Finite Group Databasebeta

← C3×#81119 #11887600

Subgroups — C3×#81119 #11887600

Order 1152.

824 conjugacy classes of subgroups.

The subgroup lattice has 529 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5730C211yesmaximal, characteristic
2C3×Q8×D12C211yesmaximal, characteristic
3C32×#477C211yesmaximal, characteristic, complemented
4C3×#5093C211yesmaximal, characteristic, complemented
5C3×C4×#216C211yesmaximal, characteristic, complemented
6C3×#4887C212yesmaximal, complemented
7C3×#4884C212yesmaximal, complemented
8C3×#4849C211yesmaximal, characteristic, complemented
9C3×#4834C211yesmaximal, characteristic
10C3×#4809C212yesmaximal, complemented
11C3×D3×#103C212yesmaximal, complemented
12C3×#3299—31nomaximal
13#81119C311yesmaximal, characteristic, direct product factor
14C2×C3×D3×Q8C2212yes—
15C32×C4⋊Q8C2211yescharacteristic
16C32×C4×Q8C2211yescharacteristic
17C3×#946—22no—
18C2×C3×#216C2211yescharacteristic
19C2×C3×Dic12C2212yes—
20C2×C3×D3×C8C2212yes—
21C3×#897—22no—
22C3×#897C2212yes—
23C3×#897C2212yes—
24C3×#893—21no—
25C3×D3×C4⋊C4C2212yes—
26C3×#890—21no—
27C3×C4×D12—21no—
28C3×C4×D12C2211yescharacteristic
29C3×#869—21no—
30C3×#869C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32C32×#107C2212yes—
33C32×C4⋊C8C2211yescharacteristic
34C32×#103C2212yes—
35C3×#835C2211yescharacteristic
36C3×(C2×D3)⋊C8C2212yes—
37C3×#816C2212yes—
38C3×#810C2211yescharacteristic
39C3×#810C2212yes—
40C3×#810C2212yes—
41C3×#807C2211yescharacteristic
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×#554—31no—
44C3×D4×Q8—31no—
45#5730C2×C311yescharacteristic
46Q8×D12C2×C311yescharacteristic
47C3×#487—31no—
48C3×#484—32no—
49C3×#477—21no—
50C3×#477D311yescharacteristic, complemented
51C3×#477C2×C311yescharacteristic, complemented
52C3×#467—32no—
53C3×#462—31no—
54C3×#451—32no—
55C3×C4×Q16—31no—
56C3×C8×D4—31no—
57C2×C3×#103—32no—
58#5093C2×C311yescharacteristic, complemented
59C4×#216C2×C311yescharacteristic, complemented
60#4887C2×C312yescomplemented
61#4884C2×C312yescomplemented
62#4849C2×C311yescharacteristic, complemented
63#4834C2×C311yescharacteristic
64#4809C2×C312yescomplemented
65D3×#103C2×C312yescomplemented
66C2×C32×Q8—21no—
67C2×C32×Q8C2311yescharacteristic
68C3×D3×Q8—24no—
69C3×D3×Q8—42no—
70C2×C3×D12D411yescharacteristic
71C2×C3×C4×D3—22no—
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3C2312yes—
74C2×C3×Dic6—22no—
75C2×C3×Dic6C2311yescharacteristic
76C2×C3×Dic6C2312yes—
77C2×C32×C8C2312yes—
78C32×C4⋊C4—21no—
79C32×C4⋊C4—21no—
80C32×C4⋊C4C2312yes—
81C32×C4⋊C4C2311yescharacteristic
82C32×C42—21no—
83C32×C42C2311yescharacteristic
84C3×#216—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×Dic3⋊C4—22no—
96C3×C4×Dic3—21no—
97C2×C3×C3⋊C8C2311yescharacteristic
98C2×C3×C3⋊C8C2311yescharacteristic
99C3×Dic12—42no—
100C3×D3×C8—42no—
101#3299—31noSylow
102C22×C3×Q8—32no—
103C2×D3×Q8C22×C312yes—
104C2×C3×Q16—31no—
105C2×C3×Q16—32no—
106C22×C3×C8—32no—
107C3×C4⋊Q8—21no—
108C3×C4⋊Q8—31no—
109C3×C4⋊Q8—61no—
110C3×C4⋊Q8C2×D311yescharacteristic
111C3×C4⋊Q8C22×C311yescharacteristic
