Subgroups — C₂×C₉×#539 #11768172

Order 1152.

1716 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#539	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₉×#126	C₂	1	2	yes	maximal, complemented
3	C₂×C₉×#125	C₂	1	2	yes	maximal, complemented
4	C₂×C₉×#123	C₂	1	2	yes	maximal, 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×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₉×#121	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄×D₄×C₉	C₂	1	2	yes	maximal, complemented
10	C₂²×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×#539	C₃	1	1	yes	maximal, characteristic
12	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
13	C₂²×D₄×C₉	C₂²	1	2	yes	—
14	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
15	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
16	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₉	C₂²	1	2	yes	—
18	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
19	C₉×#126	C₂²	1	16	yes	complemented
20	C₉×#125	C₂²	1	16	yes	complemented
21	C₉×#123	C₂²	1	16	yes	complemented
22	C₉×#123	C₂²	1	16	yes	complemented
23	C₉×C₂²⋊Q₈	C₂²	1	8	yes	complemented
24	C₉×C₂²⋊Q₈	C₂²	1	16	yes	complemented
25	C₉×#121	C₂²	1	8	yes	—
26	C₄×D₄×C₉	C₂²	1	16	yes	complemented
27	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
29	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
30	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
31	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
33	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
34	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
35	C₂×C₉×C₄⋊C₄	C₂²	1	8	yes	complemented
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	2	yes	—
39	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
40	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
41	C₂×C₄²×C₉	C₂²	1	2	yes	—
42	C₃×#539	C₂×C₃	1	16	yes	—
43	C₂×C₃×#126	C₂×C₃	1	2	yes	—
44	C₂×C₃×#125	C₂×C₃	1	2	yes	—
45	C₂×C₃×#123	C₂×C₃	1	2	yes	—
46	C₂×C₃×#123	C₂×C₃	1	2	yes	—
47	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
48	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	2	yes	—
49	C₂×C₃×#121	C₂×C₃	1	1	yes	characteristic
50	C₂×C₃×C₄×D₄	C₂×C₃	1	2	yes	—
51	C₂²×C₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
52	C₂⁴×C₉	C₂³	1	2	yes	—
53	C₂⁴×C₉	C₂³	1	1	yes	characteristic
54	C₂×Q₈×C₉	—	4	2	no	—
55	C₂×Q₈×C₉	C₂³	1	4	yes	—
56	C₂×D₄×C₉	—	2	8	no	—
57	C₂×D₄×C₉	—	4	2	no	—
58	C₂×D₄×C₉	C₂³	1	8	yes	—
59	C₂×D₄×C₉	C₂³	1	4	yes	—
60	C₂²×C₄×C₉	—	2	4	no	—
61	C₂²×C₄×C₉	—	4	2	no	—
62	C₂²×C₄×C₉	—	4	4	no	—
63	C₂²×C₄×C₉	—	4	2	no	—
64	C₂²×C₄×C₉	C₂³	1	4	yes	—
65	C₂²×C₄×C₉	C₂³	1	2	yes	—
66	C₂²×C₄×C₉	C₂³	1	2	yes	—
67	C₂²×C₄×C₉	C₂³	1	2	yes	—
68	C₂²×C₄×C₉	C₂³	1	2	yes	—
69	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₉	C₂³	1	2	yes	—
71	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₉	C₂³	1	4	yes	—
73	C₂²×C₄×C₉	C₂³	1	4	yes	—
74	C₂²×C₄×C₉	C₂³	1	8	yes	—
75	C₉×C₄⋊C₄	C₂³	1	8	yes	—
76	C₉×C₄⋊C₄	C₂³	1	8	yes	—
77	C₉×C₄⋊C₄	C₂³	1	8	yes	—
78	C₉×C₄⋊C₄	C₂³	1	4	yes	—
