Subgroups — C₃×D₃×#430 #11858630

Order 1152.

971 conjugacy classes of subgroups.

The subgroup lattice has 447 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₃×M₁₆	C₂	1	2	yes	maximal
2	C₂×C₃×D₃×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₃²×#430	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5125	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5124	C₂	1	2	yes	maximal, complemented
6	C₃×#4893	C₂	1	4	yes	maximal, complemented
7	C₃×D₃×#108	C₂	1	4	yes	maximal, complemented
8	C₂×C₃×#430	—	3	1	no	maximal
9	D₃×#430	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
11	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
12	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₃×#208	C₂²	1	2	yes	—
14	C₂×C₃×#208	C₂²	1	1	yes	characteristic
15	C₃×D₃×M₁₆	—	2	2	no	—
16	C₃×D₃×M₁₆	—	2	2	no	—
17	C₃×D₃×M₁₆	C₄	1	4	yes	—
18	C₃×D₃×M₁₆	C₄	1	4	yes	—
19	C₃×D₃×M₁₆	C₂²	1	4	yes	—
20	C₃×D₃×M₁₆	C₂²	1	4	yes	—
21	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
22	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
23	C₂×C₃×D₃×C₈	—	2	2	no	—
24	C₂×C₃×D₃×C₈	C₂²	1	2	yes	—
25	C₃²×#108	C₂²	1	4	yes	complemented
26	C₃×#822	C₂²	1	8	yes	complemented
27	C₃×#819	C₂²	1	4	yes	complemented
28	C₂²×C₃×M₁₆	—	3	1	no	—
29	C₂²×C₃×M₁₆	—	3	2	no	—
30	C₂×D₃×M₁₆	C₂×C₃	1	2	yes	—
31	C₂×D₃×M₁₆	C₂×C₃	1	1	yes	characteristic
32	C₃×#430	—	2	1	no	—
33	C₃×#430	—	3	2	no	—
34	C₃×#430	—	3	1	no	—
35	C₃×#430	—	3	4	no	—
36	C₃×#430	D₃	1	1	yes	characteristic, direct product factor
37	C₃×#430	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×C₃×#108	—	3	4	no	—
39	#5125	C₂×C₃	1	1	yes	characteristic, complemented
40	#5124	C₂×C₃	1	2	yes	complemented
41	#4893	C₂×C₃	1	4	yes	complemented
42	D₃×#108	C₂×C₃	1	4	yes	complemented
43	C₂³×C₃×D₃	Q₈	1	1	yes	characteristic
44	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
45	C₂²×C₃×Dic₃	Q₈	1	1	yes	characteristic
46	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
47	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
48	C₂×C₃×C₄×D₃	D₄	1	2	yes	—
49	C₂×C₃×C₄×D₃	D₄	1	2	yes	—
50	C₂×C₃×C₄×D₃	Q₈	1	1	yes	characteristic
51	C₂×C₃×C₄×D₃	Q₈	1	1	yes	characteristic
52	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
53	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
54	C₃²×M₁₆	—	2	2	no	—
55	C₃²×M₁₆	C₂×C₄	1	4	yes	—
56	C₃²×M₁₆	C₂³	1	4	yes	—
57	C₂×C₃²×C₈	—	2	2	no	—
58	C₂×C₃²×C₈	C₂³	1	2	yes	—
59	C₃×#208	—	2	2	no	—
60	C₃×#208	C₂×C₄	1	4	yes	—
61	C₃×#208	C₂³	1	4	yes	—
62	C₂×C₃×C₃⋊C₈	—	2	2	no	—
63	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
64	C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
