Finite Group Databasebeta

← C3×#83637 #11895210

Subgroups — C3×#83637 #11895210

Order 1152.

814 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#554C211yesmaximal, characteristic, complemented
2C3×#5584C211yesmaximal, characteristic, complemented
3C3×#5093C211yesmaximal, characteristic, complemented
4C3×#5084C211yesmaximal, characteristic, complemented
5C3×#5068C212yesmaximal, complemented
6C3×#5063C212yesmaximal, complemented
7C3×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
8C3×#5019C211yesmaximal, characteristic, complemented
9C3×C4×#214C212yesmaximal, complemented
10C3×#5016C212yesmaximal
11C3×C4×#213C211yesmaximal, characteristic
12C3×#3360—31nomaximal
13#83637C311yesmaximal, characteristic, direct product factor
14C32×C4⋊Q8C2211yescharacteristic
15C32×#125C2212yes—
16C32×C22⋊Q8—21no—
17C32×C22⋊Q8—22no—
18C32×C4×Q8C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20C32×C4×D4C2212yes—
21C2×C32×C4⋊C4—21no—
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×#808C2212yes—
38C3×#807C2211yescharacteristic
39C3×C4⋊(C3⋊C8)C2212yes—
40C3×C4⋊(C3⋊C8)C2211yescharacteristic
41C3×C4×C3⋊C8C2211yescharacteristic
42C3×C4×C3⋊C8C2212yes—
43C3×#556—31no—
44C3×#554—21no—
45C3×#554D311yescharacteristic, complemented
46C3×#554C2×C311yescharacteristic, complemented
47#5584C2×C311yescharacteristic, complemented
48C3×#488—32no—
49C3×#487—31no—
50C3×#479—32no—
51C3×#476—31no—
52C3×#463—32no—
53C3×#461—31no—
54C3×C8×Q8—31no—
55C3×C4×SD16—32no—
56C3×C4×D8—31no—
57#5093C2×C311yescharacteristic, complemented
58#5084C2×C311yescharacteristic, complemented
59#5068C2×C312yescomplemented
60#5063C2×C312yescomplemented
61Q8×C3⋊C8C2×C311yescharacteristic, complemented
62#5019C2×C311yescharacteristic, complemented
63C4×#214C2×C312yescomplemented
64#5016C2×C312yes—
65C4×#213C2×C311yescharacteristic
66C2×C32×Q8—21no—
67C2×C32×Q8D411yescharacteristic
68C2×C32×D4C2311yescharacteristic
69C22×C32×C4—21no—
70C22×C32×C4—22no—
71C2×C3×D12C2311yescharacteristic
72C2×C3×C4×D3—21no—
73C2×C3×Dic6C2312yes—
74C32×C4⋊C4—22no—
75C32×C4⋊C4—21no—
76C32×C4⋊C4—22no—
77C32×C4⋊C4D411yescharacteristic
78C32×C4⋊C4D412yes—
79C32×C4⋊C4C2311yescharacteristic
80C32×C4⋊C4C2312yes—
81C32×C22⋊C4—21no—
82C32×C22⋊C4—22no—
83C32×C42C2312yes—
84C32×C42C2311yescharacteristic
85C3×#214—24no—
86C3×#213—22no—
87C3×(C2×D3)⋊C4—22no—
88C3×(C2×D3)⋊C4—21no—
89C3×(C2×D3)⋊C4—22no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×Dic3⋊C4—22no—
94C3×C4×Dic3—22no—
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2312yes—
97C2×C3×C3⋊C8C2311yescharacteristic
98#3360—31noSylow
99C2×C3×SD16—32no—
100C2×C3×D8—31no—
101C3×C4⋊Q8—21no—
102C3×C4⋊Q8—31no—
103C3×C4⋊Q8C2×D311yescharacteristic
104C3×C4⋊Q8C22×C311yescharacteristic
105C3×#126—62no—
106C3×#125—22no—
107C3×#125C2×D312yes—
108C3×#125C22×C312yes—
109C3×#124—32no—
110C3×C22⋊Q8—22no—
111C3×C22⋊Q8—24no—
112C3×C22⋊Q8—21no—
113C3×C22⋊Q8—21no—
114C3×C22⋊Q8—22no—
115C3×C22⋊Q8—22no—
116C3×C22⋊Q8—61no—
