Finite Group Databasebeta

← C3×Dic3×#104 #11783867

Subgroups — C3×Dic3×#104 #11783867

Order 1152.

805 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Dic3×#41C211yesmaximal, characteristic
2C2×C32×#104C211yesmaximal, characteristic
3C2×C3×#837C211yesmaximal, characteristic
4C3×Dic3×M16C211yesmaximal, characteristic, complemented
5C3×C42×Dic3C211yesmaximal, characteristic, complemented
6C3×#4555C211yesmaximal, characteristic, complemented
7C3×#4523C211yesmaximal, characteristic, complemented
8C3×C4×#104—31nomaximal
9Dic3×#104C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C3×Q8×Dic3C412yescomplemented
14C3×D4×Dic3—22no—
15C3×D4×Dic3C412yescomplemented
16C3×#926—21no—
17C3×#926C2211yescharacteristic
18C2×C3×C4×Dic3—22no—
19C2×C3×C4×Dic3—21no—
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×C4×Dic3C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23C32×#104C414yescomplemented
24C3×#837C414yescomplemented
25C3×#815—21no—
26C3×C8×Dic3—21no—
27C3×C4×#41—31no—
28Dic3×#41C2×C311yescharacteristic
29C2×C3×#104—21no—
30C2×C3×#104—31no—
31C2×C3×#104D311yescharacteristic
32C2×C3×#104C2×C311yescharacteristic
33C3×C4×M16—31no—
34C3×C43—31no—
35C2×#837C2×C311yescharacteristic
36Dic3×M16C2×C311yescharacteristic, complemented
37C42×Dic3C2×C311yescharacteristic, complemented
38C3×#339—31no—
39C3×#339—31no—
40#4555C2×C311yescharacteristic, complemented
41#4523C2×C311yescharacteristic, complemented
42C32×#41—21no—
43C32×#41—21no—
44C32×#41C2×C412yes—
45C32×#41C2×C412yes—
46C2×C32×Q8C2×C411yescharacteristic
47C2×C32×D4—21no—
48C2×C32×D4C2×C411yescharacteristic
49C22×C32×C4—21no—
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3×Dic3—21no—
53C22×C3×Dic3—22no—
54C22×C3×Dic3D412yes—
55C32×M16—21no—
56C32×M16C2×C412yescomplemented
57C2×C32×C8—21no—
58C32×C42—21no—
59C32×C42C2×C412yescomplemented
60C3×#217—21no—
61C3×#217—22no—
62C3×C4⋊Dic3—22no—
63C3×C4⋊Dic3C2×C412yes—
64C3×C4×Dic3—28no—
65C3×C4×Dic3—21no—
66C3×C4×Dic3—21no—
67C3×C4×Dic3—22no—
68C3×C4×Dic3C2×C412yes—
69C3×C4×Dic3C2×C412yescomplemented
70C3×C4×Dic3D411yescharacteristic
71C3×C4×Dic3D411yescharacteristic
72C3×#208—21no—
73C3×#208C2×C412yescomplemented
74C2×C3×C3⋊C8—21no—
75C4×#104—31noSylow
76C2×C3×#41—21no—
77C2×C3×#41C2×D311yescharacteristic
78C2×C3×#41C22×C311yescharacteristic
79C2×C3×M16—21no—
80C2×C3×M16—31no—
81C2×C3×M16C2×D311yescharacteristic
82C2×C3×M16C22×C311yescharacteristic
83C3×C4×Q8—32no—
84C3×C4×D4—32no—
85C3×C4×D4—62no—
86C3×#117—31no—
87C3×#117—61no—
88C2×C3×C42—21no—
89C2×C3×C42—31no—
90C2×C3×C42—31no—
91C2×C3×C42—61no—
92C2×C3×C42—62no—
93C2×C3×C42C2×D311yescharacteristic
94C2×C3×C42C22×C311yescharacteristic
95Q8×Dic3C3×C412yescomplemented
96D4×Dic3—22no—
97D4×Dic3C3×C412yescomplemented
98#926—21no—
99#926C22×C311yescharacteristic
100C2×C4×Dic3—22no—
101C2×C4×Dic3—21no—
102C2×C4×Dic3C22×C311yescharacteristic
103C2×C4×Dic3C22×C311yescharacteristic
104C2×#208C22×C311yescharacteristic
105C3×#104—24no—
106C3×#104—34no—
107C3×#104Dic314yesdirect product factor
108C3×#104C3×C414yescomplemented
109C3×#97—61no—
110C3×C4×C8—61no—
111#837C3×C414yescomplemented
112#815—21no—
113C8×Dic3—21no—
114C23×C32—21no—
115C23×C32C2×D411yescharacteristic
116C32×Q8—21no—
117C32×Q8C4212yescomplemented
118C32×D4—22no—
119C32×D4—22no—
120C32×D4—21no—
121C32×D4C4212yescomplemented
122C2×C32×C4—24no—
123C2×C32×C4—21no—
124C2×C32×C4—22no—
125C2×C32×C4—22no—
126C2×C32×C4—22no—
127C2×C32×C4C22×C411yescharacteristic
128C2×C32×C4C22×C411yescharacteristic
129C2×C32×C4C22×C411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C3×Dic3—24no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—24no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—44no—
138C2×C3×Dic3C22⋊C412yes—
139C2×C3×Dic3C22⋊C412yes—
140C32×C8—22no—
