Finite Group Databasebeta

← C3×#80853 #11876961

Subgroups — C3×#80853 #11876961

Order 1152.

957 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5596C212yesmaximal, complemented
2C32×#469C211yesmaximal, characteristic, complemented
3C3×#5152C211yesmaximal, characteristic, complemented
4C3×#5151C211yesmaximal, characteristic, complemented
5C3×#5135C211yesmaximal, characteristic, complemented
6C3×Dic3×M16C211yesmaximal, characteristic, complemented
7C3×#5039C212yesmaximal, complemented
8C3×#4869C211yesmaximal, characteristic, complemented
9C3×#4855C211yesmaximal, characteristic, complemented
10C3×#4785C212yesmaximal, complemented
11C3×#4760C212yesmaximal, complemented
12C3×#3184—31nomaximal
13#80853C311yesmaximal, characteristic, direct product factor
14C2×C3×#237—22no—
15C2×C32×D8C2211yescharacteristic
16C2×C32×M16C2211yescharacteristic
17C32×#121C2212yes—
18C3×#940C2212yes—
19C3×#939—22no—
20C3×D4×Dic3C2212yes—
21C2×C3×#213C2212yes—
22C3×#930C2212yes—
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C2×C3×D24C2211yescharacteristic
26C3×#893C2212yes—
27C3×#888C2212yes—
28C3×#885—22no—
29C3×#67⋊C4—22no—
30C32×#106C2211yescharacteristic
31C32×#102C2212yes—
32C3×#832C2212yes—
33C3×#821C2212yes—
34C3×#817C2211yescharacteristic
35C3×#815C2211yescharacteristic
36C3×#815C2211yescharacteristic
37C3×C8×Dic3C2211yescharacteristic
38C3×C8×Dic3C2211yescharacteristic
39C3×#809C2212yes—
40C3×#808C2212yes—
41C3×#532—32no—
42#5596C2×C312yescomplemented
43C3×#498—31no—
44C3×#493—31no—
45C3×#486—32no—
46C3×#469—21no—
47C3×#469—31no—
48C3×#469—32no—
49C3×#469D311yescharacteristic, complemented
50C3×#469C2×C311yescharacteristic, complemented
51C3×#442—31no—
52C3×#442—31no—
53C3×#442—32no—
54C3×C4×M16—31no—
55#5152C2×C311yescharacteristic, complemented
56#5151C2×C311yescharacteristic, complemented
57#5135C2×C311yescharacteristic, complemented
58Dic3×M16C2×C311yescharacteristic, complemented
59#5039C2×C312yescomplemented
60#4869C2×C311yescharacteristic, complemented
61#4855C2×C311yescharacteristic, complemented
62#4785C2×C312yescomplemented
63#4760C2×C312yescomplemented
64C2×C32×D4—22no—
65C2×C32×D4C2312yes—
66C22×C32×C4C2311yescharacteristic
67C2×C3×#67—22no—
68C2×C3×#67—22no—
69C2×C3×#67—22no—
70C22×C3×Dic3—22no—
71C22×C3×Dic3D412yes—
72C3×#237—48no—
73C2×C3×D12C2312yes—
74C2×C3×C4×D3—22no—
75C2×C3×Dic6—22no—
76C32×D8—22no—
77C32×M16—22no—
78C2×C32×C8C2311yescharacteristic
79C2×C32×C8C2311yescharacteristic
80C32×C4⋊C4C2312yes—
81C32×C22⋊C4—22no—
82C3×#217—22no—
83C3×#213—24no—
84C3×(C2×D3)⋊C4—22no—
85C3×(C2×D3)⋊C4—22no—
86C3×C4⋊Dic3C2312yes—
87C3×Dic3⋊C4—22no—
88C3×C4×Dic3D412yes—
89C3×C4×Dic3C2311yescharacteristic
90C3×C4×Dic3C2311yescharacteristic
91C3×#208—22no—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94C3×D24—22no—
95#3184—31noSylow
96C2×C3×#41—62no—
97C2×#237—22no—
98C2×C3×D8—21no—
99C2×C3×D8—32no—
100C2×C3×D8—31no—
101C2×C3×D8C2×D311yescharacteristic
102C2×C3×D8C22×C311yescharacteristic
103C2×C3×M16—21no—
104C2×C3×M16—31no—
105C2×C3×M16C2×D311yescharacteristic
106C2×C3×M16C22×C311yescharacteristic
107C3×C4⋊Q8—32no—
108C3×#127—32no—
109C3×#124—62no—
110C3×#121—22no—
111C3×#121—32no—
112C3×#121—62no—
113C3×#121C2×D312yes—
114C3×#121C22×C312yes—
115C3×C4×D4—32no—
116C3×C4×D4—32no—
117C3×C4×D4—62no—
118C2×C3×C42—31no—
119#940C22×C312yes—
120#939—22no—
121D4×Dic3C22×C312yes—
122C2×#213C22×C312yes—
123#930C22×C312yes—
124C2×C4×Dic3C22×C311yescharacteristic
125C2×#208C22×C311yescharacteristic
126C2×D24C22×C311yescharacteristic
127#893C22×C312yes—
128#888C22×C312yes—
129#885—22no—
130#67⋊C4—22no—
131C3×#106—21no—
132C3×#106—31no—
133C3×#106—32no—
134C3×#106C2×D311yescharacteristic
135C3×#106C22×C311yescharacteristic
136C3×#102—22no—
137C3×#102—32no—
138C3×#102—32no—
