Finite Group Databasebeta

← #11860685

Subgroups — #11860685

Order 1152.

1122 conjugacy classes of subgroups.

The subgroup lattice has 523 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×D8C211yesmaximal, characteristic
2#10595215C212yesmaximal, complemented
3#10592851C211yesmaximal, characteristic, complemented
4C3×#5152C211yesmaximal, characteristic, complemented
5#10591435C212yesmaximal, complemented
6Dic3×#213C212yesmaximal, complemented
7#10591421C212yesmaximal, complemented
8#10590781C211yesmaximal, characteristic, complemented
9#10590771C211yesmaximal, characteristic, complemented
10#10590706C211yesmaximal, characteristic, complemented
11#10590693C211yesmaximal, characteristic, complemented
12#83823—31nomaximal
13#79867—31nomaximal
14C2×C3×D3×D4C2212yes—
15C2×C32×D8C2211yescharacteristic
16D4×C3⋊Dic3C2212yescomplemented
17C3×D4×Dic3C2212yescomplemented
18C2×C3×#213C2212yes—
19C3×D3×D8C418yescomplemented
20C2×C3×D24C2211yescharacteristic
21C2×C3×D3×C8C2211yescharacteristic
22#67⋊Dic3—22no—
23Dic3×#67—22no—
24D3×#217—22no—
25C2×(C2×D3)⋊Dic3—22no—
26#63898C2212yescomplemented
27Dic3×D12C2212yescomplemented
28#63855C2211yescharacteristic
29#63841C2212yes—
30C2×#3711C2211yescharacteristic
31#63659C2212yescomplemented
32#63644C2211yescharacteristic, complemented
33#63642C2211yescharacteristic, complemented
34C3×#832C2212yescomplemented
35C3×#817C2211yescharacteristic, complemented
36C3×#815C2211yescharacteristic, complemented
37#63575C2212yescomplemented
38#63563C2212yescomplemented
39#63562C2212yescomplemented
40#63553C2211yescharacteristic, complemented
41Dic3×C3⋊C8C2211yescharacteristic, complemented
42C22×C3×D8—31no—
43#5798—32no—
44C2×D3×D8D311yescharacteristic
45#5545—32no—
46C3×#442—31no—
47#5215—32no—
48#5152—31no—
49#5152—31no—
50#5152—31no—
51#5152—31no—
52#5152—61no—
53#5152D311yescharacteristic, complemented
54Dic3×D8—32no—
55Dic3×D8—32no—
56#5106—31no—
57#5101—31no—
58C4×#213—32no—
59#4869—31no—
60#4860—31no—
61#4770—32no—
62#4756—32no—
63#4711—31no—
64#4708—31no—
65C23×C3×D3—22no—
66C2×C32×D4C2312yes—
67C22×C3⋊Dic3—22no—
68C2×C3×#67—22no—
69C22×C3×Dic3—22no—
70C3×D3×D4—24no—
71C3×D3×D4C2×C418yescomplemented
72C2×C3×D12C2312yes—
73C2×C3×C4×D3C2311yescharacteristic
74C2×D3×Dic3—22no—
75C2×D3×Dic3—22no—
76C32×D8C2×C414yescomplemented
77C2×C32×C8C2311yescharacteristic
78#3757—22no—
79C4⋊(C3⋊Dic3)C2312yes—
80C4×C3⋊Dic3C2311yescharacteristic
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C3×#217—22no—
83C3×#213C2×C418yescomplemented
84C3×C4⋊Dic3C2312yes—
85C3×C4×Dic3C2311yescharacteristic
86C2×C3×C3⋊C8C2311yescharacteristic
87C2×C3×C3⋊C8C2311yescharacteristic
88C3×D24C2×C414yescomplemented
89C3×D3×C8C2×C414yescomplemented
90Dic3⋊Dic3D412yes—
91(C2×D3)⋊Dic3—22no—
92(C2×D3)⋊Dic3—22no—
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3D412yes—
95Dic32—22no—
96#3711—22no—
97#2948—91noSylow
98C22×C3×D4—32no—
99C2×D3×D4C2×D312yes—
100C2×C3×D8—21no—
101C2×C3×D8—32no—
102C2×C3×D8—38no—
103C2×C3×D8—31no—
104C2×C3×D8C2×D311yescharacteristic
105C2×C3×D8C2×D311yescharacteristic
106C22×C3×C8—31no—
107C3×C4×D4—32no—
108C2×#217—62no—
