Subgroups — C₃×#79081 #11858337

Order 1152.

1025 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#907	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#901	C₂	1	1	yes	maximal, characteristic
3	C₃×#5522	C₂	1	1	yes	maximal, characteristic
4	C₃²×#424	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5118	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4999	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4839	C₂	1	2	yes	maximal, complemented
9	C₃×#4839	C₂	1	2	yes	maximal, complemented
10	C₃×#4837	C₂	1	2	yes	maximal, complemented
11	C₃×D₃×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
12	C₃×#2906	—	3	1	no	maximal
13	#79081	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×#235	C₂²	1	1	yes	characteristic
15	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
17	C₃²×#117	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₃×#208	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₃×#907	—	2	4	no	—
22	C₃×#901	—	2	4	no	—
23	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
24	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
25	C₂×C₃×D₃×C₈	C₂²	1	2	yes	—
26	C₂×C₃×D₃×C₈	C₂²	1	2	yes	—
27	C₃×#893	C₄	1	1	yes	characteristic
28	C₃×#893	C₄	1	1	yes	characteristic
29	C₃×#887	C₄	1	1	yes	characteristic
30	C₃×#887	C₄	1	1	yes	characteristic
31	C₃×#67⋊C₄	C₄	1	2	yes	—
32	C₃×#67⋊C₄	C₄	1	2	yes	—
33	C₃×#872	C₂²	1	2	yes	—
34	C₃×C₄²×D₃	C₂²	1	2	yes	—
35	C₃²×C₄⋊C₈	C₂²	1	2	yes	—
36	C₃²×C₄⋊C₈	C₂²	1	2	yes	—
37	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
38	C₃×Dic₃⋊C₈	C₂²	1	2	yes	—
39	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
40	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
41	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
42	C₃×Dic₃⋊C₈	C₂²	1	2	yes	—
43	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
44	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
45	C₂×C₃×#131	—	3	1	no	—
46	C₂×C₃×#131	—	3	1	no	—
47	C₃×C₄×#41	—	3	1	no	—
48	C₂×#907	C₂×C₃	1	1	yes	characteristic
49	C₂×#901	C₂×C₃	1	1	yes	characteristic
50	#5522	C₂×C₃	1	1	yes	characteristic
51	C₃×#424	—	2	1	no	—
52	C₃×#424	—	3	1	no	—
53	C₃×#424	—	3	2	no	—
54	C₃×#424	—	3	2	no	—
55	C₃×#424	D₃	1	1	yes	characteristic, complemented
56	C₃×#424	C₂×C₃	1	1	yes	characteristic, complemented
57	C₃×#423	—	3	1	no	—
58	C₃×#423	—	3	2	no	—
59	C₂×C₃×C₄⋊C₈	—	3	1	no	—
60	C₂×C₃×C₄⋊C₈	—	3	2	no	—
61	#5118	C₂×C₃	1	1	yes	characteristic, complemented
62	C₂×Dic₃⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
63	#4999	C₂×C₃	1	1	yes	characteristic, complemented
64	#4839	C₂×C₃	1	2	yes	complemented
65	#4839	C₂×C₃	1	2	yes	complemented
66	#4837	C₂×C₃	1	2	yes	complemented
67	D₃×C₄⋊C₈	C₂×C₃	1	2	yes	complemented
68	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
69	C₂×C₃×#67	C₂×C₄	1	2	yes	—
70	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
72	C₃×#235	D₄	1	4	yes	—
73	C₃×#235	Q₈	1	4	yes	—
74	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
