Subgroups — C₉×#2440 #11767161

Order 1152.

912 conjugacy classes of subgroups.

The subgroup lattice has 441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×C₂²⋊Q₈	C₂	1	2	yes	maximal
3	C₂²×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₉×#398	C₂	1	2	yes	maximal, complemented
5	C₉×#395	C₂	1	2	yes	maximal, complemented
6	C₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#385	C₂	1	2	yes	maximal
9	C₉×#384	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#380	C₂	1	1	yes	maximal, characteristic
11	C₄×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₃×#2440	C₃	1	1	yes	maximal, characteristic
13	C₂²×Q₈×C₉	C₂²	1	2	yes	—
14	C₂³×C₄×C₉	C₂²	1	2	yes	—
15	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
16	C₉×C₄⋊Q₈	—	2	4	no	—
17	C₉×C₂²⋊Q₈	—	2	8	no	—
18	C₂×C₉×C₄⋊C₄	—	2	4	no	—
19	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
26	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
27	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
28	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
33	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
34	C₉×#95	C₂²	1	1	yes	characteristic
35	C₉×#95	C₂²	1	1	yes	characteristic
36	C₉×#95	C₂²	1	2	yes	—
37	C₉×#95	C₂²	1	2	yes	—
38	C₉×#95	C₂²	1	2	yes	—
39	C₂×C₃×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
40	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	2	yes	—
41	C₂²×C₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
42	C₃×#398	C₂×C₃	1	2	yes	—
43	C₃×#395	C₂×C₃	1	2	yes	—
44	C₃×#389	C₂×C₃	1	1	yes	characteristic
45	C₃×#389	C₂×C₃	1	1	yes	characteristic
46	C₃×#385	C₂×C₃	1	2	yes	—
47	C₃×#384	C₂×C₃	1	1	yes	characteristic
48	C₃×#380	C₂×C₃	1	1	yes	characteristic
49	C₃×C₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
50	C₂⁴×C₉	C₂³	1	1	yes	characteristic
51	C₂×Q₈×C₉	—	2	4	no	—
52	C₂×Q₈×C₉	—	2	4	no	—
53	C₂×Q₈×C₉	—	4	2	no	—
54	C₂²×C₄×C₉	—	2	2	no	—
55	C₂²×C₄×C₉	—	2	2	no	—
56	C₂²×C₄×C₉	—	2	4	no	—
57	C₂²×C₄×C₉	—	2	4	no	—
58	C₂²×C₄×C₉	—	4	2	no	—
59	C₂²×C₄×C₉	Q₈	1	4	yes	complemented
60	C₂²×C₄×C₉	C₂³	1	2	yes	—
61	C₂²×C₄×C₉	C₂³	1	2	yes	—
62	C₂²×C₄×C₉	C₂³	1	2	yes	—
63	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₉	C₂³	1	2	yes	—
66	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
68	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
70	C₉×C₄⋊C₄	—	2	4	no	—
71	C₉×C₄⋊C₄	—	2	2	no	—
72	C₉×C₄⋊C₄	—	2	4	no	—
73	C₉×C₄⋊C₄	—	2	4	no	—
74	C₉×C₄⋊C₄	—	2	4	no	—
75	C₉×C₄⋊C₄	—	2	4	no	—
76	C₉×C₄⋊C₄	—	2	2	no	—
77	C₉×C₄⋊C₄	—	2	2	no	—
78	C₉×C₄⋊C₄	—	4	2	no	—
79	C₉×C₄⋊C₄	D₄	1	4	yes	—
80	C₉×C₂²⋊C₄	—	2	4	no	—
81	C₉×C₂²⋊C₄	D₄	1	4	yes	—
82	C₉×C₂²⋊C₄	Q₈	1	4	yes	complemented
83	C₄²×C₉	—	2	2	no	—
84	C₄²×C₉	—	2	2	no	—
85	#2440	C₉	1	1	yes	characteristic, direct product factor, Sylow
86	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	—
87	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
88	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
89	C₃×C₄⋊Q₈	—	2	4	no	—
90	C₃×C₂²⋊Q₈	—	2	8	no	—
91	C₂×C₃×C₄⋊C₄	—	2	4	no	—
92	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
96	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
97	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
98	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
99	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
100	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
101	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
103	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
107	C₃×#95	C₂²×C₃	1	1	yes	characteristic
108	C₃×#95	C₂²×C₃	1	1	yes	characteristic
109	C₃×#95	C₂²×C₃	1	2	yes	—
110	C₃×#95	C₂²×C₃	1	2	yes	—
111	C₃×#95	C₂²×C₃	1	2	yes	—
112	C₂³×C₉	—	2	1	no	—
113	C₂³×C₉	—	2	1	no	—
