Subgroups — C₃×#79962 #11861500

Order 1152.

823 conjugacy classes of subgroups.

The subgroup lattice has 514 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	C₃²×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5024	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4837	C₂	1	2	yes	maximal
5	C₃×#4837	C₂	1	1	yes	maximal, characteristic
6	C₃×#4830	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4828	C₂	1	2	yes	maximal, complemented
8	C₃×#4707	C₂	1	2	yes	maximal
9	C₃×#4701	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic
11	C₃×C₈×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×Q₈×M₁₆	—	3	1	no	maximal
13	#79962	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×D₃×Q₈	C₄	1	1	yes	characteristic
15	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
16	C₃×Q₈×Dic₃	C₄	1	1	yes	characteristic
17	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
18	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
19	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
20	C₃×D₃×C₄⋊C₄	C₄	1	1	yes	characteristic
21	C₃×D₃×C₄⋊C₄	C₄	1	2	yes	—
22	C₃×#887	C₄	1	2	yes	—
23	C₃×#887	C₄	1	1	yes	characteristic
24	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
25	C₃×C₄²×D₃	C₂²	1	2	yes	—
26	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
27	C₃×C₄×Dic₆	C₂²	1	2	yes	—
28	C₃²×C₄⋊C₈	C₂²	1	2	yes	—
29	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₃²×#97	C₂²	1	2	yes	—
31	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
32	C₃×#815	C₂²	1	1	yes	characteristic
33	C₃×#815	C₂²	1	1	yes	characteristic
34	C₃×Dic₃⋊C₈	C₂²	1	2	yes	—
35	C₃×Dic₃⋊C₈	C₂²	1	2	yes	—
36	C₃×Dic₃⋊C₈	C₂²	1	2	yes	—
37	C₃×C₈×Dic₃	C₂²	1	2	yes	—
38	C₃×C₈×Dic₃	C₂²	1	2	yes	—
39	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
40	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
41	C₃×#803	C₂²	1	2	yes	—
42	C₃×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
43	C₂×C₃×C₄×Q₈	—	3	1	no	—
44	C₄×D₃×Q₈	C₂×C₃	1	1	yes	characteristic
45	C₃×#446	—	2	1	no	—
46	C₃×#446	—	3	1	no	—
47	C₃×#446	—	3	2	no	—
48	C₃×#446	—	3	2	no	—
49	C₃×#446	D₃	1	1	yes	characteristic, complemented
50	C₃×#446	C₂×C₃	1	1	yes	characteristic, complemented
51	C₃×C₈×Q₈	—	3	1	no	—
52	C₃×C₈×Q₈	—	3	1	no	—
53	C₃×#423	—	3	2	no	—
54	C₃×#423	—	3	1	no	—
55	C₃×C₄×M₁₆	—	3	2	no	—
56	C₃×C₄×M₁₆	—	3	1	no	—
57	#5024	C₂×C₃	1	1	yes	characteristic, complemented
58	#4837	C₂×C₃	1	1	yes	characteristic
59	#4837	C₂×C₃	1	2	yes	—
60	#4830	C₂×C₃	1	1	yes	characteristic, complemented
61	#4828	C₂×C₃	1	2	yes	complemented
62	#4707	C₂×C₃	1	2	yes	—
63	#4701	C₂×C₃	1	2	yes	complemented
64	C₄×ΓL(1,𝔽₂₅)	C₂×C₃	1	1	yes	characteristic
65	C₈×Dic₆	C₂×C₃	1	1	yes	characteristic, complemented
66	C₂×C₃²×Q₈	C₂×C₄	1	1	yes	characteristic
67	C₃×D₃×Q₈	—	2	4	no	—
68	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
70	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
72	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
73	C₂×C₃×Dic₆	C₂×C₄	1	2	yes	—
74	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
75	C₂×C₃²×C₈	C₂³	1	2	yes	—
76	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
77	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
