Subgroups — C₉×#3265 #11767986

Order 1152.

819 conjugacy classes of subgroups.

The subgroup lattice has 657 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	C₂²×C₉×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#548	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄²×C₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#496	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#468	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#466	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#463	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#460	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#450	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#449	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#448	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#447	C₂	1	1	yes	maximal, characteristic, complemented
14	C₉×#440	C₂	1	1	yes	maximal, characteristic, complemented
15	C₉×#435	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3265	C₃	1	1	yes	maximal, characteristic
17	C₂×C₉×#41	C₂²	1	1	yes	characteristic, complemented
18	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₄×C₉	—	2	1	no	—
20	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
21	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
22	C₉×AGL(1,ℤ/8)	—	2	4	no	—
23	C₂×C₉×SD₁₆	—	2	4	no	—
24	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic
25	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₉×SD₁₆	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	1	yes	characteristic, complemented
30	C₂×C₉×D₈	C₂²	1	1	yes	characteristic
31	C₂×C₉×D₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₉×D₈	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic, complemented
35	C₉×#127	C₂²	1	1	yes	characteristic
36	C₉×#124	—	2	1	no	—
37	C₉×#124	C₂²	1	1	yes	characteristic, complemented
38	C₉×C₂²⋊Q₈	—	2	1	no	—
39	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₉×#121	—	2	1	no	—
41	C₉×#121	—	2	1	no	—
42	C₉×#121	C₂²	1	1	yes	characteristic
43	C₉×#121	C₂²	1	1	yes	characteristic
44	C₉×#121	C₂²	1	1	yes	characteristic, complemented
45	C₉×#120	—	2	1	no	—
46	C₉×#120	—	2	1	no	—
47	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
48	C₄×D₄×C₉	—	2	1	no	—
49	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
50	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
51	C₉×#107	C₂²	1	1	yes	characteristic, complemented
52	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₉×#103	C₂²	1	1	yes	characteristic, complemented
54	C₉×#103	C₂²	1	1	yes	characteristic, complemented
55	C₉×#102	C₂²	1	1	yes	characteristic
56	C₉×#102	C₂²	1	1	yes	characteristic, complemented
57	C₉×#102	C₂²	1	1	yes	characteristic, complemented
58	C₉×#102	C₂²	1	1	yes	characteristic, complemented
59	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
61	C₉×#97	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₃×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic
63	C₂²×C₃×SD₁₆	C₂×C₃	1	1	yes	characteristic
64	C₃×#548	C₂×C₃	1	1	yes	characteristic
65	C₃×D₄²	C₂×C₃	1	1	yes	characteristic
