Subgroups — C₃×D₃×Q₈⋊C₈ #11774194

Order 1152.

595 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×D₃×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×D₃×C₈	C₂	1	1	yes	maximal, characteristic
4	C₃²×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4535	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4484	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4456	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×Q₈⋊C₈	—	3	1	no	maximal
9	D₃×Q₈⋊C₈	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂×C₃×D₃×Q₈	C₄	1	1	yes	characteristic
11	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
12	C₃×Q₈×Dic₃	C₄	1	1	yes	characteristic
13	C₂×C₃×D₃×C₈	—	2	1	no	—
14	C₂×C₃×D₃×C₈	—	2	1	no	—
15	C₃×D₃×C₄⋊C₄	—	2	1	no	—
16	C₃×D₃×C₄⋊C₄	C₄	1	1	yes	characteristic
17	C₃×#887	—	2	1	no	—
18	C₃×#887	C₄	1	1	yes	characteristic
19	C₃×C₄²×D₃	—	2	1	no	—
20	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
21	C₃×C₄×Dic₆	—	2	1	no	—
22	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
23	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
25	C₃×Dic₃⋊C₈	—	2	1	no	—
26	C₃×C₈×Dic₃	—	2	1	no	—
27	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
28	C₃×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄×Q₈	—	3	1	no	—
30	C₄×D₃×Q₈	C₂×C₃	1	1	yes	characteristic
31	C₂×C₃×C₄⋊C₈	—	3	1	no	—
32	C₂×C₃×C₄×C₈	—	3	1	no	—
33	D₃×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic
34	C₄×D₃×C₈	C₂×C₃	1	1	yes	characteristic
35	C₃×Q₈⋊C₈	—	2	1	no	—
36	C₃×Q₈⋊C₈	—	3	1	no	—
37	C₃×Q₈⋊C₈	—	3	1	no	—
38	C₃×Q₈⋊C₈	—	3	1	no	—
39	C₃×Q₈⋊C₈	D₃	1	1	yes	characteristic, direct product factor
40	C₃×Q₈⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
41	#4535	C₂×C₃	1	1	yes	characteristic, complemented
42	#4484	C₂×C₃	1	1	yes	characteristic, complemented
43	#4456	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×C₃²×Q₈	C₂×C₄	1	1	yes	characteristic
45	C₃×D₃×Q₈	—	2	2	no	—
46	C₃×D₃×Q₈	C₈	1	4	yes	complemented
47	C₂×C₃×C₄×D₃	—	2	1	no	—
48	C₂×C₃×C₄×D₃	—	2	1	no	—
49	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
51	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
52	C₂×C₃×Dic₆	—	2	1	no	—
53	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
54	C₂×C₃²×C₈	—	2	1	no	—
55	C₂×C₃²×C₈	—	2	1	no	—
56	C₃²×C₄⋊C₄	—	2	1	no	—
57	C₃²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₃²×C₄²	—	2	1	no	—
59	C₃²×C₄²	C₂³	1	1	yes	characteristic
60	C₃×C₄⋊Dic₃	—	2	1	no	—
61	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
62	C₃×Dic₃⋊C₄	—	2	1	no	—
63	C₃×Dic₃⋊C₄	—	2	1	no	—
64	C₃×Dic₃⋊C₄	—	2	1	no	—
65	C₃×C₄×Dic₃	—	2	1	no	—
66	C₃×C₄×Dic₃	—	2	1	no	—
