Finite Group Databasebeta

← #11868344

Subgroups — #11868344

Order 1152.

997 conjugacy classes of subgroups.

The subgroup lattice has 509 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#624C211yesmaximal, characteristic
2#10594482C211yesmaximal, characteristic, complemented
3C3⋊D3×#102C211yesmaximal, characteristic
4C3×#4766C212yesmaximal, complemented
5#10591416C211yesmaximal, characteristic
6#10591409C212yesmaximal, complemented
7#10590774C212yesmaximal, complemented
8#10590687C211yesmaximal, characteristic, complemented
9#10590658C211yesmaximal, characteristic, complemented
10#10590575C211yesmaximal, characteristic, complemented
11#10590470C212yesmaximal, complemented
12D3×#478—32nomaximal
13C2×D4×C3⋊D3C2211yescharacteristic
14C22×#624—21no—
15C2×C8×C3⋊D3C2211yescharacteristic
16C4⋊C4×C3⋊D3C2211yescharacteristic
17C3×D4×Dic3C2212yes—
18C3×#890C2212yescomplemented
19#63974—21no—
20#63952—22no—
21#63900—21no—
22#63900C2211yescharacteristic
23#63900C2211yescharacteristic
24#63894C2212yes—
25#63883—21no—
26C4×#624C2211yescharacteristic
27#63869C2212yescomplemented
28#63847—22no—
29C2×#3710C2211yescharacteristic
30C32×#102C2211yescharacteristic
31#63659C2211yescharacteristic
32#63648C2211yescharacteristic
33#63636C2211yescharacteristic
34C3×#832C2212yes—
35C3×#818C2212yescomplemented
36C3×Dic3⋊C8C2212yescomplemented
37C3×#808C2212yescomplemented
38#63576C2212yescomplemented
39#63573C2212yescomplemented
40Dic3⋊(C3⋊C8)C2212yescomplemented
41#63564C2212yes—
42D3×#125—32no—
43C4×D3×D4—32no—
44C3×#478—32no—
45#5066—32no—
46#5009—32no—
47#4891—32no—
48D3×#107—32no—
49#4871—32no—
50D3×#106—32no—
51#4847—32no—
52D3×C4⋊C8—32no—
53D3×#102—32no—
54D3×#102—32no—
55D3×#102—61no—
56#4766D312yescomplemented
57#4763—32no—
58C23×C3⋊D3—21no—
59C2×C32×D4C2311yescharacteristic
60C2×#638—21no—
61D4×C3⋊D3—22no—
62D4×C3⋊D3Q814yes—
63C2×C4⋊(C3⋊D3)C2311yescharacteristic
64C2×C4×C3⋊D3—21no—
65C2×C4×C3⋊D3C2311yescharacteristic
66C22×C3×Dic3—22no—
67C2×#624—21no—
68C2×#624—21no—
69C2×#624—22no—
70C2×#624—44no—
71C2×#624D411yescharacteristic
72C2×#624D411yescharacteristic
73C2×C32×C8C2311yescharacteristic
74C32×C4⋊C4C2311yescharacteristic
75C4⋊(C3⋊Dic3)C2311yescharacteristic
76#3750—21no—
77C2×C3⋊(C3⋊C8)C2311yescharacteristic
78C8×C3⋊D3—22no—
79C3×#217—22no—
80C3×C4⋊Dic3—22no—
81C3×C4⋊Dic3C2312yes—
82C3×C4⋊Dic3C2312yes—
83C3×Dic3⋊C4—22no—
84C3×C4×Dic3C2312yes—
85C2×C3×C3⋊C8C2312yes—
86#3724—21no—
87#3724—21no—
88#3724—22no—
89Dic3⋊Dic3—22no—
90#3722—22no—
91Dic32D412yes—
92#3710—22no—
93C2×#478—91noSylow
94C2×D3×D4—32no—
95C2×D3×D4—61no—
96C22×C4×D3—62no—
97C3×#125—32no—
98C3×C4×D4—32no—
99D4×Dic3C2×D312yes—
100C4×#67—62no—
101C2×D3×C8—32no—
102C2×D3×C8—32no—
103C2×D3×C8—61no—