66	C₃×#496	C₂×C₃	1	1	yes	characteristic
67	C₃×#468	C₂×C₃	1	1	yes	characteristic
68	C₃×#466	C₂×C₃	1	1	yes	characteristic
69	C₃×#463	C₂×C₃	1	1	yes	characteristic
70	C₃×#460	C₂×C₃	1	1	yes	characteristic
71	C₃×#450	C₂×C₃	1	1	yes	characteristic
72	C₃×#449	C₂×C₃	1	1	yes	characteristic
73	C₃×#448	C₂×C₃	1	1	yes	characteristic
74	C₃×#447	C₂×C₃	1	1	yes	characteristic
75	C₃×#440	C₂×C₃	1	1	yes	characteristic
76	C₃×#435	C₂×C₃	1	1	yes	characteristic
77	C₂⁴×C₉	—	2	1	no	—
78	C₂⁴×C₉	—	2	1	no	—
79	C₉×#41	—	2	2	no	—
80	C₉×#41	—	4	1	no	—
81	C₂×Q₈×C₉	—	2	1	no	—
82	C₂×Q₈×C₉	—	2	2	no	—
83	C₂×Q₈×C₉	—	4	1	no	—
84	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
85	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₉	—	2	2	no	—
87	C₂×D₄×C₉	—	2	2	no	—
88	C₂×D₄×C₉	—	2	1	no	—
89	C₂×D₄×C₉	—	2	1	no	—
90	C₂×D₄×C₉	—	2	1	no	—
91	C₂×D₄×C₉	—	2	1	no	—
92	C₂×D₄×C₉	—	2	1	no	—
93	C₂×D₄×C₉	—	2	1	no	—
94	C₂×D₄×C₉	—	2	1	no	—
95	C₂×D₄×C₉	—	2	1	no	—
96	C₂×D₄×C₉	—	4	1	no	—
97	C₂×D₄×C₉	—	4	1	no	—
98	C₂×D₄×C₉	—	4	4	no	—
99	C₂×D₄×C₉	D₄	1	1	yes	characteristic
100	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
101	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
102	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
103	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₉	—	2	1	no	—
105	C₂²×C₄×C₉	—	2	1	no	—
106	C₂²×C₄×C₉	—	2	1	no	—
107	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
108	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
109	C₉×SD₁₆	—	2	2	no	—
110	C₉×SD₁₆	—	2	2	no	—
111	C₉×SD₁₆	—	2	2	no	—
112	C₉×SD₁₆	—	2	2	no	—
113	C₉×SD₁₆	—	4	1	no	—
114	C₉×SD₁₆	D₄	1	4	yes	complemented
115	C₉×D₈	—	2	2	no	—
116	C₉×D₈	—	2	2	no	—
117	C₉×D₈	—	4	1	no	—
118	C₉×M₁₆	—	2	2	no	—
119	C₂×C₈×C₉	—	2	2	no	—
120	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
121	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
122	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
123	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
124	C₉×C₄⋊C₄	—	2	1	no	—
125	C₉×C₄⋊C₄	—	2	1	no	—
126	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
127	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₉×C₂²⋊C₄	—	2	1	no	—
130	C₉×C₂²⋊C₄	—	2	1	no	—
131	C₉×C₂²⋊C₄	—	2	1	no	—
132	C₉×C₂²⋊C₄	—	2	1	no	—
133	C₉×C₂²⋊C₄	—	2	1	no	—
134	C₉×C₂²⋊C₄	—	2	1	no	—
135	C₉×C₂²⋊C₄	—	2	1	no	—
136	C₉×C₂²⋊C₄	D₄	1	1	yes	characteristic
137	C₉×C₂²⋊C₄	D₄	1	1	yes	characteristic
138	C₄²×C₉	—	2	1	no	—
139	C₄²×C₉	C₂³	1	1	yes	characteristic
140	#3265	C₉	1	1	yes	characteristic, direct product factor, Sylow
141	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
142	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
143	C₂²×C₃×D₄	—	2	1	no	—
144	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
145	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
146	C₃×AGL(1,ℤ/8)	—	2	4	no	—
147	C₂×C₃×SD₁₆	—	2	4	no	—
148	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
149	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
150	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
151	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