67	C₃×C₄×Dic₃	—	2	1	no	—
68	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
69	C₃×C₄×Dic₃	D₄	1	1	yes	characteristic
70	C₃×C₄×Dic₃	D₄	1	1	yes	characteristic
71	C₂×C₃×C₃⋊C₈	—	2	1	no	—
72	C₂×C₃×C₃⋊C₈	—	2	1	no	—
73	C₃×D₃×C₈	—	2	4	no	—
74	C₃×D₃×C₈	—	4	2	no	—
75	C₂×Q₈⋊C₈	—	3	1	no	Sylow
76	C₂²×C₃×Q₈	—	3	1	no	—
77	C₂×D₃×Q₈	C₃×C₄	1	1	yes	characteristic
78	C₂²×C₃×C₈	—	6	1	no	—
79	C₂²×C₃×C₈	—	6	1	no	—
80	C₃×C₄×Q₈	—	2	1	no	—
81	C₃×C₄×Q₈	—	3	1	no	—
82	C₃×C₄×Q₈	—	3	1	no	—
83	C₃×C₄×Q₈	—	3	1	no	—
84	C₃×C₄×Q₈	—	6	1	no	—
85	C₃×C₄×Q₈	—	6	1	no	—
86	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic
87	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₃×C₄⋊C₄	—	3	1	no	—
89	C₂×C₃×C₄⋊C₄	—	6	1	no	—
90	C₂×C₃×C₄²	—	3	1	no	—
91	C₂×C₃×C₄²	—	6	1	no	—
92	Q₈×Dic₃	C₃×C₄	1	1	yes	characteristic
93	C₂×D₃×C₈	—	2	1	no	—
94	C₂×D₃×C₈	—	2	1	no	—
95	D₃×C₄⋊C₄	—	2	1	no	—
96	D₃×C₄⋊C₄	C₃×C₄	1	1	yes	characteristic
97	#887	—	2	1	no	—
98	#887	C₃×C₄	1	1	yes	characteristic
99	C₄²×D₃	—	2	1	no	—
100	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
101	C₄×Dic₆	—	2	1	no	—
102	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
103	C₃×C₄⋊C₈	—	2	1	no	—
104	C₃×C₄⋊C₈	—	3	1	no	—
105	C₃×C₄⋊C₈	—	6	1	no	—
106	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
107	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
108	C₃×C₄×C₈	—	2	1	no	—
109	C₃×C₄×C₈	—	3	1	no	—
110	C₃×C₄×C₈	—	6	1	no	—
111	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
112	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
113	Dic₃⋊C₈	—	2	1	no	—
114	C₈×Dic₃	—	2	1	no	—
115	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic
116	C₄×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
117	C₂²×C₃×D₃	C₂²⋊C₄	1	1	yes	characteristic
118	C₃²×Q₈	—	2	1	no	—
119	C₃²×Q₈	C₂×C₈	1	2	yes	complemented
120	C₂×C₃²×C₄	—	2	1	no	—
121	C₂×C₃²×C₄	—	2	1	no	—
122	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
124	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
125	C₂×C₃×Dic₃	—	2	1	no	—
126	C₂×C₃×Dic₃	—	2	1	no	—
127	C₂×C₃×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
128	C₂×C₃×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
129	C₂×C₃×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
130	C₃×C₄×D₃	—	2	4	no	—
131	C₃×C₄×D₃	—	2	2	no	—
132	C₃×C₄×D₃	—	4	2	no	—
133	C₃×C₄×D₃	C₂×C₈	1	2	yes	—
134	C₃×C₄×D₃	M₁₆	1	2	yes	—
135	C₃×C₄×D₃	SD₁₆	1	2	yes	—
136	C₃×C₄×D₃	Q₁₆	1	2	yes	—
137	C₃×Dic₆	—	2	1	no	—
138	C₃×Dic₆	—	2	4	no	—
139	C₃×Dic₆	C₂×C₈	1	2	yes	complemented
140	C₃²×C₈	—	2	2	no	—
141	C₃²×C₈	—	4	1	no	—
142	C₃×C₃⋊C₈	—	2	2	no	—
143	C₃×C₃⋊C₈	—	4	1	no	—
