Subgroups — C₂×#11722641 #13164944

Order 1728.

2776 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
2	#11722641	C₂	1	16	yes	maximal, direct product factor
3	C₂×#88724	C₂	1	2	yes	maximal, complemented
4	C₂×D₄×AGL(1,ℤ/9)	C₂	1	6	yes	maximal, complemented
5	C₂×#3697⋊C₃	C₂	1	3	yes	maximal, complemented
6	C₂²×C₄⋊AGL(1,ℤ/9)	C₂	1	3	yes	maximal, complemented
7	C₂×C₃×#1009	—	3	1	no	maximal
8	C₂×#63715	C₃	1	1	yes	maximal, characteristic, complemented
9	C₂³×AGL(1,ℤ/9)	C₂²	1	6	yes	complemented
10	#41×3₋¹⁺²	C₂²	1	8	yes	complemented
11	C₂×Q₈×3₋¹⁺²	C₂²	1	1	yes	characteristic, complemented
12	C₂×D₄×3₋¹⁺²	C₂²	1	3	yes	complemented
13	C₂²×C₄×3₋¹⁺²	C₂²	1	3	yes	complemented
14	C₂×#611⋊C₃	C₂²	1	6	yes	complemented
15	#88724	C₂²	1	16	yes	complemented
16	D₄×AGL(1,ℤ/9)	C₂²	1	48	yes	complemented
17	#3697⋊C₃	C₂²	1	24	yes	complemented
18	C₂×C₄⋊AGL(1,ℤ/9)	C₂²	1	3	yes	complemented
19	C₂×C₄⋊AGL(1,ℤ/9)	C₂²	1	6	yes	complemented
20	C₂×C₄⋊AGL(1,ℤ/9)	C₂²	1	24	yes	complemented
21	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	6	yes	complemented
22	C₂×3₋¹⁺²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃²×#41	D₃	1	1	yes	characteristic
24	C₃×#1009	—	3	16	no	—
25	C₂×C₃×#239	—	3	2	no	—
26	C₂×C₃×D₃×D₄	—	3	6	no	—
27	C₂×C₃×#235	—	3	3	no	—
28	C₂²×C₃×D₁₂	—	3	3	no	—
29	C₂×C₉×#41	—	2	1	no	—
30	C₂×C₉×#41	C₂×C₃	1	1	yes	characteristic, complemented
31	#63715	C₂×C₃	1	16	yes	complemented
32	C₂×#3701	C₂×C₃	1	2	yes	complemented
33	C₂×D₄×D₉	C₂×C₃	1	6	yes	complemented
34	C₂×#3697	C₂×C₃	1	3	yes	complemented
35	C₂²×D₃₆	C₂×C₃	1	3	yes	complemented
36	C₂³×3₋¹⁺²	C₂³	1	3	yes	—
37	C₂²×AGL(1,ℤ/9)	—	4	12	no	—
38	C₂²×AGL(1,ℤ/9)	C₂³	1	6	yes	—
39	C₂²×AGL(1,ℤ/9)	C₂³	1	24	yes	complemented
40	Q₈×3₋¹⁺²	C₂³	1	4	yes	complemented
41	D₄×3₋¹⁺²	C₂³	1	12	yes	complemented
42	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
43	C₂×C₄×3₋¹⁺²	C₂³	1	3	yes	—
44	C₂×C₄×3₋¹⁺²	C₂³	1	12	yes	complemented
45	#611⋊C₃	C₂³	1	24	yes	complemented
46	C₂×3₋¹⁺²⋊C₄	C₂³	1	2	yes	—
47	C₄⋊AGL(1,ℤ/9)	C₂³	1	12	yes	complemented
48	C₄⋊AGL(1,ℤ/9)	C₂³	1	24	yes	complemented
49	C₄×AGL(1,ℤ/9)	C₂³	1	24	yes	complemented
50	3₋¹⁺²⋊Q₈	C₂³	1	4	yes	complemented
