Finite Group Databasebeta

← #11860690

Subgroups — #11860690

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×D3×D24C211yesmaximal, characteristic
2#10593994C212yesmaximal, complemented
3C4×#3745C211yesmaximal, characteristic, complemented
4C3×C4×D24C211yesmaximal, characteristic, complemented
5C3×#4689C211yesmaximal, characteristic, complemented
6#10590939C212yesmaximal, complemented
7#10590763C211yesmaximal, characteristic, complemented
8Dic3×D24C211yesmaximal, characteristic, complemented
9#10590746C212yesmaximal, complemented
10#10590707C211yesmaximal, characteristic, complemented
11#10590346C212yesmaximal, complemented
12#79588—31nomaximal
13#78561—31nomaximal
14C2×D3×D12C2212yes—
15C2×#3745C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C2212yescomplemented
17C2×C3×D24C2211yescharacteristic
18C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
19C2×C3×D3×C8C2211yescharacteristic
20C3×C4×D12C2212yescomplemented
21C3×#872C2211yescharacteristic
22#63921—22no—
23D3×(C2×D3)⋊C4—22no—
24#63904—22no—
25#63894C2212yescomplemented
26Dic3×D12C2212yescomplemented
27#63881—22no—
28#63841C2212yes—
29C2×#3714C2212yes—
30D3×D24C418yescomplemented
31C32×C4×C8C2211yescharacteristic, complemented
32#63648C2212yescomplemented
33#63645C2211yescharacteristic, complemented
34C3×#821C2212yescomplemented
35C3×#818C2211yescharacteristic, complemented
36C3×#815C2211yescharacteristic, complemented
37C3×C8×Dic3C2211yescharacteristic, complemented
38C3×#803C2211yescharacteristic, complemented
39#63573C2212yescomplemented
40#63564C2212yescomplemented
41#63563C2212yescomplemented
42C2×D3×D8—31no—
43C22×D24—31no—
44#5545—32no—
45#5521—32no—
46C3×C4×D8—31no—
47C3×#405—31no—
48Dic3×D8—31no—
49#5131—32no—
50#5106—31no—
51#5014—32no—
52#4880—31no—
53#4872—31no—
54#4785—32no—
55#4770—32no—
56#4711—32no—
57#4711—32no—
58C4×D24—31no—
59C4×D24—31no—
60C4×D24—31no—
61C4×D24—31no—
62C4×D24—61no—
63C4×D24D311yescharacteristic, complemented
64#4689D311yescharacteristic, complemented
65C22×D32—22no—
66C2×C4⋊(C3⋊D3)C2312yes—
67C2×C4×C3⋊D3—22no—
68C2×C3×D12C2312yes—
69C2×C3×C4×D3—22no—
70C2×C3×C4×D3C2311yescharacteristic
71C2×#626—22no—
72C2×#624—22no—
73C2×D3×Dic3—22no—
74D3×D12—24no—
75D3×D12C2×C418yescomplemented
76C2×C32×C8C2311yescharacteristic
77C2×C32×C8C2311yescharacteristic
78C32×C42C2311yescharacteristic
79#3752—22no—
80C4⋊(C3⋊Dic3)C2312yes—
81#3745C2×C414yescomplemented
82C3×(C2×D3)⋊C4—22no—
83C3×(C2×D3)⋊C4D411yescharacteristic
84C3×(C2×D3)⋊C4D411yescharacteristic
85C3×C4⋊Dic3C2312yes—
86C3×Dic3⋊C4D411yescharacteristic
87C3×Dic3⋊C4D411yescharacteristic
88C3×C4×Dic3C2311yescharacteristic
