Subgroups — C₉×#2000 #11766721

Order 1152.

666 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×#121	C₂	1	1	yes	maximal, characteristic
4	C₂×C₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#340	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2000	C₃	1	1	yes	maximal, characteristic
9	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
10	C₂²×D₄×C₉	—	2	1	no	—
11	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
12	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
13	C₂×C₉×SD₁₆	—	2	2	no	—
14	C₂×C₉×SD₁₆	—	2	2	no	—
15	C₂×C₉×SD₁₆	—	2	2	no	—
16	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
17	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
18	C₉×C₂²⋊Q₈	—	2	2	no	—
19	C₉×C₂²⋊Q₈	—	2	2	no	—
20	C₉×#121	—	2	2	no	—
21	C₉×#121	—	2	2	no	—
22	C₂×C₉×C₄⋊C₄	—	2	1	no	—
23	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
26	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
27	C₉×#103	—	2	2	no	—
28	C₉×#102	—	2	2	no	—
29	C₉×C₂²⋊C₈	—	2	2	no	—
30	C₂²×C₃×SD₁₆	C₂×C₃	1	1	yes	characteristic
31	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
32	C₂×C₃×#121	C₂×C₃	1	1	yes	characteristic
33	C₂×C₃×#103	C₂×C₃	1	1	yes	characteristic
34	C₂×C₃×#102	C₂×C₃	1	1	yes	characteristic
35	C₂×C₃×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic
36	C₃×#340	C₂×C₃	1	1	yes	characteristic
37	C₂⁴×C₉	—	2	1	no	—
38	C₂⁴×C₉	D₄	1	1	yes	characteristic
39	C₂×Q₈×C₉	—	2	1	no	—
40	C₂×Q₈×C₉	—	2	1	no	—
41	C₂×Q₈×C₉	—	2	1	no	—
42	C₂×Q₈×C₉	—	2	1	no	—
43	C₂×Q₈×C₉	—	2	1	no	—
44	C₂×Q₈×C₉	D₄	1	2	yes	complemented
45	C₂×D₄×C₉	—	2	4	no	—
46	C₂×D₄×C₉	—	2	1	no	—
47	C₂×D₄×C₉	—	2	1	no	—
48	C₂×D₄×C₉	—	2	1	no	—
49	C₂×D₄×C₉	—	2	1	no	—
50	C₂×D₄×C₉	—	2	1	no	—
51	C₂×D₄×C₉	—	4	2	no	—
52	C₂×D₄×C₉	—	4	2	no	—
53	C₂×D₄×C₉	D₄	1	2	yes	—
54	C₂²×C₄×C₉	—	2	1	no	—
55	C₂²×C₄×C₉	—	2	1	no	—
56	C₂²×C₄×C₉	—	2	1	no	—
57	C₂²×C₄×C₉	—	2	1	no	—
58	C₂²×C₄×C₉	—	2	1	no	—
59	C₂²×C₄×C₉	—	2	1	no	—
60	C₂²×C₄×C₉	—	2	1	no	—
61	C₂²×C₄×C₉	—	2	1	no	—
62	C₂²×C₄×C₉	—	2	1	no	—
63	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
64	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
65	C₉×SD₁₆	—	2	8	no	—
66	C₂×C₈×C₉	—	2	1	no	—
67	C₂×C₈×C₉	—	2	1	no	—
68	C₂×C₈×C₉	—	2	1	no	—
69	C₂×C₈×C₉	—	2	1	no	—
70	C₂×C₈×C₉	—	2	1	no	—
71	C₂×C₈×C₉	D₄	1	2	yes	complemented
72	C₉×C₄⋊C₄	—	2	4	no	—
73	C₉×C₄⋊C₄	—	2	1	no	—
74	C₉×C₄⋊C₄	—	2	1	no	—
75	C₉×C₄⋊C₄	D₄	1	2	yes	—
76	C₉×C₄⋊C₄	D₄	1	2	yes	complemented
77	C₉×C₂²⋊C₄	—	2	4	no	—
78	C₉×C₂²⋊C₄	—	2	4	no	—
79	#2000	C₉	1	1	yes	characteristic, direct product factor, Sylow
80	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
81	C₂²×C₃×D₄	—	2	1	no	—
82	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
83	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₃×SD₁₆	—	2	2	no	—
85	C₂×C₃×SD₁₆	—	2	2	no	—
86	C₂×C₃×SD₁₆	—	2	2	no	—
