Subgroups — C₃×C₉×#547 #13154623

Order 1728.

1460 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₉×#41	C₂	1	2	yes	maximal, complemented
2	C₃×C₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×#123	C₂	1	4	yes	maximal, complemented
4	C₃×C₉×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
5	C₃×C₉×#121	C₂	1	2	yes	maximal, complemented
6	C₃×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×C₉×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
9	C₃²×#547	C₃	1	1	yes	maximal, characteristic
10	C₉×#547	C₃	1	3	yes	maximal, direct product factor
11	C₃×C₉×#41	—	2	8	no	—
12	C₂×C₃×Q₈×C₉	C₂²	1	2	yes	—
13	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
14	C₂×C₃×D₄×C₉	C₂²	1	4	yes	—
15	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₄×C₉	C₂²	1	2	yes	—
17	C₂²×C₃×C₄×C₉	C₂²	1	4	yes	—
18	C₂²×C₃×C₄×C₉	C₂²	1	2	yes	—
19	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
21	C₃×C₉×C₄⋊C₄	C₂²	1	4	yes	—
22	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
24	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₃×C₉×C₂²⋊C₄	C₂²	1	4	yes	—
27	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
28	C₂×C₃²×#41	C₂×C₃	1	2	yes	—
29	C₃²×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
30	C₃²×#123	C₂×C₃	1	4	yes	—
31	C₃²×C₂²⋊Q₈	C₂×C₃	1	2	yes	—
32	C₃²×#121	C₂×C₃	1	2	yes	—
33	C₃²×C₄×D₄	C₂×C₃	1	1	yes	characteristic
34	C₃²×C₄×D₄	C₂×C₃	1	1	yes	characteristic
35	C₂×C₃²×C₄⋊C₄	C₂×C₃	1	2	yes	—
36	C₂×C₉×#41	C₂×C₃	1	6	yes	complemented
37	C₉×C₄⋊Q₈	C₂×C₃	1	3	yes	complemented
38	C₉×#123	C₂×C₃	1	12	yes	complemented
39	C₉×C₂²⋊Q₈	C₂×C₃	1	6	yes	complemented
40	C₉×#121	C₂×C₃	1	6	yes	complemented
41	C₄×D₄×C₉	C₂×C₃	1	3	yes	complemented
42	C₄×D₄×C₉	C₂×C₃	1	3	yes	complemented
43	C₂×C₉×C₄⋊C₄	C₂×C₃	1	6	yes	complemented
44	C₂³×C₃×C₉	C₂³	1	2	yes	—
45	C₂³×C₃×C₉	C₂³	1	2	yes	—
46	C₃×Q₈×C₉	—	2	4	no	—
47	C₃×D₄×C₉	—	2	8	no	—
48	C₃×D₄×C₉	—	2	2	no	—
49	C₃×D₄×C₉	D₄	1	4	yes	complemented
50	C₂×C₃×C₄×C₉	—	2	8	no	—
51	C₂×C₃×C₄×C₉	—	2	4	no	—
52	C₂×C₃×C₄×C₉	—	2	4	no	—
53	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
54	C₂×C₃×C₄×C₉	C₂³	1	4	yes	—
55	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
56	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
59	C₃×#547	C₉	1	3	yes	direct product factor
60	C₃×#547	C₃²	1	1	yes	characteristic
