Finite Group Databasebeta

← C3×#80981 #11888009

Subgroups — C3×#80981 #11888009

Order 1152.

826 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5732C211yesmaximal, characteristic, complemented
2C3×#5555C211yesmaximal, characteristic
3C32×#474C211yesmaximal, characteristic, complemented
4C3×#5093C211yesmaximal, characteristic, complemented
5C3×C4×#214C211yesmaximal, characteristic, complemented
6C3×#4888C212yesmaximal, complemented
7C3×#4887C212yesmaximal, complemented
8C3×#4849C211yesmaximal, characteristic, complemented
9C3×#4834C211yesmaximal, characteristic, complemented
10C3×#4783C212yesmaximal, complemented
11C3×#4772C212yesmaximal, complemented
12C3×#3302—31nomaximal
13#80981C311yesmaximal, characteristic, direct product factor
14C2×C3×#237C2212yes—
15C32×C4⋊Q8C2211yescharacteristic
16C32×C4×D4C2211yescharacteristic
17C3×#947—21no—
18C3×Q8×Dic3—21no—
19C2×C3×#214C2211yescharacteristic
20C3×#930—21no—
21C2×C3×C4⋊Dic3—21no—
22C2×C3×Dic12C2212yes—
23C2×C3×D3×C8C2212yes—
24C3×#898—22no—
25C3×#897C2212yes—
26C3×#897C2212yes—
27C3×#892C2212yes—
28C3×#886—22no—
29C3×C4×D12C2211yescharacteristic
30C3×#869C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32C32×#107C2212yes—
33C32×C4⋊C8C2211yescharacteristic
34C32×#102C2212yes—
35C3×#832C2211yescharacteristic
36C3×(C2×D3)⋊C8C2212yes—
37C3×#816C2212yes—
38C3×#810C2211yescharacteristic
39C3×#810C2212yes—
40C3×#810C2212yes—
41C3×#808C2211yescharacteristic
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×#556—31no—
44C3×#547—31no—
45#5732C2×C311yescharacteristic, complemented
46#5555C2×C311yescharacteristic
47C3×#487—31no—
48C3×#485—32no—
49C3×#474—21no—
50C3×#474D311yescharacteristic, complemented
51C3×#474C2×C311yescharacteristic, complemented
52C3×#467—32no—
53C3×#462—31no—
54C3×#452—32no—
55C3×C4×SD16—31no—
56C3×C8×D4—31no—
57C3×#416—32no—
58#5093C2×C311yescharacteristic, complemented
59C4×#214C2×C311yescharacteristic, complemented
60#4888C2×C312yescomplemented
61#4887C2×C312yescomplemented
62#4849C2×C311yescharacteristic, complemented
63#4834C2×C311yescharacteristic, complemented
64#4783C2×C312yescomplemented
65#4772C2×C312yescomplemented
66C2×C32×Q8—21no—
67C2×C32×D4C2311yescharacteristic
68C22×C32×C4—21no—
69C2×C3×#67—22no—
70C22×C3×Dic3—22no—
71C3×#237—24no—
72C3×#237—42no—
73C2×C3×D12D411yescharacteristic
74C2×C3×C4×D3C2312yes—
75C2×C3×Dic6C2311yescharacteristic
76C2×C3×Dic6C2312yes—
77C2×C32×C8C2312yes—
78C32×C4⋊C4—21no—
79C32×C4⋊C4C2312yes—
80C32×C4⋊C4C2311yescharacteristic
81C32×C22⋊C4—21no—
82C32×C42C2311yescharacteristic
83C3×#214—22no—
84C3×(C2×D3)⋊C4—22no—
85C3×(C2×D3)⋊C4—22no—
86C3×(C2×D3)⋊C4—22no—
87C3×(C2×D3)⋊C4D412yes—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3—22no—
91C3×C4⋊Dic3—22no—
92C3×C4⋊Dic3D411yescharacteristic
93C3×C4⋊Dic3C2311yescharacteristic
94C3×Dic3⋊C4—21no—
95C3×C4×Dic3—21no—
96C3×C4×Dic3—22no—
97C2×C3×C3⋊C8C2311yescharacteristic
98C2×C3×C3⋊C8C2311yescharacteristic
99C3×Dic12—42no—
100C3×D3×C8—42no—
