Finite Group Databasebeta

← C3×#10619902 #14518733

Subgroups — C3×#10619902 #14518733

Order 1944.

759 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 759 conjugacy classes of subgroups — too many to draw. Only its 62 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×C3⋊((C3⋊D3)⋊C3)C212yesmaximal, complemented
2C32×#1084C211yesmaximal, characteristic, complemented
3C3×#6292—32nomaximal
4#10619902C311yesmaximal, characteristic, direct product factor
5C3×#6198—31nomaximal
6C2×C32×H(3,𝔽3)C2211yescharacteristic
7C3×C3⋊((C3⋊D3)⋊C3)—22no—
8C2×C3×C3⋊(C3⋊D3)D312yescomplemented
9C2×C32×C3⋊D3—32no—
10C33×Dic3—32no—
11C33×Dic3—61no—
12C2×C3⋊((C3⋊D3)⋊C3)—22no—
13C2×C3⋊((C3⋊D3)⋊C3)C2×C312yescomplemented
14C2×C3×(C3⋊D3)⋊C3—32no—
15C2×C3×(C3⋊D3)⋊C3—62no—
16C3×#1084—21no—
17C3×#1084D311yescharacteristic, complemented
18C3×#1084C2×C311yescharacteristic, complemented
19C32×H(3,𝔽3)D411yescharacteristic, complemented, Sylow
20C3×C4⋊(C3⋊D3)—91no—
21#6292—32no—
22C3×#626—92no—
23C3×#626—96no—
24#6198—31no—
25C2×C34—21no—
26C2×C34C2×D312yes—
27C3×C3⋊(C3⋊D3)—22no—
28C32×C3⋊D3—62no—
29C2×C3×H(3,𝔽3)—22no—
30C2×C3×H(3,𝔽3)—22no—
31C2×C3×H(3,𝔽3)—21no—
32C2×C3×H(3,𝔽3)—42no—
33C2×C3×H(3,𝔽3)—42no—
34C2×C3×H(3,𝔽3)—41no—
35C2×C3×H(3,𝔽3)—41no—
36C2×C3×H(3,𝔽3)C2×D311yescharacteristic
37C2×C3×H(3,𝔽3)C22×C311yescharacteristic
38C3⋊((C3⋊D3)⋊C3)—24no—
39C3⋊((C3⋊D3)⋊C3)—22no—
40C3×(C3⋊D3)⋊C3—64no—
41C3×(C3⋊D3)⋊C3—62no—
42C2×C3⋊(C3⋊D3)C3×D312yescomplemented
43C2×C3×C3⋊D3—32no—
44C2×C3×C3⋊D3—32no—
45C2×C3×C3⋊D3—32no—
46C2×C3×C3⋊D3—62no—
47C2×C3×C3⋊D3—62no—
48C2×C3×C3⋊D3—96no—
49C2×C32×D3—96no—
50C2×C32×D3—92no—
51C33×C4—91no—
52C32×Dic3—36no—
53C32×Dic3—32no—
54C32×Dic3—32no—
55C32×Dic3—62no—
56C32×Dic3—61no—
57C32×Dic3—61no—
58C32×Dic3—62no—
59C32×Dic3—66no—
60C32×Dic3—63no—
61C32×Dic3—66no—
62C2×(C3⋊D3)⋊C3—32no—
63C2×(C3⋊D3)⋊C3—62no—
64C2×(C3⋊D3)⋊C3—62no—
65C2×(C3⋊D3)⋊C3—64no—
66#1084C3×D311yescharacteristic, complemented
67C34—21no—
68C34#6712yescomplemented
69C3×H(3,𝔽3)—22no—
70C3×H(3,𝔽3)—22no—
71C3×H(3,𝔽3)—21no—
72C3×H(3,𝔽3)—42no—
73C3×H(3,𝔽3)—42no—
74C3×H(3,𝔽3)—41no—
75C3×H(3,𝔽3)—41no—
76C3×H(3,𝔽3)D1211yescharacteristic, complemented
77C3×H(3,𝔽3)C3×D411yescharacteristic, complemented
78C4⋊(C3⋊D3)—91no—
79C3×#67—272no—
80C3×D12—273no—
81C3×D12—271no—
82#626—92no—
83#626—96no—
84C2×C33—22no—
85C2×C33—22no—
86C2×C33—21no—
87C2×C33—22no—
88C2×C33—21no—
