Finite Group Databasebeta

← C3×#83435 #11872700

Subgroups — C3×#83435 #11872700

Order 1152.

956 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#540C211yesmaximal, characteristic, complemented
2C3×#5521C211yesmaximal, characteristic, complemented
3C3×#5072C212yesmaximal, complemented
4C3×#5066C212yesmaximal, complemented
5C3×#5036C212yesmaximal, complemented
6C3×#5035C212yesmaximal, complemented
7C3×#5014C212yesmaximal, complemented
8C3×C4×#213C212yesmaximal, complemented
9C3×#5000C211yesmaximal, characteristic, complemented
10C3×#3122—31nomaximal
11#83435C311yesmaximal, characteristic, direct product factor
12C22×C3×D12C2211yescharacteristic
13C32×#127C2211yescharacteristic, complemented
14C32×#125C2211yescharacteristic, complemented
15C32×#123—22no—
16C32×#121—22no—
17C32×#121C2212yes—
18C32×C4×D4C2212yescomplemented
19C32×#117C2211yescharacteristic
20C2×C3×#213C2212yes—
21C2×C3×#213C2212yes—
22C3×#926C2211yescharacteristic
23C3×#893—22no—
24C3×D3×C22⋊C4—22no—
25C3×C4×D12C2212yes—
26C3×C4×D12C2212yes—
27C3×#832C2212yescomplemented
28C3×#832C2212yescomplemented
29C3×#830C2212yes—
30C3×#809C2212yes—
31C3×#809C2212yes—
32C3×#808C2212yescomplemented
33C3×#807C2212yescomplemented
34C3×C4⋊(C3⋊C8)C2212yescomplemented
35C3×#803C2211yescharacteristic, complemented
36C3×C4×C3⋊C8C2211yescharacteristic, complemented
37C3×#540—21no—
38C3×#540D311yescharacteristic, complemented
39C3×#540C2×C311yescharacteristic, complemented
40C3×#518—31no—
41#5521C2×C311yescharacteristic, complemented
42C3×#482—32no—
43C3×#478—32no—
44C3×#459—32no—
45C3×#447—32no—
46C3×#442—32no—
47C3×C4×D8—32no—
48C3×#433—31no—
49#5072C2×C312yescomplemented
50#5066C2×C312yescomplemented
51#5036C2×C312yescomplemented
52#5035C2×C312yescomplemented
53#5014C2×C312yescomplemented
54C4×#213C2×C312yescomplemented
55#5000C2×C311yescharacteristic, complemented
56C23×C3×D3—21no—
57C2×C32×D4—22no—
58C2×C32×D4—22no—
59C2×C32×D4C2312yes—
60C22×C32×C4—22no—
61C22×C32×C4C2311yescharacteristic
62C2×C3×D12—21no—
63C2×C3×D12—24no—
64C2×C3×D12C2312yes—
65C2×C3×C4×D3—22no—
66C2×C3×C4×D3—22no—
67C32×C4⋊C4—22no—
68C32×C4⋊C4D412yes—
69C32×C4⋊C4C2312yes—
70C32×C22⋊C4—22no—
71C32×C22⋊C4—22no—
72C32×C22⋊C4D412yes—
73C32×C42C2311yescharacteristic
74C32×C42C2311yescharacteristic
75C3×#217—21no—
76C3×#213—24no—
77C3×#213—24no—
78C3×(C2×D3)⋊C4—22no—
79C3×(C2×D3)⋊C4—22no—
80C3×C4⋊Dic3C2312yes—
81C3×C4×Dic3—21no—
82C2×C3×C3⋊C8C2312yes—
83C2×C3×C3⋊C8C2312yes—
84#3122—31noSylow
85C22×C3×D4—31no—
86C22×D12C22×C311yescharacteristic
87C2×C3×D8—32no—
88C2×C3×D8—32no—
89C3×#127—21no—
90C3×#127C2×D311yescharacteristic, complemented
91C3×#127C22×C311yescharacteristic, complemented
92C3×#125—21no—
93C3×#125C2×D311yescharacteristic, complemented
94C3×#125C22×C311yescharacteristic, complemented
95C3×#123—24no—
96C3×#123—22no—
97C3×#123—22no—
98C3×#121—24no—
99C3×#121—22no—
100C3×#121—22no—
101C3×#121—22no—
102C3×#121C2×D312yes—
103C3×#121C22×C312yes—
104C3×C4×D4—22no—
105C3×C4×D4—32no—
106C3×C4×D4—32no—
107C3×C4×D4—62no—
108C3×C4×D4C2×D312yescomplemented
109C3×C4×D4C22×C312yescomplemented
110C3×#117—21no—
111C3×#117—31no—
112C3×#117C2×D311yescharacteristic
113C3×#117C22×C311yescharacteristic
114C2×C3×C22⋊C4—62no—
115C2×#213C22×C312yes—
116C2×#213C22×C312yes—
117#926C22×C311yescharacteristic
118#893—22no—
119D3×C22⋊C4—22no—
120C4×D12C22×C312yes—
121C4×D12C22×C312yes—
122C3×#107—32no—
123C3×#106—32no—
124C3×C4⋊C8—32no—
125C3×#102—32no—
126C3×#102—32no—
127C3×#102—32no—
128C3×#102—32no—
129C3×C22⋊C8—32no—
130C3×#97—31no—
131C3×C4×C8—31no—