78	C₃²×C₄⋊C₄	C₂×C₄	1	2	yes	—
79	C₃²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₃²×C₄²	C₂³	1	1	yes	characteristic
81	C₃²×C₄²	C₂³	1	2	yes	—
82	C₃×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
83	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
84	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
85	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
86	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
87	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
88	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
89	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
90	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
91	C₃×C₄×Dic₃	C₂³	1	2	yes	—
92	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
94	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
95	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
96	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
97	C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
98	C₃×ΓL(1,𝔽₂₅)	Q₈	1	4	yes	complemented
99	Q₈×M₁₆	—	3	1	no	Sylow
100	C₂²×C₃×Q₈	—	3	1	no	—
101	C₂×D₃×Q₈	C₃×C₄	1	1	yes	characteristic
102	C₂×C₃×M₁₆	—	3	1	no	—
103	C₂×C₃×M₁₆	—	3	2	no	—
104	C₂×C₃×M₁₆	—	3	1	no	—
105	C₃×C₄×Q₈	—	2	1	no	—
106	C₃×C₄×Q₈	—	3	1	no	—
107	C₃×C₄×Q₈	—	3	1	no	—
108	C₃×C₄×Q₈	—	3	2	no	—
109	C₃×C₄×Q₈	—	3	1	no	—
110	C₃×C₄×Q₈	—	3	2	no	—
111	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic
112	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₃×C₄⋊C₄	—	3	2	no	—
114	C₂×C₃×C₄⋊C₄	—	3	1	no	—
115	C₂×C₃×C₄²	—	3	2	no	—
116	C₂×C₃×C₄²	—	3	1	no	—
117	Q₈×Dic₃	C₃×C₄	1	1	yes	characteristic
118	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	1	yes	characteristic
119	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	—
120	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	1	yes	characteristic
121	D₃×C₄⋊C₄	C₃×C₄	1	1	yes	characteristic
122	D₃×C₄⋊C₄	C₃×C₄	1	2	yes	—
123	#887	C₃×C₄	1	2	yes	—
124	#887	C₃×C₄	1	1	yes	characteristic
125	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
126	C₄²×D₃	C₂²×C₃	1	2	yes	—
127	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
128	C₄×Dic₆	C₂²×C₃	1	2	yes	—
129	C₃×C₄⋊C₈	—	2	1	no	—
130	C₃×C₄⋊C₈	—	2	2	no	—
131	C₃×C₄⋊C₈	—	3	2	no	—
132	C₃×C₄⋊C₈	—	3	2	no	—
133	C₃×C₄⋊C₈	—	3	2	no	—
134	C₃×C₄⋊C₈	—	3	1	no	—
135	C₃×C₄⋊C₈	—	3	2	no	—
136	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
137	C₃×C₄⋊C₈	C₂×D₃	1	2	yes	—
138	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
139	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
140	C₃×#97	—	2	2	no	—
141	C₃×#97	—	3	1	no	—
142	C₃×#97	—	3	1	no	—
143	C₃×#97	—	3	2	no	—
144	C₃×#97	C₂×D₃	1	2	yes	—
145	C₃×#97	C₂²×C₃	1	2	yes	—
146	C₃×C₄×C₈	—	2	1	no	—
147	C₃×C₄×C₈	—	3	2	no	—
148	C₃×C₄×C₈	—	3	2	no	—
149	C₃×C₄×C₈	—	3	1	no	—
150	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
151	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
152	#815	C₂²×C₃	1	1	yes	characteristic
153	#815	C₂²×C₃	1	1	yes	characteristic
154	Dic₃⋊C₈	C₂²×C₃	1	2	yes	—
155	Dic₃⋊C₈	C₂²×C₃	1	2	yes	—
156	Dic₃⋊C₈	C₂²×C₃	1	2	yes	—
157	C₈×Dic₃	C₂²×C₃	1	2	yes	—
158	C₈×Dic₃	C₂²×C₃	1	2	yes	—
159	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic
