Subgroups — C₃×D₈×D₁₂ #11885734

Order 1152.

1307 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₃×D₈	C₂	1	2	yes	maximal, complemented
2	C₃×D₄×D₁₂	C₂	1	2	yes	maximal, complemented
3	C₃²×C₄×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5015	C₂	1	2	yes	maximal, complemented
5	C₃×#4883	C₂	1	2	yes	maximal, complemented
6	C₃×#4773	C₂	1	4	yes	maximal, complemented
7	C₃×#4695	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₈×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×D₄×D₈	—	3	1	no	maximal
10	D₈×D₁₂	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂×C₃×D₃×D₄	C₂²	1	4	yes	complemented
12	C₂²×C₃×D₁₂	—	2	2	no	—
13	C₂×C₃²×D₈	C₂²	1	1	yes	characteristic
14	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
15	C₂×C₃×#213	C₂²	1	4	yes	complemented
16	C₃×#930	—	2	2	no	—
17	C₃×D₃×D₈	—	2	8	no	—
18	C₂×C₃×D₂₄	C₂²	1	2	yes	complemented
19	C₂×C₃×D₂₄	C₂²	1	2	yes	complemented
20	C₂×C₃×D₃×C₈	C₂²	1	2	yes	complemented
21	C₃×#895	C₂²	1	4	yes	complemented
22	C₃×#882	—	2	4	no	—
23	C₃×#874	C₂²	1	2	yes	complemented
24	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
25	C₃²×#107	C₂²	1	1	yes	characteristic, complemented
26	C₃²×#102	C₂²	1	2	yes	complemented
27	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
28	C₃×(C₂×D₃)⋊C₈	C₂²	1	2	yes	complemented
29	C₃×#809	C₂²	1	4	yes	complemented
30	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₃×D₈	—	3	2	no	—
32	C₃×D₄²	—	3	2	no	—
33	C₂×D₃×D₈	C₂×C₃	1	2	yes	complemented
34	D₄×D₁₂	C₂×C₃	1	2	yes	complemented
35	C₃×#493	—	3	1	no	—
36	C₃×#466	—	3	2	no	—
37	C₃×#459	—	3	2	no	—
38	C₃×#447	—	3	4	no	—
39	C₃×C₄×D₈	—	2	1	no	—
40	C₃×C₄×D₈	D₃	1	1	yes	characteristic, complemented
41	C₃×C₄×D₈	C₂×C₃	1	1	yes	characteristic, complemented
42	C₃×C₈×D₄	—	3	1	no	—
43	#5015	C₂×C₃	1	2	yes	complemented
44	#4883	C₂×C₃	1	2	yes	complemented
45	#4773	C₂×C₃	1	4	yes	complemented
46	#4695	C₂×C₃	1	1	yes	characteristic, complemented
47	C₈×D₁₂	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂³×C₃×D₃	—	2	4	no	—
49	C₂×C₃²×D₄	C₂³	1	2	yes	—
50	C₂²×C₃²×C₄	—	2	2	no	—
51	C₂×C₃×#67	—	2	4	no	—
52	C₃×D₃×D₄	—	2	8	no	—
53	C₃×D₃×D₄	—	4	4	no	—
54	C₂×C₃×D₁₂	—	2	4	no	—
55	C₂×C₃×D₁₂	—	2	2	no	—
56	C₂×C₃×D₁₂	—	2	2	no	—
57	C₂×C₃×D₁₂	—	4	8	no	—
58	C₂×C₃×D₁₂	D₄	1	1	yes	characteristic
59	C₂×C₃×D₁₂	C₂³	1	4	yes	—
60	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
61	C₃²×D₈	D₄	1	4	yes	complemented
62	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