51	C₂×C₃×H(5,𝔽₂)	—	9	1	no	—
52	C₂×#1009	—	3	1	no	—
53	C₂³×C₃×D₃	—	3	6	no	—
54	C₃²×#41	C₂×D₃	1	8	yes	—
55	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
56	C₂×C₃²×D₄	C₂×D₃	1	3	yes	—
57	C₂²×C₃²×C₄	C₂×D₃	1	3	yes	—
58	C₂×C₃×#67	—	3	6	no	—
59	C₃×#239	—	3	16	no	—
60	C₃×D₃×D₄	—	3	48	no	—
61	C₃×#235	—	3	24	no	—
62	C₂×C₃×D₁₂	—	3	3	no	—
63	C₂×C₃×D₁₂	—	3	6	no	—
64	C₂×C₃×D₁₂	—	3	24	no	—
65	C₂×C₃×C₄×D₃	—	3	6	no	—
66	C₂×C₃×Dic₆	—	3	1	no	—
67	C₂³×D₉	C₂²×C₃	1	6	yes	complemented
68	C₉×#41	—	2	8	no	—
69	C₉×#41	C₂²×C₃	1	8	yes	complemented
70	C₂×Q₈×C₉	—	2	1	no	—
71	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
72	C₂×D₄×C₉	—	2	3	no	—
73	C₂×D₄×C₉	C₂²×C₃	1	3	yes	complemented
74	C₂²×C₄×C₉	—	2	3	no	—
75	C₂²×C₄×C₉	C₂²×C₃	1	3	yes	complemented
76	C₂×#611	C₂²×C₃	1	6	yes	complemented
77	#3701	C₂²×C₃	1	16	yes	complemented
78	D₄×D₉	C₂²×C₃	1	48	yes	complemented
79	#3697	C₂²×C₃	1	24	yes	complemented
80	C₂×D₃₆	C₂²×C₃	1	3	yes	complemented
81	C₂×D₃₆	C₂²×C₃	1	6	yes	complemented
82	C₂×D₃₆	C₂²×C₃	1	24	yes	complemented
83	C₂×C₄×D₉	C₂²×C₃	1	6	yes	complemented
84	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic, complemented
85	C₂²×3₋¹⁺²	—	2	6	no	—
86	C₂²×3₋¹⁺²	C₂⁴	1	6	yes	—
87	C₂²×3₋¹⁺²	C₂⁴	1	1	yes	characteristic
88	C₂×AGL(1,ℤ/9)	—	2	12	no	—
89	C₂×AGL(1,ℤ/9)	—	4	24	no	—
90	C₂×AGL(1,ℤ/9)	C₂⁴	1	12	yes	—
91	C₄×3₋¹⁺²	C₂⁴	1	2	yes	—
92	C₄×3₋¹⁺²	C₂⁴	1	6	yes	—
93	3₋¹⁺²⋊C₄	C₂⁴	1	4	yes	—
94	C₃×H(5,𝔽₂)	—	9	16	no	—
95	C₂×C₃×#41	—	3	1	no	—
96	C₂×C₃×#41	—	9	3	no	—
97	C₂×C₃×#41	—	9	2	no	—
98	C₂×C₃×#41	C₃×D₃	1	1	yes	characteristic
99	C₂²×C₃×D₄	—	9	3	no	—
100	C₂²×C₃×D₄	—	9	6	no	—
101	#1009	—	3	16	no	—
102	C₂×#239	—	3	2	no	—
103	C₂×D₃×D₄	—	3	6	no	—
104	C₂×#235	—	3	3	no	—
105	C₂²×D₁₂	—	3	3	no	—
106	C₂³×C₃²	C₂²×D₃	1	3	yes	—
107	C₂²×C₃×D₃	—	3	6	no	—
108	C₂²×C₃×D₃	—	3	24	no	—
109	C₂²×C₃×D₃	—	12	12	no	—
110	C₃²×Q₈	C₂²×D₃	1	4	yes	—
111	C₃²×D₄	C₂²×D₃	1	12	yes	—
112	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
113	C₂×C₃²×C₄	C₂²×D₃	1	3	yes	—
114	C₂×C₃²×C₄	C₂²×D₃	1	12	yes	—
115	C₃×#67	—	3	24	no	—
116	C₂×C₃×Dic₃	—	3	2	no	—
117	C₃×D₁₂	—	3	12	no	—
118	C₃×D₁₂	—	3	24	no	—
119	C₃×C₄×D₃	—	3	24	no	—
