Subgroups — C₂×C₃×(C₂×D₉)⋊C₈ #13143092

Order 1728.

682 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×C₃×C₄×D₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×(C₂×D₉)⋊C₈	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₃×(C₂×D₃)⋊C₈	—	3	1	no	maximal
6	C₂×(C₂×D₉)⋊C₈	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₂³×C₃×D₉	C₄	1	1	yes	characteristic
8	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
9	C₂²×C₃×Dic₉	C₄	1	1	yes	characteristic
10	C₂×C₃×C₄×D₉	—	2	2	no	—
11	C₂×C₃×C₄×D₉	—	2	2	no	—
12	C₂×C₃×C₄×D₉	C₄	1	2	yes	—
13	C₂×C₃×C₄×D₉	C₂²	1	2	yes	—
14	C₂×C₃×C₈×C₉	—	2	2	no	—
15	C₂×C₃×C₈×C₉	C₂²	1	2	yes	complemented
16	C₂×C₃×C₉⋊C₈	—	2	2	no	—
17	C₂×C₃×C₉⋊C₈	C₂²	1	2	yes	complemented
18	C₂²×C₃×C₄×D₃	—	3	1	no	—
19	C₂²×C₃²×C₈	D₃	1	1	yes	characteristic
20	C₂²×C₃×C₃⋊C₈	—	3	1	no	—
21	C₂²×C₄×D₉	C₂×C₃	1	1	yes	characteristic
22	C₃×(C₂×D₃)⋊C₈	—	3	4	no	—
23	C₂²×C₈×C₉	—	2	1	no	—
24	C₂²×C₈×C₉	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂²×C₉⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
26	(C₂×D₉)⋊C₈	C₂×C₃	1	4	yes	direct product factor
27	C₂³×C₃×C₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₃×D₉	—	2	2	no	—
29	C₂²×C₃×D₉	—	2	2	no	—
30	C₂²×C₃×D₉	C₈	1	4	yes	complemented
31	C₂²×C₃×D₉	C₂×C₄	1	2	yes	—
32	C₂×C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₃×C₄×C₉	D₄	1	2	yes	—
34	C₂×C₃×C₄×C₉	D₄	1	2	yes	—
35	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
36	C₂×C₃×Dic₉	—	2	2	no	—
37	C₂×C₃×Dic₉	C₂×C₄	1	2	yes	—
38	C₃×C₄×D₉	—	2	4	no	—
39	C₃×C₄×D₉	—	2	2	no	—
40	C₃×C₄×D₉	—	2	2	no	—
41	C₃×C₈×C₉	—	2	2	no	—
42	C₃×C₉⋊C₈	—	2	2	no	—
43	C₂×C₃×C₂²⋊C₈	—	9	1	no	—
44	C₂×(C₂×D₃)⋊C₈	—	3	1	no	—
45	C₂³×C₃×D₃	—	3	1	no	—
46	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
47	C₂²×C₃×Dic₃	—	3	1	no	—
48	C₂×C₃×C₄×D₃	—	3	2	no	—
49	C₂×C₃×C₄×D₃	—	3	2	no	—
50	C₂×C₃×C₄×D₃	—	6	2	no	—
51	C₂×C₃×C₄×D₃	—	6	2	no	—
52	C₂³×D₉	C₃×C₄	1	1	yes	characteristic
53	C₂×C₃²×C₈	—	2	2	no	—
54	C₂×C₃²×C₈	C₂×D₃	1	2	yes	—
55	C₂×C₃×C₃⋊C₈	—	3	2	no	—
56	C₂×C₃×C₃⋊C₈	—	6	2	no	—
57	C₂²×C₄×C₉	—	2	1	no	—
58	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
59	C₂²×Dic₉	C₃×C₄	1	1	yes	characteristic
60	C₂×C₄×D₉	—	2	2	no	—
61	C₂×C₄×D₉	—	2	2	no	—
62	C₂×C₄×D₉	C₃×C₄	1	2	yes	—
63	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
64	C₂×C₈×C₉	—	2	4	no	—
65	C₂×C₈×C₉	—	2	2	no	—
66	C₂×C₈×C₉	—	2	2	no	—
67	C₂×C₈×C₉	C₂²×C₃	1	2	yes	complemented
68	C₂×C₉⋊C₈	—	2	2	no	—
69	C₂×C₉⋊C₈	C₂²×C₃	1	2	yes	complemented
