Finite Group Databasebeta

← #11866216

Subgroups — #11866216

Order 1152.

1109 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#908C211yesmaximal, characteristic, complemented
2#10595040C211yesmaximal, characteristic, complemented
3#10594982C211yesmaximal, characteristic, complemented
4C22×#3713C211yesmaximal, characteristic, complemented
5#10592818C211yesmaximal, characteristic, complemented
6C3×#5131C211yesmaximal, characteristic, complemented
7#10591083C211yesmaximal, characteristic, complemented
8#10590750C214yesmaximal, complemented
9#10590749C214yesmaximal, complemented
10#83934—31nomaximal
11#78944—31nomaximal
12C2×C3×#235C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16#64135C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C3×#908—24no—
20C2×C3×D24C2212yescomplemented
21C2×C3×#204C2212yescomplemented
22#63976—22no—
23D3×#217—22no—
24#63914C2212yescomplemented
25#63908—22no—
26#63898C2214yescomplemented
27Dic3×D12—22no—
28#63863C2212yescomplemented
29C2×#3713—24no—
30C2×#3713C2214yes—
31#63641C2214yescomplemented
32C3×#821C2214yescomplemented
33#63565C2212yescomplemented
34#63562C2212yescomplemented
35C2×C3×AGL(1,ℤ/8)—31no—
36#5830—31no—
37#5805—31no—
38#5798—31no—
39C22×#213—31no—
40C22×#213—31no—
41C2×#908D311yescharacteristic, complemented
42#5521—31no—
43C3×#418—31no—
44#5233—31no—
45#5165—34no—
46#5150—34no—
47#5131D311yescharacteristic, complemented
48#5119—31no—
49#5119—31no—
50#5119—61no—
51#5002—31no—
52#4787—34no—
53#4786—34no—
54C23×C3×D3—21no—
55C23×C3×D3—21no—
56C22×C32×C4C2311yescharacteristic
57C2×C3×#67—21no—
58C3×#235—22no—
59C3×#235—22no—
60C2×C3×D12—21no—
61C2×C3×D12—22no—
62C2×C3×D12—22no—
63C2×C3×D12—22no—
64C2×C3×D12—21no—
65C2×C3×D12D414yescomplemented
66C2×C3×D12C2311yescharacteristic
67C2×C3×D12C2312yes—
68C2×C3×D12C2312yes—
69C2×C3×C4×D3—21no—
70C2×C3×Dic6C2311yescharacteristic
71C2×#625—24no—
72C2×D3×Dic3—24no—
73C32×M16—22no—
74C2×C32×C8C2312yes—
75#3757D412yes—
76C4⋊(C3⋊Dic3)D412yes—
77C4×C3⋊Dic3C2312yes—
78C2×C3⋊(C3⋊C8)—22no—
79C2×C3⋊(C3⋊C8)C2312yes—
80C3×#217—21no—
81C3×C4⋊Dic3C2312yes—
82C3×C4×Dic3—21no—
83C3×D24—24no—
84C3×#204—24no—
85(C2×D3)⋊Dic3—24no—
86(C2×D3)⋊Dic3—24no—
87#3713—28no—
88#3041—91noSylow
89C2×C3×#41—31no—
90C22×C3×D4—31no—
91C22×C3×D4—31no—
92C2×#235C2×D311yescharacteristic
93C22×D12C2×D311yescharacteristic
94C22×D12C2×D311yescharacteristic
95C3×AGL(1,ℤ/8)—64no—
96C2×C3×SD16—32no—
97C2×C3×D8—32no—
98C2×C3×M16—21no—
99C2×C3×M16C2×D311yescharacteristic
100C2×C3×M16C2×D311yescharacteristic
101C3×#117—31no—
102#953—62no—
103C2×#217—62no—
104#947—32no—
105#940—32no—
106#940—32no—
107#938—62no—
108#937—62no—
109#936—32no—
110D4×Dic3—34no—
111D4×Dic3—62no—
112C2×#213—34no—
113C2×#213—34no—
114C2×#213—64no—
115C2×#213—64no—