63	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
64	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
65	C₃²×C₂²⋊C₄	—	2	2	no	—
66	C₃²×C₄²	C₂³	1	1	yes	characteristic
67	C₃×#213	—	2	8	no	—
68	C₃×(C₂×D₃)⋊C₄	—	2	4	no	—
69	C₃×(C₂×D₃)⋊C₄	D₄	1	2	yes	—
70	C₃×C₄⋊Dic₃	D₄	1	1	yes	characteristic
71	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
72	C₃×D₂₄	—	2	4	no	—
73	C₃×D₂₄	—	4	2	no	—
74	C₃×D₃×C₈	—	2	4	no	—
75	D₄×D₈	—	3	1	no	Sylow
76	C₂²×C₃×D₄	—	3	4	no	—
77	C₂²×C₃×D₄	—	6	2	no	—
78	C₂×D₃×D₄	C₂²×C₃	1	4	yes	complemented
79	C₂²×D₁₂	—	2	2	no	—
80	C₂×C₃×D₈	—	2	1	no	—
81	C₂×C₃×D₈	—	3	4	no	—
82	C₂×C₃×D₈	—	3	2	no	—
83	C₂×C₃×D₈	—	3	2	no	—
84	C₂×C₃×D₈	—	6	8	no	—
85	C₂×C₃×D₈	C₂×D₃	1	1	yes	characteristic
86	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
87	C₂²×C₃×C₈	—	3	2	no	—
88	C₃×#127	—	3	2	no	—
89	C₃×#121	—	3	4	no	—
90	C₃×#121	—	6	2	no	—
91	C₃×#120	—	6	4	no	—
92	C₃×C₄×D₄	—	2	2	no	—
93	C₃×C₄×D₄	—	3	1	no	—
94	C₃×C₄×D₄	C₂×D₃	1	2	yes	complemented
95	C₃×C₄×D₄	C₂²×C₃	1	2	yes	complemented
96	C₂×#213	C₂²×C₃	1	4	yes	complemented
97	#930	—	2	2	no	—
98	D₃×D₈	—	2	8	no	—
99	C₂×D₂₄	C₂²×C₃	1	2	yes	complemented
100	C₂×D₂₄	C₂²×C₃	1	2	yes	complemented
101	C₂×D₃×C₈	C₂²×C₃	1	2	yes	complemented
102	#895	C₂²×C₃	1	4	yes	complemented
103	#882	—	2	4	no	—
104	#874	C₂²×C₃	1	2	yes	complemented
105	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
106	C₃×#107	—	2	1	no	—
107	C₃×#107	C₂×D₃	1	1	yes	characteristic, complemented
108	C₃×#107	C₂²×C₃	1	1	yes	characteristic, complemented
109	C₃×C₄⋊C₈	—	3	1	no	—
110	C₃×#102	—	2	2	no	—
111	C₃×#102	—	3	4	no	—
112	C₃×#102	C₂×D₃	1	2	yes	complemented
113	C₃×#102	C₂²×C₃	1	2	yes	complemented
114	C₃×C₂²⋊C₈	—	3	2	no	—
115	C₃×C₄×C₈	—	2	1	no	—
116	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic, complemented
117	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
118	(C₂×D₃)⋊C₈	C₂²×C₃	1	2	yes	complemented
119	#809	C₂²×C₃	1	4	yes	complemented
120	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic, complemented
121	C₂³×C₃²	—	2	2	no	—
122	C₂²×C₃×D₃	—	2	4	no	—
123	C₂²×C₃×D₃	—	4	8	no	—
124	C₂²×C₃×D₃	—	4	8	no	—
125	C₂²×C₃×D₃	—	8	4	no	—
126	C₂²×C₃×D₃	C₂×D₄	1	2	yes	—
127	C₃²×D₄	—	2	2	no	—
128	C₃²×D₄	C₂×D₄	1	4	yes	complemented
129	C₂×C₃²×C₄	—	2	2	no	—
130	C₂×C₃²×C₄	—	4	4	no	—
131	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
132	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
133	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