139C3×#102—32no—
140C3×#102C2×D312yes—
141C3×#102C22×C312yes—
142C3×#97—31no—
143C3×#97—31no—
144C3×C4×C8—31no—
145C3×C4×C8—31no—
146#832C22×C312yes—
147#821C22×C312yes—
148#817C22×C311yescharacteristic
149#815C22×C311yescharacteristic
150#815C22×C311yescharacteristic
151C8×Dic3C22×C311yescharacteristic
152C8×Dic3C22×C311yescharacteristic
153#809C22×C312yes—
154#808C22×C312yes—
155C23×C32—22no—
156C23×C32C2×D411yescharacteristic
157C22×C3×D3—22no—
158C32×D4—22no—
159C32×D4—22no—
160C32×D4—44no—
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4—22no—
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2411yescharacteristic
166C3×#67—44no—
167C3×#67—44no—
168C3×#67—44no—
169C2×C3×Dic3—24no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—44no—
172C2×C3×Dic3C2×D412yes—
173C2×C3×Dic3C2×D412yes—
174C3×D12—22no—
175C3×D12—22no—
176C3×C4×D3—44no—
177C3×Dic6—44no—
178C32×C8—21no—
179C32×C8#4112yescomplemented
180C3×C3⋊C8—21no—
181C3×C3⋊C8#4112yescomplemented
182#532—32no—
183#498—31no—
184#493—31no—
185#486—32no—
186#469—31no—
187#469—32no—
188#469C3×D311yescharacteristic, complemented
189#442—31no—
190#442—31no—
191#442—32no—
192C4×M16—31no—
193C3×#41—128no—
194C2×C3×Q8—62no—
195C2×C3×D4—22no—
196C2×C3×D4—22no—
197C2×C3×D4—22no—
198C2×C3×D4—32no—
199C2×C3×D4—42no—
200C2×C3×D4—62no—
201C2×C3×D4—62no—
202C2×C3×D4—62no—
203C2×C3×D4C22×D312yes—
204C2×C3×D4C23×C312yes—
205C22×C3×C4—21no—
206C22×C3×C4—32no—
207C22×C3×C4—62no—
208C22×C3×C4—62no—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C23×C311yescharacteristic
211C2×#67—22no—
212C2×#67—22no—
213C2×#67—22no—
214C22×Dic3—22no—
215C22×Dic3C3×D412yes—
216#237—48no—
217C2×D12C23×C312yes—
218C2×C4×D3—22no—
219C2×Dic6—22no—
220C3×D8—22no—
221C3×D8—22no—
222C3×D8—42no—
223C3×D8—64no—
224C3×D8—62no—
225C3×M16—22no—
226C3×M16—22no—
227C3×M16—42no—
228C3×M16—62no—
229C2×C3×C8—21no—
230C2×C3×C8—21no—
231C2×C3×C8—31no—
232C2×C3×C8—31no—
233C2×C3×C8C22×D311yescharacteristic
234C2×C3×C8C22×D311yescharacteristic
235C2×C3×C8C23×C311yescharacteristic
236C2×C3×C8C23×C311yescharacteristic
237C3×C4⋊C4—22no—
238C3×C4⋊C4—32no—
239C3×C4⋊C4—62no—
240C3×C4⋊C4C22×D312yes—
241C3×C4⋊C4C23×C312yes—
242C3×C22⋊C4—22no—
243C3×C22⋊C4—22no—
244C3×C22⋊C4—42no—
245C3×C22⋊C4—62no—
246C3×C22⋊C4—62no—
247C3×C22⋊C4—62no—
248C3×C42—32no—
249C3×C42—31no—
250C3×C42—31no—
251#217—22no—
252#213—24no—
253(C2×D3)⋊C4—22no—
254(C2×D3)⋊C4—22no—
255C4⋊Dic3C23×C312yes—
256Dic3⋊C4—22no—
257C4×Dic3C3×D412yes—
258C4×Dic3C23×C311yescharacteristic
259C4×Dic3C23×C311yescharacteristic
260#208—22no—
261C2×C3⋊C8C23×C311yescharacteristic
262C2×C3⋊C8C23×C311yescharacteristic
263D24—22no—
264C22×C32—21no—
265C22×C32—22no—
266C22×C32—42no—
267C22×C32—42no—
268C22×C32—42no—
269C22×C32C22×D411yescharacteristic
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C2×C3×D3—42no—
273C32×C4—21no—
274C32×C4—42no—
275C32×C4C2×#4111yescharacteristic
276C32×C4C2×#4111yescharacteristic
277C3×Dic3—22no—
278C3×Dic3—42no—
279C3×Dic3AGL(1,ℤ/8)14yes—
280C2×#41—62no—
281C2×D8—32no—
282C2×D8—31no—
283C2×D8C2×C3×D311yescharacteristic
284C2×M16—31no—
285C2×M16C2×C3×D311yescharacteristic
286C4⋊Q8—32no—
287#127—32no—
288#124—62no—
289#121—32no—
290#121—62no—
291#121C2×C3×D312yes—
292C4×D4—32no—
293C4×D4—32no—
294C4×D4—62no—
295C2×C42—31no—
296#106—31no—
297#106—32no—
298#106C2×C3×D311yescharacteristic
299#102—32no—
300#102—32no—
301#102—32no—
302#102C2×C3×D312yes—
303#97—31no—
304#97—31no—
305C4×C8—31no—
306C4×C8—31no—
307C23×C3—22no—
308C23×C3—22no—
309C23×C3—21no—
310C23×C3—42no—
311C23×C3—62no—
312C23×C3D3×D411yescharacteristic
313C23×C3C2×C3×D411yescharacteristic
314C22×D3—22no—
315C3×Q8—124no—
316C3×D4—22no—
317C3×D4—22no—
318C3×D4—22no—
319C3×D4—22no—
320C3×D4—42no—
321C3×D4—42no—
322C3×D4—44no—
