Subgroups — D₄×C₉×#41 #11768189

Order 1152.

2472 conjugacy classes of subgroups.

The subgroup lattice has 438 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	2	yes	maximal, complemented
2	C₉×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#548	C₂	1	2	yes	maximal, complemented
5	C₉×#547	C₂	1	3	yes	maximal, complemented
6	C₉×#546	C₂	1	6	yes	maximal, complemented
7	D₄²×C₉	C₂	1	3	yes	maximal, complemented
8	C₉×#532	C₂	1	3	yes	maximal, complemented
9	C₉×#525	C₂	1	6	yes	maximal, complemented
10	C₄×C₉×#41	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×D₄×C₉	C₂	1	3	yes	maximal, complemented
12	C₃×D₄×#41	C₃	1	1	yes	maximal, characteristic
13	C₂×C₉×#41	—	2	16	no	—
14	C₂×C₉×#41	C₂²	1	1	yes	characteristic
15	C₂×C₉×#41	C₂²	1	6	yes	complemented
16	C₂×C₉×#41	C₂²	1	6	yes	complemented
17	C₂×C₉×#41	C₂²	1	2	yes	complemented
18	C₂²×Q₈×C₉	C₂²	1	2	yes	complemented
19	C₂²×D₄×C₉	C₂²	1	3	yes	—
20	C₂²×D₄×C₉	C₂²	1	6	yes	complemented
21	C₂³×C₄×C₉	C₂²	1	6	yes	complemented
22	C₉×C₄⋊Q₈	C₂²	1	3	yes	complemented
23	C₉×#127	C₂²	1	3	yes	complemented
24	C₉×#124	C₂²	1	6	yes	complemented
25	C₉×#123	C₂²	1	12	yes	complemented
26	C₉×C₂²⋊Q₈	C₂²	1	6	yes	complemented
27	C₉×C₂²⋊Q₈	C₂²	1	6	yes	complemented
28	C₉×#121	C₂²	1	6	yes	complemented
29	C₉×#121	C₂²	1	6	yes	complemented
30	C₉×#121	C₂²	1	6	yes	complemented
31	C₉×#121	C₂²	1	6	yes	complemented
32	C₉×#120	C₂²	1	12	yes	complemented
33	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
34	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
35	C₄×D₄×C₉	C₂²	1	3	yes	—
36	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
37	C₄×D₄×C₉	C₂²	1	6	yes	complemented
38	C₄×D₄×C₉	C₂²	1	6	yes	complemented
39	C₄×D₄×C₉	C₂²	1	3	yes	complemented
40	C₄×D₄×C₉	C₂²	1	3	yes	complemented
41	C₄×D₄×C₉	C₂²	1	3	yes	complemented
42	C₄×D₄×C₉	C₂²	1	6	yes	complemented
43	C₄×D₄×C₉	C₂²	1	3	yes	complemented
44	C₉×#117	C₂²	1	3	yes	complemented
45	C₂×C₉×C₄⋊C₄	C₂²	1	3	yes	complemented
46	C₂×C₉×C₂²⋊C₄	C₂²	1	6	yes	complemented
47	C₂×C₄²×C₉	C₂²	1	3	yes	complemented
48	C₂²×C₃×#41	C₂×C₃	1	2	yes	—
49	C₃×#550	C₂×C₃	1	1	yes	characteristic
50	C₃×D₄×Q₈	C₂×C₃	1	1	yes	characteristic
51	C₃×#548	C₂×C₃	1	2	yes	—
52	C₃×#547	C₂×C₃	1	3	yes	—
53	C₃×#546	C₂×C₃	1	6	yes	—
54	C₃×D₄²	C₂×C₃	1	3	yes	—
55	C₃×#532	C₂×C₃	1	3	yes	—
