Finite Group Databasebeta

← C3×#80491 #11887618

Subgroups — C3×#80491 #11887618

Order 1152.

830 conjugacy classes of subgroups.

The subgroup lattice has 531 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5727C211yesmaximal, characteristic
2C3×#5579C211yesmaximal, characteristic
3C32×#462C211yesmaximal, characteristic, complemented
4C3×#5188C212yesmaximal, complemented
5C3×#5186C212yesmaximal, complemented
6C3×#5079C211yesmaximal, characteristic, complemented
7C3×C4×#216C211yesmaximal, characteristic, complemented
8C3×#4850C211yesmaximal, characteristic, complemented
9C3×#4834C211yesmaximal, characteristic
10C3×#4811C212yesmaximal, complemented
11C3×D3×#103C212yesmaximal, complemented
12C3×#3299—31nomaximal
13#80491C311yesmaximal, characteristic, direct product factor
14C2×C3×D3×Q8C2212yes—
15C2×C32×Q16C2212yes—
16C32×C4⋊Q8C2211yescharacteristic
17C32×C4×Q8C2211yescharacteristic
18C3×#946C2212yes—
19C3×#946C2212yes—
20C2×C3×#216C2211yescharacteristic
21C2×C3×D3×C8C2212yes—
22C3×#896—22no—
23C3×#896—22no—
24C3×#893—21no—
25C3×D3×C4⋊C4C2212yes—
26C3×#888—21no—
27C3×C4×D12—21no—
28C3×C4×D12C2211yescharacteristic
29C3×#870—21no—
30C3×#869C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32C32×C4⋊C8C2211yescharacteristic
33C32×#103C2212yes—
34C3×#835C2212yes—
35C3×#835C2211yescharacteristic
36C3×#835C2212yes—
37C3×(C2×D3)⋊C8C2212yes—
38C3×#818C2212yes—
39C3×#816C2212yes—
40C3×#810C2211yescharacteristic
41C3×#807C2211yescharacteristic
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×#554—31no—
44C3×D4×Q8—31no—
45#5727C2×C311yescharacteristic
46#5579C2×C311yescharacteristic
47C3×#487—31no—
48C3×#484—32no—
49C3×#477—31no—
50C3×#467—32no—
51C3×#462—21no—
52C3×#462D311yescharacteristic, complemented
53C3×#462C2×C311yescharacteristic, complemented
54C3×#451—32no—
55C3×C4×Q16—31no—
56C3×C8×D4—31no—
57C2×C3×#103—32no—
58#5188C2×C312yescomplemented
59#5186C2×C312yescomplemented
60#5079C2×C311yescharacteristic, complemented
61C4×#216C2×C311yescharacteristic, complemented
62#4850C2×C311yescharacteristic, complemented
63#4834C2×C311yescharacteristic
64#4811C2×C312yescomplemented
65D3×#103C2×C312yescomplemented
66C2×C32×Q8C2311yescharacteristic
67C2×C32×Q8C2312yes—
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×Dic6—21no—
76C2×C3×Dic6C2311yescharacteristic
77C32×Q16—42no—
78C2×C32×C8C2312yes—
79C32×C4⋊C4—21no—
80C32×C4⋊C4—21no—
81C32×C4⋊C4—21no—
82C32×C4⋊C4C2311yescharacteristic
83C32×C42—21no—
84C32×C42C2311yescharacteristic
85C3×#216—22no—
86C3×(C2×D3)⋊C4—22no—
87C3×(C2×D3)⋊C4—22no—
88C3×(C2×D3)⋊C4D412yes—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3D411yescharacteristic
91C3×C4⋊Dic3C2312yes—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×Dic3⋊C4—21no—
94C3×Dic3⋊C4—22no—
95C3×Dic3⋊C4—22no—
96C3×Dic3⋊C4—22no—
97C3×C4×Dic3—21no—
98C2×C3×C3⋊C8C2311yescharacteristic
99C2×C3×C3⋊C8C2311yescharacteristic
100C3×D3×C8—42no—
101#3299—31noSylow
102C22×C3×Q8—32no—
103C2×D3×Q8C22×C312yes—
104C2×C3×Q16—22no—
105C2×C3×Q16—31no—
106C2×C3×Q16C2×D312yes—
107C2×C3×Q16C22×C312yes—
108C22×C3×C8—32no—
109C3×C4⋊Q8—21no—
110C3×C4⋊Q8—31no—
