Finite Group Databasebeta

← C3×#82032 #11899703

Subgroups — C3×#82032 #11899703

Order 1152.

762 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
1C3×#5771C211yesmaximal, characteristic, complemented
2C3×#5769C211yesmaximal, characteristic, complemented
3C32×#508C211yesmaximal, characteristic, complemented
4C3×#5195C211yesmaximal, characteristic, complemented
5C3×#5193C211yesmaximal, characteristic, complemented
6C3×#4918C212yesmaximal, complemented
7C3×#4916C212yesmaximal, complemented
8C3×D3×SD32C212yesmaximal, complemented
9C3×#4911C212yesmaximal, complemented
10C2×C3×#800C211yesmaximal, characteristic, complemented
11C3×#4901C211yesmaximal, characteristic, complemented
12C3×#3416—31nomaximal
13#82032C311yesmaximal, characteristic, direct product factor
14C3×#1010—21no—
15C3×#1009—21no—
16C32×#135C2211yescharacteristic
17C32×#135C2211yescharacteristic, complemented
18C3×#951—21no—
19C3×#949—21no—
20C3×#919C2212yes—
21C3×D3×Q16C2212yescomplemented
22C3×#915—22no—
23C3×#914—22no—
24C3×#912C2212yescomplemented
25C3×D3×D8C2212yes—
26C2×C3×Dic12C2211yescharacteristic, complemented
27C2×C3×D24C2211yescharacteristic
28C3×#901C2211yescharacteristic
29C32×Q32C2211yescharacteristic, complemented
30C32×SD32C2211yescharacteristic, complemented
31C32×SD32C2211yescharacteristic, complemented
32C32×D16C2211yescharacteristic, complemented
33C2×C32×C16C2211yescharacteristic, complemented
34C3×#829C2212yescomplemented
35C3×#828C2212yescomplemented
36C3×#827C2212yescomplemented
37C3×#826C2212yescomplemented
38C3×#812C2211yescharacteristic, complemented
39C3×#800C2212yescomplemented
40C3×#800C2212yescomplemented
41C3×#798C2212yescomplemented
42C3×D3×C16C2212yescomplemented
43C3×#578—31no—
44C3×#576—31no—
45#5771C2×C311yescharacteristic, complemented
46#5769C2×C311yescharacteristic, complemented
47C3×#510—31no—
48C3×#510—32no—
49C3×#509—31no—
50C3×#509—32no—
51C3×#508—21no—
52C3×#508—32no—
53C3×#508D311yescharacteristic, complemented
54C3×#508C2×C311yescharacteristic, complemented
55C2×C3×SD32—32no—
56C2×C3×SD32—31no—
57C3×#504—31no—
58#5195C2×C311yescharacteristic, complemented
59#5193C2×C311yescharacteristic, complemented
60#4918C2×C312yescomplemented
61#4916C2×C312yescomplemented
62D3×SD32C2×C312yescomplemented
63#4911C2×C312yescomplemented
64C2×#800C2×C311yescharacteristic, complemented
65#4901C2×C311yescharacteristic, complemented
66C32×#41—21no—
67C32×#41—21no—
68C3×#239—22no—
69C3×D3×Q8—22no—
70C3×#237—22no—
71C3×#237—42no—
72C3×D3×D4—22no—
73C3×D3×D4—42no—
74C3×#235—41no—
75C3×#235—41no—
76C3×#235D411yescharacteristic
77C2×C3×D12—21no—
78C2×C3×D12—41no—
79C2×C3×Dic6—21no—
80C2×C3×Dic6—41no—
81C32×Q16C2311yescharacteristic
82C32×Q16C2311yescharacteristic
83C32×SD16—21no—
84C32×SD16—21no—
85C32×D8C2311yescharacteristic
86C32×D8C2311yescharacteristic
87C2×C32×C8C2311yescharacteristic
88C3×#216—22no—
89C3×#215—22no—
90C3×#214—22no—
91C3×#213—22no—
92C3×#208D411yescharacteristic
93C3×Dic12—21no—
94C3×Dic12C2312yes—
95C3×D24—21no—
96C3×D24C2312yes—
97C3×ΓL(1,𝔽25)D412yes—
98C3×D3×C8C2312yes—
99C32×C16C2311yescharacteristic
100C32×C16C2311yescharacteristic
101C3×C3⋊C16C2312yes—