144	C₂×C₄×Q₈	—	3	1	no	—
145	C₂×C₄⋊C₈	—	3	1	no	—
146	C₂×C₄×C₈	—	3	1	no	—
147	Q₈⋊C₈	—	3	1	no	—
148	Q₈⋊C₈	—	3	1	no	—
149	Q₈⋊C₈	—	3	1	no	—
150	Q₈⋊C₈	C₃×D₃	1	1	yes	characteristic, direct product factor
151	C₂×C₃×Q₈	—	2	1	no	—
152	C₂×C₃×Q₈	—	3	4	no	—
153	C₂×C₃×Q₈	—	3	1	no	—
154	C₂×C₃×Q₈	—	6	1	no	—
155	C₂×C₃×Q₈	—	6	2	no	—
156	C₂×C₃×Q₈	C₄×D₃	1	1	yes	characteristic
157	C₂×C₃×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
158	C₂²×C₃×C₄	—	3	1	no	—
159	C₂²×C₃×C₄	—	3	1	no	—
160	C₂²×C₃×C₄	—	3	1	no	—
161	C₂²×C₃×C₄	—	6	1	no	—
162	C₂²×C₃×C₄	—	6	1	no	—
163	D₃×Q₈	—	2	2	no	—
164	D₃×Q₈	C₃×C₈	1	4	yes	complemented
165	C₂×C₄×D₃	—	2	1	no	—
166	C₂×C₄×D₃	—	2	1	no	—
167	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
168	C₂×C₄×D₃	C₃×D₄	1	1	yes	characteristic
169	C₂×C₄×D₃	C₃×D₄	1	1	yes	characteristic
170	C₂×Dic₆	—	2	1	no	—
171	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
172	C₂×C₃×C₈	—	2	1	no	—
173	C₂×C₃×C₈	—	2	1	no	—
174	C₂×C₃×C₈	—	2	1	no	—
175	C₂×C₃×C₈	—	2	1	no	—
176	C₂×C₃×C₈	—	4	1	no	—
177	C₂×C₃×C₈	—	4	1	no	—
178	C₂×C₃×C₈	—	6	4	no	—
179	C₂×C₃×C₈	—	6	1	no	—
180	C₂×C₃×C₈	—	6	1	no	—
181	C₂×C₃×C₈	—	12	2	no	—
182	C₃×C₄⋊C₄	—	2	1	no	—
183	C₃×C₄⋊C₄	—	2	1	no	—
184	C₃×C₄⋊C₄	—	2	1	no	—
185	C₃×C₄⋊C₄	—	3	1	no	—
186	C₃×C₄⋊C₄	—	4	1	no	—
187	C₃×C₄⋊C₄	—	6	1	no	—
188	C₃×C₄⋊C₄	—	6	1	no	—
189	C₃×C₄⋊C₄	—	6	1	no	—
190	C₃×C₄⋊C₄	—	6	1	no	—
191	C₃×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
192	C₃×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
193	C₃×C₄²	—	2	1	no	—
194	C₃×C₄²	—	2	1	no	—
195	C₃×C₄²	—	2	1	no	—
196	C₃×C₄²	—	3	1	no	—
197	C₃×C₄²	—	3	1	no	—
198	C₃×C₄²	—	3	1	no	—
199	C₃×C₄²	—	4	1	no	—
200	C₃×C₄²	—	6	1	no	—
201	C₃×C₄²	—	6	1	no	—
202	C₃×C₄²	—	6	1	no	—
203	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
204	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
205	C₄⋊Dic₃	—	2	1	no	—
206	C₄⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
207	Dic₃⋊C₄	—	2	1	no	—
208	Dic₃⋊C₄	—	2	1	no	—
209	Dic₃⋊C₄	—	2	1	no	—
210	C₄×Dic₃	—	2	1	no	—
211	C₄×Dic₃	—	2	1	no	—
212	C₄×Dic₃	—	2	1	no	—
213	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
214	C₄×Dic₃	C₃×D₄	1	1	yes	characteristic
215	C₄×Dic₃	C₃×D₄	1	1	yes	characteristic
216	C₂×C₃⋊C₈	—	2	1	no	—
217	C₂×C₃⋊C₈	—	2	1	no	—
218	D₃×C₈	—	2	4	no	—
219	D₃×C₈	—	4	2	no	—
220	C₂²×C₃²	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₃×D₃	C₂²⋊C₈	1	2	yes	—
222	C₂×C₃×D₃	#103	1	2	yes	—
223	C₂×C₃×D₃	#104	1	2	yes	—
224	C₃²×C₄	—	2	2	no	—
225	C₃²×C₄	—	2	1	no	—
226	C₃²×C₄	—	4	1	no	—
227	C₃²×C₄	C₂²×C₈	1	1	yes	characteristic
228	C₃²×C₄	C₂×M₁₆	1	1	yes	characteristic