152	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
153	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
154	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
155	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
156	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
157	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
158	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
159	C₃×#127	C₂²×C₃	1	1	yes	characteristic
160	C₃×#124	—	2	1	no	—
161	C₃×#124	C₂²×C₃	1	1	yes	characteristic
162	C₃×C₂²⋊Q₈	—	2	1	no	—
163	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
164	C₃×#121	—	2	1	no	—
165	C₃×#121	—	2	1	no	—
166	C₃×#121	C₂²×C₃	1	1	yes	characteristic
167	C₃×#121	C₂²×C₃	1	1	yes	characteristic
168	C₃×#121	C₂²×C₃	1	1	yes	characteristic
169	C₃×#120	—	2	1	no	—
170	C₃×#120	—	2	1	no	—
171	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
172	C₃×C₄×D₄	—	2	1	no	—
173	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
174	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
175	C₃×#107	C₂²×C₃	1	1	yes	characteristic
176	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
177	C₃×#103	C₂²×C₃	1	1	yes	characteristic
178	C₃×#103	C₂²×C₃	1	1	yes	characteristic
179	C₃×#102	C₂²×C₃	1	1	yes	characteristic
180	C₃×#102	C₂²×C₃	1	1	yes	characteristic
181	C₃×#102	C₂²×C₃	1	1	yes	characteristic
182	C₃×#102	C₂²×C₃	1	1	yes	characteristic
183	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
184	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
185	C₃×#97	C₂²×C₃	1	1	yes	characteristic
186	C₂³×C₉	—	2	1	no	—
187	C₂³×C₉	—	2	1	no	—
188	C₂³×C₉	—	2	1	no	—
189	C₂³×C₉	—	2	1	no	—
190	C₂³×C₉	—	4	2	no	—
191	C₂³×C₉	—	4	2	no	—
192	C₂³×C₉	—	4	2	no	—
193	C₂³×C₉	—	4	2	no	—
194	C₂³×C₉	—	8	1	no	—
195	C₂³×C₉	—	8	1	no	—
196	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
197	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
198	Q₈×C₉	—	2	1	no	—
199	Q₈×C₉	—	2	1	no	—
200	Q₈×C₉	—	2	1	no	—
201	Q₈×C₉	—	4	2	no	—
202	Q₈×C₉	C₂×D₄	1	2	yes	complemented
203	D₄×C₉	—	2	2	no	—
204	D₄×C₉	—	2	1	no	—
205	D₄×C₉	—	2	1	no	—
206	D₄×C₉	—	2	1	no	—
207	D₄×C₉	—	2	1	no	—
208	D₄×C₉	—	2	1	no	—
209	D₄×C₉	—	2	1	no	—
210	D₄×C₉	—	2	1	no	—
211	D₄×C₉	—	4	2	no	—
212	D₄×C₉	—	4	2	no	—
213	D₄×C₉	—	4	2	no	—
214	D₄×C₉	—	4	2	no	—
215	D₄×C₉	—	4	2	no	—
216	D₄×C₉	—	4	2	no	—
217	D₄×C₉	—	4	2	no	—
218	D₄×C₉	—	8	1	no	—
219	D₄×C₉	C₂×D₄	1	2	yes	—
220	C₂×C₄×C₉	—	2	1	no	—
221	C₂×C₄×C₉	—	2	1	no	—
222	C₂×C₄×C₉	—	2	1	no	—
223	C₂×C₄×C₉	—	2	1	no	—
224	C₂×C₄×C₉	—	2	1	no	—
225	C₂×C₄×C₉	—	2	1	no	—
226	C₂×C₄×C₉	—	2	1	no	—
227	C₂×C₄×C₉	—	2	1	no	—
228	C₂×C₄×C₉	—	4	2	no	—
229	C₂×C₄×C₉	—	4	2	no	—
230	C₂×C₄×C₉	—	4	2	no	—
231	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
232	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
233	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
234	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
235	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
236	C₈×C₉	—	2	1	no	—
237	C₈×C₉	—	2	1	no	—
238	C₈×C₉	—	2	1	no	—
239	C₈×C₉	C₂×D₄	1	2	yes	complemented
240	C₂×AGL(1,ℤ/8)	C₂×C₉	1	1	yes	characteristic, complemented