79	C₉×C₄⋊C₄	C₂³	1	8	yes	—
80	C₉×C₄⋊C₄	C₂³	1	8	yes	—
81	C₉×C₄⋊C₄	C₂³	1	4	yes	—
82	C₉×C₄⋊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	8	yes	—
86	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
87	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
88	C₄²×C₉	C₂³	1	8	yes	—
89	C₂×#539	C₉	1	1	yes	characteristic, direct product factor, Sylow
90	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
91	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
92	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
93	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
94	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
95	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
96	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
97	C₃×#126	C₂²×C₃	1	16	yes	—
98	C₃×#125	C₂²×C₃	1	16	yes	—
99	C₃×#123	C₂²×C₃	1	16	yes	—
100	C₃×#123	C₂²×C₃	1	16	yes	—
101	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
102	C₃×C₂²⋊Q₈	C₂²×C₃	1	16	yes	—
103	C₃×#121	C₂²×C₃	1	8	yes	—
104	C₃×C₄×D₄	C₂²×C₃	1	16	yes	—
105	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	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	1	yes	characteristic
109	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
110	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
111	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
112	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
113	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	8	yes	—
114	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
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×C₄²	C₂²×C₃	1	2	yes	—
120	C₂³×C₉	—	2	2	no	—
121	C₂³×C₉	—	2	2	no	—
122	C₂³×C₉	—	2	4	no	—
123	C₂³×C₉	—	2	4	no	—
124	C₂³×C₉	—	2	4	no	—
125	C₂³×C₉	#41	1	4	yes	—
126	C₂³×C₉	C₂⁴	1	4	yes	—
127	C₂³×C₉	C₂⁴	1	2	yes	—
128	C₂³×C₉	C₂⁴	1	1	yes	characteristic
129	Q₈×C₉	—	4	4	no	—
130	D₄×C₉	—	2	16	no	—
131	D₄×C₉	—	4	4	no	—
132	C₂×C₄×C₉	—	2	8	no	—
133	C₂×C₄×C₉	—	2	4	no	—
134	C₂×C₄×C₉	—	2	4	no	—
135	C₂×C₄×C₉	—	2	4	no	—
136	C₂×C₄×C₉	—	2	2	no	—
137	C₂×C₄×C₉	—	2	4	no	—
138	C₂×C₄×C₉	—	2	2	no	—
139	C₂×C₄×C₉	—	2	4	no	—
140	C₂×C₄×C₉	—	4	4	no	—
141	C₂×C₄×C₉	—	4	8	no	—
142	C₂×C₄×C₉	—	4	4	no	—
143	C₂×C₄×C₉	C₂⁴	1	4	yes	—
144	C₂×C₄×C₉	C₂⁴	1	4	yes	—
145	C₂×C₄×C₉	C₂⁴	1	4	yes	—
146	C₂×C₄×C₉	C₂⁴	1	4	yes	—
147	C₂×C₄×C₉	C₂⁴	1	4	yes	—
148	C₂×C₄×C₉	C₂⁴	1	2	yes	—
149	C₂×C₄×C₉	C₂⁴	1	2	yes	—
150	#539	C₂×C₉	1	16	yes	direct product factor
151	C₂×#126	C₂×C₉	1	2	yes	complemented
152	C₂×#125	C₂×C₉	1	2	yes	complemented
153	C₂×#123	C₂×C₉	1	2	yes	complemented
154	C₂×#123	C₂×C₉	1	2	yes	complemented
155	C₂×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
156	C₂×C₂²⋊Q₈	C₂×C₉	1	2	yes	complemented
157	C₂×#121	C₂×C₉	1	1	yes	characteristic
158	C₂×C₄×D₄	C₂×C₉	1	2	yes	complemented
159	C₂²×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
160	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
161	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
162	C₂×C₃×Q₈	—	4	2	no	—
