Subgroups — C₂×C₉×#551 #11768190

Order 1152.

1992 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#551	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₉×#126	C₂	1	2	yes	maximal, complemented
3	C₂×C₉×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉×#123	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₉×#123	C₂	1	2	yes	maximal, complemented
6	C₂×C₉×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
7	C₂×C₉×#120	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×D₄×C₉	C₂	1	2	yes	maximal, complemented
9	C₂×C₉×#117	C₂	1	2	yes	maximal, complemented
10	C₂²×C₉×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
11	C₂×C₃×#551	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	1	yes	characteristic
16	C₂³×C₄×C₉	C₂²	1	2	yes	—
17	C₂³×C₄×C₉	C₂²	1	2	yes	—
18	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic, complemented
19	C₉×#126	C₂²	1	16	yes	complemented
20	C₉×#124	C₂²	1	8	yes	complemented
21	C₉×#123	C₂²	1	8	yes	complemented
22	C₉×#123	C₂²	1	16	yes	complemented
23	C₉×C₂²⋊Q₈	C₂²	1	16	yes	complemented
24	C₉×#120	C₂²	1	8	yes	—
25	C₄×D₄×C₉	C₂²	1	16	yes	complemented
26	C₉×#117	C₂²	1	16	yes	complemented
27	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	complemented
28	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	complemented
29	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	complemented
30	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	complemented
31	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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	16	yes	complemented
38	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	complemented
40	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄²×C₉	C₂²	1	2	yes	complemented
42	C₃×#551	C₂×C₃	1	16	yes	—
43	C₂×C₃×#126	C₂×C₃	1	2	yes	—
44	C₂×C₃×#124	C₂×C₃	1	1	yes	characteristic
45	C₂×C₃×#123	C₂×C₃	1	1	yes	characteristic
46	C₂×C₃×#123	C₂×C₃	1	2	yes	—
47	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	2	yes	—
48	C₂×C₃×#120	C₂×C₃	1	1	yes	characteristic
49	C₂×C₃×C₄×D₄	C₂×C₃	1	2	yes	—
50	C₂×C₃×#117	C₂×C₃	1	2	yes	—
51	C₂²×C₃×C₂²⋊C₄	C₂×C₃	1	2	yes	—
52	C₂⁴×C₉	—	2	8	no	—
53	C₂⁴×C₉	—	4	2	no	—
54	C₂⁴×C₉	C₂³	1	1	yes	characteristic
55	C₂⁴×C₉	C₂³	1	1	yes	characteristic
56	C₂⁴×C₉	C₂³	1	4	yes	—
57	C₂⁴×C₉	C₂³	1	2	yes	—
58	C₂×Q₈×C₉	—	4	2	no	—
59	C₂×Q₈×C₉	C₂³	1	4	yes	complemented
60	C₂×D₄×C₉	—	2	8	no	—
61	C₂×D₄×C₉	—	4	2	no	—
62	C₂×D₄×C₉	C₂³	1	8	yes	—
63	C₂×D₄×C₉	C₂³	1	4	yes	—
64	C₂²×C₄×C₉	—	2	8	no	—
65	C₂²×C₄×C₉	—	4	4	no	—
66	C₂²×C₄×C₉	—	4	2	no	—
67	C₂²×C₄×C₉	C₂³	1	8	yes	—
68	C₂²×C₄×C₉	C₂³	1	2	yes	—
69	C₂²×C₄×C₉	C₂³	1	2	yes	—
70	C₂²×C₄×C₉	C₂³	1	2	yes	—
71	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₉	C₂³	1	2	yes	—
73	C₂²×C₄×C₉	C₂³	1	2	yes	—
74	C₂²×C₄×C₉	C₂³	1	8	yes	—
75	C₂²×C₄×C₉	C₂³	1	4	yes	complemented
76	C₉×C₄⋊C₄	C₂³	1	8	yes	complemented
77	C₉×C₄⋊C₄	C₂³	1	8	yes	complemented
78	C₉×C₄⋊C₄	C₂³	1	8	yes	complemented