134	C₃×#67	—	4	8	no	—
135	C₂×C₃×Dic₃	C₂×D₄	1	2	yes	—
136	C₃×D₁₂	—	2	4	no	—
137	C₃×D₁₂	—	2	4	no	—
138	C₃×D₁₂	—	4	8	no	—
139	C₃×D₁₂	—	4	4	no	—
140	C₃×D₁₂	—	8	2	no	—
141	C₃×D₁₂	D₈	1	4	yes	direct product factor
142	C₃×C₄×D₃	—	2	2	no	—
143	C₃×C₄×D₃	—	2	2	no	—
144	C₃²×C₈	—	2	1	no	—
145	C₃²×C₈	C₂×D₄	1	2	yes	complemented
146	C₃×C₃⋊C₈	—	2	2	no	—
147	C₂²×D₈	—	3	2	no	—
148	D₄²	—	3	2	no	—
149	#493	—	3	1	no	—
150	#466	—	3	2	no	—
151	#459	—	3	2	no	—
152	#447	—	3	4	no	—
153	C₄×D₈	C₃×D₃	1	1	yes	characteristic, complemented
154	C₈×D₄	—	3	1	no	—
155	C₂⁴×C₃	—	6	4	no	—
156	C₂³×D₃	—	2	4	no	—
157	C₂×C₃×D₄	—	2	2	no	—
158	C₂×C₃×D₄	—	3	1	no	—
159	C₂×C₃×D₄	—	3	4	no	—
160	C₂×C₃×D₄	—	6	4	no	—
161	C₂×C₃×D₄	—	6	4	no	—
162	C₂×C₃×D₄	—	6	8	no	—
163	C₂×C₃×D₄	—	6	2	no	—
164	C₂×C₃×D₄	—	6	2	no	—
165	C₂×C₃×D₄	—	12	8	no	—
166	C₂×C₃×D₄	—	12	4	no	—
167	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
168	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
169	C₂²×C₃×C₄	—	2	2	no	—
170	C₂²×C₃×C₄	—	2	2	no	—
171	C₂²×C₃×C₄	—	3	2	no	—
172	C₂²×C₃×C₄	—	4	2	no	—
173	C₂×#67	—	2	4	no	—
174	D₃×D₄	—	2	8	no	—
175	D₃×D₄	—	4	4	no	—
176	C₂×D₁₂	—	2	4	no	—
177	C₂×D₁₂	—	2	2	no	—
178	C₂×D₁₂	—	2	2	no	—
179	C₂×D₁₂	—	4	8	no	—
180	C₂×D₁₂	C₃×D₄	1	1	yes	characteristic
181	C₂×D₁₂	C₂³×C₃	1	4	yes	—
182	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
183	C₃×D₈	—	2	4	no	—
184	C₃×D₈	—	6	8	no	—
185	C₃×D₈	—	6	4	no	—
186	C₃×D₈	—	12	2	no	—
187	C₃×D₈	D₁₂	1	4	yes	direct product factor
188	C₃×D₈	C₃×D₄	1	4	yes	complemented
189	C₂×C₃×C₈	—	2	1	no	—
190	C₂×C₃×C₈	—	2	1	no	—
191	C₂×C₃×C₈	—	3	2	no	—
192	C₂×C₃×C₈	—	6	4	no	—
193	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
194	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
195	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
196	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
197	C₃×C₄⋊C₄	—	2	2	no	—
198	C₃×C₄⋊C₄	—	3	1	no	—
199	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
200	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
201	C₃×C₂²⋊C₄	—	2	2	no	—
202	C₃×C₂²⋊C₄	—	2	2	no	—
203	C₃×C₂²⋊C₄	—	3	2	no	—
204	C₃×C₂²⋊C₄	—	4	2	no	—
205	C₃×C₂²⋊C₄	—	6	4	no	—
206	C₃×C₄²	—	2	1	no	—
207	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
208	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
209	#213	—	2	8	no	—
210	(C₂×D₃)⋊C₄	—	2	4	no	—
211	(C₂×D₃)⋊C₄	C₃×D₄	1	2	yes	—
212	C₄⋊Dic₃	C₃×D₄	1	1	yes	characteristic