116#930—62no—
117#926—31no—
118#926—31no—
119#926—61no—
120#926C2×D311yescharacteristic
121C22×C3⋊C8—31no—
122C22×C3⋊C8—31no—
123C22×C3⋊C8—61no—
124#908—24no—
125C2×D24C2×D312yescomplemented
126C2×#204C2×D312yescomplemented
127#893—34no—
128D3×C22⋊C4—62no—
129C4×D12—62no—
130C3×#102—34no—
131#835—32no—
132#832—32no—
133#821C2×D314yescomplemented
134Dic3⋊C8—34no—
135Dic3⋊C8—34no—
136Dic3⋊C8—64no—
137#810—32no—
138#809—32no—
139C23×C32C2×D411yescharacteristic
140C22×C3×D3—22no—
141C22×C3×D3—24no—
142C22×C3×D3—22no—
143C22×C3×D3—21no—
144C22×C3×D3—42no—
145C22×C3×D3—82no—
146C22×C3×D3—82no—
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D412yes—
149C2×C32×C4#4112yes—
150C2×C32×C4C2411yescharacteristic
151C2×C3⋊Dic3C2×D414yes—
152C3×#67—42no—
153C2×C3×Dic3—21no—
154C2×C3×Dic3—22no—
155C3×D12—24no—
156C3×D12—22no—
157C3×D12—21no—
158C3×D12—22no—
159C3×D12—22no—
160C3×D12—21no—
161C3×D12—42no—
162C3×D12C2×D414yes—
163C3×C4×D3—42no—
164C3×Dic6—21no—
165C3×Dic6—21no—
166#625—84no—
167D3×Dic3—84no—
168C32×C8—22no—
169C3⋊(C3⋊C8)—22no—
170C2×AGL(1,ℤ/8)—31no—
171C22×D8—91no—
172#535—91no—
173#518—91no—
174#463—94no—
175#459—94no—
176#424—91no—
177#418—31no—
178#416—91no—
179C24×C3—61no—
180C24×C3—61no—
181C23×D3—21no—
182C23×D3—21no—
183C3×#41—62no—
184C3×#41—62no—
185C2×C3×Q8—31no—
186C2×C3×D4—34no—
187C2×C3×D4—32no—
188C2×C3×D4—31no—
189C2×C3×D4—32no—
190C2×C3×D4—61no—
191C2×C3×D4—62no—
192C2×C3×D4—61no—
193C2×C3×D4—61no—
194C2×C3×D4—62no—
195C2×C3×D4—62no—
196C22×C3×C4—21no—
197C22×C3×C4—61no—
198C22×C3×C4C22×D311yescharacteristic
199C22×C3×C4C22×D311yescharacteristic
200C2×#67—21no—
201C2×#67—64no—
202C2×#67—64no—
203C22×Dic3—64no—
204#235—22no—
205#235—22no—
206C2×D12—21no—
207C2×D12—22no—
208C2×D12—22no—
209C2×D12—22no—
210C2×D12—21no—
211C2×D12#6714yescomplemented
212C2×D12C22×D311yescharacteristic
213C2×D12C22×D312yes—
214C2×D12C22×D312yes—
215C2×C4×D3—21no—
216C2×C4×D3—64no—
217C2×Dic6C22×D311yescharacteristic
218C3×SD16—64no—
219C3×D8—64no—
220C3×M16—22no—
221C3×M16—22no—
222C3×M16—42no—
223C2×C3×C8—22no—
224C2×C3×C8C22×D312yes—
225C2×C3×C8C22×D312yes—
226C3×C4⋊C4—32no—
227C3×C22⋊C4—61no—
228C3×C42—61no—
229#217—21no—
230#217—32no—
231#217—32no—
232#217—62no—
233#217—64no—
234#217—64no—
235#213—68no—
236#213—68no—
237(C2×D3)⋊C4—64no—
238(C2×D3)⋊C4—64no—
239C4⋊Dic3—32no—
240C4⋊Dic3—32no—
241C4⋊Dic3—62no—
242C4⋊Dic3C22×D312yes—
243C4×Dic3—21no—
244C4×Dic3—32no—
245C4×Dic3—32no—
246C4×Dic3—62no—
247C2×C3⋊C8—32no—
248C2×C3⋊C8—32no—
249C2×C3⋊C8—62no—
250C2×C3⋊C8—62no—
251C2×C3⋊C8—62no—
252C2×C3⋊C8—122no—
253D24—24no—
254#204—24no—
255C22×C32—22no—
256C22×C32#12112yes—
257C22×C32C22×D411yescharacteristic
258C2×C3×D3—24no—
259C2×C3×D3—44no—
260C2×C3×D3—41no—
261C2×C3×D3—42no—
262C2×C3×D3—42no—
263C2×C3×D3—44no—
