Finite Group Databasebeta

← #11867131

Subgroups — #11867131

Order 1152.

1644 conjugacy classes of subgroups.

The subgroup lattice has 519 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#525C211yesmaximal, characteristic, complemented
2C2×#64158C211yesmaximal, characteristic, complemented
3C2×#64139C211yesmaximal, characteristic, complemented
4C22×#3748C211yesmaximal, characteristic, complemented
5#10592931C211yesmaximal, characteristic, complemented
6#10592748C212yesmaximal, complemented
7#10592747C212yesmaximal, complemented
8#10592738C212yesmaximal, complemented
9#10592737C212yesmaximal, complemented
10#10592700C211yesmaximal, characteristic, complemented
11#10592694C211yesmaximal, characteristic, complemented
12#82924—34nomaximal
13C2×C32×#41C2211yescharacteristic
14C23×C32×C4C2211yescharacteristic
15C22×#638—21no—
16C22×C4⋊(C3⋊D3)C2211yescharacteristic
17C32×#123—21no—
18C32×C22⋊Q8C2211yescharacteristic, complemented
19C32×C22⋊Q8C2211yescharacteristic, complemented
20C32×#121C2211yescharacteristic, complemented
21C32×#121C2211yescharacteristic, complemented
22C32×#120—21no—
23C32×C4×D4—21no—
24C32×C4×D4—21no—
25C32×#117C2211yescharacteristic
26#64158—24no—
27C2×#3755C2212yescomplemented
28C2×#3753C2212yescomplemented
29#64139—21no—
30#64139—21no—
31#64139C2212yes—
32#64139C2212yes—
33C2×#3752—21no—
34C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
35C2×#3748—24no—
36C2×#3748C2211yescharacteristic
37C2×#3748C2211yescharacteristic
38C2×#3748C2212yescomplemented
39C22×C3⋊(C3⋊C8)C2212yescomplemented
40#63662C2212yescomplemented
41#63659C2212yescomplemented
42#63636C2212yescomplemented
43#63636C2212yescomplemented
44#63635C2212yescomplemented
45#63634C2212yescomplemented
46C3×#525D314yescomplemented
47C2×#949—34no—
48C2×#930—34no—
49C22×#208—34no—
50#5232—34no—
51#5049—38no—
52#5048—38no—
53#5039—38no—
54#5038—38no—
55#5001—34no—
56#4995—34no—
57C24×C32D411yescharacteristic
58C23×C3⋊D3—21no—
59C32×#41—22no—
60C32×#41—22no—
61C2×C32×Q8C2311yescharacteristic
62C2×C32×D4—21no—
63C2×C32×D4—21no—
64C2×C32×D4—21no—
65C2×C32×D4C2311yescharacteristic
66C22×C32×C4—22no—
67C22×C32×C4—22no—
68C22×C32×C4—21no—
69C22×C32×C4D411yescharacteristic
70C22×C32×C4D411yescharacteristic
71C22×C32×C4D411yescharacteristic
72C22×C32×C4C2311yescharacteristic
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2311yescharacteristic
75C2×#638—22no—
76C2×#638—22no—
77C2×#638—44no—
78C22×C3⋊Dic3—21no—
79C2×C4⋊(C3⋊D3)—22no—
80C2×C4⋊(C3⋊D3)—22no—
81C2×C4⋊(C3⋊D3)—21no—
82C2×C4⋊(C3⋊D3)C2312yes—
83C32×C4⋊C4—21no—
84C32×C4⋊C4—21no—
85C32×C4⋊C4C2311yescharacteristic
86C32×C4⋊C4C2311yescharacteristic
87C32×C22⋊C4—21no—
88C32×C22⋊C4—21no—
89C32×C22⋊C4—21no—
90C32×C22⋊C4—21no—
91C32×C22⋊C4—21no—
92C32×C42—21no—
93#3755—24no—
94#3753—24no—
95#3752—22no—
96#3752—22no—
97C4⋊(C3⋊Dic3)—21no—
98C4⋊(C3⋊Dic3)C2312yes—
99#3748—22no—
100#3748—24no—
101#3748D414yescomplemented
102C2×C3⋊(C3⋊C8)—24no—
103C2×C3⋊(C3⋊C8)C2312yes—
104C2×C3⋊(C3⋊C8)C2312yes—
105#3055—91noSylow
106C2×C3×#41C2×D314yes—
107C23×C3×C4C2×D314yes—