141C3×C3⋊C8—22no—
142C4×#41—31no—
143C2×#104—31no—
144C2×#104C3×D311yescharacteristic
145C4×M16—31no—
146C43—31no—
147#339—31no—
148#339—31no—
149C3×#41—21no—
150C3×#41—21no—
151C3×#41—21no—
152C3×#41—21no—
153C3×#41—22no—
154C3×#41—22no—
155C3×#41—41no—
156C3×#41—41no—
157C3×#41C4×D312yes—
158C3×#41C2×Dic312yes—
159C3×#41C2×C3×C412yes—
160C3×#41C2×C3×C412yes—
161C2×C3×Q8—21no—
162C2×C3×Q8C4×D311yescharacteristic
163C2×C3×Q8C2×C3×C411yescharacteristic
164C2×C3×D4—21no—
165C2×C3×D4—21no—
166C2×C3×D4—21no—
167C2×C3×D4—41no—
168C2×C3×D4C4×D311yescharacteristic
169C2×C3×D4C2×C3×C411yescharacteristic
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—32no—
176C22×C3×C4—41no—
177C22×C3×C4—41no—
178C22×C3×C4—62no—
179C22×C3×C4—61no—
180C22×C3×C4C22×D311yescharacteristic
181C22×C3×C4C23×C311yescharacteristic
182C22×Dic3—21no—
183C22×Dic3—22no—
184C22×Dic3C3×D412yes—
185C3×M16—21no—
186C3×M16—21no—
187C3×M16—22no—
188C3×M16—32no—
189C3×M16—41no—
190C3×M16—61no—
191C3×M16C2×Dic312yescomplemented
192C3×M16C2×C3×C412yescomplemented
193C2×C3×C8—21no—
194C2×C3×C8—21no—
195C2×C3×C8—41no—
196C2×C3×C8—61no—
197C3×C4⋊C4—32no—
198C3×C4⋊C4—62no—
199C3×C22⋊C4—62no—
200C3×C22⋊C4—61no—
201C3×C42—21no—
202C3×C42—21no—
203C3×C42—22no—
204C3×C42—32no—
205C3×C42—31no—
206C3×C42—31no—
207C3×C42—32no—
208C3×C42—41no—
209C3×C42—62no—
210C3×C42—68no—
211C3×C42—61no—
212C3×C42—61no—
213C3×C42C2×Dic312yescomplemented
214C3×C42C2×C3×C412yescomplemented
215#217—21no—
216#217—22no—
217C4⋊Dic3—22no—
218C4⋊Dic3C2×C3×C412yes—
219C4×Dic3—28no—
220C4×Dic3—21no—
221C4×Dic3—21no—
222C4×Dic3—22no—
223C4×Dic3C2×C3×C412yes—
224C4×Dic3C2×C3×C412yescomplemented
225C4×Dic3C3×D411yescharacteristic
226C4×Dic3C3×D411yescharacteristic
227#208—21no—
228#208C2×C3×C412yescomplemented
229C2×C3⋊C8—21no—
230C22×C32—22no—
231C22×C32—22no—
232C22×C32—42no—
233C22×C32C2×C22⋊C411yescharacteristic
234C22×C32C4×D411yescharacteristic
235C22×C32C4×D411yescharacteristic
236C32×C4—24no—
237C32×C4—22no—
238C32×C4C2×C4211yescharacteristic
239C32×C4#11711yescharacteristic
240C32×C4C4×D411yescharacteristic
241C32×C4C4×D411yescharacteristic
242C3×Dic3—24no—
243C3×Dic3—22no—
244C3×Dic3—42no—
245C3×Dic3#10414yesdirect product factor
246C2×#41C2×C3×D311yescharacteristic
247C2×M16—31no—
248C2×M16C2×C3×D311yescharacteristic
249C4×Q8—32no—
250C4×D4—32no—
251C4×D4—62no—
252#117—31no—
253#117—61no—
254C2×C42—31no—
255C2×C42—31no—
256C2×C42—61no—
257C2×C42—62no—
258C2×C42C2×C3×D311yescharacteristic
259#104—34no—
260#104C3×Dic314yesdirect product factor
261#97—61no—
262C4×C8—61no—
263C23×C3—21no—
264C23×C3—21no—
265C23×C3—21no—
266C23×C3—41no—
267C23×C3D3×D411yescharacteristic
268C23×C3C2×C3×D411yescharacteristic
269C3×Q8—21no—
270C3×Q8—21no—
271C3×Q8—22no—
272C3×Q8—41no—
273C3×Q8C4×Dic312yescomplemented
274C3×Q8C3×C4212yescomplemented
275C3×D4—22no—
276C3×D4—22no—
277C3×D4—22no—
278C3×D4—22no—
279C3×D4—21no—
280C3×D4—21no—
281C3×D4—22no—
282C3×D4—41no—
283C3×D4—42no—
284C3×D4—42no—
285C3×D4C4×Dic312yescomplemented
286C3×D4C3×C4212yescomplemented
287C2×C3×C4—24no—
288C2×C3×C4—24no—
289C2×C3×C4—21no—
290C2×C3×C4—22no—
291C2×C3×C4—21no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—32no—
304C2×C3×C4—32no—
305C2×C3×C4—42no—
306C2×C3×C4—42no—
307C2×C3×C4—42no—
308C2×C3×C4—41no—
309C2×C3×C4—44no—
310C2×C3×C4—64no—
311C2×C3×C4—64no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4—124no—
315C2×C3×C4C2×C4×D311yescharacteristic
316C2×C3×C4C2×C4×D311yescharacteristic
317C2×C3×C4D3×D411yescharacteristic
318C2×C3×C4#23711yescharacteristic
319C2×C3×C4#23711yescharacteristic
320C2×C3×C4C22×Dic311yescharacteristic
321C2×C3×C4C22×C3×C411yescharacteristic
322C2×C3×C4C22×C3×C411yescharacteristic
323C2×C3×C4C22×C3×C411yescharacteristic
324C2×C3×C4C2×C3×D411yescharacteristic
