Finite Group Databasebeta

← C3×#69662 #11784854

Subgroups — C3×#69662 #11784854

Order 1152.

1369 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1004C211yesmaximal, characteristic
2C32×#390C211yesmaximal, characteristic, complemented
3C2×C3×#833C211yesmaximal, characteristic, complemented
4C3×#4966C212yesmaximal, complemented
5C2×C3×#805C212yesmaximal, complemented
6C3×#1792—31nomaximal
7#69662C311yesmaximal, characteristic, direct product factor
8C22×C32×D4C2211yescharacteristic
9C22×C3×#67—22no—
10C3×#1004—22no—
11C3×#1004—24no—
12C3×#1004C414yescomplemented
13C2×C3×#237—22no—
14C2×C3×D3×D4—22no—
15C2×C3×#235C2212yes—
16C2×C32×C4⋊C4C2211yescharacteristic, complemented
17C2×C32×C22⋊C4—22no—
18C2×C32×C42C2211yescharacteristic, complemented
19C2×C3×#208C2212yescomplemented
20C3×#833—22no—
21C3×#810—22no—
22C3×#809—22no—
23C3×#805—24no—
24C2×C3×H(5,𝔽2)—31no—
25C2×#1004C2×C311yescharacteristic
26C2×C3×#104—32no—
27C3×#417—32no—
28C2×C3×#100—31no—
29C3×#390—21no—
30C3×#390D311yescharacteristic, complemented
31C3×#390C2×C311yescharacteristic, complemented
32C2×#833C2×C311yescharacteristic, complemented
33#4966C2×C312yescomplemented
34C2×#805C2×C312yescomplemented
35C24×C32D412yes—
36C23×C3×D3—22no—
37C2×C32×D4—22no—
38C2×C32×D4—22no—
39C2×C32×D4C2×C412yes—
40C2×C32×D4D412yes—
41C22×C32×C4—21no—
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C2×C3×#67—24no—
45C2×C3×#67—28no—
46C2×C3×#67—28no—
47C2×C3×#67—22no—
48C22×C3×Dic3—22no—
49C3×#237—28no—
50C3×#237—28no—
51C3×D3×D4—28no—
52C3×D3×D4—28no—
53C3×#235—22no—
54C3×#235—22no—
55C3×#235C2×C414yes—
56C3×#235D414yes—
57C2×C3×D12D412yes—
58C2×C3×C4×D3—22no—
59C2×C3×Dic6D412yes—
60C32×C4⋊C4—22no—
61C32×C22⋊C4—44no—
62C32×C42—22no—
63C3×#208—22no—
64C3×#208—22no—
65C2×C3×C3⋊C8—22no—
66#1792—31noSylow
67C3×H(5,𝔽2)—34no—
68C3×H(5,𝔽2)—64no—
69C3×H(5,𝔽2)—62no—
70C2×C3×#41—32no—
71C2×C3×#41—62no—
72C22×C3×D4—21no—
73C22×C3×D4—62no—
74C22×C3×D4—62no—
75C22×C3×D4C2×D311yescharacteristic
76C22×C3×D4C22×C311yescharacteristic
77C22×#67—22no—
78#1004—22no—
79#1004—24no—
80#1004C3×C414yescomplemented
81C2×#237—22no—
82C2×D3×D4—22no—
83C2×#235C22×C312yes—
84C2×C3×M16—32no—
85C2×C3×C4⋊C4—21no—
86C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
87C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
88C2×C3×C22⋊C4—24no—
89C2×C3×C22⋊C4—22no—
90C2×C3×C22⋊C4—22no—
91C2×C3×C42—21no—
92C2×C3×C42C2×D311yescharacteristic, complemented
93C2×C3×C42C22×C311yescharacteristic, complemented
94C2×#208C22×C312yescomplemented
95C3×#104—64no—
96C3×#103—62no—
97C3×#102—62no—
98C3×#100—62no—
99#833—22no—
100#810—22no—
101#809—22no—
102#805—24no—
103C23×C32—22no—
104C23×C32—22no—
105C23×C32—42no—
106C23×C32—42no—
107C23×C32C22⋊C414yes—
108C23×C32C2×D411yescharacteristic
109C22×C3×D3—22no—
110C22×C3×D3—28no—
111C22×C3×D3—82no—
112C22×C3×D3—82no—
113C32×D4—24no—
114C32×D4—24no—
115C2×C32×C4—22no—
116C2×C32×C4—41no—
117C2×C32×C4—41no—
118C2×C32×C4—42no—
119C2×C32×C4—41no—
120C2×C32×C4C22×C411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D412yes—
123C2×C32×C4C2×D412yes—
124C3×#67—216no—
125C3×#67—24no—
126C3×#67—24no—
127C2×C3×Dic3—28no—
128C2×C3×Dic3—22no—
129C3×D12—22no—
130C3×D12C22⋊C414yescomplemented
131C3×C4×D3—24no—
132C3×C4×D3—24no—
133C3×Dic6—22no—
134C3×Dic6C22⋊C414yescomplemented
135C3×C3⋊C8—42no—
136C2×H(5,𝔽2)—31no—
137C2×#104—32no—
138#417—32no—
139C2×#100—31no—
140#390C3×D311yescharacteristic, complemented
141C24×C3—22no—
142C24×C3—62no—
