Finite Group Databasebeta

← Dic3×#4207 #14518708

Subgroups — Dic3×#4207 #14518708

Order 1944.

449 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 449 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C2×C3×#4207C211yesmaximal, characteristic
2C3⋊#66409C211yesmaximal, characteristic, complemented
3Dic3×#737C211yesmaximal, characteristic, complemented
4C4×#4207—31nomaximal
5Dic3×C3⋊D9C311yesmaximal, characteristic, complemented
6Dic3×AGL(1,ℤ/9)—32nomaximal
7Dic3×(C3⋊D3)⋊C3—31nomaximal
8C3×Dic3×D9—31nomaximal
9C2×C3×#737C2211yescharacteristic
10C3×#4207C412yescomplemented
11C2×#4207—21no—
12C2×#4207D311yescharacteristic
13C2×C3×C3⋊D9C2×C311yescharacteristic
14C2×C3×AGL(1,ℤ/9)—32no—
15C2×C3×(C3⋊D3)⋊C3—31no—
16C2×C32×D9—31no—
17C4×#737—31no—
18C3⋊(C3⋊Dic9)C2×C311yescharacteristic, complemented
19#66409—31no—
20#66409—61no—
21#66409—61no—
22#66409—62no—
23C3⋊(3−1+2⋊C4)—32no—
24C3⋊((C3⋊Dic3)⋊C3)—31no—
25C3×C3⋊Dic9—31no—
26Dic3×3−1+2—21no—
27Dic3×3−1+2—22no—
28Dic3×3−1+2D312yescomplemented
29Dic3×H(3,𝔽3)D311yescharacteristic
30C3×C9×Dic3—21no—
31C3×C9×Dic3D311yescharacteristic, complemented
32C3×C9×Dic3C2×C311yescharacteristic, complemented
33C3×#737C2×C411yescharacteristic, complemented, Sylow
34Dic3×C3⋊D3—31no—
35C3×D3×Dic3—91no—
36C4×C3⋊D9—31no—
37C4×AGL(1,ℤ/9)—92no—
38C4×(C3⋊D3)⋊C3—91no—
39C3×C4×D9—91no—
40Dic3×D9—31no—
41Dic3×D9—32no—
42C2×#737—22no—
43C2×#737—21no—
44C2×#737—21no—
45C2×#737—21no—
46C2×#737—41no—
47C2×#737—41no—
48C2×#737—42no—
49C2×#737C2×D311yescharacteristic
50C2×C3×3−1+2—21no—
51C2×C3×3−1+2—22no—
52C2×C3×3−1+2C2×D312yes—
53C2×C3×H(3,𝔽3)C2×D311yescharacteristic
54C2×C32×C9—21no—
55C2×C32×C9C2×D311yescharacteristic
56C2×C32×C9C22×C311yescharacteristic
57#4207—22no—
58#4207Dic312yesdirect product factor
59C3×C3⋊D9C3×C412yescomplemented
60C3×AGL(1,ℤ/9)—34no—
61C3×(C3⋊D3)⋊C3—32no—
62C32×D9—32no—
63C2×C3×C3⋊D3—31no—
64C2×C32×D3—91no—
65C3⋊(C3⋊Dic3)—31no—
66C3×C3⋊Dic3—91no—
67C32×Dic3—21no—
68C32×Dic3C3×D311yescharacteristic
69C32×Dic3C3⋊D311yescharacteristic
70C2×C3⋊D9C3×D311yescharacteristic
71C2×AGL(1,ℤ/9)—32no—
72C2×AGL(1,ℤ/9)—62no—
73C2×(C3⋊D3)⋊C3—31no—
74C2×(C3⋊D3)⋊C3—61no—
75C2×C3×D9—31no—
76C2×C3×D9—31no—
77C2×C3×D9—32no—
78C2×C3×D9—61no—
79C4×3−1+2—32no—
80C4×3−1+2—62no—
81C4×3−1+2—61no—
82C4×H(3,𝔽3)—31no—
83C3×C4×C9—31no—
84C3×C4×C9—31no—
85C3×C4×C9—61no—
86C3⋊Dic9—31no—
87C3⋊Dic9—31no—
88C3⋊Dic9—32no—
89C3⋊Dic9—61no—
90C3⋊Dic9—62no—
91C3⋊Dic9—61no—
923−1+2⋊C4—92no—
933−1+2⋊C4—182no—
94(C3⋊Dic3)⋊C3—91no—
95(C3⋊Dic3)⋊C3—181no—
96C9×Dic3—22no—
97C9×Dic3—21no—
98C9×Dic3C3×D311yescharacteristic
99C9×Dic3C3×D312yes—
100C3×Dic9—91no—
101C3×Dic9—181no—
102#737—22no—
103#737—21no—
104#737—21no—
105#737—21no—
106#737—41no—
107#737—41no—