70	C₂²×C₃×C₉	C₂²⋊C₄	1	2	yes	—
71	C₂²×C₃×C₉	C₂×C₈	1	2	yes	—
72	C₂²×C₃×C₉	M₁₆	1	2	yes	—
73	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
74	C₂×C₃×D₉	—	2	8	no	—
75	C₂×C₃×D₉	—	2	2	no	—
76	C₂×C₃×D₉	—	2	2	no	—
77	C₂×C₃×D₉	C₂×C₈	1	4	yes	complemented
78	C₃×C₄×C₉	C₂²⋊C₄	1	2	yes	—
79	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
80	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
81	C₃×Dic₉	—	2	2	no	—
82	C₂³×C₃×C₄	—	9	1	no	—
83	C₂²×C₄×D₃	—	3	1	no	—
84	C₂²×C₃×C₈	—	2	1	no	—
85	C₂²×C₃×C₈	—	9	1	no	—
86	C₂²×C₃×C₈	D₉	1	1	yes	characteristic, complemented
87	C₂²×C₃×C₈	C₃×D₃	1	1	yes	characteristic
88	C₂²×C₃⋊C₈	—	3	1	no	—
89	C₃×C₂²⋊C₈	—	9	4	no	—
90	(C₂×D₃)⋊C₈	—	3	4	no	—
91	C₂³×C₃²	C₄×D₃	1	1	yes	characteristic
92	C₂²×C₃×D₃	—	3	4	no	—
93	C₂²×C₃×D₃	—	3	2	no	—
94	C₂²×C₃×D₃	—	6	2	no	—
95	C₂²×C₃×D₃	—	6	2	no	—
96	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
97	C₂×C₃²×C₄	D₁₂	1	2	yes	—
98	C₂×C₃²×C₄	#67	1	2	yes	—
99	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
100	C₂×C₃×Dic₃	—	3	2	no	—
101	C₂×C₃×Dic₃	—	6	2	no	—
102	C₃×C₄×D₃	—	6	4	no	—
103	C₃×C₄×D₃	—	6	2	no	—
104	C₃×C₄×D₃	—	6	2	no	—
105	C₂³×C₉	—	2	1	no	—
106	C₂³×C₉	C₂×C₃×C₄	1	1	yes	characteristic
107	C₂²×D₉	—	2	2	no	—
108	C₂²×D₉	—	2	2	no	—
109	C₂²×D₉	C₃×C₈	1	4	yes	complemented
110	C₂²×D₉	C₂×C₃×C₄	1	2	yes	—
111	C₃²×C₈	—	2	2	no	—
112	C₃×C₃⋊C₈	—	6	2	no	—
113	C₂×C₄×C₉	—	2	1	no	—
114	C₂×C₄×C₉	—	2	2	no	—
115	C₂×C₄×C₉	—	2	2	no	—
116	C₂×C₄×C₉	—	2	1	no	—
117	C₂×C₄×C₉	C₂×C₃×C₄	1	1	yes	characteristic
118	C₂×C₄×C₉	C₃×D₄	1	2	yes	—
119	C₂×C₄×C₉	C₃×D₄	1	2	yes	—
120	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
121	C₂×Dic₉	—	2	2	no	—
122	C₂×Dic₉	C₂×C₃×C₄	1	2	yes	—
123	C₄×D₉	—	2	4	no	—
124	C₄×D₉	—	2	2	no	—
125	C₄×D₉	—	2	2	no	—
126	C₈×C₉	—	2	4	no	—
127	C₈×C₉	—	2	2	no	—
128	C₉⋊C₈	—	2	2	no	—
129	C₂×C₂²⋊C₈	—	9	1	no	Sylow
130	C₂×C₃×C₉	C₂²⋊C₈	1	4	yes	complemented
131	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂×C₃×C₉	C₂²×C₈	1	1	yes	characteristic
133	C₂×C₃×C₉	C₂×M₁₆	1	1	yes	characteristic
134	C₃×D₉	—	2	4	no	—
135	C₂⁴×C₃	—	9	1	no	—
136	C₂³×D₃	—	3	1	no	—
137	C₂²×C₃×C₄	—	2	1	no	—
138	C₂²×C₃×C₄	—	9	1	no	—
139	C₂²×C₃×C₄	—	9	2	no	—
140	C₂²×C₃×C₄	—	9	2	no	—
141	C₂²×C₃×C₄	—	18	2	no	—
142	C₂²×C₃×C₄	—	18	2	no	—
143	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
144	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
145	C₂²×Dic₃	—	3	1	no	—
146	C₂×C₄×D₃	—	3	2	no	—
147	C₂×C₄×D₃	—	3	2	no	—