61	C₃²×#41	—	2	8	no	—
62	C₂×C₃²×Q₈	C₂²×C₃	1	2	yes	—
63	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	—
64	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
65	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
66	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
67	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
68	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
69	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
70	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
71	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	—
72	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
73	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
74	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
75	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
76	C₃²×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
77	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
78	C₉×#41	—	2	24	no	—
79	C₂×Q₈×C₉	C₂²×C₃	1	6	yes	—
80	C₂×D₄×C₉	C₂²×C₃	1	3	yes	—
81	C₂×D₄×C₉	C₂²×C₃	1	12	yes	—
82	C₂×D₄×C₉	C₂²×C₃	1	3	yes	—
83	C₂²×C₄×C₉	C₂²×C₃	1	6	yes	—
84	C₂²×C₄×C₉	C₂²×C₃	1	12	yes	—
85	C₂²×C₄×C₉	C₂²×C₃	1	6	yes	—
86	C₉×C₄⋊C₄	C₂²×C₃	1	3	yes	—
87	C₉×C₄⋊C₄	C₂²×C₃	1	6	yes	—
88	C₉×C₄⋊C₄	C₂²×C₃	1	12	yes	—
89	C₉×C₄⋊C₄	C₂²×C₃	1	3	yes	—
90	C₉×C₄⋊C₄	C₂²×C₃	1	6	yes	—
91	C₉×C₂²⋊C₄	C₂²×C₃	1	6	yes	—
92	C₉×C₂²⋊C₄	C₂²×C₃	1	6	yes	—
93	C₉×C₂²⋊C₄	C₂²×C₃	1	12	yes	—
94	C₄²×C₉	C₂²×C₃	1	3	yes	—
95	C₂²×C₃×C₉	—	2	2	no	—
96	C₂²×C₃×C₉	—	2	2	no	—
97	C₂²×C₃×C₉	—	2	2	no	—
98	C₂²×C₃×C₉	—	2	2	no	—
99	C₂²×C₃×C₉	—	2	2	no	—
100	C₂²×C₃×C₉	C₂×D₄	1	4	yes	—
101	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
102	C₃×C₄×C₉	—	2	2	no	—
103	C₃×C₄×C₉	—	2	4	no	—
104	C₃×C₄×C₉	—	2	2	no	—
105	C₃×C₄×C₉	—	2	1	no	—
106	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
107	C₃×C₄×C₉	#41	1	2	yes	complemented
108	C₂×C₃×#41	C₂×C₉	1	6	yes	complemented
109	C₂×C₃×#41	C₂×C₃²	1	2	yes	—
110	C₃×C₄⋊Q₈	C₂×C₉	1	3	yes	complemented
111	C₃×C₄⋊Q₈	C₂×C₃²	1	1	yes	characteristic
112	C₃×#123	C₂×C₉	1	12	yes	complemented
113	C₃×#123	C₂×C₃²	1	4	yes	—
114	C₃×C₂²⋊Q₈	C₂×C₉	1	6	yes	complemented
115	C₃×C₂²⋊Q₈	C₂×C₃²	1	2	yes	—
116	C₃×#121	C₂×C₉	1	6	yes	complemented
117	C₃×#121	C₂×C₃²	1	2	yes	—
118	C₃×C₄×D₄	C₂×C₉	1	3	yes	complemented
119	C₃×C₄×D₄	C₂×C₉	1	3	yes	complemented
