Subgroups — C₂×C₉×#809 #13142581

Order 1728.

698 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₉×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#809	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₃×#809	C₃	1	1	yes	maximal, characteristic
6	C₂×C₉×#102	—	3	1	no	maximal
7	C₂³×D₃×C₉	—	2	1	no	—
8	C₂²×C₃×C₄×C₉	—	2	1	no	—
9	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
10	C₂×C₉×D₁₂	—	2	1	no	—
11	C₂×C₉×D₁₂	—	2	2	no	—
12	C₂×C₉×D₁₂	C₄	1	4	yes	complemented
13	C₂×C₉×D₁₂	C₂²	1	2	yes	—
14	C₃×C₉×C₄⋊C₄	—	2	1	no	—
15	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	complemented
16	C₂×C₉×C₃⋊C₈	—	2	2	no	—
17	C₂×C₉×C₃⋊C₈	C₂²	1	2	yes	complemented
18	C₂²×C₃×D₁₂	C₂×C₃	1	1	yes	characteristic
19	C₂×C₃²×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
20	C₂²×C₃×C₃⋊C₈	C₂×C₃	1	1	yes	characteristic
21	C₂²×D₄×C₉	—	3	1	no	—
22	C₃×#809	C₂×C₃	1	4	yes	—
23	C₂²×C₈×C₉	—	3	1	no	—
24	C₂×C₉×C₄⋊C₄	—	2	1	no	—
25	C₂×C₉×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
26	C₉×#102	—	3	4	no	—
27	C₂³×C₃×C₉	D₄	1	1	yes	characteristic
28	C₂²×D₃×C₉	—	2	4	no	—
29	C₂²×D₃×C₉	—	2	2	no	—
30	C₂²×D₃×C₉	—	4	2	no	—
31	C₂²×D₃×C₉	—	4	2	no	—
32	C₂×C₃×C₄×C₉	—	2	2	no	—
33	C₂×C₃×C₄×C₉	—	4	2	no	—
34	C₂×C₃×C₄×C₉	C₂×C₄	1	2	yes	—
35	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
36	C₂×C₃×C₄×C₉	D₄	1	2	yes	—
37	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
38	C₉×D₁₂	—	2	4	no	—
39	C₉×D₁₂	—	2	2	no	—
40	C₉×D₁₂	C₂×C₄	1	4	yes	complemented
41	C₉×C₃⋊C₈	—	2	2	no	—
42	C₂×C₃×#102	—	3	1	no	—
43	C₂×#809	C₉	1	1	yes	characteristic, direct product factor
44	C₂³×C₃×D₃	—	2	1	no	—
45	C₂²×C₃²×C₄	—	2	1	no	—
46	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
47	C₂×C₃×D₁₂	—	2	1	no	—
48	C₂×C₃×D₁₂	—	2	2	no	—
49	C₂×C₃×D₁₂	C₃×C₄	1	4	yes	—
50	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
51	C₂⁴×C₉	—	6	1	no	—
52	C₃²×C₄⋊C₄	—	2	1	no	—
53	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
54	C₂×C₃×C₃⋊C₈	—	2	2	no	—
55	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	2	yes	—
56	C₂×D₄×C₉	—	3	4	no	—
57	C₂×D₄×C₉	—	3	2	no	—
58	C₂×D₄×C₉	—	6	2	no	—
59	C₂×D₄×C₉	—	6	1	no	—
60	C₂²×C₄×C₉	—	2	1	no	—
61	C₂²×C₄×C₉	—	2	2	no	—
62	C₂²×C₄×C₉	—	2	1	no	—
63	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
64	C₂×C₈×C₉	—	3	2	no	—
65	C₂×C₈×C₉	—	6	2	no	—
66	C₉×C₄⋊C₄	—	2	2	no	—
67	C₉×C₄⋊C₄	—	2	2	no	—
68	C₉×C₄⋊C₄	—	2	1	no	—
69	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
70	C₂²×C₃×C₉	C₂²⋊C₄	1	2	yes	—
71	C₂²×C₃×C₉	D₈	1	2	yes	—
72	C₂²×C₃×C₉	SD₁₆	1	2	yes	—
