Finite Group Databasebeta

← #11863957

Subgroups — #11863957

Order 1152.

2669 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C3×#5791C211yesmaximal, characteristic, complemented
3C2×#63825C212yesmaximal, complemented
4C3×#5207C211yesmaximal, characteristic, complemented
5#10591183C214yesmaximal, complemented
6#10591168C214yesmaximal, complemented
7#10591096C212yesmaximal, complemented
8#82927—31nomaximal
9#78637—31nomaximal
10C24×C3⋊D3—21no—
11C23×C32×C4C2211yescharacteristic
12C22×C4⋊(C3⋊D3)—22no—
13C22×C4⋊(C3⋊D3)—21no—
14C22×C4⋊(C3⋊D3)—28no—
15C22×C4⋊(C3⋊D3)C2214yes—
16C22×C4⋊(C3⋊D3)C2212yes—
17C2×C3×#235C2211yescharacteristic, complemented
18C3×#953—21no—
19C3×#930C2212yescomplemented
20C3×#929—21no—
21C3×C4×#67—22no—
22C3×#926C2211yescharacteristic, complemented
23C3×#924C2212yescomplemented
24C2×C3×#208C2212yescomplemented
25C2×#3717C2214yescomplemented
26#63825—28no—
27C2×#3714C2214yescomplemented
28C3×#830C2214yescomplemented
29#63564C2218yescomplemented
30C23×D12—31no—
31C23×D12—31no—
32C23×D12—61no—
33C3×#525—31no—
34C2×#949—32no—
35#5791D311yescharacteristic, complemented
36C2×#908—32no—
37C3×#407—31no—
38#5207D311yescharacteristic, complemented
39#5131—32no—
40#5046—34no—
41#5036—34no—
42#5001—32no—
43#4732—34no—
44#4731—34no—
45C24×C32D411yescharacteristic
46C23×C3⋊D3—28no—
47C23×C3⋊D3—24no—
48C23×C3⋊D3—22no—
49C23×C3⋊D3—48no—
50C22×C32×C4—24no—
51C22×C32×C4D412yes—
52C22×C32×C4D411yescharacteristic
53C22×C32×C4C2312yes—
54C22×C32×C4C2311yescharacteristic
55C2×C4⋊(C3⋊D3)—28no—
56C2×C4⋊(C3⋊D3)—216no—
57C2×C4⋊(C3⋊D3)—24no—
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)—24no—
60C2×C4⋊(C3⋊D3)—216no—
61C2×C4⋊(C3⋊D3)D418yescomplemented
62C2×C4⋊(C3⋊D3)C2314yes—
63C2×C3×#67—22no—
64C2×C3×#67—21no—
65C3×#235—24no—
66C2×C3×D12C2311yescharacteristic, complemented
67C2×C3×C4×D3—21no—
68C2×C3×Dic6C2311yescharacteristic, complemented
69C3×#217—22no—
70C3×#217—21no—
71C3×(C2×D3)⋊C4—22no—
72C3×C4⋊Dic3C2312yescomplemented
73C3×Dic3⋊C4—22no—
74C3×C4×Dic3—21no—
75C3×#208—24no—
76C2×C3×C3⋊C8C2314yescomplemented
77#3717—28no—
78#3714—28no—
79#3003—91noSylow
80C24×D3—62no—
81C24×D3—61no—
82C24×D3—61no—
83C2×C3×#41—31no—
84C23×C3×C4—21no—
85C23×C3×C4C2×D311yescharacteristic
86C23×C3×C4C2×D311yescharacteristic
87C2×#235C2×D311yescharacteristic, complemented
88C22×D12—32no—
89C22×D12—32no—
90C22×D12—34no—
91C22×D12—34no—
92C22×D12—62no—
93C22×D12—64no—
94C22×D12—68no—
95C22×D12—68no—
96C22×D12—616no—
97C22×D12—64no—
98C22×D12—62no—
99C22×D12—62no—
100C22×D12—61no—
101C22×D12—62no—
102C22×D12—61no—
103C2×C3×M16—32no—
104C3×#123—61no—
105C3×C22⋊Q8—32no—
106C3×#121—32no—
107C3×#120—61no—
108C3×C4×D4—62no—
109C3×#117—31no—
110#953—21no—
111#949—68no—
112C2×#215—34no—
113C2×#213—34no—
114#930C2×D312yescomplemented
115#929—21no—
116C4×#67—22no—
117#926C2×D311yescharacteristic, complemented
118#924C2×D312yescomplemented
119C2×#208C2×D312yescomplemented
120#908—68no—
121C2×D24—34no—
122C2×#204—34no—
123C3×C22⋊C8—34no—
124#830C2×D314yescomplemented
125#821—38no—
