Finite Group Databasebeta

← C3×#71651 #11788467

Subgroups — C3×#71651 #11788467

Order 1152.

861 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#518C211yesmaximal, characteristic, complemented
2C2×C3×#932C211yesmaximal, characteristic
3C3×#5215C211yesmaximal, characteristic, complemented
4C3×#5006C211yesmaximal, characteristic, complemented
5C3×#5005C211yesmaximal, characteristic, complemented
6C3×#4533C211yesmaximal, characteristic, complemented
7C3×#4531C211yesmaximal, characteristic, complemented
8C3×#1904—31nomaximal
9#71651C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C32×C4×D4—22no—
13C32×C4×D4—22no—
14C32×#117C2211yescharacteristic
15C32×#117C2211yescharacteristic
16C2×C32×C22⋊C4—22no—
17C2×C3×#214C412yescomplemented
18C3×#932—22no—
19C3×#932—22no—
20C2×C3×#213C412yescomplemented
21C3×#926C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C3×#832—22no—
25C3×#806—22no—
26C3×#805—22no—
27C2×C3×AGL(1,ℤ/8)—31no—
28C3×#518—21no—
29C3×#518D311yescharacteristic, complemented
30C3×#518C2×C311yescharacteristic, complemented
31C2×#932C2×C311yescharacteristic
32C3×#421—31no—
33C3×#418—31no—
34C3×#410—31no—
35#5215C2×C311yescharacteristic, complemented
36#5006C2×C311yescharacteristic, complemented
37#5005C2×C311yescharacteristic, complemented
38C3×#344—31no—
39C3×H(3,ℤ/4)—31no—
40#4533C2×C311yescharacteristic, complemented
41#4531C2×C311yescharacteristic, complemented
42C24×C32—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4C2×C412yes—
47C2×C32×D4D412yes—
48C2×C32×D4D412yes—
49C22×C32×C4—24no—
50C22×C32×C4C2311yescharacteristic
51C2×C3×#67—21no—
52C3×#235—21no—
53C3×#235—21no—
54C3×#235—21no—
55C3×#235—21no—
56C2×C3×D12C2×C411yescharacteristic, complemented
57C2×C3×C4×D3—21no—
58C2×C3×Dic6C2×C411yescharacteristic, complemented
59C32×C4⋊C4—21no—
60C32×C4⋊C4—21no—
61C32×C22⋊C4—24no—
62C32×C22⋊C4—21no—
63C32×C22⋊C4D412yes—
64C32×C42—21no—
65C32×C42D412yes—
66C3×#217—21no—
67C3×#214—24no—
68C3×#213—24no—
69C3×C4⋊Dic3—21no—
70C3×C4×Dic3—21no—
71C3×#208—21no—
72C3×#208—21no—
73C3×#208—21no—
74C3×#208—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8C2×C412yescomplemented
77#1904—31noSylow
78C2×C3×#41—31no—
79C22×C3×D4—21no—
80C22×C3×D4C2×D311yescharacteristic
81C22×C3×D4C22×C311yescharacteristic
82C2×#235C22×C311yescharacteristic
83C3×AGL(1,ℤ/8)—62no—
84C3×AGL(1,ℤ/8)—62no—
85C2×C3×SD16—32no—
86C2×C3×D8—32no—
87C2×C3×M16—31no—
88C2×C3×M16—31no—
89C3×C4×D4—24no—
90C3×C4×D4—24no—
91C3×C4×D4—22no—
92C3×C4×D4—22no—
93C3×C4×D4—22no—
94C3×C4×D4—22no—
95C3×#117—21no—
96C3×#117—21no—
97C3×#117—31no—
98C3×#117C2×D311yescharacteristic
99C3×#117C2×D311yescharacteristic
100C3×#117C22×C311yescharacteristic
101C3×#117C22×C311yescharacteristic
102C2×C3×C22⋊C4—24no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—22no—
105C2×#214C3×C412yescomplemented
106#932—22no—
107#932—22no—
108C2×#213C3×C412yescomplemented
109#926C22×C311yescharacteristic
110C2×#208C22×C311yescharacteristic
111C2×#208C22×C311yescharacteristic
112C3×#104—62no—
113C3×#102—62no—
114C3×#99—62no—
115#832—22no—
116#806—22no—
117#805—22no—
118C23×C32—22no—
119C23×C32—22no—
120C23×C32—22no—
121C23×C32—82no—
122C23×C32C2×D411yescharacteristic
123C22×C3×D3—21no—
124C32×D4—22no—
125C32×D4—22no—
126C32×D4—22no—
127C32×D4C22⋊C414yes—
128C2×C32×C4—22no—
129C2×C32×C4—22no—
130C2×C32×C4—84no—
131C2×C32×C4C22×C411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C3×#67—41no—
138C3×#67—41no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—41no—
141C3×D12—21no—
142C3×D12—21no—
143C3×C4×D3—41no—
144C3×C4×D3—41no—
145C3×Dic6—21no—
146C3×Dic6—21no—
147C3×C3⋊C8—22no—
148C3×C3⋊C8—41no—
149C2×AGL(1,ℤ/8)—31no—
150#518C3×D311yescharacteristic, complemented
