Subgroups — C₂×C₃×#4688 #11859270

Order 1152.

1185 conjugacy classes of subgroups.

The subgroup lattice has 383 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	2	yes	maximal, complemented
2	C₂×C₃×C₄×D₁₂	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃²×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×(C₂×D₃)⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4688	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×#436	—	3	1	no	maximal
8	C₂×#4688	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₃×D₁₂	C₄	1	1	yes	characteristic
10	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	—
11	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
14	C₂×C₃×(C₂×D₃)⋊C₄	C₄	1	2	yes	—
15	C₂×C₃×C₄⋊Dic₃	C₄	1	1	yes	characteristic
16	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	—
17	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	8	no	—
18	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	8	yes	complemented
19	C₃×C₄×D₁₂	C₄	1	4	yes	—
20	C₃×C₄×D₁₂	C₂²	1	4	yes	—
21	C₃²×C₄×C₈	C₂²	1	4	yes	complemented
22	C₃×(C₂×D₃)⋊C₈	C₂²	1	8	yes	complemented
23	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
24	C₂²×C₃×M₁₆	—	3	2	no	—
25	C₂×C₃×C₄×D₄	—	3	1	no	—
26	C₂²×ΓL(1,𝔽₂₅)	C₂×C₃	1	2	yes	complemented
27	C₂×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
28	C₃×#436	—	3	8	no	—
29	C₂×C₃×C₄⋊C₈	—	3	1	no	—
30	C₂×C₃×C₂²⋊C₈	—	3	2	no	—
31	C₂×C₃×C₄×C₈	—	2	1	no	—
32	C₂×C₃×C₄×C₈	D₃	1	1	yes	characteristic, complemented
33	C₂×C₃×C₄×C₈	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×(C₂×D₃)⋊C₈	C₂×C₃	1	2	yes	complemented
35	C₂×C₄⋊(C₃⋊C₈)	C₂×C₃	1	1	yes	characteristic, complemented
36	#4688	C₂×C₃	1	8	yes	direct product factor
37	C₂³×C₃×D₃	C₂×C₄	1	2	yes	—
38	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
41	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
42	C₂×C₃×D₁₂	—	2	4	no	—
43	C₂×C₃×D₁₂	C₂×C₄	1	4	yes	—
44	C₂×C₃×C₄×D₃	—	2	4	no	—
45	C₂×C₃×C₄×D₃	—	2	4	no	—
46	C₂×C₃×C₄×D₃	C₂×C₄	1	4	yes	—
47	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
48	C₂×C₃²×C₈	—	2	2	no	—
49	C₂×C₃²×C₈	D₄	1	4	yes	complemented
50	C₂×C₃²×C₈	C₂³	1	2	yes	—
51	C₂×C₃²×C₈	C₂³	1	2	yes	—
52	C₃²×C₄²	C₂×C₄	1	2	yes	—
53	C₃²×C₄²	C₂³	1	2	yes	—
54	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	—
55	C₃×C₄⋊Dic₃	C₂×C₄	1	4	yes	—
56	C₂×C₃×C₃⋊C₈	—	2	4	no	—
57	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	—
58	C₃×ΓL(1,𝔽₂₅)	—	2	16	no	—
59	C₂×#436	—	3	1	no	Sylow
60	C₂²×C₃×D₄	—	3	1	no	—
61	C₂³×C₃×C₄	—	3	2	no	—
62	C₂²×D₁₂	C₃×C₄	1	1	yes	characteristic
63	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	—
