Subgroups — C₉×#3268 #11767989

Order 1152.

765 conjugacy classes of subgroups.

The subgroup lattice has 645 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×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#550	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#546	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×#464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#459	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#449	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#449	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×#3268	C₃	1	1	yes	maximal, characteristic
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	C₂²	1	1	yes	characteristic
21	C₉×AGL(1,ℤ/8)	—	2	4	no	—
22	C₉×#135	—	2	4	no	—
23	C₂×C₉×Q₁₆	C₂²	1	1	yes	characteristic, complemented
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×D₈	C₂²	1	1	yes	characteristic
29	C₂×C₉×D₈	C₂²	1	1	yes	characteristic
30	C₂×C₉×D₈	C₂²	1	1	yes	characteristic
31	C₂×C₉×D₈	C₂²	1	1	yes	characteristic
32	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
33	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic, complemented
34	C₉×#127	—	2	1	no	—
35	C₉×#127	C₂²	1	1	yes	characteristic, complemented
36	C₉×#124	C₂²	1	1	yes	characteristic
37	C₉×#123	—	2	1	no	—
38	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
39	C₉×#121	—	2	1	no	—
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	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
47	C₄×D₄×C₉	—	2	1	no	—
48	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
49	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
50	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
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
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
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	C₂×C₃×#135	C₂×C₃	1	1	yes	characteristic
64	C₃×#550	C₂×C₃	1	1	yes	characteristic
65	C₃×#546	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×#464	C₂×C₃	1	1	yes	characteristic
70	C₃×#459	C₂×C₃	1	1	yes	characteristic
71	C₃×#452	C₂×C₃	1	1	yes	characteristic
72	C₃×#449	C₂×C₃	1	1	yes	characteristic
73	C₃×#449	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	C₉×#41	—	2	2	no	—
79	C₉×#41	—	2	2	no	—
80	C₉×#41	—	2	2	no	—
81	C₉×#41	—	4	1	no	—
82	C₉×#41	—	4	1	no	—
83	C₉×#41	—	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	1	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	D₄	1	1	yes	characteristic
98	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
99	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
100	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
101	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₉	—	2	1	no	—
103	C₂²×C₄×C₉	—	2	1	no	—
104	C₂²×C₄×C₉	—	2	1	no	—
105	C₂²×C₄×C₉	—	2	1	no	—
106	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
107	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
108	C₉×Q₁₆	—	2	2	no	—
109	C₉×SD₁₆	—	2	2	no	—
110	C₉×SD₁₆	—	2	2	no	—
111	C₉×SD₁₆	—	4	1	no	—
112	C₉×SD₁₆	D₄	1	4	yes	complemented
113	C₉×D₈	—	2	2	no	—
114	C₉×D₈	—	2	2	no	—
115	C₉×D₈	—	2	2	no	—
116	C₉×D₈	—	4	1	no	—
117	C₉×M₁₆	—	2	2	no	—
118	C₂×C₈×C₉	—	2	2	no	—
119	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
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	C₉×C₄⋊C₄	—	2	1	no	—
124	C₉×C₄⋊C₄	—	2	1	no	—
125	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
126	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
