Finite Group Databasebeta

← C3×#83563 #11895824

Subgroups — C3×#83563 #11895824

Order 1152.

884 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×D4×Q8C211yesmaximal, characteristic, complemented
2C3×#5584C211yesmaximal, characteristic, complemented
3C3×#5093C211yesmaximal, characteristic, complemented
4C3×#5091C212yesmaximal, complemented
5C3×#5089C212yesmaximal, complemented
6C3×#5087C211yesmaximal, characteristic, complemented
7C3×#5024C211yesmaximal, characteristic, complemented
8C3×#5019C211yesmaximal, characteristic, complemented
9C3×#5018C212yesmaximal, complemented
10C3×#5016C212yesmaximal
11C3×C4×#213C211yesmaximal, characteristic
12C3×#3367—31nomaximal
13#83563C311yesmaximal, characteristic, direct product factor
14C22×C32×Q8—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C32×C4⋊Q8C2212yes—
17C32×C22⋊Q8—21no—
18C32×C22⋊Q8—22no—
19C32×C4×Q8C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C32×C4×D4C2212yes—
22C3×#946—21no—
23C2×C3×#214C2212yes—
24C2×C3×#213C2211yescharacteristic
25C3×#898—22no—
26C3×#892—21no—
27C3×#875C2212yes—
28C3×C4×D12C2211yescharacteristic
29C3×#869C2211yescharacteristic
30C3×C4×Dic6C2212yes—
31C3×#832C2211yescharacteristic
32C3×#810C2212yes—
33C3×#810C2212yes—
34C3×#810C2212yes—
35C3×#809C2211yescharacteristic
36C3×#809C2212yes—
37C3×#807C2211yescharacteristic
38C3×#807C2212yes—
39C3×C4⋊(C3⋊C8)C2212yes—
40C3×C4⋊(C3⋊C8)C2211yescharacteristic
41C3×#803C2212yes—
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×#556—31no—
44C3×D4×Q8—21no—
45C3×D4×Q8D311yescharacteristic, complemented
46C3×D4×Q8C2×C311yescharacteristic, complemented
47#5584C2×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#5093C2×C311yescharacteristic, complemented
58#5091C2×C312yescomplemented
59#5089C2×C312yescomplemented
60#5087C2×C311yescharacteristic, complemented
61#5024C2×C311yescharacteristic, complemented
62#5019C2×C311yescharacteristic, complemented
63#5018C2×C312yescomplemented
64#5016C2×C312yes—
65C4×#213C2×C311yescharacteristic
66C2×C32×Q8—22no—
67C2×C32×Q8—21no—
68C2×C32×Q8—44no—
69C2×C32×Q8D411yescharacteristic
70C2×C32×D4C2311yescharacteristic
71C22×C32×C4—22no—
72C22×C32×C4—21no—
73C2×C3×D12C2311yescharacteristic
74C2×C3×C4×D3—21no—
75C2×C3×Dic6C2312yes—
76C32×C4⋊C4—22no—
77C32×C4⋊C4—21no—
78C32×C4⋊C4D411yescharacteristic
79C32×C4⋊C4D412yes—
80C32×C4⋊C4C2311yescharacteristic
81C32×C4⋊C4C2312yes—
82C32×C22⋊C4—22no—
83C32×C22⋊C4—21no—
84C32×C42C2311yescharacteristic
85C32×C42C2312yes—
86C3×#214—24no—
87C3×#213—22no—
88C3×(C2×D3)⋊C4—22no—
89C3×(C2×D3)⋊C4—21no—
90C3×(C2×D3)⋊C4—22no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×Dic3⋊C4—22no—
95C3×C4×Dic3—22no—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2312yes—
98C2×C3×C3⋊C8C2311yescharacteristic
99#3367—31noSylow
100C22×C3×Q8—22no—
101C22×C3×Q8—21no—
102C22×C3×Q8—21no—
103C2×C3×SD16—32no—
104C2×C3×D8—31no—
105C3×C4⋊Q8—21no—
106C3×C4⋊Q8—22no—
107C3×C4⋊Q8—31no—
108C3×C4⋊Q8C2×D311yescharacteristic
109C3×C4⋊Q8C2×D312yes—
110C3×C4⋊Q8C22×C311yescharacteristic
111C3×C4⋊Q8C22×C312yes—
112C3×#126—62no—
113C3×#124—32no—
114C3×C22⋊Q8—22no—
115C3×C22⋊Q8—24no—
116C3×C22⋊Q8—21no—
117C3×C22⋊Q8—22no—
