Subgroups — C₂×C₃²×#901 #13179115

Order 1728.

1900 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#235	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃³×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃²×#208	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#901	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃²×ΓL(1,𝔽₂₅)	C₂	1	2	yes	maximal, complemented
6	C₂×C₃²×D₃×C₈	C₂	1	2	yes	maximal, complemented
7	C₂×C₃²×#131	—	3	1	no	maximal
8	C₂×C₃×#901	C₃	1	4	yes	maximal, direct product factor
9	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
10	C₂×C₃²×#67	C₄	1	2	yes	—
11	C₃²×#235	C₄	1	4	yes	—
12	C₃²×#235	C₂²	1	4	yes	—
13	C₂×C₃²×D₁₂	C₄	1	1	yes	characteristic
14	C₂×C₃²×C₄×D₃	C₂²	1	2	yes	—
15	C₂×C₃²×Dic₆	C₄	1	1	yes	characteristic
16	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
17	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
18	C₂×C₃³×C₈	C₂²	1	4	yes	complemented
19	C₃²×#208	C₂²	1	4	yes	complemented
20	C₂×C₃²×C₃⋊C₈	C₂²	1	2	yes	—
21	C₃²×ΓL(1,𝔽₂₅)	C₂²	1	8	yes	complemented
22	C₃²×D₃×C₈	C₂²	1	8	yes	complemented
23	C₂×C₃²×#41	—	3	1	no	—
24	C₂×C₃×#235	C₂×C₃	1	4	yes	—
25	C₃²×#131	—	3	8	no	—
26	C₂×C₃²×M₁₆	—	3	1	no	—
27	C₂×C₃²×M₁₆	—	3	2	no	—
28	C₂²×C₃²×C₈	—	2	4	no	—
29	C₂²×C₃²×C₈	—	3	2	no	—
30	C₂²×C₃²×C₈	D₃	1	1	yes	characteristic, complemented
31	C₂²×C₃²×C₈	C₂×C₃	1	4	yes	complemented
32	C₂×C₃×#208	C₂×C₃	1	4	yes	complemented
33	C₃×#901	C₂×C₃	1	32	yes	direct product factor
34	C₂×C₃×ΓL(1,𝔽₂₅)	C₂×C₃	1	8	yes	complemented
35	C₂×C₃×D₃×C₈	C₂×C₃	1	8	yes	complemented
36	C₂³×C₃³	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₃²×D₃	C₂×C₄	1	2	yes	—
38	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic
39	C₂×C₃³×C₄	C₂×C₄	1	2	yes	—
40	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
41	C₂×C₃³×C₄	C₂³	1	2	yes	—
42	C₃²×#67	C₂×C₄	1	8	yes	—
43	C₂×C₃²×Dic₃	C₂×C₄	1	2	yes	—
44	C₃²×D₁₂	C₂×C₄	1	4	yes	—
45	C₃²×C₄×D₃	C₂×C₄	1	4	yes	—
46	C₃²×C₄×D₃	C₂³	1	4	yes	—
47	C₃²×Dic₆	C₂×C₄	1	4	yes	—
48	C₃³×C₈	C₂³	1	2	yes	—
49	C₃³×C₈	C₂³	1	2	yes	—
50	C₃²×C₃⋊C₈	C₂³	1	4	yes	—
51	C₂×C₃×#131	—	3	4	no	—
52	C₂×#901	C₃²	1	1	yes	characteristic, direct product factor
53	C₃²×#41	—	3	4	no	—
54	C₃²×#41	—	3	4	no	—
55	C₂×C₃²×Q₈	—	3	1	no	—
56	C₂×C₃²×D₄	—	3	2	no	—
57	C₂×C₃²×D₄	—	3	1	no	—