325C2×C3×C4C3×#4111yescharacteristic
326C2×C3×C4C3×#4111yescharacteristic
327C2×Dic3—24no—
328C2×Dic3—22no—
329C2×Dic3—24no—
330C2×Dic3—22no—
331C2×Dic3—44no—
332C2×Dic3C3×C22⋊C412yes—
333C2×Dic3C3×C22⋊C412yes—
334C3×C8—22no—
335C3×C8—22no—
336C3×C8—42no—
337C3×C8—62no—
338C3⋊C8—22no—
339C2×C32—21no—
340C2×C32—21no—
341C2×C32—42no—
342C2×C32C4×C22⋊C411yescharacteristic
343C2×C32C2×#10412yes—
344#41—21no—
345#41—21no—
346#41C3×C4×D312yes—
347#41C2×C3×Dic312yes—
348C2×Q8C3×C4×D311yescharacteristic
349C2×D4—21no—
350C2×D4C3×C4×D311yescharacteristic
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—32no—
354C22×C4—62no—
355C22×C4—61no—
356C22×C4C22×C3×D311yescharacteristic
357M16—21no—
358M16—32no—
359M16—61no—
360M16C2×C3×Dic312yescomplemented
361C2×C8—21no—
362C2×C8—61no—
363C4⋊C4—32no—
364C4⋊C4—62no—
365C22⋊C4—62no—
366C22⋊C4—61no—
367C42—21no—
368C42—32no—
369C42—31no—
370C42—31no—
371C42—32no—
372C42—62no—
373C42—68no—
374C42—61no—
375C42—61no—
376C42C2×C3×Dic312yescomplemented
377C22×C3—22no—
378C22×C3—22no—
379C22×C3—22no—
380C22×C3—22no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—42no—
385C22×C3—42no—
386C22×C3—42no—
387C22×C3—42no—
388C22×C3—82no—
389C22×C3D3×C22⋊C411yescharacteristic
390C22×C3#67⋊C411yescharacteristic
391C22×C3D4×Dic311yescharacteristic
392C22×C3C2×C3×C22⋊C411yescharacteristic
393C22×C3C3×C4×D411yescharacteristic
394C22×C3C3×C4×D411yescharacteristic
395C3×C4—24no—
396C3×C4—24no—
397C3×C4—22no—
398C3×C4—22no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—34no—
404C3×C4—42no—
405C3×C4—44no—
406C3×C4—64no—
407C3×C4—62no—
408C3×C4—122no—
409C3×C4#87711yescharacteristic
410C3×C4#67⋊C411yescharacteristic
411C3×C4C2×C4×Dic311yescharacteristic
412C3×C4D4×Dic311yescharacteristic
413C3×C4C2×C3×C4211yescharacteristic
414C3×C4C3×#11711yescharacteristic
415C3×C4C3×C4×D411yescharacteristic
416C3×C4C3×C4×D411yescharacteristic
417Dic3—24no—
418Dic3—22no—
419Dic3—42no—
420Dic3C3×#10414yesdirect product factor
421C32C4×#10411yescharacteristic, complemented, Sylow
422C23—21no—
423C23C3×D3×D411yescharacteristic
424Q8—21no—
425Q8C3×C4×Dic312yescomplemented
426D4—22no—
427D4—22no—
428D4—21no—
429D4C3×C4×Dic312yescomplemented
430C2×C4—24no—
431C2×C4—21no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—32no—
436C2×C4—32no—
437C2×C4—64no—
438C2×C4—64no—
439C2×C4—62no—
440C2×C4—62no—
441C2×C4—124no—
442C2×C4C2×C3×C4×D311yescharacteristic
443C2×C4C2×C3×C4×D311yescharacteristic
444C2×C4C3×D3×D411yescharacteristic
445C2×C4C3×#23711yescharacteristic
446C2×C4C3×#23711yescharacteristic
447C2×C4C22×C3×Dic311yescharacteristic
448C8—22no—
449C8—62no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—22no—
456C2×C3—41no—
457C2×C3—41no—
458C2×C3—42no—
459C2×C3—42no—
460C2×C3—82no—
461C2×C3D3×#10412yes—
462C2×C3Dic3×C22⋊C411yescharacteristic
463C2×C3C3×C4×C22⋊C411yescharacteristic
464C2×C3C2×C3×#10412yes—
465C22—22no—
466C22—22no—
467C22—42no—
468C22C3×D3×C22⋊C411yescharacteristic
469C22C3×#67⋊C411yescharacteristic
470C22C3×D4×Dic311yescharacteristic
471C4—24no—
472C4—22no—
473C4—34no—
474C4—64no—
475C4—62no—
476C4—122no—
477C4C3×#87711yescharacteristic
478C4C3×#67⋊C411yescharacteristic
479C4C2×C3×C4×Dic311yescharacteristic
480C4C3×D4×Dic311yescharacteristic
481C3—21no—
482C3Dic3×#10411yescharacteristic, direct product factor
483C3C3×C4×#10411yescharacteristic, complemented
484C2—21no—
485C2—21no—
486C2—42no—
487C2C3×D3×#10412yes—
488C2C3×Dic3×C22⋊C411yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutatorC3×C4C2×C3×C42
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#104C2
socleC22×C32C2×C22⋊C4
prime radicalC2×C32×#41C22
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#104D3
hypocenterC3C3×C4×#104
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C2×C3×#104

