Subgroups — C₃⋊D₃×#431 #11858689

Order 1152.

1584 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	#10592624	C₂	1	1	yes	maximal, characteristic, complemented
4	#10592532	C₂	1	2	yes	maximal, complemented
5	C₃⋊D₃×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
6	C₃⋊D₃×C₂²⋊C₈	C₂	1	2	yes	maximal
7	#10592417	C₂	1	2	yes	maximal, complemented
8	#10592384	C₂	1	2	yes	maximal, complemented
9	C₄×C₈×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
10	D₃×#431	—	3	4	no	maximal
11	C₂²×C₄×C₃⋊D₃	C₄	1	1	yes	characteristic
12	C₂²×C₄×C₃⋊D₃	C₄	1	1	yes	characteristic
13	C₂²×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
14	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₃⋊Dic₃	C₄	1	1	yes	characteristic
16	C₂×C₄×C₃⋊Dic₃	C₄	1	1	yes	characteristic
17	C₂×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₈×C₃⋊D₃	C₂²	1	4	yes	—
19	C₄²×C₃⋊D₃	C₄	1	1	yes	characteristic
20	C₄²×C₃⋊D₃	C₄	1	1	yes	characteristic
21	C₄²×C₃⋊D₃	C₄	1	1	yes	characteristic
22	C₄²×C₃⋊D₃	C₄	1	1	yes	characteristic
23	C₄²×C₃⋊D₃	C₂²	1	1	yes	characteristic
24	C₄²×C₃⋊D₃	C₂²	1	1	yes	characteristic
25	C₄²×C₃⋊D₃	C₂²	1	1	yes	characteristic
26	C₄²×C₃⋊D₃	C₂²	1	1	yes	characteristic
27	C₃²×C₄⋊C₈	C₂²	1	2	yes	complemented
28	C₃²×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₃²×C₄×C₈	C₂²	1	2	yes	complemented
30	#63657	C₂²	1	2	yes	—
31	#63647	C₂²	1	4	yes	—
32	#63641	C₂²	1	4	yes	complemented
33	C₈×C₃⋊Dic₃	C₂²	1	4	yes	complemented
34	C₄⋊(C₃⋊(C₃⋊C₈))	C₂²	1	2	yes	complemented
35	C₄×C₃⋊(C₃⋊C₈)	C₂²	1	2	yes	complemented
36	C₂×C₄²×D₃	—	3	4	no	—
37	C₃×#431	D₃	1	4	yes	complemented
38	#4925	—	3	4	no	—
39	#4833	—	3	8	no	—
40	D₃×C₄⋊C₈	—	3	8	no	—
41	D₃×C₂²⋊C₈	—	3	8	no	—
42	#4718	—	3	8	no	—
43	#4685	—	3	8	no	—
44	C₄×D₃×C₈	—	3	8	no	—
45	C₂³×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
49	C₂²×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×C₃⋊D₃	—	2	4	no	—
53	C₂×C₄×C₃⋊D₃	—	2	4	no	—
54	C₂×C₄×C₃⋊D₃	C₈	1	8	yes	complemented
55	C₂×C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×C₃⋊D₃	C₂³	1	1	yes	characteristic
66	C₂×C₄×C₃⋊D₃	C₂³	1	1	yes	characteristic
67	C₂×C₃²×C₈	C₂³	1	4	yes	—
68	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
69	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
70	C₃²×C₄²	C₂³	1	1	yes	characteristic
71	C₃²×C₄²	C₂³	1	1	yes	characteristic