118C3×C22⋊Q8—21no—
119C3×C22⋊Q8—22no—
120C3×C22⋊Q8—61no—
121C3×C4×Q8—21no—
122C3×C4×Q8—32no—
123C3×C4×Q8C2×D311yescharacteristic
124C3×C4×Q8C22×C311yescharacteristic
125C3×C4×D4—21no—
126C3×C4×D4—22no—
127C3×C4×D4—31no—
128C3×C4×D4C2×D311yescharacteristic
129C3×C4×D4C2×D312yes—
130C3×C4×D4C22×C311yescharacteristic
131C3×C4×D4C22×C312yes—
132C3×#117—61no—
133#946—21no—
134C2×#214C22×C312yes—
135C2×#213C22×C311yescharacteristic
136#898—22no—
137#892—21no—
138#875C22×C312yes—
139C4×D12C22×C311yescharacteristic
140#869C22×C311yescharacteristic
141C4×Dic6C22×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—31no—
151C3×#102—32no—
152C3×#97—32no—
153C3×C4×C8—31no—
154#832C22×C311yescharacteristic
155#810C22×C312yes—
156#810C22×C312yes—
157#810C22×C312yes—
158#809C22×C311yescharacteristic
159#809C22×C312yes—
160#807C22×C311yescharacteristic
161#807C22×C312yes—
162C4⋊(C3⋊C8)C22×C312yes—
163C4⋊(C3⋊C8)C22×C311yescharacteristic
164#803C22×C312yes—
165C4×C3⋊C8C22×C311yescharacteristic
166C23×C32—21no—
167C22×C3×D3—21no—
168C32×Q8—22no—
169C32×Q8—44no—
170C32×Q8—42no—
171C32×D4—21no—
172C32×D4#4112yes—
173C2×C32×C4—22no—
174C2×C32×C4—21no—
175C2×C32×C4—44no—
176C2×C32×C4—42no—
177C2×C32×C4C2×D412yes—
178C2×C32×C4C2×D412yes—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2411yescharacteristic
182C2×C3×Dic3—21no—
183C2×C3×Dic3—22no—
184C3×D12—21no—
185C3×D12—21no—
186C3×C4×D3—42no—
187C3×Dic6—22no—
188C3×Dic6—22no—
189C3×C3⋊C8—21no—
190C3×C3⋊C8—22no—
191C3×C3⋊C8—21no—
192#556—31no—
193D4×Q8C3×D311yescharacteristic, complemented
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—24no—
204C2×C3×Q8—22no—
205C2×C3×Q8—22no—
206C2×C3×Q8—21no—
207C2×C3×Q8—22no—
208C2×C3×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—32no—
211C2×C3×Q8—48no—
212C2×C3×Q8—44no—
213C2×C3×Q8—44no—
214C2×C3×Q8#6711yescharacteristic
215C2×C3×Q8C3×D411yescharacteristic
216C2×C3×D4—21no—
217C2×C3×D4—31no—
218C2×C3×D4C22×D311yescharacteristic
219C2×C3×D4C23×C311yescharacteristic
220C22×C3×C4—24no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—21no—
224C22×C3×C4—22no—
225C22×C3×C4—21no—
226C22×C3×C4—61no—
227C2×D12C23×C311yescharacteristic
228C2×C4×D3—21no—
229C2×Dic6C23×C312yes—
230C3×SD16—64no—
231C3×D8—62no—
232C2×C3×C8—31no—
233C2×C3×C8—31no—
234C2×C3×C8—32no—
235C3×C4⋊C4—24no—
236C3×C4⋊C4—22no—
237C3×C4⋊C4—22no—
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—22no—
245C3×C4⋊C4—31no—
246C3×C4⋊C4—62no—
247C3×C4⋊C4—61no—
248C3×C4⋊C4—61no—
249C3×C4⋊C4#6711yescharacteristic
250C3×C4⋊C4#6712yes—
251C3×C4⋊C4C3×D411yescharacteristic
252C3×C4⋊C4C3×D412yes—
253C3×C4⋊C4C22×D311yescharacteristic
254C3×C4⋊C4C22×D312yes—
255C3×C4⋊C4C23×C311yescharacteristic
256C3×C4⋊C4C23×C312yes—
257C3×C22⋊C4—24no—
258C3×C22⋊C4—22no—
259C3×C22⋊C4—22no—
260C3×C22⋊C4—21no—
261C3×C22⋊C4—22no—
262C3×C22⋊C4—21no—
263C3×C22⋊C4—62no—
264C3×C22⋊C4—61no—
265C3×C22⋊C4—62no—
266C3×C42—21no—
267C3×C42—22no—
268C3×C42—62no—
269C3×C42C22×D311yescharacteristic
270C3×C42C22×D312yes—
271C3×C42C23×C311yescharacteristic
272C3×C42C23×C312yes—
273#214—24no—
274#213—22no—
275(C2×D3)⋊C4—21no—
276(C2×D3)⋊C4—22no—
277(C2×D3)⋊C4—22no—
278C4⋊Dic3—21no—
279C4⋊Dic3—21no—