75	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
76	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
77	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
78	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
79	C₃²×M₁₆	—	2	2	no	—
80	C₂×C₃²×C₈	—	2	2	no	—
81	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
82	C₂×C₃²×C₈	C₂³	1	2	yes	—
83	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
84	C₃²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₃²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₃²×C₂²⋊C₄	C₂×C₄	1	2	yes	—
87	C₃²×C₄²	C₂³	1	2	yes	—
88	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
89	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
90	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
91	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
92	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
93	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
94	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
95	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
96	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
97	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
98	C₃×#208	—	2	2	no	—
99	C₂×C₃×C₃⋊C₈	—	2	2	no	—
100	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
102	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
103	C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
104	C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
105	C₃×D₃×C₈	—	2	4	no	—
106	C₃×D₃×C₈	—	2	4	no	—
107	#2906	—	3	1	no	Sylow
108	C₂×C₃×#41	—	3	1	no	—
109	C₂×#235	C₂²×C₃	1	1	yes	characteristic
110	C₃×#131	—	6	4	no	—
111	C₃×#131	—	6	4	no	—
112	C₂×C₃×M₁₆	—	2	1	no	—
113	C₂×C₃×M₁₆	—	3	1	no	—
114	C₂×C₃×M₁₆	—	3	2	no	—
115	C₂×C₃×M₁₆	—	3	2	no	—
116	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
117	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
118	C₂²×C₃×C₈	—	2	1	no	—
119	C₂²×C₃×C₈	—	3	1	no	—
120	C₂²×C₃×C₈	—	3	2	no	—
121	C₂²×C₃×C₈	—	3	2	no	—
122	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
123	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
124	C₃×C₄×Q₈	—	3	1	no	—
125	C₃×C₄×Q₈	—	3	1	no	—
126	C₃×C₄×D₄	—	3	1	no	—
127	C₃×C₄×D₄	—	3	1	no	—
128	C₃×C₄×D₄	—	3	2	no	—
129	C₃×C₄×D₄	—	3	2	no	—
130	C₃×#117	—	2	1	no	—
131	C₃×#117	—	3	2	no	—
132	C₃×#117	C₂×D₃	1	1	yes	characteristic
133	C₃×#117	C₂²×C₃	1	1	yes	characteristic
134	C₂×C₃×C₄²	—	3	1	no	—
135	C₂×C₃×C₄²	—	3	2	no	—
136	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
137	C₂×#208	C₂²×C₃	1	1	yes	characteristic
138	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
139	#907	—	2	4	no	—
140	#901	—	2	4	no	—
141	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	—
142	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	—
143	C₂×D₃×C₈	C₂²×C₃	1	2	yes	—
144	C₂×D₃×C₈	C₂²×C₃	1	2	yes	—
145	#893	C₃×C₄	1	1	yes	characteristic
146	#893	C₃×C₄	1	1	yes	characteristic
147	#887	C₃×C₄	1	1	yes	characteristic
