Finite Group Databasebeta

← #11871284

Subgroups — #11871284

Order 1152.

1131 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595948C211yesmaximal, characteristic, complemented
2C2×C3×C4×D12C211yesmaximal, characteristic, complemented
3C3×#4926C211yesmaximal, characteristic, complemented
4#10591162C212yesmaximal, complemented
5#10591125C212yesmaximal, complemented
6#10590349C212yesmaximal, complemented
7#10590346C214yesmaximal, complemented
8#10590268C212yesmaximal, complemented
9#82310—31nomaximal
10#79343—31nomaximal
11C2×#3828—21no—
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3—21no—
14C2×C32×C42C2211yescharacteristic
15#64139—21no—
16#64139C2212yes—
17#64084—21no—
18#64083C2211yescharacteristic, complemented
19C4×C4⋊(C3⋊D3)—21no—
20C4×C4⋊(C3⋊D3)C2212yescomplemented
21#64078C2211yescharacteristic, complemented
22C2×C3×(C2×D3)⋊C4—21no—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C3×C4×D12—21no—
25C3×C4×D12—21no—
26C3×C4×D12C2212yes—
27C3×C4×D12C2212yes—
28C2×#3714C2214yes—
29C3×#830C2212yes—
30C3×C4⋊(C3⋊C8)C2212yescomplemented
31C3×#803C2212yescomplemented
32#63573C2214yescomplemented
33#63564C2214yescomplemented
34#63563C2214yes—
35C2×C3×C4×D4—31no—
36#5477—31no—
37#5477—31no—
38#5477—61no—
39C2×C4×D12D311yescharacteristic, complemented
40C3×#432—31no—
41#5217—32no—
42#5015—32no—
43#5014—34no—
44#5008—32no—
45#4968—32no—
46#4926D311yescharacteristic, complemented
47#4843—32no—
48#4842—32no—
49#4735—32no—
50#4732—32no—
51#4711—34no—
52C23×C3×D3—21no—
53C22×C32×C4D411yescharacteristic
54C22×C32×C4D411yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C2×#638—22no—
57#3828—44no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)C2312yes—
61C2×C4×C3⋊D3—22no—
62C2×#634—21no—
63C22×C3×Dic3—21no—
64C2×C3×D12—21no—
65C2×C3×D12—24no—
66C2×C3×D12C2312yes—
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3—44no—
70C32×C42D411yescharacteristic
71C32×C42D411yescharacteristic
72C32×C42C2311yescharacteristic
73C32×C42C2311yescharacteristic
74#3752—22no—
75#3752—22no—
76C4⋊(C3⋊Dic3)—21no—
77C4⋊(C3⋊Dic3)C2312yes—
78C3×(C2×D3)⋊C4—22no—
79C3×(C2×D3)⋊C4—22no—
80C3×C4⋊Dic3—21no—
81C3×C4⋊Dic3C2312yes—
82C2×C3×C3⋊C8C2314yes—
83#3714—28no—
84#3109—91noSylow
85C22×C3×D4—31no—
86C23×C3×C4—61no—
87C2×#235—62no—
88C2×#235—61no—
89C2×#235—61no—
90C22×D12C2×D311yescharacteristic
91C22×C4×D3—21no—
92C3×C4×D4—32no—
93C3×C4×D4—32no—
94C3×C4×D4—61no—
95C3×C4×D4—61no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C22⋊C4—61no—
98C2×C3×C42—21no—
99C2×C3×C42C2×D311yescharacteristic
100C2×C3×C42C2×D311yescharacteristic
101C2×#213—34no—
102#930—32no—
103#930—32no—
104#930—62no—
105#930—62no—
106#930—61no—
107#930—61no—
108C2×(C2×D3)⋊C4—21no—
109C2×C4⋊Dic3C2×D311yescharacteristic
110C2×D24—34no—
111#875—62no—
112#875—61no—
113#875—61no—
114#874—31no—
115#874—31no—
116#874—61no—
117C4×D12—21no—
118C4×D12—21no—
119C4×D12—32no—
120C4×D12—32no—
121C4×D12—62no—
122C4×D12—62no—
123C4×D12—61no—