241	C₂²×SD₁₆	C₂×C₉	1	1	yes	characteristic, complemented
242	#548	C₂×C₉	1	1	yes	characteristic, complemented
243	D₄²	C₂×C₉	1	1	yes	characteristic, complemented
244	#496	C₂×C₉	1	1	yes	characteristic, complemented
245	#468	C₂×C₉	1	1	yes	characteristic, complemented
246	#466	C₂×C₉	1	1	yes	characteristic, complemented
247	#463	C₂×C₉	1	1	yes	characteristic, complemented
248	#460	C₂×C₉	1	1	yes	characteristic, complemented
249	#450	C₂×C₉	1	1	yes	characteristic, complemented
250	#449	C₂×C₉	1	1	yes	characteristic, complemented
251	#448	C₂×C₉	1	1	yes	characteristic, complemented
252	#447	C₂×C₉	1	1	yes	characteristic, complemented
253	#440	C₂×C₉	1	1	yes	characteristic, complemented
254	#435	C₂×C₉	1	1	yes	characteristic, complemented
255	C₂⁴×C₃	—	2	1	no	—
256	C₂⁴×C₃	—	2	1	no	—
257	C₃×#41	—	2	2	no	—
258	C₃×#41	—	4	1	no	—
259	C₂×C₃×Q₈	—	2	1	no	—
260	C₂×C₃×Q₈	—	2	2	no	—
261	C₂×C₃×Q₈	—	4	1	no	—
262	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
263	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
264	C₂×C₃×D₄	—	2	2	no	—
265	C₂×C₃×D₄	—	2	2	no	—
266	C₂×C₃×D₄	—	2	1	no	—
267	C₂×C₃×D₄	—	2	1	no	—
268	C₂×C₃×D₄	—	2	1	no	—
269	C₂×C₃×D₄	—	2	1	no	—
270	C₂×C₃×D₄	—	2	1	no	—
271	C₂×C₃×D₄	—	2	1	no	—
272	C₂×C₃×D₄	—	2	1	no	—
273	C₂×C₃×D₄	—	2	1	no	—
274	C₂×C₃×D₄	—	4	1	no	—
275	C₂×C₃×D₄	—	4	1	no	—
276	C₂×C₃×D₄	—	4	4	no	—
277	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
278	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
279	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
280	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
281	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
282	C₂²×C₃×C₄	—	2	1	no	—
283	C₂²×C₃×C₄	—	2	1	no	—
284	C₂²×C₃×C₄	—	2	1	no	—
285	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
286	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
287	C₃×SD₁₆	—	2	2	no	—
288	C₃×SD₁₆	—	2	2	no	—
289	C₃×SD₁₆	—	2	2	no	—
290	C₃×SD₁₆	—	2	2	no	—
291	C₃×SD₁₆	—	4	1	no	—
292	C₃×SD₁₆	C₃×D₄	1	4	yes	—
293	C₃×D₈	—	2	2	no	—
294	C₃×D₈	—	2	2	no	—
295	C₃×D₈	—	4	1	no	—
296	C₃×M₁₆	—	2	2	no	—
297	C₂×C₃×C₈	—	2	2	no	—
298	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
299	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
300	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
301	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
302	C₃×C₄⋊C₄	—	2	1	no	—
303	C₃×C₄⋊C₄	—	2	1	no	—
304	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
305	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
306	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
307	C₃×C₂²⋊C₄	—	2	1	no	—
308	C₃×C₂²⋊C₄	—	2	1	no	—
309	C₃×C₂²⋊C₄	—	2	1	no	—
310	C₃×C₂²⋊C₄	—	2	1	no	—
311	C₃×C₂²⋊C₄	—	2	1	no	—
312	C₃×C₂²⋊C₄	—	2	1	no	—
313	C₃×C₂²⋊C₄	—	2	1	no	—
314	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
315	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
316	C₃×C₄²	—	2	1	no	—
317	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
318	C₂²×C₉	—	2	1	no	—
319	C₂²×C₉	—	2	1	no	—
320	C₂²×C₉	—	2	1	no	—
321	C₂²×C₉	—	2	2	no	—
322	C₂²×C₉	—	2	1	no	—
323	C₂²×C₉	—	2	1	no	—
