Subgroups — C₉×#3055 #11767776

Order 1152.

822 conjugacy classes of subgroups.

The subgroup lattice has 519 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×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#525	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉×#121	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×#418	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#417	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3055	C₃	1	1	yes	maximal, characteristic
13	C₂×C₉×#41	C₂²	1	1	yes	characteristic
14	C₂²×D₄×C₉	—	2	1	no	—
15	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
16	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
17	C₉×AGL(1,ℤ/8)	—	2	4	no	—
18	C₂×C₉×SD₁₆	C₂²	1	2	yes	complemented
19	C₂×C₉×D₈	C₂²	1	2	yes	complemented
20	C₂×C₉×M₁₆	—	2	4	no	—
21	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
23	C₂×C₉×M₁₆	C₂²	1	2	yes	complemented
24	C₂²×C₈×C₉	C₂²	1	2	yes	complemented
25	C₉×#123	—	2	1	no	—
26	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₉×#121	—	2	1	no	—
29	C₉×#121	—	2	1	no	—
30	C₉×#121	C₂²	1	2	yes	—
31	C₉×#121	C₂²	1	2	yes	—
32	C₉×#121	C₂²	1	1	yes	characteristic, complemented
33	C₉×#121	C₂²	1	1	yes	characteristic, complemented
34	C₉×#120	—	2	1	no	—
35	C₄×D₄×C₉	—	2	1	no	—
36	C₄×D₄×C₉	—	2	1	no	—
37	C₉×#117	C₂²	1	1	yes	characteristic
38	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
40	C₉×#107	C₂²	1	2	yes	complemented
41	C₉×#106	C₂²	1	2	yes	complemented
42	C₉×#103	C₂²	1	2	yes	complemented
43	C₉×#102	C₂²	1	2	yes	complemented
44	C₉×#102	C₂²	1	2	yes	complemented
45	C₉×#102	C₂²	1	2	yes	complemented
46	C₂×C₃×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic
47	C₂²×C₃×M₁₆	C₂×C₃	1	1	yes	characteristic
48	C₃×#525	C₂×C₃	1	1	yes	characteristic
49	C₂×C₃×#121	C₂×C₃	1	1	yes	characteristic
50	C₃×#469	C₂×C₃	1	2	yes	—
51	C₃×#468	C₂×C₃	1	2	yes	—
52	C₃×#466	C₂×C₃	1	2	yes	—
53	C₃×#465	C₂×C₃	1	2	yes	—
54	C₃×#428	C₂×C₃	1	1	yes	characteristic
55	C₃×#418	C₂×C₃	1	1	yes	characteristic
56	C₃×#417	C₂×C₃	1	1	yes	characteristic
57	C₂⁴×C₉	—	2	1	no	—
58	C₂⁴×C₉	D₄	1	1	yes	characteristic
59	C₉×#41	—	2	2	no	—
60	C₉×#41	—	2	2	no	—
61	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
62	C₂×D₄×C₉	—	2	1	no	—
63	C₂×D₄×C₉	—	2	1	no	—
64	C₂×D₄×C₉	—	2	1	no	—
65	C₂×D₄×C₉	—	2	2	no	—
66	C₂×D₄×C₉	—	2	2	no	—
67	C₂×D₄×C₉	—	2	2	no	—
68	C₂×D₄×C₉	—	2	1	no	—
69	C₂×D₄×C₉	—	2	2	no	—
70	C₂×D₄×C₉	—	4	4	no	—
71	C₂×D₄×C₉	C₂³	1	2	yes	—
72	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₉	—	2	2	no	—
74	C₂²×C₄×C₉	—	2	2	no	—
75	C₂²×C₄×C₉	—	2	1	no	—
76	C₂²×C₄×C₉	—	2	1	no	—
77	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
78	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
79	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
80	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
83	C₉×SD₁₆	—	2	4	no	—
84	C₉×D₈	—	2	4	no	—
85	C₉×M₁₆	—	2	2	no	—
86	C₉×M₁₆	—	2	4	no	—
87	C₉×M₁₆	D₄	1	4	yes	complemented