64	C₂×C₃×M₁₆	—	3	8	no	—
65	C₂×C₃×M₁₆	—	6	8	no	—
66	C₂²×C₃×C₈	—	2	1	no	—
67	C₂²×C₃×C₈	—	2	1	no	—
68	C₂²×C₃×C₈	—	3	2	no	—
69	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
70	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
71	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
72	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
73	C₃×C₄×D₄	—	3	4	no	—
74	C₃×C₄×D₄	—	3	4	no	—
75	C₂×C₃×C₄⋊C₄	—	3	1	no	—
76	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
77	C₂×C₃×C₄²	—	2	1	no	—
78	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
79	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
80	C₂×(C₂×D₃)⋊C₄	C₃×C₄	1	2	yes	—
81	C₂×C₄⋊Dic₃	C₃×C₄	1	1	yes	characteristic
82	C₂²×C₃⋊C₈	C₂²×C₃	1	2	yes	—
83	C₂×ΓL(1,𝔽₂₅)	—	2	8	no	—
84	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	8	yes	complemented
85	C₄×D₁₂	C₃×C₄	1	4	yes	—
86	C₄×D₁₂	C₂²×C₃	1	4	yes	—
87	C₃×C₄⋊C₈	—	3	4	no	—
88	C₃×C₂²⋊C₈	—	3	8	no	—
89	C₃×C₄×C₈	—	2	4	no	—
90	C₃×C₄×C₈	C₂×D₃	1	4	yes	complemented
91	C₃×C₄×C₈	C₂²×C₃	1	4	yes	complemented
92	(C₂×D₃)⋊C₈	C₂²×C₃	1	8	yes	complemented
93	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	4	yes	complemented
94	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₃×D₃	—	2	4	no	—
96	C₂²×C₃×D₃	—	2	4	no	—
97	C₂²×C₃×D₃	—	2	4	no	—
98	C₂²×C₃×D₃	C₂²×C₄	1	4	yes	—
99	C₂×C₃²×C₄	—	2	2	no	—
100	C₂×C₃²×C₄	M₁₆	1	4	yes	complemented
101	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
102	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
104	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
105	C₂×C₃²×C₄	#41	1	2	yes	—
106	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
107	C₂×C₃×Dic₃	—	2	4	no	—
108	C₂×C₃×Dic₃	C₂²×C₄	1	4	yes	—
109	C₃×D₁₂	—	2	8	no	—
110	C₃×C₄×D₃	—	2	8	no	—
111	C₃×C₄×D₃	—	2	4	no	—
112	C₃×C₄×D₃	—	2	4	no	—
113	C₃²×C₈	—	2	2	no	—
114	C₃²×C₈	C₂×D₄	1	4	yes	complemented
115	C₃×C₃⋊C₈	—	2	4	no	—
116	C₂²×M₁₆	—	3	2	no	—
117	C₂×C₄×D₄	—	3	1	no	—
118	#436	—	3	8	no	—
119	C₂×C₄⋊C₈	—	3	1	no	—
120	C₂×C₂²⋊C₈	—	3	2	no	—
121	C₂×C₄×C₈	C₃×D₃	1	1	yes	characteristic, complemented
122	C₂⁴×C₃	—	3	2	no	—
123	C₂³×D₃	C₂×C₃×C₄	1	2	yes	—
124	C₂×C₃×D₄	—	3	4	no	—
125	C₂×C₃×D₄	—	6	4	no	—
126	C₂²×C₃×C₄	—	2	1	no	—
127	C₂²×C₃×C₄	—	2	1	no	—
128	C₂²×C₃×C₄	—	2	1	no	—
129	C₂²×C₃×C₄	—	3	2	no	—
130	C₂²×C₃×C₄	—	3	4	no	—
131	C₂²×C₃×C₄	—	3	4	no	—
132	C₂²×C₃×C₄	—	6	4	no	—
133	C₂²×C₃×C₄	—	6	4	no	—
134	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
135	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
136	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
137	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
