Finite Group Databasebeta

← D3×#393⋊C3 #11921172

Subgroups — D3×#393⋊C3 #11921172

Order 1152.

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

normal subgroups only

This group has 496 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
1D3×C22⋊SL(2,𝔽3)C211yesmaximal, characteristic, complemented
2C3×#393⋊C3C211yesmaximal, characteristic, complemented
3C3⋊(#393⋊C3)C211yesmaximal, characteristic, complemented
4D3×#393C311yesmaximal, characteristic, complemented
5C2×#393⋊C3—31nomaximal
6C22×D3×A4—41nomaximal
7C3×C22⋊SL(2,𝔽3)C2211yescharacteristic, complemented
8C22×D3×Q8C2×C311yescharacteristic, complemented
9C2×C22⋊SL(2,𝔽3)—31no—
10C2×D3×C22⋊C4—31no—
11C3×#393C2×C311yescharacteristic, complemented
12#5231C2×C311yescharacteristic, complemented
13#4947—31no—
14#4673—31no—
15D3×#95—31no—
16#393⋊C3—21no—
17#393⋊C3—31no—
18#393⋊C3D311yescharacteristic, direct product factor
19C22×C3×A4—41no—
20C2×D3×A4—44no—
21C2×D3×A4—41no—
22C2×D3×A4—41no—
23D3×SL(2,𝔽3)—82no—
24C2×#393—31noSylow
25C24×D3A411yescharacteristic
26C23×A4—121no—
27C22×C3×Q8C22×C311yescharacteristic, complemented
28C2×D3×Q8—62no—
29C2×D3×Q8—62no—
30C22×C4×D3—31no—
31C22×C4×D3—31no—
32C22×Dic6—31no—
33C22⋊SL(2,𝔽3)—21no—
34C22⋊SL(2,𝔽3)C2×D311yescharacteristic, complemented
35C2×C3×C22⋊C4—31no—
36C2×#217—31no—
37C2×(C2×D3)⋊C4—31no—
38C2×(C2×D3)⋊C4—31no—
39D3×C22⋊C4—62no—
40D3×C22⋊C4—62no—
41C3×#95—31no—
42C3⋊#95—32no—
43C3⋊#95—31no—
44C22×C3×D3—161no—
45C2×C3×A4—42no—
46C2×C3×A4—41no—
47D3×A4—42no—
48D3×A4—42no—
49C3×SL(2,𝔽3)—82no—
50C23×Q8—31no—
51C22×C22⋊C4—91no—
52#393—31no—
53#393—91no—
54#393—91no—
55#393C3×D311yescharacteristic, complemented
56C2×#95—91no—
57C24×C3C2×A411yescharacteristic
58C23×D3—61no—
59C23×D3—61no—
60C23×D3—62no—
61C23×D3SL(2,𝔽3)14yescomplemented
62C23×D3C2×A411yescharacteristic
63C23×D3C2×A411yescharacteristic
64C22×A4—41no—
65C22×A4—81no—
66C22×A4—121no—
67C22×A4—121no—
68C22×A4—124no—
69C2×C3×Q8—62no—
70C22×C3×C4—31no—
71C22×C3×C4—31no—
72C22×Dic3—31no—
73C22×Dic3—31no—
74D3×Q8—22no—
75D3×Q8—62no—
76D3×Q8—64no—
77D3×Q8—62no—
78D3×Q8—62no—
79C2×C4×D3—32no—
80C2×C4×D3—32no—
81C2×C4×D3—62no—
82C2×C4×D3—62no—
83C2×C4×D3—61no—
84C2×C4×D3—61no—
85C2×C4×D3—64no—
86C2×Dic6—64no—
87C2×Dic6—62no—
88C2×SL(2,𝔽3)—242no—
89C3×C22⋊C4—62no—
90#217—62no—
91(C2×D3)⋊C4—62no—
92(C2×D3)⋊C4—62no—
93C22×C32—161no—
94C2×C3×D3—161no—
95C2×C3×D3—164no—
96C2×C3×D3—161no—
97C3×A4—41no—
98C25—31no—
99C22×Q8—91no—
100C22×Q8—182no—
101C22×Q8—182no—
102C22×Q8C2×C3×D311yescharacteristic, complemented
103C23×C4—91no—
104C23×C4—91no—
105C2×C22⋊C4—31no—
106C2×C22⋊C4—91no—
107C2×C22⋊C4—91no—
108C2×C22⋊C4—91no—
109C2×C22⋊C4—182no—
110C2×C22⋊C4—182no—
111#95—31no—
112#95—91no—
113#95—92no—
114C23×C3—61no—
115C23×C3—61no—
116C23×C3—481no—
117C23×C3C2×SL(2,𝔽3)12yescomplemented
118C23×C3C22×A411yescharacteristic
119C22×D3—31no—
120C22×D3—31no—
121C22×D3—32no—
122C22×D3—41no—
123C22×D3—64no—
124C22×D3—64no—
125C22×D3—61no—
126C22×D3—61no—
127C22×D3—122no—
128C22×D3—121no—
129C22×D3—122no—
130C22×D3C2×SL(2,𝔽3)12yes—
131C22×D3C2×SL(2,𝔽3)12yescomplemented
132C2×A4—41no—
133C2×A4—42no—
134C2×A4—81no—
135C2×A4—82no—
136C2×A4—122no—
137C2×A4—122no—
138C3×Q8—22no—
139C3×Q8—62no—
140C2×C3×C4—32no—
141C2×C3×C4—62no—
142C2×C3×C4—61no—
143C2×C3×C4—62no—
144C2×Dic3—32no—
145C2×Dic3—62no—
146C2×Dic3—61no—
147C2×Dic3—62no—
148C4×D3—64no—
149C4×D3—62no—