108C22×#67—64no—
109C22×D12—34no—
110C3×#123—24no—
111C3×C22⋊Q8C2×D314yescomplemented
112C3×C22⋊Q8C2×D314yescomplemented
113C3×#121C2×D314yescomplemented
114C3×#121C2×D314yescomplemented
115C3×#120—24no—
116C3×C4×D4—24no—
117C3×C4×D4—24no—
118C3×#117C2×D314yes—
119#949—616no—
120C2×#215—38no—
121C2×#213—38no—
122#930—38no—
123#930—38no—
124#930—64no—
125#930—64no—
126C2×(C2×D3)⋊C4—64no—
127C2×C4⋊Dic3—34no—
128C2×#208—34no—
129C2×#208—34no—
130C2×#208—38no—
131C2×#208—616no—
132C22×C3⋊C8—38no—
133#835—38no—
134#832—38no—
135#809—38no—
136#809—38no—
137#808—38no—
138#807—38no—
139C23×C32—22no—
140C23×C32—22no—
141C23×C32—21no—
142C23×C32—41no—
143C23×C32C2×D411yescharacteristic
144C23×C32C2×D411yescharacteristic
145C23×C32C2×D411yescharacteristic
146C22×C3⋊D3—22no—
147C22×C3⋊D3—42no—
148C22×C3⋊D3—42no—
149C22×C3⋊D3—42no—
150C32×Q8—21no—
151C32×Q8—21no—
152C32×D4—21no—
153C32×D4—21no—
154C32×D4—42no—
155C32×D4—42no—
156C32×D4—42no—
157C2×C32×C4—22no—
158C2×C32×C4—22no—
159C2×C32×C4—22no—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4—21no—
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—42no—
168C2×C32×C4C2×D412yes—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4#4112yes—
173C2×C32×C4C2411yescharacteristic
174#638—44no—
175#638—44no—
176C2×C3⋊Dic3—22no—
177C2×C3⋊Dic3—42no—
178C4⋊(C3⋊D3)—22no—
179C4⋊(C3⋊D3)—22no—
180C4⋊(C3⋊D3)—42no—
181C3⋊(C3⋊C8)—22no—
182C3⋊(C3⋊C8)C2×D414yescomplemented
183C2×AGL(1,ℤ/8)—91no—
184C22×M16—91no—
185#525C3⋊D311yescharacteristic, complemented
186C2×#121—91no—
187#469—92no—
188#468—92no—
189#466—92no—
190#465—92no—
191#428—91no—
192#418—91no—
193#417—91no—
194C24×C3#6714yes—
195C23×D3—64no—
196C3×#41—28no—
197C3×#41—28no—
198C2×C3×Q8C22×D314yes—
199C2×C3×D4—24no—
200C2×C3×D4—24no—
201C2×C3×D4—24no—
202C2×C3×D4C22×D314yes—
203C22×C3×C4—28no—
204C22×C3×C4—28no—
205C22×C3×C4—24no—
206C22×C3×C4#6714yes—
207C22×C3×C4#6714yes—
208C22×C3×C4#6714yes—
209C22×C3×C4C22×D314yes—
210C22×C3×C4C22×D314yes—
211C22×C3×C4C22×D314yes—
212C2×#67—68no—
213C2×#67—68no—
214C2×#67—1216no—
215C22×Dic3—64no—
216C2×D12—38no—
217C2×D12—68no—
218C2×D12—68no—
219C2×D12—64no—
220C3×C4⋊C4—24no—
221C3×C4⋊C4—24no—
222C3×C4⋊C4C22×D314yes—
223C3×C4⋊C4C22×D314yes—
224C3×C22⋊C4—24no—
225C3×C22⋊C4—24no—
226C3×C22⋊C4—24no—
227C3×C22⋊C4—24no—
228C3×C22⋊C4—24no—
229C3×C42—24no—
230#215—616no—
231#213—616no—
232(C2×D3)⋊C4—68no—
233(C2×D3)⋊C4—68no—
234C4⋊Dic3—38no—
235C4⋊Dic3—64no—
236#208—316no—
237#208—616no—
238#208—68no—
239C2×C3⋊C8—38no—
240C2×C3⋊C8—38no—
241C2×C3⋊C8—616no—
242C22×C32—21no—
243C22×C32—21no—
244C22×C32—21no—
245C22×C32—21no—
246C22×C32—21no—
247C22×C32—21no—
248C22×C32—21no—
249C22×C32—44no—
250C22×C32—41no—
251C22×C32—41no—
252C22×C32—41no—
253C22×C32#12112yes—
254C22×C32AGL(1,ℤ/8)12yescomplemented
255C22×C32C22×D411yescharacteristic
256C2×C3⋊D3—42no—
257C2×C3⋊D3—42no—
258C2×C3⋊D3—42no—
259C2×C3⋊D3—84no—
260C32×C4—21no—
261C32×C4—21no—
262C32×C4—41no—
263C32×C4—41no—
264C32×C4—41no—
265C32×C4#12112yes—
266C32×C4C22×D411yescharacteristic
267C32×C4C2×#4111yescharacteristic