Complements

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

NH ≅ G/Ntype
4. C3×Dic3×M16C2semidirect
5. C3×C42×Dic3C2semidirect
6. C3×#4555C2semidirect
7. C3×#4523C2semidirect
9. Dic3×#104C3direct (N × H)
13. C3×Q8×Dic3C4semidirect
15. C3×D4×Dic3C4semidirect
23. C32×#104C4semidirect
24. C3×#837C4semidirect
36. Dic3×M16C2×C3semidirect
37. C42×Dic3C2×C3semidirect
40. #4555C2×C3semidirect
41. #4523C2×C3semidirect
56. C32×M16C2×C4semidirect
59. C32×C42C2×C4semidirect
69. C3×C4×Dic3C2×C4semidirect
73. C3×#208C2×C4semidirect
95. Q8×Dic3C3×C4semidirect
97. D4×Dic3C3×C4semidirect
107. C3×#104Dic3direct (N × H)
108. C3×#104C3×C4semidirect
111. #837C3×C4semidirect
117. C32×Q8C42semidirect
121. C32×D4C42semidirect
191. C3×M16C2×Dic3semidirect
192. C3×M16C2×C3×C4semidirect
213. C3×C42C2×Dic3semidirect
214. C3×C42C2×C3×C4semidirect
224. C4×Dic3C2×C3×C4semidirect
228. #208C2×C3×C4semidirect
245. C3×Dic3#104direct (N × H)
260. #104C3×Dic3direct (N × H)
273. C3×Q8C4×Dic3semidirect
274. C3×Q8C3×C42semidirect
285. C3×D4C4×Dic3semidirect
286. C3×D4C3×C42semidirect
360. M16C2×C3×Dic3semidirect
376. C42C2×C3×Dic3semidirect
420. Dic3C3×#104direct (N × H)
421. C32C4×#104semidirect
425. Q8C3×C4×Dic3semidirect
429. D4C3×C4×Dic3semidirect
482. C3Dic3×#104direct (N × H)
483. C3C3×C4×#104semidirect

Maximal subgroups

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

subgroupindex
C3×Dic3×#412
C2×C32×#1042
C2×C3×#8372
C3×Dic3×M162
C3×C42×Dic32
C3×#45552
C3×#45232
C3×C4×#1043
Dic3×#1043