Finite Group Databasebeta

← #11871286

Subgroups — #11871286

Order 1152.

1031 conjugacy classes of subgroups.

The subgroup lattice has 523 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5477C211yesmaximal, characteristic, complemented
2C2×C3×C4×D12C211yesmaximal, characteristic, complemented
3#10592625C211yesmaximal, characteristic, complemented
4#10591160C212yesmaximal, complemented
5#10591091C212yesmaximal, complemented
6#10590347C212yesmaximal, complemented
7#10590344C214yesmaximal, complemented
8#10590266C212yesmaximal, complemented
9#83300—31nomaximal
10#82310—31nomaximal
11C2×C3×#235—21no—
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3—21no—
14C2×C32×C42C2211yescharacteristic
15C3×#930—21no—
16C3×#930C2212yes—
17C2×C3×(C2×D3)⋊C4—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C3×#875—21no—
20C3×#874C2211yescharacteristic, complemented
21C3×C4×D12—21no—
22C3×C4×D12—21no—
23C3×C4×D12—21no—
24C3×C4×D12C2212yes—
25C3×C4×D12C2212yes—
26C3×C4×D12C2212yescomplemented
27C3×#869C2211yescharacteristic, complemented
28C2×#3713C2214yes—
29#63657C2212yes—
30C4⋊(C3⋊(C3⋊C8))C2212yescomplemented
31#63630C2212yescomplemented
32#63574C2214yescomplemented
33#63562C2214yes—
34#63562C2214yescomplemented
35C3×#532—31no—
36C2×C3×C4×D4—31no—
37#5477D311yescharacteristic, complemented
38C2×C4×D12D311yescharacteristic, complemented
39#5217—32no—
40#5084—32no—
41#5072—32no—
42#5036—32no—
43#5034—32no—
44#5015—32no—
45#5014—34no—
46#5014—34no—
47#5008—32no—
48#4968—32no—
49#4926—31no—
50#4926—31no—
51#4926—61no—
52C23×C3×D3—21no—
53C22×C32×C4D411yescharacteristic
54C22×C32×C4D411yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C2×C3×#67—22no—
57C22×C3×Dic3—21no—
58C3×#235—44no—
59C2×C3×D12—21no—
60C2×C3×D12—24no—
61C2×C3×D12—21no—
62C2×C3×D12—21no—
63C2×C3×D12C2312yes—
64C2×C3×D12C2312yes—
65C2×C3×C4×D3—22no—
66C2×C3×C4×D3—22no—
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3—44no—
69C2×C3×Dic6—21no—
70C32×C42D411yescharacteristic
71C32×C42D411yescharacteristic
72C32×C42C2311yescharacteristic
73C32×C42C2311yescharacteristic
74C2×C3⋊(C3⋊C8)C2314yes—
75C3×(C2×D3)⋊C4—22no—
76C3×(C2×D3)⋊C4—22no—
77C3×(C2×D3)⋊C4—22no—
78C3×(C2×D3)⋊C4—22no—
79C3×C4⋊Dic3—21no—
80C3×C4⋊Dic3—21no—
81C3×C4⋊Dic3C2312yes—
82C3×C4⋊Dic3C2312yes—
83#3713—28no—
84#3109—91noSylow
85C2×C3×#41—61no—
86C22×C3×D4—31no—
87C23×C3×C4—61no—
88C2×#235—21no—
89C22×D12C2×D311yescharacteristic
90C22×C4×D3—21no—
91C3×C4⋊Q8—31no—
92C3×#127—31no—
93C3×#124—61no—
94C3×#121—32no—
95C3×#121—61no—
96C3×C4×D4—32no—
97C3×C4×D4—32no—
98C3×C4×D4—32no—
99C3×C4×D4—61no—
100C3×C4×D4—61no—
101C3×C4×D4—61no—
102C2×C3×C4⋊C4—31no—
103C2×C3×C22⋊C4—61no—
104C2×C3×C42—21no—
105C2×C3×C42C2×D311yescharacteristic
106C2×C3×C42C2×D311yescharacteristic
107C2×#213—34no—
108C2×#213—34no—
109#930—21no—
110#930C2×D312yes—
111C2×(C2×D3)⋊C4—21no—
