Finite Group Databasebeta

← D3×#396⋊C3 #11921186

Subgroups — D3×#396⋊C3 #11921186

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×#396⋊C3C211yesmaximal, characteristic, complemented
2D3×#95⋊C3C211yesmaximal, characteristic, complemented
3C3⋊(#396⋊C3)C211yesmaximal, characteristic, complemented
4D3×#396C311yesmaximal, characteristic, complemented
5C2×#396⋊C3—31nomaximal
6C22×D3×A4—41nomaximal
7C3×#95⋊C3C2211yescharacteristic, complemented
8C2×D3×C4⋊C4—31no—
9C2×D3×C22⋊C4—31no—
10C3×#396C2×C311yescharacteristic, complemented
11#4994—31no—
12#4948—31no—
13#4676C2×C311yescharacteristic, complemented
14D3×#95C2×C311yescharacteristic, complemented
15#396⋊C3—21no—
16#396⋊C3—31no—
17#396⋊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×#396—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—31no—
35C2×Dic3⋊C4—31no—
36D3×C4⋊C4—64no—
37D3×C22⋊C4—64no—
38C3×#95C22×C311yescharacteristic, complemented
39C3⋊#95—31no—
40#95⋊C3—21no—
41#95⋊C3C2×D311yescharacteristic, complemented
42C22×C3×D3—161no—
43C2×C3×A4—42no—
44C2×C3×A4—41no—
45D3×A4—42no—
46D3×A4—42no—
47C22×C4⋊C4—91no—
48C22×C22⋊C4—91no—
49#396—31no—
50#396—91no—
51#396—91no—
52#396C3×D311yescharacteristic, complemented
53C2×#95—31no—
54C24×C3C2×A411yescharacteristic
55C23×D3—61no—
56C23×D3—62no—
57C23×D3—61no—
58C23×D3SL(2,𝔽3)14yes—
59C23×D3C2×A411yescharacteristic
60C23×D3C2×A411yescharacteristic
61C22×A4—41no—
62C22×A4—81no—
63C22×A4—121no—
64C22×A4—121no—
65C22×A4—124no—
66C22×C3×C4—31no—
67C22×C3×C4—31no—
68C22×Dic3—31no—
69C22×Dic3—31no—
70C2×C4×D3—34no—
71C2×C4×D3—62no—
72C2×C4×D3—61no—
73C2×C4×D3—61no—
74C2×C4×D3—62no—
75C2×C4×D3—62no—
76C2×C4×D3—61no—
77C2×C4×D3—61no—
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—62no—
85Dic3⋊C4—62no—
86C22×C32—161no—
87C2×C3×D3—161no—
88C2×C3×D3—164no—
89C2×C3×D3—161no—
90C3×A4—41no—
91C25—31no—
92C23×C4—91no—
93C23×C4—91no—
94C2×C4⋊C4—31no—
95C2×C4⋊C4—91no—
96C2×C4⋊C4—91no—
97C2×C4⋊C4—91no—
98C2×C4⋊C4—184no—
99C2×C22⋊C4—31no—
100C2×C22⋊C4—91no—
101C2×C22⋊C4—91no—
102C2×C22⋊C4—91no—
103C2×C22⋊C4—184no—
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—32no—
113C22×D3—31no—
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—61no—
132C2×C3×C4—61no—
133C2×C3×C4—61no—
134C2×C3×C4—61no—
135C2×C3×C4—61no—
136C2×Dic3—32no—
137C2×Dic3—61no—
138C2×Dic3—61no—
139C2×Dic3—61no—
140C2×Dic3—61no—
141C2×Dic3—61no—
142C4×D3—64no—
143C4×D3—64no—
144C4×D3—122no—
145C4×D3—122no—
146C2×C32—162no—
147C2×C32—161no—
148C3×D3—162no—
149C3×D3—162no—
150C24—31no—
151C24—31no—
152C24—34no—
153C24—181no—
154C24—182no—
155C24—181no—
156C24D3×A411yescharacteristic
157C22×C4—31no—
158C22×C4—31no—
159C22×C4—94no—
160C22×C4—91no—
