Finite Group Databasebeta

← C3×#83405 #11866234

Subgroups — C3×#83405 #11866234

Order 1152.

1123 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
1C32×#536C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic
3C22×C3×#215C211yesmaximal, characteristic, complemented
4C3×#5521C211yesmaximal, characteristic, complemented
5C3×#5233C211yesmaximal, characteristic, complemented
6C3×#5225C211yesmaximal, characteristic, complemented
7C3×#5083C214yesmaximal, complemented
8C3×#5057C214yesmaximal, complemented
9C3×#4999C211yesmaximal, characteristic, complemented
10C3×#3042—31nomaximal
11#83405C311yesmaximal, characteristic, direct product factor
12C2×C32×#41C2211yescharacteristic
13C22×C32×Q8C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C32×C4⋊Q8C2212yescomplemented
16C32×#124C2212yescomplemented
17C32×#123—22no—
18C32×C22⋊Q8—22no—
19C32×#117C2211yescharacteristic
20C3×#949—24no—
21C2×C3×#215—24no—
22C2×C3×#215C2214yes—
23C2×C3×#215C2212yes—
24C2×C3×#213C2212yes—
25C3×#926C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27C22×C3×C3⋊C8C2211yescharacteristic
28C3×#893—22no—
29C3×D3×C22⋊C4—22no—
30C3×C4×D12C2214yes—
31C3×#835C2214yescomplemented
32C3×#835C2212yescomplemented
33C3×#832C2212yescomplemented
34C3×C4⋊(C3⋊C8)C2214yescomplemented
35C2×C3×AGL(1,ℤ/8)—31no—
36C22×C3×SD16—31no—
37C3×#536—21no—
38C3×#536D311yescharacteristic, complemented
39C3×#536C2×C311yescharacteristic, complemented
40C3×#518—31no—
41C2×#949C2×C311yescharacteristic
42C22×#215C2×C311yescharacteristic, complemented
43#5521C2×C311yescharacteristic, complemented
44C3×#463—34no—
45C3×#461—34no—
46C3×#424—31no—
47C3×#419—31no—
48C3×#416—31no—
49#5233C2×C311yescharacteristic, complemented
50#5225C2×C311yescharacteristic, complemented
51#5083C2×C314yescomplemented
52#5057C2×C314yescomplemented
53#4999C2×C311yescharacteristic, complemented
54C23×C3×D3—21no—
55C32×#41—22no—
56C32×#41—22no—
57C2×C32×Q8—21no—
58C2×C32×Q8—22no—
59C2×C32×Q8—22no—
60C2×C32×Q8C2312yes—
61C2×C32×Q8C2311yescharacteristic
62C2×C32×D4—21no—
63C2×C32×D4C2311yescharacteristic
64C22×C32×C4—21no—
65C22×C32×C4—21no—
66C22×C32×C4C2311yescharacteristic
67C2×C3×D12—21no—
68C2×C3×D12—22no—
69C2×C3×D12D414yes—
70C2×C3×D12C2312yes—
71C2×C3×C4×D3—24no—
72C32×C4⋊C4—24no—
73C32×C4⋊C4D412yes—
74C32×C22⋊C4—24no—
75C32×C22⋊C4D412yes—
76C32×C42C2312yes—
77C3×#217—21no—
78C3×#215—28no—
79C3×#215—24no—
80C3×#213—24no—
81C3×(C2×D3)⋊C4—24no—
82C3×C4⋊Dic3C2312yes—
83C3×C4×Dic3—21no—
84C3×#208—22no—
85C2×C3×C3⋊C8—22no—
86C2×C3×C3⋊C8C2312yes—
87C2×C3×C3⋊C8C2312yes—
88#3042—31noSylow
89C2×C3×#41—21no—
90C2×C3×#41C2×D311yescharacteristic
91C2×C3×#41C22×C311yescharacteristic
92C22×C3×Q8—21no—
93C22×C3×Q8C2×D311yescharacteristic
94C22×C3×Q8C22×C311yescharacteristic
95C22×C3×D4—31no—
96C22×D12C22×C311yescharacteristic
97C3×AGL(1,ℤ/8)—64no—
98C2×C3×SD16—34no—
99C2×C3×SD16—32no—