160	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	—
161	#803	C₂²×C₃	1	2	yes	—
162	C₄×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
163	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
164	C₃²×Q₈	—	2	2	no	—
165	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
167	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
168	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
170	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
171	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
175	C₃×C₄×D₃	—	2	2	no	—
176	C₃×C₄×D₃	—	2	4	no	—
177	C₃×C₄×D₃	—	4	1	no	—
178	C₃×C₄×D₃	—	4	2	no	—
179	C₃×C₄×D₃	C₂×Q₈	1	2	yes	—
180	C₃×C₄×D₃	#41	1	2	yes	—
181	C₃×Dic₆	—	2	4	no	—
182	C₃×Dic₆	M₁₆	1	4	yes	complemented
183	C₃²×C₈	—	2	2	no	—
184	C₃²×C₈	—	2	1	no	—
185	C₃²×C₈	C₂×Q₈	1	2	yes	complemented
186	C₃×C₃⋊C₈	—	2	1	no	—
187	C₃×C₃⋊C₈	—	2	2	no	—
188	C₃×C₃⋊C₈	C₂×Q₈	1	2	yes	complemented
189	C₂×C₄×Q₈	—	3	1	no	—
190	#446	—	3	1	no	—
191	#446	—	3	2	no	—
192	#446	—	3	2	no	—
193	#446	C₃×D₃	1	1	yes	characteristic, complemented
194	C₈×Q₈	—	3	1	no	—
195	C₈×Q₈	—	3	1	no	—
196	#423	—	3	2	no	—
197	#423	—	3	1	no	—
198	C₄×M₁₆	—	3	2	no	—
199	C₄×M₁₆	—	3	1	no	—
200	C₂×C₃×Q₈	—	2	1	no	—
201	C₂×C₃×Q₈	—	3	1	no	—
202	C₂×C₃×Q₈	—	3	2	no	—
203	C₂×C₃×Q₈	—	6	4	no	—
204	C₂×C₃×Q₈	C₄×D₃	1	1	yes	characteristic
205	C₂×C₃×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
206	C₂²×C₃×C₄	—	3	1	no	—
207	C₂²×C₃×C₄	—	3	2	no	—
208	C₂²×C₃×C₄	—	3	1	no	—
209	C₂²×C₃×C₄	—	3	2	no	—
210	C₂²×C₃×C₄	—	3	1	no	—
211	D₃×Q₈	—	2	4	no	—
212	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
213	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
214	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
215	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
216	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
217	C₂×Dic₆	C₂×C₃×C₄	1	2	yes	—
218	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
219	C₃×M₁₆	—	3	4	no	—
220	C₃×M₁₆	—	6	4	no	—
221	C₃×M₁₆	—	6	2	no	—
222	C₂×C₃×C₈	—	2	1	no	—
223	C₂×C₃×C₈	—	2	1	no	—
224	C₂×C₃×C₈	—	2	2	no	—
225	C₂×C₃×C₈	—	3	1	no	—
226	C₂×C₃×C₈	—	3	2	no	—
227	C₂×C₃×C₈	—	3	1	no	—
228	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
229	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
230	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
231	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
232	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
233	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
234	C₃×C₄⋊C₄	—	2	1	no	—
235	C₃×C₄⋊C₄	—	2	2	no	—
236	C₃×C₄⋊C₄	—	3	2	no	—
237	C₃×C₄⋊C₄	—	3	2	no	—
238	C₃×C₄⋊C₄	—	3	2	no	—
239	C₃×C₄⋊C₄	—	3	2	no	—
240	C₃×C₄⋊C₄	—	3	1	no	—
241	C₃×C₄⋊C₄	C₄×D₃	1	2	yes	—
242	C₃×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
243	C₃×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
244	C₃×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
245	C₃×C₄²	—	2	1	no	—
246	C₃×C₄²	—	2	2	no	—
247	C₃×C₄²	—	3	2	no	—
248	C₃×C₄²	—	3	2	no	—
249	C₃×C₄²	—	3	1	no	—
250	C₃×C₄²	—	3	1	no	—
251	C₃×C₄²	—	3	2	no	—
252	C₃×C₄²	—	3	1	no	—
253	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
254	C₃×C₄²	C₂²×D₃	1	2	yes	—
255	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