102#3416—31noSylow
103C3×2−1+4—61no—
104C3×H(5,𝔽2)—61no—
105#1010—21no—
106#1009—21no—
107C3×#137—62no—
108C3×#137—61no—
109C3×AGL(1,ℤ/8)—62no—
110C3×AGL(1,ℤ/8)—61no—
111C3×#135—21no—
112C3×#135—21no—
113C3×#135—32no—
114C3×#135—32no—
115C3×#135C2×D311yescharacteristic
116C3×#135C2×D311yescharacteristic, complemented
117C3×#135C22×C311yescharacteristic
118C3×#135C22×C311yescharacteristic, complemented
119C2×C3×Q16—32no—
120C2×C3×Q16—31no—
121C2×C3×D8—32no—
122C2×C3×D8—31no—
123C3×#131—31no—
124#951—21no—
125#949—21no—
126#919C22×C312yes—
127D3×Q16C22×C312yescomplemented
128#915—22no—
129#914—22no—
130#912C22×C312yescomplemented
131D3×D8C22×C312yes—
132C2×Dic12C22×C311yescharacteristic, complemented
133C2×D24C22×C311yescharacteristic
134#901C22×C311yescharacteristic
135C3×Q32—21no—
136C3×Q32—32no—
137C3×Q32C2×D311yescharacteristic, complemented
138C3×Q32C22×C311yescharacteristic, complemented
139C3×SD32—21no—
140C3×SD32—21no—
141C3×SD32—32no—
142C3×SD32—32no—
143C3×SD32—32no—
144C3×SD32—32no—
145C3×SD32C2×D311yescharacteristic, complemented
146C3×SD32C2×D311yescharacteristic, complemented
147C3×SD32C22×C311yescharacteristic, complemented
148C3×SD32C22×C311yescharacteristic, complemented
149C3×D16—21no—
150C3×D16—32no—
151C3×D16C2×D311yescharacteristic, complemented
152C3×D16C22×C311yescharacteristic, complemented
153C3×M32—31no—
154C3×M32—32no—
155C2×C3×C16—21no—
156C2×C3×C16—32no—
157C2×C3×C16C2×D311yescharacteristic, complemented
158C2×C3×C16C22×C311yescharacteristic, complemented
159#829C22×C312yescomplemented
160#828C22×C312yescomplemented
161#827C22×C312yescomplemented
162#826C22×C312yescomplemented
163#812C22×C311yescharacteristic, complemented
164#800C22×C312yescomplemented
165#800C22×C312yescomplemented
166#798C22×C312yescomplemented
167D3×C16C22×C312yescomplemented
168C22×C3×D3—41no—
169C22×C3×D3—42no—
170C32×Q8—21no—
171C32×Q8—21no—
172C32×D4—21no—
173C32×D4—21no—
174C32×D4—41no—
175C32×D4—41no—
176C2×C32×C4—41no—
177C2×C32×C4—41no—
178C2×C32×C4C2×D411yescharacteristic
179C3×#67—42no—
180C3×#67—42no—
181C3×#67D812yes—
182C2×C3×Dic3—41no—
183C2×C3×Dic3—42no—
184C3×D12—22no—
185C3×D12—42no—
186C3×D12—41no—
187C3×D12D811yescharacteristic
188C3×C4×D3—42no—
189C3×C4×D3—42no—
190C3×C4×D3C2×D412yes—
191C3×Dic6—22no—
192C3×Dic6—41no—
193C3×Dic6—42no—
194C3×Dic6D811yescharacteristic
195C32×C8C2×D411yescharacteristic
196C32×C8C2411yescharacteristic
197C3×C3⋊C8C2×D412yes—
198#578—31no—
199#576—31no—
200#510—31no—
201#510—32no—
202#509—31no—
203#509—32no—
204#508—32no—
205#508C3×D311yescharacteristic, complemented
206C2×SD32—32no—
207C2×SD32—31no—
208#504—31no—
209C3×#41—21no—
210C3×#41—21no—
211C3×#41—21no—
212C3×#41—21no—
213C3×#41—31no—
214C3×#41—41no—
215C3×#41—41no—
216C3×#41—62no—
217C3×#41—62no—
218C3×#41—121no—
219C3×#41—121no—
220C3×#41—122no—
221C2×C3×Q8—62no—
222C2×C3×Q8—61no—
223C2×C3×Q8—121no—
224C2×C3×D4—62no—
225C2×C3×D4—61no—
226C2×C3×D4—121no—
227C2×C3×D4—122no—
228#239—22no—
229D3×Q8—22no—
230#237—22no—
231#237—42no—
232D3×D4—22no—
233D3×D4—42no—
234#235—41no—
235#235—41no—
236#235C3×D411yescharacteristic
237C2×D12—21no—
238C2×D12—41no—
239C2×Dic6—21no—
