Finite Group Databasebeta

← #11863958

Subgroups — #11863958

Order 1152.

2083 conjugacy classes of subgroups.

The subgroup lattice has 511 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×D12C211yesmaximal, characteristic, complemented
2C3×#5791C211yesmaximal, characteristic, complemented
3C2×#63823C212yesmaximal, complemented
4#10592906C211yesmaximal, characteristic, complemented
5#10591169C214yesmaximal, complemented
6#10591160C214yesmaximal, complemented
7#10591085C212yesmaximal, complemented
8#84038—31nomaximal
9#82927—31nomaximal
10C24×C3×D3—21no—
11C23×C32×C4C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic, complemented
13C22×C3×D12—22no—
14C22×C3×D12—21no—
15C22×C3×D12—28no—
16C22×C3×D12C2214yes—
17C22×C3×D12C2212yes—
18C2×#3748C2212yescomplemented
19C3×#953—21no—
20C3×#930C2212yescomplemented
21C3×#929—21no—
22C3×C4×#67—22no—
23C3×#926C2211yescharacteristic, complemented
24C3×#924C2212yescomplemented
25C2×#3715C2214yescomplemented
26#63823—28no—
27C2×#3713C2214yescomplemented
28#63657C2214yescomplemented
29#63562C2218yescomplemented
30C23×C3×D4—31no—
31C23×D12D311yescharacteristic, complemented
32C3×#525—31no—
33C2×#949—32no—
34C2×#932—32no—
35#5791D311yescharacteristic, complemented
36#5218—34no—
37#5217—34no—
38#5215—32no—
39#5207—31no—
40#5207—31no—
41#5207—61no—
42#5046—34no—
43#5036—34no—
44#5001—32no—
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×C3×#67—22no—
56C2×C3×#67—21no—
57C3×#235—24no—
58C2×C3×D12—28no—
59C2×C3×D12—216no—
60C2×C3×D12—24no—
61C2×C3×D12—22no—
62C2×C3×D12—24no—
63C2×C3×D12—216no—
64C2×C3×D12D418yescomplemented
65C2×C3×D12C2314yes—
66C2×C3×D12C2311yescharacteristic, complemented
67C2×C3×C4×D3—21no—
68C2×C3×Dic6C2311yescharacteristic, complemented
69#3748—24no—
70C2×C3⋊(C3⋊C8)C2314yescomplemented
71C3×#217—22no—
72C3×#217—21no—
73C3×(C2×D3)⋊C4—22no—
74C3×C4⋊Dic3C2312yescomplemented
75C3×Dic3⋊C4—22no—
76C3×C4×Dic3—21no—
77#3715—28no—
78#3713—28no—
79#3003—91noSylow
80C25×C3—61no—
81C24×D3—21no—
82C2×C3×#41—31no—
83C22×C3×D4—32no—
84C22×C3×D4—34no—
85C22×C3×D4—68no—
86C22×C3×D4—62no—
87C22×C3×D4—61no—
88C23×C3×C4—21no—
89C23×C3×C4C2×D311yescharacteristic
90C23×C3×C4C2×D311yescharacteristic
91C2×#235C2×D311yescharacteristic, complemented
92C22×D12—22no—
93C22×D12—21no—
94C22×D12—28no—
95C22×D12C2×D314yes—
96C22×D12C2×D312yes—
97C3×#123—61no—
98C3×C22⋊Q8—32no—
99C3×#121—32no—
100C3×#120—61no—
101C3×C4×D4—62no—
102C3×#117—31no—
103#953—21no—
104#949—68no—
105C2×#215—34no—
106C2×#214—34no—
107#932—68no—
108C2×#213—34no—
109C2×#213—34no—
110#930C2×D312yescomplemented
111#929—21no—
112C4×#67—22no—
113#926C2×D311yescharacteristic, complemented
114#924C2×D312yescomplemented
115C2×#208—32no—
116C2×#208—32no—
117C2×#208—62no—
118#832—38no—
119#830—34no—
120#830—34no—
121#830—64no—