88	C₂×C₈×C₉	—	2	4	no	—
89	C₂×C₈×C₉	C₂³	1	2	yes	—
90	C₂×C₈×C₉	C₂³	1	2	yes	—
91	C₉×C₄⋊C₄	—	2	1	no	—
92	C₉×C₄⋊C₄	—	2	1	no	—
93	C₉×C₄⋊C₄	—	2	1	no	—
94	C₉×C₄⋊C₄	C₂³	1	2	yes	—
95	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₉×C₂²⋊C₄	—	2	1	no	—
98	C₉×C₂²⋊C₄	—	2	1	no	—
99	C₉×C₂²⋊C₄	—	2	1	no	—
100	C₉×C₂²⋊C₄	—	2	2	no	—
101	C₉×C₂²⋊C₄	—	2	2	no	—
102	C₉×C₂²⋊C₄	—	2	1	no	—
103	C₉×C₂²⋊C₄	—	2	1	no	—
104	C₄²×C₉	—	2	1	no	—
105	#3055	C₉	1	1	yes	characteristic, direct product factor, Sylow
106	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
107	C₂²×C₃×D₄	—	2	1	no	—
108	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
109	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
110	C₃×AGL(1,ℤ/8)	—	2	4	no	—
111	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
112	C₂×C₃×D₈	C₂²×C₃	1	2	yes	—
113	C₂×C₃×M₁₆	—	2	4	no	—
114	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
115	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
117	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
118	C₃×#123	—	2	1	no	—
119	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
120	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
121	C₃×#121	—	2	1	no	—
122	C₃×#121	—	2	1	no	—
123	C₃×#121	C₂²×C₃	1	2	yes	—
124	C₃×#121	C₂²×C₃	1	2	yes	—
125	C₃×#121	C₂²×C₃	1	1	yes	characteristic
126	C₃×#121	C₂²×C₃	1	1	yes	characteristic
127	C₃×#120	—	2	1	no	—
128	C₃×C₄×D₄	—	2	1	no	—
129	C₃×C₄×D₄	—	2	1	no	—
130	C₃×#117	C₂²×C₃	1	1	yes	characteristic
131	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
132	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
133	C₃×#107	C₂²×C₃	1	2	yes	—
134	C₃×#106	C₂²×C₃	1	2	yes	—
135	C₃×#103	C₂²×C₃	1	2	yes	—
136	C₃×#102	C₂²×C₃	1	2	yes	—
137	C₃×#102	C₂²×C₃	1	2	yes	—
138	C₃×#102	C₂²×C₃	1	2	yes	—
139	C₂³×C₉	—	2	2	no	—
140	C₂³×C₉	—	2	2	no	—
141	C₂³×C₉	—	2	1	no	—
142	C₂³×C₉	—	2	2	no	—
143	C₂³×C₉	—	4	1	no	—
144	C₂³×C₉	—	4	2	no	—
145	C₂³×C₉	—	4	2	no	—
146	C₂³×C₉	—	4	2	no	—
147	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
148	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
149	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
150	Q₈×C₉	—	2	1	no	—
151	Q₈×C₉	—	2	1	no	—
152	D₄×C₉	—	2	1	no	—
153	D₄×C₉	—	2	2	no	—
154	D₄×C₉	—	2	2	no	—
155	D₄×C₉	—	2	1	no	—
156	D₄×C₉	—	4	2	no	—
157	D₄×C₉	—	4	4	no	—
158	D₄×C₉	—	4	2	no	—
159	D₄×C₉	—	4	2	no	—
160	D₄×C₉	—	4	4	no	—
161	D₄×C₉	—	4	2	no	—
162	C₂×C₄×C₉	—	2	2	no	—
163	C₂×C₄×C₉	—	2	2	no	—
164	C₂×C₄×C₉	—	2	2	no	—
165	C₂×C₄×C₉	—	2	1	no	—
166	C₂×C₄×C₉	—	2	1	no	—
167	C₂×C₄×C₉	—	2	1	no	—
168	C₂×C₄×C₉	—	2	1	no	—
169	C₂×C₄×C₉	—	2	1	no	—
170	C₂×C₄×C₉	—	2	1	no	—
171	C₂×C₄×C₉	—	2	1	no	—
172	C₂×C₄×C₉	—	2	2	no	—
173	C₂×C₄×C₉	—	4	2	no	—
174	C₂×C₄×C₉	—	4	2	no	—
175	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
176	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
177	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
178	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
