Finite Group Databasebeta

← C3×#79969 #11895729

Subgroups — C3×#79969 #11895729

Order 1152.

839 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5579C211yesmaximal, characteristic, complemented
2C3×#5577C211yesmaximal, characteristic, complemented
3C32×#446C211yesmaximal, characteristic, complemented
4C3×#4847C212yesmaximal, complemented
5C3×#4843C212yesmaximal, complemented
6C3×#4843C211yesmaximal, characteristic, complemented
7C3×#4842C211yesmaximal, characteristic, complemented
8C3×#4713C212yesmaximal, complemented
9C3×#4711C212yesmaximal, complemented
10C3×#4694C211yesmaximal, characteristic, complemented
11C3×C4×D24C211yesmaximal, characteristic, complemented
12C3×#3366—31nomaximal
13#79969C311yesmaximal, characteristic, direct product factor
14C2×C3×#239—21no—
15C32×C4×Q8C2211yescharacteristic
16C3×#946—21no—
17C2×C3×D24C2211yescharacteristic
18C2×C3×D24C2212yes—
19C3×#896—22no—
20C3×#895—21no—
21C3×#895—22no—
22C3×D3×C4⋊C4—21no—
23C3×#874C2211yescharacteristic
24C3×#874C2212yes—
25C3×C4×D12C2211yescharacteristic
26C3×C4×D12C2211yescharacteristic
27C3×C4×D12C2212yes—
28C3×C4×D12C2212yes—
29C3×#870C2212yes—
30C3×#869C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32C32×C4⋊C8C2212yes—
33C32×#97C2212yes—
34C32×C4×C8C2211yescharacteristic
35C3×#821C2211yescharacteristic
36C3×#821C2211yescharacteristic
37C3×#821C2212yes—
38C3×#821C2212yes—
39C3×#821C2212yes—
40C3×#821C2212yes—
41C3×#818C2211yescharacteristic
42C3×#817C2212yes—
43C3×#554—31no—
44C3×#550—31no—
45#5579C2×C311yescharacteristic, complemented
46#5577C2×C311yescharacteristic, complemented
47C3×#490—32no—
48C3×#486—31no—
49C3×#478—32no—
50C3×#476—31no—
51C3×#459—32no—
52C3×#459—31no—
53C3×#446—21no—
54C3×#446D311yescharacteristic, complemented
55C3×#446C2×C311yescharacteristic, complemented
56C3×#442—32no—
57C3×C4×D8—31no—
58#4847C2×C312yescomplemented
59#4843C2×C312yescomplemented
60#4843C2×C311yescharacteristic, complemented
61#4842C2×C311yescharacteristic, complemented
62#4713C2×C312yescomplemented
63#4711C2×C312yescomplemented
64#4694C2×C311yescharacteristic, complemented
65C4×D24C2×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×D12C2311yescharacteristic
75C2×C3×C4×D3—21no—
76C2×C3×C4×D3—22no—
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3—22no—
79C2×C3×Dic6—21no—
80C2×C32×C8C2312yes—
81C2×C32×C8C2311yescharacteristic
82C2×C32×C8C2311yescharacteristic
83C32×C4⋊C4D411yescharacteristic
84C32×C4⋊C4D412yes—
85C32×C42C2311yescharacteristic
86C32×C42C2312yes—
87C3×(C2×D3)⋊C4—22no—
88C3×(C2×D3)⋊C4—21no—
89C3×(C2×D3)⋊C4—21no—
90C3×(C2×D3)⋊C4—22no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×C4⋊Dic3C2312yes—
94C3×C4⋊Dic3C2311yescharacteristic
95C3×Dic3⋊C4—22no—
96C3×Dic3⋊C4—22no—
97C3×D24—22no—
98C3×D24—24no—
99#3366—31noSylow
100C2×C3×#41—61no—
101C2×#239—21no—
102C2×C3×D8—31no—
103C2×C3×D8—32no—
104C3×C4⋊Q8—31no—
105C3×#127—31no—
106C3×#127—32no—
107C3×#125—32no—
108C3×C22⋊Q8—61no—
109C3×C22⋊Q8—62no—
110C3×#121—61no—
111C3×#121—62no—
112C3×C4×Q8—21no—
113C3×C4×Q8C2×D311yescharacteristic
114C3×C4×Q8C22×C311yescharacteristic
115C3×C4×D4—31no—
116C3×C4×D4—31no—
117C3×C4×D4—32no—
