Subgroups — C₃×D₃×#424 #11858263

Order 1152.

1081 conjugacy classes of subgroups.

The subgroup lattice has 472 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	1	yes	maximal, characteristic
2	C₂²×C₃×D₃×C₈	C₂	1	1	yes	maximal, characteristic
3	C₃×D₃×#117	C₂	1	1	yes	maximal, characteristic
4	C₃²×#424	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5119	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5102	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4999	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4839	C₂	1	4	yes	maximal, complemented
9	C₃×D₃×C₄⋊C₈	C₂	1	4	yes	maximal, complemented
10	C₂×C₃×#424	—	3	1	no	maximal
11	D₃×#424	C₃	1	1	yes	maximal, characteristic, direct product factor
12	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
13	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
15	C₃²×#117	C₂²	1	1	yes	characteristic
16	C₃×#926	C₂²	1	1	yes	characteristic
17	C₂×C₃×#208	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₃×D₃×M₁₆	—	2	4	no	—
20	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
21	C₂×C₃×D₃×C₈	—	2	4	no	—
22	C₂×C₃×D₃×C₈	C₂²	1	2	yes	—
23	C₂×C₃×D₃×C₈	C₂²	1	2	yes	—
24	C₂×C₃×D₃×C₈	C₂²	1	2	yes	—
25	C₃×#892	C₄	1	2	yes	—
26	C₃×D₃×C₄⋊C₄	C₄	1	2	yes	—
27	C₃×D₃×C₂²⋊C₄	C₄	1	2	yes	—
28	C₃×#877	C₄	1	2	yes	—
29	C₃×#872	C₂²	1	2	yes	—
30	C₃×C₄²×D₃	C₂²	1	2	yes	—
31	C₃²×C₄⋊C₈	C₂²	1	4	yes	complemented
32	C₃×Dic₃⋊C₈	C₂²	1	4	yes	complemented
33	C₃×Dic₃⋊C₈	C₂²	1	4	yes	complemented
34	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
35	C₂²×C₃×M₁₆	—	3	1	no	—
36	C₂³×C₃×C₈	—	3	1	no	—
37	C₂×C₃×#117	—	3	1	no	—
38	C₂×D₃×M₁₆	C₂×C₃	1	1	yes	characteristic
39	C₂²×D₃×C₈	C₂×C₃	1	1	yes	characteristic
40	D₃×#117	C₂×C₃	1	1	yes	characteristic
41	C₃×#424	—	2	1	no	—
42	C₃×#424	—	3	1	no	—
43	C₃×#424	—	3	1	no	—
44	C₃×#424	—	3	1	no	—
45	C₃×#424	—	3	4	no	—
46	C₃×#424	D₃	1	1	yes	characteristic, direct product factor
47	C₃×#424	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂×C₃×C₄⋊C₈	—	3	4	no	—
49	#5119	C₂×C₃	1	1	yes	characteristic, complemented
50	#5102	C₂×C₃	1	1	yes	characteristic, complemented
51	#4999	C₂×C₃	1	1	yes	characteristic, complemented
52	#4839	C₂×C₃	1	4	yes	complemented
53	D₃×C₄⋊C₈	C₂×C₃	1	4	yes	complemented
54	C₂³×C₃×D₃	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
56	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₃×C₄×D₃	C₂×C₄	1	4	yes	—
58	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₃×C₄×D₃	D₄	1	4	yes	—
61	C₂×C₃×C₄×D₃	Q₈	1	4	yes	—
62	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
64	C₃²×M₁₆	—	2	2	no	—
65	C₂×C₃²×C₈	—	2	2	no	—
66	C₂×C₃²×C₈	C₂³	1	2	yes	—
67	C₂×C₃²×C₈	C₂³	1	2	yes	—
68	C₃²×C₄⋊C₄	C₂×C₄	1	2	yes	—
69	C₃²×C₂²⋊C₄	C₂×C₄	1	2	yes	—
70	C₃²×C₄²	C₂³	1	2	yes	—
71	C₃×#217	C₂×C₄	1	2	yes	—
72	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