127	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₉×C₂²⋊C₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
136	C₉×C₂²⋊C₄	D₄	1	1	yes	characteristic
137	C₄²×C₉	—	2	1	no	—
138	C₄²×C₉	C₂³	1	1	yes	characteristic
139	#3268	C₉	1	1	yes	characteristic, direct product factor, Sylow
140	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
141	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
142	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
143	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
144	C₃×AGL(1,ℤ/8)	—	2	4	no	—
145	C₃×#135	—	2	4	no	—
146	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
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×D₈	C₂²×C₃	1	1	yes	characteristic
152	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
153	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
154	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
155	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
156	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
157	C₃×#127	—	2	1	no	—
158	C₃×#127	C₂²×C₃	1	1	yes	characteristic
159	C₃×#124	C₂²×C₃	1	1	yes	characteristic
160	C₃×#123	—	2	1	no	—
161	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
162	C₃×#121	—	2	1	no	—
163	C₃×#121	—	2	1	no	—
164	C₃×#121	—	2	1	no	—
165	C₃×#121	C₂²×C₃	1	1	yes	characteristic
166	C₃×#121	C₂²×C₃	1	1	yes	characteristic
167	C₃×#121	C₂²×C₃	1	1	yes	characteristic
168	C₃×#120	—	2	1	no	—
169	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
170	C₃×C₄×D₄	—	2	1	no	—
171	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
172	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
173	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
174	C₃×#107	C₂²×C₃	1	1	yes	characteristic
175	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
176	C₃×#103	C₂²×C₃	1	1	yes	characteristic
177	C₃×#103	C₂²×C₃	1	1	yes	characteristic
178	C₃×#102	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×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
183	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
184	C₃×#97	C₂²×C₃	1	1	yes	characteristic
185	C₂³×C₉	—	2	1	no	—
186	C₂³×C₉	—	2	1	no	—
187	C₂³×C₉	—	2	1	no	—
188	C₂³×C₉	—	2	1	no	—
189	C₂³×C₉	—	4	2	no	—
190	C₂³×C₉	—	4	2	no	—
191	C₂³×C₉	—	8	1	no	—
192	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
193	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
194	Q₈×C₉	—	2	1	no	—
195	Q₈×C₉	—	2	1	no	—
196	Q₈×C₉	—	2	1	no	—
197	Q₈×C₉	C₂×D₄	1	2	yes	—
198	D₄×C₉	—	2	1	no	—
199	D₄×C₉	—	2	1	no	—
200	D₄×C₉	—	2	1	no	—
201	D₄×C₉	—	2	1	no	—
202	D₄×C₉	—	2	1	no	—
203	D₄×C₉	—	2	1	no	—
204	D₄×C₉	—	2	1	no	—
205	D₄×C₉	—	4	1	no	—
206	D₄×C₉	—	4	2	no	—
207	D₄×C₉	—	4	2	no	—
208	D₄×C₉	—	4	2	no	—
209	D₄×C₉	—	4	2	no	—
210	D₄×C₉	—	4	2	no	—
211	D₄×C₉	—	8	1	no	—
212	D₄×C₉	—	8	1	no	—
213	D₄×C₉	—	8	1	no	—
214	D₄×C₉	—	8	1	no	—
215	D₄×C₉	C₂×D₄	1	2	yes	—
216	C₂×C₄×C₉	—	2	1	no	—
217	C₂×C₄×C₉	—	2	1	no	—
218	C₂×C₄×C₉	—	2	1	no	—
219	C₂×C₄×C₉	—	2	1	no	—
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	—	4	2	no	—
225	C₂×C₄×C₉	—	4	2	no	—
226	C₂×C₄×C₉	—	4	2	no	—
227	C₂×C₄×C₉	—	8	1	no	—
228	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
229	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
230	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
231	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
232	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
233	C₈×C₉	—	2	1	no	—
234	C₈×C₉	—	2	1	no	—
235	C₈×C₉	—	2	1	no	—
236	C₈×C₉	C₂×D₄	1	2	yes	—