87	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
88	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
89	C₃×C₂²⋊Q₈	—	2	2	no	—
90	C₃×C₂²⋊Q₈	—	2	2	no	—
91	C₃×#121	—	2	2	no	—
92	C₃×#121	—	2	2	no	—
93	C₂×C₃×C₄⋊C₄	—	2	1	no	—
94	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
98	C₃×#103	—	2	2	no	—
99	C₃×#102	—	2	2	no	—
100	C₃×C₂²⋊C₈	—	2	2	no	—
101	C₂³×C₉	—	2	1	no	—
102	C₂³×C₉	—	2	1	no	—
103	C₂³×C₉	—	2	1	no	—
104	C₂³×C₉	—	2	1	no	—
105	C₂³×C₉	—	2	1	no	—
106	C₂³×C₉	—	2	1	no	—
107	C₂³×C₉	—	2	2	no	—
108	C₂³×C₉	—	4	1	no	—
109	C₂³×C₉	—	4	1	no	—
110	C₂³×C₉	—	4	1	no	—
111	C₂³×C₉	—	4	1	no	—
112	C₂³×C₉	—	4	1	no	—
113	C₂³×C₉	—	4	1	no	—
114	C₂³×C₉	SD₁₆	1	2	yes	complemented
115	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
116	Q₈×C₉	—	2	2	no	—
117	Q₈×C₉	—	2	2	no	—
118	Q₈×C₉	—	4	1	no	—
119	Q₈×C₉	—	4	1	no	—
120	D₄×C₉	—	2	2	no	—
121	D₄×C₉	—	2	2	no	—
122	D₄×C₉	—	4	8	no	—
123	D₄×C₉	—	4	1	no	—
124	D₄×C₉	—	4	1	no	—
125	C₂×C₄×C₉	—	2	1	no	—
126	C₂×C₄×C₉	—	2	2	no	—
127	C₂×C₄×C₉	—	2	2	no	—
128	C₂×C₄×C₉	—	2	2	no	—
129	C₂×C₄×C₉	—	2	1	no	—
130	C₂×C₄×C₉	—	2	1	no	—
131	C₂×C₄×C₉	—	4	1	no	—
132	C₂×C₄×C₉	—	4	1	no	—
133	C₂×C₄×C₉	—	4	1	no	—
134	C₂×C₄×C₉	—	4	1	no	—
135	C₂×C₄×C₉	—	4	1	no	—
136	C₂×C₄×C₉	—	4	1	no	—
137	C₂×C₄×C₉	—	4	1	no	—
138	C₂×C₄×C₉	—	4	1	no	—
139	C₂×C₄×C₉	—	4	1	no	—
140	C₂×C₄×C₉	—	4	1	no	—
141	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
142	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
145	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
146	C₂×C₄×C₉	#41	1	1	yes	characteristic
147	C₈×C₉	—	2	2	no	—
148	C₈×C₉	—	4	1	no	—
149	C₂²×SD₁₆	C₂×C₉	1	1	yes	characteristic, complemented
150	C₂×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
151	C₂×#121	C₂×C₉	1	1	yes	characteristic
152	C₂×#103	C₂×C₉	1	1	yes	characteristic, complemented
153	C₂×#102	C₂×C₉	1	1	yes	characteristic, complemented
154	C₂×C₂²⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
155	#340	C₂×C₉	1	1	yes	characteristic, complemented
156	C₂⁴×C₃	—	2	1	no	—
157	C₂⁴×C₃	C₃×D₄	1	1	yes	characteristic
158	C₂×C₃×Q₈	—	2	1	no	—
159	C₂×C₃×Q₈	—	2	1	no	—
160	C₂×C₃×Q₈	—	2	1	no	—
161	C₂×C₃×Q₈	—	2	1	no	—
162	C₂×C₃×Q₈	—	2	1	no	—
163	C₂×C₃×Q₈	C₃×D₄	1	2	yes	—
164	C₂×C₃×D₄	—	2	4	no	—
165	C₂×C₃×D₄	—	2	1	no	—
166	C₂×C₃×D₄	—	2	1	no	—
167	C₂×C₃×D₄	—	2	1	no	—
168	C₂×C₃×D₄	—	2	1	no	—
169	C₂×C₃×D₄	—	2	1	no	—
170	C₂×C₃×D₄	—	4	2	no	—
171	C₂×C₃×D₄	—	4	2	no	—
172	C₂×C₃×D₄	C₃×D₄	1	2	yes	—
173	C₂²×C₃×C₄	—	2	1	no	—
174	C₂²×C₃×C₄	—	2	1	no	—
175	C₂²×C₃×C₄	—	2	1	no	—
176	C₂²×C₃×C₄	—	2	1	no	—
177	C₂²×C₃×C₄	—	2	1	no	—
178	C₂²×C₃×C₄	—	2	1	no	—
179	C₂²×C₃×C₄	—	2	1	no	—
180	C₂²×C₃×C₄	—	2	1	no	—
181	C₂²×C₃×C₄	—	2	1	no	—
182	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
184	C₃×SD₁₆	—	2	8	no	—
185	C₂×C₃×C₈	—	2	1	no	—
186	C₂×C₃×C₈	—	2	1	no	—
