Subgroups — C₉×#3062 #11767783

Order 1152.

756 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#537	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#535	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#469	C₂	1	2	yes	maximal, complemented
6	C₉×#468	C₂	1	2	yes	maximal, complemented
7	C₉×#466	C₂	1	2	yes	maximal, complemented
8	C₉×#465	C₂	1	2	yes	maximal, complemented
9	C₉×#428	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#416	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3062	C₃	1	1	yes	maximal, characteristic
13	C₂×C₉×#41	C₂²	1	1	yes	characteristic
14	C₂×C₉×#41	C₂²	1	1	yes	characteristic
15	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
16	C₉×AGL(1,ℤ/8)	—	2	4	no	—
17	C₂×C₉×SD₁₆	C₂²	1	2	yes	—
18	C₂×C₉×D₈	C₂²	1	2	yes	—
19	C₉×#131	—	2	4	no	—
20	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₉×M₁₆	C₂²	1	2	yes	complemented
22	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
23	C₂²×C₈×C₉	C₂²	1	2	yes	complemented
24	C₉×#127	—	2	1	no	—
25	C₉×#124	—	2	1	no	—
26	C₉×C₂²⋊Q₈	—	2	1	no	—
27	C₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
28	C₉×#121	—	2	1	no	—
29	C₉×#121	—	2	2	no	—
30	C₉×#121	C₂²	1	2	yes	—
31	C₉×#121	C₂²	1	2	yes	—
32	C₉×#121	C₂²	1	2	yes	complemented
33	C₉×#120	—	2	2	no	—
34	C₉×#117	C₂²	1	1	yes	characteristic
35	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₉×#107	C₂²	1	2	yes	complemented
37	C₉×#106	C₂²	1	2	yes	complemented
38	C₉×#103	C₂²	1	1	yes	characteristic, complemented
39	C₉×#103	C₂²	1	1	yes	characteristic, complemented
40	C₉×#102	C₂²	1	2	yes	—
41	C₉×#102	C₂²	1	2	yes	—
42	C₉×#102	C₂²	1	1	yes	characteristic, complemented
43	C₉×#102	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₃×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic
45	C₂×C₃×#131	C₂×C₃	1	1	yes	characteristic
46	C₃×#537	C₂×C₃	1	1	yes	characteristic
47	C₃×#535	C₂×C₃	1	1	yes	characteristic
48	C₃×#469	C₂×C₃	1	2	yes	—
49	C₃×#468	C₂×C₃	1	2	yes	—
50	C₃×#466	C₂×C₃	1	2	yes	—
51	C₃×#465	C₂×C₃	1	2	yes	—
52	C₃×#428	C₂×C₃	1	1	yes	characteristic
53	C₃×#416	C₂×C₃	1	1	yes	characteristic
54	C₂×C₃×#102	C₂×C₃	1	1	yes	characteristic
55	C₂⁴×C₉	—	2	1	no	—
56	C₉×#41	—	2	2	no	—
57	C₉×#41	—	2	2	no	—
58	C₉×#41	—	2	2	no	—
59	C₉×#41	—	2	2	no	—
60	C₂×Q₈×C₉	D₄	1	1	yes	characteristic
61	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
62	C₂×D₄×C₉	—	2	1	no	—
63	C₂×D₄×C₉	—	2	2	no	—
64	C₂×D₄×C₉	—	2	2	no	—
65	C₂×D₄×C₉	—	2	2	no	—
66	C₂×D₄×C₉	—	2	2	no	—
67	C₂×D₄×C₉	—	2	1	no	—
68	C₂×D₄×C₉	—	2	2	no	—
69	C₂×D₄×C₉	D₄	1	2	yes	—
70	C₂×D₄×C₉	D₄	1	1	yes	characteristic
71	C₂×D₄×C₉	C₂³	1	2	yes	—
72	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₉	—	2	1	no	—
74	C₂²×C₄×C₉	—	2	1	no	—
75	C₂²×C₄×C₉	C₂³	1	2	yes	—
76	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
77	C₉×SD₁₆	—	2	4	no	—
78	C₉×D₈	—	2	4	no	—
79	C₉×M₁₆	—	2	4	no	—
80	C₉×M₁₆	D₄	1	4	yes	complemented
81	C₂×C₈×C₉	—	2	2	no	—
82	C₂×C₈×C₉	—	2	4	no	—
83	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
84	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
85	C₂×C₈×C₉	C₂³	1	2	yes	—
86	C₉×C₄⋊C₄	—	2	1	no	—
87	C₉×C₄⋊C₄	—	2	2	no	—