229	C₃²×C₄	C₂×SD₁₆	1	1	yes	characteristic
230	C₃²×C₄	C₂×Q₁₆	1	1	yes	characteristic
231	C₃×Dic₃	—	2	2	no	—
232	C₃×Dic₃	—	2	1	no	—
233	C₃×Dic₃	—	4	1	no	—
234	C₃×Dic₃	C₂²⋊C₈	1	2	yes	—
235	C₃×Dic₃	#103	1	2	yes	—
236	C₂²×Q₈	—	3	1	no	—
237	C₂²×C₈	—	6	1	no	—
238	C₂²×C₈	—	6	1	no	—
239	C₄×Q₈	—	3	1	no	—
240	C₄×Q₈	—	3	1	no	—
241	C₄×Q₈	—	3	1	no	—
242	C₄×Q₈	—	6	1	no	—
243	C₄×Q₈	—	6	1	no	—
244	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
245	C₂×C₄⋊C₄	—	3	1	no	—
246	C₂×C₄⋊C₄	—	6	1	no	—
247	C₂×C₄²	—	3	1	no	—
248	C₂×C₄²	—	6	1	no	—
249	C₄⋊C₈	—	3	1	no	—
250	C₄⋊C₈	—	6	1	no	—
251	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
252	C₄×C₈	—	3	1	no	—
253	C₄×C₈	—	6	1	no	—
254	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic
255	C₂³×C₃	—	3	1	no	—
256	C₂²×D₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
257	C₃×Q₈	—	2	1	no	—
258	C₃×Q₈	—	2	1	no	—
259	C₃×Q₈	—	2	2	no	—
260	C₃×Q₈	—	3	2	no	—
261	C₃×Q₈	—	4	1	no	—
262	C₃×Q₈	—	6	4	no	—
263	C₃×Q₈	—	6	1	no	—
264	C₃×Q₈	D₃×C₈	1	2	yes	complemented
265	C₃×Q₈	C₂×C₃×C₈	1	2	yes	complemented
266	C₂×C₃×C₄	—	2	1	no	—
267	C₂×C₃×C₄	—	2	1	no	—
268	C₂×C₃×C₄	—	2	1	no	—
269	C₂×C₃×C₄	—	2	1	no	—
270	C₂×C₃×C₄	—	2	1	no	—
271	C₂×C₃×C₄	—	2	1	no	—
272	C₂×C₃×C₄	—	2	1	no	—
273	C₂×C₃×C₄	—	3	1	no	—
274	C₂×C₃×C₄	—	3	1	no	—
275	C₂×C₃×C₄	—	3	2	no	—
276	C₂×C₃×C₄	—	3	2	no	—
277	C₂×C₃×C₄	—	3	2	no	—
278	C₂×C₃×C₄	—	3	2	no	—
279	C₂×C₃×C₄	—	3	1	no	—
280	C₂×C₃×C₄	—	4	1	no	—
281	C₂×C₃×C₄	—	4	1	no	—
282	C₂×C₃×C₄	—	6	2	no	—
283	C₂×C₃×C₄	—	6	4	no	—
284	C₂×C₃×C₄	—	6	1	no	—
285	C₂×C₃×C₄	—	6	1	no	—
286	C₂×C₃×C₄	—	12	2	no	—
287	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
288	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
289	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
290	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
291	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
292	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
293	C₂×Dic₃	—	2	1	no	—
294	C₂×Dic₃	—	2	1	no	—
295	C₂×Dic₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
296	C₂×Dic₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
297	C₂×Dic₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
298	C₄×D₃	—	2	4	no	—
299	C₄×D₃	—	2	2	no	—
300	C₄×D₃	—	4	2	no	—
301	C₄×D₃	C₂×C₃×C₈	1	2	yes	—
302	C₄×D₃	C₃×M₁₆	1	2	yes	—
303	C₄×D₃	C₃×SD₁₆	1	2	yes	—
304	C₄×D₃	C₃×Q₁₆	1	2	yes	—
305	Dic₆	—	2	1	no	—
306	Dic₆	—	2	4	no	—
307	Dic₆	C₂×C₃×C₈	1	2	yes	complemented
308	C₃×C₈	—	2	2	no	—
309	C₃×C₈	—	2	2	no	—
310	C₃×C₈	—	4	2	no	—
311	C₃×C₈	—	4	1	no	—
312	C₃×C₈	—	4	1	no	—
313	C₃×C₈	—	6	2	no	—
314	C₃×C₈	—	8	1	no	—
315	C₃×C₈	—	12	1	no	—
