Finite Group Databasebeta

← #11860683

Subgroups — #11860683

Order 1152.

1123 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×D8C211yesmaximal, characteristic
2#10595215C212yesmaximal, complemented
3D8×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C3×Dic3×D8C211yesmaximal, characteristic, complemented
5#10591436C212yesmaximal, complemented
6#10591430C212yesmaximal, complemented
7#10591421C212yesmaximal, complemented
8#10590777C211yesmaximal, characteristic, complemented
9Dic3×D24C211yesmaximal, characteristic, complemented
10#10590707C211yesmaximal, characteristic, complemented
11#10590692C211yesmaximal, characteristic, complemented
12#83823—31nomaximal
13#79588—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#63645C2211yescharacteristic, complemented
33C8×C3⋊Dic3C2211yescharacteristic, complemented
34C3×#832C2212yescomplemented
35C3×#818C2211yescharacteristic, complemented
36C3×C8×Dic3C2211yescharacteristic, complemented
37#63573C2212yescomplemented
38#63563C2212yescomplemented
39#63562C2212yescomplemented
40#63555C2211yescharacteristic, complemented
41#63554C2211yescharacteristic, complemented
42C22×C3×D8—31no—
43#5798—32no—
44C2×D3×D8D311yescharacteristic
45#5545—32no—
46C3×C4×D8—31no—
47#5215—32no—
48#5152—32no—
49#5152—32no—
50Dic3×D8—31no—
51Dic3×D8—31no—
52Dic3×D8—31no—
53Dic3×D8—31no—
54Dic3×D8—61no—
55Dic3×D8D311yescharacteristic, complemented
56#5106—31no—
57#5101—31no—
58#5014—32no—
59#4880—31no—
60#4872—31no—
61#4785—32no—
62#4770—32no—
63C4×D24—31no—
64#4689—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⋊Dic3D411yescharacteristic
91Dic3⋊Dic3D411yescharacteristic
92(C2×D3)⋊Dic3—22no—
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95(C2×D3)⋊Dic3D411yescharacteristic
96(C2×D3)⋊Dic3D411yescharacteristic
97Dic32—22no—
98#3711—22no—
99#2948—91noSylow
100C22×C3×D4—32no—
101C2×D3×D4C2×D312yes—
102C2×C3×D8—21no—
103C2×C3×D8—32no—
104C2×C3×D8—38no—
105C2×C3×D8—31no—
106C2×C3×D8C2×D311yescharacteristic
107C2×C3×D8C2×D311yescharacteristic
108C22×C3×C8—31no—
109C3×C4×D4—32no—
110C2×#217—62no—
111C2×#217—62no—
112D4×Dic3—32no—
113D4×Dic3—32no—
114D4×Dic3—32no—
115D4×Dic3—32no—
116D4×Dic3—62no—
117D4×Dic3—62no—
118D4×Dic3—62no—
119D4×Dic3C2×D312yescomplemented
120C2×#213C2×D312yes—
121C4×#67—62no—
122C2×(C2×D3)⋊C4—62no—
123#926—31no—
124#926—32no—
125C2×#208—31no—
126D3×D8Dic318yescomplemented
127C2×D24C2×D311yescharacteristic
128C2×ΓL(1,𝔽25)—31no—
129C2×D3×C8C2×D311yescharacteristic
130#893—32no—
131#892—32no—
132#67⋊C4—62no—
133D3×C22⋊C4—62no—
134C4×D12—32no—
135#872—31no—
136C3×#107—31no—
137C3×#102—32no—
138C3×C4×C8—31no—
139#832—32no—
140#832—32no—
141#832—32no—
142#832—32no—
143#832—62no—
144#832C2×D312yescomplemented
145#821—32no—
146#818—31no—
147#818—31no—
148#818—61no—
149#818C2×D311yescharacteristic, complemented
150#817—32no—
151#815—31no—
152#815—31no—
153#815—31no—
154C8×Dic3—31no—
155C8×Dic3—31no—
156C8×Dic3—61no—
157C8×Dic3C2×D311yescharacteristic, complemented
158#809—32no—
