Finite Group Databasebeta

← #11871285

Subgroups — #11871285

Order 1152.

1189 conjugacy classes of subgroups.

The subgroup lattice has 555 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C3×#5477C211yesmaximal, characteristic, complemented
3C3×#4926C211yesmaximal, characteristic, complemented
4#10591168C212yesmaximal, complemented
5#10591092C212yesmaximal, complemented
6#10590355C212yesmaximal, complemented
7#10590346C214yesmaximal, complemented
8#10590300C212yesmaximal, complemented
9#83300—31nomaximal
10#79343—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C4×C3⋊D3—21no—
13C2×C3×#235—21no—
14C2×C32×C42C2211yescharacteristic
15C2×#3752—21no—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C4×C4⋊(C3⋊D3)—21no—
18C4×C4⋊(C3⋊D3)—21no—
19C4×C4⋊(C3⋊D3)C2212yes—
20C4×C4⋊(C3⋊D3)C2212yes—
21C3×#930—21no—
22C3×#930C2212yes—
23C3×#875—21no—
24C3×#874C2211yescharacteristic, complemented
25C3×C4×D12—21no—
26C3×C4×D12C2212yescomplemented
27C3×#869C2211yescharacteristic, complemented
28C2×#3714C2214yes—
29C3×#830C2212yes—
30C3×C4⋊(C3⋊C8)C2212yescomplemented
31C3×#803C2212yescomplemented
32#63573C2214yescomplemented
33#63564C2214yes—
34#63563C2214yescomplemented
35C3×#532—31no—
36#5477D311yescharacteristic, complemented
37C2×C4×D12—31no—
38C2×C4×D12—31no—
39C2×C4×D12—61no—
40C3×#432—31no—
41#5084—32no—
42#5072—32no—
43#5036—32no—
44#5034—32no—
45#5014—34no—
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
56C22×C3⋊Dic3—21no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)—24no—
59C2×C4⋊(C3⋊D3)C2312yes—
60C2×C4×C3⋊D3—22no—
61C2×C4×C3⋊D3—22no—
62C2×C4×C3⋊D3—44no—
63C2×C3×#67—22no—
64C3×#235—44no—
65C2×C3×D12—21no—
66C2×C3×D12—21no—
67C2×C3×D12C2312yes—
68C2×C3×C4×D3—22no—
69C2×C3×Dic6—21no—
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
85C2×C3×#41—61no—
86C2×#235—21no—
87C22×D12—31no—
88C22×D12—31no—
89C22×D12—61no—
90C22×C4×D3—62no—
91C22×C4×D3—61no—
92C22×C4×D3—61no—
93C3×C4⋊Q8—31no—
94C3×#127—31no—
95C3×#124—61no—
96C3×#121—32no—
97C3×#121—61no—
98C3×C4×D4—32no—
99C3×C4×D4—61no—
100C2×C3×C42—21no—
101C2×C3×C42C2×D311yescharacteristic
102C2×C3×C42C2×D311yescharacteristic
103C2×#213—34no—
104#930—21no—
105#930C2×D312yes—
106C2×(C2×D3)⋊C4—62no—
107C2×(C2×D3)⋊C4—61no—
108C2×(C2×D3)⋊C4—61no—
109C2×C4⋊Dic3—31no—
110C2×C4⋊Dic3—31no—
111C2×C4⋊Dic3—61no—
112C2×D24—34no—
113#875—21no—
114#874C2×D311yescharacteristic, complemented
115C4×D12—21no—
116C4×D12—32no—
117C4×D12—32no—
118C4×D12—32no—
119C4×D12—32no—
120C4×D12—62no—
121C4×D12—62no—
122C4×D12—62no—
123C4×D12—62no—
124C4×D12—61no—
125C4×D12—61no—
126C4×D12—61no—
127C4×D12—61no—
128C4×D12C2×D312yescomplemented
129#869C2×D311yescharacteristic, complemented
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—24no—
144C22×C3⋊D3—22no—
145C22×C3⋊D3—42no—
146C22×C3⋊D3—42no—
