Finite Group Databasebeta

← #11857241

Subgroups — #11857241

Order 1152.

1199 conjugacy classes of subgroups.

The subgroup lattice has 553 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×M16C211yesmaximal, characteristic
2C2×#63855C211yesmaximal, characteristic
3C2×D3×#208C211yesmaximal, characteristic
4M16×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C3×Dic3×M16C211yesmaximal, characteristic, complemented
6#10591060C211yesmaximal, characteristic, complemented
7Dic3×#208C211yesmaximal, characteristic, complemented
8#10590909C212yesmaximal, complemented
9#10590908C212yesmaximal, complemented
10#10590693C212yesmaximal, complemented
11#10590692C212yesmaximal, complemented
12#83747—31nomaximal
13#78514—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C3×D3×M16C418yescomplemented
22C2×C3×ΓL(1,𝔽25)C2212yes—
23C2×C3×D3×C8C2212yes—
24C2×Dic3⋊Dic3C412yes—
25C2×(C2×D3)⋊Dic3C412yes—
26#63855C412yes—
27#63855C412yes—
28#63855C2211yescharacteristic
29#63855C2211yescharacteristic
30#63855C2211yescharacteristic
31#63855C2211yescharacteristic
32C2×#3711C2212yes—
33D3×#208C418yescomplemented
34C2×D3×C3⋊C8C2212yes—
35#63642C2212yescomplemented
36C8×C3⋊Dic3C2212yescomplemented
37C3×#815C2212yescomplemented
38C3×C8×Dic3C2212yescomplemented
39#63555C2212yescomplemented
40#63554C2212yescomplemented
41#63553C2212yescomplemented
42Dic3×C3⋊C8C2212yescomplemented
43C22×C3×M16—31no—
44C2×#926—31no—
45C22×#208—31no—
46C2×D3×M16—31no—
47C2×D3×M16D311yescharacteristic
48C2×#872—31no—
49C3×C4×M16—31no—
50#5122—32no—
51#5122—32no—
52Dic3×M16—31no—
53Dic3×M16—31no—
54Dic3×M16—31no—
55Dic3×M16—31no—
56Dic3×M16—31no—
57Dic3×M16—61no—
58Dic3×M16D311yescharacteristic, complemented
59#5101—32no—
60#5101—32no—
61C4×#208—31no—
62#4708—32no—
63#4708—32no—
64#4689—32no—
65#4689—32no—
66C23×C3×D3C2×C411yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3C2×C412yes—
69C22×C3×Dic3C2×C412yes—
70C22×C3×Dic3C2×C411yescharacteristic
71C2×C3×C4×D3C2×C411yescharacteristic
72C2×C3×C4×D3C2×C411yescharacteristic
73C2×C3×C4×D3C2×C414yes—
74C2×C3×C4×D3C2×C414yes—
75C2×C3×C4×D3C2311yescharacteristic
76C2×C3×C4×D3C2311yescharacteristic
77C32×M16C2×C414yes—
78C2×C32×C8C2312yes—
79C4×C3⋊Dic3C2×C412yes—
80C4×C3⋊Dic3C2311yescharacteristic
81C4×C3⋊Dic3C2311yescharacteristic
82#3748C2×C414yes—
83C2×C3⋊(C3⋊C8)C2312yes—
84C3×C4×Dic3C2×C412yes—
85C3×C4×Dic3C2311yescharacteristic
86C3×C4×Dic3C2311yescharacteristic
87C3×#208C2×C414yes—
88C3×#208C2×C414yes—
89C2×C3×C3⋊C8C2312yes—
90C2×C3×C3⋊C8C2312yes—
91C3×ΓL(1,𝔽25)C2×C418yescomplemented
92C3×D3×C8C2×C418yescomplemented
93Dic3⋊Dic3C2×C412yes—
94Dic3⋊Dic3C2×C412yes—
