Subgroups — C₂×C₃×#4689 #11857174

Order 1152.

1265 conjugacy classes of subgroups.

The subgroup lattice has 397 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×D₃×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#872	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃²×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#815	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#803	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4689	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₃×#405	—	3	1	no	maximal
10	C₂×#4689	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
12	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
13	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
15	C₂×C₃×(C₂×D₃)⋊C₄	C₄	1	2	yes	—
16	C₂×C₃×Dic₃⋊C₄	C₄	1	2	yes	—
17	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₃×ΓL(1,𝔽₂₅)	C₄	1	8	yes	complemented
21	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	—
22	C₂×C₃×D₃×C₈	C₄	1	8	yes	complemented
23	C₂×C₃×D₃×C₈	C₂²	1	4	yes	—
24	C₃×#872	C₄	1	4	yes	—
25	C₃×#872	C₂²	1	4	yes	—
26	C₃²×C₄×C₈	C₂²	1	4	yes	complemented
27	C₃×#815	C₂²	1	4	yes	complemented
28	C₃×C₈×Dic₃	C₂²	1	4	yes	complemented
29	C₃×#803	C₂²	1	4	yes	complemented
30	C₂²×C₃×M₁₆	—	3	1	no	—
31	C₂³×C₃×C₈	—	3	1	no	—
32	C₂×C₃×#117	—	3	1	no	—
33	C₂²×ΓL(1,𝔽₂₅)	C₂×C₃	1	1	yes	characteristic
34	C₂²×D₃×C₈	C₂×C₃	1	1	yes	characteristic
35	C₂×#872	C₂×C₃	1	1	yes	characteristic
36	C₃×#405	—	3	8	no	—
37	C₂×C₃×#97	—	3	1	no	—
38	C₂×C₃×#97	—	3	1	no	—
39	C₂×C₃×C₄×C₈	—	2	1	no	—
40	C₂×C₃×C₄×C₈	—	3	1	no	—
41	C₂×C₃×C₄×C₈	D₃	1	1	yes	characteristic, complemented
42	C₂×C₃×C₄×C₈	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂×#815	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×C₈×Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂×#803	C₂×C₃	1	1	yes	characteristic, complemented
46	#4689	C₂×C₃	1	8	yes	direct product factor
47	C₂³×C₃×D₃	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
49	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
50	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
51	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
53	C₂×C₃×C₄×D₃	C₂×C₄	1	4	yes	—
54	C₂×C₃×C₄×D₃	C₂×C₄	1	4	yes	—
55	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
56	C₂×C₃²×C₈	C₂×C₄	1	4	yes	—
57	C₂×C₃²×C₈	C₂×C₄	1	4	yes	—
58	C₂×C₃²×C₈	C₂³	1	2	yes	—
59	C₂×C₃²×C₈	C₂³	1	2	yes	—
60	C₃²×C₄²	C₂×C₄	1	2	yes	—
61	C₃²×C₄²	C₂³	1	2	yes	—
62	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	—
63	C₃×Dic₃⋊C₄	C₂×C₄	1	8	yes	—
64	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
65	C₃×C₄×Dic₃	C₂³	1	2	yes	—
66	C₂×C₃×C₃⋊C₈	C₂×C₄	1	4	yes	—
67	C₂×C₃×C₃⋊C₈	C₂×C₄	1	4	yes	—
68	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
69	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
70	C₃×ΓL(1,𝔽₂₅)	C₂×C₄	1	16	yes	complemented
71	C₃×D₃×C₈	C₂×C₄	1	16	yes	complemented
72	C₂×#405	—	3	1	no	Sylow
73	C₂³×C₃×C₄	—	3	1	no	—
74	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₃×M₁₆	—	3	8	no	—
76	C₂×C₃×M₁₆	—	3	4	no	—
77	C₂²×C₃×C₈	—	2	1	no	—
78	C₂²×C₃×C₈	—	2	1	no	—
79	C₂²×C₃×C₈	—	3	1	no	—
