Finite Group Databasebeta

← C3×#83356 #11878935

Subgroups — C3×#83356 #11878935

Order 1152.

899 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
1C32×#533C211yesmaximal, characteristic, complemented
2C3×#5477C211yesmaximal, characteristic
3C3×#5093C211yesmaximal, characteristic, complemented
4C3×#5092C211yesmaximal, characteristic, complemented
5C3×#5088C211yesmaximal, characteristic, complemented
6C3×#5085C211yesmaximal, characteristic, complemented
7C3×#5047C214yesmaximal, complemented
8C3×#5028C214yesmaximal, complemented
9C3×#4925C211yesmaximal, characteristic, complemented
10C3×#3210—31nomaximal
11#83356C311yesmaximal, characteristic, direct product factor
12C2×C3×#235C2212yes—
13C32×C4⋊Q8C2211yescharacteristic
14C32×C4⋊Q8C2211yescharacteristic
15C32×#125—21no—
16C32×C22⋊Q8—21no—
17C32×C22⋊Q8C2212yes—
18C32×C4×Q8—21no—
19C32×C4×Q8C2212yes—
20C32×#117—21no—
21C2×C32×C42C2211yescharacteristic
22C2×C3×#216C2214yes—
23C2×C3×#215C2214yes—
24C3×#930—21no—
25C3×#930—21no—
26C3×#875C2212yes—
27C3×#874C2211yescharacteristic
28C3×C4×D12—21no—
29C3×C4×D12—21no—
30C3×#869C2211yescharacteristic
31C3×#830C2212yes—
32C3×#810C2214yes—
33C3×#809C2214yes—
34C3×C4⋊(C3⋊C8)C2212yes—
35C3×C4×C3⋊C8C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37C3×#533—21no—
38C3×#533D311yescharacteristic, complemented
39C3×#533C2×C311yescharacteristic, complemented
40C3×#532—31no—
41#5477C2×C311yescharacteristic
42C3×#494—31no—
43C3×#492—31no—
44C3×#487—31no—
45C3×#486—31no—
46C3×#464—34no—
47C3×#452—34no—
48C3×#431—31no—
49#5093C2×C311yescharacteristic, complemented
50#5092C2×C311yescharacteristic, complemented
51#5088C2×C311yescharacteristic, complemented
52#5085C2×C311yescharacteristic, complemented
53#5047C2×C314yescomplemented
54#5028C2×C314yescomplemented
55#4925C2×C311yescharacteristic, complemented
56C2×C32×Q8—21no—
57C2×C32×Q8C2312yes—
58C22×C32×C4D411yescharacteristic
59C22×C32×C4D411yescharacteristic
60C22×C32×C4C2311yescharacteristic
61C2×C3×#67—22no—
62C3×#235—44no—
63C2×C3×D12—21no—
64C2×C3×D12—21no—
65C2×C3×D12C2312yes—
66C2×C3×C4×D3—22no—
67C2×C3×Dic6C2312yes—
68C32×C4⋊C4—21no—
69C32×C4⋊C4—21no—
70C32×C4⋊C4—21no—
71C32×C4⋊C4—22no—
72C32×C4⋊C4—22no—
73C32×C4⋊C4C2312yes—
74C32×C22⋊C4—22no—
75C32×C42—22no—
76C32×C42D411yescharacteristic
77C32×C42D411yescharacteristic
78C32×C42C2311yescharacteristic
79C32×C42C2311yescharacteristic
80C3×#216—44no—
81C3×#215—44no—
82C3×(C2×D3)⋊C4—22no—
83C3×(C2×D3)⋊C4—22no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—21no—
86C2×C3×C3⋊C8C2312yes—
87C2×C3×C3⋊C8C2312yes—
88#3210—31noSylow
89C2×C3×#41—32no—
90C2×#235C22×C312yes—
91C2×C3×Q16—34no—
92C2×C3×SD16—34no—
93C3×C4⋊Q8—21no—
94C3×C4⋊Q8—21no—
95C3×C4⋊Q8—31no—
96C3×C4⋊Q8C2×D311yescharacteristic
97C3×C4⋊Q8C2×D311yescharacteristic
98C3×C4⋊Q8C22×C311yescharacteristic
99C3×C4⋊Q8C22×C311yescharacteristic
100C3×#127—31no—
101C3×#125—22no—
102C3×#125—21no—
103C3×#125—21no—
