Subgroups — C₂×C₉×#525 #11768156

Order 1152.

2820 conjugacy classes of subgroups.

The subgroup lattice has 396 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	C₂⁴×C₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#525	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₉×#123	C₂	1	2	yes	maximal, complemented
5	C₂×C₉×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
6	C₂×C₉×#121	C₂	1	2	yes	maximal, complemented
7	C₂×C₉×#120	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×D₄×C₉	C₂	1	4	yes	maximal, complemented
9	C₂×C₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#525	C₃	1	1	yes	maximal, characteristic
11	C₂⁵×C₉	C₂²	1	1	yes	characteristic
12	C₂×C₉×#41	—	2	8	no	—
13	C₂×C₉×#41	C₂²	1	8	yes	complemented
14	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
15	C₂²×D₄×C₉	C₂²	1	4	yes	—
16	C₂²×D₄×C₉	C₂²	1	2	yes	—
17	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
18	C₂³×C₄×C₉	—	2	8	no	—
19	C₂³×C₄×C₉	C₂²	1	2	yes	—
20	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
21	C₂³×C₄×C₉	C₂²	1	2	yes	—
22	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
23	C₂³×C₄×C₉	C₂²	1	8	yes	complemented
24	C₂³×C₄×C₉	C₂²	1	2	yes	complemented
25	C₉×#123	C₂²	1	16	yes	complemented
26	C₉×C₂²⋊Q₈	C₂²	1	16	yes	complemented
27	C₉×#121	C₂²	1	16	yes	complemented
28	C₉×#120	C₂²	1	16	yes	complemented
29	C₄×D₄×C₉	C₂²	1	32	yes	complemented
30	C₉×#117	C₂²	1	8	yes	complemented
31	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	complemented
32	C₂×C₉×C₄⋊C₄	C₂²	1	4	yes	complemented
33	C₂×C₉×C₂²⋊C₄	C₂²	1	4	yes	—
34	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
35	C₂×C₉×C₂²⋊C₄	C₂²	1	4	yes	complemented
36	C₂×C₄²×C₉	C₂²	1	2	yes	complemented
37	C₂²×C₃×#41	C₂×C₃	1	1	yes	characteristic
38	C₂⁴×C₃×C₄	C₂×C₃	1	1	yes	characteristic
39	C₃×#525	C₂×C₃	1	16	yes	—
40	C₂×C₃×#123	C₂×C₃	1	2	yes	—
41	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	2	yes	—
42	C₂×C₃×#121	C₂×C₃	1	2	yes	—
43	C₂×C₃×#120	C₂×C₃	1	2	yes	—
44	C₂×C₃×C₄×D₄	C₂×C₃	1	4	yes	—
45	C₂×C₃×#117	C₂×C₃	1	1	yes	characteristic
46	C₂⁴×C₉	—	2	4	no	—
47	C₂⁴×C₉	—	2	8	no	—
48	C₂⁴×C₉	C₂³	1	2	yes	—
49	C₂⁴×C₉	C₂³	1	4	yes	—
50	C₂⁴×C₉	C₂³	1	1	yes	characteristic
51	C₂⁴×C₉	C₂³	1	2	yes	—
52	C₉×#41	—	2	32	no	—
53	C₂×Q₈×C₉	—	2	4	no	—
54	C₂×Q₈×C₉	C₂³	1	4	yes	complemented
55	C₂×D₄×C₉	—	2	8	no	—
56	C₂×D₄×C₉	—	2	16	no	—
57	C₂×D₄×C₉	—	2	4	no	—
58	C₂×D₄×C₉	C₂³	1	16	yes	—
59	C₂×D₄×C₉	C₂³	1	8	yes	—
60	C₂×D₄×C₉	C₂³	1	4	yes	complemented
61	C₂²×C₄×C₉	—	2	4	no	—
62	C₂²×C₄×C₉	—	2	8	no	—
63	C₂²×C₄×C₉	—	2	8	no	—
64	C₂²×C₄×C₉	—	2	8	no	—
65	C₂²×C₄×C₉	—	2	32	no	—
66	C₂²×C₄×C₉	D₄	1	8	yes	complemented
67	C₂²×C₄×C₉	C₂³	1	4	yes	—
68	C₂²×C₄×C₉	C₂³	1	2	yes	—
69	C₂²×C₄×C₉	C₂³	1	2	yes	—
70	C₂²×C₄×C₉	C₂³	1	8	yes	—