73	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
74	C₂×D₃×C₉	—	2	4	no	—
75	C₂×D₃×C₉	—	4	8	no	—
76	C₂×D₃×C₉	—	4	2	no	—
77	C₂×D₃×C₉	—	4	2	no	—
78	C₃×C₄×C₉	—	4	2	no	—
79	C₃×C₄×C₉	C₂²⋊C₄	1	2	yes	—
80	C₃×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
81	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₃×D₄	—	3	1	no	—
83	C₂²×D₁₂	C₂×C₉	1	1	yes	characteristic
84	C₂²×C₃×C₈	—	3	1	no	—
85	C₂×C₃×C₄⋊C₄	—	2	1	no	—
86	C₂×C₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
87	C₂×C₃×C₄⋊C₄	C₃×D₃	1	1	yes	characteristic
88	C₂²×C₃⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
89	C₃×#102	—	3	4	no	—
90	#809	C₂×C₉	1	4	yes	direct product factor
91	C₂³×C₃²	C₃×D₄	1	1	yes	characteristic
92	C₂²×C₃×D₃	—	2	4	no	—
93	C₂²×C₃×D₃	—	2	2	no	—
94	C₂²×C₃×D₃	—	4	2	no	—
95	C₂²×C₃×D₃	—	4	2	no	—
96	C₂×C₃²×C₄	—	2	2	no	—
97	C₂×C₃²×C₄	—	4	2	no	—
98	C₂×C₃²×C₄	C₂×C₃×C₄	1	2	yes	—
99	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
100	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
101	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
102	C₃×D₁₂	—	2	4	no	—
103	C₃×D₁₂	—	2	2	no	—
104	C₃×D₁₂	C₂×C₃×C₄	1	4	yes	—
105	C₂³×C₉	—	2	1	no	—
106	C₂³×C₉	—	6	4	no	—
107	C₂³×C₉	—	6	2	no	—
108	C₂³×C₉	—	12	2	no	—
109	C₂³×C₉	—	12	2	no	—
110	C₂³×C₉	#67	1	1	yes	characteristic
111	C₃×C₃⋊C₈	—	2	2	no	—
112	D₄×C₉	—	3	4	no	—
113	D₄×C₉	—	6	4	no	—
114	D₄×C₉	—	6	2	no	—
115	C₂×C₄×C₉	—	2	4	no	—
116	C₂×C₄×C₉	—	2	2	no	—
117	C₂×C₄×C₉	—	2	2	no	—
118	C₂×C₄×C₉	—	2	2	no	—
119	C₂×C₄×C₉	—	2	1	no	—
120	C₂×C₄×C₉	—	2	1	no	—
121	C₂×C₄×C₉	—	4	4	no	—
122	C₂×C₄×C₉	—	4	2	no	—
123	C₂×C₄×C₉	C₄×D₃	1	2	yes	—
124	C₂×C₄×C₉	D₁₂	1	2	yes	—
125	C₂×C₄×C₉	#67	1	1	yes	characteristic
126	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
127	C₈×C₉	—	6	2	no	—
128	C₂×#102	—	3	1	no	Sylow
129	C₂×C₃×C₉	#102	1	4	yes	complemented
130	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂×C₃×C₉	C₂×D₈	1	1	yes	characteristic
132	C₂×C₃×C₉	C₂×SD₁₆	1	1	yes	characteristic
133	D₃×C₉	—	4	4	no	—
134	C₂⁴×C₃	—	6	1	no	—
135	C₂³×D₃	—	2	1	no	—
136	C₂×C₃×D₄	—	3	4	no	—
137	C₂×C₃×D₄	—	3	2	no	—
138	C₂×C₃×D₄	—	6	2	no	—
139	C₂×C₃×D₄	—	6	1	no	—
140	C₂²×C₃×C₄	—	2	2	no	—
141	C₂²×C₃×C₄	—	2	1	no	—
142	C₂²×C₃×C₄	—	2	1	no	—
143	C₂²×C₃×C₄	—	2	1	no	—
144	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
145	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
146	C₂×D₁₂	—	2	2	no	—
147	C₂×D₁₂	—	2	1	no	—
148	C₂×D₁₂	C₄×C₉	1	4	yes	complemented
149	C₂×D₁₂	C₂²×C₉	1	2	yes	—
150	C₂×C₃×C₈	—	3	2	no	—
