Finite Group Databasebeta

← D3×#5118 #11858249

Subgroups — D3×#5118 #11858249

Order 1152.

1215 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×M16C211yesmaximal, characteristic
2C2×C4×D3×Dic3C211yesmaximal, characteristic
3C2×D3×#208C211yesmaximal, characteristic
4#10592817C211yesmaximal, characteristic, complemented
5C3×#5118C211yesmaximal, characteristic, complemented
6#10591120C211yesmaximal, characteristic, complemented
7#10591115C211yesmaximal, characteristic, complemented
8#10590663C214yesmaximal, complemented
9D3×Dic3⋊C8C214yesmaximal, complemented
10C2×#5118—31nomaximal
11D3×#423—31nomaximal
12C22×C3×C4×D3C2211yescharacteristic
13C22×D3×Dic3C412yes—
14C2×C32×M16C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C2×C3×C4×Dic3C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C3×D3×M16—24no—
21C2×C3×ΓL(1,𝔽25)C2212yes—
22C2×C3×D3×C8C2212yes—
23C2×Dic32C412yes—
24C4×D3×Dic3C411yescharacteristic
25C4×D3×Dic3C411yescharacteristic
26C4×D3×Dic3C411yescharacteristic
27C4×D3×Dic3C411yescharacteristic
28C4×D3×Dic3C2212yes—
29C4×D3×Dic3C2212yes—
30C2×#3711C2212yes—
31D3×#208—24no—
32C2×D3×C3⋊C8C2212yes—
33#63641C2214yescomplemented
34C3×Dic3⋊C8C2214yescomplemented
35#63572C2214yescomplemented
36Dic3⋊(C3⋊C8)C2214yescomplemented
37C22×C3×M16—31no—
38C22×C4×Dic3—31no—
39C22×#208—31no—
40C2×D3×M16—31no—
41C2×D3×M16D311yescharacteristic
42C2×C42×D3—31no—
43C3×#423—31no—
44#5118—31no—
45#5118—31no—
46#5118—31no—
47#5118—31no—
48#5118—31no—
49#5118—34no—
50#5118—61no—
51#5118D311yescharacteristic, direct product factor
52C2×Dic3⋊C8—34no—
53#4924—31no—
54#4837—34no—
55D3×C4⋊C8—34no—
56C23×C3×D3C2×C411yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3C2×C412yes—
59C22×C3×Dic3C2×C412yes—
60C22×C3×Dic3C2×C411yescharacteristic
61C2×C3×C4×D3C2×C411yescharacteristic
62C2×C3×C4×D3C2×C411yescharacteristic
63C2×C3×C4×D3D414yes—
64C2×C3×C4×D3Q814yes—
65C2×C3×C4×D3C2311yescharacteristic
66C2×C3×C4×D3C2311yescharacteristic
67C2×D3×Dic3—28no—
68C2×D3×Dic3C2×C412yes—
69C2×D3×Dic3C2×C412yes—
70C2×D3×Dic3C2×C412yes—
71C2×D3×Dic3C2×C412yes—
72C32×M16—22no—
73C2×C32×C8C2312yes—
74C4×C3⋊Dic3C2×C411yescharacteristic
75C4×C3⋊Dic3C2×C411yescharacteristic
76C4×C3⋊Dic3C2312yes—
77#3748—22no—
78C2×C3⋊(C3⋊C8)C2312yes—
79C3×C4×Dic3C2×C411yescharacteristic
80C3×C4×Dic3C2×C411yescharacteristic
81C3×C4×Dic3C2312yes—
82C3×#208—22no—
83C3×#208—22no—
84C2×C3×C3⋊C8C2312yes—
85C2×C3×C3⋊C8C2312yes—
86C3×ΓL(1,𝔽25)—24no—
87C3×D3×C8—24no—
88Dic32C2×C412yes—
89Dic32C2×C412yes—
90Dic32C2×C412yes—
