Subgroups — C₉×#3496 #11768217

Order 1152.

2490 conjugacy classes of subgroups.

The subgroup lattice has 390 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	2	yes	maximal, complemented
2	C₉×#547	C₂	1	4	yes	maximal, complemented
3	C₉×#546	C₂	1	8	yes	maximal, complemented
4	D₄²×C₉	C₂	1	4	yes	maximal, complemented
5	C₉×#537	C₂	1	2	yes	maximal, complemented
6	C₉×#534	C₂	1	4	yes	maximal, complemented
7	C₉×#532	C₂	1	2	yes	maximal, complemented
8	C₂×C₉×#121	C₂	1	4	yes	maximal, complemented
9	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3496	C₃	1	1	yes	maximal, characteristic
11	C₉×H(5,𝔽₂)	—	2	16	no	—
12	C₂×C₉×#41	C₂²	1	4	yes	complemented
13	C₂×C₉×#41	C₂²	1	8	yes	complemented
14	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
15	C₂²×D₄×C₉	C₂²	1	8	yes	complemented
16	C₂²×D₄×C₉	C₂²	1	8	yes	complemented
17	C₂²×D₄×C₉	C₂²	1	4	yes	complemented
18	C₂³×C₄×C₉	C₂²	1	2	yes	complemented
19	C₉×C₄⋊Q₈	C₂²	1	2	yes	complemented
20	C₉×#127	C₂²	1	2	yes	complemented
21	C₉×#124	C₂²	1	4	yes	complemented
22	C₉×#123	C₂²	1	16	yes	complemented
23	C₉×C₂²⋊Q₈	C₂²	1	8	yes	complemented
24	C₉×#121	C₂²	1	4	yes	complemented
25	C₉×#121	C₂²	1	8	yes	complemented
26	C₉×#121	C₂²	1	8	yes	complemented
27	C₉×#121	C₂²	1	8	yes	complemented
28	C₉×#121	C₂²	1	4	yes	complemented
29	C₉×#121	C₂²	1	8	yes	complemented
30	C₉×#120	C₂²	1	16	yes	complemented
31	C₄×D₄×C₉	C₂²	1	4	yes	complemented
32	C₄×D₄×C₉	C₂²	1	4	yes	complemented
33	C₄×D₄×C₉	C₂²	1	4	yes	complemented
34	C₄×D₄×C₉	C₂²	1	4	yes	complemented
35	C₂×C₉×C₄⋊C₄	C₂²	1	4	yes	complemented
36	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₉×C₂²⋊C₄	C₂²	1	8	yes	complemented
38	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	complemented
39	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₃×H(5,𝔽₂)	C₂×C₃	1	2	yes	—
41	C₃×#547	C₂×C₃	1	4	yes	—
42	C₃×#546	C₂×C₃	1	8	yes	—
43	C₃×D₄²	C₂×C₃	1	4	yes	—
44	C₃×#537	C₂×C₃	1	2	yes	—
45	C₃×#534	C₂×C₃	1	4	yes	—
46	C₃×#532	C₂×C₃	1	2	yes	—
47	C₂×C₃×#121	C₂×C₃	1	4	yes	—
48	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
49	C₂⁴×C₉	C₂³	1	8	yes	—
50	C₂⁴×C₉	C₂³	1	2	yes	—
51	C₉×#41	—	2	32	no	—
52	C₉×#41	—	2	16	no	—
53	C₂×Q₈×C₉	C₂³	1	4	yes	—
54	C₂×D₄×C₉	—	2	32	no	—
55	C₂×D₄×C₉	—	2	32	no	—
56	C₂×D₄×C₉	—	4	8	no	—
57	C₂×D₄×C₉	D₄	1	8	yes	complemented
58	C₂×D₄×C₉	C₂³	1	4	yes	—
59	C₂×D₄×C₉	C₂³	1	16	yes	—
60	C₂×D₄×C₉	C₂³	1	8	yes	—
61	C₂×D₄×C₉	C₂³	1	4	yes	—
62	C₂×D₄×C₉	C₂³	1	4	yes	—
63	C₂×D₄×C₉	C₂³	1	8	yes	—
64	C₂×D₄×C₉	C₂³	1	4	yes	—
65	C₂²×C₄×C₉	—	4	4	no	—
66	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₉	C₂³	1	8	yes	—
68	C₂²×C₄×C₉	C₂³	1	4	yes	—
69	C₂²×C₄×C₉	C₂³	1	8	yes	—
70	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₉	C₂³	1	4	yes	—
72	C₂²×C₄×C₉	C₂³	1	2	yes	—
73	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