316	C₃⋊C₈	—	2	2	no	—
317	C₃⋊C₈	—	4	1	no	—
318	C₂×C₃²	C₂×C₂²⋊C₈	1	1	yes	characteristic
319	C₂×C₃²	C₂×#103	1	1	yes	characteristic
320	C₂×C₃²	C₂×#104	1	1	yes	characteristic
321	C₃×D₃	Q₈⋊C₈	1	4	yes	direct product factor
322	C₂×Q₈	—	3	4	no	—
323	C₂×Q₈	—	3	1	no	—
324	C₂×Q₈	—	6	1	no	—
325	C₂×Q₈	—	6	2	no	—
326	C₂×Q₈	C₃×C₄×D₃	1	1	yes	characteristic
327	C₂²×C₄	—	3	1	no	—
328	C₂²×C₄	—	3	1	no	—
329	C₂²×C₄	—	3	1	no	—
330	C₂²×C₄	—	6	1	no	—
331	C₂²×C₄	—	6	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	6	4	no	—
335	C₂×C₈	—	6	1	no	—
336	C₂×C₈	—	6	1	no	—
337	C₂×C₈	—	12	2	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	3	1	no	—
340	C₄⋊C₄	—	6	1	no	—
341	C₄⋊C₄	—	6	1	no	—
342	C₄⋊C₄	—	6	1	no	—
343	C₄⋊C₄	—	6	1	no	—
344	C₄⋊C₄	C₃×C₄×D₃	1	1	yes	characteristic
345	C₄²	—	2	1	no	—
346	C₄²	—	3	1	no	—
347	C₄²	—	3	1	no	—
348	C₄²	—	3	1	no	—
349	C₄²	—	6	1	no	—
350	C₄²	—	6	1	no	—
351	C₄²	—	6	1	no	—
352	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
353	C₂²×C₃	—	2	1	no	—
354	C₂²×C₃	—	3	2	no	—
355	C₂²×C₃	—	3	2	no	—
356	C₂²×C₃	—	3	2	no	—
357	C₂²×C₃	D₃×C₂²⋊C₄	1	1	yes	characteristic
358	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
359	C₂×D₃	C₃×C₂²⋊C₈	1	2	yes	—
360	C₂×D₃	C₃×#103	1	2	yes	—
361	C₂×D₃	C₃×#104	1	2	yes	—
362	C₃×C₄	—	2	2	no	—
363	C₃×C₄	—	2	2	no	—
364	C₃×C₄	—	2	1	no	—
365	C₃×C₄	—	2	1	no	—
366	C₃×C₄	—	2	1	no	—
367	C₃×C₄	—	2	1	no	—
368	C₃×C₄	—	2	1	no	—
369	C₃×C₄	—	2	1	no	—
370	C₃×C₄	—	3	2	no	—
371	C₃×C₄	—	3	2	no	—
372	C₃×C₄	—	4	1	no	—
373	C₃×C₄	—	4	2	no	—
374	C₃×C₄	—	4	1	no	—
375	C₃×C₄	—	4	1	no	—
376	C₃×C₄	—	6	2	no	—
377	C₃×C₄	—	6	1	no	—
378	C₃×C₄	—	8	1	no	—
379	C₃×C₄	—	12	1	no	—
380	C₃×C₄	C₂×D₃×C₈	1	1	yes	characteristic
381	C₃×C₄	D₃×M₁₆	1	1	yes	characteristic
382	C₃×C₄	D₃×SD₁₆	1	1	yes	characteristic
383	C₃×C₄	D₃×Q₁₆	1	1	yes	characteristic
384	C₃×C₄	C₂²×C₃×C₈	1	1	yes	characteristic
385	C₃×C₄	C₂×C₃×M₁₆	1	1	yes	characteristic
386	C₃×C₄	C₂×C₃×SD₁₆	1	1	yes	characteristic
387	C₃×C₄	C₂×C₃×Q₁₆	1	1	yes	characteristic
388	Dic₃	—	2	2	no	—
389	Dic₃	—	2	1	no	—
390	Dic₃	—	4	1	no	—
391	Dic₃	C₃×C₂²⋊C₈	1	2	yes	—
392	Dic₃	C₃×#103	1	2	yes	—
393	C₃²	C₂×Q₈⋊C₈	1	1	yes	characteristic, complemented, Sylow
394	C₂³	—	3	1	no	—
395	Q₈	—	2	1	no	—
396	Q₈	—	3	2	no	—
397	Q₈	—	6	4	no	—
398	Q₈	—	6	1	no	—
399	Q₈	C₃×D₃×C₈	1	2	yes	complemented
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	3	1	no	—
403	C₂×C₄	—	3	1	no	—
404	C₂×C₄	—	3	2	no	—
405	C₂×C₄	—	3	2	no	—
406	C₂×C₄	—	3	2	no	—
407	C₂×C₄	—	3	2	no	—
408	C₂×C₄	—	3	1	no	—
409	C₂×C₄	—	6	2	no	—
410	C₂×C₄	—	6	4	no	—
411	C₂×C₄	—	6	1	no	—
412	C₂×C₄	—	6	1	no	—
413	C₂×C₄	—	12	2	no	—
