Subgroups — C₃×Dic₃×C₄⋊C₈ #11784167

Order 1152.

701 conjugacy classes of subgroups.

The subgroup lattice has 333 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₈×Dic₃	C₂	1	2	yes	maximal
3	C₃×C₄²×Dic₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
5	C₃×#4550	C₂	1	2	yes	maximal
6	C₃×C₄×C₄⋊C₈	—	3	1	no	maximal
7	Dic₃×C₄⋊C₈	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂²×C₃²×C₈	C₂²	1	2	yes	—
9	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₄×Dic₃	C₄	1	2	yes	—
11	C₂×C₃×C₄×Dic₃	C₄	1	2	yes	—
12	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	—
15	C₃²×C₄⋊C₈	C₄	1	4	yes	complemented
16	C₃×C₈×Dic₃	—	2	4	no	—
17	C₃×C₄⋊(C₃⋊C₈)	C₄	1	4	yes	complemented
18	C₂×C₃×C₄⋊C₈	—	2	1	no	—
19	C₂×C₃×C₄⋊C₈	—	3	1	no	—
20	C₂×C₃×C₄⋊C₈	D₃	1	1	yes	characteristic
21	C₂×C₃×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic
22	C₂×C₃×C₄×C₈	—	3	2	no	—
23	C₃×C₄³	—	3	1	no	—
24	C₂×C₈×Dic₃	C₂×C₃	1	2	yes	—
25	C₄²×Dic₃	C₂×C₃	1	1	yes	characteristic
26	C₂×C₄⋊(C₃⋊C₈)	C₂×C₃	1	1	yes	characteristic
27	C₃×#336	—	3	2	no	—
28	#4550	C₂×C₃	1	2	yes	—
29	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
32	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
33	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
34	C₂×C₃²×C₈	—	2	2	no	—
35	C₂×C₃²×C₈	—	2	2	no	—
36	C₂×C₃²×C₈	C₂×C₄	1	4	yes	—
37	C₃²×C₄²	C₂×C₄	1	2	yes	—
38	C₃²×C₄²	C₂×C₄	1	2	yes	—
39	C₃×C₄×Dic₃	—	2	1	no	—
40	C₃×C₄×Dic₃	—	2	1	no	—
41	C₃×C₄×Dic₃	—	2	4	no	—
42	C₃×C₄×Dic₃	C₈	1	8	yes	complemented
43	C₃×C₄×Dic₃	D₄	1	2	yes	—
44	C₃×C₄×Dic₃	Q₈	1	2	yes	—
45	C₂×C₃×C₃⋊C₈	—	2	2	no	—
46	C₂×C₃×C₃⋊C₈	—	2	2	no	—
47	C₂×C₃×C₃⋊C₈	C₂×C₄	1	4	yes	—
48	C₄×C₄⋊C₈	—	3	1	no	Sylow
49	C₂²×C₃×C₈	—	2	2	no	—
50	C₂²×C₃×C₈	—	3	2	no	—
51	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
52	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
53	C₂×C₃×C₄²	—	2	1	no	—
54	C₂×C₃×C₄²	—	3	2	no	—
55	C₂×C₃×C₄²	—	3	1	no	—
56	C₂×C₃×C₄²	—	3	2	no	—
57	C₂×C₃×C₄²	—	3	1	no	—
58	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
59	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
60	C₂×C₄×Dic₃	C₃×C₄	1	2	yes	—
61	C₂×C₄×Dic₃	C₃×C₄	1	2	yes	—
62	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
63	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
64	C₂²×C₃⋊C₈	C₂²×C₃	1	2	yes	—
65	C₃×C₄⋊C₈	—	2	4	no	—
66	C₃×C₄⋊C₈	—	3	4	no	—
67	C₃×C₄⋊C₈	Dic₃	1	4	yes	direct product factor
68	C₃×C₄⋊C₈	C₃×C₄	1	4	yes	complemented