268C3⋊Dic3—42no—
269C2×#41C2×C3⋊D311yescharacteristic
270C22×D4—91no—
271C22×D4—181no—
272C23×C4C2×C3⋊D311yescharacteristic
273AGL(1,ℤ/8)—184no—
274C2×SD16—92no—
275C2×D8—92no—
276C2×M16—91no—
277C2×M16—91no—
278C2×M16—92no—
279C2×M16—184no—
280C22×C8—92no—
281#123—21no—
282C22⋊Q8C2×C3⋊D311yescharacteristic, complemented
283C22⋊Q8C2×C3⋊D311yescharacteristic, complemented
284#121—92no—
285#121—92no—
286#121—181no—
287#121—181no—
288#121C2×C3⋊D311yescharacteristic, complemented
289#121C2×C3⋊D311yescharacteristic, complemented
290#120—21no—
291C4×D4—21no—
292C4×D4—21no—
293#117C2×C3⋊D311yescharacteristic
294C2×C4⋊C4—91no—
295C2×C22⋊C4—181no—
296#107—92no—
297#106—92no—
298#103—92no—
299#102—92no—
300#102—92no—
301#102—92no—
302C23×C3—28no—
303C23×C3—28no—
304C23×C3—24no—
305C23×C3—44no—
306C23×C3C2×#6714yes—
307C23×C3C2×#6714yes—
308C23×C3C2×#6714yes—
309C22×D3—68no—
310C22×D3—128no—
311C22×D3—128no—
312C22×D3—128no—
313C3×Q8—24no—
314C3×Q8—24no—
315C3×D4—24no—
316C3×D4—24no—
317C3×D4—48no—
318C3×D4—48no—
319C3×D4—48no—
320C2×C3×C4—28no—
321C2×C3×C4—28no—
322C2×C3×C4—28no—
323C2×C3×C4—24no—
324C2×C3×C4—24no—
325C2×C3×C4—24no—
326C2×C3×C4—24no—
327C2×C3×C4—24no—
328C2×C3×C4—24no—
329C2×C3×C4—24no—
330C2×C3×C4—48no—
331C2×C3×C4D3×D418yes—
332C2×C3×C4#23718yes—
333C2×C3×C4C2×#6714yes—
334C2×C3×C4C2×#6714yes—
335C2×C3×C4C2×#6714yes—
336C2×C3×C4C23×D314yes—
337#67—1216no—
338#67—1216no—
339C2×Dic3—68no—
340C2×Dic3—128no—
341D12—68no—
342D12—68no—
343D12—128no—
344C3⋊C8—316no—
345C3⋊C8—68no—
346C2×C32—22no—
347C2×C32—22no—
348C2×C32—41no—
349C2×C32—81no—
350C2×C32C2×#12111yescharacteristic
351C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
352C2×C32#57511yescharacteristic
353C3⋊D3—82no—
354C24—181no—
355C24#63811yescharacteristic
356#41—22no—
357#41—22no—
358C2×Q8C22×C3⋊D311yescharacteristic
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—92no—
363C2×D4—182no—
364C2×D4—182no—
365C2×D4—182no—
366C2×D4—182no—
367C2×D4—181no—
368C2×D4—364no—
369C2×D4C22×C3⋊D311yescharacteristic
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—181no—
374C22×C4#63811yescharacteristic
375C22×C4#63811yescharacteristic
376C22×C4#63811yescharacteristic
377C22×C4C22×C3⋊D311yescharacteristic
378C22×C4C22×C3⋊D311yescharacteristic
379C22×C4C22×C3⋊D311yescharacteristic
380SD16—184no—
381D8—184no—
382M16—94no—
383M16—184no—
384M16—182no—
385C2×C8—92no—
386C2×C8—92no—
387C2×C8—184no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—92no—
391C4⋊C4—181no—
392C4⋊C4C22×C3⋊D311yescharacteristic
393C4⋊C4C22×C3⋊D311yescharacteristic
394C22⋊C4—21no—
395C22⋊C4—21no—
396C22⋊C4—21no—
397C22⋊C4—21no—
398C22⋊C4—21no—
399C22⋊C4—182no—
400C22⋊C4—182no—
401C42—21no—
402C22×C3—24no—
403C22×C3—24no—
404C22×C3—24no—
405C22×C3—24no—
406C22×C3—24no—
407C22×C3—24no—
408C22×C3—24no—
409C22×C3—416no—
410C22×C3—44no—
411C22×C3—44no—
412C22×C3—44no—
413C22×C3#93918yes—
414C22×C3#94918yescomplemented
415C22×C3C22×#6714yes—
416C2×D3—128no—
417C2×D3—128no—
418C2×D3—128no—
419C2×D3—2416no—
420C3×C4—24no—
421C3×C4—24no—
422C3×C4—44no—