240C2×Dic6—41no—
241C3×Q16—21no—
242C3×Q16—21no—
243C3×Q16—32no—
244C3×Q16—62no—
245C3×Q16—61no—
246C3×Q16C22×D311yescharacteristic
247C3×Q16C22×D311yescharacteristic
248C3×Q16C23×C311yescharacteristic
249C3×Q16C23×C311yescharacteristic
250C3×SD16—21no—
251C3×SD16—21no—
252C3×SD16—21no—
253C3×SD16—21no—
254C3×SD16—41no—
255C3×SD16—41no—
256C3×SD16—62no—
257C3×SD16—62no—
258C3×D8—21no—
259C3×D8—21no—
260C3×D8—32no—
261C3×D8—62no—
262C3×D8—61no—
263C3×D8C22×D311yescharacteristic
264C3×D8C22×D311yescharacteristic
265C3×D8C23×C311yescharacteristic
266C3×D8C23×C311yescharacteristic
267C3×M16—31no—
268C3×M16—32no—
269C2×C3×C8—21no—
270C2×C3×C8—32no—
271C2×C3×C8C22×D311yescharacteristic
272C2×C3×C8C23×C311yescharacteristic
273#216—22no—
274#215—22no—
275#214—22no—
276#213—22no—
277#208C3×D411yescharacteristic
278Dic12—21no—
279Dic12C23×C312yes—
280D24—21no—
281D24C23×C312yes—
282ΓL(1,𝔽25)C3×D412yes—
283D3×C8C23×C312yes—
284C3×C16—21no—
285C3×C16—21no—
286C3×C16—32no—
287C3×C16C22×D311yescharacteristic
288C3×C16C22×D311yescharacteristic
289C3×C16C23×C311yescharacteristic
290C3×C16C23×C311yescharacteristic
291C3⋊C16C23×C312yes—
292C22×C32—41no—
293C22×C32—41no—
294C22×C32C2×D811yescharacteristic
295C2×C3×D3—42no—
296C2×C3×D3—162no—
297C2×C3×D3—161no—
298C2×C3×D3C2×D812yes—
299C32×C4—41no—
300C32×C4—41no—
301C32×C4C2×D811yescharacteristic
302C32×C4C22×D411yescharacteristic
303C3×Dic3—42no—
304C3×Dic3C2×D812yes—
3052−1+4—61no—
306H(5,𝔽2)—61no—
307#137—62no—
308#137—61no—
309AGL(1,ℤ/8)—62no—
310AGL(1,ℤ/8)—61no—
311#135—32no—
312#135—32no—
313#135C2×C3×D311yescharacteristic
314#135C2×C3×D311yescharacteristic, complemented
315C2×Q16—32no—
316C2×Q16—31no—
317C2×D8—32no—
318C2×D8—31no—
319#131—31no—
320Q32—32no—
321Q32C2×C3×D311yescharacteristic, complemented
322SD32—32no—
323SD32—32no—
324SD32—32no—
325SD32—32no—
326SD32C2×C3×D311yescharacteristic, complemented
327SD32C2×C3×D311yescharacteristic, complemented
328D16—32no—
329D16C2×C3×D311yescharacteristic, complemented
330M32—31no—
331M32—32no—
332C2×C16—32no—
333C2×C16C2×C3×D311yescharacteristic, complemented
334C23×C3—122no—
335C23×C3—121no—
336C22×D3—41no—
337C22×D3—42no—
338C3×Q8—21no—
339C3×Q8—21no—
340C3×Q8—21no—
341C3×Q8—21no—
342C3×Q8—31no—
343C3×Q8—41no—
344C3×Q8—41no—
345C3×Q8—62no—
346C3×Q8—122no—
347C3×Q8—121no—
348C3×D4—21no—
349C3×D4—21no—
350C3×D4—21no—
351C3×D4—21no—
352C3×D4—32no—
353C3×D4—31no—
354C3×D4—41no—
355C3×D4—41no—
356C3×D4—41no—
357C3×D4—41no—
358C3×D4—41no—
359C3×D4—41no—
360C3×D4—62no—
361C3×D4—81no—
362C3×D4—81no—
363C3×D4—122no—
364C3×D4—122no—
365C3×D4—122no—
366C3×D4—121no—
367C2×C3×C4—21no—
368C2×C3×C4—32no—
369C2×C3×C4—41no—
370C2×C3×C4—41no—
371C2×C3×C4—41no—
372C2×C3×C4—41no—
373C2×C3×C4—81no—
374C2×C3×C4—81no—
375C2×C3×C4—122no—
376C2×C3×C4—122no—
377C2×C3×C4—122no—
378C2×C3×C4—121no—
379C2×C3×C4D3×D411yescharacteristic
380C2×C3×C4C2×C3×D411yescharacteristic
381#67—42no—
382#67—42no—
383#67C3×D812yes—
384C2×Dic3—41no—
385C2×Dic3—42no—
386D12—22no—
387D12—42no—
388D12—41no—
389D12C3×D811yescharacteristic
390C4×D3—42no—
391C4×D3—42no—
392C4×D3C2×C3×D412yes—
393Dic6—22no—
394Dic6—41no—
395Dic6—42no—
