Finite Group Databasebeta

← D3×#399⋊C3 #11921194

Subgroups — D3×#399⋊C3 #11921194

Order 1152.

438 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 42 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
1C3×#399⋊C3C211yesmaximal, characteristic, complemented
2D3×#95⋊C3C211yesmaximal, characteristic, complemented
3C3⋊(#399⋊C3)C211yesmaximal, characteristic, complemented
4D3×#399C311yesmaximal, characteristic, complemented
5C2×#399⋊C3—31nomaximal
6C22×D3×A4—41nomaximal
7C3×#95⋊C3C2211yescharacteristic, complemented
8C2×D3×C4⋊C4—31no—
9C2×D3×C22⋊C4—31no—
10C3×#399C2×C311yescharacteristic, complemented
11#4993—31no—
12#4949—31no—
13#4677C2×C311yescharacteristic, complemented
14D3×#95C2×C311yescharacteristic, complemented
15#399⋊C3—21no—
16#399⋊C3—31no—
17#399⋊C3D311yescharacteristic, direct product factor
18C2×#95⋊C3—31no—
19C22×C3×A4—41no—
20C2×D3×A4—44no—
21C2×D3×A4—41no—
22C2×D3×A4—41no—
23C2×#399—31noSylow
24C24×D3A411yescharacteristic
25C23×A4—121no—
26C22×C4×D3—31no—
27C22×C4×D3—31no—
28C2×C3×C4⋊C4—31no—
29C2×C3×C22⋊C4—31no—
30C2×#217—31no—
31C2×(C2×D3)⋊C4—31no—
32C2×(C2×D3)⋊C4—31no—
33C2×C4⋊Dic3—31no—
34C2×Dic3⋊C4—32no—
35D3×C4⋊C4—62no—
36D3×C4⋊C4—62no—
37D3×C22⋊C4—62no—
38D3×C22⋊C4—62no—
39C3×#95C22×C311yescharacteristic, complemented
40C3⋊#95—31no—
41#95⋊C3—21no—
42#95⋊C3C2×D311yescharacteristic, complemented
43C22×C3×D3—161no—
44C2×C3×A4—42no—
45C2×C3×A4—41no—
46D3×A4—42no—
47D3×A4—42no—
48C22×C4⋊C4—91no—
49C22×C22⋊C4—91no—
50#399—31no—
51#399—91no—
52#399—91no—
53#399C3×D311yescharacteristic, complemented
54C2×#95—31no—
55C24×C3C2×A411yescharacteristic
56C23×D3—61no—
57C23×D3—61no—
58C23×D3—62no—
59C23×D3SL(2,𝔽3)14yes—
60C23×D3C2×A411yescharacteristic
61C23×D3C2×A411yescharacteristic
62C22×A4—41no—
63C22×A4—81no—
64C22×A4—121no—
65C22×A4—121no—
66C22×A4—124no—
67C22×C3×C4—31no—
68C22×C3×C4—31no—
69C22×Dic3—31no—
70C22×Dic3—31no—
71C2×C4×D3—32no—
72C2×C4×D3—32no—
73C2×C4×D3—64no—
74C2×C4×D3—61no—
75C2×C4×D3—61no—
76C2×C4×D3—62no—
77C2×C4×D3—62no—
78C3×C4⋊C4—62no—
79C3×C22⋊C4—62no—
80#217—62no—
81(C2×D3)⋊C4—62no—
82(C2×D3)⋊C4—62no—
83C4⋊Dic3—62no—
84Dic3⋊C4—64no—
85C22×C32—161no—
86C2×C3×D3—161no—
87C2×C3×D3—164no—
88C2×C3×D3—161no—
89C3×A4—41no—
90C25—31no—
91C23×C4—91no—
92C23×C4—91no—
93C2×C4⋊C4—31no—
94C2×C4⋊C4—91no—
95C2×C4⋊C4—92no—
96C2×C4⋊C4—182no—
97C2×C4⋊C4—182no—
98C2×C22⋊C4—31no—
99C2×C22⋊C4—91no—
100C2×C22⋊C4—91no—
101C2×C22⋊C4—91no—
102C2×C22⋊C4—182no—
103C2×C22⋊C4—182no—
104#95—91no—
105#95C2×C3×D311yescharacteristic, complemented
106C23×C3—61no—
107C23×C3—61no—
108C23×C3—481no—
109C23×C3C2×SL(2,𝔽3)12yes—
110C23×C3C22×A411yescharacteristic
111C22×D3—31no—
112C22×D3—31no—
113C22×D3—32no—
114C22×D3—41no—
115C22×D3—64no—
116C22×D3—64no—
117C22×D3—61no—
118C22×D3—61no—
119C22×D3—122no—
120C22×D3—121no—
121C22×D3—122no—
122C22×D3C2×SL(2,𝔽3)12yes—
123C22×D3C2×SL(2,𝔽3)12yes—
124C2×A4—41no—
125C2×A4—42no—
126C2×A4—81no—
127C2×A4—82no—
128C2×A4—122no—
129C2×A4—122no—
130C2×C3×C4—32no—
131C2×C3×C4—62no—
132C2×C3×C4—62no—
133C2×C3×C4—61no—