179	C₂×C₄×C₉	#41	1	2	yes	—
180	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
181	C₈×C₉	—	2	2	no	—
182	C₈×C₉	C₂×D₄	1	4	yes	complemented
183	C₂×AGL(1,ℤ/8)	C₂×C₉	1	1	yes	characteristic, complemented
184	C₂²×M₁₆	C₂×C₉	1	1	yes	characteristic, complemented
185	#525	C₂×C₉	1	1	yes	characteristic, complemented
186	C₂×#121	C₂×C₉	1	1	yes	characteristic, complemented
187	#469	C₂×C₉	1	2	yes	complemented
188	#468	C₂×C₉	1	2	yes	complemented
189	#466	C₂×C₉	1	2	yes	complemented
190	#465	C₂×C₉	1	2	yes	complemented
191	#428	C₂×C₉	1	1	yes	characteristic, complemented
192	#418	C₂×C₉	1	1	yes	characteristic, complemented
193	#417	C₂×C₉	1	1	yes	characteristic, complemented
194	C₂⁴×C₃	—	2	1	no	—
195	C₂⁴×C₃	C₃×D₄	1	1	yes	characteristic
196	C₃×#41	—	2	2	no	—
197	C₃×#41	—	2	2	no	—
198	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
199	C₂×C₃×D₄	—	2	1	no	—
200	C₂×C₃×D₄	—	2	1	no	—
201	C₂×C₃×D₄	—	2	1	no	—
202	C₂×C₃×D₄	—	2	2	no	—
203	C₂×C₃×D₄	—	2	2	no	—
204	C₂×C₃×D₄	—	2	2	no	—
205	C₂×C₃×D₄	—	2	1	no	—
206	C₂×C₃×D₄	—	2	2	no	—
207	C₂×C₃×D₄	—	4	4	no	—
208	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
209	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
210	C₂²×C₃×C₄	—	2	2	no	—
211	C₂²×C₃×C₄	—	2	2	no	—
212	C₂²×C₃×C₄	—	2	1	no	—
213	C₂²×C₃×C₄	—	2	1	no	—
214	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
215	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
216	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
217	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
218	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
219	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
220	C₃×SD₁₆	—	2	4	no	—
221	C₃×D₈	—	2	4	no	—
222	C₃×M₁₆	—	2	2	no	—
223	C₃×M₁₆	—	2	4	no	—
224	C₃×M₁₆	C₃×D₄	1	4	yes	—
225	C₂×C₃×C₈	—	2	4	no	—
226	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
227	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
228	C₃×C₄⋊C₄	—	2	1	no	—
229	C₃×C₄⋊C₄	—	2	1	no	—
230	C₃×C₄⋊C₄	—	2	1	no	—
231	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
232	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
233	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
234	C₃×C₂²⋊C₄	—	2	1	no	—
235	C₃×C₂²⋊C₄	—	2	1	no	—
236	C₃×C₂²⋊C₄	—	2	1	no	—
237	C₃×C₂²⋊C₄	—	2	2	no	—
238	C₃×C₂²⋊C₄	—	2	2	no	—
239	C₃×C₂²⋊C₄	—	2	1	no	—
240	C₃×C₂²⋊C₄	—	2	1	no	—
241	C₃×C₄²	—	2	1	no	—
242	C₂²×C₉	—	2	1	no	—
243	C₂²×C₉	—	2	1	no	—
244	C₂²×C₉	—	2	1	no	—
245	C₂²×C₉	—	2	1	no	—
246	C₂²×C₉	—	2	1	no	—
247	C₂²×C₉	—	2	1	no	—
248	C₂²×C₉	—	2	1	no	—
249	C₂²×C₉	—	4	4	no	—
250	C₂²×C₉	—	4	1	no	—
251	C₂²×C₉	—	4	2	no	—
252	C₂²×C₉	—	4	2	no	—
253	C₂²×C₉	—	4	1	no	—
254	C₂²×C₉	—	4	1	no	—
255	C₂²×C₉	—	4	2	no	—
256	C₂²×C₉	—	8	4	no	—
257	C₂²×C₉	#121	1	2	yes	—
258	C₂²×C₉	AGL(1,ℤ/8)	1	2	yes	complemented
259	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
260	C₄×C₉	—	2	1	no	—
261	C₄×C₉	—	2	1	no	—
262	C₄×C₉	—	4	1	no	—
263	C₄×C₉	—	4	2	no	—
264	C₄×C₉	—	4	1	no	—