101#3302—31noSylow
102C2×C3×#41—32no—
103C2×#237C22×C312yes—
104C2×C3×Q16—32no—
105C2×C3×SD16—31no—
106C22×C3×C8—32no—
107C3×C4⋊Q8—21no—
108C3×C4⋊Q8—31no—
109C3×C4⋊Q8C2×D311yescharacteristic
110C3×C4⋊Q8C22×C311yescharacteristic
111C3×#126—62no—
112C3×#124—61no—
113C3×#123—62no—
114C3×C22⋊Q8—32no—
115C3×C22⋊Q8—32no—
116C3×#121—61no—
117C3×C4×Q8—31no—
118C3×C4×Q8—61no—
119C3×C4×D4—21no—
120C3×C4×D4—31no—
121C3×C4×D4C2×D311yescharacteristic
122C3×C4×D4C22×C311yescharacteristic
123C3×#117—32no—
124C2×C3×C4⋊C4—61no—
125#947—21no—
126Q8×Dic3—21no—
127C2×#214C22×C311yescharacteristic
128#930—21no—
129C2×C4⋊Dic3—21no—
130C2×Dic12C22×C312yes—
131C2×D3×C8C22×C312yes—
132#898—22no—
133#897C22×C312yes—
134#897C22×C312yes—
135#892C22×C312yes—
136#886—22no—
137C4×D12C22×C311yescharacteristic
138#869C22×C311yescharacteristic
139C4×Dic6C22×C311yescharacteristic
140C3×#107—22no—
141C3×#107C2×D312yes—
142C3×#107C22×C312yes—
143C3×#106—31no—
144C3×C4⋊C8—21no—
145C3×C4⋊C8C2×D311yescharacteristic
146C3×C4⋊C8C22×C311yescharacteristic
147C3×#103—32no—
148C3×#103—32no—
149C3×#103—31no—
150C3×#103—32no—
151C3×#102—22no—
152C3×#102—31no—
153C3×#102C2×D312yes—
154C3×#102C22×C312yes—
155C3×C22⋊C8—32no—
156C3×C4×C8—31no—
157#832C22×C311yescharacteristic
158(C2×D3)⋊C8C22×C312yes—
159#816C22×C312yes—
160#810C22×C311yescharacteristic
161#810C22×C312yes—
162#810C22×C312yes—
163#808C22×C311yescharacteristic
164C4×C3⋊C8C22×C311yescharacteristic
165C23×C32—21no—
166C22×C3×D3C2×D412yes—
167C32×Q8—42no—
168C32×D4—21no—
169C32×D4#4112yes—
170C2×C32×C4—22no—
171C2×C32×C4—21no—
172C2×C32×C4—42no—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2411yescharacteristic
176C3×#67—44no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—44no—
181C2×C3×Dic3C2×D412yes—
182C3×D12—22no—
183C3×C4×D3—22no—
184C3×C4×D3—22no—
185C3×Dic6—21no—
186C3×Dic6—22no—
187C3×Dic6—21no—
188C3×Dic6—22no—
189C32×C8—22no—
190C3×C3⋊C8—21no—
191C3×C3⋊C8—21no—
192#556—31no—
193#547—31no—
194#487—31no—
195#485—32no—
196#474C3×D311yescharacteristic, complemented
197#467—32no—
198#462—31no—
199#452—32no—
200C4×SD16—31no—
201C8×D4—31no—
202#416—32no—
203C3×#41—64no—
204C3×#41—122no—
205C2×C3×Q8—21no—
206C2×C3×Q8—21no—
207C2×C3×Q8—32no—
208C2×C3×Q8—31no—
209C2×C3×Q8—41no—
210C2×C3×D4—21no—
211C2×C3×D4—31no—
212C2×C3×D4—62no—
213C2×C3×D4C22×D311yescharacteristic
214C2×C3×D4C23×C311yescharacteristic
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—32no—
218C22×C3×C4—41no—
219C22×C3×C4—62no—
220C2×#67—22no—
221C22×Dic3—22no—
222#237—24no—
223#237—42no—
224C2×D12C3×D411yescharacteristic
225C2×C4×D3C23×C312yes—
226C2×Dic6C23×C312yes—
227C2×Dic6C23×C311yescharacteristic
228C3×Q16—122no—
229C3×SD16—62no—
230C2×C3×C8—22no—
231C2×C3×C8—31no—
232C2×C3×C8—31no—
233C2×C3×C8—122no—
234C2×C3×C8C22×D312yes—
235C2×C3×C8C23×C312yes—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—22no—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—31no—
241C3×C4⋊C4—31no—
242C3×C4⋊C4—41no—
243C3×C4⋊C4—62no—