396Dic6C3×D811yescharacteristic
397C3×C8—21no—
398C3×C8—21no—
399C3×C8—32no—
400C3×C8D3×D411yescharacteristic
401C3×C8C2×C3×D411yescharacteristic
402C3×C8C23×D311yescharacteristic
403C3×C8C24×C311yescharacteristic
404C3⋊C8C2×C3×D412yes—
405C2×C32—21no—
406C2×C32—81no—
407C2×C32—81no—
408C2×C32C22×D811yescharacteristic
409C3×D3—22no—
410C3×D3—82no—
411#41—21no—
412#41—21no—
413#41—31no—
414#41—62no—
415#41—62no—
416#41—121no—
417#41—121no—
418#41—122no—
419C2×Q8—62no—
420C2×Q8—61no—
421C2×Q8—121no—
422C2×D4—62no—
423C2×D4—61no—
424C2×D4—121no—
425C2×D4—122no—
426Q16—32no—
427Q16—62no—
428Q16—61no—
429Q16C22×C3×D311yescharacteristic
430Q16C22×C3×D311yescharacteristic
431SD16—21no—
432SD16—21no—
433SD16—62no—
434SD16—62no—
435D8—32no—
436D8—62no—
437D8—61no—
438D8C22×C3×D311yescharacteristic
439D8C22×C3×D311yescharacteristic
440M16—31no—
441M16—32no—
442C2×C8—32no—
443C2×C8C22×C3×D311yescharacteristic
444C16—32no—
445C16C22×C3×D311yescharacteristic
446C16C22×C3×D311yescharacteristic
447C22×C3—21no—
448C22×C3—32no—
449C22×C3—41no—
450C22×C3—41no—
451C22×C3—41no—
452C22×C3—41no—
453C22×C3—81no—
454C22×C3—81no—
455C22×C3—122no—
456C22×C3—481no—
457C22×C3—482no—
458C22×C3D3×D811yescharacteristic
459C22×C3C2×C3×D811yescharacteristic
460C2×D3—42no—
461C2×D3—162no—
462C2×D3—161no—
463C2×D3C2×C3×D812yes—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—32no—
467C3×C4—41no—
468C3×C4—41no—
469C3×C4—41no—
470C3×C4—41no—
471C3×C4—81no—
472C3×C4—81no—
473C3×C4—122no—
474C3×C4D3×D811yescharacteristic
475C3×C4C2×C3×D811yescharacteristic
476C3×C4C2×D3×D411yescharacteristic
477C3×C4C22×C3×D411yescharacteristic
478Dic3—42no—
479Dic3C2×C3×D812yes—
480C32#341611yescharacteristic, complemented, Sylow
481C23—122no—
482C23—121no—
483Q8—21no—
484Q8—21no—
485Q8—31no—
486Q8—62no—
487Q8—122no—
488Q8—121no—
489D4—21no—
490D4—21no—
491D4—32no—
492D4—31no—
493D4—41no—
494D4—41no—
495D4—62no—
496D4—122no—
497D4—122no—
498D4—122no—
499D4—121no—
500C2×C4—32no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—122no—
504C2×C4—122no—
505C2×C4—122no—
506C2×C4—121no—
507C2×C4C3×D3×D411yescharacteristic
508C8—32no—
509C8C3×D3×D411yescharacteristic
510C8C23×C3×D311yescharacteristic
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—41no—
515C2×C3—62no—
516C2×C3—81no—
517C2×C3—81no—
518C2×C3—81no—
519C2×C3—81no—
520C2×C3—161no—
521C2×C3—161no—
522C2×C3—242no—
523C2×C3C2×D3×D811yescharacteristic
524C2×C3C22×C3×D811yescharacteristic
525D3—22no—
526D3—82no—
527C22—32no—
528C22—41no—
529C22—41no—
530C22—122no—
531C22—481no—
532C22—482no—
533C22C3×D3×D811yescharacteristic
534C4—32no—
535C4—41no—
536C4—41no—
537C4—122no—
538C4C3×D3×D811yescharacteristic
539C4C2×C3×D3×D411yescharacteristic
540C3—21no—
541C3#8203211yescharacteristic, direct product factor
542C3C3×#341611yescharacteristic, complemented
543C2—21no—
544C2—62no—
545C2—81no—
546C2—81no—
547C2—242no—
548C2C2×C3×D3×D811yescharacteristic
subgroupG/H
centerC2×C3C2×D3×D8
commutator, cosocleC3×C8C24×C3
FrattiniC8C23×C3×D3
FittingC32×#508C2
socleC2×C32C22×D8
hypercenterC3×#508D3
hypocenterC3C3×#3416
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×C8 ◁ C3×#508