120	C₃×Dic₆	—	3	4	no	—
121	C₂³×C₉	—	2	3	no	—
122	C₂³×C₉	C₂³×C₃	1	3	yes	—
123	C₂²×D₉	—	4	12	no	—
124	C₂²×D₉	C₂³×C₃	1	6	yes	—
125	C₂²×D₉	C₂³×C₃	1	24	yes	complemented
126	Q₈×C₉	—	2	4	no	—
127	Q₈×C₉	C₂³×C₃	1	4	yes	complemented
128	D₄×C₉	—	2	12	no	—
129	D₄×C₉	C₂³×C₃	1	12	yes	complemented
130	C₂×C₄×C₉	—	2	1	no	—
131	C₂×C₄×C₉	—	2	3	no	—
132	C₂×C₄×C₉	—	2	12	no	—
133	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
134	C₂×C₄×C₉	C₂³×C₃	1	3	yes	—
135	C₂×C₄×C₉	C₂³×C₃	1	12	yes	complemented
136	#611	C₂³×C₃	1	24	yes	complemented
137	C₂×Dic₉	C₂³×C₃	1	2	yes	—
138	D₃₆	C₂³×C₃	1	12	yes	complemented
139	D₃₆	C₂³×C₃	1	24	yes	complemented
140	C₄×D₉	C₂³×C₃	1	24	yes	complemented
141	Dic₁₈	C₂³×C₃	1	4	yes	complemented
142	C₂×H(5,𝔽₂)	—	9	1	no	Sylow
143	C₂×3₋¹⁺²	—	2	6	no	—
144	C₂×3₋¹⁺²	H(5,𝔽₂)	1	2	yes	complemented
145	C₂×3₋¹⁺²	C₂⁵	1	1	yes	characteristic
146	AGL(1,ℤ/9)	—	2	12	no	—
147	C₂⁴×C₃	—	9	6	no	—
148	C₂³×D₃	—	3	6	no	—
149	C₃×#41	—	3	8	no	—
150	C₃×#41	—	9	24	no	—
151	C₃×#41	—	9	16	no	—
152	C₃×#41	C₂×C₃×D₃	1	8	yes	—
153	C₂×C₃×Q₈	—	3	1	no	—
154	C₂×C₃×Q₈	—	9	1	no	—
155	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
156	C₂×C₃×D₄	—	3	3	no	—
157	C₂×C₃×D₄	—	9	3	no	—
158	C₂×C₃×D₄	—	9	6	no	—
159	C₂×C₃×D₄	—	9	24	no	—
160	C₂×C₃×D₄	—	9	48	no	—
161	C₂×C₃×D₄	—	9	6	no	—
162	C₂×C₃×D₄	C₂×C₃×D₃	1	3	yes	—
163	C₂²×C₃×C₄	—	3	3	no	—
164	C₂²×C₃×C₄	—	9	6	no	—
165	C₂²×C₃×C₄	C₂×C₃×D₃	1	3	yes	—
166	C₂×#67	—	3	6	no	—
167	#239	—	3	16	no	—
168	D₃×D₄	—	3	48	no	—
169	#235	—	3	24	no	—
170	C₂×D₁₂	—	3	3	no	—
171	C₂×D₁₂	—	3	6	no	—
172	C₂×D₁₂	—	3	24	no	—
173	C₂×C₄×D₃	—	3	6	no	—
174	C₂×Dic₆	—	3	1	no	—
175	C₂²×C₃²	—	2	6	no	—
176	C₂²×C₃²	C₂³×D₃	1	6	yes	—
177	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
178	C₂×C₃×D₃	—	3	12	no	—
179	C₂×C₃×D₃	—	6	12	no	—
180	C₂×C₃×D₃	—	12	24	no	—
181	C₃²×C₄	C₂³×D₃	1	2	yes	—
182	C₃²×C₄	C₂³×D₃	1	6	yes	—
183	C₃×Dic₃	—	3	4	no	—
184	C₂²×C₉	—	2	6	no	—
185	C₂²×C₉	—	2	1	no	—
186	C₂²×C₉	—	2	6	no	—
187	C₂²×C₉	—	4	6	no	—
188	C₂²×C₉	C₂⁴×C₃	1	6	yes	—
189	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
190	C₂×D₉	—	2	12	no	—
191	C₂×D₉	—	4	24	no	—
192	C₂×D₉	C₂⁴×C₃	1	12	yes	—
193	C₄×C₉	—	2	2	no	—
