Subgroups — C₂×C₉×#553 #11768192

Order 1152.

1878 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#553	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₉×#126	C₂	1	2	yes	maximal, complemented
3	C₂×C₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉×#123	C₂	1	2	yes	maximal, complemented
5	C₂×C₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₉×#121	C₂	1	2	yes	maximal, complemented
7	C₂×C₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄×D₄×C₉	C₂	1	2	yes	maximal, complemented
11	C₂×C₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃×#553	C₃	1	1	yes	maximal, characteristic
14	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
15	C₂²×D₄×C₉	C₂²	1	2	yes	—
16	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₉	C₂²	1	2	yes	—
18	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
19	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
20	C₂³×C₄×C₉	C₂²	1	2	yes	—
21	C₂³×C₄×C₉	C₂²	1	2	yes	—
22	C₉×#126	C₂²	1	16	yes	complemented
23	C₉×#125	C₂²	1	8	yes	complemented
24	C₉×#123	C₂²	1	16	yes	complemented
25	C₉×#121	C₂²	1	16	yes	complemented
26	C₉×#121	C₂²	1	8	yes	complemented
27	C₉×#121	C₂²	1	8	yes	complemented
28	C₄×D₄×C₉	C₂²	1	16	yes	complemented
29	C₄×D₄×C₉	C₂²	1	8	yes	complemented
30	C₄×D₄×C₉	C₂²	1	8	yes	complemented
31	C₉×#117	C₂²	1	8	yes	complemented
32	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
33	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
36	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
37	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₉×C₄⋊C₄	C₂²	1	8	yes	complemented
40	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
41	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
42	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
43	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
44	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
47	C₂×C₄²×C₉	C₂²	1	2	yes	—
48	C₃×#553	C₂×C₃	1	16	yes	—
49	C₂×C₃×#126	C₂×C₃	1	2	yes	—
50	C₂×C₃×#125	C₂×C₃	1	1	yes	characteristic
51	C₂×C₃×#123	C₂×C₃	1	2	yes	—
52	C₂×C₃×#121	C₂×C₃	1	2	yes	—
53	C₂×C₃×#121	C₂×C₃	1	1	yes	characteristic
54	C₂×C₃×#121	C₂×C₃	1	1	yes	characteristic
55	C₂×C₃×C₄×D₄	C₂×C₃	1	2	yes	—
56	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
57	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
58	C₂×C₃×#117	C₂×C₃	1	1	yes	characteristic
59	C₂²×C₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
60	C₂⁴×C₉	C₂³	1	1	yes	characteristic
61	C₂⁴×C₉	C₂³	1	2	yes	—
62	C₂⁴×C₉	C₂³	1	1	yes	characteristic
63	C₂×D₄×C₉	—	2	4	no	—
64	C₂×D₄×C₉	—	2	8	no	—
65	C₂×D₄×C₉	—	2	4	no	—
66	C₂×D₄×C₉	—	4	4	no	—
67	C₂×D₄×C₉	C₂³	1	8	yes	—
68	C₂×D₄×C₉	C₂³	1	4	yes	—
69	C₂×D₄×C₉	C₂³	1	4	yes	—
70	C₂×D₄×C₉	C₂³	1	8	yes	—
71	C₂²×C₄×C₉	—	2	4	no	—
72	C₂²×C₄×C₉	—	2	4	no	—
73	C₂²×C₄×C₉	—	4	4	no	—
74	C₂²×C₄×C₉	—	4	4	no	—
75	C₂²×C₄×C₉	C₂³	1	4	yes	—
76	C₂²×C₄×C₉	C₂³	1	4	yes	—
77	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₉	C₂³	1	2	yes	—
80	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₉	C₂³	1	2	yes	—
82	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₉	C₂³	1	2	yes	—