89C2×C3×C3⋊C8C2311yescharacteristic
90C2×C3×C3⋊C8C2311yescharacteristic
91C3×D24C2×C414yescomplemented
92C3×ΓL(1,𝔽25)—22no—
93C3×D3×C8C2×C414yescomplemented
94#3722—22no—
95(C2×D3)⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97Dic32—22no—
98#3714C2×C418yescomplemented
99#2948—91noSylow
100C2×D3×D4—32no—
101C22×D12—32no—
102C2×C3×D8—31no—
103C2×C3×M16—31no—
104C22×C3×C8—31no—
105C3×C4×D4—32no—
106C3×#117—31no—
107D4×Dic3—32no—
108C2×#213—32no—
109C4×#67—62no—
110C2×(C2×D3)⋊C4—62no—
111#926—32no—
112D3×D8—38no—
113C2×D24—32no—
114C2×D24—31no—
115C2×D24—31no—
116C2×D24—38no—
117C2×D24—61no—
118C2×D24C2×D311yescharacteristic
119C2×ΓL(1,𝔽25)C2×D311yescharacteristic
120C2×D3×C8C2×D311yescharacteristic
121#893—32no—
122#893—62no—
123#893—62no—
124#892—32no—
125#67⋊C4—62no—
126D3×C22⋊C4—62no—
127D3×C22⋊C4—62no—
128D3×C22⋊C4—62no—
129C4×D12—32no—
130C4×D12—32no—
131C4×D12—32no—
132C4×D12—32no—
133C4×D12—62no—
134C4×D12C2×D312yescomplemented
135#872C2×D311yescharacteristic
136C3×#107—31no—
137C3×#102—32no—
138C3×#97—31no—
139C3×#97—31no—
140C3×C4×C8—21no—
141C3×C4×C8—31no—
142C3×C4×C8C2×D311yescharacteristic, complemented
143C3×C4×C8C2×D311yescharacteristic, complemented
144#832—32no—
145#821—32no—
146#821—32no—
147#821—32no—
148#821—32no—
149#821—62no—
150#821C2×D312yescomplemented
151#818—31no—
152#818—31no—
153#818—61no—
154#818C2×D311yescharacteristic, complemented
155#817—32no—
156#815C2×D311yescharacteristic, complemented
157C8×Dic3C2×D311yescharacteristic, complemented
158#809—32no—
159#808—32no—
160#803C2×D311yescharacteristic, complemented
161C22×C3⋊D3—22no—
162C22×C3×D3—22no—
163C22×C3×D3C2×D411yescharacteristic
164C2×D32—28no—
165C2×D32—82no—
166C2×D32—82no—
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2411yescharacteristic
170C2×C3⋊Dic3—22no—
171C4⋊(C3⋊D3)—22no—
172C4⋊(C3⋊D3)C22×C414yes—
173C4×C3⋊D3—82no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3C2×D411yescharacteristic
176C2×C3×Dic3C2×D411yescharacteristic
177C2×C3×Dic3C2×D411yescharacteristic
178C3×D12—22no—
179C3×D12C22×C414yes—
180C3×C4×D3—82no—
181C3×C4×D3C22×C412yes—
182C3×C4×D3#4112yes—
183#626—28no—
184#624—82no—
185D3×Dic3—82no—
186C32×C8—21no—
187C32×C8C22×C412yes—
188C3×C3⋊C8—21no—
189C3×C3⋊C8C22×C412yes—
190C22×D8—91no—
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—31no—
201C23×D3—62no—
202C23×D3—62no—
203C2×C3×D4—32no—
204C22×C3×C4—31no—
205C22×C3×C4—62no—
206C2×#67—62no—
207C22×Dic3—62no—
208D3×D4—38no—
209D3×D4—64no—
210C2×D12—32no—
211C2×D12—32no—
212C2×D12—38no—
213C2×D12—62no—
214C2×D12—64no—
215C2×D12—62no—
216C2×D12C22×D312yes—
217C2×C4×D3—22no—
218C2×C4×D3—62no—