126#809—38no—
127C23×C32—22no—
128C23×C32—24no—
129C23×C32C2×D411yescharacteristic
130C23×C32C2×D412yes—
131C22×C3⋊D3—216no—
132C22×C3⋊D3—28no—
133C22×C3⋊D3—24no—
134C22×C3⋊D3—432no—
135C22×C3⋊D3—48no—
136C22×C3⋊D3—48no—
137C22×C3⋊D3—48no—
138C22×C3×D3—21no—
139C2×C32×C4—22no—
140C2×C32×C4—24no—
141C2×C32×C4—24no—
142C2×C32×C4C2×D412yes—
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D414yes—
145C2×C32×C4C2411yescharacteristic
146C4⋊(C3⋊D3)—216no—
147C4⋊(C3⋊D3)—28no—
148C4⋊(C3⋊D3)—24no—
149C4⋊(C3⋊D3)C2×D418yes—
150C3×#67—42no—
151C3×#67—44no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—21no—
154C3×D12—22no—
155C3×C4×D3—42no—
156C3×Dic6—22no—
157C3×C3⋊C8—24no—
158C23×D4—91no—
159C2×AGL(1,ℤ/8)—92no—
160#525—31no—
161#450—94no—
162#447—94no—
163#418—92no—
164#407—31no—
165C24×C3—21no—
166C24×C3D1211yescharacteristic
167C24×C3#6711yescharacteristic
168C23×D3—616no—
169C23×D3—68no—
170C23×D3—68no—
171C23×D3—68no—
172C23×D3—64no—
173C23×D3—64no—
174C23×D3—62no—
175C23×D3—64no—
176C23×D3—62no—
177C23×D3—1216no—
178C23×D3—128no—
179C23×D3—128no—
180C3×#41—64no—
181C2×C3×Q8—31no—
182C2×C3×D4—31no—
183C2×C3×D4—62no—
184C2×C3×D4—61no—
185C22×C3×C4—28no—
186C22×C3×C4—24no—
187C22×C3×C4—24no—
188C22×C3×C4—22no—
189C22×C3×C4—21no—
190C22×C3×C4—22no—
191C22×C3×C4—21no—
192C22×C3×C4—61no—
193C22×C3×C4D1212yes—
194C22×C3×C4D1211yescharacteristic
195C22×C3×C4#6712yes—
196C22×C3×C4#6711yescharacteristic
197C22×C3×C4C22×D312yes—
198C22×C3×C4C22×D312yes—
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C2×#67—22no—
202C2×#67—21no—
203#235—24no—
204C2×D12—38no—
205C2×D12—38no—
206C2×D12—34no—
207C2×D12—34no—
208C2×D12—68no—
209C2×D12—64no—
210C2×D12—616no—
211C2×D12—616no—
212C2×D12—632no—
213C2×D12—616no—
214C2×D12—632no—
215C2×D12—68no—
216C2×D12—68no—
217C2×D12—616no—
218C2×D12—616no—
219C2×D12—68no—
220C2×D12—64no—
221C2×D12—68no—
222C2×D12—64no—
223C2×D12—62no—
224C2×D12—64no—
225C2×D12—64no—
226C2×D12—64no—
227C2×D12—62no—
228C2×D12C22×D311yescharacteristic, complemented
229C2×C4×D3—21no—
230C2×Dic6C22×D311yescharacteristic, complemented
231C3×M16—64no—
232C2×C3×C8—34no—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—62no—
235C3×C22⋊C4—61no—
236C3×C22⋊C4—62no—
237C3×C22⋊C4—62no—
238C3×C42—61no—
239#217—22no—
240#217—21no—
241#215—68no—
242#213—68no—
243(C2×D3)⋊C4—22no—
244C4⋊Dic3C22×D312yescomplemented
245Dic3⋊C4—22no—
246C4×Dic3—21no—
247#208—24no—
248C2×C3⋊C8C22×D314yescomplemented
249D24—68no—
250#204—68no—
251C22×C32—28no—
252C22×C32—22no—
253C22×C32—22no—
254C22×C32—22no—
255C22×C32#12012yes—
256C22×C32AGL(1,ℤ/8)14yescomplemented
257C22×C32C22×D411yescharacteristic
258C2×C3⋊D3—28no—
259C2×C3⋊D3—416no—
260C2×C3⋊D3—432no—
261C2×C3⋊D3—48no—
262C2×C3×D3—41no—
263C2×C3×D3—42no—
264C32×C4—22no—
265C32×C4#12012yes—
266C32×C4C22×D412yes—
267C3×Dic3—41no—
268C3×Dic3—42no—
269C25—181no—
270C2×#41—31no—
271C22×D4—92no—
272C22×D4—94no—
273C22×D4—188no—
274C22×D4—182no—
275C22×D4—181no—
276C23×C4D3211yescharacteristic
277AGL(1,ℤ/8)—188no—
278C2×SD16—94no—