Complements

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

NH ≅ G/Ntype
1. C3×#5771C2semidirect
2. C3×#5769C2semidirect
3. C32×#508C2semidirect
4. C3×#5195C2semidirect
5. C3×#5193C2semidirect
6. C3×#4918C2semidirect
7. C3×#4916C2semidirect
8. C3×D3×SD32C2semidirect
9. C3×#4911C2semidirect
10. C2×C3×#800C2semidirect
11. C3×#4901C2semidirect
13. #82032C3direct (N × H)
17. C32×#135C22semidirect
21. C3×D3×Q16C22semidirect
24. C3×#912C22semidirect
26. C2×C3×Dic12C22semidirect
29. C32×Q32C22semidirect
30. C32×SD32C22semidirect
31. C32×SD32C22semidirect
32. C32×D16C22semidirect
33. C2×C32×C16C22semidirect
34. C3×#829C22semidirect
35. C3×#828C22semidirect
36. C3×#827C22semidirect
37. C3×#826C22semidirect
38. C3×#812C22semidirect
39. C3×#800C22semidirect
40. C3×#800C22semidirect
41. C3×#798C22semidirect
42. C3×D3×C16C22semidirect
45. #5771C2×C3semidirect
46. #5769C2×C3semidirect
53. C3×#508D3semidirect
54. C3×#508C2×C3semidirect
58. #5195C2×C3semidirect
59. #5193C2×C3semidirect
60. #4918C2×C3semidirect
61. #4916C2×C3semidirect
62. D3×SD32C2×C3semidirect
63. #4911C2×C3semidirect
64. C2×#800C2×C3semidirect
65. #4901C2×C3semidirect
116. C3×#135C2×D3semidirect
118. C3×#135C22×C3semidirect
127. D3×Q16C22×C3semidirect
130. #912C22×C3semidirect
132. C2×Dic12C22×C3semidirect
137. C3×Q32C2×D3semidirect
138. C3×Q32C22×C3semidirect
145. C3×SD32C2×D3semidirect
146. C3×SD32C2×D3semidirect
147. C3×SD32C22×C3semidirect
148. C3×SD32C22×C3semidirect
151. C3×D16C2×D3semidirect
152. C3×D16C22×C3semidirect
157. C2×C3×C16C2×D3semidirect
158. C2×C3×C16C22×C3semidirect
159. #829C22×C3semidirect
160. #828C22×C3semidirect
161. #827C22×C3semidirect
162. #826C22×C3semidirect
163. #812C22×C3semidirect
164. #800C22×C3semidirect
165. #800C22×C3semidirect
166. #798C22×C3semidirect
167. D3×C16C22×C3semidirect
205. #508C3×D3semidirect
314. #135C2×C3×D3semidirect
321. Q32C2×C3×D3semidirect
326. SD32C2×C3×D3semidirect
327. SD32C2×C3×D3semidirect
329. D16C2×C3×D3semidirect
333. C2×C16C2×C3×D3semidirect
480. C32#3416semidirect
541. C3#82032direct (N × H)
542. C3C3×#3416semidirect

Maximal subgroups

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

subgroupindex
C3×#57712
C3×#57692
C32×#5082
C3×#51952
C3×#51932
C3×#49182
C3×#49162
C3×D3×SD322
C3×#49112
C2×C3×#8002
C3×#49012
C3×#34163
#820323