Finite Group Databasebeta

← Dic3×#834 #11783765

Subgroups — Dic3×#834 #11783765

Order 1152.

929 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic3C211yesmaximal, characteristic
2C2×#63661C211yesmaximal, characteristic
3C2×C3×#834C211yesmaximal, characteristic
4Dic3×#217C212yesmaximal, complemented
5#10589186C212yesmaximal, complemented
6C4×#834—31nomaximal
7Dic3×#99—31nomaximal
8C22×C32×D4C2211yescharacteristic
9C23×C3×Dic3C411yescharacteristic, complemented
10C23×C3×Dic3C2211yescharacteristic
11C2×#3757C2212yes—
12C2×C3×#217C411yescharacteristic, complemented
13C2×C3×#217C2211yescharacteristic
14C2×C3×#217C2212yes—
15C3×D4×Dic3—22no—
16C3×D4×Dic3—22no—
17C2×C3×C4⋊Dic3C411yescharacteristic, complemented
18C2×C3×C4×Dic3C411yescharacteristic, complemented
19C2×Dic32—22no—
20#63661C414yescomplemented
21C3×#834C414yescomplemented
22#63579—22no—
23C2×C3×C4×D4—31no—
24C2×D4×Dic3D311yescharacteristic
25C2×C3×#99—31no—
26C2×#834—31no—
27C2×#834—31no—
28C2×#834—61no—
29C2×#834D311yescharacteristic
30C4×#217—32no—
31Dic3×C22⋊C4—32no—
32#4527—32no—
33#4526—32no—
34C24×C32C2×C411yescharacteristic
35C24×C32C2311yescharacteristic
36C2×C32×D4—22no—
37C2×C32×D4—22no—
38C2×C32×D4C2×C412yes—
39C2×C32×D4C2×C412yes—
40C22×C32×C4C2×C411yescharacteristic
41C22×C3⋊Dic3—22no—
42C22×C3×Dic3—22no—
43C22×C3×Dic3—21no—
44C22×C3×Dic3—21no—
45C22×C3×Dic3—42no—
46C22×C3×Dic3—42no—
47C22×C3×Dic3C2×C411yescharacteristic
48C22×C3×Dic3C2×C411yescharacteristic
49C22×C3×Dic3C2×C411yescharacteristic
50C22×C3×Dic3C2×C411yescharacteristic
51C22×C3×Dic3D412yes—
52C22×C3×Dic3D412yes—
53#3757—22no—
54#3757C2×C414yescomplemented
55C3×#217—22no—
56C3×#217—22no—
57C3×#217—22no—
58C3×#217C2×C414yescomplemented
59C3×C4⋊Dic3—22no—
60C3×C4×Dic3—21no—
61C3×C4×Dic3—21no—
62Dic32—44no—
63C4×#99—91noSylow
64C22×C3×D4—21no—
65C22×C3×D4C2×D311yescharacteristic
66C22×C3×D4C2×D311yescharacteristic
67C23×C3×C4—31no—
68C23×C3×C4—31no—
69C23×Dic3Dic311yescharacteristic, complemented
70C23×Dic3C2×D311yescharacteristic
71C3×C4×D4—62no—
72C3×C4×D4—62no—
73C2×C3×C4⋊C4—31no—
74C2×C3×C22⋊C4—32no—
75C2×C3×C22⋊C4—31no—
76C2×C3×C22⋊C4—31no—
77C2×C3×C42—31no—
78C2×#217—32no—
79C2×#217—32no—
80C2×#217—62no—
81C2×#217Dic311yescharacteristic, complemented
82C2×#217C2×D311yescharacteristic
83C2×#217C2×D312yes—
84D4×Dic3—22no—
85D4×Dic3—22no—
86C2×C4⋊Dic3Dic311yescharacteristic, complemented
87C2×C4×Dic3—62no—
88C2×C4×Dic3—62no—
89C2×C4×Dic3Dic311yescharacteristic, complemented
90C3×#99—34no—
