Finite Group Databasebeta

← #11866207

Subgroups — #11866207

Order 1152.

1219 conjugacy classes of subgroups.

The subgroup lattice has 553 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596301C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic, complemented
3#10594982C211yesmaximal, characteristic, complemented
4C22×#3714C211yesmaximal, characteristic, complemented
5C3×#5233C211yesmaximal, characteristic, complemented
6#10591570C214yesmaximal, complemented
7#10591433C214yesmaximal, complemented
8#10591119C211yesmaximal, characteristic, complemented
9#10591096C211yesmaximal, characteristic, complemented
10#83934—31nomaximal
11#78862—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15#64156C2212yescomplemented
16#64149C2212yescomplemented
17#64146—22no—
18#64139—22no—
19#64135C2211yescharacteristic
20C3×#949—24no—
21C2×C3×#215C2212yescomplemented
22C2×C3×#213C2212yescomplemented
23C3×#926C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26D3×#217—22no—
27#63898C2214yescomplemented
28Dic3×D12—22no—
29C2×#3714—24no—
30C2×#3714C2214yes—
31C3×#835C2212yescomplemented
32C3×#832C2212yescomplemented
33#63572C2214yescomplemented
34#63564C2214yescomplemented
35C2×C3×AGL(1,ℤ/8)—31no—
36#5830—31no—
37#5830—31no—
38#5830—61no—
39C2×#949D311yescharacteristic, complemented
40#5798—31no—
41C22×#213—31no—
42C22×D24—31no—
43#5521—31no—
44C3×#416—31no—
45#5233D311yescharacteristic, complemented
46#5165—34no—
47#5150—34no—
48#5131—31no—
49#5119—31no—
50#5102—31no—
51#5001—31no—
52#4819—34no—
53#4786—34no—
54C23×C3⋊D3—21no—
55C23×C3×D3—21no—
56C32×#41—22no—
57C32×#41—22no—
58C2×C32×Q8C2311yescharacteristic
59C2×C32×D4—21no—
60C2×C32×D4C2311yescharacteristic
61C22×C32×C4—21no—
62C22×C32×C4C2311yescharacteristic
63C2×#638—24no—
64C2×C4⋊(C3⋊D3)—22no—
65C2×C4⋊(C3⋊D3)—22no—
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)C2312yes—
68C2×C3×D12—21no—
69C2×C3×D12—22no—
70C2×C3×D12D414yescomplemented
71C2×C3×D12C2312yes—
72C2×D3×Dic3—24no—
73#3757D412yes—
74#3752—24no—
75C4⋊(C3⋊Dic3)D412yes—
76C4×C3⋊Dic3C2312yes—
77C3×#217—21no—
78C3×#215—24no—
79C3×#213—24no—
80C3×C4⋊Dic3C2312yes—
81C3×C4×Dic3—21no—
82C3×#208—22no—
83C2×C3×C3⋊C8—22no—
84C2×C3×C3⋊C8C2312yes—
85C2×C3×C3⋊C8C2312yes—
86(C2×D3)⋊Dic3—24no—
87#3714—28no—
88#3041—91noSylow
89C2×C3×#41—21no—
90C2×C3×#41C2×D311yescharacteristic
91C2×C3×#41C2×D311yescharacteristic
92C22×C3×D4—31no—
93C22×D12—31no—
94C22×D12—31no—
95C22×D12—61no—
96C22×D12C2×D311yescharacteristic
97C3×AGL(1,ℤ/8)—64no—
98C2×C3×SD16—32no—
99C2×C3×D8—32no—
100C2×C3×M16—31no—
101C22×C3×C8—31no—
102C3×#117—31no—
103C2×#217—62no—
104#949—24no—
105#947—32no—
106#947—32no—
107#947—62no—
108C2×#215C2×D312yescomplemented
109#940—32no—
110#940—32no—
111#940—62no—
112#937—62no—
113#937—62no—
114#937—64no—
115D4×Dic3—34no—
116D4×Dic3—62no—
117C2×#213—34no—
118C2×#213—64no—
119C2×#213C2×D312yescomplemented
120#930—62no—
121#930—62no—
