Finite Group Databasebeta

← C3×#83363 #11882222

Subgroups — C3×#83363 #11882222

Order 1152.

895 conjugacy classes of subgroups.

The subgroup lattice has 513 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#533C211yesmaximal, characteristic, complemented
2C3×#5477C211yesmaximal, characteristic
3C3×#5084C212yesmaximal, complemented
4C3×#5083C212yesmaximal, complemented
5C3×#5048C214yesmaximal, complemented
6C3×#5027C212yesmaximal, complemented
7C3×#5020C212yesmaximal, complemented
8C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
9C3×#3246—31nomaximal
10#83363C311yesmaximal, characteristic, direct product factor
11C2×C3×#235—21no—
12C32×C4⋊Q8C2211yescharacteristic
13C32×C4⋊Q8C2211yescharacteristic
14C32×#125—21no—
15C32×C22⋊Q8—21no—
16C32×C22⋊Q8C2212yes—
17C32×C4×Q8—21no—
18C32×C4×Q8C2212yes—
19C32×#117—21no—
20C2×C32×C42C2211yescharacteristic
21C2×C3×#215C2214yes—
22C3×#930—21no—
23C3×#930C2212yes—
24C22×C3×C3⋊C8C2212yes—
25C3×#875—21no—
26C3×#874C2211yescharacteristic
27C3×C4×D12—21no—
28C3×C4×D12C2212yes—
29C3×#869C2211yescharacteristic
30C3×#835C2214yes—
31C3×#809C2214yes—
32C3×#808C2214yes—
33C3×C4⋊(C3⋊C8)C2212yes—
34C3×C4⋊(C3⋊C8)C2212yes—
35C3×#533—21no—
36C3×#533D311yescharacteristic, complemented
37C3×#533C2×C311yescharacteristic, complemented
38C3×#532—31no—
39#5477C2×C311yescharacteristic
40C3×#476—32no—
41C3×#475—32no—
42C3×#465—34no—
43C3×#461—32no—
44C3×#460—32no—
45C2×C3×C4⋊C8—31no—
46#5084C2×C312yescomplemented
47#5083C2×C312yescomplemented
48#5048C2×C314yescomplemented
49#5027C2×C312yescomplemented
50#5020C2×C312yescomplemented
51C2×C4⋊(C3⋊C8)C2×C311yescharacteristic, complemented
52C2×C32×Q8—21no—
53C2×C32×Q8C2312yes—
54C22×C32×C4D411yescharacteristic
55C22×C32×C4D411yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C2×C3×#67—22no—
58C3×#235—44no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12C2312yes—
62C2×C3×C4×D3—22no—
63C2×C3×Dic6—21no—
64C32×C4⋊C4—21no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4—21no—
67C32×C4⋊C4—22no—
68C32×C4⋊C4—22no—
69C32×C4⋊C4C2312yes—
70C32×C22⋊C4—22no—
71C32×C42—22no—
72C32×C42D411yescharacteristic
73C32×C42D411yescharacteristic
74C32×C42C2311yescharacteristic
75C32×C42C2311yescharacteristic
76C3×#215—44no—
77C3×(C2×D3)⋊C4—22no—
78C3×(C2×D3)⋊C4—22no—
79C3×C4⋊Dic3—21no—
80C3×C4⋊Dic3C2312yes—
81C2×C3×C3⋊C8—42no—
82C2×C3×C3⋊C8C2314yes—
83#3246—31noSylow
84C2×C3×#41—61no—
85C2×#235—21no—
86C2×C3×SD16—34no—
87C22×C3×C8—32no—
88C3×C4⋊Q8—21no—
89C3×C4⋊Q8—21no—
90C3×C4⋊Q8—31no—
91C3×C4⋊Q8C2×D311yescharacteristic
92C3×C4⋊Q8C2×D311yescharacteristic
93C3×C4⋊Q8C22×C311yescharacteristic
94C3×C4⋊Q8C22×C311yescharacteristic
95C3×#127—31no—
96C3×#125—22no—
97C3×#125—21no—
98C3×#125—21no—
99C3×#124—61no—
100C3×C22⋊Q8—22no—
101C3×C22⋊Q8—21no—
102C3×C22⋊Q8—21no—
103C3×C22⋊Q8—22no—
104C3×C22⋊Q8C2×D312yes—
105C3×C22⋊Q8C22×C312yes—
106C3×#121—32no—
107C3×#121—61no—
108C3×C4×Q8—22no—
109C3×C4×Q8—21no—
110C3×C4×Q8—21no—
111C3×C4×Q8—22no—
112C3×C4×Q8C2×D312yes—