88	C₉×C₄⋊C₄	C₂³	1	2	yes	—
89	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₉×C₂²⋊C₄	—	2	1	no	—
92	C₉×C₂²⋊C₄	—	2	2	no	—
93	C₉×C₂²⋊C₄	—	2	2	no	—
94	C₉×C₂²⋊C₄	—	2	2	no	—
95	C₉×C₂²⋊C₄	—	2	2	no	—
96	C₄²×C₉	—	2	1	no	—
97	#3062	C₉	1	1	yes	characteristic, direct product factor, Sylow
98	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
100	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
101	C₃×AGL(1,ℤ/8)	—	2	4	no	—
102	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
103	C₂×C₃×D₈	C₂²×C₃	1	2	yes	—
104	C₃×#131	—	2	4	no	—
105	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
107	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
108	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
109	C₃×#127	—	2	1	no	—
110	C₃×#124	—	2	1	no	—
111	C₃×C₂²⋊Q₈	—	2	1	no	—
112	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
113	C₃×#121	—	2	1	no	—
114	C₃×#121	—	2	2	no	—
115	C₃×#121	C₂²×C₃	1	2	yes	—
116	C₃×#121	C₂²×C₃	1	2	yes	—
117	C₃×#121	C₂²×C₃	1	2	yes	—
118	C₃×#120	—	2	2	no	—
119	C₃×#117	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
121	C₃×#107	C₂²×C₃	1	2	yes	—
122	C₃×#106	C₂²×C₃	1	2	yes	—
123	C₃×#103	C₂²×C₃	1	1	yes	characteristic
124	C₃×#103	C₂²×C₃	1	1	yes	characteristic
125	C₃×#102	C₂²×C₃	1	2	yes	—
126	C₃×#102	C₂²×C₃	1	2	yes	—
127	C₃×#102	C₂²×C₃	1	1	yes	characteristic
128	C₃×#102	C₂²×C₃	1	1	yes	characteristic
129	C₂³×C₉	—	2	1	no	—
130	C₂³×C₉	—	2	2	no	—
131	C₂³×C₉	—	4	2	no	—
132	C₂³×C₉	—	8	1	no	—
133	C₂³×C₉	—	8	1	no	—
134	C₂³×C₉	C₂×D₄	1	2	yes	—
135	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
136	Q₈×C₉	—	2	2	no	—
137	Q₈×C₉	—	2	1	no	—
138	Q₈×C₉	—	2	1	no	—
139	D₄×C₉	—	2	4	no	—
140	D₄×C₉	—	2	2	no	—
141	D₄×C₉	—	2	1	no	—
142	D₄×C₉	—	2	2	no	—
143	D₄×C₉	—	2	2	no	—
144	D₄×C₉	—	2	1	no	—
145	D₄×C₉	—	4	2	no	—
146	D₄×C₉	—	4	2	no	—
147	D₄×C₉	—	8	2	no	—
148	D₄×C₉	—	8	2	no	—
149	D₄×C₉	—	8	2	no	—
150	C₂×C₄×C₉	—	2	2	no	—
151	C₂×C₄×C₉	—	2	2	no	—
152	C₂×C₄×C₉	—	2	1	no	—
153	C₂×C₄×C₉	—	2	1	no	—
154	C₂×C₄×C₉	—	2	2	no	—
155	C₂×C₄×C₉	—	2	1	no	—
156	C₂×C₄×C₉	—	4	2	no	—
157	C₂×C₄×C₉	—	8	1	no	—
158	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
159	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
160	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
161	C₂×C₄×C₉	#41	1	2	yes	—
162	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
163	C₈×C₉	—	2	1	no	—
164	C₈×C₉	—	2	1	no	—
165	C₈×C₉	C₂×D₄	1	4	yes	—
166	C₂×AGL(1,ℤ/8)	C₂×C₉	1	1	yes	characteristic, complemented
167	C₂×#131	C₂×C₉	1	1	yes	characteristic, complemented
168	#537	C₂×C₉	1	1	yes	characteristic, complemented
169	#535	C₂×C₉	1	1	yes	characteristic, complemented
170	#469	C₂×C₉	1	2	yes	complemented
171	#468	C₂×C₉	1	2	yes	complemented
172	#466	C₂×C₉	1	2	yes	complemented
173	#465	C₂×C₉	1	2	yes	complemented
174	#428	C₂×C₉	1	1	yes	characteristic, complemented
175	#416	C₂×C₉	1	1	yes	characteristic, complemented
176	C₂×#102	C₂×C₉	1	1	yes	characteristic, complemented
177	C₂⁴×C₃	—	2	1	no	—
178	C₃×#41	—	2	2	no	—
179	C₃×#41	—	2	2	no	—
180	C₃×#41	—	2	2	no	—
181	C₃×#41	—	2	2	no	—
182	C₂×C₃×Q₈	C₃×D₄	1	1	yes	characteristic