69	C₃×C₄×C₈	—	6	4	no	—
70	C₈×Dic₃	—	2	4	no	—
71	C₄⋊(C₃⋊C₈)	C₃×C₄	1	4	yes	complemented
72	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
73	C₂×C₃²×C₄	—	2	2	no	—
74	C₂×C₃²×C₄	C₄²	1	2	yes	—
75	C₂×C₃²×C₄	C₄²	1	2	yes	—
76	C₂×C₃²×C₄	C₂×C₈	1	4	yes	—
77	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
79	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
80	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
81	C₂×C₃²×C₄	#41	1	1	yes	characteristic
82	C₂×C₃²×C₄	#41	1	1	yes	characteristic
83	C₂×C₃×Dic₃	—	2	2	no	—
84	C₂×C₃×Dic₃	—	2	2	no	—
85	C₂×C₃×Dic₃	C₄⋊C₄	1	4	yes	—
86	C₂×C₃×Dic₃	C₂×C₈	1	4	yes	—
87	C₂×C₃×Dic₃	C₂×C₈	1	4	yes	—
88	C₂×C₃×Dic₃	M₁₆	1	4	yes	—
89	C₃²×C₈	—	2	4	no	—
90	C₃×C₃⋊C₈	—	2	4	no	—
91	C₂×C₄⋊C₈	—	3	1	no	—
92	C₂×C₄⋊C₈	C₃×D₃	1	1	yes	characteristic
93	C₂×C₄×C₈	—	3	2	no	—
94	C₄³	—	3	1	no	—
95	#336	—	3	2	no	—
96	C₂²×C₃×C₄	—	2	1	no	—
97	C₂²×C₃×C₄	—	2	1	no	—
98	C₂²×C₃×C₄	—	2	1	no	—
99	C₂²×C₃×C₄	—	3	2	no	—
100	C₂²×C₃×C₄	—	3	2	no	—
101	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
102	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
103	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
104	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
105	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
106	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
107	C₂²×Dic₃	C₂×C₃×C₄	1	2	yes	—
108	C₂²×Dic₃	C₂×C₃×C₄	1	2	yes	—
109	C₂×C₃×C₈	—	2	2	no	—
110	C₂×C₃×C₈	—	2	2	no	—
111	C₂×C₃×C₈	—	2	2	no	—
112	C₂×C₃×C₈	—	2	2	no	—
113	C₂×C₃×C₈	—	2	4	no	—
114	C₂×C₃×C₈	—	3	4	no	—
115	C₂×C₃×C₈	—	4	2	no	—
116	C₂×C₃×C₈	—	4	2	no	—
117	C₂×C₃×C₈	—	6	2	no	—
118	C₂×C₃×C₈	—	6	2	no	—
119	C₂×C₃×C₈	C₂×Dic₃	1	4	yes	—
120	C₂×C₃×C₈	C₂×C₃×C₄	1	4	yes	—
121	C₃×C₄²	—	2	2	no	—
122	C₃×C₄²	—	2	2	no	—
123	C₃×C₄²	—	3	8	no	—
124	C₃×C₄²	—	3	2	no	—
125	C₃×C₄²	—	3	2	no	—
126	C₃×C₄²	—	6	4	no	—
127	C₃×C₄²	—	6	1	no	—
128	C₃×C₄²	—	6	1	no	—
129	C₃×C₄²	C₄×D₃	1	2	yes	—
130	C₃×C₄²	C₂×Dic₃	1	2	yes	—
131	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
132	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
133	C₄×Dic₃	—	2	1	no	—
134	C₄×Dic₃	—	2	1	no	—
135	C₄×Dic₃	—	2	4	no	—
136	C₄×Dic₃	C₃×C₈	1	8	yes	complemented
137	C₄×Dic₃	C₃×D₄	1	2	yes	—
138	C₄×Dic₃	C₃×Q₈	1	2	yes	—
139	C₂×C₃⋊C₈	—	2	2	no	—
140	C₂×C₃⋊C₈	—	2	2	no	—
141	C₂×C₃⋊C₈	C₂×C₃×C₄	1	4	yes	—
142	C₂²×C₃²	C₂×C₄²	1	1	yes	characteristic
143	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂²×C₃²	#117	1	1	yes	characteristic