324	C₂²×C₉	—	4	1	no	—
325	C₂²×C₉	—	4	1	no	—
326	C₂²×C₉	—	4	1	no	—
327	C₂²×C₉	—	4	1	no	—
328	C₂²×C₉	—	4	1	no	—
329	C₂²×C₉	—	4	1	no	—
330	C₂²×C₉	—	4	1	no	—
331	C₂²×C₉	—	4	1	no	—
332	C₂²×C₉	—	4	1	no	—
333	C₂²×C₉	—	4	1	no	—
334	C₂²×C₉	—	4	1	no	—
335	C₂²×C₉	—	8	4	no	—
336	C₂²×C₉	—	8	4	no	—
337	C₂²×C₉	AGL(1,ℤ/8)	1	2	yes	complemented
338	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
339	C₄×C₉	—	2	1	no	—
340	C₄×C₉	—	2	1	no	—
341	C₄×C₉	—	2	2	no	—
342	C₄×C₉	—	2	1	no	—
343	C₄×C₉	—	2	1	no	—
344	C₄×C₉	—	4	1	no	—
345	C₄×C₉	—	4	1	no	—
346	C₄×C₉	—	4	1	no	—
347	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
348	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
349	C₂×#41	C₂²×C₉	1	1	yes	characteristic, complemented
350	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
351	C₂²×D₄	—	2	1	no	—
352	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
353	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
354	AGL(1,ℤ/8)	—	2	4	no	—
355	C₂×SD₁₆	—	2	4	no	—
356	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
357	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
358	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
359	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
360	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
361	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
362	C₂×D₈	C₂²×C₉	1	1	yes	characteristic
363	C₂×D₈	C₂²×C₉	1	1	yes	characteristic, complemented
364	C₂×D₈	C₂²×C₉	1	1	yes	characteristic, complemented
365	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
366	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic, complemented
367	#127	C₂²×C₉	1	1	yes	characteristic
368	#124	—	2	1	no	—
369	#124	C₂²×C₉	1	1	yes	characteristic, complemented
370	C₂²⋊Q₈	—	2	1	no	—
371	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
372	#121	—	2	1	no	—
373	#121	—	2	1	no	—
374	#121	C₂²×C₉	1	1	yes	characteristic
375	#121	C₂²×C₉	1	1	yes	characteristic
376	#121	C₂²×C₉	1	1	yes	characteristic, complemented
377	#120	—	2	1	no	—
378	#120	—	2	1	no	—
379	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
382	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
383	#107	C₂²×C₉	1	1	yes	characteristic, complemented
384	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic, complemented
385	#103	C₂²×C₉	1	1	yes	characteristic, complemented
386	#103	C₂²×C₉	1	1	yes	characteristic, complemented
387	#102	C₂²×C₉	1	1	yes	characteristic
388	#102	C₂²×C₉	1	1	yes	characteristic, complemented
389	#102	C₂²×C₉	1	1	yes	characteristic, complemented
390	#102	C₂²×C₉	1	1	yes	characteristic, complemented
391	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic, complemented
392	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic, complemented
393	#97	C₂²×C₉	1	1	yes	characteristic, complemented
394	C₂³×C₃	—	2	1	no	—
395	C₂³×C₃	—	2	1	no	—
396	C₂³×C₃	—	2	1	no	—
397	C₂³×C₃	—	2	1	no	—
398	C₂³×C₃	—	4	2	no	—
399	C₂³×C₃	—	4	2	no	—
400	C₂³×C₃	—	4	2	no	—
401	C₂³×C₃	—	4	2	no	—
402	C₂³×C₃	—	8	1	no	—
403	C₂³×C₃	—	8	1	no	—
404	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