91#834—34no—
92#834—34no—
93#834—64no—
94#834Dic314yesdirect product factor
95C3⋊#95—62no—
96C3⋊#95—62no—
97C23×C32—21no—
98C23×C32—21no—
99C23×C32—41no—
100C23×C32—41no—
101C23×C32—41no—
102C23×C32—41no—
103C23×C32C4212yescomplemented
104C23×C32C22×C411yescharacteristic
105C23×C32C22×C411yescharacteristic
106C23×C32C22×C411yescharacteristic
107C23×C32C2×D412yes—
108C23×C32#4112yes—
109C32×D4—24no—
110C32×D4—24no—
111C2×C32×C4—21no—
112C2×C32×C4—21no—
113C2×C32×C4C4212yescomplemented
114C2×C3⋊Dic3—24no—
115C2×C3⋊Dic3—42no—
116C2×C3⋊Dic3—42no—
117C2×C3×Dic3—24no—
118C2×C3×Dic3—22no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—24no—
122C2×C3×Dic3—41no—
123C2×C3×Dic3—42no—
124C2×C3×Dic3—42no—
125C2×C3×Dic3—42no—
126C2×C3×Dic3—42no—
127C2×C3×Dic3—42no—
128C2×C3×Dic3—41no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3C22⋊C411yescharacteristic
131C2×C3×Dic3C22⋊C412yes—
132C2×C3×Dic3C22⋊C411yescharacteristic
133C2×C4×D4—31no—
134C2×#99—31no—
135C2×#99—91no—
136C4×C22⋊C4—92no—
137#342—92no—
138C24×C3—21no—
139C24×C3—21no—
140C24×C3C4×D311yescharacteristic
141C24×C3C2×Dic311yescharacteristic
142C24×C3C22×D311yescharacteristic
143C24×C3C22×D311yescharacteristic
144C2×C3×D4—22no—
145C2×C3×D4—22no—
146C2×C3×D4—22no—
147C2×C3×D4—22no—
148C2×C3×D4—22no—
149C2×C3×D4—22no—
150C2×C3×D4—42no—
151C2×C3×D4—42no—
152C2×C3×D4C4×D312yes—
153C2×C3×D4C4×D312yes—
154C2×C3×D4C4×D312yes—
155C2×C3×D4C2×Dic312yes—
156C22×C3×C4—21no—
157C22×C3×C4—31no—
158C22×C3×C4—32no—
159C22×C3×C4—31no—
160C22×C3×C4—32no—
161C22×C3×C4—31no—
162C22×C3×C4—31no—
163C22×C3×C4—61no—
164C22×C3×C4—61no—
165C22×C3×C4—62no—
166C22×C3×C4—122no—
167C22×C3×C4—122no—
168C22×C3×C4C4×D311yescharacteristic
169C22×C3×C4C2×Dic311yescharacteristic
170C22×Dic3—22no—
171C22×Dic3—21no—
172C22×Dic3—21no—
173C22×Dic3—42no—
174C22×Dic3—42no—
175C22×Dic3—62no—
176C22×Dic3—62no—
177C22×Dic3—122no—
178C22×Dic3C2×Dic311yescharacteristic
179C22×Dic3C2×Dic311yescharacteristic
180C22×Dic3C2×Dic311yescharacteristic
181C22×Dic3C2×Dic311yescharacteristic
182C22×Dic3#6712yes—
183C22×Dic3#6712yes—
184C3×C4⋊C4—62no—
185C3×C22⋊C4—34no—
186C3×C22⋊C4—62no—
187C3×C22⋊C4—62no—
188C3×C22⋊C4—62no—
189C3×C42—61no—
190C3×C42—61no—
191#217—22no—
192#217—22no—
193#217—22no—
194#217—34no—
195#217—34no—
196#217—64no—
197#217—62no—
198#217—62no—
199#217—122no—
200#217C2×Dic314yescomplemented
201C4⋊Dic3—22no—
202C4×Dic3—21no—
203C4×Dic3—21no—
204C4×Dic3—124no—
205C4×Dic3—124no—
206C22×C32—22no—
207C22×C32—21no—
