Finite Group Databasebeta

← #14518852

Subgroups — #14518852

Order 1944.

494 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 67 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
2C3⋊#66409C211yesmaximal, characteristic, complemented
3C3×#66409C211yesmaximal, characteristic, complemented
4#10619908—33nomaximal
5#10619898—31nomaximal
6#10619885—31nomaximal
7C3⋊D3×Dic9—31nomaximal
8C2×C3×#737C2211yescharacteristic
9C3⋊#4208C412yescomplemented
10C2×C3⋊#272D311yescharacteristic
11C2×#4208—33no—
12C2×#4208—63no—
13C2×C9×C3⋊D3—31no—
14C2×C9×C3⋊D3—31no—
15C2×C9×C3⋊D3—61no—
16C3⋊(C3⋊Dic9)D311yescharacteristic, complemented
17#66409—33no—
18#66409—63no—
19#66409D313yescomplemented
20C3⋊(3−1+2⋊C4)—61no—
21C3⋊((C3⋊Dic3)⋊C3)—31no—
22C3×C3⋊Dic9—31no—
23C3×C3⋊Dic9D311yescharacteristic, complemented
24C3×3−1+2⋊C4—61no—
25C3×(C3⋊Dic3)⋊C3—31no—
26C32×Dic9—31no—
27C3×#737C2×C411yescharacteristic, complemented, Sylow
28#6294—91no—
29Dic3×C3⋊D3—91no—
30#6199—93no—
31D3×Dic9—93no—
32D3×Dic9—91no—
33D3×Dic9—91no—
34C2×#737—23no—
35C2×#737—23no—
36C2×#737—43no—
37C2×#737C2×D313yes—
38C2×C3×3−1+2—21no—
39C2×C3×3−1+2—21no—
40C2×C3×3−1+2—41no—
41C2×C3×H(3,𝔽3)C2×D311yescharacteristic
42C2×C32×C9—21no—
43C2×C32×C9C2×D311yescharacteristic
44C2×C32×C9C2×D311yescharacteristic
45C3⋊#272Dic312yes—
46#4208—36no—
47#4208—66no—
48C9×C3⋊D3—32no—
49C9×C3⋊D3—32no—
50C9×C3⋊D3—62no—
51C2×C3×C3⋊D3—31no—
52C2×C3×C3⋊D3—31no—
53C2×C3×C3⋊D3—61no—
54C3⋊(C3⋊Dic3)—31no—
55C3×C3⋊Dic3—31no—
56C3×C3⋊Dic3—91no—
57C32×Dic3—91no—
58C2×#272—33no—
59C2×#272—63no—
60C2×D3×C9—91no—
61C2×D3×C9—93no—
62C2×D3×C9—91no—
63C2×D3×C9—181no—
64C2×D3×C9—183no—
65C3⋊Dic9—31no—
66C3⋊Dic9—33no—
67C3⋊Dic9—61no—
68C3⋊Dic9—63no—
69C3⋊Dic9C3⋊D311yescharacteristic, complemented
703−1+2⋊C4—63no—
713−1+2⋊C4—183no—
72(C3⋊Dic3)⋊C3—33no—
73(C3⋊Dic3)⋊C3—93no—
74C3×Dic9—31no—
75C3×Dic9—33no—
76C3×Dic9—61no—
77C3×Dic9—91no—
78C3×Dic9—181no—
79#737—23no—
80#737—23no—
81#737—43no—
82#737C4×D313yescomplemented
83C3×3−1+2—21no—
84C3×3−1+2—21no—
85C3×3−1+2—41no—
86C3×H(3,𝔽3)C2×Dic311yescharacteristic
87C32×C9—21no—
88C32×C9C4×D311yescharacteristic, complemented
89C32×C9C4×D311yescharacteristic, complemented
90C4×C3⋊D3—271no—
91#624—271no—
92D3×Dic3—273no—
93D3×Dic3—271no—
94D3×Dic3—271no—
95C2×Dic9—271no—
96C2×C33—21no—
97C2×C33D3211yescharacteristic
98C2×C33D3211yescharacteristic
99C3×C3⋊D3—32no—
100C3×C3⋊D3—32no—
101C3×C3⋊D3—62no—
102C2×3−1+2—23no—
103C2×3−1+2—23no—
104C2×3−1+2—43no—
105C2×3−1+2—43no—
106C2×3−1+2—46no—
107C2×3−1+2—43no—
108C2×H(3,𝔽3)—23no—
109C2×H(3,𝔽3)D3213yes—
110C2×C3×C9—21no—
111C2×C3×C9—23no—
112C2×C3×C9—21no—
113C2×C3×C9—21no—
114C2×C3×C9—23no—
115C2×C3×C9—21no—
116C2×C3×C9—41no—
117C2×C3×C9—43no—
118C2×C3×C9—41no—
119C2×C3×C9D3211yescharacteristic
120C2×C3×C9D3213yes—
121C2×C3×C9C2×C3⋊D311yescharacteristic
122#272—36no—
123#272—66no—
124D3×C9—92no—
125D3×C9—96no—
126D3×C9—92no—
127D3×C9—182no—
128D3×C9—186no—
129C2×C3⋊D3—31no—
130C2×C3⋊D3—31no—
131C2×C3⋊D3—61no—
132C2×C3×D3—91no—
133C2×C3×D3—93no—
134C2×C3×D3—91no—