58	C₂²×C₃²×C₄	—	2	4	no	—
59	C₂²×C₃²×C₄	—	3	2	no	—
60	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
61	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
62	C₂×C₃×#67	C₃×C₄	1	8	yes	—
63	C₃×#235	C₃×C₄	1	16	yes	—
64	C₃×#235	C₂²×C₃	1	16	yes	—
65	C₂×C₃×D₁₂	C₃×C₄	1	4	yes	—
66	C₂×C₃×C₄×D₃	C₂²×C₃	1	8	yes	—
67	C₂×C₃×Dic₆	C₃×C₄	1	4	yes	—
68	C₃²×M₁₆	—	3	4	no	—
69	C₃²×M₁₆	—	3	8	no	—
70	C₂×C₃²×C₈	—	2	4	no	—
71	C₂×C₃²×C₈	—	2	4	no	—
72	C₂×C₃²×C₈	—	2	16	no	—
73	C₂×C₃²×C₈	—	3	2	no	—
74	C₂×C₃²×C₈	—	3	8	no	—
75	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
76	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
77	C₂×C₃²×C₈	C₂×D₃	1	4	yes	complemented
78	C₂×C₃²×C₈	C₂²×C₃	1	4	yes	—
79	C₂×C₃²×C₈	C₂²×C₃	1	4	yes	—
80	C₂×C₃²×C₈	C₂²×C₃	1	16	yes	complemented
81	C₃×#208	C₂²×C₃	1	16	yes	complemented
82	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	8	yes	—
83	C₃×ΓL(1,𝔽₂₅)	C₂²×C₃	1	32	yes	complemented
84	C₃×D₃×C₈	C₂²×C₃	1	32	yes	complemented
85	C₂²×C₃³	—	2	2	no	—
86	C₂²×C₃³	C₂²×C₄	1	2	yes	—
87	C₂²×C₃³	C₂²×C₄	1	1	yes	characteristic
88	C₂×C₃²×D₃	—	2	4	no	—
89	C₂×C₃²×D₃	C₂²×C₄	1	4	yes	—
90	C₃³×C₄	C₂²×C₄	1	2	yes	—
91	C₃³×C₄	C₂²×C₄	1	1	yes	characteristic
92	C₃³×C₄	C₂⁴	1	1	yes	characteristic
93	C₃²×Dic₃	C₂²×C₄	1	4	yes	—
94	C₂×C₃×#41	—	3	4	no	—
95	C₂×#235	C₂×C₃²	1	1	yes	characteristic
96	C₃×#131	—	3	32	no	—
97	C₂×C₃×M₁₆	—	3	4	no	—
98	C₂×C₃×M₁₆	—	3	8	no	—
99	C₂²×C₃×C₈	—	2	4	no	—
100	C₂²×C₃×C₈	—	3	8	no	—
101	C₂²×C₃×C₈	C₃×D₃	1	4	yes	complemented
102	C₂²×C₃×C₈	C₂×C₃²	1	1	yes	characteristic, complemented
103	C₂×#208	C₂×C₃²	1	1	yes	characteristic, complemented
104	#901	C₂×C₃²	1	8	yes	direct product factor
105	C₂×ΓL(1,𝔽₂₅)	C₂×C₃²	1	2	yes	complemented
106	C₂×D₃×C₈	C₂×C₃²	1	2	yes	complemented
107	C₂³×C₃²	—	2	4	no	—
108	C₂³×C₃²	—	3	2	no	—
109	C₂³×C₃²	C₄×D₃	1	1	yes	characteristic
110	C₂³×C₃²	C₂×C₃×C₄	1	4	yes	—
111	C₂²×C₃×D₃	C₂×C₃×C₄	1	8	yes	—
112	C₃²×Q₈	—	3	4	no	—
113	C₃²×D₄	—	3	8	no	—
114	C₃²×D₄	—	3	4	no	—
115	C₂×C₃²×C₄	—	2	4	no	—
116	C₂×C₃²×C₄	—	2	8	no	—
117	C₂×C₃²×C₄	—	2	4	no	—
118	C₂×C₃²×C₄	—	2	8	no	—
119	C₂×C₃²×C₄	—	3	2	no	—
120	C₂×C₃²×C₄	—	3	4	no	—
121	C₂×C₃²×C₄	—	3	4	no	—
122	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
123	C₂×C₃²×C₄	C₄×D₃	1	2	yes	—
124	C₂×C₃²×C₄	C₂×C₃×C₄	1	4	yes	—