244C3×C4⋊C4—62no—
245C3×C4⋊C4—61no—
246C3×C4⋊C4—61no—
247C3×C4⋊C4—61no—
248C3×C4⋊C4C22×D312yes—
249C3×C4⋊C4C22×D311yescharacteristic
250C3×C4⋊C4C23×C311yescharacteristic
251C3×C4⋊C4C23×C312yes—
252C3×C22⋊C4—21no—
253C3×C22⋊C4—21no—
254C3×C22⋊C4—32no—
255C3×C22⋊C4—41no—
256C3×C22⋊C4—62no—
257C3×C22⋊C4—62no—
258C3×C22⋊C4—62no—
259C3×C42—21no—
260C3×C42—62no—
261C3×C42—61no—
262C3×C42C22×D311yescharacteristic
263C3×C42C23×C311yescharacteristic
264#214—22no—
265(C2×D3)⋊C4—22no—
266(C2×D3)⋊C4—22no—
267(C2×D3)⋊C4—22no—
268(C2×D3)⋊C4C3×D412yes—
269C4⋊Dic3—21no—
270C4⋊Dic3—21no—
271C4⋊Dic3—22no—
272C4⋊Dic3—22no—
273C4⋊Dic3C3×D411yescharacteristic
274C4⋊Dic3C23×C311yescharacteristic
275Dic3⋊C4—21no—
276C4×Dic3—21no—
277C4×Dic3—22no—
278C2×C3⋊C8C23×C311yescharacteristic
279C2×C3⋊C8C23×C311yescharacteristic
280Dic12—42no—
281D3×C8—42no—
282C22×C32—22no—
283C22×C32—41no—
284C22×C32—41no—
285C22×C32C22×D411yescharacteristic
286C2×C3×D3—22no—
287C2×C3×D3—22no—
288C2×C3×D3—22no—
289C32×C4—21no—
290C32×C4—41no—
291C32×C4—42no—
292C32×C4#13512yes—
293C32×C4C2×#4111yescharacteristic
294C32×C4H(5,𝔽2)11yescharacteristic
295C3×Dic3—22no—
296C3×Dic3—41no—
297C3×Dic3—42no—
298C3×Dic3—41no—
299C2×#41—32no—
300C2×Q16—32no—
301C2×SD16—31no—
302C22×C8—32no—
303C4⋊Q8—31no—
304C4⋊Q8C2×C3×D311yescharacteristic
305#126—62no—
306#124—61no—
307#123—62no—
308C22⋊Q8—32no—
309C22⋊Q8—32no—
310#121—61no—
311C4×Q8—31no—
312C4×Q8—61no—
313C4×D4—31no—
314C4×D4C2×C3×D311yescharacteristic
315#117—32no—
316C2×C4⋊C4—61no—
317#107C2×C3×D312yes—
318#106—31no—
319C4⋊C8C2×C3×D311yescharacteristic
320#103—32no—
321#103—32no—
322#103—31no—
323#103—32no—
324#102—31no—
325#102C2×C3×D312yes—
326C22⋊C8—32no—
327C4×C8—31no—
328C23×C3—21no—
329C23×C3—21no—
330C23×C3—32no—
331C23×C3—41no—
332C22×D3C2×C3×D412yes—
333C3×Q8—42no—
334C3×Q8—42no—
335C3×Q8—61no—
336C3×Q8—62no—
337C3×Q8—61no—
338C3×Q8—62no—
339C3×Q8—82no—
340C3×D4—21no—
341C3×D4—21no—
342C3×D4—22no—
343C3×D4—41no—
344C3×D4—62no—
345C3×D4—124no—
346C3×D4#23912yes—
347C3×D4C3×#4112yes—
348C2×C3×C4—22no—
349C2×C3×C4—21no—
350C2×C3×C4—22no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—32no—
356C2×C3×C4—41no—
357C2×C3×C4—42no—
358C2×C3×C4—42no—
359C2×C3×C4—42no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4—61no—
363C2×C3×C4—61no—
364C2×C3×C4—62no—
365C2×C3×C4—82no—
366C2×C3×C4—124no—
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4C2×C3×D411yescharacteristic
370C2×C3×C4C2×C3×D411yescharacteristic
371C2×C3×C4C23×D311yescharacteristic
372C2×C3×C4C24×C311yescharacteristic
373#67—44no—
374C2×Dic3—21no—
375C2×Dic3—21no—
376C2×Dic3—22no—
377C2×Dic3—44no—
378C2×Dic3C2×C3×D412yes—
379D12—22no—
380C4×D3—22no—
381C4×D3—22no—
382Dic6—21no—
383Dic6—22no—
384Dic6—21no—
385Dic6—22no—
386C3×C8—22no—
387C3×C8—22no—
388C3×C8—42no—
389C3×C8—61no—
390C3×C8—61no—
391C3⋊C8—21no—
392C3⋊C8—21no—
393C2×C32—42no—
394C2×C32#54611yescharacteristic
395C2×C32C2×#13511yescharacteristic
396C2×C32#57811yescharacteristic