143C24×C3#6712yes—
144C24×C3C3×D412yes—
145C23×D3—22no—
146C3×#41—34no—
147C3×#41—34no—
148C3×#41—68no—
149C3×#41—68no—
150C3×#41—62no—
151C3×#41—62no—
152C2×C3×Q8—32no—
153C2×C3×D4—22no—
154C2×C3×D4—22no—
155C2×C3×D4—22no—
156C2×C3×D4—22no—
157C2×C3×D4—22no—
158C2×C3×D4—22no—
159C2×C3×D4—32no—
160C2×C3×D4—42no—
161C2×C3×D4—42no—
162C2×C3×D4—68no—
163C2×C3×D4—68no—
164C2×C3×D4—64no—
165C2×C3×D4—68no—
166C2×C3×D4—68no—
167C2×C3×D4—62no—
168C2×C3×D4C4×D312yes—
169C2×C3×D4D1212yes—
170C2×C3×D4C2×C3×C412yes—
171C2×C3×D4C3×D412yes—
172C22×C3×C4—22no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—22no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—62no—
180C22×C3×C4—62no—
181C22×C3×C4C22×D311yescharacteristic
182C22×C3×C4C23×C311yescharacteristic
183C2×#67—24no—
184C2×#67—28no—
185C2×#67—28no—
186C2×#67—22no—
187C22×Dic3—22no—
188#237—28no—
189#237—28no—
190D3×D4—28no—
191D3×D4—28no—
192#235—22no—
193#235—22no—
194#235C2×C3×C414yes—
195#235C3×D414yes—
196C2×D12C3×D412yes—
197C2×C4×D3—22no—
198C2×Dic6C3×D412yes—
199C3×M16—62no—
200C3×M16—62no—
201C2×C3×C8—62no—
202C3×C4⋊C4—22no—
203C3×C4⋊C4—22no—
204C3×C4⋊C4—42no—
205C3×C22⋊C4—44no—
206C3×C22⋊C4—44no—
207C3×C22⋊C4—48no—
208C3×C42—22no—
209C3×C42—22no—
210C3×C42—42no—
211#208—22no—
212#208—22no—
213C2×C3⋊C8—22no—
214C22×C32—21no—
215C22×C32—21no—
216C22×C32—24no—
217C22×C32—44no—
218C22×C32—42no—
219C22×C32—42no—
220C22×C32—82no—
221C22×C32C2×C22⋊C411yescharacteristic
222C22×C32#12011yescharacteristic
223C22×C32#12011yescharacteristic
224C2×C3×D3—24no—
225C2×C3×D3—42no—
226C2×C3×D3—42no—
227C2×C3×D3—88no—
228C32×C4—42no—
229C32×C4—81no—
230C32×C4C2×C22⋊C412yes—
231C32×C4#12012yes—
232C3×Dic3—24no—
233H(5,𝔽2)—34no—
234H(5,𝔽2)—64no—
235H(5,𝔽2)—62no—
236C2×#41—32no—
237C2×#41—62no—
238C22×D4—62no—
239C22×D4—62no—
240C22×D4C2×C3×D311yescharacteristic
241C2×M16—32no—
242C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
243C2×C22⋊C4—22no—
244C2×C42C2×C3×D311yescharacteristic, complemented
245#104—64no—
246#103—62no—
247#102—62no—
248#100—62no—
249C23×C3—22no—
250C23×C3—22no—
251C23×C3—22no—
252C23×C3—22no—
253C23×C3—24no—
254C23×C3—21no—
255C23×C3—42no—
256C23×C3—42no—
257C23×C3—42no—
258C23×C3—42no—
259C23×C3—42no—
260C23×C3—42no—
261C23×C3—44no—
262C23×C3—44no—
263C23×C3—68no—
264C23×C3—62no—
265C23×C3—242no—
266C23×C3—242no—
267C23×C3(C2×D3)⋊C414yes—
268C23×C3C3×C22⋊C414yes—
269C23×C3C2×#6711yescharacteristic
270C23×C3C2×C3×D411yescharacteristic
271C22×D3—22no—
272C22×D3—28no—
273C22×D3—82no—
274C22×D3—82no—
275C3×Q8—34no—
276C3×Q8—62no—
277C3×D4—24no—
278C3×D4—24no—
279C3×D4—24no—
280C3×D4—24no—
281C3×D4—34no—
282C3×D4—44no—
283C3×D4—44no—
284C3×D4—616no—
285C3×D4—64no—
286C3×D4—64no—
287C3×D4—62no—
288C2×C3×C4—24no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—42no—
296C2×C3×C4—42no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—44no—
302C2×C3×C4—42no—
303C2×C3×C4—42no—
304C2×C3×C4—42no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—68no—
308C2×C3×C4—62no—
309C2×C3×C4—64no—
310C2×C3×C4—64no—
311C2×C3×C4C2×C4×D311yescharacteristic
312C2×C3×C4C2×D1211yescharacteristic
313C2×C3×C4D3×D412yes—
314C2×C3×C4D3×D412yes—
315C2×C3×C4C22×C3×C411yescharacteristic
316C2×C3×C4C2×C3×D411yescharacteristic
317C2×C3×C4C2×C3×D412yes—
318C2×C3×C4C2×C3×D412yes—
319#67—216no—
320#67—24no—
321#67—24no—
322C2×Dic3—28no—
323C2×Dic3—22no—
324D12—22no—
325D12C3×C22⋊C414yescomplemented
326C4×D3—24no—
327C4×D3—24no—
328Dic6—22no—
329Dic6C3×C22⋊C414yescomplemented