280C4⋊Dic3C23×C311yescharacteristic
281Dic3⋊C4—22no—
282C4×Dic3—22no—
283C2×C3⋊C8C23×C311yescharacteristic
284C2×C3⋊C8C23×C311yescharacteristic
285C2×C3⋊C8C23×C312yes—
286C22×C32—22no—
287C22×C32—41no—
288C22×C32—41no—
289C22×C32C22×D411yescharacteristic
290C2×C3×D3—41no—
291C2×C3×D3—41no—
292C2×C3×D3—41no—
293C32×C4—22no—
294C32×C4—22no—
295C32×C4—21no—
296C32×C4—42no—
297C32×C4—41no—
298C32×C4AGL(1,ℤ/8)12yes—
299C32×C4C2×#4111yescharacteristic
300C32×C42−1+411yescharacteristic
301C3×Dic3—42no—
302C3×Dic3—41no—
303C22×Q8—21no—
304C2×SD16—32no—
305C2×D8—31no—
306C4⋊Q8—31no—
307C4⋊Q8C2×C3×D311yescharacteristic
308C4⋊Q8C2×C3×D312yes—
309#126—62no—
310#124—32no—
311C22⋊Q8—21no—
312C22⋊Q8—22no—
313C22⋊Q8—61no—
314C4×Q8—32no—
315C4×Q8C2×C3×D311yescharacteristic
316C4×D4—31no—
317C4×D4C2×C3×D311yescharacteristic
318C4×D4C2×C3×D312yes—
319#117—61no—
320#107—31no—
321#107—32no—
322C4⋊C8—31no—
323C4⋊C8—32no—
324#103—32no—
325#103—32no—
326#103—32no—
327#102—31no—
328#102—31no—
329#102—32no—
330#97—32no—
331C4×C8—31no—
332C23×C3—22no—
333C23×C3—21no—
334C23×C3—21no—
335C23×C3—61no—
336C22×D3—21no—
337C3×Q8—24no—
338C3×Q8—22no—
339C3×Q8—22no—
340C3×Q8—48no—
341C3×Q8—44no—
342C3×Q8—44no—
343C3×Q8—44no—
344C3×Q8—42no—
345C3×Q8—42no—
346C3×Q8—62no—
347C3×Q8—62no—
348C3×D4—22no—
349C3×D4—21no—
350C3×D4—21no—
351C3×D4—22no—
352C3×D4—61no—
353C3×D4—61no—
354C3×D4#23912yes—
355C3×D4C3×#4112yes—
356C2×C3×C4—24no—
357C2×C3×C4—22no—
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—21no—
367C2×C3×C4—48no—
368C2×C3×C4—44no—
369C2×C3×C4—44no—
370C2×C3×C4—44no—
371C2×C3×C4—42no—
372C2×C3×C4—42no—
373C2×C3×C4—61no—
374C2×C3×C4—62no—
375C2×C3×C4—122no—
376C2×C3×C4C2×#6712yes—
377C2×C3×C4C2×#6711yescharacteristic
378C2×C3×C4C2×#6712yes—
379C2×C3×C4C2×#6711yescharacteristic
380C2×C3×C4C2×C3×D412yes—
381C2×C3×C4C2×C3×D412yes—
382C2×C3×C4C2×C3×D411yescharacteristic
383C2×C3×C4C2×C3×D411yescharacteristic
384C2×C3×C4C23×D311yescharacteristic
385C2×C3×C4C24×C311yescharacteristic
386C2×Dic3—21no—
387C2×Dic3—22no—
388D12—21no—
389D12—21no—
390C4×D3—42no—
391Dic6—22no—
392Dic6—22no—
393C3×C8—61no—
394C3×C8—62no—
395C3×C8—61no—
396C3⋊C8—21no—
397C3⋊C8—22no—
398C3⋊C8—21no—
399C2×C32—42no—
400C2×C32#54811yescharacteristic
401C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
402C2×C32#57811yescharacteristic
403C3×D3—81no—
404C2×Q8—22no—
405C2×Q8—21no—
406C2×Q8—32no—
407C2×Q8—44no—
408C2×Q8C3×#6711yescharacteristic
409C2×D4—31no—
410C2×D4C22×C3×D311yescharacteristic
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—61no—
414SD16—64no—
415D8—62no—
416C2×C8—31no—
417C2×C8—31no—
418C2×C8—32no—
419C4⋊C4—22no—
420C4⋊C4—21no—
421C4⋊C4—31no—
422C4⋊C4—61no—
423C4⋊C4—62no—
424C4⋊C4—61no—
425C4⋊C4C3×#6711yescharacteristic
426C4⋊C4C3×#6712yes—
427C4⋊C4C22×C3×D311yescharacteristic
428C4⋊C4C22×C3×D312yes—
429C22⋊C4—22no—
430C22⋊C4—21no—
431C22⋊C4—62no—
432C22⋊C4—61no—
433C22⋊C4—62no—
434C42—62no—
435C42C22×C3×D311yescharacteristic
436C42C22×C3×D312yes—
437C22×C3—24no—
438C22×C3—22no—
439C22×C3—22no—
440C22×C3—21no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—41no—
444C22×C3—41no—
445C22×C3—41no—
446C22×C3—41no—