80	C₂²×C₃×C₈	—	3	1	no	—
81	C₂²×C₃×C₈	—	3	8	no	—
82	C₂²×C₃×C₈	—	3	4	no	—
83	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
84	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
85	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
86	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
87	C₃×#117	—	3	4	no	—
88	C₃×#117	—	3	4	no	—
89	C₂×C₃×C₄⋊C₄	—	3	2	no	—
90	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
91	C₂×C₃×C₄²	—	2	1	no	—
92	C₂×C₃×C₄²	—	3	1	no	—
93	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
94	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
95	C₂×(C₂×D₃)⋊C₄	C₃×C₄	1	2	yes	—
96	C₂×Dic₃⋊C₄	C₃×C₄	1	2	yes	—
97	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
98	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
99	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
100	C₂×ΓL(1,𝔽₂₅)	C₃×C₄	1	8	yes	complemented
101	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	4	yes	—
102	C₂×D₃×C₈	C₃×C₄	1	8	yes	complemented
103	C₂×D₃×C₈	C₂²×C₃	1	4	yes	—
104	#872	C₃×C₄	1	4	yes	—
105	#872	C₂²×C₃	1	4	yes	—
106	C₃×#97	—	3	4	no	—
107	C₃×#97	—	3	4	no	—
108	C₃×C₄×C₈	—	2	4	no	—
109	C₃×C₄×C₈	—	3	4	no	—
110	C₃×C₄×C₈	C₂×D₃	1	4	yes	complemented
111	C₃×C₄×C₈	C₂²×C₃	1	4	yes	complemented
112	#815	C₂²×C₃	1	4	yes	complemented
113	C₈×Dic₃	C₂²×C₃	1	4	yes	complemented
114	#803	C₂²×C₃	1	4	yes	complemented
115	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₃×D₃	—	2	4	no	—
117	C₂²×C₃×D₃	C₄²	1	4	yes	—
118	C₂²×C₃×D₃	C₂²×C₄	1	2	yes	—
119	C₂×C₃²×C₄	—	2	4	no	—
120	C₂×C₃²×C₄	C₂²×C₄	1	4	yes	—
121	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
123	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
124	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
125	C₂×C₃×Dic₃	—	2	4	no	—
126	C₂×C₃×Dic₃	C₄²	1	4	yes	—
127	C₂×C₃×Dic₃	C₂²×C₄	1	4	yes	—
128	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
129	C₃×C₄×D₃	C₄²	1	8	yes	—
130	C₃×C₄×D₃	C₂²×C₄	1	4	yes	—
131	C₃×C₄×D₃	C₂²×C₄	1	4	yes	—
132	C₃²×C₈	C₂²×C₄	1	4	yes	—
133	C₃²×C₈	C₂²×C₄	1	4	yes	—
134	C₃×C₃⋊C₈	C₂²×C₄	1	4	yes	—
135	C₃×C₃⋊C₈	C₂²×C₄	1	4	yes	—
136	C₂²×M₁₆	—	3	1	no	—
137	C₂³×C₈	—	3	1	no	—
138	C₂×#117	—	3	1	no	—
139	#405	—	3	8	no	—
140	C₂×#97	—	3	1	no	—
141	C₂×#97	—	3	1	no	—
142	C₂×C₄×C₈	—	3	1	no	—
143	C₂×C₄×C₈	C₃×D₃	1	1	yes	characteristic, complemented
144	C₂⁴×C₃	—	3	1	no	—
145	C₂³×D₃	C₂×C₃×C₄	1	1	yes	characteristic
146	C₂²×C₃×C₄	—	2	2	no	—
147	C₂²×C₃×C₄	—	2	1	no	—
148	C₂²×C₃×C₄	—	3	1	no	—
149	C₂²×C₃×C₄	—	3	2	no	—
150	C₂²×C₃×C₄	—	3	4	no	—
151	C₂²×C₃×C₄	—	3	4	no	—
152	C₂²×C₃×C₄	—	3	2	no	—
153	C₂²×C₃×C₄	—	3	2	no	—
154	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
155	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
156	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
157	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
158	C₂²×Dic₃	C₂×C₃×C₄	1	2	yes	—
159	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
160	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
161	C₂×C₄×D₃	C₂×C₃×C₄	1	4	yes	—
162	C₂×C₄×D₃	C₂×C₃×C₄	1	4	yes	—
163	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
