Subgroups — C₂×C₉×#546 #11768184

Order 1152.

2850 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#546	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₉×#124	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₉×#123	C₂	1	2	yes	maximal, complemented
6	C₂×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₉×#121	C₂	1	2	yes	maximal, complemented
8	C₂×C₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₉×#120	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₉×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
13	C₂×C₃×#546	C₃	1	1	yes	maximal, characteristic
14	C₂⁵×C₉	C₂²	1	2	yes	—
15	C₂×C₉×#41	—	2	8	no	—
16	C₂×C₉×#41	C₂²	1	8	yes	complemented
17	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₄×C₉	—	2	8	no	—
19	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
20	C₂²×D₄×C₉	C₂²	1	2	yes	—
21	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
22	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
23	C₂²×D₄×C₉	C₂²	1	8	yes	complemented
24	C₂²×D₄×C₉	C₂²	1	2	yes	complemented
25	C₂²×D₄×C₉	C₂²	1	2	yes	complemented
26	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
27	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic, complemented
28	C₂³×C₄×C₉	C₂²	1	2	yes	complemented
29	C₂³×C₄×C₉	C₂²	1	2	yes	complemented
30	C₉×#124	C₂²	1	8	yes	complemented
31	C₉×#123	C₂²	1	16	yes	complemented
32	C₉×C₂²⋊Q₈	C₂²	1	8	yes	complemented
33	C₉×#121	C₂²	1	8	yes	complemented
34	C₉×#121	C₂²	1	16	yes	complemented
35	C₉×#120	C₂²	1	16	yes	complemented
36	C₄×D₄×C₉	C₂²	1	8	yes	complemented
37	C₄×D₄×C₉	C₂²	1	8	yes	complemented
38	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	complemented
39	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
42	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×C₉×C₂²⋊C₄	C₂²	1	16	yes	complemented
44	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	complemented
45	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	complemented
46	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	complemented
48	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	complemented
49	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic, complemented
50	C₂²×C₃×#41	C₂×C₃	1	1	yes	characteristic
51	C₂³×C₃×D₄	C₂×C₃	1	1	yes	characteristic
52	C₃×#546	C₂×C₃	1	16	yes	—
53	C₂×C₃×#124	C₂×C₃	1	1	yes	characteristic
54	C₂×C₃×#123	C₂×C₃	1	2	yes	—
55	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
56	C₂×C₃×#121	C₂×C₃	1	1	yes	characteristic
57	C₂×C₃×#121	C₂×C₃	1	2	yes	—
58	C₂×C₃×#120	C₂×C₃	1	2	yes	—
59	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
60	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
61	C₂²×C₃×C₂²⋊C₄	C₂×C₃	1	2	yes	—
62	C₂⁴×C₉	—	2	8	no	—
63	C₂⁴×C₉	—	2	8	no	—
64	C₂⁴×C₉	—	4	4	no	—
65	C₂⁴×C₉	C₂³	1	2	yes	—
66	C₂⁴×C₉	C₂³	1	1	yes	characteristic
67	C₂⁴×C₉	C₂³	1	8	yes	—
68	C₂⁴×C₉	C₂³	1	2	yes	—
69	C₂⁴×C₉	C₂³	1	1	yes	characteristic
70	C₉×#41	—	2	32	no	—
71	C₂×Q₈×C₉	—	2	4	no	—
72	C₂×Q₈×C₉	C₂³	1	4	yes	complemented