145	C₂²×C₃²	C₂²×C₈	1	2	yes	—
146	C₂²×C₃²	C₂×M₁₆	1	2	yes	—
147	C₃²×C₄	—	2	2	no	—
148	C₃²×C₄	C₄×C₈	1	4	yes	complemented
149	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
150	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
151	C₃²×C₄	C₄×Q₈	1	1	yes	characteristic
152	C₃²×C₄	C₄×Q₈	1	1	yes	characteristic
153	C₃×Dic₃	—	2	4	no	—
154	C₃×Dic₃	C₄⋊C₈	1	8	yes	direct product factor
155	C₂²×C₈	—	3	2	no	—
156	C₂²×C₈	C₂×C₃×D₃	1	2	yes	—
157	C₂×C₄²	—	3	2	no	—
158	C₂×C₄²	—	3	1	no	—
159	C₂×C₄²	—	3	2	no	—
160	C₂×C₄²	—	3	1	no	—
161	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
162	C₄⋊C₈	—	3	4	no	—
163	C₄⋊C₈	C₃×Dic₃	1	4	yes	direct product factor
164	C₄×C₈	—	6	4	no	—
165	C₂³×C₃	—	2	1	no	—
166	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
167	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
168	C₂×C₃×C₄	—	2	2	no	—
169	C₂×C₃×C₄	—	2	2	no	—
170	C₂×C₃×C₄	—	2	4	no	—
171	C₂×C₃×C₄	—	2	2	no	—
172	C₂×C₃×C₄	—	2	2	no	—
173	C₂×C₃×C₄	—	2	1	no	—
174	C₂×C₃×C₄	—	2	1	no	—
175	C₂×C₃×C₄	—	2	1	no	—
176	C₂×C₃×C₄	—	2	1	no	—
177	C₂×C₃×C₄	—	2	1	no	—
178	C₂×C₃×C₄	—	2	1	no	—
179	C₂×C₃×C₄	—	3	4	no	—
180	C₂×C₃×C₄	—	3	4	no	—
181	C₂×C₃×C₄	—	3	4	no	—
182	C₂×C₃×C₄	—	3	4	no	—
183	C₂×C₃×C₄	—	4	2	no	—
184	C₂×C₃×C₄	—	6	2	no	—
185	C₂×C₃×C₄	—	6	2	no	—
186	C₂×C₃×C₄	D₃×C₈	1	4	yes	—
187	C₂×C₃×C₄	C₄×Dic₃	1	2	yes	—
188	C₂×C₃×C₄	C₄×Dic₃	1	2	yes	—
189	C₂×C₃×C₄	C₃×C₄²	1	2	yes	—
190	C₂×C₃×C₄	C₃×C₄²	1	2	yes	—
191	C₂×C₃×C₄	C₂×C₃×C₈	1	4	yes	—
192	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
193	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
194	C₂×C₃×C₄	#237	1	1	yes	characteristic
195	C₂×C₃×C₄	D₃×Q₈	1	1	yes	characteristic
196	C₂×C₃×C₄	#239	1	1	yes	characteristic
197	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
198	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
199	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
200	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
201	C₂×C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
202	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
203	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
204	C₂×Dic₃	—	2	2	no	—
205	C₂×Dic₃	—	2	2	no	—
206	C₂×Dic₃	C₃×C₄⋊C₄	1	4	yes	—
207	C₂×Dic₃	C₂×C₃×C₈	1	4	yes	—
208	C₂×Dic₃	C₂×C₃×C₈	1	4	yes	—
209	C₂×Dic₃	C₃×M₁₆	1	4	yes	—
210	C₃×C₈	—	2	4	no	—
211	C₃×C₈	—	2	4	no	—
212	C₃×C₈	—	4	4	no	—
