Finite Group Databasebeta

← C3×#83350 #11868640

Subgroups — C3×#83350 #11868640

Order 1152.

991 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#533C211yesmaximal, characteristic, complemented
2C2×C3×C4×D12C211yesmaximal, characteristic
3C3×#5087C212yesmaximal, complemented
4C3×#5084C212yesmaximal, complemented
5C3×#5066C214yesmaximal, complemented
6C3×#5001C212yesmaximal
7C3×#4995C212yesmaximal, complemented
8C3×#4924C211yesmaximal, characteristic, complemented
9C3×#3077—31nomaximal
10#83350C311yesmaximal, characteristic, direct product factor
11C22×C3×D12C2211yescharacteristic
12C22×C3×C4×D3—21no—
13C32×C4⋊Q8C2211yescharacteristic, complemented
14C32×C4⋊Q8C2211yescharacteristic, complemented
15C32×#125C2212yescomplemented
16C32×C22⋊Q8—21no—
17C32×C22⋊Q8—21no—
18C32×C4×Q8—21no—
19C32×C4×Q8—21no—
20C32×#117C2212yes—
21C2×C32×C42C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4—21no—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×#208C2212yes—
25C3×C4×D12—21no—
26C3×C4×D12—21no—
27C3×C4×D12C2212yes—
28C3×C4×D12C2212yes—
29C3×#809C2214yes—
30C3×#809C2214yes—
31C3×#808C2214yescomplemented
32C3×#807C2214yescomplemented
33C3×C4⋊(C3⋊C8)C2212yescomplemented
34C3×C4⋊(C3⋊C8)C2212yescomplemented
35C3×#533—21no—
36C3×#533D311yescharacteristic, complemented
37C3×#533C2×C311yescharacteristic, complemented
38C2×C3×C4×D4—31no—
39C2×C4×D12C2×C311yescharacteristic
40C3×#478—34no—
41C3×#476—32no—
42C3×#474—32no—
43C3×#428—32no—
44C3×#423—31no—
45C3×#418—32no—
46#5087C2×C312yescomplemented
47#5084C2×C312yescomplemented
48#5066C2×C314yescomplemented
49#5001C2×C312yes—
50#4995C2×C312yescomplemented
51#4924C2×C311yescharacteristic, complemented
52C23×C3×D3—21no—
53C2×C32×Q8—21no—
54C2×C32×Q8—21no—
55C22×C32×C4D411yescharacteristic
56C22×C32×C4D411yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C3×Dic3—21no—
59C2×C3×D12—21no—
60C2×C3×D12—22no—
61C2×C3×D12Q814yescomplemented
62C2×C3×D12C2312yes—
63C2×C3×C4×D3—22no—
64C2×C3×C4×D3—22no—
65C2×C3×C4×D3—44no—
66C32×C4⋊C4—22no—
67C32×C4⋊C4—22no—
68C32×C4⋊C4—21no—
69C32×C4⋊C4—21no—
70C32×C4⋊C4C2312yes—
71C32×C4⋊C4C2312yes—
72C32×C22⋊C4—22no—
73C32×C42—22no—
74C32×C42D411yescharacteristic
75C32×C42D411yescharacteristic
76C32×C42C2311yescharacteristic
77C32×C42C2311yescharacteristic
78C3×(C2×D3)⋊C4—22no—
79C3×(C2×D3)⋊C4—22no—
80C3×C4⋊Dic3—21no—
81C3×C4⋊Dic3C2312yes—
82C3×#208—24no—
83C2×C3×C3⋊C8C2314yes—
84#3077—31noSylow
85C22×C3×D4—31no—
86C23×C3×C4—61no—
87C22×D12C22×C311yescharacteristic
88C22×C4×D3—21no—
89C2×C3×M16—32no—
90C3×C4⋊Q8—21no—
91C3×C4⋊Q8—21no—
92C3×C4⋊Q8C2×D311yescharacteristic, complemented