72	C₄×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
73	C₄×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
74	C₄×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
75	C₄×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
76	C₄×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
77	C₄×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
78	C₄×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
79	C₄×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
80	C₄×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
81	C₄×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
82	C₄×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
83	C₄×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
84	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	4	yes	—
85	C₈×C₃⋊D₃	—	2	8	no	—
86	C₂×#431	—	9	1	no	Sylow
87	C₂²×C₄×D₃	—	3	4	no	—
88	C₂²×C₄×D₃	—	3	4	no	—
89	C₂²×C₄×D₃	—	3	4	no	—
90	C₂×C₃×C₄²	C₂×D₃	1	4	yes	—
91	C₂×C₄×Dic₃	—	3	4	no	—
92	C₂×C₄×Dic₃	—	3	4	no	—
93	C₂×C₄×Dic₃	—	3	4	no	—
94	C₂×D₃×C₈	—	3	16	no	—
95	C₄²×D₃	—	3	4	no	—
96	C₄²×D₃	—	3	4	no	—
97	C₄²×D₃	—	3	4	no	—
98	C₄²×D₃	—	3	4	no	—
99	C₄²×D₃	—	3	4	no	—
100	C₄²×D₃	—	3	4	no	—
101	C₄²×D₃	—	3	4	no	—
102	C₄²×D₃	—	3	4	no	—
103	C₃×C₄⋊C₈	C₂×D₃	1	8	yes	complemented
104	C₃×C₂²⋊C₈	C₂×D₃	1	8	yes	—
105	C₃×C₄×C₈	C₂×D₃	1	8	yes	complemented
106	#830	—	3	8	no	—
107	(C₂×D₃)⋊C₈	—	3	16	no	—
108	Dic₃⋊C₈	—	3	16	no	—
109	C₈×Dic₃	—	3	16	no	—
110	C₄⋊(C₃⋊C₈)	—	3	8	no	—
111	C₄×C₃⋊C₈	—	3	8	no	—
112	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₃⋊D₃	—	2	2	no	—
114	C₂²×C₃⋊D₃	—	2	2	no	—
115	C₂²×C₃⋊D₃	C₂×C₈	1	4	yes	—
116	C₂²×C₃⋊D₃	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₃⋊D₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₃²×C₄	—	2	2	no	—
119	C₂×C₃²×C₄	—	2	2	no	—
120	C₂×C₃²×C₄	C₂×C₈	1	4	yes	complemented
121	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
127	C₂×C₃⋊Dic₃	—	2	2	no	—
128	C₂×C₃⋊Dic₃	—	2	2	no	—
129	C₂×C₃⋊Dic₃	C₂×C₈	1	4	yes	complemented
130	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
136	C₄×C₃⋊D₃	—	2	2	no	—
137	C₄×C₃⋊D₃	—	2	2	no	—
138	C₄×C₃⋊D₃	—	2	2	no	—
139	C₄×C₃⋊D₃	—	2	2	no	—
140	C₄×C₃⋊D₃	—	2	2	no	—
141	C₄×C₃⋊D₃	—	2	2	no	—
142	C₄×C₃⋊D₃	C₂×C₈	1	4	yes	—
143	C₄×C₃⋊D₃	C₂×C₈	1	4	yes	—
144	C₄×C₃⋊D₃	C₂×C₈	1	4	yes	complemented