151	C₂×C₃×C₈	—	6	2	no	—
152	C₃×C₄⋊C₄	—	2	2	no	—
153	C₃×C₄⋊C₄	—	2	1	no	—
154	C₃×C₄⋊C₄	—	2	1	no	—
155	C₃×C₄⋊C₄	—	2	2	no	—
156	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	complemented
157	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
158	C₂×C₃⋊C₈	—	2	2	no	—
159	C₂×C₃⋊C₈	C₂²×C₉	1	2	yes	complemented
160	C₂²×C₃²	C₃×C₂²⋊C₄	1	2	yes	—
161	C₂²×C₃²	C₃×D₈	1	2	yes	—
162	C₂²×C₃²	C₃×SD₁₆	1	2	yes	—
163	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
164	C₂×C₃×D₃	—	2	4	no	—
165	C₂×C₃×D₃	—	4	8	no	—
166	C₂×C₃×D₃	—	4	2	no	—
167	C₂×C₃×D₃	—	4	2	no	—
168	C₃²×C₄	—	4	2	no	—
169	C₃²×C₄	C₃×C₂²⋊C₄	1	2	yes	—
170	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
171	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
172	C₂²×C₉	—	2	2	no	—
173	C₂²×C₉	—	2	2	no	—
174	C₂²×C₉	—	2	2	no	—
175	C₂²×C₉	—	2	1	no	—
176	C₂²×C₉	—	6	4	no	—
177	C₂²×C₉	—	12	8	no	—
178	C₂²×C₉	—	12	2	no	—
179	C₂²×C₉	—	12	2	no	—
180	C₂²×C₉	(C₂×D₃)⋊C₄	1	2	yes	—
181	C₂²×C₉	#213	1	2	yes	—
182	C₂²×C₉	#215	1	2	yes	—
183	C₂²×C₉	C₂×#67	1	1	yes	characteristic
184	C₄×C₉	—	2	2	no	—
185	C₄×C₉	—	2	1	no	—
186	C₄×C₉	—	2	1	no	—
187	C₄×C₉	—	4	4	no	—
188	C₄×C₉	—	4	2	no	—
189	C₄×C₉	(C₂×D₃)⋊C₄	1	2	yes	—
190	C₄×C₉	C₂×C₄×D₃	1	1	yes	characteristic
191	C₄×C₉	C₂×D₁₂	1	1	yes	characteristic
192	C₂²×D₄	—	3	1	no	—
193	C₂²×C₈	—	3	1	no	—
194	C₂×C₄⋊C₄	D₃×C₉	1	1	yes	characteristic, complemented
195	#102	—	3	4	no	—
196	C₃×C₉	C₂×#102	1	1	yes	characteristic, complemented, Sylow
197	C₂³×C₃	—	2	1	no	—
198	C₂³×C₃	—	6	4	no	—
199	C₂³×C₃	—	6	2	no	—
200	C₂³×C₃	—	12	2	no	—
201	C₂³×C₃	—	12	2	no	—
202	C₂³×C₃	D₄×C₉	1	1	yes	characteristic
203	C₂³×C₃	C₃×#67	1	1	yes	characteristic
204	C₂²×D₃	—	2	4	no	—
205	C₂²×D₃	—	2	2	no	—
206	C₂²×D₃	—	4	2	no	—
207	C₂²×D₃	—	4	2	no	—
208	C₃×D₄	—	3	4	no	—
209	C₃×D₄	—	6	4	no	—
210	C₃×D₄	—	6	2	no	—
211	C₂×C₃×C₄	—	2	4	no	—
212	C₂×C₃×C₄	—	2	2	no	—
213	C₂×C₃×C₄	—	2	2	no	—
214	C₂×C₃×C₄	—	2	2	no	—
215	C₂×C₃×C₄	—	2	2	no	—
216	C₂×C₃×C₄	—	2	1	no	—
217	C₂×C₃×C₄	—	2	1	no	—
218	C₂×C₃×C₄	—	4	4	no	—
219	C₂×C₃×C₄	—	4	2	no	—
220	C₂×C₃×C₄	—	4	2	no	—
221	C₂×C₃×C₄	C₂×C₄×C₉	1	2	yes	—
222	C₂×C₃×C₄	D₄×C₉	1	2	yes	—
223	C₂×C₃×C₄	D₄×C₉	1	1	yes	characteristic
224	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
225	C₂×C₃×C₄	C₃×C₄×D₃	1	2	yes	—
226	C₂×C₃×C₄	C₃×D₁₂	1	2	yes	—
227	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
228	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
229	D₁₂	—	2	4	no	—
230	D₁₂	—	2	2	no	—
231	D₁₂	C₂×C₄×C₉	1	4	yes	complemented
232	C₃×C₈	—	6	2	no	—
233	C₃⋊C₈	—	2	2	no	—