112C2×C4⋊Dic3C2×D311yescharacteristic
113#875—21no—
114#874C2×D311yescharacteristic, complemented
115C4×D12—21no—
116C4×D12—21no—
117C4×D12—21no—
118C4×D12C2×D312yes—
119C4×D12C2×D312yes—
120C4×D12C2×D312yescomplemented
121#869C2×D311yescharacteristic, complemented
122#832—34no—
123#832—34no—
124#830—32no—
125#830—32no—
126#830—62no—
127#809—34no—
128#809—34no—
129#808—34no—
130#808—34no—
131C4⋊(C3⋊C8)—32no—
132C4⋊(C3⋊C8)—32no—
133C4⋊(C3⋊C8)—62no—
134#803—32no—
135#803—32no—
136#803—62no—
137C23×C32C2×D411yescharacteristic
138C22×C3×D3—24no—
139C22×C3×D3—22no—
140C22×C3×D3—22no—
141C22×C3×D3—42no—
142C22×C3×D3—42no—
143C2×C32×C4—22no—
144C2×C32×C4—22no—
145C2×C32×C4—22no—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2411yescharacteristic
152C3×#67—44no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—42no—
156C3×D12—24no—
157C3×D12—22no—
158C3×D12—24no—
159C3×D12—42no—
160C3×D12—42no—
161C3×D12#4114yescomplemented
162C3×C4×D3—44no—
163C3×C4×D3—44no—
164C3×C4×D3—44no—
165C3×Dic6—42no—
166C3⋊(C3⋊C8)—24no—
167#532—31no—
168C2×C4×D4—31no—
169#481—92no—
170#476—92no—
171#459—92no—
172#447—92no—
173#442—94no—
174#432—91no—
175C24×C3—61no—
176C23×D3—21no—
177C3×#41—124no—
178C2×C3×Q8—61no—
179C2×C3×D4—32no—
180C2×C3×D4—32no—
181C2×C3×D4—64no—
182C2×C3×D4—62no—
183C2×C3×D4—61no—
184C2×C3×D4—61no—
185C2×C3×D4—61no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—61no—
190C22×C3×C4—62no—
191C22×C3×C4—62no—
192C22×C3×C4—62no—
193C22×C3×C4—124no—
194C22×C3×C4#6711yescharacteristic
195C22×C3×C4#6711yescharacteristic
196C22×C3×C4#6711yescharacteristic
197C22×C3×C4#6711yescharacteristic
198C22×C3×C4C22×D311yescharacteristic
199C22×C3×C4C22×D311yescharacteristic
200C2×#67—22no—
201C22×Dic3—21no—
202#235—44no—
203C2×D12—21no—
204C2×D12—24no—
205C2×D12—21no—
206C2×D12—21no—
207C2×D12C22×D312yes—
208C2×D12C22×D312yes—
209C2×C4×D3—22no—
210C2×C4×D3—22no—
211C2×C4×D3—22no—
212C2×C4×D3—44no—
213C2×Dic6—21no—
214C3×C4⋊C4—32no—
215C3×C4⋊C4—32no—
216C3×C4⋊C4—61no—
217C3×C4⋊C4—61no—
218C3×C22⋊C4—62no—
219C3×C22⋊C4—62no—
220C3×C22⋊C4—62no—
221C3×C22⋊C4—62no—
222C3×C42—21no—
223C3×C42—21no—
224C3×C42—21no—
225C3×C42—21no—
226C3×C42#6711yescharacteristic
227C3×C42#6711yescharacteristic
228C3×C42#6711yescharacteristic
229C3×C42#6711yescharacteristic
230C3×C42C22×D311yescharacteristic
231C3×C42C22×D311yescharacteristic
232C3×C42C22×D311yescharacteristic
233C3×C42C22×D311yescharacteristic
234#213—68no—
235#213—68no—
236(C2×D3)⋊C4—22no—
237(C2×D3)⋊C4—22no—
238(C2×D3)⋊C4—22no—
239(C2×D3)⋊C4—22no—
240C4⋊Dic3—21no—
241C4⋊Dic3—21no—
242C4⋊Dic3C22×D312yes—
243C4⋊Dic3C22×D312yes—
244C2×C3⋊C8—34no—
245C2×C3⋊C8—34no—
246C2×C3⋊C8—64no—
247C22×C32—21no—
248C22×C32—21no—
249C22×C32AGL(1,ℤ/8)12yes—
250C22×C32C22×D411yescharacteristic
251C2×C3×D3—24no—
252C2×C3×D3—48no—
253C2×C3×D3—42no—
254C2×C3×D3—42no—
255C2×C3×D3—42no—
256C2×C3×D3—42no—
