Subgroups — C₃×#79012 #11858331

Order 1152.

1037 conjugacy classes of subgroups.

The subgroup lattice has 493 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#901	C₂	1	2	yes	maximal
2	C₃×C₄×#235	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃²×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5102	C₂	1	2	yes	maximal, complemented
5	C₃×#4924	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4839	C₂	1	4	yes	maximal, complemented
7	C₃×#4837	C₂	1	2	yes	maximal, complemented
8	C₃×D₃×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
9	C₃×#2906	—	3	1	no	maximal
10	#79012	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂×C₃×#235	C₂²	1	1	yes	characteristic
12	C₂²×C₃²×C₈	C₂²	1	2	yes	—
13	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
14	C₃×C₄×#67	C₄	1	2	yes	—
15	C₃×C₄×#67	C₄	1	2	yes	—
16	C₃×#926	C₂²	1	1	yes	characteristic
17	C₂×C₃×#208	C₂²	1	2	yes	—
18	C₃×#901	—	2	8	no	—
19	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	—
20	C₂×C₃×D₃×C₈	C₂²	1	4	yes	—
21	C₃×C₄×D₁₂	C₄	1	1	yes	characteristic
22	C₃×C₄×D₁₂	C₄	1	1	yes	characteristic
23	C₃×#872	C₂²	1	2	yes	—
24	C₃×C₄²×D₃	C₂²	1	2	yes	—
25	C₃×C₄×Dic₆	C₄	1	1	yes	characteristic
26	C₃×C₄×Dic₆	C₄	1	1	yes	characteristic
27	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₃²×C₄⋊C₈	C₂²	1	2	yes	—
30	C₃×Dic₃⋊C₈	C₂²	1	4	yes	—
31	C₃×Dic₃⋊C₈	C₂²	1	4	yes	—
32	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
33	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
34	C₂×C₃×#131	—	3	2	no	—
35	C₃×C₄×#41	—	3	1	no	—
36	C₂×#901	C₂×C₃	1	2	yes	—
37	C₄×#235	C₂×C₃	1	1	yes	characteristic
38	C₃×#424	—	3	2	no	—
39	C₃×#424	—	3	4	no	—
40	C₃×#423	—	3	1	no	—
41	C₃×#423	—	3	2	no	—
42	C₂×C₃×C₄⋊C₈	—	2	1	no	—
43	C₂×C₃×C₄⋊C₈	—	3	2	no	—
44	C₂×C₃×C₄⋊C₈	D₃	1	1	yes	characteristic, complemented
45	C₂×C₃×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
46	#5102	C₂×C₃	1	2	yes	complemented
47	#4924	C₂×C₃	1	1	yes	characteristic, complemented
48	#4839	C₂×C₃	1	4	yes	complemented
49	#4837	C₂×C₃	1	2	yes	complemented
50	D₃×C₄⋊C₈	C₂×C₃	1	2	yes	complemented
51	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
54	C₂×C₃×#67	C₂×C₄	1	2	yes	—
55	C₃×#235	D₄	1	4	yes	—
56	C₃×#235	Q₈	1	4	yes	—
57	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
58	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
59	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
60	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
61	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
62	C₂×C₃²×C₈	—	2	4	no	—
63	C₂×C₃²×C₈	C₂³	1	2	yes	—
64	C₂×C₃²×C₈	C₂³	1	2	yes	—
65	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
66	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
67	C₃²×C₄²	C₂³	1	1	yes	characteristic
68	C₃²×C₄²	C₂³	1	1	yes	characteristic
69	C₃×#217	C₂×C₄	1	2	yes	—
70	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
71	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
72	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
73	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