147C22×C3×D3—22no—
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
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—42no—
159C4⋊(C3⋊D3)—24no—
160C4⋊(C3⋊D3)—22no—
161C4⋊(C3⋊D3)#4114yescomplemented
162C4×C3⋊D3—44no—
163C4×C3⋊D3—44no—
164C3×#67—44no—
165C2×C3×Dic3—22no—
166C3×D12—24no—
167C3×D12—42no—
168C3×D12—42no—
169C3×C4×D3—44no—
170C3×Dic6—42no—
171C3×C3⋊C8—24no—
172#532—31no—
173C2×C4×D4—91no—
174#481—92no—
175#476—92no—
176#459—92no—
177#447—92no—
178#442—94no—
179#432—31no—
180C23×D3—62no—
181C23×D3—61no—
182C23×D3—61no—
183C3×#41—124no—
184C2×C3×Q8—61no—
185C2×C3×D4—32no—
186C2×C3×D4—62no—
187C2×C3×D4—61no—
188C2×C3×D4—61no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—62no—
193C22×C3×C4D1211yescharacteristic
194C22×C3×C4D1211yescharacteristic
195C22×C3×C4#6711yescharacteristic
196C22×C3×C4#6711yescharacteristic
197C22×C3×C4C22×D311yescharacteristic
198C22×C3×C4C22×D311yescharacteristic
199C2×#67—22no—
200C22×Dic3—62no—
201C22×Dic3—61no—
202C22×Dic3—61no—
203#235—44no—
204C2×D12—21no—
205C2×D12—21no—
206C2×D12—32no—
207C2×D12—32no—
208C2×D12—62no—
209C2×D12—64no—
210C2×D12—64no—
211C2×D12—62no—
212C2×D12—68no—
213C2×D12—61no—
214C2×D12—61no—
215C2×D12C22×D312yes—
216C2×C4×D3—22no—
217C2×C4×D3—64no—
218C2×C4×D3—64no—
219C2×C4×D3—62no—
220C2×C4×D3—62no—
221C2×C4×D3—62no—
222C2×C4×D3—62no—
223C2×C4×D3—128no—
224C2×C4×D3—124no—
225C2×C4×D3—124no—
226C2×Dic6—21no—
227C2×C3×C8—34no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—61no—
230C3×C22⋊C4—62no—
231C3×C22⋊C4—62no—
232C3×C42—21no—
233C3×C42—21no—
234C3×C42—21no—
235C3×C42—21no—
236C3×C42D1211yescharacteristic
237C3×C42D1211yescharacteristic
238C3×C42#6711yescharacteristic
239C3×C42#6711yescharacteristic
240C3×C42C22×D311yescharacteristic
241C3×C42C22×D311yescharacteristic
242C3×C42C22×D311yescharacteristic
243C3×C42C22×D311yescharacteristic
244#213—68no—
245(C2×D3)⋊C4—22no—
246(C2×D3)⋊C4—22no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—62no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—62no—
252(C2×D3)⋊C4—62no—
253C4⋊Dic3—21no—
254C4⋊Dic3—32no—
255C4⋊Dic3—32no—
256C4⋊Dic3—62no—
257C4⋊Dic3—62no—
258C4⋊Dic3—61no—
259C4⋊Dic3—61no—
260C4⋊Dic3C22×D312yes—
261C2×C3⋊C8C22×D314yes—
262D24—68no—
263C22×C32—21no—
264C22×C32—21no—
265C22×C32AGL(1,ℤ/8)12yes—
266C22×C32C22×D411yescharacteristic
267C2×C3⋊D3—24no—
268C2×C3⋊D3—48no—
269C2×C3⋊D3—42no—
270C2×C3⋊D3—42no—
271C2×C3×D3—42no—
272C2×C3×D3—42no—
273C2×C3×D3—42no—
274C32×C4—21no—
275C32×C4—21no—
276C32×C4—21no—
277C32×C4—21no—
278C32×C4AGL(1,ℤ/8)12yes—
279C32×C4C2×#4112yes—
280C3⋊Dic3—42no—
281C3×Dic3—42no—
282C2×#41—61no—
283C22×D4—91no—
284C23×C4—181no—
285C2×D8—94no—
286C4⋊Q8—31no—
287#127—31no—
288#124—61no—
289#121—32no—
290#121—61no—
291C4×D4—32no—
292C4×D4—61no—
293C4×D4—92no—
294C4×D4—92no—