213	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
214	D₂₄	—	2	4	no	—
215	D₂₄	—	4	2	no	—
216	D₃×C₈	—	2	4	no	—
217	C₂²×C₃²	—	2	4	no	—
218	C₂²×C₃²	—	4	2	no	—
219	C₂²×C₃²	—	4	2	no	—
220	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₃×D₃	—	2	2	no	—
222	C₂×C₃×D₃	—	2	2	no	—
223	C₂×C₃×D₃	—	4	4	no	—
224	C₂×C₃×D₃	—	4	4	no	—
225	C₂×C₃×D₃	—	4	4	no	—
226	C₂×C₃×D₃	—	8	16	no	—
227	C₂×C₃×D₃	C₂×D₈	1	4	yes	complemented
228	C₃²×C₄	—	2	1	no	—
229	C₃²×C₄	—	4	2	no	—
230	C₃²×C₄	C₂×D₈	1	2	yes	complemented
231	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
232	C₃²×C₄	H(5,𝔽₂)	1	1	yes	characteristic
233	C₃×Dic₃	—	2	2	no	—
234	C₂²×D₄	—	3	4	no	—
235	C₂²×D₄	—	6	2	no	—
236	C₂×D₈	—	3	4	no	—
237	C₂×D₈	—	3	2	no	—
238	C₂×D₈	—	3	2	no	—
239	C₂×D₈	—	6	8	no	—
240	C₂×D₈	C₂×C₃×D₃	1	1	yes	characteristic
241	C₂²×C₈	—	3	2	no	—
242	#127	—	3	2	no	—
243	#121	—	3	4	no	—
244	#121	—	6	2	no	—
245	#120	—	6	4	no	—
246	C₄×D₄	—	3	1	no	—
247	C₄×D₄	C₂×C₃×D₃	1	2	yes	complemented
248	#107	C₂×C₃×D₃	1	1	yes	characteristic, complemented
249	C₄⋊C₈	—	3	1	no	—
250	#102	—	3	4	no	—
251	#102	C₂×C₃×D₃	1	2	yes	complemented
252	C₂²⋊C₈	—	3	2	no	—
253	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
254	C₂³×C₃	—	2	2	no	—
255	C₂³×C₃	—	2	2	no	—
256	C₂³×C₃	—	3	2	no	—
257	C₂³×C₃	—	4	2	no	—
258	C₂³×C₃	—	6	4	no	—
259	C₂³×C₃	—	12	8	no	—
260	C₂³×C₃	—	12	8	no	—
261	C₂³×C₃	—	24	4	no	—
262	C₂²×D₃	—	2	4	no	—
263	C₂²×D₃	—	4	8	no	—
264	C₂²×D₃	—	4	8	no	—
265	C₂²×D₃	—	8	4	no	—
266	C₂²×D₃	C₂×C₃×D₄	1	2	yes	—
267	C₃×D₄	—	2	2	no	—
268	C₃×D₄	—	2	2	no	—
269	C₃×D₄	—	2	4	no	—
270	C₃×D₄	—	3	4	no	—
271	C₃×D₄	—	4	2	no	—
272	C₃×D₄	—	6	4	no	—
273	C₃×D₄	—	6	4	no	—
274	C₃×D₄	—	12	8	no	—
275	C₃×D₄	—	12	8	no	—
276	C₃×D₄	—	12	4	no	—
277	C₃×D₄	—	24	2	no	—
278	C₃×D₄	C₂×D₁₂	1	4	yes	complemented
279	C₃×D₄	C₂×C₃×D₄	1	4	yes	complemented
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	2	2	no	—
282	C₂×C₃×C₄	—	2	1	no	—
283	C₂×C₃×C₄	—	2	1	no	—
284	C₂×C₃×C₄	—	2	1	no	—
285	C₂×C₃×C₄	—	3	2	no	—
286	C₂×C₃×C₄	—	4	2	no	—
287	C₂×C₃×C₄	—	4	4	no	—
288	C₂×C₃×C₄	—	4	4	no	—
289	C₂×C₃×C₄	—	6	2	no	—
290	C₂×C₃×C₄	—	6	2	no	—
291	C₂×C₃×C₄	—	8	4	no	—
292	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
293	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
295	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
296	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
297	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
298	#67	—	4	8	no	—
299	C₂×Dic₃	C₂×C₃×D₄	1	2	yes	—