148	C₂×C₄×D₃	—	6	2	no	—
149	C₂×C₄×D₃	—	6	2	no	—
150	C₂×C₃×C₈	—	2	4	no	—
151	C₂×C₃×C₈	—	2	2	no	—
152	C₂×C₃×C₈	—	2	2	no	—
153	C₂×C₃×C₈	—	2	2	no	—
154	C₂×C₃×C₈	—	9	2	no	—
155	C₂×C₃×C₈	—	18	2	no	—
156	C₂×C₃×C₈	C₂×D₉	1	2	yes	complemented
157	C₂×C₃×C₈	C₂×C₃×D₃	1	2	yes	—
158	C₂×C₃⋊C₈	—	3	2	no	—
159	C₂×C₃⋊C₈	—	6	2	no	—
160	C₂²×C₃²	D₃×C₈	1	2	yes	—
161	C₂²×C₃²	ΓL(1,𝔽₂₅)	1	2	yes	—
162	C₂²×C₃²	(C₂×D₃)⋊C₄	1	2	yes	—
163	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
164	C₂×C₃×D₃	—	3	4	no	—
165	C₂×C₃×D₃	—	6	8	no	—
166	C₂×C₃×D₃	—	6	2	no	—
167	C₂×C₃×D₃	—	6	2	no	—
168	C₃²×C₄	(C₂×D₃)⋊C₄	1	2	yes	—
169	C₃²×C₄	C₂×D₁₂	1	1	yes	characteristic
170	C₃²×C₄	C₂×#67	1	1	yes	characteristic
171	C₃×Dic₃	—	6	2	no	—
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	C₃×C₂²⋊C₄	1	2	yes	—
177	C₂²×C₉	C₂×C₃×C₈	1	2	yes	—
178	C₂²×C₉	C₃×M₁₆	1	2	yes	—
179	C₂²×C₉	C₂²×C₃×C₄	1	1	yes	characteristic
180	C₂×D₉	—	2	8	no	—
181	C₂×D₉	—	2	2	no	—
182	C₂×D₉	—	2	2	no	—
183	C₂×D₉	C₂×C₃×C₈	1	4	yes	complemented
184	C₄×C₉	—	2	2	no	—
185	C₄×C₉	—	2	1	no	—
186	C₄×C₉	—	2	1	no	—
187	C₄×C₉	C₃×C₂²⋊C₄	1	2	yes	—
188	C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
189	C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
190	Dic₉	—	2	2	no	—
191	C₂³×C₄	—	9	1	no	—
192	C₂²×C₈	—	9	1	no	—
193	C₂²×C₈	C₃×D₉	1	1	yes	characteristic, complemented
194	C₂²⋊C₈	—	9	4	no	—
195	C₃×C₉	C₂×C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
196	C₂³×C₃	—	2	1	no	—
197	C₂³×C₃	—	9	4	no	—
198	C₂³×C₃	—	9	2	no	—
199	C₂³×C₃	—	18	2	no	—
200	C₂³×C₃	—	18	2	no	—
201	C₂³×C₃	C₄×D₉	1	1	yes	characteristic
202	C₂³×C₃	C₃×C₄×D₃	1	1	yes	characteristic
203	C₂²×D₃	—	3	4	no	—
204	C₂²×D₃	—	3	2	no	—
205	C₂²×D₃	—	6	2	no	—
206	C₂²×D₃	—	6	2	no	—
207	C₂×C₃×C₄	—	2	1	no	—
208	C₂×C₃×C₄	—	2	2	no	—
209	C₂×C₃×C₄	—	2	2	no	—
210	C₂×C₃×C₄	—	2	1	no	—
211	C₂×C₃×C₄	—	9	2	no	—
212	C₂×C₃×C₄	—	18	2	no	—
213	C₂×C₃×C₄	—	18	4	no	—
214	C₂×C₃×C₄	—	18	2	no	—
215	C₂×C₃×C₄	—	18	2	no	—
216	C₂×C₃×C₄	C₄×D₉	1	1	yes	characteristic
217	C₂×C₃×C₄	D₃₆	1	2	yes	—
218	C₂×C₃×C₄	#611	1	2	yes	—
219	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
220	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
221	C₂×C₃×C₄	C₃×D₁₂	1	2	yes	—
222	C₂×C₃×C₄	C₃×#67	1	2	yes	—
223	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
224	C₂×Dic₃	—	3	2	no	—
225	C₂×Dic₃	—	6	2	no	—
226	C₄×D₃	—	6	4	no	—
227	C₄×D₃	—	6	2	no	—
228	C₄×D₃	—	6	2	no	—
229	C₃×C₈	—	2	4	no	—
230	C₃×C₈	—	2	2	no	—
231	C₃×C₈	—	2	2	no	—