122#809—38no—
123C23×C32—22no—
124C23×C32—24no—
125C23×C32C2×D411yescharacteristic
126C23×C32C2×D412yes—
127C22×C3×D3—216no—
128C22×C3×D3—28no—
129C22×C3×D3—24no—
130C22×C3×D3—21no—
131C22×C3×D3—432no—
132C22×C3×D3—48no—
133C22×C3×D3—48no—
134C22×C3×D3—48no—
135C2×C32×C4—22no—
136C2×C32×C4—24no—
137C2×C32×C4—24no—
138C2×C32×C4C2×D414yes—
139C2×C32×C4C2×D412yes—
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2411yescharacteristic
142C3×#67—42no—
143C3×#67—44no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—21no—
146C3×D12—216no—
147C3×D12—28no—
148C3×D12—24no—
149C3×D12—22no—
150C3×D12C2×D418yes—
151C3×C4×D3—42no—
152C3×Dic6—22no—
153C3⋊(C3⋊C8)—24no—
154C23×D4—31no—
155C2×AGL(1,ℤ/8)—92no—
156#525—31no—
157#450—94no—
158#447—94no—
159#418—92no—
160#407—91no—
161C24×C3—21no—
162C24×C3—68no—
163C24×C3—64no—
164C24×C3—62no—
165C24×C3—128no—
166C24×C3#6711yescharacteristic
167C24×C3#6711yescharacteristic
168C23×D3—28no—
169C23×D3—24no—
170C23×D3—22no—
171C23×D3—48no—
172C3×#41—64no—
173C2×C3×Q8—31no—
174C2×C3×D4—38no—
175C2×C3×D4—34no—
176C2×C3×D4—31no—
177C2×C3×D4—616no—
178C2×C3×D4—68no—
179C2×C3×D4—616no—
180C2×C3×D4—62no—
181C2×C3×D4—61no—
182C2×C3×D4—64no—
183C2×C3×D4—64no—
184C2×C3×D4—62no—
185C22×C3×C4—24no—
186C22×C3×C4—24no—
187C22×C3×C4—22no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—22no—
191C22×C3×C4—44no—
192C22×C3×C4—61no—
193C22×C3×C4#6712yes—
194C22×C3×C4#6711yescharacteristic
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—28no—
205C2×D12—216no—
206C2×D12—24no—
207C2×D12—22no—
208C2×D12—24no—
209C2×D12—216no—
210C2×D12#6718yescomplemented
211C2×D12C22×D314yes—
212C2×D12C22×D311yescharacteristic, complemented
213C2×C4×D3—21no—
214C2×Dic6C22×D311yescharacteristic, complemented
215C3×C4⋊C4—32no—
216C3×C4⋊C4—62no—
217C3×C22⋊C4—61no—
218C3×C22⋊C4—62no—
219C3×C22⋊C4—62no—
220C3×C42—61no—
221#217—22no—
222#217—21no—
223#215—68no—
224#214—68no—
225#213—68no—
226#213—68no—
227(C2×D3)⋊C4—22no—
228C4⋊Dic3C22×D312yescomplemented
229Dic3⋊C4—22no—
230C4×Dic3—21no—
231#208—64no—
232#208—64no—
233#208—124no—
234C2×C3⋊C8—34no—
235C2×C3⋊C8—34no—
236C2×C3⋊C8—64no—
237C22×C32—28no—
238C22×C32—22no—
239C22×C32—22no—
240C22×C32—22no—
241C22×C32#12012yes—
242C22×C32AGL(1,ℤ/8)14yescomplemented
243C22×C32C22×D411yescharacteristic
244C2×C3×D3—28no—
245C2×C3×D3—416no—
246C2×C3×D3—432no—
247C2×C3×D3—48no—
248C2×C3×D3—41no—
249C2×C3×D3—42no—
250C32×C4—22no—
251C32×C4#12012yes—
252C32×C4C22×D412yes—
253C3×Dic3—41no—
254C3×Dic3—42no—
255C25—61no—
256C2×#41—31no—
257C22×D4—32no—
258C22×D4—34no—
259C22×D4—68no—
260C22×D4—62no—
261C22×D4—61no—
262C23×C4D3211yescharacteristic
263AGL(1,ℤ/8)—188no—
264C2×SD16—94no—
265C2×D8—94no—
266C2×M16—92no—
267#123—61no—
268C22⋊Q8—32no—
269#121—32no—
270#120—61no—
271C4×D4—62no—