95Dic3⋊Dic3C2×C412yes—
96Dic3⋊Dic3C2×C412yes—
97(C2×D3)⋊Dic3C2×C412yes—
98(C2×D3)⋊Dic3C2×C412yes—
99(C2×D3)⋊Dic3C2×C412yes—
100(C2×D3)⋊Dic3C2×C412yes—
101#3711C2×C418yescomplemented
102D3×C3⋊C8C2×C418yescomplemented
103#2873—91noSylow
104C23×C3×C4—31no—
105C22×C4×D3C2×D311yescharacteristic
106C2×C3×M16—21no—
107C2×C3×M16—31no—
108C2×C3×M16—31no—
109C2×C3×M16—38no—
110C2×C3×M16—32no—
111C2×C3×M16C2×D311yescharacteristic
112C2×C3×M16C2×D311yescharacteristic
113C22×C3×C8—32no—
114C2×C3×C42—31no—
115C2×#217—32no—
116C2×(C2×D3)⋊C4—32no—
117#926—32no—
118#926—32no—
119#926—31no—
120#926—31no—
121#926—31no—
122#926—31no—
123C2×C4⋊Dic3—32no—
124C2×Dic3⋊C4—32no—
125C2×C4×Dic3—31no—
126C2×C4×Dic3—31no—
127C2×C4×Dic3—61no—
128C2×C4×Dic3C2×D311yescharacteristic
129C2×#208—31no—
130C2×#208—31no—
131C2×#208—38no—
132C2×#208—32no—
133C2×#208—61no—
134C2×#208C2×D311yescharacteristic
135C2×#208C2×D311yescharacteristic
136C22×C3⋊C8—32no—
137D3×M16—38no—
138D3×M16Dic318yescomplemented
139C2×ΓL(1,𝔽25)—32no—
140C2×ΓL(1,𝔽25)C2×D312yes—
141C2×D3×C8—32no—
142C2×D3×C8C2×D312yes—
143#872—32no—
144#872—32no—
145#872—31no—
146#872—31no—
147#872—31no—
148#872—31no—
149C3×#97—32no—
150C3×C4×C8—32no—
151#815—32no—
152#815—32no—
153#815—32no—
154#815—32no—
155#815—32no—
156#815—62no—
157#815C2×D312yescomplemented
158C8×Dic3—32no—
159C8×Dic3—32no—
160C8×Dic3—32no—
161C8×Dic3—32no—
162C8×Dic3—32no—
163C8×Dic3—62no—
164C8×Dic3C2×D312yescomplemented
165#803—32no—
166C4×C3⋊C8—32no—
167C23×C32C22×C411yescharacteristic
168C22×C3×D3—42no—
169C22×C3×D3C4214yes—
170C22×C3×D3C22×C411yescharacteristic
171C22×C3×D3C22×C411yescharacteristic
172C2×C32×C4C22×C411yescharacteristic
173C2×C32×C4C22×C412yes—
174C2×C32×C4C22×C412yes—
175C2×C32×C4C2411yescharacteristic
176C2×C3⋊Dic3—42no—
177C2×C3⋊Dic3C22×C412yes—
178C2×C3⋊Dic3C22×C412yes—
179C2×C3×Dic3—42no—
180C2×C3×Dic3C4214yes—
181C2×C3×Dic3C22×C412yes—
182C2×C3×Dic3C22×C412yes—
183C2×C3×Dic3C22×C411yescharacteristic
184C2×C3×Dic3C22×C411yescharacteristic
185C3×C4×D3C4214yes—
186C3×C4×D3C4214yes—
187C3×C4×D3C22×C412yes—
188C3×C4×D3C22×C412yes—
189C3×C4×D3C22×C412yes—
190C3×C4×D3C22×C412yes—
191C32×C8C22×C414yes—
192C3⋊(C3⋊C8)C22×C414yes—
193C3×C3⋊C8C22×C414yes—
194C3×C3⋊C8C22×C414yes—
195C22×M16—31no—
196C22×M16—91no—
197C2×#117—91no—
198#405—92no—
199#405—92no—
200#405—92no—
201#405—92no—
202C4×M16—31no—
203C4×M16—91no—
204C4×M16—91no—
205C4×M16—91no—
206C24×C3—31no—
207C23×D3C4×D311yescharacteristic
208C22×C3×C4—21no—
209C22×C3×C4—31no—
210C22×C3×C4—34no—
211C22×C3×C4—31no—
212C22×C3×C4—31no—
213C22×C3×C4—34no—
214C22×C3×C4—31no—
215C22×C3×C4—31no—
216C22×C3×C4—32no—