117C3×C4×Q8—21no—
118C3×C4×Q8—32no—
119C3×C4×Q8C2×D311yescharacteristic
120C3×C4×Q8C22×C311yescharacteristic
121C3×C4×D4—21no—
122C3×C4×D4—22no—
123C3×C4×D4—31no—
124C3×C4×D4C2×D311yescharacteristic
125C3×C4×D4C2×D312yes—
126C3×C4×D4C22×C311yescharacteristic
127C3×C4×D4C22×C312yes—
128C3×#117—61no—
129C2×C3×C4⋊C4—22no—
130C2×C3×C4⋊C4—21no—
131C2×C3×C4⋊C4—21no—
132#946—21no—
133C2×#214C22×C312yes—
134C2×#213C22×C311yescharacteristic
135#898—22no—
136#892—21no—
137#875C22×C312yes—
138C4×D12C22×C311yescharacteristic
139#869C22×C311yescharacteristic
140C4×Dic6C22×C312yes—
141C3×#107—31no—
142C3×#106—32no—
143C3×C4⋊C8—31no—
144C3×C4⋊C8—32no—
145C3×#103—32no—
146C3×#103—32no—
147C3×#103—32no—
148C3×#102—31no—
149C3×#102—31no—
150C3×#102—32no—
151C3×C4×C8—31no—
152C3×C4×C8—32no—
153#832C22×C311yescharacteristic
154#810C22×C312yes—
155#810C22×C312yes—
156#810C22×C312yes—
157#809C22×C311yescharacteristic
158#809C22×C312yes—
159#808C22×C312yes—
160#807C22×C311yescharacteristic
161C4⋊(C3⋊C8)C22×C312yes—
162C4⋊(C3⋊C8)C22×C311yescharacteristic
163C4×C3⋊C8C22×C311yescharacteristic
164C4×C3⋊C8C22×C312yes—
165C23×C32—21no—
166C22×C3×D3—21no—
167C32×Q8—22no—
168C32×Q8—81no—
169C32×D4—21no—
170C32×D4#4112yes—
171C2×C32×C4—21no—
172C2×C32×C4—22no—
173C2×C32×C4—42no—
174C2×C32×C4—82no—
175C2×C32×C4C2×D412yes—
176C2×C32×C4C2×D412yes—
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2411yescharacteristic
180C2×C3×Dic3—21no—
181C2×C3×Dic3—22no—
182C3×D12—21no—
183C3×D12—21no—
184C3×C4×D3—42no—
185C3×Dic6—22no—
186C3×Dic6—22no—
187C3×C3⋊C8—21no—
188C3×C3⋊C8—22no—
189C3×C3⋊C8—21no—
190#556—31no—
191#554C3×D311yescharacteristic, complemented
192#488—32no—
193#487—31no—
194#479—32no—
195#476—31no—
196#463—32no—
197#461—31no—
198C8×Q8—31no—
199C4×SD16—32no—
200C4×D8—31no—
201C2×C3×Q8—22no—
202C2×C3×Q8—21no—
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—32no—
206C2×C3×Q8#6711yescharacteristic
207C2×C3×Q8C3×D411yescharacteristic
208C2×C3×D4—21no—
209C2×C3×D4—31no—
210C2×C3×D4C22×D311yescharacteristic
211C2×C3×D4C23×C311yescharacteristic
212C22×C3×C4—22no—
213C22×C3×C4—24no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—22no—
217C22×C3×C4—22no—
218C22×C3×C4—61no—
219C2×D12C23×C311yescharacteristic
220C2×C4×D3—21no—
221C2×Dic6C23×C312yes—
222C3×SD16—64no—
223C3×D8—62no—
224C2×C3×C8—31no—
225C2×C3×C8—32no—
226C2×C3×C8—31no—
227C3×C4⋊C4—24no—
228C3×C4⋊C4—22no—
229C3×C4⋊C4—24no—
230C3×C4⋊C4—22no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—22no—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—22no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—22no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—22no—
240C3×C4⋊C4—31no—
241C3×C4⋊C4—62no—
242C3×C4⋊C4—61no—
243C3×C4⋊C4—61no—
244C3×C4⋊C4#6711yescharacteristic
245C3×C4⋊C4#6712yes—
246C3×C4⋊C4C3×D411yescharacteristic
247C3×C4⋊C4C3×D412yes—
248C3×C4⋊C4C22×D312yes—
249C3×C4⋊C4C22×D311yescharacteristic
250C3×C4⋊C4C23×C311yescharacteristic