187	C₂×C₃×C₈	—	2	1	no	—
188	C₂×C₃×C₈	—	2	1	no	—
189	C₂×C₃×C₈	—	2	1	no	—
190	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
191	C₃×C₄⋊C₄	—	2	4	no	—
192	C₃×C₄⋊C₄	—	2	1	no	—
193	C₃×C₄⋊C₄	—	2	1	no	—
194	C₃×C₄⋊C₄	C₃×D₄	1	2	yes	—
195	C₃×C₄⋊C₄	C₃×D₄	1	2	yes	—
196	C₃×C₂²⋊C₄	—	2	4	no	—
197	C₃×C₂²⋊C₄	—	2	4	no	—
198	C₂²×C₉	—	2	2	no	—
199	C₂²×C₉	—	2	2	no	—
200	C₂²×C₉	—	2	2	no	—
201	C₂²×C₉	—	4	1	no	—
202	C₂²×C₉	—	4	1	no	—
203	C₂²×C₉	—	4	1	no	—
204	C₂²×C₉	—	4	1	no	—
205	C₂²×C₉	—	4	2	no	—
206	C₂²×C₉	—	4	2	no	—
207	C₂²×C₉	—	4	2	no	—
208	C₂²×C₉	—	8	1	no	—
209	C₂²×C₉	—	8	1	no	—
210	C₂²×C₉	—	8	1	no	—
211	C₂²×C₉	—	8	1	no	—
212	C₂²×C₉	#120	1	1	yes	characteristic
213	C₂²×C₉	#120	1	1	yes	characteristic
214	C₂²×C₉	#121	1	1	yes	characteristic
215	C₂²×C₉	C₂×SD₁₆	1	1	yes	characteristic
216	C₂²×C₉	#135	1	1	yes	characteristic
217	C₂²×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
218	C₂²×C₉	#137	1	1	yes	characteristic
219	C₄×C₉	—	4	1	no	—
220	C₄×C₉	—	4	2	no	—
221	C₄×C₉	—	4	2	no	—
222	C₄×C₉	—	4	2	no	—
223	C₄×C₉	#120	1	1	yes	characteristic
224	C₄×C₉	#121	1	1	yes	characteristic
225	C₄×C₉	#121	1	1	yes	characteristic
226	C₄×C₉	#127	1	1	yes	characteristic
227	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
228	C₂²×D₄	—	2	1	no	—
229	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
230	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
231	C₂×SD₁₆	—	2	2	no	—
232	C₂×SD₁₆	—	2	2	no	—
233	C₂×SD₁₆	—	2	2	no	—
234	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
235	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
236	C₂²⋊Q₈	—	2	2	no	—
237	C₂²⋊Q₈	—	2	2	no	—
238	#121	—	2	2	no	—
239	#121	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
243	C₂×C₂²⋊C₄	—	2	1	no	—
244	C₂×C₂²⋊C₄	—	2	1	no	—
245	#103	—	2	2	no	—
246	#102	—	2	2	no	—
247	C₂²⋊C₈	—	2	2	no	—
248	C₂³×C₃	—	2	1	no	—
249	C₂³×C₃	—	2	1	no	—
250	C₂³×C₃	—	2	1	no	—
251	C₂³×C₃	—	2	1	no	—
252	C₂³×C₃	—	2	1	no	—
253	C₂³×C₃	—	2	1	no	—
254	C₂³×C₃	—	2	2	no	—
255	C₂³×C₃	—	4	1	no	—
256	C₂³×C₃	—	4	1	no	—
257	C₂³×C₃	—	4	1	no	—
258	C₂³×C₃	—	4	1	no	—
259	C₂³×C₃	—	4	1	no	—
260	C₂³×C₃	—	4	1	no	—
261	C₂³×C₃	C₃×SD₁₆	1	2	yes	—
262	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
263	C₃×Q₈	—	2	2	no	—
264	C₃×Q₈	—	2	2	no	—
265	C₃×Q₈	—	4	1	no	—
266	C₃×Q₈	—	4	1	no	—
267	C₃×D₄	—	2	2	no	—
268	C₃×D₄	—	2	2	no	—
269	C₃×D₄	—	4	8	no	—
270	C₃×D₄	—	4	1	no	—
271	C₃×D₄	—	4	1	no	—
272	C₂×C₃×C₄	—	2	1	no	—
273	C₂×C₃×C₄	—	2	2	no	—
274	C₂×C₃×C₄	—	2	2	no	—
275	C₂×C₃×C₄	—	2	2	no	—
276	C₂×C₃×C₄	—	2	1	no	—
277	C₂×C₃×C₄	—	2	1	no	—
278	C₂×C₃×C₄	—	4	1	no	—
279	C₂×C₃×C₄	—	4	1	no	—
280	C₂×C₃×C₄	—	4	1	no	—
281	C₂×C₃×C₄	—	4	1	no	—
282	C₂×C₃×C₄	—	4	1	no	—
283	C₂×C₃×C₄	—	4	1	no	—
284	C₂×C₃×C₄	—	4	1	no	—
285	C₂×C₃×C₄	—	4	1	no	—
286	C₂×C₃×C₄	—	4	1	no	—
287	C₂×C₃×C₄	—	4	1	no	—