120	C₃×C₄×D₄	C₂×C₃²	1	1	yes	characteristic
121	C₃×C₄×D₄	C₂×C₃²	1	1	yes	characteristic
122	C₂×C₃×C₄⋊C₄	C₂×C₉	1	6	yes	complemented
123	C₂×C₃×C₄⋊C₄	C₂×C₃²	1	2	yes	—
124	C₂³×C₃²	C₂³×C₃	1	2	yes	—
125	C₂³×C₃²	C₂³×C₃	1	2	yes	—
126	C₃²×Q₈	—	2	4	no	—
127	C₃²×D₄	—	2	8	no	—
128	C₃²×D₄	—	2	2	no	—
129	C₃²×D₄	C₃×D₄	1	4	yes	—
130	C₂×C₃²×C₄	—	2	8	no	—
131	C₂×C₃²×C₄	—	2	4	no	—
132	C₂×C₃²×C₄	—	2	4	no	—
133	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
134	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
135	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
136	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
137	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
138	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
139	C₂³×C₉	C₂³×C₃	1	6	yes	—
140	C₂³×C₉	C₂³×C₃	1	6	yes	—
141	Q₈×C₉	—	2	12	no	—
142	D₄×C₉	—	2	24	no	—
143	D₄×C₉	—	2	6	no	—
144	D₄×C₉	C₃×D₄	1	12	yes	complemented
145	C₂×C₄×C₉	—	2	24	no	—
146	C₂×C₄×C₉	—	2	12	no	—
147	C₂×C₄×C₉	—	2	12	no	—
148	C₂×C₄×C₉	C₂³×C₃	1	3	yes	—
149	C₂×C₄×C₉	C₂³×C₃	1	6	yes	—
150	C₂×C₄×C₉	C₂³×C₃	1	6	yes	—
151	C₂×C₄×C₉	C₂³×C₃	1	12	yes	—
152	C₂×C₄×C₉	C₂³×C₃	1	3	yes	—
153	C₂×C₄×C₉	C₂³×C₃	1	3	yes	—
154	#547	C₃×C₉	1	1	yes	characteristic, direct product factor, Sylow
155	C₂×C₃×C₉	—	2	4	no	—
156	C₂×C₃×C₉	—	4	2	no	—
157	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
159	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
160	C₃×#41	—	2	24	no	—
161	C₃×#41	—	2	8	no	—
162	C₂×C₃×Q₈	C₂²×C₉	1	6	yes	—
163	C₂×C₃×Q₈	C₂²×C₃²	1	2	yes	—
164	C₂×C₃×D₄	C₂²×C₉	1	3	yes	—
165	C₂×C₃×D₄	C₂²×C₉	1	12	yes	—
166	C₂×C₃×D₄	C₂²×C₉	1	3	yes	—
167	C₂×C₃×D₄	C₂²×C₃²	1	1	yes	characteristic
168	C₂×C₃×D₄	C₂²×C₃²	1	4	yes	—
169	C₂×C₃×D₄	C₂²×C₃²	1	1	yes	characteristic
170	C₂²×C₃×C₄	C₂²×C₉	1	6	yes	—
171	C₂²×C₃×C₄	C₂²×C₉	1	12	yes	—
172	C₂²×C₃×C₄	C₂²×C₉	1	6	yes	—
173	C₂²×C₃×C₄	C₂²×C₃²	1	2	yes	—
174	C₂²×C₃×C₄	C₂²×C₃²	1	4	yes	—
175	C₂²×C₃×C₄	C₂²×C₃²	1	2	yes	—
176	C₃×C₄⋊C₄	C₂²×C₉	1	3	yes	—
177	C₃×C₄⋊C₄	C₂²×C₉	1	6	yes	—
178	C₃×C₄⋊C₄	C₂²×C₉	1	12	yes	—
179	C₃×C₄⋊C₄	C₂²×C₉	1	3	yes	—
180	C₃×C₄⋊C₄	C₂²×C₉	1	6	yes	—
181	C₃×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
182	C₃×C₄⋊C₄	C₂²×C₃²	1	2	yes	—
183	C₃×C₄⋊C₄	C₂²×C₃²	1	4	yes	—
184	C₃×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
185	C₃×C₄⋊C₄	C₂²×C₃²	1	2	yes	—