73	C₂×D₄×C₉	—	2	8	no	—
74	C₂×D₄×C₉	—	2	8	no	—
75	C₂×D₄×C₉	—	2	4	no	—
76	C₂×D₄×C₉	—	2	32	no	—
77	C₂×D₄×C₉	—	2	4	no	—
78	C₂×D₄×C₉	—	4	4	no	—
79	C₂×D₄×C₉	D₄	1	8	yes	complemented
80	C₂×D₄×C₉	C₂³	1	4	yes	—
81	C₂×D₄×C₉	C₂³	1	8	yes	—
82	C₂×D₄×C₉	C₂³	1	4	yes	—
83	C₂×D₄×C₉	C₂³	1	4	yes	—
84	C₂×D₄×C₉	C₂³	1	8	yes	complemented
85	C₂×D₄×C₉	C₂³	1	8	yes	complemented
86	C₂²×C₄×C₉	—	2	8	no	—
87	C₂²×C₄×C₉	—	2	4	no	—
88	C₂²×C₄×C₉	—	2	4	no	—
89	C₂²×C₄×C₉	—	4	4	no	—
90	C₂²×C₄×C₉	C₂³	1	4	yes	—
91	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₉	C₂³	1	2	yes	—
94	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₉	C₂³	1	2	yes	—
96	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
98	C₂²×C₄×C₉	C₂³	1	8	yes	complemented
99	C₂²×C₄×C₉	C₂³	1	4	yes	complemented
100	C₂²×C₄×C₉	C₂³	1	8	yes	complemented
101	C₉×C₄⋊C₄	C₂³	1	4	yes	complemented
102	C₉×C₄⋊C₄	C₂³	1	4	yes	complemented
103	C₉×C₄⋊C₄	C₂³	1	8	yes	complemented
104	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
105	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
106	C₉×C₂²⋊C₄	C₂³	1	8	yes	complemented
107	C₉×C₂²⋊C₄	C₂³	1	8	yes	complemented
108	C₉×C₂²⋊C₄	C₂³	1	8	yes	complemented
109	C₉×C₂²⋊C₄	C₂³	1	4	yes	complemented
110	C₉×C₂²⋊C₄	C₂³	1	8	yes	complemented
111	C₄²×C₉	C₂³	1	4	yes	complemented
112	C₂×#546	C₉	1	1	yes	characteristic, direct product factor, Sylow
113	C₂⁵×C₃	C₂²×C₃	1	2	yes	—
114	C₂×C₃×#41	—	2	8	no	—
115	C₂×C₃×#41	C₂²×C₃	1	8	yes	—
116	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
117	C₂²×C₃×D₄	—	2	8	no	—
118	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
119	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
120	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
121	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
122	C₂²×C₃×D₄	C₂²×C₃	1	8	yes	—
123	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
124	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
125	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
126	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
127	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
128	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
129	C₃×#124	C₂²×C₃	1	8	yes	—
130	C₃×#123	C₂²×C₃	1	16	yes	—
131	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
132	C₃×#121	C₂²×C₃	1	8	yes	—
133	C₃×#121	C₂²×C₃	1	16	yes	—
134	C₃×#120	C₂²×C₃	1	16	yes	—
135	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
136	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
137	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
138	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
139	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
140	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
141	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
142	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
143	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
144	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	16	yes	—
145	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