163	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
164	C₂×C₃×D₄	—	2	8	no	—
165	C₂×C₃×D₄	—	4	2	no	—
166	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
167	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
168	C₂²×C₃×C₄	—	2	4	no	—
169	C₂²×C₃×C₄	—	4	2	no	—
170	C₂²×C₃×C₄	—	4	4	no	—
171	C₂²×C₃×C₄	—	4	2	no	—
172	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
173	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
174	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
175	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
176	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
177	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
179	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
180	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
181	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
182	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
183	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
184	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
185	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
186	C₃×C₄⋊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	4	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×C₄²	C₂³×C₃	1	8	yes	—
197	C₂²×C₉	—	2	8	no	—
198	C₂²×C₉	—	2	2	no	—
199	C₂²×C₉	—	2	2	no	—
200	C₂²×C₉	—	2	4	no	—
201	C₂²×C₉	—	2	4	no	—
202	C₂²×C₉	—	2	4	no	—
203	C₂²×C₉	—	4	8	no	—
204	C₂²×C₉	C₂×#41	1	4	yes	—
205	C₂²×C₉	C₂×#41	1	2	yes	—
206	C₂²×C₉	H(5,𝔽₂)	1	2	yes	—
207	C₂²×C₉	2₋¹⁺⁴	1	2	yes	—
208	C₂²×C₉	C₂⁵	1	1	yes	characteristic
209	C₄×C₉	—	2	4	no	—
210	C₄×C₉	—	2	4	no	—
211	C₄×C₉	—	2	4	no	—
212	C₄×C₉	—	2	2	no	—
213	C₄×C₉	—	2	4	no	—
214	C₄×C₉	—	2	2	no	—
215	C₄×C₉	—	2	4	no	—
216	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
217	C₂²×D₄	C₂²×C₉	1	2	yes	—
218	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
219	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
220	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
221	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
222	C₂³×C₄	C₂²×C₉	1	2	yes	—
223	#126	C₂²×C₉	1	16	yes	complemented
224	#125	C₂²×C₉	1	16	yes	complemented
225	#123	C₂²×C₉	1	16	yes	complemented
226	#123	C₂²×C₉	1	16	yes	complemented
227	C₂²⋊Q₈	C₂²×C₉	1	8	yes	complemented
228	C₂²⋊Q₈	C₂²×C₉	1	16	yes	complemented
229	#121	C₂²×C₉	1	8	yes	—
230	C₄×D₄	C₂²×C₉	1	16	yes	complemented
231	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
232	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
233	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
234	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
236	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
237	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
239	C₂×C₄⋊C₄	C₂²×C₉	1	8	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×C₄²	C₂²×C₉	1	2	yes	—
246	C₂³×C₃	—	2	2	no	—
247	C₂³×C₃	—	2	2	no	—
248	C₂³×C₃	—	2	4	no	—
249	C₂³×C₃	—	2	4	no	—
250	C₂³×C₃	—	2	4	no	—
251	C₂³×C₃	C₃×#41	1	4	yes	—
252	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