164	C₃×M₁₆	—	3	16	no	—
165	C₂×C₃×C₈	—	2	4	no	—
166	C₂×C₃×C₈	—	2	4	no	—
167	C₂×C₃×C₈	—	2	2	no	—
168	C₂×C₃×C₈	—	2	2	no	—
169	C₂×C₃×C₈	—	3	4	no	—
170	C₂×C₃×C₈	—	3	4	no	—
171	C₂×C₃×C₈	—	3	2	no	—
172	C₂×C₃×C₈	—	3	2	no	—
173	C₂×C₃×C₈	—	3	16	no	—
174	C₂×C₃×C₈	C₄×D₃	1	4	yes	—
175	C₂×C₃×C₈	C₄×D₃	1	4	yes	—
176	C₂×C₃×C₈	C₂×C₃×C₄	1	4	yes	—
177	C₂×C₃×C₈	C₂×C₃×C₄	1	4	yes	—
178	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
179	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
180	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
181	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
182	C₃×C₄⋊C₄	—	3	8	no	—
183	C₃×C₂²⋊C₄	—	3	8	no	—
184	C₃×C₄²	—	2	2	no	—
185	C₃×C₄²	—	2	2	no	—
186	C₃×C₄²	—	3	2	no	—
187	C₃×C₄²	—	3	2	no	—
188	C₃×C₄²	C₄×D₃	1	2	yes	—
189	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
190	C₃×C₄²	C₂²×D₃	1	2	yes	—
191	C₃×C₄²	C₂³×C₃	1	2	yes	—
192	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	8	yes	—
193	Dic₃⋊C₄	C₂×C₃×C₄	1	8	yes	—
194	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
195	C₄×Dic₃	C₂³×C₃	1	2	yes	—
196	C₂×C₃⋊C₈	C₂×C₃×C₄	1	4	yes	—
197	C₂×C₃⋊C₈	C₂×C₃×C₄	1	4	yes	—
198	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
199	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
200	ΓL(1,𝔽₂₅)	C₂×C₃×C₄	1	16	yes	complemented
201	D₃×C₈	C₂×C₃×C₄	1	16	yes	complemented
202	C₂²×C₃²	C₂×C₄²	1	2	yes	—
203	C₂²×C₃²	#131	1	4	yes	—
204	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₃×D₃	—	2	4	no	—
206	C₂×C₃×D₃	—	2	8	no	—
207	C₂×C₃×D₃	C₂×C₄²	1	4	yes	—
208	C₃²×C₄	—	2	4	no	—
209	C₃²×C₄	C₂×C₄²	1	2	yes	—
210	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
211	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
212	C₃×Dic₃	—	2	4	no	—
213	C₃×Dic₃	C₂×C₄²	1	4	yes	—
214	C₂³×C₄	—	3	1	no	—
215	C₂×M₁₆	—	3	8	no	—
216	C₂×M₁₆	—	3	4	no	—
217	C₂²×C₈	—	3	1	no	—
218	C₂²×C₈	—	3	1	no	—
219	C₂²×C₈	—	3	8	no	—
220	C₂²×C₈	—	3	4	no	—
221	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
222	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
223	#117	—	3	4	no	—
224	#117	—	3	4	no	—
225	C₂×C₄⋊C₄	—	3	2	no	—
226	C₂×C₂²⋊C₄	—	3	2	no	—
227	C₂×C₄²	—	3	1	no	—
228	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
229	#97	—	3	4	no	—
230	#97	—	3	4	no	—
231	C₄×C₈	—	3	4	no	—
232	C₄×C₈	C₂×C₃×D₃	1	4	yes	complemented
233	C₂³×C₃	—	2	1	no	—
234	C₂³×C₃	—	3	4	no	—
235	C₂³×C₃	—	3	2	no	—
236	C₂³×C₃	—	6	4	no	—
237	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
238	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
239	C₂²×D₃	—	2	4	no	—
240	C₂²×D₃	C₃×C₄²	1	4	yes	—
241	C₂²×D₃	C₂²×C₃×C₄	1	2	yes	—
242	C₂×C₃×C₄	—	2	8	no	—
243	C₂×C₃×C₄	—	2	4	no	—
244	C₂×C₃×C₄	—	2	4	no	—
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	2	4	no	—
247	C₂×C₃×C₄	—	2	1	no	—
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	—	2	2	no	—
250	C₂×C₃×C₄	—	3	4	no	—
251	C₂×C₃×C₄	—	3	2	no	—
252	C₂×C₃×C₄	—	3	8	no	—
253	C₂×C₃×C₄	—	3	4	no	—
254	C₂×C₃×C₄	—	3	4	no	—
255	C₂×C₃×C₄	—	3	4	no	—
256	C₂×C₃×C₄	—	6	4	no	—
257	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
258	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