93C3×C4⋊Q8C2×D311yescharacteristic, complemented
94C3×C4⋊Q8C22×C311yescharacteristic, complemented
95C3×C4⋊Q8C22×C311yescharacteristic, complemented
96C3×#125—22no—
97C3×#125C2×D312yescomplemented
98C3×#125C22×C312yescomplemented
99C3×C22⋊Q8—22no—
100C3×C22⋊Q8—22no—
101C3×C22⋊Q8—21no—
102C3×C22⋊Q8—21no—
103C3×C22⋊Q8—21no—
104C3×C22⋊Q8—21no—
105C3×C4×Q8—22no—
106C3×C4×Q8—22no—
107C3×C4×Q8—21no—
108C3×C4×Q8—21no—
109C3×C4×Q8—21no—
110C3×C4×Q8—21no—
111C3×C4×D4—32no—
112C3×C4×D4—32no—
113C3×C4×D4—61no—
114C3×C4×D4—61no—
115C3×#117—22no—
116C3×#117C2×D312yes—
117C3×#117C22×C312yes—
118C2×C3×C4⋊C4—31no—
119C2×C3×C22⋊C4—61no—
120C2×C3×C42—21no—
121C2×C3×C42C2×D311yescharacteristic
122C2×C3×C42C22×C311yescharacteristic
123C2×(C2×D3)⋊C4—21no—
124C2×C4⋊Dic3C22×C311yescharacteristic
125C2×#208C22×C312yes—
126C4×D12—21no—
127C4×D12—21no—
128C4×D12C22×C312yes—
129C4×D12C22×C312yes—
130C3×#107—34no—
131C3×#106—34no—
132C3×C4⋊C8—32no—
133C3×C4⋊C8—32no—
134C3×#102—34no—
135C3×#102—34no—
136#809C22×C314yes—
137#809C22×C314yes—
138#808C22×C314yescomplemented
139#807C22×C314yescomplemented
140C4⋊(C3⋊C8)C22×C312yescomplemented
141C4⋊(C3⋊C8)C22×C312yescomplemented
142C23×C32C2×D411yescharacteristic
143C22×C3×D3—24no—
144C22×C3×D3—22no—
145C22×C3×D3—42no—
146C22×C3×D3—42no—
147C32×Q8—42no—
148C32×Q8—42no—
149C2×C32×C4—22no—
150C2×C32×C4—22no—
151C2×C32×C4—22no—
152C2×C32×C4—41no—
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2×Q812yes—
159C2×C32×C4#4112yes—
160C2×C32×C4C2411yescharacteristic
161C2×C3×Dic3—22no—
162C2×C3×Dic3—42no—
163C3×D12—24no—
164C3×D12—22no—
165C3×D12C2×Q814yes—
166C3×C4×D3—44no—
167C3×C4×D3—44no—
168C3×C3⋊C8—24no—
169#533C3×D311yescharacteristic, complemented
170C2×C4×D4—31no—
171#478—34no—
172#476—32no—
173#474—32no—
174#428—32no—
175#423—31no—
176#418—32no—
177C24×C3—61no—
178C23×D3—21no—
179C2×C3×Q8—22no—
180C2×C3×Q8—22no—
181C2×C3×Q8—21no—
182C2×C3×Q8—21no—
183C2×C3×Q8—21no—
184C2×C3×Q8—21no—
185C2×C3×D4—34no—
186C2×C3×D4—32no—
187C2×C3×D4—62no—
188C2×C3×D4—61no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—61no—
193C22×C3×C4—62no—
194C22×C3×C4—62no—
195C22×C3×C4—124no—
196C22×C3×C4#6711yescharacteristic
197C22×C3×C4#6711yescharacteristic
198C22×C3×C4C3×D411yescharacteristic
199C22×C3×C4C3×D411yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C23×C311yescharacteristic
202C22×Dic3—21no—
203C2×D12—21no—
204C2×D12—22no—
205C2×D12C3×Q814yescomplemented
206C2×D12C23×C312yes—
207C2×C4×D3—22no—
208C2×C4×D3—22no—
209C2×C4×D3—44no—
210C3×M16—64no—
211C2×C3×C8—34no—
212C3×C4⋊C4—24no—
213C3×C4⋊C4—24no—