300	D₁₂	—	2	4	no	—
301	D₁₂	—	2	4	no	—
302	D₁₂	—	4	8	no	—
303	D₁₂	—	4	4	no	—
304	D₁₂	—	8	2	no	—
305	D₁₂	C₃×D₈	1	4	yes	direct product factor
306	C₄×D₃	—	2	2	no	—
307	C₄×D₃	—	2	2	no	—
308	C₃×C₈	—	2	1	no	—
309	C₃×C₈	—	2	1	no	—
310	C₃×C₈	—	2	2	no	—
311	C₃×C₈	—	4	1	no	—
312	C₃×C₈	—	6	2	no	—
313	C₃×C₈	C₂×D₁₂	1	2	yes	complemented
314	C₃×C₈	C₂×C₃×D₄	1	2	yes	complemented
315	C₃⋊C₈	—	2	2	no	—
316	C₂×C₃²	—	4	4	no	—
317	C₂×C₃²	D₄²	1	1	yes	characteristic
318	C₂×C₃²	C₂²×D₈	1	1	yes	characteristic
319	C₂×C₃²	#576	1	1	yes	characteristic
320	C₃×D₃	—	2	4	no	—
321	C₃×D₃	—	8	4	no	—
322	C₂⁴	—	6	4	no	—
323	C₂×D₄	—	3	4	no	—
324	C₂×D₄	—	3	1	no	—
325	C₂×D₄	—	6	4	no	—
326	C₂×D₄	—	6	4	no	—
327	C₂×D₄	—	6	8	no	—
328	C₂×D₄	—	6	2	no	—
329	C₂×D₄	—	6	2	no	—
330	C₂×D₄	—	12	8	no	—
331	C₂×D₄	—	12	4	no	—
332	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	3	2	no	—
335	D₈	—	6	8	no	—
336	D₈	—	6	4	no	—
337	D₈	—	12	2	no	—
338	D₈	C₃×D₁₂	1	4	yes	direct product factor
339	C₂×C₈	—	3	2	no	—
340	C₂×C₈	—	6	4	no	—
341	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
342	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
343	C₄⋊C₄	—	3	1	no	—
344	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
345	C₂²⋊C₄	—	2	2	no	—
346	C₂²⋊C₄	—	3	2	no	—
347	C₂²⋊C₄	—	6	4	no	—
348	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
349	C₂²×C₃	—	2	4	no	—
350	C₂²×C₃	—	2	4	no	—
351	C₂²×C₃	—	2	1	no	—
352	C₂²×C₃	—	3	4	no	—
353	C₂²×C₃	—	4	4	no	—
354	C₂²×C₃	—	4	2	no	—
355	C₂²×C₃	—	4	2	no	—
356	C₂²×C₃	—	4	2	no	—
357	C₂²×C₃	—	4	2	no	—
358	C₂²×C₃	—	6	2	no	—
359	C₂²×C₃	—	6	2	no	—
360	C₂²×C₃	—	8	2	no	—
361	C₂²×C₃	—	8	2	no	—
362	C₂²×C₃	—	12	4	no	—
363	C₂²×C₃	—	12	4	no	—
364	C₂²×C₃	—	12	4	no	—
365	C₂²×C₃	—	24	16	no	—
366	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
367	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
368	C₂×D₃	—	2	2	no	—
369	C₂×D₃	—	2	2	no	—
370	C₂×D₃	—	4	4	no	—
371	C₂×D₃	—	4	4	no	—
372	C₂×D₃	—	4	4	no	—
373	C₂×D₃	—	8	16	no	—
374	C₂×D₃	C₂×C₃×D₈	1	4	yes	complemented
375	C₃×C₄	—	2	1	no	—
376	C₃×C₄	—	2	1	no	—
377	C₃×C₄	—	2	2	no	—
378	C₃×C₄	—	2	1	no	—
379	C₃×C₄	—	2	1	no	—
380	C₃×C₄	—	4	1	no	—
381	C₃×C₄	—	4	2	no	—
382	C₃×C₄	—	4	2	no	—
383	C₃×C₄	—	6	2	no	—
384	C₃×C₄	—	8	2	no	—
385	C₃×C₄	D₃×D₈	1	2	yes	complemented
386	C₃×C₄	C₂×C₃×D₈	1	2	yes	complemented
387	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
388	C₃×C₄	#1009	1	1	yes	characteristic
389	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
