Finite Group Databasebeta

← C3×#83668 #11895812

Subgroups — C3×#83668 #11895812

Order 1152.

850 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
1C32×#556C211yesmaximal, characteristic, complemented
2C3×Q8×D12C211yesmaximal, characteristic, complemented
3C3×#5083C211yesmaximal, characteristic, complemented
4C3×#5079C211yesmaximal, characteristic, complemented
5C3×#5057C212yesmaximal
6C3×#5055C212yesmaximal, complemented
7C3×#5026C212yesmaximal, complemented
8C3×#5024C211yesmaximal, characteristic, complemented
9C3×#5021C212yesmaximal, complemented
10C3×C4×#213C211yesmaximal, characteristic
11C3×#5007C211yesmaximal, characteristic, complemented
12C3×#3367—31nomaximal
13#83668C311yesmaximal, characteristic, direct product factor
14C2×C3×D3×Q8—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C32×#126—22no—
17C32×#124C2212yes—
18C32×C22⋊Q8—21no—
19C32×C4×Q8C2212yes—
20C32×C4×Q8C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22C32×#117—21no—
23C2×C3×#215C2212yes—
24C2×C3×#213C2211yescharacteristic
25C3×#897—21no—
26C3×#897—22no—
27C3×C4×D12C2211yescharacteristic
28C3×C4×D12C2212yes—
29C3×#869C2211yescharacteristic
30C3×#869C2212yes—
31C3×#835C2212yes—
32C3×#835C2212yes—
33C3×#835C2212yes—
34C3×#832C2212yes—
35C3×#832C2211yescharacteristic
36C3×#809C2211yescharacteristic
37C3×#807C2212yes—
38C3×#807C2211yescharacteristic
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40C3×C4⋊(C3⋊C8)C2212yes—
41C3×#803C2212yes—
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×#556—21no—
44C3×#556D311yescharacteristic, complemented
45C3×#556C2×C311yescharacteristic, complemented
46C3×D4×Q8—31no—
47Q8×D12C2×C311yescharacteristic, complemented
48C3×#489—32no—
49C3×#487—31no—
50C3×#477—32no—
51C3×#474—31no—
52C3×#463—32no—
53C3×#461—31no—
54C3×#446—31no—
55C3×#440—32no—
56C3×C4×D8—31no—
57#5083C2×C311yescharacteristic, complemented
58#5079C2×C311yescharacteristic, complemented
59#5057C2×C312yes—
60#5055C2×C312yescomplemented
61#5026C2×C312yescomplemented
62#5024C2×C311yescharacteristic, complemented
63#5021C2×C312yescomplemented
64C4×#213C2×C311yescharacteristic
65#5007C2×C311yescharacteristic, complemented
66C2×C32×Q8D411yescharacteristic
67C2×C32×Q8C2312yes—
68C2×C32×D4C2311yescharacteristic
69C22×C32×C4—21no—
70C3×D3×Q8—44no—
71C2×C3×D12C2311yescharacteristic
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3—21no—
74C2×C3×Dic6—22no—
75C2×C3×Dic6—21no—
76C32×C4⋊C4—21no—
77C32×C4⋊C4—22no—
78C32×C4⋊C4—21no—
79C32×C4⋊C4D411yescharacteristic
80C32×C4⋊C4D412yes—
81C32×C4⋊C4C2311yescharacteristic
82C32×C22⋊C4—22no—
83C32×C22⋊C4—21no—
84C32×C22⋊C4—22no—
85C32×C42—22no—
86C32×C42C2311yescharacteristic