295C4×D4—181no—
296C4×D4—181no—
297C2×C4⋊C4—91no—
298C2×C22⋊C4—181no—
299C2×C42D3211yescharacteristic
300#106—94no—
301C4⋊C8—32no—
302#102—94no—
303#102—94no—
304C22⋊C8—32no—
305#97—32no—
306C23×C3—21no—
307C23×C3—62no—
308C23×C3C2×D1211yescharacteristic
309C23×C3C2×#6711yescharacteristic
310C22×D3—22no—
311C22×D3—64no—
312C22×D3—68no—
313C22×D3—64no—
314C22×D3—64no—
315C22×D3—62no—
316C22×D3—62no—
317C22×D3—124no—
318C22×D3—122no—
319C22×D3—122no—
320C22×D3—124no—
321C22×D3—122no—
322C22×D3—122no—
323C3×Q8—122no—
324C3×D4—64no—
325C3×D4—122no—
326C3×D4—124no—
327C3×D4—122no—
328C2×C3×C4—24no—
329C2×C3×C4—24no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—42no—
343C2×C3×C4—62no—
344C2×C3×C4—124no—
345C2×C3×C4C2×D1211yescharacteristic
346C2×C3×C4C2×D1211yescharacteristic
347C2×C3×C4C2×D1211yescharacteristic
348C2×C3×C4C2×D1211yescharacteristic
349C2×C3×C4C2×D1211yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351C2×C3×C4C2×#6711yescharacteristic
352C2×C3×C4C2×#6711yescharacteristic
353C2×C3×C4C2×#6711yescharacteristic
354C2×C3×C4C2×#6711yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356C2×C3×C4C23×D311yescharacteristic
357#67—44no—
358C2×Dic3—22no—
359C2×Dic3—64no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—124no—
363C2×Dic3—122no—
364C2×Dic3—122no—
365D12—24no—
366D12—34no—
367D12—34no—
368D12—42no—
369D12—42no—
370D12—64no—
371D12—68no—
372D12—64no—
373D12—64no—
374D12—64no—
375D12—62no—
376D12—62no—
377C4×D3—44no—
378C4×D3—128no—
379C4×D3—124no—
380C4×D3—124no—
381C4×D3—128no—
382C4×D3—124no—
383C4×D3—124no—
384Dic6—42no—
385C3×C8—64no—
386C3⋊C8—24no—
387C2×C32—22no—
388C2×C32#52511yescharacteristic
389C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
390C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
391C3⋊D3—44no—
392C3×D3—82no—
393C24—181no—
394#41—124no—
395C2×Q8—61no—
396C2×D4—32no—
397C2×D4—62no—
398C2×D4—61no—
399C2×D4—61no—
400C2×D4—92no—
401C2×D4—184no—
402C2×D4—181no—
403C22×C4—62no—
404C22×C4—181no—
405C22×C4—182no—
406C22×C4—182no—
407C22×C4—364no—
408C22×C4#62611yescharacteristic
409C22×C4#62611yescharacteristic
410C22×C4C2×D3211yescharacteristic
411D8—188no—
412C2×C8—34no—
413C4⋊C4—32no—
414C4⋊C4—61no—
415C4⋊C4—92no—
416C4⋊C4—181no—
417C22⋊C4—62no—
418C22⋊C4—62no—
419C22⋊C4—182no—
420C22⋊C4—182no—
421C42#62611yescharacteristic
422C42#62611yescharacteristic
423C42C2×D3211yescharacteristic
424C42C2×D3211yescharacteristic
425C22×C3—22no—
426C22×C3—22no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—22no—
433C22×C3—122no—
434C22×C3—122no—
435C22×C3—122no—
436C22×C3#90812yes—
437C22×C3#93212yes—
438C22×C3C22×D1211yescharacteristic
439C22×C3C22×#6711yescharacteristic
440C2×D3—42no—
441C2×D3—42no—
442C2×D3—42no—
443C2×D3—68no—
444C2×D3—64no—
445C2×D3—64no—
446C2×D3—124no—