71	C₂²×C₄×C₉	C₂³	1	8	yes	—
72	C₂²×C₄×C₉	C₂³	1	4	yes	—
73	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₉	C₂³	1	4	yes	—
75	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₉	C₂³	1	8	yes	complemented
77	C₉×C₄⋊C₄	C₂³	1	8	yes	complemented
78	C₉×C₄⋊C₄	C₂³	1	16	yes	complemented
79	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
80	C₉×C₂²⋊C₄	C₂³	1	16	yes	—
81	C₉×C₂²⋊C₄	C₂³	1	16	yes	complemented
82	C₄²×C₉	C₂³	1	8	yes	complemented
83	C₂×#525	C₉	1	1	yes	characteristic, direct product factor, Sylow
84	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₃×#41	—	2	8	no	—
86	C₂×C₃×#41	C₂²×C₃	1	8	yes	—
87	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
88	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
89	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
90	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
91	C₂³×C₃×C₄	—	2	8	no	—
92	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
93	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
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	8	yes	—
97	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
98	C₃×#123	C₂²×C₃	1	16	yes	—
99	C₃×C₂²⋊Q₈	C₂²×C₃	1	16	yes	—
100	C₃×#121	C₂²×C₃	1	16	yes	—
101	C₃×#120	C₂²×C₃	1	16	yes	—
102	C₃×C₄×D₄	C₂²×C₃	1	32	yes	—
103	C₃×#117	C₂²×C₃	1	8	yes	—
104	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
105	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
106	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
107	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
108	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
109	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
110	C₂³×C₉	—	2	32	no	—
111	C₂³×C₉	—	2	8	no	—
112	C₂³×C₉	—	2	4	no	—
113	C₂³×C₉	—	2	4	no	—
114	C₂³×C₉	—	2	4	no	—
115	C₂³×C₉	—	2	16	no	—
116	C₂³×C₉	—	2	4	no	—
117	C₂³×C₉	—	2	8	no	—
118	C₂³×C₉	C₂×D₄	1	4	yes	—
119	C₂³×C₉	#41	1	8	yes	complemented
120	C₂³×C₉	C₂⁴	1	4	yes	—
121	C₂³×C₉	C₂⁴	1	2	yes	—
122	C₂³×C₉	C₂⁴	1	4	yes	—
123	C₂³×C₉	C₂⁴	1	1	yes	characteristic
124	Q₈×C₉	—	2	8	no	—
125	D₄×C₉	—	2	16	no	—
126	D₄×C₉	—	2	32	no	—
127	D₄×C₉	—	2	8	no	—
128	C₂×C₄×C₉	—	2	8	no	—
129	C₂×C₄×C₉	—	2	4	no	—
130	C₂×C₄×C₉	—	2	4	no	—
131	C₂×C₄×C₉	—	2	8	no	—
132	C₂×C₄×C₉	—	2	16	no	—
133	C₂×C₄×C₉	—	2	16	no	—
134	C₂×C₄×C₉	—	2	16	no	—
135	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
136	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
137	C₂×C₄×C₉	C₂×D₄	1	16	yes	complemented
138	C₂×C₄×C₉	C₂⁴	1	8	yes	—
139	C₂×C₄×C₉	C₂⁴	1	4	yes	—
140	C₂×C₄×C₉	C₂⁴	1	4	yes	—
141	C₂×C₄×C₉	C₂⁴	1	2	yes	—
142	C₂×C₄×C₉	C₂⁴	1	2	yes	—
143	C₂²×#41	C₂×C₉	1	1	yes	characteristic, complemented
144	C₂⁴×C₄	C₂×C₉	1	1	yes	characteristic, complemented
145	#525	C₂×C₉	1	16	yes	direct product factor