208C22×C32—22no—
209C22×C32—21no—
210C22×C32—22no—
211C22×C32—41no—
212C22×C32—41no—
213C22×C32—42no—
214C22×C32—42no—
215C22×C32—42no—
216C22×C32—41no—
217C22×C32—41no—
218C22×C32C2×C4211yescharacteristic
219C22×C32C2×C22⋊C411yescharacteristic
220C22×C32#11711yescharacteristic
221C22×C32C4×D412yes—
222C22×C32C4×D412yes—
223C32×C4—22no—
224C3⋊Dic3—44no—
225C3×Dic3—21no—
226C3×Dic3—22no—
227C3×Dic3—44no—
228C3×Dic3—41no—
229C3×Dic3—41no—
230C3×Dic3#9912yescomplemented
231C22×D4D3211yescharacteristic
232C23×C4—31no—
233C23×C4—31no—
234C4×D4—62no—
235C4×D4—62no—
236C2×C4⋊C4—31no—
237C2×C22⋊C4—32no—
238C2×C22⋊C4—31no—
239C2×C22⋊C4—31no—
240C2×C22⋊C4—92no—
241C2×C42—31no—
242C2×C42—182no—
243#99—34no—
244#99—94no—
245#95—182no—
246C23×C3—21no—
247C23×C3—21no—
248C23×C3—21no—
249C23×C3—21no—
250C23×C3—22no—
251C23×C3—21no—
252C23×C3—21no—
253C23×C3—22no—
254C23×C3—21no—
255C23×C3—22no—
256C23×C3—41no—
257C23×C3—41no—
258C23×C3—41no—
259C23×C3—41no—
260C23×C3—41no—
261C23×C3—41no—
262C23×C3—41no—
263C23×C3—41no—
264C23×C3—41no—
265C23×C3—41no—
266C23×C3—81no—
267C23×C3—81no—
268C23×C3—81no—
269C23×C3—81no—
270C23×C3C4×Dic312yescomplemented
271C23×C3C4×Dic312yescomplemented
272C23×C3C2×C4×D311yescharacteristic
273C23×C3C2×C4×D311yescharacteristic
274C23×C3C2×C4×D311yescharacteristic
275C23×C3C2×C4×D311yescharacteristic
276C23×C3#23512yes—
277C23×C3D3×D412yes—
278C23×C3#23712yes—
279C23×C3C22×Dic311yescharacteristic
280C23×C3C22×Dic311yescharacteristic
281C23×C3C2×#6712yes—
282C3×D4—24no—
283C3×D4—24no—
284C3×D4—24no—
285C3×D4—24no—
286C3×D4—44no—
287C3×D4—44no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—22no—
293C2×C3×C4—31no—
294C2×C3×C4—31no—
295C2×C3×C4—32no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—64no—
299C2×C3×C4—62no—
300C2×C3×C4—61no—
301C2×C3×C4—61no—
302C2×C3×C4—64no—
303C2×C3×C4—122no—
304C2×C3×C4—122no—
305C2×C3×C4—121no—
306C2×C3×C4—122no—
307C2×C3×C4—122no—
308C2×C3×C4—122no—
309C2×C3×C4—121no—
310C2×C3×C4—121no—
311C2×C3×C4C4×Dic312yescomplemented
312C2×C3×C4C4×Dic312yescomplemented
313C2×Dic3—24no—
314C2×Dic3—22no—
315C2×Dic3—24no—
316C2×Dic3—21no—
317C2×Dic3—21no—
318C2×Dic3—41no—
319C2×Dic3—42no—
320C2×Dic3—42no—
321C2×Dic3—42no—
322C2×Dic3—42no—
323C2×Dic3—42no—
324C2×Dic3—41no—
325C2×Dic3—41no—
326C2×Dic3—64no—
327C2×Dic3—64no—
328C2×Dic3—124no—
329C2×Dic3—122no—
330C2×Dic3—122no—
331C2×Dic3—122no—
332C2×Dic3—122no—
333C2×Dic3—242no—
334C2×Dic3—242no—
335C2×Dic3#21711yescharacteristic