146	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
148	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
149	C₂³×C₉	—	2	2	no	—
150	C₂³×C₉	—	2	4	no	—
151	C₂³×C₉	—	2	4	no	—
152	C₂³×C₉	—	2	2	no	—
153	C₂³×C₉	—	2	2	no	—
154	C₂³×C₉	—	2	16	no	—
155	C₂³×C₉	—	2	4	no	—
156	C₂³×C₉	—	2	2	no	—
157	C₂³×C₉	—	2	4	no	—
158	C₂³×C₉	—	2	16	no	—
159	C₂³×C₉	—	2	2	no	—
160	C₂³×C₉	—	2	4	no	—
161	C₂³×C₉	—	4	8	no	—
162	C₂³×C₉	—	4	32	no	—
163	C₂³×C₉	C₂×D₄	1	8	yes	—
164	C₂³×C₉	#41	1	4	yes	complemented
165	C₂³×C₉	C₂⁴	1	4	yes	—
166	C₂³×C₉	C₂⁴	1	2	yes	—
167	C₂³×C₉	C₂⁴	1	4	yes	—
168	C₂³×C₉	C₂⁴	1	2	yes	—
169	C₂³×C₉	C₂⁴	1	1	yes	characteristic
170	Q₈×C₉	—	2	8	no	—
171	D₄×C₉	—	2	16	no	—
172	D₄×C₉	—	2	16	no	—
173	D₄×C₉	—	2	8	no	—
174	D₄×C₉	—	2	8	no	—
175	D₄×C₉	—	4	8	no	—
176	D₄×C₉	C₂×D₄	1	16	yes	complemented
177	C₂×C₄×C₉	—	2	2	no	—
178	C₂×C₄×C₉	—	2	2	no	—
179	C₂×C₄×C₉	—	2	4	no	—
180	C₂×C₄×C₉	—	2	16	no	—
181	C₂×C₄×C₉	—	2	2	no	—
182	C₂×C₄×C₉	—	2	2	no	—
183	C₂×C₄×C₉	—	2	4	no	—
184	C₂×C₄×C₉	—	2	8	no	—
185	C₂×C₄×C₉	—	2	8	no	—
186	C₂×C₄×C₉	—	4	8	no	—
187	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
188	C₂×C₄×C₉	C₂⁴	1	2	yes	—
189	C₂×C₄×C₉	C₂⁴	1	2	yes	—
190	C₂×C₄×C₉	C₂⁴	1	4	yes	—
191	C₂×C₄×C₉	C₂⁴	1	2	yes	—
192	C₂×C₄×C₉	C₂⁴	1	4	yes	—
193	C₂×C₄×C₉	C₂⁴	1	2	yes	—
194	C₂×C₄×C₉	C₂⁴	1	2	yes	—
195	C₂²×#41	C₂×C₉	1	1	yes	characteristic, complemented
196	C₂³×D₄	C₂×C₉	1	1	yes	characteristic, complemented
197	#546	C₂×C₉	1	16	yes	direct product factor
198	C₂×#124	C₂×C₉	1	1	yes	characteristic, complemented
199	C₂×#123	C₂×C₉	1	2	yes	complemented
200	C₂×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
201	C₂×#121	C₂×C₉	1	1	yes	characteristic, complemented
202	C₂×#121	C₂×C₉	1	2	yes	complemented
203	C₂×#120	C₂×C₉	1	2	yes	complemented
204	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic, complemented
205	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic, complemented
206	C₂²×C₂²⋊C₄	C₂×C₉	1	2	yes	complemented
207	C₂⁴×C₃	—	2	8	no	—
208	C₂⁴×C₃	—	2	8	no	—
209	C₂⁴×C₃	—	4	4	no	—
210	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
211	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
212	C₂⁴×C₃	C₂³×C₃	1	8	yes	—
213	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
214	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
215	C₃×#41	—	2	32	no	—
216	C₂×C₃×Q₈	—	2	4	no	—
217	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
218	C₂×C₃×D₄	—	2	8	no	—
219	C₂×C₃×D₄	—	2	8	no	—
220	C₂×C₃×D₄	—	2	4	no	—
221	C₂×C₃×D₄	—	2	32	no	—
222	C₂×C₃×D₄	—	2	4	no	—
223	C₂×C₃×D₄	—	4	4	no	—
224	C₂×C₃×D₄	C₃×D₄	1	8	yes	—
225	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
226	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
227	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
228	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
229	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
230	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
231	C₂²×C₃×C₄	—	2	8	no	—
232	C₂²×C₃×C₄	—	2	4	no	—