146	C₂×#123	C₂×C₉	1	2	yes	complemented
147	C₂×C₂²⋊Q₈	C₂×C₉	1	2	yes	complemented
148	C₂×#121	C₂×C₉	1	2	yes	complemented
149	C₂×#120	C₂×C₉	1	2	yes	complemented
150	C₂×C₄×D₄	C₂×C₉	1	4	yes	complemented
151	C₂×#117	C₂×C₉	1	1	yes	characteristic, complemented
152	C₂⁴×C₃	—	2	4	no	—
153	C₂⁴×C₃	—	2	8	no	—
154	C₂⁴×C₃	C₂³×C₃	1	4	yes	—
155	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
156	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
157	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
158	C₃×#41	—	2	32	no	—
159	C₂×C₃×Q₈	—	2	4	no	—
160	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
161	C₂×C₃×D₄	—	2	8	no	—
162	C₂×C₃×D₄	—	2	16	no	—
163	C₂×C₃×D₄	—	2	4	no	—
164	C₂×C₃×D₄	C₂³×C₃	1	16	yes	—
165	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
166	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
167	C₂²×C₃×C₄	—	2	4	no	—
168	C₂²×C₃×C₄	—	2	8	no	—
169	C₂²×C₃×C₄	—	2	8	no	—
170	C₂²×C₃×C₄	—	2	32	no	—
171	C₂²×C₃×C₄	—	2	8	no	—
172	C₂²×C₃×C₄	C₃×D₄	1	8	yes	—
173	C₂²×C₃×C₄	C₂³×C₃	1	4	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	8	yes	—
177	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
178	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
179	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
180	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
181	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
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	16	yes	—
185	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
186	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
187	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
188	C₃×C₄²	C₂³×C₃	1	8	yes	—
189	C₂²×C₉	—	2	32	no	—
190	C₂²×C₉	—	2	8	no	—
191	C₂²×C₉	—	2	16	no	—
192	C₂²×C₉	—	2	4	no	—
193	C₂²×C₉	—	2	4	no	—
194	C₂²×C₉	—	2	4	no	—
195	C₂²×C₉	—	2	4	no	—
196	C₂²×C₉	—	2	8	no	—
197	C₂²×C₉	—	4	8	no	—
198	C₂²×C₉	C₂²×D₄	1	4	yes	—
199	C₂²×C₉	C₂²×D₄	1	2	yes	—
200	C₂²×C₉	C₂×#41	1	4	yes	—
201	C₂²×C₉	C₂×#41	1	8	yes	complemented
202	C₂²×C₉	C₂⁵	1	1	yes	characteristic
203	C₄×C₉	—	2	4	no	—
204	C₄×C₉	—	2	4	no	—
205	C₄×C₉	—	2	8	no	—
206	C₄×C₉	C₂²×D₄	1	4	yes	—
207	C₄×C₉	C₂²×D₄	1	4	yes	—
208	C₂⁵	C₂²×C₉	1	1	yes	characteristic
209	C₂×#41	—	2	8	no	—
210	C₂×#41	C₂²×C₉	1	8	yes	complemented
211	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
212	C₂²×D₄	C₂²×C₉	1	4	yes	—
213	C₂²×D₄	C₂²×C₉	1	2	yes	—
214	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic, complemented
215	C₂³×C₄	—	2	8	no	—
216	C₂³×C₄	C₂²×C₉	1	2	yes	—
217	C₂³×C₄	C₂²×C₉	1	2	yes	—
218	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
219	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
220	C₂³×C₄	C₂²×C₉	1	8	yes	complemented
221	C₂³×C₄	C₂²×C₉	1	2	yes	complemented
222	#123	C₂²×C₉	1	16	yes	complemented
