Subgroups — C₉×#3012 #11767733

Order 1152.

1146 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×#135	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#537	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#452	C₂	1	2	yes	maximal, complemented
6	C₉×#450	C₂	1	2	yes	maximal, complemented
7	C₉×#449	C₂	1	2	yes	maximal, complemented
8	C₉×#447	C₂	1	2	yes	maximal, complemented
9	C₉×#417	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#408	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3012	C₃	1	1	yes	maximal, characteristic
13	C₉×H(5,𝔽₂)	—	2	4	no	—
14	C₉×H(5,𝔽₂)	—	2	4	no	—
15	C₂×C₉×#41	—	2	1	no	—
16	C₂×C₉×#41	C₂²	1	2	yes	—
17	C₂×C₉×#41	C₂²	1	1	yes	characteristic
18	C₂×C₉×#41	C₂²	1	1	yes	characteristic
19	C₂×C₉×#41	C₂²	1	1	yes	characteristic, complemented
20	C₂²×D₄×C₉	—	2	2	no	—
21	C₂²×D₄×C₉	—	2	1	no	—
22	C₂²×D₄×C₉	C₂²	1	2	yes	—
23	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
24	C₉×AGL(1,ℤ/8)	—	2	4	no	—
25	C₉×#135	—	2	4	no	—
26	C₂×C₉×Q₁₆	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₉×SD₁₆	C₂²	1	2	yes	complemented
30	C₂×C₉×D₈	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₉×D₈	C₂²	1	2	yes	complemented
32	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic, complemented
34	C₉×C₂²⋊Q₈	—	2	1	no	—
35	C₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
36	C₉×#121	—	2	1	no	—
37	C₉×#121	—	2	2	no	—
38	C₉×#121	C₂²	1	2	yes	complemented
39	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₉×#103	C₂²	1	2	yes	complemented
41	C₉×#102	C₂²	1	2	yes	complemented
42	C₉×#102	C₂²	1	2	yes	complemented
43	C₉×#102	C₂²	1	2	yes	complemented
44	C₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
45	C₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
46	C₂×C₃×H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic
47	C₂×C₃×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic
48	C₂×C₃×#135	C₂×C₃	1	1	yes	characteristic
49	C₃×#537	C₂×C₃	1	1	yes	characteristic
50	C₃×#452	C₂×C₃	1	2	yes	—
51	C₃×#450	C₂×C₃	1	2	yes	—
52	C₃×#449	C₂×C₃	1	2	yes	—
53	C₃×#447	C₂×C₃	1	2	yes	—
54	C₃×#417	C₂×C₃	1	1	yes	characteristic
55	C₂×C₃×#102	C₂×C₃	1	1	yes	characteristic
56	C₃×#408	C₂×C₃	1	1	yes	characteristic
57	C₂⁴×C₉	—	2	2	no	—
58	C₂⁴×C₉	—	2	1	no	—
59	C₉×#41	—	2	8	no	—
60	C₉×#41	—	2	4	no	—
61	C₉×#41	—	2	4	no	—
62	C₉×#41	—	2	2	no	—
63	C₉×#41	—	2	2	no	—
64	C₉×#41	—	2	2	no	—
65	C₉×#41	—	2	2	no	—
66	C₉×#41	—	2	2	no	—
67	C₉×#41	D₄	1	4	yes	complemented
68	C₂×Q₈×C₉	D₄	1	1	yes	characteristic
69	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
70	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
71	C₂×D₄×C₉	—	2	16	no	—
72	C₂×D₄×C₉	—	2	8	no	—
73	C₂×D₄×C₉	—	2	2	no	—