233	C₂²×C₃×C₄	—	2	4	no	—
234	C₂²×C₃×C₄	—	4	4	no	—
235	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
236	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
237	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
238	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
239	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
240	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
241	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
242	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
243	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
244	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
245	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
246	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
247	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
248	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
249	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
250	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
251	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
252	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
253	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
254	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
255	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
256	C₃×C₄²	C₂³×C₃	1	4	yes	—
257	C₂²×C₉	—	2	8	no	—
258	C₂²×C₉	—	2	16	no	—
259	C₂²×C₉	—	2	2	no	—
260	C₂²×C₉	—	2	4	no	—
261	C₂²×C₉	—	2	4	no	—
262	C₂²×C₉	—	2	2	no	—
263	C₂²×C₉	—	2	2	no	—
264	C₂²×C₉	—	2	4	no	—
265	C₂²×C₉	—	2	2	no	—
266	C₂²×C₉	—	2	4	no	—
267	C₂²×C₉	—	2	2	no	—
268	C₂²×C₉	—	2	4	no	—
269	C₂²×C₉	—	4	32	no	—
270	C₂²×C₉	—	4	4	no	—
271	C₂²×C₉	—	4	8	no	—
272	C₂²×C₉	C₂²×D₄	1	8	yes	—
273	C₂²×C₉	C₂²×D₄	1	2	yes	—
274	C₂²×C₉	C₂×#41	1	2	yes	—
275	C₂²×C₉	C₂×#41	1	4	yes	complemented
276	C₂²×C₉	H(5,𝔽₂)	1	2	yes	—
277	C₂²×C₉	C₂⁵	1	1	yes	characteristic
278	C₄×C₉	—	2	2	no	—
279	C₄×C₉	—	2	2	no	—
280	C₄×C₉	—	2	4	no	—
281	C₄×C₉	—	2	2	no	—
282	C₄×C₉	—	2	2	no	—
283	C₄×C₉	—	2	4	no	—
284	C₄×C₉	C₂²×D₄	1	4	yes	—
285	C₂⁵	C₂²×C₉	1	2	yes	—
286	C₂×#41	—	2	8	no	—
287	C₂×#41	C₂²×C₉	1	8	yes	complemented
288	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
289	C₂²×D₄	—	2	8	no	—
290	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
291	C₂²×D₄	C₂²×C₉	1	2	yes	—
292	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
293	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
294	C₂²×D₄	C₂²×C₉	1	8	yes	complemented
295	C₂²×D₄	C₂²×C₉	1	2	yes	complemented
296	C₂²×D₄	C₂²×C₉	1	2	yes	complemented
297	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
298	C₂³×C₄	C₂²×C₉	1	2	yes	complemented
299	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic, complemented
300	C₂³×C₄	C₂²×C₉	1	2	yes	complemented
301	#124	C₂²×C₉	1	8	yes	complemented
302	#123	C₂²×C₉	1	16	yes	complemented
303	C₂²⋊Q₈	C₂²×C₉	1	8	yes	complemented
304	#121	C₂²×C₉	1	8	yes	complemented
305	#121	C₂²×C₉	1	16	yes	complemented
306	#120	C₂²×C₉	1	16	yes	complemented
307	C₄×D₄	C₂²×C₉	1	8	yes	complemented