183	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
184	C₂×C₃×D₄	—	2	1	no	—
185	C₂×C₃×D₄	—	2	2	no	—
186	C₂×C₃×D₄	—	2	2	no	—
187	C₂×C₃×D₄	—	2	2	no	—
188	C₂×C₃×D₄	—	2	2	no	—
189	C₂×C₃×D₄	—	2	1	no	—
190	C₂×C₃×D₄	—	2	2	no	—
191	C₂×C₃×D₄	C₃×D₄	1	2	yes	—
192	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
193	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
194	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
195	C₂²×C₃×C₄	—	2	1	no	—
196	C₂²×C₃×C₄	—	2	1	no	—
197	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
198	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
199	C₃×SD₁₆	—	2	4	no	—
200	C₃×D₈	—	2	4	no	—
201	C₃×M₁₆	—	2	4	no	—
202	C₃×M₁₆	C₃×D₄	1	4	yes	—
203	C₂×C₃×C₈	—	2	2	no	—
204	C₂×C₃×C₈	—	2	4	no	—
205	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
206	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
207	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
208	C₃×C₄⋊C₄	—	2	1	no	—
209	C₃×C₄⋊C₄	—	2	2	no	—
210	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
211	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
212	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
213	C₃×C₂²⋊C₄	—	2	1	no	—
214	C₃×C₂²⋊C₄	—	2	2	no	—
215	C₃×C₂²⋊C₄	—	2	2	no	—
216	C₃×C₂²⋊C₄	—	2	2	no	—
217	C₃×C₂²⋊C₄	—	2	2	no	—
218	C₃×C₄²	—	2	1	no	—
219	C₂²×C₉	—	2	1	no	—
220	C₂²×C₉	—	2	1	no	—
221	C₂²×C₉	—	2	2	no	—
222	C₂²×C₉	—	2	2	no	—
223	C₂²×C₉	—	2	2	no	—
224	C₂²×C₉	—	4	1	no	—
225	C₂²×C₉	—	4	2	no	—
226	C₂²×C₉	—	4	1	no	—
227	C₂²×C₉	—	4	2	no	—
228	C₂²×C₉	—	4	2	no	—
229	C₂²×C₉	—	4	1	no	—
230	C₂²×C₉	—	8	4	no	—
231	C₂²×C₉	#121	1	2	yes	—
232	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
233	C₄×C₉	—	2	2	no	—
234	C₄×C₉	—	4	1	no	—
235	C₄×C₉	—	4	2	no	—
236	C₄×C₉	—	4	1	no	—
237	C₄×C₉	—	4	1	no	—
238	C₄×C₉	#121	1	2	yes	—
239	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
240	C₄×C₉	C₂×#41	1	1	yes	characteristic
241	C₂×#41	C₂²×C₉	1	1	yes	characteristic
242	C₂×#41	C₂²×C₉	1	1	yes	characteristic
243	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
244	AGL(1,ℤ/8)	—	2	4	no	—
245	C₂×SD₁₆	C₂²×C₉	1	2	yes	—
246	C₂×D₈	C₂²×C₉	1	2	yes	—
247	#131	—	2	4	no	—
248	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
249	C₂×M₁₆	C₂²×C₉	1	2	yes	complemented
250	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
251	C₂²×C₈	C₂²×C₉	1	2	yes	complemented
252	#127	—	2	1	no	—
253	#124	—	2	1	no	—
254	C₂²⋊Q₈	—	2	1	no	—
255	C₂²⋊Q₈	C₂²×C₉	1	2	yes	complemented
256	#121	—	2	1	no	—
257	#121	—	2	2	no	—
258	#121	C₂²×C₉	1	2	yes	—
259	#121	C₂²×C₉	1	2	yes	—
260	#121	C₂²×C₉	1	2	yes	complemented
261	#120	—	2	2	no	—
262	#117	C₂²×C₉	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
264	#107	C₂²×C₉	1	2	yes	complemented
265	#106	C₂²×C₉	1	2	yes	complemented
266	#103	C₂²×C₉	1	1	yes	characteristic, complemented
267	#103	C₂²×C₉	1	1	yes	characteristic, complemented
268	#102	C₂²×C₉	1	2	yes	—
269	#102	C₂²×C₉	1	2	yes	—
270	#102	C₂²×C₉	1	1	yes	characteristic, complemented
271	#102	C₂²×C₉	1	1	yes	characteristic, complemented
272	C₂³×C₃	—	2	1	no	—
273	C₂³×C₃	—	2	2	no	—
274	C₂³×C₃	—	4	2	no	—
275	C₂³×C₃	—	8	1	no	—