148	#887	C₃×C₄	1	1	yes	characteristic
149	#67⋊C₄	C₃×C₄	1	2	yes	—
150	#67⋊C₄	C₃×C₄	1	2	yes	—
151	#872	C₂²×C₃	1	2	yes	—
152	C₄²×D₃	C₂²×C₃	1	2	yes	—
153	C₃×C₄⋊C₈	—	2	2	no	—
154	C₃×C₄⋊C₈	—	2	2	no	—
155	C₃×C₄⋊C₈	—	3	1	no	—
156	C₃×C₄⋊C₈	—	3	2	no	—
157	C₃×C₄⋊C₈	—	3	1	no	—
158	C₃×C₄⋊C₈	—	3	1	no	—
159	C₃×C₄⋊C₈	—	3	1	no	—
160	C₃×C₄⋊C₈	—	3	2	no	—
161	C₃×C₄⋊C₈	—	3	2	no	—
162	C₃×C₄⋊C₈	—	3	2	no	—
163	C₃×C₄⋊C₈	C₂×D₃	1	2	yes	—
164	C₃×C₄⋊C₈	C₂×D₃	1	2	yes	—
165	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
166	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
167	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
168	Dic₃⋊C₈	C₂²×C₃	1	2	yes	—
169	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
170	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
171	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
172	Dic₃⋊C₈	C₂²×C₃	1	2	yes	—
173	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	—
174	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	—
175	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₃×D₃	C₂²×C₄	1	2	yes	—
177	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
178	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
179	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
181	C₂×C₃²×C₄	C₂×Q₈	1	2	yes	—
182	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
183	C₃×#67	C₄⋊C₄	1	8	yes	—
184	C₂×C₃×Dic₃	—	2	2	no	—
185	C₂×C₃×Dic₃	—	4	1	no	—
186	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
190	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
191	C₃×D₁₂	C₄⋊C₄	1	4	yes	—
192	C₃×C₄×D₃	—	2	4	no	—
193	C₃×C₄×D₃	—	4	2	no	—
194	C₃×C₄×D₃	C₂×D₄	1	4	yes	—
195	C₃×C₄×D₃	C₂×Q₈	1	4	yes	—
196	C₃×Dic₆	C₄⋊C₄	1	4	yes	—
197	C₃²×C₈	—	2	1	no	—
198	C₃²×C₈	—	2	2	no	—
199	C₃²×C₈	—	2	1	no	—
200	C₃×C₃⋊C₈	—	2	1	no	—
201	C₃×C₃⋊C₈	—	2	2	no	—
202	C₃×C₃⋊C₈	—	2	1	no	—
203	C₂×#131	—	3	1	no	—
204	C₂×#131	—	3	1	no	—
205	C₄×#41	—	3	1	no	—
206	#424	—	3	1	no	—
207	#424	—	3	2	no	—
208	#424	—	3	2	no	—
209	#424	C₃×D₃	1	1	yes	characteristic, complemented
210	#423	—	3	1	no	—
211	#423	—	3	2	no	—
212	C₂×C₄⋊C₈	—	3	1	no	—
213	C₂×C₄⋊C₈	—	3	2	no	—
214	C₃×#41	—	3	4	no	—
215	C₃×#41	—	3	4	no	—
216	C₂×C₃×Q₈	—	3	1	no	—
217	C₂×C₃×D₄	—	3	2	no	—
218	C₂×C₃×D₄	—	3	1	no	—
219	C₂²×C₃×C₄	—	2	1	no	—
220	C₂²×C₃×C₄	—	3	2	no	—
221	C₂²×C₃×C₄	—	3	1	no	—
222	C₂²×C₃×C₄	—	3	1	no	—
223	C₂²×C₃×C₄	—	3	2	no	—
224	C₂²×C₃×C₄	—	3	2	no	—
225	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
227	C₂×#67	C₂×C₃×C₄	1	2	yes	—
228	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
229	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
230	#235	C₃×D₄	1	4	yes	—
231	#235	C₃×Q₈	1	4	yes	—
232	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
233	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
234	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
235	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
236	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