186	C₃×C₂²⋊C₄	C₂²×C₉	1	6	yes	—
187	C₃×C₂²⋊C₄	C₂²×C₉	1	6	yes	—
188	C₃×C₂²⋊C₄	C₂²×C₉	1	12	yes	—
189	C₃×C₂²⋊C₄	C₂²×C₃²	1	2	yes	—
190	C₃×C₂²⋊C₄	C₂²×C₃²	1	2	yes	—
191	C₃×C₂²⋊C₄	C₂²×C₃²	1	4	yes	—
192	C₃×C₄²	C₂²×C₉	1	3	yes	—
193	C₃×C₄²	C₂²×C₃²	1	1	yes	characteristic
194	C₂²×C₃²	—	2	2	no	—
195	C₂²×C₃²	—	2	2	no	—
196	C₂²×C₃²	—	2	2	no	—
197	C₂²×C₃²	—	2	2	no	—
198	C₂²×C₃²	—	2	2	no	—
199	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
200	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
201	C₃²×C₄	—	2	2	no	—
202	C₃²×C₄	—	2	4	no	—
203	C₃²×C₄	—	2	2	no	—
204	C₃²×C₄	—	2	1	no	—
205	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
206	C₃²×C₄	C₃×#41	1	2	yes	—
207	C₂²×C₉	—	2	6	no	—
208	C₂²×C₉	—	2	6	no	—
209	C₂²×C₉	—	2	6	no	—
210	C₂²×C₉	—	2	6	no	—
211	C₂²×C₉	—	2	6	no	—
212	C₂²×C₉	C₂×C₃×D₄	1	12	yes	—
213	C₂²×C₉	C₂⁴×C₃	1	3	yes	—
214	C₄×C₉	—	2	6	no	—
215	C₄×C₉	—	2	12	no	—
216	C₄×C₉	—	2	6	no	—
217	C₄×C₉	—	2	3	no	—
218	C₄×C₉	C₂×C₃×D₄	1	6	yes	—
219	C₄×C₉	C₃×#41	1	6	yes	complemented
220	C₂×#41	C₂×C₃×C₉	1	2	yes	complemented
221	C₄⋊Q₈	C₂×C₃×C₉	1	1	yes	characteristic, complemented
222	#123	C₂×C₃×C₉	1	4	yes	complemented
223	C₂²⋊Q₈	C₂×C₃×C₉	1	2	yes	complemented
224	#121	C₂×C₃×C₉	1	2	yes	complemented
225	C₄×D₄	C₂×C₃×C₉	1	1	yes	characteristic, complemented
226	C₄×D₄	C₂×C₃×C₉	1	1	yes	characteristic, complemented
227	C₂×C₄⋊C₄	C₂×C₃×C₉	1	2	yes	complemented
228	C₃×C₉	#547	1	1	yes	characteristic, direct product factor, Sylow
229	C₂³×C₃	C₂³×C₉	1	6	yes	—
230	C₂³×C₃	C₂³×C₉	1	6	yes	—
231	C₂³×C₃	C₂³×C₃²	1	2	yes	—
232	C₂³×C₃	C₂³×C₃²	1	2	yes	—
233	C₃×Q₈	—	2	12	no	—
234	C₃×Q₈	—	2	4	no	—
235	C₃×D₄	—	2	24	no	—
236	C₃×D₄	—	2	8	no	—
237	C₃×D₄	—	2	6	no	—
238	C₃×D₄	—	2	2	no	—
239	C₃×D₄	D₄×C₉	1	12	yes	complemented
240	C₃×D₄	C₃²×D₄	1	4	yes	—
241	C₂×C₃×C₄	—	2	24	no	—
242	C₂×C₃×C₄	—	2	8	no	—
243	C₂×C₃×C₄	—	2	12	no	—
244	C₂×C₃×C₄	—	2	12	no	—
245	C₂×C₃×C₄	—	2	4	no	—
246	C₂×C₃×C₄	—	2	4	no	—
247	C₂×C₃×C₄	C₂³×C₉	1	3	yes	—
248	C₂×C₃×C₄	C₂³×C₉	1	6	yes	—
249	C₂×C₃×C₄	C₂³×C₉	1	6	yes	—
250	C₂×C₃×C₄	C₂³×C₉	1	12	yes	—
251	C₂×C₃×C₄	C₂³×C₉	1	3	yes	—
252	C₂×C₃×C₄	C₂³×C₉	1	3	yes	—
253	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
255	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
256	C₂×C₃×C₄	C₂³×C₃²	1	4	yes	—
257	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