223	C₂²⋊Q₈	C₂²×C₉	1	16	yes	complemented
224	#121	C₂²×C₉	1	16	yes	complemented
225	#120	C₂²×C₉	1	16	yes	complemented
226	C₄×D₄	C₂²×C₉	1	32	yes	complemented
227	#117	C₂²×C₉	1	8	yes	complemented
228	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	complemented
229	C₂×C₄⋊C₄	C₂²×C₉	1	4	yes	complemented
230	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
231	C₂×C₂²⋊C₄	C₂²×C₉	1	4	yes	—
232	C₂×C₂²⋊C₄	C₂²×C₉	1	4	yes	complemented
233	C₂×C₄²	C₂²×C₉	1	2	yes	complemented
234	C₂³×C₃	—	2	32	no	—
235	C₂³×C₃	—	2	8	no	—
236	C₂³×C₃	—	2	4	no	—
237	C₂³×C₃	—	2	4	no	—
238	C₂³×C₃	—	2	4	no	—
239	C₂³×C₃	—	2	16	no	—
240	C₂³×C₃	—	2	4	no	—
241	C₂³×C₃	—	2	8	no	—
242	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
243	C₂³×C₃	C₃×#41	1	8	yes	—
244	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
245	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
246	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
247	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
248	C₃×Q₈	—	2	8	no	—
249	C₃×D₄	—	2	16	no	—
250	C₃×D₄	—	2	32	no	—
251	C₃×D₄	—	2	8	no	—
252	C₂×C₃×C₄	—	2	8	no	—
253	C₂×C₃×C₄	—	2	4	no	—
254	C₂×C₃×C₄	—	2	4	no	—
255	C₂×C₃×C₄	—	2	8	no	—
256	C₂×C₃×C₄	—	2	16	no	—
257	C₂×C₃×C₄	—	2	16	no	—
258	C₂×C₃×C₄	—	2	16	no	—
259	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
260	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
261	C₂×C₃×C₄	C₂×C₃×D₄	1	16	yes	—
262	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
263	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
264	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
265	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
266	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
267	C₂×C₉	—	2	4	no	—
268	C₂×C₉	—	2	8	no	—
269	C₂×C₉	—	4	4	no	—
270	C₂×C₉	#525	1	4	yes	direct product factor
271	C₂×C₉	C₂³×D₄	1	1	yes	characteristic
272	C₂×C₉	C₂²×#41	1	2	yes	—
273	C₂⁴	—	2	4	no	—
274	C₂⁴	—	2	8	no	—
275	C₂⁴	C₂³×C₉	1	2	yes	—
276	C₂⁴	C₂³×C₉	1	4	yes	—
277	C₂⁴	C₂³×C₉	1	1	yes	characteristic
278	C₂⁴	C₂³×C₉	1	2	yes	—
279	#41	—	2	32	no	—
280	C₂×Q₈	—	2	4	no	—
281	C₂×Q₈	C₂³×C₉	1	4	yes	complemented
282	C₂×D₄	—	2	8	no	—
283	C₂×D₄	—	2	16	no	—
284	C₂×D₄	—	2	4	no	—
285	C₂×D₄	C₂³×C₉	1	16	yes	—
286	C₂×D₄	C₂³×C₉	1	8	yes	—
287	C₂×D₄	C₂³×C₉	1	4	yes	complemented
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	8	no	—
290	C₂²×C₄	—	2	8	no	—
291	C₂²×C₄	—	2	8	no	—
292	C₂²×C₄	—	2	32	no	—
293	C₂²×C₄	D₄×C₉	1	8	yes	complemented
294	C₂²×C₄	C₂³×C₉	1	4	yes	—
295	C₂²×C₄	C₂³×C₉	1	2	yes	—
296	C₂²×C₄	C₂³×C₉	1	2	yes	—
297	C₂²×C₄	C₂³×C₉	1	8	yes	—
298	C₂²×C₄	C₂³×C₉	1	8	yes	—
299	C₂²×C₄	C₂³×C₉	1	4	yes	—
300	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
301	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
302	C₂²×C₄	C₂³×C₉	1	4	yes	—