100C2×C3×SD16—64no—
101C2×C3×D8—32no—
102C2×C3×M16—31no—
103C22×C3×C8—31no—
104C3×C4⋊Q8—22no—
105C3×C4⋊Q8C2×D312yescomplemented
106C3×C4⋊Q8C22×C312yescomplemented
107C3×#124—22no—
108C3×#124C2×D312yescomplemented
109C3×#124C22×C312yescomplemented
110C3×#123—24no—
111C3×#123—22no—
112C3×#123—22no—
113C3×C22⋊Q8—24no—
114C3×C22⋊Q8—22no—
115C3×C22⋊Q8—22no—
116C3×C4×D4—34no—
117C3×C4×D4—62no—
118C3×#117—21no—
119C3×#117—31no—
120C3×#117C2×D311yescharacteristic
121C3×#117C22×C311yescharacteristic
122C2×C3×C22⋊C4—62no—
123#949—24no—
124C2×#215—24no—
125C2×#215C22×C314yes—
126C2×#215C22×C312yes—
127C2×#213C22×C312yes—
128#926C22×C311yescharacteristic
129C2×#208C22×C311yescharacteristic
130C22×C3⋊C8C22×C311yescharacteristic
131#893—22no—
132D3×C22⋊C4—22no—
133C4×D12C22×C314yes—
134C3×C4⋊C8—34no—
135C3×#103—32no—
136C3×#103—34no—
137C3×#102—32no—
138#835C22×C314yescomplemented
139#835C22×C312yescomplemented
140#832C22×C312yescomplemented
141C4⋊(C3⋊C8)C22×C314yescomplemented
142C23×C32—21no—
143C23×C32C2×D411yescharacteristic
144C22×C3×D3—22no—
145C22×C3×D3—24no—
146C22×C3×D3—82no—
147C32×Q8—22no—
148C32×Q8—21no—
149C32×Q8—22no—
150C32×Q8—21no—
151C32×Q8—42no—
152C32×D4—21no—
153C32×D4—21no—
154C32×D4—42no—
155C2×C32×C4—22no—
156C2×C32×C4—21no—
157C2×C32×C4—42no—
158C2×C32×C4—42no—
159C2×C32×C4C2×D412yes—
160C2×C32×C4C2×D414yes—
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4#4112yes—
163C2×C32×C4C2411yescharacteristic
164C2×C3×Dic3—22no—
165C3×D12—24no—
166C3×D12—22no—
167C3×D12C2×D414yes—
168C3×C4×D3—84no—
169C3×C3⋊C8—22no—
170C3×C3⋊C8—22no—
171C2×AGL(1,ℤ/8)—31no—
172C22×SD16—31no—
173#536C3×D311yescharacteristic, complemented
174#518—31no—
175#463—34no—
176#461—34no—
177#424—31no—
178#419—31no—
179#416—31no—
180C24×C3—61no—
181C23×D3—21no—
182C3×#41—22no—
183C3×#41—22no—
184C3×#41—22no—
185C3×#41—22no—
186C3×#41—42no—
187C3×#41—42no—
188C2×C3×Q8—22no—
189C2×C3×Q8—21no—
190C2×C3×Q8—21no—
191C2×C3×Q8—22no—
192C2×C3×Q8—22no—
193C2×C3×Q8—22no—
194C2×C3×Q8—22no—
195C2×C3×Q8—22no—
196C2×C3×Q8—21no—
197C2×C3×Q8—42no—
198C2×C3×Q8—42no—
199C2×C3×Q8C22×D312yes—
200C2×C3×Q8C22×D311yescharacteristic
201C2×C3×Q8C23×C312yes—
202C2×C3×Q8C23×C311yescharacteristic
203C2×C3×D4—22no—
204C2×C3×D4—21no—
205C2×C3×D4—21no—
206C2×C3×D4—21no—
207C2×C3×D4—34no—
208C2×C3×D4—32no—
209C2×C3×D4—62no—
210C2×C3×D4—61no—
211C2×C3×D4C22×D311yescharacteristic
212C2×C3×D4C23×C311yescharacteristic
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—64no—
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C23×C311yescharacteristic
223C2×D12—21no—
224C2×D12—22no—
225C2×D12C3×D414yes—
226C2×D12C23×C312yes—
227C2×C4×D3—24no—
228C3×SD16—68no—
229C3×SD16—64no—
230C3×D8—64no—
231C3×M16—62no—
232C2×C3×C8—32no—
233C2×C3×C8—32no—
234C2×C3×C8—62no—
235C3×C4⋊C4—28no—
236C3×C4⋊C4—24no—
237C3×C4⋊C4—24no—
238C3×C4⋊C4—22no—