79	C₉×C₄⋊C₄	C₂³	1	8	yes	complemented
80	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
81	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
82	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
83	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
84	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
85	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
86	C₉×C₂²⋊C₄	C₂³	1	8	yes	complemented
87	C₉×C₂²⋊C₄	C₂³	1	4	yes	complemented
88	C₄²×C₉	C₂³	1	4	yes	complemented
89	C₄²×C₉	C₂³	1	8	yes	complemented
90	C₂×#551	C₉	1	1	yes	characteristic, direct product factor, Sylow
91	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic
92	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
93	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
94	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
95	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
96	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
97	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
98	C₃×#126	C₂²×C₃	1	16	yes	—
99	C₃×#124	C₂²×C₃	1	8	yes	—
100	C₃×#123	C₂²×C₃	1	8	yes	—
101	C₃×#123	C₂²×C₃	1	16	yes	—
102	C₃×C₂²⋊Q₈	C₂²×C₃	1	16	yes	—
103	C₃×#120	C₂²×C₃	1	8	yes	—
104	C₃×C₄×D₄	C₂²×C₃	1	16	yes	—
105	C₃×#117	C₂²×C₃	1	16	yes	—
106	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
107	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
108	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
109	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
110	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
111	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
112	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
113	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
114	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
115	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	16	yes	—
117	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
118	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
119	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
121	C₂³×C₉	—	2	4	no	—
122	C₂³×C₉	—	2	4	no	—
123	C₂³×C₉	—	2	4	no	—
124	C₂³×C₉	—	2	16	no	—
125	C₂³×C₉	—	2	4	no	—
126	C₂³×C₉	—	2	2	no	—
127	C₂³×C₉	—	2	2	no	—
128	C₂³×C₉	—	4	4	no	—
129	C₂³×C₉	—	4	16	no	—
130	C₂³×C₉	#41	1	8	yes	—
131	C₂³×C₉	C₂⁴	1	2	yes	—
132	C₂³×C₉	C₂⁴	1	2	yes	—
133	C₂³×C₉	C₂⁴	1	4	yes	—
134	C₂³×C₉	C₂⁴	1	1	yes	characteristic
135	Q₈×C₉	—	4	4	no	—
136	D₄×C₉	—	2	16	no	—
137	D₄×C₉	—	4	4	no	—
138	C₂×C₄×C₉	—	2	16	no	—
139	C₂×C₄×C₉	—	2	4	no	—
140	C₂×C₄×C₉	—	2	4	no	—
141	C₂×C₄×C₉	—	2	4	no	—
142	C₂×C₄×C₉	—	2	4	no	—
143	C₂×C₄×C₉	—	2	4	no	—
144	C₂×C₄×C₉	—	2	2	no	—
145	C₂×C₄×C₉	—	4	8	no	—
146	C₂×C₄×C₉	—	4	4	no	—
147	C₂×C₄×C₉	C₂⁴	1	4	yes	—
148	C₂×C₄×C₉	C₂⁴	1	4	yes	—
149	C₂×C₄×C₉	C₂⁴	1	4	yes	—
150	C₂×C₄×C₉	C₂⁴	1	2	yes	—
151	C₂×C₄×C₉	C₂⁴	1	4	yes	—
152	C₂×C₄×C₉	C₂⁴	1	4	yes	—
153	#551	C₂×C₉	1	16	yes	direct product factor
154	C₂×#126	C₂×C₉	1	2	yes	complemented
155	C₂×#124	C₂×C₉	1	1	yes	characteristic, complemented