74	C₉×C₄⋊C₄	C₂³	1	4	yes	—
75	C₉×C₄⋊C₄	C₂³	1	4	yes	—
76	C₉×C₄⋊C₄	C₂³	1	8	yes	—
77	C₉×C₄⋊C₄	C₂³	1	4	yes	—
78	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
79	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
80	C₉×C₂²⋊C₄	C₂³	1	16	yes	—
81	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
82	C₄²×C₉	C₂³	1	2	yes	—
83	C₄²×C₉	C₂³	1	2	yes	—
84	#3496	C₉	1	1	yes	characteristic, direct product factor, Sylow
85	C₃×H(5,𝔽₂)	—	2	16	no	—
86	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
87	C₂×C₃×#41	C₂²×C₃	1	8	yes	—
88	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
89	C₂²×C₃×D₄	C₂²×C₃	1	8	yes	—
90	C₂²×C₃×D₄	C₂²×C₃	1	8	yes	—
91	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
92	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
93	C₃×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
94	C₃×#127	C₂²×C₃	1	2	yes	—
95	C₃×#124	C₂²×C₃	1	4	yes	—
96	C₃×#123	C₂²×C₃	1	16	yes	—
97	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
98	C₃×#121	C₂²×C₃	1	4	yes	—
99	C₃×#121	C₂²×C₃	1	8	yes	—
100	C₃×#121	C₂²×C₃	1	8	yes	—
101	C₃×#121	C₂²×C₃	1	8	yes	—
102	C₃×#121	C₂²×C₃	1	4	yes	—
103	C₃×#121	C₂²×C₃	1	8	yes	—
104	C₃×#120	C₂²×C₃	1	16	yes	—
105	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
106	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
107	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
108	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
109	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
110	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
111	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
112	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
113	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
114	C₂³×C₉	—	2	16	no	—
115	C₂³×C₉	—	4	2	no	—
116	C₂³×C₉	—	4	2	no	—
117	C₂³×C₉	—	4	8	no	—
118	C₂³×C₉	—	4	8	no	—
119	C₂³×C₉	C₂×D₄	1	8	yes	complemented
120	C₂³×C₉	C₂⁴	1	8	yes	—
121	C₂³×C₉	C₂⁴	1	4	yes	—
122	C₂³×C₉	C₂⁴	1	1	yes	characteristic
123	Q₈×C₉	—	2	8	no	—
124	D₄×C₉	—	2	32	no	—
125	D₄×C₉	—	2	16	no	—
126	D₄×C₉	—	2	8	no	—
127	D₄×C₉	—	2	8	no	—
128	D₄×C₉	—	4	8	no	—
129	D₄×C₉	—	4	4	no	—
130	D₄×C₉	C₂×D₄	1	16	yes	complemented
131	C₂×C₄×C₉	—	2	16	no	—
132	C₂×C₄×C₉	—	2	16	no	—
133	C₂×C₄×C₉	—	2	2	no	—
134	C₂×C₄×C₉	—	2	8	no	—
135	C₂×C₄×C₉	—	4	4	no	—
136	C₂×C₄×C₉	—	4	2	no	—
137	C₂×C₄×C₉	—	4	1	no	—
138	C₂×C₄×C₉	C₂×D₄	1	4	yes	complemented
139	C₂×C₄×C₉	C₂⁴	1	2	yes	—
140	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
141	C₂×C₄×C₉	C₂⁴	1	4	yes	—
142	C₂×C₄×C₉	C₂⁴	1	8	yes	—
143	C₂×C₄×C₉	C₂⁴	1	2	yes	—
144	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
145	C₂×H(5,𝔽₂)	C₂×C₉	1	2	yes	complemented
146	#547	C₂×C₉	1	4	yes	complemented
147	#546	C₂×C₉	1	8	yes	complemented
148	D₄²	C₂×C₉	1	4	yes	complemented
149	#537	C₂×C₉	1	2	yes	complemented