124C4×D12—61no—
125C4×D12C2×D312yes—
126C4×D12C2×D312yes—
127#869—31no—
128#869—31no—
129#869—61no—
130C3×C4⋊C8—32no—
131C3×C22⋊C8—32no—
132C3×#97—32no—
133#832—34no—
134#830C2×D312yes—
135#821—34no—
136#821—34no—
137#817—34no—
138#809—34no—
139#808—34no—
140C4⋊(C3⋊C8)C2×D312yescomplemented
141#803C2×D312yescomplemented
142C23×C32C2×D411yescharacteristic
143C22×C3⋊D3—22no—
144C22×C3×D3—24no—
145C22×C3×D3—22no—
146C22×C3×D3—42no—
147C22×C3×D3—42no—
148C2×C32×C4—22no—
149C2×C32×C4—22no—
150C2×C32×C4—22no—
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2411yescharacteristic
157#638—44no—
158C2×C3⋊Dic3—22no—
159C4⋊(C3⋊D3)—24no—
160C4⋊(C3⋊D3)—42no—
161C4⋊(C3⋊D3)—42no—
162C4×C3⋊D3—44no—
163#634—42no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—42no—
166C3×D12—24no—
167C3×D12—22no—
168C3×D12#4114yescomplemented
169C3×C4×D3—44no—
170C3×C4×D3—44no—
171C3×C3⋊C8—24no—
172#532—91no—
173C2×C4×D4—31no—
174#481—92no—
175#476—92no—
176#459—92no—
177#447—92no—
178#442—94no—
179#432—31no—
180C24×C3—61no—
181C23×D3—21no—
182C2×C3×D4—32no—
183C2×C3×D4—64no—
184C2×C3×D4—61no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—61no—
189C22×C3×C4—62no—
190C22×C3×C4—62no—
191C22×C3×C4—124no—
192C22×C3×C4D1211yescharacteristic
193C22×C3×C4D1211yescharacteristic
194C22×C3×C4#6711yescharacteristic
195C22×C3×C4#6711yescharacteristic
196C22×C3×C4C22×D311yescharacteristic
197C22×C3×C4C22×D311yescharacteristic
198C2×#67—64no—
199C2×#67—62no—
200C2×#67—62no—
201C22×Dic3—21no—
202#235—128no—
203#235—124no—
204#235—124no—
205C2×D12—21no—
206C2×D12—24no—
207C2×D12—32no—
208C2×D12—32no—
209C2×D12—62no—
210C2×D12—62no—
211C2×D12—62no—
212C2×D12—61no—
213C2×D12—61no—
214C2×D12—61no—
215C2×D12—61no—
216C2×D12C22×D312yes—
217C2×C4×D3—22no—
218C2×C4×D3—22no—
219C2×C4×D3—44no—
220C2×C4×D3—64no—
221C2×C4×D3—62no—
222C2×C4×D3—62no—
223C2×Dic6—62no—
224C2×Dic6—61no—
225C2×Dic6—61no—
226C2×C3×C8—34no—
227C3×C4⋊C4—32no—
228C3×C4⋊C4—61no—
229C3×C22⋊C4—62no—
230C3×C22⋊C4—62no—
231C3×C42—21no—
232C3×C42—21no—
233C3×C42—21no—
234C3×C42—21no—
235C3×C42D1211yescharacteristic
236C3×C42D1211yescharacteristic
237C3×C42#6711yescharacteristic
238C3×C42#6711yescharacteristic
239C3×C42C22×D311yescharacteristic
240C3×C42C22×D311yescharacteristic
241C3×C42C22×D311yescharacteristic
242C3×C42C22×D311yescharacteristic
243#213—68no—
244(C2×D3)⋊C4—22no—
245(C2×D3)⋊C4—22no—
246(C2×D3)⋊C4—64no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4—62no—
249(C2×D3)⋊C4—62no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—62no—
252C4⋊Dic3—21no—
253C4⋊Dic3—32no—
254C4⋊Dic3—32no—
255C4⋊Dic3—62no—
256C4⋊Dic3—62no—
257C4⋊Dic3—61no—
258C4⋊Dic3—61no—
259C4⋊Dic3C22×D312yes—
260C2×C3⋊C8C22×D314yes—
261D24—68no—
262C22×C32—21no—
263C22×C32—21no—
264C22×C32AGL(1,ℤ/8)12yes—
265C22×C32C22×D411yescharacteristic
266C2×C3⋊D3—42no—
267C2×C3⋊D3—42no—
268C2×C3⋊D3—42no—
269C2×C3×D3—24no—
270C2×C3×D3—48no—
271C2×C3×D3—42no—
272C2×C3×D3—42no—
273C32×C4—21no—
