—
121C23×C32C2×D411yescharacteristic
122C22×C3×D3—22no—
123C22×C3×D3—22no—
124C22×C3×D3—22no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C22×C3×D3—41no—
129C32×Q8—22no—
130C32×Q8—22no—
131C32×Q8—41no—
132C32×Q8—41no—
133C2×C32×C4—22no—
134C2×C32×C4—41no—
135C2×C32×C4—41no—
136C2×C32×C4C22×C411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3—21no—
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3—21no—
146C2×C3⋊Dic3—21no—
147C2×C3⋊Dic3—41no—
148C2×C3⋊Dic3—41no—
149C2×C3⋊Dic3—41no—
150C2×C3⋊Dic3SD1612yescomplemented
151C2×C3×Dic3—22no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C3×D12—22no—
155C3×D12—22no—
156C3×D12—22no—
157C3×D12C22⋊C414yes—
158D3×Dic3—48no—
159C3×C3⋊C8—22no—
160C3×C3⋊C8—41no—
161C22×SD16—31no—
162C2×C4×D4—91no—
163C2×#103—31no—
164C2×#102—91no—
165#391—91no—
166#340—91no—
167#336—91no—
168C24×C3—61no—
169C23×D3—21no—
170C2×C3×Q8—22no—
171C2×C3×Q8—21no—
172C2×C3×Q8—21no—
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×Q8—41no—
186C2×C3×Q8C4×D312yescomplemented
187C2×C3×Q8C2×Dic312yescomplemented
188C2×C3×D4—32no—
189C2×C3×D4—32no—
190C2×C3×D4—32no—
191C2×C3×D4—61no—
192C2×C3×D4—61no—
193C2×C3×D4—61no—
194C22×C3×C4—22no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—61no—
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C22×Dic3—21no—
202C22×Dic3—31no—
203C22×Dic3—31no—
204C22×Dic3—31no—
205C22×Dic3—31no—
206C22×Dic3—61no—
207C22×Dic3—61no—
208C22×Dic3—64no—
209C22×Dic3—62no—
210C22×Dic3—61no—
211C22×Dic3—61no—
212C22×Dic3—122no—
213C22×Dic3—122no—
214C2×D12—21no—
215C2×D12—21no—
216C2×D12—21no—
217C2×D12C2×Dic312yes—
218C2×D12#6712yes—
219C2×D12#6712yes—
220C2×C4×D3—64no—
221C2×C4×D3—122no—
222C2×C4×D3—122no—
223C3×SD16—68no—
224C2×C3×C8—32no—
225C2×C3×C8—61no—
226C2×C3×C8—61no—
227C2×C3×C8—61no—
228C2×C3×C8—61no—
229C2×C3×C8—61no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—61no—
232#217—64no—
233#215—28no—
234(C2×D3)⋊C4—64no—
235C4⋊Dic3—21no—
236C4⋊Dic3—61no—
237C4⋊Dic3—61no—
238C4⋊Dic3—61no—
239C4⋊Dic3—61no—
240C4⋊Dic3—121no—
241C4⋊Dic3—121no—
242C4⋊Dic3#6712yes—
243C4×Dic3—61no—
244C4×Dic3—61no—
245C4×Dic3—61no—
246C4×Dic3—61no—
247C4×Dic3—121no—
248C4×Dic3—121no—
249C2×C3⋊C8—21no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8C2×Dic312yescomplemented
255C22×C32C4×D411yescharacteristic
256C22×C32#12011yescharacteristic
257C22×C32#12111yescharacteristic
258C22×C32C2×SD1611yescharacteristic
259C22×C32#13511yescharacteristic
260C22×C32AGL(1,ℤ/8)11yescharacteristic
261C22×C32#13711yescharacteristic
262C2×C3×D3—24no—
263C2×C3×D3—42no—
264C2×C3×D3—42no—
265C2×C3×D3—42no—
266C2×C3×D3—42no—
267C2×C3×D3—42no—
268C2×C3×D3—42no—
269C32×C4—42no—
270C32×C4C2×C22⋊C411yescharacteristic
271C32×C4C4×D411yescharacteristic
272C32×C4#12111yescharacteristic
273C32×C4#12311yescharacteristic
274C3⋊Dic3—22no—
275C3⋊Dic3—41no—
276C3⋊Dic3—81no—
277C3×Dic3—42no—
278C22×Q8D3211yescharacteristic
279C22×D4—31no—
280C23×C4—181no—
281C2×SD16—34no—
282C2×SD16—62no—
283C2×SD16—62no—
284C22×C8—31no—
285C22×C8—31no—
286C4×D4—182no—
287C4×D4—182no—
288C2×C4⋊C4—31no—
289C2×C4⋊C4—91no—
290C2×C22⋊C4—181no—
291C2×C42—91no—
292#103—62no—
293#102—182no—
294#95—181no—
295#95—181no—
296C23×C3—21no—
297C23×C3—62no—
298C23×C3—62no—
299C23×C3—62no—
300C23×C3—121no—
301C23×C3—121no—
302C23×C3—121no—