323C3×D4—44no—
324C3×D4—62no—
325C3×D4—62no—
326C3×D4—84no—
327C3×D4—124no—
328C3×D4—124no—
329C3×D4—124no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—32no—
339C2×C3×C4—32no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—42no—
343C2×C3×C4—64no—
344C2×C3×C4—62no—
345C2×C3×C4—124no—
346C2×C3×C4—124no—
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4C2×C3×D411yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350C2×C3×C4C24×C311yescharacteristic
351#67—44no—
352#67—44no—
353#67—44no—
354C2×Dic3—24no—
355C2×Dic3—22no—
356C2×Dic3—44no—
357C2×Dic3C2×C3×D412yes—
358C2×Dic3C2×C3×D412yes—
359D12—22no—
360D12—22no—
361C4×D3—44no—
362Dic6—44no—
363C3×C8—21no—
364C3×C8—21no—
365C3×C8—22no—
366C3×C8—32no—
367C3×C8—41no—
368C3×C8—61no—
369C3×C8#23712yescomplemented
370C3×C8C3×#4112yescomplemented
371C3⋊C8—21no—
372C3⋊C8C3×#4112yescomplemented
373C2×C32—41no—
374C2×C32—82no—
375C2×C32#53211yescharacteristic
376C2×C32C2×AGL(1,ℤ/8)12yes—
377C3×D3—82no—
378#41—128no—
379C2×Q8—62no—
380C2×D4—22no—
381C2×D4—32no—
382C2×D4—62no—
383C2×D4—62no—
384C2×D4—62no—
385C2×D4C22×C3×D312yes—
386C22×C4—32no—
387C22×C4—62no—
388C22×C4—62no—
389C22×C4C22×C3×D311yescharacteristic
390D8—22no—
391D8—64no—
392D8—62no—
393M16—22no—
394M16—62no—
395C2×C8—31no—
396C2×C8—31no—
397C2×C8C22×C3×D311yescharacteristic
398C2×C8C22×C3×D311yescharacteristic
399C4⋊C4—32no—
400C4⋊C4—62no—
401C4⋊C4C22×C3×D312yes—
402C22⋊C4—22no—
403C22⋊C4—62no—
404C22⋊C4—62no—
405C22⋊C4—62no—
406C42—31no—
407C42—31no—
408C42—32no—
409C22×C3—22no—
410C22×C3—22no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—41no—
415C22×C3—42no—
416C22×C3—42no—
417C22×C3—42no—
418C22×C3—42no—
419C22×C3—42no—
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—82no—
423C22×C3—82no—
424C22×C3—82no—
425C22×C3—122no—
426C22×C3—122no—
427C22×C3—122no—
428C22×C3C2×D3×D411yescharacteristic
429C22×C3C22×C3×D411yescharacteristic
430C2×D3—42no—
431C2×D3—42no—
432C2×D3—42no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—34no—
438C3×C4—41no—
439C3×C4—42no—
440C3×C4—42no—
441C3×C4—62no—
442C3×C4—82no—
443C3×C4—122no—
444C3×C4C2×#23711yescharacteristic
445C3×C4D3×#4111yescharacteristic
446C3×C4C2×C3×#4111yescharacteristic
447C3×C4C2×C3×#4111yescharacteristic
448Dic3—22no—
449Dic3—42no—
450Dic3C3×AGL(1,ℤ/8)14yes—
451C32#318411yescharacteristic, complemented, Sylow
452C23—22no—
453C23—62no—
454C23C3×D3×D411yescharacteristic
455Q8—124no—
456D4—22no—
457D4—22no—
458D4—44no—
459D4—62no—
460D4—62no—
461D4—124no—
462D4—124no—
463D4—124no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—32no—
468C2×C4—32no—
469C2×C4—64no—
470C2×C4—62no—
471C2×C4—124no—
472C2×C4—124no—
473C2×C4C3×D3×D411yescharacteristic
474C2×C4C23×C3×D311yescharacteristic
475C8—21no—
476C8—32no—
477C8—61no—
478C8C3×#23712yescomplemented
479C2×C3—22no—
480C2×C3—21no—
481C2×C3—41no—
482C2×C3—41no—
483C2×C3—81no—
484C2×C3—82no—
485C2×C3—82no—
486C2×C3—162no—
487C2×C3—242no—
488C2×C3#559611yescharacteristic
489C2×C3D3×AGL(1,ℤ/8)12yes—
490C2×C3C3×#53211yescharacteristic
491C2×C3C2×C3×AGL(1,ℤ/8)12yes—
492D3—82no—
493C22—22no—
494C22—21no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—122no—
499C22—122no—
500C22—122no—
501C22C2×C3×D3×D411yescharacteristic
502C4—21no—
503C4—34no—
504C4—42no—
505C4—62no—
506C4—122no—
507C4C2×C3×#23711yescharacteristic
508C4C3×D3×#4111yescharacteristic
509C3—21no—
510C3#8085311yescharacteristic, direct product factor
511C3C3×#318411yescharacteristic, complemented
512C2—41no—
513C2—82no—
514C2—242no—
515C2C3×#559611yescharacteristic
516C2C3×D3×AGL(1,ℤ/8)12yes—
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#469C2
socleC22×C32C22×D4
hypercenterC3×#469D3
hypocenterC3C3×#3184
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#469