219C2×C4×D3—62no—
220C2×C4×D3—62no—
221C2×C4×D3—62no—
222C2×C4×D3—62no—
223C2×C4×D3—122no—
224C2×C4×D3C22×D311yescharacteristic
225C3×D8—34no—
226C3×M16—62no—
227C2×C3×C8—21no—
228C2×C3×C8—21no—
229C2×C3×C8—31no—
230C2×C3×C8—34no—
231C2×C3×C8—31no—
232C2×C3×C8C22×D311yescharacteristic
233C2×C3×C8C22×D311yescharacteristic
234C2×C3×C8C22×D311yescharacteristic
235C2×C3×C8C22×D311yescharacteristic
236C3×C4⋊C4—31no—
237C3×C4⋊C4—31no—
238C3×C4⋊C4—32no—
239C3×C22⋊C4—31no—
240C3×C22⋊C4—31no—
241C3×C22⋊C4—62no—
242C3×C42—21no—
243C3×C42—31no—
244C3×C42C22×D311yescharacteristic
245C3×C42C22×D311yescharacteristic
246#217—62no—
247#217—62no—
248#213—38no—
249(C2×D3)⋊C4—22no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—62no—
252(C2×D3)⋊C4—62no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—62no—
255(C2×D3)⋊C4—62no—
256(C2×D3)⋊C4—122no—
257(C2×D3)⋊C4D1211yescharacteristic
258(C2×D3)⋊C4D1211yescharacteristic
259C4⋊Dic3—32no—
260C4⋊Dic3—32no—
261C4⋊Dic3—62no—
262C4⋊Dic3C22×D312yes—
263Dic3⋊C4D1211yescharacteristic
264Dic3⋊C4D1211yescharacteristic
265C4×Dic3—62no—
266C4×Dic3—62no—
267C4×Dic3C22×D311yescharacteristic
268C2×C3⋊C8C22×D311yescharacteristic
269C2×C3⋊C8C22×D311yescharacteristic
270D24—38no—
271D24—34no—
272D24—34no—
273D24—64no—
274D24C4×D314yescomplemented
275ΓL(1,𝔽25)—22no—
276D3×C8C4×D314yescomplemented
277C22×C32C22×D411yescharacteristic
278C2×C3⋊D3—24no—
279C2×C3⋊D3—42no—
280C2×C3⋊D3—42no—
281C2×C3×D3—21no—
282C2×C3×D3—21no—
283C2×C3×D3—24no—
284C2×C3×D3—42no—
285C2×C3×D3—42no—
286C2×C3×D3C4×D412yes—
287D32—88no—
288C32×C4—21no—
289C32×C4—21no—
290C32×C4C23×C411yescharacteristic
291C32×C4C2×#4111yescharacteristic
292C3⋊Dic3—42no—
293C3×Dic3—21no—
294C3×Dic3—21no—
295C3×Dic3—42no—
296C3×Dic3C4×D412yes—
297C22×D4—92no—
298C2×D8—31no—
299C2×D8—98no—
300C2×D8—92no—
301C2×D8—91no—
302C2×M16—31no—
303C22×C8—31no—
304C4×D4—32no—
305C4×D4—92no—
306C4×D4—92no—
307C4×D4—92no—
308C4×D4—182no—
309C4×D4—182no—
310#117—31no—
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—31no—
322#97—31no—
323C4×C8—31no—
324C4×C8D3211yescharacteristic, complemented
325C23×C3—31no—
326C23×C3—62no—
327C22×D3—22no—
328C22×D3—68no—
329C22×D3—62no—
330C22×D3—62no—
331C22×D3—68no—
332C22×D3—122no—
333C22×D3—242no—
334C22×D3—242no—
335C22×D3—242no—
336C22×D3—242no—
337C22×D3C2×D1211yescharacteristic
338C3×D4—34no—
339C3×D4—62no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—31no—
344C2×C3×C4—32no—
345C2×C3×C4—32no—
346C2×C3×C4—31no—
347C2×C3×C4—31no—
348C2×C3×C4—62no—
349C2×C3×C4—242no—
350C2×C3×C4C2×D1211yescharacteristic