114	C₂³×C₉	—	2	1	no	—
115	C₂³×C₉	—	2	1	no	—
116	C₂³×C₉	C₂×D₄	1	2	yes	—
117	C₂³×C₉	C₂×Q₈	1	2	yes	—
118	C₂³×C₉	C₂×Q₈	1	2	yes	—
119	C₂³×C₉	C₂⁴	1	1	yes	characteristic
120	Q₈×C₉	—	4	8	no	—
121	C₂×C₄×C₉	—	2	1	no	—
122	C₂×C₄×C₉	—	2	1	no	—
123	C₂×C₄×C₉	—	2	1	no	—
124	C₂×C₄×C₉	—	2	2	no	—
125	C₂×C₄×C₉	—	2	1	no	—
126	C₂×C₄×C₉	—	2	1	no	—
127	C₂×C₄×C₉	—	2	1	no	—
128	C₂×C₄×C₉	—	2	1	no	—
129	C₂×C₄×C₉	—	2	2	no	—
130	C₂×C₄×C₉	—	2	1	no	—
131	C₂×C₄×C₉	—	2	1	no	—
132	C₂×C₄×C₉	—	2	1	no	—
133	C₂×C₄×C₉	—	2	8	no	—
134	C₂×C₄×C₉	—	2	2	no	—
135	C₂×C₄×C₉	—	2	2	no	—
136	C₂×C₄×C₉	—	2	2	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	—	2	2	no	—
141	C₂×C₄×C₉	—	2	2	no	—
142	C₂×C₄×C₉	—	2	2	no	—
143	C₂×C₄×C₉	—	4	8	no	—
144	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
145	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
146	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
147	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
148	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
149	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
150	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
151	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
152	C₂×C₄×C₉	#41	1	2	yes	—
153	C₂×C₄⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
154	C₂×C₂²⋊Q₈	C₂×C₉	1	2	yes	—
155	C₂²×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic
156	#398	C₂×C₉	1	2	yes	complemented
157	#395	C₂×C₉	1	2	yes	complemented
158	#389	C₂×C₉	1	1	yes	characteristic, complemented
159	#389	C₂×C₉	1	1	yes	characteristic, complemented
160	#385	C₂×C₉	1	2	yes	—
161	#384	C₂×C₉	1	1	yes	characteristic, complemented
162	#380	C₂×C₉	1	1	yes	characteristic
163	C₄×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic
164	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
165	C₂×C₃×Q₈	—	2	4	no	—
166	C₂×C₃×Q₈	—	2	4	no	—
167	C₂×C₃×Q₈	—	4	2	no	—
168	C₂²×C₃×C₄	—	2	2	no	—
169	C₂²×C₃×C₄	—	2	2	no	—
170	C₂²×C₃×C₄	—	2	4	no	—
171	C₂²×C₃×C₄	—	2	4	no	—
172	C₂²×C₃×C₄	—	4	2	no	—
173	C₂²×C₃×C₄	C₃×Q₈	1	4	yes	—
174	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
175	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
176	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
177	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
179	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
180	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
181	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
184	C₃×C₄⋊C₄	—	2	4	no	—
185	C₃×C₄⋊C₄	—	2	2	no	—
186	C₃×C₄⋊C₄	—	2	4	no	—
187	C₃×C₄⋊C₄	—	2	4	no	—
188	C₃×C₄⋊C₄	—	2	4	no	—
189	C₃×C₄⋊C₄	—	2	4	no	—
190	C₃×C₄⋊C₄	—	2	2	no	—
191	C₃×C₄⋊C₄	—	2	2	no	—
192	C₃×C₄⋊C₄	—	4	2	no	—
193	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
194	C₃×C₂²⋊C₄	—	2	4	no	—
195	C₃×C₂²⋊C₄	C₃×D₄	1	4	yes	—
196	C₃×C₂²⋊C₄	C₃×Q₈	1	4	yes	—
197	C₃×C₄²	—	2	2	no	—
198	C₃×C₄²	—	2	2	no	—
199	C₂²×C₉	—	2	2	no	—
200	C₂²×C₉	—	2	2	no	—
201	C₂²×C₉	—	2	2	no	—
202	C₂²×C₉	—	2	2	no	—
203	C₂²×C₉	—	2	2	no	—
204	C₂²×C₉	—	2	2	no	—
205	C₂²×C₉	C₄⋊Q₈	1	4	yes	complemented
206	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
207	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
208	C₂²×C₉	C₂²×Q₈	1	1	yes	characteristic
209	C₂²×C₉	C₂²×Q₈	1	1	yes	characteristic
210	C₂²×C₉	C₂×#41	1	1	yes	characteristic
211	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
213	C₄×C₉	—	2	2	no	—
214	C₄×C₉	—	2	4	no	—
215	C₄×C₉	—	2	2	no	—
216	C₄×C₉	—	2	2	no	—
217	C₄×C₉	—	2	2	no	—
218	C₄×C₉	—	2	2	no	—
219	C₄×C₉	—	4	2	no	—
220	C₄×C₉	—	4	2	no	—
221	C₄×C₉	—	4	2	no	—
222	C₄×C₉	C₂²⋊Q₈	1	4	yes	complemented
223	C₂²×Q₈	C₂²×C₉	1	2	yes	—
224	C₂³×C₄	C₂²×C₉	1	2	yes	—
225	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
226	C₄⋊Q₈	—	2	4	no	—