112C3×#125—61no—
113C3×C22⋊Q8—32no—
114C3×C22⋊Q8—32no—
115C3×C22⋊Q8—62no—
116C3×C22⋊Q8—62no—
117C3×C4×Q8—21no—
118C3×C4×Q8—31no—
119C3×C4×Q8C2×D311yescharacteristic
120C3×C4×Q8C22×C311yescharacteristic
121C3×C4×D4—31no—
122C3×C4×D4—61no—
123C3×C4×D4—61no—
124C2×C3×C4⋊C4—32no—
125#946—22no—
126C2×#216C22×C311yescharacteristic
127C2×Dic12C22×C312yes—
128C2×D3×C8C22×C312yes—
129#897—22no—
130#897C22×C312yes—
131#897C22×C312yes—
132#893—21no—
133D3×C4⋊C4C22×C312yes—
134#890—21no—
135C4×D12—21no—
136C4×D12C22×C311yescharacteristic
137#869—21no—
138#869C22×C311yescharacteristic
139C4×Dic6C22×C311yescharacteristic
140C3×#107—22no—
141C3×#107—31no—
142C3×#107C2×D312yes—
143C3×#107C22×C312yes—
144C3×C4⋊C8—21no—
145C3×C4⋊C8C2×D311yescharacteristic
146C3×C4⋊C8C22×C311yescharacteristic
147C3×#103—22no—
148C3×#103—31no—
149C3×#103—32no—
150C3×#103—32no—
151C3×#103—31no—
152C3×#103—32no—
153C3×#103C2×D312yes—
154C3×#103C22×C312yes—
155C3×C22⋊C8—32no—
156C3×C4×C8—31no—
157#835C22×C311yescharacteristic
158(C2×D3)⋊C8C22×C312yes—
159#816C22×C312yes—
160#810C22×C312yes—
161#810C22×C311yescharacteristic
162#810C22×C312yes—
163#807C22×C311yescharacteristic
164C4×C3⋊C8C22×C311yescharacteristic
165C22×C3×D3C2×D412yes—
166C32×Q8—21no—
167C32×Q8—81no—
168C32×Q8#4112yes—
169C2×C32×C4—21no—
170C2×C32×C4—22no—
171C2×C32×C4—21no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2411yescharacteristic
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3C2×D412yes—
179C3×D12Q1614yescomplemented
180C3×C4×D3—22no—
181C3×C4×D3—22no—
182C3×C4×D3—44no—
183C3×C4×D3—82no—
184C3×Dic6—21no—
185C3×Dic6—22no—
186C3×Dic6—21no—
187C3×Dic6—22no—
188C3×Dic6—44no—
189C32×C8—22no—
190C3×C3⋊C8—21no—
191C3×C3⋊C8—21no—
192#554—31no—
193D4×Q8—31no—
194#487—31no—
195#484—32no—
196#477C3×D311yescharacteristic, complemented
197#467—32no—
198#462—31no—
199#451—32no—
200C4×Q16—31no—
201C8×D4—31no—
202C2×#103—32no—
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—21no—
206C2×C3×Q8—32no—
207C2×C3×Q8—31no—
208C2×C3×Q8—41no—
209C2×C3×Q8—62no—
210C2×C3×Q8—64no—
211C2×C3×Q8—122no—
212C2×C3×Q8C22×D311yescharacteristic
213C2×C3×Q8C23×C311yescharacteristic
214C2×C3×D4—31no—
215C22×C3×C4—32no—
216C22×C3×C4—62no—
217C22×C3×C4—62no—
218D3×Q8—24no—
219D3×Q8—42no—
220C2×D12C3×D411yescharacteristic
221C2×C4×D3—22no—
222C2×C4×D3—22no—
223C2×C4×D3C23×C312yes—
224C2×Dic6—22no—
225C2×Dic6C23×C312yes—
226C2×Dic6C23×C311yescharacteristic
227C3×Q16—62no—
228C3×Q16—122no—
229C2×C3×C8—22no—
230C2×C3×C8—31no—
231C2×C3×C8—31no—
232C2×C3×C8—122no—
233C2×C3×C8C22×D312yes—
234C2×C3×C8C23×C312yes—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—22no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—31no—
242C3×C4⋊C4—31no—
243C3×C4⋊C4—41no—
244C3×C4⋊C4—41no—
245C3×C4⋊C4—62no—
246C3×C4⋊C4—62no—
247C3×C4⋊C4—62no—
248C3×C4⋊C4—61no—
249C3×C4⋊C4—61no—
250C3×C4⋊C4—61no—
251C3×C4⋊C4C22×D312yes—
252C3×C4⋊C4C22×D311yescharacteristic
253C3×C4⋊C4C23×C311yescharacteristic
254C3×C4⋊C4C23×C312yes—
255C3×C22⋊C4—32no—
256C3×C22⋊C4—62no—
257C3×C22⋊C4—62no—
258C3×C42—21no—
