Finite Group Databasebeta

← C3×#82548 #11860730

Subgroups — C3×#82548 #11860730

Order 1152.

1117 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#519C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic
3C3×#5521C211yesmaximal, characteristic
4C3×#5225C211yesmaximal, characteristic, complemented
5C3×#5026C214yesmaximal, complemented
6C3×C4×#215C214yesmaximal, complemented
7C3×#5001C211yesmaximal, characteristic
8C3×#4998C211yesmaximal, characteristic, complemented
9C3×#4997C211yesmaximal, characteristic, complemented
10C3×#2949—31nomaximal
11#82548C311yesmaximal, characteristic, direct product factor
12C22×C32×Q8C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C32×C4×Q8—22no—
15C32×C4×Q8C2214yescomplemented
16C32×#117—22no—
17C32×#117C2211yescharacteristic
18C32×#117C2211yescharacteristic
19C2×C3×#215C418yescomplemented
20C2×C3×#215C2212yes—
21C2×C3×#215C2212yes—
22C3×#926C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C3×#893—22no—
26C3×D3×C22⋊C4—22no—
27C3×C4×D12C2214yes—
28C3×#835C2214yescomplemented
29C3×#809C2214yes—
30C3×#808C2212yescomplemented
31C3×#807C2212yescomplemented
32C3×#803C2212yescomplemented
33C3×C4×C3⋊C8C2212yescomplemented
34C22×C3×SD16—31no—
35C3×#519—21no—
36C3×#519D311yescharacteristic, complemented
37C3×#519C2×C311yescharacteristic, complemented
38C3×#518—31no—
39C22×#215C2×C311yescharacteristic
40#5521C2×C311yescharacteristic
41C3×#440—34no—
42C3×C4×SD16—34no—
43C3×#427—31no—
44C3×#419—31no—
45C3×#418—31no—
46C3×#405—31no—
47#5225C2×C311yescharacteristic, complemented
48#5026C2×C314yescomplemented
49C4×#215C2×C314yescomplemented
50#5001C2×C311yescharacteristic
51#4998C2×C311yescharacteristic, complemented
52#4997C2×C311yescharacteristic, complemented
53C23×C3×D3—21no—
54C2×C32×Q8—21no—
55C2×C32×Q8—22no—
56C2×C32×Q8C2×C414yescomplemented
57C2×C32×Q8C2312yes—
58C22×C32×C4—21no—
59C22×C32×C4C2311yescharacteristic
60C2×C3×D12—21no—
61C2×C3×D12—22no—
62C2×C3×D12C2×C414yes—
63C2×C3×D12C2312yes—
64C2×C3×C4×D3—24no—
65C32×C4⋊C4—24no—
66C32×C4⋊C4D412yes—
67C32×C4⋊C4C2312yes—
68C32×C22⋊C4—21no—
69C32×C22⋊C4D412yes—
70C32×C42—24no—
71C32×C42—21no—
72C32×C42C2312yes—
73C3×#217—21no—
74C3×#215C2×C418yescomplemented
75C3×#215C2×C418yescomplemented
76C3×(C2×D3)⋊C4—24no—
77C3×C4⋊Dic3C2312yes—
78C3×C4×Dic3—21no—
79C3×#208—22no—
80C2×C3×C3⋊C8C2×C414yescomplemented
81C2×C3×C3⋊C8C2312yes—
82C2×C3×C3⋊C8C2311yescharacteristic
83C2×C3×C3⋊C8C2311yescharacteristic
84#2949—31noSylow
85C22×C3×Q8—21no—
86C22×C3×Q8C2×D311yescharacteristic
87C22×C3×Q8C22×C311yescharacteristic
88C22×C3×D4—31no—
89C22×D12C22×C311yescharacteristic
90C2×C3×SD16—38no—
91C2×C3×SD16—32no—
92C2×C3×SD16—32no—
93C2×C3×M16—31no—
94C22×C3×C8—31no—
95C3×C4×Q8—24no—
96C3×C4×Q8—22no—
97C3×C4×Q8—22no—
98C3×C4×Q8—24no—
99C3×C4×Q8C2×D314yescomplemented
100C3×C4×Q8C22×C314yescomplemented
101C3×C4×D4—34no—
102C3×C4×D4—62no—
103C3×#117—24no—
104C3×#117—22no—
105C3×#117—22no—
106C3×#117—21no—
107C3×#117—21no—
108C3×#117—31no—
109C3×#117C2×D311yescharacteristic
110C3×#117C2×D311yescharacteristic
111C3×#117C22×C311yescharacteristic
112C3×#117C22×C311yescharacteristic
113C2×C3×C22⋊C4—62no—
114C2×#215C3×C418yescomplemented
115C2×#215C22×C312yes—
116C2×#215C22×C312yes—
117#926C22×C311yescharacteristic
118C2×#208C22×C311yescharacteristic
119C22×C3⋊C8C22×C311yescharacteristic
120#893—22no—
121D3×C22⋊C4—22no—
122C4×D12C22×C314yes—
123C3×#107—32no—
124C3×#106—32no—
125C3×#103—34no—
126C3×#102—34no—
127C3×#97—32no—
128C3×C4×C8—32no—
129#835C22×C314yescomplemented