156	C₂×#123	C₂×C₉	1	1	yes	characteristic, complemented
157	C₂×#123	C₂×C₉	1	2	yes	complemented
158	C₂×C₂²⋊Q₈	C₂×C₉	1	2	yes	complemented
159	C₂×#120	C₂×C₉	1	1	yes	characteristic
160	C₂×C₄×D₄	C₂×C₉	1	2	yes	complemented
161	C₂×#117	C₂×C₉	1	2	yes	complemented
162	C₂²×C₂²⋊C₄	C₂×C₉	1	2	yes	complemented
163	C₂⁴×C₃	—	2	8	no	—
164	C₂⁴×C₃	—	4	2	no	—
165	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
166	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
167	C₂⁴×C₃	C₂³×C₃	1	4	yes	—
168	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
169	C₂×C₃×Q₈	—	4	2	no	—
170	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
171	C₂×C₃×D₄	—	2	8	no	—
172	C₂×C₃×D₄	—	4	2	no	—
173	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
174	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
175	C₂²×C₃×C₄	—	2	8	no	—
176	C₂²×C₃×C₄	—	4	4	no	—
177	C₂²×C₃×C₄	—	4	2	no	—
178	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
179	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
180	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
181	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
183	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
184	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
185	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
186	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
187	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
188	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
189	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
190	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
191	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
192	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
193	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
194	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
195	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
196	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
197	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
198	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
199	C₃×C₄²	C₂³×C₃	1	4	yes	—
200	C₃×C₄²	C₂³×C₃	1	8	yes	—
201	C₂²×C₉	—	2	16	no	—
202	C₂²×C₉	—	2	4	no	—
203	C₂²×C₉	—	2	4	no	—
204	C₂²×C₉	—	2	4	no	—
205	C₂²×C₉	—	2	4	no	—
206	C₂²×C₉	—	2	2	no	—
207	C₂²×C₉	—	2	2	no	—
208	C₂²×C₉	—	4	16	no	—
209	C₂²×C₉	—	4	4	no	—
210	C₂²×C₉	—	4	4	no	—
211	C₂²×C₉	C₂×#41	1	8	yes	—
212	C₂²×C₉	C₂×#41	1	4	yes	—
213	C₂²×C₉	H(5,𝔽₂)	1	2	yes	—
214	C₂²×C₉	C₂⁵	1	1	yes	characteristic
215	C₄×C₉	—	2	4	no	—
216	C₄×C₉	—	2	4	no	—
217	C₄×C₉	—	2	4	no	—
218	C₄×C₉	—	2	4	no	—
219	C₄×C₉	—	2	4	no	—
220	C₄×C₉	—	2	2	no	—
221	C₂⁵	C₂²×C₉	1	1	yes	characteristic
222	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
223	C₂²×D₄	C₂²×C₉	1	2	yes	—
224	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
225	C₂³×C₄	C₂²×C₉	1	2	yes	—
226	C₂³×C₄	C₂²×C₉	1	2	yes	—
227	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic, complemented
