Finite Group Databasebeta

← C3×#79980 #11895931

Subgroups — C3×#79980 #11895931

Order 1152.

811 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5577C211yesmaximal, characteristic
2C3×#5567C211yesmaximal, characteristic, complemented
3C32×#446C211yesmaximal, characteristic, complemented
4C3×#4848C212yesmaximal, complemented
5C3×#4848C211yesmaximal, characteristic, complemented
6C3×#4847C212yesmaximal, complemented
7C3×#4846C211yesmaximal, characteristic, complemented
8C3×#4713C212yesmaximal, complemented
9C3×#4710C212yesmaximal, complemented
10C3×#4694C211yesmaximal, characteristic, complemented
11C3×C4×#204C211yesmaximal, characteristic, complemented
12C3×#3368—31nomaximal
13#79980C311yesmaximal, characteristic, direct product factor
14C2×C3×#239—21no—
15C32×C4×Q8C2211yescharacteristic
16C3×#944—21no—
17C2×C3×#204C2211yescharacteristic
18C2×C3×#204C2212yes—
19C3×#895—21no—
20C3×#895—22no—
21C3×#889—22no—
22C3×#887—21no—
23C3×#874C2211yescharacteristic
24C3×#874C2212yes—
25C3×C4×D12C2211yescharacteristic
26C3×C4×D12C2212yes—
27C3×#870C2212yes—
28C3×#869C2211yescharacteristic
29C3×C4×Dic6C2211yescharacteristic
30C3×C4×Dic6C2212yes—
31C32×C4⋊C8C2211yescharacteristic
32C32×C4⋊C8C2212yes—
33C32×#97C2212yes—
34C32×C4×C8C2211yescharacteristic
35C3×#821C2211yescharacteristic
36C3×#821C2212yes—
37C3×#821C2212yes—
38C3×#821C2212yes—
39C3×#821C2212yes—
40C3×#818C2212yes—
41C3×#817C2211yescharacteristic
42C3×#816C2211yescharacteristic
43C3×#557—31no—
44C3×#550—31no—
45#5577C2×C311yescharacteristic
46#5567C2×C311yescharacteristic, complemented
47C3×#490—32no—
48C3×#486—31no—
49C3×#478—32no—
50C3×#474—31no—
51C3×#460—32no—
52C3×#460—31no—
53C3×#446—21no—
54C3×#446D311yescharacteristic, complemented
55C3×#446C2×C311yescharacteristic, complemented
56C3×#440—32no—
57C3×C4×SD16—31no—
58#4848C2×C312yescomplemented
59#4848C2×C311yescharacteristic, complemented
60#4847C2×C312yescomplemented
61#4846C2×C311yescharacteristic, complemented
62#4713C2×C312yescomplemented
63#4710C2×C312yescomplemented
64#4694C2×C311yescharacteristic, complemented
65C4×#204C2×C311yescharacteristic, complemented
66C2×C32×Q8D411yescharacteristic
67C3×#239—44no—
68C2×C3×D12—22no—
69C2×C3×D12—21no—
70C2×C3×D12—22no—
71C2×C3×D12—21no—
72C2×C3×D12C2311yescharacteristic
73C2×C3×D12C2312yes—
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3—21no—
76C2×C3×Dic6—21no—
77C2×C3×Dic6C2311yescharacteristic
78C2×C32×C8C2311yescharacteristic
79C2×C32×C8C2312yes—
80C2×C32×C8C2311yescharacteristic
81C32×C4⋊C4D411yescharacteristic
82C32×C4⋊C4D412yes—
83C32×C42C2311yescharacteristic
84C32×C42C2312yes—
85C3×(C2×D3)⋊C4—22no—
86C3×(C2×D3)⋊C4—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3C2311yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4—21no—
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4—22no—
95C3×C4×Dic3—22no—
96C3×C4×Dic3—21no—
97C3×#204—22no—
98C3×#204—24no—
99#3368—31noSylow
100C2×C3×#41—61no—
101C2×#239—21no—
