Subgroups — C₃×Q₁₆×C₃⋊C₈ #11777225

Order 1152.

383 conjugacy classes of subgroups.

The subgroup lattice has 247 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×Q₈×C₃⋊C₈	C₂	1	2	yes	maximal
3	C₃×#4535	C₂	1	2	yes	maximal
4	C₃×#4458	C₂	1	1	yes	maximal, characteristic
5	C₃×C₈×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₃×C₈×Q₁₆	—	3	1	no	maximal
7	Q₁₆×C₃⋊C₈	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃²×Q₁₆	C₄	1	1	yes	characteristic
9	C₃²×C₄×Q₈	C₂²	1	2	yes	—
10	C₃²×#107	C₄	1	1	yes	characteristic
11	C₃²×#103	C₄	1	2	yes	—
12	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
13	C₃×C₄⋊(C₃⋊C₈)	—	2	2	no	—
14	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
15	C₃×C₄×C₃⋊C₈	—	2	2	no	—
16	C₃×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
17	C₃×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
18	C₃×C₈×Q₈	—	3	2	no	—
19	C₃×C₄×Q₁₆	—	2	1	no	—
20	C₃×C₄×Q₁₆	D₃	1	1	yes	characteristic
21	C₃×C₄×Q₁₆	C₂×C₃	1	1	yes	characteristic
22	Q₈×C₃⋊C₈	C₂×C₃	1	2	yes	—
23	C₃×#335	—	3	1	no	—
24	C₃×Q₈⋊C₈	—	3	2	no	—
25	C₃×C₈²	—	3	1	no	—
26	#4535	C₂×C₃	1	2	yes	—
27	#4458	C₂×C₃	1	1	yes	characteristic
28	C₈×C₃⋊C₈	C₂×C₃	1	1	yes	characteristic
29	C₂×C₃²×Q₈	C₂×C₄	1	2	yes	—
30	C₃²×Q₁₆	C₈	1	4	yes	complemented
31	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
32	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
33	C₃²×C₄⋊C₄	—	2	2	no	—
34	C₃²×C₄⋊C₄	C₂×C₄	1	2	yes	—
35	C₃²×C₄²	—	2	2	no	—
36	C₃²×C₄²	C₂³	1	1	yes	characteristic
37	C₂×C₃×C₃⋊C₈	—	2	1	no	—
38	C₂×C₃×C₃⋊C₈	—	2	2	no	—
39	C₂×C₃×C₃⋊C₈	D₄	1	1	yes	characteristic
40	C₂×C₃×C₃⋊C₈	D₄	1	1	yes	characteristic
41	C₈×Q₁₆	—	3	1	no	Sylow
42	C₂×C₃×Q₁₆	—	2	1	no	—
43	C₂×C₃×Q₁₆	Dic₃	1	1	yes	characteristic
44	C₂×C₃×Q₁₆	C₃×C₄	1	1	yes	characteristic
45	C₃×C₄×Q₈	—	2	2	no	—
46	C₃×C₄×Q₈	C₂×D₃	1	2	yes	—
47	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
48	C₃×#107	—	2	1	no	—
49	C₃×#107	Dic₃	1	1	yes	characteristic
50	C₃×#107	C₃×C₄	1	1	yes	characteristic
51	C₃×C₄⋊C₈	—	3	2	no	—
52	C₃×C₄⋊C₈	—	6	2	no	—
53	C₃×#103	—	2	2	no	—
54	C₃×#103	Dic₃	1	2	yes	—
55	C₃×#103	C₃×C₄	1	2	yes	—
56	C₃×C₄×C₈	—	2	1	no	—
57	C₃×C₄×C₈	—	3	1	no	—
58	C₃×C₄×C₈	—	3	1	no	—
59	C₃×C₄×C₈	—	6	2	no	—
60	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
61	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