253	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
254	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
255	C₃×Q₈	—	4	4	no	—
256	C₃×D₄	—	2	16	no	—
257	C₃×D₄	—	4	4	no	—
258	C₂×C₃×C₄	—	2	8	no	—
259	C₂×C₃×C₄	—	2	4	no	—
260	C₂×C₃×C₄	—	2	4	no	—
261	C₂×C₃×C₄	—	2	4	no	—
262	C₂×C₃×C₄	—	2	2	no	—
263	C₂×C₃×C₄	—	2	4	no	—
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	2	4	no	—
266	C₂×C₃×C₄	—	4	4	no	—
267	C₂×C₃×C₄	—	4	8	no	—
268	C₂×C₃×C₄	—	4	4	no	—
269	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
270	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
271	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
272	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
273	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
274	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
275	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
276	C₂×C₉	—	2	4	no	—
277	C₂×C₉	—	4	4	no	—
278	C₂×C₉	#539	1	4	yes	direct product factor
279	C₂×C₉	C₂²×#41	1	1	yes	characteristic
280	C₂×C₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
281	C₂×C₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
282	C₂⁴	C₂³×C₉	1	2	yes	—
283	C₂⁴	C₂³×C₉	1	1	yes	characteristic
284	C₂×Q₈	—	4	2	no	—
285	C₂×Q₈	C₂³×C₉	1	4	yes	—
286	C₂×D₄	—	2	8	no	—
287	C₂×D₄	—	4	2	no	—
288	C₂×D₄	C₂³×C₉	1	8	yes	—
289	C₂×D₄	C₂³×C₉	1	4	yes	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	4	4	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	C₂³×C₉	1	2	yes	—
295	C₂²×C₄	C₂³×C₉	1	2	yes	—
296	C₂²×C₄	C₂³×C₉	1	2	yes	—
297	C₂²×C₄	C₂³×C₉	1	2	yes	—
298	C₂²×C₄	C₂³×C₉	1	2	yes	—
299	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
300	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
301	C₂²×C₄	C₂³×C₉	1	4	yes	—
302	C₂²×C₄	C₂³×C₉	1	4	yes	—
303	C₂²×C₄	C₂³×C₉	1	4	yes	—
304	C₂²×C₄	C₂³×C₉	1	8	yes	—
305	C₄⋊C₄	C₂³×C₉	1	8	yes	—
306	C₄⋊C₄	C₂³×C₉	1	8	yes	—
307	C₄⋊C₄	C₂³×C₉	1	8	yes	—
308	C₄⋊C₄	C₂³×C₉	1	4	yes	—
309	C₄⋊C₄	C₂³×C₉	1	8	yes	—
310	C₄⋊C₄	C₂³×C₉	1	8	yes	—
311	C₄⋊C₄	C₂³×C₉	1	4	yes	—
312	C₄⋊C₄	C₂³×C₉	1	8	yes	—
313	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
314	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
315	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
316	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
317	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
318	C₄²	C₂³×C₉	1	8	yes	—
319	C₂²×C₃	—	2	2	no	—
320	C₂²×C₃	—	2	2	no	—
321	C₂²×C₃	—	2	8	no	—
322	C₂²×C₃	—	2	4	no	—
323	C₂²×C₃	—	2	4	no	—
324	C₂²×C₃	—	2	4	no	—
325	C₂²×C₃	—	4	8	no	—
326	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
327	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
328	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
329	C₂²×C₃	C₃×2₋¹⁺⁴	1	2	yes	—
330	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
331	C₃×C₄	—	2	4	no	—
332	C₃×C₄	—	2	4	no	—
333	C₃×C₄	—	2	4	no	—
334	C₃×C₄	—	2	2	no	—
335	C₃×C₄	—	2	4	no	—
336	C₃×C₄	—	2	2	no	—
337	C₃×C₄	—	2	4	no	—