279C2×D8—94no—
280C2×M16—32no—
281#123—61no—
282C22⋊Q8—32no—
283#121—32no—
284#120—61no—
285C4×D4—62no—
286#117—31no—
287#102—98no—
288C22⋊C8—34no—
289C23×C3—24no—
290C23×C3—28no—
291C23×C3—22no—
292C23×C3—24no—
293C23×C3—22no—
294C23×C3—24no—
295C23×C3—22no—
296C23×C3—21no—
297C23×C3—61no—
298C23×C3C2×D1211yescharacteristic
299C23×C3C2×D1212yes—
300C23×C3C2×#6711yescharacteristic
301C23×C3C2×#6712yes—
302C22×D3—21no—
303C22×D3—632no—
304C22×D3—616no—
305C22×D3—616no—
306C22×D3—68no—
307C22×D3—616no—
308C22×D3—68no—
309C22×D3—68no—
310C22×D3—64no—
311C22×D3—64no—
312C22×D3—1264no—
313C22×D3—1232no—
314C22×D3—1232no—
315C22×D3—1216no—
316C22×D3—1216no—
317C22×D3—128no—
318C22×D3—128no—
319C22×D3—128no—
320C22×D3—128no—
321C22×D3—1216no—
322C22×D3—128no—
323C22×D3—128no—
324C3×Q8—62no—
325C3×D4—62no—
326C3×D4—122no—
327C3×D4—124no—
328C2×C3×C4—24no—
329C2×C3×C4—28no—
330C2×C3×C4—28no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—24no—
334C2×C3×C4—24no—
335C2×C3×C4—24no—
336C2×C3×C4—24no—
337C2×C3×C4—21no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—24no—
341C2×C3×C4—62no—
342C2×C3×C4—61no—
343C2×C3×C4—122no—
344C2×C3×C4C2×D1212yes—
345C2×C3×C4C2×D1211yescharacteristic
346C2×C3×C4D3×D414yes—
347C2×C3×C4D3×D414yes—
348C2×C3×C4C2×#6712yes—
349C2×C3×C4C2×#6711yescharacteristic
350C2×C3×C4C23×D311yescharacteristic
351C2×C3×C4C23×D311yescharacteristic
352#67—42no—
353#67—44no—
354C2×Dic3—22no—
355C2×Dic3—21no—
356D12—22no—
357D12—38no—
358D12—38no—
359D12—68no—
360D12—632no—
361D12—616no—
362D12—616no—
363D12—68no—
364D12—616no—
365D12—68no—
366D12—68no—
367D12—64no—
368D12—64no—
369C4×D3—42no—
370Dic6—22no—
371C3×C8—64no—
372C3⋊C8—24no—
373C2×C32—22no—
374C2×C32—24no—
375C2×C32C2×#12011yescharacteristic
376C2×C32C2×AGL(1,ℤ/8)12yes—
377C3⋊D3—48no—
378C3×D3—81no—
379C24—188no—
380C24—184no—
381C24—182no—
382C24—368no—
383C24#62611yescharacteristic
384#41—64no—
385C2×Q8—31no—
386C2×D4—31no—
387C2×D4—62no—
388C2×D4—61no—
389C2×D4—94no—
390C2×D4—98no—
391C2×D4—1816no—
392C2×D4—188no—
393C2×D4—1816no—
394C2×D4—184no—
395C2×D4—182no—
396C2×D4—184no—
397C22×C4—24no—
398C22×C4—61no—
399C22×C4#62612yes—
400C22×C4#62611yescharacteristic
401C22×C4C2×D3212yes—
402C22×C4C2×D3211yescharacteristic
403SD16—188no—
404D8—188no—
405M16—64no—
406C2×C8—34no—
407C4⋊C4—32no—
408C4⋊C4—62no—
409C22⋊C4—61no—
410C22⋊C4—62no—
411C22⋊C4—62no—
412C42—61no—
413C22×C3—24no—
414C22×C3—216no—
415C22×C3—28no—
416C22×C3—28no—
417C22×C3—24no—
418C22×C3—24no—
419C22×C3—22no—
420C22×C3—22no—
421C22×C3—22no—
422C22×C3—22no—
423C22×C3—22no—
424C22×C3—22no—
425C22×C3—21no—
426C22×C3—24no—
427C22×C3—22no—
428C22×C3—121no—
429C22×C3—122no—
430C22×C3#88212yes—
431C22×C3#90814yescomplemented
432C22×C3#93712yes—
433C22×C3#94914yescomplemented
434C22×C3C22×D1211yescharacteristic
435C22×C3C22×#6711yescharacteristic
436C2×D3—41no—
437C2×D3—42no—
438C2×D3—616no—
439C2×D3—68no—
440C2×D3—68no—
441C2×D3—1264no—
442C2×D3—1232no—
443C2×D3—1216no—
444C2×D3—1232no—
445C2×D3—1216no—
446C2×D3—1232no—