73	C₃×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
74	C₃×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
75	C₃×C₄×Dic₃	C₂×C₄	1	4	yes	—
76	C₃×C₄×Dic₃	C₂³	1	2	yes	—
77	C₃×#208	—	2	2	no	—
78	C₂×C₃×C₃⋊C₈	—	2	2	no	—
79	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
80	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
81	C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
82	C₃×D₃×C₈	—	2	4	no	—
83	C₃×D₃×C₈	—	2	4	no	—
84	C₃×D₃×C₈	—	2	4	no	—
85	C₂×#424	—	3	1	no	Sylow
86	C₂³×C₃×C₄	—	3	1	no	—
87	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₃×M₁₆	—	2	1	no	—
89	C₂×C₃×M₁₆	—	3	1	no	—
90	C₂×C₃×M₁₆	—	3	2	no	—
91	C₂×C₃×M₁₆	—	6	4	no	—
92	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
93	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
94	C₂²×C₃×C₈	—	2	1	no	—
95	C₂²×C₃×C₈	—	3	1	no	—
96	C₂²×C₃×C₈	—	3	2	no	—
97	C₂²×C₃×C₈	—	3	2	no	—
98	C₂²×C₃×C₈	—	3	2	no	—
99	C₂²×C₃×C₈	—	6	4	no	—
100	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
101	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
102	C₃×#117	—	2	1	no	—
103	C₃×#117	—	3	1	no	—
104	C₃×#117	—	3	2	no	—
105	C₃×#117	—	3	2	no	—
106	C₃×#117	—	3	2	no	—
107	C₃×#117	C₂×D₃	1	1	yes	characteristic
108	C₃×#117	C₂²×C₃	1	1	yes	characteristic
109	C₂×C₃×C₄⋊C₄	—	3	2	no	—
110	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
111	C₂×C₃×C₄²	—	3	2	no	—
112	#926	C₂²×C₃	1	1	yes	characteristic
113	C₂×#208	C₂²×C₃	1	1	yes	characteristic
114	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
115	D₃×M₁₆	—	2	4	no	—
116	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	—
117	C₂×D₃×C₈	—	2	4	no	—
118	C₂×D₃×C₈	C₂²×C₃	1	2	yes	—
119	C₂×D₃×C₈	C₂²×C₃	1	2	yes	—
120	C₂×D₃×C₈	C₂²×C₃	1	2	yes	—
121	#892	C₃×C₄	1	2	yes	—
122	D₃×C₄⋊C₄	C₃×C₄	1	2	yes	—
123	D₃×C₂²⋊C₄	C₃×C₄	1	2	yes	—
124	#877	C₃×C₄	1	2	yes	—
125	#872	C₂²×C₃	1	2	yes	—
126	C₄²×D₃	C₂²×C₃	1	2	yes	—
127	C₃×C₄⋊C₈	—	2	4	no	—
128	C₃×C₄⋊C₈	—	3	4	no	—
129	C₃×C₄⋊C₈	—	3	4	no	—
130	C₃×C₄⋊C₈	—	3	4	no	—
131	C₃×C₄⋊C₈	C₂×D₃	1	4	yes	complemented
132	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
133	Dic₃⋊C₈	C₂²×C₃	1	4	yes	complemented
134	Dic₃⋊C₈	C₂²×C₃	1	4	yes	complemented
135	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	4	yes	complemented
136	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₃×D₃	—	2	4	no	—
138	C₂²×C₃×D₃	C₄⋊C₄	1	4	yes	—
139	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₃²×C₄	C₂²×C₄	1	4	yes	—
142	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
144	C₂×C₃²×C₄	C₂×Q₈	1	2	yes	—
145	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
146	C₂×C₃×Dic₃	C₄⋊C₄	1	4	yes	—
147	C₂×C₃×Dic₃	C₂²×C₄	1	4	yes	—
148	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
150	C₃×C₄×D₃	—	2	8	no	—
151	C₃×C₄×D₃	C₄⋊C₄	1	4	yes	—
152	C₃×C₄×D₃	C₄⋊C₄	1	4	yes	—
153	C₃×C₄×D₃	C₂×D₄	1	2	yes	—