308	C₄×D₄	C₂²×C₉	1	8	yes	complemented
309	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
310	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
311	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	complemented
312	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
314	C₂×C₂²⋊C₄	C₂²×C₉	1	16	yes	complemented
315	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	complemented
316	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	complemented
317	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	complemented
318	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
319	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	complemented
320	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic, complemented
321	C₂³×C₃	—	2	2	no	—
322	C₂³×C₃	—	2	4	no	—
323	C₂³×C₃	—	2	4	no	—
324	C₂³×C₃	—	2	2	no	—
325	C₂³×C₃	—	2	2	no	—
326	C₂³×C₃	—	2	16	no	—
327	C₂³×C₃	—	2	4	no	—
328	C₂³×C₃	—	2	2	no	—
329	C₂³×C₃	—	2	4	no	—
330	C₂³×C₃	—	2	16	no	—
331	C₂³×C₃	—	2	2	no	—
332	C₂³×C₃	—	2	4	no	—
333	C₂³×C₃	—	4	8	no	—
334	C₂³×C₃	—	4	32	no	—
335	C₂³×C₃	C₂×C₃×D₄	1	8	yes	—
336	C₂³×C₃	C₃×#41	1	4	yes	—
337	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
338	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
339	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
340	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
341	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
342	C₃×Q₈	—	2	8	no	—
343	C₃×D₄	—	2	16	no	—
344	C₃×D₄	—	2	16	no	—
345	C₃×D₄	—	2	8	no	—
346	C₃×D₄	—	2	8	no	—
347	C₃×D₄	—	4	8	no	—
348	C₃×D₄	C₂×C₃×D₄	1	16	yes	—
349	C₂×C₃×C₄	—	2	2	no	—
350	C₂×C₃×C₄	—	2	2	no	—
351	C₂×C₃×C₄	—	2	4	no	—
352	C₂×C₃×C₄	—	2	16	no	—
353	C₂×C₃×C₄	—	2	2	no	—
354	C₂×C₃×C₄	—	2	2	no	—
355	C₂×C₃×C₄	—	2	4	no	—
356	C₂×C₃×C₄	—	2	8	no	—
357	C₂×C₃×C₄	—	2	8	no	—
358	C₂×C₃×C₄	—	4	8	no	—
359	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
360	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
361	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
362	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
363	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
364	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
365	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
366	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
367	C₂×C₉	—	2	4	no	—
368	C₂×C₉	—	2	8	no	—
369	C₂×C₉	—	4	2	no	—
370	C₂×C₉	—	4	4	no	—
371	C₂×C₉	#546	1	4	yes	direct product factor
372	C₂×C₉	C₂³×D₄	1	1	yes	characteristic
373	C₂×C₉	C₂²×#41	1	1	yes	characteristic
374	C₂×C₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
375	C₂⁴	—	2	8	no	—
376	C₂⁴	—	2	8	no	—
377	C₂⁴	—	4	4	no	—
378	C₂⁴	C₂³×C₉	1	2	yes	—
379	C₂⁴	C₂³×C₉	1	1	yes	characteristic
380	C₂⁴	C₂³×C₉	1	8	yes	—
381	C₂⁴	C₂³×C₉	1	2	yes	—
382	C₂⁴	C₂³×C₉	1	1	yes	characteristic
383	#41	—	2	32	no	—
384	C₂×Q₈	—	2	4	no	—
385	C₂×Q₈	C₂³×C₉	1	4	yes	complemented
386	C₂×D₄	—	2	8	no	—
387	C₂×D₄	—	2	8	no	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	2	32	no	—