336C2×Dic3#21712yes—
337C2×Dic3#21711yescharacteristic
338C2×C32—22no—
339C2×C32—22no—
340C2×C32—21no—
341C2×C32—21no—
342C2×C32—42no—
343C2×C32C4×C22⋊C411yescharacteristic
344C2×C32C2×#9911yescharacteristic
345C2×C32#41011yescharacteristic
346C24D3×Dic311yescharacteristic
347C24C2×D3211yescharacteristic
348C2×D4—22no—
349C2×D4—22no—
350C2×D4D3×Dic312yes—
351C2×D4#62412yes—
352C22×C4—31no—
353C22×C4—32no—
354C22×C4—31no—
355C22×C4—32no—
356C22×C4—31no—
357C22×C4—31no—
358C22×C4—61no—
359C22×C4—61no—
360C22×C4—62no—
361C22×C4—122no—
362C22×C4—122no—
363C22×C4—182no—
364C22×C4D3×Dic311yescharacteristic
365C4⋊C4—62no—
366C22⋊C4—34no—
367C22⋊C4—62no—
368C22⋊C4—62no—
369C22⋊C4—62no—
370C22⋊C4—94no—
371C22⋊C4—182no—
372C42—61no—
373C42—61no—
374C42—364no—
375C22×C3—21no—
376C22×C3—22no—
377C22×C3—21no—
378C22×C3—22no—
379C22×C3—22no—
380C22×C3—21no—
381C22×C3—22no—
382C22×C3—21no—
383C22×C3—22no—
384C22×C3—22no—
385C22×C3—22no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—22no—
390C22×C3—42no—
391C22×C3—42no—
392C22×C3—41no—
393C22×C3—41no—
394C22×C3—42no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—42no—
399C22×C3—42no—
400C22×C3—41no—
401C22×C3—42no—
402C22×C3—42no—
403C22×C3—42no—
404C22×C3—42no—
405C22×C3—41no—
406C22×C3—41no—
407C22×C3—41no—
408C22×C3—41no—
409C22×C3—81no—
410C22×C3—81no—
411C22×C3—81no—
412C22×C3—82no—
413C22×C3—81no—
414C22×C3—82no—
415C22×C3—82no—
416C22×C3#87711yescharacteristic
417C22×C3D3×C22⋊C411yescharacteristic
418C22×C3#67⋊C412yes—
419C22×C3C2×C4×Dic311yescharacteristic
420C22×C3C2×C4×Dic311yescharacteristic
421C22×C3#92611yescharacteristic
422C22×C3C4×#6712yes—
423C22×C3C4×#6712yes—
424C22×C3D4×Dic312yes—
425C22×C3C2×#21711yescharacteristic
426C3×C4—22no—
427C3×C4—22no—
428C3×C4—32no—
429C3×C4—42no—
430C3×C4—61no—
431C3×C4—62no—
432C3×C4—124no—
433C3×C4—121no—
434C3×C4—121no—
435Dic3—21no—
436Dic3—22no—
437Dic3—44no—
438Dic3—41no—
439Dic3—41no—
440Dic3—124no—
441Dic3—124no—
442Dic3—244no—
443Dic3#83412yesdirect product factor
444C32C4×#9911yescharacteristic, complemented, Sylow
445C23—21no—
446C23—21no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23Dic3212yescomplemented
452C23C2×D3×Dic311yescharacteristic
453C23C2×D3×Dic311yescharacteristic
454C23#380412yes—
455C23C2×#62411yescharacteristic
456C23D3×#6712yes—
457D4—24no—
458D4—24no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—31no—
462C2×C4—31no—
463C2×C4—32no—
464C2×C4—64no—
465C2×C4—62no—
466C2×C4—61no—
467C2×C4—61no—
