Subgroups — C₂×C₉×#538 #11768171

Order 1152.

2004 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

Subgroups — C2×C9×#538 #11768171

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#538 #11768171