91Dic32C2×C412yes—
92#3711—24no—
93D3×C3⋊C8—24no—
94C2×#423—91noSylow
95C23×C3×C4—31no—
96C23×Dic3—32no—
97C22×C4×D3—32no—
98C22×C4×D3C2×D311yescharacteristic
99C2×C3×M16—21no—
100C2×C3×M16—31no—
101C2×C3×M16—31no—
102C2×C3×M16—32no—
103C2×C3×M16—64no—
104C2×C3×M16C2×D311yescharacteristic
105C2×C3×M16C2×D311yescharacteristic
106C22×C3×C8—32no—
107C2×C3×C42—31no—
108C2×C4×Dic3—31no—
109C2×C4×Dic3—31no—
110C2×C4×Dic3—32no—
111C2×C4×Dic3—32no—
112C2×C4×Dic3—31no—
113C2×C4×Dic3—31no—
114C2×C4×Dic3—31no—
115C2×C4×Dic3—31no—
116C2×C4×Dic3—32no—
117C2×C4×Dic3—32no—
118C2×C4×Dic3—61no—
119C2×C4×Dic3C2×D311yescharacteristic
120C2×#208—31no—
121C2×#208—31no—
122C2×#208—32no—
123C2×#208—61no—
124C2×#208—64no—
125C2×#208C2×D311yescharacteristic
126C2×#208C2×D311yescharacteristic
127C22×C3⋊C8—32no—
128D3×M16—24no—
129D3×M16—64no—
130C2×ΓL(1,𝔽25)—32no—
131C2×ΓL(1,𝔽25)C2×D312yes—
132C2×D3×C8—32no—
133C2×D3×C8C2×D312yes—
134C42×D3—31no—
135C42×D3—31no—
136C42×D3—31no—
137C42×D3—31no—
138C42×D3—32no—
139C42×D3—32no—
140C3×C4⋊C8—34no—
141Dic3⋊C8—34no—
142Dic3⋊C8—34no—
143Dic3⋊C8—34no—
144Dic3⋊C8—34no—
145Dic3⋊C8—34no—
146Dic3⋊C8—64no—
147Dic3⋊C8C2×D314yescomplemented
148C4⋊(C3⋊C8)—34no—
149C23×C32C22×C411yescharacteristic
150C22×C3×D3—24no—
151C22×C3×D3C4⋊C414yes—
152C22×C3×D3C22×C411yescharacteristic
153C22×C3×D3C22×C411yescharacteristic
154C2×C32×C4C22×C411yescharacteristic
155C2×C32×C4C2×D412yes—
156C2×C32×C4C2×Q812yes—
157C2×C32×C4C2411yescharacteristic
158C2×C3⋊Dic3—24no—
159C2×C3⋊Dic3C22×C412yes—
160C2×C3⋊Dic3C22×C412yes—
161C2×C3×Dic3—24no—
162C2×C3×Dic3C4⋊C414yes—
163C2×C3×Dic3C22×C412yes—
164C2×C3×Dic3C22×C411yescharacteristic
165C2×C3×Dic3C22×C411yescharacteristic
166C2×C3×Dic3C22×C412yes—
167C3×C4×D3C4⋊C414yes—
168C3×C4×D3C4⋊C414yes—
169C3×C4×D3C2×D412yes—
170C3×C4×D3C2×D412yes—
171C3×C4×D3C2×Q812yes—
172C3×C4×D3C2×Q812yes—
173D3×Dic3—24no—
174D3×Dic3—24no—
175D3×Dic3—24no—
176D3×Dic3M1618yescomplemented
177C32×C8—22no—
178C3⋊(C3⋊C8)—22no—
179C3×C3⋊C8—22no—
180C3×C3⋊C8—22no—
181C22×M16—31no—
182C22×M16—91no—
183C22×C42—91no—
184#423—31no—
185#423—94no—
186#423—91no—
187#423—91no—
188#423—91no—
189C2×C4⋊C8—94no—
190C24×C3—31no—
191C23×D3C4×D311yescharacteristic
192C22×C3×C4—21no—
193C22×C3×C4—31no—
194C22×C3×C4—31no—
195C22×C3×C4—31no—
196C22×C3×C4—34no—
197C22×C3×C4—34no—
198C22×C3×C4—31no—
199C22×C3×C4—31no—
200C22×C3×C4—32no—
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C22×Dic3—32no—
204C22×Dic3—32no—
205C22×Dic3—32no—
206C22×Dic3—32no—
207C22×Dic3—32no—
208C22×Dic3—32no—