89C2×C33—22no—
90C2×C33—36no—
91C2×C33—42no—
92C2×C33—42no—
93C2×C33—41no—
94C2×C33—41no—
95C2×C33—66no—
96C2×C33—66no—
97C2×C33—63no—
98C2×C33D3211yescharacteristic
99C2×C33D3212yes—
100C2×C33C2×C3×D312yes—
101C3⋊(C3⋊D3)—22no—
102C3×C3⋊D3—64no—
103C3×C3⋊D3—62no—
104C3×C3⋊D3—62no—
105C3×C3⋊D3—64no—
106C3×C3⋊D3—62no—
107C3×C3⋊D3—186no—
108C32×D3—186no—
109C32×D3—182no—
110C2×H(3,𝔽3)—24no—
111C2×H(3,𝔽3)—22no—
112C2×H(3,𝔽3)—22no—
113C2×H(3,𝔽3)—41no—
114C2×H(3,𝔽3)—41no—
115C2×H(3,𝔽3)—44no—
116C2×H(3,𝔽3)—44no—
117C2×H(3,𝔽3)—42no—
118C2×H(3,𝔽3)—42no—
119C2×H(3,𝔽3)—42no—
120C2×H(3,𝔽3)C2×C3×D311yescharacteristic
121(C3⋊D3)⋊C3—68no—
122(C3⋊D3)⋊C3—64no—
123(C3⋊D3)⋊C3—64no—
124(C3⋊D3)⋊C3—62no—
125C22×C32—272no—
126C2×C3⋊D3—32no—
127C2×C3⋊D3—32no—
128C2×C3⋊D3—62no—
129C2×C3⋊D3—96no—
130C2×C3×D3—96no—
131C2×C3×D3—96no—
132C2×C3×D3—92no—
133C2×C3×D3—92no—
134C2×C3×D3—182no—
135C2×C3×D3—186no—
136C2×C3×D3—272no—
137C2×C3×D3—542no—
138C32×C4—91no—
139C32×C4—93no—
140C32×C4—91no—
141C32×C4—183no—
142C32×C4—181no—
143C3×Dic3—32no—
144C3×Dic3—36no—
145C3×Dic3—32no—
146C3×Dic3—62no—
147C3×Dic3—66no—
148C3×Dic3—61no—
149C3×Dic3—63no—
150C3×Dic3—61no—
151C3×Dic3—62no—
152C3×Dic3—66no—
153C33—22no—
154C33—22no—
155C33—21no—
156C33—22no—
157C33—21no—
158C33—22no—
159C33—36no—
160C33—42no—
161C33—42no—
162C33—41no—
163C33—41no—
164C33—66no—
165C33—66no—
166C33—63no—
167C33#62511yescharacteristic
168C33#62612yescomplemented
169C33C3×#6712yescomplemented
170H(3,𝔽3)—24no—
171H(3,𝔽3)—22no—
172H(3,𝔽3)—22no—
173H(3,𝔽3)—41no—
174H(3,𝔽3)—41no—
175H(3,𝔽3)—44no—
176H(3,𝔽3)—44no—
177H(3,𝔽3)—42no—
178H(3,𝔽3)—42no—
179H(3,𝔽3)—42no—
180H(3,𝔽3)C3×D1211yescharacteristic, complemented
181C3×D4—811no—
182#67—272no—
183D12—273no—
184D12—271no—
185C2×C32—23no—
186C2×C32—21no—
187C2×C32—22no—
188C2×C32—22no—
189C2×C32—21no—
190C2×C32—36no—
191C2×C32—32no—
192C2×C32—42no—
193C2×C32—41no—
194C2×C32—41no—
195C2×C32—42no—
196C2×C32—62no—
197C2×C32—66no—
198C2×C32—66no—
199C2×C32—62no—
200C2×C32—66no—
201C2×C32—63no—
202C2×C32—62no—
203C2×C32—61no—
204C2×C32—126no—
205C2×C32—122no—
206C2×C32—126no—
207C2×C32—122no—
208C2×C32—123no—
209C2×C32—121no—
210C2×C32—542no—
211C2×C32((C3⋊D3)⋊C3)⋊C213yes—
212C2×C32C3×D3212yes—
213C2×C32C3×D3211yescharacteristic
214C2×C32#111311yescharacteristic
215C3⋊D3—62no—
216C3⋊D3—64no—
217C3⋊D3—62no—
218C3⋊D3—186no—
219C3×D3—184no—
220C3×D3—186no—