62	C₄⋊(C₃⋊C₈)	—	2	2	no	—
63	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	—
64	C₄×C₃⋊C₈	—	2	2	no	—
65	C₄×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
66	C₄×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
67	C₃²×Q₈	—	2	2	no	—
68	C₃²×Q₈	C₂×C₈	1	4	yes	—
69	C₂×C₃²×C₄	—	2	2	no	—
70	C₂×C₃²×C₄	—	2	2	no	—
71	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
72	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
73	C₂×C₃²×C₄	#41	1	1	yes	characteristic
74	C₃²×C₈	—	2	1	no	—
75	C₃²×C₈	C₂×C₈	1	2	yes	—
76	C₃×C₃⋊C₈	—	2	2	no	—
77	C₃×C₃⋊C₈	—	2	1	no	—
78	C₃×C₃⋊C₈	—	4	2	no	—
79	C₃×C₃⋊C₈	Q₁₆	1	2	yes	direct product factor
80	C₈×Q₈	—	3	2	no	—
81	C₄×Q₁₆	C₃×D₃	1	1	yes	characteristic
82	#335	—	3	1	no	—
83	Q₈⋊C₈	—	3	2	no	—
84	C₈²	—	3	1	no	—
85	C₂×C₃×Q₈	—	2	2	no	—
86	C₂×C₃×Q₈	C₂×Dic₃	1	2	yes	—
87	C₂×C₃×Q₈	C₂×C₃×C₄	1	2	yes	—
88	C₃×Q₁₆	—	2	4	no	—
89	C₃×Q₁₆	C₃⋊C₈	1	4	yes	direct product factor
90	C₃×Q₁₆	C₃×C₈	1	4	yes	complemented
91	C₂×C₃×C₈	—	2	1	no	—
92	C₂×C₃×C₈	—	2	1	no	—
93	C₂×C₃×C₈	—	3	1	no	—
94	C₂×C₃×C₈	—	3	1	no	—
95	C₂×C₃×C₈	—	6	1	no	—
96	C₂×C₃×C₈	—	6	2	no	—
97	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
98	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
99	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
100	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
101	C₃×C₄⋊C₄	—	2	2	no	—
102	C₃×C₄⋊C₄	—	2	2	no	—
103	C₃×C₄⋊C₄	—	2	2	no	—
104	C₃×C₄⋊C₄	—	4	2	no	—
105	C₃×C₄⋊C₄	C₂×Dic₃	1	2	yes	—
106	C₃×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
107	C₃×C₄²	—	2	2	no	—
108	C₃×C₄²	—	2	2	no	—
109	C₃×C₄²	—	2	1	no	—
110	C₃×C₄²	—	4	2	no	—
111	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
112	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
113	C₂×C₃⋊C₈	—	2	1	no	—
114	C₂×C₃⋊C₈	—	2	2	no	—
115	C₂×C₃⋊C₈	C₃×D₄	1	1	yes	characteristic
116	C₂×C₃⋊C₈	C₃×D₄	1	1	yes	characteristic
117	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
118	C₃²×C₄	—	2	4	no	—
119	C₃²×C₄	—	2	1	no	—
120	C₃²×C₄	—	4	2	no	—
121	C₃²×C₄	C₂²×C₈	1	1	yes	characteristic
122	C₃²×C₄	#131	1	1	yes	characteristic
123	C₃²×C₄	C₂×Q₁₆	1	1	yes	characteristic
124	C₃²×C₄	#135	1	1	yes	characteristic
125	C₂×Q₁₆	C₃×Dic₃	1	1	yes	characteristic
126	C₄×Q₈	C₂×C₃×D₃	1	2	yes	—
127	#107	C₃×Dic₃	1	1	yes	characteristic