74	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
75	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
76	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
77	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
78	C₃×C₄×Dic₃	C₂³	1	2	yes	—
79	C₃×#208	—	2	4	no	—
80	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	—
81	C₃×ΓL(1,𝔽₂₅)	—	2	8	no	—
82	C₃×D₃×C₈	—	2	8	no	—
83	#2906	—	3	1	no	Sylow
84	C₂×C₃×#41	—	3	1	no	—
85	C₂×#235	C₂²×C₃	1	1	yes	characteristic
86	C₃×#131	—	6	8	no	—
87	C₂×C₃×M₁₆	—	3	2	no	—
88	C₂×C₃×M₁₆	—	3	4	no	—
89	C₂²×C₃×C₈	—	2	2	no	—
90	C₂²×C₃×C₈	—	3	4	no	—
91	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
92	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
93	C₃×C₄×Q₈	—	3	1	no	—
94	C₃×C₄×Q₈	—	3	1	no	—
95	C₃×C₄×D₄	—	3	2	no	—
96	C₃×C₄×D₄	—	3	2	no	—
97	C₃×C₄×D₄	—	3	1	no	—
98	C₃×C₄×D₄	—	3	1	no	—
99	C₃×#117	—	3	1	no	—
100	C₃×#117	—	3	2	no	—
101	C₂×C₃×C₄²	—	2	1	no	—
102	C₂×C₃×C₄²	—	3	2	no	—
103	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
104	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
105	C₄×#67	C₃×C₄	1	2	yes	—
106	C₄×#67	C₃×C₄	1	2	yes	—
107	#926	C₂²×C₃	1	1	yes	characteristic
108	C₂×#208	C₂²×C₃	1	2	yes	—
109	#901	—	2	8	no	—
110	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	4	yes	—
111	C₂×D₃×C₈	C₂²×C₃	1	4	yes	—
112	C₄×D₁₂	C₃×C₄	1	1	yes	characteristic
113	C₄×D₁₂	C₃×C₄	1	1	yes	characteristic
114	#872	C₂²×C₃	1	2	yes	—
115	C₄²×D₃	C₂²×C₃	1	2	yes	—
116	C₄×Dic₆	C₃×C₄	1	1	yes	characteristic
117	C₄×Dic₆	C₃×C₄	1	1	yes	characteristic
118	C₃×C₄⋊C₈	—	2	1	no	—
119	C₃×C₄⋊C₈	—	2	1	no	—
120	C₃×C₄⋊C₈	—	2	2	no	—
121	C₃×C₄⋊C₈	—	3	4	no	—
122	C₃×C₄⋊C₈	—	3	4	no	—
123	C₃×C₄⋊C₈	—	3	2	no	—
124	C₃×C₄⋊C₈	—	3	2	no	—
125	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
126	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
127	C₃×C₄⋊C₈	C₂×D₃	1	2	yes	—
128	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
129	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
130	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
131	Dic₃⋊C₈	C₂²×C₃	1	4	yes	—
132	Dic₃⋊C₈	C₂²×C₃	1	4	yes	—
133	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	—
134	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	—
135	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₃×D₃	C₂²×C₄	1	2	yes	—
137	C₂×C₃²×C₄	—	2	2	no	—
138	C₂×C₃²×C₄	—	4	1	no	—
139	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
145	C₂×C₃²×C₄	C₂×Q₈	1	2	yes	—
146	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
147	C₃×#67	C₄⋊C₄	1	8	yes	—
148	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
149	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
150	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
151	C₃×D₁₂	C₄⋊C₄	1	4	yes	—
152	C₃×C₄×D₃	—	2	4	no	—
153	C₃×C₄×D₃	—	4	2	no	—
154	C₃×C₄×D₃	C₂×D₄	1	4	yes	—
155	C₃×C₄×D₃	C₂×Q₈	1	4	yes	—
156	C₃×Dic₆	C₄⋊C₄	1	4	yes	—
157	C₃²×C₈	—	2	2	no	—
158	C₃²×C₈	—	2	2	no	—
159	C₃×C₃⋊C₈	—	2	4	no	—
160	C₂×#131	—	3	2	no	—
161	C₄×#41	—	3	1	no	—
162	#424	—	3	2	no	—