56	C₃×#525	C₂×C₃	1	6	yes	—
57	C₃×C₄×#41	C₂×C₃	1	1	yes	characteristic
58	C₂×C₃×C₄×D₄	C₂×C₃	1	3	yes	—
59	C₂⁴×C₉	C₂³	1	6	yes	—
60	C₉×#41	—	2	8	no	—
61	C₉×#41	—	2	24	no	—
62	C₉×#41	—	2	24	no	—
63	C₉×#41	D₄	1	8	yes	direct product factor
64	C₂×Q₈×C₉	—	2	8	no	—
65	C₂×Q₈×C₉	C₂³	1	6	yes	—
66	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
67	C₂×D₄×C₉	—	2	24	no	—
68	C₂×D₄×C₉	—	2	12	no	—
69	C₂×D₄×C₉	C₂³	1	6	yes	—
70	C₂×D₄×C₉	C₂³	1	3	yes	—
71	C₂×D₄×C₉	C₂³	1	12	yes	—
72	C₂×D₄×C₉	C₂³	1	6	yes	—
73	C₂×D₄×C₉	C₂³	1	6	yes	—
74	C₂×D₄×C₉	C₂³	1	3	yes	—
75	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₉	—	2	24	no	—
77	C₂²×C₄×C₉	C₂³	1	3	yes	—
78	C₂²×C₄×C₉	C₂³	1	6	yes	—
79	C₂²×C₄×C₉	C₂³	1	6	yes	—
80	C₂²×C₄×C₉	C₂³	1	6	yes	—
81	C₂²×C₄×C₉	C₂³	1	2	yes	—
82	C₂²×C₄×C₉	C₂³	1	6	yes	—
83	C₂²×C₄×C₉	C₂³	1	3	yes	—
84	C₂²×C₄×C₉	C₂³	1	3	yes	—
85	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₉×C₄⋊C₄	C₂³	1	3	yes	—
87	C₉×C₄⋊C₄	C₂³	1	6	yes	—
88	C₉×C₄⋊C₄	C₂³	1	3	yes	—
89	C₉×C₄⋊C₄	C₂³	1	3	yes	—
90	C₉×C₄⋊C₄	C₂³	1	6	yes	—
91	C₉×C₂²⋊C₄	C₂³	1	2	yes	—
92	C₉×C₂²⋊C₄	C₂³	1	6	yes	—
93	C₉×C₂²⋊C₄	C₂³	1	6	yes	—
94	C₉×C₂²⋊C₄	C₂³	1	6	yes	—
95	C₉×C₂²⋊C₄	C₂³	1	6	yes	—
96	C₉×C₂²⋊C₄	C₂³	1	12	yes	—
97	C₄²×C₉	C₂³	1	3	yes	—
98	C₄²×C₉	C₂³	1	3	yes	—
99	C₄²×C₉	C₂³	1	1	yes	characteristic
100	C₄²×C₉	C₂³	1	3	yes	—
101	D₄×#41	C₉	1	1	yes	characteristic, direct product factor, Sylow
102	C₂×C₃×#41	—	2	16	no	—
103	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₃×#41	C₂²×C₃	1	6	yes	—
105	C₂×C₃×#41	C₂²×C₃	1	6	yes	—
106	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
107	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	—
108	C₂²×C₃×D₄	C₂²×C₃	1	3	yes	—
109	C₂²×C₃×D₄	C₂²×C₃	1	6	yes	—
110	C₂³×C₃×C₄	C₂²×C₃	1	6	yes	—
111	C₃×C₄⋊Q₈	C₂²×C₃	1	3	yes	—
112	C₃×#127	C₂²×C₃	1	3	yes	—
113	C₃×#124	C₂²×C₃	1	6	yes	—
114	C₃×#123	C₂²×C₃	1	12	yes	—
115	C₃×C₂²⋊Q₈	C₂²×C₃	1	6	yes	—
116	C₃×C₂²⋊Q₈	C₂²×C₃	1	6	yes	—
117	C₃×#121	C₂²×C₃	1	6	yes	—
118	C₃×#121	C₂²×C₃	1	6	yes	—
119	C₃×#121	C₂²×C₃	1	6	yes	—
120	C₃×#121	C₂²×C₃	1	6	yes	—
121	C₃×#120	C₂²×C₃	1	12	yes	—
122	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
123	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
124	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
125	C₃×C₄×D₄	C₂²×C₃	1	3	yes	—
126	C₃×C₄×D₄	C₂²×C₃	1	6	yes	—