154	C₃×C₄×D₃	C₂×D₄	1	2	yes	—
155	C₃×C₄×D₃	C₂×Q₈	1	2	yes	—
156	C₃×C₄×D₃	C₂×Q₈	1	2	yes	—
157	C₃²×C₈	—	2	2	no	—
158	C₃²×C₈	—	2	2	no	—
159	C₃×C₃⋊C₈	—	2	2	no	—
160	C₃×C₃⋊C₈	—	2	2	no	—
161	C₂²×M₁₆	—	3	1	no	—
162	C₂³×C₈	—	3	1	no	—
163	C₂×#117	—	3	1	no	—
164	#424	—	3	1	no	—
165	#424	—	3	1	no	—
166	#424	—	3	1	no	—
167	#424	—	3	4	no	—
168	#424	C₃×D₃	1	1	yes	characteristic, direct product factor
169	C₂×C₄⋊C₈	—	3	4	no	—
170	C₂⁴×C₃	—	3	1	no	—
171	C₂³×D₃	C₂×C₃×C₄	1	1	yes	characteristic
172	C₂²×C₃×C₄	—	2	1	no	—
173	C₂²×C₃×C₄	—	3	1	no	—
174	C₂²×C₃×C₄	—	3	1	no	—
175	C₂²×C₃×C₄	—	3	1	no	—
176	C₂²×C₃×C₄	—	3	4	no	—
177	C₂²×C₃×C₄	—	3	4	no	—
178	C₂²×C₃×C₄	—	3	1	no	—
179	C₂²×C₃×C₄	—	3	1	no	—
180	C₂²×C₃×C₄	—	3	4	no	—
181	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
183	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
184	C₂×C₄×D₃	C₂×C₃×C₄	1	4	yes	—
185	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
186	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
187	C₂×C₄×D₃	C₃×D₄	1	4	yes	—
188	C₂×C₄×D₃	C₃×Q₈	1	4	yes	—
189	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
190	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
191	C₃×M₁₆	—	2	2	no	—
192	C₃×M₁₆	—	2	2	no	—
193	C₃×M₁₆	—	4	2	no	—
194	C₃×M₁₆	—	6	4	no	—
195	C₃×M₁₆	—	6	2	no	—
196	C₂×C₃×C₈	—	2	2	no	—
197	C₂×C₃×C₈	—	2	2	no	—
198	C₂×C₃×C₈	—	2	2	no	—
199	C₂×C₃×C₈	—	2	2	no	—
200	C₂×C₃×C₈	—	3	2	no	—
201	C₂×C₃×C₈	—	3	2	no	—
202	C₂×C₃×C₈	—	4	2	no	—
203	C₂×C₃×C₈	—	6	4	no	—
204	C₂×C₃×C₈	—	6	4	no	—
205	C₂×C₃×C₈	—	6	4	no	—
206	C₂×C₃×C₈	—	6	2	no	—
207	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
208	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
209	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
210	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
211	C₃×C₄⋊C₄	—	2	2	no	—
212	C₃×C₄⋊C₄	—	3	4	no	—
213	C₃×C₄⋊C₄	—	3	2	no	—
214	C₃×C₄⋊C₄	C₄×D₃	1	2	yes	—
215	C₃×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
216	C₃×C₂²⋊C₄	—	2	2	no	—
217	C₃×C₂²⋊C₄	—	3	2	no	—
218	C₃×C₂²⋊C₄	—	3	4	no	—
219	C₃×C₂²⋊C₄	C₄×D₃	1	2	yes	—
220	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
221	C₃×C₄²	—	2	2	no	—
222	C₃×C₄²	—	3	4	no	—
223	C₃×C₄²	—	3	2	no	—
224	C₃×C₄²	C₂²×D₃	1	2	yes	—
225	C₃×C₄²	C₂³×C₃	1	2	yes	—
226	#217	C₂×C₃×C₄	1	2	yes	—
227	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	4	yes	—
228	C₄⋊Dic₃	C₂×C₃×C₄	1	2	yes	—
229	Dic₃⋊C₄	C₂×C₃×C₄	1	4	yes	—
230	C₄×Dic₃	C₂×C₃×C₄	1	4	yes	—
231	C₄×Dic₃	C₂³×C₃	1	2	yes	—
232	#208	—	2	2	no	—
233	C₂×C₃⋊C₈	—	2	2	no	—
234	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
235	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
236	ΓL(1,𝔽₂₅)	—	2	4	no	—
237	D₃×C₈	—	2	4	no	—
238	D₃×C₈	—	2	4	no	—
239	D₃×C₈	—	2	4	no	—
240	C₂²×C₃²	—	2	2	no	—
241	C₂²×C₃²	C₂×C₄⋊C₄	1	2	yes	—
242	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