163	#424	—	3	4	no	—
164	#423	—	3	1	no	—
165	#423	—	3	2	no	—
166	C₂×C₄⋊C₈	—	3	2	no	—
167	C₂×C₄⋊C₈	C₃×D₃	1	1	yes	characteristic, complemented
168	C₃×#41	—	3	4	no	—
169	C₃×#41	—	3	4	no	—
170	C₂×C₃×Q₈	—	3	1	no	—
171	C₂×C₃×D₄	—	3	2	no	—
172	C₂×C₃×D₄	—	3	1	no	—
173	C₂²×C₃×C₄	—	2	1	no	—
174	C₂²×C₃×C₄	—	2	1	no	—
175	C₂²×C₃×C₄	—	2	1	no	—
176	C₂²×C₃×C₄	—	3	2	no	—
177	C₂²×C₃×C₄	—	3	2	no	—
178	C₂²×C₃×C₄	—	3	2	no	—
179	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
180	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
181	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
184	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
185	C₂×#67	C₂×C₃×C₄	1	2	yes	—
186	#235	C₃×D₄	1	4	yes	—
187	#235	C₃×Q₈	1	4	yes	—
188	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
189	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
190	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
191	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
192	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
193	C₃×M₁₆	—	6	8	no	—
194	C₃×M₁₆	—	6	4	no	—
195	C₂×C₃×C₈	—	2	4	no	—
196	C₂×C₃×C₈	—	2	4	no	—
197	C₂×C₃×C₈	—	2	2	no	—
198	C₂×C₃×C₈	—	2	2	no	—
199	C₂×C₃×C₈	—	3	4	no	—
200	C₂×C₃×C₈	—	4	4	no	—
201	C₂×C₃×C₈	—	6	8	no	—
202	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
203	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
204	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
205	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
206	C₃×C₄⋊C₄	—	3	2	no	—
207	C₃×C₄⋊C₄	—	3	2	no	—
208	C₃×C₄⋊C₄	—	3	1	no	—
209	C₃×C₄⋊C₄	—	3	1	no	—
210	C₃×C₂²⋊C₄	—	3	2	no	—
211	C₃×C₂²⋊C₄	—	3	2	no	—
212	C₃×C₂²⋊C₄	—	3	2	no	—
213	C₃×C₄²	—	2	1	no	—
214	C₃×C₄²	—	2	1	no	—
215	C₃×C₄²	—	2	1	no	—
216	C₃×C₄²	—	2	1	no	—
217	C₃×C₄²	—	3	2	no	—
218	C₃×C₄²	—	3	2	no	—
219	C₃×C₄²	—	3	2	no	—
220	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
221	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
222	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
223	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
224	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
225	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
226	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
227	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
228	#217	C₂×C₃×C₄	1	2	yes	—
229	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	2	yes	—
230	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	2	yes	—
231	C₄⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
232	C₄⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
233	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
234	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
235	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
236	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
237	C₄×Dic₃	C₂³×C₃	1	2	yes	—
238	#208	—	2	4	no	—
239	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
240	ΓL(1,𝔽₂₅)	—	2	8	no	—
241	D₃×C₈	—	2	8	no	—
242	C₂²×C₃²	—	2	1	no	—
243	C₂²×C₃²	—	2	1	no	—