237	C₂×AGL(1,ℤ/8)	C₂×C₉	1	1	yes	characteristic, complemented
238	C₂×#135	C₂×C₉	1	1	yes	characteristic, complemented
239	#550	C₂×C₉	1	1	yes	characteristic, complemented
240	#546	C₂×C₉	1	1	yes	characteristic, complemented
241	#496	C₂×C₉	1	1	yes	characteristic, complemented
242	#468	C₂×C₉	1	1	yes	characteristic, complemented
243	#466	C₂×C₉	1	1	yes	characteristic, complemented
244	#464	C₂×C₉	1	1	yes	characteristic, complemented
245	#459	C₂×C₉	1	1	yes	characteristic, complemented
246	#452	C₂×C₉	1	1	yes	characteristic, complemented
247	#449	C₂×C₉	1	1	yes	characteristic, complemented
248	#449	C₂×C₉	1	1	yes	characteristic, complemented
249	#447	C₂×C₉	1	1	yes	characteristic, complemented
250	#440	C₂×C₉	1	1	yes	characteristic, complemented
251	#435	C₂×C₉	1	1	yes	characteristic, complemented
252	C₂⁴×C₃	—	2	1	no	—
253	C₃×#41	—	2	2	no	—
254	C₃×#41	—	2	2	no	—
255	C₃×#41	—	2	2	no	—
256	C₃×#41	—	4	1	no	—
257	C₃×#41	—	4	1	no	—
258	C₃×#41	—	4	1	no	—
259	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
260	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
261	C₂×C₃×D₄	—	2	2	no	—
262	C₂×C₃×D₄	—	2	1	no	—
263	C₂×C₃×D₄	—	2	1	no	—
264	C₂×C₃×D₄	—	2	1	no	—
265	C₂×C₃×D₄	—	2	1	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	—	4	1	no	—
272	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
273	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
274	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
275	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
276	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
277	C₂²×C₃×C₄	—	2	1	no	—
278	C₂²×C₃×C₄	—	2	1	no	—
279	C₂²×C₃×C₄	—	2	1	no	—
280	C₂²×C₃×C₄	—	2	1	no	—
281	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
282	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
283	C₃×Q₁₆	—	2	2	no	—
284	C₃×SD₁₆	—	2	2	no	—
285	C₃×SD₁₆	—	2	2	no	—
286	C₃×SD₁₆	—	4	1	no	—
287	C₃×SD₁₆	C₃×D₄	1	4	yes	—
288	C₃×D₈	—	2	2	no	—
289	C₃×D₈	—	2	2	no	—
290	C₃×D₈	—	2	2	no	—
291	C₃×D₈	—	4	1	no	—
292	C₃×M₁₆	—	2	2	no	—
293	C₂×C₃×C₈	—	2	2	no	—
294	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
295	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
296	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
297	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
298	C₃×C₄⋊C₄	—	2	1	no	—
299	C₃×C₄⋊C₄	—	2	1	no	—
300	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
301	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
302	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
303	C₃×C₂²⋊C₄	—	2	1	no	—
304	C₃×C₂²⋊C₄	—	2	1	no	—
305	C₃×C₂²⋊C₄	—	2	1	no	—
306	C₃×C₂²⋊C₄	—	2	1	no	—
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	C₃×D₄	1	1	yes	characteristic
311	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
312	C₃×C₄²	—	2	1	no	—
313	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
314	C₂²×C₉	—	2	1	no	—
315	C₂²×C₉	—	2	1	no	—
316	C₂²×C₉	—	2	2	no	—
317	C₂²×C₉	—	2	1	no	—
318	C₂²×C₉	—	2	1	no	—
319	C₂²×C₉	—	2	1	no	—
320	C₂²×C₉	—	2	1	no	—
321	C₂²×C₉	—	4	1	no	—
322	C₂²×C₉	—	4	1	no	—
323	C₂²×C₉	—	4	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	—	8	4	no	—
333	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
334	C₄×C₉	—	2	1	no	—
335	C₄×C₉	—	2	1	no	—
336	C₄×C₉	—	2	2	no	—
337	C₄×C₉	—	2	1	no	—
338	C₄×C₉	—	2	1	no	—
339	C₄×C₉	—	4	1	no	—
340	C₄×C₉	—	4	1	no	—
341	C₄×C₉	—	4	1	no	—
342	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
343	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