102C2×C3×SD16—31no—
103C2×C3×SD16—32no—
104C3×C4⋊Q8—31no—
105C3×C4⋊Q8—61no—
106C3×#127—31no—
107C3×#127—32no—
108C3×#125—32no—
109C3×#125—62no—
110C3×#121—61no—
111C3×#121—62no—
112C3×C4×Q8—21no—
113C3×C4×Q8—31no—
114C3×C4×Q8—32no—
115C3×C4×Q8—61no—
116C3×C4×Q8C2×D311yescharacteristic
117C3×C4×Q8C22×C311yescharacteristic
118C3×C4×D4—31no—
119C3×C4×D4—32no—
120#944—21no—
121C2×#204C22×C311yescharacteristic
122C2×#204C22×C312yes—
123#895—21no—
124#895—22no—
125#889—22no—
126#887—21no—
127#874C22×C311yescharacteristic
128#874C22×C312yes—
129C4×D12C22×C311yescharacteristic
130C4×D12C22×C312yes—
131#870C22×C312yes—
132#869C22×C311yescharacteristic
133C4×Dic6C22×C311yescharacteristic
134C4×Dic6C22×C312yes—
135C3×#107—32no—
136C3×#106—31no—
137C3×C4⋊C8—21no—
138C3×C4⋊C8—22no—
139C3×C4⋊C8C2×D311yescharacteristic
140C3×C4⋊C8C2×D312yes—
141C3×C4⋊C8C22×C311yescharacteristic
142C3×C4⋊C8C22×C312yes—
143C3×#103—31no—
144C3×#102—31no—
145C3×#102—32no—
146C3×#102—32no—
147C3×#102—32no—
148C3×#102—32no—
149C3×#97—22no—
150C3×#97C2×D312yes—
151C3×#97C22×C312yes—
152C3×C4×C8—21no—
153C3×C4×C8C2×D311yescharacteristic
154C3×C4×C8C22×C311yescharacteristic
155#821C22×C311yescharacteristic
156#821C22×C312yes—
157#821C22×C312yes—
158#821C22×C312yes—
159#821C22×C312yes—
160#818C22×C312yes—
161#817C22×C311yescharacteristic
162#816C22×C311yescharacteristic
163C22×C3×D3—22no—
164C22×C3×D3—21no—
165C32×Q8—22no—
166C2×C32×C4C2×D412yes—
167C2×C32×C4C2×D412yes—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—21no—
175C3×D12—21no—
176C3×D12—22no—
177C3×D12—21no—
178C3×D12—22no—
179C3×D12—44no—
180C3×D12—42no—
181C3×D12—82no—
182C3×D12—81no—
183C3×C4×D3—44no—
184C3×C4×D3—42no—
185C3×Dic6—21no—
186C3×Dic6—42no—
187C3×Dic6#4112yescomplemented
188C32×C8—21no—
189C32×C8—21no—
190C32×C8—22no—
191#557—31no—
192#550—31no—
193#490—32no—
194#486—31no—
195#478—32no—
196#474—31no—
197#460—32no—
198#460—31no—
199#446C3×D311yescharacteristic, complemented
200#440—32no—
201C4×SD16—31no—
202C3×#41—124no—
203C2×C3×Q8—21no—
204C2×C3×Q8—31no—
205C2×C3×Q8—61no—
206C2×C3×Q8D1211yescharacteristic
207C2×C3×Q8C3×D411yescharacteristic
208C2×C3×D4—31no—
209C2×C3×D4—32no—
210C2×C3×D4—62no—
211C2×C3×D4—61no—
212C2×C3×D4—62no—
213C2×C3×D4—61no—
214C22×C3×C4—62no—
215C22×C3×C4—61no—
216#239—44no—
217C2×D12—22no—
218C2×D12—21no—
219C2×D12—22no—
220C2×D12—21no—
221C2×D12C23×C311yescharacteristic
222C2×D12C23×C312yes—
223C2×C4×D3—22no—
224C2×C4×D3—21no—
225C2×Dic6—21no—
226C2×Dic6C23×C311yescharacteristic
227C3×SD16—62no—
228C3×SD16—64no—
229C2×C3×C8—21no—
230C2×C3×C8—21no—
231C2×C3×C8—22no—
232C2×C3×C8C22×D311yescharacteristic
233C2×C3×C8C22×D311yescharacteristic
234C2×C3×C8C22×D312yes—
235C2×C3×C8C23×C311yescharacteristic
236C2×C3×C8C23×C311yescharacteristic
237C2×C3×C8C23×C312yes—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—22no—
240C3×C4⋊C4—31no—
241C3×C4⋊C4—32no—
242C3×C4⋊C4—31no—
243C3×C4⋊C4—61no—
244C3×C4⋊C4—62no—
245C3×C4⋊C4—62no—