132#832C22×C312yescomplemented
133#832C22×C312yescomplemented
134#830C22×C312yes—
135#809C22×C312yes—
136#809C22×C312yes—
137#808C22×C312yescomplemented
138#807C22×C312yescomplemented
139C4⋊(C3⋊C8)C22×C312yescomplemented
140#803C22×C311yescharacteristic, complemented
141C4×C3⋊C8C22×C311yescharacteristic, complemented
142C23×C32—22no—
143C23×C32C2×D411yescharacteristic
144C22×C3×D3—22no—
145C22×C3×D3—24no—
146C22×C3×D3—82no—
147C32×D4—22no—
148C32×D4—22no—
149C32×D4—82no—
150C32×D4—82no—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4—82no—
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D412yes—
156C2×C32×C4C2×D412yes—
157C2×C32×C4C2411yescharacteristic
158C2×C3×Dic3—22no—
159C3×D12—24no—
160C3×D12—22no—
161C3×D12#4114yes—
162C3×C4×D3—82no—
163C3×C4×D3—82no—
164C3×C3⋊C8—22no—
165C3×C3⋊C8—22no—
166#540C3×D311yescharacteristic, complemented
167#518—31no—
168#482—32no—
169#478—32no—
170#459—32no—
171#447—32no—
172#442—32no—
173C4×D8—32no—
174#433—31no—
175C24×C3—61no—
176C23×D3—21no—
177C2×C3×D4—24no—
178C2×C3×D4—24no—
179C2×C3×D4—22no—
180C2×C3×D4—22no—
181C2×C3×D4—22no—
182C2×C3×D4—22no—
183C2×C3×D4—22no—
184C2×C3×D4—32no—
185C2×C3×D4—64no—
186C2×C3×D4—61no—
187C2×C3×D4C22×D312yes—
188C2×C3×D4C23×C312yes—
189C22×C3×C4—24no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—21no—
193C22×C3×C4—62no—
194C22×C3×C4—62no—
195C22×C3×C4C22×D311yescharacteristic
196C22×C3×C4C23×C311yescharacteristic
197C2×D12—21no—
198C2×D12—24no—
199C2×D12C23×C312yes—
200C2×C4×D3—22no—
201C2×C4×D3—22no—
202C3×D8—64no—
203C3×D8—64no—
204C2×C3×C8—32no—
205C2×C3×C8—32no—
206C3×C4⋊C4—24no—
207C3×C4⋊C4—22no—
208C3×C4⋊C4—22no—
209C3×C4⋊C4—22no—
210C3×C4⋊C4—22no—
211C3×C4⋊C4—32no—
212C3×C4⋊C4#6712yes—
213C3×C4⋊C4C3×D412yes—
214C3×C4⋊C4C22×D312yes—
215C3×C4⋊C4C23×C312yes—
216C3×C22⋊C4—24no—
217C3×C22⋊C4—24no—
218C3×C22⋊C4—22no—
219C3×C22⋊C4—22no—
220C3×C22⋊C4—22no—
221C3×C22⋊C4—22no—
222C3×C22⋊C4—22no—
223C3×C22⋊C4—61no—
224C3×C22⋊C4—62no—
225C3×C22⋊C4—62no—
226C3×C22⋊C4#6712yes—
227C3×C22⋊C4C3×D412yes—
228C3×C42—21no—
229C3×C42—21no—
230C3×C42—61no—
231C3×C42C22×D311yescharacteristic
232C3×C42C22×D311yescharacteristic
233C3×C42C23×C311yescharacteristic
234C3×C42C23×C311yescharacteristic
235#217—21no—
236#213—24no—
237#213—24no—
238(C2×D3)⋊C4—22no—
239(C2×D3)⋊C4—22no—
240C4⋊Dic3C23×C312yes—
241C4×Dic3—21no—
242C2×C3⋊C8C23×C312yes—
243C2×C3⋊C8C23×C312yes—
244C22×C32—21no—
245C22×C32—22no—
246C22×C32—42no—
247C22×C32—42no—
248C22×C32—42no—
249C22×C32C22×D411yescharacteristic
250C2×C3×D3—24no—
251C2×C3×D3—42no—
252C2×C3×D3—42no—
253C2×C3×D3—84no—
254C32×C4—21no—
255C32×C4—22no—
256C32×C4—22no—
257C32×C4—42no—
258C32×C4C2×#4112yes—
259C3×Dic3—42no—
260C22×D4—31no—
261C2×D8—32no—
262C2×D8—32no—
263#127C2×C3×D311yescharacteristic, complemented
264#125C2×C3×D311yescharacteristic, complemented
265#123—22no—
266#121—22no—
267#121C2×C3×D312yes—
268C4×D4—32no—
269C4×D4—32no—
270C4×D4—62no—
271C4×D4C2×C3×D312yescomplemented
272#117—31no—
273#117C2×C3×D311yescharacteristic
274C2×C22⋊C4—62no—
275#107—32no—
276#106—32no—
277C4⋊C8—32no—
278#102—32no—
279#102—32no—
280#102—32no—
281#102—32no—
282C22⋊C8—32no—
283#97—31no—
284C4×C8—31no—
285C23×C3—24no—
286C23×C3—22no—
287C23×C3—22no—
288C23×C3—21no—
289C23×C3—64no—
290C23×C3—62no—
291C23×C3—242no—
292C23×C3C2×#6711yescharacteristic
293C23×C3C2×C3×D411yescharacteristic
294C22×D3—22no—
295C22×D3—24no—
296C22×D3—82no—
297C3×D4—22no—
298C3×D4—22no—
299C3×D4—22no—
300C3×D4—22no—
301C3×D4—34no—
302C3×D4—42no—
303C3×D4—42no—
304C3×D4—64no—
