Subgroups — C₉×#3484 #11768205

Order 1152.

2850 conjugacy classes of subgroups.

The subgroup lattice has 435 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#546	C₂	1	8	yes	maximal, complemented
4	D₄²×C₉	C₂	1	8	yes	maximal, complemented
5	C₉×#535	C₂	1	2	yes	maximal, complemented
6	C₉×#534	C₂	1	4	yes	maximal, complemented
7	C₉×#525	C₂	1	2	yes	maximal, complemented
8	C₂×C₉×#120	C₂	1	4	yes	maximal, complemented
9	C₉×#518	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3484	C₃	1	1	yes	maximal, characteristic
11	C₂⁵×C₉	C₂²	1	2	yes	complemented
12	C₉×H(5,𝔽₂)	—	2	8	no	—
13	C₂×C₉×#41	C₂²	1	2	yes	complemented
14	C₂×C₉×#41	C₂²	1	4	yes	complemented
15	C₂²×D₄×C₉	—	2	8	no	—
16	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₉	C₂²	1	2	yes	complemented
18	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₄×C₉	C₂²	1	8	yes	complemented
20	C₂²×D₄×C₉	C₂²	1	4	yes	complemented
21	C₂²×D₄×C₉	C₂²	1	4	yes	complemented
22	C₂²×D₄×C₉	C₂²	1	8	yes	complemented
23	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic, complemented
24	C₉×#127	C₂²	1	4	yes	complemented
25	C₉×#124	C₂²	1	4	yes	complemented
26	C₉×#123	C₂²	1	4	yes	complemented
27	C₉×#123	C₂²	1	8	yes	complemented
28	C₉×C₂²⋊Q₈	C₂²	1	4	yes	complemented
29	C₉×#121	C₂²	1	4	yes	complemented
30	C₉×#121	C₂²	1	16	yes	complemented
31	C₉×#121	C₂²	1	8	yes	complemented
32	C₉×#120	C₂²	1	4	yes	complemented
33	C₉×#120	C₂²	1	8	yes	complemented
34	C₉×#120	C₂²	1	16	yes	complemented
35	C₉×#120	C₂²	1	8	yes	complemented
36	C₄×D₄×C₉	C₂²	1	8	yes	complemented
37	C₄×D₄×C₉	C₂²	1	8	yes	complemented
38	C₉×#117	C₂²	1	2	yes	complemented
39	C₂×C₉×C₂²⋊C₄	C₂²	1	4	yes	complemented
40	C₂×C₉×C₂²⋊C₄	C₂²	1	8	yes	complemented
41	C₂×C₃×H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic
42	C₂³×C₃×D₄	C₂×C₃	1	1	yes	characteristic
43	C₃×#546	C₂×C₃	1	8	yes	—
44	C₃×D₄²	C₂×C₃	1	8	yes	—
45	C₃×#535	C₂×C₃	1	2	yes	—
46	C₃×#534	C₂×C₃	1	4	yes	—
47	C₃×#525	C₂×C₃	1	2	yes	—
48	C₂×C₃×#120	C₂×C₃	1	4	yes	—
49	C₃×#518	C₂×C₃	1	1	yes	characteristic
50	C₂⁴×C₉	—	2	8	no	—
51	C₂⁴×C₉	—	4	8	no	—
52	C₂⁴×C₉	C₂³	1	1	yes	characteristic
53	C₂⁴×C₉	C₂³	1	8	yes	—
54	C₂⁴×C₉	C₂³	1	2	yes	—
55	C₂⁴×C₉	C₂³	1	2	yes	—
56	C₂⁴×C₉	C₂³	1	4	yes	complemented
57	C₉×#41	—	2	16	no	—
58	C₉×#41	—	2	8	no	—
59	C₂×Q₈×C₉	C₂³	1	2	yes	complemented
60	C₂×D₄×C₉	—	2	8	no	—
61	C₂×D₄×C₉	—	2	16	no	—
62	C₂×D₄×C₉	—	2	32	no	—
63	C₂×D₄×C₉	—	2	16	no	—
64	C₂×D₄×C₉	—	2	4	no	—
65	C₂×D₄×C₉	—	4	16	no	—
66	C₂×D₄×C₉	D₄	1	8	yes	complemented
67	C₂×D₄×C₉	C₂³	1	8	yes	—
68	C₂×D₄×C₉	C₂³	1	4	yes	—
69	C₂×D₄×C₉	C₂³	1	8	yes	—
70	C₂×D₄×C₉	C₂³	1	4	yes	—
71	C₂×D₄×C₉	C₂³	1	4	yes	—
72	C₂×D₄×C₉	C₂³	1	8	yes	complemented