118C3×C4×D4—32no—
119C2×C3×C4⋊C4—61no—
120#946—21no—
121C2×D24C22×C311yescharacteristic
122C2×D24C22×C312yes—
123#896—22no—
124#895—21no—
125#895—22no—
126D3×C4⋊C4—21no—
127#874C22×C311yescharacteristic
128#874C22×C312yes—
129C4×D12C22×C311yescharacteristic
130C4×D12C22×C311yescharacteristic
131C4×D12C22×C312yes—
132C4×D12C22×C312yes—
133#870C22×C312yes—
134#869C22×C311yescharacteristic
135C3×#107—31no—
136C3×#106—32no—
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×#102—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×C311yescharacteristic
157#821C22×C312yes—
158#821C22×C312yes—
159#821C22×C312yes—
160#821C22×C312yes—
161#818C22×C311yescharacteristic
162#817C22×C312yes—
163C22×C3×D3—21no—
164C22×C3×D3—22no—
165C22×C3×D3—21no—
166C32×Q8—22no—
167C2×C32×C4C2×D412yes—
168C2×C32×C4C2×D412yes—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3×Dic3—21no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—21no—
175C3×D12—21no—
176C3×D12—22no—
177C3×D12—21no—
178C3×D12—21no—
179C3×D12—22no—
180C3×D12—44no—
181C3×D12—42no—
182C3×D12—81no—
183C3×D12—82no—
184C3×D12#4112yescomplemented
185C3×C4×D3—44no—
186C3×C4×D3—42no—
187C3×C4×D3—42no—
188C3×C4×D3—82no—
189C3×Dic6—81no—
190C32×C8—21no—
191C32×C8—22no—
192C32×C8—21no—
193#554—31no—
194#550—31no—
195#490—32no—
196#486—31no—
197#478—32no—
198#476—31no—
199#459—32no—
200#459—31no—
201#446C3×D311yescharacteristic, complemented
202#442—32no—
203C4×D8—31no—
204C3×#41—124no—
205C2×C3×Q8—21no—
206C2×C3×Q8—61no—
207C2×C3×Q8D1211yescharacteristic
208C2×C3×Q8C3×D411yescharacteristic
209C2×C3×D4—31no—
210C2×C3×D4—31no—
211C2×C3×D4—32no—
212C2×C3×D4—62no—
213C2×C3×D4—61no—
214C2×C3×D4—61no—
215C2×C3×D4—62no—
216C22×C3×C4—61no—
217C22×C3×C4—62no—
218C22×C3×C4—61no—
219C22×C3×C4—62no—
220#239—44no—
221C2×D12—22no—
222C2×D12—21no—
223C2×D12—22no—
224C2×D12—21no—
225C2×D12C23×C311yescharacteristic
226C2×D12C23×C312yes—
227C2×D12C23×C311yescharacteristic
228C2×C4×D3—21no—
229C2×C4×D3—22no—
230C2×C4×D3—21no—
231C2×C4×D3—22no—
232C2×Dic6—21no—
233C3×D8—62no—
234C3×D8—64no—
235C2×C3×C8—21no—
236C2×C3×C8—21no—
237C2×C3×C8—22no—
238C2×C3×C8C22×D311yescharacteristic
239C2×C3×C8C22×D311yescharacteristic
240C2×C3×C8C22×D312yes—
241C2×C3×C8C23×C312yes—
242C2×C3×C8C23×C311yescharacteristic
243C2×C3×C8C23×C311yescharacteristic
244C3×C4⋊C4—21no—
245C3×C4⋊C4—22no—
246C3×C4⋊C4—32no—
247C3×C4⋊C4—31no—
248C3×C4⋊C4—31no—
249C3×C4⋊C4—62no—
250C3×C4⋊C4—62no—
251C3×C4⋊C4—61no—
252C3×C4⋊C4D1211yescharacteristic
253C3×C4⋊C4D1212yes—
254C3×C4⋊C4C3×D411yescharacteristic
255C3×C4⋊C4C3×D412yes—
256C3×C22⋊C4—61no—
257C3×C22⋊C4—62no—
258C3×C22⋊C4—61no—
259C3×C22⋊C4—62no—
260C3×C42—21no—
261C3×C42—22no—
262C3×C42C22×D311yescharacteristic
263C3×C42C22×D312yes—
264C3×C42C23×C311yescharacteristic
265C3×C42C23×C312yes—
266(C2×D3)⋊C4—22no—
267(C2×D3)⋊C4—21no—
268(C2×D3)⋊C4—21no—
269(C2×D3)⋊C4—22no—
270C4⋊Dic3—21no—
271C4⋊Dic3C23×C311yescharacteristic
272C4⋊Dic3C23×C312yes—
273C4⋊Dic3C23×C311yescharacteristic
274Dic3⋊C4—22no—
275Dic3⋊C4—22no—
276D24—22no—
277D24—24no—
278C22×C32C22×D411yescharacteristic
279C2×C3×D3—22no—
280C2×C3×D3—41no—
281C2×C3×D3—41no—