244	C₂²×C₃²	C₂×C₄⋊C₄	1	2	yes	—
245	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
246	C₂×C₃×D₃	—	2	2	no	—
247	C₂×C₃×D₃	—	2	2	no	—
248	C₂×C₃×D₃	C₂×C₄⋊C₄	1	4	yes	—
249	C₃²×C₄	—	2	1	no	—
250	C₃²×C₄	—	2	1	no	—
251	C₃²×C₄	—	2	1	no	—
252	C₃²×C₄	C₂×C₄⋊C₄	1	2	yes	—
253	C₃²×C₄	#131	1	2	yes	complemented
254	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
255	C₃²×C₄	C₂²×Q₈	1	1	yes	characteristic
256	C₃×Dic₃	—	2	2	no	—
257	C₃×Dic₃	—	2	2	no	—
258	C₃×Dic₃	C₂×C₄⋊C₄	1	4	yes	—
259	C₂×#41	—	3	1	no	—
260	#131	—	6	8	no	—
261	C₂×M₁₆	—	3	2	no	—
262	C₂×M₁₆	—	3	4	no	—
263	C₂²×C₈	—	3	4	no	—
264	C₂²×C₈	C₂×C₃×D₃	1	2	yes	—
265	C₄×Q₈	—	3	1	no	—
266	C₄×Q₈	—	3	1	no	—
267	C₄×D₄	—	3	2	no	—
268	C₄×D₄	—	3	2	no	—
269	C₄×D₄	—	3	1	no	—
270	C₄×D₄	—	3	1	no	—
271	#117	—	3	1	no	—
272	#117	—	3	2	no	—
273	C₂×C₄²	—	3	2	no	—
274	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
275	C₄⋊C₈	—	3	4	no	—
276	C₄⋊C₈	—	3	4	no	—
277	C₄⋊C₈	—	3	2	no	—
278	C₄⋊C₈	—	3	2	no	—
279	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
280	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
281	C₄⋊C₈	C₂×C₃×D₃	1	2	yes	—
282	C₂³×C₃	—	2	1	no	—
283	C₂³×C₃	—	3	2	no	—
284	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
285	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
286	C₂²×D₃	C₂²×C₃×C₄	1	2	yes	—
287	C₃×Q₈	—	3	4	no	—
288	C₃×D₄	—	3	8	no	—
289	C₃×D₄	—	3	4	no	—
290	C₂×C₃×C₄	—	2	4	no	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	2	2	no	—
293	C₂×C₃×C₄	—	2	1	no	—
294	C₂×C₃×C₄	—	2	1	no	—
295	C₂×C₃×C₄	—	2	1	no	—
296	C₂×C₃×C₄	—	2	1	no	—
297	C₂×C₃×C₄	—	2	1	no	—
298	C₂×C₃×C₄	—	2	1	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	—	3	2	no	—
302	C₂×C₃×C₄	—	3	4	no	—
303	C₂×C₃×C₄	—	3	4	no	—
304	C₂×C₃×C₄	—	3	2	no	—
305	C₂×C₃×C₄	—	3	2	no	—
306	C₂×C₃×C₄	—	4	1	no	—
307	C₂×C₃×C₄	—	4	1	no	—
308	C₂×C₃×C₄	—	4	2	no	—
309	C₂×C₃×C₄	—	6	4	no	—
310	C₂×C₃×C₄	—	12	2	no	—
311	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
312	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
313	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
314	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
315	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
316	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
317	C₂×C₃×C₄	D₃×Q₈	1	2	yes	—
318	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
319	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
320	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
321	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
322	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
323	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
324	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
325	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
326	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
327	#67	C₃×C₄⋊C₄	1	8	yes	—
328	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
329	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
330	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
331	D₁₂	C₃×C₄⋊C₄	1	4	yes	—