351C2×C3×C4C2×D1211yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4C23×D311yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356#67—68no—
357C2×Dic3—22no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—122no—
361C2×Dic3—242no—
362C2×Dic3C2×D1211yescharacteristic
363C2×Dic3C2×D1211yescharacteristic
364C2×Dic3C2×D1211yescharacteristic
365D12—22no—
366D12—34no—
367D12—34no—
368D12—64no—
369D12—68no—
370D12—62no—
371D12—62no—
372D12—122no—
373D12C2×C4×D314yes—
374C4×D3—82no—
375C4×D3—242no—
376C4×D3—242no—
377C4×D3—242no—
378C4×D3—242no—
379C4×D3—242no—
380C4×D3—244no—
381C4×D3C2×C4×D312yes—
382C4×D3#23512yes—
383C3×C8—21no—
384C3×C8—21no—
385C3×C8—22no—
386C3×C8—32no—
387C3×C8—41no—
388C3×C8—61no—
389C3×C8C2×C4×D312yes—
390C3×C8C2×C4×D312yes—
391C3⋊C8—21no—
392C3⋊C8C2×C4×D312yes—
393C2×C32C2×C4×D411yescharacteristic
394C2×C32#57611yescharacteristic
395C2×C32#57611yescharacteristic
396C3⋊D3—44no—
397C3×D3—22no—
398C3×D3—44no—
399C24—182no—
400C2×D4—32no—
401C2×D4—98no—
402C2×D4—92no—
403C2×D4—184no—
404C2×D4—182no—
405C22×C4—31no—
406C22×C4—62no—
407C22×C4—182no—
408C22×C4—182no—
409C22×C4—182no—
410D8—34no—
411D8—98no—
412D8—94no—
413M16—62no—
414C2×C8—31no—
415C2×C8—34no—
416C2×C8—31no—
417C2×C8C2×D3211yescharacteristic
418C2×C8C2×D3211yescharacteristic
419C4⋊C4—31no—
420C4⋊C4—31no—
421C4⋊C4—32no—
422C4⋊C4—92no—
423C22⋊C4—31no—
424C22⋊C4—31no—
425C22⋊C4—62no—
426C22⋊C4—182no—
427C22⋊C4—182no—
428C22⋊C4—182no—
429C22⋊C4—182no—
430C42—31no—
431C42—182no—
432C42C2×D3211yescharacteristic
433C22×C3—21no—
434C22×C3—32no—
435C22×C3—61no—
436C22×C3—61no—
437C22×C3—64no—
438C22×C3—122no—
439C22×C3—122no—
440C22×C3C22×D1211yescharacteristic
441C22×C3C2×D3×D411yescharacteristic
442C2×D3—21no—
443C2×D3—21no—
444C2×D3—24no—
445C2×D3—42no—
446C2×D3—42no—
447C2×D3—64no—
448C2×D3—64no—
449C2×D3—124no—
450C2×D3—122no—
451C2×D3—122no—
452C2×D3—122no—
453C2×D3—122no—
454C2×D3—242no—
455C2×D3—242no—
456C2×D3—248no—
457C2×D3—248no—
458C2×D3C4×D1212yes—
459C3×C4—22no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—32no—
467C3×C4—41no—
468C3×C4—61no—
469C3×C4—61no—
470C3×C4—122no—
471C3×C4C22×C4×D311yescharacteristic
472C3×C4C22×C4×D311yescharacteristic
473C3×C4C2×#23511yescharacteristic
474C3×C4D3×#4111yescharacteristic
475Dic3—21no—
476Dic3—21no—
477Dic3—42no—
478Dic3—122no—
479Dic3—122no—
480Dic3—242no—
481Dic3C4×D1212yes—
482C32#294811yescharacteristic, complemented, Sylow
483C23—31no—
484C23—62no—
485C23—188no—
486C23—182no—
487C23—722no—
488C23—722no—
489D4—34no—
490D4—62no—
491D4—94no—
492D4—188no—
493D4—182no—
494C2×C4—31no—
495C2×C4—32no—
496C2×C4—32no—
497C2×C4—31no—
498C2×C4—31no—
499C2×C4—62no—
500C2×C4—182no—
501C2×C4—242no—
