Finite Group Databasebeta

← C2×#4184⋊D3 #14518342

Subgroups — C2×#4184⋊D3 #14518342

Order 1944.

534 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 51 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⋊#4177C211yesmaximal, characteristic, complemented
2C2×C3⋊#4176C211yesmaximal, characteristic, complemented
3C2×C3×#4184C211yesmaximal, characteristic, complemented
4#4184⋊D3C214yesmaximal, direct product factor
5C2×((C3⋊D3)⋊C3)⋊D3—31nomaximal
6C2×D9×C3⋊D3—31nomaximal
7C2×#4176⋊C2—31nomaximal
8C2×C3×#731C2211yescharacteristic, complemented
9C3⋊#4177C2212yescomplemented
10C3⋊#4176C2212yescomplemented
11C3×#4184C2212yescomplemented
12C2×C3⋊#272D311yescharacteristic
13C2×C3⋊(C3⋊D9)D311yescharacteristic, complemented
14C2×C3⋊((C3⋊D3)⋊C3)—31no—
15C2×C9×C3⋊D3—31no—
16C2×C3×AGL(1,ℤ/9)—61no—
17C2×C3×(C3⋊D3)⋊C3—31no—
18C2×C32×D9—31no—
19((C3⋊D3)⋊C3)⋊D3—34no—
20D9×C3⋊D3—34no—
21C2×#4184D311yescharacteristic, complemented
22C2×#4177—31no—
23C2×#4177—61no—
24C2×#4176—31no—
25C2×#4176—61no—
26#4176⋊C2—34no—
27C3×#731C2311yescharacteristic, complemented, Sylow
28C2×#1113—91no—
29C2×D3×C3⋊D3—91no—
30C2×((C3⋊D3)⋊C3)⋊C2—91no—
31C2×((C3⋊D3)⋊C3)⋊C2—92no—
32C2×D3×D9—91no—
33C2×D3×D9—92no—
34C2×D3×D9—91no—
35C2×C3×3−1+2—21no—
36C2×C3×H(3,𝔽3)C2×D311yescharacteristic
37C2×C32×C9C2×D311yescharacteristic, complemented
38C3⋊#272C2×D312yes—
39C3⋊(C3⋊D9)C2×D312yescomplemented
40C3⋊((C3⋊D3)⋊C3)—32no—
41C9×C3⋊D3—32no—
42C3×AGL(1,ℤ/9)—62no—
43C3×(C3⋊D3)⋊C3—32no—
44C32×D9—32no—
45C2×#731—21no—
46C2×#731—21no—
47C2×#731—41no—
48C2×#731C2×D311yescharacteristic, complemented
49#4184C2×D312yescomplemented
50#4177—32no—
51#4177—62no—
52#4176—32no—
53#4176—62no—
54C2×C3⋊(C3⋊D3)—31no—
55C2×C3×C3⋊D3—31no—
56C2×C3×C3⋊D3—31no—
57C2×C3×C3⋊D3—91no—
58C2×C3×C3⋊D3—91no—
59C2×C32×D3—91no—
60#1113—94no—
61D3×C3⋊D3—94no—
62C2×#272—31no—
63C2×#272—61no—
64C2×#272—92no—
65C2×C3⋊D9—31no—
66C2×C3⋊D9—61no—
67C2×C3⋊D9—91no—
68C2×C3⋊D9—92no—
69C2×AGL(1,ℤ/9)—61no—
70C2×AGL(1,ℤ/9)—62no—
71C2×(C3⋊D3)⋊C3—32no—
72C2×(C3⋊D3)⋊C3—31no—
73C2×(C3⋊D3)⋊C3—92no—
74C2×(C3⋊D3)⋊C3—91no—
75C2×D3×C9—92no—
76C2×D3×C9—91no—
77C2×D3×C9—91no—
78C2×C3×D9—31no—
79C2×C3×D9—32no—
80C2×C3×D9—31no—
81C2×C3×D9—61no—
82((C3⋊D3)⋊C3)⋊C2—94no—
83((C3⋊D3)⋊C3)⋊C2—98no—
84D3×D9—94no—
85D3×D9—98no—
86D3×D9—94no—
87C3×3−1+2—21no—
88C3×H(3,𝔽3)C22×D311yescharacteristic
89C32×C9C22×D311yescharacteristic, complemented