138	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
139	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
140	C₂²×Dic₃	C₂×C₃×C₄	1	2	yes	—
141	C₂×D₁₂	—	2	4	no	—
142	C₂×D₁₂	C₂×C₃×C₄	1	4	yes	—
143	C₂×C₄×D₃	—	2	4	no	—
144	C₂×C₄×D₃	—	2	4	no	—
145	C₂×C₄×D₃	C₂×C₃×C₄	1	4	yes	—
146	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
147	C₃×M₁₆	—	6	16	no	—
148	C₂×C₃×C₈	—	2	4	no	—
149	C₂×C₃×C₈	—	2	2	no	—
150	C₂×C₃×C₈	—	2	2	no	—
151	C₂×C₃×C₈	—	2	4	no	—
152	C₂×C₃×C₈	—	2	2	no	—
153	C₂×C₃×C₈	—	2	2	no	—
154	C₂×C₃×C₈	—	3	4	no	—
155	C₂×C₃×C₈	—	6	4	no	—
156	C₂×C₃×C₈	D₁₂	1	4	yes	complemented
157	C₂×C₃×C₈	C₃×D₄	1	4	yes	complemented
158	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
159	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
160	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
161	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
162	C₃×C₄⋊C₄	—	3	4	no	—
163	C₃×C₂²⋊C₄	—	3	8	no	—
164	C₃×C₄²	—	2	2	no	—
165	C₃×C₄²	—	2	2	no	—
166	C₃×C₄²	C₄×D₃	1	2	yes	—
167	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
168	C₃×C₄²	C₂²×D₃	1	2	yes	—
169	C₃×C₄²	C₂³×C₃	1	2	yes	—
170	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	8	yes	—
171	C₄⋊Dic₃	C₂×C₃×C₄	1	4	yes	—
172	C₂×C₃⋊C₈	—	2	4	no	—
173	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
174	ΓL(1,𝔽₂₅)	—	2	16	no	—
175	C₂²×C₃²	C₄×D₄	1	2	yes	—
176	C₂²×C₃²	C₂×M₁₆	1	2	yes	—
177	C₂²×C₃²	#131	1	2	yes	—
178	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₃×D₃	—	2	4	no	—
180	C₂×C₃×D₃	—	2	4	no	—
181	C₂×C₃×D₃	—	2	4	no	—
182	C₂×C₃×D₃	—	4	8	no	—
183	C₃²×C₄	—	2	2	no	—
184	C₃²×C₄	C₄×D₄	1	2	yes	—
185	C₃²×C₄	C₂×M₁₆	1	4	yes	complemented
186	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
187	C₃²×C₄	C₂×#41	1	1	yes	characteristic
188	C₃×Dic₃	—	2	4	no	—
189	C₂²×D₄	—	3	1	no	—
190	C₂³×C₄	—	3	2	no	—
191	C₂×M₁₆	—	3	8	no	—
192	C₂×M₁₆	—	6	8	no	—
193	C₂²×C₈	—	3	2	no	—
194	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
195	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
196	C₄×D₄	—	3	4	no	—
197	C₄×D₄	—	3	4	no	—
198	C₂×C₄⋊C₄	—	3	1	no	—
199	C₂×C₂²⋊C₄	—	3	2	no	—
200	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
201	C₄⋊C₈	—	3	4	no	—
202	C₂²⋊C₈	—	3	8	no	—
203	C₄×C₈	C₂×C₃×D₃	1	4	yes	complemented
204	C₂³×C₃	—	2	1	no	—
205	C₂³×C₃	—	3	4	no	—
206	C₂³×C₃	—	6	4	no	—
207	C₂³×C₃	—	6	4	no	—
208	C₂³×C₃	—	6	4	no	—
209	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
210	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
211	C₂²×D₃	—	2	4	no	—
212	C₂²×D₃	—	2	4	no	—
213	C₂²×D₃	—	2	4	no	—
214	C₂²×D₃	C₂²×C₃×C₄	1	4	yes	—
215	C₃×D₄	—	6	8	no	—
