Subgroups — #10588483⋊C₃ #13141948

Order 1728.

507 conjugacy classes of subgroups.

The subgroup lattice has 373 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#88724	C₂	1	1	yes	maximal, characteristic
2	C₂×#3663⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊C₄×AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic, complemented
4	3₋¹⁺²×#103	C₂	1	1	yes	maximal, characteristic, complemented
5	#63395⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#63380⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#63369⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4803	—	3	1	no	maximal
9	#10588483	C₃	1	1	yes	maximal, characteristic, complemented
10	C₂×Q₈×3₋¹⁺²	C₂²	1	1	yes	characteristic
11	#88724	—	2	2	no	—
12	#88724	C₄	1	4	yes	complemented
13	C₂×C₄⋊AGL(1,ℤ/9)	—	2	1	no	—
14	C₂×C₄⋊AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
15	C₂×C₄×AGL(1,ℤ/9)	—	2	1	no	—
16	C₂×C₄×AGL(1,ℤ/9)	—	2	1	no	—
17	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
18	C₂×C₈×3₋¹⁺²	C₂²	1	1	yes	characteristic
19	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
20	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
21	(3₋¹⁺²⋊C₄)⋊C₄	—	2	1	no	—
22	C₂×3₋¹⁺²⋊C₈	C₂²	1	1	yes	characteristic
23	#3663⋊C₃	—	2	2	no	—
24	C₂×C₃×#239	—	3	1	no	—
25	C₂×C₃×ΓL(1,𝔽₂₅)	—	3	1	no	—
26	C₃×D₃×C₄⋊C₄	—	3	1	no	—
27	C₂×#3701	C₂×C₃	1	1	yes	characteristic
28	C₃²×#103	D₃	1	1	yes	characteristic
29	C₃×#835	—	3	1	no	—
30	C₃×#821	—	3	1	no	—
31	C₃×#809	—	3	1	no	—
32	C₂×#3663	C₂×C₃	1	1	yes	characteristic, complemented
33	C₄⋊C₄×D₉	C₂×C₃	1	1	yes	characteristic, complemented
34	C₉×#103	—	2	1	no	—
35	C₉×#103	C₂×C₃	1	1	yes	characteristic, complemented
36	#63395	C₂×C₃	1	1	yes	characteristic, complemented
37	#63380	C₂×C₃	1	1	yes	characteristic, complemented
38	#63369	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂²×AGL(1,ℤ/9)	—	2	1	no	—
40	C₂²×AGL(1,ℤ/9)	D₄	1	1	yes	characteristic
41	Q₈×3₋¹⁺²	—	2	1	no	—
42	Q₈×3₋¹⁺²	C₂×C₄	1	2	yes	complemented
43	C₂×C₄×3₋¹⁺²	—	2	1	no	—
44	C₂×C₄×3₋¹⁺²	—	2	1	no	—
45	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
46	C₂×3₋¹⁺²⋊C₄	—	2	1	no	—
47	C₂×3₋¹⁺²⋊C₄	D₄	1	1	yes	characteristic
48	C₄⋊AGL(1,ℤ/9)	—	2	4	no	—
49	C₄⋊AGL(1,ℤ/9)	—	2	1	no	—
50	C₄⋊AGL(1,ℤ/9)	C₂×C₄	1	2	yes	complemented
51	C₄×AGL(1,ℤ/9)	—	2	4	no	—
52	C₄×AGL(1,ℤ/9)	—	4	2	no	—
53	C₄×AGL(1,ℤ/9)	C₂×C₄	1	2	yes	—
54	C₄×AGL(1,ℤ/9)	D₄	1	2	yes	—
55	C₈×3₋¹⁺²	—	2	1	no	—
56	3₋¹⁺²⋊C₈	—	2	1	no	—
57	C₃×#417	—	9	1	no	—
58	#4803	—	3	1	no	—
59	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