113C3×C4×Q8C22×C312yes—
114C3×C4×D4—32no—
115C3×C4×D4—61no—
116C3×#117—22no—
117C3×#117—21no—
118C3×#117—21no—
119C2×C3×C42—21no—
120C2×C3×C42C2×D311yescharacteristic
121C2×C3×C42C22×C311yescharacteristic
122C2×#215C22×C314yes—
123#930—21no—
124#930C22×C312yes—
125C22×C3⋊C8C22×C312yes—
126#875—21no—
127#874C22×C311yescharacteristic
128C4×D12—21no—
129C4×D12C22×C312yes—
130#869C22×C311yescharacteristic
131C3×#106—34no—
132C3×C4⋊C8—32no—
133C3×C4⋊C8—32no—
134C3×#103—34no—
135C3×#102—34no—
136#835C22×C314yes—
137#809C22×C314yes—
138#808C22×C314yes—
139C4⋊(C3⋊C8)C22×C312yes—
140C4⋊(C3⋊C8)C22×C312yes—
141C23×C32C2×D411yescharacteristic
142C22×C3×D3—22no—
143C32×Q8—22no—
144C32×Q8—22no—
145C32×Q8—42no—
146C2×C32×C4—22no—
147C2×C32×C4—22no—
148C2×C32×C4—21no—
149C2×C32×C4—21no—
150C2×C32×C4—41no—
151C2×C32×C4SD1614yescomplemented
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2411yescharacteristic
158C3×#67—44no—
159C2×C3×Dic3—22no—
160C3×D12—22no—
161C3×D12—22no—
162C3×D12—42no—
163C3×D12—42no—
164C3×C4×D3—44no—
165C3×Dic6—42no—
166C3×C3⋊C8—24no—
167#533C3×D311yescharacteristic, complemented
168#532—31no—
169#476—32no—
170#475—32no—
171#465—34no—
172#461—32no—
173#460—32no—
174C2×C4⋊C8—31no—
175C3×#41—124no—
176C2×C3×Q8—22no—
177C2×C3×Q8—21no—
178C2×C3×Q8—21no—
179C2×C3×Q8—22no—
180C2×C3×Q8—61no—
181C2×C3×Q8C22×D312yes—
182C2×C3×Q8C23×C312yes—
183C2×C3×D4—32no—
184C2×C3×D4—62no—
185C2×C3×D4—61no—
186C2×C3×D4—61no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—62no—
191C22×C3×C4#6711yescharacteristic
192C22×C3×C4#6711yescharacteristic
193C22×C3×C4C3×D411yescharacteristic
194C22×C3×C4C3×D411yescharacteristic
195C22×C3×C4C22×D311yescharacteristic
196C22×C3×C4C23×C311yescharacteristic
197C2×#67—22no—
198#235—44no—
199C2×D12—21no—
200C2×D12—21no—
201C2×D12C23×C312yes—
202C2×C4×D3—22no—
203C2×Dic6—21no—
204C3×SD16—124no—
205C2×C3×C8—34no—
206C2×C3×C8—122no—
207C3×C4⋊C4—22no—
208C3×C4⋊C4—22no—
209C3×C4⋊C4—24no—
210C3×C4⋊C4—24no—
211C3×C4⋊C4—22no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—22no—
216C3×C4⋊C4—22no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—22no—
221C3×C4⋊C4—22no—
222C3×C4⋊C4—22no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4—61no—
225C3×C4⋊C4C22×D312yes—
226C3×C4⋊C4C23×C312yes—
227C3×C22⋊C4—24no—
228C3×C22⋊C4—22no—
229C3×C22⋊C4—22no—
230C3×C22⋊C4—62no—
231C3×C22⋊C4—62no—
232C3×C42—24no—
233C3×C42—22no—
234C3×C42—22no—
235C3×C42—21no—
236C3×C42—21no—
237C3×C42—21no—
238C3×C42—21no—
239C3×C42#6711yescharacteristic
240C3×C42#6711yescharacteristic
241C3×C42C3×D411yescharacteristic
242C3×C42C3×D411yescharacteristic
243C3×C42C22×D311yescharacteristic
244C3×C42C22×D311yescharacteristic
245C3×C42C23×C311yescharacteristic
246C3×C42C23×C311yescharacteristic
247#215—44no—
248(C2×D3)⋊C4—22no—
249(C2×D3)⋊C4—22no—
250C4⋊Dic3—21no—
251C4⋊Dic3C23×C312yes—
252C2×C3⋊C8—42no—
253C2×C3⋊C8C23×C314yes—
254C22×C32—21no—
255C22×C32—21no—
256C22×C32C2×SD1612yes—
257C22×C32C22×D411yescharacteristic