216	C₂×C₃×C₄	—	2	4	no	—
217	C₂×C₃×C₄	—	2	2	no	—
218	C₂×C₃×C₄	—	2	2	no	—
219	C₂×C₃×C₄	—	2	1	no	—
220	C₂×C₃×C₄	—	2	4	no	—
221	C₂×C₃×C₄	—	2	2	no	—
222	C₂×C₃×C₄	—	2	2	no	—
223	C₂×C₃×C₄	—	2	1	no	—
224	C₂×C₃×C₄	—	2	2	no	—
225	C₂×C₃×C₄	—	2	2	no	—
226	C₂×C₃×C₄	—	3	4	no	—
227	C₂×C₃×C₄	—	6	4	no	—
228	C₂×C₃×C₄	—	6	8	no	—
229	C₂×C₃×C₄	—	6	4	no	—
230	C₂×C₃×C₄	—	6	4	no	—
231	C₂×C₃×C₄	ΓL(1,𝔽₂₅)	1	4	yes	complemented
232	C₂×C₃×C₄	C₃×M₁₆	1	4	yes	complemented
233	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
234	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
235	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
236	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
237	C₂×C₃×C₄	#235	1	2	yes	—
238	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
239	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
240	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
241	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
242	C₂×C₃×C₄	C₃×#41	1	2	yes	—
243	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
244	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
245	C₂×Dic₃	—	2	4	no	—
246	C₂×Dic₃	C₂²×C₃×C₄	1	4	yes	—
247	D₁₂	—	2	8	no	—
248	C₄×D₃	—	2	8	no	—
249	C₄×D₃	—	2	4	no	—
250	C₄×D₃	—	2	4	no	—
251	C₃×C₈	—	2	4	no	—
252	C₃×C₈	—	2	2	no	—
253	C₃×C₈	—	2	2	no	—
254	C₃×C₈	—	2	4	no	—
255	C₃×C₈	—	6	4	no	—
256	C₃×C₈	C₂×D₁₂	1	4	yes	complemented
257	C₃×C₈	C₂×C₃×D₄	1	4	yes	complemented
258	C₃⋊C₈	—	2	4	no	—
259	C₂×C₃²	#436	1	4	yes	complemented
260	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
261	C₂×C₃²	C₂²×M₁₆	1	1	yes	characteristic
262	C₂×C₃²	C₂×#131	1	1	yes	characteristic
263	C₃×D₃	—	4	4	no	—
264	C₂⁴	—	3	2	no	—
265	C₂×D₄	—	3	4	no	—
266	C₂×D₄	—	6	4	no	—
267	C₂²×C₄	—	3	2	no	—
268	C₂²×C₄	—	3	4	no	—
269	C₂²×C₄	—	3	4	no	—
270	C₂²×C₄	—	6	4	no	—
271	C₂²×C₄	—	6	4	no	—
272	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
273	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
274	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
275	M₁₆	—	6	16	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	3	4	no	—
278	C₂×C₈	—	6	4	no	—
279	C₂×C₈	C₃×D₁₂	1	4	yes	complemented
280	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
281	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
282	C₄⋊C₄	—	3	4	no	—
283	C₂²⋊C₄	—	3	8	no	—
284	C₄²	C₃×C₄×D₃	1	2	yes	—
285	C₄²	C₂²×C₃×D₃	1	2	yes	—
286	C₂²×C₃	—	2	2	no	—
287	C₂²×C₃	—	2	2	no	—
288	C₂²×C₃	—	2	1	no	—
289	C₂²×C₃	—	2	2	no	—
290	C₂²×C₃	—	6	4	no	—
291	C₂²×C₃	—	6	4	no	—
292	C₂²×C₃	—	6	4	no	—
293	C₂²×C₃	—	12	8	no	—
294	C₂²×C₃	C₄×D₁₂	1	2	yes	—