282C2×C3×D3—42no—
283C2×C3×D3—41no—
284C2×C3×D3—42no—
285C2×C3×D3—41no—
286C2×C3×D3—42no—
287C2×C3×D3—41no—
288C32×C4—22no—
289C32×C4—21no—
290C32×C4—22no—
291C32×C4AGL(1,ℤ/8)12yes—
292C32×C4C2×#4111yescharacteristic
293C32×C42−1+411yescharacteristic
294C3×Dic3—41no—
295C3×Dic3—41no—
296C3×Dic3—42no—
297C2×#41—61no—
298C2×D8—31no—
299C2×D8—32no—
300C4⋊Q8—31no—
301#127—31no—
302#127—32no—
303#125—32no—
304C22⋊Q8—61no—
305C22⋊Q8—62no—
306#121—61no—
307#121—62no—
308C4×Q8C2×C3×D311yescharacteristic
309C4×D4—31no—
310C4×D4—32no—
311C4×D4—31no—
312C4×D4—32no—
313C2×C4⋊C4—61no—
314#107—31no—
315#106—32no—
316C4⋊C8C2×C3×D311yescharacteristic
317C4⋊C8C2×C3×D312yes—
318#102—31no—
319#102—31no—
320#102—32no—
321#102—32no—
322#102—32no—
323#102—32no—
324#97C2×C3×D312yes—
325C4×C8C2×C3×D311yescharacteristic
326C23×C3—61no—
327C23×C3—62no—
328C23×C3—61no—
329C22×D3—21no—
330C22×D3—22no—
331C22×D3—21no—
332C3×Q8—22no—
333C3×Q8—22no—
334C3×Q8—42no—
335C3×Q8—241no—
336C3×D4—32no—
337C3×D4—61no—
338C3×D4—61no—
339C3×D4—62no—
340C3×D4—61no—
341C3×D4—62no—
342C3×D4—124no—
343C3×D4—122no—
344C3×D4—242no—
345C3×D4—241no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—62no—
354C2×C3×C4—124no—
355C2×C3×C4—122no—
356C2×C3×C4—122no—
357C2×C3×C4—242no—
358C2×C3×C4C2×D1211yescharacteristic
359C2×C3×C4C2×D1212yes—
360C2×C3×C4C2×D1212yes—
361C2×C3×C4C2×D1211yescharacteristic
362C2×C3×C4C2×C3×D412yes—
363C2×C3×C4C2×C3×D412yes—
364C2×C3×C4C2×C3×D411yescharacteristic
365C2×C3×C4C2×C3×D411yescharacteristic
366C2×C3×C4C23×D311yescharacteristic
367C2×C3×C4C24×C311yescharacteristic
368C2×Dic3—21no—
369C2×Dic3—22no—
370C2×Dic3—21no—
371D12—21no—
372D12—22no—
373D12—21no—
374D12—21no—
375D12—22no—
376D12—44no—
377D12—42no—
378D12—81no—
379D12—82no—
380D12C3×#4112yescomplemented
381C4×D3—44no—
382C4×D3—42no—
383C4×D3—42no—
384C4×D3—82no—
385Dic6—81no—
386C3×C8—22no—
387C3×C8—21no—
388C3×C8—21no—
389C3×C8—22no—
390C3×C8—22no—
391C3×C8—21no—
392C3×C8—21no—
393C3×C8—41no—
394C3×C8—42no—
395C2×C32#54811yescharacteristic
396C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
397C2×C32#57611yescharacteristic
398C3×D3—42no—
399C3×D3—82no—
400C3×D3—81no—
401#41—124no—
402C2×Q8—61no—
403C2×Q8C3×D1211yescharacteristic
404C2×D4—31no—
405C2×D4—31no—
406C2×D4—32no—
407C2×D4—62no—
408C2×D4—61no—
409C2×D4—61no—
410C2×D4—62no—
411C22×C4—61no—
412C22×C4—62no—
413C22×C4—61no—
414C22×C4—62no—
415D8—62no—
416D8—64no—
417C2×C8C22×C3×D311yescharacteristic
418C2×C8C22×C3×D311yescharacteristic
419C2×C8C22×C3×D312yes—
420C4⋊C4—32no—
421C4⋊C4—31no—
422C4⋊C4—31no—
423C4⋊C4—62no—
424C4⋊C4—61no—
425C4⋊C4—62no—
426C4⋊C4C3×D1211yescharacteristic
427C4⋊C4C3×D1212yes—
428C22⋊C4—61no—
429C22⋊C4—62no—
430C22⋊C4—61no—
431C22⋊C4—62no—
432C42C22×C3×D311yescharacteristic
433C42C22×C3×D312yes—
434C22×C3—21no—
435C22×C3—62no—
436C22×C3—121no—
437C22×C3—121no—
438C22×C3—122no—
439C22×C3—121no—
440C22×C3—121no—
441C22×C3—122no—
442C22×C3—122no—
443C22×C3—121no—
444C22×C3C22×D1211yescharacteristic
445C22×C3C22×C3×D411yescharacteristic
446C2×D3—22no—
447C2×D3—41no—
448C2×D3—41no—
449C2×D3—42no—
450C2×D3—41no—
451C2×D3—42no—
452C2×D3—41no—
453C2×D3—42no—