214C3×C4⋊C4—22no—
215C3×C4⋊C4—22no—
216C3×C4⋊C4—22no—
217C3×C4⋊C4—22no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—22no—
221C3×C4⋊C4—22no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—22no—
225C3×C4⋊C4—22no—
226C3×C4⋊C4—32no—
227C3×C4⋊C4—61no—
228C3×C4⋊C4C22×D312yes—
229C3×C4⋊C4C22×D312yes—
230C3×C4⋊C4C23×C312yes—
231C3×C4⋊C4C23×C312yes—
232C3×C22⋊C4—24no—
233C3×C22⋊C4—22no—
234C3×C22⋊C4—22no—
235C3×C22⋊C4—62no—
236C3×C22⋊C4—62no—
237C3×C42—24no—
238C3×C42—22no—
239C3×C42—22no—
240C3×C42—21no—
241C3×C42—21no—
242C3×C42—21no—
243C3×C42—21no—
244C3×C42#6711yescharacteristic
245C3×C42#6711yescharacteristic
246C3×C42C3×D411yescharacteristic
247C3×C42C3×D411yescharacteristic
248C3×C42C22×D311yescharacteristic
249C3×C42C22×D311yescharacteristic
250C3×C42C23×C311yescharacteristic
251C3×C42C23×C311yescharacteristic
252(C2×D3)⋊C4—22no—
253(C2×D3)⋊C4—22no—
254C4⋊Dic3—21no—
255C4⋊Dic3C23×C312yes—
256#208—24no—
257C2×C3⋊C8C23×C314yes—
258C22×C32—21no—
259C22×C32—21no—
260C22×C32C22⋊Q812yes—
261C22×C32C22×D411yescharacteristic
262C2×C3×D3—24no—
263C2×C3×D3—48no—
264C2×C3×D3—42no—
265C2×C3×D3—42no—
266C32×C4—21no—
267C32×C4—21no—
268C32×C4—21no—
269C32×C4—42no—
270C32×C4—42no—
271C32×C4C22⋊Q812yes—
272C32×C4AGL(1,ℤ/8)12yes—
273C32×C4C22×Q811yescharacteristic
274C32×C4C2×#4111yescharacteristic
275C3×Dic3—42no—
276C22×D4—31no—
277C23×C4—61no—
278C2×M16—32no—
279C4⋊Q8C2×C3×D311yescharacteristic, complemented
280C4⋊Q8C2×C3×D311yescharacteristic, complemented
281#125C2×C3×D312yescomplemented
282C22⋊Q8—21no—
283C22⋊Q8—21no—
284C4×Q8—21no—
285C4×Q8—21no—
286C4×D4—32no—
287C4×D4—32no—
288C4×D4—61no—
289C4×D4—61no—
290#117C2×C3×D312yes—
291C2×C4⋊C4—31no—
292C2×C22⋊C4—61no—
293C2×C42C2×C3×D311yescharacteristic
294#107—34no—
295#106—34no—
296C4⋊C8—32no—
297C4⋊C8—32no—
298#102—34no—
299#102—34no—
300C23×C3—21no—
301C23×C3—64no—
302C23×C3—62no—
303C23×C3—122no—
304C23×C3—122no—
305C23×C3C2×#6711yescharacteristic
306C23×C3C2×C3×D411yescharacteristic
307C22×D3—24no—
308C22×D3—22no—
309C22×D3—42no—
310C22×D3—42no—
311C3×Q8—44no—
312C3×Q8—42no—
313C3×Q8—42no—
314C3×Q8—44no—
315C3×Q8—42no—
316C3×Q8—42no—
317C3×D4—34no—
318C3×D4—64no—
319C3×D4—62no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—24no—
323C2×C3×C4—24no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—21no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—42no—
337C2×C3×C4—41no—
338C2×C3×C4—41no—
339C2×C3×C4—42no—
340C2×C3×C4—62no—
341C2×C3×C4—124no—
342C2×C3×C4—122no—
343C2×C3×C4—124no—
344C2×C3×C4D3×Q812yes—
345C2×C3×C4#23912yes—
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C2×#6711yescharacteristic