111C3×C4⋊Q8—61no—
112C3×C4⋊Q8C2×D311yescharacteristic
113C3×C4⋊Q8C22×C311yescharacteristic
114C3×#125—61no—
115C3×C22⋊Q8—32no—
116C3×C22⋊Q8—32no—
117C3×C22⋊Q8—62no—
118C3×C22⋊Q8—62no—
119C3×C4×Q8—21no—
120C3×C4×Q8—31no—
121C3×C4×Q8C2×D311yescharacteristic
122C3×C4×Q8C22×C311yescharacteristic
123C3×C4×D4—31no—
124C3×C4×D4—61no—
125C3×C4×D4—61no—
126C2×C3×C4⋊C4—32no—
127#946C22×C312yes—
128#946C22×C312yes—
129C2×#216C22×C311yescharacteristic
130C2×D3×C8C22×C312yes—
131#896—22no—
132#896—22no—
133#893—21no—
134D3×C4⋊C4C22×C312yes—
135#888—21no—
136C4×D12—21no—
137C4×D12C22×C311yescharacteristic
138#870—21no—
139#869C22×C311yescharacteristic
140C4×Dic6C22×C311yescharacteristic
141C3×#107—32no—
142C3×#107—31no—
143C3×C4⋊C8—21no—
144C3×C4⋊C8C2×D311yescharacteristic
145C3×C4⋊C8C22×C311yescharacteristic
146C3×#103—22no—
147C3×#103—32no—
148C3×#103—31no—
149C3×#103—32no—
150C3×#103—32no—
151C3×#103—31no—
152C3×#103C2×D312yes—
153C3×#103C22×C312yes—
154C3×C22⋊C8—32no—
155C3×C4×C8—31no—
156#835C22×C312yes—
157#835C22×C311yescharacteristic
158#835C22×C312yes—
159(C2×D3)⋊C8C22×C312yes—
160#818C22×C312yes—
161#816C22×C312yes—
162#810C22×C311yescharacteristic
163#807C22×C311yescharacteristic
164C4×C3⋊C8C22×C311yescharacteristic
165C22×C3×D3C2×D412yes—
166C32×Q8—21no—
167C32×Q8—21no—
168C32×Q8—22no—
169C32×Q8—22no—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—22no—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2411yescharacteristic
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3C2×D412yes—
180C3×D12Q1614yescomplemented
181C3×C4×D3—22no—
182C3×C4×D3—22no—
183C3×C4×D3—44no—
184C3×C4×D3—82no—
185C3×Dic6—21no—
186C3×Dic6—44no—
187C3×Dic6—81no—
188C3×Dic6#4112yes—
189C32×C8—22no—
190C3×C3⋊C8—21no—
191C3×C3⋊C8—21no—
192#554—31no—
193D4×Q8—31no—
194#487—31no—
195#484—32no—
196#477—31no—
197#467—32no—
198#462C3×D311yescharacteristic, complemented
199#451—32no—
200C4×Q16—31no—
201C8×D4—31no—
202C2×#103—32no—
203C2×C3×Q8—21no—
204C2×C3×Q8—22no—
205C2×C3×Q8—31no—
206C2×C3×Q8—62no—
207C2×C3×Q8—61no—
208C2×C3×Q8—64no—
209C2×C3×Q8—122no—
210C2×C3×Q8C22×D312yes—
211C2×C3×Q8C22×D311yescharacteristic
212C2×C3×Q8C23×C312yes—
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×Dic6—21no—
226C2×Dic6C23×C311yescharacteristic
227C3×Q16—42no—
228C3×Q16—42no—
229C3×Q16—44no—
230C3×Q16—62no—
231C2×C3×C8—22no—
232C2×C3×C8—31no—
233C2×C3×C8—31no—
234C2×C3×C8—122no—
235C2×C3×C8C22×D312yes—
236C2×C3×C8C23×C312yes—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—21no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—31no—
245C3×C4⋊C4—32no—
246C3×C4⋊C4—31no—
247C3×C4⋊C4—41no—
248C3×C4⋊C4—41no—
249C3×C4⋊C4—41no—
250C3×C4⋊C4—62no—
251C3×C4⋊C4—62no—
252C3×C4⋊C4—62no—
253C3×C4⋊C4—61no—
254C3×C4⋊C4—61no—
255C3×C4⋊C4C22×D311yescharacteristic
256C3×C4⋊C4C23×C311yescharacteristic
257C3×C22⋊C4—32no—
258C3×C22⋊C4—62no—
259C3×C22⋊C4—62no—
260C3×C42—21no—
261C3×C42—21no—
262C3×C42—21no—
263C3×C42—41no—
264C3×C42—61no—
265C3×C42C22×D311yescharacteristic
266C3×C42C23×C311yescharacteristic
267#216—22no—
268(C2×D3)⋊C4—22no—
269(C2×D3)⋊C4—22no—
270(C2×D3)⋊C4C3×D412yes—