104#893—32no—
105D3×C4⋊C4—32no—
106D3×C4⋊C4—32no—
107D3×C4⋊C4—32no—
108D3×C4⋊C4—61no—
109D3×C4⋊C4—62no—
110D3×C4⋊C4—62no—
111#890—32no—
112#890C2×D312yescomplemented
113#889—62no—
114#889—62no—
115#67⋊C4—62no—
116D3×C22⋊C4—62no—
117C4×D12—32no—
118C42×D3—32no—
119#870—32no—
120C3×#107—32no—
121C3×#106—32no—
122C3×C4⋊C8—32no—
123C3×#102—21no—
124C3×#102—32no—
125C3×#102C2×D312yes—
126#832—32no—
127#832—61no—
128#832C2×D312yes—
129#821—32no—
130#821—32no—
131#821—61no—
132#818C2×D312yescomplemented
133#817—32no—
134Dic3⋊C8—32no—
135Dic3⋊C8C2×D312yescomplemented
136#809—32no—
137#809—32no—
138#809—61no—
139#808—32no—
140#808C2×D312yescomplemented
141#807—32no—
142#807—32no—
143C4⋊(C3⋊C8)—32no—
144C23×C32—21no—
145C22×C3⋊D3—21no—
146C22×C3⋊D3—24no—
147C22×C3⋊D3—42no—
148C22×C3⋊D3—42no—
149C22×C3⋊D3C2×D411yescharacteristic
150C32×D4—21no—
151C32×D4C2×Q812yes—
152C2×C32×C4—21no—
153C2×C32×C4C2411yescharacteristic
154#638—24no—
155C2×C3⋊Dic3—21no—
156C2×C3⋊Dic3C2×D411yescharacteristic
157C4⋊(C3⋊D3)—21no—
158C4⋊(C3⋊D3)C2×Q812yes—
159C4×C3⋊D3—42no—
160C4×C3⋊D3C2×Q812yes—
161C4×C3⋊D3#4112yes—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—44no—
165C2×C3×Dic3C2×D412yes—
166C2×C3×Dic3C2×D412yes—
167#624—22no—
168#624—22no—
169#624—44no—
170#624—42no—
171#624—42no—
172C32×C8—21no—
173C3⋊(C3⋊C8)—21no—
174C3×C3⋊C8—22no—
175C2×#125—91no—
176C2×C4×D4—91no—
177#478—32no—
178#478—92no—
179#478—92no—
180#478—92no—
181C2×#107—91no—
182C2×#106—91no—
183C2×C4⋊C8—91no—
184C2×#102—91no—
185C2×#102—91no—
186C23×D3—62no—
187C23×D3—121no—
188C2×C3×D4—21no—
189C2×C3×D4C22×D312yes—
190C22×C3×C4—62no—
191C2×#67—62no—
192C2×#67—121no—
193C22×Dic3—22no—
194D3×D4—38no—
195D3×D4—64no—
196D3×D4—64no—
197D3×D4—122no—
198C2×D12—32no—
199C2×D12—61no—
200C2×C4×D3—32no—
201C2×C4×D3—32no—
202C2×C4×D3—32no—
203C2×C4×D3—61no—
204C2×C4×D3—62no—
205C2×C4×D3—62no—
206C2×C4×D3—62no—
207C2×C4×D3—62no—
208C2×C4×D3—62no—
209C2×C4×D3—121no—
210C2×C4×D3—128no—
211C2×C3×C8—21no—
212C2×C3×C8—32no—
213C2×C3×C8C22×D312yes—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—32no—
216C3×C4⋊C4—32no—
217C3×C4⋊C4—62no—
218C3×C4⋊C4—62no—
219C3×C4⋊C4C22×D312yes—
220C3×C22⋊C4—62no—
221C3×C42—32no—
222#217—22no—
223(C2×D3)⋊C4—62no—
224(C2×D3)⋊C4—62no—
225C4⋊Dic3—22no—
226C4⋊Dic3—32no—
227C4⋊Dic3—61no—
228C4⋊Dic3—62no—
229C4⋊Dic3C22×D312yes—
230C4⋊Dic3C22×D312yes—
231Dic3⋊C4—22no—
232Dic3⋊C4—62no—
233Dic3⋊C4—62no—
234Dic3⋊C4—62no—
235Dic3⋊C4—62no—
236Dic3⋊C4—62no—
237Dic3⋊C4—62no—
238Dic3⋊C4—121no—
239C4×Dic3—32no—
240C4×Dic3—32no—
241C4×Dic3C22×D312yes—
242C2×C3⋊C8—32no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8C22×D312yes—
245D3×C8—64no—
246D3×C8—64no—
247D3×C8—122no—
248C22×C32—22no—
249C22×C32—41no—
