Subgroups — C₂×C₉×#449 #11767721

Order 1152.

1218 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂³×C₉	C₂×D₄
commutator	C₂×C₄	C₂⁴×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂³×C₃	C₂×C₃×D₄
prime radical	C₂×C₃×#449	C₃
LCS	G ▷ C₂×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×#41	C₂	semidirect
2. C₂²×C₉×SD₁₆	C₂	semidirect
3. C₂²×C₉×D₈	C₂	semidirect
4. C₂×C₉×#121	C₂	semidirect
5. C₉×#449	C₂	direct (N × H)
6. C₂×C₉×#103	C₂	semidirect
7. C₂×C₉×#102	C₂	semidirect
8. C₂×C₉×C₂²⋊C₈	C₂	semidirect
13. C₂×C₉×#41	C₂²	semidirect
22. C₂×C₉×SD₁₆	C₂²	semidirect
24. C₂×C₉×D₈	C₂²	semidirect
28. C₉×#121	C₂²	semidirect
31. C₉×#103	C₂²	semidirect
32. C₉×#102	C₂²	semidirect
33. C₉×C₂²⋊C₈	C₂²	semidirect
50. C₂×Q₈×C₉	D₄	semidirect
61. C₂×D₄×C₉	D₄	semidirect
83. C₂×#449	C₉	direct (N × H)
123. Q₈×C₉	C₂×D₄	semidirect
131. D₄×C₉	C₂×D₄	semidirect
148. C₂²×#41	C₂×C₉	semidirect
149. C₂²×SD₁₆	C₂×C₉	semidirect
150. C₂²×D₈	C₂×C₉	semidirect
151. C₂×#121	C₂×C₉	semidirect
152. #449	C₂×C₉	direct (N × H)
153. C₂×#103	C₂×C₉	semidirect
154. C₂×#102	C₂×C₉	semidirect
155. C₂×C₂²⋊C₈	C₂×C₉	semidirect
222. C₂×#41	C₂²×C₉	semidirect
231. C₂×SD₁₆	C₂²×C₉	semidirect
233. C₂×D₈	C₂²×C₉	semidirect
237. #121	C₂²×C₉	semidirect
240. #103	C₂²×C₉	semidirect
241. #102	C₂²×C₉	semidirect
242. C₂²⋊C₈	C₂²×C₉	semidirect
286. C₂×C₉	#449	direct (N × H)
298. C₂×Q₈	D₄×C₉	semidirect
309. C₂×D₄	D₄×C₉	semidirect
353. C₉	C₂×#449	direct (N × H)
369. Q₈	C₂×D₄×C₉	semidirect
377. D₄	C₂×D₄×C₉	semidirect
427. C₂	C₉×#449	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₉×#41	2
C₂²×C₉×SD₁₆	2
C₂²×C₉×D₈	2
C₂×C₉×#121	2
C₉×#449	2
C₂×C₉×#103	2
C₂×C₉×#102	2
C₂×C₉×C₂²⋊C₈	2
C₂×C₃×#449	3

Subgroups — C2×C9×#449 #11767721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#449 #11767721