Finite Group Databasebeta

← C3×#81622 #11895839

Subgroups — C3×#81622 #11895839

Order 1152.

793 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5732C211yesmaximal, characteristic, complemented
2C3×#5727C211yesmaximal, characteristic, complemented
3C32×#487C211yesmaximal, characteristic, complemented
4C3×#5087C211yesmaximal, characteristic, complemented
5C3×#5083C211yesmaximal, characteristic, complemented
6C3×#4819C212yesmaximal
7C3×#4817C212yesmaximal, complemented
8C3×#4794C212yesmaximal, complemented
9C3×#4793C212yesmaximal, complemented
10C3×C4×D24C211yesmaximal, characteristic
11C3×#4679C211yesmaximal, characteristic, complemented
12C3×#3367—31nomaximal
13#81622C311yesmaximal, characteristic, direct product factor
14C2×C3×D3×Q8—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C32×C4⋊Q8C2211yescharacteristic
17C3×#947C2212yes—
18C3×#946—21no—
19C3×Q8×Dic3C2212yes—
20C2×C3×#215C2212yes—
21C2×C3×D24C2211yescharacteristic
22C3×#898—22no—
23C3×#897—21no—
24C3×#896—22no—
25C3×#893C2212yes—
26C3×#892—21no—
27C3×#888C2212yes—
28C3×C4×D12C2211yescharacteristic
29C3×C4×D12C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C32×#103C2212yes—
32C32×#103C2212yes—
33C32×C4×C8C2211yescharacteristic
34C3×#835C2212yes—
35C3×#821C2211yescharacteristic
36C3×#821C2211yescharacteristic
37C3×#818C2211yescharacteristic
38C3×#815C2212yes—
39C3×Dic3⋊C8C2212yes—
40C3×#809C2212yes—
41C3×#807C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43C3×#556—31no—
44C3×D4×Q8—31no—
45#5732C2×C311yescharacteristic, complemented
46#5727C2×C311yescharacteristic, complemented
47C3×#489—32no—
48C3×#487—21no—
49C3×#487D311yescharacteristic, complemented
50C3×#487C2×C311yescharacteristic, complemented
51C3×#477—32no—
52C3×#474—31no—
53C3×#463—32no—
54C3×#461—31no—
55C3×#446—31no—
56C3×#440—32no—
57C3×C4×D8—31no—
58#5087C2×C311yescharacteristic, complemented
59#5083C2×C311yescharacteristic, complemented
60#4819C2×C312yes—
61#4817C2×C312yescomplemented
62#4794C2×C312yescomplemented
63#4793C2×C312yescomplemented
64C4×D24C2×C311yescharacteristic
65#4679C2×C311yescharacteristic, complemented
66C2×C32×Q8—21no—
67C2×C32×Q8C2312yes—
68C3×D3×Q8—44no—
69C2×C3×D12C2311yescharacteristic
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×C4×D3—21no—
73C2×C3×C4×D3—22no—
74C2×C3×Dic6—22no—
75C2×C3×Dic6D411yescharacteristic
76C2×C32×C8C2311yescharacteristic
77C2×C32×C8C2311yescharacteristic
78C32×C4⋊C4—21no—
79C32×C4⋊C4—21no—
80C32×C4⋊C4—21no—
81C32×C4⋊C4C2312yes—
82C32×C42C2311yescharacteristic
83C3×#215—24no—
84C3×(C2×D3)⋊C4—21no—
85C3×(C2×D3)⋊C4—21no—
86C3×(C2×D3)⋊C4—22no—
87C3×(C2×D3)⋊C4—22no—
88C3×(C2×D3)⋊C4—22no—
89C3×C4⋊Dic3—22no—
90C3×C4⋊Dic3D411yescharacteristic
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4⋊Dic3C2311yescharacteristic
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4D412yes—
95C3×C4×Dic3—22no—
96C3×C4×Dic3C2312yes—
97C2×C3×C3⋊C8C2312yes—
98C3×D24—22no—
99#3367—31noSylow
100C22×C3×Q8—61no—
101C2×D3×Q8—21no—
102C2×C3×SD16—32no—
103C2×C3×D8—31no—
104C3×C4⋊Q8—21no—
105C3×C4⋊Q8—21no—
106C3×C4⋊Q8—32no—