390	C₂×D₄	—	2	4	no	—
391	C₂×D₄	—	4	4	no	—
392	C₂×D₄	D₄×C₉	1	8	yes	complemented
393	C₂×D₄	C₂³×C₉	1	4	yes	—
394	C₂×D₄	C₂³×C₉	1	8	yes	—
395	C₂×D₄	C₂³×C₉	1	4	yes	—
396	C₂×D₄	C₂³×C₉	1	4	yes	—
397	C₂×D₄	C₂³×C₉	1	8	yes	complemented
398	C₂×D₄	C₂³×C₉	1	8	yes	complemented
399	C₂²×C₄	—	2	8	no	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	4	4	no	—
403	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
404	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
405	C₂²×C₄	C₂³×C₉	1	2	yes	—
406	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
407	C₂²×C₄	C₂³×C₉	1	2	yes	—
408	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
409	C₂²×C₄	C₂³×C₉	1	4	yes	—
410	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
411	C₂²×C₄	C₂³×C₉	1	8	yes	complemented
412	C₂²×C₄	C₂³×C₉	1	4	yes	complemented
413	C₂²×C₄	C₂³×C₉	1	8	yes	complemented
414	C₄⋊C₄	C₂³×C₉	1	4	yes	complemented
415	C₄⋊C₄	C₂³×C₉	1	4	yes	complemented
416	C₄⋊C₄	C₂³×C₉	1	8	yes	complemented
417	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
418	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
419	C₂²⋊C₄	C₂³×C₉	1	8	yes	complemented
420	C₂²⋊C₄	C₂³×C₉	1	8	yes	complemented
421	C₂²⋊C₄	C₂³×C₉	1	8	yes	complemented
422	C₂²⋊C₄	C₂³×C₉	1	4	yes	complemented
423	C₂²⋊C₄	C₂³×C₉	1	8	yes	complemented
424	C₄²	C₂³×C₉	1	4	yes	complemented
425	C₂²×C₃	—	2	2	no	—
426	C₂²×C₃	—	2	4	no	—
427	C₂²×C₃	—	2	4	no	—
428	C₂²×C₃	—	2	2	no	—
429	C₂²×C₃	—	2	8	no	—
430	C₂²×C₃	—	2	16	no	—
431	C₂²×C₃	—	2	2	no	—
432	C₂²×C₃	—	2	4	no	—
433	C₂²×C₃	—	2	2	no	—
434	C₂²×C₃	—	2	4	no	—
435	C₂²×C₃	—	2	2	no	—
436	C₂²×C₃	—	2	4	no	—
437	C₂²×C₃	—	4	32	no	—
438	C₂²×C₃	—	4	8	no	—
439	C₂²×C₃	—	4	4	no	—
440	C₂²×C₃	C₂²×C₃×D₄	1	8	yes	—
441	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
442	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
443	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
444	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
445	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
446	C₃×C₄	—	2	2	no	—
447	C₃×C₄	—	2	2	no	—
448	C₃×C₄	—	2	4	no	—
449	C₃×C₄	—	2	2	no	—
450	C₃×C₄	—	2	2	no	—
451	C₃×C₄	—	2	4	no	—
452	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
453	C₉	C₂×#546	1	1	yes	characteristic, direct product factor, Sylow
454	C₂³	—	2	2	no	—
455	C₂³	—	2	4	no	—
456	C₂³	—	2	4	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	16	no	—
460	C₂³	—	2	4	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	4	no	—
463	C₂³	—	2	16	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	4	no	—
466	C₂³	—	4	8	no	—
467	C₂³	—	4	32	no	—
468	C₂³	C₂×D₄×C₉	1	8	yes	—
469	C₂³	C₉×#41	1	4	yes	complemented
470	C₂³	C₂⁴×C₉	1	4	yes	—
471	C₂³	C₂⁴×C₉	1	2	yes	—
472	C₂³	C₂⁴×C₉	1	4	yes	—
473	C₂³	C₂⁴×C₉	1	2	yes	—
474	C₂³	C₂⁴×C₉	1	1	yes	characteristic
475	Q₈	—	2	8	no	—
476	D₄	—	2	16	no	—
477	D₄	—	2	16	no	—
478	D₄	—	2	8	no	—
479	D₄	—	2	8	no	—
480	D₄	—	4	8	no	—
481	D₄	C₂×D₄×C₉	1	16	yes	complemented