151#421—31no—
152#418—31no—
153#410—31no—
154#344—31no—
155H(3,ℤ/4)—31no—
156C24×C3—22no—
157C24×C3—21no—
158C24×C3—21no—
159C3×#41—61no—
160C3×#41—61no—
161C3×#41—61no—
162C3×#41—61no—
163C2×C3×Q8—31no—
164C2×C3×D4—22no—
165C2×C3×D4—22no—
166C2×C3×D4—22no—
167C2×C3×D4—21no—
168C2×C3×D4—21no—
169C2×C3×D4—21no—
170C2×C3×D4—21no—
171C2×C3×D4—21no—
172C2×C3×D4—21no—
173C2×C3×D4—22no—
174C2×C3×D4—22no—
175C2×C3×D4—22no—
176C2×C3×D4—31no—
177C2×C3×D4—61no—
178C2×C3×D4C4×D312yes—
179C2×C3×D4D1212yes—
180C2×C3×D4#6712yes—
181C2×C3×D4C2×C3×C412yes—
182C2×C3×D4C3×D412yes—
183C2×C3×D4C3×D412yes—
184C22×C3×C4—28no—
185C22×C3×C4—24no—
186C22×C3×C4—24no—
187C22×C3×C4—21no—
188C22×C3×C4—61no—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C23×C311yescharacteristic
191C2×#67—21no—
192#235—21no—
193#235—21no—
194#235—21no—
195#235—21no—
196C2×D12C2×C3×C411yescharacteristic, complemented
197C2×C4×D3—21no—
198C2×Dic6C2×C3×C411yescharacteristic, complemented
199C3×SD16—64no—
200C3×D8—64no—
201C3×M16—61no—
202C3×M16—61no—
203C3×M16—61no—
204C3×M16—61no—
205C2×C3×C8—32no—
206C2×C3×C8—61no—
207C3×C4⋊C4—22no—
208C3×C4⋊C4—22no—
209C3×C4⋊C4—21no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—61no—
214C3×C22⋊C4—22no—
215C3×C22⋊C4—28no—
216C3×C22⋊C4—24no—
217C3×C22⋊C4—24no—
218C3×C22⋊C4—21no—
219C3×C22⋊C4—21no—
220C3×C22⋊C4—22no—
221C3×C22⋊C4—61no—
222C3×C22⋊C4#6712yes—
223C3×C22⋊C4C3×D412yes—
224C3×C42—22no—
225C3×C42—21no—
226C3×C42—21no—
227C3×C42—22no—
228C3×C42—61no—
229C3×C42#6712yes—
230C3×C42C3×D412yes—
231#217—21no—
232#214—24no—
233#213—24no—
234C4⋊Dic3—21no—
235C4×Dic3—21no—
236#208—21no—
237#208—21no—
238#208—21no—
239#208—21no—
240C2×C3⋊C8—21no—
241C2×C3⋊C8C2×C3×C412yescomplemented
242C22×C32—24no—
243C22×C32—41no—
244C22×C32—44no—
245C22×C32—82no—
246C22×C32—82no—
247C22×C32C4×D411yescharacteristic
248C22×C32#12011yescharacteristic
249C22×C32#12111yescharacteristic
250C2×C3×D3—41no—
251C2×C3×D3—81no—
252C32×C4—42no—
253C32×C4—42no—
254C32×C4C2×C22⋊C411yescharacteristic
255C32×C4C4×D411yescharacteristic
256C32×C4#12111yescharacteristic
257C32×C4#12311yescharacteristic
258C3×Dic3—41no—
259C3×Dic3—81no—
260C2×#41—31no—
261C22×D4C2×C3×D311yescharacteristic
262AGL(1,ℤ/8)—62no—
263AGL(1,ℤ/8)—62no—
264C2×SD16—32no—
265C2×D8—32no—
266C2×M16—31no—
267C2×M16—31no—
268C4×D4—22no—
269C4×D4—22no—
270#117—31no—
271#117C2×C3×D311yescharacteristic
272#117C2×C3×D311yescharacteristic
273C2×C22⋊C4—22no—
274#104—62no—
275#102—62no—
276#99—62no—
277C23×C3—24no—
278C23×C3—24no—
279C23×C3—24no—
280C23×C3—22no—
281C23×C3—22no—
282C23×C3—22no—
283C23×C3—22no—
284C23×C3—22no—
285C23×C3—22no—
286C23×C3—21no—
287C23×C3—61no—
288C23×C3—82no—
289C23×C3—82no—
290C23×C3—84no—
291C23×C3C2×#6711yescharacteristic
292C23×C3C2×C3×D411yescharacteristic
293C22×D3—21no—
294C3×Q8—61no—
295C3×Q8—61no—
296C3×D4—24no—
297C3×D4—24no—
298C3×D4—24no—
299C3×D4—22no—
300C3×D4—22no—
301C3×D4—22no—
302C3×D4—22no—
303C3×D4—22no—
304C3×D4—22no—
305C3×D4—24no—
306C3×D4—61no—
307C3×D4—61no—
308C3×D4—121no—
309C3×D4—121no—
310C3×D4(C2×D3)⋊C414yes—
311C3×D4C3×C22⋊C414yes—
312C2×C3×C4—24no—
313C2×C3×C4—24no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—61no—
325C2×C3×C4—88no—
326C2×C3×C4—84no—
327C2×C3×C4—84no—
328C2×C3×C4—121no—
329C2×C3×C4—121no—
330C2×C3×C4—121no—
331C2×C3×C4C2×C4×D311yescharacteristic
332C2×C3×C4C2×D1211yescharacteristic
333C2×C3×C4#23511yescharacteristic
334C2×C3×C4#23511yescharacteristic
335C2×C3×C4C2×#6711yescharacteristic
336C2×C3×C4C2×#6711yescharacteristic
337C2×C3×C4C22×C3×C411yescharacteristic
338C2×C3×C4C2×C3×D411yescharacteristic
339C2×C3×C4C2×C3×D411yescharacteristic
340C2×C3×C4C2×C3×D411yescharacteristic
341C2×C3×C4C3×#4111yescharacteristic
