Finite Group Databasebeta

← #10619902⋊C3 #14518751

Subgroups — #10619902⋊C3 #14518751

Order 1944.

474 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 48 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×#92391C212yesmaximal, complemented
2#11758013C211yesmaximal, characteristic, complemented
3#10619902C311yesmaximal, characteristic, complemented
4C3×#6198—31nomaximal
5#6292⋊C3—32nomaximal
6C2×H(5,𝔽3)C2211yescharacteristic
7#92391—22no—
8C2×C3⋊((C3⋊D3)⋊C3)—22no—
9C2×C3⋊((C3⋊D3)⋊C3)D312yescomplemented
10C2×C3⋊((C3⋊D3)⋊C3)C2×C312yescomplemented
11C2×C3×(C3⋊D3)⋊C3—32no—
12C2×C3×(C3⋊D3)⋊C3—32no—
13C2×C3×(C3⋊D3)⋊C3—62no—
14C3×#1084—21no—
15C3×#1084D311yescharacteristic, complemented
16C3×#1084C2×C311yescharacteristic, complemented
17Dic3×H(3,𝔽3)—32no—
18Dic3×H(3,𝔽3)—61no—
19H(5,𝔽3)D411yescharacteristic, complemented, Sylow
20#6292—32no—
21C3×#626—92no—
22C4⋊((C3⋊D3)⋊C3)—91no—
23#6198—31no—
24C2×C3×H(3,𝔽3)—22no—
25C2×C3×H(3,𝔽3)—22no—
26C2×C3×H(3,𝔽3)—21no—
27C2×C3×H(3,𝔽3)—21no—
28C2×C3×H(3,𝔽3)—41no—
29C2×C3×H(3,𝔽3)—42no—
30C2×C3×H(3,𝔽3)—41no—
31C2×C3×H(3,𝔽3)—42no—
32C2×C3×H(3,𝔽3)C2×D312yes—
33C2×C3×H(3,𝔽3)C2×D311yescharacteristic
34C2×C3×H(3,𝔽3)C22×C311yescharacteristic
35C3⋊((C3⋊D3)⋊C3)—24no—
36C3⋊((C3⋊D3)⋊C3)—22no—
37C3⋊((C3⋊D3)⋊C3)—22no—
38C3×(C3⋊D3)⋊C3—64no—
39C3×(C3⋊D3)⋊C3—62no—
40C3×(C3⋊D3)⋊C3—62no—
41C2×C3⋊(C3⋊D3)C3×D312yescomplemented
42C2×C3×C3⋊D3—32no—
43C2×C3×C3⋊D3—32no—
44C2×C3×C3⋊D3—62no—
45C2×C32×D3—92no—
46C32×Dic3—32no—
47C32×Dic3—32no—
48C32×Dic3—62no—
49C32×Dic3—61no—
50C32×Dic3—61no—
51C32×Dic3—62no—
52C2×(C3⋊D3)⋊C3—32no—
53C2×(C3⋊D3)⋊C3—32no—
54C2×(C3⋊D3)⋊C3—62no—
55C2×(C3⋊D3)⋊C3—62no—
56C2×(C3⋊D3)⋊C3—62no—
57C2×(C3⋊D3)⋊C3—62no—
58C2×(C3⋊D3)⋊C3—62no—
59C4×H(3,𝔽3)—91no—
60#1084C3×D311yescharacteristic, complemented
61C3×H(3,𝔽3)—22no—
62C3×H(3,𝔽3)—22no—
63C3×H(3,𝔽3)—21no—
64C3×H(3,𝔽3)—21no—
65C3×H(3,𝔽3)—41no—
66C3×H(3,𝔽3)—42no—
67C3×H(3,𝔽3)—41no—
68C3×H(3,𝔽3)—42no—
69C3×H(3,𝔽3)D1211yescharacteristic, complemented
70C3×H(3,𝔽3)#6712yescomplemented
71C3×H(3,𝔽3)C3×D411yescharacteristic, complemented
72C4⋊(C3⋊D3)—91no—
73C3×#67—272no—
74C3×D12—271no—