338	C₉	C₂×#539	1	1	yes	characteristic, direct product factor, Sylow
339	C₂³	—	2	2	no	—
340	C₂³	—	2	2	no	—
341	C₂³	—	2	4	no	—
342	C₂³	—	2	4	no	—
343	C₂³	—	2	4	no	—
344	C₂³	C₉×#41	1	4	yes	—
345	C₂³	C₂⁴×C₉	1	4	yes	—
346	C₂³	C₂⁴×C₉	1	2	yes	—
347	C₂³	C₂⁴×C₉	1	1	yes	characteristic
348	Q₈	—	4	4	no	—
349	D₄	—	2	16	no	—
350	D₄	—	4	4	no	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	4	8	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	C₂⁴×C₉	1	4	yes	—
363	C₂×C₄	C₂⁴×C₉	1	4	yes	—
364	C₂×C₄	C₂⁴×C₉	1	4	yes	—
365	C₂×C₄	C₂⁴×C₉	1	4	yes	—
366	C₂×C₄	C₂⁴×C₉	1	4	yes	—
367	C₂×C₄	C₂⁴×C₉	1	2	yes	—
368	C₂×C₄	C₂⁴×C₉	1	2	yes	—
369	C₂×C₃	—	2	4	no	—
370	C₂×C₃	—	4	4	no	—
371	C₂×C₃	C₃×#539	1	4	yes	—
372	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
373	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
374	C₂×C₃	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
375	C₂²	—	2	8	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	4	no	—
379	C₂²	—	2	4	no	—
380	C₂²	—	2	4	no	—
381	C₂²	—	4	8	no	—
382	C₂²	C₂×C₉×#41	1	4	yes	—
383	C₂²	C₂×C₉×#41	1	2	yes	—
384	C₂²	C₉×H(5,𝔽₂)	1	2	yes	—
385	C₂²	C₉×2₋¹⁺⁴	1	2	yes	—
386	C₂²	C₂⁵×C₉	1	1	yes	characteristic
387	C₄	—	2	4	no	—
388	C₄	—	2	4	no	—
389	C₄	—	2	4	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	4	no	—
392	C₄	—	2	2	no	—
393	C₄	—	2	4	no	—
394	C₃	C₂×C₃×#539	1	1	yes	characteristic
395	C₂	—	2	4	no	—
396	C₂	—	4	4	no	—
397	C₂	C₉×#539	1	4	yes	direct product factor
398	C₂	C₂²×C₉×#41	1	1	yes	characteristic
399	C₂	C₂×C₉×H(5,𝔽₂)	1	1	yes	characteristic
400	C₂	C₂×C₉×2₋¹⁺⁴	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×#121	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×#539	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×#123	C₂	semidirect
6. C₂×C₉×C₂²⋊Q₈	C₂	semidirect
7. C₂×C₉×C₂²⋊Q₈	C₂	semidirect
9. C₂×C₄×D₄×C₉	C₂	semidirect
10. C₂²×C₉×C₄⋊C₄	C₂	semidirect
19. C₉×#126	C₂²	semidirect
20. C₉×#125	C₂²	semidirect
21. C₉×#123	C₂²	semidirect
22. C₉×#123	C₂²	semidirect
23. C₉×C₂²⋊Q₈	C₂²	semidirect
24. C₉×C₂²⋊Q₈	C₂²	semidirect
26. C₄×D₄×C₉	C₂²	semidirect
35. C₂×C₉×C₄⋊C₄	C₂²	semidirect
89. C₂×#539	C₉	direct (N × H)
150. #539	C₂×C₉	direct (N × H)
151. C₂×#126	C₂×C₉	semidirect
152. C₂×#125	C₂×C₉	semidirect
153. C₂×#123	C₂×C₉	semidirect
154. C₂×#123	C₂×C₉	semidirect
155. C₂×C₂²⋊Q₈	C₂×C₉	semidirect
156. C₂×C₂²⋊Q₈	C₂×C₉	semidirect
158. C₂×C₄×D₄	C₂×C₉	semidirect
159. C₂²×C₄⋊C₄	C₂×C₉	semidirect
223. #126	C₂²×C₉	semidirect
224. #125	C₂²×C₉	semidirect
225. #123	C₂²×C₉	semidirect
226. #123	C₂²×C₉	semidirect
227. C₂²⋊Q₈	C₂²×C₉	semidirect
228. C₂²⋊Q₈	C₂²×C₉	semidirect
230. C₄×D₄	C₂²×C₉	semidirect
239. C₂×C₄⋊C₄	C₂²×C₉	semidirect
278. C₂×C₉	#539	direct (N × H)
338. C₉	C₂×#539	direct (N × H)
397. C₂	C₉×#539	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×#539	2
C₂×C₉×#126	2
C₂×C₉×#125	2
C₂×C₉×#123	2
C₂×C₉×C₂²⋊Q₈	2
C₂×C₉×#121	2
C₂×C₄×D₄×C₉	2
C₂²×C₉×C₄⋊C₄	2
C₂×C₃×#539	3

Subgroups — C2×C9×#539 #11768172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#539 #11768172