257C2×C3×D3—42no—
258C32×C4—21no—
259C32×C4—21no—
260C32×C4—21no—
261C32×C4—21no—
262C32×C4AGL(1,ℤ/8)12yes—
263C32×C4C2×#4112yes—
264C3×Dic3—42no—
265C3×Dic3—42no—
266C2×#41—61no—
267C22×D4—31no—
268C23×C4—61no—
269C2×D8—94no—
270C4⋊Q8—31no—
271#127—31no—
272#124—61no—
273#121—32no—
274#121—61no—
275C4×D4—32no—
276C4×D4—32no—
277C4×D4—32no—
278C4×D4—61no—
279C4×D4—61no—
280C4×D4—61no—
281C2×C4⋊C4—31no—
282C2×C22⋊C4—61no—
283C2×C42D3211yescharacteristic
284#106—94no—
285C4⋊C8—92no—
286#102—94no—
287#102—94no—
288C22⋊C8—92no—
289#97—92no—
290C23×C3—21no—
291C23×C3—64no—
292C23×C3—62no—
293C23×C3—62no—
294C23×C3—122no—
295C23×C3—122no—
296C23×C3C2×#6711yescharacteristic
297C23×C3C2×#6711yescharacteristic
298C22×D3—24no—
299C22×D3—22no—
300C22×D3—22no—
301C22×D3—42no—
302C22×D3—42no—
303C3×Q8—122no—
304C3×D4—34no—
305C3×D4—64no—
306C3×D4—64no—
307C3×D4—62no—
308C3×D4—122no—
309C3×D4—124no—
310C3×D4—122no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—42no—
324C2×C3×C4—42no—
325C2×C3×C4—42no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—124no—
329C2×C3×C4—124no—
330C2×C3×C4—122no—
331C2×C3×C4—124no—
332C2×C3×C4C2×#6711yescharacteristic
333C2×C3×C4C2×#6711yescharacteristic
334C2×C3×C4C2×#6711yescharacteristic
335C2×C3×C4C2×#6711yescharacteristic
336C2×C3×C4C2×#6711yescharacteristic
337C2×C3×C4C2×#6711yescharacteristic
338C2×C3×C4C2×#6711yescharacteristic
339C2×C3×C4C2×#6711yescharacteristic
340C2×C3×C4C2×#6711yescharacteristic
341C2×C3×C4C2×#6711yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343C2×C3×C4C23×D311yescharacteristic
344#67—44no—
345C2×Dic3—22no—
346C2×Dic3—22no—
347C2×Dic3—42no—
348D12—24no—
349D12—22no—
350D12—24no—
351D12—42no—
352D12—42no—
353D12#23514yescomplemented
354C4×D3—44no—
355C4×D3—44no—
356C4×D3—44no—
357Dic6—42no—
358C3⋊C8—64no—
359C3⋊C8—64no—
360C3⋊C8—124no—
361C2×C32—22no—
362C2×C32#52511yescharacteristic
363C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
364C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
365C3×D3—44no—
366C3×D3—82no—
367C24—61no—
368#41—124no—
369C2×Q8—61no—
370C2×D4—32no—
371C2×D4—32no—
372C2×D4—64no—
373C2×D4—62no—
374C2×D4—61no—
375C2×D4—61no—
376C2×D4—61no—
377C22×C4—61no—
378C22×C4—62no—
379C22×C4—62no—
380C22×C4—62no—
381C22×C4—124no—
382C22×C4#62511yescharacteristic
383C22×C4#62511yescharacteristic
384C22×C4C2×D3211yescharacteristic
385D8—188no—
386C2×C8—94no—
387C4⋊C4—32no—
388C4⋊C4—32no—
389C4⋊C4—61no—
390C4⋊C4—61no—
391C22⋊C4—62no—
392C22⋊C4—62no—
393C22⋊C4—62no—
394C22⋊C4—62no—
395C42#62511yescharacteristic
396C42#62511yescharacteristic
397C42C2×D3211yescharacteristic
398C42C2×D3211yescharacteristic
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—22no—
405C22×C3—41no—
406C22×C3—41no—
407C22×C3—64no—
408C22×C3—128no—
409C22×C3—122no—
410C22×C3—122no—
411C22×C3—122no—
412C22×C3—122no—
413C22×C3—122no—