243	C₂×C₃×D₃	—	2	2	no	—
244	C₂×C₃×D₃	—	2	8	no	—
245	C₂×C₃×D₃	C₂×C₄⋊C₄	1	2	yes	—
246	C₂×C₃×D₃	C₂×C₄⋊C₄	1	2	yes	—
247	C₂×C₃×D₃	#131	1	4	yes	—
248	C₃²×C₄	—	2	4	no	—
249	C₃²×C₄	C₂×C₄⋊C₄	1	2	yes	—
250	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
251	C₃²×C₄	C₂²×Q₈	1	1	yes	characteristic
252	C₃×Dic₃	—	2	4	no	—
253	C₃×Dic₃	C₂×C₄⋊C₄	1	2	yes	—
254	C₃×Dic₃	C₂×C₄⋊C₄	1	2	yes	—
255	C₂³×C₄	—	3	1	no	—
256	C₂×M₁₆	—	3	1	no	—
257	C₂×M₁₆	—	3	2	no	—
258	C₂×M₁₆	—	6	4	no	—
259	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
260	C₂²×C₈	—	3	1	no	—
261	C₂²×C₈	—	3	2	no	—
262	C₂²×C₈	—	3	2	no	—
263	C₂²×C₈	—	3	2	no	—
264	C₂²×C₈	—	6	4	no	—
265	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
266	#117	—	3	1	no	—
267	#117	—	3	2	no	—
268	#117	—	3	2	no	—
269	#117	—	3	2	no	—
270	#117	C₂×C₃×D₃	1	1	yes	characteristic
271	C₂×C₄⋊C₄	—	3	2	no	—
272	C₂×C₂²⋊C₄	—	3	2	no	—
273	C₂×C₄²	—	3	2	no	—
274	C₄⋊C₈	—	3	4	no	—
275	C₄⋊C₈	—	3	4	no	—
276	C₄⋊C₈	—	3	4	no	—
277	C₄⋊C₈	C₂×C₃×D₃	1	4	yes	complemented
278	C₂³×C₃	—	2	1	no	—
279	C₂³×C₃	—	3	1	no	—
280	C₂³×C₃	—	3	4	no	—
281	C₂³×C₃	—	3	1	no	—
282	C₂³×C₃	—	6	4	no	—
283	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
284	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
285	C₂²×D₃	—	2	4	no	—
286	C₂²×D₃	C₃×C₄⋊C₄	1	4	yes	—
287	C₂²×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
288	C₂²×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
289	C₂×C₃×C₄	—	2	1	no	—
290	C₂×C₃×C₄	—	2	1	no	—
291	C₂×C₃×C₄	—	2	4	no	—
292	C₂×C₃×C₄	—	2	2	no	—
293	C₂×C₃×C₄	—	2	2	no	—
294	C₂×C₃×C₄	—	3	4	no	—
295	C₂×C₃×C₄	—	3	1	no	—
296	C₂×C₃×C₄	—	3	1	no	—
297	C₂×C₃×C₄	—	3	4	no	—
298	C₂×C₃×C₄	—	3	4	no	—
299	C₂×C₃×C₄	—	3	2	no	—
300	C₂×C₃×C₄	—	3	2	no	—
301	C₂×C₃×C₄	—	3	2	no	—
302	C₂×C₃×C₄	—	3	2	no	—
303	C₂×C₃×C₄	—	3	4	no	—
304	C₂×C₃×C₄	—	6	8	no	—
305	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
306	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
307	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
308	C₂×C₃×C₄	D₃×Q₈	1	2	yes	—
309	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
310	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
311	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
312	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
313	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
314	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
315	C₂×Dic₃	C₃×C₄⋊C₄	1	4	yes	—
316	C₂×Dic₃	C₂²×C₃×C₄	1	4	yes	—
317	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
318	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
319	C₄×D₃	—	2	8	no	—
320	C₄×D₃	C₃×C₄⋊C₄	1	4	yes	—
321	C₄×D₃	C₃×C₄⋊C₄	1	4	yes	—
322	C₄×D₃	C₂×C₃×D₄	1	2	yes	—
323	C₄×D₃	C₂×C₃×D₄	1	2	yes	—
324	C₄×D₃	C₂×C₃×Q₈	1	2	yes	—
325	C₄×D₃	C₂×C₃×Q₈	1	2	yes	—
326	C₃×C₈	—	2	2	no	—
327	C₃×C₈	—	2	2	no	—
328	C₃×C₈	—	2	2	no	—