73	C₂×D₄×C₉	C₂³	1	2	yes	complemented
74	C₂×D₄×C₉	C₂³	1	16	yes	complemented
75	C₂²×C₄×C₉	—	2	4	no	—
76	C₂²×C₄×C₉	C₂³	1	4	yes	—
77	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₉	C₂³	1	4	yes	complemented
80	C₂²×C₄×C₉	C₂³	1	4	yes	complemented
81	C₂²×C₄×C₉	C₂³	1	8	yes	complemented
82	C₉×C₄⋊C₄	C₂³	1	4	yes	complemented
83	C₉×C₄⋊C₄	C₂³	1	8	yes	complemented
84	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
85	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
86	C₉×C₂²⋊C₄	C₂³	1	8	yes	complemented
87	C₉×C₂²⋊C₄	C₂³	1	16	yes	complemented
88	C₉×C₂²⋊C₄	C₂³	1	8	yes	complemented
89	C₄²×C₉	C₂³	1	4	yes	complemented
90	#3484	C₉	1	1	yes	characteristic, direct product factor, Sylow
91	C₂⁵×C₃	C₂²×C₃	1	2	yes	—
92	C₃×H(5,𝔽₂)	—	2	8	no	—
93	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
94	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
95	C₂²×C₃×D₄	—	2	8	no	—
96	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
97	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
98	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
99	C₂²×C₃×D₄	C₂²×C₃	1	8	yes	—
100	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
101	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
102	C₂²×C₃×D₄	C₂²×C₃	1	8	yes	—
103	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
104	C₃×#127	C₂²×C₃	1	4	yes	—
105	C₃×#124	C₂²×C₃	1	4	yes	—
106	C₃×#123	C₂²×C₃	1	4	yes	—
107	C₃×#123	C₂²×C₃	1	8	yes	—
108	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
109	C₃×#121	C₂²×C₃	1	4	yes	—
110	C₃×#121	C₂²×C₃	1	16	yes	—
111	C₃×#121	C₂²×C₃	1	8	yes	—
112	C₃×#120	C₂²×C₃	1	4	yes	—
113	C₃×#120	C₂²×C₃	1	8	yes	—
114	C₃×#120	C₂²×C₃	1	16	yes	—
115	C₃×#120	C₂²×C₃	1	8	yes	—
116	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
117	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
118	C₃×#117	C₂²×C₃	1	2	yes	—
119	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
120	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
121	C₂³×C₉	—	2	2	no	—
122	C₂³×C₉	—	2	4	no	—
123	C₂³×C₉	—	2	16	no	—
124	C₂³×C₉	—	2	4	no	—
125	C₂³×C₉	—	2	16	no	—
126	C₂³×C₉	—	2	8	no	—
127	C₂³×C₉	—	4	4	no	—
128	C₂³×C₉	—	4	8	no	—
129	C₂³×C₉	—	4	4	no	—
130	C₂³×C₉	—	4	8	no	—
131	C₂³×C₉	—	4	32	no	—
132	C₂³×C₉	C₂×D₄	1	8	yes	complemented
133	C₂³×C₉	C₂⁴	1	4	yes	—
134	C₂³×C₉	C₂⁴	1	4	yes	—
135	C₂³×C₉	C₂⁴	1	1	yes	characteristic
136	C₂³×C₉	C₂⁴	1	4	yes	—
137	C₂³×C₉	C₂⁴	1	2	yes	—
138	Q₈×C₉	—	2	4	no	—
139	D₄×C₉	—	2	16	no	—
140	D₄×C₉	—	2	8	no	—
141	D₄×C₉	—	2	16	no	—
142	D₄×C₉	—	2	16	no	—
143	D₄×C₉	—	2	8	no	—
144	D₄×C₉	—	2	4	no	—
145	D₄×C₉	—	4	16	no	—
146	D₄×C₉	C₂×D₄	1	16	yes	complemented
147	C₂×C₄×C₉	—	2	2	no	—
148	C₂×C₄×C₉	—	2	8	no	—