330C3×C8—122no—
331C3⋊C8—42no—
332C2×C32—21no—
333C2×C32—21no—
334C2×C32—44no—
335C2×C32#37911yescharacteristic
336C2×C32#45311yescharacteristic
337C2×C32#45511yescharacteristic
338C3×D3—44no—
339C24—62no—
340C24C3×#6712yes—
341#41—34no—
342#41—34no—
343#41—68no—
344#41—68no—
345#41—62no—
346#41—62no—
347C2×Q8—32no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—32no—
351C2×D4—68no—
352C2×D4—68no—
353C2×D4—64no—
354C2×D4—68no—
355C2×D4—68no—
356C2×D4—62no—
357C2×D4C3×C4×D312yes—
358C2×D4C3×D1212yes—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—62no—
362C22×C4—62no—
363C22×C4C22×C3×D311yescharacteristic
364M16—62no—
365M16—62no—
366C2×C8—62no—
367C4⋊C4—22no—
368C22⋊C4—44no—
369C42—22no—
370C22×C3—22no—
371C22×C3—22no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—24no—
377C22×C3—24no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—44no—
382C22×C3—44no—
383C22×C3—44no—
384C22×C3—48no—
385C22×C3—42no—
386C22×C3—42no—
387C22×C3—42no—
388C22×C3—42no—
389C22×C3—64no—
390C22×C3—82no—
391C22×C3—82no—
392C22×C3—82no—
393C22×C3—82no—
394C22×C3—84no—
395C22×C3—122no—
396C22×C3—122no—
397C22×C3—248no—
398C22×C3C2×(C2×D3)⋊C411yescharacteristic
399C22×C3#93711yescharacteristic
400C22×C3#93711yescharacteristic
401C22×C3C2×C3×C22⋊C411yescharacteristic
402C22×C3C3×#12011yescharacteristic
403C22×C3C3×#12011yescharacteristic
404C2×D3—24no—
405C2×D3—42no—
406C2×D3—42no—
407C2×D3—88no—
408C3×C4—22no—
409C3×C4—22no—
410C3×C4—44no—
411C3×C4—42no—
412C3×C4—42no—
413C3×C4—64no—
414C3×C4—82no—
415C3×C4—81no—
416C3×C4—81no—
417C3×C4D3×C22⋊C412yes—
418C3×C4#88212yes—
419C3×C4C2×C3×C22⋊C412yes—
420C3×C4C3×#12012yes—
421Dic3—24no—
422C32#179211yescharacteristic, complemented, Sylow
423C23—22no—
424C23—22no—
425C23—42no—
426C23—42no—
427C23—68no—
428C23—62no—
429C23—242no—
430C23—242no—
431C23C3×(C2×D3)⋊C414yes—
432C23C2×C3×#6711yescharacteristic
433Q8—34no—
434Q8—62no—
435D4—24no—
436D4—24no—
437D4—34no—
438D4—616no—
439D4—64no—
440D4—64no—
441D4—62no—
442C2×C4—22no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—68no—
448C2×C4—62no—
449C2×C4—64no—
450C2×C4—64no—
451C2×C4C2×C3×C4×D311yescharacteristic
452C2×C4C2×C3×D1211yescharacteristic
453C2×C4C3×D3×D412yes—
454C2×C4C3×D3×D412yes—
455C8—122no—
456C2×C3—22no—
457C2×C3—22no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—44no—
466C2×C3—44no—
467C2×C3—84no—
468C2×C3—124no—
469C2×C3#495511yescharacteristic
470C2×C3#506111yescharacteristic
471C2×C3#507711yescharacteristic
472C2×C3C3×#37911yescharacteristic
473C2×C3C3×#45311yescharacteristic
474C2×C3C3×#45511yescharacteristic
475D3—44no—
476C22—21no—
477C22—21no—
478C22—24no—
479C22—44no—
480C22—42no—
481C22—42no—
482C22—64no—
483C22—82no—
484C22—122no—
485C22—122no—
486C22—248no—
487C22C2×C3×(C2×D3)⋊C411yescharacteristic
488C22C3×#93711yescharacteristic
489C22C3×#93711yescharacteristic
490C4—42no—
491C4—64no—
492C4—81no—
493C4C3×D3×C22⋊C412yes—
494C4C3×#88212yes—
495C3—21no—
496C3#6966211yescharacteristic, direct product factor
497C3C3×#179211yescharacteristic, complemented
498C2—21no—
499C2—21no—
500C2—44no—
501C2—124no—
502C2C3×#495511yescharacteristic
503C2C3×#506111yescharacteristic
504C2C3×#507711yescharacteristic
subgroupG/H
centerC22×C3#937
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#390C2
socleC22×C32#120
prime radicalC2×C3×#1004C2
cosocleC22×C3×C4C23×C3
hypercenterC3×#390D3
hypocenterC3C3×#1792
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#390

