Finite Group Databasebeta

← D3×#352 #69142

Subgroups — D3×#352 #69142

Order 384.

278 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 57 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×#123C211yesmaximal, characteristic
2D3×#100C211yesmaximal, characteristic
3D3×#99C211yesmaximal, characteristic
4C3×#352C211yesmaximal, characteristic, complemented
5#4539C211yesmaximal, characteristic, complemented
6#4476C211yesmaximal, characteristic, complemented
7#4472C211yesmaximal, characteristic, complemented
8C2×#352—31nomaximal, Sylow
9C2×D3×D4C2211yescharacteristic
10C22×C4×D3C411yescharacteristic, complemented
11C3×#123C2211yescharacteristic
12#935C2211yescharacteristic
13#929C411yescharacteristic, complemented
14D3×M16—21no—
15#894—21no—
16D3×C4⋊C4—21no—
17#886C411yescharacteristic, complemented
18#883—21no—
19D3×C22⋊C4—21no—
20D3×C22⋊C4—21no—
21D3×C22⋊C4C411yescharacteristic, complemented
22C3×#100C2211yescharacteristic
23C3×#99C2211yescharacteristic
24#834C2211yescharacteristic
25#833C2211yescharacteristic
26#823—21no—
27#806—21no—
28C2×#123—31no—
29C2×#100—31no—
30C2×#99—31no—
31#352—31no—
32#352—31no—
33#352—31no—
34#352D311yescharacteristic, direct product factor
35C23×D3C2×C411yescharacteristic
36C23×D3D411yescharacteristic
37C2×C3×D4C2311yescharacteristic
38C22×C3×C4C2×C411yescharacteristic, complemented
39C2×#67C2×C411yescharacteristic
40C2×#67D411yescharacteristic
41C22×Dic3C2×C411yescharacteristic, complemented
42D3×D4—41no—
43D3×D4—41no—
44C2×D12D411yescharacteristic
45C2×C4×D3—21no—
46C2×C4×D3—21no—
47C2×C4×D3—21no—
48C2×C4×D3—41no—
49C2×C4×D3—41no—
50C2×C4×D3—41no—
51C2×C4×D3D411yescharacteristic
52C3×M16—21no—
53C3×C4⋊C4—21no—
54C3×C22⋊C4—21no—
55C3×C22⋊C4—21no—
56C3×C22⋊C4C2×C411yescharacteristic, complemented
57#217—21no—
58#217—21no—
59#217C2×C411yescharacteristic, complemented
60(C2×D3)⋊C4—21no—
61(C2×D3)⋊C4—21no—
62(C2×D3)⋊C4—21no—
63(C2×D3)⋊C4—41no—
64C4⋊Dic3—21no—
65Dic3⋊C4—21no—
66Dic3⋊C4—21no—
67#208—21no—
68ΓL(1,𝔽25)—41no—
69D3×C8—41no—
70C22×D4—31no—
71C23×C4—31no—
72C2×M16—61no—
73#123—31no—
74#123—31no—
75#123—31no—
76#123—61no—
77#123—61no—
78#123C2×D311yescharacteristic
79C2×C4⋊C4—61no—
80C2×C22⋊C4—31no—
81C2×C22⋊C4—61no—
82C2×C22⋊C4—61no—
83#100—31no—
84#100—61no—
85#100C2×D311yescharacteristic
86#99—31no—
87#99—61no—
88#99C2×D311yescharacteristic
89C23×C3C22×C411yescharacteristic
90C23×C3C2×D411yescharacteristic
91C22×D3—21no—
92C22×D3—21no—
93C22×D3—21no—
94C22×D3—21no—
95C22×D3—42no—
96C22×D3—42no—
97C22×D3C22⋊C411yescharacteristic
98C22×D3C22⋊C411yescharacteristic
99C22×D3C22⋊C411yescharacteristic
100C3×D4—41no—
101C2×C3×C4—21no—
102C2×C3×C4—21no—
103C2×C3×C4—41no—
104C2×C3×C4—41no—
105C2×C3×C4C2×D411yescharacteristic
106#67—41no—
107#67—41no—
108C2×Dic3—21no—
109C2×Dic3—21no—
110C2×Dic3—41no—
111C2×Dic3—41no—
112C2×Dic3C22⋊C411yescharacteristic
113D12—41no—
114C4×D3—21no—
115C4×D3—21no—
116C4×D3—42no—
117C4×D3—42no—
118C4×D3—41no—
119C4×D3—41no—
120C4×D3—82no—
121C3×C8—41no—
122C3⋊C8—41no—
123C24—31no—
124C24—31no—
125C2×D4—31no—
126C2×D4—31no—