405	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
406	C₃×Q₈	—	2	1	no	—
407	C₃×Q₈	—	2	1	no	—
408	C₃×Q₈	—	2	1	no	—
409	C₃×Q₈	—	4	2	no	—
410	C₃×Q₈	C₂×C₃×D₄	1	2	yes	—
411	C₃×D₄	—	2	2	no	—
412	C₃×D₄	—	2	1	no	—
413	C₃×D₄	—	2	1	no	—
414	C₃×D₄	—	2	1	no	—
415	C₃×D₄	—	2	1	no	—
416	C₃×D₄	—	2	1	no	—
417	C₃×D₄	—	2	1	no	—
418	C₃×D₄	—	2	1	no	—
419	C₃×D₄	—	4	2	no	—
420	C₃×D₄	—	4	2	no	—
421	C₃×D₄	—	4	2	no	—
422	C₃×D₄	—	4	2	no	—
423	C₃×D₄	—	4	2	no	—
424	C₃×D₄	—	4	2	no	—
425	C₃×D₄	—	4	2	no	—
426	C₃×D₄	—	8	1	no	—
427	C₃×D₄	C₂×C₃×D₄	1	2	yes	—
428	C₂×C₃×C₄	—	2	1	no	—
429	C₂×C₃×C₄	—	2	1	no	—
430	C₂×C₃×C₄	—	2	1	no	—
431	C₂×C₃×C₄	—	2	1	no	—
432	C₂×C₃×C₄	—	2	1	no	—
433	C₂×C₃×C₄	—	2	1	no	—
434	C₂×C₃×C₄	—	2	1	no	—
435	C₂×C₃×C₄	—	2	1	no	—
436	C₂×C₃×C₄	—	4	2	no	—
437	C₂×C₃×C₄	—	4	2	no	—
438	C₂×C₃×C₄	—	4	2	no	—
439	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
440	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
441	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
442	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
443	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
444	C₃×C₈	—	2	1	no	—
445	C₃×C₈	—	2	1	no	—
446	C₃×C₈	—	2	1	no	—
447	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
448	C₂×C₉	—	2	2	no	—
449	C₂×C₉	—	4	1	no	—
450	C₂×C₉	—	4	2	no	—
451	C₂×C₉	—	8	1	no	—
452	C₂×C₉	—	8	1	no	—
453	C₂×C₉	—	8	1	no	—
454	C₂×C₉	D₄²	1	1	yes	characteristic
455	C₂×C₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
456	C₂×C₉	#577	1	1	yes	characteristic
457	C₂⁴	—	2	1	no	—
458	C₂⁴	—	2	1	no	—
459	#41	—	2	2	no	—
460	#41	—	4	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	2	no	—
463	C₂×Q₈	—	4	1	no	—
464	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
465	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	4	1	no	—
477	C₂×D₄	—	4	1	no	—
478	C₂×D₄	—	4	4	no	—
479	C₂×D₄	D₄×C₉	1	1	yes	characteristic
480	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
481	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
482	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
483	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
488	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
489	SD₁₆	—	2	2	no	—
490	SD₁₆	—	2	2	no	—
491	SD₁₆	—	2	2	no	—
492	SD₁₆	—	2	2	no	—
493	SD₁₆	—	4	1	no	—
494	SD₁₆	D₄×C₉	1	4	yes	complemented
495	D₈	—	2	2	no	—
496	D₈	—	2	2	no	—
497	D₈	—	4	1	no	—
498	M₁₆	—	2	2	no	—
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
501	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
502	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
503	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
507	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
508	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
509	C₂²⋊C₄	—	2	1	no	—
510	C₂²⋊C₄	—	2	1	no	—
511	C₂²⋊C₄	—	2	1	no	—
512	C₂²⋊C₄	—	2	1	no	—
513	C₂²⋊C₄	—	2	1	no	—
514	C₂²⋊C₄	—	2	1	no	—
515	C₂²⋊C₄	—	2	1	no	—
516	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
517	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
518	C₄²	—	2	1	no	—
519	C₄²	C₂³×C₉	1	1	yes	characteristic
520	C₂²×C₃	—	2	1	no	—