108#737—42no—
109#737C2×Dic311yescharacteristic, complemented
110C3×3−1+2—21no—
111C3×3−1+2—22no—
112C3×3−1+2C4×D312yescomplemented
113C3×H(3,𝔽3)C4×D311yescharacteristic
114C32×C9—21no—
115C32×C9C4×D311yescharacteristic, complemented
116C32×C9C2×C3×C411yescharacteristic, complemented
117C4×C3⋊D3—91no—
118C2×C3×Dic3—271no—
119C3×C4×D3—271no—
120D3×Dic3—91no—
121D3×Dic3—271no—
122C4×D9—91no—
123C4×D9—92no—
124C2×C33—21no—
125C2×C33C2×C3×D311yescharacteristic
126C2×C33C2×C3⋊D311yescharacteristic
127C3×C3⋊D3—32no—
128C32×D3—92no—
129C2×3−1+2—21no—
130C2×3−1+2—22no—
131C2×3−1+2—22no—
132C2×3−1+2—22no—
133C2×3−1+2—42no—
134C2×3−1+2—42no—
135C2×3−1+2—42no—
136C2×3−1+2—42no—
137C2×3−1+2—42no—
138C2×3−1+2—41no—
139C2×3−1+2—41no—
140C2×3−1+2—42no—
141C2×3−1+2D3212yes—
142C2×H(3,𝔽3)—21no—
143C2×H(3,𝔽3)—21no—
144C2×H(3,𝔽3)—41no—
145C2×H(3,𝔽3)D3211yescharacteristic
146C2×C3×C9—21no—
147C2×C3×C9—22no—
148C2×C3×C9—21no—
149C2×C3×C9—21no—
150C2×C3×C9—21no—
151C2×C3×C9—22no—
152C2×C3×C9—21no—
153C2×C3×C9—21no—
154C2×C3×C9—41no—
155C2×C3×C9—42no—
156C2×C3×C9—41no—
157C2×C3×C9—41no—
158C2×C3×C9D3211yescharacteristic
159C2×C3×C9C2×C3×D311yescharacteristic
160C2×C3×C9C2×C3×D312yes—
161C2×C3×C9C2×C3×D311yescharacteristic
162C3⋊D9C3×Dic312yescomplemented
163AGL(1,ℤ/9)—34no—
164AGL(1,ℤ/9)—64no—
165(C3⋊D3)⋊C3—32no—
166(C3⋊D3)⋊C3—62no—
167C3×D9—32no—
168C3×D9—32no—
169C3×D9—34no—
170C3×D9—62no—
171C22×C32—271no—
172C2×C3⋊D3—31no—
173C2×C3×D3—91no—
174C2×C3×D3—91no—
175C2×C3×D3—181no—
176C2×C3×D3—271no—
177C32×C4—31no—
178C32×C4—31no—
179C32×C4—61no—
180C3⋊Dic3—91no—
181C3⋊Dic3—91no—
182C3⋊Dic3—181no—
183C3⋊Dic3—271no—
184C3⋊Dic3—541no—
185C3×Dic3—31no—
186C3×Dic3—31no—
187C3×Dic3—61no—
188C3×Dic3—271no—
189C3×Dic3—271no—
190C3×Dic3—541no—
191C3×Dic3C3×C3⋊D311yescharacteristic
192C2×D9—31no—
193C2×D9—32no—
194C4×C9—31no—
195C4×C9—32no—
196C4×C9—61no—
197C4×C9—62no—
198Dic9—91no—
199Dic9—92no—
200Dic9—181no—
201Dic9—182no—
202C33—21no—
203C33C3×C4×D311yescharacteristic
204C33C4×C3⋊D311yescharacteristic
2053−1+2—21no—
2063−1+2—22no—
2073−1+2—22no—
2083−1+2—22no—
2093−1+2—42no—
2103−1+2—42no—
2113−1+2—42no—
2123−1+2—42no—
2133−1+2—42no—
2143−1+2—41no—
2153−1+2—41no—
2163−1+2—42no—
2173−1+2D3×Dic312yescomplemented
218H(3,𝔽3)—21no—
219H(3,𝔽3)—21no—
220H(3,𝔽3)—41no—
221H(3,𝔽3)D3×Dic311yescharacteristic
222C3×C9—21no—
223C3×C9—21no—
224C3×C9—22no—
225C3×C9—21no—
226C3×C9—21no—
227C3×C9—22no—
228C3×C9—21no—
229C3×C9—21no—
230C3×C9—41no—
231C3×C9—42no—
232C3×C9—41no—
233C3×C9—41no—
234C3×C9D3×Dic311yescharacteristic, complemented
235C3×C9C3×C4×D311yescharacteristic
236C3×C9C3×C4×D312yes—
237C3×C9C2×C3×Dic311yescharacteristic, complemented
238C2×C3×C4—811no—
239C2×Dic3—271no—
240C4×D3—271no—
241C4×D3—811no—