130#809C22×C314yes—
131#808C22×C312yescomplemented
132#807C22×C312yescomplemented
133#803C22×C312yescomplemented
134C4×C3⋊C8C22×C312yescomplemented
135C23×C32C2×D411yescharacteristic
136C22×C3×D3—22no—
137C22×C3×D3—24no—
138C22×C3×D3—82no—
139C32×Q8—24no—
140C32×Q8—22no—
141C32×Q8C22×C414yes—
142C2×C32×C4—24no—
143C2×C32×C4—22no—
144C2×C32×C4—22no—
145C2×C32×C4C22×C412yes—
146C2×C32×C4C2×D414yes—
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4#4112yes—
149C2×C32×C4C2411yescharacteristic
150C2×C3×Dic3—22no—
151C3×D12—24no—
152C3×D12—22no—
153C3×D12C22×C414yes—
154C3×C4×D3—84no—
155C3×C3⋊C8—22no—
156C3×C3⋊C8C22×C412yes—
157C3×C3⋊C8C22×C412yes—
158C22×SD16—31no—
159#519C3×D311yescharacteristic, complemented
160#518—31no—
161#440—34no—
162C4×SD16—34no—
163#427—31no—
164#419—31no—
165#418—31no—
166#405—31no—
167C24×C3—61no—
168C23×D3—21no—
169C2×C3×Q8—22no—
170C2×C3×Q8—24no—
171C2×C3×Q8—22no—
172C2×C3×Q8—21no—
173C2×C3×Q8—21no—
174C2×C3×Q8—22no—
175C2×C3×Q8—24no—
176C2×C3×Q8—22no—
177C2×C3×Q8C4×D314yescomplemented
178C2×C3×Q8C2×C3×C414yescomplemented
179C2×C3×Q8C22×D312yes—
180C2×C3×Q8C23×C312yes—
181C2×C3×D4—34no—
182C2×C3×D4—32no—
183C2×C3×D4—62no—
184C2×C3×D4—61no—
185C22×C3×C4—22no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—64no—
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C23×C311yescharacteristic
192C2×D12—21no—
193C2×D12—22no—
194C2×D12C2×C3×C414yes—
195C2×D12C23×C312yes—
196C2×C4×D3—24no—
197C3×SD16—38no—
198C3×SD16—38no—
199C3×M16—62no—
200C2×C3×C8—34no—
201C2×C3×C8—31no—
202C2×C3×C8—31no—
203C2×C3×C8—32no—
204C3×C4⋊C4—28no—
205C3×C4⋊C4—24no—
206C3×C4⋊C4—24no—
207C3×C4⋊C4—22no—
208C3×C4⋊C4—22no—
209C3×C4⋊C4—32no—
210C3×C4⋊C4#6712yes—
211C3×C4⋊C4C3×D412yes—
212C3×C4⋊C4C22×D312yes—
213C3×C4⋊C4C23×C312yes—
214C3×C22⋊C4—22no—
215C3×C22⋊C4—21no—
216C3×C22⋊C4—21no—
217C3×C22⋊C4—22no—
218C3×C22⋊C4—61no—
219C3×C22⋊C4—64no—
220C3×C22⋊C4#6712yes—
221C3×C22⋊C4C3×D412yes—
222C3×C42—28no—
223C3×C42—22no—
224C3×C42—24no—
225C3×C42—21no—
226C3×C42—24no—
227C3×C42—21no—
228C3×C42—22no—
229C3×C42—61no—
230C3×C42C22×D312yes—
231C3×C42C23×C312yes—
232#217—21no—
233#215C2×C3×C418yescomplemented
234#215C2×C3×C418yescomplemented
235(C2×D3)⋊C4—24no—
236C4⋊Dic3C23×C312yes—
237C4×Dic3—21no—
238#208—22no—
239C2×C3⋊C8C2×C3×C414yescomplemented
240C2×C3⋊C8C23×C312yes—
241C2×C3⋊C8C23×C311yescharacteristic
242C2×C3⋊C8C23×C311yescharacteristic
243C22×C32—22no—
244C22×C32C4×D412yes—
245C22×C32C22×D411yescharacteristic
246C2×C3×D3—24no—
247C2×C3×D3—44no—
248C2×C3×D3—84no—
249C32×C4—24no—
250C32×C4—24no—
251C32×C4—42no—
252C32×C4C4×D412yes—
253C32×C4C23×C411yescharacteristic
254C32×C4C2×#4111yescharacteristic
255C3×Dic3—42no—
256C22×Q8C2×C3×D311yescharacteristic
257C22×D4—31no—
258C2×SD16—38no—
259C2×SD16—32no—
260C2×SD16—32no—
261C2×M16—31no—
262C22×C8—31no—
263C4×Q8—22no—
264C4×Q8C2×C3×D314yescomplemented
265C4×D4—34no—
266C4×D4—62no—
267#117—22no—
268#117—31no—
269#117C2×C3×D311yescharacteristic
270#117C2×C3×D311yescharacteristic
271C2×C22⋊C4—62no—
272#107—32no—
273#106—32no—
274#103—34no—
275#102—34no—
276#97—32no—
277C4×C8—32no—
278C23×C3—21no—
279C23×C3—62no—
280C23×C3—64no—
281C23×C3—242no—
282C23×C3C2×#6711yescharacteristic
283C23×C3C2×C3×D411yescharacteristic
284C22×D3—22no—
285C22×D3—24no—
286C22×D3—82no—
287C3×Q8—28no—
288C3×Q8—24no—
289C3×Q8—24no—
290C3×Q8—24no—
291C3×Q8—22no—
292C3×Q8—22no—
293C3×Q8—24no—
294C3×Q8C2×C4×D314yes—
295C3×Q8C22×C3×C414yes—
296C3×D4—34no—
297C3×D4—64no—
298C3×D4—62no—
299C2×C3×C4—24no—
300C2×C3×C4—28no—
301C2×C3×C4—24no—