74	C₂×D₄×C₉	—	2	1	no	—
75	C₂×D₄×C₉	—	2	4	no	—
76	C₂×D₄×C₉	—	2	4	no	—
77	C₂×D₄×C₉	—	2	1	no	—
78	C₂×D₄×C₉	—	2	2	no	—
79	C₂×D₄×C₉	—	2	2	no	—
80	C₂×D₄×C₉	—	2	1	no	—
81	C₂×D₄×C₉	—	2	2	no	—
82	C₂×D₄×C₉	D₄	1	2	yes	—
83	C₂×D₄×C₉	D₄	1	1	yes	characteristic
84	C₂×D₄×C₉	D₄	1	4	yes	complemented
85	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
87	C₂×D₄×C₉	C₂³	1	2	yes	—
88	C₂²×C₄×C₉	—	2	2	no	—
89	C₂²×C₄×C₉	—	2	1	no	—
90	C₂²×C₄×C₉	—	2	1	no	—
91	C₂²×C₄×C₉	—	2	1	no	—
92	C₂²×C₄×C₉	C₂³	1	2	yes	—
93	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
94	C₉×Q₁₆	—	2	2	no	—
95	C₉×SD₁₆	—	2	2	no	—
96	C₉×SD₁₆	—	2	2	no	—
97	C₉×SD₁₆	—	2	4	no	—
98	C₉×D₈	—	2	2	no	—
99	C₉×D₈	—	2	4	no	—
100	C₉×M₁₆	—	2	2	no	—
101	C₂×C₈×C₉	—	2	2	no	—
102	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
103	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
104	C₂×C₈×C₉	C₂³	1	2	yes	—
105	C₉×C₄⋊C₄	—	2	1	no	—
106	C₉×C₄⋊C₄	—	2	2	no	—
107	C₉×C₄⋊C₄	C₂³	1	2	yes	—
108	C₉×C₂²⋊C₄	—	2	2	no	—
109	C₉×C₂²⋊C₄	—	2	2	no	—
110	#3012	C₉	1	1	yes	characteristic, direct product factor, Sylow
111	C₃×H(5,𝔽₂)	—	2	4	no	—
112	C₃×H(5,𝔽₂)	—	2	4	no	—
113	C₂×C₃×#41	—	2	1	no	—
114	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
115	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
118	C₂²×C₃×D₄	—	2	2	no	—
119	C₂²×C₃×D₄	—	2	1	no	—
120	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
121	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
122	C₃×AGL(1,ℤ/8)	—	2	4	no	—
123	C₃×#135	—	2	4	no	—
124	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
125	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
126	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
128	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₃×D₈	C₂²×C₃	1	2	yes	—
130	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
131	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
132	C₃×C₂²⋊Q₈	—	2	1	no	—
133	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
134	C₃×#121	—	2	1	no	—
135	C₃×#121	—	2	2	no	—
136	C₃×#121	C₂²×C₃	1	2	yes	—
137	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
138	C₃×#103	C₂²×C₃	1	2	yes	—
139	C₃×#102	C₂²×C₃	1	2	yes	—
140	C₃×#102	C₂²×C₃	1	2	yes	—
141	C₃×#102	C₂²×C₃	1	2	yes	—
142	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
143	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
144	C₂³×C₉	—	2	8	no	—
145	C₂³×C₉	—	2	2	no	—
146	C₂³×C₉	—	2	1	no	—
147	C₂³×C₉	—	2	4	no	—
148	C₂³×C₉	—	2	1	no	—
149	C₂³×C₉	—	8	1	no	—
150	C₂³×C₉	—	8	1	no	—
151	C₂³×C₉	—	8	2	no	—
152	C₂³×C₉	—	8	2	no	—
153	C₂³×C₉	C₂×D₄	1	2	yes	—
154	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
155	Q₈×C₉	—	2	2	no	—
156	Q₈×C₉	—	2	1	no	—