145	C₄×C₃⋊D₃	C₂×C₈	1	4	yes	complemented
146	C₄×C₃⋊D₃	M₁₆	1	4	yes	—
147	C₄×C₃⋊D₃	#41	1	4	yes	—
148	C₃²×C₈	—	2	4	no	—
149	C₃⋊(C₃⋊C₈)	—	2	4	no	—
150	C₂²×C₄²	—	9	1	no	—
151	#431	—	9	1	no	—
152	#431	—	9	2	no	—
153	#431	—	9	2	no	—
154	#431	—	9	2	no	—
155	#431	C₃⋊D₃	1	1	yes	characteristic, direct product factor
156	C₂×C₄⋊C₈	—	9	2	no	—
157	C₂×C₂²⋊C₈	—	9	2	no	—
158	C₂×C₄×C₈	—	9	2	no	—
159	C₂³×D₃	—	3	4	no	—
160	C₂²×C₃×C₄	C₄×D₃	1	4	yes	—
161	C₂²×C₃×C₄	C₄×D₃	1	4	yes	—
162	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
163	C₂²×Dic₃	—	3	4	no	—
164	C₂²×Dic₃	—	3	4	no	—
165	C₂²×Dic₃	—	3	4	no	—
166	C₂×C₄×D₃	—	3	32	no	—
167	C₂×C₄×D₃	—	3	4	no	—
168	C₂×C₄×D₃	—	3	4	no	—
169	C₂×C₄×D₃	—	3	4	no	—
170	C₂×C₄×D₃	—	3	4	no	—
171	C₂×C₄×D₃	—	3	4	no	—
172	C₂×C₄×D₃	—	3	4	no	—
173	C₂×C₄×D₃	—	3	4	no	—
174	C₂×C₄×D₃	—	3	4	no	—
175	C₂×C₄×D₃	—	3	4	no	—
176	C₂×C₄×D₃	—	3	4	no	—
177	C₂×C₄×D₃	—	3	4	no	—
178	C₂×C₄×D₃	—	3	4	no	—
179	C₂×C₄×D₃	—	6	16	no	—
180	C₂×C₄×D₃	—	6	16	no	—
181	C₂×C₃×C₈	C₂²×D₃	1	16	yes	—
182	C₃×C₄²	C₄×D₃	1	4	yes	—
183	C₃×C₄²	C₄×D₃	1	4	yes	—
184	C₃×C₄²	C₂²×D₃	1	4	yes	—
185	C₃×C₄²	C₂²×D₃	1	4	yes	—
186	C₄×Dic₃	—	3	4	no	—
187	C₄×Dic₃	—	3	4	no	—
188	C₄×Dic₃	—	3	4	no	—
189	C₄×Dic₃	—	3	4	no	—
190	C₄×Dic₃	—	3	4	no	—
191	C₄×Dic₃	—	3	4	no	—
192	C₄×Dic₃	—	3	4	no	—
193	C₄×Dic₃	—	3	4	no	—
194	C₄×Dic₃	—	3	4	no	—
195	C₄×Dic₃	—	3	4	no	—
196	C₄×Dic₃	—	3	4	no	—
197	C₄×Dic₃	—	3	4	no	—
198	C₂×C₃⋊C₈	—	3	16	no	—
199	D₃×C₈	—	6	32	no	—
200	C₂²×C₃²	—	2	1	no	—
201	C₂²×C₃²	—	2	1	no	—
202	C₂²×C₃²	C₂²×C₈	1	2	yes	—
203	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₃⋊D₃	—	2	1	no	—
205	C₂×C₃⋊D₃	—	2	1	no	—
206	C₂×C₃⋊D₃	—	2	8	no	—
207	C₂×C₃⋊D₃	#117	1	2	yes	—
208	C₂×C₃⋊D₃	C₂²×C₈	1	2	yes	—
209	C₂×C₃⋊D₃	C₂²×C₈	1	2	yes	—
210	C₂×C₃⋊D₃	C₂×M₁₆	1	2	yes	—
211	C₃²×C₄	—	2	1	no	—
212	C₃²×C₄	—	2	1	no	—
213	C₃²×C₄	C₂²×C₈	1	2	yes	—
214	C₃²×C₄	C₂²×C₈	1	2	yes	—
215	C₃²×C₄	C₂×M₁₆	1	2	yes	—
216	C₃²×C₄	C₂×#41	1	2	yes	—
217	C₃⋊Dic₃	—	2	1	no	—
218	C₃⋊Dic₃	—	2	1	no	—
219	C₃⋊Dic₃	#117	1	2	yes	—
220	C₃⋊Dic₃	C₂²×C₈	1	2	yes	—
221	C₃⋊Dic₃	C₂²×C₈	1	2	yes	—
222	C₃⋊Dic₃	C₂×M₁₆	1	2	yes	—
223	C₂³×C₄	—	9	1	no	—
224	C₂³×C₄	—	9	1	no	—
225	C₂³×C₄	—	9	1	no	—
226	C₂²×C₈	—	9	4	no	—
227	C₂×C₄²	—	9	1	no	—
228	C₂×C₄²	—	9	1	no	—
229	C₂×C₄²	—	9	1	no	—
230	C₂×C₄²	—	9	1	no	—
231	C₂×C₄²	—	9	1	no	—
