Finite Group Databasebeta

← C3×D3×#638 #13049647

Subgroups — C3×D3×#638 #13049647

Order 1296.

1220 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 1220 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C33×D3C211yesmaximal, characteristic, complemented
2C2×C3×D3×C3⋊D3C211yesmaximal, characteristic, complemented
3C3×#6312C211yesmaximal, characteristic, complemented
4C32×#638C211yesmaximal, characteristic, complemented
5C3×#6291C211yesmaximal, characteristic, complemented
6C3×#6290C211yesmaximal, characteristic, complemented
7C3×D3×C3⋊Dic3C211yesmaximal, characteristic, complemented
8C2×C3×#638—31nomaximal
9D3×#638C311yesmaximal, characteristic, direct product factor
10C3×D3×#67—34nomaximal
11C22×C34C2211yescharacteristic, complemented
12C2×C3×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
13C2×C32×C3⋊D3C2211yescharacteristic, complemented
14C2×C33×D3—22no—
15C2×C33×D3C2211yescharacteristic
16C2×C33×D3C2211yescharacteristic, complemented
17C3×D3×C3⋊D3—22no—
18C3×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
19C32×C3⋊Dic3C2211yescharacteristic, complemented
20C23×C33—31no—
21C22×C3×C3⋊D3—31no—
22C22×C32×D3—24no—
23C22×C32×D3D314yescomplemented
24C22×C32×D3C2×C311yescharacteristic, complemented
25C2×D3×C3⋊D3C2×C311yescharacteristic, complemented
26C2×C3×D32—34no—
27#6312C2×C311yescharacteristic, complemented
28C3×#638—21no—
29C3×#638—31no—
30C3×#638—34no—
31C3×#638—31no—
32C3×#638—31no—
33C3×#638—64no—
34C3×#638D311yescharacteristic, direct product factor
35C3×#638C2×C311yescharacteristic, complemented
36C2×C3×C3⋊Dic3—31no—
37C32×#67—34no—
38#6291C2×C311yescharacteristic, complemented
39#6290C2×C311yescharacteristic, complemented
40D3×C3⋊Dic3C2×C311yescharacteristic, complemented
41C3×#626—34no—
42C3×#625—34no—
43C3×D3×Dic3—34no—
44C2×C34—21no—
45C2×C34C2311yescharacteristic
46C3×C3⋊(C3⋊D3)—21no—
47C32×C3⋊D3—21no—
48C33×D3—21no—
49C33×D3D412yescomplemented
50C2×#638—31no—
51C2×C3×#67—94no—
52C3×D3×D4—91no—
53D3×#67—34no—
54C22×C33—24no—
55C22×C33—24no—
56C22×C33—21no—
57C22×C33—31no—
58C22×C33—31no—
59C22×C33—44no—
60C22×C33—62no—
61C22×C33C2×D311yescharacteristic, complemented
62C22×C33C2×D314yescomplemented
63C22×C33C22×C311yescharacteristic, complemented
64C2×C3⋊(C3⋊D3)C22×C311yescharacteristic, complemented
65C2×C3×C3⋊D3—21no—
66C2×C3×C3⋊D3—31no—
67C2×C3×C3⋊D3—34no—
68C2×C3×C3⋊D3—62no—
69C2×C3×C3⋊D3—64no—
70C2×C3×C3⋊D3C2×D311yescharacteristic, complemented
71C2×C3×C3⋊D3C22×C311yescharacteristic, complemented
72C2×C32×D3—216no—
73C2×C32×D3—24no—
74C2×C32×D3—24no—
75C2×C32×D3—28no—
76C2×C32×D3—22no—
77C2×C32×D3—34no—
78C2×C32×D3C2×D314yes—
79C2×C32×D3C2×D314yescomplemented
80C2×C32×D3C22×C311yescharacteristic
81C2×C32×D3C22×C311yescharacteristic, complemented
82D3×C3⋊D3—22no—
83C3×D32—68no—
84C3⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
85C3×C3⋊Dic3—21no—
86C3×C3⋊Dic3—31no—