127	C₃×C₄×D₄	C₂²×C₃	1	3	yes	—
128	C₃×C₄×D₄	C₂²×C₃	1	6	yes	—
129	C₃×C₄×D₄	C₂²×C₃	1	3	yes	—
130	C₃×C₄×D₄	C₂²×C₃	1	3	yes	—
131	C₃×C₄×D₄	C₂²×C₃	1	3	yes	—
132	C₃×C₄×D₄	C₂²×C₃	1	6	yes	—
133	C₃×#117	C₂²×C₃	1	3	yes	—
134	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	3	yes	—
135	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	6	yes	—
136	C₂×C₃×C₄²	C₂²×C₃	1	3	yes	—
137	C₂³×C₉	—	2	12	no	—
138	C₂³×C₉	—	2	12	no	—
139	C₂³×C₉	—	4	6	no	—
140	C₂³×C₉	C₂⁴	1	6	yes	—
141	C₂³×C₉	C₂⁴	1	3	yes	—
142	C₂³×C₉	C₂⁴	1	2	yes	—
143	Q₈×C₉	—	2	12	no	—
144	Q₈×C₉	C₂×D₄	1	4	yes	complemented
145	D₄×C₉	—	2	24	no	—
146	D₄×C₉	—	2	12	no	—
147	D₄×C₉	—	2	12	no	—
148	D₄×C₉	—	2	6	no	—
149	D₄×C₉	—	4	6	no	—
150	D₄×C₉	C₂×D₄	1	12	yes	complemented
151	D₄×C₉	#41	1	4	yes	direct product factor
152	C₂×C₄×C₉	—	2	12	no	—
153	C₂×C₄×C₉	—	2	4	no	—
154	C₂×C₄×C₉	—	2	12	no	—
155	C₂×C₄×C₉	—	2	12	no	—
156	C₂×C₄×C₉	—	2	12	no	—
157	C₂×C₄×C₉	—	2	6	no	—
158	C₂×C₄×C₉	—	4	3	no	—
159	C₂×C₄×C₉	C₂×D₄	1	12	yes	complemented
160	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
161	C₂×C₄×C₉	C₂⁴	1	3	yes	—
162	C₂×C₄×C₉	C₂⁴	1	3	yes	—
163	C₂×C₄×C₉	C₂⁴	1	2	yes	—
164	C₂×C₄×C₉	C₂⁴	1	6	yes	—
165	C₂×C₄×C₉	C₂⁴	1	3	yes	—
166	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
167	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
168	C₂²×#41	C₂×C₉	1	2	yes	complemented
169	#550	C₂×C₉	1	1	yes	characteristic, complemented
170	D₄×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
171	#548	C₂×C₉	1	2	yes	complemented
172	#547	C₂×C₉	1	3	yes	complemented
173	#546	C₂×C₉	1	6	yes	complemented
174	D₄²	C₂×C₉	1	3	yes	complemented
175	#532	C₂×C₉	1	3	yes	complemented
176	#525	C₂×C₉	1	6	yes	complemented
177	C₄×#41	C₂×C₉	1	1	yes	characteristic, complemented
178	C₂×C₄×D₄	C₂×C₉	1	3	yes	complemented
179	C₂⁴×C₃	C₂³×C₃	1	6	yes	—
180	C₃×#41	—	2	8	no	—
181	C₃×#41	—	2	24	no	—
182	C₃×#41	—	2	24	no	—
183	C₃×#41	C₃×D₄	1	8	yes	—
184	C₂×C₃×Q₈	—	2	8	no	—
185	C₂×C₃×Q₈	C₂³×C₃	1	6	yes	—
186	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
187	C₂×C₃×D₄	—	2	24	no	—
188	C₂×C₃×D₄	—	2	12	no	—
189	C₂×C₃×D₄	C₂³×C₃	1	6	yes	—
190	C₂×C₃×D₄	C₂³×C₃	1	3	yes	—
191	C₂×C₃×D₄	C₂³×C₃	1	12	yes	—
192	C₂×C₃×D₄	C₂³×C₃	1	6	yes	—
193	C₂×C₃×D₄	C₂³×C₃	1	6	yes	—
194	C₂×C₃×D₄	C₂³×C₃	1	3	yes	—
195	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
