Finite Group Databasebeta

← #11865442

Subgroups — #11865442

Order 1152.

1509 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#63926C212yesmaximal, complemented
3#10594008C211yesmaximal, characteristic, complemented
4C3×#5015C212yesmaximal, complemented
5#10591486C212yesmaximal, complemented
6#10590593C212yesmaximal, complemented
7#10590551C212yesmaximal, complemented
8#10590355C212yesmaximal, complemented
9#10590331C211yesmaximal, characteristic, complemented
10D3×#459—32nomaximal
11C2×D4×C3⋊D3C2211yescharacteristic
12C22×C4×C3⋊D3—21no—
13C2×#3802—21no—
14C2×#3802—21no—
15C2×#3802C2212yes—
16C32×C4×D4C2211yescharacteristic, complemented
17D4×C3⋊Dic3C2211yescharacteristic, complemented
18C4×#638—21no—
19#64102C2211yescharacteristic, complemented
20C4⋊C4×C3⋊D3C2211yescharacteristic
21#64090—21no—
22C22⋊C4×C3⋊D3—21no—
23C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
24C42×C3⋊D3C2211yescharacteristic
25C2×C3×#213C2214yescomplemented
26C3×#874C2212yescomplemented
27#63926—28no—
28#63914—21no—
29#63914—21no—
30#63914C2212yescomplemented
31C2×#3714C2214yescomplemented
32C2×#3710C2212yes—
33C3×#809C2214yescomplemented
34C3×C4⋊(C3⋊C8)C2212yescomplemented
35#63572C2212yescomplemented
36#63563C2214yescomplemented
37C2×D3×D8—34no—
38D3×#127—32no—
39C4×D3×D4—32no—
40C4×D3×D4—61no—
41C3×#459—32no—
42#5150—34no—
43#5072—32no—
44#5015D312yescomplemented
45#4843—32no—
46D3×C4⋊C8—32no—
47#4786—34no—
48D3×#102—34no—
49C23×C3⋊D3—21no—
50C22×D32—22no—
51C2×C32×D4C2311yescharacteristic
52C22×C32×C4—21no—
53C2×#638—21no—
54C22×C3⋊Dic3—21no—
55D4×C3⋊D3—22no—
56D4×C3⋊D3D414yescomplemented
57C2×C4⋊(C3⋊D3)C2311yescharacteristic
58C2×C4×C3⋊D3—21no—
59C2×C4×C3⋊D3—21no—
60C2×C4×C3⋊D3—21no—
61C2×C4×C3⋊D3—44no—
62C2×C4×C3⋊D3D411yescharacteristic
63C2×C4×C3⋊D3D411yescharacteristic
64C2×C4×C3⋊D3C2311yescharacteristic
65C2×C3×D12—22no—
66C2×C3×D12—22no—
67C2×C3×D12C2314yes—
68C2×#625—22no—
69C2×#625—22no—
70C2×#625—22no—
71#3802—24no—
72#3802—24no—
73#3802—44no—
74#3802—44no—
75C32×C4⋊C4C2311yescharacteristic
76C32×C22⋊C4—21no—
77C32×C42C2311yescharacteristic
78#3757—21no—
79#3752—21no—
80#3752—21no—
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82#3750—21no—
83C4×C3⋊Dic3D411yescharacteristic
84C4×C3⋊Dic3D411yescharacteristic
85C4×C3⋊Dic3C2311yescharacteristic
86C3×#213—28no—
87C2×C3×C3⋊C8C2314yes—
88#3714—28no—
89#3710—24no—
90C2×#459—91noSylow
91C2×D3×D4—32no—
92C2×D3×D4—34no—
93C2×D3×D4—61no—
94C2×D3×D4—62no—
95C2×D3×D4—62no—
96C22×C4×D3—62no—
97C22×C4×D3—62no—
98C2×C3×D8—34no—
99C3×#127—32no—
100C3×C4×D4—21no—
101C3×C4×D4C2×D312yescomplemented
102#940—34no—
103#940—62no—
104#940—62no—
105D4×Dic3—32no—
106D4×Dic3—61no—
107C2×#213—34no—
108C2×#213C2×D314yescomplemented
109C4×#67—62no—
110C4×#67—62no—
111D3×D8—616no—
112C2×D24—34no—
113C2×D3×C8—34no—
114#893—32no—
115#893—61no—
116D3×C4⋊C4—32no—
117D3×C4⋊C4—61no—
118#67⋊C4—62no—
119#67⋊C4—62no—
120D3×C22⋊C4—62no—
121D3×C22⋊C4—62no—
122#874C2×D312yescomplemented
123C4×D12—32no—
124C4×D12—61no—
125C42×D3—32no—
126C42×D3—61no—