65	C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
66	C₃×ΓL(1,𝔽₂₅)	C₂×C₄	1	8	yes	—
67	C₃×D₃×C₈	—	2	4	no	—
68	C₃×D₃×C₈	—	2	4	no	—
69	C₃×D₃×C₈	C₂×C₄	1	4	yes	—
70	C₃×D₃×C₈	C₂×C₄	1	4	yes	—
71	C₂×#430	—	3	1	no	Sylow
72	C₂³×C₃×C₄	—	3	1	no	—
73	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₃×M₁₆	—	2	1	no	—
75	C₂×C₃×M₁₆	—	2	2	no	—
76	C₂×C₃×M₁₆	—	3	1	no	—
77	C₂×C₃×M₁₆	—	3	4	no	—
78	C₂×C₃×M₁₆	—	3	4	no	—
79	C₂×C₃×M₁₆	—	3	2	no	—
80	C₂×C₃×M₁₆	—	3	2	no	—
81	C₂×C₃×M₁₆	—	3	4	no	—
82	C₂×C₃×M₁₆	—	3	4	no	—
83	C₂×C₃×M₁₆	—	6	2	no	—
84	C₂×C₃×M₁₆	—	6	2	no	—
85	C₂×C₃×M₁₆	—	6	2	no	—
86	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
87	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
88	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
89	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
90	C₂²×C₃×C₈	—	3	2	no	—
91	C₂²×C₃×C₈	—	6	2	no	—
92	C₂×#208	C₂²×C₃	1	2	yes	—
93	C₂×#208	C₂²×C₃	1	1	yes	characteristic
94	D₃×M₁₆	—	2	2	no	—
95	D₃×M₁₆	—	2	2	no	—
96	D₃×M₁₆	C₃×C₄	1	4	yes	—
97	D₃×M₁₆	C₃×C₄	1	4	yes	—
98	D₃×M₁₆	C₂²×C₃	1	4	yes	—
99	D₃×M₁₆	C₂²×C₃	1	4	yes	—
100	C₂×ΓL(1,𝔽₂₅)	—	2	2	no	—
101	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	—
102	C₂×D₃×C₈	—	2	2	no	—
103	C₂×D₃×C₈	C₂²×C₃	1	2	yes	—
104	C₃×#108	—	2	4	no	—
105	C₃×#108	—	3	8	no	—
106	C₃×#108	—	3	4	no	—
107	C₃×#108	C₂×D₃	1	4	yes	complemented
108	C₃×#108	C₂²×C₃	1	4	yes	complemented
109	#822	C₂²×C₃	1	8	yes	complemented
110	#819	C₂²×C₃	1	4	yes	complemented
111	C₂³×C₃²	C₂×Q₈	1	1	yes	characteristic
112	C₂²×C₃×D₃	—	4	2	no	—
113	C₂²×C₃×D₃	C₄⋊C₄	1	2	yes	—
114	C₂²×C₃×D₃	C₄⋊C₄	1	2	yes	—
115	C₂²×C₃×D₃	C₂×Q₈	1	1	yes	characteristic
116	C₂²×C₃×D₃	C₂×Q₈	1	1	yes	characteristic
117	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
118	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
119	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
120	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
121	C₂×C₃×Dic₃	C₄⋊C₄	1	2	yes	—
122	C₂×C₃×Dic₃	C₄⋊C₄	1	2	yes	—
123	C₂×C₃×Dic₃	C₂×Q₈	1	1	yes	characteristic
124	C₂×C₃×Dic₃	C₂×Q₈	1	1	yes	characteristic
125	C₃×C₄×D₃	C₄⋊C₄	1	2	yes	—
126	C₃×C₄×D₃	C₄⋊C₄	1	2	yes	—
127	C₃×C₄×D₃	C₄⋊C₄	1	2	yes	—
128	C₃×C₄×D₃	C₄⋊C₄	1	2	yes	—
129	C₃×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
130	C₃×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
131	C₃×C₄×D₃	C₂²×C₄	1	2	yes	—
132	C₃×C₄×D₃	C₂×D₄	1	1	yes	characteristic
133	C₃×C₄×D₃	C₂×D₄	1	2	yes	—
134	C₃×C₄×D₃	C₂×D₄	1	1	yes	characteristic
135	C₃²×C₈	—	2	4	no	—
136	C₃²×C₈	C₂²×C₄	1	4	yes	—
137	C₃×C₃⋊C₈	—	2	4	no	—
138	C₃×C₃⋊C₈	C₂²×C₄	1	4	yes	—
139	C₂²×M₁₆	—	3	1	no	—
140	C₂²×M₁₆	—	3	2	no	—
141	#430	—	3	2	no	—
142	#430	—	3	1	no	—