237	C₃×M₁₆	—	2	2	no	—
238	C₃×M₁₆	—	2	2	no	—
239	C₃×M₁₆	—	4	2	no	—
240	C₃×M₁₆	—	6	4	no	—
241	C₃×M₁₆	—	6	4	no	—
242	C₃×M₁₆	—	6	2	no	—
243	C₂×C₃×C₈	—	2	2	no	—
244	C₂×C₃×C₈	—	2	2	no	—
245	C₂×C₃×C₈	—	2	1	no	—
246	C₂×C₃×C₈	—	2	1	no	—
247	C₂×C₃×C₈	—	2	2	no	—
248	C₂×C₃×C₈	—	3	1	no	—
249	C₂×C₃×C₈	—	3	1	no	—
250	C₂×C₃×C₈	—	3	2	no	—
251	C₂×C₃×C₈	—	4	2	no	—
252	C₂×C₃×C₈	—	6	4	no	—
253	C₂×C₃×C₈	—	6	4	no	—
254	C₂×C₃×C₈	—	6	2	no	—
255	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
256	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
257	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
258	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
259	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
260	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
261	C₃×C₄⋊C₄	—	2	1	no	—
262	C₃×C₄⋊C₄	—	2	1	no	—
263	C₃×C₄⋊C₄	—	3	2	no	—
264	C₃×C₄⋊C₄	—	3	2	no	—
265	C₃×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
266	C₃×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
267	C₃×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
268	C₃×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
269	C₃×C₂²⋊C₄	—	2	2	no	—
270	C₃×C₂²⋊C₄	—	3	2	no	—
271	C₃×C₂²⋊C₄	—	3	2	no	—
272	C₃×C₂²⋊C₄	C₄×D₃	1	2	yes	—
273	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
274	C₃×C₄²	—	2	2	no	—
275	C₃×C₄²	—	3	2	no	—
276	C₃×C₄²	—	3	1	no	—
277	C₃×C₄²	—	3	2	no	—
278	C₃×C₄²	—	3	1	no	—
279	C₃×C₄²	—	3	1	no	—
280	C₃×C₄²	—	3	1	no	—
281	C₃×C₄²	C₂²×D₃	1	2	yes	—
282	C₃×C₄²	C₂³×C₃	1	2	yes	—
283	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	2	yes	—
284	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	2	yes	—
285	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
286	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
287	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
288	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
289	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
290	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
291	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
292	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
293	#208	—	2	2	no	—
294	C₂×C₃⋊C₈	—	2	2	no	—
295	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
296	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
297	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
298	ΓL(1,𝔽₂₅)	—	2	4	no	—
299	ΓL(1,𝔽₂₅)	—	2	4	no	—
300	D₃×C₈	—	2	4	no	—
301	D₃×C₈	—	2	4	no	—
302	C₂²×C₃²	—	2	1	no	—
303	C₂²×C₃²	—	2	1	no	—
304	C₂²×C₃²	C₂×C₄⋊C₄	1	2	yes	—
305	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
306	C₂×C₃×D₃	—	2	2	no	—
307	C₂×C₃×D₃	—	2	2	no	—
308	C₂×C₃×D₃	C₂×C₄⋊C₄	1	4	yes	—
309	C₃²×C₄	—	2	2	no	—
310	C₃²×C₄	—	2	2	no	—
311	C₃²×C₄	C₂×C₄⋊C₄	1	2	yes	—
312	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
313	C₃²×C₄	C₂²×Q₈	1	1	yes	characteristic
314	C₃×Dic₃	—	2	1	no	—
315	C₃×Dic₃	—	2	1	no	—
316	C₃×Dic₃	—	2	1	no	—