454C2×D3—41no—
455C3×C4—22no—
456C3×C4—21no—
457C3×C4—22no—
458C3×C4—22no—
459C3×C4—22no—
460C3×C4—21no—
461C3×C4—22no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—42no—
465C3×C4—42no—
466C3×C4—41no—
467C3×C4—121no—
468C3×C4—121no—
469C3×C4—122no—
470C3×C4#90812yes—
471C3×C4C3×AGL(1,ℤ/8)12yes—
472C3×C4#100711yescharacteristic
473C3×C4D3×#4111yescharacteristic
474C3×C4C2×C3×#4111yescharacteristic
475C3×C4C3×2−1+411yescharacteristic
476Dic3—41no—
477Dic3—41no—
478Dic3—42no—
479C32#336611yescharacteristic, complemented, Sylow
480C23—61no—
481C23—62no—
482C23—61no—
483Q8—22no—
484Q8—241no—
485D4—32no—
486D4—61no—
487D4—61no—
488D4—62no—
489D4—61no—
490D4—62no—
491D4—124no—
492D4—122no—
493D4—242no—
494D4—241no—
495C2×C4—61no—
496C2×C4—61no—
497C2×C4—62no—
498C2×C4—124no—
499C2×C4—122no—
500C2×C4—122no—
501C2×C4—242no—
502C2×C4C2×C3×D1211yescharacteristic
503C2×C4C2×C3×D1212yes—
504C2×C4C2×C3×D1212yes—
505C2×C4C2×C3×D1211yescharacteristic
506C2×C4C23×C3×D311yescharacteristic
507C8—21no—
508C8—21no—
509C8—22no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—122no—
514C2×C3—242no—
515C2×C3—241no—
516C2×C3#557611yescharacteristic
517C2×C3C2×#90811yescharacteristic
518C2×C3#575211yescharacteristic
519C2×C3C3×#54811yescharacteristic
520C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
521C2×C3C3×#57611yescharacteristic
522D3—42no—
523D3—82no—
524D3—81no—
525C22—62no—
526C22—121no—
527C22—121no—
528C22—122no—
529C22—121no—
530C22—121no—
531C22—122no—
532C22—122no—
533C22—121no—
534C22C22×C3×D1211yescharacteristic
535C4—22no—
536C4—22no—
537C4—21no—
538C4—121no—
539C4—121no—
540C4—122no—
541C4C3×#90812yes—
542C4C3×#100711yescharacteristic
543C4C3×D3×#4111yescharacteristic
544C3—21no—
545C3#7996911yescharacteristic, direct product factor
546C3C3×#336611yescharacteristic, complemented
547C2—122no—
548C2—242no—
549C2—241no—
550C2C3×#557611yescharacteristic
551C2C2×C3×#90811yescharacteristic
552C2C3×#575211yescharacteristic
subgroupG/H
centerC22×C3C22×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#446C2
socleC22×C32C22×D4
hypercenterC3×#446D3
hypocenterC3C3×#3366
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
1. C3×#5579C2semidirect
2. C3×#5577C2semidirect
3. C32×#446C2semidirect
4. C3×#4847C2semidirect
5. C3×#4843C2semidirect
6. C3×#4843C2semidirect
7. C3×#4842C2semidirect
8. C3×#4713C2semidirect
9. C3×#4711C2semidirect
10. C3×#4694C2semidirect
11. C3×C4×D24C2semidirect
13. #79969C3direct (N × H)
45. #5579C2×C3semidirect
46. #5577C2×C3semidirect
54. C3×#446D3semidirect
55. C3×#446C2×C3semidirect
58. #4847C2×C3semidirect
59. #4843C2×C3semidirect
60. #4843C2×C3semidirect
61. #4842C2×C3semidirect
62. #4713C2×C3semidirect
63. #4711C2×C3semidirect
64. #4694C2×C3semidirect
65. C4×D24C2×C3semidirect
184. C3×D12#41semidirect
201. #446C3×D3semidirect
380. D12C3×#41semidirect
479. C32#3366semidirect
545. C3#79969direct (N × H)
546. C3C3×#3366semidirect

Maximal subgroups

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

subgroupindex
C3×#55792
C3×#55772
C32×#4462
C3×#48472
C3×#48432
C3×#48422
C3×#47132
C3×#47112
C3×#46942
C3×C4×D242
C3×#33663
#799693