104C3×#124—32no—
105C3×C22⋊Q8—22no—
106C3×C22⋊Q8—21no—
107C3×C22⋊Q8—21no—
108C3×C22⋊Q8—22no—
109C3×C22⋊Q8C2×D312yes—
110C3×C22⋊Q8C22×C312yes—
111C3×#121—61no—
112C3×#121—61no—
113C3×C4×Q8—22no—
114C3×C4×Q8—21no—
115C3×C4×Q8—21no—
116C3×C4×Q8—22no—
117C3×C4×Q8C2×D312yes—
118C3×C4×Q8C22×C312yes—
119C3×C4×D4—61no—
120C3×C4×D4—61no—
121C3×#117—22no—
122C3×#117—21no—
123C3×#117—21no—
124C2×C3×C42—21no—
125C2×C3×C42C2×D311yescharacteristic
126C2×C3×C42C22×C311yescharacteristic
127C2×#216C22×C314yes—
128C2×#215C22×C314yes—
129#930—21no—
130#930—21no—
131#875C22×C312yes—
132#874C22×C311yescharacteristic
133C4×D12—21no—
134C4×D12—21no—
135#869C22×C311yescharacteristic
136C3×C4⋊C8—32no—
137C3×#103—34no—
138C3×#102—34no—
139C3×C22⋊C8—32no—
140C3×C4×C8—31no—
141C3×C4×C8—31no—
142#830C22×C312yes—
143#810C22×C314yes—
144#809C22×C314yes—
145C4⋊(C3⋊C8)C22×C312yes—
146C4×C3⋊C8C22×C311yescharacteristic
147C4×C3⋊C8C22×C311yescharacteristic
148C23×C32C2×D411yescharacteristic
149C22×C3×D3—22no—
150C32×Q8—24no—
151C32×Q8—42no—
152C2×C32×C4—22no—
153C2×C32×C4—22no—
154C2×C32×C4—22no—
155C2×C32×C4—22no—
156C2×C32×C4—22no—
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2411yescharacteristic
163C3×#67—44no—
164C2×C3×Dic3—22no—
165C3×D12—24no—
166C3×D12—42no—
167C3×D12—42no—
168C3×C4×D3—44no—
169C3×Dic6—24no—
170C3×C3⋊C8—22no—
171C3×C3⋊C8—22no—
172#533C3×D311yescharacteristic, complemented
173#532—31no—
174#494—31no—
175#492—31no—
176#487—31no—
177#486—31no—
178#464—34no—
179#452—34no—
180#431—31no—
181C3×#41—124no—
182C2×C3×Q8—22no—
183C2×C3×Q8—21no—
184C2×C3×Q8—21no—
185C2×C3×Q8—22no—
186C2×C3×Q8—32no—
187C2×C3×Q8C22×D312yes—
188C2×C3×Q8C23×C312yes—
189C2×C3×D4—32no—
190C2×C3×D4—62no—
191C2×C3×D4—61no—
192C2×C3×D4—61no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—62no—
197C22×C3×C4#6711yescharacteristic
198C22×C3×C4#6711yescharacteristic
199C22×C3×C4C3×D411yescharacteristic
200C22×C3×C4C3×D411yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C23×C311yescharacteristic
203C2×#67—22no—
204#235—44no—
205C2×D12—21no—
206C2×D12—21no—
207C2×D12C23×C312yes—
208C2×C4×D3—22no—
209C2×Dic6C23×C312yes—
210C3×Q16—124no—
211C3×SD16—124no—
212C2×C3×C8—32no—
213C2×C3×C8—32no—
214C3×C4⋊C4—22no—
215C3×C4⋊C4—22no—
216C3×C4⋊C4—24no—
217C3×C4⋊C4—24no—
218C3×C4⋊C4—22no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—22no—
223C3×C4⋊C4—22no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—22no—
228C3×C4⋊C4—22no—
229C3×C4⋊C4—22no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4—61no—
232C3×C4⋊C4C22×D312yes—
233C3×C4⋊C4C23×C312yes—
234C3×C22⋊C4—24no—
235C3×C22⋊C4—22no—
236C3×C22⋊C4—22no—
237C3×C22⋊C4—62no—
238C3×C22⋊C4—62no—
239C3×C42—24no—
240C3×C42—22no—
241C3×C42—22no—
242C3×C42—21no—
243C3×C42—21no—
244C3×C42—21no—
245C3×C42—21no—
246C3×C42#6711yescharacteristic
247C3×C42#6711yescharacteristic
248C3×C42C3×D411yescharacteristic
249C3×C42C3×D411yescharacteristic
250C3×C42C22×D311yescharacteristic