143	#430	—	3	4	no	—
144	#430	C₃×D₃	1	1	yes	characteristic, direct product factor
145	C₂×#108	—	3	4	no	—
146	C₂⁴×C₃	—	3	1	no	—
147	C₂³×D₃	C₃×Q₈	1	1	yes	characteristic
148	C₂²×C₃×C₄	—	2	1	no	—
149	C₂²×C₃×C₄	—	3	1	no	—
150	C₂²×C₃×C₄	—	3	2	no	—
151	C₂²×C₃×C₄	—	3	2	no	—
152	C₂²×C₃×C₄	—	3	2	no	—
153	C₂²×C₃×C₄	—	3	2	no	—
154	C₂²×C₃×C₄	—	3	1	no	—
155	C₂²×C₃×C₄	—	3	1	no	—
156	C₂²×C₃×C₄	—	3	1	no	—
157	C₂²×C₃×C₄	—	3	1	no	—
158	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
159	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
160	C₂²×Dic₃	C₃×Q₈	1	1	yes	characteristic
161	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
162	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
163	C₂×C₄×D₃	C₃×D₄	1	2	yes	—
164	C₂×C₄×D₃	C₃×D₄	1	2	yes	—
165	C₂×C₄×D₃	C₃×Q₈	1	1	yes	characteristic
166	C₂×C₄×D₃	C₃×Q₈	1	1	yes	characteristic
167	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
168	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
169	C₃×M₁₆	—	2	2	no	—
170	C₃×M₁₆	—	2	2	no	—
171	C₃×M₁₆	—	2	4	no	—
172	C₃×M₁₆	—	2	4	no	—
173	C₃×M₁₆	—	3	4	no	—
174	C₃×M₁₆	—	3	8	no	—
175	C₃×M₁₆	—	3	4	no	—
176	C₃×M₁₆	—	4	2	no	—
177	C₃×M₁₆	—	6	4	no	—
178	C₃×M₁₆	—	6	4	no	—
179	C₃×M₁₆	—	6	2	no	—
180	C₃×M₁₆	C₄×D₃	1	4	yes	—
181	C₃×M₁₆	C₂×C₃×C₄	1	4	yes	—
182	C₃×M₁₆	C₂²×D₃	1	4	yes	—
183	C₃×M₁₆	C₂³×C₃	1	4	yes	—
184	C₂×C₃×C₈	—	2	2	no	—
185	C₂×C₃×C₈	—	2	2	no	—
186	C₂×C₃×C₈	—	2	2	no	—
187	C₂×C₃×C₈	—	3	2	no	—
188	C₂×C₃×C₈	—	3	4	no	—
189	C₂×C₃×C₈	—	3	4	no	—
190	C₂×C₃×C₈	—	4	2	no	—
191	C₂×C₃×C₈	—	6	4	no	—
192	C₂×C₃×C₈	—	6	4	no	—
193	C₂×C₃×C₈	—	6	2	no	—
194	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
195	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
196	#208	—	2	2	no	—
197	#208	C₂×C₃×C₄	1	4	yes	—
198	#208	C₂³×C₃	1	4	yes	—
199	C₂×C₃⋊C₈	—	2	2	no	—
200	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
201	ΓL(1,𝔽₂₅)	—	2	4	no	—
202	ΓL(1,𝔽₂₅)	—	2	4	no	—
203	ΓL(1,𝔽₂₅)	C₂×C₃×C₄	1	8	yes	—
204	D₃×C₈	—	2	4	no	—
205	D₃×C₈	—	2	4	no	—
206	D₃×C₈	C₂×C₃×C₄	1	4	yes	—
207	D₃×C₈	C₂×C₃×C₄	1	4	yes	—
208	C₂²×C₃²	—	4	1	no	—
209	C₂²×C₃²	C₂×C₄⋊C₄	1	2	yes	—
210	C₂²×C₃²	C₂²×Q₈	1	1	yes	characteristic
211	C₂×C₃×D₃	—	2	4	no	—
212	C₂×C₃×D₃	—	2	2	no	—
213	C₂×C₃×D₃	—	4	2	no	—
214	C₂×C₃×D₃	—	4	1	no	—
215	C₂×C₃×D₃	C₂×C₄⋊C₄	1	1	yes	characteristic
216	C₂×C₃×D₃	C₂×C₄⋊C₄	1	2	yes	—
217	C₂×C₃×D₃	C₂×C₄⋊C₄	1	1	yes	characteristic
218	C₃²×C₄	C₂×C₄⋊C₄	1	2	yes	—
219	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
220	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
221	C₃×Dic₃	C₂×C₄⋊C₄	1	1	yes	characteristic
222	C₃×Dic₃	C₂×C₄⋊C₄	1	1	yes	characteristic
223	C₃×Dic₃	C₂×C₄⋊C₄	1	2	yes	—
224	C₂³×C₄	—	3	1	no	—