125	C₂×C₃²×C₄	C₂×C₃×C₄	1	8	yes	—
126	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
127	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
128	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
129	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
130	C₃×#67	C₂×C₃×C₄	1	32	yes	—
131	C₂×C₃×Dic₃	C₂×C₃×C₄	1	8	yes	—
132	C₃×D₁₂	C₂×C₃×C₄	1	16	yes	—
133	C₃×C₄×D₃	C₂×C₃×C₄	1	16	yes	—
134	C₃×C₄×D₃	C₂³×C₃	1	16	yes	—
135	C₃×Dic₆	C₂×C₃×C₄	1	16	yes	—
136	C₃²×C₈	—	2	8	no	—
137	C₃²×C₈	—	2	8	no	—
138	C₃²×C₈	—	3	4	no	—
139	C₃²×C₈	C₂²×D₃	1	2	yes	—
140	C₃²×C₈	C₂²×D₃	1	2	yes	—
141	C₃²×C₈	C₂³×C₃	1	8	yes	—
142	C₃²×C₈	C₂³×C₃	1	8	yes	—
143	C₃×C₃⋊C₈	C₂³×C₃	1	16	yes	—
144	C₂×#131	—	3	1	no	Sylow
145	C₂×C₃³	—	2	2	no	—
146	C₂×C₃³	#131	1	2	yes	complemented
147	C₂×C₃³	C₂³×C₄	1	1	yes	characteristic
148	C₃²×D₃	—	2	4	no	—
149	C₃×#41	—	3	16	no	—
150	C₃×#41	—	3	16	no	—
151	C₂×C₃×Q₈	—	3	4	no	—
152	C₂×C₃×D₄	—	3	8	no	—
153	C₂×C₃×D₄	—	3	4	no	—
154	C₂²×C₃×C₄	—	2	4	no	—
155	C₂²×C₃×C₄	—	3	8	no	—
156	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
157	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
158	C₂×#67	C₃²×C₄	1	2	yes	—
159	#235	C₃²×C₄	1	4	yes	—
160	#235	C₂²×C₃²	1	4	yes	—
161	C₂×D₁₂	C₃²×C₄	1	1	yes	characteristic
162	C₂×C₄×D₃	C₂²×C₃²	1	2	yes	—
163	C₂×Dic₆	C₃²×C₄	1	1	yes	characteristic
164	C₃×M₁₆	—	3	16	no	—
165	C₃×M₁₆	—	3	32	no	—
166	C₂×C₃×C₈	—	2	4	no	—
167	C₂×C₃×C₈	—	2	4	no	—
168	C₂×C₃×C₈	—	2	16	no	—
169	C₂×C₃×C₈	—	3	8	no	—
170	C₂×C₃×C₈	—	3	32	no	—
171	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
172	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
173	C₂×C₃×C₈	C₂×C₃×D₃	1	16	yes	complemented
174	C₂×C₃×C₈	C₂²×C₃²	1	1	yes	characteristic
175	C₂×C₃×C₈	C₂²×C₃²	1	1	yes	characteristic
176	C₂×C₃×C₈	C₂²×C₃²	1	4	yes	complemented
177	#208	C₂²×C₃²	1	4	yes	complemented
178	C₂×C₃⋊C₈	C₂²×C₃²	1	2	yes	—
179	ΓL(1,𝔽₂₅)	C₂²×C₃²	1	8	yes	complemented
180	D₃×C₈	C₂²×C₃²	1	8	yes	complemented
181	C₂²×C₃²	—	2	16	no	—
182	C₂²×C₃²	—	2	2	no	—
183	C₂²×C₃²	—	2	8	no	—
184	C₂²×C₃²	—	2	8	no	—
185	C₂²×C₃²	—	2	4	no	—
186	C₂²×C₃²	—	3	4	no	—
187	C₂²×C₃²	—	6	4	no	—
188	C₂²×C₃²	C₂×C₄×D₃	1	2	yes	—
189	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
190	C₂²×C₃²	C₂²×C₃×C₄	1	8	yes	—
191	C₂²×C₃²	C₂²×C₃×C₄	1	4	yes	—
192	C₂×C₃×D₃	—	2	16	no	—