150	#534	C₂×C₉	1	4	yes	complemented
151	#532	C₂×C₉	1	2	yes	complemented
152	C₂×#121	C₂×C₉	1	4	yes	complemented
153	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic, complemented
154	C₂⁴×C₃	C₂³×C₃	1	8	yes	—
155	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
156	C₃×#41	—	2	32	no	—
157	C₃×#41	—	2	16	no	—
158	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
159	C₂×C₃×D₄	—	2	32	no	—
160	C₂×C₃×D₄	—	2	32	no	—
161	C₂×C₃×D₄	—	4	8	no	—
162	C₂×C₃×D₄	C₃×D₄	1	8	yes	—
163	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
164	C₂×C₃×D₄	C₂³×C₃	1	16	yes	—
165	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
166	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
167	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
168	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
169	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
170	C₂²×C₃×C₄	—	4	4	no	—
171	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
172	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
173	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
174	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
175	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
176	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
177	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
178	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
179	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
180	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
181	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
182	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
183	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
184	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
185	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
186	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
187	C₃×C₄²	C₂³×C₃	1	2	yes	—
188	C₃×C₄²	C₂³×C₃	1	2	yes	—
189	C₂²×C₉	—	2	1	no	—
190	C₂²×C₉	—	2	4	no	—
191	C₂²×C₉	—	2	1	no	—
192	C₂²×C₉	—	2	4	no	—
193	C₂²×C₉	—	2	8	no	—
194	C₂²×C₉	—	2	8	no	—
195	C₂²×C₉	—	2	8	no	—
196	C₂²×C₉	—	4	8	no	—
197	C₂²×C₉	—	8	16	no	—
198	C₂²×C₉	C₂²×D₄	1	8	yes	—
199	C₂²×C₉	C₂²×D₄	1	2	yes	—
200	C₂²×C₉	C₂⁵	1	1	yes	characteristic
201	C₄×C₉	—	2	8	no	—
202	C₄×C₉	—	2	1	no	—
203	C₄×C₉	—	2	4	no	—
204	C₄×C₉	—	2	2	no	—
205	C₄×C₉	C₂²×D₄	1	4	yes	—
206	C₄×C₉	H(5,𝔽₂)	1	2	yes	complemented
207	H(5,𝔽₂)	—	2	16	no	—
208	C₂×#41	C₂²×C₉	1	4	yes	complemented
209	C₂×#41	C₂²×C₉	1	8	yes	complemented
210	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
211	C₂²×D₄	C₂²×C₉	1	8	yes	complemented
212	C₂²×D₄	C₂²×C₉	1	8	yes	complemented
213	C₂²×D₄	C₂²×C₉	1	4	yes	complemented
214	C₂³×C₄	C₂²×C₉	1	2	yes	complemented
215	C₄⋊Q₈	C₂²×C₉	1	2	yes	complemented
216	#127	C₂²×C₉	1	2	yes	complemented
217	#124	C₂²×C₉	1	4	yes	complemented