250C22×C32—41no—
251C22×C32C22×D411yescharacteristic
252C2×C3⋊D3—22no—
253C2×C3⋊D3—41no—
254C2×C3⋊D3—41no—
255C2×C3⋊D3—48no—
256C2×C3⋊D3C22⋊Q812yes—
257C2×C3⋊D3#13512yes—
258C2×C3⋊D3AGL(1,ℤ/8)12yes—
259C32×C4—41no—
260C32×C4C22×Q811yescharacteristic
261C32×C4C2×#4111yescharacteristic
262C3⋊Dic3—41no—
263C3⋊Dic3C22⋊Q812yes—
264C3×Dic3—22no—
265C3×Dic3—22no—
266C3×Dic3—42no—
267C3×Dic3—42no—
268C22×D4—91no—
269C23×C4—181no—
270C22×C8—91no—
271C22×C8—91no—
272#125—32no—
273#125—92no—
274#125—182no—
275C4×D4—32no—
276C4×D4—92no—
277C4×D4—182no—
278C2×C4⋊C4—91no—
279C2×C4⋊C4—91no—
280C2×C4⋊C4—91no—
281C2×C4⋊C4—181no—
282C2×C4⋊C4—181no—
283C2×C22⋊C4—181no—
284C2×C42—91no—
285#107—32no—
286#107—92no—
287#106—32no—
288#106—92no—
289C4⋊C8—32no—
290C4⋊C8—92no—
291#102—32no—
292#102—92no—
293#102—91no—
294#102—91no—
295#102—91no—
296#102D3211yescharacteristic
297C23×C3—22no—
298C23×C3—41no—
299C22×D3—32no—
300C22×D3—61no—
301C22×D3—68no—
302C22×D3—62no—
303C22×D3—124no—
304C22×D3—121no—
305C22×D3—124no—
306C22×D3—124no—
307C22×D3—242no—
308C22×D3—242no—
309C3×D4—22no—
310C3×D4—22no—
311C3×D4—41no—
312C3×D4D3×Q814yes—
313C2×C3×C4—22no—
314C2×C3×C4—21no—
315C2×C3×C4—32no—
316C2×C3×C4—32no—
317C2×C3×C4—41no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—124no—
321C2×C3×C4C23×D312yes—
322#67—68no—
323#67—124no—
324C2×Dic3—22no—
325C2×Dic3—22no—
326C2×Dic3—32no—
327C2×Dic3—44no—
328C2×Dic3—61no—
329C2×Dic3—62no—
330C2×Dic3—121no—
331C2×Dic3D3×D412yes—
332C2×Dic3D3×D412yes—
333D12—34no—
334D12—62no—
335D12—62no—
336D12—121no—
337C4×D3—34no—
338C4×D3—34no—
339C4×D3—62no—
340C4×D3—62no—
341C4×D3—64no—
342C4×D3—64no—
343C4×D3—124no—
344C4×D3—124no—
345C4×D3—124no—
346C4×D3—124no—
347C4×D3—124no—
348C4×D3—242no—
349C3×C8—22no—
350C3×C8—41no—
351C3×C8—62no—
352C3⋊C8—22no—
353C3⋊C8—62no—
354C3⋊C8—121no—
355C2×C32—42no—
356C2×C32C2×C22⋊Q811yescharacteristic
357C2×C32C2×#13511yescharacteristic
358C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
359C3⋊D3—42no—
360C3⋊D3#47814yescomplemented
361C24—181no—
362C2×D4—94no—
363C2×D4—91no—
364C2×D4—182no—
365C2×D4—181no—
366C2×D4C2×D3211yescharacteristic
367C22×C4—62no—
368C22×C4—91no—
369C22×C4—91no—
370C22×C4—91no—
371C22×C4—181no—
372C22×C4—182no—
373C22×C4—181no—
374C22×C4—181no—
375C22×C4—364no—
376C2×C8—32no—
377C2×C8—91no—
378C2×C8—182no—
379C2×C8—182no—
380C2×C8C2×D3211yescharacteristic
381C4⋊C4—32no—
382C4⋊C4—32no—
383C4⋊C4—62no—
384C4⋊C4—62no—
385C4⋊C4—91no—
386C4⋊C4—181no—
387C4⋊C4—182no—
388C4⋊C4—182no—
389C4⋊C4—181no—
390C4⋊C4—181no—
391C4⋊C4C2×D3211yescharacteristic
392C22⋊C4—62no—
393C22⋊C4—182no—
394C42—32no—
395C42—92no—
396C22×C3—24no—
397C22×C3—21no—
398C22×C3—42no—
399C22×C3—42no—
400C22×C3—42no—
401C22×C3—81no—