303C23×C3—121no—
304C23×C3D3×D411yescharacteristic
305C23×C3D3×D411yescharacteristic
306C22×D3—22no—
307C22×D3—22no—
308C22×D3—22no—
309C22×D3—41no—
310C22×D3—41no—
311C22×D3—41no—
312C22×D3—41no—
313C3×Q8—22no—
314C3×Q8—22no—
315C3×Q8—22no—
316C3×Q8—22no—
317C3×Q8—42no—
318C3×Q8—42no—
319C3×Q8—42no—
320C3×Q8—42no—
321C3×Q8—41no—
322C3×Q8—41no—
323C3×Q8—41no—
324C3×Q8—41no—
325C3×D4—34no—
326C3×D4—62no—
327C3×D4—62no—
328C3×D4—62no—
329C2×C3×C4—24no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—42no—
339C2×C3×C4—42no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—41no—
343C2×C3×C4—41no—
344C2×C3×C4—62no—
345C2×C3×C4—121no—
346C2×C3×C4—121no—
347C2×C3×C4C2×C4×D311yescharacteristic
348C2×C3×C4#23511yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4#23711yescharacteristic
353C2×C3×C4#23711yescharacteristic
354C2×C3×C4#23711yescharacteristic
355C2×C3×C4C22×Dic311yescharacteristic
356C2×C3×C4C2×#6711yescharacteristic
357C2×C3×C4C2×#6711yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359C2×Dic3—22no—
360C2×Dic3—32no—
361C2×Dic3—32no—
362C2×Dic3—41no—
363C2×Dic3—41no—
364C2×Dic3—62no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—62no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—61no—
373C2×Dic3—61no—
374C2×Dic3—61no—
375C2×Dic3—61no—
376C2×Dic3—121no—
377C2×Dic3—121no—
378C2×Dic3—121no—
379C2×Dic3—121no—
380C2×Dic3—128no—
381C2×Dic3—122no—
382C2×Dic3—122no—
383C2×Dic3—122no—
384C2×Dic3—121no—
385C2×Dic3—121no—
386C2×Dic3—121no—
387C2×Dic3—121no—
388C2×Dic3—121no—
389C2×Dic3—121no—
390D12—22no—
391D12—22no—
392D12—22no—
393D12#21714yes—
394C4×D3—128no—
395C3×C8—62no—
396C3×C8—121no—
397C3⋊C8—22no—
398C3⋊C8—41no—
399C2×C32#38611yescharacteristic
400C2×C32C4×SD1611yescharacteristic
401C2×C32#44011yescharacteristic
402C2×C32#45011yescharacteristic
403C2×C32#45211yescharacteristic
404C2×C32#46111yescharacteristic
405C2×C32#46311yescharacteristic
406C3×D3—44no—
407C24—61no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8D3×Dic312yescomplemented
414C2×D4—32no—
415C2×D4—32no—
416C2×D4—32no—
417C2×D4—61no—
418C2×D4—61no—
419C2×D4—61no—
420C22×C4—21no—
421C22×C4—61no—
422C22×C4—91no—
423C22×C4—91no—
424C22×C4—184no—
425C22×C4—181no—
426C22×C4—362no—
427C22×C4—362no—
428C22×C4C2×D3211yescharacteristic
429SD16—68no—
430C2×C8—32no—
431C2×C8—61no—
432C2×C8—61no—
433C2×C8—61no—
434C2×C8—61no—
435C2×C8—61no—
436C4⋊C4—32no—
437C4⋊C4—61no—
438C4⋊C4—181no—
439C4⋊C4—181no—
440C22⋊C4—184no—
441C42—181no—
442C42—181no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—64no—
451C22×C3—122no—
452C22×C3—122no—
453C22×C3—122no—
454C22×C3—122no—
455C22×C3—122no—
456C22×C3—122no—
457C22×C3#67⋊C411yescharacteristic
458C22×C3#88411yescharacteristic
459C22×C3D3×SD1611yescharacteristic
460C22×C3D3×SD1611yescharacteristic
461C22×C3#91411yescharacteristic
462C22×C3#91411yescharacteristic
463C22×C3#91511yescharacteristic
464C22×C3#91611yescharacteristic
465C22×C3#91811yescharacteristic
466C22×C3#91911yescharacteristic
467C22×C3D4×Dic311yescharacteristic
468C22×C3#93711yescharacteristic
469C22×C3#93711yescharacteristic
470C22×C3#93911yescharacteristic
471C2×D3—24no—
472C2×D3—42no—
473C2×D3—42no—
474C2×D3—42no—
475C2×D3—42no—
476C2×D3—42no—
477C2×D3—42no—
478C3×C4—21no—
479C3×C4—21no—
480C3×C4—21no—
481C3×C4—21no—
482C3×C4—44no—