194	C₄×C₉	—	2	6	no	—
195	C₄×C₉	C₂⁴×C₃	1	2	yes	—
196	C₄×C₉	C₂⁴×C₃	1	6	yes	—
197	Dic₉	C₂⁴×C₃	1	4	yes	—
198	H(5,𝔽₂)	—	9	16	no	—
199	C₂×#41	—	9	2	no	—
200	C₂×#41	—	9	3	no	—
201	C₂×#41	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
202	C₂²×D₄	—	9	6	no	—
203	C₂²×D₄	—	9	3	no	—
204	3₋¹⁺²	C₂×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
205	C₂³×C₃	—	3	3	no	—
206	C₂³×C₃	—	9	6	no	—
207	C₂³×C₃	—	9	24	no	—
208	C₂³×C₃	—	36	12	no	—
209	C₂³×C₃	C₂²×C₃×D₃	1	3	yes	—
210	C₂²×D₃	—	3	6	no	—
211	C₂²×D₃	—	3	24	no	—
212	C₂²×D₃	—	12	12	no	—
213	C₃×Q₈	—	3	4	no	—
214	C₃×Q₈	—	9	4	no	—
215	C₃×Q₈	C₂²×C₃×D₃	1	4	yes	—
216	C₃×D₄	—	3	12	no	—
217	C₃×D₄	—	9	12	no	—
218	C₃×D₄	—	9	24	no	—
219	C₃×D₄	—	9	24	no	—
220	C₃×D₄	C₂²×C₃×D₃	1	12	yes	—
221	C₂×C₃×C₄	—	3	1	no	—
222	C₂×C₃×C₄	—	3	3	no	—
223	C₂×C₃×C₄	—	3	12	no	—
224	C₂×C₃×C₄	—	9	24	no	—
225	C₂×C₃×C₄	—	9	2	no	—
226	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
227	C₂×C₃×C₄	C₂²×C₃×D₃	1	3	yes	—
228	C₂×C₃×C₄	C₂²×C₃×D₃	1	12	yes	—
229	#67	—	3	24	no	—
230	C₂×Dic₃	—	3	2	no	—
231	D₁₂	—	3	12	no	—
232	D₁₂	—	3	24	no	—
233	C₄×D₃	—	3	24	no	—
234	Dic₆	—	3	4	no	—
235	C₂×C₃²	—	2	6	no	—
236	C₂×C₃²	#1009	1	2	yes	—
237	C₂×C₃²	C₂⁴×D₃	1	1	yes	characteristic
238	C₃×D₃	—	6	12	no	—
239	C₂×C₉	—	2	6	no	—
240	C₂×C₉	—	2	2	no	—
241	C₂×C₉	—	2	1	no	—
242	C₂×C₉	—	4	6	no	—
243	C₂×C₉	C₃×H(5,𝔽₂)	1	2	yes	complemented
244	C₂×C₉	C₂⁵×C₃	1	1	yes	characteristic
245	D₉	—	2	12	no	—
246	C₂⁴	—	9	6	no	—
247	#41	—	9	16	no	—
248	#41	—	9	24	no	—
249	#41	C₂×AGL(1,ℤ/9)	1	8	yes	complemented
250	C₂×Q₈	—	9	1	no	—
251	C₂×Q₈	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
252	C₂×D₄	—	9	6	no	—
253	C₂×D₄	—	9	48	no	—
254	C₂×D₄	—	9	6	no	—
255	C₂×D₄	—	9	3	no	—
256	C₂×D₄	—	9	24	no	—
257	C₂×D₄	C₂×AGL(1,ℤ/9)	1	3	yes	complemented
258	C₂²×C₄	—	9	6	no	—
259	C₂²×C₄	C₂×AGL(1,ℤ/9)	1	3	yes	complemented
260	C₂²×C₃	—	2	6	no	—
261	C₂²×C₃	—	3	6	no	—
262	C₂²×C₃	—	3	1	no	—
263	C₂²×C₃	—	6	6	no	—
264	C₂²×C₃	—	9	12	no	—
265	C₂²×C₃	—	18	12	no	—
266	C₂²×C₃	—	36	24	no	—
267	C₂²×C₃	C₂³×C₃×D₃	1	6	yes	—
268	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
269	C₂×D₃	—	3	12	no	—
270	C₂×D₃	—	6	12	no	—