87C32×C42C2312yes—
88C3×#215—24no—
89C3×#213—22no—
90C3×(C2×D3)⋊C4—22no—
91C3×(C2×D3)⋊C4—21no—
92C3×C4⋊Dic3—22no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3C2312yes—
95C3×C4⋊Dic3C2311yescharacteristic
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2312yes—
98C2×C3×C3⋊C8C2311yescharacteristic
99#3367—31noSylow
100C22×C3×Q8—61no—
101C2×D3×Q8—21no—
102C2×C3×SD16—32no—
103C2×C3×D8—31no—
104C3×C4⋊Q8—21no—
105C3×C4⋊Q8—31no—
106C3×C4⋊Q8—32no—
107C3×C4⋊Q8C2×D311yescharacteristic
108C3×C4⋊Q8C22×C311yescharacteristic
109C3×#126—24no—
110C3×#126—22no—
111C3×#126—22no—
112C3×#124—22no—
113C3×#124C2×D312yes—
114C3×#124C22×C312yes—
115C3×C22⋊Q8—22no—
116C3×C22⋊Q8—21no—
117C3×C22⋊Q8—21no—
118C3×C22⋊Q8—61no—
119C3×C22⋊Q8—62no—
120C3×C4×Q8—22no—
121C3×C4×Q8—21no—
122C3×C4×Q8C2×D312yes—
123C3×C4×Q8C2×D311yescharacteristic
124C3×C4×Q8C22×C312yes—
125C3×C4×Q8C22×C311yescharacteristic
126C3×C4×D4—21no—
127C3×C4×D4—31no—
128C3×C4×D4—32no—
129C3×C4×D4C2×D311yescharacteristic
130C3×C4×D4C22×C311yescharacteristic
131C3×#117—22no—
132C3×#117—21no—
133C3×#117—21no—
134C2×#215C22×C312yes—
135C2×#213C22×C311yescharacteristic
136#897—21no—
137#897—22no—
138C4×D12C22×C311yescharacteristic
139C4×D12C22×C312yes—
140#869C22×C311yescharacteristic
141#869C22×C312yes—
142C3×#107—31no—
143C3×#107—32no—
144C3×C4⋊C8—31no—
145C3×C4⋊C8—32no—
146C3×#103—32no—
147C3×#103—32no—
148C3×#103—32no—
149C3×#102—31no—
150C3×#102—32no—
151C3×#102—31no—
152C3×#97—32no—
153C3×C4×C8—31no—
154#835C22×C312yes—
155#835C22×C312yes—
156#835C22×C312yes—
157#832C22×C312yes—
158#832C22×C311yescharacteristic
159#809C22×C311yescharacteristic
160#807C22×C312yes—
161#807C22×C311yescharacteristic
162C4⋊(C3⋊C8)C22×C311yescharacteristic
163C4⋊(C3⋊C8)C22×C312yes—
164#803C22×C312yes—
165C4×C3⋊C8C22×C311yescharacteristic
166C23×C32—21no—
167C22×C3×D3—21no—
168C32×Q8—22no—
169C32×Q8—22no—
170C32×Q8—22no—
171C32×D4—21no—
172C32×D4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—22no—
175C2×C32×C4—42no—
176C2×C32×C4C2×D412yes—
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×D412yes—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2411yescharacteristic
181C2×C3×Dic3—21no—
182C2×C3×Dic3—22no—
183C3×D12—21no—
184C3×D12#4112yes—
185C3×C4×D3—44no—
186C3×C4×D3—42no—
187C3×Dic6—44no—
188C3×Dic6—42no—
189C3×C3⋊C8—21no—
190C3×C3⋊C8—22no—
191C3×C3⋊C8—21no—
192#556C3×D311yescharacteristic, complemented
193D4×Q8—31no—
194#489—32no—
195#487—31no—
196#477—32no—
197#474—31no—
198#463—32no—
199#461—31no—
200#446—31no—
201#440—32no—
202C4×D8—31no—
203C2×C3×Q8—21no—
204C2×C3×Q8—22no—
205C2×C3×Q8—62no—
206C2×C3×Q8—61no—
207C2×C3×Q8—124no—
208C2×C3×Q8#6711yescharacteristic