87C3×C3⋊Dic3—34no—
88C3×C3⋊Dic3—64no—
89C3×C3⋊Dic3C2×D311yescharacteristic, complemented
90C3×C3⋊Dic3C22×C311yescharacteristic, complemented
91C32×Dic3—34no—
92C34C2×D411yescharacteristic, complemented, Sylow
93C23×C32—31no—
94C23×C32—34no—
95C23×C32—64no—
96C22×C3⋊D3—31no—
97C22×C3×D3—24no—
98C22×C3×D3—94no—
99C22×C3×D3—91no—
100C22×C3×D3C3×D314yescomplemented
101C22×C3×D3C3⋊D311yescharacteristic, complemented
102C2×D32—34no—
103C32×D4—91no—
104#638—31no—
105#638—31no—
106#638—31no—
107#638—34no—
108#638—64no—
109#638C3×D311yescharacteristic, direct product factor
110C2×C3⋊Dic3—31no—
111C3×#67—34no—
112C3×#67—34no—
113C3×#67—64no—
114C3×#67—94no—
115C3×#67—94no—
116C3×#67—94no—
117C3×#67—91no—
118C3×#67—91no—
119C3×#67—184no—
120C2×C3×Dic3—94no—
121C3×D12—91no—
122C3×C4×D3—91no—
123#626—34no—
124#625—34no—
125D3×Dic3—34no—
126C2×C33—21no—
127C2×C33—28no—
128C2×C33—24no—
129C2×C33—21no—
130C2×C33—24no—
131C2×C33—21no—
132C2×C33—24no—
133C2×C33—32no—
134C2×C33—44no—
135C2×C33—44no—
136C2×C33—41no—
137C2×C33—48no—
138C2×C33—61no—
139C2×C33C22×D311yescharacteristic
140C2×C33C22×D314yes—
141C2×C33C23×C311yescharacteristic
142C3⋊(C3⋊D3)—21no—
143C3×C3⋊D3—21no—
144C3×C3⋊D3—21no—
145C3×C3⋊D3—41no—
146C3×C3⋊D3—61no—
147C3×C3⋊D3—64no—
148C3×C3⋊D3—124no—
149C32×D3—28no—
150C32×D3—24no—
151C32×D3—21no—
152C32×D3—28no—
153C32×D3—64no—
154C32×D3#6718yescomplemented
155C32×D3C3×D412yescomplemented
156C2×C3×D4—271no—
157C2×#67—94no—
158D3×D4—91no—
159C22×C32—24no—
160C22×C32—24no—
161C22×C32—24no—
162C22×C32—24no—
163C22×C32—24no—
164C22×C32—31no—
165C22×C32—31no—
166C22×C32—34no—
167C22×C32—34no—
168C22×C32—44no—
169C22×C32—412no—
170C22×C32—44no—
171C22×C32—64no—
172C22×C32—64no—
173C22×C32—62no—
174C22×C32—68no—
175C22×C32—616no—
176C22×C32—91no—
177C22×C32D3214yescomplemented
178C22×C32C2×C3×D314yescomplemented
179C22×C32C2×C3×D311yescharacteristic, complemented
180C22×C32C2×C3⋊D311yescharacteristic, complemented
181C2×C3⋊D3—31no—
182C2×C3⋊D3—34no—
183C2×C3⋊D3—64no—
184C2×C3⋊D3—62no—
185C2×C3⋊D3C2×C3×D311yescharacteristic, complemented
186C2×C3×D3—216no—
187C2×C3×D3—28no—
188C2×C3×D3—22no—
189C2×C3×D3—24no—
190C2×C3×D3—24no—
191C2×C3×D3—34no—
192C2×C3×D3—34no—
193C2×C3×D3—64no—
194C2×C3×D3—94no—
195C2×C3×D3—91no—
196C2×C3×D3—184no—
197C2×C3×D3—188no—
198C2×C3×D3—182no—
199C2×C3×D3C2×C3×D314yes—
200C2×C3×D3C2×C3×D314yescomplemented
201C2×C3×D3C2×C3⋊D311yescharacteristic
202C2×C3×D3C2×C3⋊D311yescharacteristic, complemented
203D32—68no—
204C32×C4—91no—
205C3⋊Dic3—31no—
206C3⋊Dic3—34no—
207C3⋊Dic3—64no—
208C3⋊Dic3C2×C3×D311yescharacteristic, complemented
209C3×Dic3—34no—
210C3×Dic3—34no—
211C3×Dic3—64no—
212C3×Dic3—94no—
213C3×Dic3—91no—
214C3×Dic3—184no—
215C33—24no—
216C33—21no—
217C33—24no—
218C33—44no—
219C33D3×D411yescharacteristic, complemented
220C33C2×#6714yescomplemented
221C33C2×C3×D411yescharacteristic, complemented
222C23×C3—34no—