225	C₂×M₁₆	—	3	1	no	—
226	C₂×M₁₆	—	3	4	no	—
227	C₂×M₁₆	—	3	4	no	—
228	C₂×M₁₆	—	3	2	no	—
229	C₂×M₁₆	—	3	2	no	—
230	C₂×M₁₆	—	3	4	no	—
231	C₂×M₁₆	—	3	4	no	—
232	C₂×M₁₆	—	6	2	no	—
233	C₂×M₁₆	—	6	2	no	—
234	C₂×M₁₆	—	6	2	no	—
235	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	—
236	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
237	C₂²×C₈	—	3	2	no	—
238	C₂²×C₈	—	6	2	no	—
239	#108	—	3	8	no	—
240	#108	—	3	4	no	—
241	#108	C₂×C₃×D₃	1	4	yes	complemented
242	C₂³×C₃	—	2	1	no	—
243	C₂³×C₃	—	3	2	no	—
244	C₂³×C₃	—	3	1	no	—
245	C₂³×C₃	—	3	2	no	—
246	C₂³×C₃	—	3	1	no	—
247	C₂³×C₃	—	12	2	no	—
248	C₂³×C₃	D₃×Q₈	1	1	yes	characteristic
249	C₂³×C₃	C₂×C₃×Q₈	1	1	yes	characteristic
250	C₂²×D₃	—	4	2	no	—
251	C₂²×D₃	C₃×C₄⋊C₄	1	2	yes	—
252	C₂²×D₃	C₃×C₄⋊C₄	1	2	yes	—
253	C₂²×D₃	C₂×C₃×Q₈	1	1	yes	characteristic
254	C₂²×D₃	C₂×C₃×Q₈	1	1	yes	characteristic
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	2	no	—
258	C₂×C₃×C₄	—	2	1	no	—
259	C₂×C₃×C₄	—	3	2	no	—
260	C₂×C₃×C₄	—	3	2	no	—
261	C₂×C₃×C₄	—	3	1	no	—
262	C₂×C₃×C₄	—	3	1	no	—
263	C₂×C₃×C₄	—	3	2	no	—
264	C₂×C₃×C₄	—	3	2	no	—
265	C₂×C₃×C₄	—	3	2	no	—
266	C₂×C₃×C₄	—	3	2	no	—
267	C₂×C₃×C₄	—	3	1	no	—
268	C₂×C₃×C₄	—	3	1	no	—
269	C₂×C₃×C₄	—	3	2	no	—
270	C₂×C₃×C₄	—	3	1	no	—
271	C₂×C₃×C₄	—	3	2	no	—
272	C₂×C₃×C₄	—	3	1	no	—
273	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
274	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
275	C₂×C₃×C₄	D₃×Q₈	1	1	yes	characteristic
276	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
277	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
278	C₂×C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
279	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
281	C₂×Dic₃	C₃×C₄⋊C₄	1	2	yes	—
282	C₂×Dic₃	C₃×C₄⋊C₄	1	2	yes	—
283	C₂×Dic₃	C₂×C₃×Q₈	1	1	yes	characteristic
284	C₂×Dic₃	C₂×C₃×Q₈	1	1	yes	characteristic
285	C₄×D₃	C₃×C₄⋊C₄	1	2	yes	—
286	C₄×D₃	C₃×C₄⋊C₄	1	2	yes	—
287	C₄×D₃	C₃×C₄⋊C₄	1	2	yes	—
288	C₄×D₃	C₃×C₄⋊C₄	1	2	yes	—
289	C₄×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
290	C₄×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
291	C₄×D₃	C₂²×C₃×C₄	1	2	yes	—
292	C₄×D₃	C₂×C₃×D₄	1	1	yes	characteristic
293	C₄×D₃	C₂×C₃×D₄	1	2	yes	—
294	C₄×D₃	C₂×C₃×D₄	1	1	yes	characteristic
295	C₃×C₈	—	2	4	no	—
296	C₃×C₈	—	2	4	no	—
297	C₃×C₈	—	2	4	no	—
298	C₃×C₈	—	3	4	no	—
299	C₃×C₈	—	4	4	no	—
300	C₃×C₈	—	6	4	no	—
301	C₃×C₈	C₂×C₄×D₃	1	4	yes	—
302	C₃×C₈	C₂²×C₃×C₄	1	4	yes	—
303	C₃⋊C₈	—	2	4	no	—
304	C₃⋊C₈	C₂²×C₃×C₄	1	4	yes	—
305	C₂×C₃²	—	2	2	no	—
306	C₂×C₃²	—	2	1	no	—
307	C₂×C₃²	C₂²×C₄⋊C₄	1	1	yes	characteristic
308	C₃×D₃	—	2	2	no	—
309	C₃×D₃	—	2	1	no	—
310	C₃×D₃	#430	1	2	yes	direct product factor