127C3×C4⋊C8—32no—
128C3×#102—34no—
129#832—34no—
130#821—34no—
131Dic3⋊C8—34no—
132#809C2×D314yescomplemented
133C4⋊(C3⋊C8)C2×D312yescomplemented
134C23×C32—21no—
135C22×C3⋊D3—21no—
136C22×C3⋊D3—24no—
137C22×C3⋊D3—42no—
138C22×C3⋊D3—42no—
139C22×C3⋊D3C2×D411yescharacteristic
140C22×C3×D3—24no—
141C2×D32—44no—
142C2×D32—44no—
143C2×D32—44no—
144C32×D4—21no—
145C32×D4C2×D412yescomplemented
146C2×C32×C4—21no—
147C2×C32×C4—42no—
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2411yescharacteristic
151#638—24no—
152C2×C3⋊Dic3—21no—
153C2×C3⋊Dic3—42no—
154C2×C3⋊Dic3C2×D411yescharacteristic
155C2×C3⋊Dic3C2×D411yescharacteristic
156C2×C3⋊Dic3C2×D411yescharacteristic
157C4⋊(C3⋊D3)—21no—
158C4⋊(C3⋊D3)C2×D412yescomplemented
159C4×C3⋊D3—22no—
160C4×C3⋊D3—42no—
161C4×C3⋊D3—42no—
162C4×C3⋊D3—42no—
163C4×C3⋊D3D814yescomplemented
164C4×C3⋊D3C2×D412yes—
165C4×C3⋊D3#4112yes—
166C3×D12—24no—
167C3×D12—24no—
168C3×D12—44no—
169C3×D12—44no—
170#625—44no—
171#625—44no—
172#625—44no—
173C3×C3⋊C8—24no—
174C22×D8—92no—
175C2×#127—91no—
176C2×C4×D4—91no—
177#459—32no—
178#459—92no—
179#459—92no—
180#459—92no—
181C2×C4⋊C8—91no—
182C2×#102—92no—
183C23×D3—64no—
184C23×D3—62no—
185C23×D3—62no—
186C2×C3×D4—21no—
187C2×C3×D4—34no—
188C2×C3×D4—62no—
189C2×C3×D4—62no—
190C2×C3×D4C22×D312yes—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C2×#67—62no—
194C2×#67—64no—
195C2×#67—64no—
196C2×#67—64no—
197C2×#67—62no—
198C22×Dic3—62no—
199C22×Dic3—62no—
200D3×D4—38no—
201D3×D4—64no—
202D3×D4—68no—
203D3×D4—68no—
204D3×D4—64no—
205D3×D4—64no—
206D3×D4—128no—
207D3×D4—128no—
208C2×D12—22no—
209C2×D12—22no—
210C2×D12—32no—
211C2×D12—61no—
212C2×D12C22×D314yes—
213C2×C4×D3—32no—
214C2×C4×D3—32no—
215C2×C4×D3—32no—
216C2×C4×D3—61no—
217C2×C4×D3—61no—
218C2×C4×D3—61no—
219C2×C4×D3—62no—
220C2×C4×D3—62no—
221C2×C4×D3—62no—
222C2×C4×D3—62no—
223C2×C4×D3—62no—
224C2×C4×D3—62no—
225C2×C4×D3—128no—
226C2×C4×D3—128no—
227C3×D8—68no—
228C2×C3×C8—34no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4C22×D312yes—
231C3×C22⋊C4—22no—
232C3×C22⋊C4—22no—
233C3×C42—21no—
234C3×C42C22×D312yes—
235#217—62no—
236#217—62no—
237#213—28no—
238#213—68no—
239(C2×D3)⋊C4—62no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—62no—
242(C2×D3)⋊C4—62no—
243C4⋊Dic3—32no—
244C4⋊Dic3—61no—
245Dic3⋊C4—62no—
246Dic3⋊C4—62no—
247C4×Dic3—32no—
248C4×Dic3—32no—
249C4×Dic3—32no—
250C4×Dic3—61no—
251C4×Dic3—61no—
252C4×Dic3—61no—
253C2×C3⋊C8C22×D314yes—
254D24—68no—
255D3×C8—68no—
256C22×C32—22no—
257C22×C32—41no—
258C22×C32—41no—
259C22×C32C22×D411yescharacteristic
260C2×C3⋊D3—22no—
261C2×C3⋊D3—41no—
262C2×C3⋊D3—41no—
263C2×C3⋊D3—48no—
264C2×C3⋊D3#12112yes—
265C2×C3⋊D3C2×D812yes—
266C2×C3⋊D3AGL(1,ℤ/8)12yes—
267C2×C3×D3—44no—
268C2×C3×D3—44no—
269C2×C3×D3—44no—
270D32—88no—
271C32×C4—21no—
272C32×C4—41no—
273C32×C4C2×D812yescomplemented
274C32×C4C22×D411yescharacteristic
275C32×C4C2×#4111yescharacteristic
276C3⋊Dic3—21no—
277C3⋊Dic3—41no—
278C3⋊Dic3#12112yes—
279C3⋊Dic3C2×D812yescomplemented
280C22×D4—92no—
281C22×D4—91no—
282C22×D4—181no—