288	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
290	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
291	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
292	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
293	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
294	C₃×C₈	—	2	2	no	—
295	C₃×C₈	—	4	1	no	—
296	C₂×C₉	—	4	2	no	—
297	C₂×C₉	—	8	2	no	—
298	C₂×C₉	#392	1	1	yes	characteristic
299	C₂×C₉	#448	1	1	yes	characteristic
300	C₂×C₉	#449	1	1	yes	characteristic
301	C₂×C₉	#450	1	1	yes	characteristic
302	C₂×C₉	#452	1	1	yes	characteristic
303	C₂×C₉	#465	1	1	yes	characteristic
304	C₂×C₉	#468	1	1	yes	characteristic
305	C₂⁴	—	2	1	no	—
306	C₂⁴	D₄×C₉	1	1	yes	characteristic
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	D₄×C₉	1	2	yes	complemented
313	C₂×D₄	—	2	4	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	4	2	no	—
320	C₂×D₄	—	4	2	no	—
321	C₂×D₄	D₄×C₉	1	2	yes	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
332	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
333	SD₁₆	—	2	8	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	D₄×C₉	1	2	yes	complemented
340	C₄⋊C₄	—	2	4	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	D₄×C₉	1	2	yes	—
344	C₄⋊C₄	D₄×C₉	1	2	yes	complemented
345	C₂²⋊C₄	—	2	4	no	—
346	C₂²⋊C₄	—	2	4	no	—
347	C₂²×C₃	—	2	2	no	—
348	C₂²×C₃	—	2	2	no	—
349	C₂²×C₃	—	2	2	no	—
350	C₂²×C₃	—	4	1	no	—
351	C₂²×C₃	—	4	1	no	—
352	C₂²×C₃	—	4	1	no	—
353	C₂²×C₃	—	4	1	no	—
354	C₂²×C₃	—	4	2	no	—
355	C₂²×C₃	—	4	2	no	—
356	C₂²×C₃	—	4	2	no	—
357	C₂²×C₃	—	8	1	no	—
358	C₂²×C₃	—	8	1	no	—
359	C₂²×C₃	—	8	1	no	—
360	C₂²×C₃	—	8	1	no	—
361	C₂²×C₃	C₃×#120	1	1	yes	characteristic
362	C₂²×C₃	C₃×#120	1	1	yes	characteristic
363	C₂²×C₃	C₃×#121	1	1	yes	characteristic
364	C₂²×C₃	C₂×C₃×SD₁₆	1	1	yes	characteristic
365	C₂²×C₃	C₃×#135	1	1	yes	characteristic
366	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
367	C₂²×C₃	C₃×#137	1	1	yes	characteristic
368	C₃×C₄	—	4	1	no	—
369	C₃×C₄	—	4	2	no	—
370	C₃×C₄	—	4	2	no	—
371	C₃×C₄	—	4	2	no	—
372	C₃×C₄	C₃×#120	1	1	yes	characteristic
373	C₃×C₄	C₃×#121	1	1	yes	characteristic
374	C₃×C₄	C₃×#121	1	1	yes	characteristic
375	C₃×C₄	C₃×#127	1	1	yes	characteristic
376	C₉	#2000	1	1	yes	characteristic, direct product factor, Sylow
377	C₂³	—	2	1	no	—
378	C₂³	—	2	1	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	1	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	4	1	no	—
385	C₂³	—	4	1	no	—
386	C₂³	—	4	1	no	—
387	C₂³	—	4	1	no	—
388	C₂³	—	4	1	no	—
389	C₂³	—	4	1	no	—
390	C₂³	C₉×SD₁₆	1	2	yes	complemented
391	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
392	Q₈	—	2	2	no	—
393	Q₈	—	2	2	no	—
394	Q₈	—	4	1	no	—
395	Q₈	—	4	1	no	—
396	D₄	—	2	2	no	—
397	D₄	—	2	2	no	—
398	D₄	—	4	8	no	—
399	D₄	—	4	1	no	—
400	D₄	—	4	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