414	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
415	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
416	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
417	C₈	—	2	2	no	—
418	C₈	—	4	1	no	—
419	C₈	—	6	2	no	—
420	C₈	—	12	1	no	—
421	C₂×C₃	—	2	1	no	—
422	C₂×C₃	—	2	1	no	—
423	C₂×C₃	—	2	1	no	—
424	C₂×C₃	—	3	4	no	—
425	C₂×C₃	D₃×C₂²⋊C₈	1	1	yes	characteristic
426	C₂×C₃	D₃×#103	1	1	yes	characteristic
427	C₂×C₃	D₃×#104	1	1	yes	characteristic
428	C₂×C₃	C₂×C₃×C₂²⋊C₈	1	1	yes	characteristic
429	C₂×C₃	C₂×C₃×#103	1	1	yes	characteristic
430	C₂×C₃	C₂×C₃×#104	1	1	yes	characteristic
431	D₃	C₃×Q₈⋊C₈	1	4	yes	direct product factor
432	C₂²	—	3	2	no	—
433	C₂²	—	3	2	no	—
434	C₂²	—	3	2	no	—
435	C₂²	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	2	1	no	—
438	C₄	—	3	2	no	—
439	C₄	—	3	2	no	—
440	C₄	—	4	1	no	—
441	C₄	—	6	2	no	—
442	C₄	—	6	1	no	—
443	C₄	—	12	1	no	—
444	C₄	C₂×C₃×D₃×C₈	1	1	yes	characteristic
445	C₄	C₃×D₃×M₁₆	1	1	yes	characteristic
446	C₄	C₃×D₃×SD₁₆	1	1	yes	characteristic
447	C₄	C₃×D₃×Q₁₆	1	1	yes	characteristic
448	C₃	—	2	1	no	—
449	C₃	D₃×Q₈⋊C₈	1	1	yes	characteristic, direct product factor
450	C₃	C₂×C₃×Q₈⋊C₈	1	1	yes	characteristic, complemented
451	C₂	—	3	4	no	—
452	C₂	C₃×D₃×C₂²⋊C₈	1	1	yes	characteristic
453	C₂	C₃×D₃×#103	1	1	yes	characteristic
454	C₂	C₃×D₃×#104	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×Q₈⋊C₈	C₂
socle	C₂²×C₃²	C₂×C₂²⋊C₄
prime radical	C₂²×C₃×D₃	C₂²⋊C₄
cosocle	C₃×C₄²	C₂³×C₃
hypercenter	C₃×Q₈⋊C₈	D₃
hypocenter	C₃	C₂×C₃×Q₈⋊C₈
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄² ◁ C₃×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
4. C₃²×Q₈⋊C₈	C₂	semidirect
5. C₃×#4535	C₂	semidirect
6. C₃×#4484	C₂	semidirect
7. C₃×#4456	C₂	semidirect
9. D₃×Q₈⋊C₈	C₃	direct (N × H)
39. C₃×Q₈⋊C₈	D₃	direct (N × H)
40. C₃×Q₈⋊C₈	C₂×C₃	semidirect
41. #4535	C₂×C₃	semidirect
42. #4484	C₂×C₃	semidirect
43. #4456	C₂×C₃	semidirect
46. C₃×D₃×Q₈	C₈	semidirect
119. C₃²×Q₈	C₂×C₈	semidirect
139. C₃×Dic₆	C₂×C₈	semidirect
150. Q₈⋊C₈	C₃×D₃	direct (N × H)
164. D₃×Q₈	C₃×C₈	semidirect
264. C₃×Q₈	D₃×C₈	semidirect
265. C₃×Q₈	C₂×C₃×C₈	semidirect
307. Dic₆	C₂×C₃×C₈	semidirect
321. C₃×D₃	Q₈⋊C₈	direct (N × H)
393. C₃²	C₂×Q₈⋊C₈	semidirect
399. Q₈	C₃×D₃×C₈	semidirect
431. D₃	C₃×Q₈⋊C₈	direct (N × H)
449. C₃	D₃×Q₈⋊C₈	direct (N × H)
450. C₃	C₂×C₃×Q₈⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×D₃×Q₈	2
C₃×D₃×C₄⋊C₈	2
C₃×C₄×D₃×C₈	2
C₃²×Q₈⋊C₈	2
C₃×#4535	2
C₃×#4484	2
C₃×#4456	2
C₂×C₃×Q₈⋊C₈	3
D₃×Q₈⋊C₈	3

Subgroups — C3×D3×Q8⋊C8 #11774194

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×Q₈⋊C₈ #11774194