Finite Group Databasebeta

← #11788856

Subgroups — #11788856

Order 1152.

929 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596269C211yesmaximal, characteristic, complemented
2C3×#5804C211yesmaximal, characteristic
3C2×C3×#834C211yesmaximal, characteristic, complemented
4C2×#63580C212yesmaximal, complemented
5#10589186C212yesmaximal, complemented
6#71848—31nomaximal
7#70024—31nomaximal
8C22×C32×D4C2211yescharacteristic
9C22×C3×#67C2211yescharacteristic
10C2×#3757—21no—
11C2×#3757C2212yes—
12D4×C3⋊Dic3—24no—
13#64135—21no—
14C3×#953—21no—
15C2×C3×#217C2212yes—
16C2×C3×#217C2211yescharacteristic
17C3×#939—22no—
18C3×#937C412yescomplemented
19C3×#935C412yescomplemented
20C3×#929—21no—
21C3×#834—22no—
22#63580—24no—
23C3×#534—31no—
24#5804D311yescharacteristic
25#5798—31no—
26#5798—31no—
27#5798—61no—
28C2×C3×#99—31no—
29C2×#834—32no—
30C2×#834D311yescharacteristic, complemented
31C2×#806—32no—
32#4527—32no—
33#4526—32no—
34C24×C32D411yescharacteristic
35C24×C32C2311yescharacteristic
36C23×C3×D3C2×C411yescharacteristic, complemented
37C2×C32×D4—22no—
38C2×C32×D4—22no—
39C2×C32×D4C2×C412yes—
40C2×C32×D4D412yes—
41C22×C32×C4D411yescharacteristic
42C22×C3⋊Dic3—22no—
43C22×C3⋊Dic3—22no—
44C2×C3×#67—21no—
45C2×C3×#67—21no—
46C2×C3×#67—22no—
47C2×C3×#67—22no—
48C2×C3×#67—22no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3—22no—
51C22×C3×Dic3C2×C411yescharacteristic, complemented
52#3757—22no—
53#3757—22no—
54#3757D414yescomplemented
55C4⋊(C3⋊Dic3)—22no—
56C4×C3⋊Dic3—22no—
57C3×#217—22no—
58C3×#217—21no—
59C3×#217—22no—
60C3×#217—22no—
61C3×#217C2×C412yescomplemented
62C3×(C2×D3)⋊C4—22no—
63C3×Dic3⋊C4—22no—
64#1913—91noSylow
65C22×C3×D4—21no—
66C22×C3×D4—31no—
67C22×C3×D4C2×D311yescharacteristic
68C22×C3×D4C2×D311yescharacteristic
69C22×#67C2×D311yescharacteristic
70C3×#123—32no—
71C3×#123—61no—
72C3×#121—62no—
73C3×#120—32no—
74C3×#120—61no—
75C2×C3×C22⋊C4—31no—
76C2×C3×C22⋊C4—32no—
77#953—21no—
78C2×#217—32no—
79C2×#217—32no—
80C2×#217—62no—
81C2×#217—62no—
82C2×#217—61no—
83C2×#217—61no—
84C2×#217C2×D312yes—
85C2×#217C2×D311yescharacteristic
86#939—22no—
87#937Dic312yescomplemented
88#935Dic312yescomplemented
89D4×Dic3—64no—
90D4×Dic3—64no—
91D4×Dic3—68no—
92#929—21no—
93#926—62no—
94#926—61no—
95#926—61no—
96C3×#99—62no—
97#834—22no—
98#834—64no—
99#806—64no—
100C23×C32—21no—
101C23×C32—21no—
102C23×C32—81no—
103C23×C32—81no—
104C23×C32C22⋊C412yes—
105C23×C32C22×C411yescharacteristic
106C23×C32C2×D411yescharacteristic
107C23×C32C2×D412yes—
108C23×C32C2×D411yescharacteristic
109C23×C32#4112yes—
110C22×C3×D3—21no—
111C22×C3×D3—22no—
112C22×C3×D3—81no—
113C32×D4—24no—
114C32×D4—24no—
115C2×C32×C4—21no—
116C2×C32×C4—21no—
117C2×C32×C4C22⋊C412yes—