149	C₂×C₄×C₉	—	2	8	no	—
150	C₂×C₄×C₉	—	2	8	no	—
151	C₂×C₄×C₉	—	4	8	no	—
152	C₂×C₄×C₉	C₂×D₄	1	4	yes	complemented
153	C₂×C₄×C₉	C₂⁴	1	8	yes	—
154	C₂×C₄×C₉	C₂⁴	1	4	yes	—
155	C₂×C₄×C₉	C₂⁴	1	2	yes	—
156	C₂×C₄×C₉	C₂⁴	1	2	yes	—
157	C₂×H(5,𝔽₂)	C₂×C₉	1	1	yes	characteristic, complemented
158	C₂³×D₄	C₂×C₉	1	1	yes	characteristic, complemented
159	#546	C₂×C₉	1	8	yes	complemented
160	D₄²	C₂×C₉	1	8	yes	complemented
161	#535	C₂×C₉	1	2	yes	complemented
162	#534	C₂×C₉	1	4	yes	complemented
163	#525	C₂×C₉	1	2	yes	complemented
164	C₂×#120	C₂×C₉	1	4	yes	complemented
165	#518	C₂×C₉	1	1	yes	characteristic, complemented
166	C₂⁴×C₃	—	2	8	no	—
167	C₂⁴×C₃	—	4	8	no	—
168	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
169	C₂⁴×C₃	C₂³×C₃	1	8	yes	—
170	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
171	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
172	C₂⁴×C₃	C₂³×C₃	1	4	yes	—
173	C₃×#41	—	2	16	no	—
174	C₃×#41	—	2	8	no	—
175	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
176	C₂×C₃×D₄	—	2	8	no	—
177	C₂×C₃×D₄	—	2	16	no	—
178	C₂×C₃×D₄	—	2	32	no	—
179	C₂×C₃×D₄	—	2	16	no	—
180	C₂×C₃×D₄	—	2	4	no	—
181	C₂×C₃×D₄	—	4	16	no	—
182	C₂×C₃×D₄	C₃×D₄	1	8	yes	—
183	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
184	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
185	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
186	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
187	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
188	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
189	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
190	C₂×C₃×D₄	C₂³×C₃	1	16	yes	—
191	C₂²×C₃×C₄	—	2	4	no	—
192	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
193	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
194	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
195	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
196	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
197	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
198	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
199	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
200	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
201	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
202	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
203	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
204	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
205	C₃×C₄²	C₂³×C₃	1	4	yes	—
206	C₂²×C₉	—	2	8	no	—
207	C₂²×C₉	—	2	2	no	—
208	C₂²×C₉	—	2	8	no	—
209	C₂²×C₉	—	2	2	no	—
210	C₂²×C₉	—	2	2	no	—
211	C₂²×C₉	—	2	4	no	—
212	C₂²×C₉	—	2	4	no	—
213	C₂²×C₉	—	2	8	no	—