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C22×D311yescharacteristic
219C22×Dic3—32no—
220C22×Dic3—32no—
221C22×Dic3—62no—
222C22×Dic3C4×D312yes—
223C22×Dic3C4×D311yescharacteristic
224C2×C4×D3C4×D311yescharacteristic
225C2×C4×D3C4×D311yescharacteristic
226C2×C4×D3C4×D314yes—
227C2×C4×D3C2×Dic314yes—
228C2×C4×D3C22×D311yescharacteristic
229C2×C4×D3C22×D311yescharacteristic
230C3×M16—24no—
231C3×M16—34no—
232C3×M16—34no—
233C3×M16—38no—
234C3×M16C4×D314yes—
235C3×M16C2×Dic314yes—
236C2×C3×C8—22no—
237C2×C3×C8—32no—
238C2×C3×C8—32no—
239C2×C3×C8—38no—
240C2×C3×C8C22×D312yes—
241C2×C3×C8C22×D312yes—
242C3×C42—32no—
243C3×C42—31no—
244C3×C42—31no—
245#217—32no—
246#217—32no—
247#217—32no—
248#217—32no—
249(C2×D3)⋊C4—32no—
250(C2×D3)⋊C4—32no—
251(C2×D3)⋊C4—32no—
252(C2×D3)⋊C4—32no—
253C4⋊Dic3—32no—
254C4⋊Dic3—32no—
255C4⋊Dic3—32no—
256C4⋊Dic3—32no—
257Dic3⋊C4—32no—
258Dic3⋊C4—32no—
259Dic3⋊C4—32no—
260Dic3⋊C4—32no—
261C4×Dic3—32no—
262C4×Dic3—32no—
263C4×Dic3—31no—
264C4×Dic3—31no—
265C4×Dic3—31no—
266C4×Dic3—31no—
267C4×Dic3—61no—
268C4×Dic3—61no—
269C4×Dic3—62no—
270C4×Dic3C4×D312yes—
271C4×Dic3C22×D311yescharacteristic
272C4×Dic3C22×D311yescharacteristic
273#208—34no—
274#208—34no—
275#208—38no—
276#208—64no—
277#208C4×D314yes—
278#208C2×Dic314yes—
279C2×C3⋊C8—32no—
280C2×C3⋊C8—32no—
281C2×C3⋊C8—38no—
282C2×C3⋊C8—62no—
283C2×C3⋊C8C22×D312yes—
284C2×C3⋊C8C22×D312yes—
285ΓL(1,𝔽25)—38no—
286ΓL(1,𝔽25)C2×Dic318yescomplemented
287D3×C8—38no—
288D3×C8C2×Dic318yescomplemented
289C22×C32—22no—
290C22×C32C2×C4212yes—
291C22×C32C23×C411yescharacteristic
292C2×C3×D3—22no—
293C2×C3×D3—22no—
294C2×C3×D3—44no—
295C2×C3×D3C2×C4212yes—
296C2×C3×D3C2×C4212yes—
297C32×C4C2×C4212yes—
298C32×C4C23×C411yescharacteristic
299C32×C4C23×C411yescharacteristic
300C3⋊Dic3—22no—
301C3⋊Dic3—22no—
302C3×Dic3—22no—
303C3×Dic3—22no—
304C3×Dic3C2×C4212yes—
305C3×Dic3C2×C4212yes—
306C23×C4—31no—
307C2×M16—31no—
308C2×M16—31no—
309C2×M16—38no—
310C2×M16—32no—
311C2×M16—92no—
312C2×M16—98no—
313C2×M16—91no—
314C2×M16D3211yescharacteristic
315C22×C8—32no—
316C22×C8—92no—
317#117—91no—
318#117—91no—
319#117—91no—
320#117—91no—
321#117—92no—
322#117—92no—
323C2×C4⋊C4—92no—
324C2×C22⋊C4—92no—
325C2×C42—31no—
326C2×C42—91no—
327#97—32no—
328#97—92no—
329#97—92no—
330#97—92no—
331C4×C8—32no—
332C4×C8—92no—
333C4×C8—92no—
334C4×C8—92no—
335C23×C3—21no—
336C23×C3—31no—
337C23×C3—31no—
338C23×C3—34no—
339C23×C3—122no—
340C23×C3C2×C4×D311yescharacteristic
341C23×C3C2×C4×D311yescharacteristic
342C22×D3—42no—
343C22×D3C4×Dic314yes—
344C22×D3C2×C4×D311yescharacteristic
345C22×D3C2×C4×D311yescharacteristic
