Finite Group Databasebeta

← #14518855

Subgroups — #14518855

Order 1944.

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

normal subgroups only

This group has 506 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⋊#4208C211yesmaximal, characteristic, complemented
2C2×C3×#4207C211yesmaximal, characteristic, complemented
3C3⋊#66409C211yesmaximal, characteristic, complemented
4#10619909—33nomaximal
5#10619899—31nomaximal
6#10619886—31nomaximal
7#10619877—31nomaximal
8C2×C3×#737C2211yescharacteristic
9C3⋊#4208—21no—
10C3×#4207—21no—
11C2×C3⋊#272D311yescharacteristic
12C2×#4208—33no—
13C2×#4208—63no—
14C2×#4207D313yescomplemented
15C2×C9×C3⋊D3—31no—
16C2×C9×C3⋊D3—31no—
17C2×C9×C3⋊D3—61no—
18C2×C3×C3⋊D9D311yescharacteristic, complemented
19C2×C3×AGL(1,ℤ/9)—61no—
20C2×C3×(C3⋊D3)⋊C3—31no—
21C2×C32×D9—31no—
22C3⋊(C3⋊Dic9)D311yescharacteristic, complemented
23#66409—33no—
24#66409—63no—
25C3⋊(3−1+2⋊C4)—61no—
26C3⋊((C3⋊Dic3)⋊C3)—31no—
27C3×C3⋊Dic9—31no—
28C3×#737D411yescharacteristic, complemented, Sylow
29#6295—91no—
30#6290—91no—
31#6200—93no—
32#6195—91no—
33#6194—93no—
34#6194—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⋊#272—21no—
47#4208—66no—
48#4208—63no—
49#4207—23no—
50C9×C3⋊D3—62no—
51C9×C3⋊D3—61no—
52C9×C3⋊D3—61no—
53C3×C3⋊D9—21no—
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—31no—
60C2×C3×C3⋊D3—61no—
61C2×C32×D3—91no—
62C3⋊(C3⋊Dic3)—31no—
63C3×C3⋊Dic3—91no—
64C2×#272—33no—
65C2×#272—63no—
66C2×C3⋊D9C3⋊D311yescharacteristic, complemented
67C2×AGL(1,ℤ/9)—63no—
68C2×(C3⋊D3)⋊C3—33no—
69C2×D3×C9—91no—
70C2×D3×C9—93no—
71C2×D3×C9—91no—
72C2×D3×C9—181no—
73C2×D3×C9—183no—
74C2×C3×D9—31no—
75C2×C3×D9—33no—
76C2×C3×D9—61no—
77C3⋊Dic9—31no—
78C3⋊Dic9—33no—
79C3⋊Dic9—61no—
80C3⋊Dic9—63no—
813−1+2⋊C4—183no—
82(C3⋊Dic3)⋊C3—93no—
83C3×Dic9—91no—
84C3×Dic9—181no—
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)#6711yescharacteristic
93C32×C9—21no—
94C32×C9D1211yescharacteristic, complemented
95C32×C9#6711yescharacteristic, complemented
96#638—271no—
97#626—271no—
98#626—271no—
99#625—273no—
100#625—271no—
101#611—271no—
102C2×C33—21no—
103C2×C33D3211yescharacteristic
104C2×C33D3211yescharacteristic
105C3×C3⋊D3—62no—
106C3×C3⋊D3—61no—
107C3×C3⋊D3—61no—
108C3×C3⋊D3—61no—
109C32×D3—181no—
110C2×3−1+2—23no—
111C2×3−1+2—23no—
112C2×3−1+2—43no—
113C2×3−1+2—43no—
114C2×3−1+2—46no—
115C2×3−1+2—43no—
116C2×H(3,𝔽3)—23no—
117C2×H(3,𝔽3)D3213yes—
118C2×C3×C9—21no—
119C2×C3×C9—23no—
120C2×C3×C9—21no—
121C2×C3×C9—21no—
122C2×C3×C9—23no—
123C2×C3×C9—21no—
124C2×C3×C9—41no—
125C2×C3×C9—43no—
126C2×C3×C9—41no—
127C2×C3×C9D3211yescharacteristic
128C2×C3×C9D3213yes—
129C2×C3×C9C2×C3⋊D311yescharacteristic
130#272—66no—
131#272—63no—
132C3⋊D9—21no—
133AGL(1,ℤ/9)—66no—