228	#126	C₂²×C₉	1	16	yes	complemented
229	#124	C₂²×C₉	1	8	yes	complemented
230	#123	C₂²×C₉	1	8	yes	complemented
231	#123	C₂²×C₉	1	16	yes	complemented
232	C₂²⋊Q₈	C₂²×C₉	1	16	yes	complemented
233	#120	C₂²×C₉	1	8	yes	—
234	C₄×D₄	C₂²×C₉	1	16	yes	complemented
235	#117	C₂²×C₉	1	16	yes	complemented
236	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	complemented
237	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	complemented
238	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	complemented
239	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	complemented
240	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
241	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
242	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
243	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
244	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
245	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
246	C₂×C₂²⋊C₄	C₂²×C₉	1	16	yes	complemented
247	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	complemented
248	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
249	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic, complemented
250	C₂×C₄²	C₂²×C₉	1	2	yes	complemented
251	C₂³×C₃	—	2	4	no	—
252	C₂³×C₃	—	2	4	no	—
253	C₂³×C₃	—	2	4	no	—
254	C₂³×C₃	—	2	16	no	—
255	C₂³×C₃	—	2	4	no	—
256	C₂³×C₃	—	2	2	no	—
257	C₂³×C₃	—	2	2	no	—
258	C₂³×C₃	—	4	4	no	—
259	C₂³×C₃	—	4	16	no	—
260	C₂³×C₃	C₃×#41	1	8	yes	—
261	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
262	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
263	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
264	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
265	C₃×Q₈	—	4	4	no	—
266	C₃×D₄	—	2	16	no	—
267	C₃×D₄	—	4	4	no	—
268	C₂×C₃×C₄	—	2	16	no	—
269	C₂×C₃×C₄	—	2	4	no	—
270	C₂×C₃×C₄	—	2	4	no	—
271	C₂×C₃×C₄	—	2	4	no	—
272	C₂×C₃×C₄	—	2	4	no	—
273	C₂×C₃×C₄	—	2	4	no	—
274	C₂×C₃×C₄	—	2	2	no	—
275	C₂×C₃×C₄	—	4	8	no	—
276	C₂×C₃×C₄	—	4	4	no	—
277	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
278	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
279	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
280	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
281	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
282	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
283	C₂×C₉	—	2	8	no	—
284	C₂×C₉	—	4	2	no	—
285	C₂×C₉	—	4	2	no	—
286	C₂×C₉	#551	1	4	yes	direct product factor
287	C₂×C₉	C₂²×#41	1	2	yes	—
288	C₂×C₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
289	C₂⁴	—	2	8	no	—
290	C₂⁴	—	4	2	no	—
291	C₂⁴	C₂³×C₉	1	1	yes	characteristic
292	C₂⁴	C₂³×C₉	1	1	yes	characteristic
293	C₂⁴	C₂³×C₉	1	4	yes	—
294	C₂⁴	C₂³×C₉	1	2	yes	—
295	C₂×Q₈	—	4	2	no	—
296	C₂×Q₈	C₂³×C₉	1	4	yes	complemented
297	C₂×D₄	—	2	8	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	C₂³×C₉	1	8	yes	—
300	C₂×D₄	C₂³×C₉	1	4	yes	—
301	C₂²×C₄	—	2	8	no	—
302	C₂²×C₄	—	4	4	no	—