348C2×C3×C4C2×#6711yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351C2×C3×C4C2×C3×D411yescharacteristic
352C2×C3×C4C2×C3×D411yescharacteristic
353C2×C3×C4C2×C3×D411yescharacteristic
354C2×C3×C4C2×C3×D411yescharacteristic
355C2×C3×C4C2×C3×D411yescharacteristic
356C2×C3×C4C2×C3×Q812yes—
357C2×C3×C4C3×#4112yes—
358C2×C3×C4C23×D311yescharacteristic
359C2×C3×C4C24×C311yescharacteristic
360C2×Dic3—22no—
361C2×Dic3—42no—
362D12—24no—
363D12—22no—
364D12C2×C3×Q814yes—
365C4×D3—44no—
366C4×D3—44no—
367C3×C8—64no—
368C3⋊C8—24no—
369C2×C32—22no—
370C2×C32C2×C22⋊Q811yescharacteristic
371C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
372C2×C32#57511yescharacteristic
373C3×D3—44no—
374C24—61no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×D4—32no—
378C2×D4—34no—
379C2×D4—62no—
380C2×D4—61no—
381C22×C4—61no—
382C22×C4—62no—
383C22×C4—62no—
384C22×C4—124no—
385C22×C4C3×#6711yescharacteristic
386C22×C4C3×#6711yescharacteristic
387C22×C4C22×C3×D311yescharacteristic
388M16—64no—
389C2×C8—34no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—32no—
395C4⋊C4—61no—
396C4⋊C4C22×C3×D312yes—
397C4⋊C4C22×C3×D312yes—
398C22⋊C4—22no—
399C22⋊C4—62no—
400C22⋊C4—62no—
401C42—22no—
402C42C3×#6711yescharacteristic
403C42C3×#6711yescharacteristic
404C42C22×C3×D311yescharacteristic
405C42C22×C3×D311yescharacteristic
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—22no—
411C22×C3—21no—
412C22×C3—41no—
413C22×C3—41no—
414C22×C3—64no—
415C22×C3—128no—
416C22×C3—122no—
417C22×C3—122no—
418C22×C3#94612yes—
419C22×C3C3×C22⋊Q812yes—
420C22×C3C22×#6711yescharacteristic
421C22×C3C22×C3×D411yescharacteristic
422C2×D3—24no—
423C2×D3—48no—
424C2×D3—42no—
425C2×D3—42no—
426C3×C4—22no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—22no—
434C3×C4—22no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—41no—
438C3×C4—41no—
439C3×C4—44no—
440C3×C4—44no—
441C3×C4—42no—
442C3×C4—42no—
443C3×C4—42no—
444C3×C4—42no—
445C3×C4—122no—
446C3×C4#94612yes—
447C3×C4#94912yes—
448C3×C4C3×C22⋊Q812yes—
449C3×C4C3×AGL(1,ℤ/8)12yes—
450C3×C4C2×D3×Q811yescharacteristic
451C3×C4C2×#23911yescharacteristic
452C3×C4C22×C3×Q811yescharacteristic
453C3×C4C2×C3×#4111yescharacteristic
454Dic3—42no—
455C32#307711yescharacteristic, complemented, Sylow
456C23—64no—
457C23—62no—
458C23—122no—
459C23—122no—
460C23C2×C3×#6711yescharacteristic
461Q8—42no—
462Q8—42no—
463D4—34no—
464D4—64no—
465D4—62no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—41no—
470C2×C4—62no—
471C2×C4—124no—
472C2×C4—122no—
473C2×C4—124no—
474C2×C4C3×D3×Q812yes—