283C22×D4—181no—
284C23×C4—181no—
285C2×D8—34no—
286C2×D8—94no—
287C2×D8—188no—
288C22×C8—92no—
289#127—32no—
290#127—92no—
291#127—181no—
292#127—181no—
293C4×D4—91no—
294C4×D4—91no—
295C4×D4—91no—
296C4×D4—181no—
297C4×D4—181no—
298C4×D4D3211yescharacteristic, complemented
299C2×C4⋊C4—91no—
300C2×C22⋊C4—181no—
301C2×C42—91no—
302C4⋊C8—32no—
303C4⋊C8—92no—
304#102—34no—
305#102—94no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—64no—
309C22×D3—24no—
310C22×D3—32no—
311C22×D3—61no—
312C22×D3—68no—
313C22×D3—62no—
314C22×D3—68no—
315C22×D3—62no—
316C22×D3—128no—
317C22×D3—128no—
318C22×D3—128no—
319C22×D3—124no—
320C22×D3—124no—
321C22×D3—124no—
322C22×D3—124no—
323C3×D4—22no—
324C3×D4—22no—
325C3×D4—22no—
326C3×D4—64no—
327C3×D4—64no—
328C3×D4—124no—
329C3×D4—124no—
330C3×D4D3×D414yescomplemented
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—44no—
337C2×C3×C4—44no—
338C2×C3×C4D3×D412yes—
339C2×C3×C4D3×D412yes—
340C2×C3×C4C23×D312yes—
341#67—68no—
342#67—68no—
343#67—128no—
344#67—128no—
345#67—128no—
346C2×Dic3—32no—
347C2×Dic3—32no—
348C2×Dic3—32no—
349C2×Dic3—61no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—124no—
355C2×Dic3—124no—
356D12—24no—
357D12—24no—
358D12—34no—
359D12—44no—
360D12—44no—
361D12—62no—
362D12—62no—
363D12—62no—
364C4×D3—38no—
365C4×D3—34no—
366C4×D3—34no—
367C4×D3—64no—
368C4×D3—62no—
369C4×D3—62no—
370C4×D3—64no—
371C4×D3—122no—
372C4×D3—124no—
373C4×D3—124no—
374C4×D3—124no—
375C4×D3—124no—
376C4×D3—124no—
377C4×D3—124no—
378C3×C8—64no—
379C3⋊C8—24no—
380C2×C32—42no—
381C2×C32C2×#12111yescharacteristic
382C2×C32C22×D811yescharacteristic
383C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
384C3⋊D3—42no—
385C3⋊D3#45914yescomplemented
386C3×D3—84no—
387C24—181no—
388C24—182no—
389C2×D4—34no—
390C2×D4—62no—
391C2×D4—62no—
392C2×D4—94no—
393C2×D4—91no—
394C2×D4—182no—
395C2×D4—184no—
396C2×D4—184no—
397C2×D4—181no—
398C2×D4—182no—
399C2×D4—182no—
400C2×D4—182no—
401C2×D4—364no—
402C2×D4—364no—
403C2×D4C2×D3211yescharacteristic
404C22×C4—21no—
405C22×C4—91no—
406C22×C4—91no—
407C22×C4—91no—
408C22×C4—181no—
409C22×C4—181no—
410C22×C4—181no—
411C22×C4—181no—
412C22×C4—364no—
413D8—68no—
414D8—188no—
415C2×C8—34no—
416C2×C8—184no—
417C4⋊C4—91no—
418C4⋊C4—181no—
419C4⋊C4C2×D3211yescharacteristic
420C22⋊C4—21no—
421C22⋊C4—181no—
422C22⋊C4—181no—
423C22⋊C4—181no—
424C42—91no—
425C42—91no—
426C42—91no—
427C42C2×D3211yescharacteristic
428C22×C3—24no—
429C22×C3—24no—
430C22×C3—21no—
431C22×C3—42no—
432C22×C3—42no—
433C22×C3—42no—
434C22×C3—42no—
435C22×C3—124no—
436C22×C3—124no—
437C22×C3—124no—
438C22×C3C2×D3×D412yes—
439C2×D3—34no—
440C2×D3—34no—
441C2×D3—34no—
442C2×D3—44no—
443C2×D3—44no—
444C2×D3—44no—
445C2×D3—62no—
446C2×D3—62no—
447C2×D3—62no—
448C2×D3—64no—
449C2×D3—64no—
450C2×D3—1216no—
451C2×D3—1216no—
452C2×D3—122no—
453C2×D3—122no—
454C2×D3—122no—
455C2×D3—122no—
456C2×D3—2416no—
457C3×C4—22no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—22no—
461C3×C4—41no—
462C3×C4—42no—
463C3×C4—42no—
464C3×C4D3×D814yescomplemented