311	C₂⁴	—	3	1	no	—
312	C₂²×C₄	—	3	1	no	—
313	C₂²×C₄	—	3	1	no	—
314	C₂²×C₄	—	3	1	no	—
315	C₂²×C₄	—	3	2	no	—
316	C₂²×C₄	—	3	2	no	—
317	C₂²×C₄	—	3	2	no	—
318	C₂²×C₄	—	3	2	no	—
319	C₂²×C₄	—	3	1	no	—
320	C₂²×C₄	—	3	1	no	—
321	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
322	M₁₆	—	2	2	no	—
323	M₁₆	—	3	4	no	—
324	M₁₆	—	3	8	no	—
325	M₁₆	—	3	4	no	—
326	M₁₆	—	6	4	no	—
327	M₁₆	—	6	4	no	—
328	M₁₆	—	6	2	no	—
329	M₁₆	C₃×C₄×D₃	1	4	yes	—
330	M₁₆	C₂²×C₃×D₃	1	4	yes	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	3	2	no	—
333	C₂×C₈	—	3	4	no	—
334	C₂×C₈	—	3	4	no	—
335	C₂×C₈	—	6	4	no	—
336	C₂×C₈	—	6	4	no	—
337	C₂×C₈	—	6	2	no	—
338	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
339	C₂²×C₃	—	2	2	no	—
340	C₂²×C₃	—	2	1	no	—
341	C₂²×C₃	—	3	1	no	—
342	C₂²×C₃	—	3	1	no	—
343	C₂²×C₃	—	3	2	no	—
344	C₂²×C₃	—	4	1	no	—
345	C₂²×C₃	—	4	1	no	—
346	C₂²×C₃	—	6	4	no	—
347	C₂²×C₃	—	6	2	no	—
348	C₂²×C₃	—	8	1	no	—
349	C₂²×C₃	—	12	2	no	—
350	C₂²×C₃	—	12	1	no	—
351	C₂²×C₃	D₃×C₄⋊C₄	1	2	yes	—
352	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	2	yes	—
353	C₂²×C₃	C₂×D₃×Q₈	1	1	yes	characteristic
354	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
355	C₂×D₃	—	2	4	no	—
356	C₂×D₃	—	2	2	no	—
357	C₂×D₃	—	4	2	no	—
358	C₂×D₃	—	4	1	no	—
359	C₂×D₃	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
360	C₂×D₃	C₂×C₃×C₄⋊C₄	1	2	yes	—
361	C₂×D₃	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
362	C₃×C₄	—	2	2	no	—
363	C₃×C₄	—	2	1	no	—
364	C₃×C₄	—	2	1	no	—
365	C₃×C₄	—	3	1	no	—
366	C₃×C₄	—	3	1	no	—
367	C₃×C₄	—	3	2	no	—
368	C₃×C₄	D₃×C₄⋊C₄	1	2	yes	—
369	C₃×C₄	C₂×C₃×C₄⋊C₄	1	2	yes	—
370	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
371	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
372	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
373	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
374	Dic₃	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
375	Dic₃	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
376	Dic₃	C₂×C₃×C₄⋊C₄	1	2	yes	—
377	C₃²	C₂×#430	1	1	yes	characteristic, complemented, Sylow
378	C₂³	—	3	2	no	—
379	C₂³	—	3	1	no	—
380	C₂³	—	3	2	no	—
381	C₂³	—	3	1	no	—
382	C₂³	—	12	2	no	—
383	C₂³	C₃×D₃×Q₈	1	1	yes	characteristic
384	C₂×C₄	—	3	2	no	—
385	C₂×C₄	—	3	2	no	—
386	C₂×C₄	—	3	1	no	—
387	C₂×C₄	—	3	1	no	—
388	C₂×C₄	—	3	2	no	—
389	C₂×C₄	—	3	2	no	—
390	C₂×C₄	—	3	2	no	—
391	C₂×C₄	—	3	2	no	—
392	C₂×C₄	—	3	1	no	—
393	C₂×C₄	—	3	1	no	—
394	C₂×C₄	—	3	2	no	—
395	C₂×C₄	—	3	1	no	—
396	C₂×C₄	—	3	2	no	—
397	C₂×C₄	—	3	1	no	—
398	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
399	C₂×C₄	C₃×D₃×D₄	1	2	yes	—