447C2×D3—1216no—
448C2×D3—128no—
449C2×D3—128no—
450C2×D3—124no—
451C2×D3—122no—
452C2×D3—122no—
453C2×D3—122no—
454C2×D3—122no—
455C3×C4—22no—
456C3×C4—22no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—22no—
466C3×C4—22no—
467C3×C4—41no—
468C3×C4—41no—
469C3×C4—122no—
470C3×C4#90812yes—
471C3×C4#94912yes—
472C3×C4D3×#4112yes—
473C3×C4D3×#4112yes—
474Dic3—42no—
475Dic3—124no—
476Dic3—122no—
477Dic3—122no—
478C32#310911yescharacteristic, complemented, Sylow
479C23—62no—
480C23—184no—
481C23—182no—
482C23—362no—
483C23—362no—
484C23C2×#62611yescharacteristic
485Q8—122no—
486D4—64no—
487D4—94no—
488D4—122no—
489D4—124no—
490D4—122no—
491D4—184no—
492D4—182no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—62no—
497C2×C4—124no—
498C2×C4—182no—
499C2×C4—364no—
500C2×C4—362no—
501C2×C4—364no—
502C2×C4C2×#62611yescharacteristic
503C2×C4C2×#62611yescharacteristic
504C2×C4C2×#62611yescharacteristic
505C2×C4C2×#62611yescharacteristic
506C2×C4C2×#62611yescharacteristic
507C2×C4C22×D3211yescharacteristic
508C8—64no—
509C2×C3—24no—
510C2×C3—22no—
511C2×C3—22no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—242no—
516C2×C3#552411yescharacteristic
517C2×C3C2×#90811yescharacteristic
518C2×C3C2×#90811yescharacteristic
519C2×C3C2×#93211yescharacteristic
520C2×C3C2×#94911yescharacteristic
521C2×C3#582811yescharacteristic
522D3—82no—
523D3—128no—
524D3—124no—
525D3—124no—
526C22—21no—
527C22—21no—
528C22—122no—
529C22—122no—
530C22—122no—
531C22—184no—
532C22—368no—
533C22—362no—
534C22—362no—
535C22#6383012yes—
536C22C22×#62611yescharacteristic
537C4—21no—
538C4—21no—
539C4—21no—
540C4—21no—
541C4—122no—
542C4—362no—
543C4#6382512yes—
544C4#6430612yes—
545C3—21no—
546C3#7934311yescharacteristic, complemented
547C3#8330011yescharacteristic, complemented
548C2—22no—
549C2—242no—
550C2—364no—
551C2C2×#6382511yescharacteristic
552C2C2×#6383011yescharacteristic
553C2#1059503411yescharacteristic
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. C2×C4×C4⋊(C3⋊D3)C2semidirect
2. C3×#5477C2semidirect
3. C3×#4926C2semidirect
4. #10591168C2semidirect
5. #10591092C2semidirect
6. #10590355C2semidirect
7. #10590346C2semidirect
8. #10590300C2semidirect
24. C3×#874C22semidirect
26. C3×C4×D12C22semidirect
27. C3×#869C22semidirect
30. C3×C4⋊(C3⋊C8)C22semidirect
31. C3×#803C22semidirect
32. #63573C22semidirect
34. #63563C22semidirect
36. #5477D3semidirect
46. #4926D3semidirect
114. #874C2×D3semidirect
128. C4×D12C2×D3semidirect
129. #869C2×D3semidirect
140. C4⋊(C3⋊C8)C2×D3semidirect
141. #803C2×D3semidirect
161. C4⋊(C3⋊D3)#41semidirect
478. C32#3109semidirect
546. C3#79343semidirect
547. C3#83300semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊(C3⋊D3)2
C3×#54772
C3×#49262
#105911682
#105910922
#105903552
#105903462
#105903002
#833003
#793433