Subgroups — C₂×C₃×#4837 #11858236

Order 1152.

1221 conjugacy classes of subgroups.

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

Subgroups — C2×C3×#4837 #11858236

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4837 #11858236