397C3×D3—42no—
398#41—64no—
399#41—122no—
400C2×Q8—21no—
401C2×Q8—32no—
402C2×Q8—31no—
403C2×D4—31no—
404C2×D4—62no—
405C2×D4C22×C3×D311yescharacteristic
406C22×C4—21no—
407C22×C4—32no—
408C22×C4—62no—
409Q16—122no—
410SD16—62no—
411C2×C8—31no—
412C2×C8—31no—
413C2×C8—122no—
414C2×C8C22×C3×D312yes—
415C4⋊C4—21no—
416C4⋊C4—31no—
417C4⋊C4—31no—
418C4⋊C4—62no—
419C4⋊C4—62no—
420C4⋊C4—61no—
421C4⋊C4—61no—
422C4⋊C4—61no—
423C4⋊C4C22×C3×D312yes—
424C4⋊C4C22×C3×D311yescharacteristic
425C22⋊C4—21no—
426C22⋊C4—32no—
427C22⋊C4—62no—
428C22⋊C4—62no—
429C22⋊C4—62no—
430C42—62no—
431C42—61no—
432C42C22×C3×D311yescharacteristic
433C22×C3—22no—
434C22×C3—22no—
435C22×C3—21no—
436C22×C3—42no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3—62no—
442C22×C3—62no—
443C22×C3—62no—
444C22×C3—81no—
445C22×C3—81no—
446C22×C3C2×D3×D411yescharacteristic
447C22×C3C22×C3×D411yescharacteristic
448C2×D3—22no—
449C2×D3—22no—
450C2×D3—22no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—22no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—41no—
457C3×C4—41no—
458C3×C4—42no—
459C3×C4—41no—
460C3×C4—42no—
461C3×C4—62no—
462C3×C4—81no—
463C3×C4—82no—
464C3×C4—121no—
465C3×C4—122no—
466C3×C4—121no—
467C3×C4#91212yes—
468C3×C4C3×#13512yes—
469C3×C4C2×#23911yescharacteristic
470C3×C4#100911yescharacteristic
471C3×C4C2×C3×#4111yescharacteristic
472C3×C4C3×H(5,𝔽2)11yescharacteristic
473Dic3—22no—
474Dic3—41no—
475Dic3—42no—
476Dic3—41no—
477C32#330211yescharacteristic, complemented, Sylow
478C23—21no—
479C23—32no—
480Q8—42no—
481Q8—61no—
482Q8—62no—
483Q8—61no—
484Q8—62no—
485D4—21no—
486D4—62no—
487D4—124no—
488D4C3×#23912yes—
489C2×C4—22no—
490C2×C4—21no—
491C2×C4—32no—
492C2×C4—42no—
493C2×C4—62no—
494C2×C4—62no—
495C2×C4—61no—
496C2×C4—61no—
497C2×C4—62no—
498C2×C4—124no—
499C2×C4C3×D3×D411yescharacteristic
500C2×C4C3×D3×D411yescharacteristic
501C2×C4C23×C3×D311yescharacteristic
502C8—22no—
503C8—61no—
504C8—61no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—42no—
509C2×C3—42no—
510C2×C3—82no—
511C2×C3—122no—
512C2×C3#563011yescharacteristic
513C2×C3C2×#91211yescharacteristic
514C2×C3#577911yescharacteristic
515C2×C3C3×#54611yescharacteristic
516C2×C3C2×C3×#13511yescharacteristic
517C2×C3C3×#57811yescharacteristic
518D3—42no—
519C22—22no—
520C22—41no—
521C22—41no—
522C22—62no—
523C22—62no—
524C22—62no—
525C22C2×C3×D3×D411yescharacteristic
526C4—21no—
527C4—41no—
528C4—42no—
529C4—62no—
530C4—121no—
531C4—122no—
532C4—121no—
533C4C3×#91212yes—
534C4C2×C3×#23911yescharacteristic
535C4C3×#100911yescharacteristic
536C3—21no—
537C3#8098111yescharacteristic, direct product factor
538C3C3×#330211yescharacteristic, complemented
539C2—42no—
540C2—122no—
541C2C3×#563011yescharacteristic
542C2C2×C3×#91211yescharacteristic
543C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#474C2
socleC22×C32C22×D4
prime radicalC3×#5555C2
hypercenterC3×#474D3
hypocenterC3C3×#3302
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#474