302C2×C3×C4—24no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—24no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—21no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—21no—
312C2×C3×C4—24no—
313C2×C3×C4—62no—
314C2×C3×C4—244no—
315C2×C3×C4C2×C4×D312yes—
316C2×C3×C4#23512yes—
317C2×C3×C4C2×#6714yes—
318C2×C3×C4C2×#6711yescharacteristic
319C2×C3×C4C22×C3×C412yes—
320C2×C3×C4C2×C3×D414yes—
321C2×C3×C4C2×C3×D411yescharacteristic
322C2×C3×C4C3×#4112yes—
323C2×C3×C4C23×D311yescharacteristic
324C2×C3×C4C24×C311yescharacteristic
325C2×Dic3—22no—
326D12—24no—
327D12—22no—
328D12C22×C3×C414yes—
329C4×D3—84no—
330C3×C8—32no—
331C3×C8—32no—
332C3×C8—62no—
333C3⋊C8—22no—
334C3⋊C8C22×C3×C412yes—
335C3⋊C8C22×C3×C412yes—
336C2×C32—22no—
337C2×C32C2×C4×D411yescharacteristic
338C2×C32#57712yes—
339C3×D3—44no—
340C24—61no—
341C2×Q8—22no—
342C2×Q8—21no—
343C2×Q8C3×C4×D314yescomplemented
344C2×Q8C22×C3×D312yes—
345C2×D4—32no—
346C2×D4—34no—
347C2×D4—62no—
348C2×D4—61no—
349C22×C4—21no—
350C22×C4—64no—
351C22×C4C22×C3×D311yescharacteristic
352SD16—38no—
353SD16—38no—
354M16—62no—
355C2×C8—31no—
356C2×C8—31no—
357C2×C8—34no—
358C2×C8—32no—
359C4⋊C4—24no—
360C4⋊C4—32no—
361C4⋊C4C3×#6712yes—
362C4⋊C4C22×C3×D312yes—
363C22⋊C4—21no—
364C22⋊C4—61no—
365C22⋊C4—64no—
366C22⋊C4C3×#6712yes—
367C42—24no—
368C42—21no—
369C42—61no—
370C42C22×C3×D312yes—
371C22×C3—22no—
372C22×C3—22no—
373C22×C3—22no—
374C22×C3—21no—
375C22×C3—42no—
376C22×C3—64no—
377C22×C3—124no—
378C22×C3—244no—
379C22×C3C4×#6712yes—
380C22×C3C3×C4×D412yes—
381C22×C3C22×#6711yescharacteristic
382C22×C3C22×C3×D411yescharacteristic
383C2×D3—24no—
384C2×D3—44no—
385C2×D3—84no—
386C3×C4—28no—
387C3×C4—24no—
388C3×C4—24no—
389C3×C4—24no—
390C3×C4—24no—
391C3×C4—22no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—44no—
395C3×C4—44no—
396C3×C4—42no—
397C3×C4—42no—
398C3×C4—122no—
399C3×C4C4×#6712yes—
400C3×C4C3×C4×D412yes—
401C3×C4C22×C4×D311yescharacteristic
402C3×C4C2×#23511yescharacteristic
403C3×C4C23×C3×C411yescharacteristic
404C3×C4C2×C3×#4111yescharacteristic
405Dic3—42no—
406C32#294911yescharacteristic, complemented, Sylow
407C23—62no—
408C23—64no—
409C23—242no—
410C23C2×C3×#6711yescharacteristic
411Q8—24no—
412Q8—22no—
413Q8C2×C3×C4×D314yes—
414D4—34no—
415D4—64no—
416D4—62no—
417C2×C4—24no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—62no—
421C2×C4—244no—
422C2×C4C2×C3×C4×D312yes—
423C2×C4C3×#23512yes—
424C2×C4C2×C3×#6714yes—
425C2×C4C2×C3×#6711yescharacteristic
426C2×C4C23×C3×D311yescharacteristic
427C8—32no—
428C8—32no—
429C8—62no—
430C2×C3—22no—
431C2×C3—22no—
432C2×C3—21no—
433C2×C3—22no—
434C2×C3—42no—
435C2×C3—124no—
436C2×C3C2×C4×#6711yescharacteristic
437C2×C3#583712yes—
438C2×C3C2×C3×C4×D411yescharacteristic
439C2×C3C3×#57712yes—
440D3—44no—
441C22—22no—
442C22—64no—
443C22—124no—
444C22—244no—
445C22C3×C4×#6712yes—
446C22C22×C3×#6711yescharacteristic
447C4—24no—
448C4—24no—
449C4—42no—
450C4—122no—
451C4C3×C4×#6712yes—
452C4C22×C3×C4×D311yescharacteristic
453C4C2×C3×#23511yescharacteristic
454C3—21no—
455C3#8254811yescharacteristic, direct product factor
456C3C3×#294911yescharacteristic, complemented
457C2—22no—
458C2—124no—
459C2C2×C3×C4×#6711yescharacteristic
460C2C3×#583712yes—
subgroupG/H
centerC22×C3C22×#67
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×#519C2
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
cosocleC2×C3×C4C24×C3
hypercenterC3×#519D3
hypocenterC3C3×#2949
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#117 ◁ C3×#519

