Finite Group Databasebeta

← #14518851

Subgroups — #14518851

Order 1944.

502 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 63 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, complemented
2C2×C3×#4207C211yesmaximal, characteristic, complemented
3C3⋊#66410C211yesmaximal, characteristic, complemented
4#10619907—33nomaximal
5#10619897—31nomaximal
6#10619884—31nomaximal
7#10619873—31nomaximal
8C2×C3×#737C2211yescharacteristic
9C3⋊#4207—21no—
10C3×#4207—21no—
11C2×C3⋊(C3⋊D9)D311yescharacteristic, complemented
12C2×#4207—33no—
13C2×#4207—63no—
14C2×#4207D313yescomplemented
15C2×C3⋊AGL(1,ℤ/9)—61no—
16C2×C3⋊((C3⋊D3)⋊C3)—31no—
17C2×C3×C3⋊D9—31no—
18C2×C3×C3⋊D9D311yescharacteristic, complemented
19C2×C3×AGL(1,ℤ/9)—61no—
20C2×C3×(C3⋊D3)⋊C3—31no—
21C2×C32×D9—31no—
22C3⋊#1084D311yescharacteristic
23#66410—33no—
24#66410—63no—
25C9×C3⋊Dic3—31no—
26C9×C3⋊Dic3—31no—
27C9×C3⋊Dic3—61no—
28C3×#737D411yescharacteristic, complemented, Sylow
29#6295—91no—
30#6291—91no—
31#6198—93no—
32#6192—93no—
33#6192—91no—
34#6192—91no—
35C2×#737—23no—
36C2×#737—23no—
37C2×#737—43no—
38C2×#737C2×D313yes—
39C2×C3×3−1+2—21no—
40C2×C3×3−1+2—21no—
41C2×C3×3−1+2—41no—
42C2×C3×H(3,𝔽3)C2×D311yescharacteristic
43C2×C32×C9—21no—
44C2×C32×C9C2×D311yescharacteristic
45C2×C32×C9C2×D311yescharacteristic
46C3⋊(C3⋊D9)—21no—
47#4207—23no—
48#4207—66no—
49#4207—63no—
50C3⋊AGL(1,ℤ/9)—62no—
51C3⋊((C3⋊D3)⋊C3)—61no—
52C3×C3⋊D9—21no—
53C3×C3⋊D9—61no—
54C3×AGL(1,ℤ/9)—62no—
55C3×(C3⋊D3)⋊C3—61no—
56C32×D9—61no—
57C2×C3⋊(C3⋊D3)—31no—
58C2×C3×C3⋊D3—31no—
59C2×C3×C3⋊D3—91no—
60C2×C32×D3—91no—
61C3×C3⋊Dic3—31no—
62C3×C3⋊Dic3—31no—
63C3×C3⋊Dic3—61no—
64C2×C3⋊D9—31no—
65C2×C3⋊D9—33no—
66C2×C3⋊D9—61no—
67C2×C3⋊D9—63no—
68C2×C3⋊D9C3⋊D311yescharacteristic, complemented
69C2×AGL(1,ℤ/9)—63no—
70C2×AGL(1,ℤ/9)—183no—
71C2×(C3⋊D3)⋊C3—33no—
72C2×(C3⋊D3)⋊C3—93no—
73C2×C3×D9—31no—
74C2×C3×D9—33no—
75C2×C3×D9—61no—
76C2×C3×D9—91no—
77C2×C3×D9—181no—
78#1084—33no—
79#1084—63no—
80C9×Dic3—91no—
81C9×Dic3—93no—
82C9×Dic3—91no—
83C9×Dic3—181no—
84C9×Dic3—183no—
85#737—23no—
86#737—23no—
87#737—43no—
88#737#6713yescomplemented
89C3×3−1+2—21no—
90C3×3−1+2—21no—
91C3×3−1+2—41no—
92C3×H(3,𝔽3)D1211yescharacteristic
93C32×C9—21no—
94C32×C9#6711yescharacteristic, complemented
95C32×C9#6711yescharacteristic, complemented
96#638—271no—
97#626—273no—
98#626—271no—
99#626—271no—
100#625—271no—
101D36—271no—
102C2×C33—21no—
103C2×C33D3211yescharacteristic
104C2×C33D3211yescharacteristic
105C3⋊(C3⋊D3)—61no—
106C3×C3⋊D3—61no—
107C3×C3⋊D3—181no—
108C32×D3—181no—
109C2×3−1+2—23no—
110C2×3−1+2—23no—
111C2×3−1+2—43no—
112C2×3−1+2—43no—
113C2×3−1+2—46no—
114C2×3−1+2—43no—
115C2×H(3,𝔽3)—23no—
116C2×H(3,𝔽3)D3213yes—
117C2×C3×C9—21no—
118C2×C3×C9—23no—
119C2×C3×C9—21no—
120C2×C3×C9—21no—
121C2×C3×C9—23no—
122C2×C3×C9—21no—
123C2×C3×C9—41no—
124C2×C3×C9—43no—
125C2×C3×C9—41no—
126C2×C3×C9D3211yescharacteristic
127C2×C3×C9D3213yes—
128C2×C3×C9C2×C3⋊D311yescharacteristic
129C3⋊D9—21no—
130C3⋊D9—62no—
131C3⋊D9—66no—
132C3⋊D9—61no—
133C3⋊D9—63no—
134AGL(1,ℤ/9)—66no—
135AGL(1,ℤ/9)—186no—
136(C3⋊D3)⋊C3—63no—
137(C3⋊D3)⋊C3—183no—
138C3×D9—62no—
139C3×D9—61no—
140C3×D9—63no—
141C3×D9—182no—
142C3×D9—181no—
143C22×C32—271no—
144C2×C3⋊D3—31no—
145C2×C3⋊D3—91no—
