Finite Group Databasebeta

← #11783259

Subgroups — #11783259

Order 1152.

905 conjugacy classes of subgroups.

The subgroup lattice has 549 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#892C211yesmaximal, characteristic
2C2×#63841C211yesmaximal, characteristic
3C22×D3×C3⋊C8C211yesmaximal, characteristic
4#10589395C211yesmaximal, characteristic, complemented
5C3×#4529C211yesmaximal, characteristic, complemented
6#10589164C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#71580—31nomaximal
9#68866—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4—21no—
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4×Dic3—21no—
18C22×C3×C3⋊C8C2211yescharacteristic
19C3×#892—22no—
20C3×#892C414yescomplemented
21C2×(C2×D3)⋊Dic3—21no—
22C2×Dic32—21no—
23#63841—22no—
24#63841C414yescomplemented
25C2×D3×C3⋊C8—22no—
26C2×D3×C3⋊C8—22no—
27C2×D3×C3⋊C8C414yescomplemented
28C2×C3×#117—31no—
29C2×#926—31no—
30C23×C3⋊C8—31no—
31C22×D3×C8—31no—
32C2×#892—31no—
33C2×#892D311yescharacteristic
34C3×#340—31no—
35#4551—31no—
36#4529—31no—
37#4529—31no—
38#4529—31no—
39#4529—31no—
40#4529—31no—
41#4529—61no—
42#4529D311yescharacteristic, complemented
43C23×C3×D3D411yescharacteristic
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C2×C3×C4×D3C2×C412yes—
51C2×C3×C4×D3C2×C412yes—
52C2×C3×C4×D3C2×C412yes—
53C2×C3×C4×D3D412yes—
54C2×C3×C4×D3D412yes—
55C2×C3×C4×D3Q812yes—
56C32×C4⋊C4—21no—
57C32×C4⋊C4C2×C412yes—
58C4⋊(C3⋊Dic3)—21no—
59C4⋊(C3⋊Dic3)C2×C412yes—
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)C2×C412yes—
63C3×(C2×D3)⋊C4—24no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3C2×C412yes—
67C3×C4⋊Dic3C2×C412yes—
68C3×C4×Dic3—24no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8C2×C412yes—
72(C2×D3)⋊Dic3—24no—
73Dic32—24no—
74D3×C3⋊C8—28no—
75#1735—91noSylow
76C23×C3×C4—31no—
77C22×C4×D3C2×D311yescharacteristic
78C22×C3×C8—31no—
79C3×#117—34no—
80C3×#117—62no—
81C2×C3×C4⋊C4—21no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C4⋊C4—31no—
84C2×C3×C4⋊C4C2×D311yescharacteristic
85C2×C3×C4⋊C4C2×D311yescharacteristic
86C2×C3×C22⋊C4—61no—
87C2×C3×C42—61no—
88C2×#217—61no—
89C2×(C2×D3)⋊C4—21no—
90C2×(C2×D3)⋊C4—61no—
91#926—34no—
92#926—62no—
93C2×C4⋊Dic3—31no—
94C2×C4⋊Dic3—31no—
95C2×C4⋊Dic3—61no—
96C2×C4⋊Dic3C2×D311yescharacteristic
97C2×C4⋊Dic3C2×D311yescharacteristic
98C2×C4×Dic3—21no—
99C2×C4×Dic3—61no—
100C2×C4×Dic3—61no—
101C22×C3⋊C8—31no—
102C22×C3⋊C8—31no—
103C22×C3⋊C8—34no—
104C22×C3⋊C8—61no—
105C22×C3⋊C8—62no—
106C22×C3⋊C8—62no—
107C22×C3⋊C8C2×D311yescharacteristic
108C2×D3×C8—34no—
109C2×D3×C8—62no—
110C2×D3×C8—62no—
111#892—22no—
112#892—34no—
113#892—62no—
114#892Dic314yescomplemented
115C23×C32C2×D411yescharacteristic
116C22×C3×D3—21no—
117C22×C3×D3—21no—
118C22×C3×D3—21no—
119C22×C3×D3—21no—
120C22×C3×D3C22⋊C412yes—
121C22×C3×D3C22⋊C412yes—
122C22×C3×D3C4⋊C412yes—
123C2×C32×C4—22no—
124C2×C32×C4—41no—
125C2×C32×C4—41no—
126C2×C32×C4C22×C411yescharacteristic
127C2×C32×C4C22×C411yescharacteristic
128C2×C32×C4C22×C411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×Q811yescharacteristic