468C2×C4—64no—
469C2×C4—122no—
470C2×C4—122no—
471C2×C4—121no—
472C2×C4—122no—
473C2×C4—122no—
474C2×C4—122no—
475C2×C4—121no—
476C2×C4—121no—
477C2×C4—184no—
478C2×C4—362no—
479C2×C4—362no—
480C2×C4Dic3212yescomplemented
481C2×C3—22no—
482C2×C3—22no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—22no—
486C2×C3—22no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—42no—
493C2×C3—41no—
494C2×C3—41no—
495C2×C3—42no—
496C2×C3—42no—
497C2×C3—42no—
498C2×C3—82no—
499C2×C3#474011yescharacteristic
500C2×C3D3×#9911yescharacteristic
501C2×C3Dic3×C22⋊C411yescharacteristic
502C2×C3C4×#21711yescharacteristic
503C2×C3C2×#83411yescharacteristic
504C2×C3#524011yescharacteristic
505C22—22no—
506C22—21no—
507C22—22no—
508C22—21no—
509C22—22no—
510C22—41no—
511C22—42no—
512C22—41no—
513C22—42no—
514C22—42no—
515C22—41no—
516C22—41no—
517C22#6395212yes—
518C22C2×Dic3211yescharacteristic
519C22#6395511yescharacteristic
520C22D3×#21711yescharacteristic
521C22Dic3×#6712yes—
522C4—22no—
523C4—32no—
524C4—61no—
525C4—62no—
526C4—124no—
527C4—121no—
528C4—121no—
529C4—364no—
530C3—21no—
531C3Dic3×#9911yescharacteristic, complemented
532C3C4×#83411yescharacteristic, complemented
533C2—22no—
534C2—22no—
535C2—21no—
536C2—21no—
537C2—42no—
538C2D3×#83411yescharacteristic
539C2#1059152811yescharacteristic
540C2Dic3×#21711yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC22×C32C2×C42
FrattiniC24C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32C2×C22⋊C4
cosocleC24×C32C23
hypercenterC22×D4D32
hypocenterC32C4×#99
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. Dic3×#217C2semidirect
5. #10589186C2semidirect
9. C23×C3×Dic3C4semidirect
12. C2×C3×#217C4semidirect
17. C2×C3×C4⋊Dic3C4semidirect
18. C2×C3×C4×Dic3C4semidirect
20. #63661C4semidirect
21. C3×#834C4semidirect
54. #3757C2×C4semidirect
58. C3×#217C2×C4semidirect
69. C23×Dic3Dic3semidirect
81. C2×#217Dic3semidirect
86. C2×C4⋊Dic3Dic3semidirect
89. C2×C4×Dic3Dic3semidirect
94. #834Dic3direct (N × H)
103. C23×C32C42semidirect
113. C2×C32×C4C42semidirect
200. #217C2×Dic3semidirect
230. C3×Dic3#99semidirect
270. C23×C3C4×Dic3semidirect
271. C23×C3C4×Dic3semidirect
311. C2×C3×C4C4×Dic3semidirect
312. C2×C3×C4C4×Dic3semidirect
443. Dic3#834direct (N × H)
444. C32C4×#99semidirect
451. C23Dic32semidirect
480. C2×C4Dic32semidirect
531. C3Dic3×#99semidirect
532. C3C4×#834semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic32
C2×#636612
C2×C3×#8342
Dic3×#2172
#105891862
C4×#8343
Dic3×#993