264C2×C3×D3—84no—
265C2×C3×D3—84no—
266C32×C4#12112yes—
267C32×C4C22×D411yescharacteristic
268C32×C4C2×#4111yescharacteristic
269C3⋊Dic3—24no—
270C3×Dic3—41no—
271C3×Dic3—42no—
272C2×#41—31no—
273C22×D4—31no—
274C22×D4—31no—
275AGL(1,ℤ/8)—64no—
276C2×SD16—32no—
277C2×D8—32no—
278C2×D8—94no—
279C2×D8—184no—
280C2×M16D3211yescharacteristic
281C22×C8—91no—
282#127—92no—
283#124—92no—
284#121—182no—
285#120—182no—
286C4×D4—94no—
287C4×D4—182no—
288#117—31no—
289#117—91no—
290C2×C22⋊C4—182no—
291C4⋊C8—94no—
292#103—92no—
293#102—34no—
294#102—92no—
295C23×C3—21no—
296C23×C3—62no—
297C23×C3—64no—
298C23×C3—62no—
299C23×C3—61no—
300C23×C3—122no—
301C23×C3—242no—
302C23×C3—242no—
303C23×C3D3×D411yescharacteristic
304C23×C3D3×D411yescharacteristic
305C22×D3—22no—
306C22×D3—24no—
307C22×D3—22no—
308C22×D3—21no—
309C22×D3—42no—
310C22×D3—82no—
311C22×D3—82no—
312C3×Q8—61no—
313C3×Q8—61no—
314C3×D4—34no—
315C3×D4—64no—
316C3×D4—62no—
317C3×D4—61no—
318C3×D4—61no—
319C3×D4—62no—
320C3×D4—62no—
321C3×D4—122no—
322C3×D4—122no—
323C2×C3×C4—21no—
324C2×C3×C4—22no—
325C2×C3×C4—21no—
326C2×C3×C4—22no—
327C2×C3×C4—61no—
328C2×C3×C4—62no—
329C2×C3×C4—122no—
330C2×C3×C4#23512yes—
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4D3×D412yes—
334C2×C3×C4#23712yes—
335C2×C3×C4C2×#6712yes—
336C2×C3×C4C23×D311yescharacteristic
337C2×C3×C4C23×D311yescharacteristic
338#67—42no—
339#67—244no—
340#67—244no—
341C2×Dic3—22no—
342C2×Dic3—21no—
343C2×Dic3—34no—
344C2×Dic3—34no—
345C2×Dic3—64no—
346C2×Dic3—244no—
347D12—24no—
348D12—22no—
349D12—22no—
350D12—22no—
351D12—21no—
352D12—21no—
353D12—42no—
354D12C2×#6714yes—
355C4×D3—42no—
356C4×D3—244no—
357Dic6—21no—
358Dic6—21no—
359C3×C8—22no—
360C3×C8—22no—
361C3×C8—42no—
362C3⋊C8—62no—
363C3⋊C8—62no—
364C3⋊C8—122no—
365C2×C32—22no—
366C2×C32C2×#12111yescharacteristic
367C2×C32#57612yes—
368C3×D3—44no—
369C3×D3—81no—
370C3×D3—82no—
371C24—61no—
372C24—61no—
373#41—62no—
374#41—62no—
375C2×Q8—31no—
376C2×D4—32no—
377C2×D4—32no—
378C2×D4—31no—
379C2×D4—34no—
380C2×D4—61no—
381C2×D4—62no—
382C2×D4—62no—
383C2×D4—61no—
384C2×D4—61no—
385C2×D4—62no—
386C2×D4—184no—
387C22×C4—61no—
388C22×C4—184no—
389C22×C4C2×D3211yescharacteristic
390SD16—64no—
391D8—64no—
392D8—188no—
393M16—22no—
394C2×C8—92no—
395C2×C8—182no—
396C2×C8C2×D3212yes—
397C4⋊C4—32no—
398C4⋊C4—92no—
399C22⋊C4—61no—
400C22⋊C4—92no—
401C22⋊C4—184no—
402C22⋊C4—184no—
403C42—61no—
404C42—92no—
405C22×C3—22no—
406C22×C3—22no—
407C22×C3—21no—
408C22×C3—22no—
409C22×C3—42no—
410C22×C3—64no—
411C22×C3—124no—
412C22×C3—121no—
413C22×C3—122no—
414C22×C3—124no—
415C22×C3—122no—
416C22×C3—244no—
417C22×C3—244no—
418C22×C3#88412yes—
419C22×C3#93912yes—
420C22×C3C2×D3×D411yescharacteristic
421C22×C3C2×D3×D411yescharacteristic