146C2×C3⋊D3—93no—
147C2×C3⋊D3—271no—
148C2×C3⋊D3—541no—
149C2×C3×D3—91no—
150C2×C3×D3—93no—
151C2×C3×D3—271no—
152C2×C3×D3—271no—
153C2×C3×D3—271no—
154C2×C3×D3—541no—
155C3⋊Dic3—31no—
156C3⋊Dic3—31no—
157C3⋊Dic3—61no—
158C3×Dic3—91no—
159C3×Dic3—93no—
160C3×Dic3—91no—
161C3×Dic3—183no—
162C3×Dic3—181no—
163C2×D9—31no—
164C2×D9—61no—
165C2×D9—91no—
166C2×D9—181no—
167C2×D9—183no—
168C4×C9—271no—
169C33—21no—
170C33#62611yescharacteristic
171C33#62611yescharacteristic
1723−1+2—23no—
1733−1+2—23no—
1743−1+2—43no—
1753−1+2—43no—
1763−1+2—46no—
1773−1+2—43no—
178H(3,𝔽3)—23no—
179H(3,𝔽3)#62613yes—
180C3×C9—21no—
181C3×C9—23no—
182C3×C9—21no—
183C3×C9—21no—
184C3×C9—23no—
185C3×C9—21no—
186C3×C9—41no—
187C3×C9—43no—
188C3×C9—41no—
189C3×C9#62511yescharacteristic
190C3×C9#62513yescomplemented
191C3×C9#63811yescharacteristic, complemented
192#67—811no—
193#67—811no—
194#67—813no—
195D12—811no—
196C2×C32—21no—
197C2×C32—23no—
198C2×C32—31no—
199C2×C32—31no—
200C2×C32—61no—
201C2×C32—61no—
202C2×C32—61no—
203C2×C32—121no—
204C2×C32—541no—
205C2×C32D3×C3⋊D311yescharacteristic
206C2×C32#111311yescharacteristic
207C2×C32#111313yes—
208C3⋊D3—61no—
209C3⋊D3—181no—
210C3⋊D3—183no—
211C3⋊D3—541no—
212C3⋊D3—542no—
213C3×D3—181no—
214C3×D3—183no—
215C3×D3—541no—
216C3×D3—541no—
217C3×D3—542no—
218C3×D3—541no—
219C2×C9—21no—
220C2×C9—23no—
221C2×C9—21no—
222C2×C9—41no—
223C2×C9—43no—
224C2×C9D3×C3⋊D311yescharacteristic
225D9—62no—
226D9—61no—
227D9—182no—
228D9—186no—
229D9—181no—
230C22×C3—273no—
231C22×C3—271no—
232C22×C3—811no—
233C2×D3—91no—
234C2×D3—271no—
235C2×D3—271no—
236C2×D3—271no—
237C2×D3—541no—
238C2×D3—813no—
239C3×C4—271no—
240Dic3—91no—
241Dic3—93no—
242Dic3—91no—
243Dic3—181no—
244Dic3—183no—
245C32—21no—
246C32—23no—
247C32—31no—
248C32—31no—
249C32—61no—
250C32—61no—
251C32—61no—
252C32—121no—
253C32#629111yescharacteristic
254C32#629511yescharacteristic
255C32#629513yes—
256C9—21no—
257C9—21no—
258C9—23no—
259C9—41no—
260C9—43no—
261C9#629011yescharacteristic
262D4—2431noSylow
263C2×C3—21no—
264C2×C3—31no—
265C2×C3—33no—
266C2×C3—61no—
267C2×C3—63no—
268C2×C3—543no—
269C2×C3—541no—
270C2×C3—1621no—
271C2×C3#4207⋊C211yescharacteristic
272C2×C3C3⋊#111311yescharacteristic
273D3—181no—
274D3—541no—
275D3—542no—
276D3—541no—
277D3—541no—
278D3—1623no—
279C22—271no—
280C22—811no—
281C4—271no—
282C3—21no—
283C3—31no—
284C3—33no—
285C3—61no—
286C3—63no—
287C3#1061990711yescharacteristic, complemented
288C3#1062015711yescharacteristic
289C2—541no—
290C2—1621no—
291C2#4207⋊D311yescharacteristic
subgroupG/H
center, hypercenterC2#4207⋊D3
commutator, Fitting, cosocleC2×C3×#737C22
FrattiniC2×C3C3⋊#1113
socleC2×C32#1113
hypocenterC3×#737D4
LCSG ▷ C2×C3×#737 ▷ C3×#737
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊#4207C2semidirect
2. C2×C3×#4207C2semidirect
3. C3⋊#66410C2semidirect
11. C2×C3⋊(C3⋊D9)D3semidirect
14. C2×#4207D3semidirect
18. C2×C3×C3⋊D9D3semidirect
28. C3×#737D4semidirect
68. C2×C3⋊D9C3⋊D3semidirect
88. #737#67semidirect
94. C32×C9#67semidirect
95. C32×C9#67semidirect
190. C3×C9#625semidirect
191. C3×C9#638semidirect
287. C3#10619907semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊#42072
C2×C3×#42072
C3⋊#664102
#106199073
#106198973
#106198843
#106198733