475C2×C4C3×#23912yes—
476C2×C4C2×C3×#6711yescharacteristic
477C2×C4C2×C3×#6711yescharacteristic
478C2×C4C2×C3×#6711yescharacteristic
479C2×C4C2×C3×#6711yescharacteristic
480C2×C4C2×C3×#6711yescharacteristic
481C2×C4C23×C3×D311yescharacteristic
482C8—64no—
483C2×C3—22no—
484C2×C3—22no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—42no—
489C2×C3—124no—
490C2×C3C2×#94611yescharacteristic
491C2×C3C2×#94911yescharacteristic
492C2×C3#582211yescharacteristic
493C2×C3C2×C3×C22⋊Q811yescharacteristic
494C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
495C2×C3C3×#57511yescharacteristic
496D3—44no—
497C22—21no—
498C22—21no—
499C22—64no—
500C22—128no—
501C22—122no—
502C22—122no—
503C22C3×#94612yes—
504C22C22×C3×#6711yescharacteristic
505C4—21no—
506C4—21no—
507C4—21no—
508C4—42no—
509C4—42no—
510C4—122no—
511C4C3×#94612yes—
512C4C3×#94912yes—
513C4C2×C3×D3×Q811yescharacteristic
514C4C2×C3×#23911yescharacteristic
515C3—21no—
516C3#8335011yescharacteristic, direct product factor
517C3C3×#307711yescharacteristic, complemented
518C2—22no—
519C2—124no—
520C2C2×C3×#94611yescharacteristic
521C2C2×C3×#94911yescharacteristic
522C2C3×#582211yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#533C2
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
hypercenterC3×#533D3
hypocenterC3C3×#3077
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×#5087C2semidirect
4. C3×#5084C2semidirect
5. C3×#5066C2semidirect
7. C3×#4995C2semidirect
8. C3×#4924C2semidirect
10. #83350C3direct (N × H)
13. C32×C4⋊Q8C22semidirect
14. C32×C4⋊Q8C22semidirect
15. C32×#125C22semidirect
31. C3×#808C22semidirect
32. C3×#807C22semidirect
33. C3×C4⋊(C3⋊C8)C22semidirect
34. C3×C4⋊(C3⋊C8)C22semidirect
36. C3×#533D3semidirect
37. C3×#533C2×C3semidirect
46. #5087C2×C3semidirect
47. #5084C2×C3semidirect
48. #5066C2×C3semidirect
50. #4995C2×C3semidirect
51. #4924C2×C3semidirect
61. C2×C3×D12Q8semidirect
92. C3×C4⋊Q8C2×D3semidirect
93. C3×C4⋊Q8C2×D3semidirect
94. C3×C4⋊Q8C22×C3semidirect
95. C3×C4⋊Q8C22×C3semidirect
97. C3×#125C2×D3semidirect
98. C3×#125C22×C3semidirect
138. #808C22×C3semidirect
139. #807C22×C3semidirect
140. C4⋊(C3⋊C8)C22×C3semidirect
141. C4⋊(C3⋊C8)C22×C3semidirect
169. #533C3×D3semidirect
205. C2×D12C3×Q8semidirect
279. C4⋊Q8C2×C3×D3semidirect
280. C4⋊Q8C2×C3×D3semidirect
281. #125C2×C3×D3semidirect
455. C32#3077semidirect
516. C3#83350direct (N × H)
517. C3C3×#3077semidirect

Maximal subgroups

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

subgroupindex
C32×#5332
C2×C3×C4×D122
C3×#50872
C3×#50842
C3×#50662
C3×#50012
C3×#49952
C3×#49242
C3×#30773
#833503