346C2×C3×C4—21no—
347C2×C3×C4—22no—
348C2×C3×C4—21no—
349C2×C3×C4—22no—
350C2×C3×C4—34no—
351C2×C3×C4—31no—
352C2×C3×C4—31no—
353C2×C3×C4—34no—
354C2×C3×C4—34no—
355C2×C3×C4—32no—
356C2×C3×C4—32no—
357C2×C3×C4—32no—
358C2×C3×C4—32no—
359C2×C3×C4—32no—
360C2×C3×C4—32no—
361C2×C3×C4—122no—
362C2×C3×C4C2×C4×D311yescharacteristic
363C2×C3×C4C2×C4×D312yes—
364C2×C3×C4C2×C4×D311yescharacteristic
365C2×C3×C4C2×C4×D312yes—
366C2×C3×C4C2×C4×D312yes—
367C2×C3×C4C22×Dic312yes—
368C2×C3×C4C23×D311yescharacteristic
369C2×C3×C4C23×D311yescharacteristic
370C2×Dic3—32no—
371C2×Dic3—32no—
372C2×Dic3—32no—
373C2×Dic3—32no—
374C2×Dic3—42no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—122no—
378C2×Dic3—122no—
379C2×Dic3—124no—
380C2×Dic3C4×Dic314yes—
381C2×Dic3C2×C4×D312yes—
382C2×Dic3C2×C4×D312yes—
383C2×Dic3C2×C4×D311yescharacteristic
384C2×Dic3C2×C4×D311yescharacteristic
385C4×D3C4×Dic314yes—
386C4×D3C4×Dic314yes—
387C4×D3C2×C4×D312yes—
388C4×D3C2×C4×D312yes—
389C4×D3C22×Dic312yes—
390C4×D3C22×Dic312yes—
391C3×C8—24no—
392C3×C8—34no—
393C3×C8—34no—
394C3×C8C2×C4×D314yes—
395C3×C8C22×Dic314yes—
396C3⋊C8—34no—
397C3⋊C8—34no—
398C3⋊C8—64no—
399C3⋊C8C2×C4×D314yes—
400C3⋊C8C22×Dic314yes—
401C2×C32—22no—
402C2×C32C22×C4211yescharacteristic
403C2×C32#56812yes—
404C3×D3—22no—
405C3×D3—22no—
406C24—31no—
407C22×C4—31no—
408C22×C4—31no—
409C22×C4—31no—
410C22×C4—31no—
411C22×C4—31no—
412C22×C4—34no—
413C22×C4—34no—
414C22×C4—32no—
415C22×C4—92no—
416C22×C4C2×D3211yescharacteristic
417M16—34no—
418M16—34no—
419M16—38no—
420M16—98no—
421M16—94no—
422M16D3×Dic314yes—
423C2×C8—32no—
424C2×C8—32no—
425C2×C8—38no—
426C2×C8—98no—
427C2×C8—92no—
428C2×C8C2×D3212yes—
429C4⋊C4—92no—
430C4⋊C4—92no—
431C4⋊C4—92no—
432C4⋊C4—92no—
433C22⋊C4—92no—
434C22⋊C4—92no—
435C22⋊C4—92no—
436C22⋊C4—92no—
437C42—31no—
438C42—31no—
439C42—32no—
440C42—91no—
441C42—91no—
442C42—92no—
443C22×C3—22no—
444C22×C3—22no—
445C22×C3—21no—
446C22×C3—22no—
447C22×C3—32no—
448C22×C3—32no—
449C22×C3—42no—
450C22×C3—62no—
451C22×C3—62no—
452C22×C3—124no—
453C22×C3C42×D312yes—
454C22×C3C2×C4×Dic312yes—
455C22×C3C22×C4×D311yescharacteristic
456C22×C3C22×C4×D311yescharacteristic
457C2×D3—22no—
458C2×D3—22no—
459C2×D3—44no—
460C2×D3C2×C4×Dic312yes—
461C2×D3C2×C4×Dic312yes—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—22no—
465C3×C4—32no—
466C3×C4—32no—
467C3×C4—62no—
468C3×C4—62no—
469C3×C4C42×D312yes—
470C3×C4C2×C4×Dic312yes—
471C3×C4C22×C4×D311yescharacteristic
472C3×C4C22×C4×D311yescharacteristic
473C3×C4C22×C4×D311yescharacteristic
474C3×C4C23×Dic311yescharacteristic
475Dic3—22no—
476Dic3—22no—
477Dic3—64no—
478Dic3—62no—