260	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
261	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
262	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
264	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
265	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
267	C₂×Dic₃	—	2	4	no	—
268	C₂×Dic₃	C₃×C₄²	1	4	yes	—
269	C₂×Dic₃	C₂²×C₃×C₄	1	4	yes	—
270	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
271	C₄×D₃	C₃×C₄²	1	8	yes	—
272	C₄×D₃	C₂²×C₃×C₄	1	4	yes	—
273	C₄×D₃	C₂²×C₃×C₄	1	4	yes	—
274	C₃×C₈	—	2	4	no	—
275	C₃×C₈	—	2	4	no	—
276	C₃×C₈	—	3	4	no	—
277	C₃×C₈	—	3	4	no	—
278	C₃×C₈	C₂×C₄×D₃	1	4	yes	—
279	C₃×C₈	C₂×C₄×D₃	1	4	yes	—
280	C₃×C₈	C₂²×C₃×C₄	1	4	yes	—
281	C₃×C₈	C₂²×C₃×C₄	1	4	yes	—
282	C₃⋊C₈	C₂²×C₃×C₄	1	4	yes	—
283	C₃⋊C₈	C₂²×C₃×C₄	1	4	yes	—
284	C₂×C₃²	#405	1	4	yes	complemented
285	C₂×C₃²	C₂²×C₄²	1	1	yes	characteristic
286	C₂×C₃²	C₂×#131	1	2	yes	—
287	C₃×D₃	—	2	4	no	—
288	C₂⁴	—	3	1	no	—
289	C₂²×C₄	—	3	1	no	—
290	C₂²×C₄	—	3	2	no	—
291	C₂²×C₄	—	3	2	no	—
292	C₂²×C₄	—	3	4	no	—
293	C₂²×C₄	—	3	4	no	—
294	C₂²×C₄	—	3	2	no	—
295	C₂²×C₄	C₃×C₄×D₃	1	2	yes	—
296	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
297	M₁₆	—	3	16	no	—
298	C₂×C₈	—	3	2	no	—
299	C₂×C₈	—	3	2	no	—
300	C₂×C₈	—	3	4	no	—
301	C₂×C₈	—	3	4	no	—
302	C₂×C₈	—	3	16	no	—
303	C₂×C₈	C₃×C₄×D₃	1	4	yes	—
304	C₂×C₈	C₃×C₄×D₃	1	4	yes	—
305	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
306	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
307	C₄⋊C₄	—	3	8	no	—
308	C₂²⋊C₄	—	3	8	no	—
309	C₄²	—	3	2	no	—
310	C₄²	—	3	2	no	—
311	C₄²	C₃×C₄×D₃	1	2	yes	—
312	C₄²	C₂²×C₃×D₃	1	2	yes	—
313	C₂²×C₃	—	2	4	no	—
314	C₂²×C₃	—	2	1	no	—
315	C₂²×C₃	—	2	2	no	—
316	C₂²×C₃	—	3	4	no	—
317	C₂²×C₃	—	6	8	no	—
318	C₂²×C₃	—	6	4	no	—
319	C₂²×C₃	C₄²×D₃	1	2	yes	—
320	C₂²×C₃	#901	1	4	yes	—
321	C₂²×C₃	C₂×C₃×C₄²	1	2	yes	—
322	C₂²×C₃	C₃×#131	1	4	yes	—
323	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
324	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
325	C₂×D₃	—	2	4	no	—
326	C₂×D₃	—	2	8	no	—
327	C₂×D₃	C₂×C₃×C₄²	1	4	yes	—
328	C₃×C₄	—	2	8	no	—
329	C₃×C₄	—	2	4	no	—
330	C₃×C₄	—	2	4	no	—
331	C₃×C₄	—	2	1	no	—
332	C₃×C₄	—	2	1	no	—
333	C₃×C₄	—	2	2	no	—
334	C₃×C₄	—	3	4	no	—
335	C₃×C₄	—	6	4	no	—
336	C₃×C₄	C₄²×D₃	1	2	yes	—
337	C₃×C₄	C₂×C₃×C₄²	1	2	yes	—
338	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
339	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
340	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
341	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
342	Dic₃	—	2	4	no	—
343	Dic₃	C₂×C₃×C₄²	1	4	yes	—
344	C₃²	C₂×#405	1	1	yes	characteristic, complemented, Sylow
345	C₂³	—	3	2	no	—
346	C₂³	—	3	4	no	—
347	C₂³	—	6	4	no	—
348	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	3	2	no	—
351	C₂×C₄	—	3	4	no	—
352	C₂×C₄	—	3	4	no	—
353	C₂×C₄	—	3	4	no	—
354	C₂×C₄	—	3	8	no	—
355	C₂×C₄	—	3	4	no	—
356	C₂×C₄	—	6	4	no	—
357	C₂×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
358	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
359	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