344	C₂×#41	C₂²×C₉	1	1	yes	characteristic
345	C₂×#41	C₂²×C₉	1	1	yes	characteristic
346	C₂×#41	C₂²×C₉	1	1	yes	characteristic, complemented
347	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
348	AGL(1,ℤ/8)	—	2	4	no	—
349	#135	—	2	4	no	—
350	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
351	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
352	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
353	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
354	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
355	C₂×D₈	C₂²×C₉	1	1	yes	characteristic
356	C₂×D₈	C₂²×C₉	1	1	yes	characteristic
357	C₂×D₈	C₂²×C₉	1	1	yes	characteristic
358	C₂×D₈	C₂²×C₉	1	1	yes	characteristic
359	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
360	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic, complemented
361	#127	—	2	1	no	—
362	#127	C₂²×C₉	1	1	yes	characteristic, complemented
363	#124	C₂²×C₉	1	1	yes	characteristic
364	#123	—	2	1	no	—
365	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
366	#121	—	2	1	no	—
367	#121	—	2	1	no	—
368	#121	—	2	1	no	—
369	#121	C₂²×C₉	1	1	yes	characteristic
370	#121	C₂²×C₉	1	1	yes	characteristic
371	#121	C₂²×C₉	1	1	yes	characteristic, complemented
372	#120	—	2	1	no	—
373	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
374	C₄×D₄	—	2	1	no	—
375	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
376	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	#107	C₂²×C₉	1	1	yes	characteristic, complemented
379	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic, complemented
380	#103	C₂²×C₉	1	1	yes	characteristic, complemented
381	#103	C₂²×C₉	1	1	yes	characteristic, complemented
382	#102	C₂²×C₉	1	1	yes	characteristic
383	#102	C₂²×C₉	1	1	yes	characteristic
384	#102	C₂²×C₉	1	1	yes	characteristic, complemented
385	#102	C₂²×C₉	1	1	yes	characteristic, complemented
386	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
387	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic, complemented
388	#97	C₂²×C₉	1	1	yes	characteristic, complemented
389	C₂³×C₃	—	2	1	no	—
390	C₂³×C₃	—	2	1	no	—
391	C₂³×C₃	—	2	1	no	—
392	C₂³×C₃	—	2	1	no	—
393	C₂³×C₃	—	4	2	no	—
394	C₂³×C₃	—	4	2	no	—
395	C₂³×C₃	—	8	1	no	—
396	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
397	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
398	C₃×Q₈	—	2	1	no	—
399	C₃×Q₈	—	2	1	no	—
400	C₃×Q₈	—	2	1	no	—
401	C₃×Q₈	C₂×C₃×D₄	1	2	yes	—
402	C₃×D₄	—	2	1	no	—
403	C₃×D₄	—	2	1	no	—
404	C₃×D₄	—	2	1	no	—
405	C₃×D₄	—	2	1	no	—
406	C₃×D₄	—	2	1	no	—
407	C₃×D₄	—	2	1	no	—
408	C₃×D₄	—	2	1	no	—
409	C₃×D₄	—	4	1	no	—
410	C₃×D₄	—	4	2	no	—
411	C₃×D₄	—	4	2	no	—
412	C₃×D₄	—	4	2	no	—
413	C₃×D₄	—	4	2	no	—
414	C₃×D₄	—	4	2	no	—
415	C₃×D₄	—	8	1	no	—
416	C₃×D₄	—	8	1	no	—
417	C₃×D₄	—	8	1	no	—
418	C₃×D₄	—	8	1	no	—
419	C₃×D₄	C₂×C₃×D₄	1	2	yes	—
420	C₂×C₃×C₄	—	2	1	no	—
421	C₂×C₃×C₄	—	2	1	no	—
422	C₂×C₃×C₄	—	2	1	no	—
423	C₂×C₃×C₄	—	2	1	no	—
424	C₂×C₃×C₄	—	2	1	no	—
425	C₂×C₃×C₄	—	2	1	no	—
426	C₂×C₃×C₄	—	2	1	no	—
427	C₂×C₃×C₄	—	2	1	no	—
428	C₂×C₃×C₄	—	4	2	no	—
429	C₂×C₃×C₄	—	4	2	no	—
430	C₂×C₃×C₄	—	4	2	no	—
431	C₂×C₃×C₄	—	8	1	no	—
432	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
433	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
434	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
435	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
436	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
437	C₃×C₈	—	2	1	no	—
438	C₃×C₈	—	2	1	no	—
439	C₃×C₈	—	2	1	no	—