258C2×C3×D3—42no—
259C2×C3×D3—42no—
260C2×C3×D3—42no—
261C32×C4—21no—
262C32×C4—21no—
263C32×C4—21no—
264C32×C4—42no—
265C32×C4—42no—
266C32×C4C2×SD1612yes—
267C32×C4C2×SD1612yes—
268C32×C4H(5,𝔽2)11yescharacteristic
269C32×C42−1+411yescharacteristic
270C3×Dic3—42no—
271C2×#41—61no—
272C2×SD16—34no—
273C22×C8—32no—
274C4⋊Q8—31no—
275C4⋊Q8C2×C3×D311yescharacteristic
276C4⋊Q8C2×C3×D311yescharacteristic
277#127—31no—
278#125—21no—
279#124—61no—
280C22⋊Q8—21no—
281C22⋊Q8C2×C3×D312yes—
282#121—32no—
283#121—61no—
284C4×Q8—21no—
285C4×Q8C2×C3×D312yes—
286C4×D4—32no—
287C4×D4—61no—
288#117—21no—
289C2×C42C2×C3×D311yescharacteristic
290#106—34no—
291C4⋊C8—32no—
292C4⋊C8—32no—
293#103—34no—
294#102—34no—
295C23×C3—21no—
296C23×C3—62no—
297C23×C3C2×#6711yescharacteristic
298C23×C3C2×C3×D411yescharacteristic
299C22×D3—22no—
300C3×Q8—22no—
301C3×Q8—22no—
302C3×Q8—22no—
303C3×Q8—22no—
304C3×Q8—42no—
305C3×Q8—42no—
306C3×Q8—44no—
307C3×Q8—42no—
308C3×Q8—42no—
309C3×Q8—122no—
310C3×D4—62no—
311C3×D4—62no—
312C3×D4—122no—
313C3×D4—124no—
314C3×D4—122no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—24no—
320C2×C3×C4—24no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—21no—
326C2×C3×C4—24no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—41no—
333C2×C3×C4—41no—
334C2×C3×C4—41no—
335C2×C3×C4—41no—
336C2×C3×C4—42no—
337C2×C3×C4—62no—
338C2×C3×C4—124no—
339C2×C3×C4#21514yescomplemented
340C2×C3×C4C3×SD1614yescomplemented
341C2×C3×C4C2×#6711yescharacteristic
342C2×C3×C4C2×#6711yescharacteristic
343C2×C3×C4C2×#6711yescharacteristic
344C2×C3×C4C2×#6711yescharacteristic
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C2×C3×D411yescharacteristic
347C2×C3×C4C2×C3×D411yescharacteristic
348C2×C3×C4C2×C3×D411yescharacteristic
349C2×C3×C4C2×C3×D411yescharacteristic
350C2×C3×C4C2×C3×D411yescharacteristic
351C2×C3×C4C23×D311yescharacteristic
352C2×C3×C4C24×C311yescharacteristic
353#67—44no—
354C2×Dic3—22no—
355D12—22no—
356D12—22no—
357D12—42no—
358D12—42no—
359C4×D3—44no—
360Dic6—42no—
361C3×C8—64no—
362C3⋊C8—24no—
363C2×C32—22no—
364C2×C32#53711yescharacteristic
365C2×C32C22×SD1611yescharacteristic
366C2×C32#57511yescharacteristic
367C3×D3—82no—
368#41—124no—
369C2×Q8—21no—
370C2×Q8—61no—
371C2×Q8C22×C3×D312yes—
372C2×D4—32no—
373C2×D4—62no—
374C2×D4—61no—
375C2×D4—61no—
376C22×C4—62no—
377C22×C4C3×#6711yescharacteristic
378C22×C4C3×#6711yescharacteristic
379C22×C4C22×C3×D311yescharacteristic
380SD16—124no—
381C2×C8—34no—
382C2×C8—122no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—32no—
389C4⋊C4—61no—
390C4⋊C4C22×C3×D312yes—
391C22⋊C4—22no—
392C22⋊C4—62no—
393C22⋊C4—62no—
394C42—22no—
395C42C3×#6711yescharacteristic
396C42C3×#6711yescharacteristic
397C42C22×C3×D311yescharacteristic
398C42C22×C3×D311yescharacteristic
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—22no—
404C22×C3—21no—
405C22×C3—41no—
406C22×C3—41no—
407C22×C3—122no—
408C22×C3—122no—
409C22×C3—122no—
410C22×C3C2×#21512yes—