232	C₂×C₄²	—	9	1	no	—
233	C₂×C₄²	—	9	1	no	—
234	C₂×C₄²	—	9	1	no	—
235	C₂×C₄²	—	9	1	no	—
236	C₂×C₄²	—	9	1	no	—
237	C₂×C₄²	—	9	1	no	—
238	C₂×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
239	C₄⋊C₈	—	9	4	no	—
240	C₄⋊C₈	—	9	2	no	—
241	C₄⋊C₈	C₂×C₃⋊D₃	1	2	yes	complemented
242	C₂²⋊C₈	—	9	2	no	—
243	C₂²⋊C₈	—	9	4	no	—
244	C₂²⋊C₈	C₂×C₃⋊D₃	1	2	yes	—
245	C₄×C₈	—	9	4	no	—
246	C₄×C₈	—	9	2	no	—
247	C₄×C₈	C₂×C₃⋊D₃	1	2	yes	complemented
248	C₂³×C₃	C₂×C₄×D₃	1	4	yes	—
249	C₂²×D₃	—	3	4	no	—
250	C₂²×D₃	—	3	16	no	—
251	C₂²×D₃	—	3	4	no	—
252	C₂²×D₃	—	6	8	no	—
253	C₂²×D₃	—	6	8	no	—
254	C₂×C₃×C₄	—	2	8	no	—
255	C₂×C₃×C₄	—	2	8	no	—
256	C₂×C₃×C₄	D₃×C₈	1	16	yes	complemented
257	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
258	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
259	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
260	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
261	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
262	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
263	C₂×Dic₃	—	3	16	no	—
264	C₂×Dic₃	—	3	4	no	—
265	C₂×Dic₃	—	3	4	no	—
266	C₂×Dic₃	—	3	4	no	—
267	C₂×Dic₃	—	3	4	no	—
268	C₂×Dic₃	—	3	4	no	—
269	C₂×Dic₃	—	3	4	no	—
270	C₂×Dic₃	—	6	8	no	—
271	C₂×Dic₃	—	6	8	no	—
272	C₄×D₃	—	3	16	no	—
273	C₄×D₃	—	3	16	no	—
274	C₄×D₃	—	3	16	no	—
275	C₄×D₃	—	3	16	no	—
276	C₄×D₃	—	3	16	no	—
277	C₄×D₃	—	3	16	no	—
278	C₄×D₃	—	6	8	no	—
279	C₄×D₃	—	6	8	no	—
280	C₄×D₃	—	6	8	no	—
281	C₄×D₃	—	6	8	no	—
282	C₄×D₃	—	6	8	no	—
283	C₄×D₃	—	6	8	no	—
284	C₃×C₈	—	2	16	no	—
285	C₃⋊C₈	—	6	16	no	—
286	C₂×C₃²	—	2	2	no	—
287	C₂×C₃²	C₂×#117	1	1	yes	characteristic
288	C₂×C₃²	C₂³×C₈	1	1	yes	characteristic
289	C₂×C₃²	C₂²×M₁₆	1	1	yes	characteristic
290	C₃⋊D₃	—	2	2	no	—
291	C₃⋊D₃	#431	1	4	yes	direct product factor
292	C₂⁴	—	9	1	no	—
293	C₂²×C₄	—	9	1	no	—
294	C₂²×C₄	—	9	1	no	—
295	C₂²×C₄	—	9	8	no	—
296	C₂²×C₄	—	9	1	no	—
297	C₂²×C₄	—	9	1	no	—
298	C₂²×C₄	—	9	1	no	—
299	C₂²×C₄	—	9	1	no	—
300	C₂²×C₄	—	9	1	no	—
301	C₂²×C₄	—	9	1	no	—
302	C₂²×C₄	—	9	1	no	—
303	C₂²×C₄	—	9	1	no	—
304	C₂²×C₄	—	9	1	no	—
305	C₂²×C₄	—	9	1	no	—
306	C₂²×C₄	—	9	1	no	—
307	C₂²×C₄	—	9	1	no	—
308	C₂²×C₄	—	9	1	no	—
309	C₂²×C₄	—	18	4	no	—
310	C₂²×C₄	—	18	4	no	—
311	C₂²×C₄	C₄×C₃⋊D₃	1	1	yes	characteristic
312	C₂²×C₄	C₄×C₃⋊D₃	1	1	yes	characteristic