118C2×C3⋊Dic3—24no—
119C2×C3⋊Dic3—82no—
120C2×C3⋊Dic3—82no—
121C3×#67—41no—
122C3×#67—42no—
123C3×#67—41no—
124C3×#67—82no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—42no—
129C2×C3×Dic3—81no—
130C2×C3×Dic3—82no—
131#534—31no—
132#518—91no—
133C2×#99—31no—
134C2×#99—92no—
135#342—92no—
136C24×C3—21no—
137C24×C3—21no—
138C24×C3—31no—
139C24×C3D1211yescharacteristic
140C24×C3#6711yescharacteristic
141C24×C3C22×D311yescharacteristic
142C24×C3C22×D311yescharacteristic
143C23×D3C2×Dic311yescharacteristic, complemented
144C2×C3×D4—24no—
145C2×C3×D4—24no—
146C2×C3×D4—22no—
147C2×C3×D4—22no—
148C2×C3×D4—22no—
149C2×C3×D4—22no—
150C2×C3×D4—22no—
151C2×C3×D4—22no—
152C2×C3×D4—61no—
153C2×C3×D4—62no—
154C2×C3×D4—62no—
155C2×C3×D4—61no—
156C2×C3×D4—62no—
157C2×C3×D4C4×D312yes—
158C2×C3×D4C2×Dic312yes—
159C2×C3×D4#6712yes—
160C2×C3×D4#6712yes—
161C22×C3×C4—21no—
162C22×C3×C4—31no—
163C22×C3×C4—61no—
164C22×C3×C4—62no—
165C22×C3×C4D1211yescharacteristic
166C22×C3×C4#6711yescharacteristic
167C2×#67—22no—
168C2×#67—22no—
169C2×#67—21no—
170C2×#67—21no—
171C2×#67—22no—
172C22×Dic3—21no—
173C22×Dic3—22no—
174C22×Dic3—64no—
175C22×Dic3—62no—
176C22×Dic3—62no—
177C22×Dic3—64no—
178C22×Dic3—62no—
179C22×Dic3—62no—
180C22×Dic3C2×Dic311yescharacteristic, complemented
181C3×C4⋊C4—62no—
182C3×C22⋊C4—32no—
183C3×C22⋊C4—62no—
184C3×C22⋊C4—61no—
185C3×C22⋊C4—62no—
186C3×C22⋊C4—62no—
187C3×C22⋊C4—62no—
188#217—22no—
189#217—21no—
190#217—22no—
191#217—22no—
192#217—34no—
193#217—34no—
194#217—64no—
195#217—64no—
196#217—64no—
197#217—62no—
198#217—62no—
199#217—62no—
200#217—62no—
201#217C2×Dic312yescomplemented
202(C2×D3)⋊C4—22no—
203C4⋊Dic3—64no—
204C4⋊Dic3—62no—
205C4⋊Dic3—62no—
206Dic3⋊C4—22no—
207C4×Dic3—64no—
208C4×Dic3—62no—
209C4×Dic3—62no—
210C22×C32—22no—
211C22×C32—42no—
212C22×C32—41no—
213C22×C32—42no—
214C22×C32—41no—
215C22×C32—42no—
216C22×C32—41no—
217C22×C32—42no—
218C22×C32—81no—
219C22×C32C2×C22⋊C411yescharacteristic
220C22×C32C4×D412yes—
221C22×C32#12011yescharacteristic
222C22×C32#12112yes—
223C22×C32#12311yescharacteristic
224C2×C3×D3—42no—
225C2×C3×D3—41no—
226C2×C3×D3—82no—
227C32×C4—22no—
228C3⋊Dic3—44no—
229C3×Dic3—42no—
230C3×Dic3—41no—
231C3×Dic3—82no—
232C22×D4—31no—
233C22×D4D3211yescharacteristic
234#123—32no—
235#123—61no—
236#121—62no—
237#120—32no—
238#120—61no—
239C4×D4—184no—
240#117—181no—
241C2×C22⋊C4—31no—
242C2×C22⋊C4—32no—
243C2×C22⋊C4—92no—
244C2×C22⋊C4—181no—
245#99—62no—
246#99—184no—
247C23×C3—22no—
248C23×C3—22no—
249C23×C3—21no—
250C23×C3—21no—
251C23×C3—21no—
252C23×C3—21no—
253C23×C3—22no—
254C23×C3—21no—
255C23×C3—22no—
256C23×C3—21no—
257C23×C3—21no—
258C23×C3—22no—
259C23×C3—61no—
260C23×C3—62no—
261C23×C3—81no—
262C23×C3—81no—