251C3×C4⋊C4C23×C312yes—
252C3×C22⋊C4—22no—
253C3×C22⋊C4—24no—
254C3×C22⋊C4—21no—
255C3×C22⋊C4—22no—
256C3×C22⋊C4—21no—
257C3×C22⋊C4—22no—
258C3×C22⋊C4—62no—
259C3×C22⋊C4—61no—
260C3×C22⋊C4—62no—
261C3×C42—22no—
262C3×C42—21no—
263C3×C42—62no—
264C3×C42C22×D311yescharacteristic
265C3×C42C22×D312yes—
266C3×C42C23×C312yes—
267C3×C42C23×C311yescharacteristic
268#214—24no—
269#213—22no—
270(C2×D3)⋊C4—21no—
271(C2×D3)⋊C4—22no—
272(C2×D3)⋊C4—22no—
273C4⋊Dic3—21no—
274C4⋊Dic3—21no—
275C4⋊Dic3C23×C311yescharacteristic
276Dic3⋊C4—22no—
277C4×Dic3—22no—
278C2×C3⋊C8C23×C311yescharacteristic
279C2×C3⋊C8C23×C311yescharacteristic
280C2×C3⋊C8C23×C312yes—
281C22×C32—22no—
282C22×C32—41no—
283C22×C32—41no—
284C22×C32C22×D411yescharacteristic
285C2×C3×D3—41no—
286C2×C3×D3—41no—
287C2×C3×D3—41no—
288C32×C4—22no—
289C32×C4—22no—
290C32×C4—21no—
291C32×C4—41no—
292C32×C4—42no—
293C32×C4#13512yes—
294C32×C4C2×#4111yescharacteristic
295C32×C42−1+411yescharacteristic
296C3×Dic3—42no—
297C3×Dic3—41no—
298C2×SD16—32no—
299C2×D8—31no—
300C4⋊Q8—31no—
301C4⋊Q8C2×C3×D311yescharacteristic
302#126—62no—
303#125C2×C3×D312yes—
304#124—32no—
305C22⋊Q8—21no—
306C22⋊Q8—22no—
307C22⋊Q8—61no—
308C4×Q8—32no—
309C4×Q8C2×C3×D311yescharacteristic
310C4×D4—31no—
311C4×D4C2×C3×D311yescharacteristic
312C4×D4C2×C3×D312yes—
313#117—61no—
314C2×C4⋊C4—21no—
315#107—31no—
316#106—32no—
317C4⋊C8—31no—
318C4⋊C8—32no—
319#103—32no—
320#103—32no—
321#103—32no—
322#102—31no—
323#102—31no—
324#102—32no—
325C4×C8—31no—
326C4×C8—32no—
327C23×C3—22no—
328C23×C3—21no—
329C23×C3—21no—
330C23×C3—61no—
331C22×D3—21no—
332C3×Q8—22no—
333C3×Q8—22no—
334C3×Q8—42no—
335C3×Q8—62no—
336C3×Q8—62no—
337C3×Q8—81no—
338C3×Q8—81no—
339C3×Q8—82no—
340C3×D4—22no—
341C3×D4—21no—
342C3×D4—21no—
343C3×D4—22no—
344C3×D4—61no—
345C3×D4—61no—
346C3×D4#23912yes—
347C3×D4C3×#4112yes—
348C2×C3×C4—22no—
349C2×C3×C4—24no—
350C2×C3×C4—21no—
351C2×C3×C4—22no—
352C2×C3×C4—21no—
353C2×C3×C4—22no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—22no—
357C2×C3×C4—21no—
358C2×C3×C4—22no—
359C2×C3×C4—44no—
360C2×C3×C4—42no—
361C2×C3×C4—42no—
362C2×C3×C4—61no—
363C2×C3×C4—62no—
364C2×C3×C4—82no—
365C2×C3×C4—82no—
366C2×C3×C4—84no—
367C2×C3×C4—122no—
368C2×C3×C4C2×#6712yes—
369C2×C3×C4C2×#6712yes—
370C2×C3×C4C2×#6711yescharacteristic
371C2×C3×C4C2×#6711yescharacteristic
372C2×C3×C4C2×C3×D412yes—
373C2×C3×C4C2×C3×D412yes—
374C2×C3×C4C2×C3×D411yescharacteristic
375C2×C3×C4C2×C3×D411yescharacteristic
376C2×C3×C4C23×D311yescharacteristic
377C2×C3×C4C24×C311yescharacteristic
378C2×Dic3—21no—
379C2×Dic3—22no—
380D12—21no—
381D12—21no—
382C4×D3—42no—
383Dic6—22no—
384Dic6—22no—
385C3×C8—61no—
386C3×C8—62no—
387C3×C8—61no—
388C3⋊C8—21no—
389C3⋊C8—22no—
390C3⋊C8—21no—
391C2×C32—42no—
392C2×C32#54811yescharacteristic
393C2×C32C2×#13511yescharacteristic
394C2×C32#57711yescharacteristic
395C3×D3—81no—
396C2×Q8—21no—
397C2×Q8—32no—
398C2×Q8C3×#6711yescharacteristic
399C2×D4—31no—