259C3×C42—21no—
260C3×C42—21no—
261C3×C42—41no—
262C3×C42—61no—
263C3×C42C22×D311yescharacteristic
264C3×C42C23×C311yescharacteristic
265#216—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—
276Dic3⋊C4—22no—
277C4×Dic3—21no—
278C2×C3⋊C8C23×C311yescharacteristic
279C2×C3⋊C8C23×C311yescharacteristic
280Dic12—42no—
281D3×C8—42no—
282C22×C32C22×D411yescharacteristic
283C2×C3×D3—22no—
284C2×C3×D3—22no—
285C2×C3×D3C2×Q1614yes—
286C32×C4—22no—
287C32×C4—21no—
288C32×C4—42no—
289C32×C4—41no—
290C32×C4C2×Q1612yes—
291C32×C4C2×#4111yescharacteristic
292C32×C4H(5,𝔽2)11yescharacteristic
293C3×Dic3—22no—
294C3×Dic3—42no—
295C3×Dic3—41no—
296C3×Dic3—41no—
297C22×Q8—32no—
298C2×Q16—31no—
299C2×Q16—32no—
300C22×C8—32no—
301C4⋊Q8—31no—
302C4⋊Q8—61no—
303C4⋊Q8C2×C3×D311yescharacteristic
304#125—61no—
305C22⋊Q8—32no—
306C22⋊Q8—32no—
307C22⋊Q8—62no—
308C22⋊Q8—62no—
309C4×Q8—31no—
310C4×Q8C2×C3×D311yescharacteristic
311C4×D4—31no—
312C4×D4—61no—
313C4×D4—61no—
314C2×C4⋊C4—32no—
315#107—31no—
316#107C2×C3×D312yes—
317C4⋊C8C2×C3×D311yescharacteristic
318#103—31no—
319#103—32no—
320#103—32no—
321#103—31no—
322#103—32no—
323#103C2×C3×D312yes—
324C22⋊C8—32no—
325C4×C8—31no—
326C23×C3—32no—
327C22×D3C2×C3×D412yes—
328C3×Q8—21no—
329C3×Q8—21no—
330C3×Q8—22no—
331C3×Q8—41no—
332C3×Q8—61no—
333C3×Q8—62no—
334C3×Q8—61no—
335C3×Q8—62no—
336C3×Q8—81no—
337C3×Q8—81no—
338C3×Q8—82no—
339C3×Q8—124no—
340C3×Q8#23912yes—
341C3×Q8C3×#4112yes—
342C3×D4—34no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—32no—
353C2×C3×C4—41no—
354C2×C3×C4—41no—
355C2×C3×C4—42no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—61no—
359C2×C3×C4—61no—
360C2×C3×C4—62no—
361C2×C3×C4—124no—
362C2×C3×C4—242no—
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4C2×C3×D411yescharacteristic
366C2×C3×C4C2×C3×D411yescharacteristic
367C2×C3×C4C23×D311yescharacteristic
368C2×C3×C4C24×C311yescharacteristic
369C2×Dic3—21no—
370C2×Dic3—21no—
371C2×Dic3—22no—
372C2×Dic3C2×C3×D412yes—
373D12C3×Q1614yescomplemented
374C4×D3—22no—
375C4×D3—22no—
376C4×D3—44no—
377C4×D3—82no—
378Dic6—21no—
379Dic6—22no—
380Dic6—21no—
381Dic6—22no—
382Dic6—44no—
383C3×C8—22no—
384C3×C8—22no—
385C3×C8—42no—
386C3×C8—61no—
387C3×C8—61no—
388C3⋊C8—21no—
389C3⋊C8—21no—
390C2×C32#54611yescharacteristic
391C2×C32C22×Q1611yescharacteristic
392C2×C32#57711yescharacteristic
393C3×D3—24no—
394C2×Q8—21no—
395C2×Q8—32no—
396C2×Q8—31no—
397C2×Q8—62no—
398C2×Q8—64no—
399C2×Q8—122no—
400C2×Q8C22×C3×D311yescharacteristic
401C2×D4—31no—
402C22×C4—32no—
403C22×C4—62no—
404C22×C4—62no—
405Q16—62no—
406Q16—122no—
407C2×C8—31no—
408C2×C8—31no—
409C2×C8—122no—
410C2×C8C22×C3×D312yes—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—31no—
414C4⋊C4—31no—
415C4⋊C4—62no—
416C4⋊C4—62no—
417C4⋊C4—62no—
418C4⋊C4—61no—
419C4⋊C4—61no—
420C4⋊C4—61no—
421C4⋊C4C22×C3×D312yes—
422C4⋊C4C22×C3×D311yescharacteristic
423C22⋊C4—32no—
424C22⋊C4—62no—
425C22⋊C4—62no—
426C42—21no—
427C42—61no—
428C42C22×C3×D311yescharacteristic
429C22×C3—21no—
430C22×C3—34no—
431C22×C3—62no—
432C22×C3—62no—
433C22×C3C2×D3×D411yescharacteristic