218	#123	C₂²×C₉	1	16	yes	complemented
219	C₂²⋊Q₈	C₂²×C₉	1	8	yes	complemented
220	#121	C₂²×C₉	1	4	yes	complemented
221	#121	C₂²×C₉	1	8	yes	complemented
222	#121	C₂²×C₉	1	8	yes	complemented
223	#121	C₂²×C₉	1	8	yes	complemented
224	#121	C₂²×C₉	1	4	yes	complemented
225	#121	C₂²×C₉	1	8	yes	complemented
226	#120	C₂²×C₉	1	16	yes	complemented
227	C₄×D₄	C₂²×C₉	1	4	yes	complemented
228	C₄×D₄	C₂²×C₉	1	4	yes	complemented
229	C₄×D₄	C₂²×C₉	1	4	yes	complemented
230	C₄×D₄	C₂²×C₉	1	4	yes	complemented
231	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
232	C₂×C₄⋊C₄	C₂²×C₉	1	4	yes	complemented
233	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	complemented
234	C₂×C₂²⋊C₄	C₂²×C₉	1	8	yes	complemented
235	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic, complemented
236	C₂³×C₃	—	2	16	no	—
237	C₂³×C₃	—	4	2	no	—
238	C₂³×C₃	—	4	2	no	—
239	C₂³×C₃	—	4	8	no	—
240	C₂³×C₃	—	4	8	no	—
241	C₂³×C₃	C₂×C₃×D₄	1	8	yes	—
242	C₂³×C₃	C₂⁴×C₃	1	8	yes	—
243	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
244	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
245	C₃×Q₈	—	2	8	no	—
246	C₃×D₄	—	2	32	no	—
247	C₃×D₄	—	2	16	no	—
248	C₃×D₄	—	2	8	no	—
249	C₃×D₄	—	2	8	no	—
250	C₃×D₄	—	4	8	no	—
251	C₃×D₄	—	4	4	no	—
252	C₃×D₄	C₂×C₃×D₄	1	16	yes	—
253	C₂×C₃×C₄	—	2	16	no	—
254	C₂×C₃×C₄	—	2	16	no	—
255	C₂×C₃×C₄	—	2	2	no	—
256	C₂×C₃×C₄	—	2	8	no	—
257	C₂×C₃×C₄	—	4	4	no	—
258	C₂×C₃×C₄	—	4	2	no	—
259	C₂×C₃×C₄	—	4	1	no	—
260	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
261	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
262	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
264	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
265	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
266	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
267	C₂×C₉	—	2	2	no	—
268	C₂×C₉	—	2	8	no	—
269	C₂×C₉	—	4	8	no	—
270	C₂×C₉	C₂³×D₄	1	1	yes	characteristic
271	C₂×C₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
272	C₂×C₉	#585	1	1	yes	characteristic
273	C₂⁴	C₂³×C₉	1	8	yes	—
274	C₂⁴	C₂³×C₉	1	2	yes	—
275	#41	—	2	32	no	—
276	#41	—	2	16	no	—
277	C₂×Q₈	C₂³×C₉	1	4	yes	—
278	C₂×D₄	—	2	32	no	—
279	C₂×D₄	—	2	32	no	—
280	C₂×D₄	—	4	8	no	—
281	C₂×D₄	D₄×C₉	1	8	yes	complemented
282	C₂×D₄	C₂³×C₉	1	4	yes	—
283	C₂×D₄	C₂³×C₉	1	16	yes	—
284	C₂×D₄	C₂³×C₉	1	8	yes	—
285	C₂×D₄	C₂³×C₉	1	4	yes	—
286	C₂×D₄	C₂³×C₉	1	4	yes	—
287	C₂×D₄	C₂³×C₉	1	8	yes	—
288	C₂×D₄	C₂³×C₉	1	4	yes	—
289	C₂²×C₄	—	4	4	no	—
290	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
291	C₂²×C₄	C₂³×C₉	1	8	yes	—
292	C₂²×C₄	C₂³×C₉	1	4	yes	—
293	C₂²×C₄	C₂³×C₉	1	8	yes	—
294	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
295	C₂²×C₄	C₂³×C₉	1	4	yes	—
296	C₂²×C₄	C₂³×C₉	1	2	yes	—
297	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
298	C₄⋊C₄	C₂³×C₉	1	4	yes	—
299	C₄⋊C₄	C₂³×C₉	1	4	yes	—