276	C₂³×C₃	—	8	1	no	—
277	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
278	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
279	C₃×Q₈	—	2	2	no	—
280	C₃×Q₈	—	2	1	no	—
281	C₃×Q₈	—	2	1	no	—
282	C₃×D₄	—	2	4	no	—
283	C₃×D₄	—	2	2	no	—
284	C₃×D₄	—	2	1	no	—
285	C₃×D₄	—	2	2	no	—
286	C₃×D₄	—	2	2	no	—
287	C₃×D₄	—	2	1	no	—
288	C₃×D₄	—	4	2	no	—
289	C₃×D₄	—	4	2	no	—
290	C₃×D₄	—	8	2	no	—
291	C₃×D₄	—	8	2	no	—
292	C₃×D₄	—	8	2	no	—
293	C₂×C₃×C₄	—	2	2	no	—
294	C₂×C₃×C₄	—	2	2	no	—
295	C₂×C₃×C₄	—	2	1	no	—
296	C₂×C₃×C₄	—	2	1	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	—	2	1	no	—
299	C₂×C₃×C₄	—	4	2	no	—
300	C₂×C₃×C₄	—	8	1	no	—
301	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
302	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
303	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
304	C₂×C₃×C₄	C₃×#41	1	2	yes	—
305	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
306	C₃×C₈	—	2	1	no	—
307	C₃×C₈	—	2	1	no	—
308	C₃×C₈	C₂×C₃×D₄	1	4	yes	—
309	C₂×C₉	—	2	2	no	—
310	C₂×C₉	—	4	2	no	—
311	C₂×C₉	—	8	1	no	—
312	C₂×C₉	—	8	2	no	—
313	C₂×C₉	C₂×#121	1	1	yes	characteristic
314	C₂×C₉	#576	1	1	yes	characteristic
315	C₂×C₉	#577	1	1	yes	characteristic
316	C₂⁴	—	2	1	no	—
317	#41	—	2	2	no	—
318	#41	—	2	2	no	—
319	#41	—	2	2	no	—
320	#41	—	2	2	no	—
321	C₂×Q₈	D₄×C₉	1	1	yes	characteristic
322	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	D₄×C₉	1	2	yes	—
331	C₂×D₄	D₄×C₉	1	1	yes	characteristic
332	C₂×D₄	C₂³×C₉	1	2	yes	—
333	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	C₂³×C₉	1	2	yes	—
337	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
338	SD₁₆	—	2	4	no	—
339	D₈	—	2	4	no	—
340	M₁₆	—	2	4	no	—
341	M₁₆	D₄×C₉	1	4	yes	complemented
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	4	no	—
344	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
345	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
346	C₂×C₈	C₂³×C₉	1	2	yes	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	C₂³×C₉	1	2	yes	—
350	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
351	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
352	C₂²⋊C₄	—	2	1	no	—
353	C₂²⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	2	2	no	—
355	C₂²⋊C₄	—	2	2	no	—
356	C₂²⋊C₄	—	2	2	no	—
357	C₄²	—	2	1	no	—
358	C₂²×C₃	—	2	1	no	—
359	C₂²×C₃	—	2	1	no	—
360	C₂²×C₃	—	2	2	no	—
361	C₂²×C₃	—	2	2	no	—
362	C₂²×C₃	—	2	2	no	—
363	C₂²×C₃	—	4	1	no	—
364	C₂²×C₃	—	4	2	no	—
365	C₂²×C₃	—	4	2	no	—
366	C₂²×C₃	—	4	1	no	—
367	C₂²×C₃	—	4	1	no	—
368	C₂²×C₃	—	4	2	no	—
369	C₂²×C₃	—	8	4	no	—
370	C₂²×C₃	C₃×#121	1	2	yes	—
371	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
372	C₃×C₄	—	2	2	no	—
373	C₃×C₄	—	4	2	no	—
374	C₃×C₄	—	4	1	no	—
375	C₃×C₄	—	4	1	no	—
376	C₃×C₄	—	4	1	no	—
377	C₃×C₄	C₃×#121	1	2	yes	—
378	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
379	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
380	C₉	#3062	1	1	yes	characteristic, direct product factor, Sylow
381	C₂³	—	2	1	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	4	2	no	—
384	C₂³	—	8	1	no	—
385	C₂³	—	8	1	no	—
386	C₂³	C₂×D₄×C₉	1	2	yes	—