75#626—92no—
76#626—272no—
77C2×C33—22no—
78C2×C33—22no—
79C2×C33—22no—
80C2×C33—21no—
81C2×C33—21no—
82C2×C33—42no—
83C2×C33—42no—
84C2×C33—41no—
85C2×C33D3212yes—
86C2×C33C2×C3×D312yes—
87C3⋊(C3⋊D3)—22no—
88C3×C3⋊D3—64no—
89C3×C3⋊D3—62no—
90C3×C3⋊D3—62no—
91C32×D3—182no—
92C2×H(3,𝔽3)—22no—
93C2×H(3,𝔽3)—22no—
94C2×H(3,𝔽3)—22no—
95C2×H(3,𝔽3)—22no—
96C2×H(3,𝔽3)—22no—
97C2×H(3,𝔽3)—41no—
98C2×H(3,𝔽3)—42no—
99C2×H(3,𝔽3)—41no—
100C2×H(3,𝔽3)—42no—
101C2×H(3,𝔽3)—42no—
102C2×H(3,𝔽3)—42no—
103C2×H(3,𝔽3)—42no—
104C2×H(3,𝔽3)—41no—
105C2×H(3,𝔽3)—41no—
106C2×H(3,𝔽3)—42no—
107C2×H(3,𝔽3)—41no—
108C2×H(3,𝔽3)D3211yescharacteristic
109C2×H(3,𝔽3)C2×C3×D311yescharacteristic
110(C3⋊D3)⋊C3—64no—
111(C3⋊D3)⋊C3—64no—
112(C3⋊D3)⋊C3—64no—
113(C3⋊D3)⋊C3—64no—
114(C3⋊D3)⋊C3—64no—
115(C3⋊D3)⋊C3—62no—
116(C3⋊D3)⋊C3—62no—
117C22×C32—272no—
118C2×C3⋊D3—32no—
119C2×C3⋊D3—32no—
120C2×C3⋊D3—62no—
121C2×C3⋊D3—272no—
122C2×C3×D3—92no—
123C2×C3×D3—92no—
124C2×C3×D3—182no—
125C2×C3×D3—272no—
126C2×C3×D3—272no—
127C2×C3×D3—542no—
128C32×C4—91no—
129C32×C4—91no—
130C32×C4—181no—
131C3×Dic3—32no—
132C3×Dic3—61no—
133C3×Dic3—92no—
134C3×Dic3—92no—
135C3×Dic3—182no—
136C3×Dic3—181no—
137C3×Dic3—181no—
138C3×Dic3—182no—
139C33—22no—
140C33—22no—
141C33—21no—
142C33—22no—
143C33—21no—
144C33—42no—
145C33—42no—
146C33—41no—
147C33#62612yescomplemented
148C33C3×#6712yescomplemented
149H(3,𝔽3)—22no—
150H(3,𝔽3)—22no—
151H(3,𝔽3)—22no—
152H(3,𝔽3)—22no—
153H(3,𝔽3)—22no—
154H(3,𝔽3)—41no—
155H(3,𝔽3)—42no—
156H(3,𝔽3)—41no—
157H(3,𝔽3)—42no—
158H(3,𝔽3)—42no—
159H(3,𝔽3)—42no—
160H(3,𝔽3)—42no—
161H(3,𝔽3)—41no—
162H(3,𝔽3)—41no—
163H(3,𝔽3)—42no—
164H(3,𝔽3)—41no—
165H(3,𝔽3)#62511yescharacteristic
166H(3,𝔽3)C3×D1211yescharacteristic
167C3×D4—811no—
168#67—272no—
169D12—271no—
170D12—811no—
171C2×C32—22no—
172C2×C32—22no—
173C2×C32—21no—
174C2×C32—21no—
175C2×C32—41no—
176C2×C32—42no—
177C2×C32—41no—
178C2×C32—42no—
179C2×C32—92no—
180C2×C32—92no—
181C2×C32—182no—
182C2×C32—181no—
183C2×C32—181no—
184C2×C32—182no—
185C2×C32—182no—
186C2×C32—362no—
187C2×C32—362no—
188C2×C32—361no—
189C2×C32—542no—
190C2×C32C3×D3211yescharacteristic