196	C₂²×C₃×C₄	—	2	24	no	—
197	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
198	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
199	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
200	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
201	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
202	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
203	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
204	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
205	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
206	C₃×C₄⋊C₄	C₂³×C₃	1	3	yes	—
207	C₃×C₄⋊C₄	C₂³×C₃	1	6	yes	—
208	C₃×C₄⋊C₄	C₂³×C₃	1	3	yes	—
209	C₃×C₄⋊C₄	C₂³×C₃	1	3	yes	—
210	C₃×C₄⋊C₄	C₂³×C₃	1	6	yes	—
211	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
212	C₃×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
213	C₃×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
214	C₃×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
215	C₃×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
216	C₃×C₂²⋊C₄	C₂³×C₃	1	12	yes	—
217	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
218	C₃×C₄²	C₂³×C₃	1	3	yes	—
219	C₃×C₄²	C₂³×C₃	1	3	yes	—
220	C₃×C₄²	C₂³×C₃	1	3	yes	—
221	C₂²×C₉	—	2	2	no	—
222	C₂²×C₉	—	2	3	no	—
223	C₂²×C₉	—	2	3	no	—
224	C₂²×C₉	—	2	2	no	—
225	C₂²×C₉	—	2	6	no	—
226	C₂²×C₉	—	2	6	no	—
227	C₂²×C₉	—	2	6	no	—
228	C₂²×C₉	—	4	24	no	—
229	C₂²×C₉	C₂²×D₄	1	6	yes	—
230	C₂²×C₉	C₂×#41	1	4	yes	complemented
231	C₂²×C₉	C₂⁵	1	1	yes	characteristic
232	C₄×C₉	—	2	2	no	—
233	C₄×C₉	—	2	6	no	—
234	C₄×C₉	—	2	3	no	—
235	C₄×C₉	—	2	1	no	—
236	C₄×C₉	—	2	3	no	—
237	C₄×C₉	C₂²×D₄	1	2	yes	—
238	C₄×C₉	C₂²×D₄	1	6	yes	—
239	C₄×C₉	C₂×#41	1	2	yes	complemented
240	C₂×#41	—	2	16	no	—
241	C₂×#41	C₂²×C₉	1	1	yes	characteristic
242	C₂×#41	C₂²×C₉	1	6	yes	complemented
243	C₂×#41	C₂²×C₉	1	6	yes	complemented
244	C₂×#41	C₂²×C₉	1	2	yes	complemented
245	C₂²×Q₈	C₂²×C₉	1	2	yes	complemented
246	C₂²×D₄	C₂²×C₉	1	3	yes	—
247	C₂²×D₄	C₂²×C₉	1	6	yes	complemented
248	C₂³×C₄	C₂²×C₉	1	6	yes	complemented
249	C₄⋊Q₈	C₂²×C₉	1	3	yes	complemented
250	#127	C₂²×C₉	1	3	yes	complemented
251	#124	C₂²×C₉	1	6	yes	complemented
252	#123	C₂²×C₉	1	12	yes	complemented
253	C₂²⋊Q₈	C₂²×C₉	1	6	yes	complemented
254	C₂²⋊Q₈	C₂²×C₉	1	6	yes	complemented