317	C₃×Dic₃	C₂×C₄⋊C₄	1	4	yes	—
318	C₃×Dic₃	#131	1	2	yes	complemented
319	C₂×#41	—	3	1	no	—
320	#131	—	6	4	no	—
321	#131	—	6	4	no	—
322	C₂×M₁₆	—	3	1	no	—
323	C₂×M₁₆	—	3	2	no	—
324	C₂×M₁₆	—	3	2	no	—
325	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
326	C₂²×C₈	—	3	1	no	—
327	C₂²×C₈	—	3	2	no	—
328	C₂²×C₈	—	3	2	no	—
329	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
330	C₄×Q₈	—	3	1	no	—
331	C₄×Q₈	—	3	1	no	—
332	C₄×D₄	—	3	1	no	—
333	C₄×D₄	—	3	1	no	—
334	C₄×D₄	—	3	2	no	—
335	C₄×D₄	—	3	2	no	—
336	#117	—	3	2	no	—
337	#117	C₂×C₃×D₃	1	1	yes	characteristic
338	C₂×C₄²	—	3	1	no	—
339	C₂×C₄²	—	3	2	no	—
340	C₄⋊C₈	—	3	1	no	—
341	C₄⋊C₈	—	3	2	no	—
342	C₄⋊C₈	—	3	1	no	—
343	C₄⋊C₈	—	3	1	no	—
344	C₄⋊C₈	—	3	1	no	—
345	C₄⋊C₈	—	3	2	no	—
346	C₄⋊C₈	—	3	2	no	—
347	C₄⋊C₈	—	3	2	no	—
348	C₄⋊C₈	C₂×C₃×D₃	1	2	yes	—
349	C₄⋊C₈	C₂×C₃×D₃	1	2	yes	—
350	C₂³×C₃	—	2	1	no	—
351	C₂³×C₃	—	3	2	no	—
352	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
353	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
354	C₂²×D₃	C₂²×C₃×C₄	1	2	yes	—
355	C₃×Q₈	—	3	4	no	—
356	C₃×D₄	—	3	8	no	—
357	C₃×D₄	—	3	4	no	—
358	C₂×C₃×C₄	—	2	1	no	—
359	C₂×C₃×C₄	—	2	1	no	—
360	C₂×C₃×C₄	—	2	2	no	—
361	C₂×C₃×C₄	—	2	2	no	—
362	C₂×C₃×C₄	—	2	2	no	—
363	C₂×C₃×C₄	—	2	2	no	—
364	C₂×C₃×C₄	—	3	1	no	—
365	C₂×C₃×C₄	—	3	2	no	—
366	C₂×C₃×C₄	—	3	4	no	—
367	C₂×C₃×C₄	—	3	4	no	—
368	C₂×C₃×C₄	—	3	1	no	—
369	C₂×C₃×C₄	—	3	1	no	—
370	C₂×C₃×C₄	—	3	1	no	—
371	C₂×C₃×C₄	—	6	4	no	—
372	C₂×C₃×C₄	—	6	2	no	—
373	C₂×C₃×C₄	—	12	2	no	—
374	C₂×C₃×C₄	—	12	1	no	—
375	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
376	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
377	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
378	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
379	C₂×C₃×C₄	D₃×Q₈	1	2	yes	—
380	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
381	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
382	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
383	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
384	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
385	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
386	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
387	#67	C₃×C₄⋊C₄	1	8	yes	—
388	C₂×Dic₃	—	2	2	no	—
389	C₂×Dic₃	—	4	1	no	—
390	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
391	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
392	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
393	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
394	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
395	D₁₂	C₃×C₄⋊C₄	1	4	yes	—
396	C₄×D₃	—	2	4	no	—
397	C₄×D₃	—	4	2	no	—
398	C₄×D₃	C₂×C₃×D₄	1	4	yes	—
399	C₄×D₃	C₂×C₃×Q₈	1	4	yes	—
400	Dic₆	C₃×C₄⋊C₄	1	4	yes	—
401	C₃×C₈	—	2	1	no	—
402	C₃×C₈	—	2	1	no	—
403	C₃×C₈	—	2	2	no	—
404	C₃×C₈	—	2	1	no	—
405	C₃×C₈	—	2	2	no	—
406	C₃×C₈	—	2	1	no	—
407	C₃×C₈	—	4	1	no	—
408	C₃×C₈	—	4	1	no	—
409	C₃×C₈	—	4	2	no	—