447C22×C3—121no—
448C22×C3—121no—
449C22×C3—121no—
450C22×C3C22×#6711yescharacteristic
451C22×C3C22×C3×D411yescharacteristic
452C2×D3—41no—
453C2×D3—41no—
454C2×D3—41no—
455C3×C4—24no—
456C3×C4—22no—
457C3×C4—22no—
458C3×C4—21no—
459C3×C4—22no—
460C3×C4—22no—
461C3×C4—21no—
462C3×C4—22no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—42no—
466C3×C4—41no—
467C3×C4—44no—
468C3×C4—42no—
469C3×C4—42no—
470C3×C4—41no—
471C3×C4—42no—
472C3×C4—41no—
473C3×C4—121no—
474C3×C4—122no—
475C3×C4#93212yes—
476C3×C4C3×AGL(1,ℤ/8)12yes—
477C3×C4C2×#23911yescharacteristic
478C3×C4#100711yescharacteristic
479C3×C4C2×C3×#4111yescharacteristic
480C3×C4C3×2−1+411yescharacteristic
481Dic3—41no—
482Dic3—42no—
483C32#336711yescharacteristic, complemented, Sylow
484C23—21no—
485C23—61no—
486Q8—22no—
487Q8—44no—
488Q8—42no—
489Q8—62no—
490Q8—62no—
491D4—21no—
492D4—61no—
493D4—61no—
494D4C3×#23912yes—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—44no—
498C2×C4—42no—
499C2×C4—61no—
500C2×C4—62no—
501C2×C4—122no—
502C2×C4C2×C3×#6712yes—
503C2×C4C2×C3×#6711yescharacteristic
504C2×C4C2×C3×#6712yes—
505C2×C4C2×C3×#6711yescharacteristic
506C2×C4C23×C3×D311yescharacteristic
507C8—61no—
508C8—62no—
509C8—61no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—44no—
514C2×C3—42no—
515C2×C3—42no—
516C2×C3—241no—
517C2×C3C2×#93211yescharacteristic
518C2×C3#581711yescharacteristic
519C2×C3#583811yescharacteristic
520C2×C3C3×#54811yescharacteristic
521C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
522C2×C3C3×#57811yescharacteristic
523D3—81no—
524C22—22no—
525C22—41no—
526C22—41no—
527C22—121no—
528C22—121no—
529C22—121no—
530C22C22×C3×#6711yescharacteristic
531C4—22no—
532C4—22no—
533C4—21no—
534C4—42no—
535C4—41no—
536C4—121no—
537C4—122no—
538C4C3×#93212yes—
539C4C2×C3×#23911yescharacteristic
540C4C3×#100711yescharacteristic
541C3—21no—
542C3#8356311yescharacteristic, direct product factor
543C3C3×#336711yescharacteristic, complemented
544C2—42no—
545C2—241no—
546C2C2×C3×#93211yescharacteristic
547C2C3×#581711yescharacteristic
548C2C3×#583811yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×D4×Q8C2
socleC22×C32C22×D4
prime radicalC2×C3×#213C22
hypercenterC3×D4×Q8D3
hypocenterC3C3×#3367
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×Q8 ◁ C3×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C32×D4×Q8C2semidirect
2. C3×#5584C2semidirect
3. C3×#5093C2semidirect
4. C3×#5091C2semidirect
5. C3×#5089C2semidirect
6. C3×#5087C2semidirect
7. C3×#5024C2semidirect
8. C3×#5019C2semidirect
9. C3×#5018C2semidirect
13. #83563C3direct (N × H)
45. C3×D4×Q8D3semidirect
46. C3×D4×Q8C2×C3semidirect
47. #5584C2×C3semidirect
57. #5093C2×C3semidirect
58. #5091C2×C3semidirect
59. #5089C2×C3semidirect
60. #5087C2×C3semidirect
61. #5024C2×C3semidirect
62. #5019C2×C3semidirect
63. #5018C2×C3semidirect
193. D4×Q8C3×D3semidirect
483. C32#3367semidirect
542. C3#83563direct (N × H)
543. C3C3×#3367semidirect

Maximal subgroups

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

subgroupindex
C32×D4×Q82
C3×#55842
C3×#50932
C3×#50912
C3×#50892
C3×#50872
C3×#50242
C3×#50192
C3×#50182
C3×#50162
C3×C4×#2132
C3×#33673
#835633