Finite Group Databasebeta

← C3×#83849 #11866312

Subgroups — C3×#83849 #11866312

Order 1152.

1129 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×SD16C211yesmaximal, characteristic, complemented
2C3×#5812C211yesmaximal, characteristic, complemented
3C2×C3×#942C211yesmaximal, characteristic, complemented
4C3×#5805C211yesmaximal, characteristic
5C3×#5215C211yesmaximal, characteristic, complemented
6C3×#5166C214yesmaximal, complemented
7C3×#5163C214yesmaximal, complemented
8C3×#5113C211yesmaximal, characteristic, complemented
9C3×#5102C211yesmaximal, characteristic, complemented
10C3×#3043—31nomaximal
11#83849C311yesmaximal, characteristic, direct product factor
12C22×C32×Q8C2211yescharacteristic
13C22×C32×D4C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic
15C2×C32×SD16—24no—
16C2×C32×SD16C2214yes—
17C22×C32×C8C2211yescharacteristic
18C3×#953—22no—
19C3×Q8×Dic3—22no—
20C3×Q8×Dic3C2214yescomplemented
21C2×C3×#216C2212yescomplemented
22C3×#942—24no—
23C2×C3×#215C2212yescomplemented
24C3×#940C2212yes—
25C3×#938—22no—
26C3×#936C2212yes—
27C3×#926—22no—
28C3×#926C2211yescharacteristic
29C3×#926C2211yescharacteristic
30C2×C3×#208C2211yescharacteristic
31C3×#832C2214yes—
32C3×#821C2212yescomplemented
33C3×#816C2212yescomplemented
34C3×Dic3⋊C8C2214yescomplemented
35C2×C3×#137—31no—
36C22×C3×SD16—21no—
37C22×C3×SD16D311yescharacteristic, complemented
38C22×C3×SD16C2×C311yescharacteristic, complemented
39C3×#535—31no—
40C3×#519—31no—
41#5812C2×C311yescharacteristic, complemented
42C2×#942C2×C311yescharacteristic, complemented
43#5805C2×C311yescharacteristic
44C3×#464—34no—
45C3×#460—34no—
46C3×#424—31no—
47C3×#418—31no—
48C3×#416—31no—
49#5215C2×C311yescharacteristic, complemented
50#5166C2×C314yescomplemented
51#5163C2×C314yescomplemented
52#5113C2×C311yescharacteristic, complemented
53#5102C2×C311yescharacteristic, complemented
54C24×C32—21no—
55C2×C32×Q8—21no—
56C2×C32×Q8—22no—
57C2×C32×Q8D414yescomplemented
58C2×C32×Q8C2312yes—
59C2×C32×D4—22no—
60C2×C32×D4—21no—
61C2×C32×D4—22no—
62C2×C32×D4C2312yes—
63C22×C32×C4—21no—
64C22×C32×C4C2311yescharacteristic
65C2×C3×#67—21no—
66C2×C3×#67—24no—
67C3×#235—22no—
68C3×#235—22no—
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×Dic6C2311yescharacteristic
72C32×SD16—28no—
73C2×C32×C8—22no—
74C2×C32×C8C2312yes—
75C3×#217—21no—
76C3×#217—24no—
77C3×#217D412yes—
78C3×#216—24no—
79C3×#215—24no—
80C3×C4⋊Dic3—24no—
81C3×C4⋊Dic3D412yes—
82C3×C4⋊Dic3C2312yes—
83C3×C4×Dic3—21no—
84C3×C4×Dic3—24no—
85C3×C4×Dic3C2312yes—
86C3×#208—22no—
87C2×C3×C3⋊C8C2312yes—
88#3043—31noSylow
89C2×C3×#41—31no—
90C22×C3×Q8—21no—
91C22×C3×Q8C2×D311yescharacteristic
92C22×C3×Q8C22×C311yescharacteristic
93C22×C3×D4—21no—
94C22×C3×D4C2×D311yescharacteristic
95C22×C3×D4C22×C311yescharacteristic
96C2×#235C22×C311yescharacteristic
97C3×#137—64no—
98C2×C3×Q16—32no—
99C2×C3×SD16—28no—
100C2×C3×SD16—24no—
101C2×C3×SD16—24no—
102C2×C3×SD16—24no—
103C2×C3×SD16—32no—
104C2×C3×SD16C2×D314yes—
105C2×C3×SD16C22×C314yes—
106C2×C3×M16—31no—
107C22×C3×C8—21no—
108C22×C3×C8C2×D311yescharacteristic
109C22×C3×C8C22×C311yescharacteristic
110C3×#127—32no—
111C3×#124—32no—
112C3×#121—62no—
113C3×#120—62no—
114C3×C4×Q8—34no—
115C3×C4×Q8—62no—
116C3×#117—31no—
117C3×#117—31no—
118C3×#117—62no—
119#953—22no—
120Q8×Dic3—22no—
121Q8×Dic3C22×C314yescomplemented
122C2×#216C22×C312yescomplemented
123#942—24no—
124C2×#215C22×C312yescomplemented
125#940C22×C312yes—
126#938—22no—
127#936C22×C312yes—
128#926—22no—
129#926C22×C311yescharacteristic
130#926C22×C311yescharacteristic
131C2×#208C22×C311yescharacteristic
132C3×C4⋊C8—34no—
133C3×#103—32no—
134C3×#102—34no—
135C3×#102—32no—
136#832C22×C314yes—
137#821C22×C312yescomplemented