255	#121	C₂²×C₉	1	6	yes	complemented
256	#121	C₂²×C₉	1	6	yes	complemented
257	#121	C₂²×C₉	1	6	yes	complemented
258	#121	C₂²×C₉	1	6	yes	complemented
259	#120	C₂²×C₉	1	12	yes	complemented
260	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
261	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
262	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
263	C₄×D₄	C₂²×C₉	1	3	yes	—
264	C₄×D₄	C₂²×C₉	1	6	yes	complemented
265	C₄×D₄	C₂²×C₉	1	3	yes	complemented
266	C₄×D₄	C₂²×C₉	1	6	yes	complemented
267	C₄×D₄	C₂²×C₉	1	3	yes	complemented
268	C₄×D₄	C₂²×C₉	1	3	yes	complemented
269	C₄×D₄	C₂²×C₉	1	3	yes	complemented
270	C₄×D₄	C₂²×C₉	1	6	yes	complemented
271	#117	C₂²×C₉	1	3	yes	complemented
272	C₂×C₄⋊C₄	C₂²×C₉	1	3	yes	complemented
273	C₂×C₂²⋊C₄	C₂²×C₉	1	6	yes	complemented
274	C₂×C₄²	C₂²×C₉	1	3	yes	complemented
275	C₂³×C₃	—	2	12	no	—
276	C₂³×C₃	—	2	12	no	—
277	C₂³×C₃	—	4	6	no	—
278	C₂³×C₃	C₂⁴×C₃	1	6	yes	—
279	C₂³×C₃	C₂⁴×C₃	1	3	yes	—
280	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
281	C₃×Q₈	—	2	12	no	—
282	C₃×Q₈	C₂×C₃×D₄	1	4	yes	—
283	C₃×D₄	—	2	24	no	—
284	C₃×D₄	—	2	12	no	—
285	C₃×D₄	—	2	12	no	—
286	C₃×D₄	—	2	6	no	—
287	C₃×D₄	—	4	6	no	—
288	C₃×D₄	C₂×C₃×D₄	1	12	yes	—
289	C₃×D₄	C₃×#41	1	4	yes	—
290	C₂×C₃×C₄	—	2	12	no	—
291	C₂×C₃×C₄	—	2	4	no	—
292	C₂×C₃×C₄	—	2	12	no	—
293	C₂×C₃×C₄	—	2	12	no	—
294	C₂×C₃×C₄	—	2	12	no	—
295	C₂×C₃×C₄	—	2	6	no	—
296	C₂×C₃×C₄	—	4	3	no	—
297	C₂×C₃×C₄	C₂×C₃×D₄	1	12	yes	—
298	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
299	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
300	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
301	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
302	C₂×C₃×C₄	C₂⁴×C₃	1	6	yes	—
303	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
304	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
305	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
306	C₂×C₉	—	2	4	no	—
307	C₂×C₉	—	2	6	no	—
308	C₂×C₉	—	4	6	no	—
309	C₂×C₉	C₂³×D₄	1	1	yes	characteristic
310	C₂×C₉	C₂²×#41	1	1	yes	characteristic
311	C₂×C₉	#585	1	1	yes	characteristic
312	C₂⁴	C₂³×C₉	1	6	yes	—
313	#41	—	2	8	no	—
314	#41	—	2	24	no	—
315	#41	—	2	24	no	—
316	#41	D₄×C₉	1	8	yes	direct product factor
317	C₂×Q₈	—	2	8	no	—
318	C₂×Q₈	C₂³×C₉	1	6	yes	—
319	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