127C2×D4—31no—
128C2×D4—121no—
129C2×D4—121no—
130C2×D4C22×D311yescharacteristic
131C22×C4—31no—
132C22×C4—31no—
133C22×C4—61no—
134C22×C4—61no—
135C22×C4—61no—
136C22×C4—121no—
137C22×C4—121no—
138C22×C4—121no—
139C22×C4C4×D311yescharacteristic, complemented
140M16—21no—
141M16—61no—
142M16—121no—
143C2×C8—121no—
144C4⋊C4—21no—
145C4⋊C4—61no—
146C4⋊C4—61no—
147C4⋊C4—61no—
148C22⋊C4—21no—
149C22⋊C4—21no—
150C22⋊C4—31no—
151C22⋊C4—61no—
152C22⋊C4—61no—
153C22⋊C4—61no—
154C22⋊C4—61no—
155C22⋊C4—61no—
156C22⋊C4—121no—
157C22⋊C4C4×D311yescharacteristic, complemented
158C22×C3—21no—
159C22×C3—21no—
160C22×C3—41no—
161C22×C3—41no—
162C22×C3C2×C22⋊C411yescharacteristic
163C2×D3—22no—
164C2×D3—21no—
165C2×D3—21no—
166C2×D3—42no—
167C2×D3—42no—
168C2×D3—42no—
169C2×D3—41no—
170C2×D3—41no—
171C2×D3—81no—
172C2×D3#9911yescharacteristic
173C2×D3#9911yescharacteristic
174C3×C4—21no—
175C3×C4—41no—
176C3×C4—41no—
177C3×C4—81no—
178Dic3—21no—
179Dic3—41no—
180Dic3—41no—
181Dic3—81no—
182C23—31no—
183C23—31no—
184C23—31no—
185C23—61no—
186C23—61no—
187C23—61no—
188C23—61no—
189C23—122no—
190C23—122no—
191C23C2×C4×D311yescharacteristic
192C23D3×D411yescharacteristic
193D4—41no—
194D4—121no—
195D4—121no—
196D4—121no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—31no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—61no—
203C2×C4—61no—
204C2×C4—61no—
205C2×C4—61no—
206C2×C4—121no—
207C2×C4—121no—
208C2×C4—122no—
209C2×C4—122no—
210C2×C4—121no—
211C2×C4—121no—
212C2×C4—242no—
213C2×C4D3×D411yescharacteristic
214C8—41no—
215C8—121no—
216C2×C3—21no—
217C2×C3—41no—
218C2×C3—41no—
219C2×C3C2×#9911yescharacteristic
220D3—21no—
221D3—41no—
222D3—41no—
223D3#35212yesdirect product factor
224C22—21no—
225C22—21no—
226C22—31no—
227C22—31no—
228C22—41no—
229C22—41no—
230C22—62no—
231C22—61no—
232C22—61no—
233C22—121no—
234C22—121no—
235C22—122no—
236C22—122no—
237C22—122no—
238C22—241no—
239C22D3×C22⋊C411yescharacteristic
240C4—21no—
241C4—41no—
242C4—41no—
243C4—61no—
244C4—81no—
245C4—121no—
246C4—121no—
247C4—241no—
248C3C2×#35211yescharacteristic, complemented, Sylow
249C2—21no—
250C2—32no—
251C2—41no—
252C2—41no—
253C2—61no—
254C2—121no—
255C2—121no—
256C2D3×#9911yescharacteristic
subgroupG/H
centerC2D3×#99
commutatorC23×C3C22×C4
FrattiniC2×D4C22×D3
FittingC3×#352C2
socleC2×C3C2×#99
prime radicalC2×D3×D4C22
cosocleC2×C3×D4C23
hypercenter#352D3
hypocenterC3C2×#352
LCSG ▷ C23×C3 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
4. C3×#352C2semidirect
5. #4539C2semidirect
6. #4476C2semidirect
7. #4472C2semidirect
10. C22×C4×D3C4semidirect
13. #929C4semidirect
17. #886C4semidirect
21. D3×C22⋊C4C4semidirect
34. #352D3direct (N × H)
38. C22×C3×C4C2×C4semidirect
41. C22×Dic3C2×C4semidirect
56. C3×C22⋊C4C2×C4semidirect
59. #217C2×C4semidirect
139. C22×C4C4×D3semidirect
157. C22⋊C4C4×D3semidirect
223. D3#352direct (N × H)
248. C3C2×#352semidirect

Maximal subgroups

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

subgroupindex
D3×#1232
D3×#1002
D3×#992
C3×#3522
#45392
#44762
#44722
C2×#3523