109C2×#217—62no—
110D4×Dic3—32no—
111D4×Dic3—32no—
112D4×Dic3—32no—
113D4×Dic3—32no—
114D4×Dic3—62no—
115D4×Dic3—62no—
116D4×Dic3—62no—
117D4×Dic3C2×D312yescomplemented
118C2×#213C2×D312yes—
119C4×#67—62no—
120C2×(C2×D3)⋊C4—62no—
121#926—31no—
122#926—32no—
123C2×#208—31no—
124D3×D8Dic318yescomplemented
125C2×D24C2×D311yescharacteristic
126C2×ΓL(1,𝔽25)—31no—
127C2×D3×C8C2×D311yescharacteristic
128#893—32no—
129#892—32no—
130#67⋊C4—62no—
131D3×C22⋊C4—62no—
132C4×D12—32no—
133#872—31no—
134C3×#106—31no—
135C3×#102—32no—
136C3×#97—31no—
137#832—32no—
138#832—32no—
139#832—32no—
140#832—32no—
141#832—62no—
142#832C2×D312yescomplemented
143#821—32no—
144#818—32no—
145#817—31no—
146#817—31no—
147#817—61no—
148#817C2×D311yescharacteristic, complemented
149#815—31no—
150#815—31no—
151#815—61no—
152#815C2×D311yescharacteristic, complemented
153C8×Dic3—31no—
154C8×Dic3—31no—
155C8×Dic3—31no—
156#809—32no—
157#807—32no—
158C4×C3⋊C8—31no—
159C23×C32—22no—
160C22×C3×D3—22no—
161C22×C3×D3—28no—
162C22×C3×D3—82no—
163C22×C3×D3—82no—
164C22×C3×D3C2×D411yescharacteristic
165C32×D4—22no—
166C32×D4C22×C414yes—
167C2×C32×C4C2411yescharacteristic
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—82no—
170C2×C3⋊Dic3C2×D412yes—
171C3×#67—28no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—82no—
174C2×C3×Dic3C2×D412yes—
175C2×C3×Dic3C2×D411yescharacteristic
176C3×D12—22no—
177C3×D12C22×C414yes—
178C3×C4×D3C22×C412yes—
179C3×C4×D3#4112yes—
180D3×Dic3—82no—
181D3×Dic3—82no—
182C32×C8C22×C412yes—
183C3⋊(C3⋊C8)—21no—
184C3×C3⋊C8—21no—
185C3×C3⋊C8C22×C412yes—
186C22×D8—31no—
187#518—92no—
188#442—31no—
189#442—91no—
190#442—91no—
191#442—91no—
192C4×D8—92no—
193C4×D8—92no—
194#427—91no—
195#418—92no—
196#405—91no—
197C24×C3—62no—
198C23×D3—22no—
199C2×C3×D4—22no—
200C2×C3×D4—38no—
201C2×C3×D4—32no—
202C2×C3×D4—64no—
203C2×C3×D4—62no—
204C2×C3×D4C22×D312yes—
205C2×C3×D4C22×D312yes—
206C22×C3×C4—31no—
207C22×C3×C4—62no—
208C2×#67—22no—
209C22×Dic3—22no—
210C22×Dic3—62no—
211C22×Dic3—62no—
212C22×Dic3—62no—
213C22×Dic3—62no—
214C22×Dic3—122no—
215D3×D4—24no—
216D3×D4C2×Dic318yescomplemented
217C2×D12C22×D312yes—
218C2×C4×D3—62no—
219C2×C4×D3—62no—
220C2×C4×D3C22×D311yescharacteristic
221C3×D8—24no—
222C3×D8—38no—
223C3×D8—34no—
224C3×D8C4×D314yescomplemented
225C3×D8C2×Dic314yescomplemented
226C2×C3×C8—21no—
227C2×C3×C8—31no—
228C2×C3×C8—34no—
229C2×C3×C8—31no—
230C2×C3×C8C22×D311yescharacteristic
231C2×C3×C8C22×D311yescharacteristic
232C3×C4⋊C4—32no—
233C3×C22⋊C4—62no—
234C3×C42—31no—
235#217—22no—
236#217—32no—
237#217—62no—
238#217—62no—
239#217—62no—
240#217—62no—
241#217—62no—
242#217—122no—
243#213C2×Dic318yescomplemented
244(C2×D3)⋊C4—32no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—62no—
248C4⋊Dic3—32no—
249C4⋊Dic3—32no—
250C4⋊Dic3—32no—
251C4⋊Dic3—62no—
252C4⋊Dic3C22×D312yes—
253Dic3⋊C4—32no—
254C4×Dic3—31no—
255C4×Dic3—31no—
256C4×Dic3—61no—
257C4×Dic3—62no—
258C4×Dic3—62no—
259C4×Dic3C22×D311yescharacteristic
260#208—62no—
261C2×C3⋊C8—31no—
262C2×C3⋊C8—31no—
263C2×C3⋊C8—61no—
264C2×C3⋊C8C22×D311yescharacteristic
265C2×C3⋊C8C22×D311yescharacteristic