265	C₄×C₉	—	4	1	no	—
266	C₄×C₉	#121	1	2	yes	—
267	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
268	C₄×C₉	C₂×#41	1	1	yes	characteristic
269	C₂×#41	C₂²×C₉	1	1	yes	characteristic
270	C₂²×D₄	—	2	1	no	—
271	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
272	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
273	AGL(1,ℤ/8)	—	2	4	no	—
274	C₂×SD₁₆	C₂²×C₉	1	2	yes	complemented
275	C₂×D₈	C₂²×C₉	1	2	yes	complemented
276	C₂×M₁₆	—	2	4	no	—
277	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
278	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
279	C₂×M₁₆	C₂²×C₉	1	2	yes	complemented
280	C₂²×C₈	C₂²×C₉	1	2	yes	complemented
281	#123	—	2	1	no	—
282	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
283	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
284	#121	—	2	1	no	—
285	#121	—	2	1	no	—
286	#121	C₂²×C₉	1	2	yes	—
287	#121	C₂²×C₉	1	2	yes	—
288	#121	C₂²×C₉	1	1	yes	characteristic, complemented
289	#121	C₂²×C₉	1	1	yes	characteristic, complemented
290	#120	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	2	1	no	—
293	#117	C₂²×C₉	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	#107	C₂²×C₉	1	2	yes	complemented
297	#106	C₂²×C₉	1	2	yes	complemented
298	#103	C₂²×C₉	1	2	yes	complemented
299	#102	C₂²×C₉	1	2	yes	complemented
300	#102	C₂²×C₉	1	2	yes	complemented
301	#102	C₂²×C₉	1	2	yes	complemented
302	C₂³×C₃	—	2	2	no	—
303	C₂³×C₃	—	2	2	no	—
304	C₂³×C₃	—	2	1	no	—
305	C₂³×C₃	—	2	2	no	—
306	C₂³×C₃	—	4	1	no	—
307	C₂³×C₃	—	4	2	no	—
308	C₂³×C₃	—	4	2	no	—
309	C₂³×C₃	—	4	2	no	—
310	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
311	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
312	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
313	C₃×Q₈	—	2	1	no	—
314	C₃×Q₈	—	2	1	no	—
315	C₃×D₄	—	2	1	no	—
316	C₃×D₄	—	2	2	no	—
317	C₃×D₄	—	2	2	no	—
318	C₃×D₄	—	2	1	no	—
319	C₃×D₄	—	4	2	no	—
320	C₃×D₄	—	4	4	no	—
321	C₃×D₄	—	4	2	no	—
322	C₃×D₄	—	4	2	no	—
323	C₃×D₄	—	4	4	no	—
324	C₃×D₄	—	4	2	no	—
325	C₂×C₃×C₄	—	2	2	no	—
326	C₂×C₃×C₄	—	2	2	no	—
327	C₂×C₃×C₄	—	2	2	no	—
328	C₂×C₃×C₄	—	2	1	no	—
329	C₂×C₃×C₄	—	2	1	no	—
330	C₂×C₃×C₄	—	2	1	no	—
331	C₂×C₃×C₄	—	2	1	no	—
332	C₂×C₃×C₄	—	2	1	no	—
333	C₂×C₃×C₄	—	2	1	no	—
334	C₂×C₃×C₄	—	2	1	no	—
335	C₂×C₃×C₄	—	2	2	no	—
336	C₂×C₃×C₄	—	4	2	no	—
337	C₂×C₃×C₄	—	4	2	no	—
338	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
339	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
340	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
341	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
342	C₂×C₃×C₄	C₃×#41	1	2	yes	—
343	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
344	C₃×C₈	—	2	2	no	—
345	C₃×C₈	C₂×C₃×D₄	1	4	yes	—
346	C₂×C₉	—	2	2	no	—
347	C₂×C₉	—	2	2	no	—
348	C₂×C₉	—	4	1	no	—
349	C₂×C₉	—	8	1	no	—
350	C₂×C₉	—	8	2	no	—
351	C₂×C₉	C₂×#121	1	1	yes	characteristic
352	C₂×C₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
353	C₂×C₉	#575	1	1	yes	characteristic
354	C₂⁴	—	2	1	no	—