332	C₄×D₃	—	2	4	no	—
333	C₄×D₃	—	4	2	no	—
334	C₄×D₃	C₂×C₃×D₄	1	4	yes	—
335	C₄×D₃	C₂×C₃×Q₈	1	4	yes	—
336	Dic₆	C₃×C₄⋊C₄	1	4	yes	—
337	C₃×C₈	—	2	2	no	—
338	C₃×C₈	—	2	2	no	—
339	C₃×C₈	—	2	2	no	—
340	C₃×C₈	—	2	2	no	—
341	C₃×C₈	—	4	2	no	—
342	C₃×C₈	—	4	2	no	—
343	C₃×C₈	—	6	4	no	—
344	C₃⋊C₈	—	2	4	no	—
345	C₂×C₃²	—	2	2	no	—
346	C₂×C₃²	C₂²×C₄⋊C₄	1	1	yes	characteristic
347	C₂×C₃²	C₂×#131	1	1	yes	characteristic
348	C₂×C₃²	#568	1	1	yes	characteristic
349	C₃×D₃	—	2	4	no	—
350	#41	—	3	4	no	—
351	#41	—	3	4	no	—
352	C₂×Q₈	—	3	1	no	—
353	C₂×D₄	—	3	2	no	—
354	C₂×D₄	—	3	1	no	—
355	C₂²×C₄	—	3	2	no	—
356	C₂²×C₄	—	3	2	no	—
357	C₂²×C₄	—	3	2	no	—
358	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
359	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
360	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
361	M₁₆	—	6	8	no	—
362	M₁₆	—	6	4	no	—
363	C₂×C₈	—	2	4	no	—
364	C₂×C₈	—	3	4	no	—
365	C₂×C₈	—	6	8	no	—
366	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
367	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
368	C₄⋊C₄	—	3	2	no	—
369	C₄⋊C₄	—	3	2	no	—
370	C₄⋊C₄	—	3	1	no	—
371	C₄⋊C₄	—	3	1	no	—
372	C₂²⋊C₄	—	3	2	no	—
373	C₂²⋊C₄	—	3	2	no	—
374	C₂²⋊C₄	—	3	2	no	—
375	C₄²	—	3	2	no	—
376	C₄²	—	3	2	no	—
377	C₄²	—	3	2	no	—
378	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
379	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
380	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
381	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
382	C₂²×C₃	—	2	2	no	—
383	C₂²×C₃	—	2	2	no	—
384	C₂²×C₃	—	2	1	no	—
385	C₂²×C₃	—	2	1	no	—
386	C₂²×C₃	—	2	1	no	—
387	C₂²×C₃	—	2	1	no	—
388	C₂²×C₃	—	2	2	no	—
389	C₂²×C₃	—	2	1	no	—
390	C₂²×C₃	—	3	4	no	—
391	C₂²×C₃	—	6	2	no	—
392	C₂²×C₃	—	6	2	no	—
393	C₂²×C₃	D₃×C₄⋊C₄	1	2	yes	—
394	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	2	yes	—
395	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
396	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
397	C₂×D₃	—	2	2	no	—
398	C₂×D₃	—	2	2	no	—
399	C₂×D₃	C₂×C₃×C₄⋊C₄	1	4	yes	—
400	C₃×C₄	—	2	2	no	—
401	C₃×C₄	—	2	1	no	—
402	C₃×C₄	—	2	1	no	—
403	C₃×C₄	—	2	1	no	—
404	C₃×C₄	—	2	1	no	—
405	C₃×C₄	—	2	1	no	—
406	C₃×C₄	—	2	1	no	—
407	C₃×C₄	—	2	2	no	—
408	C₃×C₄	—	2	2	no	—
409	C₃×C₄	—	2	1	no	—
410	C₃×C₄	—	2	1	no	—
411	C₃×C₄	—	3	4	no	—
412	C₃×C₄	—	4	1	no	—
413	C₃×C₄	—	4	1	no	—
414	C₃×C₄	—	6	2	no	—
415	C₃×C₄	—	6	2	no	—
416	C₃×C₄	D₃×C₄⋊C₄	1	2	yes	—
417	C₃×C₄	#901	1	2	yes	complemented
418	C₃×C₄	C₂×C₃×C₄⋊C₄	1	2	yes	—
419	C₃×C₄	C₃×#131	1	2	yes	complemented
420	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
421	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
422	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
423	C₃×C₄	C₂²×C₃×Q₈	1	1	yes	characteristic
424	Dic₃	—	2	2	no	—
425	Dic₃	—	2	2	no	—
426	Dic₃	C₂×C₃×C₄⋊C₄	1	4	yes	—
427	C₃²	#2906	1	1	yes	characteristic, complemented, Sylow
428	C₂³	—	3	2	no	—
429	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
430	Q₈	—	3	4	no	—
431	D₄	—	3	8	no	—