479Dic3—62no—
480Dic3—62no—
481Dic3—62no—
482Dic3—122no—
483Dic3C2×C4×Dic312yes—
484Dic3C2×C4×Dic312yes—
485C32#287311yescharacteristic, complemented, Sylow
486C23—31no—
487C23—31no—
488C23—34no—
489C23—122no—
490C23C4×D3211yescharacteristic
491C2×C4—31no—
492C2×C4—31no—
493C2×C4—34no—
494C2×C4—32no—
495C2×C4—32no—
496C2×C4—32no—
497C2×C4—32no—
498C2×C4—34no—
499C2×C4—34no—
500C2×C4—32no—
501C2×C4—32no—
502C2×C4—92no—
503C2×C4—92no—
504C2×C4—122no—
505C2×C4—362no—
506C2×C4C4×D3212yes—
507C2×C4C4×D3211yescharacteristic
508C2×C4C2×D3×Dic312yes—
509C2×C4C22×D3211yescharacteristic
510C8—34no—
511C8—34no—
512C8—94no—
513C8C2×D3×Dic314yes—
514C2×C3—22no—
515C2×C3—22no—
516C2×C3—21no—
517C2×C3—22no—
518C2×C3—42no—
519C2×C3—62no—
520C2×C3—62no—
521C2×C3C2×C42×D311yescharacteristic
522C2×C3#574512yes—
523C2×C3#574512yes—
524C2×C3C22×C4×Dic311yescharacteristic
525D3—22no—
526D3—22no—
527C22—22no—
528C22—32no—
529C22—32no—
530C22—62no—
531C22—62no—
532C22—124no—
533C22C4×D3×Dic312yes—
534C22C2×C4×D3211yescharacteristic
535C4—32no—
536C4—32no—
537C4—62no—
538C4—62no—
539C4—182no—
540C4—182no—
541C4C4×D3×Dic312yes—
542C4C2×C4×D3211yescharacteristic
543C4C22×D3×Dic311yescharacteristic
544C3—21no—
545C3#7851411yescharacteristic, complemented
546C3#8374711yescharacteristic, complemented
547C2—22no—
548C2—62no—
549C2—62no—
550C2#1059472212yes—
551C2C2×C4×D3×Dic311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutatorC2×C32C22×C42
FittingC2×C32×M16C22
socleC22×C32C23×C4
prime radicalC23×C3×D3C2×C4
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2873
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. M16×C3⋊Dic3C2semidirect
5. C3×Dic3×M16C2semidirect
6. #10591060C2semidirect
7. Dic3×#208C2semidirect
8. #10590909C2semidirect
9. #10590908C2semidirect
10. #10590693C2semidirect
11. #10590692C2semidirect
21. C3×D3×M16C4semidirect
33. D3×#208C4semidirect
35. #63642C22semidirect
36. C8×C3⋊Dic3C22semidirect
37. C3×#815C22semidirect
38. C3×C8×Dic3C22semidirect
39. #63555C22semidirect
40. #63554C22semidirect
41. #63553C22semidirect
42. Dic3×C3⋊C8C22semidirect
58. Dic3×M16D3semidirect
91. C3×ΓL(1,𝔽25)C2×C4semidirect
92. C3×D3×C8C2×C4semidirect
101. #3711C2×C4semidirect
102. D3×C3⋊C8C2×C4semidirect
138. D3×M16Dic3semidirect
157. #815C2×D3semidirect
164. C8×Dic3C2×D3semidirect
286. ΓL(1,𝔽25)C2×Dic3semidirect
288. D3×C8C2×Dic3semidirect
485. C32#2873semidirect
545. C3#78514semidirect
546. C3#83747semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×M162
C2×#638552
C2×D3×#2082
M16×C3⋊Dic32
C3×Dic3×M162
#105910602
Dic3×#2082
#105909092
#105909082
#105906932
#105906922
#837473
#785143