138#816C22×C312yescomplemented
139Dic3⋊C8C22×C314yescomplemented
140C23×C32—22no—
141C23×C32—42no—
142C23×C32—82no—
143C23×C32C2×D411yescharacteristic
144C22×C3×D3—21no—
145C32×Q8—24no—
146C32×Q8—22no—
147C32×Q8C2×D414yes—
148C32×D4—22no—
149C32×D4—22no—
150C32×D4—42no—
151C2×C32×C4—24no—
152C2×C32×C4—22no—
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D412yes—
155C2×C32×C4#4112yes—
156C2×C32×C4C2411yescharacteristic
157C3×#67—42no—
158C3×#67—84no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—21no—
161C2×C3×Dic3C2×D414yes—
162C3×D12—21no—
163C3×D12—21no—
164C3×C4×D3—42no—
165C3×Dic6—21no—
166C3×Dic6—21no—
167C32×C8—22no—
168C3×C3⋊C8—22no—
169C2×#137—31no—
170C22×SD16C3×D311yescharacteristic, complemented
171#535—31no—
172#519—31no—
173#464—34no—
174#460—34no—
175#424—31no—
176#418—31no—
177#416—31no—
178C24×C3—21no—
179C24×C3—21no—
180C24×C3—41no—
181C3×#41—62no—
182C3×#41—62no—
183C2×C3×Q8—21no—
184C2×C3×Q8—22no—
185C2×C3×Q8—21no—
186C2×C3×Q8—22no—
187C2×C3×Q8—24no—
188C2×C3×Q8—22no—
189C2×C3×Q8—31no—
190C2×C3×Q8—41no—
191C2×C3×Q8—42no—
192C2×C3×Q8#6714yescomplemented
193C2×C3×Q8C3×D414yescomplemented
194C2×C3×Q8C22×D312yes—
195C2×C3×Q8C23×C312yes—
196C2×C3×D4—24no—
197C2×C3×D4—21no—
198C2×C3×D4—22no—
199C2×C3×D4—22no—
200C2×C3×D4—22no—
201C2×C3×D4—21no—
202C2×C3×D4—22no—
203C2×C3×D4—22no—
204C2×C3×D4—31no—
205C2×C3×D4—41no—
206C2×C3×D4—42no—
207C2×C3×D4—64no—
208C2×C3×D4—61no—
209C2×C3×D4C22×D312yes—
210C2×C3×D4C23×C312yes—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—41no—
215C22×C3×C4—61no—
216C22×C3×C4C22×D311yescharacteristic
217C22×C3×C4C23×C311yescharacteristic
218C2×#67—21no—
219C2×#67—24no—
220#235—22no—
221#235—22no—
222C2×D12C23×C311yescharacteristic
223C2×C4×D3—21no—
224C2×Dic6C23×C311yescharacteristic
225C3×Q16—64no—
226C3×SD16—216no—
227C3×SD16—28no—
228C3×SD16—28no—
229C3×SD16—64no—
230C3×M16—62no—
231C2×C3×C8—24no—
232C2×C3×C8—22no—
233C2×C3×C8—22no—
234C2×C3×C8—22no—
235C2×C3×C8—32no—
236C2×C3×C8C22×D312yes—
237C2×C3×C8C23×C312yes—
238C3×C4⋊C4—32no—
239C3×C4⋊C4—32no—
240C3×C4⋊C4—64no—
241C3×C22⋊C4—32no—
242C3×C22⋊C4—64no—
243C3×C22⋊C4—61no—
244C3×C42—32no—
245C3×C42—64no—
246C3×C42—61no—
247#217—21no—
248#217—24no—
249#217C3×D412yes—
250#216—24no—
251#215—24no—
252C4⋊Dic3—24no—
253C4⋊Dic3C3×D412yes—
254C4⋊Dic3C23×C312yes—
255C4×Dic3—21no—
256C4×Dic3—24no—
257C4×Dic3C23×C312yes—
258#208—22no—
259C2×C3⋊C8C23×C312yes—
260C22×C32—22no—
261C22×C32—42no—
262C22×C32—44no—
263C22×C32—84no—
264C22×C32#12112yes—
265C22×C32C22×D411yescharacteristic
266C2×C3×D3—41no—
267C2×C3×D3—42no—
268C32×C4—24no—
269C32×C4#12112yes—
270C32×C4C22×D411yescharacteristic
271C32×C4C2×#4111yescharacteristic
272C3×Dic3—24no—
273C3×Dic3—41no—
274C3×Dic3—42no—
275C2×#41—31no—
276C22×Q8C2×C3×D311yescharacteristic
277C22×D4C2×C3×D311yescharacteristic
278#137—64no—
279C2×Q16—32no—
280C2×SD16—24no—
281C2×SD16—32no—
282C2×SD16C2×C3×D314yes—
283C2×M16—31no—
284C22×C8C2×C3×D311yescharacteristic
285#127—32no—
286#124—32no—
287#121—62no—
288#120—62no—
289C4×Q8—34no—
290C4×Q8—62no—
291#117—31no—
292#117—31no—
293#117—62no—
294C4⋊C8—34no—
295#103—32no—
296#102—34no—
297#102—32no—
298C23×C3—22no—
299C23×C3—22no—
300C23×C3—21no—
301C23×C3—42no—
302C23×C3—44no—
303C23×C3—42no—
304C23×C3—42no—
305C23×C3—61no—
306C23×C3—82no—
307C23×C3—82no—
308C23×C3—84no—
309C23×C3D3×D411yescharacteristic
310C23×C3C2×C3×D411yescharacteristic
311C22×D3—21no—
312C3×Q8—24no—
313C3×Q8—24no—
314C3×Q8—22no—
315C3×Q8—22no—
316C3×Q8—24no—
317C3×Q8—44no—
318C3×Q8—42no—
319C3×Q8—61no—
320C3×Q8—61no—
321C3×Q8C2×#6714yes—
322C3×Q8C2×C3×D414yes—
323C3×D4—24no—
324C3×D4—22no—
325C3×D4—22no—
326C3×D4—22no—
327C3×D4—22no—
328C3×D4—42no—
329C3×D4—44no—
330C3×D4—42no—