232	C₃×C₈	—	18	2	no	—
233	C₃⋊C₈	—	6	2	no	—
234	C₂×C₃²	(C₂×D₃)⋊C₈	1	4	yes	—
235	C₂×C₃²	C₂×D₃×C₈	1	1	yes	characteristic
236	C₂×C₃²	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
237	C₂×C₃²	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
238	C₃×D₃	—	6	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	C₃×C₂²⋊C₈	1	4	yes	complemented
244	C₂×C₉	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
245	C₂×C₉	C₂²×C₃×C₈	1	1	yes	characteristic
246	C₂×C₉	C₂×C₃×M₁₆	1	1	yes	characteristic
247	D₉	—	2	4	no	—
248	C₂⁴	—	9	1	no	—
249	C₂²×C₄	—	9	1	no	—
250	C₂²×C₄	—	9	2	no	—
251	C₂²×C₄	—	9	2	no	—
252	C₂²×C₄	—	18	2	no	—
253	C₂²×C₄	—	18	2	no	—
254	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
255	C₂×C₈	—	2	2	no	—
256	C₂×C₈	—	9	2	no	—
257	C₂×C₈	—	18	2	no	—
258	C₂×C₈	C₂×C₃×D₉	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	—	9	4	no	—
264	C₂²×C₃	—	18	2	no	—
265	C₂²×C₃	—	18	8	no	—
266	C₂²×C₃	—	18	2	no	—
267	C₂²×C₃	C₈×D₉	1	2	yes	—
268	C₂²×C₃	#3663	1	2	yes	—
269	C₂²×C₃	(C₂×D₉)⋊C₄	1	2	yes	—
270	C₂²×C₃	C₂×C₄×D₉	1	1	yes	characteristic
271	C₂²×C₃	C₃×D₃×C₈	1	2	yes	—
272	C₂²×C₃	C₃×ΓL(1,𝔽₂₅)	1	2	yes	—
273	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	2	yes	—
274	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
275	C₂×D₃	—	3	4	no	—
276	C₂×D₃	—	6	2	no	—
277	C₂×D₃	—	6	2	no	—
278	C₂×D₃	—	6	8	no	—
279	C₃×C₄	—	2	1	no	—
280	C₃×C₄	—	2	1	no	—
281	C₃×C₄	—	2	2	no	—
282	C₃×C₄	—	18	2	no	—
283	C₃×C₄	(C₂×D₉)⋊C₄	1	2	yes	—
284	C₃×C₄	C₂×D₃₆	1	1	yes	characteristic
285	C₃×C₄	C₂×#611	1	1	yes	characteristic
286	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	2	yes	—
287	C₃×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
288	C₃×C₄	C₂×C₃×#67	1	1	yes	characteristic
289	Dic₃	—	6	2	no	—
290	C₃²	C₂×(C₂×D₃)⋊C₈	1	1	yes	characteristic
291	C₉	—	2	1	no	—
292	C₉	C₂×C₃×C₂²⋊C₈	1	1	yes	characteristic, complemented
293	C₂³	—	9	2	no	—
294	C₂³	—	9	4	no	—
295	C₂³	—	18	2	no	—
296	C₂³	—	18	2	no	—
297	C₂³	C₃×C₄×D₉	1	1	yes	characteristic
298	C₂×C₄	—	9	2	no	—
299	C₂×C₄	—	18	2	no	—
300	C₂×C₄	—	18	2	no	—
301	C₂×C₄	—	18	2	no	—
302	C₂×C₄	—	18	4	no	—
303	C₂×C₄	C₃×C₄×D₉	1	1	yes	characteristic
304	C₂×C₄	C₃×D₃₆	1	2	yes	—
305	C₂×C₄	C₃×#611	1	2	yes	—
306	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
307	C₈	—	2	2	no	—
308	C₈	—	18	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	—	18	4	no	—
314	C₂×C₃	(C₂×D₉)⋊C₈	1	4	yes	direct product factor
315	C₂×C₃	C₂×C₈×D₉	1	1	yes	characteristic