84	C₂²×C₄×C₉	C₂³	1	8	yes	—
85	C₂²×C₄×C₉	C₂³	1	8	yes	—
86	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
87	C₉×C₄⋊C₄	C₂³	1	4	yes	—
88	C₉×C₄⋊C₄	C₂³	1	4	yes	—
89	C₉×C₄⋊C₄	C₂³	1	8	yes	—
90	C₉×C₄⋊C₄	C₂³	1	4	yes	—
91	C₉×C₄⋊C₄	C₂³	1	8	yes	—
92	C₉×C₄⋊C₄	C₂³	1	4	yes	—
93	C₉×C₄⋊C₄	C₂³	1	8	yes	—
94	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
95	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
96	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
97	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
98	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
99	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
100	C₄²×C₉	C₂³	1	8	yes	—
101	C₄²×C₉	C₂³	1	4	yes	—
102	C₂×#553	C₉	1	1	yes	characteristic, direct product factor, Sylow
103	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
104	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
105	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
106	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
107	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
108	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
109	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
110	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
111	C₃×#126	C₂²×C₃	1	16	yes	—
112	C₃×#125	C₂²×C₃	1	8	yes	—
113	C₃×#123	C₂²×C₃	1	16	yes	—
114	C₃×#121	C₂²×C₃	1	16	yes	—
115	C₃×#121	C₂²×C₃	1	8	yes	—
116	C₃×#121	C₂²×C₃	1	8	yes	—
117	C₃×C₄×D₄	C₂²×C₃	1	16	yes	—
118	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
119	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
120	C₃×#117	C₂²×C₃	1	8	yes	—
121	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
123	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
124	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
126	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
128	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	8	yes	—
129	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
130	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
131	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
132	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
133	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
134	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
135	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
136	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
137	C₂³×C₉	—	2	2	no	—
138	C₂³×C₉	—	2	2	no	—
139	C₂³×C₉	—	2	2	no	—
140	C₂³×C₉	—	2	2	no	—
141	C₂³×C₉	—	2	4	no	—
142	C₂³×C₉	—	2	4	no	—
143	C₂³×C₉	—	2	4	no	—
144	C₂³×C₉	—	2	2	no	—
145	C₂³×C₉	#41	1	4	yes	—
146	C₂³×C₉	C₂⁴	1	2	yes	—
147	C₂³×C₉	C₂⁴	1	4	yes	—
148	C₂³×C₉	C₂⁴	1	2	yes	—
149	C₂³×C₉	C₂⁴	1	1	yes	characteristic
150	D₄×C₉	—	2	16	no	—
151	D₄×C₉	—	2	8	no	—
152	D₄×C₉	—	2	8	no	—
153	D₄×C₉	—	4	8	no	—
154	C₂×C₄×C₉	—	2	2	no	—
155	C₂×C₄×C₉	—	2	2	no	—
156	C₂×C₄×C₉	—	2	2	no	—
157	C₂×C₄×C₉	—	2	4	no	—
158	C₂×C₄×C₉	—	2	2	no	—
159	C₂×C₄×C₉	—	2	4	no	—
160	C₂×C₄×C₉	—	2	4	no	—
161	C₂×C₄×C₉	—	2	8	no	—
162	C₂×C₄×C₉	—	2	8	no	—
163	C₂×C₄×C₉	—	4	8	no	—
164	C₂×C₄×C₉	—	4	8	no	—
165	C₂×C₄×C₉	#41	1	4	yes	—