90#731—21no—
91#731—21no—
92#731—41no—
93#731C22×D311yescharacteristic, complemented
94C22×C3⋊D3—271no—
95C2×D32—272no—
96C2×D32—271no—
97C2×D32—271no—
98C2×D32—271no—
99C2×D32—271no—
100C22×D9—271no—
101C2×C33—31no—
102C2×C33D3211yescharacteristic
103C3⋊(C3⋊D3)—32no—
104C3×C3⋊D3—32no—
105C3×C3⋊D3—32no—
106C3×C3⋊D3—92no—
107C3×C3⋊D3—92no—
108C32×D3—92no—
109C2×3−1+2—21no—
110C2×3−1+2—41no—
111C2×3−1+2—62no—
112C2×H(3,𝔽3)—21no—
113C2×H(3,𝔽3)—32no—
114C2×H(3,𝔽3)D3211yescharacteristic
115C2×C3×C9—21no—
116C2×C3×C9—31no—
117C2×C3×C9—32no—
118C2×C3×C9—61no—
119C2×C3×C9D3211yescharacteristic, complemented
120#272—32no—
121#272—62no—
122#272—94no—
123C3⋊D9—32no—
124C3⋊D9—62no—
125C3⋊D9—92no—
126C3⋊D9—94no—
127AGL(1,ℤ/9)—62no—
128AGL(1,ℤ/9)—64no—
129(C3⋊D3)⋊C3—34no—
130(C3⋊D3)⋊C3—32no—
131(C3⋊D3)⋊C3—94no—
132(C3⋊D3)⋊C3—92no—
133D3×C9—94no—
134D3×C9—92no—
135D3×C9—92no—
136C3×D9—32no—
137C3×D9—34no—
138C3×D9—32no—
139C3×D9—62no—
140C22×C32—271no—
141C2×C3⋊D3—31no—
142C2×C3⋊D3—31no—
143C2×C3⋊D3—91no—
144C2×C3⋊D3—91no—
145C2×C3⋊D3—92no—
146C2×C3⋊D3—91no—
147C2×C3⋊D3—271no—
148C2×C3⋊D3—274no—
149C2×C3⋊D3—541no—
150C2×C3×D3—91no—
151C2×C3×D3—92no—
152C2×C3×D3—92no—
153C2×C3×D3—91no—
154C2×C3×D3—91no—
155C2×C3×D3—91no—
156C2×C3×D3—271no—
157C2×C3×D3—271no—
158C2×C3×D3—271no—
159C2×C3×D3—271no—
160C2×C3×D3—541no—
161C2×C3×D3—541no—
162D32—278no—
163D32—274no—
164D32—274no—
165D32—274no—
166D32—274no—
167C22×C9—271no—
168C2×D9—31no—
169C2×D9—61no—
170C2×D9—271no—
171C2×D9—274no—
172C2×D9—541no—
173C33—31no—
174C33C2×D3211yescharacteristic
1753−1+2—21no—
1763−1+2—41no—
1773−1+2—62no—
178H(3,𝔽3)—21no—
179H(3,𝔽3)—32no—
180H(3,𝔽3)C2×D3211yescharacteristic
181C3×C9—21no—
182C3×C9—31no—
183C3×C9—32no—
184C3×C9—61no—
185C3×C9C2×D3211yescharacteristic, complemented
186C22×D3—811no—
187C22×D3—811no—
188C22×D3—812no—
189C22×D3—811no—
190C22×D3—811no—
191C2×C32—31no—
192C2×C32—31no—
193C2×C32—61no—
194C2×C32—61no—
195C2×C32—91no—
196C2×C32—181no—
197C2×C32—272no—
198C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
199C2×C32((C3⋊D3)⋊C3)⋊C212yes—
200C2×C32#111311yescharacteristic
201C3⋊D3—32no—
202C3⋊D3—32no—
203C3⋊D3—92no—
204C3⋊D3—92no—
205C3⋊D3—94no—
206C3⋊D3—92no—
207C3⋊D3—272no—
208C3⋊D3—542no—
209C3×D3—92no—
210C3×D3—94no—
211C3×D3—94no—
212C3×D3—92no—
213C3×D3—92no—
214C3×D3—92no—
215C3×D3—272no—
216C3×D3—272no—
217C3×D3—272no—
218C3×D3—272no—
219C3×D3—542no—