303	C₂²×C₄	C₂³×C₉	1	8	yes	complemented
304	C₄⋊C₄	C₂³×C₉	1	8	yes	complemented
305	C₄⋊C₄	C₂³×C₉	1	16	yes	complemented
306	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
307	C₂²⋊C₄	C₂³×C₉	1	16	yes	—
308	C₂²⋊C₄	C₂³×C₉	1	16	yes	complemented
309	C₄²	C₂³×C₉	1	8	yes	complemented
310	C₂²×C₃	—	2	32	no	—
311	C₂²×C₃	—	2	4	no	—
312	C₂²×C₃	—	2	4	no	—
313	C₂²×C₃	—	2	4	no	—
314	C₂²×C₃	—	2	8	no	—
315	C₂²×C₃	—	2	16	no	—
316	C₂²×C₃	—	2	4	no	—
317	C₂²×C₃	—	2	8	no	—
318	C₂²×C₃	—	4	8	no	—
319	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
320	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
321	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
322	C₂²×C₃	C₂×C₃×#41	1	8	yes	—
323	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
324	C₃×C₄	—	2	4	no	—
325	C₃×C₄	—	2	4	no	—
326	C₃×C₄	—	2	8	no	—
327	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
328	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
329	C₉	C₂×#525	1	1	yes	characteristic, direct product factor, Sylow
330	C₂³	—	2	32	no	—
331	C₂³	—	2	8	no	—
332	C₂³	—	2	4	no	—
333	C₂³	—	2	4	no	—
334	C₂³	—	2	4	no	—
335	C₂³	—	2	16	no	—
336	C₂³	—	2	4	no	—
337	C₂³	—	2	8	no	—
338	C₂³	C₂×D₄×C₉	1	4	yes	—
339	C₂³	C₉×#41	1	8	yes	complemented
340	C₂³	C₂⁴×C₉	1	4	yes	—
341	C₂³	C₂⁴×C₉	1	2	yes	—
342	C₂³	C₂⁴×C₉	1	4	yes	—
343	C₂³	C₂⁴×C₉	1	1	yes	characteristic
344	Q₈	—	2	8	no	—
345	D₄	—	2	16	no	—
346	D₄	—	2	32	no	—
347	D₄	—	2	8	no	—
348	C₂×C₄	—	2	8	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	2	16	no	—
353	C₂×C₄	—	2	16	no	—
354	C₂×C₄	—	2	16	no	—
355	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
356	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
357	C₂×C₄	C₂×D₄×C₉	1	16	yes	complemented
358	C₂×C₄	C₂⁴×C₉	1	8	yes	—
359	C₂×C₄	C₂⁴×C₉	1	4	yes	—
360	C₂×C₄	C₂⁴×C₉	1	4	yes	—
361	C₂×C₄	C₂⁴×C₉	1	2	yes	—
362	C₂×C₄	C₂⁴×C₉	1	2	yes	—
363	C₂×C₃	—	2	4	no	—
364	C₂×C₃	—	2	8	no	—
365	C₂×C₃	—	4	4	no	—
366	C₂×C₃	C₃×#525	1	4	yes	—
367	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
368	C₂×C₃	C₂²×C₃×#41	1	2	yes	—
369	C₂²	—	2	32	no	—
370	C₂²	—	2	8	no	—
371	C₂²	—	2	16	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	2	4	no	—
375	C₂²	—	2	4	no	—
376	C₂²	—	2	8	no	—
377	C₂²	—	4	8	no	—
378	C₂²	C₂²×D₄×C₉	1	4	yes	—
379	C₂²	C₂²×D₄×C₉	1	2	yes	—
380	C₂²	C₂×C₉×#41	1	4	yes	—
381	C₂²	C₂×C₉×#41	1	8	yes	complemented
382	C₂²	C₂⁵×C₉	1	1	yes	characteristic
383	C₄	—	2	4	no	—
384	C₄	—	2	4	no	—
385	C₄	—	2	8	no	—
386	C₄	C₂²×D₄×C₉	1	4	yes	—
387	C₄	C₂²×D₄×C₉	1	4	yes	—
388	C₃	C₂×C₃×#525	1	1	yes	characteristic
389	C₂	—	2	4	no	—
390	C₂	—	2	8	no	—
391	C₂	—	4	4	no	—
392	C₂	C₉×#525	1	4	yes	direct product factor
393	C₂	C₂³×D₄×C₉	1	1	yes	characteristic
394	C₂	C₂²×C₉×#41	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₉	C₂³