400C2×D4C22×C3×D311yescharacteristic
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—61no—
404SD16—64no—
405D8—62no—
406C2×C8—31no—
407C2×C8—32no—
408C2×C8—31no—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—22no—
412C4⋊C4—31no—
413C4⋊C4—61no—
414C4⋊C4—62no—
415C4⋊C4—61no—
416C4⋊C4C3×#6711yescharacteristic
417C4⋊C4C3×#6712yes—
418C4⋊C4C22×C3×D312yes—
419C4⋊C4C22×C3×D311yescharacteristic
420C22⋊C4—21no—
421C22⋊C4—22no—
422C22⋊C4—62no—
423C22⋊C4—61no—
424C22⋊C4—62no—
425C42—62no—
426C42C22×C3×D311yescharacteristic
427C42C22×C3×D312yes—
428C22×C3—24no—
429C22×C3—22no—
430C22×C3—22no—
431C22×C3—21no—
432C22×C3—42no—
433C22×C3—42no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—41no—
437C22×C3—41no—
438C22×C3—121no—
439C22×C3—121no—
440C22×C3—121no—
441C22×C3C22×#6711yescharacteristic
442C22×C3C22×C3×D411yescharacteristic
443C2×D3—41no—
444C2×D3—41no—
445C2×D3—41no—
446C3×C4—22no—
447C3×C4—22no—
448C3×C4—21no—
449C3×C4—22no—
450C3×C4—22no—
451C3×C4—21no—
452C3×C4—22no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—42no—
456C3×C4—42no—
457C3×C4—41no—
458C3×C4—42no—
459C3×C4—44no—
460C3×C4—41no—
461C3×C4—42no—
462C3×C4—41no—
463C3×C4—42no—
464C3×C4—122no—
465C3×C4—121no—
466C3×C4#95012yes—
467C3×C4C3×#13512yes—
468C3×C4C2×#23911yescharacteristic
469C3×C4#100711yescharacteristic
470C3×C4C2×C3×#4111yescharacteristic
471C3×C4C3×2−1+411yescharacteristic
472Dic3—41no—
473Dic3—42no—
474C32#336011yescharacteristic, complemented, Sylow
475C23—21no—
476C23—61no—
477Q8—22no—
478Q8—62no—
479Q8—62no—
480Q8—81no—
481D4—21no—
482D4—61no—
483D4—61no—
484D4C3×#23912yes—
485C2×C4—21no—
486C2×C4—22no—
487C2×C4—42no—
488C2×C4—61no—
489C2×C4—62no—
490C2×C4—82no—
491C2×C4—122no—
492C2×C4C2×C3×#6712yes—
493C2×C4C2×C3×#6712yes—
494C2×C4C2×C3×#6711yescharacteristic
495C2×C4C2×C3×#6711yescharacteristic
496C2×C4C23×C3×D311yescharacteristic
497C8—61no—
498C8—62no—
499C8—61no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—44no—
504C2×C3—42no—
505C2×C3—42no—
506C2×C3—241no—
507C2×C3#581711yescharacteristic
508C2×C3C2×#95011yescharacteristic
509C2×C3#583611yescharacteristic
510C2×C3C3×#54811yescharacteristic
511C2×C3C2×C3×#13511yescharacteristic
512C2×C3C3×#57711yescharacteristic
513D3—81no—
514C22—22no—
515C22—41no—
516C22—41no—
517C22—121no—
518C22—121no—
519C22—121no—
520C22C22×C3×#6711yescharacteristic
521C4—22no—
522C4—22no—
523C4—21no—
524C4—41no—
525C4—42no—
526C4—122no—
527C4—121no—
528C4C3×#95012yes—
529C4C2×C3×#23911yescharacteristic
530C4C3×#100711yescharacteristic
531C3—21no—
532C3#8363711yescharacteristic, direct product factor
533C3C3×#336011yescharacteristic, complemented
534C2—42no—
535C2—241no—
536C2C3×#581711yescharacteristic
537C2C2×C3×#95011yescharacteristic
538C2C3×#583611yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#554C2
socleC22×C32C22×D4
prime radicalC2×C3×#213C22
hypercenterC3×#554D3
hypocenterC3C3×#3360
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×Q8 ◁ C3×#554