483C3×C4—42no—
484C3×C4—42no—
485C3×C4—122no—
486C3×C4D3×C22⋊C411yescharacteristic
487C3×C4#88311yescharacteristic
488C3×C4C4×#6711yescharacteristic
489C3×C4D4×Dic311yescharacteristic
490C3×C4#93511yescharacteristic
491C3×C4#93811yescharacteristic
492C3×C4#93911yescharacteristic
493C3×C4C2×#21711yescharacteristic
494Dic3—42no—
495Dic3—62no—
496Dic3—62no—
497Dic3—122no—
498Dic3—122no—
499Dic3—121no—
500Dic3—121no—
501Dic3—242no—
502Dic3—241no—
503Dic3—241no—
504C32#187711yescharacteristic, complemented, Sylow
505C23—62no—
506C23—62no—
507C23—62no—
508C23—121no—
509C23—121no—
510C23—121no—
511C23—121no—
512C23#381111yescharacteristic
513Q8—22no—
514Q8—22no—
515Q8—41no—
516Q8—41no—
517D4—34no—
518D4—62no—
519D4—62no—
520D4—62no—
521C2×C4—22no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—62no—
525C2×C4—92no—
526C2×C4—121no—
527C2×C4—121no—
528C2×C4—181no—
529C2×C4—181no—
530C2×C4—181no—
531C2×C4—181no—
532C2×C4—181no—
533C2×C4—368no—
534C2×C4—361no—
535C2×C4—361no—
536C2×C4—361no—
537C2×C4C2×D3×Dic311yescharacteristic
538C2×C4#380411yescharacteristic
539C2×C4#380511yescharacteristic
540C2×C4D3×#6711yescharacteristic
541C2×C4D3×#6711yescharacteristic
542C2×C4D3×#6711yescharacteristic
543C8—62no—
544C8—121no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—124no—
553C2×C3#478811yescharacteristic
554C2×C3#481711yescharacteristic
555C2×C3#481811yescharacteristic
556C2×C3#481911yescharacteristic
557C2×C3#495611yescharacteristic
558C2×C3Dic3×SD1611yescharacteristic
559C2×C3#516211yescharacteristic
560C2×C3#516411yescharacteristic
561C2×C3#516511yescharacteristic
562C2×C3#516911yescharacteristic
563C2×C3#516911yescharacteristic
564C2×C3#517311yescharacteristic
565C2×C3#518711yescharacteristic
566C2×C3#522011yescharacteristic
567D3—44no—
568C22—64no—
569C22—122no—
570C22—122no—
571C22—122no—
572C22—122no—
573C22—122no—
574C22—122no—
575C22#6394011yescharacteristic
576C22#6394111yescharacteristic
577C22#6395011yescharacteristic
578C22#6395111yescharacteristic
579C22#6397111yescharacteristic
580C22#67⋊Dic311yescharacteristic
581C22#6398311yescharacteristic
582C4—42no—
583C4—122no—
584C4—182no—
585C4—361no—
586C4—721no—
587C4D3×#21711yescharacteristic
588C4#6396911yescharacteristic
589C4#6397011yescharacteristic
590C4Dic3×#6711yescharacteristic
591C3—21no—
592C3#7027611yescharacteristic, complemented
593C3#7204711yescharacteristic, complemented
594C2—124no—
595C2#1059156911yescharacteristic
596C2#1059157011yescharacteristic
597C2#1059157111yescharacteristic
598C2#1059157211yescharacteristic
599C2#1059165211yescharacteristic
600C2#1059165611yescharacteristic
601C2#1059172111yescharacteristic
subgroupG/H
centerC23#3811
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. #10592928C2semidirect
4. C2×C3×#835C2semidirect
6. #10589164C2semidirect
7. #10589156C2semidirect
17. C2×C3×#215C4semidirect
36. C2×#835D3semidirect
49. C2×C32×Q8C2×C4semidirect
77. C2×C3×C3⋊C8C2×C4semidirect
96. C2×#215Dic3semidirect
150. C2×C3⋊Dic3SD16semidirect
186. C2×C3×Q8C4×D3semidirect
187. C2×C3×Q8C2×Dic3semidirect
254. C2×C3⋊C8C2×Dic3semidirect
413. C2×Q8D3×Dic3semidirect
504. C32#1877semidirect
592. C3#70276semidirect
593. 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×#638982
#105929282
C2×C3×#8352
C2×#635632
#105891642
#105891562
#720473
#702763