272#117—31no—
273#102—98no—
274C22⋊C8—94no—
275C23×C3—24no—
276C23×C3—22no—
277C23×C3—24no—
278C23×C3—22no—
279C23×C3—22no—
280C23×C3—21no—
281C23×C3—42no—
282C23×C3—44no—
283C23×C3—616no—
284C23×C3—68no—
285C23×C3—64no—
286C23×C3—61no—
287C23×C3—1232no—
288C23×C3—128no—
289C23×C3—128no—
290C23×C3—128no—
291C23×C3C2×#6712yes—
292C23×C3C2×#6711yescharacteristic
293C23×C3C2×#6712yes—
294C23×C3C2×#6711yescharacteristic
295C22×D3—216no—
296C22×D3—28no—
297C22×D3—24no—
298C22×D3—21no—
299C22×D3—432no—
300C22×D3—48no—
301C22×D3—48no—
302C22×D3—48no—
303C3×Q8—62no—
304C3×D4—38no—
305C3×D4—616no—
306C3×D4—68no—
307C3×D4—64no—
308C3×D4—62no—
309C3×D4—124no—
310C3×D4—122no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—24no—
314C2×C3×C4—24no—
315C2×C3×C4—24no—
316C2×C3×C4—24no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—22no—
320C2×C3×C4—24no—
321C2×C3×C4—44no—
322C2×C3×C4—44no—
323C2×C3×C4—42no—
324C2×C3×C4—62no—
325C2×C3×C4—61no—
326C2×C3×C4—122no—
327C2×C3×C4D3×D414yes—
328C2×C3×C4C2×#6712yes—
329C2×C3×C4C2×#6712yes—
330C2×C3×C4C2×#6711yescharacteristic
331C2×C3×C4C2×#6711yescharacteristic
332C2×C3×C4C2×#6714yes—
333C2×C3×C4C23×D311yescharacteristic
334C2×C3×C4C23×D311yescharacteristic
335#67—42no—
336#67—44no—
337C2×Dic3—22no—
338C2×Dic3—21no—
339D12—216no—
340D12—28no—
341D12—22no—
342D12—24no—
343D12C2×#6718yes—
344C4×D3—42no—
345Dic6—22no—
346C3⋊C8—64no—
347C3⋊C8—64no—
348C3⋊C8—124no—
349C2×C32—22no—
350C2×C32—24no—
351C2×C32C2×#12011yescharacteristic
352C2×C32C2×AGL(1,ℤ/8)12yes—
353C3×D3—48no—
354C3×D3—81no—
355C24—68no—
356C24—64no—
357C24—62no—
358C24—128no—
359C24#62511yescharacteristic
360#41—64no—
361C2×Q8—31no—
362C2×D4—34no—
363C2×D4—31no—
364C2×D4—38no—
365C2×D4—616no—
366C2×D4—68no—
367C2×D4—616no—
368C2×D4—62no—
369C2×D4—61no—
370C2×D4—64no—
371C2×D4—62no—
372C2×D4—64no—
373C22×C4—24no—
374C22×C4—61no—
375C22×C4#62512yes—
376C22×C4#62511yescharacteristic
377C22×C4C2×D3212yes—
378C22×C4C2×D3211yescharacteristic
379SD16—188no—
380D8—188no—
381M16—184no—
382C2×C8—94no—
383C4⋊C4—32no—
384C4⋊C4—62no—
385C22⋊C4—61no—
386C22⋊C4—62no—
387C22⋊C4—62no—
388C42—61no—
389C22×C3—28no—
390C22×C3—28no—
391C22×C3—22no—
392C22×C3—22no—
393C22×C3—22no—
394C22×C3—22no—
395C22×C3—22no—
396C22×C3—22no—
397C22×C3—21no—
398C22×C3—24no—
399C22×C3—22no—
400C22×C3—42no—
401C22×C3—42no—
402C22×C3—42no—
403C22×C3—48no—
404C22×C3—68no—
405C22×C3—1216no—
406C22×C3—1232no—
407C22×C3—128no—
408C22×C3—122no—
409C22×C3—121no—
410C22×C3#93214yescomplemented
411C22×C3#93712yes—
412C22×C3#94914yescomplemented
413C22×C3#95312yes—
414C22×C3C22×#6711yescharacteristic
415C22×C3C22×#6711yescharacteristic
416C2×D3—28no—
417C2×D3—432no—
418C2×D3—416no—
419C2×D3—48no—
420C2×D3—41no—
421C2×D3—42no—
422C3×C4—22no—
423C3×C4—22no—
424C3×C4—22no—