342C2×C3×C4C3×#4111yescharacteristic
343#67—41no—
344#67—41no—
345C2×Dic3—21no—
346C2×Dic3—41no—
347D12—21no—
348D12—21no—
349C4×D3—41no—
350C4×D3—41no—
351Dic6—21no—
352Dic6—21no—
353C3×C8—62no—
354C3×C8—121no—
355C3⋊C8—22no—
356C3⋊C8—41no—
357C2×C32—21no—
358C2×C32—21no—
359C2×C32—21no—
360C2×C32—44no—
361C2×C32#38611yescharacteristic
362C3×D3—81no—
363C24—21no—
364#41—61no—
365#41—61no—
366#41—61no—
367#41—61no—
368C2×Q8—31no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—31no—
373C2×D4—61no—
374C2×D4C3×C4×D312yes—
375C2×D4C3×D1212yes—
376C2×D4C3×#6712yes—
377C22×C4—24no—
378C22×C4—61no—
379C22×C4C22×C3×D311yescharacteristic
380SD16—64no—
381D8—64no—
382M16—61no—
383M16—61no—
384M16—61no—
385M16—61no—
386C2×C8—32no—
387C2×C8—61no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—61no—
391C22⋊C4—24no—
392C22⋊C4—21no—
393C22⋊C4—61no—
394C22⋊C4C3×#6712yes—
395C42—21no—
396C42—61no—
397C42C3×#6712yes—
398C22×C3—28no—
399C22×C3—24no—
400C22×C3—24no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—41no—
405C22×C3—41no—
406C22×C3—48no—
407C22×C3—44no—
408C22×C3—44no—
409C22×C3—42no—
410C22×C3—82no—
411C22×C3—82no—
412C22×C3—82no—
413C22×C3—82no—
414C22×C3—84no—
415C22×C3—84no—
416C22×C3—121no—
417C22×C3—241no—
418C22×C3C4×#6711yescharacteristic
419C22×C3#93011yescharacteristic
420C22×C3#95311yescharacteristic
421C22×C3C3×C4×D411yescharacteristic
422C22×C3C3×#12011yescharacteristic
423C22×C3C3×#12111yescharacteristic
424C2×D3—41no—
425C2×D3—81no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—44no—
431C3×C4—44no—
432C3×C4—42no—
433C3×C4—42no—
434C3×C4—42no—
435C3×C4—42no—
436C3×C4—121no—
437C3×C4—241no—
438C3×C4C2×(C2×D3)⋊C411yescharacteristic
439C3×C4C4×#6711yescharacteristic
440C3×C4#92911yescharacteristic
441C3×C4#93011yescharacteristic
442C3×C4C2×C3×C22⋊C411yescharacteristic
443C3×C4C3×C4×D411yescharacteristic
444C3×C4C3×#12111yescharacteristic
445C3×C4C3×#12311yescharacteristic
446Dic3—41no—
447Dic3—81no—
448C32#190411yescharacteristic, complemented, Sylow
449C23—22no—
450C23—22no—
451C23—22no—
452C23—61no—
453C23—82no—
454C23C2×C3×#6711yescharacteristic
455Q8—61no—
456Q8—61no—
457D4—22no—
458D4—22no—
459D4—22no—
460D4—61no—
461D4—61no—
462D4—121no—
463D4—121no—
464D4C3×(C2×D3)⋊C414yes—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—61no—
468C2×C4—84no—
469C2×C4—121no—
470C2×C4—121no—
471C2×C4—121no—
472C2×C4C2×C3×C4×D311yescharacteristic
473C2×C4C2×C3×D1211yescharacteristic
474C2×C4C3×#23511yescharacteristic
475C2×C4C3×#23511yescharacteristic
476C2×C4C2×C3×#6711yescharacteristic
477C2×C4C2×C3×#6711yescharacteristic
478C8—62no—
479C8—121no—
480C2×C3—22no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—41no—
489C2×C3—41no—
490C2×C3—48no—
491C2×C3—44no—
492C2×C3—44no—
493C2×C3—241no—
494C2×C3#521311yescharacteristic
495C2×C3C3×#38611yescharacteristic
496D3—81no—
497C22—24no—
498C22—41no—
499C22—44no—
500C22—82no—
501C22—82no—
502C22—121no—
503C22—241no—
504C22C3×C4×#6711yescharacteristic
505C22C3×#93011yescharacteristic
506C22C3×#95311yescharacteristic
507C4—42no—
508C4—42no—
509C4—121no—
510C4—241no—
511C4C2×C3×(C2×D3)⋊C411yescharacteristic
512C4C3×C4×#6711yescharacteristic
513C4C3×#92911yescharacteristic
514C4C3×#93011yescharacteristic
515C3—21no—
516C3#7165111yescharacteristic, direct product factor
517C3C3×#190411yescharacteristic, complemented
518C2—21no—
519C2—21no—
520C2—21no—
521C2—44no—
522C2—241no—
523C2C3×#521311yescharacteristic
subgroupG/H
centerC2×C3#5213
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#518C2
socleC2×C32#386
prime radicalC2×C3×#932C2
cosocleC22×C3×C4C23×C3
hypercenterC3×#518D3
hypocenterC3C3×#1904
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#518