157	Q₈×C₉	—	2	1	no	—
158	Q₈×C₉	—	2	1	no	—
159	Q₈×C₉	C₂×D₄	1	2	yes	—
160	D₄×C₉	—	2	8	no	—
161	D₄×C₉	—	2	8	no	—
162	D₄×C₉	—	2	4	no	—
163	D₄×C₉	—	2	4	no	—
164	D₄×C₉	—	2	2	no	—
165	D₄×C₉	—	2	4	no	—
166	D₄×C₉	—	2	2	no	—
167	D₄×C₉	—	2	1	no	—
168	D₄×C₉	—	2	1	no	—
169	D₄×C₉	—	2	1	no	—
170	D₄×C₉	—	4	2	no	—
171	D₄×C₉	—	8	2	no	—
172	D₄×C₉	C₂×D₄	1	2	yes	—
173	D₄×C₉	C₂×D₄	1	4	yes	—
174	C₂×C₄×C₉	—	2	8	no	—
175	C₂×C₄×C₉	—	2	1	no	—
176	C₂×C₄×C₉	—	2	4	no	—
177	C₂×C₄×C₉	—	2	2	no	—
178	C₂×C₄×C₉	—	2	2	no	—
179	C₂×C₄×C₉	—	2	2	no	—
180	C₂×C₄×C₉	—	2	1	no	—
181	C₂×C₄×C₉	—	4	2	no	—
182	C₂×C₄×C₉	—	8	1	no	—
183	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
184	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
185	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
186	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
187	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
188	C₈×C₉	—	2	1	no	—
189	C₈×C₉	—	2	1	no	—
190	C₈×C₉	—	2	2	no	—
191	C₂×H(5,𝔽₂)	C₂×C₉	1	1	yes	characteristic, complemented
192	C₂×AGL(1,ℤ/8)	C₂×C₉	1	1	yes	characteristic, complemented
193	C₂×#135	C₂×C₉	1	1	yes	characteristic, complemented
194	#537	C₂×C₉	1	1	yes	characteristic, complemented
195	#452	C₂×C₉	1	2	yes	complemented
196	#450	C₂×C₉	1	2	yes	complemented
197	#449	C₂×C₉	1	2	yes	complemented
198	#447	C₂×C₉	1	2	yes	complemented
199	#417	C₂×C₉	1	1	yes	characteristic, complemented
200	C₂×#102	C₂×C₉	1	1	yes	characteristic, complemented
201	#408	C₂×C₉	1	1	yes	characteristic, complemented
202	C₂⁴×C₃	—	2	2	no	—
203	C₂⁴×C₃	—	2	1	no	—
204	C₃×#41	—	2	8	no	—
205	C₃×#41	—	2	4	no	—
206	C₃×#41	—	2	4	no	—
207	C₃×#41	—	2	2	no	—
208	C₃×#41	—	2	2	no	—
209	C₃×#41	—	2	2	no	—
210	C₃×#41	—	2	2	no	—
211	C₃×#41	—	2	2	no	—
212	C₃×#41	C₃×D₄	1	4	yes	—
213	C₂×C₃×Q₈	C₃×D₄	1	1	yes	characteristic
214	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
215	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
216	C₂×C₃×D₄	—	2	16	no	—
217	C₂×C₃×D₄	—	2	8	no	—
218	C₂×C₃×D₄	—	2	2	no	—
219	C₂×C₃×D₄	—	2	1	no	—
220	C₂×C₃×D₄	—	2	4	no	—
221	C₂×C₃×D₄	—	2	4	no	—
222	C₂×C₃×D₄	—	2	1	no	—
223	C₂×C₃×D₄	—	2	2	no	—
224	C₂×C₃×D₄	—	2	2	no	—
225	C₂×C₃×D₄	—	2	1	no	—
226	C₂×C₃×D₄	—	2	2	no	—
227	C₂×C₃×D₄	C₃×D₄	1	2	yes	—
228	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
229	C₂×C₃×D₄	C₃×D₄	1	4	yes	—
230	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
231	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
232	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
233	C₂²×C₃×C₄	—	2	2	no	—
234	C₂²×C₃×C₄	—	2	1	no	—
235	C₂²×C₃×C₄	—	2	1	no	—
236	C₂²×C₃×C₄	—	2	1	no	—
237	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