Complements

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

NH ≅ G/Ntype
2. C32×#390C2semidirect
3. C2×C3×#833C2semidirect
4. C3×#4966C2semidirect
5. C2×C3×#805C2semidirect
7. #69662C3direct (N × H)
12. C3×#1004C4semidirect
16. C2×C32×C4⋊C4C22semidirect
18. C2×C32×C42C22semidirect
19. C2×C3×#208C22semidirect
30. C3×#390D3semidirect
31. C3×#390C2×C3semidirect
32. C2×#833C2×C3semidirect
33. #4966C2×C3semidirect
34. C2×#805C2×C3semidirect
80. #1004C3×C4semidirect
86. C2×C3×C4⋊C4C2×D3semidirect
87. C2×C3×C4⋊C4C22×C3semidirect
92. C2×C3×C42C2×D3semidirect
93. C2×C3×C42C22×C3semidirect
94. C2×#208C22×C3semidirect
130. C3×D12C22⋊C4semidirect
134. C3×Dic6C22⋊C4semidirect
140. #390C3×D3semidirect
242. C2×C4⋊C4C2×C3×D3semidirect
244. C2×C42C2×C3×D3semidirect
325. D12C3×C22⋊C4semidirect
329. Dic6C3×C22⋊C4semidirect
422. C32#1792semidirect
496. C3#69662direct (N × H)
497. C3C3×#1792semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10042
C32×#3902
C2×C3×#8332
C3×#49662
C2×C3×#8052
C3×#17923
#696623