223C23×C3—31no—
224C23×C3—64no—
225C23×C3—271no—
226C22×D3—94no—
227C22×D3—91no—
228C22×D3C3×C3⋊D311yescharacteristic, complemented
229C3×D4—91no—
230C3×D4—91no—
231C3×D4—181no—
232C3×D4—271no—
233C3×D4—271no—
234C3×D4—271no—
235C2×C3×C4—271no—
236#67—34no—
237#67—94no—
238#67—94no—
239#67—94no—
240#67—91no—
241#67—91no—
242#67—184no—
243C2×Dic3—94no—
244D12—91no—
245C4×D3—91no—
246C2×C32—28no—
247C2×C32—24no—
248C2×C32—21no—
249C2×C32—24no—
250C2×C32—24no—
251C2×C32—28no—
252C2×C32—24no—
253C2×C32—21no—
254C2×C32—24no—
255C2×C32—24no—
256C2×C32—24no—
257C2×C32—32no—
258C2×C32—38no—
259C2×C32—44no—
260C2×C32—412no—
261C2×C32—44no—
262C2×C32—44no—
263C2×C32—44no—
264C2×C32—48no—
265C2×C32—424no—
266C2×C32—48no—
267C2×C32—44no—
268C2×C32—68no—
269C2×C32—68no—
270C2×C32—64no—
271C2×C32—61no—
272C2×C32—181no—
273C2×C32C2×D3214yes—
274C2×C32C22×C3×D314yes—
275C2×C32C22×C3×D311yescharacteristic
276C2×C32C22×C3⋊D311yescharacteristic
277C3⋊D3—21no—
278C3⋊D3—61no—
279C3⋊D3—64no—
280C3⋊D3—124no—
281C3×D3—28no—
282C3×D3—24no—
283C3×D3—21no—
284C3×D3—28no—
285C3×D3—64no—
286C3×D3—64no—
287C3×D3—124no—
288C3×D3—184no—
289C3×D3—181no—
290C3×D3—364no—
291C3×D3C3×#6718yescomplemented
292C3×D3#63812yesdirect product factor
293C2×D4—271noSylow
294C22×C3—24no—
295C22×C3—24no—
296C22×C3—21no—
297C22×C3—34no—
298C22×C3—31no—
299C22×C3—34no—
300C22×C3—31no—
301C22×C3—44no—
302C22×C3—64no—
303C22×C3—64no—
304C22×C3—68no—
305C22×C3—62no—
306C22×C3—616no—
307C22×C3—91no—
308C22×C3—91no—
309C22×C3—181no—
310C22×C3—271no—
311C22×C3—542no—
312C22×C3C3×D3214yescomplemented
313C22×C3D3×C3⋊D311yescharacteristic, complemented
314C22×C3C2×C3×C3⋊D311yescharacteristic, complemented
315C2×D3—22no—
316C2×D3—34no—
317C2×D3—94no—
318C2×D3—91no—
319C2×D3—184no—
320C2×D3—188no—
321C2×D3—182no—
322C2×D3C2×C3×C3⋊D311yescharacteristic
323C2×D3C2×C3×C3⋊D311yescharacteristic, complemented
324C3×C4—91no—
325C3×C4—91no—
326C3×C4—181no—
327C3×C4—271no—
328Dic3—34no—
329Dic3—94no—
330Dic3—91no—
331Dic3—184no—
332C32—24no—
333C32—24no—
334C32—24no—
335C32—24no—
336C32—24no—
337C32—44no—
338C32—412no—
339C32—44no—
340C32D3×#6714yescomplemented
341C32C3×D3×D411yescharacteristic, complemented
342C32C2×C3×#6714yescomplemented
343C32C2×#63811yescharacteristic, complemented
344C23—31no—
345C23—271no—
346D4—91no—
347D4—271no—
348D4—271no—
349D4—271no—
350C2×C4—271no—
351C2×C3—28no—
352C2×C3—24no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—24no—
356C2×C3—21no—
357C2×C3—24no—
358C2×C3—38no—
359C2×C3—32no—
360C2×C3—44no—
361C2×C3—41no—
362C2×C3—48no—
363C2×C3—44no—
364C2×C3—68no—
365C2×C3—68no—
366C2×C3—64no—
367C2×C3—61no—
368C2×C3—181no—
369C2×C3—181no—
370C2×C3—361no—
371C2×C3—541no—
372C2×C3C2×C3×D3214yes—
373C2×C3C2×D3×C3⋊D311yescharacteristic
374C2×C3C22×C3×C3⋊D311yescharacteristic
375D3—21no—
376D3—64no—
377D3—184no—
378D3—181no—
379D3—364no—
380D3C3×#63812yesdirect product factor