Complements

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

NH ≅ G/Ntype
1. C3×#5732C2semidirect
3. C32×#474C2semidirect
4. C3×#5093C2semidirect
5. C3×C4×#214C2semidirect
6. C3×#4888C2semidirect
7. C3×#4887C2semidirect
8. C3×#4849C2semidirect
9. C3×#4834C2semidirect
10. C3×#4783C2semidirect
11. C3×#4772C2semidirect
13. #80981C3direct (N × H)
45. #5732C2×C3semidirect
50. C3×#474D3semidirect
51. C3×#474C2×C3semidirect
58. #5093C2×C3semidirect
59. C4×#214C2×C3semidirect
60. #4888C2×C3semidirect
61. #4887C2×C3semidirect
62. #4849C2×C3semidirect
63. #4834C2×C3semidirect
64. #4783C2×C3semidirect
65. #4772C2×C3semidirect
196. #474C3×D3semidirect
477. C32#3302semidirect
537. C3#80981direct (N × H)
538. C3C3×#3302semidirect

Maximal subgroups

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

subgroupindex
C3×#57322
C3×#55552
C32×#4742
C3×#50932
C3×C4×#2142
C3×#48882
C3×#48872
C3×#48492
C3×#48342
C3×#47832
C3×#47722
C3×#33023
#809813