60	C₃×#239	—	3	4	no	—
61	C₃×#239	—	6	2	no	—
62	C₂×C₃×D₁₂	—	3	1	no	—
63	C₂×C₃×D₁₂	—	6	1	no	—
64	C₂×C₃×C₄×D₃	—	3	1	no	—
65	C₂×C₃×C₄×D₃	—	6	1	no	—
66	C₂×C₃×C₄×D₃	—	6	1	no	—
67	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
68	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
69	C₃×C₄⋊Dic₃	—	3	1	no	—
70	C₃×Dic₃⋊C₄	—	6	1	no	—
71	C₂×C₃×C₃⋊C₈	—	3	1	no	—
72	C₃×ΓL(1,𝔽₂₅)	—	6	2	no	—
73	C₂×Q₈×C₉	—	2	1	no	—
74	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic
75	#3701	—	2	2	no	—
76	#3701	C₃×C₄	1	4	yes	complemented
77	C₂×D₃₆	—	2	1	no	—
78	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₄×D₉	—	2	1	no	—
80	C₂×C₄×D₉	—	2	1	no	—
81	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₈×C₉	—	2	1	no	—
83	C₂×C₈×C₉	C₂²×C₃	1	1	yes	characteristic
84	C₉×C₄⋊C₄	—	2	1	no	—
85	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
87	Dic₉⋊C₄	—	2	1	no	—
88	C₂×C₉⋊C₈	C₂²×C₃	1	1	yes	characteristic
89	#3663	—	2	2	no	—
90	C₂²×3₋¹⁺²	C₂×D₄	1	1	yes	characteristic
91	C₂×AGL(1,ℤ/9)	—	2	1	no	—
92	C₂×AGL(1,ℤ/9)	—	2	1	no	—
93	C₂×AGL(1,ℤ/9)	—	2	2	no	—
94	C₂×AGL(1,ℤ/9)	—	4	1	no	—
95	C₂×AGL(1,ℤ/9)	—	4	1	no	—
96	C₂×AGL(1,ℤ/9)	C₂²⋊C₄	1	2	yes	—
97	C₄×3₋¹⁺²	—	2	2	no	—
98	C₄×3₋¹⁺²	—	4	1	no	—
99	C₄×3₋¹⁺²	C₂²×C₄	1	1	yes	characteristic
100	C₄×3₋¹⁺²	C₂×D₄	1	1	yes	characteristic
101	3₋¹⁺²⋊C₄	—	4	1	no	—
102	3₋¹⁺²⋊C₄	C₂²⋊C₄	1	2	yes	—
103	C₂×C₃×#41	—	9	1	no	—
104	C₂×#239	—	3	1	no	—
105	C₂×C₃×M₁₆	—	9	1	no	—
106	C₂×C₃×C₄⋊C₄	—	9	1	no	—
107	C₂×ΓL(1,𝔽₂₅)	—	3	1	no	—
108	D₃×C₄⋊C₄	—	3	1	no	—
109	C₃×#103	—	3	1	no	—
110	C₃×#103	—	9	1	no	—
111	C₃×#103	C₃×D₃	1	1	yes	characteristic
112	C₃×#102	—	9	1	no	—
113	C₃×#102	—	9	1	no	—
114	#835	—	3	1	no	—
115	#821	—	3	1	no	—
116	#809	—	3	1	no	—
117	C₂²×C₃×D₃	—	3	1	no	—
118	C₂²×C₃×D₃	—	6	1	no	—
119	C₃²×Q₈	—	2	1	no	—
120	C₃²×Q₈	C₄×D₃	1	2	yes	—
121	C₂×C₃²×C₄	—	2	1	no	—
122	C₂×C₃²×C₄	—	2	1	no	—
123	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
124	C₂×C₃×Dic₃	—	3	1	no	—
125	C₂×C₃×Dic₃	—	6	1	no	—
126	C₃×D₁₂	—	3	2	no	—
127	C₃×D₁₂	—	6	4	no	—
128	C₃×D₁₂	—	6	1	no	—
129	C₃×C₄×D₃	—	3	2	no	—
130	C₃×C₄×D₃	—	3	2	no	—
131	C₃×C₄×D₃	—	6	4	no	—
132	C₃×C₄×D₃	—	12	2	no	—
133	C₂²×D₉	—	2	1	no	—
134	C₂²×D₉	C₃×D₄	1	1	yes	characteristic
135	C₃²×C₈	—	2	1	no	—
136	C₃×C₃⋊C₈	—	6	1	no	—
137	Q₈×C₉	—	2	1	no	—
138	Q₈×C₉	—	2	2	no	—
139	Q₈×C₉	—	4	1	no	—
140	Q₈×C₉	C₂×C₃×C₄	1	2	yes	complemented
141	C₂×C₄×C₉	—	2	1	no	—
142	C₂×C₄×C₉	—	2	1	no	—
143	C₂×C₄×C₉	—	2	1	no	—
144	C₂×C₄×C₉	—	4	1	no	—
145	C₂×C₄×C₉	—	4	1	no	—
146	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
147	C₂×Dic₉	—	2	1	no	—