209C22×Dic3—62no—
210C22×Dic3—68no—
211C22×Dic3C4×D312yes—
212C22×Dic3C4×D311yescharacteristic
213C2×C4×D3—32no—
214C2×C4×D3—32no—
215C2×C4×D3—32no—
216C2×C4×D3—32no—
217C2×C4×D3—68no—
218C2×C4×D3Dic614yes—
219C2×C4×D3C4×D311yescharacteristic
220C2×C4×D3C4×D311yescharacteristic
221C2×C4×D3#6714yes—
222C2×C4×D3C22×D311yescharacteristic
223C2×C4×D3C22×D311yescharacteristic
224C3×M16—22no—
225C3×M16—22no—
226C3×M16—42no—
227C3×M16—64no—
228C3×M16—62no—
229C3×M16—62no—
230C2×C3×C8—22no—
231C2×C3×C8—32no—
232C2×C3×C8—32no—
233C2×C3×C8—64no—
234C2×C3×C8C22×D312yes—
235C2×C3×C8C22×D312yes—
236C3×C42—31no—
237C3×C42—31no—
238C3×C42—32no—
239C4×Dic3—31no—
240C4×Dic3—31no—
241C4×Dic3—31no—
242C4×Dic3—31no—
243C4×Dic3—32no—
244C4×Dic3—32no—
245C4×Dic3—32no—
246C4×Dic3—32no—
247C4×Dic3—32no—
248C4×Dic3—32no—
249C4×Dic3—32no—
250C4×Dic3—32no—
251C4×Dic3—32no—
252C4×Dic3—32no—
253C4×Dic3—62no—
254C4×Dic3—61no—
255C4×Dic3—61no—
256C4×Dic3C4×D311yescharacteristic
257C4×Dic3C4×D311yescharacteristic
258C4×Dic3C22×D312yes—
259#208—22no—
260#208—22no—
261#208—64no—
262#208—62no—
263#208—62no—
264#208—122no—
265C2×C3⋊C8—32no—
266C2×C3⋊C8—32no—
267C2×C3⋊C8—62no—
268C2×C3⋊C8—64no—
269C2×C3⋊C8C22×D312yes—
270C2×C3⋊C8C22×D312yes—
271ΓL(1,𝔽25)—24no—
272ΓL(1,𝔽25)—64no—
273D3×C8—24no—
274D3×C8—64no—
275C22×C32—22no—
276C22×C32C2×C4⋊C412yes—
277C22×C32C23×C411yescharacteristic
278C2×C3×D3—22no—
279C2×C3×D3—28no—
280C2×C3×D3C2×C4⋊C412yes—
281C2×C3×D3C2×C4⋊C412yes—
282C2×C3×D3C2×M1614yes—
283C32×C4C2×C4⋊C412yes—
284C32×C4C22×D411yescharacteristic
285C32×C4C22×Q811yescharacteristic
286C3⋊Dic3—22no—
287C3⋊Dic3C2×M1614yescomplemented
288C3×Dic3—22no—
289C3×Dic3C2×C4⋊C412yes—
290C3×Dic3C2×C4⋊C412yes—
291C3×Dic3C2×M1614yescomplemented
292C23×C4—31no—
293C23×C4—92no—
294C2×M16—31no—
295C2×M16—31no—
296C2×M16—32no—
297C2×M16—64no—
298C2×M16—92no—
299C2×M16—91no—
300C2×M16—184no—
301C2×M16D3211yescharacteristic
302C22×C8—32no—
303C22×C8—92no—
304C2×C42—31no—
305C2×C42—92no—
306C2×C42—92no—
307C2×C42—91no—
308C2×C42—91no—
309C2×C42—91no—
310C2×C42—91no—
311C2×C42—92no—
312C2×C42—91no—
313C4⋊C8—34no—
314C4⋊C8—94no—
315C4⋊C8—94no—
316C4⋊C8—94no—
317C23×C3—21no—
318C23×C3—31no—
319C23×C3—34no—
320C23×C3—31no—
321C23×C3—64no—
322C23×C3C2×C4×D311yescharacteristic
323C23×C3C2×C4×D311yescharacteristic
324C22×D3—24no—
325C22×D3Dic3⋊C414yes—
326C22×D3C2×C4×D311yescharacteristic
327C22×D3C2×C4×D311yescharacteristic
328C2×C3×C4—21no—
329C2×C3×C4—22no—
330C2×C3×C4—21no—
331C2×C3×C4—22no—
332C2×C3×C4—34no—