295	C₂²×C₃	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
296	C₂²×C₃	#901	1	2	yes	—
297	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
298	C₂²×C₃	C₂×C₃×M₁₆	1	2	yes	—
299	C₂²×C₃	C₃×#131	1	2	yes	—
300	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
301	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
302	C₂×D₃	—	2	4	no	—
303	C₂×D₃	—	2	4	no	—
304	C₂×D₃	—	2	4	no	—
305	C₂×D₃	—	4	8	no	—
306	C₃×C₄	—	2	4	no	—
307	C₃×C₄	—	2	2	no	—
308	C₃×C₄	—	2	2	no	—
309	C₃×C₄	—	2	4	no	—
310	C₃×C₄	—	2	1	no	—
311	C₃×C₄	—	2	1	no	—
312	C₃×C₄	—	2	2	no	—
313	C₃×C₄	—	6	4	no	—
314	C₃×C₄	C₄×D₁₂	1	2	yes	—
315	C₃×C₄	C₂×ΓL(1,𝔽₂₅)	1	4	yes	complemented
316	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
317	C₃×C₄	C₂×C₃×M₁₆	1	4	yes	complemented
318	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
319	C₃×C₄	C₂×#235	1	1	yes	characteristic
320	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
321	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
322	Dic₃	—	2	4	no	—
323	C₃²	C₂×#436	1	1	yes	characteristic, complemented, Sylow
324	C₂³	—	3	4	no	—
325	C₂³	—	6	4	no	—
326	C₂³	—	6	4	no	—
327	C₂³	—	6	4	no	—
328	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
329	D₄	—	6	8	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	3	4	no	—
332	C₂×C₄	—	6	4	no	—
333	C₂×C₄	—	6	4	no	—
334	C₂×C₄	—	6	4	no	—
335	C₂×C₄	—	6	8	no	—
336	C₂×C₄	C₃×ΓL(1,𝔽₂₅)	1	4	yes	complemented
337	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
338	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
339	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
340	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
341	C₂×C₄	C₃×#235	1	2	yes	—
342	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
343	C₈	—	2	2	no	—
344	C₈	—	6	4	no	—
345	C₈	C₂×C₃×D₁₂	1	4	yes	complemented
346	C₂×C₃	—	2	4	no	—
347	C₂×C₃	—	2	1	no	—
348	C₂×C₃	—	2	1	no	—
349	C₂×C₃	—	2	1	no	—
350	C₂×C₃	—	12	4	no	—
351	C₂×C₃	#4688	1	4	yes	direct product factor
352	C₂×C₃	C₃×#436	1	4	yes	complemented
353	C₂×C₃	C₂×C₄×D₁₂	1	1	yes	characteristic
354	C₂×C₃	C₂²×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
355	C₂×C₃	C₂×#901	1	1	yes	characteristic
356	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
357	C₂×C₃	C₂²×C₃×M₁₆	1	1	yes	characteristic
358	C₂×C₃	C₂×C₃×#131	1	1	yes	characteristic
359	D₃	—	4	4	no	—
360	C₂²	—	6	4	no	—
361	C₂²	—	6	4	no	—
362	C₂²	—	6	4	no	—
363	C₂²	—	12	8	no	—
364	C₂²	C₃×C₄×D₁₂	1	2	yes	—
365	C₂²	C₂×C₃×ΓL(1,𝔽₂₅)	1	2	yes	—
366	C₂²	C₃×#901	1	2	yes	—
367	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
368	C₄	—	2	2	no	—
369	C₄	—	6	4	no	—
370	C₄	C₃×C₄×D₁₂	1	2	yes	—
