Finite Group Databasebeta

← C3×#83304 #11878746

Subgroups — C3×#83304 #11878746

Order 1152.

1031 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#532C211yesmaximal, characteristic, complemented
2C3×#5477C211yesmaximal, characteristic, complemented
3C3×#5093C211yesmaximal, characteristic, complemented
4C3×#5088C211yesmaximal, characteristic, complemented
5C3×#5076C211yesmaximal, characteristic, complemented
6C3×#5073C211yesmaximal, characteristic, complemented
7C3×#5037C214yesmaximal, complemented
8C3×#5016C214yesmaximal, complemented
9C3×#4925C211yesmaximal, characteristic, complemented
10C3×#3207—31nomaximal
11#83304C311yesmaximal, characteristic, direct product factor
12C2×C32×#41—21no—
13C2×C3×#235C2212yes—
14C32×C4⋊Q8C2211yescharacteristic
15C32×#127C2211yescharacteristic
16C32×#124—21no—
17C32×#121—21no—
18C32×#121C2212yes—
19C32×C4×D4—21no—
20C32×C4×D4C2212yes—
21C2×C32×C42C2211yescharacteristic
22C2×C3×#214C2214yes—
23C2×C3×#213C2214yes—
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×#532—21no—
38C3×#532—31no—
39C3×#532D311yescharacteristic, complemented
40C3×#532C2×C311yescharacteristic, complemented
41#5477C2×C311yescharacteristic, complemented
42C3×#493—31no—
43C3×#492—31no—
44C3×#487—31no—
45C3×#486—31no—
46C3×#463—34no—
47C3×#449—34no—
48C3×#431—31no—
49#5093C2×C311yescharacteristic, complemented
50#5088C2×C311yescharacteristic, complemented
51#5076C2×C311yescharacteristic, complemented
52#5073C2×C311yescharacteristic, complemented
53#5037C2×C314yescomplemented
54#5016C2×C314yescomplemented
55#4925C2×C311yescharacteristic, complemented
56C32×#41—44no—
57C2×C32×Q8—21no—
58C2×C32×D4—22no—
59C2×C32×D4—21no—
60C2×C32×D4—21no—
61C2×C32×D4C2312yes—
62C22×C32×C4—22no—
63C22×C32×C4D411yescharacteristic
64C22×C32×C4D411yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C2×C3×#67—22no—
67C3×#235—44no—
68C2×C3×D12—21no—
69C2×C3×D12—21no—
70C2×C3×D12C2312yes—
71C2×C3×C4×D3—22no—
72C2×C3×Dic6C2312yes—
73C32×C4⋊C4—21no—
74C32×C4⋊C4C2312yes—
75C32×C22⋊C4—22no—
76C32×C22⋊C4—22no—
77C32×C42D411yescharacteristic
78C32×C42D411yescharacteristic
79C32×C42C2311yescharacteristic
80C32×C42C2311yescharacteristic
81C3×#214—44no—
82C3×#213—44no—
83C3×(C2×D3)⋊C4—22no—
84C3×(C2×D3)⋊C4—22no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3—21no—
87C2×C3×C3⋊C8C2312yes—
88C2×C3×C3⋊C8C2312yes—
89#3207—31noSylow
90C2×C3×#41—22no—
91C2×C3×#41—21no—
92C2×C3×#41—21no—
93C2×C3×#41—32no—
94C2×#235C22×C312yes—
95C2×C3×SD16—34no—
96C2×C3×D8—34no—
97C3×C4⋊Q8—21no—
98C3×C4⋊Q8—31no—
99C3×C4⋊Q8C2×D311yescharacteristic
100C3×C4⋊Q8C22×C311yescharacteristic
101C3×#127—21no—
102C3×#127—31no—
103C3×#127C2×D311yescharacteristic
104C3×#127C22×C311yescharacteristic
105C3×#124—22no—
106C3×#124—21no—
107C3×#124—21no—
108C3×#124—32no—
109C3×#121—22no—
110C3×#121—21no—
111C3×#121—21no—
112C3×#121—22no—
113C3×#121—61no—
114C3×#121—61no—
115C3×#121C2×D312yes—
116C3×#121C22×C312yes—
117C3×C4×D4—22no—
118C3×C4×D4—21no—
119C3×C4×D4—21no—
120C3×C4×D4—22no—
121C3×C4×D4—61no—
122C3×C4×D4—61no—
123C3×C4×D4C2×D312yes—