400	C₂×C₄	C₃×D₃×Q₈	1	1	yes	characteristic
401	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
402	C₈	—	2	4	no	—
403	C₈	—	3	4	no	—
404	C₈	—	6	4	no	—
405	C₈	C₂×C₃×C₄×D₃	1	4	yes	—
406	C₂×C₃	—	2	2	no	—
407	C₂×C₃	—	2	1	no	—
408	C₂×C₃	—	2	2	no	—
409	C₂×C₃	—	2	1	no	—
410	C₂×C₃	—	2	1	no	—
411	C₂×C₃	—	3	2	no	—
412	C₂×C₃	—	4	2	no	—
413	C₂×C₃	—	4	1	no	—
414	C₂×C₃	—	6	1	no	—
415	C₂×C₃	—	6	2	no	—
416	C₂×C₃	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
417	C₂×C₃	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
418	D₃	—	2	2	no	—
419	D₃	—	2	1	no	—
420	D₃	C₃×#430	1	2	yes	direct product factor
421	C₂²	—	3	1	no	—
422	C₂²	—	3	1	no	—
423	C₂²	—	3	2	no	—
424	C₂²	—	4	1	no	—
425	C₂²	—	6	4	no	—
426	C₂²	—	6	2	no	—
427	C₂²	—	12	2	no	—
428	C₂²	—	12	1	no	—
429	C₂²	C₃×D₃×C₄⋊C₄	1	2	yes	—
430	C₂²	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
431	C₄	—	3	1	no	—
432	C₄	—	3	1	no	—
433	C₄	—	3	2	no	—
434	C₄	C₃×D₃×C₄⋊C₄	1	2	yes	—
435	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
436	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
437	C₃	—	2	1	no	—
438	C₃	D₃×#430	1	1	yes	characteristic, direct product factor
439	C₃	C₂×C₃×#430	1	1	yes	characteristic, complemented
440	C₂	—	2	2	no	—
441	C₂	—	2	1	no	—
442	C₂	—	3	2	no	—
443	C₂	—	6	1	no	—
444	C₂	—	6	2	no	—
445	C₂	C₂×C₃×D₃×C₄⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#430	C₂
socle	C₂×C₃²	C₂²×C₄⋊C₄
prime radical	C₂³×C₃×D₃	Q₈
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#430	D₃
hypocenter	C₃	C₂×C₃×#430
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₃×#430

Complements

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

N	H ≅ G/N	type
3. C₃²×#430	C₂	semidirect
4. C₃×#5125	C₂	semidirect
5. C₃×#5124	C₂	semidirect
6. C₃×#4893	C₂	semidirect
7. C₃×D₃×#108	C₂	semidirect
9. D₃×#430	C₃	direct (N × H)
25. C₃²×#108	C₂²	semidirect
26. C₃×#822	C₂²	semidirect
27. C₃×#819	C₂²	semidirect
36. C₃×#430	D₃	direct (N × H)
37. C₃×#430	C₂×C₃	semidirect
39. #5125	C₂×C₃	semidirect
40. #5124	C₂×C₃	semidirect
41. #4893	C₂×C₃	semidirect
42. D₃×#108	C₂×C₃	semidirect
107. C₃×#108	C₂×D₃	semidirect
108. C₃×#108	C₂²×C₃	semidirect
109. #822	C₂²×C₃	semidirect
110. #819	C₂²×C₃	semidirect
144. #430	C₃×D₃	direct (N × H)
241. #108	C₂×C₃×D₃	semidirect
310. C₃×D₃	#430	direct (N × H)
377. C₃²	C₂×#430	semidirect
420. D₃	C₃×#430	direct (N × H)
438. C₃	D₃×#430	direct (N × H)
439. C₃	C₂×C₃×#430	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×M₁₆	2
C₃²×#430	2
C₃×#5125	2
C₃×#5124	2
C₃×#4893	2
C₃×D₃×#108	2
C₂×C₃×#430	3
D₃×#430	3

Subgroups — C3×D3×#430 #11858630

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×#430 #11858630