214	C₂²×C₉	—	2	8	no	—
215	C₂²×C₉	—	4	8	no	—
216	C₂²×C₉	—	4	32	no	—
217	C₂²×C₉	—	4	8	no	—
218	C₂²×C₉	—	8	8	no	—
219	C₂²×C₉	C₂²×D₄	1	2	yes	—
220	C₂²×C₉	C₂²×D₄	1	8	yes	—
221	C₂²×C₉	H(5,𝔽₂)	1	4	yes	complemented
222	C₂²×C₉	C₂⁵	1	1	yes	characteristic
223	C₄×C₉	—	2	2	no	—
224	C₄×C₉	—	2	4	no	—
225	C₄×C₉	—	2	8	no	—
226	C₄×C₉	C₂²×D₄	1	4	yes	—
227	C₂⁵	C₂²×C₉	1	2	yes	complemented
228	H(5,𝔽₂)	—	2	8	no	—
229	C₂×#41	C₂²×C₉	1	2	yes	complemented
230	C₂×#41	C₂²×C₉	1	4	yes	complemented
231	C₂²×D₄	—	2	8	no	—
232	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
233	C₂²×D₄	C₂²×C₉	1	2	yes	complemented
234	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic, complemented
235	C₂²×D₄	C₂²×C₉	1	8	yes	complemented
236	C₂²×D₄	C₂²×C₉	1	4	yes	complemented
237	C₂²×D₄	C₂²×C₉	1	4	yes	complemented
238	C₂²×D₄	C₂²×C₉	1	8	yes	complemented
239	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic, complemented
240	#127	C₂²×C₉	1	4	yes	complemented
241	#124	C₂²×C₉	1	4	yes	complemented
242	#123	C₂²×C₉	1	4	yes	complemented
243	#123	C₂²×C₉	1	8	yes	complemented
244	C₂²⋊Q₈	C₂²×C₉	1	4	yes	complemented
245	#121	C₂²×C₉	1	4	yes	complemented
246	#121	C₂²×C₉	1	16	yes	complemented
247	#121	C₂²×C₉	1	8	yes	complemented
248	#120	C₂²×C₉	1	4	yes	complemented
249	#120	C₂²×C₉	1	8	yes	complemented
250	#120	C₂²×C₉	1	16	yes	complemented
251	#120	C₂²×C₉	1	8	yes	complemented
252	C₄×D₄	C₂²×C₉	1	8	yes	complemented
253	C₄×D₄	C₂²×C₉	1	8	yes	complemented
254	#117	C₂²×C₉	1	2	yes	complemented
255	C₂×C₂²⋊C₄	C₂²×C₉	1	4	yes	complemented
256	C₂×C₂²⋊C₄	C₂²×C₉	1	8	yes	complemented
257	C₂³×C₃	—	2	2	no	—
258	C₂³×C₃	—	2	4	no	—
259	C₂³×C₃	—	2	16	no	—
260	C₂³×C₃	—	2	4	no	—
261	C₂³×C₃	—	2	16	no	—
262	C₂³×C₃	—	2	8	no	—
263	C₂³×C₃	—	4	4	no	—
264	C₂³×C₃	—	4	8	no	—
265	C₂³×C₃	—	4	4	no	—
266	C₂³×C₃	—	4	8	no	—
267	C₂³×C₃	—	4	32	no	—
268	C₂³×C₃	C₂×C₃×D₄	1	8	yes	—
269	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
270	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
271	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
272	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
273	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
274	C₃×Q₈	—	2	4	no	—
275	C₃×D₄	—	2	16	no	—
276	C₃×D₄	—	2	8	no	—
277	C₃×D₄	—	2	16	no	—
278	C₃×D₄	—	2	16	no	—
279	C₃×D₄	—	2	8	no	—
280	C₃×D₄	—	2	4	no	—
281	C₃×D₄	—	4	16	no	—
282	C₃×D₄	C₂×C₃×D₄	1	16	yes	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	—	2	8	no	—
285	C₂×C₃×C₄	—	2	8	no	—
286	C₂×C₃×C₄	—	2	8	no	—
287	C₂×C₃×C₄	—	4	8	no	—
288	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
289	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
290	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