410	C₃×C₈	—	6	1	no	—
411	C₃×C₈	—	6	2	no	—
412	C₃×C₈	—	6	1	no	—
413	C₃⋊C₈	—	2	1	no	—
414	C₃⋊C₈	—	2	2	no	—
415	C₃⋊C₈	—	2	1	no	—
416	C₂×C₃²	—	2	2	no	—
417	C₂×C₃²	C₂²×C₄⋊C₄	1	1	yes	characteristic
418	C₂×C₃²	C₂×#131	1	1	yes	characteristic
419	C₂×C₃²	#568	1	1	yes	characteristic
420	C₃×D₃	—	2	4	no	—
421	#41	—	3	4	no	—
422	#41	—	3	4	no	—
423	C₂×Q₈	—	3	1	no	—
424	C₂×D₄	—	3	2	no	—
425	C₂×D₄	—	3	1	no	—
426	C₂²×C₄	—	3	2	no	—
427	C₂²×C₄	—	3	1	no	—
428	C₂²×C₄	—	3	1	no	—
429	C₂²×C₄	—	3	2	no	—
430	C₂²×C₄	—	3	2	no	—
431	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
432	M₁₆	—	2	2	no	—
433	M₁₆	—	6	4	no	—
434	M₁₆	—	6	4	no	—
435	M₁₆	—	6	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	3	1	no	—
438	C₂×C₈	—	3	1	no	—
439	C₂×C₈	—	3	2	no	—
440	C₂×C₈	—	6	4	no	—
441	C₂×C₈	—	6	4	no	—
442	C₂×C₈	—	6	2	no	—
443	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
444	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
445	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
446	C₄⋊C₄	—	3	2	no	—
447	C₄⋊C₄	—	3	2	no	—
448	C₄⋊C₄	C₃×C₄×D₃	1	1	yes	characteristic
449	C₄⋊C₄	C₃×C₄×D₃	1	1	yes	characteristic
450	C₂²⋊C₄	—	3	2	no	—
451	C₂²⋊C₄	—	3	2	no	—
452	C₂²⋊C₄	C₃×C₄×D₃	1	2	yes	—
453	C₄²	—	3	1	no	—
454	C₄²	—	3	1	no	—
455	C₄²	—	3	2	no	—
456	C₄²	—	3	1	no	—
457	C₄²	—	3	2	no	—
458	C₄²	—	3	1	no	—
459	C₄²	C₂²×C₃×D₃	1	2	yes	—
460	C₂²×C₃	—	2	1	no	—
461	C₂²×C₃	—	2	1	no	—
462	C₂²×C₃	—	2	1	no	—
463	C₂²×C₃	—	2	1	no	—
464	C₂²×C₃	—	2	2	no	—
465	C₂²×C₃	—	2	1	no	—
466	C₂²×C₃	—	3	4	no	—
467	C₂²×C₃	—	4	1	no	—
468	C₂²×C₃	—	4	1	no	—
469	C₂²×C₃	—	6	2	no	—
470	C₂²×C₃	—	6	2	no	—
471	C₂²×C₃	D₃×C₄⋊C₄	1	2	yes	—
472	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	2	yes	—
473	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
474	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
475	C₂×D₃	—	2	2	no	—
476	C₂×D₃	—	2	2	no	—
477	C₂×D₃	C₂×C₃×C₄⋊C₄	1	4	yes	—
478	C₃×C₄	—	2	2	no	—
479	C₃×C₄	—	2	2	no	—
480	C₃×C₄	—	2	2	no	—
481	C₃×C₄	—	2	2	no	—
482	C₃×C₄	—	2	2	no	—
483	C₃×C₄	—	2	1	no	—
484	C₃×C₄	—	2	1	no	—
485	C₃×C₄	—	3	2	no	—
486	C₃×C₄	—	3	4	no	—
487	C₃×C₄	—	4	2	no	—
488	C₃×C₄	—	4	2	no	—
489	C₃×C₄	—	6	1	no	—
490	C₃×C₄	—	6	1	no	—
491	C₃×C₄	—	6	1	no	—
492	C₃×C₄	D₃×C₄⋊C₄	1	2	yes	—
493	C₃×C₄	C₂×C₃×C₄⋊C₄	1	2	yes	—
494	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
495	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
496	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
497	C₃×C₄	C₂²×C₃×Q₈	1	1	yes	characteristic
498	Dic₃	—	2	1	no	—
499	Dic₃	—	2	1	no	—
500	Dic₃	—	2	1	no	—
501	Dic₃	C₂×C₃×C₄⋊C₄	1	4	yes	—
502	Dic₃	C₃×#131	1	2	yes	complemented
503	C₃²	#2906	1	1	yes	characteristic, complemented, Sylow
504	C₂³	—	3	2	no	—
505	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
506	Q₈	—	3	4	no	—
507	D₄	—	3	8	no	—
508	D₄	—	3	4	no	—
509	C₂×C₄	—	3	1	no	—
510	C₂×C₄	—	3	2	no	—
511	C₂×C₄	—	3	4	no	—
512	C₂×C₄	—	3	4	no	—
513	C₂×C₄	—	3	1	no	—
514	C₂×C₄	—	3	1	no	—