209C2×C3×Q8C3×D411yescharacteristic
210C2×C3×Q8C22×D312yes—
211C2×C3×Q8C23×C312yes—
212C2×C3×D4—21no—
213C2×C3×D4—31no—
214C2×C3×D4C22×D311yescharacteristic
215C2×C3×D4C23×C311yescharacteristic
216C22×C3×C4—22no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—62no—
220C22×C3×C4—61no—
221D3×Q8—44no—
222C2×D12C23×C311yescharacteristic
223C2×C4×D3—22no—
224C2×C4×D3—21no—
225C2×Dic6—22no—
226C2×Dic6—21no—
227C3×SD16—64no—
228C3×D8—62no—
229C2×C3×C8—31no—
230C2×C3×C8—31no—
231C2×C3×C8—32no—
232C3×C4⋊C4—22no—
233C3×C4⋊C4—24no—
234C3×C4⋊C4—22no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—22no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—22no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—21no—
242C3×C4⋊C4—22no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—31no—
245C3×C4⋊C4—32no—
246C3×C4⋊C4—62no—
247C3×C4⋊C4—61no—
248C3×C4⋊C4#6711yescharacteristic
249C3×C4⋊C4#6712yes—
250C3×C4⋊C4C3×D411yescharacteristic
251C3×C4⋊C4C3×D412yes—
252C3×C4⋊C4C22×D311yescharacteristic
253C3×C4⋊C4C23×C311yescharacteristic
254C3×C22⋊C4—24no—
255C3×C22⋊C4—22no—
256C3×C22⋊C4—24no—
257C3×C22⋊C4—22no—
258C3×C22⋊C4—21no—
259C3×C22⋊C4—22no—
260C3×C22⋊C4—22no—
261C3×C22⋊C4—21no—
262C3×C22⋊C4—22no—
263C3×C22⋊C4—62no—
264C3×C22⋊C4—61no—
265C3×C42—24no—
266C3×C42—22no—
267C3×C42—22no—
268C3×C42—21no—
269C3×C42—22no—
270C3×C42C22×D311yescharacteristic
271C3×C42C22×D312yes—
272C3×C42C23×C311yescharacteristic
273C3×C42C23×C312yes—
274#215—24no—
275#213—22no—
276(C2×D3)⋊C4—22no—
277(C2×D3)⋊C4—21no—
278C4⋊Dic3—22no—
279C4⋊Dic3—21no—
280C4⋊Dic3C23×C312yes—
281C4⋊Dic3C23×C311yescharacteristic
282C2×C3⋊C8C23×C311yescharacteristic
283C2×C3⋊C8C23×C311yescharacteristic
284C2×C3⋊C8C23×C312yes—
285C22×C32—41no—
286C22×C32—41no—
287C22×C32—41no—
288C22×C32C22×D411yescharacteristic
289C2×C3×D3—22no—
290C2×C3×D3—41no—
291C2×C3×D3—41no—
292C32×C4—22no—
293C32×C4—22no—
294C32×C4—21no—
295C32×C4—42no—
296C32×C4—41no—
297C32×C4AGL(1,ℤ/8)12yes—
298C32×C4C2×#4111yescharacteristic
299C32×C42−1+411yescharacteristic
300C3×Dic3—41no—
301C3×Dic3—42no—
302C22×Q8—61no—
303C2×SD16—32no—
304C2×D8—31no—
305C4⋊Q8—31no—
306C4⋊Q8—32no—
307C4⋊Q8C2×C3×D311yescharacteristic
308#126—22no—
309#124C2×C3×D312yes—
310C22⋊Q8—21no—
311C22⋊Q8—61no—
312C22⋊Q8—62no—
313C4×Q8C2×C3×D312yes—
314C4×Q8C2×C3×D311yescharacteristic
315C4×D4—31no—
316C4×D4—32no—
317C4×D4C2×C3×D311yescharacteristic
318#117—21no—
319#107—31no—
320#107—32no—
321C4⋊C8—31no—
322C4⋊C8—32no—
323#103—32no—
324#103—32no—
325#103—32no—
326#102—31no—
327#102—32no—
328#102—31no—
329#97—32no—
330C4×C8—31no—
331C23×C3—22no—
332C23×C3—21no—
333C23×C3—21no—
334C23×C3—61no—
335C22×D3—21no—
