Finite Group Databasebeta

← C3×#82442 #11870711

Subgroups — C3×#82442 #11870711

Order 1152.

1005 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×Q8C211yesmaximal, characteristic, complemented
2C3×#5477C211yesmaximal, characteristic
3C3×#5227C212yesmaximal, complemented
4C3×#5027C212yesmaximal, complemented
5C3×C4×#215C214yesmaximal, complemented
6C3×#5020C212yesmaximal, complemented
7C3×#4968C212yesmaximal, complemented
8C3×#4925C211yesmaximal, characteristic, complemented
9C3×#3103—31nomaximal
10#82442C311yesmaximal, characteristic, direct product factor
11C22×C32×Q8C2211yescharacteristic
12C2×C3×#235—21no—
13C32×C4×Q8—21no—
14C32×C4×Q8—21no—
15C32×C4×Q8C2212yes—
16C32×C4×Q8C2212yes—
17C2×C32×C4⋊C4—21no—
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C32×C42—21no—
20C2×C32×C42C2211yescharacteristic
21C2×C3×#215C2214yes—
22C3×#930—21no—
23C3×#930C2212yes—
24C3×#875—21no—
25C3×#874C2211yescharacteristic
26C3×C4×D12—21no—
27C3×C4×D12C2212yes—
28C3×#869C2211yescharacteristic
29C3×#835C2214yes—
30C3×#830C2212yes—
31C3×#809C2214yes—
32C3×#808C2214yes—
33C3×C4⋊(C3⋊C8)C2212yes—
34C3×C4×C3⋊C8C2212yes—
35C3×#532—31no—
36C2×C3×C4×Q8—21no—
37C2×C3×C4×Q8D311yescharacteristic, complemented
38C2×C3×C4×Q8C2×C311yescharacteristic, complemented
39#5477C2×C311yescharacteristic
40C3×#481—32no—
41C3×#475—32no—
42C3×#460—32no—
43C3×#448—32no—
44C3×C4×SD16—34no—
45C3×#431—31no—
46#5227C2×C312yescomplemented
47#5027C2×C312yescomplemented
48C4×#215C2×C314yescomplemented
49#5020C2×C312yescomplemented
50#4968C2×C312yescomplemented
51#4925C2×C311yescharacteristic, complemented
52C2×C32×Q8—24no—
53C2×C32×Q8—21no—
54C2×C32×Q8C2312yes—
55C22×C32×C4—21no—
56C22×C32×C4—21no—
57C22×C32×C4D411yescharacteristic
58C22×C32×C4D411yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C2×C3×#67—22no—
61C3×#235—44no—
62C2×C3×D12—21no—
63C2×C3×D12—21no—
64C2×C3×D12C2312yes—
65C2×C3×C4×D3—22no—
66C2×C3×Dic6—21no—
67C32×C4⋊C4—22no—
68C32×C4⋊C4—22no—
69C32×C4⋊C4—21no—
70C32×C4⋊C4C2312yes—
71C32×C42—22no—
72C32×C42—22no—
73C32×C42D411yescharacteristic
74C32×C42D411yescharacteristic
75C32×C42C2311yescharacteristic
76C32×C42C2311yescharacteristic
77C3×#215—28no—
78C3×(C2×D3)⋊C4—22no—
79C3×(C2×D3)⋊C4—22no—
80C3×C4⋊Dic3—21no—
81C3×C4⋊Dic3C2312yes—
82C2×C3×C3⋊C8C2314yes—
83#3103—31noSylow
84C2×C3×#41—61no—
85C22×C3×Q8—21no—
86C22×C3×Q8C2×D311yescharacteristic
87C22×C3×Q8C22×C311yescharacteristic
88C2×#235—21no—
89C2×C3×SD16—34no—
90C3×C4⋊Q8—31no—
91C3×#127—31no—
92C3×#124—61no—
93C3×#121—32no—
94C3×#121—61no—
95C3×C4×Q8—22no—
96C3×C4×Q8—22no—
97C3×C4×Q8—21no—
98C3×C4×Q8—21no—
99C3×C4×Q8—21no—
100C3×C4×Q8—21no—
101C3×C4×Q8—22no—
102C3×C4×Q8—22no—
103C3×C4×Q8C2×D312yes—
104C3×C4×Q8C2×D312yes—
105C3×C4×Q8C22×C312yes—
106C3×C4×Q8C22×C312yes—
107C3×C4×D4—32no—
108C3×C4×D4—61no—
109C2×C3×C4⋊C4—22no—
110C2×C3×C4⋊C4—21no—
111C2×C3×C4⋊C4—21no—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4C2×D311yescharacteristic
114C2×C3×C4⋊C4C22×C311yescharacteristic
115C2×C3×C42—22no—
116C2×C3×C42—21no—
117C2×C3×C42—21no—
118C2×C3×C42—21no—