Complements

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

NH ≅ G/Ntype
1. C32×#519C2semidirect
4. C3×#5225C2semidirect
5. C3×#5026C2semidirect
6. C3×C4×#215C2semidirect
8. C3×#4998C2semidirect
9. C3×#4997C2semidirect
11. #82548C3direct (N × H)
15. C32×C4×Q8C22semidirect
19. C2×C3×#215C4semidirect
28. C3×#835C22semidirect
30. C3×#808C22semidirect
31. C3×#807C22semidirect
32. C3×#803C22semidirect
33. C3×C4×C3⋊C8C22semidirect
36. C3×#519D3semidirect
37. C3×#519C2×C3semidirect
47. #5225C2×C3semidirect
48. #5026C2×C3semidirect
49. C4×#215C2×C3semidirect
51. #4998C2×C3semidirect
52. #4997C2×C3semidirect
56. C2×C32×Q8C2×C4semidirect
74. C3×#215C2×C4semidirect
75. C3×#215C2×C4semidirect
80. C2×C3×C3⋊C8C2×C4semidirect
99. C3×C4×Q8C2×D3semidirect
100. C3×C4×Q8C22×C3semidirect
114. C2×#215C3×C4semidirect
129. #835C22×C3semidirect
131. #808C22×C3semidirect
132. #807C22×C3semidirect
133. #803C22×C3semidirect
134. C4×C3⋊C8C22×C3semidirect
159. #519C3×D3semidirect
177. C2×C3×Q8C4×D3semidirect
178. C2×C3×Q8C2×C3×C4semidirect
233. #215C2×C3×C4semidirect
234. #215C2×C3×C4semidirect
239. C2×C3⋊C8C2×C3×C4semidirect
264. C4×Q8C2×C3×D3semidirect
343. C2×Q8C3×C4×D3semidirect
406. C32#2949semidirect
455. C3#82548direct (N × H)
456. C3C3×#2949semidirect

Maximal subgroups

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

subgroupindex
C32×#5192
C22×C3×#2152
C3×#55212
C3×#52252
C3×#50262
C3×C4×#2152
C3×#50012
C3×#49982
C3×#49972
C3×#29493
#825483