336C3×Q8—22no—
337C3×Q8—22no—
338C3×Q8—22no—
339C3×Q8—22no—
340C3×Q8—22no—
341C3×Q8—22no—
342C3×Q8—42no—
343C3×Q8—42no—
344C3×Q8—42no—
345C3×Q8—124no—
346C3×Q8—122no—
347C3×D4—21no—
348C3×D4—21no—
349C3×D4—21no—
350C3×D4—21no—
351C3×D4—32no—
352C3×D4—41no—
353C3×D4—41no—
354C3×D4—61no—
355C2×C3×C4—22no—
356C2×C3×C4—24no—
357C2×C3×C4—21no—
358C2×C3×C4—22no—
359C2×C3×C4—21no—
360C2×C3×C4—22no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—22no—
364C2×C3×C4—21no—
365C2×C3×C4—22no—
366C2×C3×C4—44no—
367C2×C3×C4—42no—
368C2×C3×C4—42no—
369C2×C3×C4—62no—
370C2×C3×C4—61no—
371C2×C3×C4—124no—
372C2×C3×C4—122no—
373C2×C3×C4C2×#6712yes—
374C2×C3×C4C2×#6711yescharacteristic
375C2×C3×C4C2×#6712yes—
376C2×C3×C4C2×#6711yescharacteristic
377C2×C3×C4C2×C3×D412yes—
378C2×C3×C4C2×C3×D411yescharacteristic
379C2×C3×C4C2×C3×D412yes—
380C2×C3×C4C2×C3×D411yescharacteristic
381C2×C3×C4C23×D311yescharacteristic
382C2×C3×C4C24×C311yescharacteristic
383C2×Dic3—21no—
384C2×Dic3—22no—
385D12—21no—
386D12C3×#4112yes—
387C4×D3—44no—
388C4×D3—42no—
389Dic6—44no—
390Dic6—42no—
391C3×C8—61no—
392C3×C8—62no—
393C3×C8—61no—
394C3⋊C8—21no—
395C3⋊C8—22no—
396C3⋊C8—21no—
397C2×C32—81no—
398C2×C32#54811yescharacteristic
399C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
400C2×C32#57811yescharacteristic
401C3×D3—42no—
402C2×Q8—62no—
403C2×Q8—61no—
404C2×Q8—124no—
405C2×Q8C3×#6711yescharacteristic
406C2×Q8C22×C3×D312yes—
407C2×D4—31no—
408C2×D4C22×C3×D311yescharacteristic
409C22×C4—21no—
410C22×C4—62no—
411C22×C4—61no—
412SD16—64no—
413D8—62no—
414C2×C8—31no—
415C2×C8—31no—
416C2×C8—32no—
417C4⋊C4—21no—
418C4⋊C4—22no—
419C4⋊C4—21no—
420C4⋊C4—31no—
421C4⋊C4—32no—
422C4⋊C4—62no—
423C4⋊C4—61no—
424C4⋊C4C3×#6711yescharacteristic
425C4⋊C4C3×#6712yes—
426C4⋊C4C22×C3×D311yescharacteristic
427C22⋊C4—22no—
428C22⋊C4—21no—
429C22⋊C4—22no—
430C22⋊C4—62no—
431C22⋊C4—61no—
432C42—22no—
433C42C22×C3×D311yescharacteristic
434C42C22×C3×D312yes—
435C22×C3—21no—
436C22×C3—42no—
437C22×C3—42no—
438C22×C3—42no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3—41no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—41no—
445C22×C3—62no—
446C22×C3—121no—
447C22×C3—121no—
448C22×C3C22×#6711yescharacteristic
449C22×C3C22×C3×D411yescharacteristic
450C2×D3—22no—
451C2×D3—41no—
452C2×D3—41no—
453C3×C4—22no—
454C3×C4—22no—
455C3×C4—21no—
456C3×C4—22no—
457C3×C4—22no—
458C3×C4—21no—
459C3×C4—22no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—42no—
463C3×C4—42no—
464C3×C4—41no—
465C3×C4—42no—
466C3×C4—44no—
467C3×C4—41no—
468C3×C4—41no—
469C3×C4—42no—
470C3×C4—42no—
471C3×C4—122no—
472C3×C4—121no—
473C3×C4#94912yes—
474C3×C4C3×AGL(1,ℤ/8)12yes—