227	C₂²⋊Q₈	—	2	8	no	—
228	C₂×C₄⋊C₄	—	2	4	no	—
229	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
231	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
232	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
233	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
234	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
236	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
238	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
239	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
240	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
241	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
242	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
243	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
244	#95	C₂²×C₉	1	1	yes	characteristic
245	#95	C₂²×C₉	1	1	yes	characteristic
246	#95	C₂²×C₉	1	2	yes	—
247	#95	C₂²×C₉	1	2	yes	—
248	#95	C₂²×C₉	1	2	yes	—
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	C₂×C₃×D₄	1	2	yes	—
254	C₂³×C₃	C₂×C₃×Q₈	1	2	yes	—
255	C₂³×C₃	C₂×C₃×Q₈	1	2	yes	—
256	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
257	C₃×Q₈	—	4	8	no	—
258	C₂×C₃×C₄	—	2	1	no	—
259	C₂×C₃×C₄	—	2	1	no	—
260	C₂×C₃×C₄	—	2	1	no	—
261	C₂×C₃×C₄	—	2	2	no	—
262	C₂×C₃×C₄	—	2	1	no	—
263	C₂×C₃×C₄	—	2	1	no	—
264	C₂×C₃×C₄	—	2	1	no	—
265	C₂×C₃×C₄	—	2	1	no	—
266	C₂×C₃×C₄	—	2	2	no	—
267	C₂×C₃×C₄	—	2	1	no	—
268	C₂×C₃×C₄	—	2	1	no	—
269	C₂×C₃×C₄	—	2	1	no	—
270	C₂×C₃×C₄	—	2	8	no	—
271	C₂×C₃×C₄	—	2	2	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	—	2	2	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	2	2	no	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	4	8	no	—
281	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
282	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
283	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
284	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
285	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
286	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
287	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
288	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
289	C₂×C₃×C₄	C₃×#41	1	2	yes	—
290	C₂×C₉	—	2	4	no	—
291	C₂×C₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
292	C₂×C₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
293	C₂×C₉	#544	1	1	yes	characteristic
294	C₂×C₉	D₄²	1	1	yes	characteristic
295	C₂×C₉	#547	1	1	yes	characteristic
296	C₂×C₉	D₄×Q₈	1	1	yes	characteristic
297	C₂×C₉	#554	1	1	yes	characteristic
298	C₂⁴	C₂³×C₉	1	1	yes	characteristic
299	C₂×Q₈	—	2	4	no	—
300	C₂×Q₈	—	2	4	no	—
301	C₂×Q₈	—	4	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	Q₈×C₉	1	4	yes	complemented
308	C₂²×C₄	C₂³×C₉	1	2	yes	—
309	C₂²×C₄	C₂³×C₉	1	2	yes	—
310	C₂²×C₄	C₂³×C₉	1	2	yes	—
311	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
312	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
313	C₂²×C₄	C₂³×C₉	1	2	yes	—
314	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
315	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
316	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
317	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	D₄×C₉	1	4	yes	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	D₄×C₉	1	4	yes	—
330	C₂²⋊C₄	Q₈×C₉	1	4	yes	complemented
331	C₄²	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₂²×C₃	—	2	2	no	—
334	C₂²×C₃	—	2	2	no	—
335	C₂²×C₃	—	2	2	no	—
336	C₂²×C₃	—	2	2	no	—
337	C₂²×C₃	—	2	2	no	—
338	C₂²×C₃	—	2	2	no	—
339	C₂²×C₃	C₃×C₄⋊Q₈	1	4	yes	—
340	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
341	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
342	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