107C3×C4⋊Q8C2×D311yescharacteristic
108C3×C4⋊Q8C2×D311yescharacteristic
109C3×C4⋊Q8C22×C311yescharacteristic
110C3×C4⋊Q8C22×C311yescharacteristic
111C3×#126—62no—
112C3×#124—32no—
113C3×C22⋊Q8—62no—
114C3×C22⋊Q8—61no—
115C3×C22⋊Q8—61no—
116C3×C4×Q8—31no—
117C3×C4×Q8—32no—
118C3×C4×D4—32no—
119C3×C4×D4—31no—
120C3×C4×D4—31no—
121C3×#117—61no—
122#947C22×C312yes—
123#946—21no—
124Q8×Dic3C22×C312yes—
125C2×#215C22×C312yes—
126C2×D24C22×C311yescharacteristic
127#898—22no—
128#897—21no—
129#896—22no—
130#893C22×C312yes—
131#892—21no—
132#888C22×C312yes—
133C4×D12C22×C311yescharacteristic
134C4×D12C22×C311yescharacteristic
135C4×Dic6C22×C311yescharacteristic
136C3×#107—31no—
137C3×#107—32no—
138C3×C4⋊C8—32no—
139C3×C4⋊C8—31no—
140C3×#103—22no—
141C3×#103—22no—
142C3×#103—32no—
143C3×#103C2×D312yes—
144C3×#103C2×D312yes—
145C3×#103C22×C312yes—
146C3×#103C22×C312yes—
147C3×#102—31no—
148C3×#102—31no—
149C3×#102—32no—
150C3×#97—32no—
151C3×C4×C8—21no—
152C3×C4×C8C2×D311yescharacteristic
153C3×C4×C8C22×C311yescharacteristic
154#835C22×C312yes—
155#821C22×C311yescharacteristic
156#821C22×C311yescharacteristic
157#818C22×C311yescharacteristic
158#815C22×C312yes—
159Dic3⋊C8C22×C312yes—
160#809C22×C312yes—
161#807C22×C312yes—
162C4⋊(C3⋊C8)C22×C311yescharacteristic
163C22×C3×D3—21no—
164C22×C3×D3—21no—
165C32×Q8—22no—
166C32×Q8—22no—
167C32×Q8—42no—
168C2×C32×C4—22no—
169C2×C32×C4—22no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C3×D12—21no—
178C3×D12—21no—
179C3×D12—21no—
180C3×D12#4112yes—
181C3×C4×D3—44no—
182C3×C4×D3—42no—
183C3×C4×D3—42no—
184C3×Dic6—22no—
185C3×Dic6—44no—
186C32×C8—21no—
187C32×C8—21no—
188C3×C3⋊C8—22no—
189#556—31no—
190D4×Q8—31no—
191#489—32no—
192#487C3×D311yescharacteristic, complemented
193#477—32no—
194#474—31no—
195#463—32no—
196#461—31no—
197#446—31no—
198#440—32no—
199C4×D8—31no—
200C2×C3×Q8—21no—
201C2×C3×Q8—21no—
202C2×C3×Q8—22no—
203C2×C3×Q8—31no—
204C2×C3×Q8—41no—
205C2×C3×Q8—62no—
206C2×C3×Q8—124no—
207C2×C3×Q8C22×D312yes—
208C2×C3×Q8C23×C312yes—
209C2×C3×D4—31no—
210C2×C3×D4—31no—
211C22×C3×C4—62no—
212C22×C3×C4—61no—
213C22×C3×C4—61no—
214D3×Q8—44no—
215C2×D12C23×C311yescharacteristic
216C2×D12C23×C311yescharacteristic
217C2×C4×D3—21no—
218C2×C4×D3—21no—
219C2×C4×D3—22no—
220C2×Dic6—22no—
221C2×Dic6C3×D411yescharacteristic
222C3×SD16—64no—
223C3×D8—62no—
224C2×C3×C8—21no—
225C2×C3×C8—21no—
226C2×C3×C8—32no—
227C2×C3×C8C22×D311yescharacteristic
228C2×C3×C8C22×D311yescharacteristic
229C2×C3×C8C23×C311yescharacteristic
230C2×C3×C8C23×C311yescharacteristic
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—22no—
238C3×C4⋊C4—32no—
239C3×C4⋊C4—31no—
240C3×C4⋊C4—31no—
241C3×C4⋊C4—31no—
242C3×C4⋊C4—41no—
243C3×C4⋊C4—41no—
244C3×C4⋊C4—41no—
245C3×C4⋊C4—62no—
246C3×C4⋊C4—62no—
247C3×C4⋊C4C22×D312yes—
248C3×C4⋊C4C23×C312yes—
249C3×C22⋊C4—62no—
250C3×C22⋊C4—62no—
251C3×C22⋊C4—62no—
252C3×C22⋊C4—61no—
253C3×C22⋊C4—61no—
254C3×C42—21no—
255C3×C42—32no—
256C3×C42—62no—
257C3×C42C22×D311yescharacteristic
258C3×C42C23×C311yescharacteristic
259#215—24no—
260(C2×D3)⋊C4—21no—
261(C2×D3)⋊C4—21no—