440	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
441	C₂×C₉	—	4	1	no	—
442	C₂×C₉	—	4	1	no	—
443	C₂×C₉	—	4	2	no	—
444	C₂×C₉	—	8	1	no	—
445	C₂×C₉	—	8	1	no	—
446	C₂×C₉	—	8	1	no	—
447	C₂×C₉	D₄²	1	1	yes	characteristic
448	C₂×C₉	#575	1	1	yes	characteristic
449	C₂×C₉	#576	1	1	yes	characteristic
450	C₂⁴	—	2	1	no	—
451	#41	—	2	2	no	—
452	#41	—	2	2	no	—
453	#41	—	2	2	no	—
454	#41	—	4	1	no	—
455	#41	—	4	1	no	—
456	#41	—	4	1	no	—
457	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
458	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	4	1	no	—
470	C₂×D₄	D₄×C₉	1	1	yes	characteristic
471	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
472	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
473	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
474	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
480	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
481	Q₁₆	—	2	2	no	—
482	SD₁₆	—	2	2	no	—
483	SD₁₆	—	2	2	no	—
484	SD₁₆	—	4	1	no	—
485	SD₁₆	D₄×C₉	1	4	yes	complemented
486	D₈	—	2	2	no	—
487	D₈	—	2	2	no	—
488	D₈	—	2	2	no	—
489	D₈	—	4	1	no	—
490	M₁₆	—	2	2	no	—
491	C₂×C₈	—	2	2	no	—
492	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
493	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
494	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
495	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
499	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
500	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	2	1	no	—
504	C₂²⋊C₄	—	2	1	no	—
505	C₂²⋊C₄	—	2	1	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	1	no	—
508	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
509	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
510	C₄²	—	2	1	no	—
511	C₄²	C₂³×C₉	1	1	yes	characteristic
512	C₂²×C₃	—	2	1	no	—
513	C₂²×C₃	—	2	1	no	—
514	C₂²×C₃	—	2	1	no	—
515	C₂²×C₃	—	2	1	no	—
516	C₂²×C₃	—	2	1	no	—
517	C₂²×C₃	—	2	1	no	—
518	C₂²×C₃	—	2	2	no	—
519	C₂²×C₃	—	4	1	no	—
520	C₂²×C₃	—	4	1	no	—
521	C₂²×C₃	—	4	1	no	—
522	C₂²×C₃	—	4	1	no	—
523	C₂²×C₃	—	4	1	no	—
524	C₂²×C₃	—	4	1	no	—
525	C₂²×C₃	—	4	1	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	—	8	4	no	—
531	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
532	C₃×C₄	—	2	1	no	—
533	C₃×C₄	—	2	1	no	—
534	C₃×C₄	—	2	1	no	—
535	C₃×C₄	—	2	1	no	—
536	C₃×C₄	—	2	2	no	—
537	C₃×C₄	—	4	1	no	—
538	C₃×C₄	—	4	1	no	—
539	C₃×C₄	—	4	1	no	—
540	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
541	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
542	C₉	#3268	1	1	yes	characteristic, direct product factor, Sylow
543	C₂³	—	2	1	no	—
544	C₂³	—	2	1	no	—
545	C₂³	—	2	1	no	—
546	C₂³	—	2	1	no	—
547	C₂³	—	4	2	no	—
548	C₂³	—	4	2	no	—
549	C₂³	—	8	1	no	—
550	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
551	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
552	Q₈	—	2	1	no	—
553	Q₈	—	2	1	no	—
554	Q₈	—	2	1	no	—
555	Q₈	C₂×D₄×C₉	1	2	yes	—
556	D₄	—	2	1	no	—
557	D₄	—	2	1	no	—
558	D₄	—	2	1	no	—
559	D₄	—	2	1	no	—
560	D₄	—	2	1	no	—
561	D₄	—	2	1	no	—
562	D₄	—	2	1	no	—
563	D₄	—	4	1	no	—
564	D₄	—	4	2	no	—
565	D₄	—	4	2	no	—
566	D₄	—	4	2	no	—
567	D₄	—	4	2	no	—
568	D₄	—	4	2	no	—
569	D₄	—	8	1	no	—
570	D₄	—	8	1	no	—
571	D₄	—	8	1	no	—
572	D₄	—	8	1	no	—
573	D₄	C₂×D₄×C₉	1	2	yes	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	8	1	no	—
586	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
587	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
588	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