343	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
344	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
345	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
346	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
347	C₃×C₄	—	2	2	no	—
348	C₃×C₄	—	2	4	no	—
349	C₃×C₄	—	2	2	no	—
350	C₃×C₄	—	2	2	no	—
351	C₃×C₄	—	2	2	no	—
352	C₃×C₄	—	2	2	no	—
353	C₃×C₄	—	4	2	no	—
354	C₃×C₄	—	4	2	no	—
355	C₃×C₄	—	4	2	no	—
356	C₃×C₄	C₃×C₂²⋊Q₈	1	4	yes	—
357	C₉	#2440	1	1	yes	characteristic, direct product factor, Sylow
358	C₂³	—	2	1	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	2	1	no	—
361	C₂³	—	2	1	no	—
362	C₂³	C₂×D₄×C₉	1	2	yes	—
363	C₂³	C₂×Q₈×C₉	1	2	yes	—
364	C₂³	C₂×Q₈×C₉	1	2	yes	—
365	C₂³	C₂⁴×C₉	1	1	yes	characteristic
366	Q₈	—	4	8	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	8	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	8	no	—
390	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
391	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
392	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
393	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
394	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
395	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
396	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
397	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
398	C₂×C₄	C₉×#41	1	2	yes	—
399	C₂×C₃	—	2	4	no	—
400	C₂×C₃	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
401	C₂×C₃	C₂×C₃×C₄⋊Q₈	1	1	yes	characteristic
402	C₂×C₃	C₃×#544	1	1	yes	characteristic
403	C₂×C₃	C₃×D₄²	1	1	yes	characteristic
404	C₂×C₃	C₃×#547	1	1	yes	characteristic
405	C₂×C₃	C₃×D₄×Q₈	1	1	yes	characteristic
406	C₂×C₃	C₃×#554	1	1	yes	characteristic
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	C₉×C₄⋊Q₈	1	4	yes	complemented
414	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
415	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
416	C₂²	C₂²×Q₈×C₉	1	1	yes	characteristic
417	C₂²	C₂²×Q₈×C₉	1	1	yes	characteristic
418	C₂²	C₂×C₉×#41	1	1	yes	characteristic
419	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
420	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
421	C₄	—	2	2	no	—
422	C₄	—	2	4	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	2	no	—
430	C₄	C₉×C₂²⋊Q₈	1	4	yes	complemented
431	C₃	C₃×#2440	1	1	yes	characteristic
432	C₂	—	2	4	no	—
433	C₂	C₂×C₉×C₂²⋊Q₈	1	1	yes	characteristic
434	C₂	C₂×C₉×C₄⋊Q₈	1	1	yes	characteristic
435	C₂	C₉×#544	1	1	yes	characteristic
436	C₂	D₄²×C₉	1	1	yes	characteristic
437	C₂	C₉×#547	1	1	yes	characteristic
438	C₂	D₄×Q₈×C₉	1	1	yes	characteristic
439	C₂	C₉×#554	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂³	C₂⁴×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂⁴×C₃	C₂³×C₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×C₄⋊Q₈	C₂	semidirect
4. C₉×#398	C₂	semidirect
5. C₉×#395	C₂	semidirect
6. C₉×#389	C₂	semidirect
7. C₉×#389	C₂	semidirect
9. C₉×#384	C₂	semidirect
59. C₂²×C₄×C₉	Q₈	semidirect
82. C₉×C₂²⋊C₄	Q₈	semidirect
85. #2440	C₉	direct (N × H)
153. C₂×C₄⋊Q₈	C₂×C₉	semidirect
156. #398	C₂×C₉	semidirect
157. #395	C₂×C₉	semidirect
158. #389	C₂×C₉	semidirect
159. #389	C₂×C₉	semidirect
161. #384	C₂×C₉	semidirect
205. C₂²×C₉	C₄⋊Q₈	semidirect
222. C₄×C₉	C₂²⋊Q₈	semidirect
307. C₂²×C₄	Q₈×C₉	semidirect
330. C₂²⋊C₄	Q₈×C₉	semidirect
357. C₉	#2440	direct (N × H)
413. C₂²	C₉×C₄⋊Q₈	semidirect
430. C₄	C₉×C₂²⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×C₄⋊Q₈	2
C₂×C₉×C₂²⋊Q₈	2
C₂²×C₉×C₄⋊C₄	2
C₉×#398	2
C₉×#395	2
C₉×#389	2
C₉×#385	2
C₉×#384	2
C₉×#380	2
C₄×C₉×C₂²⋊C₄	2
C₃×#2440	3

Subgroups — C9×#2440 #11767161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2440 #11767161