271C4⋊Dic3—21no—
272C4⋊Dic3C3×D411yescharacteristic
273C4⋊Dic3C23×C311yescharacteristic
274C4⋊Dic3C23×C312yes—
275Dic3⋊C4—21no—
276Dic3⋊C4—22no—
277Dic3⋊C4—22no—
278Dic3⋊C4—22no—
279C4×Dic3—21no—
280C2×C3⋊C8C23×C311yescharacteristic
281C2×C3⋊C8C23×C311yescharacteristic
282D3×C8—42no—
283C22×C32C22×D411yescharacteristic
284C2×C3×D3—22no—
285C2×C3×D3—22no—
286C2×C3×D3C2×Q1614yes—
287C32×C4—21no—
288C32×C4—41no—
289C32×C4—42no—
290C32×C4—41no—
291C32×C4C2×Q1612yes—
292C32×C4C2×#4111yescharacteristic
293C32×C4H(5,𝔽2)11yescharacteristic
294C3×Dic3—22no—
295C3×Dic3—22no—
296C3×Dic3—42no—
297C3×Dic3—41no—
298C22×Q8—32no—
299C2×Q16—31no—
300C2×Q16C2×C3×D312yes—
301C22×C8—32no—
302C4⋊Q8—31no—
303C4⋊Q8—61no—
304C4⋊Q8C2×C3×D311yescharacteristic
305#125—61no—
306C22⋊Q8—32no—
307C22⋊Q8—32no—
308C22⋊Q8—62no—
309C22⋊Q8—62no—
310C4×Q8—31no—
311C4×Q8C2×C3×D311yescharacteristic
312C4×D4—31no—
313C4×D4—61no—
314C4×D4—61no—
315C2×C4⋊C4—32no—
316#107—32no—
317#107—31no—
318C4⋊C8C2×C3×D311yescharacteristic
319#103—32no—
320#103—31no—
321#103—32no—
322#103—32no—
323#103—31no—
324#103C2×C3×D312yes—
325C22⋊C8—32no—
326C4×C8—31no—
327C23×C3—32no—
328C22×D3C2×C3×D412yes—
329C3×Q8—22no—
330C3×Q8—21no—
331C3×Q8—22no—
332C3×Q8—21no—
333C3×Q8—22no—
334C3×Q8—21no—
335C3×Q8—22no—
336C3×Q8—21no—
337C3×Q8—22no—
338C3×Q8—32no—
339C3×Q8—41no—
340C3×Q8—42no—
341C3×Q8—42no—
342C3×Q8—61no—
343C3×Q8—124no—
344C3×Q8—241no—
345C3×D4—34no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—22no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—22no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—32no—
356C2×C3×C4—41no—
357C2×C3×C4—41no—
358C2×C3×C4—42no—
359C2×C3×C4—61no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4—61no—
363C2×C3×C4—62no—
364C2×C3×C4—124no—
365C2×C3×C4—242no—
366C2×C3×C4D3×D411yescharacteristic
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4C2×C3×D411yescharacteristic
369C2×C3×C4C2×C3×D411yescharacteristic
370C2×C3×C4C23×D311yescharacteristic
371C2×C3×C4C24×C311yescharacteristic
372C2×Dic3—21no—
373C2×Dic3—21no—
374C2×Dic3—22no—
375C2×Dic3C2×C3×D412yes—
376D12C3×Q1614yescomplemented
377C4×D3—22no—
378C4×D3—22no—
379C4×D3—44no—
380C4×D3—82no—
381Dic6—21no—
382Dic6—44no—
383Dic6—81no—
384Dic6C3×#4112yes—
385C3×C8—22no—
386C3×C8—22no—
387C3×C8—42no—
388C3×C8—61no—
389C3×C8—61no—
390C3⋊C8—21no—
391C3⋊C8—21no—
392C2×C32#54611yescharacteristic
393C2×C32C22×Q1611yescharacteristic
394C2×C32#57711yescharacteristic
395C3×D3—24no—
396C2×Q8—31no—
397C2×Q8—62no—
398C2×Q8—61no—
399C2×Q8—64no—
400C2×Q8—122no—
401C2×Q8C22×C3×D312yes—
402C2×Q8C22×C3×D311yescharacteristic
403C2×D4—31no—
404C22×C4—32no—
405C22×C4—62no—
406C22×C4—62no—
407Q16—42no—
408Q16—62no—
409C2×C8—31no—
410C2×C8—31no—
411C2×C8—122no—
412C2×C8C22×C3×D312yes—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—31no—
417C4⋊C4—32no—
418C4⋊C4—31no—
419C4⋊C4—62no—
420C4⋊C4—62no—
421C4⋊C4—62no—
422C4⋊C4—61no—
423C4⋊C4—61no—
424C4⋊C4C22×C3×D311yescharacteristic
425C22⋊C4—32no—
426C22⋊C4—62no—
427C22⋊C4—62no—
428C42—21no—
429C42—61no—
430C42C22×C3×D311yescharacteristic
431C22×C3—21no—