166	C₂×C₄×C₉	C₂⁴	1	2	yes	—
167	C₂×C₄×C₉	C₂⁴	1	4	yes	—
168	C₂×C₄×C₉	C₂⁴	1	2	yes	—
169	C₂×C₄×C₉	C₂⁴	1	4	yes	—
170	C₂×C₄×C₉	C₂⁴	1	2	yes	—
171	C₂×C₄×C₉	C₂⁴	1	2	yes	—
172	C₂×C₄×C₉	C₂⁴	1	4	yes	—
173	C₂×C₄×C₉	C₂⁴	1	2	yes	—
174	#553	C₂×C₉	1	16	yes	direct product factor
175	C₂×#126	C₂×C₉	1	2	yes	complemented
176	C₂×#125	C₂×C₉	1	1	yes	characteristic, complemented
177	C₂×#123	C₂×C₉	1	2	yes	complemented
178	C₂×#121	C₂×C₉	1	2	yes	complemented
179	C₂×#121	C₂×C₉	1	1	yes	characteristic, complemented
180	C₂×#121	C₂×C₉	1	1	yes	characteristic, complemented
181	C₂×C₄×D₄	C₂×C₉	1	2	yes	complemented
182	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic, complemented
183	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic, complemented
184	C₂×#117	C₂×C₉	1	1	yes	characteristic, complemented
185	C₂²×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
186	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
187	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
188	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
189	C₂×C₃×D₄	—	2	8	no	—
190	C₂×C₃×D₄	—	2	4	no	—
191	C₂×C₃×D₄	—	2	4	no	—
192	C₂×C₃×D₄	—	4	4	no	—
193	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
194	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
195	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
196	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
197	C₂²×C₃×C₄	—	2	4	no	—
198	C₂²×C₃×C₄	—	2	4	no	—
199	C₂²×C₃×C₄	—	4	4	no	—
200	C₂²×C₃×C₄	—	4	4	no	—
201	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
202	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
203	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
204	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
205	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
206	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
207	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
208	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
209	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
210	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
211	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
212	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
213	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
214	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
215	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
216	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
217	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
218	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
219	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
220	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
221	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
222	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
223	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
224	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
225	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
226	C₃×C₄²	C₂³×C₃	1	8	yes	—
227	C₃×C₄²	C₂³×C₃	1	4	yes	—
228	C₂²×C₉	—	2	8	no	—
229	C₂²×C₉	—	2	2	no	—
230	C₂²×C₉	—	2	2	no	—