161C22×C4—91no—
162C22×C4—182no—
163C22×C4—181no—
164C22×C4—181no—
165C22×C4—182no—
166C22×C4—182no—
167C22×C4—181no—
168C22×C4—181no—
169C4⋊C4—62no—
170C4⋊C4—182no—
171C4⋊C4—182no—
172C4⋊C4—182no—
173C22⋊C4—62no—
174C22⋊C4—182no—
175C22⋊C4—182no—
176C22⋊C4—182no—
177C22×C3—31no—
178C22×C3—31no—
179C22×C3—41no—
180C22×C3—62no—
181C22×C3—121no—
182C22×C3—161no—
183C22×C3—321no—
184C22×C3—481no—
185C22×C3—484no—
186C22×C3—481no—
187C22×C3C22×SL(2,𝔽3)11yescharacteristic
188C2×D3—32no—
189C2×D3—31no—
190C2×D3—32no—
191C2×D3—32no—
192C2×D3—32no—
193C2×D3—41no—
194C2×D3—44no—
195C2×D3—62no—
196C2×D3—124no—
197C2×D3—121no—
198C2×D3#126⋊C311yescharacteristic
199A4—41no—
200A4—81no—
201C3×C4—62no—
202C3×C4—121no—
203Dic3—62no—
204Dic3—121no—
205C32—161noSylow
206C23—32no—
207C23—32no—
208C23—61no—
209C23—61no—
210C23—91no—
211C23—92no—
212C23—91no—
213C23—121no—
214C23—181no—
215C23—181no—
216C23—184no—
217C23—184no—
218C23—361no—
219C23—362no—
220C23—362no—
221C23D3×SL(2,𝔽3)12yes—
222C23C2×D3×A411yescharacteristic
223C2×C4—32no—
224C2×C4—61no—
225C2×C4—61no—
226C2×C4—61no—
227C2×C4—61no—
228C2×C4—61no—
229C2×C4—92no—
230C2×C4—184no—
231C2×C4—184no—
232C2×C4—181no—
233C2×C4—181no—
234C2×C4—181no—
235C2×C4—181no—
236C2×C4—181no—
237C2×C4—362no—
238C2×C4—362no—
239C2×C3—31no—
240C2×C3—31no—
241C2×C3—42no—
242C2×C3—162no—
243C2×C3—161no—
244C2×C3—322no—
245C2×C3—321no—
246C2×C3—482no—
247C2×C3—482no—
248C2×C3C2×#126⋊C311yescharacteristic
249D3—32no—
250D3—42no—
251D3#396⋊C312yesdirect product factor
252C22—31no—
253C22—31no—
254C22—31no—
255C22—41no—
256C22—62no—
257C22—92no—
258C22—92no—
259C22—92no—
260C22—92no—
261C22—91no—
262C22—121no—
263C22—124no—
264C22—121no—
265C22—182no—
266C22—361no—
267C22—364no—
268C22C2×D3×SL(2,𝔽3)11yescharacteristic
269C4—62no—
270C4—121no—
271C4—182no—
272C4—361no—
273C3—161no—
274C3—321no—
275C3C2×#396⋊C311yescharacteristic, complemented
276C2—31no—
277C2—31no—
278C2—32no—
279C2—42no—
280C2—92no—
281C2—122no—
282C2D3×#126⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#126⋊C3
commutator, cosocle, hypocenterC3×#95C22×C3
FrattiniC23C2×D3×A4
FittingC3×#396C2×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×#396⋊C3C2semidirect
2. D3×#95⋊C3C2semidirect
3. C3⋊(#396⋊C3)C2semidirect
4. D3×#396C3semidirect
7. C3×#95⋊C3C22semidirect
10. C3×#396C2×C3semidirect
13. #4676C2×C3semidirect
14. D3×#95C2×C3semidirect
17. #396⋊C3D3direct (N × H)
38. C3×#95C22×C3semidirect
41. #95⋊C3C2×D3semidirect
52. #396C3×D3semidirect
105. #95C2×C3×D3semidirect
251. D3#396⋊C3direct (N × H)
275. C3C2×#396⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×#396⋊C32
D3×#95⋊C32
C3⋊(#396⋊C3)2
D3×#3963
C2×#396⋊C33
C22×D3×A44