266D24C2×Dic314yescomplemented
267ΓL(1,𝔽25)—62no—
268D3×C8C2×Dic314yescomplemented
269C22×C32—24no—
270C22×C32—42no—
271C22×C32—42no—
272C22×C32C22×D411yescharacteristic
273C2×C3×D3—22no—
274C2×C3×D3—24no—
275C2×C3×D3—42no—
276C2×C3×D3—42no—
277C2×C3×D3—88no—
278C2×C3×D3C4×D412yes—
279C32×C4C23×C411yescharacteristic
280C32×C4C2×#4111yescharacteristic
281C3⋊Dic3—22no—
282C3⋊Dic3—42no—
283C3×Dic3—22no—
284C3×Dic3—42no—
285C3×Dic3C4×D412yes—
286C22×D4—32no—
287C2×D8—32no—
288C2×D8—38no—
289C2×D8—31no—
290C2×D8D3211yescharacteristic
291C2×M16—91no—
292C22×C8—31no—
293C4×D4—32no—
294C4×D4—92no—
295C4×D4—92no—
296C4×D4—92no—
297C4×D4—182no—
298C4×D4—182no—
299#117—91no—
300#117—92no—
301C2×C22⋊C4—182no—
302C2×C22⋊C4—182no—
303#107—92no—
304#106—31no—
305#106—91no—
306#102—32no—
307#102—92no—
308#102—92no—
309#102—92no—
310#97—31no—
311#97—91no—
312C4×C8—91no—
313C4×C8—91no—
314C23×C3—22no—
315C23×C3—22no—
316C23×C3—31no—
317C23×C3—42no—
318C23×C3—68no—
319C23×C3—62no—
320C23×C3—242no—
321C23×C3—242no—
322C22×D3—22no—
323C22×D3—28no—
324C22×D3—82no—
325C22×D3—82no—
326C22×D3D3×D411yescharacteristic
327C3×D4—22no—
328C3×D4—22no—
329C3×D4—24no—
330C3×D4—34no—
331C3×D4—42no—
332C3×D4—68no—
333C3×D4—62no—
334C3×D4C2×C4×D314yes—
335C3×D4C22×Dic314yes—
336C2×C3×C4—21no—
337C2×C3×C4—31no—
338C2×C3×C4—32no—
339C2×C3×C4—32no—
340C2×C3×C4—32no—
341C2×C3×C4—62no—
342C2×C3×C4—242no—
343C2×C3×C4C23×D311yescharacteristic
344C2×C3×C4C23×D311yescharacteristic
345#67—28no—
346C2×Dic3—22no—
347C2×Dic3—32no—
348C2×Dic3—32no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—82no—
353C2×Dic3—122no—
354C2×Dic3—242no—
355C2×Dic3—242no—
356C2×Dic3—242no—
357C2×Dic3—242no—
358C2×Dic3—244no—
359C2×Dic3D3×D412yes—
360C2×Dic3D3×D411yescharacteristic
361D12—22no—
362D12C22×Dic314yes—
363C4×D3—242no—
364C4×D3—242no—
365C4×D3#23712yes—
366C4×D3C22×Dic312yes—
367C3×C8—22no—
368C3×C8—32no—
369C3×C8—61no—
370C3×C8C2×C4×D312yes—
371C3×C8C22×Dic312yes—
372C3⋊C8—21no—
373C3⋊C8—61no—
374C3⋊C8—61no—
375C3⋊C8—121no—
376C3⋊C8C22×Dic312yes—
377C2×C32—44no—
378C2×C32C2×C4×D411yescharacteristic
379C2×C32#57612yes—
380C3×D3—22no—
381C3×D3—44no—
382C24—62no—
383C2×D4—38no—
384C2×D4—32no—
385C2×D4—64no—
386C2×D4—62no—
387C2×D4C2×D3212yes—
388C22×C4—31no—
389C22×C4—62no—
390C22×C4—182no—
391C22×C4—182no—
392C22×C4—182no—
393D8—38no—
394D8—34no—
395D8D3×Dic314yescomplemented
396M16—182no—
397C2×C8—31no—
398C2×C8—34no—
399C2×C8—31no—
400C2×C8—91no—
401C2×C8C2×D3211yescharacteristic
402C4⋊C4—32no—
403C4⋊C4—92no—
404C4⋊C4—92no—
405C22⋊C4—62no—
406C22⋊C4—92no—
407C22⋊C4—182no—
408C22⋊C4—182no—
409C22⋊C4—182no—
410C22⋊C4—182no—
411C42—31no—
412C42—91no—
413C42—182no—
414C22×C3—24no—
415C22×C3—24no—
416C22×C3—21no—
417C22×C3—32no—
418C22×C3—44no—
419C22×C3—42no—
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—42no—
423C22×C3—62no—
424C22×C3—64no—
425C22×C3—82no—
426C22×C3—82no—
427C22×C3—122no—
428C22×C3—122no—
429C22×C3—248no—
430C22×C3C2×D3×D411yescharacteristic
431C22×C3C2×D3×D411yescharacteristic
432C2×D3—22no—
433C2×D3—24no—
434C2×D3—42no—
435C2×D3—42no—
436C2×D3—88no—