159#808—32no—
160#803—31no—
161C23×C32—22no—
162C22×C3×D3—22no—
163C22×C3×D3—28no—
164C22×C3×D3—82no—
165C22×C3×D3—82no—
166C22×C3×D3C2×D411yescharacteristic
167C32×D4—22no—
168C32×D4C22×C414yes—
169C2×C32×C4C2411yescharacteristic
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3—82no—
172C2×C3⋊Dic3C2×D411yescharacteristic
173C2×C3⋊Dic3C2×D411yescharacteristic
174C3×#67—28no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—82no—
177C2×C3×Dic3C2×D411yescharacteristic
178C2×C3×Dic3C2×D411yescharacteristic
179C2×C3×Dic3C2×D411yescharacteristic
180C3×D12—22no—
181C3×D12C22×C414yes—
182C3×C4×D3C22×C412yes—
183C3×C4×D3#4112yes—
184D3×Dic3—82no—
185D3×Dic3—82no—
186C32×C8C22×C412yes—
187C3⋊(C3⋊C8)—21no—
188C3×C3⋊C8—21no—
189C3×C3⋊C8C22×C412yes—
190C22×D8—31no—
191#518—92no—
192#442—92no—
193#442—92no—
194C4×D8—31no—
195C4×D8—91no—
196C4×D8—91no—
197C4×D8—91no—
198#427—91no—
199#418—92no—
200#405—91no—
201C24×C3—62no—
202C23×D3—22no—
203C2×C3×D4—22no—
204C2×C3×D4—38no—
205C2×C3×D4—32no—
206C2×C3×D4—64no—
207C2×C3×D4—62no—
208C2×C3×D4C22×D312yes—
209C2×C3×D4C22×D312yes—
210C22×C3×C4—31no—
211C22×C3×C4—62no—
212C2×#67—22no—
213C22×Dic3—22no—
214C22×Dic3—62no—
215C22×Dic3—62no—
216C22×Dic3—62no—
217C22×Dic3—62no—
218C22×Dic3—122no—
219D3×D4—24no—
220D3×D4C2×Dic318yescomplemented
221C2×D12C22×D312yes—
222C2×C4×D3—62no—
223C2×C4×D3—62no—
224C2×C4×D3C22×D311yescharacteristic
225C3×D8—24no—
226C3×D8—38no—
227C3×D8—34no—
228C3×D8C4×D314yescomplemented
229C3×D8C2×Dic314yescomplemented
230C2×C3×C8—21no—
231C2×C3×C8—31no—
232C2×C3×C8—34no—
233C2×C3×C8—31no—
234C2×C3×C8C22×D311yescharacteristic
235C2×C3×C8C22×D311yescharacteristic
236C3×C4⋊C4—32no—
237C3×C22⋊C4—62no—
238C3×C42—31no—
239#217—22no—
240#217—31no—
241#217—31no—
242#217—62no—
243#217—62no—
244#217—62no—
245#217—62no—
246#217—62no—
247#217—122no—
248#213C2×Dic318yescomplemented
249(C2×D3)⋊C4—31no—
250(C2×D3)⋊C4—31no—
251(C2×D3)⋊C4—62no—
252(C2×D3)⋊C4—62no—
253(C2×D3)⋊C4—62no—
254C4⋊Dic3—31no—
255C4⋊Dic3—31no—
256C4⋊Dic3—32no—
257C4⋊Dic3—32no—
258C4⋊Dic3—62no—
259C4⋊Dic3C22×D312yes—
260Dic3⋊C4—31no—
261Dic3⋊C4—31no—
262C4×Dic3—31no—
263C4×Dic3—31no—
264C4×Dic3—61no—
265C4×Dic3—62no—
266C4×Dic3—62no—
267C4×Dic3C22×D311yescharacteristic
268#208—62no—
269C2×C3⋊C8—31no—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—61no—
272C2×C3⋊C8C22×D311yescharacteristic
273C2×C3⋊C8C22×D311yescharacteristic
274D24C2×Dic314yescomplemented
275ΓL(1,𝔽25)—62no—
276D3×C8C2×Dic314yescomplemented
277C22×C32—24no—
278C22×C32—42no—
279C22×C32—42no—
280C22×C32C22×D411yescharacteristic
281C2×C3×D3—21no—
282C2×C3×D3—21no—
283C2×C3×D3—24no—
284C2×C3×D3—42no—
285C2×C3×D3—42no—
286C2×C3×D3—88no—
287C2×C3×D3C4×D412yes—
288C32×C4C23×C411yescharacteristic
289C32×C4C2×#4111yescharacteristic
290C3⋊Dic3—21no—
291C3⋊Dic3—21no—
292C3⋊Dic3—42no—
293C3×Dic3—21no—
294C3×Dic3—21no—
295C3×Dic3—42no—
296C3×Dic3C4×D412yes—
297C22×D4—32no—
298C2×D8—32no—
299C2×D8—38no—
300C2×D8—31no—
301C2×D8D3211yescharacteristic
302C2×M16—91no—