331C3×D4—42no—
332C3×D4—61no—
333C3×D4—61no—
334C3×D4—122no—
335C3×D4—244no—
336C2×C3×C4—24no—
337C2×C3×C4—24no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—34no—
345C2×C3×C4—44no—
346C2×C3×C4—42no—
347C2×C3×C4—62no—
348C2×C3×C4—61no—
349C2×C3×C4—122no—
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4#23712yes—
352C2×C3×C4C2×#6712yes—
353C2×C3×C4C2×C3×D411yescharacteristic
354C2×C3×C4C2×C3×D412yes—
355C2×C3×C4C3×#4112yes—
356C2×C3×C4C23×D311yescharacteristic
357C2×C3×C4C24×C311yescharacteristic
358#67—42no—
359#67—84no—
360C2×Dic3—22no—
361C2×Dic3—21no—
362C2×Dic3C2×C3×D414yes—
363D12—21no—
364D12—21no—
365C4×D3—42no—
366Dic6—21no—
367Dic6—21no—
368C3×C8—24no—
369C3×C8—22no—
370C3×C8—22no—
371C3×C8—62no—
372C3⋊C8—22no—
373C2×C32—22no—
374C2×C32—82no—
375C2×C32C2×#12111yescharacteristic
376C2×C32#57712yes—
377C3×D3—81no—
378C24—21no—
379#41—62no—
380#41—62no—
381C2×Q8—21no—
382C2×Q8—22no—
383C2×Q8—31no—
384C2×Q8C3×#6714yescomplemented
385C2×Q8C22×C3×D312yes—
386C2×D4—21no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—31no—
390C2×D4—64no—
391C2×D4—61no—
392C2×D4C22×C3×D312yes—
393C22×C4—21no—
394C22×C4—61no—
395C22×C4C22×C3×D311yescharacteristic
396Q16—64no—
397SD16—28no—
398SD16—64no—
399M16—62no—
400C2×C8—22no—
401C2×C8—32no—
402C2×C8C22×C3×D312yes—
403C4⋊C4—32no—
404C4⋊C4—32no—
405C4⋊C4—64no—
406C22⋊C4—32no—
407C22⋊C4—64no—
408C22⋊C4—61no—
409C42—32no—
410C42—64no—
411C42—61no—
412C22×C3—24no—
413C22×C3—22no—
414C22×C3—22no—
415C22×C3—22no—
416C22×C3—21no—
417C22×C3—44no—
418C22×C3—44no—
419C22×C3—44no—
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—84no—
423C22×C3—88no—
424C22×C3—84no—
425C22×C3—84no—
426C22×C3—122no—
427C22×C3—121no—
428C22×C3#93912yes—
429C22×C3C3×#12112yes—
430C22×C3C2×D3×D411yescharacteristic
431C22×C3C22×C3×D411yescharacteristic
432C2×D3—42no—
433C2×D3—41no—
434C3×C4—24no—
435C3×C4—24no—
436C3×C4—22no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—44no—
440C3×C4—64no—
441C3×C4—122no—
442C3×C4—121no—
443C3×C4#93912yes—
444C3×C4C3×#12112yes—
445C3×C4C2×#23711yescharacteristic
446C3×C4C22×#6711yescharacteristic
447C3×C4C22×C3×D411yescharacteristic
448C3×C4C2×C3×#4111yescharacteristic
449Dic3—24no—
450Dic3—42no—
451Dic3—41no—
452C32#304311yescharacteristic, complemented, Sylow
453C23—22no—
454C23—42no—
455C23—61no—
456C23—82no—
457C23C3×D3×D411yescharacteristic
458Q8—24no—
459Q8—22no—
460Q8—61no—
461Q8—61no—
462Q8C2×C3×#6714yes—
463D4—22no—
464D4—22no—
465D4—42no—
466D4—61no—
467D4—61no—
468D4—122no—
469D4—244no—
470C2×C4—24no—
471C2×C4—22no—
472C2×C4—34no—
473C2×C4—62no—
474C2×C4—61no—
475C2×C4—122no—
476C2×C4C3×D3×D411yescharacteristic
477C2×C4C3×#23712yes—
478C2×C4C2×C3×#6712yes—
479C2×C4C23×C3×D311yescharacteristic
480C8—22no—
481C8—62no—
482C2×C3—24no—
483C2×C3—22no—
484C2×C3—22no—
485C2×C3—22no—
486C2×C3—21no—
487C2×C3—84no—
488C2×C3—82no—
489C2×C3—82no—
490C2×C3—241no—
491C2×C3#576212yes—
492C2×C3C2×#93911yescharacteristic
493C2×C3C2×C3×#12111yescharacteristic
494C2×C3C3×#57712yes—
495D3—81no—
496C22—22no—
497C22—44no—
498C22—42no—
499C22—84no—
500C22—122no—
501C22—121no—
502C22C3×#93912yes—
503C22C2×C3×D3×D411yescharacteristic
504C4—24no—
505C4—64no—
506C4—122no—
507C4—121no—
508C4C3×#93912yes—
509C4C2×C3×#23711yescharacteristic
510C4C22×C3×#6711yescharacteristic
511C3—21no—
512C3#8384911yescharacteristic, direct product factor
513C3C3×#304311yescharacteristic, complemented
514C2—22no—
515C2—82no—
516C2—241no—
517C2C3×#576212yes—
518C2C2×C3×#93911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC22×C32×SD16C2
socleC22×C32C22×D4
prime radicalC3×#5805C2
hypercenterC22×C3×SD16D3
hypocenterC3C3×#3043
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×SD16