390	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
391	Dic₃	—	2	2	no	—
392	C₃²	D₄×D₈	1	1	yes	characteristic, complemented, Sylow
393	C₂³	—	2	2	no	—
394	C₂³	—	3	2	no	—
395	C₂³	—	6	4	no	—
396	C₂³	—	12	8	no	—
397	C₂³	—	12	8	no	—
398	C₂³	—	24	4	no	—
399	D₄	—	2	2	no	—
400	D₄	—	3	4	no	—
401	D₄	—	6	4	no	—
402	D₄	—	6	4	no	—
403	D₄	—	12	8	no	—
404	D₄	—	12	8	no	—
405	D₄	—	12	4	no	—
406	D₄	—	24	2	no	—
407	D₄	C₂×C₃×D₁₂	1	4	yes	complemented
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	3	2	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	6	2	no	—
412	C₂×C₄	—	6	2	no	—
413	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
414	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
415	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
416	C₈	—	2	1	no	—
417	C₈	—	6	2	no	—
418	C₈	C₂×C₃×D₁₂	1	2	yes	complemented
419	C₂×C₃	—	2	1	no	—
420	C₂×C₃	—	2	1	no	—
421	C₂×C₃	—	2	1	no	—
422	C₂×C₃	—	4	4	no	—
423	C₂×C₃	—	4	4	no	—
424	C₂×C₃	—	6	4	no	—
425	C₂×C₃	—	8	4	no	—
426	C₂×C₃	—	24	4	no	—
427	C₂×C₃	D₄×D₁₂	1	1	yes	characteristic
428	C₂×C₃	C₂×D₃×D₈	1	1	yes	characteristic
429	C₂×C₃	#5769	1	1	yes	characteristic
430	C₂×C₃	C₃×D₄²	1	1	yes	characteristic
431	C₂×C₃	C₂²×C₃×D₈	1	1	yes	characteristic
432	C₂×C₃	C₃×#576	1	1	yes	characteristic
433	D₃	—	2	4	no	—
434	D₃	—	8	4	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	3	4	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	6	2	no	—
440	C₂²	—	6	2	no	—
441	C₂²	—	12	4	no	—
442	C₂²	—	12	4	no	—
443	C₂²	—	12	4	no	—
444	C₂²	—	24	16	no	—
445	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
446	C₄	—	2	1	no	—
447	C₄	—	4	2	no	—
448	C₄	—	6	2	no	—
449	C₄	C₃×D₃×D₈	1	2	yes	complemented
450	C₄	C₂²×C₃×D₁₂	1	1	yes	characteristic
451	C₄	C₃×#1009	1	1	yes	characteristic
452	C₃	—	2	1	no	—
453	C₃	D₈×D₁₂	1	1	yes	characteristic, direct product factor
454	C₃	C₃×D₄×D₈	1	1	yes	characteristic, complemented
455	C₂	—	4	4	no	—
456	C₂	—	6	4	no	—
457	C₂	—	24	4	no	—
458	C₂	C₃×D₄×D₁₂	1	1	yes	characteristic
459	C₂	C₂×C₃×D₃×D₈	1	1	yes	characteristic
460	C₂	C₃×#5769	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×C₄×D₈	C₂
socle	C₂²×C₃²	C₂²×D₄
hypercenter	C₃×C₄×D₈	D₃
hypocenter	C₃	C₃×D₄×D₈
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×C₄×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₃×D₈	C₂	semidirect
2. C₃×D₄×D₁₂	C₂	semidirect
3. C₃²×C₄×D₈	C₂	semidirect
4. C₃×#5015	C₂	semidirect
5. C₃×#4883	C₂	semidirect