521	C₂²×C₃	—	2	1	no	—
522	C₂²×C₃	—	2	1	no	—
523	C₂²×C₃	—	2	1	no	—
524	C₂²×C₃	—	2	1	no	—
525	C₂²×C₃	—	2	2	no	—
526	C₂²×C₃	—	4	1	no	—
527	C₂²×C₃	—	4	1	no	—
528	C₂²×C₃	—	4	1	no	—
529	C₂²×C₃	—	4	1	no	—
530	C₂²×C₃	—	4	1	no	—
531	C₂²×C₃	—	4	1	no	—
532	C₂²×C₃	—	4	1	no	—
533	C₂²×C₃	—	4	1	no	—
534	C₂²×C₃	—	4	1	no	—
535	C₂²×C₃	—	4	1	no	—
536	C₂²×C₃	—	4	1	no	—
537	C₂²×C₃	—	8	4	no	—
538	C₂²×C₃	—	8	4	no	—
539	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	2	yes	—
540	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
541	C₃×C₄	—	2	1	no	—
542	C₃×C₄	—	2	1	no	—
543	C₃×C₄	—	2	1	no	—
544	C₃×C₄	—	2	1	no	—
545	C₃×C₄	—	2	2	no	—
546	C₃×C₄	—	4	1	no	—
547	C₃×C₄	—	4	1	no	—
548	C₃×C₄	—	4	1	no	—
549	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
550	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
551	C₉	#3265	1	1	yes	characteristic, direct product factor, Sylow
552	C₂³	—	2	1	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	2	1	no	—
556	C₂³	—	4	2	no	—
557	C₂³	—	4	2	no	—
558	C₂³	—	4	2	no	—
559	C₂³	—	4	2	no	—
560	C₂³	—	8	1	no	—
561	C₂³	—	8	1	no	—
562	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
563	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
564	Q₈	—	2	1	no	—
565	Q₈	—	2	1	no	—
566	Q₈	—	2	1	no	—
567	Q₈	—	4	2	no	—
568	Q₈	C₂×D₄×C₉	1	2	yes	complemented
569	D₄	—	2	2	no	—
570	D₄	—	2	1	no	—
571	D₄	—	2	1	no	—
572	D₄	—	2	1	no	—
573	D₄	—	2	1	no	—
574	D₄	—	2	1	no	—
575	D₄	—	2	1	no	—
576	D₄	—	2	1	no	—
577	D₄	—	4	2	no	—
578	D₄	—	4	2	no	—
579	D₄	—	4	2	no	—
580	D₄	—	4	2	no	—
581	D₄	—	4	2	no	—
582	D₄	—	4	2	no	—
583	D₄	—	4	2	no	—
584	D₄	—	8	1	no	—
585	D₄	C₂×D₄×C₉	1	2	yes	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
598	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
599	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
600	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
601	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
602	C₈	—	2	1	no	—
603	C₈	—	2	1	no	—
604	C₈	—	2	1	no	—
605	C₈	C₂×D₄×C₉	1	2	yes	complemented
606	C₂×C₃	—	2	2	no	—
607	C₂×C₃	—	4	1	no	—
608	C₂×C₃	—	4	2	no	—
609	C₂×C₃	—	8	1	no	—
610	C₂×C₃	—	8	1	no	—
611	C₂×C₃	—	8	1	no	—
612	C₂×C₃	C₃×D₄²	1	1	yes	characteristic
613	C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
614	C₂×C₃	C₃×#577	1	1	yes	characteristic
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	1	no	—
624	C₂²	—	4	1	no	—
625	C₂²	—	4	1	no	—
626	C₂²	—	4	1	no	—
627	C₂²	—	4	1	no	—
628	C₂²	—	4	1	no	—
629	C₂²	—	4	1	no	—
630	C₂²	—	4	1	no	—
631	C₂²	—	4	1	no	—
632	C₂²	—	8	4	no	—
633	C₂²	—	8	4	no	—
634	C₂²	C₉×AGL(1,ℤ/8)	1	2	yes	complemented
635	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
636	C₄	—	2	1	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	2	no	—
639	C₄	—	2	1	no	—
640	C₄	—	2	1	no	—
641	C₄	—	4	1	no	—
642	C₄	—	4	1	no	—
643	C₄	—	4	1	no	—
644	C₄	C₂²×D₄×C₉	1	1	yes	characteristic
645	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
646	C₃	C₃×#3265	1	1	yes	characteristic
647	C₂	—	2	2	no	—
648	C₂	—	4	1	no	—
649	C₂	—	4	2	no	—
650	C₂	—	8	1	no	—
651	C₂	—	8	1	no	—
652	C₂	—	8	1	no	—