291	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
292	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
293	C₂×C₉	—	2	2	no	—
294	C₂×C₉	—	2	4	no	—
295	C₂×C₉	—	2	8	no	—
296	C₂×C₉	—	4	4	no	—
297	C₂×C₉	—	4	4	no	—
298	C₂×C₉	C₂³×D₄	1	1	yes	characteristic
299	C₂×C₉	C₂×H(5,𝔽₂)	1	2	yes	—
300	C₂⁴	—	2	8	no	—
301	C₂⁴	—	4	8	no	—
302	C₂⁴	C₂³×C₉	1	1	yes	characteristic
303	C₂⁴	C₂³×C₉	1	8	yes	—
304	C₂⁴	C₂³×C₉	1	2	yes	—
305	C₂⁴	C₂³×C₉	1	2	yes	—
306	C₂⁴	C₂³×C₉	1	4	yes	complemented
307	#41	—	2	16	no	—
308	#41	—	2	8	no	—
309	C₂×Q₈	C₂³×C₉	1	2	yes	complemented
310	C₂×D₄	—	2	8	no	—
311	C₂×D₄	—	2	16	no	—
312	C₂×D₄	—	2	32	no	—
313	C₂×D₄	—	2	16	no	—
314	C₂×D₄	—	2	4	no	—
315	C₂×D₄	—	4	16	no	—
316	C₂×D₄	D₄×C₉	1	8	yes	complemented
317	C₂×D₄	C₂³×C₉	1	8	yes	—
318	C₂×D₄	C₂³×C₉	1	4	yes	—
319	C₂×D₄	C₂³×C₉	1	8	yes	—
320	C₂×D₄	C₂³×C₉	1	4	yes	—
321	C₂×D₄	C₂³×C₉	1	4	yes	—
322	C₂×D₄	C₂³×C₉	1	8	yes	complemented
323	C₂×D₄	C₂³×C₉	1	2	yes	complemented
324	C₂×D₄	C₂³×C₉	1	16	yes	complemented
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	C₂³×C₉	1	4	yes	—
327	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
328	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
329	C₂²×C₄	C₂³×C₉	1	4	yes	complemented
330	C₂²×C₄	C₂³×C₉	1	4	yes	complemented
331	C₂²×C₄	C₂³×C₉	1	8	yes	complemented
332	C₄⋊C₄	C₂³×C₉	1	4	yes	complemented
333	C₄⋊C₄	C₂³×C₉	1	8	yes	complemented
334	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
335	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
336	C₂²⋊C₄	C₂³×C₉	1	8	yes	complemented
337	C₂²⋊C₄	C₂³×C₉	1	16	yes	complemented
338	C₂²⋊C₄	C₂³×C₉	1	8	yes	complemented
339	C₄²	C₂³×C₉	1	4	yes	complemented
340	C₂²×C₃	—	2	8	no	—
341	C₂²×C₃	—	2	2	no	—
342	C₂²×C₃	—	2	8	no	—
343	C₂²×C₃	—	2	2	no	—
344	C₂²×C₃	—	2	2	no	—
345	C₂²×C₃	—	2	4	no	—
346	C₂²×C₃	—	2	4	no	—
347	C₂²×C₃	—	2	8	no	—
348	C₂²×C₃	—	2	8	no	—
349	C₂²×C₃	—	4	8	no	—
350	C₂²×C₃	—	4	32	no	—
351	C₂²×C₃	—	4	8	no	—
352	C₂²×C₃	—	8	8	no	—
353	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
354	C₂²×C₃	C₂²×C₃×D₄	1	8	yes	—
355	C₂²×C₃	C₃×H(5,𝔽₂)	1	4	yes	—
356	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
357	C₃×C₄	—	2	2	no	—
358	C₃×C₄	—	2	4	no	—
359	C₃×C₄	—	2	8	no	—
360	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
361	C₉	#3484	1	1	yes	characteristic, direct product factor, Sylow
362	C₂³	—	2	2	no	—
363	C₂³	—	2	4	no	—
364	C₂³	—	2	16	no	—
365	C₂³	—	2	4	no	—
366	C₂³	—	2	16	no	—
367	C₂³	—	2	8	no	—
368	C₂³	—	4	4	no	—
369	C₂³	—	4	8	no	—
370	C₂³	—	4	4	no	—
371	C₂³	—	4	8	no	—
372	C₂³	—	4	32	no	—
373	C₂³	C₂×D₄×C₉	1	8	yes	complemented
374	C₂³	C₂⁴×C₉	1	4	yes	—
375	C₂³	C₂⁴×C₉	1	4	yes	—