262(C2×D3)⋊C4—22no—
263(C2×D3)⋊C4—22no—
264(C2×D3)⋊C4—22no—
265C4⋊Dic3—22no—
266C4⋊Dic3C3×D411yescharacteristic
267C4⋊Dic3C23×C311yescharacteristic
268C4⋊Dic3C23×C311yescharacteristic
269Dic3⋊C4—22no—
270Dic3⋊C4C3×D412yes—
271C4×Dic3—22no—
272C4×Dic3C23×C312yes—
273C2×C3⋊C8C23×C312yes—
274D24—22no—
275C22×C32C22×D411yescharacteristic
276C2×C3×D3—22no—
277C2×C3×D3—41no—
278C2×C3×D3—41no—
279C2×C3×D3—41no—
280C2×C3×D3—41no—
281C2×C3×D3—41no—
282C32×C4—21no—
283C32×C4—42no—
284C32×C4—42no—
285C32×C4AGL(1,ℤ/8)12yes—
286C32×C4C2×#4111yescharacteristic
287C32×C42−1+411yescharacteristic
288C3×Dic3—22no—
289C3×Dic3—22no—
290C3×Dic3—41no—
291C3×Dic3—41no—
292C22×Q8—61no—
293C2×SD16—32no—
294C2×D8—31no—
295C4⋊Q8—32no—
296C4⋊Q8C2×C3×D311yescharacteristic
297C4⋊Q8C2×C3×D311yescharacteristic
298#126—62no—
299#124—32no—
300C22⋊Q8—62no—
301C22⋊Q8—61no—
302C22⋊Q8—61no—
303C4×Q8—31no—
304C4×Q8—32no—
305C4×D4—32no—
306C4×D4—31no—
307C4×D4—31no—
308#117—61no—
309#107—31no—
310#107—32no—
311C4⋊C8—32no—
312C4⋊C8—31no—
313#103—32no—
314#103C2×C3×D312yes—
315#103C2×C3×D312yes—
316#102—31no—
317#102—31no—
318#102—32no—
319#97—32no—
320C4×C8C2×C3×D311yescharacteristic
321C23×C3—61no—
322C23×C3—61no—
323C22×D3—21no—
324C22×D3—21no—
325C3×Q8—22no—
326C3×Q8—22no—
327C3×Q8—22no—
328C3×Q8—22no—
329C3×Q8—42no—
330C3×Q8—42no—
331C3×Q8—42no—
332C3×Q8—42no—
333C3×Q8—62no—
334C3×Q8—82no—
335C3×Q8—124no—
336C3×D4—32no—
337C3×D4—61no—
338C3×D4—61no—
339C3×D4—61no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—32no—
348C2×C3×C4—32no—
349C2×C3×C4—42no—
350C2×C3×C4—42no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—124no—
354C2×C3×C4—122no—
355C2×C3×C4—122no—
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4C2×C3×D411yescharacteristic
359C2×C3×C4C2×C3×D411yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361C2×C3×C4C24×C311yescharacteristic
362C2×Dic3—21no—
363C2×Dic3—21no—
364C2×Dic3C2×C3×D412yes—
365C2×Dic3C2×C3×D412yes—
366D12—21no—
367D12—21no—
368D12—21no—
369D12C3×#4112yes—
370C4×D3—44no—
371C4×D3—42no—
372C4×D3—42no—
373Dic6—22no—
374Dic6—44no—
375C3×C8—21no—
376C3×C8—21no—
377C3×C8—21no—
378C3×C8—21no—
379C3×C8—41no—
380C3×C8—41no—
381C3×C8—62no—
382C3⋊C8—22no—
383C2×C32#54811yescharacteristic
384C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
385C2×C32#57811yescharacteristic
386C3×D3—42no—
387C3×D3—81no—
388C2×Q8—21no—
389C2×Q8—31no—
390C2×Q8—62no—
391C2×Q8—124no—
392C2×Q8C22×C3×D312yes—
393C2×D4—31no—
394C2×D4—31no—
395C22×C4—62no—
396C22×C4—61no—
397C22×C4—61no—
398SD16—64no—
399D8—62no—
400C2×C8—32no—
401C2×C8C22×C3×D311yescharacteristic
402C2×C8C22×C3×D311yescharacteristic
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—31no—
407C4⋊C4—32no—
408C4⋊C4—31no—
409C4⋊C4—31no—
410C4⋊C4—62no—
411C4⋊C4—62no—
412C4⋊C4C22×C3×D312yes—
413C22⋊C4—62no—
414C22⋊C4—62no—
415C22⋊C4—62no—
416C22⋊C4—61no—
417C22⋊C4—61no—
418C42—32no—
419C42—62no—
420C42C22×C3×D311yescharacteristic
421C22×C3—21no—
422C22×C3—62no—
423C22×C3—121no—
424C22×C3—121no—
425C22×C3—121no—
426C22×C3—121no—
427C22×C3—121no—
428C22×C3C2×D3×D411yescharacteristic