653	C₂	D₄²×C₉	1	1	yes	characteristic
654	C₂	C₂×C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
655	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×#3265	C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₄×D₄×C₉ ◁ 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. C₂²×C₉×SD₁₆	C₂	semidirect
3. C₉×#548	C₂	semidirect
4. D₄²×C₉	C₂	semidirect
5. C₉×#496	C₂	semidirect
6. C₉×#468	C₂	semidirect
7. C₉×#466	C₂	semidirect
8. C₉×#463	C₂	semidirect
9. C₉×#460	C₂	semidirect
10. C₉×#450	C₂	semidirect
11. C₉×#449	C₂	semidirect
12. C₉×#448	C₂	semidirect
13. C₉×#447	C₂	semidirect
14. C₉×#440	C₂	semidirect
15. C₉×#435	C₂	semidirect
17. C₂×C₉×#41	C₂²	semidirect
18. C₂²×Q₈×C₉	C₂²	semidirect
26. C₂×C₉×SD₁₆	C₂²	semidirect
27. C₂×C₉×SD₁₆	C₂²	semidirect
28. C₂×C₉×SD₁₆	C₂²	semidirect
29. C₂×C₉×SD₁₆	C₂²	semidirect
31. C₂×C₉×D₈	C₂²	semidirect
32. C₂×C₉×D₈	C₂²	semidirect
33. C₂×C₉×M₁₆	C₂²	semidirect
34. C₂²×C₈×C₉	C₂²	semidirect
37. C₉×#124	C₂²	semidirect
39. C₉×C₂²⋊Q₈	C₂²	semidirect
44. C₉×#121	C₂²	semidirect
47. C₄×Q₈×C₉	C₂²	semidirect
51. C₉×#107	C₂²	semidirect
52. C₉×C₄⋊C₈	C₂²	semidirect
53. C₉×#103	C₂²	semidirect
54. C₉×#103	C₂²	semidirect
56. C₉×#102	C₂²	semidirect
57. C₉×#102	C₂²	semidirect
58. C₉×#102	C₂²	semidirect
59. C₉×C₂²⋊C₈	C₂²	semidirect
60. C₉×C₂²⋊C₈	C₂²	semidirect
61. C₉×#97	C₂²	semidirect
114. C₉×SD₁₆	D₄	semidirect
140. #3265	C₉	direct (N × H)
202. Q₈×C₉	C₂×D₄	semidirect
239. C₈×C₉	C₂×D₄	semidirect
240. C₂×AGL(1,ℤ/8)	C₂×C₉	semidirect
241. C₂²×SD₁₆	C₂×C₉	semidirect
242. #548	C₂×C₉	semidirect
243. D₄²	C₂×C₉	semidirect
244. #496	C₂×C₉	semidirect
245. #468	C₂×C₉	semidirect
246. #466	C₂×C₉	semidirect
247. #463	C₂×C₉	semidirect
248. #460	C₂×C₉	semidirect
249. #450	C₂×C₉	semidirect
250. #449	C₂×C₉	semidirect
251. #448	C₂×C₉	semidirect
252. #447	C₂×C₉	semidirect
253. #440	C₂×C₉	semidirect
254. #435	C₂×C₉	semidirect
337. C₂²×C₉	AGL(1,ℤ/8)	semidirect
349. C₂×#41	C₂²×C₉	semidirect
350. C₂²×Q₈	C₂²×C₉	semidirect
358. C₂×SD₁₆	C₂²×C₉	semidirect
359. C₂×SD₁₆	C₂²×C₉	semidirect
360. C₂×SD₁₆	C₂²×C₉	semidirect
361. C₂×SD₁₆	C₂²×C₉	semidirect
363. C₂×D₈	C₂²×C₉	semidirect
364. C₂×D₈	C₂²×C₉	semidirect
365. C₂×M₁₆	C₂²×C₉	semidirect
366. C₂²×C₈	C₂²×C₉	semidirect
369. #124	C₂²×C₉	semidirect
371. C₂²⋊Q₈	C₂²×C₉	semidirect
376. #121	C₂²×C₉	semidirect
379. C₄×Q₈	C₂²×C₉	semidirect
383. #107	C₂²×C₉	semidirect
384. C₄⋊C₈	C₂²×C₉	semidirect
385. #103	C₂²×C₉	semidirect
386. #103	C₂²×C₉	semidirect
388. #102	C₂²×C₉	semidirect
389. #102	C₂²×C₉	semidirect
390. #102	C₂²×C₉	semidirect
391. C₂²⋊C₈	C₂²×C₉	semidirect
392. C₂²⋊C₈	C₂²×C₉	semidirect
393. #97	C₂²×C₉	semidirect
494. SD₁₆	D₄×C₉	semidirect
551. C₉	#3265	direct (N × H)
568. Q₈	C₂×D₄×C₉	semidirect
605. C₈	C₂×D₄×C₉	semidirect
634. C₂²	C₉×AGL(1,ℤ/8)	semidirect

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
C₂²×C₉×SD₁₆	2
C₉×#548	2
D₄²×C₉	2
C₉×#496	2
C₉×#468	2
C₉×#466	2
C₉×#463	2
C₉×#460	2
C₉×#450	2
C₉×#449	2
C₉×#448	2
C₉×#447	2
C₉×#440	2
C₉×#435	2
C₃×#3265	3

Subgroups — C9×#3265 #11767986

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3265 #11767986