259	C₂×C₃²	—	2	4	no	—
260	C₂×C₃²	—	4	2	no	—
261	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
262	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
263	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
264	C₂×C₉	—	2	12	no	—
265	C₂×C₉	—	4	6	no	—
266	C₂×C₉	C₂²×C₃×D₄	1	3	yes	—
267	C₂×C₉	C₂×C₃×#41	1	3	yes	—
268	C₂×C₉	C₃×2₋¹⁺⁴	1	3	yes	—
269	#41	—	2	8	no	—
270	C₂×Q₈	C₂²×C₃×C₉	1	2	yes	—
271	C₂×D₄	C₂²×C₃×C₉	1	1	yes	characteristic
272	C₂×D₄	C₂²×C₃×C₉	1	4	yes	—
273	C₂×D₄	C₂²×C₃×C₉	1	1	yes	characteristic
274	C₂²×C₄	C₂²×C₃×C₉	1	2	yes	—
275	C₂²×C₄	C₂²×C₃×C₉	1	4	yes	—
276	C₂²×C₄	C₂²×C₃×C₉	1	2	yes	—
277	C₄⋊C₄	C₂²×C₃×C₉	1	1	yes	characteristic
278	C₄⋊C₄	C₂²×C₃×C₉	1	2	yes	—
279	C₄⋊C₄	C₂²×C₃×C₉	1	4	yes	—
280	C₄⋊C₄	C₂²×C₃×C₉	1	1	yes	characteristic
281	C₄⋊C₄	C₂²×C₃×C₉	1	2	yes	—
282	C₂²⋊C₄	C₂²×C₃×C₉	1	2	yes	—
283	C₂²⋊C₄	C₂²×C₃×C₉	1	2	yes	—
284	C₂²⋊C₄	C₂²×C₃×C₉	1	4	yes	—
285	C₄²	C₂²×C₃×C₉	1	1	yes	characteristic
286	C₂²×C₃	—	2	2	no	—
287	C₂²×C₃	—	2	2	no	—
288	C₂²×C₃	—	2	6	no	—
289	C₂²×C₃	—	2	6	no	—
290	C₂²×C₃	—	2	2	no	—
291	C₂²×C₃	—	2	2	no	—
292	C₂²×C₃	—	2	2	no	—
293	C₂²×C₃	—	2	6	no	—
294	C₂²×C₃	—	2	6	no	—
295	C₂²×C₃	—	2	6	no	—
296	C₂²×C₃	C₂×D₄×C₉	1	12	yes	—
297	C₂²×C₃	C₂⁴×C₉	1	3	yes	—
298	C₂²×C₃	C₂×C₃²×D₄	1	4	yes	—
299	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
300	C₃×C₄	—	2	2	no	—
301	C₃×C₄	—	2	4	no	—
302	C₃×C₄	—	2	2	no	—
303	C₃×C₄	—	2	1	no	—
304	C₃×C₄	—	2	6	no	—
305	C₃×C₄	—	2	12	no	—
306	C₃×C₄	—	2	6	no	—
307	C₃×C₄	—	2	3	no	—
308	C₃×C₄	C₂×D₄×C₉	1	6	yes	—
309	C₃×C₄	C₉×#41	1	6	yes	complemented
310	C₃×C₄	C₂×C₃²×D₄	1	2	yes	—
311	C₃×C₄	C₃²×#41	1	2	yes	—
312	C₃²	C₃×#547	1	1	yes	characteristic
313	C₉	C₃×#547	1	3	yes	direct product factor
314	C₂³	C₂³×C₃×C₉	1	2	yes	—
315	C₂³	C₂³×C₃×C₉	1	2	yes	—
316	Q₈	—	2	4	no	—
317	D₄	—	2	8	no	—
318	D₄	—	2	2	no	—
319	D₄	C₃×D₄×C₉	1	4	yes	complemented
320	C₂×C₄	—	2	8	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	C₂³×C₃×C₉	1	1	yes	characteristic
324	C₂×C₄	C₂³×C₃×C₉	1	2	yes	—
325	C₂×C₄	C₂³×C₃×C₉	1	2	yes	—
326	C₂×C₄	C₂³×C₃×C₉	1	4	yes	—
327	C₂×C₄	C₂³×C₃×C₉	1	1	yes	characteristic
328	C₂×C₄	C₂³×C₃×C₉	1	1	yes	characteristic
329	C₂×C₃	—	2	12	no	—
330	C₂×C₃	—	2	4	no	—
331	C₂×C₃	—	4	6	no	—
332	C₂×C₃	—	4	2	no	—
333	C₂×C₃	C₂²×D₄×C₉	1	3	yes	—
334	C₂×C₃	C₂×C₉×#41	1	3	yes	—