305C3×D4—62no—
306C3×D4—82no—
307C3×D4—82no—
308C3×D4—82no—
309C3×D4—82no—
310C3×D4—84no—
311C3×D4—84no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—24no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—21no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—21no—
321C2×C3×C4—42no—
322C2×C3×C4—62no—
323C2×C3×C4—82no—
324C2×C3×C4—82no—
325C2×C3×C4—84no—
326C2×C3×C4—242no—
327C2×C3×C4—242no—
328C2×C3×C4C2×#6711yescharacteristic
329C2×C3×C4C2×#6712yes—
330C2×C3×C4C2×#6712yes—
331C2×C3×C4C2×C3×D411yescharacteristic
332C2×C3×C4C2×C3×D412yes—
333C2×C3×C4C2×C3×D412yes—
334C2×C3×C4C23×D311yescharacteristic
335C2×C3×C4C24×C311yescharacteristic
336C2×Dic3—22no—
337D12—24no—
338D12—22no—
339D12C3×#4114yes—
340C4×D3—82no—
341C4×D3—82no—
342C3×C8—62no—
343C3×C8—62no—
344C3⋊C8—22no—
345C3⋊C8—22no—
346C2×C32—41no—
347C2×C32—82no—
348C2×C32#52511yescharacteristic
349C2×C32#57612yes—
350C3×D3—44no—
351C24—61no—
352C2×D4—22no—
353C2×D4—22no—
354C2×D4—32no—
355C2×D4—64no—
356C2×D4—61no—
357C2×D4C22×C3×D312yes—
358C22×C4—22no—
359C22×C4—62no—
360C22×C4—62no—
361C22×C4C22×C3×D311yescharacteristic
362D8—64no—
363D8—64no—
364C2×C8—32no—
365C2×C8—32no—
366C4⋊C4—22no—
367C4⋊C4—32no—
368C4⋊C4C3×#6712yes—
369C4⋊C4C22×C3×D312yes—
370C22⋊C4—22no—
371C22⋊C4—22no—
372C22⋊C4—61no—
373C22⋊C4—62no—
374C22⋊C4—62no—
375C22⋊C4C3×#6712yes—
376C42—61no—
377C42C22×C3×D311yescharacteristic
378C42C22×C3×D311yescharacteristic
379C22×C3—22no—
380C22×C3—21no—
381C22×C3—22no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—41no—
385C22×C3—42no—
386C22×C3—44no—
387C22×C3—44no—
388C22×C3—44no—
389C22×C3—42no—
390C22×C3—42no—
391C22×C3—42no—
392C22×C3—42no—
393C22×C3—42no—
394C22×C3—42no—
395C22×C3—64no—
396C22×C3—122no—
397C22×C3—122no—
398C22×C3—244no—
399C22×C3C22×#6711yescharacteristic
400C22×C3C22×C3×D411yescharacteristic
401C2×D3—24no—
402C2×D3—42no—
403C2×D3—42no—
404C2×D3—84no—
405C3×C4—22no—
406C3×C4—22no—
407C3×C4—21no—
408C3×C4—22no—
409C3×C4—22no—
410C3×C4—21no—
411C3×C4—22no—
412C3×C4—41no—
413C3×C4—42no—
414C3×C4—42no—
415C3×C4—44no—
416C3×C4—42no—
417C3×C4—42no—
418C3×C4—122no—
419C3×C4D3×#4112yes—
420C3×C4C2×C3×#4112yes—
421Dic3—42no—
422C32#312211yescharacteristic, complemented, Sylow
423C23—22no—
424C23—64no—
425C23—62no—
426C23—242no—
427C23C2×C3×#6711yescharacteristic
428D4—22no—
429D4—22no—
430D4—34no—
431D4—64no—
432D4—62no—
433D4—82no—
434D4—82no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—62no—
438C2×C4—82no—
439C2×C4—242no—
440C2×C4—242no—
441C2×C4C2×C3×#6711yescharacteristic
442C2×C4C2×C3×#6712yes—
443C2×C4C2×C3×#6712yes—
444C2×C4C23×C3×D311yescharacteristic
445C8—62no—
446C8—62no—
447C2×C3—21no—
448C2×C3—22no—
449C2×C3—41no—
450C2×C3—41no—
451C2×C3—81no—
452C2×C3—84no—
453C2×C3—82no—
454C2×C3—82no—
455C2×C3—124no—
456C2×C3#582811yescharacteristic
457C2×C3#583512yes—
458C2×C3C3×#52511yescharacteristic
459C2×C3C3×#57612yes—
460D3—44no—
461C22—21no—
462C22—22no—
463C22—42no—
464C22—42no—
465C22—42no—
466C22—64no—
467C22—122no—
468C22—122no—
469C22—244no—
470C22C22×C3×#6711yescharacteristic
471C4—21no—
472C4—22no—
473C4—22no—
474C4—42no—
475C4—122no—
476C4C3×D3×#4112yes—
477C3—21no—
478C3#8343511yescharacteristic, direct product factor
479C3C3×#312211yescharacteristic, complemented
480C2—41no—
481C2—82no—
482C2—124no—
483C2C3×#582811yescharacteristic
484C2C3×#583512yes—
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#540C2
socleC22×C32C22×D4
hypercenterC3×#540D3
hypocenterC3C3×#3122
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#117 ◁ C3×#540