124C3×C4×D4C22×C312yes—
125C2×C3×C42—21no—
126C2×C3×C42C2×D311yescharacteristic
127C2×C3×C42C22×C311yescharacteristic
128C2×#214C22×C314yes—
129C2×#213C22×C314yes—
130#930—21no—
131#930—21no—
132#875C22×C312yes—
133#874C22×C311yescharacteristic
134C4×D12—21no—
135C4×D12—21no—
136#869C22×C311yescharacteristic
137C3×C4⋊C8—32no—
138C3×#103—34no—
139C3×#102—34no—
140C3×C22⋊C8—32no—
141C3×C4×C8—31no—
142C3×C4×C8—31no—
143#830C22×C312yes—
144#810C22×C314yes—
145#809C22×C314yes—
146C4⋊(C3⋊C8)C22×C312yes—
147C4×C3⋊C8C22×C311yescharacteristic
148C4×C3⋊C8C22×C311yescharacteristic
149C23×C32—22no—
150C23×C32C2×D411yescharacteristic
151C22×C3×D3—22no—
152C32×Q8—42no—
153C32×D4—24no—
154C32×D4—44no—
155C32×D4—42no—
156C32×D4—42no—
157C2×C32×C4—22no—
158C2×C32×C4—22no—
159C2×C32×C4—22no—
160C2×C32×C4—22no—
161C2×C32×C4—44no—
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2411yescharacteristic
168C3×#67—44no—
169C2×C3×Dic3—22no—
170C3×D12—24no—
171C3×D12—42no—
172C3×D12—42no—
173C3×C4×D3—44no—
174C3×Dic6—24no—
175C3×C3⋊C8—22no—
176C3×C3⋊C8—22no—
177#532—31no—
178#532C3×D311yescharacteristic, complemented
179#493—31no—
180#492—31no—
181#487—31no—
182#486—31no—
183#463—34no—
184#449—34no—
185#431—31no—
186C3×#41—48no—
187C3×#41—44no—
188C3×#41—44no—
189C3×#41—124no—
190C2×C3×Q8—22no—
191C2×C3×Q8—21no—
192C2×C3×Q8—21no—
193C2×C3×Q8—32no—
194C2×C3×D4—22no—
195C2×C3×D4—24no—
196C2×C3×D4—22no—
197C2×C3×D4—22no—
198C2×C3×D4—22no—
199C2×C3×D4—21no—
200C2×C3×D4—21no—
201C2×C3×D4—21no—
202C2×C3×D4—21no—
203C2×C3×D4—22no—
204C2×C3×D4—32no—
205C2×C3×D4—62no—
206C2×C3×D4—61no—
207C2×C3×D4—61no—
208C2×C3×D4C22×D312yes—
209C2×C3×D4C23×C312yes—
210C22×C3×C4—24no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—62no—
217C22×C3×C4#6711yescharacteristic
218C22×C3×C4#6711yescharacteristic
219C22×C3×C4C3×D411yescharacteristic
220C22×C3×C4C3×D411yescharacteristic
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C23×C311yescharacteristic
223C2×#67—22no—
224#235—44no—
225C2×D12—21no—
226C2×D12—21no—
227C2×D12C23×C312yes—
228C2×C4×D3—22no—
229C2×Dic6C23×C312yes—
230C3×SD16—124no—
231C3×D8—124no—
232C2×C3×C8—32no—
233C2×C3×C8—32no—
234C3×C4⋊C4—22no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—22no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4—61no—
240C3×C4⋊C4C22×D312yes—
241C3×C4⋊C4C23×C312yes—
242C3×C22⋊C4—24no—
243C3×C22⋊C4—24no—
244C3×C22⋊C4—22no—
245C3×C22⋊C4—22no—
246C3×C22⋊C4—22no—
247C3×C22⋊C4—22no—
248C3×C22⋊C4—62no—
249C3×C22⋊C4—62no—
250C3×C42—21no—
251C3×C42—21no—
252C3×C42—21no—
253C3×C42—21no—
254C3×C42#6711yescharacteristic
255C3×C42#6711yescharacteristic
256C3×C42C3×D411yescharacteristic
257C3×C42C3×D411yescharacteristic
258C3×C42C22×D311yescharacteristic
259C3×C42C22×D311yescharacteristic
260C3×C42C23×C311yescharacteristic
261C3×C42C23×C311yescharacteristic
262#214—44no—
263#213—44no—
264(C2×D3)⋊C4—22no—
265(C2×D3)⋊C4—22no—
266C4⋊Dic3—21no—
267C4⋊Dic3—21no—
268C2×C3⋊C8C23×C312yes—
269C2×C3⋊C8C23×C312yes—
270C22×C32—21no—
271C22×C32—21no—
272C22×C32—21no—
273C22×C32—42no—
274C22×C32—42no—
275C22×C32—42no—