193	C₂×C₃×D₃	C₂²×C₃×C₄	1	16	yes	—
194	C₃²×C₄	—	2	4	no	—
195	C₃²×C₄	—	2	4	no	—
196	C₃²×C₄	—	2	8	no	—
197	C₃²×C₄	—	3	4	no	—
198	C₃²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
199	C₃²×C₄	C₂×C₄×D₃	1	2	yes	—
200	C₃²×C₄	C₂²×C₃×C₄	1	8	yes	—
201	C₃²×C₄	C₂²×C₃×C₄	1	4	yes	—
202	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
203	C₃²×C₄	C₂⁴×C₃	1	4	yes	—
204	C₃×Dic₃	C₂²×C₃×C₄	1	16	yes	—
205	C₂×#41	—	3	1	no	—
206	#131	—	3	8	no	—
207	C₂×M₁₆	—	3	1	no	—
208	C₂×M₁₆	—	3	2	no	—
209	C₂²×C₈	—	3	2	no	—
210	C₂²×C₈	C₃²×D₃	1	1	yes	characteristic, complemented
211	C₃³	C₂×#131	1	1	yes	characteristic, complemented, Sylow
212	C₂³×C₃	—	2	4	no	—
213	C₂³×C₃	—	3	8	no	—
214	C₂³×C₃	C₃×C₄×D₃	1	4	yes	—
215	C₂³×C₃	C₂×C₃²×C₄	1	1	yes	characteristic
216	C₂²×D₃	C₂×C₃²×C₄	1	2	yes	—
217	C₃×Q₈	—	3	16	no	—
218	C₃×D₄	—	3	32	no	—
219	C₃×D₄	—	3	16	no	—
220	C₂×C₃×C₄	—	2	4	no	—
221	C₂×C₃×C₄	—	2	8	no	—
222	C₂×C₃×C₄	—	2	4	no	—
223	C₂×C₃×C₄	—	2	8	no	—
224	C₂×C₃×C₄	—	3	8	no	—
225	C₂×C₃×C₄	—	3	16	no	—
226	C₂×C₃×C₄	—	3	16	no	—
227	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
228	C₂×C₃×C₄	C₃×C₄×D₃	1	8	yes	—
229	C₂×C₃×C₄	C₂×C₃²×C₄	1	1	yes	characteristic
230	C₂×C₃×C₄	C₂×C₃²×C₄	1	2	yes	—
231	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
232	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
233	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
234	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
235	#67	C₂×C₃²×C₄	1	8	yes	—
236	C₂×Dic₃	C₂×C₃²×C₄	1	2	yes	—
237	D₁₂	C₂×C₃²×C₄	1	4	yes	—
238	C₄×D₃	C₂×C₃²×C₄	1	4	yes	—
239	C₄×D₃	C₂³×C₃²	1	4	yes	—
240	Dic₆	C₂×C₃²×C₄	1	4	yes	—
241	C₃×C₈	—	2	8	no	—
242	C₃×C₈	—	2	8	no	—
243	C₃×C₈	—	3	16	no	—
244	C₃×C₈	C₂²×C₃×D₃	1	8	yes	—
245	C₃×C₈	C₂²×C₃×D₃	1	8	yes	—
246	C₃×C₈	C₂³×C₃²	1	2	yes	—
247	C₃×C₈	C₂³×C₃²	1	2	yes	—
248	C₃⋊C₈	C₂³×C₃²	1	4	yes	—
249	C₂×C₃²	—	2	16	no	—
250	C₂×C₃²	—	2	8	no	—
251	C₂×C₃²	—	2	2	no	—
252	C₂×C₃²	—	2	8	no	—
253	C₂×C₃²	—	2	4	no	—
254	C₂×C₃²	—	6	4	no	—
255	C₂×C₃²	#901	1	2	yes	direct product factor
256	C₂×C₃²	C₃×#131	1	8	yes	complemented
257	C₂×C₃²	C₂²×C₄×D₃	1	1	yes	characteristic
258	C₂×C₃²	C₂³×C₃×C₄	1	4	yes	—
259	C₃×D₃	—	2	16	no	—
260	#41	—	3	4	no	—
261	#41	—	3	4	no	—
262	C₂×Q₈	—	3	1	no	—
263	C₂×D₄	—	3	2	no	—
264	C₂×D₄	—	3	1	no	—
265	C₂²×C₄	—	3	2	no	—