239C3×C4⋊C4—32no—
240C3×C4⋊C4#6712yes—
241C3×C4⋊C4C3×D412yes—
242C3×C22⋊C4—28no—
243C3×C22⋊C4—24no—
244C3×C22⋊C4—24no—
245C3×C22⋊C4—22no—
246C3×C22⋊C4—61no—
247C3×C22⋊C4—64no—
248C3×C22⋊C4#6712yes—
249C3×C22⋊C4C3×D412yes—
250C3×C42—22no—
251C3×C42—61no—
252C3×C42C22×D312yes—
253C3×C42C23×C312yes—
254#217—21no—
255#215—28no—
256#215—24no—
257#213—24no—
258(C2×D3)⋊C4—24no—
259C4⋊Dic3C23×C312yes—
260C4×Dic3—21no—
261#208—22no—
262C2×C3⋊C8—22no—
263C2×C3⋊C8C23×C312yes—
264C2×C3⋊C8C23×C312yes—
265C22×C32—22no—
266C22×C32—41no—
267C22×C32—42no—
268C22×C32#12112yes—
269C22×C32C22×D411yescharacteristic
270C2×C3×D3—24no—
271C2×C3×D3—44no—
272C2×C3×D3—84no—
273C32×C4—24no—
274C32×C4—41no—
275C32×C4—42no—
276C32×C4#12112yes—
277C32×C4C22×D411yescharacteristic
278C32×C4C2×#4111yescharacteristic
279C3×Dic3—42no—
280C2×#41C2×C3×D311yescharacteristic
281C22×Q8C2×C3×D311yescharacteristic
282C22×D4—31no—
283AGL(1,ℤ/8)—64no—
284C2×SD16—34no—
285C2×SD16—32no—
286C2×SD16—64no—
287C2×D8—32no—
288C2×M16—31no—
289C22×C8—31no—
290C4⋊Q8C2×C3×D312yescomplemented
291#124C2×C3×D312yescomplemented
292#123—22no—
293C22⋊Q8—22no—
294C4×D4—34no—
295C4×D4—62no—
296#117—31no—
297#117C2×C3×D311yescharacteristic
298C2×C22⋊C4—62no—
299C4⋊C8—34no—
300#103—32no—
301#103—34no—
302#102—32no—
303C23×C3—22no—
304C23×C3—21no—
305C23×C3—21no—
306C23×C3—21no—
307C23×C3—62no—
308C23×C3—64no—
309C23×C3—242no—
310C23×C3C2×#6711yescharacteristic
311C23×C3C2×C3×D411yescharacteristic
312C22×D3—22no—
313C22×D3—24no—
314C22×D3—82no—
315C3×Q8—22no—
316C3×Q8—21no—
317C3×Q8—22no—
318C3×Q8—21no—
319C3×Q8—22no—
320C3×Q8—21no—
321C3×Q8—22no—
322C3×Q8—21no—
323C3×Q8—42no—
324C3×Q8—42no—
325C3×Q8—41no—
326C3×Q8—41no—
327C3×Q8—44no—
328C3×Q8—42no—
329C3×Q8—42no—
330C3×D4—21no—
331C3×D4—21no—
332C3×D4—21no—
333C3×D4—21no—
334C3×D4—34no—
335C3×D4—41no—
336C3×D4—41no—
337C3×D4—44no—
338C3×D4—42no—
339C3×D4—42no—
340C3×D4—64no—
341C3×D4—62no—
342C2×C3×C4—24no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—21no—
346C2×C3×C4—22no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—21no—
352C2×C3×C4—24no—
353C2×C3×C4—44no—
354C2×C3×C4—44no—
355C2×C3×C4—42no—
356C2×C3×C4—42no—
357C2×C3×C4—42no—
358C2×C3×C4—42no—
359C2×C3×C4—62no—
360C2×C3×C4—244no—
361C2×C3×C4D3×D412yes—
362C2×C3×C4#23712yes—
363C2×C3×C4C2×#6714yes—
364C2×C3×C4C2×#6711yescharacteristic
365C2×C3×C4C2×C3×D412yes—
366C2×C3×C4C2×C3×D414yes—
367C2×C3×C4C2×C3×D411yescharacteristic
368C2×C3×C4C3×#4112yes—
369C2×C3×C4C23×D311yescharacteristic
370C2×C3×C4C24×C311yescharacteristic
371C2×Dic3—22no—
372D12—24no—
373D12—22no—
374D12C2×C3×D414yes—
375C4×D3—84no—
376C3×C8—62no—
377C3×C8—62no—
378C3⋊C8—22no—
379C3⋊C8—22no—
380C2×C32—22no—
381C2×C32—81no—
382C2×C32C2×#12111yescharacteristic
383C2×C32#57712yes—
384C3×D3—44no—
385C24—61no—
386#41—22no—
387#41—22no—
388C2×Q8—21no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8C22×C3×D312yes—