148	C₂×Dic₉	C₃×D₄	1	1	yes	characteristic
149	D₃₆	—	2	4	no	—
150	D₃₆	—	2	1	no	—
151	D₃₆	C₂×C₃×C₄	1	2	yes	complemented
152	C₄×D₉	—	2	4	no	—
153	C₄×D₉	—	4	2	no	—
154	C₄×D₉	C₂×C₃×C₄	1	2	yes	—
155	C₄×D₉	C₃×D₄	1	2	yes	—
156	C₈×C₉	—	2	1	no	—
157	C₈×C₉	—	4	1	no	—
158	C₉⋊C₈	—	2	1	no	—
159	#417	—	9	1	no	Sylow
160	C₂×3₋¹⁺²	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂×3₋¹⁺²	AGL(1,ℤ/8)	1	1	yes	characteristic
162	C₂×3₋¹⁺²	#137	1	1	yes	characteristic
163	AGL(1,ℤ/9)	—	2	2	no	—
164	AGL(1,ℤ/9)	—	4	2	no	—
165	C₃×#41	—	9	4	no	—
166	C₃×#41	—	18	2	no	—
167	C₂×C₃×Q₈	—	3	1	no	—
168	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
169	C₂×C₃×D₄	—	9	1	no	—
170	C₂×C₃×D₄	—	18	1	no	—
171	C₂²×C₃×C₄	—	9	1	no	—
172	C₂²×C₃×C₄	—	18	1	no	—
173	C₂²×C₃×C₄	—	18	1	no	—
174	#239	—	3	4	no	—
175	#239	—	6	2	no	—
176	C₂×D₁₂	—	3	1	no	—
177	C₂×D₁₂	—	6	1	no	—
178	C₂×C₄×D₃	—	3	1	no	—
179	C₂×C₄×D₃	—	6	1	no	—
180	C₂×C₄×D₃	—	6	1	no	—
181	C₃×M₁₆	—	18	2	no	—
182	C₂×C₃×C₈	—	3	1	no	—
183	C₂×C₃×C₈	—	9	1	no	—
184	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
185	C₃×C₄⋊C₄	—	3	1	no	—
186	C₃×C₄⋊C₄	—	9	1	no	—
187	C₃×C₄⋊C₄	—	18	1	no	—
188	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
189	C₄⋊Dic₃	—	3	1	no	—
190	Dic₃⋊C₄	—	6	1	no	—
191	C₂×C₃⋊C₈	—	3	1	no	—
192	ΓL(1,𝔽₂₅)	—	6	2	no	—
193	C₂²×C₃²	D₃×D₄	1	1	yes	characteristic
194	C₂×C₃×D₃	—	3	2	no	—
195	C₂×C₃×D₃	—	6	1	no	—
196	C₂×C₃×D₃	—	6	1	no	—
197	C₂×C₃×D₃	—	6	2	no	—
198	C₂×C₃×D₃	—	12	1	no	—
199	C₂×C₃×D₃	—	12	1	no	—
200	C₃²×C₄	—	2	2	no	—
201	C₃²×C₄	—	4	1	no	—
202	C₃²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
203	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
204	C₃×Dic₃	—	3	2	no	—
205	C₃×Dic₃	—	12	1	no	—
206	C₂²×C₉	—	2	1	no	—
207	C₂²×C₉	C₂×C₃×D₄	1	1	yes	characteristic
208	C₂×D₉	—	2	1	no	—
209	C₂×D₉	—	2	1	no	—
210	C₂×D₉	—	2	2	no	—
211	C₂×D₉	—	4	1	no	—
212	C₂×D₉	—	4	1	no	—
213	C₂×D₉	C₃×C₂²⋊C₄	1	2	yes	—
214	C₄×C₉	—	2	2	no	—
215	C₄×C₉	—	2	1	no	—
216	C₄×C₉	—	2	1	no	—
217	C₄×C₉	—	4	2	no	—
218	C₄×C₉	—	4	1	no	—
219	C₄×C₉	—	8	1	no	—
220	C₄×C₉	C₂²×C₃×C₄	1	1	yes	characteristic
221	C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
222	Dic₉	—	4	1	no	—
223	Dic₉	C₃×C₂²⋊C₄	1	2	yes	—
224	C₂×#41	—	9	1	no	—
225	C₂×M₁₆	—	9	1	no	—
226	C₂×C₄⋊C₄	—	9	1	no	—
227	#103	—	9	1	no	—
228	#103	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
229	#102	—	9	1	no	—
230	#102	—	9	1	no	—
231	3₋¹⁺²	#417	1	1	yes	characteristic, complemented, Sylow
232	C₂³×C₃	—	9	1	no	—
233	C₂³×C₃	—	18	1	no	—
234	C₂²×D₃	—	3	1	no	—
235	C₂²×D₃	—	6	1	no	—
236	C₃×Q₈	—	2	1	no	—