300	C₄⋊C₄	C₂³×C₉	1	8	yes	—
301	C₄⋊C₄	C₂³×C₉	1	4	yes	—
302	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
303	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
304	C₂²⋊C₄	C₂³×C₉	1	16	yes	—
305	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
306	C₄²	C₂³×C₉	1	2	yes	—
307	C₄²	C₂³×C₉	1	2	yes	—
308	C₂²×C₃	—	2	1	no	—
309	C₂²×C₃	—	2	4	no	—
310	C₂²×C₃	—	2	1	no	—
311	C₂²×C₃	—	2	4	no	—
312	C₂²×C₃	—	2	8	no	—
313	C₂²×C₃	—	2	8	no	—
314	C₂²×C₃	—	2	8	no	—
315	C₂²×C₃	—	4	8	no	—
316	C₂²×C₃	—	8	16	no	—
317	C₂²×C₃	C₂²×C₃×D₄	1	8	yes	—
318	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
319	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
320	C₃×C₄	—	2	8	no	—
321	C₃×C₄	—	2	1	no	—
322	C₃×C₄	—	2	4	no	—
323	C₃×C₄	—	2	2	no	—
324	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
325	C₃×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
326	C₉	#3496	1	1	yes	characteristic, direct product factor, Sylow
327	C₂³	—	2	16	no	—
328	C₂³	—	4	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	8	no	—
331	C₂³	—	4	8	no	—
332	C₂³	C₂×D₄×C₉	1	8	yes	complemented
333	C₂³	C₂⁴×C₉	1	8	yes	—
334	C₂³	C₂⁴×C₉	1	4	yes	—
335	C₂³	C₂⁴×C₉	1	1	yes	characteristic
336	Q₈	—	2	8	no	—
337	D₄	—	2	32	no	—
338	D₄	—	2	16	no	—
339	D₄	—	2	8	no	—
340	D₄	—	2	8	no	—
341	D₄	—	4	8	no	—
342	D₄	—	4	4	no	—
343	D₄	C₂×D₄×C₉	1	16	yes	complemented
344	C₂×C₄	—	2	16	no	—
345	C₂×C₄	—	2	16	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	8	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	C₂×D₄×C₉	1	4	yes	complemented
352	C₂×C₄	C₂⁴×C₉	1	2	yes	—
353	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
354	C₂×C₄	C₂⁴×C₉	1	4	yes	—
355	C₂×C₄	C₂⁴×C₉	1	8	yes	—
356	C₂×C₄	C₂⁴×C₉	1	2	yes	—
357	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
358	C₂×C₃	—	2	2	no	—
359	C₂×C₃	—	2	8	no	—
360	C₂×C₃	—	4	8	no	—
361	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
362	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
363	C₂×C₃	C₃×#585	1	1	yes	characteristic
364	C₂²	—	2	1	no	—
365	C₂²	—	2	4	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	4	no	—
368	C₂²	—	2	8	no	—
369	C₂²	—	2	8	no	—
370	C₂²	—	2	8	no	—
371	C₂²	—	4	8	no	—
372	C₂²	—	8	16	no	—
373	C₂²	C₂²×D₄×C₉	1	8	yes	—
374	C₂²	C₂²×D₄×C₉	1	2	yes	—
375	C₂²	C₂⁵×C₉	1	1	yes	characteristic
376	C₄	—	2	8	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	4	no	—
379	C₄	—	2	2	no	—
380	C₄	C₂²×D₄×C₉	1	4	yes	—
381	C₄	C₉×H(5,𝔽₂)	1	2	yes	complemented
382	C₃	C₃×#3496	1	1	yes	characteristic
383	C₂	—	2	2	no	—
384	C₂	—	2	8	no	—
385	C₂	—	4	8	no	—
386	C₂	C₂³×D₄×C₉	1	1	yes	characteristic
387	C₂	C₂×C₉×H(5,𝔽₂)	1	1	yes	characteristic
388	C₂	C₉×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂⁵
commutator	C₂²	C₂⁵×C₉
Frattini, socle, cosocle	C₂²×C₃	C₂⁵×C₃