238	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
239	C₃×Q₁₆	—	2	2	no	—
240	C₃×SD₁₆	—	2	2	no	—
241	C₃×SD₁₆	—	2	2	no	—
242	C₃×SD₁₆	—	2	4	no	—
243	C₃×D₈	—	2	2	no	—
244	C₃×D₈	—	2	4	no	—
245	C₃×M₁₆	—	2	2	no	—
246	C₂×C₃×C₈	—	2	2	no	—
247	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
248	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
249	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
250	C₃×C₄⋊C₄	—	2	1	no	—
251	C₃×C₄⋊C₄	—	2	2	no	—
252	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
253	C₃×C₂²⋊C₄	—	2	2	no	—
254	C₃×C₂²⋊C₄	—	2	2	no	—
255	C₂²×C₉	—	2	1	no	—
256	C₂²×C₉	—	2	1	no	—
257	C₂²×C₉	—	2	2	no	—
258	C₂²×C₉	—	2	4	no	—
259	C₂²×C₉	—	2	2	no	—
260	C₂²×C₉	—	2	2	no	—
261	C₂²×C₉	—	2	2	no	—
262	C₂²×C₉	—	4	2	no	—
263	C₂²×C₉	—	4	1	no	—
264	C₂²×C₉	—	4	2	no	—
265	C₂²×C₉	—	4	1	no	—
266	C₂²×C₉	—	4	1	no	—
267	C₂²×C₉	—	4	1	no	—
268	C₂²×C₉	—	4	1	no	—
269	C₂²×C₉	—	8	4	no	—
270	C₂²×C₉	—	8	8	no	—
271	C₂²×C₉	#120	1	2	yes	—
272	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
273	C₄×C₉	—	2	2	no	—
274	C₄×C₉	—	2	2	no	—
275	C₄×C₉	—	4	1	no	—
276	C₄×C₉	—	4	2	no	—
277	C₄×C₉	#120	1	2	yes	—
278	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
279	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
280	H(5,𝔽₂)	—	2	4	no	—
281	H(5,𝔽₂)	—	2	4	no	—
282	C₂×#41	—	2	1	no	—
283	C₂×#41	C₂²×C₉	1	2	yes	—
284	C₂×#41	C₂²×C₉	1	1	yes	characteristic
285	C₂×#41	C₂²×C₉	1	1	yes	characteristic
286	C₂×#41	C₂²×C₉	1	1	yes	characteristic, complemented
287	C₂²×D₄	—	2	2	no	—
288	C₂²×D₄	—	2	1	no	—
289	C₂²×D₄	C₂²×C₉	1	2	yes	—
290	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
291	AGL(1,ℤ/8)	—	2	4	no	—
292	#135	—	2	4	no	—
293	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
294	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
295	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
296	C₂×SD₁₆	C₂²×C₉	1	2	yes	complemented
297	C₂×D₈	C₂²×C₉	1	1	yes	characteristic, complemented
298	C₂×D₈	C₂²×C₉	1	2	yes	complemented
299	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
300	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic, complemented
301	C₂²⋊Q₈	—	2	1	no	—
302	C₂²⋊Q₈	C₂²×C₉	1	2	yes	complemented
303	#121	—	2	1	no	—
304	#121	—	2	2	no	—
305	#121	C₂²×C₉	1	2	yes	complemented
306	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
307	#103	C₂²×C₉	1	2	yes	complemented
308	#102	C₂²×C₉	1	2	yes	complemented
309	#102	C₂²×C₉	1	2	yes	complemented
310	#102	C₂²×C₉	1	2	yes	complemented
311	C₂²⋊C₈	C₂²×C₉	1	2	yes	complemented
312	C₂²⋊C₈	C₂²×C₉	1	2	yes	complemented
313	C₂³×C₃	—	2	8	no	—
314	C₂³×C₃	—	2	2	no	—
315	C₂³×C₃	—	2	1	no	—
316	C₂³×C₃	—	2	4	no	—
317	C₂³×C₃	—	2	1	no	—
318	C₂³×C₃	—	8	1	no	—
319	C₂³×C₃	—	8	1	no	—