213	C₃×C₈	—	6	4	no	—
214	C₃⋊C₈	—	2	4	no	—
215	C₂×C₃²	C₄×C₄⋊C₄	1	1	yes	characteristic
216	C₂×C₃²	C₂×C₄×C₈	1	1	yes	characteristic
217	C₂×C₃²	C₄×M₁₆	1	1	yes	characteristic
218	C₂×C₃²	C₂×C₄⋊C₈	1	2	yes	—
219	C₂×C₃²	#431	1	2	yes	—
220	C₂²×C₄	—	3	2	no	—
221	C₂²×C₄	—	3	2	no	—
222	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
223	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
224	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
225	C₂×C₈	—	2	2	no	—
226	C₂×C₈	—	2	2	no	—
227	C₂×C₈	—	3	4	no	—
228	C₂×C₈	—	6	2	no	—
229	C₂×C₈	—	6	2	no	—
230	C₂×C₈	C₂×C₃×Dic₃	1	4	yes	—
231	C₄²	—	3	8	no	—
232	C₄²	—	3	2	no	—
233	C₄²	—	3	2	no	—
234	C₄²	—	6	4	no	—
235	C₄²	—	6	1	no	—
236	C₄²	—	6	1	no	—
237	C₄²	C₃×C₄×D₃	1	2	yes	—
238	C₄²	C₂×C₃×Dic₃	1	2	yes	—
239	C₂²×C₃	—	2	1	no	—
240	C₂²×C₃	—	2	1	no	—
241	C₂²×C₃	—	2	2	no	—
242	C₂²×C₃	—	2	2	no	—
243	C₂²×C₃	—	2	1	no	—
244	C₂²×C₃	D₃×C₄⋊C₄	1	1	yes	characteristic
245	C₂²×C₃	#892	1	1	yes	characteristic
246	C₂²×C₃	C₂×D₃×C₈	1	2	yes	—
247	C₂²×C₃	D₃×M₁₆	1	2	yes	—
248	C₂²×C₃	C₂×C₄×Dic₃	1	1	yes	characteristic
249	C₂²×C₃	C₂×C₃×C₄²	1	1	yes	characteristic
250	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
251	C₂²×C₃	C₃×#117	1	1	yes	characteristic
252	C₂²×C₃	C₂²×C₃×C₈	1	2	yes	—
253	C₂²×C₃	C₂×C₃×M₁₆	1	2	yes	—
254	C₃×C₄	—	2	2	no	—
255	C₃×C₄	—	2	2	no	—
256	C₃×C₄	—	2	1	no	—
257	C₃×C₄	—	2	1	no	—
258	C₃×C₄	—	2	1	no	—
259	C₃×C₄	—	2	1	no	—
260	C₃×C₄	—	2	4	no	—
261	C₃×C₄	—	3	8	no	—
262	C₃×C₄	—	4	2	no	—
263	C₃×C₄	—	6	4	no	—
264	C₃×C₄	C₈×Dic₃	1	4	yes	complemented
265	C₃×C₄	C₃×C₄×C₈	1	4	yes	complemented
266	C₃×C₄	#887	1	1	yes	characteristic
267	C₃×C₄	#893	1	1	yes	characteristic
268	C₃×C₄	D₄×Dic₃	1	1	yes	characteristic
269	C₃×C₄	Q₈×Dic₃	1	1	yes	characteristic
270	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
271	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
272	C₃×C₄	C₃×C₄×Q₈	1	1	yes	characteristic
273	C₃×C₄	C₃×C₄×Q₈	1	1	yes	characteristic
274	Dic₃	—	2	4	no	—
275	Dic₃	C₃×C₄⋊C₈	1	8	yes	direct product factor
276	C₃²	C₄×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
277	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	3	4	no	—
280	C₂×C₄	—	3	4	no	—
281	C₂×C₄	—	3	4	no	—
282	C₂×C₄	—	3	4	no	—
283	C₂×C₄	—	6	2	no	—
284	C₂×C₄	—	6	2	no	—
285	C₂×C₄	C₃×D₃×C₈	1	4	yes	—
286	C₂×C₄	C₃×C₄×Dic₃	1	2	yes	—
287	C₂×C₄	C₃×C₄×Dic₃	1	2	yes	—
288	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