Complements

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

NH ≅ G/Ntype
1. C32×#540C2semidirect
2. C3×#5521C2semidirect
3. C3×#5072C2semidirect
4. C3×#5066C2semidirect
5. C3×#5036C2semidirect
6. C3×#5035C2semidirect
7. C3×#5014C2semidirect
8. C3×C4×#213C2semidirect
9. C3×#5000C2semidirect
11. #83435C3direct (N × H)
13. C32×#127C22semidirect
14. C32×#125C22semidirect
18. C32×C4×D4C22semidirect
27. C3×#832C22semidirect
28. C3×#832C22semidirect
32. C3×#808C22semidirect
33. C3×#807C22semidirect
34. C3×C4⋊(C3⋊C8)C22semidirect
35. C3×#803C22semidirect
36. C3×C4×C3⋊C8C22semidirect
38. C3×#540D3semidirect
39. C3×#540C2×C3semidirect
41. #5521C2×C3semidirect
49. #5072C2×C3semidirect
50. #5066C2×C3semidirect
51. #5036C2×C3semidirect
52. #5035C2×C3semidirect
53. #5014C2×C3semidirect
54. C4×#213C2×C3semidirect
55. #5000C2×C3semidirect
90. C3×#127C2×D3semidirect
91. C3×#127C22×C3semidirect
93. C3×#125C2×D3semidirect
94. C3×#125C22×C3semidirect
108. C3×C4×D4C2×D3semidirect
109. C3×C4×D4C22×C3semidirect
132. #832C22×C3semidirect
133. #832C22×C3semidirect
137. #808C22×C3semidirect
138. #807C22×C3semidirect
139. C4⋊(C3⋊C8)C22×C3semidirect
140. #803C22×C3semidirect
141. C4×C3⋊C8C22×C3semidirect
166. #540C3×D3semidirect
263. #127C2×C3×D3semidirect
264. #125C2×C3×D3semidirect
271. C4×D4C2×C3×D3semidirect
422. C32#3122semidirect
478. C3#83435direct (N × H)
479. C3C3×#3122semidirect

Maximal subgroups

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

subgroupindex
C32×#5402
C3×#55212
C3×#50722
C3×#50662
C3×#50362
C3×#50352
C3×#50142
C3×C4×#2132
C3×#50002
C3×#31223
#834353