303C22×C8—31no—
304C4×D4—32no—
305C4×D4—92no—
306C4×D4—92no—
307C4×D4—92no—
308C4×D4—182no—
309C4×D4—182no—
310#117—91no—
311#117—92no—
312C2×C22⋊C4—182no—
313C2×C22⋊C4—182no—
314#107—31no—
315#107—91no—
316#106—92no—
317#102—32no—
318#102—92no—
319#102—92no—
320#102—92no—
321#97—91no—
322#97—91no—
323C4×C8—31no—
324C4×C8—91no—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3—31no—
328C23×C3—42no—
329C23×C3—68no—
330C23×C3—62no—
331C23×C3—242no—
332C23×C3—242no—
333C22×D3—22no—
334C22×D3—28no—
335C22×D3—82no—
336C22×D3—82no—
337C22×D3D3×D411yescharacteristic
338C3×D4—22no—
339C3×D4—22no—
340C3×D4—24no—
341C3×D4—34no—
342C3×D4—42no—
343C3×D4—68no—
344C3×D4—62no—
345C3×D4C2×C4×D314yes—
346C3×D4C22×Dic314yes—
347C2×C3×C4—21no—
348C2×C3×C4—31no—
349C2×C3×C4—32no—
350C2×C3×C4—32no—
351C2×C3×C4—31no—
352C2×C3×C4—31no—
353C2×C3×C4—62no—
354C2×C3×C4—242no—
355C2×C3×C4C23×D311yescharacteristic
356C2×C3×C4C23×D311yescharacteristic
357#67—28no—
358C2×Dic3—22no—
359C2×Dic3—31no—
360C2×Dic3—31no—
361C2×Dic3—31no—
362C2×Dic3—31no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—82no—
368C2×Dic3—122no—
369C2×Dic3—242no—
370C2×Dic3—242no—
371C2×Dic3—242no—
372C2×Dic3—242no—
373C2×Dic3—244no—
374C2×Dic3D3×D411yescharacteristic
375C2×Dic3D3×D411yescharacteristic
376C2×Dic3D3×D411yescharacteristic
377D12—22no—
378D12C22×Dic314yes—
379C4×D3—242no—
380C4×D3—242no—
381C4×D3#23712yes—
382C4×D3C22×Dic312yes—
383C3×C8—22no—
384C3×C8—32no—
385C3×C8—61no—
386C3×C8C2×C4×D312yes—
387C3×C8C22×Dic312yes—
388C3⋊C8—21no—
389C3⋊C8—61no—
390C3⋊C8—61no—
391C3⋊C8—121no—
392C3⋊C8C22×Dic312yes—
393C2×C32—44no—
394C2×C32C2×C4×D411yescharacteristic
395C2×C32#57611yescharacteristic
396C2×C32#57611yescharacteristic
397C3×D3—22no—
398C3×D3—44no—
399C24—62no—
400C2×D4—38no—
401C2×D4—32no—
402C2×D4—64no—
403C2×D4—62no—
404C2×D4C2×D3212yes—
405C22×C4—31no—
406C22×C4—62no—
407C22×C4—182no—
408C22×C4—182no—
409C22×C4—182no—
410D8—38no—
411D8—34no—
412D8D3×Dic314yescomplemented
413M16—182no—
414C2×C8—31no—
415C2×C8—34no—
416C2×C8—31no—
417C2×C8—91no—
418C2×C8C2×D3211yescharacteristic
419C4⋊C4—32no—
420C4⋊C4—91no—
421C4⋊C4—91no—
422C4⋊C4—92no—
423C22⋊C4—62no—
424C22⋊C4—91no—
425C22⋊C4—91no—
426C22⋊C4—182no—
427C22⋊C4—182no—
428C22⋊C4—182no—
429C22⋊C4—182no—
430C42—31no—
431C42—91no—
432C42—182no—
433C22×C3—24no—
434C22×C3—24no—
435C22×C3—21no—
436C22×C3—32no—
437C22×C3—44no—
438C22×C3—42no—
439C22×C3—42no—
440C22×C3—42no—
441C22×C3—42no—
442C22×C3—61no—
443C22×C3—61no—
444C22×C3—64no—
445C22×C3—82no—
446C22×C3—82no—
447C22×C3—122no—
448C22×C3—122no—
449C22×C3—248no—
450C22×C3C2×D3×D411yescharacteristic
451C22×C3C2×D3×D411yescharacteristic
452C2×D3—21no—
453C2×D3—21no—
454C2×D3—24no—
455C2×D3—42no—
456C2×D3—42no—
457C2×D3—88no—
458C2×D3D4×Dic312yes—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—32no—
462C3×C4—61no—
463C3×C4—61no—
464C3×C4—122no—
465C3×C4C22×C4×D311yescharacteristic
466C3×C4C2×#23711yescharacteristic
467C3×C4D3×#4111yescharacteristic