266	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
267	M₁₆	—	3	4	no	—
268	M₁₆	—	3	8	no	—
269	C₂×C₈	—	3	2	no	—
270	C₂×C₈	—	3	8	no	—
271	C₂×C₈	C₂×C₃²×D₃	1	1	yes	characteristic
272	C₂×C₈	C₂×C₃²×D₃	1	1	yes	characteristic
273	C₂×C₈	C₂×C₃²×D₃	1	4	yes	complemented
274	C₂²×C₃	—	2	16	no	—
275	C₂²×C₃	—	2	8	no	—
276	C₂²×C₃	—	2	2	no	—
277	C₂²×C₃	—	2	8	no	—
278	C₂²×C₃	—	2	4	no	—
279	C₂²×C₃	—	3	16	no	—
280	C₂²×C₃	—	6	16	no	—
281	C₂²×C₃	C₂×C₃×C₄×D₃	1	8	yes	—
282	C₂²×C₃	C₂×C₃×C₄×D₃	1	4	yes	—
283	C₂²×C₃	C₂²×C₃²×C₄	1	2	yes	—
284	C₂²×C₃	C₂²×C₃²×C₄	1	1	yes	characteristic
285	C₂×D₃	—	2	4	no	—
286	C₂×D₃	C₂²×C₃²×C₄	1	4	yes	—
287	C₃×C₄	—	2	4	no	—
288	C₃×C₄	—	2	4	no	—
289	C₃×C₄	—	2	8	no	—
290	C₃×C₄	—	3	16	no	—
291	C₃×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
292	C₃×C₄	C₂×C₃×C₄×D₃	1	8	yes	—
293	C₃×C₄	C₂²×C₃²×C₄	1	2	yes	—
294	C₃×C₄	C₂²×C₃²×C₄	1	1	yes	characteristic
295	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
296	C₃×C₄	C₂⁴×C₃²	1	1	yes	characteristic
297	Dic₃	C₂²×C₃²×C₄	1	4	yes	—
298	C₃²	—	2	4	no	—
299	C₃²	C₂×#901	1	1	yes	characteristic, direct product factor
300	C₃²	C₂×C₃×#131	1	4	yes	complemented
301	C₂³	—	3	2	no	—
302	C₂³	C₃²×C₄×D₃	1	1	yes	characteristic
303	Q₈	—	3	4	no	—
304	D₄	—	3	8	no	—
305	D₄	—	3	4	no	—
306	C₂×C₄	—	3	2	no	—
307	C₂×C₄	—	3	4	no	—
308	C₂×C₄	—	3	4	no	—
309	C₂×C₄	C₃²×C₄×D₃	1	1	yes	characteristic
310	C₂×C₄	C₃²×C₄×D₃	1	2	yes	—
311	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
312	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
313	C₈	—	3	4	no	—
314	C₈	C₂²×C₃²×D₃	1	2	yes	—
315	C₈	C₂²×C₃²×D₃	1	2	yes	—
316	C₂×C₃	—	2	16	no	—
317	C₂×C₃	—	2	2	no	—
318	C₂×C₃	—	2	8	no	—
319	C₂×C₃	—	2	4	no	—
320	C₂×C₃	—	2	8	no	—
321	C₂×C₃	—	6	16	no	—
322	C₂×C₃	C₃×#901	1	8	yes	direct product factor
323	C₂×C₃	C₃²×#131	1	2	yes	complemented
324	C₂×C₃	C₂²×C₃×C₄×D₃	1	4	yes	—
325	C₂×C₃	C₂³×C₃²×C₄	1	1	yes	characteristic
326	D₃	—	2	4	no	—
327	C₂²	—	2	2	no	—
328	C₂²	—	3	4	no	—
329	C₂²	—	6	4	no	—
330	C₂²	C₂×C₃²×C₄×D₃	1	2	yes	—
331	C₂²	C₂×C₃²×C₄×D₃	1	1	yes	characteristic
332	C₄	—	3	4	no	—
333	C₄	C₂×C₃²×C₄×D₃	1	1	yes	characteristic
334	C₄	C₂×C₃²×C₄×D₃	1	2	yes	—
335	C₄	C₂³×C₃²×D₃	1	1	yes	characteristic
336	C₃	—	2	4	no	—
337	C₃	C₂×C₃×#901	1	4	yes	direct product factor