360	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
361	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
362	C₈	—	3	4	no	—
363	C₈	—	3	4	no	—
364	C₈	C₂×C₃×C₄×D₃	1	4	yes	—
365	C₈	C₂×C₃×C₄×D₃	1	4	yes	—
366	C₂×C₃	—	2	4	no	—
367	C₂×C₃	—	2	1	no	—
368	C₂×C₃	—	2	2	no	—
369	C₂×C₃	—	6	4	no	—
370	C₂×C₃	#4689	1	4	yes	direct product factor
371	C₂×C₃	C₃×#405	1	4	yes	complemented
372	C₂×C₃	C₂×C₄²×D₃	1	1	yes	characteristic
373	C₂×C₃	C₂×#901	1	2	yes	—
374	C₂×C₃	C₂²×C₃×C₄²	1	1	yes	characteristic
375	C₂×C₃	C₂×C₃×#131	1	2	yes	—
376	D₃	—	2	4	no	—
377	C₂²	—	3	4	no	—
378	C₂²	—	6	8	no	—
379	C₂²	—	6	4	no	—
380	C₂²	C₃×C₄²×D₃	1	2	yes	—
381	C₂²	C₃×#901	1	4	yes	—
382	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
383	C₄	—	2	4	no	—
384	C₄	—	3	4	no	—
385	C₄	—	6	4	no	—
386	C₄	C₃×C₄²×D₃	1	2	yes	—
387	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
388	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
389	C₃	—	2	1	no	—
390	C₃	C₂×#4689	1	1	yes	characteristic, direct product factor
391	C₃	C₂×C₃×#405	1	1	yes	characteristic, complemented
392	C₂	—	6	4	no	—
393	C₂	C₃×#4689	1	4	yes	direct product factor
394	C₂	C₂×C₃×C₄²×D₃	1	1	yes	characteristic
395	C₂	C₂×C₃×#901	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₈	C₂×D₃
commutator	C₂×C₃	C₂²×C₃×C₄²
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×C₄×C₈	C₂
socle	C₂³×C₃²	C₂²×C₄
prime radical	C₂³×C₃×D₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×C₄×C₈	D₃
hypocenter	C₃	C₂×C₃×#405
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃×C₈ ◁ C₂×C₃×C₄×C₈

Complements

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

N	H ≅ G/N	type
4. C₂×C₃²×C₄×C₈	C₂	semidirect
5. C₂×C₃×#815	C₂	semidirect
6. C₂×C₃×C₈×Dic₃	C₂	semidirect
7. C₂×C₃×#803	C₂	semidirect
8. C₃×#4689	C₂	direct (N × H)
10. C₂×#4689	C₃	direct (N × H)
20. C₂×C₃×ΓL(1,𝔽₂₅)	C₄	semidirect
22. C₂×C₃×D₃×C₈	C₄	semidirect
26. C₃²×C₄×C₈	C₂²	semidirect
27. C₃×#815	C₂²	semidirect
28. C₃×C₈×Dic₃	C₂²	semidirect
29. C₃×#803	C₂²	semidirect
41. C₂×C₃×C₄×C₈	D₃	semidirect
42. C₂×C₃×C₄×C₈	C₂×C₃	semidirect
43. C₂×#815	C₂×C₃	semidirect
44. C₂×C₈×Dic₃	C₂×C₃	semidirect
45. C₂×#803	C₂×C₃	semidirect
46. #4689	C₂×C₃	direct (N × H)
70. C₃×ΓL(1,𝔽₂₅)	C₂×C₄	semidirect
71. C₃×D₃×C₈	C₂×C₄	semidirect
100. C₂×ΓL(1,𝔽₂₅)	C₃×C₄	semidirect
102. C₂×D₃×C₈	C₃×C₄	semidirect
110. C₃×C₄×C₈	C₂×D₃	semidirect
111. C₃×C₄×C₈	C₂²×C₃	semidirect
112. #815	C₂²×C₃	semidirect
113. C₈×Dic₃	C₂²×C₃	semidirect
114. #803	C₂²×C₃	semidirect
143. C₂×C₄×C₈	C₃×D₃	semidirect
200. ΓL(1,𝔽₂₅)	C₂×C₃×C₄	semidirect
201. D₃×C₈	C₂×C₃×C₄	semidirect
232. C₄×C₈	C₂×C₃×D₃	semidirect
284. C₂×C₃²	#405	semidirect
344. C₃²	C₂×#405	semidirect
370. C₂×C₃	#4689	direct (N × H)
371. C₂×C₃	C₃×#405	semidirect
390. C₃	C₂×#4689	direct (N × H)
391. C₃	C₂×C₃×#405	semidirect
393. C₂	C₃×#4689	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×ΓL(1,𝔽₂₅)	2
C₂²×C₃×D₃×C₈	2
C₂×C₃×#872	2
C₂×C₃²×C₄×C₈	2
C₂×C₃×#815	2
C₂×C₃×C₈×Dic₃	2
C₂×C₃×#803	2
C₃×#4689	2
C₂×C₃×#405	3
C₂×#4689	3

Subgroups — C2×C3×#4689 #11857174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4689 #11857174