303	C₂²×C₄	—	4	2	no	—
304	C₂²×C₄	C₂³×C₉	1	2	yes	—
305	C₂²×C₄	C₂³×C₉	1	2	yes	—
306	C₂²×C₄	C₂³×C₉	1	2	yes	—
307	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
308	C₂²×C₄	C₂³×C₉	1	2	yes	—
309	C₂²×C₄	C₂³×C₉	1	2	yes	—
310	C₂²×C₄	C₂³×C₉	1	8	yes	—
311	C₂²×C₄	C₂³×C₉	1	8	yes	—
312	C₂²×C₄	C₂³×C₉	1	4	yes	complemented
313	C₄⋊C₄	C₂³×C₉	1	8	yes	complemented
314	C₄⋊C₄	C₂³×C₉	1	8	yes	complemented
315	C₄⋊C₄	C₂³×C₉	1	8	yes	complemented
316	C₄⋊C₄	C₂³×C₉	1	8	yes	complemented
317	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
318	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
319	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
320	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
321	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
322	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
323	C₂²⋊C₄	C₂³×C₉	1	8	yes	complemented
324	C₂²⋊C₄	C₂³×C₉	1	4	yes	complemented
325	C₄²	C₂³×C₉	1	4	yes	complemented
326	C₄²	C₂³×C₉	1	8	yes	complemented
327	C₂²×C₃	—	2	4	no	—
328	C₂²×C₃	—	2	4	no	—
329	C₂²×C₃	—	2	16	no	—
330	C₂²×C₃	—	2	4	no	—
331	C₂²×C₃	—	2	4	no	—
332	C₂²×C₃	—	2	2	no	—
333	C₂²×C₃	—	2	2	no	—
334	C₂²×C₃	—	4	16	no	—
335	C₂²×C₃	—	4	4	no	—
336	C₂²×C₃	—	4	4	no	—
337	C₂²×C₃	C₂×C₃×#41	1	8	yes	—
338	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
339	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
340	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
341	C₃×C₄	—	2	4	no	—
342	C₃×C₄	—	2	4	no	—
343	C₃×C₄	—	2	4	no	—
344	C₃×C₄	—	2	4	no	—
345	C₃×C₄	—	2	4	no	—
346	C₃×C₄	—	2	2	no	—
347	C₉	C₂×#551	1	1	yes	characteristic, direct product factor, Sylow
348	C₂³	—	2	4	no	—
349	C₂³	—	2	4	no	—
350	C₂³	—	2	4	no	—
351	C₂³	—	2	16	no	—
352	C₂³	—	2	4	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	4	4	no	—
356	C₂³	—	4	16	no	—
357	C₂³	C₉×#41	1	8	yes	—
358	C₂³	C₂⁴×C₉	1	2	yes	—
359	C₂³	C₂⁴×C₉	1	2	yes	—
360	C₂³	C₂⁴×C₉	1	4	yes	—
361	C₂³	C₂⁴×C₉	1	1	yes	characteristic
362	Q₈	—	4	4	no	—
363	D₄	—	2	16	no	—
364	D₄	—	4	4	no	—
365	C₂×C₄	—	2	16	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	4	8	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	C₂⁴×C₉	1	4	yes	—
375	C₂×C₄	C₂⁴×C₉	1	4	yes	—
376	C₂×C₄	C₂⁴×C₉	1	4	yes	—
377	C₂×C₄	C₂⁴×C₉	1	2	yes	—
378	C₂×C₄	C₂⁴×C₉	1	4	yes	—
379	C₂×C₄	C₂⁴×C₉	1	4	yes	—
380	C₂×C₃	—	2	8	no	—
381	C₂×C₃	—	4	2	no	—
382	C₂×C₃	—	4	2	no	—
383	C₂×C₃	C₃×#551	1	4	yes	—
384	C₂×C₃	C₂²×C₃×#41	1	2	yes	—
385	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
386	C₂²	—	2	16	no	—
387	C₂²	—	2	4	no	—
388	C₂²	—	2	4	no	—
389	C₂²	—	2	4	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	4	16	no	—
394	C₂²	—	4	4	no	—
395	C₂²	—	4	4	no	—
396	C₂²	C₂×C₉×#41	1	8	yes	—
397	C₂²	C₂×C₉×#41	1	4	yes	—
398	C₂²	C₉×H(5,𝔽₂)	1	2	yes	—
399	C₂²	C₂⁵×C₉	1	1	yes	characteristic
400	C₄	—	2	4	no	—
401	C₄	—	2	4	no	—
402	C₄	—	2	4	no	—
403	C₄	—	2	4	no	—
404	C₄	—	2	4	no	—
405	C₄	—	2	2	no	—
406	C₃	C₂×C₃×#551	1	1	yes	characteristic
407	C₂	—	2	8	no	—