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—41no—
134C2×C3⋊Dic3—41no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3C22⋊C412yes—
142C2×C3×Dic3C22⋊C412yes—
143C2×C3×Dic3C4⋊C412yes—
144C3×C4×D3C4214yes—
145C3×C4×D3C22⋊C414yes—
146C3×C4×D3C4⋊C414yes—
147C3×C4×D3C4⋊C414yes—
148C3⋊(C3⋊C8)—22no—
149C3×C3⋊C8—22no—
150C23×C8—91no—
151C2×#117—31no—
152C2×#117—91no—
153#340—31no—
154#340—91no—
155#340—91no—
156#340—91no—
157C24×C3—31no—
158C23×D3#6711yescharacteristic
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—31no—
163C22×C3×C4—32no—
164C22×C3×C4—32no—
165C22×C3×C4—32no—
166C22×C3×C4—32no—
167C22×C3×C4—32no—
168C22×C3×C4—32no—
169C22×C3×C4—41no—
170C22×C3×C4—61no—
171C22×C3×C4—61no—
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C22×D311yescharacteristic
174C22×Dic3—21no—
175C22×Dic3—21no—
176C22×Dic3—61no—
177C22×Dic3—61no—
178C22×Dic3—121no—
179C22×Dic3#6711yescharacteristic
180C2×C4×D3Dic612yes—
181C2×C4×D3C4×D312yes—
182C2×C4×D3C4×D312yes—
183C2×C4×D3D1212yes—
184C2×C4×D3C2×Dic312yes—
185C2×C4×D3#6712yes—
186C2×C3×C8—32no—
187C2×C3×C8—61no—
188C2×C3×C8—61no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—22no—
192C3×C4⋊C4—32no—
193C3×C4⋊C4—32no—
194C3×C4⋊C4—41no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4—61no—
197C3×C4⋊C4C4×D312yes—
198C3×C4⋊C4C2×Dic312yes—
199C3×C22⋊C4—64no—
200C3×C42—64no—
201#217—64no—
202(C2×D3)⋊C4—24no—
203(C2×D3)⋊C4—64no—
204C4⋊Dic3—21no—
205C4⋊Dic3—21no—
206C4⋊Dic3—32no—
207C4⋊Dic3—32no—
208C4⋊Dic3—62no—
209C4⋊Dic3—61no—
210C4⋊Dic3—61no—
211C4⋊Dic3—121no—
212C4⋊Dic3C4×D312yes—
213C4⋊Dic3C2×Dic312yes—
214C4×Dic3—24no—
215C4×Dic3—64no—
216C4×Dic3—64no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—21no—
219C2×C3⋊C8—32no—
220C2×C3⋊C8—32no—
221C2×C3⋊C8—62no—
222C2×C3⋊C8—68no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—121no—
228C2×C3⋊C8—121no—
229C2×C3⋊C8C4×D312yes—
230D3×C8—68no—
231C22×C32C2×C22⋊C411yescharacteristic
232C22×C32C2×C22⋊C411yescharacteristic
233C22×C32C2×C4⋊C411yescharacteristic
234C22×C32#13511yescharacteristic
235C22×C32#13511yescharacteristic
236C22×C32#13511yescharacteristic
237C22×C32#13511yescharacteristic
238C2×C3×D3—22no—
239C2×C3×D3—22no—
240C2×C3×D3—22no—
241C2×C3×D3—22no—
242C2×C3×D3—22no—
243C2×C3×D3—22no—
244C2×C3×D3#9514yes—
245C32×C4—42no—
246C32×C4C2×C4211yescharacteristic
247C32×C4C2×C22⋊C411yescharacteristic
248C32×C4C2×C4⋊C411yescharacteristic
249C32×C4C2×C4⋊C411yescharacteristic
250C3⋊Dic3—42no—
251C3×Dic3—42no—
252C3×Dic3—42no—
253C3×Dic3#9514yes—
254C23×C4—31no—
255C22×C8—31no—
256C22×C8—94no—
257C22×C8—91no—
258C22×C8—182no—
259C22×C8—182no—
260#117—34no—
261#117—62no—
262#117—94no—
263#117—182no—
264C2×C4⋊C4—31no—
265C2×C4⋊C4—31no—
266C2×C4⋊C4—91no—
267C2×C4⋊C4D3211yescharacteristic
268C2×C22⋊C4—61no—
269C2×C22⋊C4—181no—
270C2×C42—61no—
271C2×C42—181no—
272C23×C3—21no—
273C23×C3—32no—
274C23×C3—32no—
275C23×C3—32no—
276C23×C3—61no—
277C23×C3—61no—
278C23×C3—61no—
279C23×C3—61no—
280C23×C3D3×D411yescharacteristic
281C23×C3C2×#6711yescharacteristic
282C22×D3—21no—
283C22×D3—21no—