122#930—64no—
123#926—31no—
124#926—31no—
125#926—61no—
126#926C2×D311yescharacteristic
127C2×#208C2×D311yescharacteristic
128C22×C3⋊C8C2×D311yescharacteristic
129C2×D24—34no—
130C2×D24—64no—
131#893—34no—
132D3×C22⋊C4—62no—
133C4×D12—62no—
134C3×#103—32no—
135C3×#102—32no—
136#835C2×D312yescomplemented
137#832C2×D312yescomplemented
138#821—34no—
139Dic3⋊C8—34no—
140Dic3⋊C8—34no—
141#809—34no—
142C23×C32—21no—
143C23×C32C2×D411yescharacteristic
144C22×C3⋊D3—22no—
145C22×C3⋊D3—42no—
146C22×C3⋊D3—82no—
147C22×C3×D3—22no—
148C22×C3×D3—24no—
149C22×C3×D3—82no—
150C32×Q8—21no—
151C32×Q8—21no—
152C32×D4—21no—
153C32×D4—21no—
154C32×D4—42no—
155C2×C32×C4—21no—
156C2×C32×C4—42no—
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2×D412yes—
159C2×C32×C4#4112yes—
160C2×C32×C4C2411yescharacteristic
161#638—84no—
162C2×C3⋊Dic3C2×D414yes—
163C4⋊(C3⋊D3)—22no—
164C4⋊(C3⋊D3)—22no—
165C4⋊(C3⋊D3)—42no—
166C2×C3×Dic3—22no—
167C3×D12—24no—
168C3×D12—22no—
169C3×D12C2×D414yes—
170D3×Dic3—84no—
171C3×C3⋊C8—22no—
172C3×C3⋊C8—22no—
173C2×AGL(1,ℤ/8)—31no—
174C22×D8—91no—
175#535—91no—
176#518—91no—
177#463—94no—
178#459—94no—
179#424—91no—
180#418—91no—
181#416—31no—
182C24×C3—61no—
183C23×D3—21no—
184C23×D3—62no—
185C23×D3—61no—
186C23×D3—61no—
187C3×#41—22no—
188C3×#41—22no—
189C3×#41—22no—
190C3×#41—22no—
191C3×#41—42no—
192C3×#41—42no—
193C2×C3×Q8—21no—
194C2×C3×Q8C22×D311yescharacteristic
195C2×C3×Q8C22×D311yescharacteristic
196C2×C3×D4—22no—
197C2×C3×D4—21no—
198C2×C3×D4—21no—
199C2×C3×D4—21no—
200C2×C3×D4—34no—
201C2×C3×D4—32no—
202C2×C3×D4—62no—
203C2×C3×D4—61no—
204C2×C3×D4C22×D311yescharacteristic
205C2×C3×D4C22×D311yescharacteristic
206C22×C3×C4—22no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C2×#67—64no—
213C2×#67—64no—
214C2×#67—68no—
215C22×Dic3—64no—
216C2×D12—21no—
217C2×D12—22no—
218C2×D12—32no—
219C2×D12—32no—
220C2×D12—62no—
221C2×D12—62no—
222C2×D12—62no—
223C2×D12—62no—
224C2×D12—62no—
225C2×D12—62no—
226C2×D12—61no—
227C2×D12—61no—
228C2×D12—122no—
229C2×D12—122no—
230C2×D12#6714yescomplemented
231C2×D12C22×D312yes—
232C2×C4×D3—64no—
233C3×SD16—64no—
234C3×D8—64no—
235C3×M16—62no—
236C2×C3×C8—32no—
237C2×C3×C8—32no—
238C2×C3×C8—62no—
239C3×C4⋊C4—32no—
240C3×C22⋊C4—61no—
241C3×C42—61no—
242#217—21no—
243#217—32no—
244#217—32no—
245#217—62no—
246#217—64no—
247#215—24no—
248#213—24no—
249#213—68no—
250(C2×D3)⋊C4—64no—
251(C2×D3)⋊C4—64no—
252(C2×D3)⋊C4—64no—
253(C2×D3)⋊C4—68no—
254C4⋊Dic3—32no—
255C4⋊Dic3—32no—
256C4⋊Dic3—62no—
257C4⋊Dic3C22×D312yes—
258C4×Dic3—21no—
259C4×Dic3—32no—
260C4×Dic3—32no—
261C4×Dic3—62no—
262#208—22no—
263C2×C3⋊C8—22no—
264C2×C3⋊C8C22×D312yes—
265C2×C3⋊C8C22×D312yes—
266D24—68no—
267C22×C32—22no—
268C22×C32—41no—
269C22×C32—42no—
270C22×C32#12112yes—
271C22×C32C22×D411yescharacteristic
272C2×C3⋊D3—42no—
273C2×C3⋊D3—44no—
274C2×C3⋊D3—84no—
275C2×C3×D3—24no—
276C2×C3×D3—44no—
277C2×C3×D3—84no—
278C32×C4—41no—