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	16	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	8	no	—
490	C₂×C₄	—	2	8	no	—
491	C₂×C₄	—	4	8	no	—
492	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
493	C₂×C₄	C₂⁴×C₉	1	2	yes	—
494	C₂×C₄	C₂⁴×C₉	1	2	yes	—
495	C₂×C₄	C₂⁴×C₉	1	4	yes	—
496	C₂×C₄	C₂⁴×C₉	1	2	yes	—
497	C₂×C₄	C₂⁴×C₉	1	4	yes	—
498	C₂×C₄	C₂⁴×C₉	1	2	yes	—
499	C₂×C₄	C₂⁴×C₉	1	2	yes	—
500	C₂×C₃	—	2	4	no	—
501	C₂×C₃	—	2	8	no	—
502	C₂×C₃	—	4	4	no	—
503	C₂×C₃	—	4	2	no	—
504	C₂×C₃	C₃×#546	1	4	yes	—
505	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
506	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
507	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
508	C₂²	—	2	8	no	—
509	C₂²	—	2	16	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	4	no	—
512	C₂²	—	2	4	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	2	4	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	2	4	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	4	no	—
520	C₂²	—	4	32	no	—
521	C₂²	—	4	8	no	—
522	C₂²	—	4	4	no	—
523	C₂²	C₂²×D₄×C₉	1	8	yes	—
524	C₂²	C₂²×D₄×C₉	1	2	yes	—
525	C₂²	C₂×C₉×#41	1	2	yes	—
526	C₂²	C₂×C₉×#41	1	4	yes	complemented
527	C₂²	C₉×H(5,𝔽₂)	1	2	yes	—
528	C₂²	C₂⁵×C₉	1	1	yes	characteristic
529	C₄	—	2	2	no	—
530	C₄	—	2	2	no	—
531	C₄	—	2	4	no	—
532	C₄	—	2	2	no	—
533	C₄	—	2	2	no	—
534	C₄	—	2	4	no	—
535	C₄	C₂²×D₄×C₉	1	4	yes	—
536	C₃	C₂×C₃×#546	1	1	yes	characteristic
537	C₂	—	2	4	no	—
538	C₂	—	2	8	no	—
539	C₂	—	4	4	no	—
540	C₂	—	4	2	no	—
541	C₂	C₉×#546	1	4	yes	direct product factor
542	C₂	C₂³×D₄×C₉	1	1	yes	characteristic
543	C₂	C₂²×C₉×#41	1	1	yes	characteristic
544	C₂	C₂×C₉×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂²	C₂⁵×C₉
Frattini, cosocle	C₂²×C₃	C₂⁵×C₃
socle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂×C₃×#546	C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₉×#41	C₂	semidirect
2. C₂³×D₄×C₉	C₂	semidirect
3. C₉×#546	C₂	direct (N × H)
4. C₂×C₉×#124	C₂	semidirect
5. C₂×C₉×#123	C₂	semidirect
6. C₂×C₉×C₂²⋊Q₈	C₂	semidirect
7. C₂×C₉×#121	C₂	semidirect
8. C₂×C₉×#121	C₂	semidirect
9. C₂×C₉×#120	C₂	semidirect
10. C₂×C₄×D₄×C₉	C₂	semidirect
11. C₂×C₄×D₄×C₉	C₂	semidirect
12. C₂²×C₉×C₂²⋊C₄	C₂	semidirect
16. C₂×C₉×#41	C₂²	semidirect
17. C₂²×Q₈×C₉	C₂²	semidirect
23. C₂²×D₄×C₉	C₂²	semidirect
24. C₂²×D₄×C₉	C₂²	semidirect
25. C₂²×D₄×C₉	C₂²	semidirect
27. C₂³×C₄×C₉	C₂²	semidirect
28. C₂³×C₄×C₉	C₂²	semidirect
29. C₂³×C₄×C₉	C₂²	semidirect
30. C₉×#124	C₂²	semidirect
31. C₉×#123	C₂²	semidirect
32. C₉×C₂²⋊Q₈	C₂²	semidirect
33. C₉×#121	C₂²	semidirect
34. C₉×#121	C₂²	semidirect
35. C₉×#120	C₂²	semidirect
36. C₄×D₄×C₉	C₂²	semidirect
37. C₄×D₄×C₉	C₂²	semidirect
38. C₂×C₉×C₄⋊C₄	C₂²	semidirect
39. C₂×C₉×C₄⋊C₄	C₂²	semidirect
40. C₂×C₉×C₄⋊C₄	C₂²	semidirect
43. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
44. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
45. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
46. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
47. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
48. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
49. C₂×C₄²×C₉	C₂²	semidirect
72. C₂×Q₈×C₉	C₂³	semidirect
79. C₂×D₄×C₉	D₄	semidirect
84. C₂×D₄×C₉	C₂³	semidirect
85. C₂×D₄×C₉	C₂³	semidirect
98. C₂²×C₄×C₉	C₂³	semidirect
99. C₂²×C₄×C₉	C₂³	semidirect
100. C₂²×C₄×C₉	C₂³	semidirect
101. C₉×C₄⋊C₄	C₂³	semidirect
102. C₉×C₄⋊C₄	C₂³	semidirect
103. C₉×C₄⋊C₄	C₂³	semidirect
106. C₉×C₂²⋊C₄	C₂³	semidirect
107. C₉×C₂²⋊C₄	C₂³	semidirect
108. C₉×C₂²⋊C₄	C₂³	semidirect
109. C₉×C₂²⋊C₄	C₂³	semidirect
110. C₉×C₂²⋊C₄	C₂³	semidirect
111. C₄²×C₉	C₂³	semidirect
112. C₂×#546	C₉	direct (N × H)
164. C₂³×C₉	#41	semidirect
176. D₄×C₉	C₂×D₄	semidirect
195. C₂²×#41	C₂×C₉	semidirect
196. C₂³×D₄	C₂×C₉	semidirect
197. #546	C₂×C₉	direct (N × H)
198. C₂×#124	C₂×C₉	semidirect
199. C₂×#123	C₂×C₉	semidirect
200. C₂×C₂²⋊Q₈	C₂×C₉	semidirect
201. C₂×#121	C₂×C₉	semidirect
202. C₂×#121	C₂×C₉	semidirect
203. C₂×#120	C₂×C₉	semidirect
204. C₂×C₄×D₄	C₂×C₉	semidirect
205. C₂×C₄×D₄	C₂×C₉	semidirect
206. C₂²×C₂²⋊C₄	C₂×C₉	semidirect
275. C₂²×C₉	C₂×#41	semidirect
287. C₂×#41	C₂²×C₉	semidirect
288. C₂²×Q₈	C₂²×C₉	semidirect
294. C₂²×D₄	C₂²×C₉	semidirect
295. C₂²×D₄	C₂²×C₉	semidirect
296. C₂²×D₄	C₂²×C₉	semidirect
298. C₂³×C₄	C₂²×C₉	semidirect
299. C₂³×C₄	C₂²×C₉	semidirect
300. C₂³×C₄	C₂²×C₉	semidirect
301. #124	C₂²×C₉	semidirect
302. #123	C₂²×C₉	semidirect
303. C₂²⋊Q₈	C₂²×C₉	semidirect
304. #121	C₂²×C₉	semidirect
305. #121	C₂²×C₉	semidirect
306. #120	C₂²×C₉	semidirect
307. C₄×D₄	C₂²×C₉	semidirect
308. C₄×D₄	C₂²×C₉	semidirect
309. C₂×C₄⋊C₄	C₂²×C₉	semidirect
310. C₂×C₄⋊C₄	C₂²×C₉	semidirect
311. C₂×C₄⋊C₄	C₂²×C₉	semidirect
314. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
315. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
316. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
317. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
318. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
319. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
320. C₂×C₄²	C₂²×C₉	semidirect
371. C₂×C₉	#546	direct (N × H)
385. C₂×Q₈	C₂³×C₉	semidirect
392. C₂×D₄	D₄×C₉	semidirect
397. C₂×D₄	C₂³×C₉	semidirect
398. C₂×D₄	C₂³×C₉	semidirect
411. C₂²×C₄	C₂³×C₉	semidirect
412. C₂²×C₄	C₂³×C₉	semidirect
413. C₂²×C₄	C₂³×C₉	semidirect
414. C₄⋊C₄	C₂³×C₉	semidirect
415. C₄⋊C₄	C₂³×C₉	semidirect
416. C₄⋊C₄	C₂³×C₉	semidirect
419. C₂²⋊C₄	C₂³×C₉	semidirect
420. C₂²⋊C₄	C₂³×C₉	semidirect
421. C₂²⋊C₄	C₂³×C₉	semidirect
422. C₂²⋊C₄	C₂³×C₉	semidirect
423. C₂²⋊C₄	C₂³×C₉	semidirect
424. C₄²	C₂³×C₉	semidirect
453. C₉	C₂×#546	direct (N × H)
469. C₂³	C₉×#41	semidirect
481. D₄	C₂×D₄×C₉	semidirect
526. C₂²	C₂×C₉×#41	semidirect
541. C₂	C₉×#546	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×C₉×#41	2
C₂³×D₄×C₉	2
C₉×#546	2
C₂×C₉×#124	2
C₂×C₉×#123	2
C₂×C₉×C₂²⋊Q₈	2
C₂×C₉×#121	2
C₂×C₉×#120	2
C₂×C₄×D₄×C₉	2
C₂²×C₉×C₂²⋊C₄	2
C₂×C₃×#546	3

Subgroups — C2×C9×#546 #11768184

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#546 #11768184