320	C₂³×C₃	—	8	2	no	—
321	C₂³×C₃	—	8	2	no	—
322	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
323	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
324	C₃×Q₈	—	2	2	no	—
325	C₃×Q₈	—	2	1	no	—
326	C₃×Q₈	—	2	1	no	—
327	C₃×Q₈	—	2	1	no	—
328	C₃×Q₈	C₂×C₃×D₄	1	2	yes	—
329	C₃×D₄	—	2	8	no	—
330	C₃×D₄	—	2	8	no	—
331	C₃×D₄	—	2	4	no	—
332	C₃×D₄	—	2	4	no	—
333	C₃×D₄	—	2	2	no	—
334	C₃×D₄	—	2	4	no	—
335	C₃×D₄	—	2	2	no	—
336	C₃×D₄	—	2	1	no	—
337	C₃×D₄	—	2	1	no	—
338	C₃×D₄	—	2	1	no	—
339	C₃×D₄	—	4	2	no	—
340	C₃×D₄	—	8	2	no	—
341	C₃×D₄	C₂×C₃×D₄	1	2	yes	—
342	C₃×D₄	C₂×C₃×D₄	1	4	yes	—
343	C₂×C₃×C₄	—	2	8	no	—
344	C₂×C₃×C₄	—	2	1	no	—
345	C₂×C₃×C₄	—	2	4	no	—
346	C₂×C₃×C₄	—	2	2	no	—
347	C₂×C₃×C₄	—	2	2	no	—
348	C₂×C₃×C₄	—	2	2	no	—
349	C₂×C₃×C₄	—	2	1	no	—
350	C₂×C₃×C₄	—	4	2	no	—
351	C₂×C₃×C₄	—	8	1	no	—
352	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
353	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
354	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
355	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
356	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
357	C₃×C₈	—	2	1	no	—
358	C₃×C₈	—	2	1	no	—
359	C₃×C₈	—	2	2	no	—
360	C₂×C₉	—	2	2	no	—
361	C₂×C₉	—	4	2	no	—
362	C₂×C₉	—	4	4	no	—
363	C₂×C₉	—	4	2	no	—
364	C₂×C₉	—	8	1	no	—
365	C₂×C₉	C₂×#120	1	1	yes	characteristic
366	C₂×C₉	#576	1	1	yes	characteristic
367	C₂×C₉	#577	1	1	yes	characteristic
368	C₂⁴	—	2	2	no	—
369	C₂⁴	—	2	1	no	—
370	#41	—	2	8	no	—
371	#41	—	2	4	no	—
372	#41	—	2	4	no	—
373	#41	—	2	2	no	—
374	#41	—	2	2	no	—
375	#41	—	2	2	no	—
376	#41	—	2	2	no	—
377	#41	—	2	2	no	—
378	#41	D₄×C₉	1	4	yes	complemented
379	C₂×Q₈	D₄×C₉	1	1	yes	characteristic
380	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
381	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
382	C₂×D₄	—	2	16	no	—
383	C₂×D₄	—	2	8	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	2	4	no	—
387	C₂×D₄	—	2	4	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	D₄×C₉	1	2	yes	—
394	C₂×D₄	D₄×C₉	1	1	yes	characteristic
395	C₂×D₄	D₄×C₉	1	4	yes	complemented
396	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
397	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
398	C₂×D₄	C₂³×C₉	1	2	yes	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	C₂³×C₉	1	2	yes	—
404	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
405	Q₁₆	—	2	2	no	—
406	SD₁₆	—	2	2	no	—
407	SD₁₆	—	2	2	no	—
408	SD₁₆	—	2	4	no	—
409	D₈	—	2	2	no	—
410	D₈	—	2	4	no	—
411	M₁₆	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
414	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
415	C₂×C₈	C₂³×C₉	1	2	yes	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	C₂³×C₉	1	2	yes	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²×C₃	—	2	1	no	—