279C32×C4#12112yes—
280C32×C4C22×D411yescharacteristic
281C32×C4C2×#4111yescharacteristic
282C3⋊Dic3—24no—
283C3×Dic3—42no—
284C2×#41D3211yescharacteristic
285C22×D4—31no—
286C22×D4—91no—
287AGL(1,ℤ/8)—64no—
288C2×SD16—32no—
289C2×D8—32no—
290C2×D8—94no—
291C2×D8—184no—
292C2×M16—31no—
293C22×C8—31no—
294#127—92no—
295#124—92no—
296#121—182no—
297#120—182no—
298C4×D4—94no—
299C4×D4—182no—
300#117—31no—
301#117—91no—
302C2×C22⋊C4—182no—
303C4⋊C8—94no—
304#103—32no—
305#102—32no—
306#102—94no—
307C23×C3—22no—
308C23×C3—21no—
309C23×C3—21no—
310C23×C3—21no—
311C23×C3—62no—
312C23×C3—64no—
313C23×C3—242no—
314C23×C3D3×D411yescharacteristic
315C23×C3D3×D411yescharacteristic
316C22×D3—22no—
317C22×D3—24no—
318C22×D3—64no—
319C22×D3—62no—
320C22×D3—62no—
321C22×D3—82no—
322C22×D3—124no—
323C22×D3—122no—
324C22×D3—122no—
325C22×D3—242no—
326C22×D3—242no—
327C22×D3—244no—
328C3×Q8—21no—
329C3×Q8—21no—
330C3×Q8—21no—
331C3×Q8—21no—
332C3×Q8—41no—
333C3×Q8—41no—
334C3×D4—21no—
335C3×D4—21no—
336C3×D4—21no—
337C3×D4—21no—
338C3×D4—34no—
339C3×D4—41no—
340C3×D4—41no—
341C3×D4—44no—
342C3×D4—42no—
343C3×D4—42no—
344C3×D4—64no—
345C3×D4—62no—
346C2×C3×C4—22no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—21no—
353C2×C3×C4—44no—
354C2×C3×C4—42no—
355C2×C3×C4—42no—
356C2×C3×C4—62no—
357C2×C3×C4#23512yes—
358C2×C3×C4D3×D412yes—
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4#23712yes—
362C2×C3×C4C2×#6712yes—
363C2×C3×C4C23×D311yescharacteristic
364C2×C3×C4C23×D311yescharacteristic
365#67—244no—
366#67—244no—
367#67—248no—
368C2×Dic3—22no—
369C2×Dic3—34no—
370C2×Dic3—34no—
371C2×Dic3—64no—
372C2×Dic3—244no—
373D12—24no—
374D12—22no—
375D12—62no—
376D12—62no—
377D12—62no—
378D12—62no—
379D12—122no—
380D12—122no—
381D12—124no—
382D12—122no—
383D12—122no—
384D12C2×#6714yes—
385C4×D3—244no—
386C3×C8—62no—
387C3×C8—62no—
388C3⋊C8—22no—
389C3⋊C8—22no—
390C2×C32—22no—
391C2×C32—81no—
392C2×C32C2×#12111yescharacteristic
393C2×C32#57612yes—
394C3⋊D3—82no—
395C3×D3—44no—
396C24—61no—
397C24—181no—
398#41—22no—
399#41—22no—
400C2×Q8C2×D3211yescharacteristic
401C2×D4—21no—
402C2×D4—32no—
403C2×D4—34no—
404C2×D4—62no—
405C2×D4—61no—
406C2×D4—92no—
407C2×D4—184no—
408C2×D4—182no—
409C2×D4—182no—
410C2×D4—181no—
411C2×D4C2×D3211yescharacteristic
412C22×C4—21no—
413C22×C4—184no—
414C22×C4C2×D3211yescharacteristic
415SD16—64no—
416D8—64no—
417D8—188no—
418M16—62no—
419C2×C8—32no—
420C2×C8—32no—
421C2×C8—62no—
422C4⋊C4—32no—
423C4⋊C4—92no—
424C22⋊C4—61no—
425C22⋊C4—92no—
426C22⋊C4—184no—
427C22⋊C4—184no—
428C42—61no—
429C42—92no—
430C22×C3—22no—
431C22×C3—22no—
432C22×C3—21no—
433C22×C3—22no—
434C22×C3—42no—
435C22×C3—44no—
436C22×C3—42no—
437C22×C3—41no—
438C22×C3—42no—
439C22×C3—42no—
440C22×C3—41no—
441C22×C3—64no—
442C22×C3—124no—
443C22×C3—244no—
444C22×C3#88412yes—
445C22×C3#93912yes—
446C22×C3C2×D3×D411yescharacteristic
447C22×C3C2×D3×D411yescharacteristic