414C22×C3#93212yes—
415C22×C3#94912yes—
416C22×C3C22×#6711yescharacteristic
417C22×C3C22×#6711yescharacteristic
418C2×D3—24no—
419C2×D3—48no—
420C2×D3—42no—
421C2×D3—42no—
422C2×D3—42no—
423C2×D3—42no—
424C2×D3—42no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—22no—
434C3×C4—22no—
435C3×C4—41no—
436C3×C4—41no—
437C3×C4—41no—
438C3×C4—41no—
439C3×C4—122no—
440C3×C4—122no—
441C3×C4#93212yes—
442C3×C4#94912yes—
443C3×C4C2×#23512yes—
444C3×C4D3×#4112yes—
445Dic3—42no—
446Dic3—42no—
447C32#310911yescharacteristic, complemented, Sylow
448C23—64no—
449C23—62no—
450C23—62no—
451C23—122no—
452C23—122no—
453C23C2×#62511yescharacteristic
454Q8—122no—
455D4—34no—
456D4—64no—
457D4—62no—
458D4—64no—
459D4—122no—
460D4—124no—
461D4—122no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—124no—
468C2×C4—124no—
469C2×C4—122no—
470C2×C4—124no—
471C2×C4C2×#62511yescharacteristic
472C2×C4C2×#62511yescharacteristic
473C2×C4C2×#62511yescharacteristic
474C2×C4C2×#62511yescharacteristic
475C2×C4C2×#62511yescharacteristic
476C2×C4C22×D3211yescharacteristic
477C8—184no—
478C2×C3—22no—
479C2×C3—22no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—42no—
484C2×C3—124no—
485C2×C3—242no—
486C2×C3#579111yescharacteristic
487C2×C3C2×#93211yescharacteristic
488C2×C3C2×#93211yescharacteristic
489C2×C3C2×#94911yescharacteristic
490C2×C3C2×#94911yescharacteristic
491C2×C3#582811yescharacteristic
492D3—44no—
493D3—82no—
494C22—21no—
495C22—21no—
496C22—64no—
497C22—128no—
498C22—122no—
499C22—122no—
500C22—122no—
501C22—122no—
502C22—122no—
503C22#6382312yes—
504C22C22×#62511yescharacteristic
505C4—21no—
506C4—21no—
507C4—21no—
508C4—21no—
509C4—122no—
510C4—122no—
511C4#6382312yes—
512C4D3×#23512yes—
513C3—21no—
514C3#8231011yescharacteristic, complemented
515C3#8330011yescharacteristic, complemented
516C2—22no—
517C2—124no—
518C2—242no—
519C2C2×#6382311yescharacteristic
520C2C2×#6382311yescharacteristic
521C2#1059502211yescharacteristic
subgroupG/H
centerC22C22×#625
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. C3×#5477C2semidirect
2. C2×C3×C4×D12C2semidirect
3. #10592625C2semidirect
4. #10591160C2semidirect
5. #10591091C2semidirect
6. #10590347C2semidirect
7. #10590344C2semidirect
8. #10590266C2semidirect
20. C3×#874C22semidirect
26. C3×C4×D12C22semidirect
27. C3×#869C22semidirect
30. C4⋊(C3⋊(C3⋊C8))C22semidirect
31. #63630C22semidirect
32. #63574C22semidirect
34. #63562C22semidirect
37. #5477D3semidirect
38. C2×C4×D12D3semidirect
114. #874C2×D3semidirect
120. C4×D12C2×D3semidirect
121. #869C2×D3semidirect
161. C3×D12#41semidirect
353. D12#235semidirect
447. C32#3109semidirect
514. C3#82310semidirect
515. C3#83300semidirect

Maximal subgroups

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

subgroupindex
C3×#54772
C2×C3×C4×D122
#105926252
#105911602
#105910912
#105903472
#105903442
#105902662
#833003
#823103