422	C₂²×C₃	—	2	1	no	—
423	C₂²×C₃	—	2	2	no	—
424	C₂²×C₃	—	2	2	no	—
425	C₂²×C₃	—	2	2	no	—
426	C₂²×C₃	—	2	4	no	—
427	C₂²×C₃	—	2	2	no	—
428	C₂²×C₃	—	4	2	no	—
429	C₂²×C₃	—	4	1	no	—
430	C₂²×C₃	—	4	2	no	—
431	C₂²×C₃	—	4	1	no	—
432	C₂²×C₃	—	4	1	no	—
433	C₂²×C₃	—	4	1	no	—
434	C₂²×C₃	—	4	1	no	—
435	C₂²×C₃	—	8	4	no	—
436	C₂²×C₃	—	8	8	no	—
437	C₂²×C₃	C₃×#120	1	2	yes	—
438	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
439	C₃×C₄	—	2	2	no	—
440	C₃×C₄	—	2	2	no	—
441	C₃×C₄	—	4	2	no	—
442	C₃×C₄	—	4	1	no	—
443	C₃×C₄	C₃×#120	1	2	yes	—
444	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
445	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
446	C₉	#3012	1	1	yes	characteristic, direct product factor, Sylow
447	C₂³	—	2	8	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	1	no	—
450	C₂³	—	2	4	no	—
451	C₂³	—	2	1	no	—
452	C₂³	—	8	1	no	—
453	C₂³	—	8	1	no	—
454	C₂³	—	8	2	no	—
455	C₂³	—	8	2	no	—
456	C₂³	C₂×D₄×C₉	1	2	yes	—
457	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
458	Q₈	—	2	2	no	—
459	Q₈	—	2	1	no	—
460	Q₈	—	2	1	no	—
461	Q₈	—	2	1	no	—
462	Q₈	C₂×D₄×C₉	1	2	yes	—
463	D₄	—	2	8	no	—
464	D₄	—	2	8	no	—
465	D₄	—	2	4	no	—
466	D₄	—	2	4	no	—
467	D₄	—	2	2	no	—
468	D₄	—	2	4	no	—
469	D₄	—	2	2	no	—
470	D₄	—	2	1	no	—
471	D₄	—	2	1	no	—
472	D₄	—	2	1	no	—
473	D₄	—	4	2	no	—
474	D₄	—	8	2	no	—
475	D₄	C₂×D₄×C₉	1	2	yes	—
476	D₄	C₂×D₄×C₉	1	4	yes	—
477	C₂×C₄	—	2	8	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	8	1	no	—
486	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
487	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
488	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
489	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
490	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
491	C₈	—	2	1	no	—
492	C₈	—	2	1	no	—
493	C₈	—	2	2	no	—
494	C₂×C₃	—	2	2	no	—
495	C₂×C₃	—	4	2	no	—
496	C₂×C₃	—	4	4	no	—
497	C₂×C₃	—	4	2	no	—
498	C₂×C₃	—	8	1	no	—
499	C₂×C₃	C₂×C₃×#120	1	1	yes	characteristic
500	C₂×C₃	C₃×#576	1	1	yes	characteristic
501	C₂×C₃	C₃×#577	1	1	yes	characteristic
502	C₂²	—	2	1	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	4	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	2	2	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	1	no	—
513	C₂²	—	4	1	no	—
514	C₂²	—	4	1	no	—
515	C₂²	—	4	1	no	—
516	C₂²	—	8	4	no	—
517	C₂²	—	8	8	no	—
518	C₂²	C₉×#120	1	2	yes	—
519	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
520	C₄	—	2	2	no	—
521	C₄	—	2	2	no	—
522	C₄	—	4	1	no	—
523	C₄	—	4	2	no	—
524	C₄	C₉×#120	1	2	yes	—
525	C₄	C₂²×D₄×C₉	1	1	yes	characteristic
526	C₄	C₂²×D₄×C₉	1	1	yes	characteristic