448C2×D3—24no—
449C2×D3—44no—
450C2×D3—84no—
451C2×D3—124no—
452C2×D3—128no—
453C2×D3—122no—
454C2×D3—124no—
455C2×D3—124no—
456C2×D3—122no—
457C2×D3—244no—
458C2×D3—244no—
459C2×D3—248no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—22no—
463C3×C4—42no—
464C3×C4—41no—
465C3×C4—41no—
466C3×C4—122no—
467C3×C4#88412yes—
468C3×C4#93912yes—
469C3×C4C2×#23511yescharacteristic
470C3×C4C2×D3×D411yescharacteristic
471C3×C4C2×#23711yescharacteristic
472C3×C4C22×#6711yescharacteristic
473Dic3—42no—
474Dic3—64no—
475Dic3—64no—
476Dic3—124no—
477C32#304111yescharacteristic, complemented, Sylow
478C23—21no—
479C23—62no—
480C23—64no—
481C23—182no—
482C23—242no—
483C23—362no—
484C23—722no—
485C23#381111yescharacteristic
486Q8—21no—
487Q8—21no—
488D4—21no—
489D4—21no—
490D4—34no—
491D4—42no—
492D4—62no—
493D4—64no—
494D4—182no—
495D4—182no—
496D4—362no—
497D4—724no—
498C2×C4—21no—
499C2×C4—42no—
500C2×C4—62no—
501C2×C4—94no—
502C2×C4—724no—
503C2×C4#380412yes—
504C2×C4D3×#6712yes—
505C2×C4#381111yescharacteristic
506C2×C4C22×D3211yescharacteristic
507C8—62no—
508C8—62no—
509C2×C3—22no—
510C2×C3—22no—
511C2×C3—22no—
512C2×C3—21no—
513C2×C3—42no—
514C2×C3—82no—
515C2×C3—81no—
516C2×C3—81no—
517C2×C3—124no—
518C2×C3C2×#88411yescharacteristic
519C2×C3#576912yes—
520C2×C3#577412yes—
521C2×C3C2×#93911yescharacteristic
522D3—44no—
523D3—244no—
524D3—242no—
525D3—242no—
526C22—22no—
527C22—42no—
528C22—41no—
529C22—64no—
530C22—124no—
531C22—244no—
532C22—364no—
533C22—362no—
534C22—724no—
535C22#6397112yes—
536C22C2×#381111yescharacteristic
537C4—41no—
538C4—122no—
539C4—184no—
540C4#6397112yes—
541C4C2×#380411yescharacteristic
542C4C2×D3×#6711yescharacteristic
543C3—21no—
544C3#7886211yescharacteristic, complemented
545C3#8393411yescharacteristic, complemented
546C2—22no—
547C2—81no—
548C2—124no—
549C2—722no—
550C2#1059546112yes—
551C2C2×#6397111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3041
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #10596301C2semidirect
2. C2×C3×#949C2semidirect
3. #10594982C2semidirect
4. C22×#3714C2semidirect
5. C3×#5233C2semidirect
6. #10591570C2semidirect
7. #10591433C2semidirect
8. #10591119C2semidirect
9. #10591096C2semidirect
15. #64156C22semidirect
16. #64149C22semidirect
21. C2×C3×#215C22semidirect
22. C2×C3×#213C22semidirect
27. #63898C22semidirect
31. C3×#835C22semidirect
32. C3×#832C22semidirect
33. #63572C22semidirect
34. #63564C22semidirect
39. C2×#949D3semidirect
45. #5233D3semidirect
70. C2×C3×D12D4semidirect
108. C2×#215C2×D3semidirect
119. C2×#213C2×D3semidirect
136. #835C2×D3semidirect
137. #832C2×D3semidirect
230. C2×D12#67semidirect
477. C32#3041semidirect
544. C3#78862semidirect
545. C3#83934semidirect

Maximal subgroups

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

subgroupindex
#105963012
C2×C3×#9492
#105949822
C22×#37142
C3×#52332
#105915702
#105914332
#105911192
#105910962
#839343
#788623