256	C₃×C₄²	C₂³×C₃	1	2	yes	—
257	C₄⋊Dic₃	C₂×C₃×C₄	1	2	yes	—
258	C₄⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
259	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
260	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
261	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
262	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
263	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
264	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
265	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
266	C₄×Dic₃	C₂³×C₃	1	2	yes	—
267	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
268	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
269	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
270	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
271	ΓL(1,𝔽₂₅)	—	2	2	no	—
272	ΓL(1,𝔽₂₅)	—	2	4	no	—
273	ΓL(1,𝔽₂₅)	C₃×Q₈	1	4	yes	complemented
274	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
275	C₂×C₃×D₃	—	2	1	no	—
276	C₂×C₃×D₃	—	2	1	no	—
277	C₂×C₃×D₃	C₄×Q₈	1	2	yes	—
278	C₃²×C₄	—	2	2	no	—
279	C₃²×C₄	—	2	1	no	—
280	C₃²×C₄	—	2	2	no	—
281	C₃²×C₄	C₂×M₁₆	1	2	yes	—
282	C₃²×C₄	C₂²×Q₈	1	1	yes	characteristic
283	C₃²×C₄	C₂×#41	1	1	yes	characteristic
284	C₃×Dic₃	—	2	1	no	—
285	C₃×Dic₃	—	2	2	no	—
286	C₃×Dic₃	—	2	1	no	—
287	C₃×Dic₃	C₄×Q₈	1	2	yes	—
288	C₃×Dic₃	C₂×M₁₆	1	4	yes	—
289	C₂²×Q₈	—	3	1	no	—
290	C₂×M₁₆	—	3	1	no	—
291	C₂×M₁₆	—	3	2	no	—
292	C₂×M₁₆	—	3	1	no	—
293	C₄×Q₈	—	3	1	no	—
294	C₄×Q₈	—	3	1	no	—
295	C₄×Q₈	—	3	2	no	—
296	C₄×Q₈	—	3	1	no	—
297	C₄×Q₈	—	3	2	no	—
298	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
299	C₂×C₄⋊C₄	—	3	2	no	—
300	C₂×C₄⋊C₄	—	3	1	no	—
301	C₂×C₄²	—	3	2	no	—
302	C₂×C₄²	—	3	1	no	—
303	C₄⋊C₈	—	3	2	no	—
304	C₄⋊C₈	—	3	2	no	—
305	C₄⋊C₈	—	3	2	no	—
306	C₄⋊C₈	—	3	1	no	—
307	C₄⋊C₈	—	3	2	no	—
308	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
309	C₄⋊C₈	C₂×C₃×D₃	1	2	yes	—
310	#97	—	3	1	no	—
311	#97	—	3	1	no	—
312	#97	—	3	2	no	—
313	#97	C₂×C₃×D₃	1	2	yes	—
314	C₄×C₈	—	3	2	no	—
315	C₄×C₈	—	3	2	no	—
316	C₄×C₈	—	3	1	no	—
317	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic
318	C₂³×C₃	—	3	1	no	—
319	C₂²×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
320	C₃×Q₈	—	2	2	no	—
321	C₃×Q₈	—	2	2	no	—
322	C₃×Q₈	—	3	4	no	—
323	C₃×Q₈	—	4	2	no	—
324	C₃×Q₈	—	6	4	no	—
325	C₂×C₃×C₄	—	2	1	no	—
326	C₂×C₃×C₄	—	2	1	no	—
327	C₂×C₃×C₄	—	2	1	no	—
328	C₂×C₃×C₄	—	2	2	no	—
329	C₂×C₃×C₄	—	2	2	no	—
330	C₂×C₃×C₄	—	3	1	no	—
331	C₂×C₃×C₄	—	3	2	no	—
332	C₂×C₃×C₄	—	3	2	no	—
333	C₂×C₃×C₄	—	3	2	no	—
334	C₂×C₃×C₄	—	3	2	no	—
335	C₂×C₃×C₄	—	3	1	no	—
336	C₂×C₃×C₄	—	3	1	no	—
337	C₂×C₃×C₄	—	6	4	no	—
338	C₂×C₃×C₄	—	6	2	no	—
339	C₂×C₃×C₄	—	12	1	no	—
340	C₂×C₃×C₄	—	12	2	no	—
341	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
342	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
343	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
344	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
345	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
346	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
347	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
348	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