246C3×C4⋊C4—62no—
247C3×C4⋊C4—61no—
248C3×C4⋊C4D1211yescharacteristic
249C3×C4⋊C4D1212yes—
250C3×C4⋊C4C3×D411yescharacteristic
251C3×C4⋊C4C3×D412yes—
252C3×C22⋊C4—62no—
253C3×C22⋊C4—61no—
254C3×C42—21no—
255C3×C42—22no—
256C3×C42—62no—
257C3×C42—61no—
258C3×C42C22×D311yescharacteristic
259C3×C42C22×D312yes—
260C3×C42C23×C311yescharacteristic
261C3×C42C23×C312yes—
262(C2×D3)⋊C4—22no—
263(C2×D3)⋊C4—21no—
264C4⋊Dic3—21no—
265C4⋊Dic3C23×C311yescharacteristic
266C4⋊Dic3C23×C311yescharacteristic
267C4⋊Dic3C23×C312yes—
268Dic3⋊C4—21no—
269Dic3⋊C4—22no—
270Dic3⋊C4—22no—
271Dic3⋊C4—22no—
272C4×Dic3—22no—
273C4×Dic3—21no—
274#204—22no—
275#204—24no—
276C22×C32C22×D411yescharacteristic
277C2×C3×D3—42no—
278C2×C3×D3—41no—
279C2×C3×D3—42no—
280C2×C3×D3—41no—
281C2×C3×D3—42no—
282C2×C3×D3—41no—
283C32×C4—22no—
284C32×C4—22no—
285C32×C4—21no—
286C32×C4AGL(1,ℤ/8)12yes—
287C32×C4C2×#4111yescharacteristic
288C32×C42−1+411yescharacteristic
289C3×Dic3—22no—
290C3×Dic3—42no—
291C3×Dic3—41no—
292C3×Dic3—41no—
293C2×#41—61no—
294C2×SD16—31no—
295C2×SD16—32no—
296C4⋊Q8—31no—
297C4⋊Q8—61no—
298#127—31no—
299#127—32no—
300#125—32no—
301#125—62no—
302#121—61no—
303#121—62no—
304C4×Q8—31no—
305C4×Q8—32no—
306C4×Q8—61no—
307C4×Q8C2×C3×D311yescharacteristic
308C4×D4—31no—
309C4×D4—32no—
310#107—32no—
311#106—31no—
312C4⋊C8C2×C3×D311yescharacteristic
313C4⋊C8C2×C3×D312yes—
314#103—31no—
315#102—31no—
316#102—32no—
317#102—32no—
318#102—32no—
319#102—32no—
320#97C2×C3×D312yes—
321C4×C8C2×C3×D311yescharacteristic
322C23×C3—62no—
323C23×C3—61no—
324C22×D3—22no—
325C22×D3—21no—
326C3×Q8—22no—
327C3×Q8—22no—
328C3×Q8—32no—
329C3×Q8—42no—
330C3×Q8—61no—
331C3×Q8—122no—
332C3×D4—61no—
333C3×D4—62no—
334C3×D4—61no—
335C3×D4—62no—
336C3×D4—124no—
337C3×D4—122no—
338C3×D4—242no—
339C3×D4—241no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—22no—
343C2×C3×C4—21no—
344C2×C3×C4—22no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—62no—
348C2×C3×C4—61no—
349C2×C3×C4—124no—
350C2×C3×C4—122no—
351C2×C3×C4C2×D1212yes—
352C2×C3×C4C2×D1211yescharacteristic
353C2×C3×C4C2×D1212yes—
354C2×C3×C4C2×D1211yescharacteristic
355C2×C3×C4C2×C3×D412yes—
356C2×C3×C4C2×C3×D412yes—
357C2×C3×C4C2×C3×D411yescharacteristic
358C2×C3×C4C2×C3×D411yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×C3×C4C24×C311yescharacteristic
361C2×Dic3—21no—
362C2×Dic3—21no—
363C2×Dic3—22no—
364C2×Dic3—21no—
365D12—21no—
366D12—22no—
367D12—21no—
368D12—22no—
369D12—44no—
370D12—42no—
371D12—82no—
372D12—81no—
373C4×D3—44no—
374C4×D3—42no—
375Dic6—21no—
376Dic6—42no—
377Dic6C3×#4112yescomplemented
378C3×C8—22no—
379C3×C8—21no—
380C3×C8—21no—
381C3×C8—22no—
382C3×C8—21no—
383C3×C8—22no—
384C3×C8—21no—
385C3×C8—41no—
386C3×C8—42no—
387C2×C32#54811yescharacteristic
388C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
389C2×C32#57711yescharacteristic
390C3×D3—82no—
391C3×D3—81no—
392#41—124no—
393C2×Q8—31no—
394C2×Q8—61no—
395C2×Q8C3×D1211yescharacteristic