355	C₂⁴	D₄×C₉	1	1	yes	characteristic
356	#41	—	2	2	no	—
357	#41	—	2	2	no	—
358	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	4	4	no	—
368	C₂×D₄	C₂³×C₉	1	2	yes	—
369	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
375	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
376	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
377	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
378	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
379	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
380	SD₁₆	—	2	4	no	—
381	D₈	—	2	4	no	—
382	M₁₆	—	2	2	no	—
383	M₁₆	—	2	4	no	—
384	M₁₆	D₄×C₉	1	4	yes	complemented
385	C₂×C₈	—	2	4	no	—
386	C₂×C₈	C₂³×C₉	1	2	yes	—
387	C₂×C₈	C₂³×C₉	1	2	yes	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
392	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
393	C₄⋊C₄	C₂³×C₉	1	2	yes	—
394	C₂²⋊C₄	—	2	1	no	—
395	C₂²⋊C₄	—	2	1	no	—
396	C₂²⋊C₄	—	2	1	no	—
397	C₂²⋊C₄	—	2	2	no	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	2	1	no	—
400	C₂²⋊C₄	—	2	1	no	—
401	C₄²	—	2	1	no	—
402	C₂²×C₃	—	2	1	no	—
403	C₂²×C₃	—	2	1	no	—
404	C₂²×C₃	—	2	1	no	—
405	C₂²×C₃	—	2	1	no	—
406	C₂²×C₃	—	2	1	no	—
407	C₂²×C₃	—	2	1	no	—
408	C₂²×C₃	—	2	1	no	—
409	C₂²×C₃	—	4	4	no	—
410	C₂²×C₃	—	4	2	no	—
411	C₂²×C₃	—	4	1	no	—
412	C₂²×C₃	—	4	1	no	—
413	C₂²×C₃	—	4	2	no	—
414	C₂²×C₃	—	4	1	no	—
415	C₂²×C₃	—	4	2	no	—
416	C₂²×C₃	—	8	4	no	—
417	C₂²×C₃	C₃×#121	1	2	yes	—
418	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	2	yes	—
419	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
420	C₃×C₄	—	2	1	no	—
421	C₃×C₄	—	2	1	no	—
422	C₃×C₄	—	4	2	no	—
423	C₃×C₄	—	4	1	no	—
424	C₃×C₄	—	4	1	no	—
425	C₃×C₄	—	4	1	no	—
426	C₃×C₄	C₃×#121	1	2	yes	—
427	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
428	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
429	C₉	#3055	1	1	yes	characteristic, direct product factor, Sylow
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	2	1	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	4	2	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	2	no	—
438	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
439	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
440	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
441	Q₈	—	2	1	no	—
442	Q₈	—	2	1	no	—
443	D₄	—	2	1	no	—
444	D₄	—	2	2	no	—
445	D₄	—	2	2	no	—
446	D₄	—	2	1	no	—
447	D₄	—	4	4	no	—
448	D₄	—	4	2	no	—
449	D₄	—	4	2	no	—
450	D₄	—	4	4	no	—
451	D₄	—	4	2	no	—
452	D₄	—	4	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
467	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
468	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
469	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
470	C₂×C₄	C₉×#41	1	2	yes	—
471	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
472	C₈	—	2	2	no	—
473	C₈	C₂×D₄×C₉	1	4	yes	complemented
474	C₂×C₃	—	2	2	no	—
475	C₂×C₃	—	2	2	no	—
476	C₂×C₃	—	4	1	no	—
477	C₂×C₃	—	8	2	no	—
478	C₂×C₃	—	8	1	no	—