271	C₂×D₃	—	12	24	no	—
272	C₃×C₄	—	3	2	no	—
273	C₃×C₄	—	3	6	no	—
274	C₃×C₄	—	9	4	no	—
275	C₃×C₄	C₂³×C₃×D₃	1	2	yes	—
276	C₃×C₄	C₂³×C₃×D₃	1	6	yes	—
277	Dic₃	—	3	4	no	—
278	C₃²	C₂×#1009	1	1	yes	characteristic
279	C₉	—	2	1	no	—
280	C₉	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic, complemented
281	C₂³	—	9	6	no	—
282	C₂³	—	9	24	no	—
283	C₂³	—	36	12	no	—
284	C₂³	C₂²×AGL(1,ℤ/9)	1	3	yes	—
285	Q₈	—	9	4	no	—
286	Q₈	C₂²×AGL(1,ℤ/9)	1	4	yes	complemented
287	D₄	—	9	24	no	—
288	D₄	—	9	24	no	—
289	D₄	—	9	12	no	—
290	D₄	C₂²×AGL(1,ℤ/9)	1	12	yes	complemented
291	C₂×C₄	—	9	2	no	—
292	C₂×C₄	—	9	24	no	—
293	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	3	yes	—
294	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
295	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	12	yes	complemented
296	C₂×C₃	—	2	6	no	—
297	C₂×C₃	—	3	1	no	—
298	C₂×C₃	—	3	2	no	—
299	C₂×C₃	—	6	6	no	—
300	C₂×C₃	—	18	12	no	—
301	C₂×C₃	C₃×#1009	1	2	yes	—
302	C₂×C₃	C₂⁴×C₃×D₃	1	1	yes	characteristic
303	D₃	—	6	12	no	—
304	C₂²	—	2	6	no	—
305	C₂²	—	9	12	no	—
306	C₂²	—	18	12	no	—
307	C₂²	—	36	24	no	—
308	C₂²	C₂³×AGL(1,ℤ/9)	1	6	yes	—
309	C₂²	C₂³×AGL(1,ℤ/9)	1	1	yes	characteristic
310	C₄	—	9	4	no	—
311	C₄	C₂³×AGL(1,ℤ/9)	1	6	yes	—
312	C₄	C₂³×AGL(1,ℤ/9)	1	2	yes	—
313	C₃	—	3	1	no	—
314	C₃	C₂×C₃×#1009	1	1	yes	characteristic
315	C₂	—	2	6	no	—
316	C₂	—	18	12	no	—
317	C₂	#11722641	1	2	yes	direct product factor
318	C₂	C₂⁴×AGL(1,ℤ/9)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×AGL(1,ℤ/9)
commutator, cosocle	C₂×C₉	C₂⁵×C₃
Frattini	C₂×C₃	C₂⁴×C₃×D₃
Fitting	C₂×#41×3₋¹⁺²	C₂
socle	C₂²×C₃	C₂³×C₃×D₃
hypercenter	C₂×#41	AGL(1,ℤ/9)
hypocenter	C₉	C₂×C₃×H(5,𝔽₂)
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
1. C₂×#41×3₋¹⁺²	C₂	semidirect
2. #11722641	C₂	direct (N × H)
3. C₂×#88724	C₂	semidirect
4. C₂×D₄×AGL(1,ℤ/9)	C₂	semidirect
5. C₂×#3697⋊C₃	C₂	semidirect
6. C₂²×C₄⋊AGL(1,ℤ/9)	C₂	semidirect
8. C₂×#63715	C₃	semidirect
9. C₂³×AGL(1,ℤ/9)	C₂²	semidirect
10. #41×3₋¹⁺²	C₂²	semidirect
11. C₂×Q₈×3₋¹⁺²	C₂²	semidirect
12. C₂×D₄×3₋¹⁺²	C₂²	semidirect
13. C₂²×C₄×3₋¹⁺²	C₂²	semidirect
14. C₂×#611⋊C₃	C₂²	semidirect