284C22×D3—21no—
285C22×D3—21no—
286C22×D3Dic3⋊C412yes—
287C22×D3(C2×D3)⋊C412yes—
288C22×D3#21712yes—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—32no—
298C2×C3×C4—32no—
299C2×C3×C4—32no—
300C2×C3×C4—34no—
301C2×C3×C4—34no—
302C2×C3×C4—34no—
303C2×C3×C4—34no—
304C2×C3×C4—42no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4—62no—
310C2×C3×C4—62no—
311C2×C3×C4—81no—
312C2×C3×C4—81no—
313C2×C3×C4—121no—
314C2×C3×C4—121no—
315C2×C3×C4—121no—
316C2×C3×C4—121no—
317C2×C3×C4C2×Dic611yescharacteristic
318C2×C3×C4C2×C4×D311yescharacteristic
319C2×C3×C4C2×C4×D311yescharacteristic
320C2×C3×C4C2×C4×D311yescharacteristic
321C2×C3×C4C2×C4×D311yescharacteristic
322C2×C3×C4C2×C4×D311yescharacteristic
323C2×C3×C4C2×D1211yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4D3×Q811yescharacteristic
327C2×C3×C4C22×Dic311yescharacteristic
328C2×C3×C4C2×#6711yescharacteristic
329C2×Dic3—22no—
330C2×Dic3—22no—
331C2×Dic3—41no—
332C2×Dic3—41no—
333C2×Dic3—41no—
334C2×Dic3—41no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—122no—
338C2×Dic3—121no—
339C2×Dic3—121no—
340C2×Dic3—121no—
341C2×Dic3—121no—
342C2×Dic3—241no—
343C2×Dic3—241no—
344C2×Dic3Dic3⋊C412yes—
345C2×Dic3(C2×D3)⋊C412yes—
346C2×Dic3#21712yes—
347C4×D3C4×Dic314yes—
348C4×D3Dic3⋊C414yes—
349C4×D3C4⋊Dic314yes—
350C4×D3(C2×D3)⋊C414yes—
351C3×C8—62no—
352C3⋊C8—22no—
353C3⋊C8—62no—
354C3⋊C8—62no—
355C3⋊C8—122no—
356C2×C32C2×#9511yescharacteristic
357C2×C32#41611yescharacteristic
358C2×C32#41611yescharacteristic
359C2×C32#41611yescharacteristic
360C2×C32#41611yescharacteristic
361C2×C32#42711yescharacteristic
362C2×C32#42711yescharacteristic
363C3×D3—24no—
364C24—31no—
365C22×C4—21no—
366C22×C4—31no—
367C22×C4—32no—
368C22×C4—32no—
369C22×C4—32no—
370C22×C4—32no—
371C22×C4—32no—
372C22×C4—32no—
373C22×C4—61no—
374C22×C4—61no—
375C22×C4—181no—
376C22×C4C2×D3211yescharacteristic
377C2×C8—32no—
378C2×C8—61no—
379C2×C8—61no—
380C2×C8—92no—
381C2×C8—188no—
382C2×C8—181no—
383C2×C8—181no—
384C4⋊C4—21no—
385C4⋊C4—32no—
386C4⋊C4—32no—
387C4⋊C4—61no—
388C4⋊C4—61no—
389C4⋊C4—92no—
390C4⋊C4—181no—
391C4⋊C4D3×Dic312yes—
392C22⋊C4—64no—
393C22⋊C4—184no—
394C42—64no—
395C42—184no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—34no—
404C22×C3—62no—
405C22×C3—62no—
406C22×C3—62no—
407C22×C3—62no—
408C22×C3—62no—
409C22×C3—62no—
410C22×C3D3×C22⋊C411yescharacteristic
411C22×C3D3×C22⋊C411yescharacteristic
412C22×C3D3×C4⋊C411yescharacteristic
413C22×C3#91211yescharacteristic
414C22×C3#91611yescharacteristic
415C22×C3#91611yescharacteristic
416C22×C3#91911yescharacteristic
417C22×C3C2×Dic3⋊C411yescharacteristic
418C22×C3C2×(C2×D3)⋊C411yescharacteristic
419C22×C3#95011yescharacteristic
420C22×C3#95011yescharacteristic
421C22×C3#95011yescharacteristic
422C22×C3#95011yescharacteristic
423C22×C3C2×#21711yescharacteristic
424C2×D3—22no—
425C2×D3—22no—
426C2×D3—22no—
427C2×D3—22no—
428C2×D3—22no—
429C2×D3—22no—
430C2×D3C3⋊#9514yes—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—34no—
436C3×C4—42no—
437C3×C4—42no—
438C3×C4—82no—
439C3×C4—122no—
440C3×C4—122no—