221C3×D3—1812no—
222C3×D3—186no—
223C3×D3—182no—
224C3×D3—182no—
225C3×D3—542no—
226C3×D3—544no—
227C22×C3—272no—
228C22×C3—272no—
229C22×C3—542no—
230C2×D3—96no—
231C2×D3—92no—
232C2×D3—272no—
233C2×D3—542no—
234C3×C4—93no—
235C3×C4—91no—
236C3×C4—91no—
237C3×C4—183no—
238C3×C4—181no—
239Dic3—32no—
240Dic3—61no—
241C32—23no—
242C32—21no—
243C32—22no—
244C32—22no—
245C32—21no—
246C32—36no—
247C32—32no—
248C32—42no—
249C32—41no—
250C32—41no—
251C32—42no—
252C32—62no—
253C32—66no—
254C32—66no—
255C32—62no—
256C32—66no—
257C32—63no—
258C32—62no—
259C32—61no—
260C32—126no—
261C32—122no—
262C32—126no—
263C32—122no—
264C32—123no—
265C32—121no—
266C32#619813yescomplemented
267C32C3×#62511yescharacteristic
268C32C3×#62612yescomplemented
269C32#629511yescharacteristic
270D4—811noSylow
271C2×C3—23no—
272C2×C3—21no—
273C2×C3—32no—
274C2×C3—61no—
275C2×C3—62no—
276C2×C3—62no—
277C2×C3—122no—
278C2×C3—122no—
279C2×C3—121no—
280C2×C3—121no—
281C2×C3—542no—
282C2×C3—544no—
283C2×C3—542no—
284C2×C3C3×((C3⋊D3)⋊C3)⋊C213yes—
285C2×C3#6643211yescharacteristic
286C2×C3C3×#111311yescharacteristic
287D3—186no—
288D3—182no—
289D3—542no—
290D3—544no—
291C22—272no—
292C4—91no—
293C3—23no—
294C3—21no—
295C3—32no—
296C3—62no—
297C3—62no—
298C3—61no—
299C3—122no—
300C3—122no—
301C3—121no—
302C3—121no—
303C3C3×#619813yescomplemented
304C3#1061990211yescharacteristic, direct product factor
305C3C3×#629511yescharacteristic
306C2—542no—
307C2C3×#6643211yescharacteristic
subgroupG/H
center, hypercenterC2×C3#66432
commutator, cosocleC2×C3×H(3,𝔽3)C22×C3
FrattiniC2×C3C3×#1113
FittingC2×C32×H(3,𝔽3)C22
socleC2×C33D32
hypocenterC3×H(3,𝔽3)C3×D4
LCSG ▷ C2×C3×H(3,𝔽3) ▷ C3×H(3,𝔽3)
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×C3⋊((C3⋊D3)⋊C3)C2semidirect
2. C32×#1084C2semidirect
4. #10619902C3direct (N × H)
8. C2×C3×C3⋊(C3⋊D3)D3semidirect
13. C2×C3⋊((C3⋊D3)⋊C3)C2×C3semidirect
17. C3×#1084D3semidirect
18. C3×#1084C2×C3semidirect
19. C32×H(3,𝔽3)D4semidirect
42. C2×C3⋊(C3⋊D3)C3×D3semidirect
66. #1084C3×D3semidirect
68. C34#67semidirect
76. C3×H(3,𝔽3)D12semidirect
77. C3×H(3,𝔽3)C3×D4semidirect
168. C33#626semidirect
169. C33C3×#67semidirect
180. H(3,𝔽3)C3×D12semidirect
266. C32#6198semidirect
268. C32C3×#626semidirect
303. C3C3×#6198semidirect
304. C3#10619902direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C3⋊((C3⋊D3)⋊C3)2
C32×#10842
C3×#62923
#106199023
C3×#61983