432C22×C3—34no—
433C22×C3—62no—
434C22×C3—62no—
435C22×C3C2×D3×D411yescharacteristic
436C22×C3C22×C3×D411yescharacteristic
437C2×D3—22no—
438C2×D3—22no—
439C2×D3C2×C3×Q1614yes—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—22no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—41no—
446C3×C4—42no—
447C3×C4—41no—
448C3×C4—41no—
449C3×C4—42no—
450C3×C4—41no—
451C3×C4—42no—
452C3×C4—41no—
453C3×C4—62no—
454C3×C4—62no—
455C3×C4—82no—
456C3×C4—81no—
457C3×C4—122no—
458C3×C4—121no—
459C3×C4D3×Q1612yes—
460C3×C4C2×C3×Q1612yes—
461C3×C4#100411yescharacteristic
462C3×C4D3×#4111yescharacteristic
463C3×C4C2×C3×#4111yescharacteristic
464C3×C4C3×H(5,𝔽2)11yescharacteristic
465Dic3—22no—
466Dic3—22no—
467Dic3—42no—
468Dic3—41no—
469C32#329911yescharacteristic, complemented, Sylow
470C23—32no—
471Q8—21no—
472Q8—22no—
473Q8—21no—
474Q8—22no—
475Q8—32no—
476Q8—61no—
477Q8—124no—
478Q8—241no—
479D4—34no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—32no—
484C2×C4—61no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—61no—
488C2×C4—62no—
489C2×C4—124no—
490C2×C4—242no—
491C2×C4C3×D3×D411yescharacteristic
492C2×C4C3×D3×D411yescharacteristic
493C2×C4C23×C3×D311yescharacteristic
494C8—22no—
495C8—61no—
496C8—61no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—64no—
501C2×C3#561211yescharacteristic
502C2×C3C2×D3×Q1611yescharacteristic
503C2×C3#577811yescharacteristic
504C2×C3C3×#54611yescharacteristic
505C2×C3C22×C3×Q1611yescharacteristic
506C2×C3C3×#57711yescharacteristic
507D3—24no—
508C22—34no—
509C22—62no—
510C22—62no—
511C22C2×C3×D3×D411yescharacteristic
512C4—21no—
513C4—41no—
514C4—42no—
515C4—41no—
516C4—62no—
517C4—62no—
518C4—122no—
519C4—121no—
520C4C3×D3×Q1612yes—
521C4C3×#100411yescharacteristic
522C4C3×D3×#4111yescharacteristic
523C3—21no—
524C3#8049111yescharacteristic, direct product factor
525C3C3×#329911yescharacteristic, complemented
526C2—64no—
527C2C3×#561211yescharacteristic
528C2C2×C3×D3×Q1611yescharacteristic
529C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#462C2
socleC22×C32C22×D4
prime radicalC2×C3×D12D4
hypercenterC3×#462D3
hypocenterC3C3×#3299
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#462

Complements

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

NH ≅ G/Ntype
3. C32×#462C2semidirect
4. C3×#5188C2semidirect
5. C3×#5186C2semidirect
6. C3×#5079C2semidirect
7. C3×C4×#216C2semidirect
8. C3×#4850C2semidirect
10. C3×#4811C2semidirect
11. C3×D3×#103C2semidirect
13. #80491C3direct (N × H)
52. C3×#462D3semidirect
53. C3×#462C2×C3semidirect
58. #5188C2×C3semidirect
59. #5186C2×C3semidirect
60. #5079C2×C3semidirect
61. C4×#216C2×C3semidirect
62. #4850C2×C3semidirect
64. #4811C2×C3semidirect
65. D3×#103C2×C3semidirect
180. C3×D12Q16semidirect
198. #462C3×D3semidirect
376. D12C3×Q16semidirect
469. C32#3299semidirect
524. C3#80491direct (N × H)
525. C3C3×#3299semidirect

Maximal subgroups

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

subgroupindex
C3×#57272
C3×#55792
C32×#4622
C3×#51882
C3×#51862
C3×#50792
C3×C4×#2162
C3×#48502
C3×#48342
C3×#48112
C3×D3×#1032
C3×#32993
#804913