Complements

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

NH ≅ G/Ntype
1. C22×C32×SD16C2semidirect
2. C3×#5812C2semidirect
3. C2×C3×#942C2semidirect
5. C3×#5215C2semidirect
6. C3×#5166C2semidirect
7. C3×#5163C2semidirect
8. C3×#5113C2semidirect
9. C3×#5102C2semidirect
11. #83849C3direct (N × H)
20. C3×Q8×Dic3C22semidirect
21. C2×C3×#216C22semidirect
23. C2×C3×#215C22semidirect
32. C3×#821C22semidirect
33. C3×#816C22semidirect
34. C3×Dic3⋊C8C22semidirect
37. C22×C3×SD16D3semidirect
38. C22×C3×SD16C2×C3semidirect
41. #5812C2×C3semidirect
42. C2×#942C2×C3semidirect
49. #5215C2×C3semidirect
50. #5166C2×C3semidirect
51. #5163C2×C3semidirect
52. #5113C2×C3semidirect
53. #5102C2×C3semidirect
57. C2×C32×Q8D4semidirect
121. Q8×Dic3C22×C3semidirect
122. C2×#216C22×C3semidirect
124. C2×#215C22×C3semidirect
137. #821C22×C3semidirect
138. #816C22×C3semidirect
139. Dic3⋊C8C22×C3semidirect
170. C22×SD16C3×D3semidirect
192. C2×C3×Q8#67semidirect
193. C2×C3×Q8C3×D4semidirect
384. C2×Q8C3×#67semidirect
452. C32#3043semidirect
512. C3#83849direct (N × H)
513. C3C3×#3043semidirect

Maximal subgroups

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

subgroupindex
C22×C32×SD162
C3×#58122
C2×C3×#9422
C3×#58052
C3×#52152
C3×#51662
C3×#51632
C3×#51132
C3×#51022
C3×#30433
#838493