381C22—31no—
382C22—31no—
383C22—62no—
384C22—91no—
385C22—271no—
386C22—542no—
387C22C3×D3×C3⋊D311yescharacteristic, complemented
388C4—91no—
389C4—271no—
390C3—24no—
391C3—24no—
392C3—21no—
393C3—44no—
394C3C3×D3×#6714yescomplemented
395C3D3×#63811yescharacteristic, direct product factor
396C3C2×C3×#63811yescharacteristic, complemented
397C2—21no—
398C2—32no—
399C2—61no—
400C2—181no—
401C2—541no—
402C2C2×C3×D3×C3⋊D311yescharacteristic
subgroupG/H
centerC2×C3C2×D3×C3⋊D3
commutator, cosocleC2×C33C23×C3
FrattiniC2C2×C3×D3×C3⋊D3
FittingC22×C34C22
socleC2×C34C23
hypercenterC22×C3D3×C3⋊D3
hypocenterC33C2×C3×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C3 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C22×C33×D3C2semidirect
2. C2×C3×D3×C3⋊D3C2semidirect
3. C3×#6312C2semidirect
4. C32×#638C2semidirect
5. C3×#6291C2semidirect
6. C3×#6290C2semidirect
7. C3×D3×C3⋊Dic3C2semidirect
9. D3×#638C3direct (N × H)
11. C22×C34C22semidirect
12. C2×C3×C3⋊(C3⋊D3)C22semidirect
13. C2×C32×C3⋊D3C22semidirect
16. C2×C33×D3C22semidirect
18. C3×C3⋊(C3⋊Dic3)C22semidirect
19. C32×C3⋊Dic3C22semidirect
23. C22×C32×D3D3semidirect
24. C22×C32×D3C2×C3semidirect
25. C2×D3×C3⋊D3C2×C3semidirect
27. #6312C2×C3semidirect
34. C3×#638D3direct (N × H)
35. C3×#638C2×C3semidirect
38. #6291C2×C3semidirect
39. #6290C2×C3semidirect
40. D3×C3⋊Dic3C2×C3semidirect
49. C33×D3D4semidirect
61. C22×C33C2×D3semidirect
62. C22×C33C2×D3semidirect
63. C22×C33C22×C3semidirect
64. C2×C3⋊(C3⋊D3)C22×C3semidirect
70. C2×C3×C3⋊D3C2×D3semidirect
71. C2×C3×C3⋊D3C22×C3semidirect
79. C2×C32×D3C2×D3semidirect
81. C2×C32×D3C22×C3semidirect
84. C3⋊(C3⋊Dic3)C22×C3semidirect
89. C3×C3⋊Dic3C2×D3semidirect
90. C3×C3⋊Dic3C22×C3semidirect
92. C34C2×D4semidirect
100. C22×C3×D3C3×D3semidirect
101. C22×C3×D3C3⋊D3semidirect
109. #638C3×D3direct (N × H)
154. C32×D3#67semidirect
155. C32×D3C3×D4semidirect
177. C22×C32D32semidirect
178. C22×C32C2×C3×D3semidirect
179. C22×C32C2×C3×D3semidirect
180. C22×C32C2×C3⋊D3semidirect
185. C2×C3⋊D3C2×C3×D3semidirect
200. C2×C3×D3C2×C3×D3semidirect
202. C2×C3×D3C2×C3⋊D3semidirect
208. C3⋊Dic3C2×C3×D3semidirect
219. C33D3×D4semidirect
220. C33C2×#67semidirect
221. C33C2×C3×D4semidirect
228. C22×D3C3×C3⋊D3semidirect
291. C3×D3C3×#67semidirect
292. C3×D3#638direct (N × H)
312. C22×C3C3×D32semidirect
313. C22×C3D3×C3⋊D3semidirect
314. C22×C3C2×C3×C3⋊D3semidirect
323. C2×D3C2×C3×C3⋊D3semidirect
340. C32D3×#67semidirect
341. C32C3×D3×D4semidirect
342. C32C2×C3×#67semidirect
343. C32C2×#638semidirect
380. D3C3×#638direct (N × H)
387. C22C3×D3×C3⋊D3semidirect
394. C3C3×D3×#67semidirect
395. C3D3×#638direct (N × H)
396. C3C2×C3×#638semidirect

Maximal subgroups

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

subgroupindex
C22×C33×D32
C2×C3×D3×C3⋊D32
C3×#63122
C32×#6382
C3×#62912
C3×#62902
C3×D3×C3⋊Dic32
C2×C3×#6383
D3×#6383
C3×D3×#673