251C3×C42C22×D311yescharacteristic
252C3×C42C23×C311yescharacteristic
253C3×C42C23×C311yescharacteristic
254#216—44no—
255#215—44no—
256(C2×D3)⋊C4—22no—
257(C2×D3)⋊C4—22no—
258C4⋊Dic3—21no—
259C4⋊Dic3—21no—
260C2×C3⋊C8C23×C312yes—
261C2×C3⋊C8C23×C312yes—
262C22×C32—21no—
263C22×C32—21no—
264C22×C32—21no—
265C22×C32C22×D411yescharacteristic
266C2×C3×D3—42no—
267C2×C3×D3—42no—
268C2×C3×D3—42no—
269C32×C4—21no—
270C32×C4—21no—
271C32×C4—21no—
272C32×C4—42no—
273C32×C4—42no—
274C32×C4#13512yes—
275C32×C4#13712yes—
276C32×C4H(5,𝔽2)12yes—
277C3×Dic3—42no—
278C2×#41—32no—
279C2×Q16—34no—
280C2×SD16—34no—
281C4⋊Q8—31no—
282C4⋊Q8C2×C3×D311yescharacteristic
283C4⋊Q8C2×C3×D311yescharacteristic
284#127—31no—
285#125—21no—
286#124—32no—
287C22⋊Q8—21no—
288C22⋊Q8C2×C3×D312yes—
289#121—61no—
290#121—61no—
291C4×Q8—21no—
292C4×Q8C2×C3×D312yes—
293C4×D4—61no—
294C4×D4—61no—
295#117—21no—
296C2×C42C2×C3×D311yescharacteristic
297C4⋊C8—32no—
298#103—34no—
299#102—34no—
300C22⋊C8—32no—
301C4×C8—31no—
302C4×C8—31no—
303C23×C3—21no—
304C23×C3—62no—
305C23×C3C2×#6711yescharacteristic
306C23×C3C2×C3×D411yescharacteristic
307C22×D3—22no—
308C3×Q8—24no—
309C3×Q8—24no—
310C3×Q8—44no—
311C3×Q8—44no—
312C3×Q8—42no—
313C3×Q8—42no—
314C3×Q8—64no—
315C3×D4—64no—
316C3×D4—124no—
317C3×D4—122no—
318C3×D4—122no—
319C2×C3×C4—24no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—24no—
327C2×C3×C4—24no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—42no—
339C2×C3×C4—42no—
340C2×C3×C4—62no—
341C2×C3×C4—124no—
342C2×C3×C4C2×#6711yescharacteristic
343C2×C3×C4C2×#6711yescharacteristic
344C2×C3×C4C2×#6711yescharacteristic
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C2×C3×D411yescharacteristic
348C2×C3×C4C2×C3×D411yescharacteristic
349C2×C3×C4C2×C3×D411yescharacteristic
350C2×C3×C4C2×C3×D411yescharacteristic
351C2×C3×C4C2×C3×D411yescharacteristic
352C2×C3×C4C23×D311yescharacteristic
353C2×C3×C4C24×C311yescharacteristic
354#67—44no—
355C2×Dic3—22no—
356D12—24no—
357D12—42no—
358D12—42no—
359C4×D3—44no—
360Dic6—24no—
361C3×C8—62no—
362C3×C8—62no—
363C3⋊C8—22no—
364C3⋊C8—22no—
365C2×C32—41no—
366C2×C32#53511yescharacteristic
367C2×C32C2×#13511yescharacteristic
368C2×C32C2×#13711yescharacteristic
369C3×D3—82no—
370#41—124no—
371C2×Q8—21no—
372C2×Q8—32no—
373C2×Q8C22×C3×D312yes—
374C2×D4—32no—
375C2×D4—62no—
376C2×D4—61no—
377C2×D4—61no—
378C22×C4—62no—
379C22×C4C3×#6711yescharacteristic
380C22×C4C3×#6711yescharacteristic
381C22×C4C22×C3×D311yescharacteristic
382Q16—124no—
383SD16—124no—
384C2×C8—32no—
385C2×C8—32no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—61no—
392C4⋊C4—61no—
393C4⋊C4C22×C3×D312yes—
394C22⋊C4—22no—
395C22⋊C4—62no—
396C22⋊C4—62no—
397C42—22no—
398C42C3×#6711yescharacteristic
399C42C3×#6711yescharacteristic
400C42C22×C3×D311yescharacteristic
401C42C22×C3×D311yescharacteristic
402C22×C3—22no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—41no—