263C23×C3—81no—
264C23×C3—81no—
265C23×C3—82no—
266C23×C3—82no—
267C23×C3—241no—
268C23×C3(C2×D3)⋊C412yes—
269C23×C3#21712yes—
270C23×C3C2×C4×D311yescharacteristic
271C23×C3C2×D1211yescharacteristic
272C23×C3D3×D412yes—
273C23×C3D3×D412yes—
274C23×C3#23712yes—
275C23×C3#23712yes—
276C23×C3C22×Dic311yescharacteristic
277C23×C3C2×#6711yescharacteristic
278C23×C3C2×#6711yescharacteristic
279C23×C3C2×#6711yescharacteristic
280C22×D3—21no—
281C22×D3—22no—
282C22×D3—81no—
283C3×D4—28no—
284C3×D4—28no—
285C3×D4—24no—
286C3×D4—24no—
287C3×D4—24no—
288C3×D4—24no—
289C3×D4—121no—
290C3×D4—121no—
291C3×D4—122no—
292C3×D4—242no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—22no—
300C2×C3×C4—62no—
301C2×C3×C4—62no—
302C2×C3×C4—61no—
303C2×C3×C4—122no—
304C2×C3×C4—241no—
305C2×C3×C4—242no—
306C2×C3×C4(C2×D3)⋊C412yes—
307C2×C3×C4#21712yes—
308#67—41no—
309#67—41no—
310#67—42no—
311#67—82no—
312C2×Dic3—22no—
313C2×Dic3—21no—
314C2×Dic3—22no—
315C2×Dic3—42no—
316C2×Dic3—68no—
317C2×Dic3—64no—
318C2×Dic3—64no—
319C2×Dic3—81no—
320C2×Dic3—82no—
321C2×Dic3—242no—
322C2×Dic3—242no—
323C2×Dic3—244no—
324C2×Dic3—244no—
325C2×Dic3—242no—
326C2×Dic3—242no—
327C2×C32—21no—
328C2×C32—21no—
329C2×C32—22no—
330C2×C32—22no—
331C2×C32—21no—
332C2×C32—42no—
333C2×C32#38611yescharacteristic
334C3×D3—81no—
335C24—31no—
336C24#62611yescharacteristic
337C24C2×D3211yescharacteristic
338C2×D4—22no—
339C2×D4—22no—
340C2×D4—62no—
341C2×D4—61no—
342C2×D4—61no—
343C2×D4—62no—
344C2×D4—62no—
345C2×D4D3×Dic312yes—
346C2×D4#62512yes—
347C22×C4—31no—
348C22×C4—61no—
349C22×C4—62no—
350C22×C4—182no—
351C22×C4—182no—
352C22×C4#62611yescharacteristic
353C4⋊C4—62no—
354C4⋊C4—182no—
355C22⋊C4—32no—
356C22⋊C4—62no—
357C22⋊C4—61no—
358C22⋊C4—62no—
359C22⋊C4—62no—
360C22⋊C4—62no—
361C22⋊C4—94no—
362C22⋊C4—182no—
363C22⋊C4—182no—
364C42—182no—
365C22×C3—24no—
366C22×C3—22no—
367C22×C3—22no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—22no—
371C22×C3—22no—
372C22×C3—21no—
373C22×C3—42no—
374C22×C3—41no—
375C22×C3—42no—
376C22×C3—42no—
377C22×C3—42no—
378C22×C3—41no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3—41no—
382C22×C3—41no—
383C22×C3—42no—
384C22×C3—42no—
385C22×C3—44no—
386C22×C3—44no—
387C22×C3—42no—
388C22×C3—42no—
389C22×C3—42no—
390C22×C3—82no—
391C22×C3—81no—
392C22×C3—81no—
393C22×C3—82no—
394C22×C3—81no—
395C22×C3—81no—
396C22×C3—82no—
397C22×C3—122no—
398C22×C3—121no—
399C22×C3—242no—
400C22×C3#67⋊C412yes—
401C22×C3#88211yescharacteristic
402C22×C3#88611yescharacteristic
403C22×C3C2×(C2×D3)⋊C411yescharacteristic
404C22×C3D4×Dic312yes—
405C22×C3#93511yescharacteristic
406C22×C3#93711yescharacteristic
407C22×C3#93912yes—
408C22×C3#93912yes—
409C22×C3C2×#21711yescharacteristic