274C32×C4—21no—
275C32×C4—21no—
276C32×C4—21no—
277C32×C4AGL(1,ℤ/8)12yes—
278C32×C4C2×#4112yes—
279C3⋊Dic3—42no—
280C3×Dic3—42no—
281C2×#41—181no—
282C22×D4—31no—
283C23×C4—61no—
284C2×D8—94no—
285C4⋊Q8—91no—
286#127—91no—
287#124—181no—
288#121—92no—
289#121—181no—
290C4×D4—32no—
291C4×D4—32no—
292C4×D4—61no—
293C4×D4—61no—
294C4×D4—92no—
295C4×D4—181no—
296C2×C4⋊C4—31no—
297C2×C22⋊C4—61no—
298C2×C42D3211yescharacteristic
299#106—94no—
300C4⋊C8—32no—
301#102—94no—
302#102—94no—
303C22⋊C8—32no—
304#97—32no—
305C23×C3—21no—
306C23×C3—64no—
307C23×C3—62no—
308C23×C3—122no—
309C23×C3—122no—
310C23×C3C2×D1211yescharacteristic
311C23×C3C2×#6711yescharacteristic
312C22×D3—24no—
313C22×D3—22no—
314C22×D3—42no—
315C22×D3—42no—
316C22×D3—64no—
317C22×D3—62no—
318C22×D3—62no—
319C3×D4—34no—
320C3×D4—64no—
321C3×D4—62no—
322C2×C3×C4—24no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—42no—
336C2×C3×C4—42no—
337C2×C3×C4—62no—
338C2×C3×C4—124no—
339C2×C3×C4—122no—
340C2×C3×C4—124no—
341C2×C3×C4C2×D1211yescharacteristic
342C2×C3×C4C2×D1211yescharacteristic
343C2×C3×C4C2×D1211yescharacteristic
344C2×C3×C4C2×D1211yescharacteristic
345C2×C3×C4C2×D1211yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C2×#6711yescharacteristic
348C2×C3×C4C2×#6711yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351C2×C3×C4C23×D311yescharacteristic
352C2×C3×C4C23×D311yescharacteristic
353#67—128no—
354#67—124no—
355#67—124no—
356C2×Dic3—22no—
357C2×Dic3—42no—
358C2×Dic3—64no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361D12—24no—
362D12—22no—
363D12—64no—
364D12—64no—
365D12—124no—
366D12—124no—
367D12—124no—
368D12—122no—
369D12—122no—
370D12—122no—
371D12—122no—
372D12#23514yescomplemented
373C4×D3—44no—
374C4×D3—44no—
375C4×D3—128no—
376C4×D3—124no—
377C4×D3—124no—
378Dic6—124no—
379Dic6—122no—
380Dic6—122no—
381C3×C8—64no—
382C3⋊C8—24no—
383C2×C32—22no—
384C2×C32#52511yescharacteristic
385C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
386C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
387C3⋊D3—82no—
388C3×D3—44no—
389C24—61no—
390#41—364no—
391C2×Q8—181no—
392C2×D4—32no—
393C2×D4—64no—
394C2×D4—61no—
395C2×D4—92no—
396C2×D4—182no—
397C2×D4—181no—
398C2×D4—181no—
399C22×C4—61no—
400C22×C4—62no—
401C22×C4—62no—
402C22×C4—124no—
403C22×C4—182no—
404C22×C4#62611yescharacteristic
405C22×C4#62611yescharacteristic
406C22×C4C2×D3211yescharacteristic
407D8—188no—
408C2×C8—34no—
409C4⋊C4—32no—
410C4⋊C4—61no—
411C4⋊C4—92no—
412C4⋊C4—181no—
413C22⋊C4—62no—
414C22⋊C4—62no—
415C22⋊C4—182no—
416C22⋊C4—182no—
417C42#62611yescharacteristic
418C42#62611yescharacteristic
419C42C2×D3211yescharacteristic
420C42C2×D3211yescharacteristic
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—22no—
427C22×C3—41no—
428C22×C3—41no—
429C22×C3—64no—
430C22×C3—128no—
431C22×C3—122no—
432C22×C3—122no—
433C22×C3#90812yes—
434C22×C3#94912yes—
435C22×C3C22×D1211yescharacteristic
436C22×C3C22×#6711yescharacteristic