349	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
350	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
351	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
352	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
353	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
354	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
355	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
356	C₄×D₃	—	2	2	no	—
357	C₄×D₃	—	2	4	no	—
358	C₄×D₃	—	4	1	no	—
359	C₄×D₃	—	4	2	no	—
360	C₄×D₃	C₂×C₃×Q₈	1	2	yes	—
361	C₄×D₃	C₃×#41	1	2	yes	—
362	Dic₆	—	2	4	no	—
363	Dic₆	C₃×M₁₆	1	4	yes	complemented
364	C₃×C₈	—	2	2	no	—
365	C₃×C₈	—	2	1	no	—
366	C₃×C₈	—	2	2	no	—
367	C₃×C₈	—	2	1	no	—
368	C₃×C₈	—	2	2	no	—
369	C₃×C₈	—	3	2	no	—
370	C₃×C₈	—	4	1	no	—
371	C₃×C₈	—	4	2	no	—
372	C₃×C₈	—	6	1	no	—
373	C₃×C₈	—	6	2	no	—
374	C₃×C₈	D₃×Q₈	1	2	yes	complemented
375	C₃×C₈	C₂×C₃×Q₈	1	2	yes	complemented
376	C₃⋊C₈	—	2	1	no	—
377	C₃⋊C₈	—	2	2	no	—
378	C₃⋊C₈	C₂×C₃×Q₈	1	2	yes	complemented
379	C₂×C₃²	C₂×C₄×Q₈	1	1	yes	characteristic
380	C₂×C₃²	C₂²×M₁₆	1	1	yes	characteristic
381	C₂×C₃²	#568	1	1	yes	characteristic
382	C₃×D₃	—	2	2	no	—
383	C₂×Q₈	—	3	1	no	—
384	C₂×Q₈	—	3	2	no	—
385	C₂×Q₈	—	6	4	no	—
386	C₂×Q₈	C₃×C₄×D₃	1	1	yes	characteristic
387	C₂²×C₄	—	3	1	no	—
388	C₂²×C₄	—	3	2	no	—
389	C₂²×C₄	—	3	1	no	—
390	C₂²×C₄	—	3	2	no	—
391	C₂²×C₄	—	3	1	no	—
392	M₁₆	—	3	4	no	—
393	M₁₆	—	6	4	no	—
394	M₁₆	—	6	2	no	—
395	C₂×C₈	—	3	1	no	—
396	C₂×C₈	—	3	2	no	—
397	C₂×C₈	—	3	1	no	—
398	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
399	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
400	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
401	C₄⋊C₄	—	3	2	no	—
402	C₄⋊C₄	—	3	2	no	—
403	C₄⋊C₄	—	3	2	no	—
404	C₄⋊C₄	—	3	2	no	—
405	C₄⋊C₄	—	3	1	no	—
406	C₄⋊C₄	C₃×C₄×D₃	1	2	yes	—
407	C₄⋊C₄	C₃×C₄×D₃	1	1	yes	characteristic
408	C₄²	—	3	2	no	—
409	C₄²	—	3	1	no	—
410	C₄²	—	3	2	no	—
411	C₄²	—	3	2	no	—
412	C₄²	—	3	1	no	—
413	C₄²	—	3	1	no	—
414	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
415	C₄²	C₂²×C₃×D₃	1	2	yes	—
416	C₂²×C₃	—	2	1	no	—
417	C₂²×C₃	—	3	2	no	—
418	C₂²×C₃	—	6	1	no	—
419	C₂²×C₃	—	6	1	no	—
420	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
421	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
422	C₂×D₃	—	2	1	no	—
423	C₂×D₃	—	2	1	no	—
424	C₂×D₃	C₃×C₄×Q₈	1	2	yes	—
425	C₃×C₄	—	2	2	no	—
426	C₃×C₄	—	2	1	no	—
427	C₃×C₄	—	2	2	no	—
428	C₃×C₄	—	2	2	no	—
429	C₃×C₄	—	2	1	no	—
430	C₃×C₄	—	2	2	no	—
431	C₃×C₄	—	2	2	no	—
432	C₃×C₄	—	2	1	no	—
433	C₃×C₄	—	2	1	no	—
434	C₃×C₄	—	3	4	no	—
435	C₃×C₄	—	3	2	no	—
436	C₃×C₄	—	4	2	no	—
437	C₃×C₄	—	4	1	no	—
438	C₃×C₄	—	4	2	no	—
439	C₃×C₄	—	6	1	no	—
440	C₃×C₄	—	6	2	no	—
441	C₃×C₄	—	6	1	no	—
442	C₃×C₄	D₃×M₁₆	1	2	yes	—
443	C₃×C₄	C₂×C₃×M₁₆	1	2	yes	—
444	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
445	C₃×C₄	D₃×#41	1	1	yes	characteristic
446	C₃×C₄	C₂²×C₃×Q₈	1	1	yes	characteristic
447	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
448	Dic₃	—	2	1	no	—
449	Dic₃	—	2	2	no	—
450	Dic₃	—	2	1	no	—
451	Dic₃	C₃×C₄×Q₈	1	2	yes	—
452	Dic₃	C₂×C₃×M₁₆	1	4	yes	—
453	C₃²	Q₈×M₁₆	1	1	yes	characteristic, complemented, Sylow
454	C₂³	—	3	1	no	—
455	Q₈	—	2	2	no	—