475C3×C4D3×#4111yescharacteristic
476C3×C4#101011yescharacteristic
477C3×C4C2×C3×#4111yescharacteristic
478C3×C4C3×2−1+411yescharacteristic
479Dic3—41no—
480Dic3—42no—
481C32#336711yescharacteristic, complemented, Sylow
482C23—21no—
483C23—61no—
484Q8—22no—
485Q8—22no—
486Q8—22no—
487Q8—124no—
488Q8—122no—
489D4—21no—
490D4—21no—
491D4—32no—
492D4—61no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—42no—
496C2×C4—62no—
497C2×C4—61no—
498C2×C4—124no—
499C2×C4—122no—
500C2×C4C2×C3×#6712yes—
501C2×C4C2×C3×#6711yescharacteristic
502C2×C4C2×C3×#6712yes—
503C2×C4C2×C3×#6711yescharacteristic
504C2×C4C23×C3×D311yescharacteristic
505C8—61no—
506C8—62no—
507C8—61no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—82no—
512C2×C3—81no—
513C2×C3—81no—
514C2×C3—122no—
515C2×C3C2×#94911yescharacteristic
516C2×C3#583111yescharacteristic
517C2×C3#583811yescharacteristic
518C2×C3C3×#54811yescharacteristic
519C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
520C2×C3C3×#57811yescharacteristic
521D3—42no—
522C22—41no—
523C22—41no—
524C22—41no—
525C22—62no—
526C22—121no—
527C22—121no—
528C22C22×C3×#6711yescharacteristic
529C4—22no—
530C4—22no—
531C4—21no—
532C4—41no—
533C4—42no—
534C4—122no—
535C4—121no—
536C4C3×#94912yes—
537C4C3×D3×#4111yescharacteristic
538C4C3×#101011yescharacteristic
539C3—21no—
540C3#8366811yescharacteristic, direct product factor
541C3C3×#336711yescharacteristic, complemented
542C2—81no—
543C2—122no—
544C2C2×C3×#94911yescharacteristic
545C2C3×#583111yescharacteristic
546C2C3×#583811yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#556C2
socleC22×C32C22×D4
prime radicalC2×C3×#213C22
hypercenterC3×#556D3
hypocenterC3C3×#3367
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×Q8 ◁ C3×#556

Complements

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

NH ≅ G/Ntype
1. C32×#556C2semidirect
2. C3×Q8×D12C2semidirect
3. C3×#5083C2semidirect
4. C3×#5079C2semidirect
6. C3×#5055C2semidirect
7. C3×#5026C2semidirect
8. C3×#5024C2semidirect
9. C3×#5021C2semidirect
11. C3×#5007C2semidirect
13. #83668C3direct (N × H)
44. C3×#556D3semidirect
45. C3×#556C2×C3semidirect
47. Q8×D12C2×C3semidirect
57. #5083C2×C3semidirect
58. #5079C2×C3semidirect
60. #5055C2×C3semidirect
61. #5026C2×C3semidirect
62. #5024C2×C3semidirect
63. #5021C2×C3semidirect
65. #5007C2×C3semidirect
192. #556C3×D3semidirect
481. C32#3367semidirect
540. C3#83668direct (N × H)
541. C3C3×#3367semidirect

Maximal subgroups

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

subgroupindex
C32×#5562
C3×Q8×D122
C3×#50832
C3×#50792
C3×#50572
C3×#50552
C3×#50262
C3×#50242
C3×#50212
C3×C4×#2132
C3×#50072
C3×#33673
#836683