Complements

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

NH ≅ G/Ntype
1. C32×#518C2semidirect
3. C3×#5215C2semidirect
4. C3×#5006C2semidirect
5. C3×#5005C2semidirect
6. C3×#4533C2semidirect
7. C3×#4531C2semidirect
9. #71651C3direct (N × H)
17. C2×C3×#214C4semidirect
20. C2×C3×#213C4semidirect
29. C3×#518D3semidirect
30. C3×#518C2×C3semidirect
35. #5215C2×C3semidirect
36. #5006C2×C3semidirect
37. #5005C2×C3semidirect
40. #4533C2×C3semidirect
41. #4531C2×C3semidirect
56. C2×C3×D12C2×C4semidirect
58. C2×C3×Dic6C2×C4semidirect
76. C2×C3×C3⋊C8C2×C4semidirect
105. C2×#214C3×C4semidirect
108. C2×#213C3×C4semidirect
150. #518C3×D3semidirect
196. C2×D12C2×C3×C4semidirect
198. C2×Dic6C2×C3×C4semidirect
241. C2×C3⋊C8C2×C3×C4semidirect
448. C32#1904semidirect
516. C3#71651direct (N × H)
517. C3C3×#1904semidirect

Maximal subgroups

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

subgroupindex
C32×#5182
C2×C3×#9322
C3×#52152
C3×#50062
C3×#50052
C3×#45332
C3×#45312
C3×#19043
#716513