220C3×D3—542no—
221C2×C9—31no—
222C2×C9—61no—
223C2×C9—61no—
224C2×C9—121no—
225C2×C9—272no—
226D9—32no—
227D9—62no—
228D9—272no—
229D9—542no—
230C22×C3—272no—
231C22×C3—271no—
232C22×C3—271no—
233C22×C3—271no—
234C22×C3—811no—
235C2×D3—92no—
236C2×D3—91no—
237C2×D3—91no—
238C2×D3—91no—
239C2×D3—271no—
240C2×D3—271no—
241C2×D3—271no—
242C2×D3—271no—
243C2×D3—541no—
244C2×D3—541no—
245C2×D3—812no—
246C2×D3—811no—
247C2×D3—814no—
248C2×D3—814no—
249C2×D3—818no—
250C2×D3—814no—
251C2×D3—814no—
252C32—31no—
253C32—31no—
254C32—61no—
255C32—61no—
256C32—91no—
257C32—181no—
258C32C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
259C32C2×((C3⋊D3)⋊C3)⋊C212yes—
260C32C2×#111311yescharacteristic
261C9—31no—
262C9—61no—
263C9—61no—
264C9—121no—
265C23—2431noSylow
266C2×C3—21no—
267C2×C3—32no—
268C2×C3—31no—
269C2×C3—91no—
270C2×C3—181no—
271C2×C3—274no—
272C2×C3—272no—
273C2×C3—272no—
274C2×C3—272no—
275C2×C3—812no—
276C2×C3#4176⋊C211yescharacteristic, complemented
277C2×C3#6643211yescharacteristic
278D3—94no—
279D3—92no—
280D3—92no—
281D3—92no—
282D3—272no—
283D3—272no—
284D3—272no—
285D3—272no—
286D3—542no—
287D3—542no—
288D3—814no—
289D3—812no—
290C22—271no—
291C22—271no—
292C22—811no—
293C22—2434no—
294C3—21no—
295C3—32no—
296C3—31no—
297C3—91no—
298C3—181no—
299C3C2×#4176⋊C211yescharacteristic, complemented
300C3C2×#6643211yescharacteristic
301C2—272no—
302C2—272no—
303C2—812no—
304C2#4184⋊D311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2#4184⋊D3
commutator, cosocle, hypocenterC3×#731C23
FrattiniC32C2×#1113
FittingC2×C3×#731C22
socleC2×C32((C3⋊D3)⋊C3)⋊C2
LCSG ▷ C3×#731
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊#4177C2semidirect
2. C2×C3⋊#4176C2semidirect
3. C2×C3×#4184C2semidirect
4. #4184⋊D3C2direct (N × H)
8. C2×C3×#731C22semidirect
9. C3⋊#4177C22semidirect
10. C3⋊#4176C22semidirect
11. C3×#4184C22semidirect
13. C2×C3⋊(C3⋊D9)D3semidirect
21. C2×#4184D3semidirect
27. C3×#731C23semidirect
37. C2×C32×C9C2×D3semidirect
39. C3⋊(C3⋊D9)C2×D3semidirect
48. C2×#731C2×D3semidirect
49. #4184C2×D3semidirect
89. C32×C9C22×D3semidirect
93. #731C22×D3semidirect
119. C2×C3×C9D32semidirect
185. C3×C9C2×D32semidirect
276. C2×C3#4176⋊C2semidirect
299. C3C2×#4176⋊C2semidirect
304. C2#4184⋊D3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3⋊#41772
C2×C3⋊#41762
C2×C3×#41842
#4184⋊D32
C2×((C3⋊D3)⋊C3)⋊D33
C2×D9×C3⋊D33
C2×#4176⋊C23