234	C₂×C₃²	C₃×#102	1	4	yes	—
235	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
236	C₂×C₃²	C₂×C₃×D₈	1	1	yes	characteristic
237	C₂×C₃²	C₂×C₃×SD₁₆	1	1	yes	characteristic
238	C₃×D₃	—	4	4	no	—
239	C₂×C₉	—	2	1	no	—
240	C₂×C₉	—	2	1	no	—
241	C₂×C₉	—	2	1	no	—
242	C₂×C₉	—	2	4	no	—
243	C₂×C₉	—	12	4	no	—
244	C₂×C₉	#809	1	4	yes	direct product factor
245	C₂×C₉	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
246	C₂×C₉	C₂×#213	1	1	yes	characteristic
247	C₂×C₉	C₂×#215	1	1	yes	characteristic
248	C₂⁴	—	6	1	no	—
249	C₂×D₄	—	3	4	no	—
250	C₂×D₄	—	3	2	no	—
251	C₂×D₄	—	6	2	no	—
252	C₂×D₄	—	6	1	no	—
253	C₂²×C₄	—	2	1	no	—
254	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
255	C₂×C₈	—	3	2	no	—
256	C₂×C₈	—	6	2	no	—
257	C₄⋊C₄	—	2	1	no	—
258	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
259	C₂²×C₃	—	2	1	no	—
260	C₂²×C₃	—	2	2	no	—
261	C₂²×C₃	—	2	2	no	—
262	C₂²×C₃	—	2	2	no	—
263	C₂²×C₃	—	6	4	no	—
264	C₂²×C₃	—	12	2	no	—
265	C₂²×C₃	—	12	2	no	—
266	C₂²×C₃	—	12	8	no	—
267	C₂²×C₃	C₉×C₂²⋊C₄	1	2	yes	—
268	C₂²×C₃	C₉×D₈	1	2	yes	—
269	C₂²×C₃	C₉×SD₁₆	1	2	yes	—
270	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
271	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	2	yes	—
272	C₂²×C₃	C₃×#213	1	2	yes	—
273	C₂²×C₃	C₃×#215	1	2	yes	—
274	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
275	C₂×D₃	—	2	4	no	—
276	C₂×D₃	—	4	2	no	—
277	C₂×D₃	—	4	2	no	—
278	C₂×D₃	—	4	8	no	—
279	C₃×C₄	—	2	1	no	—
280	C₃×C₄	—	2	1	no	—
281	C₃×C₄	—	2	2	no	—
282	C₃×C₄	—	4	4	no	—
283	C₃×C₄	—	4	2	no	—
284	C₃×C₄	—	4	2	no	—
285	C₃×C₄	C₉×C₂²⋊C₄	1	2	yes	—
286	C₃×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
287	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
288	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	2	yes	—
289	C₃×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
290	C₃×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
291	C₃²	C₂×C₃×#102	1	1	yes	characteristic
292	C₉	—	2	1	no	—
293	C₉	C₂×#809	1	1	yes	characteristic, direct product factor
294	C₂³	—	6	2	no	—
295	C₂³	—	6	4	no	—
296	C₂³	—	12	2	no	—
297	C₂³	—	12	2	no	—
298	C₂³	C₉×#67	1	1	yes	characteristic
299	D₄	—	3	4	no	—
300	D₄	—	6	2	no	—
301	D₄	—	6	4	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	4	2	no	—
304	C₂×C₄	C₄×D₃×C₉	1	2	yes	—
305	C₂×C₄	C₉×D₁₂	1	2	yes	—
306	C₂×C₄	C₉×#67	1	1	yes	characteristic
307	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
308	C₈	—	6	2	no	—
309	C₂×C₃	—	2	1	no	—
310	C₂×C₃	—	2	1	no	—
311	C₂×C₃	—	2	1	no	—
312	C₂×C₃	—	2	4	no	—