237	C₃×Q₈	—	3	2	no	—
238	C₃×Q₈	—	6	1	no	—
239	C₃×Q₈	C₃×C₄×D₃	1	2	yes	—
240	C₃×D₄	—	9	2	no	—
241	C₃×D₄	—	18	1	no	—
242	C₃×D₄	—	18	4	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	3	1	no	—
246	C₂×C₃×C₄	—	6	1	no	—
247	C₂×C₃×C₄	—	6	1	no	—
248	C₂×C₃×C₄	—	9	2	no	—
249	C₂×C₃×C₄	—	9	2	no	—
250	C₂×C₃×C₄	—	9	1	no	—
251	C₂×C₃×C₄	—	18	4	no	—
252	C₂×C₃×C₄	—	18	1	no	—
253	C₂×C₃×C₄	—	36	2	no	—
254	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
255	C₂×Dic₃	—	3	1	no	—
256	C₂×Dic₃	—	6	1	no	—
257	D₁₂	—	3	2	no	—
258	D₁₂	—	6	4	no	—
259	D₁₂	—	6	1	no	—
260	C₄×D₃	—	3	2	no	—
261	C₄×D₃	—	3	2	no	—
262	C₄×D₃	—	6	4	no	—
263	C₄×D₃	—	12	2	no	—
264	C₃×C₈	—	2	1	no	—
265	C₃×C₈	—	6	1	no	—
266	C₃×C₈	—	18	1	no	—
267	C₃⋊C₈	—	6	1	no	—
268	C₂×C₃²	D₃×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₃²	#914	1	1	yes	characteristic
270	C₂×C₃²	#918	1	1	yes	characteristic
271	C₃×D₃	—	6	2	no	—
272	C₃×D₃	—	12	2	no	—
273	C₂×C₉	—	2	1	no	—
274	C₂×C₉	—	2	1	no	—
275	C₂×C₉	—	2	1	no	—
276	C₂×C₉	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
277	C₂×C₉	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
278	C₂×C₉	C₃×#137	1	1	yes	characteristic
279	D₉	—	2	2	no	—
280	D₉	—	4	2	no	—
281	#41	—	9	4	no	—
282	#41	—	18	2	no	—
283	C₂×Q₈	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
284	C₂×D₄	—	9	1	no	—
285	C₂×D₄	—	18	1	no	—
286	C₂²×C₄	—	9	1	no	—
287	C₂²×C₄	—	18	1	no	—
288	C₂²×C₄	—	18	1	no	—
289	M₁₆	—	18	2	no	—
290	C₂×C₈	—	9	1	no	—
291	C₂×C₈	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
292	C₄⋊C₄	—	9	1	no	—
293	C₄⋊C₄	—	18	1	no	—
294	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
295	C₂²×C₃	—	3	1	no	—
296	C₂²×C₃	—	9	2	no	—
297	C₂²×C₃	—	18	1	no	—
298	C₂²×C₃	—	18	1	no	—
299	C₂²×C₃	—	18	2	no	—
300	C₂²×C₃	—	36	1	no	—
301	C₂²×C₃	—	36	1	no	—
302	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
303	C₂×D₃	—	3	2	no	—
304	C₂×D₃	—	6	1	no	—
305	C₂×D₃	—	6	1	no	—
306	C₂×D₃	—	6	2	no	—
307	C₂×D₃	—	12	1	no	—
308	C₂×D₃	—	12	1	no	—
309	C₃×C₄	—	2	2	no	—
310	C₃×C₄	—	3	1	no	—
311	C₃×C₄	—	3	1	no	—
312	C₃×C₄	—	4	1	no	—
313	C₃×C₄	—	6	2	no	—
314	C₃×C₄	—	9	2	no	—
315	C₃×C₄	—	12	1	no	—
316	C₃×C₄	—	36	1	no	—
317	C₃×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
318	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
319	Dic₃	—	3	2	no	—
320	Dic₃	—	12	1	no	—
321	C₃²	#4803	1	1	yes	characteristic
322	C₉	—	2	1	no	—
323	C₉	C₃×#417	1	1	yes	characteristic, complemented
324	C₂³	—	9	1	no	—
325	C₂³	—	18	1	no	—
326	Q₈	—	2	1	no	—
327	Q₈	C₄×AGL(1,ℤ/9)	1	2	yes	complemented
328	D₄	—	9	2	no	—