135C2×C3×D3—183no—
136C2×C3×D3—181no—
137C32×C4—271no—
138C3⋊Dic3—31no—
139C3⋊Dic3—91no—
140C3⋊Dic3—93no—
141C3⋊Dic3—271no—
142C3⋊Dic3—541no—
143C3×Dic3—91no—
144C3×Dic3—93no—
145C3×Dic3—271no—
146C3×Dic3—271no—
147C3×Dic3—271no—
148C3×Dic3—541no—
149C22×C9—271no—
150Dic9—31no—
151Dic9—61no—
152Dic9—91no—
153Dic9—181no—
154Dic9—183no—
155C33—21no—
156C33D3×Dic311yescharacteristic
157C33D3×Dic311yescharacteristic
1583−1+2—23no—
1593−1+2—23no—
1603−1+2—43no—
1613−1+2—43no—
1623−1+2—46no—
1633−1+2—43no—
164H(3,𝔽3)—23no—
165H(3,𝔽3)D3×Dic313yes—
166C3×C9—21no—
167C3×C9—23no—
168C3×C9—21no—
169C3×C9—21no—
170C3×C9—23no—
171C3×C9—21no—
172C3×C9—41no—
173C3×C9—43no—
174C3×C9—41no—
175C3×C9#62411yescharacteristic
176C3×C9#62413yescomplemented
177C3×C9C4×C3⋊D311yescharacteristic, complemented
178C2×Dic3—811no—
179C4×D3—811no—
180C4×D3—811no—
181C4×D3—813no—
182C2×C32—21no—
183C2×C32—23no—
184C2×C32—31no—
185C2×C32—31no—
186C2×C32—61no—
187C2×C32—61no—
188C2×C32—61no—
189C2×C32—121no—
190C2×C32D3×C3⋊D311yescharacteristic
191C2×C32#111311yescharacteristic
192C2×C32#111313yes—
193C3⋊D3—32no—
194C3⋊D3—32no—
195C3⋊D3—62no—
196C3×D3—92no—
197C3×D3—96no—
198C3×D3—92no—
199C3×D3—186no—
200C3×D3—182no—
201C2×C9—21no—
202C2×C9—23no—
203C2×C9—21no—
204C2×C9—41no—
205C2×C9—43no—
206C2×C9—272no—
207C2×C9D3×C3⋊D311yescharacteristic
208C22×C3—271no—
209C2×D3—91no—
210C2×D3—93no—
211C2×D3—91no—
212C2×D3—181no—
213C2×D3—183no—
214C3×C4—273no—
215C3×C4—271no—
216C3×C4—811no—
217Dic3—91no—
218Dic3—271no—
219Dic3—271no—
220Dic3—271no—
221Dic3—541no—
222Dic3—813no—
223C32—21no—
224C32—23no—
225C32—31no—
226C32—31no—
227C32—61no—
228C32—61no—
229C32—61no—
230C32—121no—
231C32Dic3×C3⋊D311yescharacteristic
232C32#629411yescharacteristic
233C32#629413yes—
234C9—21no—
235C9—23no—
236C9—21no—
237C9—41no—
238C9—43no—
239C9#628911yescharacteristic
240C2×C4—2431noSylow
241C2×C3—21no—
242C2×C3—31no—
243C2×C3—33no—
244C2×C3—61no—
245C2×C3—63no—
246C2×C3—272no—
247C2×C3#4207⋊C211yescharacteristic
248C2×C3C3⋊#111311yescharacteristic
249D3—92no—
250D3—96no—
251D3—92no—
252D3—182no—
253D3—186no—
254C22—271no—
255C4—271no—
256C4—811no—
257C3—21no—
258C3—31no—
259C3—33no—
260C3—61no—
261C3—63no—
262C3#1061990811yescharacteristic, complemented
263C3#1062015411yescharacteristic
264C2—272no—
265C2#4207⋊D311yescharacteristic
subgroupG/H
center, hypercenterC2#4207⋊D3
commutator, hypocenterC3×#737C2×C4
FrattiniC2×C3C3⋊#1113
Fitting, cosocleC2×C3×#737C22
socleC2×C32#1113
prime radicalC2×C3⋊#272D3
LCSG ▷ C3×#737
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3⋊#66409C2semidirect
3. C3×#66409C2semidirect
9. C3⋊#4208C4semidirect
16. C3⋊(C3⋊Dic9)D3semidirect
19. #66409D3semidirect
23. C3×C3⋊Dic9D3semidirect
27. C3×#737C2×C4semidirect
69. C3⋊Dic9C3⋊D3semidirect
82. #737C4×D3semidirect
88. C32×C9C4×D3semidirect
89. C32×C9C4×D3semidirect
176. C3×C9#624semidirect
177. C3×C9C4×C3⋊D3semidirect
262. C3#10619908semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊#42082
C3⋊#664092
C3×#664092
#106199083
#106198983
#106198853
C3⋊D3×Dic93