Complements

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

NH ≅ G/Ntype
1. C32×#554C2semidirect
2. C3×#5584C2semidirect
3. C3×#5093C2semidirect
4. C3×#5084C2semidirect
5. C3×#5068C2semidirect
6. C3×#5063C2semidirect
7. C3×Q8×C3⋊C8C2semidirect
8. C3×#5019C2semidirect
9. C3×C4×#214C2semidirect
13. #83637C3direct (N × H)
45. C3×#554D3semidirect
46. C3×#554C2×C3semidirect
47. #5584C2×C3semidirect
57. #5093C2×C3semidirect
58. #5084C2×C3semidirect
59. #5068C2×C3semidirect
60. #5063C2×C3semidirect
61. Q8×C3⋊C8C2×C3semidirect
62. #5019C2×C3semidirect
63. C4×#214C2×C3semidirect
191. #554C3×D3semidirect
474. C32#3360semidirect
532. C3#83637direct (N × H)
533. C3C3×#3360semidirect

Maximal subgroups

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

subgroupindex
C32×#5542
C3×#55842
C3×#50932
C3×#50842
C3×#50682
C3×#50632
C3×Q8×C3⋊C82
C3×#50192
C3×C4×#2142
C3×#50162
C3×C4×#2132
C3×#33603
#836373