150C4×D3—62no—
151C4×D3—122no—
152C4×D3—122no—
153Dic6—64no—
154Dic6—62no—
155Dic6—62no—
156SL(2,𝔽3)—82no—
157SL(2,𝔽3)—162no—
158C2×C32—162no—
159C2×C32—161no—
160C3×D3—162no—
161C3×D3—162no—
162C24—31no—
163C24—31no—
164C24—34no—
165C24—181no—
166C24—181no—
167C24—182no—
168C24D3×A411yescharacteristic
169C2×Q8—62no—
170C2×Q8—62no—
171C2×Q8—182no—
172C2×Q8—184no—
173C2×Q8—182no—
174C2×Q8—182no—
175C2×Q8—184no—
176C2×Q8—182no—
177C22×C4—31no—
178C22×C4—31no—
179C22×C4—92no—
180C22×C4—92no—
181C22×C4—91no—
182C22×C4—91no—
183C22×C4—182no—
184C22×C4—182no—
185C22×C4—181no—
186C22×C4—181no—
187C22×C4—184no—
188C22⋊C4—62no—
189C22⋊C4—182no—
190C22⋊C4—182no—
191C22⋊C4—182no—
192C22×C3—31no—
193C22×C3—31no—
194C22×C3—41no—
195C22×C3—62no—
196C22×C3—121no—
197C22×C3—161no—
198C22×C3—321no—
199C22×C3—481no—
200C22×C3—484no—
201C22×C3—481no—
202C22×C3C22×SL(2,𝔽3)11yescharacteristic
203C2×D3—32no—
204C2×D3—31no—
205C2×D3—32no—
206C2×D3—32no—
207C2×D3—32no—
208C2×D3—41no—
209C2×D3—44no—
210C2×D3—62no—
211C2×D3—124no—
212C2×D3—121no—
213C2×D3#120⋊C311yescharacteristic
214A4—41no—
215A4—81no—
216C3×C4—62no—
217C3×C4—121no—
218Dic3—62no—
219Dic3—121no—
220C32—161noSylow
221C23—32no—
222C23—32no—
223C23—61no—
224C23—61no—
225C23—91no—
226C23—91no—
227C23—92no—
228C23—121no—
229C23—181no—
230C23—181no—
231C23—184no—
232C23—184no—
233C23—361no—
234C23—362no—
235C23—362no—
236C23D3×SL(2,𝔽3)12yescomplemented
237C23C2×D3×A411yescharacteristic
238Q8—22no—
239Q8—62no—
240Q8—182no—
241Q8—182no—
242Q8—184no—
243C2×C4—32no—
244C2×C4—62no—
245C2×C4—61no—
246C2×C4—62no—
247C2×C4—92no—
248C2×C4—182no—
249C2×C4—182no—
250C2×C4—184no—
251C2×C4—182no—
252C2×C4—181no—
253C2×C4—182no—
254C2×C4—362no—
255C2×C4—362no—
256C2×C3—31no—
257C2×C3—31no—
258C2×C3—42no—
259C2×C3—162no—
260C2×C3—161no—
261C2×C3—322no—
262C2×C3—321no—
263C2×C3—482no—
264C2×C3—482no—
265C2×C3C2×#120⋊C311yescharacteristic
266D3—32no—
267D3—42no—
268D3#393⋊C312yesdirect product factor
269C22—31no—
270C22—31no—
271C22—31no—
272C22—41no—
273C22—62no—
274C22—92no—
275C22—92no—
276C22—92no—
277C22—92no—
278C22—91no—
279C22—121no—
280C22—124no—
281C22—121no—
282C22—182no—
283C22—361no—
284C22—364no—
285C22C2×D3×SL(2,𝔽3)11yescharacteristic
286C4—62no—
287C4—121no—
288C4—182no—
289C4—361no—
290C3—161no—
291C3—321no—
292C3C2×#393⋊C311yescharacteristic, complemented
293C2—31no—
294C2—31no—
295C2—32no—
296C2—42no—
297C2—92no—
298C2—122no—
299C2D3×#120⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#120⋊C3
commutator, cosocle, hypocenterC22×C3×Q8C22×C3
FrattiniC23C2×D3×A4
FittingC3×#393C2×C3
socleC23×C3C22×A4
LCSG ▷ C22×C3×Q8
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. D3×C22⋊SL(2,𝔽3)C2semidirect
2. C3×#393⋊C3C2semidirect
3. C3⋊(#393⋊C3)C2semidirect
4. D3×#393C3semidirect
7. C3×C22⋊SL(2,𝔽3)C22semidirect
8. C22×D3×Q8C2×C3semidirect
11. C3×#393C2×C3semidirect
12. #5231C2×C3semidirect
18. #393⋊C3D3direct (N × H)
27. C22×C3×Q8C22×C3semidirect
34. C22⋊SL(2,𝔽3)C2×D3semidirect
55. #393C3×D3semidirect
61. C23×D3SL(2,𝔽3)semidirect
102. C22×Q8C2×C3×D3semidirect
117. C23×C3C2×SL(2,𝔽3)semidirect
131. C22×D3C2×SL(2,𝔽3)semidirect
236. C23D3×SL(2,𝔽3)semidirect
268. D3#393⋊C3direct (N × H)
292. C3C2×#393⋊C3semidirect

Maximal subgroups

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

subgroupindex
D3×C22⋊SL(2,𝔽3)2
C3×#393⋊C32
C3⋊(#393⋊C3)2
D3×#3933
C2×#393⋊C33
C22×D3×A44