6. C₃×#4773	C₂	semidirect
7. C₃×#4695	C₂	semidirect
8. C₃×C₈×D₁₂	C₂	semidirect
10. D₈×D₁₂	C₃	direct (N × H)
11. C₂×C₃×D₃×D₄	C₂²	semidirect
14. C₃²×C₄×D₄	C₂²	semidirect
15. C₂×C₃×#213	C₂²	semidirect
18. C₂×C₃×D₂₄	C₂²	semidirect
19. C₂×C₃×D₂₄	C₂²	semidirect
20. C₂×C₃×D₃×C₈	C₂²	semidirect
21. C₃×#895	C₂²	semidirect
23. C₃×#874	C₂²	semidirect
25. C₃²×#107	C₂²	semidirect
26. C₃²×#102	C₂²	semidirect
27. C₃²×C₄×C₈	C₂²	semidirect
28. C₃×(C₂×D₃)⋊C₈	C₂²	semidirect
29. C₃×#809	C₂²	semidirect
30. C₃×C₄⋊(C₃⋊C₈)	C₂²	semidirect
33. C₂×D₃×D₈	C₂×C₃	semidirect
34. D₄×D₁₂	C₂×C₃	semidirect
40. C₃×C₄×D₈	D₃	semidirect
41. C₃×C₄×D₈	C₂×C₃	semidirect
43. #5015	C₂×C₃	semidirect
44. #4883	C₂×C₃	semidirect
45. #4773	C₂×C₃	semidirect
46. #4695	C₂×C₃	semidirect
47. C₈×D₁₂	C₂×C₃	semidirect
61. C₃²×D₈	D₄	semidirect
78. C₂×D₃×D₄	C₂²×C₃	semidirect
94. C₃×C₄×D₄	C₂×D₃	semidirect
95. C₃×C₄×D₄	C₂²×C₃	semidirect
96. C₂×#213	C₂²×C₃	semidirect
99. C₂×D₂₄	C₂²×C₃	semidirect
100. C₂×D₂₄	C₂²×C₃	semidirect
101. C₂×D₃×C₈	C₂²×C₃	semidirect
102. #895	C₂²×C₃	semidirect
104. #874	C₂²×C₃	semidirect
107. C₃×#107	C₂×D₃	semidirect
108. C₃×#107	C₂²×C₃	semidirect
112. C₃×#102	C₂×D₃	semidirect
113. C₃×#102	C₂²×C₃	semidirect
116. C₃×C₄×C₈	C₂×D₃	semidirect
117. C₃×C₄×C₈	C₂²×C₃	semidirect
118. (C₂×D₃)⋊C₈	C₂²×C₃	semidirect
119. #809	C₂²×C₃	semidirect
120. C₄⋊(C₃⋊C₈)	C₂²×C₃	semidirect
128. C₃²×D₄	C₂×D₄	semidirect
141. C₃×D₁₂	D₈	direct (N × H)
145. C₃²×C₈	C₂×D₄	semidirect
153. C₄×D₈	C₃×D₃	semidirect
187. C₃×D₈	D₁₂	direct (N × H)
188. C₃×D₈	C₃×D₄	semidirect
227. C₂×C₃×D₃	C₂×D₈	semidirect
230. C₃²×C₄	C₂×D₈	semidirect
247. C₄×D₄	C₂×C₃×D₃	semidirect
248. #107	C₂×C₃×D₃	semidirect
251. #102	C₂×C₃×D₃	semidirect
253. C₄×C₈	C₂×C₃×D₃	semidirect
278. C₃×D₄	C₂×D₁₂	semidirect
279. C₃×D₄	C₂×C₃×D₄	semidirect
305. D₁₂	C₃×D₈	direct (N × H)
313. C₃×C₈	C₂×D₁₂	semidirect
314. C₃×C₈	C₂×C₃×D₄	semidirect
338. D₈	C₃×D₁₂	direct (N × H)
374. C₂×D₃	C₂×C₃×D₈	semidirect
385. C₃×C₄	D₃×D₈	semidirect
386. C₃×C₄	C₂×C₃×D₈	semidirect
392. C₃²	D₄×D₈	semidirect
407. D₄	C₂×C₃×D₁₂	semidirect
418. C₈	C₂×C₃×D₁₂	semidirect
449. C₄	C₃×D₃×D₈	semidirect
453. C₃	D₈×D₁₂	direct (N × H)
454. C₃	C₃×D₄×D₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₃×D₈	2
C₃×D₄×D₁₂	2
C₃²×C₄×D₈	2
C₃×#5015	2
C₃×#4883	2
C₃×#4773	2
C₃×#4695	2
C₃×C₈×D₁₂	2
C₃×D₄×D₈	3
D₈×D₁₂	3

Subgroups — C3×D8×D12 #11885734

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₈×D₁₂ #11885734