376	C₂³	C₂⁴×C₉	1	1	yes	characteristic
377	C₂³	C₂⁴×C₉	1	4	yes	—
378	C₂³	C₂⁴×C₉	1	2	yes	—
379	Q₈	—	2	4	no	—
380	D₄	—	2	16	no	—
381	D₄	—	2	8	no	—
382	D₄	—	2	16	no	—
383	D₄	—	2	16	no	—
384	D₄	—	2	8	no	—
385	D₄	—	2	4	no	—
386	D₄	—	4	16	no	—
387	D₄	C₂×D₄×C₉	1	16	yes	complemented
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	8	no	—
390	C₂×C₄	—	2	8	no	—
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	4	8	no	—
393	C₂×C₄	C₂×D₄×C₉	1	4	yes	complemented
394	C₂×C₄	C₂⁴×C₉	1	8	yes	—
395	C₂×C₄	C₂⁴×C₉	1	4	yes	—
396	C₂×C₄	C₂⁴×C₉	1	2	yes	—
397	C₂×C₄	C₂⁴×C₉	1	2	yes	—
398	C₂×C₃	—	2	2	no	—
399	C₂×C₃	—	2	4	no	—
400	C₂×C₃	—	2	8	no	—
401	C₂×C₃	—	4	4	no	—
402	C₂×C₃	—	4	4	no	—
403	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
404	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
405	C₂²	—	2	8	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	8	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	4	no	—
411	C₂²	—	2	4	no	—
412	C₂²	—	2	8	no	—
413	C₂²	—	2	8	no	—
414	C₂²	—	4	8	no	—
415	C₂²	—	4	32	no	—
416	C₂²	—	4	8	no	—
417	C₂²	—	8	8	no	—
418	C₂²	C₂²×D₄×C₉	1	2	yes	—
419	C₂²	C₂²×D₄×C₉	1	8	yes	—
420	C₂²	C₉×H(5,𝔽₂)	1	4	yes	complemented
421	C₂²	C₂⁵×C₉	1	1	yes	characteristic
422	C₄	—	2	2	no	—
423	C₄	—	2	4	no	—
424	C₄	—	2	8	no	—
425	C₄	C₂²×D₄×C₉	1	4	yes	—
426	C₃	C₃×#3484	1	1	yes	characteristic
427	C₂	—	2	2	no	—
428	C₂	—	2	4	no	—
429	C₂	—	2	8	no	—
430	C₂	—	4	4	no	—
431	C₂	—	4	4	no	—
432	C₂	C₂³×D₄×C₉	1	1	yes	characteristic
433	C₂	C₂×C₉×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center	C₂²×C₉	C₂⁵
commutator	C₂²	C₂⁵×C₉
Frattini, socle, cosocle	C₂²×C₃	C₂⁵×C₃
prime radical	C₃×#3484	C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×H(5,𝔽₂)	C₂	semidirect
2. C₂³×D₄×C₉	C₂	semidirect
3. C₉×#546	C₂	semidirect
4. D₄²×C₉	C₂	semidirect
5. C₉×#535	C₂	semidirect
6. C₉×#534	C₂	semidirect
7. C₉×#525	C₂	semidirect
8. C₂×C₉×#120	C₂	semidirect
9. C₉×#518	C₂	semidirect
11. C₂⁵×C₉	C₂²	semidirect
13. C₂×C₉×#41	C₂²	semidirect
14. C₂×C₉×#41	C₂²	semidirect
17. C₂²×D₄×C₉	C₂²	semidirect
18. C₂²×D₄×C₉	C₂²	semidirect
19. C₂²×D₄×C₉	C₂²	semidirect
20. C₂²×D₄×C₉	C₂²	semidirect
21. C₂²×D₄×C₉	C₂²	semidirect
22. C₂²×D₄×C₉	C₂²	semidirect
23. C₂³×C₄×C₉	C₂²	semidirect
24. C₉×#127	C₂²	semidirect
25. C₉×#124	C₂²	semidirect
26. C₉×#123	C₂²	semidirect
27. C₉×#123	C₂²	semidirect
28. C₉×C₂²⋊Q₈	C₂²	semidirect
29. C₉×#121	C₂²	semidirect
30. C₉×#121	C₂²	semidirect
31. C₉×#121	C₂²	semidirect
32. C₉×#120	C₂²	semidirect
33. C₉×#120	C₂²	semidirect
34. C₉×#120	C₂²	semidirect
35. C₉×#120	C₂²	semidirect
36. C₄×D₄×C₉	C₂²	semidirect
37. C₄×D₄×C₉	C₂²	semidirect
38. C₉×#117	C₂²	semidirect
39. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
40. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
56. C₂⁴×C₉	C₂³	semidirect
59. C₂×Q₈×C₉	C₂³	semidirect
66. C₂×D₄×C₉	D₄	semidirect
72. C₂×D₄×C₉	C₂³	semidirect
73. C₂×D₄×C₉	C₂³	semidirect
74. C₂×D₄×C₉	C₂³	semidirect
79. C₂²×C₄×C₉	C₂³	semidirect
80. C₂²×C₄×C₉	C₂³	semidirect
81. C₂²×C₄×C₉	C₂³	semidirect
82. C₉×C₄⋊C₄	C₂³	semidirect
83. C₉×C₄⋊C₄	C₂³	semidirect
86. C₉×C₂²⋊C₄	C₂³	semidirect
87. C₉×C₂²⋊C₄	C₂³	semidirect
88. C₉×C₂²⋊C₄	C₂³	semidirect
89. C₄²×C₉	C₂³	semidirect
90. #3484	C₉	direct (N × H)
132. C₂³×C₉	C₂×D₄	semidirect
146. D₄×C₉	C₂×D₄	semidirect
152. C₂×C₄×C₉	C₂×D₄	semidirect
157. C₂×H(5,𝔽₂)	C₂×C₉	semidirect
158. C₂³×D₄	C₂×C₉	semidirect
159. #546	C₂×C₉	semidirect
160. D₄²	C₂×C₉	semidirect
161. #535	C₂×C₉	semidirect
162. #534	C₂×C₉	semidirect
163. #525	C₂×C₉	semidirect
164. C₂×#120	C₂×C₉	semidirect
165. #518	C₂×C₉	semidirect
221. C₂²×C₉	H(5,𝔽₂)	semidirect
227. C₂⁵	C₂²×C₉	semidirect
229. C₂×#41	C₂²×C₉	semidirect
230. C₂×#41	C₂²×C₉	semidirect
233. C₂²×D₄	C₂²×C₉	semidirect
234. C₂²×D₄	C₂²×C₉	semidirect
235. C₂²×D₄	C₂²×C₉	semidirect
236. C₂²×D₄	C₂²×C₉	semidirect
237. C₂²×D₄	C₂²×C₉	semidirect
238. C₂²×D₄	C₂²×C₉	semidirect
239. C₂³×C₄	C₂²×C₉	semidirect
240. #127	C₂²×C₉	semidirect
241. #124	C₂²×C₉	semidirect
242. #123	C₂²×C₉	semidirect
243. #123	C₂²×C₉	semidirect
244. C₂²⋊Q₈	C₂²×C₉	semidirect
245. #121	C₂²×C₉	semidirect
246. #121	C₂²×C₉	semidirect
247. #121	C₂²×C₉	semidirect
248. #120	C₂²×C₉	semidirect
249. #120	C₂²×C₉	semidirect
250. #120	C₂²×C₉	semidirect
251. #120	C₂²×C₉	semidirect
252. C₄×D₄	C₂²×C₉	semidirect
253. C₄×D₄	C₂²×C₉	semidirect
254. #117	C₂²×C₉	semidirect
255. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
256. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
306. C₂⁴	C₂³×C₉	semidirect
309. C₂×Q₈	C₂³×C₉	semidirect
316. C₂×D₄	D₄×C₉	semidirect
322. C₂×D₄	C₂³×C₉	semidirect
323. C₂×D₄	C₂³×C₉	semidirect
324. C₂×D₄	C₂³×C₉	semidirect
329. C₂²×C₄	C₂³×C₉	semidirect
330. C₂²×C₄	C₂³×C₉	semidirect
331. C₂²×C₄	C₂³×C₉	semidirect
332. C₄⋊C₄	C₂³×C₉	semidirect
333. C₄⋊C₄	C₂³×C₉	semidirect
336. C₂²⋊C₄	C₂³×C₉	semidirect
337. C₂²⋊C₄	C₂³×C₉	semidirect
338. C₂²⋊C₄	C₂³×C₉	semidirect
339. C₄²	C₂³×C₉	semidirect
361. C₉	#3484	direct (N × H)
373. C₂³	C₂×D₄×C₉	semidirect
387. D₄	C₂×D₄×C₉	semidirect
393. C₂×C₄	C₂×D₄×C₉	semidirect
420. C₂²	C₉×H(5,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×H(5,𝔽₂)	2
C₂³×D₄×C₉	2
C₉×#546	2
D₄²×C₉	2
C₉×#535	2
C₉×#534	2
C₉×#525	2
C₂×C₉×#120	2
C₉×#518	2
C₃×#3484	3

Subgroups — C9×#3484 #11768205

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3484 #11768205