410C2×D3—42no—
411C2×D3—41no—
412C2×D3—82no—
413C3×C4—24no—
414C3×C4—22no—
415C3×C4—22no—
416C3×C4—122no—
417C3×C4—121no—
418C3×C4—242no—
419Dic3—42no—
420Dic3—41no—
421Dic3—82no—
422Dic3—128no—
423Dic3—124no—
424Dic3—124no—
425C32#191311yescharacteristic, complemented, Sylow
426C23—21no—
427C23—21no—
428C23—61no—
429C23—62no—
430C23—81no—
431C23—81no—
432C23—241no—
433C23(C2×D3)⋊Dic312yes—
434C23C2×D3×Dic311yescharacteristic
435C23#380512yes—
436C23C2×#62511yescharacteristic
437C23C2×#62611yescharacteristic
438C23#381112yes—
439D4—24no—
440D4—24no—
441D4—121no—
442D4—122no—
443D4—121no—
444D4—242no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—62no—
448C2×C4—61no—
449C2×C4—62no—
450C2×C4—122no—
451C2×C4—184no—
452C2×C4—241no—
453C2×C4—242no—
454C2×C4—722no—
455C2×C4—722no—
456C2×C4(C2×D3)⋊Dic312yes—
457C2×C3—22no—
458C2×C3—22no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—22no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—22no—
466C2×C3—22no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—41no—
470C2×C3—41no—
471C2×C3—42no—
472C2×C3—42no—
473C2×C3—44no—
474C2×C3—42no—
475C2×C3—42no—
476C2×C3—241no—
477C2×C3#495811yescharacteristic
478C2×C3#522011yescharacteristic
479D3—81no—
480C22—22no—
481C22—42no—
482C22—41no—
483C22—42no—
484C22—41no—
485C22—41no—
486C22—42no—
487C22—42no—
488C22—81no—
489C22—122no—
490C22—121no—
491C22—242no—
492C22C2×(C2×D3)⋊Dic311yescharacteristic
493C22#6396211yescharacteristic
494C22#67⋊Dic312yes—
495C22#6398012yes—
496C22#6398111yescharacteristic
497C4—22no—
498C4—122no—
499C4—121no—
500C4—242no—
501C4—364no—
502C3—21no—
503C3#7002411yescharacteristic, complemented
504C3#7184811yescharacteristic, complemented
505C2—21no—
506C2—22no—
507C2—21no—
508C2—21no—
509C2—22no—
510C2—42no—
511C2—241no—
512C2#1059171311yescharacteristic
subgroupG/H
centerC2#10591713
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC22×C32×D4C22
socleC2×C32#386
prime radicalC3×#5804C2
cosocleC24×C32C23
hypercenterC22×D4D32
hypocenterC32#1913
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #10596269C2semidirect
3. C2×C3×#834C2semidirect
4. C2×#63580C2semidirect
5. #10589186C2semidirect
18. C3×#937C4semidirect
19. C3×#935C4semidirect
30. C2×#834D3semidirect
36. C23×C3×D3C2×C4semidirect
51. C22×C3×Dic3C2×C4semidirect
54. #3757D4semidirect
61. C3×#217C2×C4semidirect
87. #937Dic3semidirect
88. #935Dic3semidirect
143. C23×D3C2×Dic3semidirect
180. C22×Dic3C2×Dic3semidirect
201. #217C2×Dic3semidirect
425. C32#1913semidirect
503. C3#70024semidirect
504. C3#71848semidirect

Maximal subgroups

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

subgroupindex
#105962692
C3×#58042
C2×C3×#8342
C2×#635802
#105891862
#718483
#700243