231	C₂²×C₉	—	2	2	no	—
232	C₂²×C₉	—	2	2	no	—
233	C₂²×C₉	—	2	4	no	—
234	C₂²×C₉	—	2	4	no	—
235	C₂²×C₉	—	2	4	no	—
236	C₂²×C₉	—	2	2	no	—
237	C₂²×C₉	—	4	4	no	—
238	C₂²×C₉	—	4	8	no	—
239	C₂²×C₉	C₂×#41	1	4	yes	—
240	C₂²×C₉	C₂×#41	1	2	yes	—
241	C₂²×C₉	C₂×#41	1	2	yes	—
242	C₂²×C₉	H(5,𝔽₂)	1	2	yes	—
243	C₂²×C₉	C₂⁵	1	1	yes	characteristic
244	C₄×C₉	—	2	2	no	—
245	C₄×C₉	—	2	2	no	—
246	C₄×C₉	—	2	4	no	—
247	C₄×C₉	—	2	2	no	—
248	C₄×C₉	—	2	2	no	—
249	C₄×C₉	—	2	4	no	—
250	C₄×C₉	—	2	4	no	—
251	C₄×C₉	C₂×#41	1	4	yes	—
252	C₂²×D₄	C₂²×C₉	1	2	yes	—
253	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
254	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
255	C₂²×D₄	C₂²×C₉	1	2	yes	—
256	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
257	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
258	C₂³×C₄	C₂²×C₉	1	2	yes	—
259	C₂³×C₄	C₂²×C₉	1	2	yes	—
260	#126	C₂²×C₉	1	16	yes	complemented
261	#125	C₂²×C₉	1	8	yes	complemented
262	#123	C₂²×C₉	1	16	yes	complemented
263	#121	C₂²×C₉	1	16	yes	complemented
264	#121	C₂²×C₉	1	8	yes	complemented
265	#121	C₂²×C₉	1	8	yes	complemented
266	C₄×D₄	C₂²×C₉	1	16	yes	complemented
267	C₄×D₄	C₂²×C₉	1	8	yes	complemented
268	C₄×D₄	C₂²×C₉	1	8	yes	complemented
269	#117	C₂²×C₉	1	8	yes	complemented
270	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
273	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
275	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
277	C₂×C₄⋊C₄	C₂²×C₉	1	8	yes	complemented
278	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
279	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
280	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
281	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
282	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
283	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
284	C₂×C₄²	C₂²×C₉	1	2	yes	—
285	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
286	C₂³×C₃	—	2	2	no	—
287	C₂³×C₃	—	2	2	no	—
288	C₂³×C₃	—	2	2	no	—
289	C₂³×C₃	—	2	2	no	—
290	C₂³×C₃	—	2	4	no	—
291	C₂³×C₃	—	2	4	no	—
292	C₂³×C₃	—	2	4	no	—
293	C₂³×C₃	—	2	2	no	—
294	C₂³×C₃	C₃×#41	1	4	yes	—
295	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
296	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
297	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
298	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
299	C₃×D₄	—	2	16	no	—
300	C₃×D₄	—	2	8	no	—
301	C₃×D₄	—	2	8	no	—
302	C₃×D₄	—	4	8	no	—
303	C₂×C₃×C₄	—	2	2	no	—
304	C₂×C₃×C₄	—	2	2	no	—
305	C₂×C₃×C₄	—	2	4	no	—
306	C₂×C₃×C₄	—	2	2	no	—
307	C₂×C₃×C₄	—	2	2	no	—
308	C₂×C₃×C₄	—	2	4	no	—
309	C₂×C₃×C₄	—	2	4	no	—
310	C₂×C₃×C₄	—	2	8	no	—
311	C₂×C₃×C₄	—	2	8	no	—
312	C₂×C₃×C₄	—	4	8	no	—
313	C₂×C₃×C₄	—	4	8	no	—
314	C₂×C₃×C₄	C₃×#41	1	4	yes	—
315	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
316	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
317	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
318	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
319	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
320	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