437C2×D3D4×Dic312yes—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—32no—
441C3×C4—62no—
442C3×C4—122no—
443C3×C4C22×C4×D311yescharacteristic
444C3×C4C2×#23711yescharacteristic
445C3×C4D3×#4111yescharacteristic
446C3×C4C23×Dic311yescharacteristic
447Dic3—22no—
448Dic3—42no—
449Dic3—62no—
450Dic3—62no—
451Dic3—122no—
452Dic3—122no—
453Dic3—122no—
454Dic3—242no—
455Dic3D4×Dic312yes—
456C32#294811yescharacteristic, complemented, Sylow
457C23—22no—
458C23—31no—
459C23—68no—
460C23—62no—
461C23—242no—
462C23—242no—
463D4—22no—
464D4—34no—
465D4—68no—
466D4—62no—
467D4C2×D3×Dic314yes—
468C2×C4—31no—
469C2×C4—32no—
470C2×C4—32no—
471C2×C4—32no—
472C2×C4—62no—
473C2×C4—92no—
474C2×C4—182no—
475C2×C4—242no—
476C2×C4—722no—
477C2×C4—722no—
478C2×C4—722no—
479C2×C4C22×D3211yescharacteristic
480C8—32no—
481C8—61no—
482C8—181no—
483C8C2×D3×Dic312yes—
484C2×C3—21no—
485C2×C3—22no—
486C2×C3—44no—
487C2×C3—44no—
488C2×C3—62no—
489C2×C3—84no—
490C2×C3—124no—
491C2×C3C4×D3×D411yescharacteristic
492C2×C3#575712yes—
493C2×C3#577412yes—
494C2×C3C2×D4×Dic311yescharacteristic
495D3—22no—
496D3—44no—
497C22—24no—
498C22—32no—
499C22—42no—
500C22—42no—
501C22—62no—
502C22—64no—
503C22—122no—
504C22—122no—
505C22—248no—
506C22D32×D411yescharacteristic
507C4—32no—
508C4—62no—
509C4—122no—
510C4—182no—
511C4—362no—
512C4D3×#23711yescharacteristic
513C4C22×D3×Dic311yescharacteristic
514C3—21no—
515C3#7986711yescharacteristic, complemented
516C3#8382311yescharacteristic, complemented
517C2—44no—
518C2—62no—
519C2—124no—
520C2#1059473212yes—
521C2D3×D4×Dic311yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×D8C2
cosocleC2×C32×C4C24
hypercenterC2×D8D32
hypocenterC32#2948
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. #10595215C2semidirect
3. #10592851C2semidirect
4. C3×#5152C2semidirect
5. #10591435C2semidirect
6. Dic3×#213C2semidirect
7. #10591421C2semidirect
8. #10590781C2semidirect
9. #10590771C2semidirect
10. #10590706C2semidirect
11. #10590693C2semidirect
16. D4×C3⋊Dic3C22semidirect
17. C3×D4×Dic3C22semidirect
19. C3×D3×D8C4semidirect
26. #63898C22semidirect
27. Dic3×D12C22semidirect
31. #63659C22semidirect
32. #63644C22semidirect
33. #63642C22semidirect
34. C3×#832C22semidirect
35. C3×#817C22semidirect
36. C3×#815C22semidirect
37. #63575C22semidirect
38. #63563C22semidirect
39. #63562C22semidirect
40. #63553C22semidirect
41. Dic3×C3⋊C8C22semidirect
53. #5152D3semidirect
71. C3×D3×D4C2×C4semidirect
76. C32×D8C2×C4semidirect
83. C3×#213C2×C4semidirect
88. C3×D24C2×C4semidirect
89. C3×D3×C8C2×C4semidirect
117. D4×Dic3C2×D3semidirect
124. D3×D8Dic3semidirect
142. #832C2×D3semidirect
148. #817C2×D3semidirect
152. #815C2×D3semidirect
216. D3×D4C2×Dic3semidirect
224. C3×D8C4×D3semidirect
225. C3×D8C2×Dic3semidirect
243. #213C2×Dic3semidirect
266. D24C2×Dic3semidirect
268. D3×C8C2×Dic3semidirect
395. D8D3×Dic3semidirect
456. C32#2948semidirect
515. C3#79867semidirect
516. C3#83823semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×D82
#105952152
#105928512
C3×#51522
#105914352
Dic3×#2132
#105914212
#105907812
#105907712
#105907062
#105906932
#838233
#798673