333C2×C3×C4—31no—
334C2×C3×C4—31no—
335C2×C3×C4—32no—
336C2×C3×C4—34no—
337C2×C3×C4—34no—
338C2×C3×C4—32no—
339C2×C3×C4—32no—
340C2×C3×C4—32no—
341C2×C3×C4—32no—
342C2×C3×C4—32no—
343C2×C3×C4—64no—
344C2×C3×C4C2×Dic612yes—
345C2×C3×C4C2×C4×D311yescharacteristic
346C2×C3×C4C2×C4×D311yescharacteristic
347C2×C3×C4D3×D412yes—
348C2×C3×C4D3×Q812yes—
349C2×C3×C4C2×#6712yes—
350C2×C3×C4C23×D311yescharacteristic
351C2×C3×C4C23×D311yescharacteristic
352C2×Dic3—24no—
353C2×Dic3—32no—
354C2×Dic3—32no—
355C2×Dic3—38no—
356C2×Dic3—32no—
357C2×Dic3—32no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—64no—
361C2×Dic3—64no—
362C2×Dic3—64no—
363C2×Dic3—64no—
364C2×Dic3—64no—
365C2×Dic3—124no—
366C2×Dic3Dic3⋊C414yes—
367C2×Dic3C2×C4×D312yes—
368C2×Dic3C2×C4×D312yes—
369C2×Dic3C2×C4×D311yescharacteristic
370C2×Dic3C2×C4×D311yescharacteristic
371C4×D3—38no—
372C4×D3—64no—
373C4×D3—64no—
374C4×D3—64no—
375C4×D3Dic3⋊C414yes—
376C4×D3Dic3⋊C414yes—
377C4×D3C2×Dic612yes—
378C4×D3C2×Dic612yes—
379C4×D3C2×#6712yes—
380C4×D3C2×#6712yes—
381C3×C8—22no—
382C3×C8—22no—
383C3×C8—42no—
384C3×C8—62no—
385C3×C8—62no—
386C3⋊C8—22no—
387C3⋊C8—22no—
388C3⋊C8—62no—
389C3⋊C8—62no—
390C3⋊C8—122no—
391C2×C32—22no—
392C2×C32C22×C4⋊C411yescharacteristic
393C2×C32C22×M1612yes—
394C3×D3—22no—
395C3×D3#42314yescomplemented
396C24—31no—
397C22×C4—31no—
398C22×C4—31no—
399C22×C4—31no—
400C22×C4—34no—
401C22×C4—31no—
402C22×C4—31no—
403C22×C4—34no—
404C22×C4—32no—
405C22×C4—92no—
406C22×C4—92no—
407C22×C4—92no—
408C22×C4—92no—
409C22×C4—92no—
410C22×C4—188no—
411C22×C4C2×D3211yescharacteristic
412M16—22no—
413M16—64no—
414M16—62no—
415M16—62no—
416M16—184no—
417M16—182no—
418C2×C8—32no—
419C2×C8—32no—
420C2×C8—64no—
421C2×C8—92no—
422C2×C8—184no—
423C2×C8C2×D3212yes—
424C42—32no—
425C42—31no—
426C42—31no—
427C42—92no—
428C42—92no—
429C42—92no—
430C42—92no—
431C42—92no—
432C42—91no—
433C42—91no—
434C22×C3—22no—
435C22×C3—22no—
436C22×C3—21no—
437C22×C3—22no—
438C22×C3—34no—
439C22×C3—32no—
440C22×C3—32no—
441C22×C3—42no—
442C22×C3—68no—
443C22×C3—62no—
444C22×C3D3×C4⋊C412yes—
445C22×C3C2×Dic3⋊C412yes—
446C22×C3C22×C4×D311yescharacteristic
447C22×C3C22×C4×D311yescharacteristic
448C2×D3—22no—
449C2×D3—28no—
450C2×D3D3×M1614yes—
451C2×D3C2×Dic3⋊C412yes—
452C2×D3C2×Dic3⋊C412yes—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—22no—
456C3×C4—34no—
457C3×C4—32no—
458C3×C4—32no—
459C3×C4—62no—
460C3×C4D3×C4⋊C412yes—
461C3×C4C2×Dic3⋊C412yes—
462C3×C4C22×Dic611yescharacteristic
463C3×C4C2×D3×D411yescharacteristic