447C2×D3—1216no—
448C2×D3—128no—
449C2×D3—128no—
450C3×C4—24no—
451C3×C4—22no—
452C3×C4—22no—
453C3×C4—22no—
454C3×C4—22no—
455C3×C4—121no—
456C3×C4—122no—
457C3×C4#88212yes—
458C3×C4#93712yes—
459C3×C4C2×D3×D412yes—
460C3×C4C2×D3×D412yes—
461Dic3—41no—
462Dic3—42no—
463C32#300311yescharacteristic, complemented, Sylow
464C23—24no—
465C23—22no—
466C23—61no—
467C23—1816no—
468C23—184no—
469C23—188no—
470C23—3632no—
471C23—368no—
472C23—368no—
473C23—368no—
474C23C2×#62612yes—
475C23C2×#62611yescharacteristic
476Q8—62no—
477D4—62no—
478D4—98no—
479D4—124no—
480D4—122no—
481D4—1816no—
482D4—184no—
483D4—188no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—62no—
488C2×C4—61no—
489C2×C4—122no—
490C2×C4C2×#62612yes—
491C2×C4C2×#62611yescharacteristic
492C2×C4#381114yes—
493C2×C4C22×D3211yescharacteristic
494C8—64no—
495C2×C3—28no—
496C2×C3—24no—
497C2×C3—22no—
498C2×C3—24no—
499C2×C3—22no—
500C2×C3—24no—
501C2×C3—21no—
502C2×C3—22no—
503C2×C3—241no—
504C2×C3C2×#88211yescharacteristic
505C2×C3C2×#90812yes—
506C2×C3C2×#93711yescharacteristic
507C2×C3C2×#94912yes—
508D3—81no—
509D3—1216no—
510D3—128no—
511D3—128no—
512C22—28no—
513C22—22no—
514C22—22no—
515C22—22no—
516C22—121no—
517C22—122no—
518C22—188no—
519C22—3632no—
520C22—3616no—
521C22—368no—
522C22#6382514yescomplemented
523C22#6398112yes—
524C22C22×#62611yescharacteristic
525C4—22no—
526C4—121no—
527C4—122no—
528C4#6398112yes—
529C4C2×#381112yes—
530C3—21no—
531C3#7863711yescharacteristic, complemented
532C3#8292711yescharacteristic, complemented
533C2—24no—
534C2—22no—
535C2—241no—
536C2—368no—
537C2C2×#6382512yes—
538C2C2×#6398111yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC22×C32C22×D4
hypercenterC23×C4D32
hypocenterC32#3003
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×C4⋊(C3⋊D3)C2semidirect
2. C3×#5791C2semidirect
3. C2×#63825C2semidirect
4. C3×#5207C2semidirect
5. #10591183C2semidirect
6. #10591168C2semidirect
7. #10591096C2semidirect
17. C2×C3×#235C22semidirect
19. C3×#930C22semidirect
22. C3×#926C22semidirect
23. C3×#924C22semidirect
24. C2×C3×#208C22semidirect
25. C2×#3717C22semidirect
27. C2×#3714C22semidirect
28. C3×#830C22semidirect
29. #63564C22semidirect
35. #5791D3semidirect
38. #5207D3semidirect
61. C2×C4⋊(C3⋊D3)D4semidirect
66. C2×C3×D12C23semidirect
68. C2×C3×Dic6C23semidirect
72. C3×C4⋊Dic3C23semidirect
76. C2×C3×C3⋊C8C23semidirect
87. C2×#235C2×D3semidirect
114. #930C2×D3semidirect
117. #926C2×D3semidirect
118. #924C2×D3semidirect
119. C2×#208C2×D3semidirect
124. #830C2×D3semidirect
228. C2×D12C22×D3semidirect
230. C2×Dic6C22×D3semidirect
244. C4⋊Dic3C22×D3semidirect
248. C2×C3⋊C8C22×D3semidirect
256. C22×C32AGL(1,ℤ/8)semidirect
431. C22×C3#908semidirect
433. C22×C3#949semidirect
463. C32#3003semidirect
522. C22#63825semidirect
531. C3#78637semidirect
532. C3#82927semidirect

Maximal subgroups

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

subgroupindex
C23×C4⋊(C3⋊D3)2
C3×#57912
C2×#638252
C3×#52072
#105911832
#105911682
#105910962
#829273
#786373