434C22×C3C22×C3×D411yescharacteristic
435C2×D3—22no—
436C2×D3—22no—
437C2×D3C2×C3×Q1614yes—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—22no—
441C3×C4—22no—
442C3×C4—22no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—41no—
446C3×C4—42no—
447C3×C4—42no—
448C3×C4—41no—
449C3×C4—42no—
450C3×C4—41no—
451C3×C4—62no—
452C3×C4—82no—
453C3×C4—81no—
454C3×C4—121no—
455C3×C4—122no—
456C3×C4—121no—
457C3×C4D3×Q1612yes—
458C3×C4C2×C3×Q1612yes—
459C3×C4C2×#23911yescharacteristic
460C3×C4#100911yescharacteristic
461C3×C4C2×C3×#4111yescharacteristic
462C3×C4C3×H(5,𝔽2)11yescharacteristic
463Dic3—22no—
464Dic3—41no—
465Dic3—42no—
466Dic3—41no—
467C32#329911yescharacteristic, complemented, Sylow
468C23—32no—
469Q8—21no—
470Q8—61no—
471Q8—62no—
472Q8—61no—
473Q8—62no—
474Q8—81no—
475Q8—124no—
476Q8C3×#23912yes—
477D4—34no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—22no—
481C2×C4—32no—
482C2×C4—62no—
483C2×C4—62no—
484C2×C4—61no—
485C2×C4—61no—
486C2×C4—62no—
487C2×C4—124no—
488C2×C4—242no—
489C2×C4C3×D3×D411yescharacteristic
490C2×C4C3×D3×D411yescharacteristic
491C2×C4C23×C3×D311yescharacteristic
492C8—22no—
493C8—61no—
494C8—61no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—64no—
499C2×C3#563011yescharacteristic
500C2×C3C2×D3×Q1611yescharacteristic
501C2×C3#577511yescharacteristic
502C2×C3C3×#54611yescharacteristic
503C2×C3C22×C3×Q1611yescharacteristic
504C2×C3C3×#57711yescharacteristic
505D3—24no—
506C22—34no—
507C22—62no—
508C22—62no—
509C22C2×C3×D3×D411yescharacteristic
510C4—21no—
511C4—22no—
512C4—42no—
513C4—41no—
514C4—62no—
515C4—121no—
516C4—122no—
517C4—121no—
518C4C3×D3×Q1612yes—
519C4C2×C3×#23911yescharacteristic
520C4C3×#100911yescharacteristic
521C3—21no—
522C3#8111911yescharacteristic, direct product factor
523C3C3×#329911yescharacteristic, complemented
524C2—64no—
525C2C3×#563011yescharacteristic
526C2C2×C3×D3×Q1611yescharacteristic
527C2C3×#577511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#477C2
socleC22×C32C22×D4
prime radicalC2×C3×D12D4
hypercenterC3×#477D3
hypocenterC3C3×#3299
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#477

Complements

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

NH ≅ G/Ntype
3. C32×#477C2semidirect
4. C3×#5093C2semidirect
5. C3×C4×#216C2semidirect
6. C3×#4887C2semidirect
7. C3×#4884C2semidirect
8. C3×#4849C2semidirect
10. C3×#4809C2semidirect
11. C3×D3×#103C2semidirect
13. #81119C3direct (N × H)
50. C3×#477D3semidirect
51. C3×#477C2×C3semidirect
58. #5093C2×C3semidirect
59. C4×#216C2×C3semidirect
60. #4887C2×C3semidirect
61. #4884C2×C3semidirect
62. #4849C2×C3semidirect
64. #4809C2×C3semidirect
65. D3×#103C2×C3semidirect
179. C3×D12Q16semidirect
196. #477C3×D3semidirect
373. D12C3×Q16semidirect
467. C32#3299semidirect
522. C3#81119direct (N × H)
523. C3C3×#3299semidirect

Maximal subgroups

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

subgroupindex
C3×#57302
C3×Q8×D122
C32×#4772
C3×#50932
C3×C4×#2162
C3×#48872
C3×#48842
C3×#48492
C3×#48342
C3×#48092
C3×D3×#1032
C3×#32993
#811193