276C22×C32C22×D411yescharacteristic
277C2×C3×D3—42no—
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C32×C4—21no—
281C32×C4—21no—
282C32×C4—21no—
283C32×C4—42no—
284C32×C4#13512yes—
285C32×C4AGL(1,ℤ/8)12yes—
286C32×C4H(5,𝔽2)12yes—
287C3×Dic3—42no—
288C2×#41—21no—
289C2×#41—32no—
290C2×SD16—34no—
291C2×D8—34no—
292C4⋊Q8—31no—
293C4⋊Q8C2×C3×D311yescharacteristic
294#127—31no—
295#127C2×C3×D311yescharacteristic
296#124—21no—
297#124—32no—
298#121—21no—
299#121—61no—
300#121—61no—
301#121C2×C3×D312yes—
302C4×D4—21no—
303C4×D4—61no—
304C4×D4—61no—
305C4×D4C2×C3×D312yes—
306C2×C42C2×C3×D311yescharacteristic
307C4⋊C8—32no—
308#103—34no—
309#102—34no—
310C22⋊C8—32no—
311C4×C8—31no—
312C4×C8—31no—
313C23×C3—24no—
314C23×C3—22no—
315C23×C3—22no—
316C23×C3—21no—
317C23×C3—62no—
318C23×C3C2×#6711yescharacteristic
319C23×C3C2×C3×D411yescharacteristic
320C22×D3—22no—
321C3×Q8—44no—
322C3×Q8—42no—
323C3×Q8—42no—
324C3×Q8—64no—
325C3×D4—24no—
326C3×D4—24no—
327C3×D4—44no—
328C3×D4—44no—
329C3×D4—44no—
330C3×D4—48no—
331C3×D4—44no—
332C3×D4—44no—
333C3×D4—42no—
334C3×D4—42no—
335C3×D4—42no—
336C3×D4—42no—
337C3×D4—64no—
338C3×D4—124no—
339C3×D4—122no—
340C3×D4—122no—
341C2×C3×C4—24no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—24no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—42no—
358C2×C3×C4—42no—
359C2×C3×C4—48no—
360C2×C3×C4—44no—
361C2×C3×C4—44no—
362C2×C3×C4—62no—
363C2×C3×C4—124no—
364C2×C3×C4C2×#6711yescharacteristic
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C2×#6711yescharacteristic
367C2×C3×C4C2×#6711yescharacteristic
368C2×C3×C4C2×#6711yescharacteristic
369C2×C3×C4C2×C3×D411yescharacteristic
370C2×C3×C4C2×C3×D411yescharacteristic
371C2×C3×C4C2×C3×D411yescharacteristic
372C2×C3×C4C2×C3×D411yescharacteristic
373C2×C3×C4C2×C3×D411yescharacteristic
374C2×C3×C4C23×D311yescharacteristic
375C2×C3×C4C24×C311yescharacteristic
376#67—44no—
377C2×Dic3—22no—
378D12—24no—
379D12—42no—
380D12—42no—
381C4×D3—44no—
382Dic6—24no—
383C3×C8—62no—
384C3×C8—62no—
385C3⋊C8—22no—
386C3⋊C8—22no—
387C2×C32—41no—
388C2×C32—82no—
389C2×C32#53511yescharacteristic
390C2×C32C2×#13511yescharacteristic
391C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
392C3×D3—82no—
393#41—44no—
394#41—124no—
395C2×Q8—21no—
396C2×Q8—32no—
397C2×D4—22no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—32no—
401C2×D4—62no—
402C2×D4—61no—
403C2×D4—61no—
404C2×D4C22×C3×D312yes—
405C22×C4—22no—
406C22×C4—62no—
407C22×C4C3×#6711yescharacteristic
408C22×C4C3×#6711yescharacteristic
409C22×C4C22×C3×D311yescharacteristic
410SD16—124no—
411D8—124no—
412C2×C8—32no—
413C2×C8—32no—
414C4⋊C4—21no—
415C4⋊C4—61no—
416C4⋊C4—61no—
417C4⋊C4C22×C3×D312yes—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—62no—
421C22⋊C4—62no—
422C42C3×#6711yescharacteristic
423C42C3×#6711yescharacteristic
424C42C22×C3×D311yescharacteristic
425C42C22×C3×D311yescharacteristic
426C22×C3—22no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—44no—
437C22×C3—44no—
438C22×C3—44no—
439C22×C3—42no—
440C22×C3—42no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—42no—