329	C₃×C₈	—	2	2	no	—
330	C₃×C₈	—	4	2	no	—
331	C₃×C₈	—	4	2	no	—
332	C₃×C₈	—	6	2	no	—
333	C₃×C₈	—	6	2	no	—
334	C₃⋊C₈	—	2	2	no	—
335	C₃⋊C₈	—	2	2	no	—
336	C₂×C₃²	—	2	2	no	—
337	C₂×C₃²	C₂²×C₄⋊C₄	1	1	yes	characteristic
338	C₂×C₃²	C₂×#131	1	2	yes	—
339	C₃×D₃	—	2	2	no	—
340	C₃×D₃	#424	1	4	yes	direct product factor
341	C₂⁴	—	3	1	no	—
342	C₂²×C₄	—	3	1	no	—
343	C₂²×C₄	—	3	1	no	—
344	C₂²×C₄	—	3	1	no	—
345	C₂²×C₄	—	3	1	no	—
346	C₂²×C₄	—	3	1	no	—
347	C₂²×C₄	—	3	4	no	—
348	C₂²×C₄	—	3	4	no	—
349	C₂²×C₄	—	3	4	no	—
350	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
351	M₁₆	—	2	2	no	—
352	M₁₆	—	6	4	no	—
353	M₁₆	—	6	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	3	2	no	—
356	C₂×C₈	—	3	2	no	—
357	C₂×C₈	—	6	4	no	—
358	C₂×C₈	—	6	4	no	—
359	C₂×C₈	—	6	4	no	—
360	C₂×C₈	—	6	2	no	—
361	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
362	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
363	C₄⋊C₄	—	3	4	no	—
364	C₄⋊C₄	—	3	2	no	—
365	C₄⋊C₄	C₃×C₄×D₃	1	2	yes	—
366	C₂²⋊C₄	—	3	2	no	—
367	C₂²⋊C₄	—	3	4	no	—
368	C₂²⋊C₄	C₃×C₄×D₃	1	2	yes	—
369	C₄²	—	3	2	no	—
370	C₄²	—	3	4	no	—
371	C₄²	C₂²×C₃×D₃	1	2	yes	—
372	C₂²×C₃	—	2	2	no	—
373	C₂²×C₃	—	2	2	no	—
374	C₂²×C₃	—	2	2	no	—
375	C₂²×C₃	—	2	1	no	—
376	C₂²×C₃	—	3	4	no	—
377	C₂²×C₃	—	3	2	no	—
378	C₂²×C₃	—	3	2	no	—
379	C₂²×C₃	—	4	2	no	—
380	C₂²×C₃	—	6	8	no	—
381	C₂²×C₃	—	6	2	no	—
382	C₂²×C₃	D₃×C₄⋊C₄	1	2	yes	—
383	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	2	yes	—
384	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
385	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
386	C₂×D₃	—	2	2	no	—
387	C₂×D₃	—	2	8	no	—
388	C₂×D₃	C₂×C₃×C₄⋊C₄	1	2	yes	—
389	C₂×D₃	C₂×C₃×C₄⋊C₄	1	2	yes	—
390	C₂×D₃	C₃×#131	1	4	yes	—
391	C₃×C₄	—	2	4	no	—
392	C₃×C₄	—	2	4	no	—
393	C₃×C₄	—	2	2	no	—
394	C₃×C₄	—	2	1	no	—
395	C₃×C₄	—	2	1	no	—
396	C₃×C₄	—	3	2	no	—
397	C₃×C₄	—	3	2	no	—
398	C₃×C₄	—	4	4	no	—
399	C₃×C₄	—	6	4	no	—
400	C₃×C₄	D₃×C₄⋊C₄	1	2	yes	—
401	C₃×C₄	C₂×C₃×C₄⋊C₄	1	2	yes	—
402	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
403	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
404	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
405	C₃×C₄	C₂²×C₃×Q₈	1	1	yes	characteristic
406	Dic₃	—	2	4	no	—
407	Dic₃	C₂×C₃×C₄⋊C₄	1	2	yes	—
408	Dic₃	C₂×C₃×C₄⋊C₄	1	2	yes	—
409	C₃²	C₂×#424	1	1	yes	characteristic, complemented, Sylow
410	C₂³	—	3	1	no	—
411	C₂³	—	3	4	no	—
412	C₂³	—	3	1	no	—
413	C₂³	—	6	4	no	—
414	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
415	C₂×C₄	—	3	4	no	—
416	C₂×C₄	—	3	1	no	—
417	C₂×C₄	—	3	1	no	—
418	C₂×C₄	—	3	4	no	—
419	C₂×C₄	—	3	4	no	—
420	C₂×C₄	—	3	2	no	—
421	C₂×C₄	—	3	2	no	—
422	C₂×C₄	—	3	2	no	—
423	C₂×C₄	—	3	2	no	—
424	C₂×C₄	—	3	4	no	—
425	C₂×C₄	—	6	8	no	—
426	C₂×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
427	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