502C2×C4—722no—
503C2×C4—722no—
504C2×C4—722no—
505C2×C4D3×D1211yescharacteristic
506C2×C4D3×D1211yescharacteristic
507C2×C4C22×D3211yescharacteristic
508C8—21no—
509C8—32no—
510C8—61no—
511C8C4×D3212yes—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—62no—
516C2×C3—124no—
517C2×C3C2×C4×D1211yescharacteristic
518C2×C3C4×D3×D411yescharacteristic
519C2×C3#575211yescharacteristic
520C2×C3#575211yescharacteristic
521C2×C3#575711yescharacteristic
522C2×C3#576911yescharacteristic
523D3—22no—
524D3—44no—
525D3—124no—
526D3—124no—
527D3—244no—
528C22—32no—
529C22—61no—
530C22—61no—
531C22—64no—
532C22—122no—
533C22—122no—
534C22—184no—
535C22—362no—
536C22—362no—
537C22—728no—
538C22C2×D3×D1211yescharacteristic
539C4—21no—
540C4—21no—
541C4—32no—
542C4—61no—
543C4—61no—
544C4—122no—
545C4—362no—
546C4C2×C4×D3211yescharacteristic
547C4D3×#23511yescharacteristic
548C3—21no—
549C3#7856111yescharacteristic, complemented
550C3#7958811yescharacteristic, complemented
551C2—62no—
552C2—124no—
553C2—364no—
554C2C4×D3×D1211yescharacteristic
555C2#1059467811yescharacteristic
556C2#1059468011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×D3×D24C2
cosocleC2×C32×C4C24
hypercenterC4×C8D32
hypocenterC32#2948
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10593994C2semidirect
3. C4×#3745C2semidirect
4. C3×C4×D24C2semidirect
5. C3×#4689C2semidirect
6. #10590939C2semidirect
7. #10590763C2semidirect
8. Dic3×D24C2semidirect
9. #10590746C2semidirect
10. #10590707C2semidirect
11. #10590346C2semidirect
16. C4×C4⋊(C3⋊D3)C22semidirect
20. C3×C4×D12C22semidirect
25. #63894C22semidirect
26. Dic3×D12C22semidirect
30. D3×D24C4semidirect
31. C32×C4×C8C22semidirect
32. #63648C22semidirect
33. #63645C22semidirect
34. C3×#821C22semidirect
35. C3×#818C22semidirect
36. C3×#815C22semidirect
37. C3×C8×Dic3C22semidirect
38. C3×#803C22semidirect
39. #63573C22semidirect
40. #63564C22semidirect
41. #63563C22semidirect
63. C4×D24D3semidirect
64. #4689D3semidirect
75. D3×D12C2×C4semidirect
81. #3745C2×C4semidirect
91. C3×D24C2×C4semidirect
93. C3×D3×C8C2×C4semidirect
98. #3714C2×C4semidirect
134. C4×D12C2×D3semidirect
142. C3×C4×C8C2×D3semidirect
143. C3×C4×C8C2×D3semidirect
150. #821C2×D3semidirect
154. #818C2×D3semidirect
156. #815C2×D3semidirect
157. C8×Dic3C2×D3semidirect
160. #803C2×D3semidirect
274. D24C4×D3semidirect
276. D3×C8C4×D3semidirect
324. C4×C8D32semidirect
482. C32#2948semidirect
549. C3#78561semidirect
550. C3#79588semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D242
#105939942
C4×#37452
C3×C4×D242
C3×#46892
#105909392
#105907632
Dic3×D242
#105907462
#105907072
#105903462
#795883
#785613