242C2×C32—21no—
243C2×C32—21no—
244C2×C32—21no—
245C2×C32—31no—
246C2×C32—31no—
247C2×C32—41no—
248C2×C32—61no—
249C2×C32—61no—
250C2×C32—61no—
251C2×C32—121no—
252C2×C32—272no—
253C2×C32C3×D3211yescharacteristic
254C2×C32D3×C3⋊D311yescharacteristic
255C2×C32C2×C3×C3⋊D311yescharacteristic
256C3⋊D3—32no—
257C3×D3—92no—
258C3×D3—92no—
259C3×D3—182no—
260C3×D3—272no—
261C2×C9—21no—
262C2×C9—22no—
263C2×C9—22no—
264C2×C9—21no—
265C2×C9—41no—
266C2×C9—42no—
267C2×C9C3×D3211yescharacteristic
268C2×C9C3×D3212yes—
269D9—32no—
270D9—34no—
271C22×C3—271no—
272C22×C3—271no—
273C22×C3—541no—
274C2×D3—91no—
275C2×D3—271no—
276C3×C4—31no—
277C3×C4—91no—
278C3×C4—91no—
279C3×C4—181no—
280C3×C4—811no—
281Dic3—271no—
282Dic3—271no—
283Dic3—541no—
284Dic3—811no—
285Dic3—1621no—
286Dic3#420711yescharacteristic, direct product factor
287C32—21no—
288C32—21no—
289C32—21no—
290C32—31no—
291C32—31no—
292C32—41no—
293C32—61no—
294C32—61no—
295C32—61no—
296C32—121no—
297C32C3×D3×Dic311yescharacteristic
298C32Dic3×C3⋊D311yescharacteristic
299C32C3×C4×C3⋊D311yescharacteristic
300C9—21no—
301C9—22no—
302C9—22no—
303C9—21no—
304C9—41no—
305C9—42no—
306C9C3×D3×Dic311yescharacteristic
307C9C3×D3×Dic312yes—
308C2×C4—811noSylow
309C2×C3—21no—
310C2×C3—31no—
311C2×C3—31no—
312C2×C3—61no—
313C2×C3—61no—
314C2×C3—61no—
315C2×C3—121no—
316C2×C3—272no—
317C2×C3—272no—
318C2×C3—542no—
319C2×C3C2×#420711yescharacteristic
320C2×C3C3×D3×C3⋊D311yescharacteristic
321D3—92no—
322D3—272no—
323C22—271no—
324C4—31no—
325C4—811no—
326C3—21no—
327C3—31no—
328C3—31no—
329C3—61no—
330C3—61no—
331C3—61no—
332C3—121no—
333C3C4×#420711yescharacteristic, complemented
334C3C3×Dic3×C3⋊D311yescharacteristic
335C2—272no—
336C2D3×#420711yescharacteristic
subgroupG/H
center, hypercenterC2D3×#4207
commutator, hypocenterC32×C9C2×C3×C4
FrattiniC2×C3C3×D3×C3⋊D3
FittingC2×C3×#737C22
socleC2×C32C2×C3×C3⋊D3
prime radicalC2×C3×#4207C2
cosocleC2×C32×C9C22×C3
LCSG ▷ C32×C9
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3⋊#66409C2semidirect
3. Dic3×#737C2semidirect
5. Dic3×C3⋊D9C3semidirect
10. C3×#4207C4semidirect
18. C3⋊(C3⋊Dic9)C2×C3semidirect
28. Dic3×3−1+2D3semidirect
31. C3×C9×Dic3D3semidirect
32. C3×C9×Dic3C2×C3semidirect
33. C3×#737C2×C4semidirect
58. #4207Dic3direct (N × H)
59. C3×C3⋊D9C3×C4semidirect
109. #737C2×Dic3semidirect
112. C3×3−1+2C4×D3semidirect
115. C32×C9C4×D3semidirect
116. C32×C9C2×C3×C4semidirect
162. C3⋊D9C3×Dic3semidirect
217. 3−1+2D3×Dic3semidirect
234. C3×C9D3×Dic3semidirect
237. C3×C9C2×C3×Dic3semidirect
286. Dic3#4207direct (N × H)
333. C3C4×#4207semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#42072
C3⋊#664092
Dic3×#7372
C4×#42073
Dic3×C3⋊D93
Dic3×AGL(1,ℤ/9)3
Dic3×(C3⋊D3)⋊C33
C3×Dic3×D93