119C2×C3×C42C2×D311yescharacteristic
120C2×C3×C42C22×C311yescharacteristic
121C2×#215C22×C314yes—
122#930—21no—
123#930C22×C312yes—
124#875—21no—
125#874C22×C311yescharacteristic
126C4×D12—21no—
127C4×D12C22×C312yes—
128#869C22×C311yescharacteristic
129C3×#106—34no—
130C3×C4⋊C8—32no—
131C3×#103—34no—
132C3×#102—34no—
133C3×C22⋊C8—32no—
134C3×C4×C8—32no—
135#835C22×C314yes—
136#830C22×C312yes—
137#809C22×C314yes—
138#808C22×C314yes—
139C4⋊(C3⋊C8)C22×C312yes—
140C4×C3⋊C8C22×C312yes—
141C23×C32C2×D411yescharacteristic
142C22×C3×D3—22no—
143C32×Q8—24no—
144C32×Q8—22no—
145C32×Q8#4114yescomplemented
146C2×C32×C4—24no—
147C2×C32×C4—22no—
148C2×C32×C4—22no—
149C2×C32×C4—22no—
150C2×C32×C4—41no—
151C2×C32×C4—42no—
152C2×C32×C4SD1614yescomplemented
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2411yescharacteristic
159C3×#67—44no—
160C2×C3×Dic3—22no—
161C3×D12—24no—
162C3×D12—42no—
163C3×D12—42no—
164C3×C4×D3—44no—
165C3×Dic6—42no—
166C3×C3⋊C8—24no—
167#532—31no—
168C2×C4×Q8C3×D311yescharacteristic, complemented
169#481—32no—
170#475—32no—
171#460—32no—
172#448—32no—
173C4×SD16—34no—
174#431—31no—
175C3×#41—124no—
176C2×C3×Q8—22no—
177C2×C3×Q8—28no—
178C2×C3×Q8—24no—
179C2×C3×Q8—24no—
180C2×C3×Q8—21no—
181C2×C3×Q8—21no—
182C2×C3×Q8—22no—
183C2×C3×Q8—61no—
184C2×C3×Q8C22×D312yes—
185C2×C3×Q8C23×C312yes—
186C2×C3×D4—32no—
187C2×C3×D4—62no—
188C2×C3×D4—61no—
189C2×C3×D4—61no—
190C22×C3×C4—22no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—22no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—62no—
200C22×C3×C4#6711yescharacteristic
201C22×C3×C4#6711yescharacteristic
202C22×C3×C4C3×D411yescharacteristic
203C22×C3×C4C3×D411yescharacteristic
204C22×C3×C4C22×D311yescharacteristic
205C22×C3×C4C23×C311yescharacteristic
206C2×#67—22no—
207#235—44no—
208C2×D12—21no—
209C2×D12—21no—
210C2×D12C23×C312yes—
211C2×C4×D3—22no—
212C2×Dic6—21no—
213C3×SD16—68no—
214C2×C3×C8—34no—
215C3×C4⋊C4—24no—
216C3×C4⋊C4—24no—
217C3×C4⋊C4—22no—
218C3×C4⋊C4—22no—
219C3×C4⋊C4—22no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—22no—
222C3×C4⋊C4—22no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—22no—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4C22×D312yes—
228C3×C4⋊C4C23×C312yes—
229C3×C22⋊C4—62no—
230C3×C22⋊C4—62no—
231C3×C42—24no—
232C3×C42—24no—
233C3×C42—22no—
234C3×C42—22no—
235C3×C42—22no—
236C3×C42—22no—
237C3×C42—21no—
238C3×C42—21no—
239C3×C42—21no—
240C3×C42—21no—
241C3×C42#6711yescharacteristic
242C3×C42#6711yescharacteristic
243C3×C42C3×D411yescharacteristic
244C3×C42C3×D411yescharacteristic
245C3×C42C22×D311yescharacteristic
246C3×C42C22×D311yescharacteristic
247C3×C42C23×C311yescharacteristic
248C3×C42C23×C311yescharacteristic
249#215—28no—
250(C2×D3)⋊C4—22no—
251(C2×D3)⋊C4—22no—
252C4⋊Dic3—21no—
253C4⋊Dic3C23×C312yes—
254C2×C3⋊C8C23×C314yes—
255C22×C32—21no—
256C22×C32—21no—
257C22×C32C2×SD1612yes—
258C22×C32C22×D411yescharacteristic
259C2×C3×D3—42no—
260C2×C3×D3—42no—
261C2×C3×D3—42no—
262C32×C4—24no—
263C32×C4—21no—
264C32×C4—21no—
265C32×C4—21no—
266C32×C4—42no—