320	C₂×D₄	—	2	24	no	—
321	C₂×D₄	—	2	12	no	—
322	C₂×D₄	C₂³×C₉	1	6	yes	—
323	C₂×D₄	C₂³×C₉	1	3	yes	—
324	C₂×D₄	C₂³×C₉	1	12	yes	—
325	C₂×D₄	C₂³×C₉	1	6	yes	—
326	C₂×D₄	C₂³×C₉	1	6	yes	—
327	C₂×D₄	C₂³×C₉	1	3	yes	—
328	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
329	C₂²×C₄	—	2	24	no	—
330	C₂²×C₄	C₂³×C₉	1	3	yes	—
331	C₂²×C₄	C₂³×C₉	1	6	yes	—
332	C₂²×C₄	C₂³×C₉	1	2	yes	—
333	C₂²×C₄	C₂³×C₉	1	6	yes	—
334	C₂²×C₄	C₂³×C₉	1	6	yes	—
335	C₂²×C₄	C₂³×C₉	1	6	yes	—
336	C₂²×C₄	C₂³×C₉	1	3	yes	—
337	C₂²×C₄	C₂³×C₉	1	3	yes	—
338	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
339	C₄⋊C₄	C₂³×C₉	1	3	yes	—
340	C₄⋊C₄	C₂³×C₉	1	6	yes	—
341	C₄⋊C₄	C₂³×C₉	1	3	yes	—
342	C₄⋊C₄	C₂³×C₉	1	3	yes	—
343	C₄⋊C₄	C₂³×C₉	1	6	yes	—
344	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
345	C₂²⋊C₄	C₂³×C₉	1	6	yes	—
346	C₂²⋊C₄	C₂³×C₉	1	6	yes	—
347	C₂²⋊C₄	C₂³×C₉	1	6	yes	—
348	C₂²⋊C₄	C₂³×C₉	1	6	yes	—
349	C₂²⋊C₄	C₂³×C₉	1	12	yes	—
350	C₄²	C₂³×C₉	1	1	yes	characteristic
351	C₄²	C₂³×C₉	1	3	yes	—
352	C₄²	C₂³×C₉	1	3	yes	—
353	C₄²	C₂³×C₉	1	3	yes	—
354	C₂²×C₃	—	2	2	no	—
355	C₂²×C₃	—	2	3	no	—
356	C₂²×C₃	—	2	3	no	—
357	C₂²×C₃	—	2	2	no	—
358	C₂²×C₃	—	2	6	no	—
359	C₂²×C₃	—	2	6	no	—
360	C₂²×C₃	—	2	6	no	—
361	C₂²×C₃	—	4	24	no	—
362	C₂²×C₃	C₂²×C₃×D₄	1	6	yes	—
363	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
364	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
365	C₃×C₄	—	2	2	no	—
366	C₃×C₄	—	2	6	no	—
367	C₃×C₄	—	2	3	no	—
368	C₃×C₄	—	2	1	no	—
369	C₃×C₄	—	2	3	no	—
370	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
371	C₃×C₄	C₂²×C₃×D₄	1	6	yes	—
372	C₃×C₄	C₂×C₃×#41	1	2	yes	—
373	C₉	D₄×#41	1	1	yes	characteristic, direct product factor, Sylow
374	C₂³	—	2	12	no	—
375	C₂³	—	2	12	no	—
376	C₂³	—	4	6	no	—
377	C₂³	C₂⁴×C₉	1	6	yes	—
378	C₂³	C₂⁴×C₉	1	3	yes	—
379	C₂³	C₂⁴×C₉	1	2	yes	—
380	Q₈	—	2	12	no	—
381	Q₈	C₂×D₄×C₉	1	4	yes	complemented
382	D₄	—	2	24	no	—
383	D₄	—	2	12	no	—
384	D₄	—	2	12	no	—
385	D₄	—	2	6	no	—
386	D₄	—	4	6	no	—
387	D₄	C₂×D₄×C₉	1	12	yes	complemented
388	D₄	C₉×#41	1	4	yes	direct product factor
389	C₂×C₄	—	2	12	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	12	no	—
392	C₂×C₄	—	2	12	no	—
393	C₂×C₄	—	2	12	no	—
394	C₂×C₄	—	2	6	no	—
395	C₂×C₄	—	4	3	no	—
396	C₂×C₄	C₂×D₄×C₉	1	12	yes	complemented
397	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