Complements

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

NH ≅ G/Ntype
1. C3×#5596C2semidirect
2. C32×#469C2semidirect
3. C3×#5152C2semidirect
4. C3×#5151C2semidirect
5. C3×#5135C2semidirect
6. C3×Dic3×M16C2semidirect
7. C3×#5039C2semidirect
8. C3×#4869C2semidirect
9. C3×#4855C2semidirect
10. C3×#4785C2semidirect
11. C3×#4760C2semidirect
13. #80853C3direct (N × H)
42. #5596C2×C3semidirect
49. C3×#469D3semidirect
50. C3×#469C2×C3semidirect
55. #5152C2×C3semidirect
56. #5151C2×C3semidirect
57. #5135C2×C3semidirect
58. Dic3×M16C2×C3semidirect
59. #5039C2×C3semidirect
60. #4869C2×C3semidirect
61. #4855C2×C3semidirect
62. #4785C2×C3semidirect
63. #4760C2×C3semidirect
179. C32×C8#41semidirect
181. C3×C3⋊C8#41semidirect
188. #469C3×D3semidirect
369. C3×C8#237semidirect
370. C3×C8C3×#41semidirect
372. C3⋊C8C3×#41semidirect
451. C32#3184semidirect
478. C8C3×#237semidirect
510. C3#80853direct (N × H)
511. C3C3×#3184semidirect

Maximal subgroups

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

subgroupindex
C3×#55962
C32×#4692
C3×#51522
C3×#51512
C3×#51352
C3×Dic3×M162
C3×#50392
C3×#48692
C3×#48552
C3×#47852
C3×#47602
C3×#31843
#808533