371	C₄	C₂×C₃×ΓL(1,𝔽₂₅)	1	4	yes	complemented
372	C₄	C₂²×C₃×D₁₂	1	1	yes	characteristic
373	C₄	C₂×C₃×#235	1	1	yes	characteristic
374	C₃	—	2	1	no	—
375	C₃	C₂×#4688	1	1	yes	characteristic, direct product factor
376	C₃	C₂×C₃×#436	1	1	yes	characteristic, complemented
377	C₂	—	12	4	no	—
378	C₂	C₃×#4688	1	4	yes	direct product factor
379	C₂	C₂×C₃×C₄×D₁₂	1	1	yes	characteristic
380	C₂	C₂²×C₃×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
381	C₂	C₂×C₃×#901	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×C₄×C₈	C₂
socle	C₂³×C₃²	C₂²×C₄
prime radical	C₂²×C₃×D₁₂	C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×C₄×C₈	D₃
hypocenter	C₃	C₂×C₃×#436
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×C₄×C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×ΓL(1,𝔽₂₅)	C₂	semidirect
3. C₂×C₃²×C₄×C₈	C₂	semidirect
4. C₂×C₃×(C₂×D₃)⋊C₈	C₂	semidirect
5. C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	semidirect
6. C₃×#4688	C₂	direct (N × H)
8. C₂×#4688	C₃	direct (N × H)
18. C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	semidirect
21. C₃²×C₄×C₈	C₂²	semidirect
22. C₃×(C₂×D₃)⋊C₈	C₂²	semidirect
23. C₃×C₄⋊(C₃⋊C₈)	C₂²	semidirect
26. C₂²×ΓL(1,𝔽₂₅)	C₂×C₃	semidirect
32. C₂×C₃×C₄×C₈	D₃	semidirect
33. C₂×C₃×C₄×C₈	C₂×C₃	semidirect
34. C₂×(C₂×D₃)⋊C₈	C₂×C₃	semidirect
35. C₂×C₄⋊(C₃⋊C₈)	C₂×C₃	semidirect
36. #4688	C₂×C₃	direct (N × H)
49. C₂×C₃²×C₈	D₄	semidirect
84. C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	semidirect
90. C₃×C₄×C₈	C₂×D₃	semidirect
91. C₃×C₄×C₈	C₂²×C₃	semidirect
92. (C₂×D₃)⋊C₈	C₂²×C₃	semidirect
93. C₄⋊(C₃⋊C₈)	C₂²×C₃	semidirect
100. C₂×C₃²×C₄	M₁₆	semidirect
114. C₃²×C₈	C₂×D₄	semidirect
121. C₂×C₄×C₈	C₃×D₃	semidirect
156. C₂×C₃×C₈	D₁₂	semidirect
157. C₂×C₃×C₈	C₃×D₄	semidirect
185. C₃²×C₄	C₂×M₁₆	semidirect
203. C₄×C₈	C₂×C₃×D₃	semidirect
231. C₂×C₃×C₄	ΓL(1,𝔽₂₅)	semidirect
232. C₂×C₃×C₄	C₃×M₁₆	semidirect
256. C₃×C₈	C₂×D₁₂	semidirect
257. C₃×C₈	C₂×C₃×D₄	semidirect
259. C₂×C₃²	#436	semidirect
279. C₂×C₈	C₃×D₁₂	semidirect
315. C₃×C₄	C₂×ΓL(1,𝔽₂₅)	semidirect
317. C₃×C₄	C₂×C₃×M₁₆	semidirect
323. C₃²	C₂×#436	semidirect
336. C₂×C₄	C₃×ΓL(1,𝔽₂₅)	semidirect
345. C₈	C₂×C₃×D₁₂	semidirect
351. C₂×C₃	#4688	direct (N × H)
352. C₂×C₃	C₃×#436	semidirect
371. C₄	C₂×C₃×ΓL(1,𝔽₂₅)	semidirect
375. C₃	C₂×#4688	direct (N × H)
376. C₃	C₂×C₃×#436	semidirect
378. C₂	C₃×#4688	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
C₂×C₃×C₄×D₁₂	2
C₂×C₃²×C₄×C₈	2
C₂×C₃×(C₂×D₃)⋊C₈	2
C₂×C₃×C₄⋊(C₃⋊C₈)	2
C₃×#4688	2
C₂×C₃×#436	3
C₂×#4688	3

Subgroups — C2×C3×#4688 #11859270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4688 #11859270