408	C₂	—	4	2	no	—
409	C₂	—	4	2	no	—
410	C₂	C₉×#551	1	4	yes	direct product factor
411	C₂	C₂²×C₉×#41	1	2	yes	—
412	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×#120	C₂×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×#551	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×#123	C₂	semidirect
6. C₂×C₉×C₂²⋊Q₈	C₂	semidirect
8. C₂×C₄×D₄×C₉	C₂	semidirect
9. C₂×C₉×#117	C₂	semidirect
10. C₂²×C₉×C₂²⋊C₄	C₂	semidirect
13. C₂²×Q₈×C₉	C₂²	semidirect
18. C₂³×C₄×C₉	C₂²	semidirect
19. C₉×#126	C₂²	semidirect
20. C₉×#124	C₂²	semidirect
21. C₉×#123	C₂²	semidirect
22. C₉×#123	C₂²	semidirect
23. C₉×C₂²⋊Q₈	C₂²	semidirect
25. C₄×D₄×C₉	C₂²	semidirect
26. C₉×#117	C₂²	semidirect
27. C₂×C₉×C₄⋊C₄	C₂²	semidirect
28. C₂×C₉×C₄⋊C₄	C₂²	semidirect
29. C₂×C₉×C₄⋊C₄	C₂²	semidirect
30. C₂×C₉×C₄⋊C₄	C₂²	semidirect
37. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
38. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
39. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
40. C₂×C₄²×C₉	C₂²	semidirect
41. C₂×C₄²×C₉	C₂²	semidirect
59. C₂×Q₈×C₉	C₂³	semidirect
75. C₂²×C₄×C₉	C₂³	semidirect
76. C₉×C₄⋊C₄	C₂³	semidirect
77. C₉×C₄⋊C₄	C₂³	semidirect
78. C₉×C₄⋊C₄	C₂³	semidirect
79. C₉×C₄⋊C₄	C₂³	semidirect
86. C₉×C₂²⋊C₄	C₂³	semidirect
87. C₉×C₂²⋊C₄	C₂³	semidirect
88. C₄²×C₉	C₂³	semidirect
89. C₄²×C₉	C₂³	semidirect
90. C₂×#551	C₉	direct (N × H)
153. #551	C₂×C₉	direct (N × H)
154. C₂×#126	C₂×C₉	semidirect
155. C₂×#124	C₂×C₉	semidirect
156. C₂×#123	C₂×C₉	semidirect
157. C₂×#123	C₂×C₉	semidirect
158. C₂×C₂²⋊Q₈	C₂×C₉	semidirect
160. C₂×C₄×D₄	C₂×C₉	semidirect
161. C₂×#117	C₂×C₉	semidirect
162. C₂²×C₂²⋊C₄	C₂×C₉	semidirect
222. C₂²×Q₈	C₂²×C₉	semidirect
227. C₂³×C₄	C₂²×C₉	semidirect
228. #126	C₂²×C₉	semidirect
229. #124	C₂²×C₉	semidirect
230. #123	C₂²×C₉	semidirect
231. #123	C₂²×C₉	semidirect
232. C₂²⋊Q₈	C₂²×C₉	semidirect
234. C₄×D₄	C₂²×C₉	semidirect
235. #117	C₂²×C₉	semidirect
236. C₂×C₄⋊C₄	C₂²×C₉	semidirect
237. C₂×C₄⋊C₄	C₂²×C₉	semidirect
238. C₂×C₄⋊C₄	C₂²×C₉	semidirect
239. C₂×C₄⋊C₄	C₂²×C₉	semidirect
246. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
247. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
248. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
249. C₂×C₄²	C₂²×C₉	semidirect
250. C₂×C₄²	C₂²×C₉	semidirect
286. C₂×C₉	#551	direct (N × H)
296. C₂×Q₈	C₂³×C₉	semidirect
312. C₂²×C₄	C₂³×C₉	semidirect
313. C₄⋊C₄	C₂³×C₉	semidirect
314. C₄⋊C₄	C₂³×C₉	semidirect
315. C₄⋊C₄	C₂³×C₉	semidirect
316. C₄⋊C₄	C₂³×C₉	semidirect
323. C₂²⋊C₄	C₂³×C₉	semidirect
324. C₂²⋊C₄	C₂³×C₉	semidirect
325. C₄²	C₂³×C₉	semidirect
326. C₄²	C₂³×C₉	semidirect
347. C₉	C₂×#551	direct (N × H)
410. C₂	C₉×#551	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×#551	2
C₂×C₉×#126	2
C₂×C₉×#124	2
C₂×C₉×#123	2
C₂×C₉×C₂²⋊Q₈	2
C₂×C₉×#120	2
C₂×C₄×D₄×C₉	2
C₂×C₉×#117	2
C₂²×C₉×C₂²⋊C₄	2
C₂×C₃×#551	3

Subgroups — C2×C9×#551 #11768190

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#551 #11768190