128	C₄⋊C₈	—	3	2	no	—
129	C₄⋊C₈	—	6	2	no	—
130	#103	C₃×Dic₃	1	2	yes	—
131	C₄×C₈	—	3	1	no	—
132	C₄×C₈	—	3	1	no	—
133	C₄×C₈	—	6	2	no	—
134	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic
135	C₃×Q₈	—	2	2	no	—
136	C₃×Q₈	—	2	2	no	—
137	C₃×Q₈	—	2	4	no	—
138	C₃×Q₈	—	4	2	no	—
139	C₃×Q₈	C₂×C₃⋊C₈	1	4	yes	—
140	C₃×Q₈	C₂×C₃×C₈	1	4	yes	—
141	C₂×C₃×C₄	—	2	2	no	—
142	C₂×C₃×C₄	—	2	2	no	—
143	C₂×C₃×C₄	—	2	2	no	—
144	C₂×C₃×C₄	—	2	2	no	—
145	C₂×C₃×C₄	—	2	1	no	—
146	C₂×C₃×C₄	—	2	1	no	—
147	C₂×C₃×C₄	—	2	1	no	—
148	C₂×C₃×C₄	—	4	2	no	—
149	C₂×C₃×C₄	—	4	2	no	—
150	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
151	C₂×C₃×C₄	#237	1	1	yes	characteristic
152	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
153	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
154	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
155	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
156	C₃×C₈	—	2	1	no	—
157	C₃×C₈	—	2	1	no	—
158	C₃×C₈	—	2	2	no	—
159	C₃×C₈	—	3	2	no	—
160	C₃×C₈	—	4	1	no	—
161	C₃×C₈	—	6	2	no	—
162	C₃×C₈	—	6	1	no	—
163	C₃×C₈	—	12	2	no	—
164	C₃×C₈	C₂×C₃⋊C₈	1	2	yes	—
165	C₃×C₈	C₂×C₃×C₈	1	2	yes	—
166	C₃⋊C₈	—	2	2	no	—
167	C₃⋊C₈	—	2	1	no	—
168	C₃⋊C₈	—	4	2	no	—
169	C₃⋊C₈	C₃×Q₁₆	1	2	yes	direct product factor
170	C₂×C₃²	C₈×D₄	1	1	yes	characteristic
171	C₂×C₃²	C₄×Q₁₆	1	1	yes	characteristic
172	C₂×C₃²	#443	1	1	yes	characteristic
173	C₂×Q₈	C₂×C₃×Dic₃	1	2	yes	—
174	Q₁₆	C₃×C₃⋊C₈	1	4	yes	direct product factor
175	C₂×C₈	—	3	1	no	—
176	C₂×C₈	—	3	1	no	—
177	C₂×C₈	—	6	1	no	—
178	C₂×C₈	—	6	2	no	—
179	C₂×C₈	C₂×C₃×Dic₃	1	1	yes	characteristic
180	C₂×C₈	C₂×C₃×Dic₃	1	1	yes	characteristic
181	C₄⋊C₄	—	2	2	no	—
182	C₄⋊C₄	C₂×C₃×Dic₃	1	2	yes	—
183	C₄²	—	2	2	no	—
184	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
185	C₂²×C₃	—	2	1	no	—
186	C₂²×C₃	D₄×Dic₃	1	1	yes	characteristic
187	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
188	C₃×C₄	—	2	1	no	—
189	C₃×C₄	—	2	4	no	—
190	C₃×C₄	—	2	4	no	—
191	C₃×C₄	—	2	1	no	—
192	C₃×C₄	—	2	1	no	—
193	C₃×C₄	—	2	1	no	—
194	C₃×C₄	—	2	1	no	—
195	C₃×C₄	—	2	1	no	—
196	C₃×C₄	—	4	1	no	—
197	C₃×C₄	—	4	4	no	—
198	C₃×C₄	—	4	2	no	—
199	C₃×C₄	—	4	2	no	—
200	C₃×C₄	—	8	2	no	—
201	C₃×C₄	D₃×Q₁₆	1	1	yes	characteristic
202	C₃×C₄	#919	1	1	yes	characteristic
203	C₃×C₄	C₂²×C₃⋊C₈	1	1	yes	characteristic
204	C₃×C₄	#948	1	1	yes	characteristic