387	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
388	Q₈	—	2	2	no	—
389	Q₈	—	2	1	no	—
390	Q₈	—	2	1	no	—
391	D₄	—	2	4	no	—
392	D₄	—	2	2	no	—
393	D₄	—	2	1	no	—
394	D₄	—	2	2	no	—
395	D₄	—	2	2	no	—
396	D₄	—	2	1	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	8	2	no	—
400	D₄	—	8	2	no	—
401	D₄	—	8	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	8	1	no	—
410	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
411	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
412	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
413	C₂×C₄	C₉×#41	1	2	yes	—
414	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
415	C₈	—	2	1	no	—
416	C₈	—	2	1	no	—
417	C₈	C₂×D₄×C₉	1	4	yes	—
418	C₂×C₃	—	2	2	no	—
419	C₂×C₃	—	4	2	no	—
420	C₂×C₃	—	8	2	no	—
421	C₂×C₃	—	8	1	no	—
422	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
423	C₂×C₃	C₃×#576	1	1	yes	characteristic
424	C₂×C₃	C₃×#577	1	1	yes	characteristic
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	8	4	no	—
437	C₂²	C₉×#121	1	2	yes	—
438	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	2	no	—
442	C₄	—	4	1	no	—
443	C₄	—	4	1	no	—
444	C₄	C₉×#121	1	2	yes	—
445	C₄	C₂²×D₄×C₉	1	1	yes	characteristic
446	C₄	C₂×C₉×#41	1	1	yes	characteristic
447	C₃	C₃×#3062	1	1	yes	characteristic
448	C₂	—	2	2	no	—
449	C₂	—	4	2	no	—
450	C₂	—	8	2	no	—
451	C₂	—	8	1	no	—
452	C₂	C₂×C₉×#121	1	1	yes	characteristic
453	C₂	C₉×#576	1	1	yes	characteristic
454	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×#3062	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×AGL(1,ℤ/8)	C₂	semidirect
2. C₂×C₉×#131	C₂	semidirect
3. C₉×#537	C₂	semidirect
4. C₉×#535	C₂	semidirect
5. C₉×#469	C₂	semidirect
6. C₉×#468	C₂	semidirect
7. C₉×#466	C₂	semidirect
8. C₉×#465	C₂	semidirect
9. C₉×#428	C₂	semidirect
10. C₉×#416	C₂	semidirect
11. C₂×C₉×#102	C₂	semidirect
21. C₂×C₉×M₁₆	C₂²	semidirect
23. C₂²×C₈×C₉	C₂²	semidirect
27. C₉×C₂²⋊Q₈	C₂²	semidirect
32. C₉×#121	C₂²	semidirect
36. C₉×#107	C₂²	semidirect
37. C₉×#106	C₂²	semidirect
38. C₉×#103	C₂²	semidirect
39. C₉×#103	C₂²	semidirect
42. C₉×#102	C₂²	semidirect
43. C₉×#102	C₂²	semidirect
80. C₉×M₁₆	D₄	semidirect
97. #3062	C₉	direct (N × H)
166. C₂×AGL(1,ℤ/8)	C₂×C₉	semidirect
167. C₂×#131	C₂×C₉	semidirect
168. #537	C₂×C₉	semidirect
169. #535	C₂×C₉	semidirect
170. #469	C₂×C₉	semidirect
171. #468	C₂×C₉	semidirect
172. #466	C₂×C₉	semidirect
173. #465	C₂×C₉	semidirect
174. #428	C₂×C₉	semidirect
175. #416	C₂×C₉	semidirect
176. C₂×#102	C₂×C₉	semidirect
249. C₂×M₁₆	C₂²×C₉	semidirect
251. C₂²×C₈	C₂²×C₉	semidirect
255. C₂²⋊Q₈	C₂²×C₉	semidirect
260. #121	C₂²×C₉	semidirect
264. #107	C₂²×C₉	semidirect
265. #106	C₂²×C₉	semidirect
266. #103	C₂²×C₉	semidirect
267. #103	C₂²×C₉	semidirect
270. #102	C₂²×C₉	semidirect
271. #102	C₂²×C₉	semidirect
341. M₁₆	D₄×C₉	semidirect
380. C₉	#3062	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×AGL(1,ℤ/8)	2
C₂×C₉×#131	2
C₉×#537	2
C₉×#535	2
C₉×#469	2
C₉×#468	2
C₉×#466	2
C₉×#465	2
C₉×#428	2
C₉×#416	2
C₂×C₉×#102	2
C₃×#3062	3

Subgroups — C9×#3062 #11767783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3062 #11767783