338	C₃	C₂×C₃²×#131	1	1	yes	characteristic, complemented
339	C₂	—	2	2	no	—
340	C₂	—	6	4	no	—
341	C₂	C₃²×#901	1	2	yes	direct product factor
342	C₂	C₂²×C₃²×C₄×D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃²×C₈	C₂×D₃
commutator	C₂×C₃	C₂³×C₃²×C₄
Frattini	C₄	C₂³×C₃²×D₃
Fitting	C₂²×C₃³×C₈	C₂
socle	C₂²×C₃³	C₂²×C₄
prime radical	C₂×C₃²×#235	C₂
cosocle	C₃×C₄	C₂⁴×C₃²
hypercenter	C₂²×C₃²×C₈	D₃
hypocenter	C₃	C₂×C₃²×#131
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃²×C₈ ◁ C₂²×C₃²×C₈

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃³×C₈	C₂	semidirect
3. C₂×C₃²×#208	C₂	semidirect
4. C₃²×#901	C₂	direct (N × H)
5. C₂×C₃²×ΓL(1,𝔽₂₅)	C₂	semidirect
6. C₂×C₃²×D₃×C₈	C₂	semidirect
8. C₂×C₃×#901	C₃	direct (N × H)
18. C₂×C₃³×C₈	C₂²	semidirect
19. C₃²×#208	C₂²	semidirect
21. C₃²×ΓL(1,𝔽₂₅)	C₂²	semidirect
22. C₃²×D₃×C₈	C₂²	semidirect
30. C₂²×C₃²×C₈	D₃	semidirect
31. C₂²×C₃²×C₈	C₂×C₃	semidirect
32. C₂×C₃×#208	C₂×C₃	semidirect
33. C₃×#901	C₂×C₃	direct (N × H)
34. C₂×C₃×ΓL(1,𝔽₂₅)	C₂×C₃	semidirect
35. C₂×C₃×D₃×C₈	C₂×C₃	semidirect
52. C₂×#901	C₃²	direct (N × H)
77. C₂×C₃²×C₈	C₂×D₃	semidirect
80. C₂×C₃²×C₈	C₂²×C₃	semidirect
81. C₃×#208	C₂²×C₃	semidirect
83. C₃×ΓL(1,𝔽₂₅)	C₂²×C₃	semidirect
84. C₃×D₃×C₈	C₂²×C₃	semidirect
101. C₂²×C₃×C₈	C₃×D₃	semidirect
102. C₂²×C₃×C₈	C₂×C₃²	semidirect
103. C₂×#208	C₂×C₃²	semidirect
104. #901	C₂×C₃²	direct (N × H)
105. C₂×ΓL(1,𝔽₂₅)	C₂×C₃²	semidirect
106. C₂×D₃×C₈	C₂×C₃²	semidirect
146. C₂×C₃³	#131	semidirect
173. C₂×C₃×C₈	C₂×C₃×D₃	semidirect
176. C₂×C₃×C₈	C₂²×C₃²	semidirect
177. #208	C₂²×C₃²	semidirect
179. ΓL(1,𝔽₂₅)	C₂²×C₃²	semidirect
180. D₃×C₈	C₂²×C₃²	semidirect
210. C₂²×C₈	C₃²×D₃	semidirect
211. C₃³	C₂×#131	semidirect
255. C₂×C₃²	#901	direct (N × H)
256. C₂×C₃²	C₃×#131	semidirect
273. C₂×C₈	C₂×C₃²×D₃	semidirect
299. C₃²	C₂×#901	direct (N × H)
300. C₃²	C₂×C₃×#131	semidirect
322. C₂×C₃	C₃×#901	direct (N × H)
323. C₂×C₃	C₃²×#131	semidirect
337. C₃	C₂×C₃×#901	direct (N × H)
338. C₃	C₂×C₃²×#131	semidirect
341. C₂	C₃²×#901	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×#235	2
C₂²×C₃³×C₈	2
C₂×C₃²×#208	2
C₃²×#901	2
C₂×C₃²×ΓL(1,𝔽₂₅)	2
C₂×C₃²×D₃×C₈	2
C₂×C₃²×#131	3
C₂×C₃×#901	3

Subgroups — C2×C32×#901 #13179115

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×#901 #13179115