515	C₂×C₄	—	3	1	no	—
516	C₂×C₄	—	6	4	no	—
517	C₂×C₄	—	6	2	no	—
518	C₂×C₄	—	12	2	no	—
519	C₂×C₄	—	12	1	no	—
520	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
521	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
522	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
523	C₂×C₄	C₃×D₃×D₄	1	2	yes	—
524	C₂×C₄	C₃×D₃×Q₈	1	2	yes	—
525	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
526	C₈	—	2	1	no	—
527	C₈	—	2	1	no	—
528	C₈	—	2	2	no	—
529	C₈	—	6	1	no	—
530	C₈	—	6	2	no	—
531	C₈	—	6	1	no	—
532	C₂×C₃	—	2	2	no	—
533	C₂×C₃	—	2	2	no	—
534	C₂×C₃	—	2	1	no	—
535	C₂×C₃	—	2	1	no	—
536	C₂×C₃	—	2	1	no	—
537	C₂×C₃	—	4	2	no	—
538	C₂×C₃	—	6	4	no	—
539	C₂×C₃	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
540	C₂×C₃	D₃×#131	1	1	yes	characteristic
541	C₂×C₃	#5750	1	1	yes	characteristic
542	C₂×C₃	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
543	C₂×C₃	C₂×C₃×#131	1	1	yes	characteristic
544	C₂×C₃	C₃×#568	1	1	yes	characteristic
545	D₃	—	2	4	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	3	4	no	—
549	C₂²	—	6	2	no	—
550	C₂²	—	6	2	no	—
551	C₂²	C₃×D₃×C₄⋊C₄	1	2	yes	—
552	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
553	C₄	—	2	2	no	—
554	C₄	—	2	2	no	—
555	C₄	—	3	2	no	—
556	C₄	—	3	4	no	—
557	C₄	—	6	1	no	—
558	C₄	—	6	1	no	—
559	C₄	—	6	1	no	—
560	C₄	C₃×D₃×C₄⋊C₄	1	2	yes	—
561	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
562	C₄	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
563	C₃	—	2	1	no	—
564	C₃	#79081	1	1	yes	characteristic, direct product factor
565	C₃	C₃×#2906	1	1	yes	characteristic, complemented
566	C₂	—	2	2	no	—
567	C₂	—	6	4	no	—
568	C₂	C₂×C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
569	C₂	C₃×D₃×#131	1	1	yes	characteristic
570	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×#424	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂×C₃×#235	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#424	D₃
hypocenter	C₃	C₃×#2906
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×#5118	C₂	semidirect
6. C₂×C₃×Dic₃⋊C₈	C₂	semidirect
7. C₃×#4999	C₂	semidirect
8. C₃×#4839	C₂	semidirect
9. C₃×#4839	C₂	semidirect
10. C₃×#4837	C₂	semidirect
11. C₃×D₃×C₄⋊C₈	C₂	semidirect
13. #79081	C₃	direct (N × H)
55. C₃×#424	D₃	semidirect
56. C₃×#424	C₂×C₃	semidirect
61. #5118	C₂×C₃	semidirect
62. C₂×Dic₃⋊C₈	C₂×C₃	semidirect
63. #4999	C₂×C₃	semidirect
64. #4839	C₂×C₃	semidirect
65. #4839	C₂×C₃	semidirect
66. #4837	C₂×C₃	semidirect
67. D₃×C₄⋊C₈	C₂×C₃	semidirect
209. #424	C₃×D₃	semidirect
318. C₃×Dic₃	#131	semidirect
502. Dic₃	C₃×#131	semidirect
503. C₃²	#2906	semidirect
564. C₃	#79081	direct (N × H)
565. C₃	C₃×#2906	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#907	2
C₂×C₃×#901	2
C₃×#5522	2
C₃²×#424	2
C₃×#5118	2
C₂×C₃×Dic₃⋊C₈	2
C₃×#4999	2
C₃×#4839	2
C₃×#4837	2
C₃×D₃×C₄⋊C₈	2
C₃×#2906	3
#79081	3

Subgroups — C3×#79081 #11858337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79081 #11858337