commutator	C₂²	C₂⁵×C₉
Frattini, cosocle	C₂²×C₃	C₂⁵×C₃
socle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂×C₃×#525	C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×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. C₂⁴×C₄×C₉	C₂	semidirect
3. C₉×#525	C₂	direct (N × H)
4. C₂×C₉×#123	C₂	semidirect
5. C₂×C₉×C₂²⋊Q₈	C₂	semidirect
6. C₂×C₉×#121	C₂	semidirect
7. C₂×C₉×#120	C₂	semidirect
8. C₂×C₄×D₄×C₉	C₂	semidirect
9. C₂×C₉×#117	C₂	semidirect
13. C₂×C₉×#41	C₂²	semidirect
14. C₂²×Q₈×C₉	C₂²	semidirect
17. C₂²×D₄×C₉	C₂²	semidirect
23. C₂³×C₄×C₉	C₂²	semidirect
24. C₂³×C₄×C₉	C₂²	semidirect
25. C₉×#123	C₂²	semidirect
26. C₉×C₂²⋊Q₈	C₂²	semidirect
27. C₉×#121	C₂²	semidirect
28. C₉×#120	C₂²	semidirect
29. C₄×D₄×C₉	C₂²	semidirect
30. C₉×#117	C₂²	semidirect
31. C₂×C₉×C₄⋊C₄	C₂²	semidirect
32. C₂×C₉×C₄⋊C₄	C₂²	semidirect
35. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
36. C₂×C₄²×C₉	C₂²	semidirect
54. C₂×Q₈×C₉	C₂³	semidirect
60. C₂×D₄×C₉	C₂³	semidirect
66. C₂²×C₄×C₉	D₄	semidirect
76. C₂²×C₄×C₉	C₂³	semidirect
77. C₉×C₄⋊C₄	C₂³	semidirect
78. C₉×C₄⋊C₄	C₂³	semidirect
81. C₉×C₂²⋊C₄	C₂³	semidirect
82. C₄²×C₉	C₂³	semidirect
83. C₂×#525	C₉	direct (N × H)
119. C₂³×C₉	#41	semidirect
137. C₂×C₄×C₉	C₂×D₄	semidirect
143. C₂²×#41	C₂×C₉	semidirect
144. C₂⁴×C₄	C₂×C₉	semidirect
145. #525	C₂×C₉	direct (N × H)
146. C₂×#123	C₂×C₉	semidirect
147. C₂×C₂²⋊Q₈	C₂×C₉	semidirect
148. C₂×#121	C₂×C₉	semidirect
149. C₂×#120	C₂×C₉	semidirect
150. C₂×C₄×D₄	C₂×C₉	semidirect
151. C₂×#117	C₂×C₉	semidirect
201. C₂²×C₉	C₂×#41	semidirect
210. C₂×#41	C₂²×C₉	semidirect
211. C₂²×Q₈	C₂²×C₉	semidirect
214. C₂²×D₄	C₂²×C₉	semidirect
220. C₂³×C₄	C₂²×C₉	semidirect
221. C₂³×C₄	C₂²×C₉	semidirect
222. #123	C₂²×C₉	semidirect
223. C₂²⋊Q₈	C₂²×C₉	semidirect
224. #121	C₂²×C₉	semidirect
225. #120	C₂²×C₉	semidirect
226. C₄×D₄	C₂²×C₉	semidirect
227. #117	C₂²×C₉	semidirect
228. C₂×C₄⋊C₄	C₂²×C₉	semidirect
229. C₂×C₄⋊C₄	C₂²×C₉	semidirect
232. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
233. C₂×C₄²	C₂²×C₉	semidirect
270. C₂×C₉	#525	direct (N × H)
281. C₂×Q₈	C₂³×C₉	semidirect
287. C₂×D₄	C₂³×C₉	semidirect
293. C₂²×C₄	D₄×C₉	semidirect
303. C₂²×C₄	C₂³×C₉	semidirect
304. C₄⋊C₄	C₂³×C₉	semidirect
305. C₄⋊C₄	C₂³×C₉	semidirect
308. C₂²⋊C₄	C₂³×C₉	semidirect
309. C₄²	C₂³×C₉	semidirect
329. C₉	C₂×#525	direct (N × H)
339. C₂³	C₉×#41	semidirect
357. C₂×C₄	C₂×D₄×C₉	semidirect
381. C₂²	C₂×C₉×#41	semidirect
392. C₂	C₉×#525	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
C₂⁴×C₄×C₉	2
C₉×#525	2
C₂×C₉×#123	2
C₂×C₉×C₂²⋊Q₈	2
C₂×C₉×#121	2
C₂×C₉×#120	2
C₂×C₄×D₄×C₉	2
C₂×C₉×#117	2
C₂×C₃×#525	3

Subgroups — C2×C9×#525 #11768156

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#525 #11768156