428	C₂×C₄	C₃×D₃×D₄	1	2	yes	—
429	C₂×C₄	C₃×D₃×Q₈	1	2	yes	—
430	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	2	2	no	—
433	C₈	—	6	2	no	—
434	C₈	—	6	2	no	—
435	C₂×C₃	—	2	2	no	—
436	C₂×C₃	—	2	2	no	—
437	C₂×C₃	—	2	2	no	—
438	C₂×C₃	—	2	1	no	—
439	C₂×C₃	—	3	4	no	—
440	C₂×C₃	—	4	2	no	—
441	C₂×C₃	—	6	2	no	—
442	C₂×C₃	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
443	C₂×C₃	D₃×#131	1	2	yes	—
444	C₂×C₃	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
445	C₂×C₃	C₂×C₃×#131	1	2	yes	—
446	D₃	—	2	2	no	—
447	D₃	C₃×#424	1	4	yes	direct product factor
448	C₂²	—	2	2	no	—
449	C₂²	—	3	4	no	—
450	C₂²	—	3	2	no	—
451	C₂²	—	3	2	no	—
452	C₂²	—	6	8	no	—
453	C₂²	—	6	2	no	—
454	C₂²	C₃×D₃×C₄⋊C₄	1	2	yes	—
455	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
456	C₄	—	2	4	no	—
457	C₄	—	3	2	no	—
458	C₄	—	3	2	no	—
459	C₄	—	6	4	no	—
460	C₄	C₃×D₃×C₄⋊C₄	1	2	yes	—
461	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
462	C₄	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
463	C₃	—	2	1	no	—
464	C₃	D₃×#424	1	1	yes	characteristic, direct product factor
465	C₃	C₂×C₃×#424	1	1	yes	characteristic, complemented
466	C₂	—	2	2	no	—
467	C₂	—	3	4	no	—
468	C₂	—	6	2	no	—
469	C₂	C₂×C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
470	C₂	C₃×D₃×#131	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#424	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂³×C₃×D₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#424	D₃
hypocenter	C₃	C₂×C₃×#424
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#424

Complements

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

N	H ≅ G/N	type
4. C₃²×#424	C₂	semidirect
5. C₃×#5119	C₂	semidirect
6. C₃×#5102	C₂	semidirect
7. C₃×#4999	C₂	semidirect
8. C₃×#4839	C₂	semidirect
9. C₃×D₃×C₄⋊C₈	C₂	semidirect
11. D₃×#424	C₃	direct (N × H)
31. C₃²×C₄⋊C₈	C₂²	semidirect
32. C₃×Dic₃⋊C₈	C₂²	semidirect
33. C₃×Dic₃⋊C₈	C₂²	semidirect
34. C₃×C₄⋊(C₃⋊C₈)	C₂²	semidirect
46. C₃×#424	D₃	direct (N × H)
47. C₃×#424	C₂×C₃	semidirect
49. #5119	C₂×C₃	semidirect
50. #5102	C₂×C₃	semidirect
51. #4999	C₂×C₃	semidirect
52. #4839	C₂×C₃	semidirect
53. D₃×C₄⋊C₈	C₂×C₃	semidirect
131. C₃×C₄⋊C₈	C₂×D₃	semidirect
132. C₃×C₄⋊C₈	C₂²×C₃	semidirect
133. Dic₃⋊C₈	C₂²×C₃	semidirect
134. Dic₃⋊C₈	C₂²×C₃	semidirect
135. C₄⋊(C₃⋊C₈)	C₂²×C₃	semidirect
168. #424	C₃×D₃	direct (N × H)
277. C₄⋊C₈	C₂×C₃×D₃	semidirect
340. C₃×D₃	#424	direct (N × H)
409. C₃²	C₂×#424	semidirect
447. D₃	C₃×#424	direct (N × H)
464. C₃	D₃×#424	direct (N × H)
465. C₃	C₂×C₃×#424	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
C₂²×C₃×D₃×C₈	2
C₃×D₃×#117	2
C₃²×#424	2
C₃×#5119	2
C₃×#5102	2
C₃×#4999	2
C₃×#4839	2
C₃×D₃×C₄⋊C₈	2
C₂×C₃×#424	3
D₃×#424	3

Subgroups — C3×D3×#424 #11858263

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×#424 #11858263