465C3×C4C2×D3×D412yes—
466C3×C4D3×#4112yes—
467Dic3—34no—
468Dic3—34no—
469Dic3—62no—
470Dic3—62no—
471Dic3—62no—
472Dic3—121no—
473Dic3—122no—
474Dic3—122no—
475C32C2×#45911yescharacteristic, complemented, Sylow
476C23—21no—
477C23—64no—
478C23—91no—
479C23—184no—
480C23—181no—
481C23—362no—
482C23—362no—
483C23—364no—
484C23—364no—
485C23—364no—
486D4—21no—
487D4—64no—
488D4—64no—
489D4—92no—
490D4—124no—
491D4—124no—
492D4—184no—
493D4—181no—
494D4—364no—
495D4—364no—
496D4—364no—
497D4#380212yescomplemented
498C2×C4—21no—
499C2×C4—42no—
500C2×C4—91no—
501C2×C4—91no—
502C2×C4—92no—
503C2×C4—92no—
504C2×C4—94no—
505C2×C4—91no—
506C2×C4—182no—
507C2×C4—181no—
508C2×C4—362no—
509C2×C4—362no—
510C2×C4—362no—
511C2×C4—362no—
512C2×C4#381111yescharacteristic
513C2×C4#381111yescharacteristic
514C2×C4C22×D3211yescharacteristic
515C8—64no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—44no—
520C2×C3—44no—
521C2×C3—244no—
522C2×C3D3×#12112yes—
523C2×C3C2×D3×D812yes—
524C2×C3D3×AGL(1,ℤ/8)12yes—
525D3—38no—
526D3—64no—
527D3—84no—
528D3—124no—
529D3—124no—
530C22—22no—
531C22—41no—
532C22—41no—
533C22—92no—
534C22—92no—
535C22—92no—
536C22—124no—
537C22—124no—
538C22—124no—
539C22—182no—
540C22—368no—
541C22—361no—
542C22—361no—
543C22—728no—
544C22C2×#381111yescharacteristic
545C4—21no—
546C4—41no—
547C4—92no—
548C4—92no—
549C4—181no—
550C4—361no—
551C4#6392612yescomplemented
552C4C2×#380211yescharacteristic
553C4#6430611yescharacteristic
554C3—21no—
555C3D3×#45912yescomplemented
556C2—42no—
557C2—94no—
558C2—244no—
559C2—362no—
560C2#1059508111yescharacteristic
561C2C2×#6392611yescharacteristic
562C2#1059545811yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32C2×#459
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C4×D4×C3⋊D3C2semidirect
2. C2×#63926C2semidirect
3. #10594008C2semidirect
4. C3×#5015C2semidirect
5. #10591486C2semidirect
6. #10590593C2semidirect
7. #10590551C2semidirect
8. #10590355C2semidirect
9. #10590331C2semidirect
16. C32×C4×D4C22semidirect
17. D4×C3⋊Dic3C22semidirect
19. #64102C22semidirect
23. C4×C4⋊(C3⋊D3)C22semidirect
25. C2×C3×#213C22semidirect
26. C3×#874C22semidirect
30. #63914C22semidirect
31. C2×#3714C22semidirect
33. C3×#809C22semidirect
34. C3×C4⋊(C3⋊C8)C22semidirect
35. #63572C22semidirect
36. #63563C22semidirect
44. #5015D3semidirect
56. D4×C3⋊D3D4semidirect
101. C3×C4×D4C2×D3semidirect
108. C2×#213C2×D3semidirect
122. #874C2×D3semidirect
132. #809C2×D3semidirect
133. C4⋊(C3⋊C8)C2×D3semidirect
145. C32×D4C2×D4semidirect
158. C4⋊(C3⋊D3)C2×D4semidirect
163. C4×C3⋊D3D8semidirect
273. C32×C4C2×D8semidirect
279. C3⋊Dic3C2×D8semidirect
298. C4×D4D32semidirect
330. C3×D4D3×D4semidirect
385. C3⋊D3#459semidirect
464. C3×C4D3×D8semidirect
475. C32C2×#459semidirect
497. D4#3802semidirect
551. C4#63926semidirect
555. C3D3×#459semidirect

Maximal subgroups

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

subgroupindex
C4×D4×C3⋊D32
C2×#639262
#105940082
C3×#50152
#105914862
#105905932
#105905512
#105903552
#105903312
D3×#4593