289	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
290	C₂×C₄	C₃×#237	1	1	yes	characteristic
291	C₂×C₄	C₃×D₃×Q₈	1	1	yes	characteristic
292	C₂×C₄	C₃×#239	1	1	yes	characteristic
293	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
294	C₈	—	2	4	no	—
295	C₈	—	6	4	no	—
296	C₂×C₃	—	2	1	no	—
297	C₂×C₃	—	2	2	no	—
298	C₂×C₃	—	2	2	no	—
299	C₂×C₃	—	2	1	no	—
300	C₂×C₃	—	2	1	no	—
301	C₂×C₃	D₃×C₄⋊C₈	1	2	yes	—
302	C₂×C₃	#4833	1	2	yes	—
303	C₂×C₃	Dic₃×C₄⋊C₄	1	1	yes	characteristic
304	C₂×C₃	C₂×C₈×Dic₃	1	1	yes	characteristic
305	C₂×C₃	Dic₃×M₁₆	1	1	yes	characteristic
306	C₂×C₃	C₃×C₄×C₄⋊C₄	1	1	yes	characteristic
307	C₂×C₃	C₂×C₃×C₄×C₈	1	1	yes	characteristic
308	C₂×C₃	C₃×C₄×M₁₆	1	1	yes	characteristic
309	C₂×C₃	C₂×C₃×C₄⋊C₈	1	2	yes	—
310	C₂×C₃	C₃×#431	1	2	yes	—
311	C₂²	C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
312	C₂²	C₃×#892	1	1	yes	characteristic
313	C₂²	C₂×C₃×D₃×C₈	1	2	yes	—
314	C₂²	C₃×D₃×M₁₆	1	2	yes	—
315	C₂²	C₂×C₃×C₄×Dic₃	1	1	yes	characteristic
316	C₄	—	2	2	no	—
317	C₄	—	3	8	no	—
318	C₄	—	6	4	no	—
319	C₄	C₃×C₈×Dic₃	1	4	yes	complemented
320	C₄	C₃×#887	1	1	yes	characteristic
321	C₄	C₃×#893	1	1	yes	characteristic
322	C₄	C₃×D₄×Dic₃	1	1	yes	characteristic
323	C₄	C₃×Q₈×Dic₃	1	1	yes	characteristic
324	C₃	—	2	1	no	—
325	C₃	Dic₃×C₄⋊C₈	1	1	yes	characteristic, direct product factor
326	C₃	C₃×C₄×C₄⋊C₈	1	1	yes	characteristic, complemented
327	C₂	C₃×D₃×C₄⋊C₈	1	2	yes	—
328	C₂	C₃×#4833	1	2	yes	—
329	C₂	C₃×Dic₃×C₄⋊C₄	1	1	yes	characteristic
330	C₂	C₂×C₃×C₈×Dic₃	1	1	yes	characteristic
331	C₂	C₃×Dic₃×M₁₆	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
7. Dic₃×C₄⋊C₈	C₃	direct (N × H)
15. C₃²×C₄⋊C₈	C₄	semidirect
17. C₃×C₄⋊(C₃⋊C₈)	C₄	semidirect
42. C₃×C₄×Dic₃	C₈	semidirect
67. C₃×C₄⋊C₈	Dic₃	direct (N × H)
68. C₃×C₄⋊C₈	C₃×C₄	semidirect
71. C₄⋊(C₃⋊C₈)	C₃×C₄	semidirect
136. C₄×Dic₃	C₃×C₈	semidirect
148. C₃²×C₄	C₄×C₈	semidirect
154. C₃×Dic₃	C₄⋊C₈	direct (N × H)
163. C₄⋊C₈	C₃×Dic₃	direct (N × H)
264. C₃×C₄	C₈×Dic₃	semidirect
265. C₃×C₄	C₃×C₄×C₈	semidirect
275. Dic₃	C₃×C₄⋊C₈	direct (N × H)
276. C₃²	C₄×C₄⋊C₈	semidirect
319. C₄	C₃×C₈×Dic₃	semidirect
325. C₃	Dic₃×C₄⋊C₈	direct (N × H)
326. C₃	C₃×C₄×C₄⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₄⋊C₈	2
C₂×C₃×C₈×Dic₃	2
C₃×C₄²×Dic₃	2
C₂×C₃×C₄⋊(C₃⋊C₈)	2
C₃×#4550	2
C₃×C₄×C₄⋊C₈	3
Dic₃×C₄⋊C₈	3

Subgroups — C3×Dic3×C4⋊C8 #11784167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Dic₃×C₄⋊C₈ #11784167