396C2×D4—31no—
397C2×D4—32no—
398C2×D4—62no—
399C2×D4—61no—
400C2×D4—62no—
401C2×D4—61no—
402C22×C4—62no—
403C22×C4—61no—
404SD16—62no—
405SD16—64no—
406C2×C8C22×C3×D311yescharacteristic
407C2×C8C22×C3×D311yescharacteristic
408C2×C8C22×C3×D312yes—
409C4⋊C4—31no—
410C4⋊C4—32no—
411C4⋊C4—31no—
412C4⋊C4—61no—
413C4⋊C4—62no—
414C4⋊C4—62no—
415C4⋊C4—62no—
416C4⋊C4—61no—
417C4⋊C4C3×D1211yescharacteristic
418C4⋊C4C3×D1212yes—
419C22⋊C4—62no—
420C22⋊C4—61no—
421C42—62no—
422C42—61no—
423C42C22×C3×D311yescharacteristic
424C42C22×C3×D312yes—
425C22×C3—21no—
426C22×C3—122no—
427C22×C3—121no—
428C22×C3—122no—
429C22×C3—121no—
430C22×C3—122no—
431C22×C3—121no—
432C22×C3C22×D1211yescharacteristic
433C22×C3C22×C3×D411yescharacteristic
434C2×D3—42no—
435C2×D3—41no—
436C2×D3—42no—
437C2×D3—41no—
438C2×D3—42no—
439C2×D3—41no—
440C3×C4—22no—
441C3×C4—22no—
442C3×C4—21no—
443C3×C4—22no—
444C3×C4—22no—
445C3×C4—21no—
446C3×C4—22no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—42no—
450C3×C4—42no—
451C3×C4—41no—
452C3×C4—62no—
453C3×C4—121no—
454C3×C4—122no—
455C3×C4—121no—
456C3×C4#90812yes—
457C3×C4C3×AGL(1,ℤ/8)12yes—
458C3×C4#100711yescharacteristic
459C3×C4D3×#4111yescharacteristic
460C3×C4C2×C3×#4111yescharacteristic
461C3×C4C3×2−1+411yescharacteristic
462Dic3—22no—
463Dic3—42no—
464Dic3—41no—
465Dic3—41no—
466C32#336811yescharacteristic, complemented, Sylow
467C23—62no—
468C23—61no—
469Q8—22no—
470Q8—32no—
471Q8—61no—
472Q8—122no—
473D4—61no—
474D4—62no—
475D4—61no—
476D4—62no—
477D4—124no—
478D4—122no—
479D4—242no—
480D4—241no—
481C2×C4—61no—
482C2×C4—61no—
483C2×C4—62no—
484C2×C4—61no—
485C2×C4—124no—
486C2×C4—122no—
487C2×C4C2×C3×D1212yes—
488C2×C4C2×C3×D1211yescharacteristic
489C2×C4C2×C3×D1212yes—
490C2×C4C2×C3×D1211yescharacteristic
491C2×C4C23×C3×D311yescharacteristic
492C8—21no—
493C8—21no—
494C8—22no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—242no—
499C2×C3—241no—
500C2×C3#557611yescharacteristic
501C2×C3C2×#90811yescharacteristic
502C2×C3#575111yescharacteristic
503C2×C3C3×#54811yescharacteristic
504C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
505C2×C3C3×#57711yescharacteristic
506D3—82no—
507D3—81no—
508C22—122no—
509C22—121no—
510C22—122no—
511C22—121no—
512C22—122no—
513C22—121no—
514C22C22×C3×D1211yescharacteristic
515C4—22no—
516C4—22no—
517C4—21no—
518C4—62no—
519C4—121no—
520C4—122no—
521C4—121no—
522C4C3×#90812yes—
523C4C3×#100711yescharacteristic
524C4C3×D3×#4111yescharacteristic
525C3—21no—
526C3#7998011yescharacteristic, direct product factor
527C3C3×#336811yescharacteristic, complemented
528C2—242no—
529C2—241no—
530C2C3×#557611yescharacteristic
531C2C2×C3×#90811yescharacteristic
532C2C3×#575111yescharacteristic
subgroupG/H
centerC22×C3C22×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#446C2
socleC22×C32C22×D4
prime radicalC3×#5577C2
hypercenterC3×#446D3
hypocenterC3C3×#3368
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×Q8 ◁ C3×#446