437C2×D3—24no—
438C2×D3—48no—
439C2×D3—42no—
440C2×D3—42no—
441C2×D3—124no—
442C2×D3—124no—
443C2×D3—124no—
444C2×D3—122no—
445C2×D3—122no—
446C2×D3—122no—
447C2×D3—122no—
448C2×D3—122no—
449C2×D3—122no—
450C3×C4—22no—
451C3×C4—22no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—22no—
461C3×C4—22no—
462C3×C4—41no—
463C3×C4—41no—
464C3×C4—122no—
465C3×C4#90812yes—
466C3×C4#93212yes—
467C3×C4C2×#23512yes—
468C3×C4D3×#4112yes—
469Dic3—42no—
470Dic3—124no—
471Dic3—122no—
472Dic3—122no—
473C32#310911yescharacteristic, complemented, Sylow
474C23—64no—
475C23—62no—
476C23—122no—
477C23—122no—
478C23—182no—
479C23C2×#62611yescharacteristic
480Q8—362no—
481D4—34no—
482D4—64no—
483D4—62no—
484D4—184no—
485D4—362no—
486D4—364no—
487D4—362no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—62no—
492C2×C4—124no—
493C2×C4—122no—
494C2×C4—124no—
495C2×C4—182no—
496C2×C4—364no—
497C2×C4C2×#62611yescharacteristic
498C2×C4C2×#62611yescharacteristic
499C2×C4C2×#62611yescharacteristic
500C2×C4C2×#62611yescharacteristic
501C2×C4C2×#62611yescharacteristic
502C2×C4C22×D3211yescharacteristic
503C8—64no—
504C2×C3—22no—
505C2×C3—22no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—42no—
510C2×C3—124no—
511C2×C3#552411yescharacteristic
512C2×C3C2×#90811yescharacteristic
513C2×C3C2×#90811yescharacteristic
514C2×C3#579111yescharacteristic
515C2×C3C2×#93211yescharacteristic
516C2×C3C2×#94911yescharacteristic
517D3—44no—
518D3—244no—
519D3—242no—
520D3—242no—
521C22—21no—
522C22—21no—
523C22—64no—
524C22—128no—
525C22—122no—
526C22—122no—
527C22—362no—
528C22—362no—
529C22—362no—
530C22#6382512yes—
531C22C22×#62611yescharacteristic
532C4—21no—
533C4—21no—
534C4—21no—
535C4—21no—
536C4—122no—
537C4—362no—
538C4#6383012yes—
539C4D3×#23512yes—
540C3—21no—
541C3#7934311yescharacteristic, complemented
542C3#8231011yescharacteristic, complemented
543C2—22no—
544C2—124no—
545C2—722no—
546C2C2×#6382511yescharacteristic
547C2C2×#6383011yescharacteristic
548C2#1059502311yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
hypercenterC2×C42D32
hypocenterC32#3109
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #10595948C2semidirect
2. C2×C3×C4×D12C2semidirect
3. C3×#4926C2semidirect
4. #10591162C2semidirect
5. #10591125C2semidirect
6. #10590349C2semidirect
7. #10590346C2semidirect
8. #10590268C2semidirect
18. #64083C22semidirect
20. C4×C4⋊(C3⋊D3)C22semidirect
21. #64078C22semidirect
30. C3×C4⋊(C3⋊C8)C22semidirect
31. C3×#803C22semidirect
32. #63573C22semidirect
33. #63564C22semidirect
39. C2×C4×D12D3semidirect
46. #4926D3semidirect
140. C4⋊(C3⋊C8)C2×D3semidirect
141. #803C2×D3semidirect
168. C3×D12#41semidirect
372. D12#235semidirect
473. C32#3109semidirect
541. C3#79343semidirect
542. C3#82310semidirect

Maximal subgroups

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

subgroupindex
#105959482
C2×C3×C4×D122
C3×#49262
#105911622
#105911252
#105903492
#105903462
#105902682
#823103
#793433