15. #88724	C₂²	semidirect
16. D₄×AGL(1,ℤ/9)	C₂²	semidirect
17. #3697⋊C₃	C₂²	semidirect
18. C₂×C₄⋊AGL(1,ℤ/9)	C₂²	semidirect
19. C₂×C₄⋊AGL(1,ℤ/9)	C₂²	semidirect
20. C₂×C₄⋊AGL(1,ℤ/9)	C₂²	semidirect
21. C₂×C₄×AGL(1,ℤ/9)	C₂²	semidirect
22. C₂×3₋¹⁺²⋊Q₈	C₂²	semidirect
30. C₂×C₉×#41	C₂×C₃	semidirect
31. #63715	C₂×C₃	semidirect
32. C₂×#3701	C₂×C₃	semidirect
33. C₂×D₄×D₉	C₂×C₃	semidirect
34. C₂×#3697	C₂×C₃	semidirect
35. C₂²×D₃₆	C₂×C₃	semidirect
39. C₂²×AGL(1,ℤ/9)	C₂³	semidirect
40. Q₈×3₋¹⁺²	C₂³	semidirect
41. D₄×3₋¹⁺²	C₂³	semidirect
44. C₂×C₄×3₋¹⁺²	C₂³	semidirect
45. #611⋊C₃	C₂³	semidirect
47. C₄⋊AGL(1,ℤ/9)	C₂³	semidirect
48. C₄⋊AGL(1,ℤ/9)	C₂³	semidirect
49. C₄×AGL(1,ℤ/9)	C₂³	semidirect
50. 3₋¹⁺²⋊Q₈	C₂³	semidirect
67. C₂³×D₉	C₂²×C₃	semidirect
69. C₉×#41	C₂²×C₃	semidirect
71. C₂×Q₈×C₉	C₂²×C₃	semidirect
73. C₂×D₄×C₉	C₂²×C₃	semidirect
75. C₂²×C₄×C₉	C₂²×C₃	semidirect
76. C₂×#611	C₂²×C₃	semidirect
77. #3701	C₂²×C₃	semidirect
78. D₄×D₉	C₂²×C₃	semidirect
79. #3697	C₂²×C₃	semidirect
80. C₂×D₃₆	C₂²×C₃	semidirect
81. C₂×D₃₆	C₂²×C₃	semidirect
82. C₂×D₃₆	C₂²×C₃	semidirect
83. C₂×C₄×D₉	C₂²×C₃	semidirect
84. C₂×Dic₁₈	C₂²×C₃	semidirect
125. C₂²×D₉	C₂³×C₃	semidirect
127. Q₈×C₉	C₂³×C₃	semidirect
129. D₄×C₉	C₂³×C₃	semidirect
135. C₂×C₄×C₉	C₂³×C₃	semidirect
136. #611	C₂³×C₃	semidirect
138. D₃₆	C₂³×C₃	semidirect
139. D₃₆	C₂³×C₃	semidirect
140. C₄×D₉	C₂³×C₃	semidirect
141. Dic₁₈	C₂³×C₃	semidirect
144. C₂×3₋¹⁺²	H(5,𝔽₂)	semidirect
201. C₂×#41	AGL(1,ℤ/9)	semidirect
204. 3₋¹⁺²	C₂×H(5,𝔽₂)	semidirect
243. C₂×C₉	C₃×H(5,𝔽₂)	semidirect
249. #41	C₂×AGL(1,ℤ/9)	semidirect
251. C₂×Q₈	C₂×AGL(1,ℤ/9)	semidirect
257. C₂×D₄	C₂×AGL(1,ℤ/9)	semidirect
259. C₂²×C₄	C₂×AGL(1,ℤ/9)	semidirect
280. C₉	C₂×C₃×H(5,𝔽₂)	semidirect
286. Q₈	C₂²×AGL(1,ℤ/9)	semidirect
290. D₄	C₂²×AGL(1,ℤ/9)	semidirect
295. C₂×C₄	C₂²×AGL(1,ℤ/9)	semidirect
317. C₂	#11722641	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#41×3₋¹⁺²	2
#11722641	2
C₂×#88724	2
C₂×D₄×AGL(1,ℤ/9)	2
C₂×#3697⋊C₃	2
C₂²×C₄⋊AGL(1,ℤ/9)	2
C₂×C₃×#1009	3
C₂×#63715	3

Subgroups — C2×#11722641 #13164944

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11722641 #13164944