441C3×C4C42×D311yescharacteristic
442C3×C4D3×C22⋊C411yescharacteristic
443C3×C4D3×C4⋊C411yescharacteristic
444C3×C4D3×C4⋊C411yescharacteristic
445C3×C4C2×C4×Dic311yescharacteristic
446C3×C4C2×Dic3⋊C411yescharacteristic
447C3×C4C2×C4⋊Dic311yescharacteristic
448C3×C4C2×(C2×D3)⋊C411yescharacteristic
449Dic3—42no—
450Dic3—42no—
451Dic3—122no—
452Dic3—122no—
453Dic3—242no—
454Dic3C3⋊#9514yes—
455C32#173511yescharacteristic, complemented, Sylow
456C23—32no—
457C23—32no—
458C23—32no—
459C23—61no—
460C23—61no—
461C23—61no—
462C23—61no—
463C23D3×#6711yescharacteristic
464C2×C4—22no—
465C2×C4—32no—
466C2×C4—32no—
467C2×C4—32no—
468C2×C4—34no—
469C2×C4—34no—
470C2×C4—34no—
471C2×C4—34no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—62no—
475C2×C4—62no—
476C2×C4—121no—
477C2×C4—121no—
478C2×C4—121no—
479C2×C4—121no—
480C2×C4—182no—
481C2×C4—361no—
482C2×C4—361no—
483C2×C4D3×Dic611yescharacteristic
484C2×C4C4×D3211yescharacteristic
485C2×C4C4×D3211yescharacteristic
486C2×C4D3×D1211yescharacteristic
487C2×C4C2×D3×Dic311yescharacteristic
488C2×C4D3×#6711yescharacteristic
489C8—62no—
490C8—182no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—64no—
499C2×C3D3×#9511yescharacteristic
500C2×C3#477211yescharacteristic
501C2×C3#477211yescharacteristic
502C2×C3#480411yescharacteristic
503C2×C3#480411yescharacteristic
504C2×C3#486011yescharacteristic
505C2×C3#488011yescharacteristic
506C2×C3#499811yescharacteristic
507C2×C3#499811yescharacteristic
508C2×C3#500211yescharacteristic
509C2×C3#500211yescharacteristic
510C2×C3C2×C3⋊#9511yescharacteristic
511C2×C3#523311yescharacteristic
512C2×C3#523311yescharacteristic
513D3—24no—
514C22—34no—
515C22—62no—
516C22—62no—
517C22—62no—
518C22—62no—
519C22—62no—
520C22—62no—
521C22D3×Dic3⋊C411yescharacteristic
522C22D3×(C2×D3)⋊C411yescharacteristic
523C22#6393311yescharacteristic
524C22#6393511yescharacteristic
525C22#6394711yescharacteristic
526C22#6394911yescharacteristic
527C22D3×#21711yescharacteristic
528C4—34no—
529C4—42no—
530C4—122no—
531C4—122no—
532C4—362no—
533C4C4×D3×Dic311yescharacteristic
534C4D3×Dic3⋊C411yescharacteristic
535C4D3×C4⋊Dic311yescharacteristic
536C4D3×(C2×D3)⋊C411yescharacteristic
537C3—21no—
538C3#6886611yescharacteristic, complemented
539C3#7158011yescharacteristic, complemented
540C2—64no—
541C2#1059057111yescharacteristic
542C2#1059057211yescharacteristic
543C2#1059060811yescharacteristic
544C2#1059061011yescharacteristic
545C2D3×C3⋊#9511yescharacteristic
546C2#1059142011yescharacteristic
547C2#1059155611yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1735
LCSG ▷ 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
4. #10589395C2semidirect
5. C3×#4529C2semidirect
6. #10589164C2semidirect
7. #10589163C2semidirect
20. C3×#892C4semidirect
24. #63841C4semidirect
27. C2×D3×C3⋊C8C4semidirect
42. #4529D3semidirect
114. #892Dic3semidirect
455. C32#1735semidirect
538. C3#68866semidirect
539. C3#71580semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8922
C2×#638412
C22×D3×C3⋊C82
#105893952
C3×#45292
#105891642
#105891632
#715803
#688663