313	C₂×C₃	—	12	4	no	—
314	C₂×C₃	C₉×#102	1	4	yes	complemented
315	C₂×C₃	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
316	C₂×C₃	C₂×C₉×D₈	1	1	yes	characteristic
317	C₂×C₃	C₂×C₉×SD₁₆	1	1	yes	characteristic
318	C₂×C₃	C₃×#809	1	4	yes	—
319	C₂×C₃	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
320	C₂×C₃	C₂×C₃×#213	1	1	yes	characteristic
321	C₂×C₃	C₂×C₃×#215	1	1	yes	characteristic
322	D₃	—	4	4	no	—
323	C₂²	—	6	4	no	—
324	C₂²	—	12	2	no	—
325	C₂²	—	12	2	no	—
326	C₂²	—	12	8	no	—
327	C₂²	C₉×(C₂×D₃)⋊C₄	1	2	yes	—
328	C₂²	C₉×#213	1	2	yes	—
329	C₂²	C₉×#215	1	2	yes	—
330	C₂²	C₂×C₉×#67	1	1	yes	characteristic
331	C₄	—	4	2	no	—
332	C₄	C₉×(C₂×D₃)⋊C₄	1	2	yes	—
333	C₄	C₂×C₄×D₃×C₉	1	1	yes	characteristic
334	C₄	C₂×C₉×D₁₂	1	1	yes	characteristic
335	C₃	—	2	1	no	—
336	C₃	C₂×C₉×#102	1	1	yes	characteristic, complemented
337	C₃	C₂×C₃×#809	1	1	yes	characteristic
338	C₂	—	12	4	no	—
339	C₂	C₉×#809	1	4	yes	direct product factor
340	C₂	C₂×C₉×(C₂×D₃)⋊C₄	1	1	yes	characteristic
341	C₂	C₂×C₉×#213	1	1	yes	characteristic
342	C₂	C₂×C₉×#215	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	#67
commutator	C₃×C₄	C₂²×C₄×C₉
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₂×C₃×C₉×C₄⋊C₄	C₂
socle	C₂³×C₃²	C₃×D₄
prime radical	C₂²×C₃×D₁₂	C₂×C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₂×C₉×C₄⋊C₄	D₃
hypocenter	C₃	C₂×C₉×#102
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₉ ◁ C₂²×C₄×C₉ ◁ C₂×C₉×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₉×C₄⋊C₄	C₂	semidirect
3. C₂²×C₉×C₃⋊C₈	C₂	semidirect
4. C₉×#809	C₂	direct (N × H)
12. C₂×C₉×D₁₂	C₄	semidirect
15. C₃×C₉×C₄⋊C₄	C₂²	semidirect
17. C₂×C₉×C₃⋊C₈	C₂²	semidirect
25. C₂×C₉×C₄⋊C₄	D₃	semidirect
40. C₉×D₁₂	C₂×C₄	semidirect
43. C₂×#809	C₉	direct (N × H)
69. C₉×C₄⋊C₄	C₂×D₃	semidirect
86. C₂×C₃×C₄⋊C₄	C₂×C₉	semidirect
88. C₂²×C₃⋊C₈	C₂×C₉	semidirect
90. #809	C₂×C₉	direct (N × H)
129. C₂×C₃×C₉	#102	semidirect
148. C₂×D₁₂	C₄×C₉	semidirect
156. C₃×C₄⋊C₄	C₂²×C₉	semidirect
159. C₂×C₃⋊C₈	C₂²×C₉	semidirect
194. C₂×C₄⋊C₄	D₃×C₉	semidirect
196. C₃×C₉	C₂×#102	semidirect
231. D₁₂	C₂×C₄×C₉	semidirect
244. C₂×C₉	#809	direct (N × H)
258. C₄⋊C₄	C₂×D₃×C₉	semidirect
293. C₉	C₂×#809	direct (N × H)
314. C₂×C₃	C₉×#102	semidirect
336. C₃	C₂×C₉×#102	semidirect
339. C₂	C₉×#809	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×D₁₂	2
C₂×C₃×C₉×C₄⋊C₄	2
C₂²×C₉×C₃⋊C₈	2
C₉×#809	2
C₂×C₃×#809	3
C₂×C₉×#102	3

Subgroups — C2×C9×#809 #13142581

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#809 #13142581