418	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
419	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
420	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
421	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
422	C₂×C₄	C₉×#41	1	1	yes	characteristic
423	C₈	—	2	2	no	—
424	C₈	—	4	1	no	—
425	C₂×C₃	—	4	2	no	—
426	C₂×C₃	—	8	2	no	—
427	C₂×C₃	C₃×#392	1	1	yes	characteristic
428	C₂×C₃	C₃×#448	1	1	yes	characteristic
429	C₂×C₃	C₃×#449	1	1	yes	characteristic
430	C₂×C₃	C₃×#450	1	1	yes	characteristic
431	C₂×C₃	C₃×#452	1	1	yes	characteristic
432	C₂×C₃	C₃×#465	1	1	yes	characteristic
433	C₂×C₃	C₃×#468	1	1	yes	characteristic
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	8	1	no	—
445	C₂²	—	8	1	no	—
446	C₂²	—	8	1	no	—
447	C₂²	—	8	1	no	—
448	C₂²	C₉×#120	1	1	yes	characteristic
449	C₂²	C₉×#120	1	1	yes	characteristic
450	C₂²	C₉×#121	1	1	yes	characteristic
451	C₂²	C₂×C₉×SD₁₆	1	1	yes	characteristic
452	C₂²	C₉×#135	1	1	yes	characteristic
453	C₂²	C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
454	C₂²	C₉×#137	1	1	yes	characteristic
455	C₄	—	4	1	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	2	no	—
459	C₄	C₉×#120	1	1	yes	characteristic
460	C₄	C₉×#121	1	1	yes	characteristic
461	C₄	C₉×#121	1	1	yes	characteristic
462	C₄	C₉×#127	1	1	yes	characteristic
463	C₃	C₃×#2000	1	1	yes	characteristic
464	C₂	—	4	2	no	—
465	C₂	—	8	2	no	—
466	C₂	C₉×#392	1	1	yes	characteristic
467	C₂	C₉×#448	1	1	yes	characteristic
468	C₂	C₉×#449	1	1	yes	characteristic
469	C₂	C₉×#450	1	1	yes	characteristic
470	C₂	C₉×#452	1	1	yes	characteristic
471	C₂	C₉×#465	1	1	yes	characteristic
472	C₂	C₉×#468	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂×D₄
commutator	C₂²×C₄	C₂³×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle	C₂³×C₃	C₂×C₃×D₄
prime radical	C₂×C₃×#121	C₂×C₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ C₂³×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₉×SD₁₆	C₂	semidirect
2. C₂×C₉×C₂²⋊Q₈	C₂	semidirect
4. C₂×C₉×#103	C₂	semidirect
5. C₂×C₉×#102	C₂	semidirect
6. C₂×C₉×C₂²⋊C₈	C₂	semidirect
7. C₉×#340	C₂	semidirect
44. C₂×Q₈×C₉	D₄	semidirect
71. C₂×C₈×C₉	D₄	semidirect
76. C₉×C₄⋊C₄	D₄	semidirect
79. #2000	C₉	direct (N × H)
114. C₂³×C₉	SD₁₆	semidirect
149. C₂²×SD₁₆	C₂×C₉	semidirect
150. C₂×C₂²⋊Q₈	C₂×C₉	semidirect
152. C₂×#103	C₂×C₉	semidirect
153. C₂×#102	C₂×C₉	semidirect
154. C₂×C₂²⋊C₈	C₂×C₉	semidirect
155. #340	C₂×C₉	semidirect
312. C₂×Q₈	D₄×C₉	semidirect
339. C₂×C₈	D₄×C₉	semidirect
344. C₄⋊C₄	D₄×C₉	semidirect
376. C₉	#2000	direct (N × H)
390. C₂³	C₉×SD₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₉×SD₁₆	2
C₂×C₉×C₂²⋊Q₈	2
C₂×C₉×#121	2
C₂×C₉×#103	2
C₂×C₉×#102	2
C₂×C₉×C₂²⋊C₈	2
C₉×#340	2
C₃×#2000	3

Subgroups — C9×#2000 #11766721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2000 #11766721