479	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
480	C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
481	C₂×C₃	C₃×#575	1	1	yes	characteristic
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	2	1	no	—
489	C₂²	—	4	4	no	—
490	C₂²	—	4	1	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	1	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	8	4	no	—
497	C₂²	C₉×#121	1	2	yes	—
498	C₂²	C₉×AGL(1,ℤ/8)	1	2	yes	complemented
499	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
500	C₄	—	2	1	no	—
501	C₄	—	2	1	no	—
502	C₄	—	4	1	no	—
503	C₄	—	4	2	no	—
504	C₄	—	4	1	no	—
505	C₄	—	4	1	no	—
506	C₄	C₉×#121	1	2	yes	—
507	C₄	C₂²×D₄×C₉	1	1	yes	characteristic
508	C₄	C₂×C₉×#41	1	1	yes	characteristic
509	C₃	C₃×#3055	1	1	yes	characteristic
510	C₂	—	2	2	no	—
511	C₂	—	2	2	no	—
512	C₂	—	4	1	no	—
513	C₂	—	8	2	no	—
514	C₂	—	8	1	no	—
515	C₂	C₂×C₉×#121	1	1	yes	characteristic
516	C₂	C₂×C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
517	C₂	C₉×#575	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×#3055	C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂³×C₄×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×M₁₆	C₂	semidirect
3. C₉×#525	C₂	semidirect
4. C₂×C₉×#121	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×#418	C₂	semidirect
11. C₉×#417	C₂	semidirect
18. C₂×C₉×SD₁₆	C₂²	semidirect
19. C₂×C₉×D₈	C₂²	semidirect
23. C₂×C₉×M₁₆	C₂²	semidirect
24. C₂²×C₈×C₉	C₂²	semidirect
26. C₉×C₂²⋊Q₈	C₂²	semidirect
27. C₉×C₂²⋊Q₈	C₂²	semidirect
32. C₉×#121	C₂²	semidirect
33. C₉×#121	C₂²	semidirect
40. C₉×#107	C₂²	semidirect
41. C₉×#106	C₂²	semidirect
42. C₉×#103	C₂²	semidirect
43. C₉×#102	C₂²	semidirect
44. C₉×#102	C₂²	semidirect
45. C₉×#102	C₂²	semidirect
87. C₉×M₁₆	D₄	semidirect
105. #3055	C₉	direct (N × H)
182. C₈×C₉	C₂×D₄	semidirect
183. C₂×AGL(1,ℤ/8)	C₂×C₉	semidirect
184. C₂²×M₁₆	C₂×C₉	semidirect
185. #525	C₂×C₉	semidirect
186. C₂×#121	C₂×C₉	semidirect
187. #469	C₂×C₉	semidirect
188. #468	C₂×C₉	semidirect
189. #466	C₂×C₉	semidirect
190. #465	C₂×C₉	semidirect
191. #428	C₂×C₉	semidirect
192. #418	C₂×C₉	semidirect
193. #417	C₂×C₉	semidirect
258. C₂²×C₉	AGL(1,ℤ/8)	semidirect
274. C₂×SD₁₆	C₂²×C₉	semidirect
275. C₂×D₈	C₂²×C₉	semidirect
279. C₂×M₁₆	C₂²×C₉	semidirect
280. C₂²×C₈	C₂²×C₉	semidirect
282. C₂²⋊Q₈	C₂²×C₉	semidirect
283. C₂²⋊Q₈	C₂²×C₉	semidirect
288. #121	C₂²×C₉	semidirect
289. #121	C₂²×C₉	semidirect
296. #107	C₂²×C₉	semidirect
297. #106	C₂²×C₉	semidirect
298. #103	C₂²×C₉	semidirect
299. #102	C₂²×C₉	semidirect
300. #102	C₂²×C₉	semidirect
301. #102	C₂²×C₉	semidirect
384. M₁₆	D₄×C₉	semidirect
429. C₉	#3055	direct (N × H)
473. C₈	C₂×D₄×C₉	semidirect
498. 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×M₁₆	2
C₉×#525	2
C₂×C₉×#121	2
C₉×#469	2
C₉×#468	2
C₉×#466	2
C₉×#465	2
C₉×#428	2
C₉×#418	2
C₉×#417	2
C₃×#3055	3

Subgroups — C9×#3055 #11767776

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3055 #11767776