527	C₃	C₃×#3012	1	1	yes	characteristic
528	C₂	—	2	2	no	—
529	C₂	—	4	2	no	—
530	C₂	—	4	4	no	—
531	C₂	—	4	2	no	—
532	C₂	—	8	1	no	—
533	C₂	C₂×C₉×#120	1	1	yes	characteristic
534	C₂	C₉×#576	1	1	yes	characteristic
535	C₂	C₉×#577	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂²×D₄
commutator	C₂×C₄	C₂⁴×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂²×C₃×D₄
prime radical	C₃×#3012	C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₉×#41 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₉×H(5,𝔽₂)	C₂	semidirect
2. C₂×C₉×AGL(1,ℤ/8)	C₂	semidirect
3. C₂×C₉×#135	C₂	semidirect
4. C₉×#537	C₂	semidirect
5. C₉×#452	C₂	semidirect
6. C₉×#450	C₂	semidirect
7. C₉×#449	C₂	semidirect
8. C₉×#447	C₂	semidirect
9. C₉×#417	C₂	semidirect
10. C₂×C₉×#102	C₂	semidirect
11. C₉×#408	C₂	semidirect
19. C₂×C₉×#41	C₂²	semidirect
26. C₂×C₉×Q₁₆	C₂²	semidirect
27. C₂×C₉×SD₁₆	C₂²	semidirect
28. C₂×C₉×SD₁₆	C₂²	semidirect
29. C₂×C₉×SD₁₆	C₂²	semidirect
30. C₂×C₉×D₈	C₂²	semidirect
31. C₂×C₉×D₈	C₂²	semidirect
32. C₂×C₉×M₁₆	C₂²	semidirect
33. C₂²×C₈×C₉	C₂²	semidirect
35. C₉×C₂²⋊Q₈	C₂²	semidirect
38. C₉×#121	C₂²	semidirect
39. C₂×C₉×C₄⋊C₄	C₂²	semidirect
40. C₉×#103	C₂²	semidirect
41. C₉×#102	C₂²	semidirect
42. C₉×#102	C₂²	semidirect
43. C₉×#102	C₂²	semidirect
44. C₉×C₂²⋊C₈	C₂²	semidirect
45. C₉×C₂²⋊C₈	C₂²	semidirect
67. C₉×#41	D₄	semidirect
84. C₂×D₄×C₉	D₄	semidirect
110. #3012	C₉	direct (N × H)
191. C₂×H(5,𝔽₂)	C₂×C₉	semidirect
192. C₂×AGL(1,ℤ/8)	C₂×C₉	semidirect
193. C₂×#135	C₂×C₉	semidirect
194. #537	C₂×C₉	semidirect
195. #452	C₂×C₉	semidirect
196. #450	C₂×C₉	semidirect
197. #449	C₂×C₉	semidirect
198. #447	C₂×C₉	semidirect
199. #417	C₂×C₉	semidirect
200. C₂×#102	C₂×C₉	semidirect
201. #408	C₂×C₉	semidirect
286. C₂×#41	C₂²×C₉	semidirect
293. C₂×Q₁₆	C₂²×C₉	semidirect
294. C₂×SD₁₆	C₂²×C₉	semidirect
295. C₂×SD₁₆	C₂²×C₉	semidirect
296. C₂×SD₁₆	C₂²×C₉	semidirect
297. C₂×D₈	C₂²×C₉	semidirect
298. C₂×D₈	C₂²×C₉	semidirect
299. C₂×M₁₆	C₂²×C₉	semidirect
300. C₂²×C₈	C₂²×C₉	semidirect
302. C₂²⋊Q₈	C₂²×C₉	semidirect
305. #121	C₂²×C₉	semidirect
306. C₂×C₄⋊C₄	C₂²×C₉	semidirect
307. #103	C₂²×C₉	semidirect
308. #102	C₂²×C₉	semidirect
309. #102	C₂²×C₉	semidirect
310. #102	C₂²×C₉	semidirect
311. C₂²⋊C₈	C₂²×C₉	semidirect
312. C₂²⋊C₈	C₂²×C₉	semidirect
378. #41	D₄×C₉	semidirect
395. C₂×D₄	D₄×C₉	semidirect
446. C₉	#3012	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₉×H(5,𝔽₂)	2
C₂×C₉×AGL(1,ℤ/8)	2
C₂×C₉×#135	2
C₉×#537	2
C₉×#452	2
C₉×#450	2
C₉×#449	2
C₉×#447	2
C₉×#417	2
C₂×C₉×#102	2
C₉×#408	2
C₃×#3012	3

Subgroups — C9×#3012 #11767733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3012 #11767733