432	D₄	—	3	4	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	3	2	no	—
435	C₂×C₄	—	3	4	no	—
436	C₂×C₄	—	3	4	no	—
437	C₂×C₄	—	3	2	no	—
438	C₂×C₄	—	3	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	6	4	no	—
441	C₂×C₄	—	12	2	no	—
442	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
443	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
444	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
445	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
446	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
447	C₂×C₄	C₃×D₃×D₄	1	2	yes	—
448	C₂×C₄	C₃×D₃×Q₈	1	2	yes	—
449	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
450	C₈	—	2	2	no	—
451	C₈	—	2	2	no	—
452	C₈	—	6	4	no	—
453	C₂×C₃	—	2	4	no	—
454	C₂×C₃	—	2	2	no	—
455	C₂×C₃	—	2	2	no	—
456	C₂×C₃	—	2	1	no	—
457	C₂×C₃	—	2	1	no	—
458	C₂×C₃	—	2	1	no	—
459	C₂×C₃	—	6	4	no	—
460	C₂×C₃	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
461	C₂×C₃	C₂×#901	1	1	yes	characteristic
462	C₂×C₃	#5745	1	1	yes	characteristic
463	C₂×C₃	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
464	C₂×C₃	C₂×C₃×#131	1	1	yes	characteristic
465	C₂×C₃	C₃×#568	1	1	yes	characteristic
466	D₃	—	2	4	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	3	4	no	—
470	C₂²	—	6	2	no	—
471	C₂²	—	6	2	no	—
472	C₂²	C₃×D₃×C₄⋊C₄	1	2	yes	—
473	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	3	4	no	—
478	C₄	—	6	2	no	—
479	C₄	—	6	2	no	—
480	C₄	C₃×D₃×C₄⋊C₄	1	2	yes	—
481	C₄	C₃×#901	1	2	yes	complemented
482	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
483	C₄	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
484	C₃	—	2	1	no	—
485	C₃	#79012	1	1	yes	characteristic, direct product factor
486	C₃	C₃×#2906	1	1	yes	characteristic, complemented
487	C₂	—	2	2	no	—
488	C₂	—	6	4	no	—
489	C₂	C₂×C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
490	C₂	C₂×C₃×#901	1	1	yes	characteristic
491	C₂	C₃×#5745	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	C₂×C₃²×C₄⋊C₈	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂×C₃×#235	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×C₄⋊C₈	D₃
hypocenter	C₃	C₃×#2906
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. C₂×C₃²×C₄⋊C₈	C₂	semidirect
4. C₃×#5102	C₂	semidirect
5. C₃×#4924	C₂	semidirect
6. C₃×#4839	C₂	semidirect
7. C₃×#4837	C₂	semidirect
8. C₃×D₃×C₄⋊C₈	C₂	semidirect
10. #79012	C₃	direct (N × H)
44. C₂×C₃×C₄⋊C₈	D₃	semidirect
45. C₂×C₃×C₄⋊C₈	C₂×C₃	semidirect
46. #5102	C₂×C₃	semidirect
47. #4924	C₂×C₃	semidirect
48. #4839	C₂×C₃	semidirect
49. #4837	C₂×C₃	semidirect
50. D₃×C₄⋊C₈	C₂×C₃	semidirect
167. C₂×C₄⋊C₈	C₃×D₃	semidirect
253. C₃²×C₄	#131	semidirect
417. C₃×C₄	#901	semidirect
419. C₃×C₄	C₃×#131	semidirect
427. C₃²	#2906	semidirect
481. C₄	C₃×#901	semidirect
485. C₃	#79012	direct (N × H)
486. 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×#901	2
C₃×C₄×#235	2
C₂×C₃²×C₄⋊C₈	2
C₃×#5102	2
C₃×#4924	2
C₃×#4839	2
C₃×#4837	2
C₃×D₃×C₄⋊C₈	2
C₃×#2906	3
#79012	3

Subgroups — C3×#79012 #11858331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79012 #11858331