398	C₂×C₄	C₂⁴×C₉	1	3	yes	—
399	C₂×C₄	C₂⁴×C₉	1	3	yes	—
400	C₂×C₄	C₂⁴×C₉	1	2	yes	—
401	C₂×C₄	C₂⁴×C₉	1	6	yes	—
402	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
403	C₂×C₄	C₂⁴×C₉	1	3	yes	—
404	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
405	C₂×C₃	—	2	4	no	—
406	C₂×C₃	—	2	6	no	—
407	C₂×C₃	—	4	6	no	—
408	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
409	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
410	C₂×C₃	C₃×#585	1	1	yes	characteristic
411	C₂²	—	2	2	no	—
412	C₂²	—	2	3	no	—
413	C₂²	—	2	3	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	2	6	no	—
416	C₂²	—	2	6	no	—
417	C₂²	—	2	6	no	—
418	C₂²	—	4	24	no	—
419	C₂²	C₂²×D₄×C₉	1	6	yes	—
420	C₂²	C₂×C₉×#41	1	4	yes	complemented
421	C₂²	C₂⁵×C₉	1	1	yes	characteristic
422	C₄	—	2	2	no	—
423	C₄	—	2	6	no	—
424	C₄	—	2	3	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	3	no	—
427	C₄	C₂²×D₄×C₉	1	2	yes	—
428	C₄	C₂²×D₄×C₉	1	6	yes	—
429	C₄	C₂×C₉×#41	1	2	yes	complemented
430	C₃	C₃×D₄×#41	1	1	yes	characteristic
431	C₂	—	2	4	no	—
432	C₂	—	2	6	no	—
433	C₂	—	4	6	no	—
434	C₂	C₂³×D₄×C₉	1	1	yes	characteristic
435	C₂	C₂²×C₉×#41	1	1	yes	characteristic
436	C₂	C₉×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₉	C₂⁴
commutator	C₂²	C₂⁵×C₉
Frattini, socle, cosocle	C₂²×C₃	C₂⁵×C₃
prime radical	C₃×D₄×#41	C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×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. C₉×#550	C₂	semidirect
3. D₄×Q₈×C₉	C₂	semidirect
4. C₉×#548	C₂	semidirect
5. C₉×#547	C₂	semidirect
6. C₉×#546	C₂	semidirect
7. D₄²×C₉	C₂	semidirect
8. C₉×#532	C₂	semidirect
9. C₉×#525	C₂	semidirect
10. C₄×C₉×#41	C₂	semidirect
11. C₂×C₄×D₄×C₉	C₂	semidirect
15. C₂×C₉×#41	C₂²	semidirect
16. C₂×C₉×#41	C₂²	semidirect
17. C₂×C₉×#41	C₂²	semidirect
18. C₂²×Q₈×C₉	C₂²	semidirect
20. C₂²×D₄×C₉	C₂²	semidirect
21. C₂³×C₄×C₉	C₂²	semidirect
22. C₉×C₄⋊Q₈	C₂²	semidirect
23. C₉×#127	C₂²	semidirect
24. C₉×#124	C₂²	semidirect
25. C₉×#123	C₂²	semidirect
26. C₉×C₂²⋊Q₈	C₂²	semidirect
27. C₉×C₂²⋊Q₈	C₂²	semidirect
28. C₉×#121	C₂²	semidirect
29. C₉×#121	C₂²	semidirect
30. C₉×#121	C₂²	semidirect
31. C₉×#121	C₂²	semidirect
32. C₉×#120	C₂²	semidirect
33. C₄×Q₈×C₉	C₂²	semidirect
34. C₄×Q₈×C₉	C₂²	semidirect
37. C₄×D₄×C₉	C₂²	semidirect
38. C₄×D₄×C₉	C₂²	semidirect