313	C₂²×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
314	C₂×C₈	—	9	4	no	—
315	C₂×C₈	—	18	8	no	—
316	C₂×C₈	C₂²×C₃⋊D₃	1	4	yes	—
317	C₄²	—	9	1	no	—
318	C₄²	—	9	1	no	—
319	C₄²	—	9	1	no	—
320	C₄²	—	9	1	no	—
321	C₄²	—	9	1	no	—
322	C₄²	—	9	1	no	—
323	C₄²	—	9	1	no	—
324	C₄²	—	9	1	no	—
325	C₄²	—	9	1	no	—
326	C₄²	—	9	1	no	—
327	C₄²	—	9	1	no	—
328	C₄²	—	9	1	no	—
329	C₄²	C₄×C₃⋊D₃	1	1	yes	characteristic
330	C₄²	C₄×C₃⋊D₃	1	1	yes	characteristic
331	C₄²	C₂²×C₃⋊D₃	1	1	yes	characteristic
332	C₄²	C₂²×C₃⋊D₃	1	1	yes	characteristic
333	C₂²×C₃	—	2	4	no	—
334	C₂²×C₃	—	2	4	no	—
335	C₂²×C₃	C₂×D₃×C₈	1	8	yes	—
336	C₂²×C₃	C₂²×C₄×D₃	1	4	yes	—
337	C₂×D₃	—	3	8	no	—
338	C₂×D₃	—	3	8	no	—
339	C₂×D₃	—	3	8	no	—
340	C₂×D₃	—	3	8	no	—
341	C₂×D₃	—	6	32	no	—
342	C₂×D₃	—	6	4	no	—
343	C₂×D₃	—	6	4	no	—
344	C₃×C₄	—	2	4	no	—
345	C₃×C₄	—	2	4	no	—
346	C₃×C₄	C₂×D₃×C₈	1	8	yes	—
347	C₃×C₄	C₂×D₃×C₈	1	8	yes	—
348	C₃×C₄	D₃×M₁₆	1	8	yes	—
349	C₃×C₄	D₃×#41	1	8	yes	—
350	Dic₃	—	3	8	no	—
351	Dic₃	—	3	8	no	—
352	Dic₃	—	3	8	no	—
353	Dic₃	—	3	8	no	—
354	Dic₃	—	6	4	no	—
355	Dic₃	—	6	4	no	—
356	C₃²	C₂×#431	1	1	yes	characteristic, complemented, Sylow
357	C₂³	—	9	1	no	—
358	C₂³	—	9	1	no	—
359	C₂³	—	9	4	no	—
360	C₂³	—	18	2	no	—
361	C₂³	—	18	2	no	—
362	C₂³	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	9	1	no	—
366	C₂×C₄	—	9	1	no	—
367	C₂×C₄	—	9	1	no	—
368	C₂×C₄	—	9	1	no	—
369	C₂×C₄	—	9	4	no	—
370	C₂×C₄	—	9	4	no	—
371	C₂×C₄	—	9	4	no	—
372	C₂×C₄	—	9	4	no	—
373	C₂×C₄	—	9	4	no	—
374	C₂×C₄	—	9	4	no	—
375	C₂×C₄	—	9	4	no	—
376	C₂×C₄	—	9	1	no	—
377	C₂×C₄	—	9	1	no	—
378	C₂×C₄	—	18	2	no	—
379	C₂×C₄	—	18	2	no	—
380	C₂×C₄	—	18	2	no	—
381	C₂×C₄	—	18	2	no	—
382	C₂×C₄	—	18	2	no	—
383	C₂×C₄	—	18	2	no	—
384	C₂×C₄	—	18	2	no	—
385	C₂×C₄	—	18	2	no	—
386	C₂×C₄	C₈×C₃⋊D₃	1	4	yes	complemented
387	C₂×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
388	C₂×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
389	C₂×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
390	C₂×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
391	C₂×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
392	C₂×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
393	C₈	—	2	4	no	—
394	C₈	—	18	4	no	—
395	C₂×C₃	—	2	8	no	—
396	C₂×C₃	D₃×#117	1	4	yes	—
397	C₂×C₃	C₂²×D₃×C₈	1	4	yes	—
398	C₂×C₃	C₂×D₃×M₁₆	1	4	yes	—