Complements

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

NH ≅ G/Ntype
2. C3×#5567C2semidirect
3. C32×#446C2semidirect
4. C3×#4848C2semidirect
5. C3×#4848C2semidirect
6. C3×#4847C2semidirect
7. C3×#4846C2semidirect
8. C3×#4713C2semidirect
9. C3×#4710C2semidirect
10. C3×#4694C2semidirect
11. C3×C4×#204C2semidirect
13. #79980C3direct (N × H)
46. #5567C2×C3semidirect
54. C3×#446D3semidirect
55. C3×#446C2×C3semidirect
58. #4848C2×C3semidirect
59. #4848C2×C3semidirect
60. #4847C2×C3semidirect
61. #4846C2×C3semidirect
62. #4713C2×C3semidirect
63. #4710C2×C3semidirect
64. #4694C2×C3semidirect
65. C4×#204C2×C3semidirect
187. C3×Dic6#41semidirect
199. #446C3×D3semidirect
377. Dic6C3×#41semidirect
466. C32#3368semidirect
526. C3#79980direct (N × H)
527. C3C3×#3368semidirect

Maximal subgroups

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

subgroupindex
C3×#55772
C3×#55672
C32×#4462
C3×#48482
C3×#48472
C3×#48462
C3×#47132
C3×#47102
C3×#46942
C3×C4×#2042
C3×#33683
#799803