321	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
322	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
323	C₂×C₉	—	2	4	no	—
324	C₂×C₉	—	4	2	no	—
325	C₂×C₉	—	4	4	no	—
326	C₂×C₉	#553	1	4	yes	direct product factor
327	C₂×C₉	C₂²×#41	1	1	yes	characteristic
328	C₂×C₉	C₂²×#41	1	1	yes	characteristic
329	C₂×C₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
330	C₂⁴	C₂³×C₉	1	1	yes	characteristic
331	C₂⁴	C₂³×C₉	1	2	yes	—
332	C₂⁴	C₂³×C₉	1	1	yes	characteristic
333	C₂×D₄	—	2	8	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	4	4	no	—
337	C₂×D₄	C₂³×C₉	1	8	yes	—
338	C₂×D₄	C₂³×C₉	1	4	yes	—
339	C₂×D₄	C₂³×C₉	1	4	yes	—
340	C₂×D₄	C₂³×C₉	1	8	yes	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	4	4	no	—
344	C₂²×C₄	—	4	4	no	—
345	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
346	C₂²×C₄	C₂³×C₉	1	2	yes	—
347	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
348	C₂²×C₄	C₂³×C₉	1	2	yes	—
349	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
350	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
351	C₂²×C₄	C₂³×C₉	1	2	yes	—
352	C₂²×C₄	C₂³×C₉	1	4	yes	—
353	C₂²×C₄	C₂³×C₉	1	4	yes	—
354	C₂²×C₄	C₂³×C₉	1	8	yes	—
355	C₂²×C₄	C₂³×C₉	1	8	yes	—
356	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
357	C₄⋊C₄	C₂³×C₉	1	4	yes	—
358	C₄⋊C₄	C₂³×C₉	1	4	yes	—
359	C₄⋊C₄	C₂³×C₉	1	8	yes	—
360	C₄⋊C₄	C₂³×C₉	1	4	yes	—
361	C₄⋊C₄	C₂³×C₉	1	8	yes	—
362	C₄⋊C₄	C₂³×C₉	1	4	yes	—
363	C₄⋊C₄	C₂³×C₉	1	8	yes	—
364	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
365	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
366	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
367	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
368	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
369	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
370	C₄²	C₂³×C₉	1	8	yes	—
371	C₄²	C₂³×C₉	1	4	yes	—
372	C₂²×C₃	—	2	2	no	—
373	C₂²×C₃	—	2	2	no	—
374	C₂²×C₃	—	2	8	no	—
375	C₂²×C₃	—	2	2	no	—
376	C₂²×C₃	—	2	2	no	—
377	C₂²×C₃	—	2	4	no	—
378	C₂²×C₃	—	2	4	no	—
379	C₂²×C₃	—	2	4	no	—
380	C₂²×C₃	—	2	2	no	—
381	C₂²×C₃	—	4	4	no	—
382	C₂²×C₃	—	4	8	no	—
383	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
384	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
385	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
386	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
387	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
388	C₃×C₄	—	2	2	no	—
389	C₃×C₄	—	2	2	no	—
390	C₃×C₄	—	2	4	no	—
391	C₃×C₄	—	2	2	no	—
392	C₃×C₄	—	2	2	no	—
393	C₃×C₄	—	2	4	no	—
394	C₃×C₄	—	2	4	no	—
395	C₃×C₄	C₂×C₃×#41	1	4	yes	—
396	C₉	C₂×#553	1	1	yes	characteristic, direct product factor, Sylow
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	2	4	no	—
403	C₂³	—	2	4	no	—
404	C₂³	—	2	2	no	—
405	C₂³	C₉×#41	1	4	yes	—
406	C₂³	C₂⁴×C₉	1	2	yes	—
407	C₂³	C₂⁴×C₉	1	4	yes	—
408	C₂³	C₂⁴×C₉	1	2	yes	—
409	C₂³	C₂⁴×C₉	1	1	yes	characteristic
410	D₄	—	2	16	no	—
411	D₄	—	2	8	no	—
412	D₄	—	2	8	no	—
413	D₄	—	4	8	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	8	no	—
422	C₂×C₄	—	2	8	no	—
423	C₂×C₄	—	4	8	no	—
424	C₂×C₄	—	4	8	no	—