191C2×C32C3×D3212yes—
192C2×C32#111311yescharacteristic
193C3⋊D3—64no—
194C3⋊D3—62no—
195C3⋊D3—62no—
196C3⋊D3—542no—
197C3×D3—184no—
198C3×D3—182no—
199C3×D3—182no—
200C3×D3—542no—
201C3×D3—542no—
202C3×D3—544no—
203C22×C3—272no—
204C22×C3—272no—
205C22×C3—542no—
206C2×D3—92no—
207C2×D3—272no—
208C2×D3—272no—
209C2×D3—542no—
210C3×C4—91no—
211C3×C4—271no—
212C3×C4—271no—
213C3×C4—541no—
214Dic3—32no—
215Dic3—61no—
216C32—22no—
217C32—22no—
218C32—21no—
219C32—21no—
220C32—42no—
221C32—41no—
222C32—41no—
223C32—42no—
224C32—92no—
225C32—92no—
226C32—181no—
227C32—182no—
228C32—181no—
229C32—182no—
230C32—182no—
231C32—362no—
232C32—362no—
233C32—361no—
234C32C3×#62511yescharacteristic
235C32C3×#62612yes—
236C32#629511yescharacteristic
237D4—811noSylow
238C2×C3—32no—
239C2×C3—31no—
240C2×C3—31no—
241C2×C3—61no—
242C2×C3—61no—
243C2×C3—62no—
244C2×C3—62no—
245C2×C3—122no—
246C2×C3—121no—
247C2×C3—122no—
248C2×C3—121no—
249C2×C3—542no—
250C2×C3—542no—
251C2×C3—544no—
252C2×C3C3×#111311yescharacteristic
253D3—182no—
254D3—542no—
255D3—542no—
256D3—544no—
257C22—272no—
258C4—91no—
259C3—31no—
260C3—32no—
261C3—31no—
262C3—62no—
263C3—62no—
264C3—61no—
265C3—61no—
266C3—122no—
267C3—122no—
268C3—121no—
269C3—121no—
270C3C3×#629511yescharacteristic
271C2—542no—
272C2#66432⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2#66432⋊C3
commutator, cosocleC2×C3×H(3,𝔽3)C22×C3
Frattini, socleC2×C3C3×#1113
FittingC2×H(5,𝔽3)C22
hypocenterC3×H(3,𝔽3)C3×D4
LCSG ▷ C2×C3×H(3,𝔽3) ▷ C3×H(3,𝔽3)
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×#92391C2semidirect
2. #11758013C2semidirect
3. #10619902C3semidirect
9. C2×C3⋊((C3⋊D3)⋊C3)D3semidirect
10. C2×C3⋊((C3⋊D3)⋊C3)C2×C3semidirect
15. C3×#1084D3semidirect
16. C3×#1084C2×C3semidirect
19. H(5,𝔽3)D4semidirect
41. C2×C3⋊(C3⋊D3)C3×D3semidirect
60. #1084C3×D3semidirect
69. C3×H(3,𝔽3)D12semidirect
70. C3×H(3,𝔽3)#67semidirect
71. C3×H(3,𝔽3)C3×D4semidirect
147. C33#626semidirect
148. C33C3×#67semidirect

Maximal subgroups

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

subgroupindex
C2×#923912
#117580132
#106199023
C3×#61983
#6292⋊C33