392C2×Q8C22×C3×D311yescharacteristic
393C2×D4—21no—
394C2×D4—32no—
395C2×D4—34no—
396C2×D4—62no—
397C2×D4—61no—
398C2×D4C22×C3×D311yescharacteristic
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—64no—
402C22×C4C22×C3×D311yescharacteristic
403SD16—68no—
404SD16—64no—
405D8—64no—
406M16—62no—
407C2×C8—32no—
408C2×C8—32no—
409C2×C8—62no—
410C4⋊C4—24no—
411C4⋊C4—32no—
412C4⋊C4C3×#6712yes—
413C22⋊C4—24no—
414C22⋊C4—61no—
415C22⋊C4—64no—
416C22⋊C4C3×#6712yes—
417C42—61no—
418C42C22×C3×D312yes—
419C22×C3—22no—
420C22×C3—22no—
421C22×C3—22no—
422C22×C3—21no—
423C22×C3—42no—
424C22×C3—42no—
425C22×C3—44no—
426C22×C3—42no—
427C22×C3—41no—
428C22×C3—42no—
429C22×C3—41no—
430C22×C3—64no—
431C22×C3—124no—
432C22×C3—244no—
433C22×C3#93812yes—
434C22×C3C3×#12112yes—
435C22×C3C22×#6711yescharacteristic
436C22×C3C22×C3×D411yescharacteristic
437C2×D3—24no—
438C2×D3—44no—
439C2×D3—84no—
440C3×C4—24no—
441C3×C4—24no—
442C3×C4—22no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—44no—
446C3×C4—42no—
447C3×C4—44no—
448C3×C4—41no—
449C3×C4—42no—
450C3×C4—41no—
451C3×C4—42no—
452C3×C4—122no—
453C3×C4#93812yes—
454C3×C4C3×#12112yes—
455C3×C4C2×D3×D411yescharacteristic
456C3×C4C2×#23711yescharacteristic
457C3×C4C22×C3×D411yescharacteristic
458C3×C4C2×C3×#4111yescharacteristic
459Dic3—42no—
460C32#304211yescharacteristic, complemented, Sylow
461C23—21no—
462C23—62no—
463C23—64no—
464C23—242no—
465C23C2×C3×#6711yescharacteristic
466Q8—22no—
467Q8—21no—
468Q8—22no—
469Q8—21no—
470Q8—42no—
471D4—21no—
472D4—21no—
473D4—34no—
474D4—42no—
475D4—64no—
476D4—62no—
477C2×C4—22no—
478C2×C4—21no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—62no—
482C2×C4—244no—
483C2×C4C3×D3×D412yes—
484C2×C4C3×#23712yes—
485C2×C4C2×C3×#6714yes—
486C2×C4C2×C3×#6711yescharacteristic
487C2×C4C23×C3×D311yescharacteristic
488C8—62no—
489C8—62no—
490C2×C3—22no—
491C2×C3—22no—
492C2×C3—21no—
493C2×C3—22no—
494C2×C3—42no—
495C2×C3—82no—
496C2×C3—81no—
497C2×C3—81no—
498C2×C3—124no—
499C2×C3C2×#93811yescharacteristic
500C2×C3#583712yes—
501C2×C3C2×C3×#12111yescharacteristic
502C2×C3C3×#57712yes—
503D3—44no—
504C22—22no—
505C22—41no—
506C22—42no—
507C22—64no—
508C22—124no—
509C22—244no—
510C22C3×#93812yes—
511C22C22×C3×#6711yescharacteristic
512C4—24no—
513C4—41no—
514C4—42no—
515C4—122no—
516C4C3×#93812yes—
517C4C2×C3×D3×D411yescharacteristic
518C4C2×C3×#23711yescharacteristic
519C3—21no—
520C3#8340511yescharacteristic, direct product factor
521C3C3×#304211yescharacteristic, complemented
522C2—22no—
523C2—81no—
524C2—124no—
525C2C2×C3×#93811yescharacteristic
526C2C3×#583712yes—
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#536C2
socleC22×C32C22×D4
prime radicalC2×C3×#949C2
hypercenterC3×#536D3
hypocenterC3C3×#3042
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#117 ◁ C3×#536