425	C₂×C₄	C₉×#41	1	4	yes	—
426	C₂×C₄	C₂⁴×C₉	1	2	yes	—
427	C₂×C₄	C₂⁴×C₉	1	4	yes	—
428	C₂×C₄	C₂⁴×C₉	1	2	yes	—
429	C₂×C₄	C₂⁴×C₉	1	4	yes	—
430	C₂×C₄	C₂⁴×C₉	1	2	yes	—
431	C₂×C₄	C₂⁴×C₉	1	2	yes	—
432	C₂×C₄	C₂⁴×C₉	1	4	yes	—
433	C₂×C₄	C₂⁴×C₉	1	2	yes	—
434	C₂×C₃	—	2	4	no	—
435	C₂×C₃	—	4	2	no	—
436	C₂×C₃	—	4	4	no	—
437	C₂×C₃	C₃×#553	1	4	yes	—
438	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
439	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
440	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
441	C₂²	—	2	8	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	4	no	—
447	C₂²	—	2	4	no	—
448	C₂²	—	2	4	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	4	8	no	—
452	C₂²	C₂×C₉×#41	1	4	yes	—
453	C₂²	C₂×C₉×#41	1	2	yes	—
454	C₂²	C₂×C₉×#41	1	2	yes	—
455	C₂²	C₉×H(5,𝔽₂)	1	2	yes	—
456	C₂²	C₂⁵×C₉	1	1	yes	characteristic
457	C₄	—	2	2	no	—
458	C₄	—	2	2	no	—
459	C₄	—	2	4	no	—
460	C₄	—	2	2	no	—
461	C₄	—	2	2	no	—
462	C₄	—	2	4	no	—
463	C₄	—	2	4	no	—
464	C₄	C₂×C₉×#41	1	4	yes	—
465	C₃	C₂×C₃×#553	1	1	yes	characteristic
466	C₂	—	2	4	no	—
467	C₂	—	4	2	no	—
468	C₂	—	4	4	no	—
469	C₂	C₉×#553	1	4	yes	direct product factor
470	C₂	C₂²×C₉×#41	1	1	yes	characteristic
471	C₂	C₂²×C₉×#41	1	1	yes	characteristic
472	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×#553	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. C₉×#553	C₂	direct (N × H)
2. C₂×C₉×#126	C₂	semidirect
3. C₂×C₉×#125	C₂	semidirect
4. C₂×C₉×#123	C₂	semidirect
5. C₂×C₉×#121	C₂	semidirect
6. C₂×C₉×#121	C₂	semidirect
7. C₂×C₉×#121	C₂	semidirect
8. C₂×C₄×D₄×C₉	C₂	semidirect
9. C₂×C₄×D₄×C₉	C₂	semidirect
10. C₂×C₄×D₄×C₉	C₂	semidirect
11. C₂×C₉×#117	C₂	semidirect
12. C₂²×C₉×C₄⋊C₄	C₂	semidirect
22. C₉×#126	C₂²	semidirect
23. C₉×#125	C₂²	semidirect
24. C₉×#123	C₂²	semidirect
25. C₉×#121	C₂²	semidirect
26. C₉×#121	C₂²	semidirect
27. C₉×#121	C₂²	semidirect
28. C₄×D₄×C₉	C₂²	semidirect
29. C₄×D₄×C₉	C₂²	semidirect
30. C₄×D₄×C₉	C₂²	semidirect
31. C₉×#117	C₂²	semidirect
39. C₂×C₉×C₄⋊C₄	C₂²	semidirect
102. C₂×#553	C₉	direct (N × H)
174. #553	C₂×C₉	direct (N × H)
175. C₂×#126	C₂×C₉	semidirect
176. C₂×#125	C₂×C₉	semidirect
177. C₂×#123	C₂×C₉	semidirect
178. C₂×#121	C₂×C₉	semidirect
179. C₂×#121	C₂×C₉	semidirect
180. C₂×#121	C₂×C₉	semidirect
181. C₂×C₄×D₄	C₂×C₉	semidirect
182. C₂×C₄×D₄	C₂×C₉	semidirect
183. C₂×C₄×D₄	C₂×C₉	semidirect
184. C₂×#117	C₂×C₉	semidirect
185. C₂²×C₄⋊C₄	C₂×C₉	semidirect
260. #126	C₂²×C₉	semidirect
261. #125	C₂²×C₉	semidirect
262. #123	C₂²×C₉	semidirect
263. #121	C₂²×C₉	semidirect
264. #121	C₂²×C₉	semidirect
265. #121	C₂²×C₉	semidirect
266. C₄×D₄	C₂²×C₉	semidirect
267. C₄×D₄	C₂²×C₉	semidirect
268. C₄×D₄	C₂²×C₉	semidirect
269. #117	C₂²×C₉	semidirect
277. C₂×C₄⋊C₄	C₂²×C₉	semidirect
326. C₂×C₉	#553	direct (N × H)
396. C₉	C₂×#553	direct (N × H)
469. C₂	C₉×#553	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×#553	2
C₂×C₉×#126	2
C₂×C₉×#125	2
C₂×C₉×#123	2
C₂×C₉×#121	2
C₂×C₄×D₄×C₉	2
C₂×C₉×#117	2
C₂²×C₉×C₄⋊C₄	2
C₂×C₃×#553	3

Subgroups — C2×C9×#553 #11768192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#553 #11768192