468C3×C4C23×Dic311yescharacteristic
469Dic3—21no—
470Dic3—21no—
471Dic3—42no—
472Dic3—62no—
473Dic3—61no—
474Dic3—61no—
475Dic3—61no—
476Dic3—61no—
477Dic3—121no—
478Dic3—122no—
479Dic3—122no—
480Dic3—242no—
481Dic3D4×Dic312yes—
482C32#294811yescharacteristic, complemented, Sylow
483C23—22no—
484C23—31no—
485C23—68no—
486C23—62no—
487C23—242no—
488C23—242no—
489D4—22no—
490D4—34no—
491D4—68no—
492D4—62no—
493D4C2×D3×Dic314yes—
494C2×C4—31no—
495C2×C4—32no—
496C2×C4—32no—
497C2×C4—31no—
498C2×C4—31no—
499C2×C4—62no—
500C2×C4—91no—
501C2×C4—91no—
502C2×C4—182no—
503C2×C4—242no—
504C2×C4—722no—
505C2×C4—722no—
506C2×C4—722no—
507C2×C4C22×D3211yescharacteristic
508C8—32no—
509C8—61no—
510C8—181no—
511C8C2×D3×Dic312yes—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—44no—
516C2×C3—44no—
517C2×C3—62no—
518C2×C3—84no—
519C2×C3—124no—
520C2×C3C4×D3×D411yescharacteristic
521C2×C3#575711yescharacteristic
522C2×C3#575711yescharacteristic
523C2×C3#575711yescharacteristic
524C2×C3#576911yescharacteristic
525C2×C3C2×D4×Dic311yescharacteristic
526D3—22no—
527D3—44no—
528C22—24no—
529C22—32no—
530C22—42no—
531C22—42no—
532C22—61no—
533C22—61no—
534C22—64no—
535C22—122no—
536C22—122no—
537C22—248no—
538C22D32×D411yescharacteristic
539C4—32no—
540C4—61no—
541C4—61no—
542C4—122no—
543C4—181no—
544C4—181no—
545C4—362no—
546C4D3×#23711yescharacteristic
547C4C22×D3×Dic311yescharacteristic
548C3—21no—
549C3#7958811yescharacteristic, complemented
550C3#8382311yescharacteristic, complemented
551C2—44no—
552C2—62no—
553C2—124no—
554C2#1059473111yescharacteristic
555C2#1059473411yescharacteristic
556C2D3×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. D8×C3⋊Dic3C2semidirect
4. C3×Dic3×D8C2semidirect
5. #10591436C2semidirect
6. #10591430C2semidirect
7. #10591421C2semidirect
8. #10590777C2semidirect
9. Dic3×D24C2semidirect
10. #10590707C2semidirect
11. #10590692C2semidirect
16. D4×C3⋊Dic3C22semidirect
17. C3×D4×Dic3C22semidirect
19. C3×D3×D8C4semidirect
26. #63898C22semidirect
27. Dic3×D12C22semidirect
31. #63659C22semidirect
32. #63645C22semidirect
33. C8×C3⋊Dic3C22semidirect
34. C3×#832C22semidirect
35. C3×#818C22semidirect
36. C3×C8×Dic3C22semidirect
37. #63573C22semidirect
38. #63563C22semidirect
39. #63562C22semidirect
40. #63555C22semidirect
41. #63554C22semidirect
55. Dic3×D8D3semidirect
71. C3×D3×D4C2×C4semidirect
76. C32×D8C2×C4semidirect
83. C3×#213C2×C4semidirect
88. C3×D24C2×C4semidirect
89. C3×D3×C8C2×C4semidirect
119. D4×Dic3C2×D3semidirect
126. D3×D8Dic3semidirect
144. #832C2×D3semidirect
149. #818C2×D3semidirect
157. C8×Dic3C2×D3semidirect
220. D3×D4C2×Dic3semidirect
228. C3×D8C4×D3semidirect
229. C3×D8C2×Dic3semidirect
248. #213C2×Dic3semidirect
274. D24C2×Dic3semidirect
276. D3×C8C2×Dic3semidirect
412. D8D3×Dic3semidirect
482. C32#2948semidirect
549. C3#79588semidirect
550. 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
D8×C3⋊Dic32
C3×Dic3×D82
#105914362
#105914302
#105914212
#105907772
Dic3×D242
#105907072
#105906922
#838233
#795883