411C22×C3—41no—
412C22×C3—122no—
413C22×C3—122no—
414C22×C3—122no—
415C22×C3C22×#6711yescharacteristic
416C22×C3C22×C3×D411yescharacteristic
417C2×D3—42no—
418C2×D3—42no—
419C2×D3—42no—
420C3×C4—22no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—22no—
428C3×C4—22no—
429C3×C4—22no—
430C3×C4—41no—
431C3×C4—41no—
432C3×C4—44no—
433C3×C4—44no—
434C3×C4—42no—
435C3×C4—42no—
436C3×C4—42no—
437C3×C4—42no—
438C3×C4—122no—
439C3×C4#94212yes—
440C3×C4#95012yes—
441C3×C4C3×#13512yes—
442C3×C4C3×#13712yes—
443C3×C4#100912yes—
444C3×C4C3×H(5,𝔽2)12yes—
445Dic3—42no—
446C32#321011yescharacteristic, complemented, Sylow
447C23—62no—
448C23C2×C3×#6711yescharacteristic
449Q8—24no—
450Q8—42no—
451Q8—64no—
452D4—64no—
453D4—124no—
454D4—122no—
455D4—122no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—62no—
462C2×C4—124no—
463C2×C4C2×C3×#6711yescharacteristic
464C2×C4C2×C3×#6711yescharacteristic
465C2×C4C2×C3×#6711yescharacteristic
466C2×C4C2×C3×#6711yescharacteristic
467C2×C4C2×C3×#6711yescharacteristic
468C2×C4C23×C3×D311yescharacteristic
469C8—62no—
470C8—62no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—42no—
475C2×C3—41no—
476C2×C3—41no—
477C2×C3—242no—
478C2×C3C2×#94211yescharacteristic
479C2×C3C2×#95011yescharacteristic
480C2×C3#583011yescharacteristic
481C2×C3C3×#53511yescharacteristic
482C2×C3C2×C3×#13511yescharacteristic
483C2×C3C2×C3×#13711yescharacteristic
484D3—82no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—122no—
489C22—122no—
490C22—122no—
491C22C22×C3×#6711yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—42no—
496C4—42no—
497C4—122no—
498C4C3×#94212yes—
499C4C3×#95012yes—
500C4C3×#100912yes—
501C3—21no—
502C3#8335611yescharacteristic, direct product factor
503C3C3×#321011yescharacteristic, complemented
504C2—41no—
505C2—242no—
506C2C2×C3×#94211yescharacteristic
507C2C2×C3×#95011yescharacteristic
508C2C3×#583011yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#533C2
socleC22×C32C22×D4
prime radicalC3×#5477C2
hypercenterC3×#533D3
hypocenterC3C3×#3210
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C3×#533

Complements

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

NH ≅ G/Ntype
1. C32×#533C2semidirect
3. C3×#5093C2semidirect
4. C3×#5092C2semidirect
5. C3×#5088C2semidirect
6. C3×#5085C2semidirect
7. C3×#5047C2semidirect
8. C3×#5028C2semidirect
9. C3×#4925C2semidirect
11. #83356C3direct (N × H)
38. C3×#533D3semidirect
39. C3×#533C2×C3semidirect
49. #5093C2×C3semidirect
50. #5092C2×C3semidirect
51. #5088C2×C3semidirect
52. #5085C2×C3semidirect
53. #5047C2×C3semidirect
54. #5028C2×C3semidirect
55. #4925C2×C3semidirect
172. #533C3×D3semidirect
446. C32#3210semidirect
502. C3#83356direct (N × H)
503. C3C3×#3210semidirect

Maximal subgroups

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

subgroupindex
C32×#5332
C3×#54772
C3×#50932
C3×#50922
C3×#50882
C3×#50852
C3×#50472
C3×#50282
C3×#49252
C3×#32103
#833563