464C3×C4C2×D3×Q811yescharacteristic
465C3×C4C22×#6711yescharacteristic
466Dic3—22no—
467Dic3—34no—
468Dic3—34no—
469Dic3—64no—
470Dic3—62no—
471Dic3—62no—
472Dic3—122no—
473Dic3D3×M1614yescomplemented
474Dic3C2×Dic3⋊C412yes—
475Dic3C2×Dic3⋊C412yes—
476C32C2×#42311yescharacteristic, complemented, Sylow
477C23—31no—
478C23—31no—
479C23—34no—
480C23—64no—
481C23C4×D3211yescharacteristic
482C2×C4—32no—
483C2×C4—31no—
484C2×C4—31no—
485C2×C4—34no—
486C2×C4—32no—
487C2×C4—32no—
488C2×C4—32no—
489C2×C4—32no—
490C2×C4—34no—
491C2×C4—34no—
492C2×C4—32no—
493C2×C4—64no—
494C2×C4—98no—
495C2×C4—92no—
496C2×C4—92no—
497C2×C4—184no—
498C2×C4—184no—
499C2×C4—184no—
500C2×C4—184no—
501C2×C4D3×Dic612yes—
502C2×C4C4×D3211yescharacteristic
503C2×C4D3×#6712yes—
504C2×C4C22×D3211yescharacteristic
505C8—22no—
506C8—62no—
507C8—62no—
508C8—182no—
509C2×C3—22no—
510C2×C3—22no—
511C2×C3—21no—
512C2×C3—22no—
513C2×C3—34no—
514C2×C3—42no—
515C2×C3—62no—
516C2×C3C2×D3×C4⋊C411yescharacteristic
517C2×C3C2×D3×M1612yes—
518C2×C3C2×D3×M1612yes—
519C2×C3C22×Dic3⋊C411yescharacteristic
520D3—22no—
521D3#511814yesdirect product factor
522C22—22no—
523C22—32no—
524C22—34no—
525C22—32no—
526C22—68no—
527C22—62no—
528C22D3×Dic3⋊C412yes—
529C22C2×C4×D3211yescharacteristic
530C4—32no—
531C4—32no—
532C4—34no—
533C4—62no—
534C4—94no—
535C4—182no—
536C4D3×Dic3⋊C412yes—
537C4C2×D3×Dic611yescharacteristic
538C4C2×D3×#6711yescharacteristic
539C3—21no—
540C3D3×#42311yescharacteristic, complemented
541C3C2×#511811yescharacteristic, complemented
542C2—22no—
543C2—34no—
544C2—62no—
545C2D32×M1612yes—
546C2C2×D3×Dic3⋊C411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC2×C32×M16C22
prime radicalC23×C3×D3C2×C4
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32C2×#423
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. #10592817C2semidirect
5. C3×#5118C2semidirect
6. #10591120C2semidirect
7. #10591115C2semidirect
8. #10590663C2semidirect
9. D3×Dic3⋊C8C2semidirect
33. #63641C22semidirect
34. C3×Dic3⋊C8C22semidirect
35. #63572C22semidirect
36. Dic3⋊(C3⋊C8)C22semidirect
51. #5118D3direct (N × H)
147. Dic3⋊C8C2×D3semidirect
176. D3×Dic3M16semidirect
287. C3⋊Dic3C2×M16semidirect
291. C3×Dic3C2×M16semidirect
395. C3×D3#423semidirect
473. Dic3D3×M16semidirect
476. C32C2×#423semidirect
521. D3#5118direct (N × H)
540. C3D3×#423semidirect
541. C3C2×#5118semidirect

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×C4×D3×Dic32
C2×D3×#2082
#105928172
C3×#51182
#105911202
#105911152
#105906632
D3×Dic3⋊C82
C2×#51183
D3×#4233