prime radical	C₃×#3496	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. C₉×#547	C₂	semidirect
3. C₉×#546	C₂	semidirect
4. D₄²×C₉	C₂	semidirect
5. C₉×#537	C₂	semidirect
6. C₉×#534	C₂	semidirect
7. C₉×#532	C₂	semidirect
8. C₂×C₉×#121	C₂	semidirect
9. C₂×C₄×D₄×C₉	C₂	semidirect
12. C₂×C₉×#41	C₂²	semidirect
13. C₂×C₉×#41	C₂²	semidirect
15. C₂²×D₄×C₉	C₂²	semidirect
16. C₂²×D₄×C₉	C₂²	semidirect
17. C₂²×D₄×C₉	C₂²	semidirect
18. C₂³×C₄×C₉	C₂²	semidirect
19. C₉×C₄⋊Q₈	C₂²	semidirect
20. C₉×#127	C₂²	semidirect
21. C₉×#124	C₂²	semidirect
22. C₉×#123	C₂²	semidirect
23. C₉×C₂²⋊Q₈	C₂²	semidirect
24. C₉×#121	C₂²	semidirect
25. C₉×#121	C₂²	semidirect
26. C₉×#121	C₂²	semidirect
27. C₉×#121	C₂²	semidirect
28. C₉×#121	C₂²	semidirect
29. C₉×#121	C₂²	semidirect
30. C₉×#120	C₂²	semidirect
31. C₄×D₄×C₉	C₂²	semidirect
32. C₄×D₄×C₉	C₂²	semidirect
33. C₄×D₄×C₉	C₂²	semidirect
34. C₄×D₄×C₉	C₂²	semidirect
35. C₂×C₉×C₄⋊C₄	C₂²	semidirect
36. C₂×C₉×C₄⋊C₄	C₂²	semidirect
37. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
38. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
39. C₂×C₄²×C₉	C₂²	semidirect
57. C₂×D₄×C₉	D₄	semidirect
84. #3496	C₉	direct (N × H)
119. C₂³×C₉	C₂×D₄	semidirect
130. D₄×C₉	C₂×D₄	semidirect
138. C₂×C₄×C₉	C₂×D₄	semidirect
145. C₂×H(5,𝔽₂)	C₂×C₉	semidirect
146. #547	C₂×C₉	semidirect
147. #546	C₂×C₉	semidirect
148. D₄²	C₂×C₉	semidirect
149. #537	C₂×C₉	semidirect
150. #534	C₂×C₉	semidirect
151. #532	C₂×C₉	semidirect
152. C₂×#121	C₂×C₉	semidirect
153. C₂×C₄×D₄	C₂×C₉	semidirect
206. C₄×C₉	H(5,𝔽₂)	semidirect
208. C₂×#41	C₂²×C₉	semidirect
209. C₂×#41	C₂²×C₉	semidirect
211. C₂²×D₄	C₂²×C₉	semidirect
212. C₂²×D₄	C₂²×C₉	semidirect
213. C₂²×D₄	C₂²×C₉	semidirect
214. C₂³×C₄	C₂²×C₉	semidirect
215. C₄⋊Q₈	C₂²×C₉	semidirect
216. #127	C₂²×C₉	semidirect
217. #124	C₂²×C₉	semidirect
218. #123	C₂²×C₉	semidirect
219. C₂²⋊Q₈	C₂²×C₉	semidirect
220. #121	C₂²×C₉	semidirect
221. #121	C₂²×C₉	semidirect
222. #121	C₂²×C₉	semidirect
223. #121	C₂²×C₉	semidirect
224. #121	C₂²×C₉	semidirect
225. #121	C₂²×C₉	semidirect
226. #120	C₂²×C₉	semidirect
227. C₄×D₄	C₂²×C₉	semidirect
228. C₄×D₄	C₂²×C₉	semidirect
229. C₄×D₄	C₂²×C₉	semidirect
230. C₄×D₄	C₂²×C₉	semidirect
231. C₂×C₄⋊C₄	C₂²×C₉	semidirect
232. C₂×C₄⋊C₄	C₂²×C₉	semidirect
233. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
234. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
235. C₂×C₄²	C₂²×C₉	semidirect
281. C₂×D₄	D₄×C₉	semidirect
326. C₉	#3496	direct (N × H)
332. C₂³	C₂×D₄×C₉	semidirect
343. D₄	C₂×D₄×C₉	semidirect
351. C₂×C₄	C₂×D₄×C₉	semidirect
381. C₄	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
C₉×#547	2
C₉×#546	2
D₄²×C₉	2
C₉×#537	2
C₉×#534	2
C₉×#532	2
C₂×C₉×#121	2
C₂×C₄×D₄×C₉	2
C₃×#3496	3

Subgroups — C9×#3496 #11768217

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3496 #11768217