456	Q₈	—	3	4	no	—
457	Q₈	—	6	4	no	—
458	C₂×C₄	—	3	1	no	—
459	C₂×C₄	—	3	2	no	—
460	C₂×C₄	—	3	2	no	—
461	C₂×C₄	—	3	2	no	—
462	C₂×C₄	—	3	2	no	—
463	C₂×C₄	—	3	1	no	—
464	C₂×C₄	—	3	1	no	—
465	C₂×C₄	—	6	4	no	—
466	C₂×C₄	—	6	2	no	—
467	C₂×C₄	—	12	1	no	—
468	C₂×C₄	—	12	2	no	—
469	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
470	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
471	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
472	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
473	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
474	C₈	—	2	2	no	—
475	C₈	—	2	1	no	—
476	C₈	—	3	2	no	—
477	C₈	—	6	2	no	—
478	C₈	—	6	1	no	—
479	C₈	C₃×D₃×Q₈	1	2	yes	complemented
480	C₂×C₃	—	2	1	no	—
481	C₂×C₃	—	2	1	no	—
482	C₂×C₃	—	2	1	no	—
483	C₂×C₃	—	6	2	no	—
484	C₂×C₃	C₄×D₃×Q₈	1	1	yes	characteristic
485	C₂×C₃	C₂×D₃×M₁₆	1	1	yes	characteristic
486	C₂×C₃	#5750	1	1	yes	characteristic
487	C₂×C₃	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
488	C₂×C₃	C₂²×C₃×M₁₆	1	1	yes	characteristic
489	C₂×C₃	C₃×#568	1	1	yes	characteristic
490	D₃	—	2	2	no	—
491	C₂²	—	3	2	no	—
492	C₂²	—	6	1	no	—
493	C₂²	—	6	1	no	—
494	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
495	C₄	—	2	2	no	—
496	C₄	—	2	1	no	—
497	C₄	—	2	2	no	—
498	C₄	—	3	4	no	—
499	C₄	—	3	2	no	—
500	C₄	—	6	1	no	—
501	C₄	—	6	2	no	—
502	C₄	—	6	1	no	—
503	C₄	C₃×D₃×M₁₆	1	2	yes	—
504	C₄	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
505	C₄	C₃×D₃×#41	1	1	yes	characteristic
506	C₃	—	2	1	no	—
507	C₃	#79962	1	1	yes	characteristic, direct product factor
508	C₃	C₃×Q₈×M₁₆	1	1	yes	characteristic, complemented
509	C₂	—	6	2	no	—
510	C₂	C₃×C₄×D₃×Q₈	1	1	yes	characteristic
511	C₂	C₂×C₃×D₃×M₁₆	1	1	yes	characteristic
512	C₂	C₃×#5750	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#446	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂²×C₃×D₃	C₂²×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#446	D₃
hypocenter	C₃	C₃×Q₈×M₁₆
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#446

Complements

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

N	H ≅ G/N	type
2. C₃²×#446	C₂	semidirect
3. C₃×#5024	C₂	semidirect
6. C₃×#4830	C₂	semidirect
7. C₃×#4828	C₂	semidirect
9. C₃×#4701	C₂	semidirect
11. C₃×C₈×Dic₆	C₂	semidirect
13. #79962	C₃	direct (N × H)
49. C₃×#446	D₃	semidirect
50. C₃×#446	C₂×C₃	semidirect
57. #5024	C₂×C₃	semidirect
60. #4830	C₂×C₃	semidirect
61. #4828	C₂×C₃	semidirect
63. #4701	C₂×C₃	semidirect
65. C₈×Dic₆	C₂×C₃	semidirect
98. C₃×ΓL(1,𝔽₂₅)	Q₈	semidirect
182. C₃×Dic₆	M₁₆	semidirect
185. C₃²×C₈	C₂×Q₈	semidirect
188. C₃×C₃⋊C₈	C₂×Q₈	semidirect
193. #446	C₃×D₃	semidirect
273. ΓL(1,𝔽₂₅)	C₃×Q₈	semidirect
363. Dic₆	C₃×M₁₆	semidirect
374. C₃×C₈	D₃×Q₈	semidirect
375. C₃×C₈	C₂×C₃×Q₈	semidirect
378. C₃⋊C₈	C₂×C₃×Q₈	semidirect
453. C₃²	Q₈×M₁₆	semidirect
479. C₈	C₃×D₃×Q₈	semidirect
507. C₃	#79962	direct (N × H)
508. C₃	C₃×Q₈×M₁₆	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
C₃²×#446	2
C₃×#5024	2
C₃×#4837	2
C₃×#4830	2
C₃×#4828	2
C₃×#4707	2
C₃×#4701	2
C₃×C₄×ΓL(1,𝔽₂₅)	2
C₃×C₈×Dic₆	2
C₃×Q₈×M₁₆	3
#79962	3

Subgroups — C3×#79962 #11861500

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79962 #11861500