444C22×C3—42no—
445C22×C3—122no—
446C22×C3—122no—
447C22×C3—122no—
448C22×C3C22×#6711yescharacteristic
449C22×C3C22×C3×D411yescharacteristic
450C2×D3—42no—
451C2×D3—42no—
452C2×D3—42no—
453C3×C4—22no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—22no—
461C3×C4—22no—
462C3×C4—22no—
463C3×C4—41no—
464C3×C4—41no—
465C3×C4—44no—
466C3×C4—42no—
467C3×C4—42no—
468C3×C4—122no—
469C3×C4#93212yes—
470C3×C4#95012yes—
471C3×C4C3×#13512yes—
472C3×C4C3×AGL(1,ℤ/8)12yes—
473C3×C4#100912yes—
474C3×C4C3×H(5,𝔽2)12yes—
475Dic3—42no—
476C32#320711yescharacteristic, complemented, Sylow
477C23—22no—
478C23—62no—
479C23C2×C3×#6711yescharacteristic
480Q8—42no—
481Q8—64no—
482D4—24no—
483D4—44no—
484D4—42no—
485D4—42no—
486D4—64no—
487D4—124no—
488D4—122no—
489D4—122no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—44no—
495C2×C4—62no—
496C2×C4—124no—
497C2×C4C2×C3×#6711yescharacteristic
498C2×C4C2×C3×#6711yescharacteristic
499C2×C4C2×C3×#6711yescharacteristic
500C2×C4C2×C3×#6711yescharacteristic
501C2×C4C2×C3×#6711yescharacteristic
502C2×C4C23×C3×D311yescharacteristic
503C8—62no—
504C8—62no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—42no—
509C2×C3—41no—
510C2×C3—41no—
511C2×C3—84no—
512C2×C3—82no—
513C2×C3—82no—
514C2×C3—242no—
515C2×C3C2×#93211yescharacteristic
516C2×C3C2×#95011yescharacteristic
517C2×C3#583011yescharacteristic
518C2×C3C3×#53511yescharacteristic
519C2×C3C2×C3×#13511yescharacteristic
520C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
521D3—82no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—122no—
529C22—122no—
530C22—122no—
531C22C22×C3×#6711yescharacteristic
532C4—21no—
533C4—21no—
534C4—21no—
535C4—42no—
536C4—122no—
537C4C3×#93212yes—
538C4C3×#95012yes—
539C4C3×#100912yes—
540C3—21no—
541C3#8330411yescharacteristic, direct product factor
542C3C3×#320711yescharacteristic, complemented
543C2—41no—
544C2—82no—
545C2—242no—
546C2C2×C3×#93211yescharacteristic
547C2C2×C3×#95011yescharacteristic
548C2C3×#583011yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#532C2
socleC22×C32C22×D4
hypercenterC3×#532D3
hypocenterC3C3×#3207
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C3×#532

Complements

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

NH ≅ G/Ntype
1. C32×#532C2semidirect
2. C3×#5477C2semidirect
3. C3×#5093C2semidirect
4. C3×#5088C2semidirect
5. C3×#5076C2semidirect
6. C3×#5073C2semidirect
7. C3×#5037C2semidirect
8. C3×#5016C2semidirect
9. C3×#4925C2semidirect
11. #83304C3direct (N × H)
39. C3×#532D3semidirect
40. C3×#532C2×C3semidirect
41. #5477C2×C3semidirect
49. #5093C2×C3semidirect
50. #5088C2×C3semidirect
51. #5076C2×C3semidirect
52. #5073C2×C3semidirect
53. #5037C2×C3semidirect
54. #5016C2×C3semidirect
55. #4925C2×C3semidirect
178. #532C3×D3semidirect
476. C32#3207semidirect
541. C3#83304direct (N × H)
542. C3C3×#3207semidirect

Maximal subgroups

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

subgroupindex
C32×#5322
C3×#54772
C3×#50932
C3×#50882
C3×#50762
C3×#50732
C3×#50372
C3×#50162
C3×#49252
C3×#32073
#833043