39. C₄×D₄×C₉	C₂²	semidirect
40. C₄×D₄×C₉	C₂²	semidirect
41. C₄×D₄×C₉	C₂²	semidirect
42. C₄×D₄×C₉	C₂²	semidirect
43. C₄×D₄×C₉	C₂²	semidirect
44. C₉×#117	C₂²	semidirect
45. C₂×C₉×C₄⋊C₄	C₂²	semidirect
46. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
47. C₂×C₄²×C₉	C₂²	semidirect
63. C₉×#41	D₄	direct (N × H)
101. D₄×#41	C₉	direct (N × H)
144. Q₈×C₉	C₂×D₄	semidirect
150. D₄×C₉	C₂×D₄	semidirect
151. D₄×C₉	#41	direct (N × H)
159. C₂×C₄×C₉	C₂×D₄	semidirect
168. C₂²×#41	C₂×C₉	semidirect
169. #550	C₂×C₉	semidirect
170. D₄×Q₈	C₂×C₉	semidirect
171. #548	C₂×C₉	semidirect
172. #547	C₂×C₉	semidirect
173. #546	C₂×C₉	semidirect
174. D₄²	C₂×C₉	semidirect
175. #532	C₂×C₉	semidirect
176. #525	C₂×C₉	semidirect
177. C₄×#41	C₂×C₉	semidirect
178. C₂×C₄×D₄	C₂×C₉	semidirect
230. C₂²×C₉	C₂×#41	semidirect
239. C₄×C₉	C₂×#41	semidirect
242. C₂×#41	C₂²×C₉	semidirect
243. C₂×#41	C₂²×C₉	semidirect
244. C₂×#41	C₂²×C₉	semidirect
245. C₂²×Q₈	C₂²×C₉	semidirect
247. C₂²×D₄	C₂²×C₉	semidirect
248. C₂³×C₄	C₂²×C₉	semidirect
249. C₄⋊Q₈	C₂²×C₉	semidirect
250. #127	C₂²×C₉	semidirect
251. #124	C₂²×C₉	semidirect
252. #123	C₂²×C₉	semidirect
253. C₂²⋊Q₈	C₂²×C₉	semidirect
254. C₂²⋊Q₈	C₂²×C₉	semidirect
255. #121	C₂²×C₉	semidirect
256. #121	C₂²×C₉	semidirect
257. #121	C₂²×C₉	semidirect
258. #121	C₂²×C₉	semidirect
259. #120	C₂²×C₉	semidirect
260. C₄×Q₈	C₂²×C₉	semidirect
261. C₄×Q₈	C₂²×C₉	semidirect
264. C₄×D₄	C₂²×C₉	semidirect
265. C₄×D₄	C₂²×C₉	semidirect
266. C₄×D₄	C₂²×C₉	semidirect
267. C₄×D₄	C₂²×C₉	semidirect
268. C₄×D₄	C₂²×C₉	semidirect
269. C₄×D₄	C₂²×C₉	semidirect
270. C₄×D₄	C₂²×C₉	semidirect
271. #117	C₂²×C₉	semidirect
272. C₂×C₄⋊C₄	C₂²×C₉	semidirect
273. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
274. C₂×C₄²	C₂²×C₉	semidirect
316. #41	D₄×C₉	direct (N × H)
373. C₉	D₄×#41	direct (N × H)
381. Q₈	C₂×D₄×C₉	semidirect
387. D₄	C₂×D₄×C₉	semidirect
388. D₄	C₉×#41	direct (N × H)
396. C₂×C₄	C₂×D₄×C₉	semidirect
420. C₂²	C₂×C₉×#41	semidirect
429. C₄	C₂×C₉×#41	semidirect

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
C₉×#550	2
D₄×Q₈×C₉	2
C₉×#548	2
C₉×#547	2
C₉×#546	2
D₄²×C₉	2
C₉×#532	2
C₉×#525	2
C₄×C₉×#41	2
C₂×C₄×D₄×C₉	2
C₃×D₄×#41	3

Subgroups — D4×C9×#41 #11768189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₉×#41 #11768189