134C2×Dic3—32no—
135C2×Dic3—62no—
136C2×Dic3—62no—
137C2×Dic3—61no—
138C4×D3—64no—
139C4×D3—64no—
140C4×D3—122no—
141C4×D3—121no—
142C4×D3—121no—
143C2×C32—162no—
144C2×C32—161no—
145C3×D3—162no—
146C3×D3—162no—
147C24—31no—
148C24—31no—
149C24—34no—
150C24—181no—
151C24—181no—
152C24—182no—
153C24D3×A411yescharacteristic
154C22×C4—31no—
155C22×C4—31no—
156C22×C4—92no—
157C22×C4—92no—
158C22×C4—91no—
159C22×C4—91no—
160C22×C4—184no—
161C22×C4—181no—
162C22×C4—181no—
163C22×C4—182no—
164C22×C4—182no—
165C4⋊C4—62no—
166C4⋊C4—182no—
167C4⋊C4—184no—
168C22⋊C4—62no—
169C22⋊C4—182no—
170C22⋊C4—182no—
171C22⋊C4—182no—
172C22×C3—31no—
173C22×C3—31no—
174C22×C3—41no—
175C22×C3—62no—
176C22×C3—121no—
177C22×C3—161no—
178C22×C3—321no—
179C22×C3—481no—
180C22×C3—484no—
181C22×C3—481no—
182C22×C3C22×SL(2,𝔽3)11yescharacteristic
183C2×D3—32no—
184C2×D3—31no—
185C2×D3—32no—
186C2×D3—32no—
187C2×D3—32no—
188C2×D3—41no—
189C2×D3—44no—
190C2×D3—62no—
191C2×D3—124no—
192C2×D3—121no—
193C2×D3#127⋊C311yescharacteristic
194A4—41no—
195A4—81no—
196C3×C4—62no—
197C3×C4—121no—
198Dic3—62no—
199Dic3—121no—
200C32—161noSylow
201C23—32no—
202C23—32no—
203C23—61no—
204C23—61no—
205C23—91no—
206C23—91no—
207C23—92no—
208C23—121no—
209C23—181no—
210C23—181no—
211C23—184no—
212C23—184no—
213C23—361no—
214C23—362no—
215C23—362no—
216C23D3×SL(2,𝔽3)12yes—
217C23C2×D3×A411yescharacteristic
218C2×C4—32no—
219C2×C4—62no—
220C2×C4—61no—
221C2×C4—62no—
222C2×C4—92no—
223C2×C4—184no—
224C2×C4—184no—
225C2×C4—182no—
226C2×C4—181no—
227C2×C4—182no—
228C2×C4—361no—
229C2×C4—361no—
230C2×C4—362no—
231C2×C3—31no—
232C2×C3—31no—
233C2×C3—42no—
234C2×C3—162no—
235C2×C3—161no—
236C2×C3—322no—
237C2×C3—321no—
238C2×C3—482no—
239C2×C3—482no—
240C2×C3C2×#127⋊C311yescharacteristic
241D3—32no—
242D3—42no—
243D3#399⋊C312yesdirect product factor
244C22—31no—
245C22—31no—
246C22—31no—
247C22—41no—
248C22—62no—
249C22—92no—
250C22—92no—
251C22—92no—
252C22—92no—
253C22—91no—
254C22—121no—
255C22—124no—
256C22—121no—
257C22—182no—
258C22—361no—
259C22—364no—
260C22C2×D3×SL(2,𝔽3)11yescharacteristic
261C4—62no—
262C4—121no—
263C4—182no—
264C4—361no—
265C3—161no—
266C3—321no—
267C3C2×#399⋊C311yescharacteristic, complemented
268C2—31no—
269C2—31no—
270C2—32no—
271C2—42no—
272C2—92no—
273C2—122no—
274C2D3×#127⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#127⋊C3
commutator, cosocle, hypocenterC3×#95C22×C3
FrattiniC23C2×D3×A4
FittingC3×#399C2×C3
socleC23×C3C22×A4
LCSG ▷ C3×#95
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C3×#399⋊C3C2semidirect
2. D3×#95⋊C3C2semidirect
3. C3⋊(#399⋊C3)C2semidirect
4. D3×#399C3semidirect
7. C3×#95⋊C3C22semidirect
10. C3×#399C2×C3semidirect
13. #4677C2×C3semidirect
14. D3×#95C2×C3semidirect
17. #399⋊C3D3direct (N × H)
39. C3×#95C22×C3semidirect
42. #95⋊C3C2×D3semidirect
53. #399C3×D3semidirect
105. #95C2×C3×D3semidirect
243. D3#399⋊C3direct (N × H)
267. C3C2×#399⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×#399⋊C32
D3×#95⋊C32
C3⋊(#399⋊C3)2
D3×#3993
C2×#399⋊C33
C22×D3×A44