316	C₂×C₃	C₂×#3663	1	1	yes	characteristic
317	C₂×C₃	C₂×(C₂×D₉)⋊C₄	1	1	yes	characteristic
318	C₂×C₃	C₃×(C₂×D₃)⋊C₈	1	4	yes	—
319	C₂×C₃	C₂×C₃×D₃×C₈	1	1	yes	characteristic
320	C₂×C₃	C₂×C₃×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
321	C₂×C₃	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
322	D₃	—	6	4	no	—
323	C₂²	—	9	4	no	—
324	C₂²	—	18	2	no	—
325	C₂²	—	18	2	no	—
326	C₂²	—	18	8	no	—
327	C₂²	C₃×C₈×D₉	1	2	yes	—
328	C₂²	C₃×#3663	1	2	yes	—
329	C₂²	C₃×(C₂×D₉)⋊C₄	1	2	yes	—
330	C₂²	C₂×C₃×C₄×D₉	1	1	yes	characteristic
331	C₄	—	18	2	no	—
332	C₄	C₃×(C₂×D₉)⋊C₄	1	2	yes	—
333	C₄	C₂×C₃×D₃₆	1	1	yes	characteristic
334	C₄	C₂×C₃×#611	1	1	yes	characteristic
335	C₃	—	2	1	no	—
336	C₃	C₂×(C₂×D₉)⋊C₈	1	1	yes	characteristic, direct product factor
337	C₃	C₂×C₃×(C₂×D₃)⋊C₈	1	1	yes	characteristic
338	C₂	—	18	4	no	—
339	C₂	C₃×(C₂×D₉)⋊C₈	1	4	yes	direct product factor
340	C₂	C₂×C₃×C₈×D₉	1	1	yes	characteristic
341	C₂	C₂×C₃×#3663	1	1	yes	characteristic
342	C₂	C₂×C₃×(C₂×D₉)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂×D₉
commutator	C₂×C₉	C₂²×C₃×C₈
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₂²×C₃×C₈×C₉	C₂
socle	C₂³×C₃²	C₄×D₃
prime radical	C₂³×C₃×D₉	C₄
cosocle	C₂×C₄×C₉	C₂³×C₃
hypercenter	C₂²×C₃×C₈	D₉
hypocenter	C₉	C₂×C₃×C₂²⋊C₈
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×C₈

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₈×C₉	C₂	semidirect
3. C₂²×C₃×C₉⋊C₈	C₂	semidirect
4. C₃×(C₂×D₉)⋊C₈	C₂	direct (N × H)
6. C₂×(C₂×D₉)⋊C₈	C₃	direct (N × H)
15. C₂×C₃×C₈×C₉	C₂²	semidirect
17. C₂×C₃×C₉⋊C₈	C₂²	semidirect
24. C₂²×C₈×C₉	C₂×C₃	semidirect
25. C₂²×C₉⋊C₈	C₂×C₃	semidirect
26. (C₂×D₉)⋊C₈	C₂×C₃	direct (N × H)
30. C₂²×C₃×D₉	C₈	semidirect
67. C₂×C₈×C₉	C₂²×C₃	semidirect
69. C₂×C₉⋊C₈	C₂²×C₃	semidirect
77. C₂×C₃×D₉	C₂×C₈	semidirect
86. C₂²×C₃×C₈	D₉	semidirect
109. C₂²×D₉	C₃×C₈	semidirect
130. C₂×C₃×C₉	C₂²⋊C₈	semidirect
156. C₂×C₃×C₈	C₂×D₉	semidirect
183. C₂×D₉	C₂×C₃×C₈	semidirect
193. C₂²×C₈	C₃×D₉	semidirect
195. C₃×C₉	C₂×C₂²⋊C₈	semidirect
243. C₂×C₉	C₃×C₂²⋊C₈	semidirect
258. C₂×C₈	C₂×C₃×D₉	semidirect
292. C₉	C₂×C₃×C₂²⋊C₈	semidirect
314. C₂×C₃	(C₂×D₉)⋊C₈	direct (N × H)
336. C₃	C₂×(C₂×D₉)⋊C₈	direct (N × H)
339. C₂	C₃×(C₂×D₉)⋊C₈	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×C₃×C₄×D₉	2
C₂²×C₃×C₈×C₉	2
C₂²×C₃×C₉⋊C₈	2
C₃×(C₂×D₉)⋊C₈	2
C₂×C₃×(C₂×D₃)⋊C₈	3
C₂×(C₂×D₉)⋊C₈	3

Subgroups — C2×C3×(C2×D9)⋊C8 #13143092

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×(C₂×D₉)⋊C₈ #13143092