267C32×C4C2×SD1612yes—
268C32×C4C2×SD1612yes—
269C32×C4C2×#4112yes—
270C3×Dic3—42no—
271C2×#41—61no—
272C22×Q8C2×C3×D311yescharacteristic
273C2×SD16—34no—
274C4⋊Q8—31no—
275#127—31no—
276#124—61no—
277#121—32no—
278#121—61no—
279C4×Q8—21no—
280C4×Q8—21no—
281C4×Q8C2×C3×D312yes—
282C4×Q8C2×C3×D312yes—
283C4×D4—32no—
284C4×D4—61no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4C2×C3×D311yescharacteristic
287C2×C42—21no—
288C2×C42C2×C3×D311yescharacteristic
289#106—34no—
290C4⋊C8—32no—
291#103—34no—
292#102—34no—
293C22⋊C8—32no—
294C4×C8—32no—
295C23×C3—21no—
296C23×C3—62no—
297C23×C3C2×#6711yescharacteristic
298C23×C3C2×C3×D411yescharacteristic
299C22×D3—22no—
300C3×Q8—28no—
301C3×Q8—24no—
302C3×Q8—24no—
303C3×Q8—24no—
304C3×Q8—22no—
305C3×Q8—22no—
306C3×Q8—24no—
307C3×Q8—122no—
308C3×Q8#23514yescomplemented
309C3×Q8C3×#4114yescomplemented
310C3×D4—64no—
311C3×D4—122no—
312C3×D4—124no—
313C3×D4—122no—
314C2×C3×C4—24no—
315C2×C3×C4—28no—
316C2×C3×C4—24no—
317C2×C3×C4—24no—
318C2×C3×C4—24no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—24no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—21no—
327C2×C3×C4—24no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—41no—
334C2×C3×C4—41no—
335C2×C3×C4—42no—
336C2×C3×C4—44no—
337C2×C3×C4—42no—
338C2×C3×C4—42no—
339C2×C3×C4—62no—
340C2×C3×C4—124no—
341C2×C3×C4#21514yescomplemented
342C2×C3×C4C3×SD1614yescomplemented
343C2×C3×C4C2×#6711yescharacteristic
344C2×C3×C4C2×#6711yescharacteristic
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C2×#6711yescharacteristic
348C2×C3×C4C2×C3×D411yescharacteristic
349C2×C3×C4C2×C3×D411yescharacteristic
350C2×C3×C4C2×C3×D411yescharacteristic
351C2×C3×C4C2×C3×D411yescharacteristic
352C2×C3×C4C2×C3×D411yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354C2×C3×C4C24×C311yescharacteristic
355#67—44no—
356C2×Dic3—22no—
357D12—24no—
358D12—42no—
359D12—42no—
360C4×D3—44no—
361Dic6—42no—
362C3×C8—64no—
363C3⋊C8—24no—
364C2×C32—22no—
365C2×C32#52511yescharacteristic
366C2×C32C22×SD1611yescharacteristic
367C2×C32#57511yescharacteristic
368C3×D3—82no—
369#41—124no—
370C2×Q8—24no—
371C2×Q8—21no—
372C2×Q8—61no—
373C2×Q8C22×C3×D312yes—
374C2×D4—32no—
375C2×D4—62no—
376C2×D4—61no—
377C2×D4—61no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—62no—
381C22×C4C3×#6711yescharacteristic
382C22×C4C3×#6711yescharacteristic
383C22×C4C22×C3×D311yescharacteristic
384SD16—68no—
385C2×C8—34no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—21no—
389C4⋊C4—32no—
390C4⋊C4—61no—
391C4⋊C4C22×C3×D312yes—
392C22⋊C4—62no—
393C22⋊C4—62no—
394C42—22no—
395C42—22no—
396C42C3×#6711yescharacteristic
397C42C3×#6711yescharacteristic
398C42C22×C3×D311yescharacteristic
399C42C22×C3×D311yescharacteristic
400C22×C3—22no—
401C22×C3—22no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—22no—
407C22×C3—21no—
408C22×C3—122no—
409C22×C3—122no—
410C22×C3—122no—
411C22×C3C2×#21512yes—
412C22×C3C2×C3×SD1612yes—
413C22×C3C22×#6711yescharacteristic
414C22×C3C22×C3×D411yescharacteristic
415C2×D3—42no—
416C2×D3—42no—
417C2×D3—42no—
418C3×C4—28no—