423C3×C4—44no—
424C3×C4—44no—
425C3×C4#93918yes—
426C3×C4C2×D3×D414yes—
427C3×C4C2×#23714yes—
428Dic3—128no—
429C32#305511yescharacteristic, complemented, Sylow
430C23—22no—
431C23—22no—
432C23—21no—
433C23—41no—
434C23—182no—
435C23—362no—
436C23—362no—
437C23—362no—
438C23C2×#63811yescharacteristic
439C23C2×#63811yescharacteristic
440C23C2×#63811yescharacteristic
441Q8—21no—
442Q8—21no—
443D4—21no—
444D4—21no—
445D4—42no—
446D4—42no—
447D4—42no—
448D4—182no—
449D4—182no—
450D4—364no—
451D4—364no—
452D4—362no—
453C2×C4—22no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—42no—
464C2×C4—182no—
465C2×C4—362no—
466C2×C4D4×C3⋊D312yes—
467C2×C4#383012yes—
468C2×C4C2×#63811yescharacteristic
469C2×C4C2×#63811yescharacteristic
470C2×C4C2×#63811yescharacteristic
471C2×C4C23×C3⋊D311yescharacteristic
472C8—94no—
473C8—182no—
474C2×C3—28no—
475C2×C3—28no—
476C2×C3—44no—
477C2×C3—84no—
478C2×C3C2×#93914yes—
479C2×C3C2×#94914yes—
480C2×C3#582214yes—
481D3—248no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—44no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—362no—
494C22—362no—
495C22—362no—
496C22—724no—
497C22#6414812yes—
498C22#6415812yescomplemented
499C22C22×#63811yescharacteristic
500C4—21no—
501C4—21no—
502C4—41no—
503C4—41no—
504C4—41no—
505C4—362no—
506C4#6414812yes—
507C4C2×D4×C3⋊D311yescharacteristic
508C4C2×#383011yescharacteristic
509C3#8292414yescomplemented
510C2—22no—
511C2—22no—
512C2—41no—
513C2—81no—
514C2—722no—
515C2C2×#6414811yescharacteristic
516C2C2×#6415811yescharacteristic
517C2#1059629311yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#525C2
socleC22×C32C22×D4
hypercenter#525C3⋊D3
hypocenterC32#3055
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C32×#525C2semidirect
2. C2×#64158C2semidirect
3. C2×#64139C2semidirect
4. C22×#3748C2semidirect
5. #10592931C2semidirect
6. #10592748C2semidirect
7. #10592747C2semidirect
8. #10592738C2semidirect
9. #10592737C2semidirect
10. #10592700C2semidirect
11. #10592694C2semidirect
18. C32×C22⋊Q8C22semidirect
19. C32×C22⋊Q8C22semidirect
20. C32×#121C22semidirect
21. C32×#121C22semidirect
27. C2×#3755C22semidirect
28. C2×#3753C22semidirect
38. C2×#3748C22semidirect
39. C22×C3⋊(C3⋊C8)C22semidirect
40. #63662C22semidirect
41. #63659C22semidirect
42. #63636C22semidirect
43. #63636C22semidirect
44. #63635C22semidirect
45. #63634C22semidirect
46. C3×#525D3semidirect
101. #3748D4semidirect
111. C3×C22⋊Q8C2×D3semidirect
112. C3×C22⋊Q8C2×D3semidirect
113. C3×#121C2×D3semidirect
114. C3×#121C2×D3semidirect
182. C3⋊(C3⋊C8)C2×D4semidirect
185. #525C3⋊D3semidirect
254. C22×C32AGL(1,ℤ/8)semidirect
282. C22⋊Q8C2×C3⋊D3semidirect
283. C22⋊Q8C2×C3⋊D3semidirect
288. #121C2×C3⋊D3semidirect
289. #121C2×C3⋊D3semidirect
414. C22×C3#949semidirect
429. C32#3055semidirect
498. C22#64158semidirect
509. C3#82924semidirect

Maximal subgroups

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

subgroupindex
C32×#5252
C2×#641582
C2×#641392
C22×#37482
#105929312
#105927482
#105927472
#105927382
#105927372
#105927002
#105926942
#829243