Complements

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

NH ≅ G/Ntype
1. C32×#536C2semidirect
3. C22×C3×#215C2semidirect
4. C3×#5521C2semidirect
5. C3×#5233C2semidirect
6. C3×#5225C2semidirect
7. C3×#5083C2semidirect
8. C3×#5057C2semidirect
9. C3×#4999C2semidirect
11. #83405C3direct (N × H)
15. C32×C4⋊Q8C22semidirect
16. C32×#124C22semidirect
31. C3×#835C22semidirect
32. C3×#835C22semidirect
33. C3×#832C22semidirect
34. C3×C4⋊(C3⋊C8)C22semidirect
38. C3×#536D3semidirect
39. C3×#536C2×C3semidirect
42. C22×#215C2×C3semidirect
43. #5521C2×C3semidirect
49. #5233C2×C3semidirect
50. #5225C2×C3semidirect
51. #5083C2×C3semidirect
52. #5057C2×C3semidirect
53. #4999C2×C3semidirect
105. C3×C4⋊Q8C2×D3semidirect
106. C3×C4⋊Q8C22×C3semidirect
108. C3×#124C2×D3semidirect
109. C3×#124C22×C3semidirect
138. #835C22×C3semidirect
139. #835C22×C3semidirect
140. #832C22×C3semidirect
141. C4⋊(C3⋊C8)C22×C3semidirect
173. #536C3×D3semidirect
290. C4⋊Q8C2×C3×D3semidirect
291. #124C2×C3×D3semidirect
460. C32#3042semidirect
520. C3#83405direct (N × H)
521. C3C3×#3042semidirect

Maximal subgroups

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

subgroupindex
C32×#5362
C2×C3×#9492
C22×C3×#2152
C3×#55212
C3×#52332
C3×#52252
C3×#50832
C3×#50572
C3×#49992
C3×#30423
#834053