399	D₃	—	3	16	no	—
400	D₃	—	6	8	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	9	2	no	—
404	C₂²	—	9	2	no	—
405	C₂²	—	9	2	no	—
406	C₂²	—	9	2	no	—
407	C₂²	—	18	8	no	—
408	C₂²	—	18	1	no	—
409	C₂²	—	18	1	no	—
410	C₂²	C₂×C₈×C₃⋊D₃	1	2	yes	—
411	C₂²	C₂²×C₄×C₃⋊D₃	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	9	2	no	—
415	C₄	—	9	2	no	—
416	C₄	—	9	2	no	—
417	C₄	—	9	2	no	—
418	C₄	—	18	1	no	—
419	C₄	—	18	1	no	—
420	C₄	C₂×C₈×C₃⋊D₃	1	2	yes	—
421	C₄	C₂×C₈×C₃⋊D₃	1	2	yes	—
422	C₄	M₁₆×C₃⋊D₃	1	2	yes	—
423	C₄	#41×C₃⋊D₃	1	2	yes	—
424	C₃	D₃×#431	1	4	yes	complemented
425	C₂	—	2	2	no	—
426	C₂	—	9	4	no	—
427	C₂	—	18	2	no	—
428	C₂	C₃⋊D₃×#117	1	1	yes	characteristic
429	C₂	C₂²×C₈×C₃⋊D₃	1	1	yes	characteristic
430	C₂	C₂×M₁₆×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂²×C₃⋊D₃
commutator	C₂×C₃²	C₂³×C₈
Frattini	C₂×C₄	C₂³×C₃⋊D₃
Fitting	C₃²×#431	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂³×C₃⋊D₃	C₂×C₄
cosocle	C₂×C₃²×C₄	C₂⁴
hypercenter	#431	C₃⋊D₃
hypocenter	C₃²	C₂×#431
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₄² ◁ #431

Complements

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

N	H ≅ G/N	type
2. C₃²×#431	C₂	semidirect
3. #10592624	C₂	semidirect
4. #10592532	C₂	semidirect
5. C₃⋊D₃×C₄⋊C₈	C₂	semidirect
7. #10592417	C₂	semidirect
8. #10592384	C₂	semidirect
9. C₄×C₈×C₃⋊D₃	C₂	semidirect
27. C₃²×C₄⋊C₈	C₂²	semidirect
29. C₃²×C₄×C₈	C₂²	semidirect
32. #63641	C₂²	semidirect
33. C₈×C₃⋊Dic₃	C₂²	semidirect
34. C₄⋊(C₃⋊(C₃⋊C₈))	C₂²	semidirect
35. C₄×C₃⋊(C₃⋊C₈)	C₂²	semidirect
37. C₃×#431	D₃	semidirect
54. C₂×C₄×C₃⋊D₃	C₈	semidirect
103. C₃×C₄⋊C₈	C₂×D₃	semidirect
105. C₃×C₄×C₈	C₂×D₃	semidirect
120. C₂×C₃²×C₄	C₂×C₈	semidirect
129. C₂×C₃⋊Dic₃	C₂×C₈	semidirect
144. C₄×C₃⋊D₃	C₂×C₈	semidirect
145. C₄×C₃⋊D₃	C₂×C₈	semidirect
155. #431	C₃⋊D₃	direct (N × H)
241. C₄⋊C₈	C₂×C₃⋊D₃	semidirect
247. C₄×C₈	C₂×C₃⋊D₃	semidirect
256. C₂×C₃×C₄	D₃×C₈	semidirect
291. C₃⋊D₃	#431	direct (N × H)
356. C₃²	C₂×#431	semidirect
386. C₂×C₄	C₈×C₃⋊D₃	semidirect
424. C₃	D₃×#431	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄²×C₃⋊D₃	2
C₃²×#431	2
#10592624	2
#10592532	2
C₃⋊D₃×C₄⋊C₈	2
C₃⋊D₃×C₂²⋊C₈	2
#10592417	2
#10592384	2
C₄×C₈×C₃⋊D₃	2
D₃×#431	3

Subgroups — C3⋊D3×#431 #11858689

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊D₃×#431 #11858689