425C3×C4—22no—
426C3×C4—42no—
427C3×C4—122no—
428C3×C4—121no—
429C3×C4#93712yes—
430C3×C4#95312yes—
431C3×C4C2×D3×D412yes—
432C3×C4C22×#6712yes—
433Dic3—41no—
434Dic3—42no—
435C32#300311yescharacteristic, complemented, Sylow
436C23—24no—
437C23—22no—
438C23—616no—
439C23—64no—
440C23—68no—
441C23—61no—
442C23—1232no—
443C23—128no—
444C23—128no—
445C23—128no—
446C23C2×#62512yes—
447C23C2×#62511yescharacteristic
448Q8—62no—
449D4—38no—
450D4—616no—
451D4—64no—
452D4—62no—
453D4—68no—
454D4—124no—
455D4—122no—
456C2×C4—22no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—62no—
460C2×C4—61no—
461C2×C4—122no—
462C2×C4C2×#62512yes—
463C2×C4C2×#62511yescharacteristic
464C2×C4D3×#6714yes—
465C2×C4C22×D3211yescharacteristic
466C8—184no—
467C2×C3—24no—
468C2×C3—22no—
469C2×C3—22no—
470C2×C3—24no—
471C2×C3—21no—
472C2×C3—22no—
473C2×C3—44no—
474C2×C3—42no—
475C2×C3—128no—
476C2×C3—241no—
477C2×C3C2×#93212yes—
478C2×C3C2×#93711yescharacteristic
479C2×C3C2×#94912yes—
480C2×C3C2×#95311yescharacteristic
481D3—48no—
482D3—81no—
483C22—28no—
484C22—22no—
485C22—22no—
486C22—22no—
487C22—68no—
488C22—1232no—
489C22—1216no—
490C22—128no—
491C22—121no—
492C22—122no—
493C22#6382314yescomplemented
494C22#6397612yes—
495C22C22×#62511yescharacteristic
496C4—22no—
497C4—121no—
498C4—122no—
499C4#6397612yes—
500C4C2×D3×#6712yes—
501C3—21no—
502C3#8292711yescharacteristic, complemented
503C3#8403811yescharacteristic, complemented
504C2—24no—
505C2—22no—
506C2—128no—
507C2—241no—
508C2C2×#6382312yes—
509C2C2×#6397611yescharacteristic
subgroupG/H
centerC22C22×#625
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×C3×D12C2semidirect
2. C3×#5791C2semidirect
3. C2×#63823C2semidirect
4. #10592906C2semidirect
5. #10591169C2semidirect
6. #10591160C2semidirect
7. #10591085C2semidirect
12. C2×C3×#235C22semidirect
18. C2×#3748C22semidirect
20. C3×#930C22semidirect
23. C3×#926C22semidirect
24. C3×#924C22semidirect
25. C2×#3715C22semidirect
27. C2×#3713C22semidirect
28. #63657C22semidirect
29. #63562C22semidirect
31. C23×D12D3semidirect
35. #5791D3semidirect
64. C2×C3×D12D4semidirect
66. C2×C3×D12C23semidirect
68. C2×C3×Dic6C23semidirect
70. C2×C3⋊(C3⋊C8)C23semidirect
74. C3×C4⋊Dic3C23semidirect
91. C2×#235C2×D3semidirect
110. #930C2×D3semidirect
113. #926C2×D3semidirect
114. #924C2×D3semidirect
210. C2×D12#67semidirect
212. C2×D12C22×D3semidirect
214. C2×Dic6C22×D3semidirect
228. C4⋊Dic3C22×D3semidirect
242. C22×C32AGL(1,ℤ/8)semidirect
410. C22×C3#932semidirect
412. C22×C3#949semidirect
435. C32#3003semidirect
493. C22#63823semidirect
502. C3#82927semidirect
503. C3#84038semidirect

Maximal subgroups

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

subgroupindex
C23×C3×D122
C3×#57912
C2×#638232
#105929062
#105911692
#105911602
#105910852
#840383
#829273