205	C₃×C₄	C₂²×C₃×C₈	1	1	yes	characteristic
206	C₃×C₄	C₃×#131	1	1	yes	characteristic
207	C₃×C₄	C₂×C₃×Q₁₆	1	1	yes	characteristic
208	C₃×C₄	C₃×#135	1	1	yes	characteristic
209	C₃²	C₈×Q₁₆	1	1	yes	characteristic, complemented, Sylow
210	Q₈	—	2	2	no	—
211	Q₈	C₂×C₃×C₃⋊C₈	1	4	yes	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
215	C₂×C₄	C₃×#237	1	1	yes	characteristic
216	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
217	C₈	—	2	1	no	—
218	C₈	—	3	2	no	—
219	C₈	—	6	2	no	—
220	C₈	—	6	1	no	—
221	C₈	—	12	2	no	—
222	C₈	C₂×C₃×C₃⋊C₈	1	2	yes	—
223	C₂×C₃	—	2	1	no	—
224	C₂×C₃	—	2	1	no	—
225	C₂×C₃	—	2	1	no	—
226	C₂×C₃	D₄×C₃⋊C₈	1	1	yes	characteristic
227	C₂×C₃	Dic₃×Q₁₆	1	1	yes	characteristic
228	C₂×C₃	#5196	1	1	yes	characteristic
229	C₂×C₃	C₃×C₈×D₄	1	1	yes	characteristic
230	C₂×C₃	C₃×C₄×Q₁₆	1	1	yes	characteristic
231	C₂×C₃	C₃×#443	1	1	yes	characteristic
232	C₂²	C₃×D₄×Dic₃	1	1	yes	characteristic
233	C₄	—	2	1	no	—
234	C₄	—	2	4	no	—
235	C₄	—	4	2	no	—
236	C₄	C₃×D₃×Q₁₆	1	1	yes	characteristic
237	C₄	C₃×#919	1	1	yes	characteristic
238	C₄	C₂²×C₃×C₃⋊C₈	1	1	yes	characteristic
239	C₄	C₃×#948	1	1	yes	characteristic
240	C₃	—	2	1	no	—
241	C₃	Q₁₆×C₃⋊C₈	1	1	yes	characteristic, direct product factor
242	C₃	C₃×C₈×Q₁₆	1	1	yes	characteristic, complemented
243	C₂	C₃×D₄×C₃⋊C₈	1	1	yes	characteristic
244	C₂	C₃×Dic₃×Q₁₆	1	1	yes	characteristic
245	C₂	C₃×#5196	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	D₃×D₄
commutator	C₃×C₄	C₂²×C₃×C₈
Frattini	C₄²	C₂²×C₃×D₃
Fitting	C₃²×C₄×Q₁₆	C₂
socle, prime radical	C₂²×C₃²	C₄×D₄
cosocle	C₃×C₄²	C₂³×C₃
hypercenter	C₃×C₄×Q₁₆	D₃
hypocenter	C₃	C₃×C₈×Q₁₆
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄² ◁ C₃×C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
7. Q₁₆×C₃⋊C₈	C₃	direct (N × H)
30. C₃²×Q₁₆	C₈	semidirect
79. C₃×C₃⋊C₈	Q₁₆	direct (N × H)
89. C₃×Q₁₆	C₃⋊C₈	direct (N × H)
90. C₃×Q₁₆	C₃×C₈	semidirect
169. C₃⋊C₈	C₃×Q₁₆	direct (N × H)
174. Q₁₆	C₃×C₃⋊C₈	direct (N × H)
209. C₃²	C₈×Q₁₆	semidirect
241. C₃	Q₁₆×C₃⋊C₈	direct (N × H)
242. C₃	C₃×C₈×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₄×Q₁₆	2
C₃×Q₈×C₃⋊C₈	2
C₃×#4535	2
C₃×#4458	2
C₃×C₈×C₃⋊C₈	2
C₃×C₈×Q₁₆	3
Q₁₆×C₃⋊C₈	3

Subgroups — C3×Q16×C3⋊C8 #11777225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Q₁₆×C₃⋊C₈ #11777225