402C22×C3—81no—
403C22×C3C2×D3×D412yes—
404C2×D3—34no—
405C2×D3—34no—
406C2×D3—34no—
407C2×D3—62no—
408C2×D3—62no—
409C2×D3—62no—
410C2×D3—64no—
411C2×D3—122no—
412C2×D3—1216no—
413C2×D3—122no—
414C2×D3—122no—
415C2×D3—248no—
416C2×D3—241no—
417C2×D3—241no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—42no—
421C3×C4—62no—
422C3×C4—62no—
423C3×C4—81no—
424C3×C4—122no—
425C3×C4—122no—
426C3×C4C2×D3×Q812yes—
427C3×C4D3×#4112yes—
428Dic3—22no—
429Dic3—22no—
430Dic3—34no—
431Dic3—42no—
432Dic3—42no—
433Dic3—62no—
434Dic3—122no—
435Dic3—241no—
436C32C2×#47811yescharacteristic, complemented, Sylow
437C23—21no—
438C23—91no—
439C23—184no—
440C23—181no—
441C23—362no—
442C23—362no—
443D4—21no—
444D4—92no—
445D4—184no—
446D4—181no—
447D4#379712yes—
448C2×C4—21no—
449C2×C4—32no—
450C2×C4—32no—
451C2×C4—62no—
452C2×C4—62no—
453C2×C4—91no—
454C2×C4—92no—
455C2×C4—92no—
456C2×C4—124no—
457C2×C4—182no—
458C2×C4—182no—
459C2×C4—181no—
460C2×C4—362no—
461C2×C4—364no—
462C2×C4—362no—
463C2×C4—362no—
464C2×C4C22×D3211yescharacteristic
465C8—21no—
466C8—62no—
467C8—181no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—44no—
472C2×C3—82no—
473C2×C3D3×C22⋊Q812yes—
474C2×C3D3×#13512yes—
475C2×C3D3×AGL(1,ℤ/8)12yes—
476D3—38no—
477D3—64no—
478D3—124no—
479D3—242no—
480C22—22no—
481C22—41no—
482C22—41no—
483C22—92no—
484C22—92no—
485C22—92no—
486C22—182no—
487C22—368no—
488C22—361no—
489C22—361no—
490C22D32×D411yescharacteristic
491C4—41no—
492C4—62no—
493C4—62no—
494C4—92no—
495C4—122no—
496C4—122no—
497C4—361no—
498C4C2×#379711yescharacteristic
499C4#6431211yescharacteristic
500C3—21no—
501C3D3×#47812yescomplemented
502C2—42no—
503C2—94no—
504C2—362no—
505C2#1059406711yescharacteristic
506C2#1059473011yescharacteristic
507C2#1059474011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
hypercenter#102D32
hypocenterC32C2×#478
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10594482C2semidirect
4. C3×#4766C2semidirect
6. #10591409C2semidirect
7. #10590774C2semidirect
8. #10590687C2semidirect
9. #10590658C2semidirect
10. #10590575C2semidirect
11. #10590470C2semidirect
18. C3×#890C22semidirect
27. #63869C22semidirect
35. C3×#818C22semidirect
36. C3×Dic3⋊C8C22semidirect
37. C3×#808C22semidirect
38. #63576C22semidirect
39. #63573C22semidirect
40. Dic3⋊(C3⋊C8)C22semidirect
56. #4766D3semidirect
112. #890C2×D3semidirect
132. #818C2×D3semidirect
135. Dic3⋊C8C2×D3semidirect
140. #808C2×D3semidirect
360. C3⋊D3#478semidirect
436. C32C2×#478semidirect
501. C3D3×#478semidirect

Maximal subgroups

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

subgroupindex
D4×#6242
#105944822
C3⋊D3×#1022
C3×#47662
#105914162
#105914092
#105907742
#105906872
#105906582
#105905752
#105904702
D3×#4783