422C2×D3—24no—
423C2×D3—44no—
424C2×D3—42no—
425C2×D3—42no—
426C2×D3—44no—
427C2×D3—41no—
428C2×D3—84no—
429C2×D3—84no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—22no—
433C3×C4—121no—
434C3×C4—122no—
435C3×C4#88412yes—
436C3×C4#93912yes—
437C3×C4C2×#23511yescharacteristic
438C3×C4C2×D3×D411yescharacteristic
439C3×C4C2×#23711yescharacteristic
440C3×C4C22×#6711yescharacteristic
441Dic3—42no—
442Dic3—41no—
443Dic3—64no—
444Dic3—64no—
445Dic3—124no—
446C32#304111yescharacteristic, complemented, Sylow
447C23—62no—
448C23—64no—
449C23—62no—
450C23—61no—
451C23—122no—
452C23—242no—
453C23—242no—
454C23#380211yescharacteristic
455Q8—61no—
456Q8—61no—
457D4—34no—
458D4—62no—
459D4—62no—
460D4—61no—
461D4—61no—
462D4—62no—
463D4—64no—
464D4—122no—
465D4—122no—
466D4—724no—
467C2×C4—62no—
468C2×C4—61no—
469C2×C4—94no—
470C2×C4—122no—
471C2×C4—724no—
472C2×C4#379512yes—
473C2×C4#380211yescharacteristic
474C2×C4D3×#6712yes—
475C2×C4C22×D3211yescharacteristic
476C8—22no—
477C8—182no—
478C2×C3—22no—
479C2×C3—22no—
480C2×C3—21no—
481C2×C3—22no—
482C2×C3—42no—
483C2×C3—124no—
484C2×C3—241no—
485C2×C3—242no—
486C2×C3C2×#88411yescharacteristic
487C2×C3#577412yes—
488C2×C3#577412yes—
489C2×C3C2×#93911yescharacteristic
490D3—44no—
491D3—82no—
492D3—81no—
493C22—22no—
494C22—64no—
495C22—124no—
496C22—121no—
497C22—122no—
498C22—122no—
499C22—124no—
500C22—244no—
501C22—244no—
502C22#6388512yes—
503C22C2×#380211yescharacteristic
504C4—121no—
505C4—122no—
506C4—184no—
507C4#6388512yes—
508C4C2×#379511yescharacteristic
509C4C2×D3×#6711yescharacteristic
510C3—21no—
511C3#7894411yescharacteristic, complemented
512C3#8393411yescharacteristic, complemented
513C2—22no—
514C2—124no—
515C2—242no—
516C2—241no—
517C2#1059472012yes—
518C2C2×#6388511yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
hypercenterC2×M16D32
hypocenterC32#3041
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#908C2semidirect
2. #10595040C2semidirect
3. #10594982C2semidirect
4. C22×#3713C2semidirect
5. #10592818C2semidirect
6. C3×#5131C2semidirect
7. #10591083C2semidirect
8. #10590750C2semidirect
9. #10590749C2semidirect
20. C2×C3×D24C22semidirect
21. C2×C3×#204C22semidirect
24. #63914C22semidirect
26. #63898C22semidirect
28. #63863C22semidirect
31. #63641C22semidirect
32. C3×#821C22semidirect
33. #63565C22semidirect
34. #63562C22semidirect
41. C2×#908D3semidirect
47. #5131D3semidirect
65. C2×C3×D12D4semidirect
125. C2×D24C2×D3semidirect
126. C2×#204C2×D3semidirect
133. #821C2×D3semidirect
211. C2×D12#67semidirect
446. C32#3041semidirect
511. C3#78944semidirect
512. C3#83934semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9082
#105950402
#105949822
C22×#37132
#105928182
C3×#51312
#105910832
#105907502
#105907492
#839343
#789443