329	D₄	—	18	4	no	—
330	D₄	—	18	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	9	1	no	—
334	C₂×C₄	—	9	2	no	—
335	C₂×C₄	—	9	2	no	—
336	C₂×C₄	—	18	4	no	—
337	C₂×C₄	—	18	1	no	—
338	C₂×C₄	—	36	2	no	—
339	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
340	C₈	—	2	1	no	—
341	C₈	—	18	1	no	—
342	C₂×C₃	—	3	1	no	—
343	C₂×C₃	—	3	1	no	—
344	C₂×C₃	—	3	1	no	—
345	C₂×C₃	—	18	2	no	—
346	C₂×C₃	—	36	2	no	—
347	C₂×C₃	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
348	C₂×C₃	C₃×#914	1	1	yes	characteristic
349	C₂×C₃	C₃×#918	1	1	yes	characteristic
350	D₃	—	6	2	no	—
351	D₃	—	12	2	no	—
352	C₂²	—	9	2	no	—
353	C₂²	—	18	1	no	—
354	C₂²	—	18	1	no	—
355	C₂²	—	18	2	no	—
356	C₂²	—	36	1	no	—
357	C₂²	—	36	1	no	—
358	C₂²	D₄×AGL(1,ℤ/9)	1	1	yes	characteristic
359	C₄	—	2	2	no	—
360	C₄	—	4	1	no	—
361	C₄	—	9	2	no	—
362	C₄	—	36	1	no	—
363	C₄	C₂×C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
364	C₄	D₄×AGL(1,ℤ/9)	1	1	yes	characteristic
365	C₃	—	3	1	no	—
366	C₃	C₃×#4803	1	1	yes	characteristic
367	C₂	—	18	2	no	—
368	C₂	—	36	2	no	—
369	C₂	C₂²⋊C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
370	C₂	#63476⋊C₃	1	1	yes	characteristic
371	C₂	#63480⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×AGL(1,ℤ/9)
commutator	C₄×C₉	C₂²×C₃×C₄
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	3₋¹⁺²×#103	C₂
socle	C₂²×C₃	C₃×D₃×D₄
prime radical	C₂×#88724	C₂
cosocle	C₂×C₄×C₉	C₂³×C₃
hypercenter	#103	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#417
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
2. C₂×#3663⋊C₃	C₂	semidirect
3. C₄⋊C₄×AGL(1,ℤ/9)	C₂	semidirect
4. 3₋¹⁺²×#103	C₂	semidirect
5. #63395⋊C₃	C₂	semidirect
6. #63380⋊C₃	C₂	semidirect
7. #63369⋊C₃	C₂	semidirect
9. #10588483	C₃	semidirect
12. #88724	C₄	semidirect
32. C₂×#3663	C₂×C₃	semidirect
33. C₄⋊C₄×D₉	C₂×C₃	semidirect
35. C₉×#103	C₂×C₃	semidirect
36. #63395	C₂×C₃	semidirect
37. #63380	C₂×C₃	semidirect
38. #63369	C₂×C₃	semidirect
42. Q₈×3₋¹⁺²	C₂×C₄	semidirect
50. C₄⋊AGL(1,ℤ/9)	C₂×C₄	semidirect
76. #3701	C₃×C₄	semidirect
140. Q₈×C₉	C₂×C₃×C₄	semidirect
151. D₃₆	C₂×C₃×C₄	semidirect
228. #103	AGL(1,ℤ/9)	semidirect
231. 3₋¹⁺²	#417	semidirect
323. C₉	C₃×#417	semidirect
327. Q₈	C₄×AGL(1,ℤ/9)	semidirect

Maximal subgroups

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

subgroup	index
C₂×#88724	2
C₂×#3663⋊C₃	2
C₄⋊C₄×AGL(1,ℤ/9)	2
3₋¹⁺²×#103	2
#63395⋊C₃	2
#63380⋊C₃	2
#63369⋊C₃	2
C₃×#4803	3
#10588483	3

Subgroups — #10588483⋊C3 #13141948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10588483⋊C₃ #13141948