429C22×C3C22×C3×D411yescharacteristic
430C2×D3—22no—
431C2×D3—41no—
432C2×D3—41no—
433C2×D3—41no—
434C2×D3—41no—
435C2×D3—41no—
436C3×C4—22no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—22no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—42no—
443C3×C4—42no—
444C3×C4—42no—
445C3×C4—42no—
446C3×C4—62no—
447C3×C4—62no—
448C3×C4—82no—
449C3×C4—82no—
450C3×C4—121no—
451C3×C4—121no—
452C3×C4#91412yes—
453C3×C4C3×AGL(1,ℤ/8)12yes—
454C3×C4D3×#4111yescharacteristic
455C3×C4#101011yescharacteristic
456C3×C4C2×C3×#4111yescharacteristic
457C3×C4C3×2−1+411yescharacteristic
458Dic3—22no—
459Dic3—22no—
460Dic3—41no—
461Dic3—41no—
462C32#336711yescharacteristic, complemented, Sylow
463C23—61no—
464C23—61no—
465Q8—22no—
466Q8—22no—
467Q8—42no—
468Q8—62no—
469Q8—124no—
470D4—32no—
471D4—61no—
472D4—61no—
473D4—61no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—32no—
477C2×C4—32no—
478C2×C4—61no—
479C2×C4—61no—
480C2×C4—124no—
481C2×C4—122no—
482C2×C4—122no—
483C2×C4C3×D3×D411yescharacteristic
484C2×C4C3×D3×D411yescharacteristic
485C2×C4C23×C3×D311yescharacteristic
486C8—21no—
487C8—21no—
488C8—62no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—122no—
493C2×C3—241no—
494C2×C3#567711yescharacteristic
495C2×C3C2×#91411yescharacteristic
496C2×C3#576611yescharacteristic
497C2×C3C3×#54811yescharacteristic
498C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
499C2×C3C3×#57811yescharacteristic
500D3—42no—
501D3—81no—
502C22—62no—
503C22—121no—
504C22—121no—
505C22—121no—
506C22—121no—
507C22—121no—
508C22C2×C3×D3×D411yescharacteristic
509C4—21no—
510C4—42no—
511C4—42no—
512C4—62no—
513C4—62no—
514C4—121no—
515C4—121no—
516C4C3×#91412yes—
517C4C3×D3×#4111yescharacteristic
518C4C3×#101011yescharacteristic
519C3—21no—
520C3#8162211yescharacteristic, direct product factor
521C3C3×#336711yescharacteristic, complemented
522C2—122no—
523C2—241no—
524C2C3×#567711yescharacteristic
525C2C2×C3×#91411yescharacteristic
526C2C3×#576611yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#487C2
socleC22×C32C22×D4
prime radicalC2×C3×D24C22
hypercenterC3×#487D3
hypocenterC3C3×#3367
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#487

Complements

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

NH ≅ G/Ntype
1. C3×#5732C2semidirect
2. C3×#5727C2semidirect
3. C32×#487C2semidirect
4. C3×#5087C2semidirect
5. C3×#5083C2semidirect
7. C3×#4817C2semidirect
8. C3×#4794C2semidirect
9. C3×#4793C2semidirect
11. C3×#4679C2semidirect
13. #81622C3direct (N × H)
45. #5732C2×C3semidirect
46. #5727C2×C3semidirect
49. C3×#487D3semidirect
50. C3×#487C2×C3semidirect
58. #5087C2×C3semidirect
59. #5083C2×C3semidirect
61. #4817C2×C3semidirect
62. #4794C2×C3semidirect
63. #4793C2×C3semidirect
65. #4679C2×C3semidirect
192. #487C3×D3semidirect
462. C32#3367semidirect
520. C3#81622direct (N × H)
521. C3C3×#3367semidirect

Maximal subgroups

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

subgroupindex
C3×#57322
C3×#57272
C32×#4872
C3×#50872
C3×#50832
C3×#48192
C3×#48172
C3×#47942
C3×#47932
C3×C4×D242
C3×#46792
C3×#33673
#816223