411C22×C3C2×C3×SD1612yes—
412C22×C3C22×#6711yescharacteristic
413C22×C3C22×C3×D411yescharacteristic
414C2×D3—42no—
415C2×D3—42no—
416C2×D3—42no—
417C3×C4—22no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—22no—
425C3×C4—22no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—41no—
429C3×C4—41no—
430C3×C4—44no—
431C3×C4—44no—
432C3×C4—42no—
433C3×C4—42no—
434C3×C4—42no—
435C3×C4—42no—
436C3×C4—122no—
437C3×C4C2×#21512yes—
438C3×C4C2×#21512yes—
439C3×C4C2×C3×SD1612yes—
440C3×C4C2×C3×SD1612yes—
441C3×C4#100911yescharacteristic
442C3×C4#101011yescharacteristic
443C3×C4C3×H(5,𝔽2)11yescharacteristic
444C3×C4C3×2−1+411yescharacteristic
445Dic3—42no—
446C32#324611yescharacteristic, complemented, Sylow
447C23—62no—
448C23C2×C3×#6711yescharacteristic
449Q8—22no—
450Q8—22no—
451Q8—42no—
452Q8—122no—
453D4—62no—
454D4—62no—
455D4—122no—
456D4—124no—
457D4—122no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—41no—
463C2×C4—62no—
464C2×C4—124no—
465C2×C4C3×#21514yescomplemented
466C2×C4C2×C3×#6711yescharacteristic
467C2×C4C2×C3×#6711yescharacteristic
468C2×C4C2×C3×#6711yescharacteristic
469C2×C4C2×C3×#6711yescharacteristic
470C2×C4C2×C3×#6711yescharacteristic
471C2×C4C23×C3×D311yescharacteristic
472C8—64no—
473C2×C3—22no—
474C2×C3—22no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—42no—
479C2×C3—242no—
480C2×C3C22×#21511yescharacteristic
481C2×C3#582211yescharacteristic
482C2×C3#583311yescharacteristic
483C2×C3C3×#53711yescharacteristic
484C2×C3C22×C3×SD1611yescharacteristic
485C2×C3C3×#57511yescharacteristic
486D3—82no—
487C22—21no—
488C22—21no—
489C22—122no—
490C22—122no—
491C22—122no—
492C22C2×C3×#21512yes—
493C22C22×C3×#6711yescharacteristic
494C4—21no—
495C4—21no—
496C4—21no—
497C4—42no—
498C4—42no—
499C4—122no—
500C4C2×C3×#21512yes—
501C4C2×C3×#21512yes—
502C4C3×#100911yescharacteristic
503C4C3×#101011yescharacteristic
504C3—21no—
505C3#8336311yescharacteristic, direct product factor
506C3C3×#324611yescharacteristic, complemented
507C2—22no—
508C2—242no—
509C2C22×C3×#21511yescharacteristic
510C2C3×#582211yescharacteristic
511C2C3×#583311yescharacteristic
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×#3246
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×#5084C2semidirect
4. C3×#5083C2semidirect
5. C3×#5048C2semidirect
6. C3×#5027C2semidirect
7. C3×#5020C2semidirect
8. C2×C3×C4⋊(C3⋊C8)C2semidirect
10. #83363C3direct (N × H)
36. C3×#533D3semidirect
37. C3×#533C2×C3semidirect
46. #5084C2×C3semidirect
47. #5083C2×C3semidirect
48. #5048C2×C3semidirect
49. #5027C2×C3semidirect
50. #5020C2×C3semidirect
51. C2×C4⋊(C3⋊C8)C2×C3semidirect
151. C2×C32×C4SD16semidirect
167. #533C3×D3semidirect
339. C2×C3×C4#215semidirect
340. C2×C3×C4C3×SD16semidirect
446. C32#3246semidirect
465. C2×C4C3×#215semidirect
505. C3#83363direct (N × H)
506. C3C3×#3246semidirect

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×#50842
C3×#50832
C3×#50482
C3×#50272
C3×#50202
C2×C3×C4⋊(C3⋊C8)2
C3×#32463
#833633