419C3×C4—22no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—24no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—24no—
427C3×C4—21no—
428C3×C4—22no—
429C3×C4—22no—
430C3×C4—22no—
431C3×C4—41no—
432C3×C4—41no—
433C3×C4—44no—
434C3×C4—42no—
435C3×C4—42no—
436C3×C4—122no—
437C3×C4C2×#21512yes—
438C3×C4C2×#21512yes—
439C3×C4C2×C3×SD1612yes—
440C3×C4C2×C3×SD1612yes—
441C3×C4C2×#23512yes—
442C3×C4C2×C3×#4112yes—
443Dic3—42no—
444C32#310311yescharacteristic, complemented, Sylow
445C23—62no—
446C23C2×C3×#6711yescharacteristic
447Q8—24no—
448Q8—22no—
449Q8—122no—
450Q8C3×#23514yescomplemented
451D4—64no—
452D4—122no—
453D4—124no—
454D4—122no—
455C2×C4—24no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—41no—
460C2×C4—42no—
461C2×C4—62no—
462C2×C4—124no—
463C2×C4C3×#21514yescomplemented
464C2×C4C2×C3×#6711yescharacteristic
465C2×C4C2×C3×#6711yescharacteristic
466C2×C4C2×C3×#6711yescharacteristic
467C2×C4C2×C3×#6711yescharacteristic
468C2×C4C2×C3×#6711yescharacteristic
469C2×C4C23×C3×D311yescharacteristic
470C8—64no—
471C2×C3—24no—
472C2×C3—22no—
473C2×C3—22no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—242no—
478C2×C3#579111yescharacteristic
479C2×C3C22×#21511yescharacteristic
480C2×C3#582211yescharacteristic
481C2×C3C3×#52511yescharacteristic
482C2×C3C22×C3×SD1611yescharacteristic
483C2×C3C3×#57511yescharacteristic
484D3—82no—
485C22—21no—
486C22—21no—
487C22—122no—
488C22—122no—
489C22—122no—
490C22C2×C3×#21512yes—
491C22C22×C3×#6711yescharacteristic
492C4—24no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—42no—
497C4—122no—
498C4C2×C3×#21512yes—
499C4C2×C3×#21512yes—
500C4C2×C3×#23512yes—
501C3—21no—
502C3#8244211yescharacteristic, direct product factor
503C3C3×#310311yescharacteristic, complemented
504C2—22no—
505C2—242no—
506C2C3×#579111yescharacteristic
507C2C22×C3×#21511yescharacteristic
508C2C3×#582211yescharacteristic
subgroupG/H
centerC2×C3×C4C2×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×C4×Q8C2
socleC22×C32C22×D4
prime radicalC3×#5477C2
hypercenterC2×C3×C4×Q8D3
hypocenterC3C3×#3103
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C2×C3×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×Q8C2semidirect
3. C3×#5227C2semidirect
4. C3×#5027C2semidirect
5. C3×C4×#215C2semidirect
6. C3×#5020C2semidirect
7. C3×#4968C2semidirect
8. C3×#4925C2semidirect
10. #82442C3direct (N × H)
37. C2×C3×C4×Q8D3semidirect
38. C2×C3×C4×Q8C2×C3semidirect
46. #5227C2×C3semidirect
47. #5027C2×C3semidirect
48. C4×#215C2×C3semidirect
49. #5020C2×C3semidirect
50. #4968C2×C3semidirect
51. #4925C2×C3semidirect
145. C32×Q8#41semidirect
152. C2×C32×C4SD16semidirect
168. C2×C4×Q8C3×D3semidirect
308. C3×Q8#235semidirect
309. C3×Q8C3×#41semidirect
341. C2×C3×C4#215semidirect
342. C2×C3×C4C3×SD16semidirect
444. C32#3103semidirect
450. Q8C3×#235semidirect
463. C2×C4C3×#215semidirect
502. C3#82442direct (N × H)
503. C3C3×#3103semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×Q82
C3×#54772
C3×#52272
C3×#50272
C3×C4×#2152
C3×#50202
C3×#49682
C3×#49252
C3×#31033
#824423