134(C3⋊D3)⋊C3—63no—
135D3×C9—186no—
136D3×C9—182no—
137D3×C9—181no—
138D3×C9—183no—
139D3×C9—181no—
140C3×D9—62no—
141C3×D9—61no—
142C3×D9—63no—
143C22×C32—271no—
144C2×C3⋊D3—31no—
145C2×C3⋊D3—31no—
146C2×C3⋊D3—31no—
147C2×C3⋊D3—61no—
148C2×C3×D3—91no—
149C2×C3×D3—91no—
150C2×C3×D3—93no—
151C2×C3×D3—93no—
152C2×C3×D3—91no—
153C2×C3×D3—183no—
154C2×C3×D3—181no—
155C2×C3×D3—271no—
156C3⋊Dic3—91no—
157C3⋊Dic3—93no—
158C3⋊Dic3—271no—
159C3⋊Dic3—541no—
160C3×Dic3—271no—
161C3×Dic3—271no—
162C3×Dic3—541no—
163C22×C9—271no—
164C2×D9—31no—
165C2×D9—61no—
166Dic9—91no—
167Dic9—181no—
168Dic9—183no—
169C33—21no—
170C33#62511yescharacteristic
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)#62513yes—
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#62611yescharacteristic
190C3×C9#62613yescomplemented
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—61no—
210C3⋊D3—62no—
211C3⋊D3—61no—
212C3×D3—182no—
213C3×D3—186no—
214C3×D3—181no—
215C3×D3—181no—
216C3×D3—183no—
217C3×D3—183no—
218C3×D3—181no—
219C3×D3—541no—
220C2×C9—21no—
221C2×C9—23no—
222C2×C9—21no—
223C2×C9—41no—
224C2×C9—43no—
225C2×C9—541no—
226C2×C9D3×C3⋊D311yescharacteristic
227D9—62no—
228D9—61no—
229C22×C3—273no—
230C22×C3—271no—
231C22×C3—271no—
232C2×D3—91no—
233C2×D3—93no—
234C2×D3—91no—
235C2×D3—91no—
236C2×D3—181no—
237C2×D3—183no—
238C2×D3—271no—
239C3×C4—811no—
240Dic3—271no—
241Dic3—271no—
242Dic3—541no—
243Dic3—813no—
244C32—21no—
245C32—23no—
246C32—31no—
247C32—31no—
248C32—61no—
249C32—61no—
250C32—61no—
251C32—121no—
252C32#629011yescharacteristic
253C32#629511yescharacteristic
254C32#629513yes—
255C9—21no—
256C9—21no—
257C9—23no—
258C9—41no—
259C9—43no—
260C9#629111yescharacteristic
261D4—2431noSylow
262C2×C3—21no—
263C2×C3—33no—
264C2×C3—31no—
265C2×C3—61no—
266C2×C3—63no—
267C2×C3—543no—
268C2×C3—541no—
269C2×C3—541no—
270C2×C3#4207⋊C211yescharacteristic
271C2×C3C3⋊#111311yescharacteristic
272D3—181no—
273D3—183no—
274D3—182no—
275D3—186no—
276D3—181no—
277D3—181no—
278D3—541no—
279C22—271no—
280C22—271no—
281C4—811no—
282C3—21no—
283C3—31no—
284C3—33no—
285C3—61no—
286C3—63no—
287C3#1061990911yescharacteristic, complemented
288C3#1062015711yescharacteristic
289C2—541no—
290C2—541no—
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⋊#4208C2semidirect
2. C2×C3×#4207C2semidirect
3. C3⋊#66409C2semidirect
14. C2×#4207D3semidirect
18. C2×C3×C3⋊D9D3semidirect
22. C3⋊(C3⋊Dic9)D3semidirect
28. C3×#737D4semidirect
66. C2×C3⋊D9C3⋊D3semidirect
88. #737#67semidirect
94. C32×C9D12semidirect
95. C32×C9#67semidirect
190. C3×C9#626semidirect
191. C3×C9#638semidirect
287. C3#10619909semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊#42082
C2×C3×#42072
C3⋊#664092
#106199093
#106198993
#106198863
#106198773