589	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
590	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
591	C₈	—	2	1	no	—
592	C₈	—	2	1	no	—
593	C₈	—	2	1	no	—
594	C₈	C₂×D₄×C₉	1	2	yes	—
595	C₂×C₃	—	4	1	no	—
596	C₂×C₃	—	4	1	no	—
597	C₂×C₃	—	4	2	no	—
598	C₂×C₃	—	8	1	no	—
599	C₂×C₃	—	8	1	no	—
600	C₂×C₃	—	8	1	no	—
601	C₂×C₃	C₃×D₄²	1	1	yes	characteristic
602	C₂×C₃	C₃×#575	1	1	yes	characteristic
603	C₂×C₃	C₃×#576	1	1	yes	characteristic
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	1	no	—
611	C₂²	—	4	1	no	—
612	C₂²	—	4	1	no	—
613	C₂²	—	4	1	no	—
614	C₂²	—	4	1	no	—
615	C₂²	—	4	1	no	—
616	C₂²	—	4	1	no	—
617	C₂²	—	4	1	no	—
618	C₂²	—	4	1	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	8	4	no	—
623	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
624	C₄	—	2	1	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	2	no	—
627	C₄	—	2	1	no	—
628	C₄	—	2	1	no	—
629	C₄	—	4	1	no	—
630	C₄	—	4	1	no	—
631	C₄	—	4	1	no	—
632	C₄	C₂²×D₄×C₉	1	1	yes	characteristic
633	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
634	C₃	C₃×#3268	1	1	yes	characteristic
635	C₂	—	4	1	no	—
636	C₂	—	4	1	no	—
637	C₂	—	4	2	no	—
638	C₂	—	8	1	no	—
639	C₂	—	8	1	no	—
640	C₂	—	8	1	no	—
641	C₂	D₄²×C₉	1	1	yes	characteristic
642	C₂	C₉×#575	1	1	yes	characteristic
643	C₂	C₉×#576	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×#3268	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. C₂×C₉×#135	C₂	semidirect
3. C₉×#550	C₂	semidirect
4. C₉×#546	C₂	semidirect
5. C₉×#496	C₂	semidirect
6. C₉×#468	C₂	semidirect
7. C₉×#466	C₂	semidirect
8. C₉×#464	C₂	semidirect
9. C₉×#459	C₂	semidirect
10. C₉×#452	C₂	semidirect
11. C₉×#449	C₂	semidirect
12. C₉×#449	C₂	semidirect
13. C₉×#447	C₂	semidirect
14. C₉×#440	C₂	semidirect
15. C₉×#435	C₂	semidirect
19. C₂×C₉×#41	C₂²	semidirect
23. C₂×C₉×Q₁₆	C₂²	semidirect
26. C₂×C₉×SD₁₆	C₂²	semidirect
27. C₂×C₉×SD₁₆	C₂²	semidirect
33. C₂²×C₈×C₉	C₂²	semidirect
35. C₉×#127	C₂²	semidirect
44. C₉×#121	C₂²	semidirect
46. 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
57. C₉×#102	C₂²	semidirect
58. C₉×#102	C₂²	semidirect
60. C₉×C₂²⋊C₈	C₂²	semidirect
61. C₉×#97	C₂²	semidirect
112. C₉×SD₁₆	D₄	semidirect
139. #3268	C₉	direct (N × H)
237. C₂×AGL(1,ℤ/8)	C₂×C₉	semidirect
238. C₂×#135	C₂×C₉	semidirect
239. #550	C₂×C₉	semidirect
240. #546	C₂×C₉	semidirect
241. #496	C₂×C₉	semidirect
242. #468	C₂×C₉	semidirect
243. #466	C₂×C₉	semidirect
244. #464	C₂×C₉	semidirect
245. #459	C₂×C₉	semidirect
246. #452	C₂×C₉	semidirect
247. #449	C₂×C₉	semidirect
248. #449	C₂×C₉	semidirect
249. #447	C₂×C₉	semidirect
250. #440	C₂×C₉	semidirect
251. #435	C₂×C₉	semidirect
346. C₂×#41	C₂²×C₉	semidirect
350. C₂×Q₁₆	C₂²×C₉	semidirect
353. C₂×SD₁₆	C₂²×C₉	semidirect
354. C₂×SD₁₆	C₂²×C₉	semidirect
360. C₂²×C₈	C₂²×C₉	semidirect
362. #127	C₂²×C₉	semidirect
371. #121	C₂²×C₉	semidirect
373. C₄×Q₈	C₂²×C₉	semidirect
378. #107	C₂²×C₉	semidirect
379. C₄⋊C₈	C₂²×C₉	semidirect
380. #103	C₂²×C₉	semidirect
381. #103	C₂²×C₉	semidirect
384. #102	C₂²×C₉	semidirect
385. #102	C₂²×C₉	semidirect
387. C₂²⋊C₈	C₂²×C₉	semidirect
388. #97	C₂²×C₉	semidirect
485. SD₁₆	D₄×C₉	semidirect
542. C₉	#3268	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×#135	2
C₉×#550	2
C₉×#546	2
C₉×#496	2
C₉×#468	2
C₉×#466	2
C₉×#464	2
C₉×#459	2
C₉×#452	2
C₉×#449	2
C₉×#447	2
C₉×#440	2
C₉×#435	2
C₃×#3268	3

Subgroups — C9×#3268 #11767989

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3268 #11767989