335	C₂×C₃	C₉×2₋¹⁺⁴	1	3	yes	—
336	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
337	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
338	C₂×C₃	C₃²×2₋¹⁺⁴	1	1	yes	characteristic
339	C₂²	—	2	2	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	2	no	—
344	C₂²	C₂×C₃×D₄×C₉	1	4	yes	—
345	C₂²	C₂⁴×C₃×C₉	1	1	yes	characteristic
346	C₄	—	2	2	no	—
347	C₄	—	2	4	no	—
348	C₄	—	2	2	no	—
349	C₄	—	2	1	no	—
350	C₄	C₂×C₃×D₄×C₉	1	2	yes	—
351	C₄	C₃×C₉×#41	1	2	yes	complemented
352	C₃	C₉×#547	1	3	yes	direct product factor
353	C₃	C₃²×#547	1	1	yes	characteristic
354	C₂	—	2	4	no	—
355	C₂	—	4	2	no	—
356	C₂	C₂²×C₃×D₄×C₉	1	1	yes	characteristic
357	C₂	C₂×C₃×C₉×#41	1	1	yes	characteristic
358	C₂	C₃×C₉×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₉	C₂⁴
commutator	C₂²	C₂⁴×C₃×C₉
Frattini, cosocle	C₂²×C₃	C₂⁴×C₃²
socle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃²×#547	C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₉×#41	C₂	semidirect
2. C₃×C₉×C₄⋊Q₈	C₂	semidirect
3. C₃×C₉×#123	C₂	semidirect
4. C₃×C₉×C₂²⋊Q₈	C₂	semidirect
5. C₃×C₉×#121	C₂	semidirect
6. C₃×C₄×D₄×C₉	C₂	semidirect
7. C₃×C₄×D₄×C₉	C₂	semidirect
8. C₂×C₃×C₉×C₄⋊C₄	C₂	semidirect
10. C₉×#547	C₃	direct (N × H)
36. C₂×C₉×#41	C₂×C₃	semidirect
37. C₉×C₄⋊Q₈	C₂×C₃	semidirect
38. C₉×#123	C₂×C₃	semidirect
39. C₉×C₂²⋊Q₈	C₂×C₃	semidirect
40. C₉×#121	C₂×C₃	semidirect
41. C₄×D₄×C₉	C₂×C₃	semidirect
42. C₄×D₄×C₉	C₂×C₃	semidirect
43. C₂×C₉×C₄⋊C₄	C₂×C₃	semidirect
49. C₃×D₄×C₉	D₄	semidirect
59. C₃×#547	C₉	direct (N × H)
107. C₃×C₄×C₉	#41	semidirect
108. C₂×C₃×#41	C₂×C₉	semidirect
110. C₃×C₄⋊Q₈	C₂×C₉	semidirect
112. C₃×#123	C₂×C₉	semidirect
114. C₃×C₂²⋊Q₈	C₂×C₉	semidirect
116. C₃×#121	C₂×C₉	semidirect
118. C₃×C₄×D₄	C₂×C₉	semidirect
119. C₃×C₄×D₄	C₂×C₉	semidirect
122. C₂×C₃×C₄⋊C₄	C₂×C₉	semidirect
144. D₄×C₉	C₃×D₄	semidirect
154. #547	C₃×C₉	direct (N × H)
219. C₄×C₉	C₃×#41	semidirect
220. C₂×#41	C₂×C₃×C₉	semidirect
221. C₄⋊Q₈	C₂×C₃×C₉	semidirect
222. #123	C₂×C₃×C₉	semidirect
223. C₂²⋊Q₈	C₂×C₃×C₉	semidirect
224. #121	C₂×C₃×C₉	semidirect
225. C₄×D₄	C₂×C₃×C₉	semidirect
226. C₄×D₄	C₂×C₃×C₉	semidirect
227. C₂×C₄⋊C₄	C₂×C₃×C₉	semidirect
228. C₃×C₉	#547	direct (N × H)
239. C₃×D₄	D₄×C₉	semidirect
309. C₃×C₄	C₉×#41	semidirect
313. C₉	C₃×#547	direct (N × H)
319. D₄	C₃×D₄×C₉	semidirect
351. C₄	C₃×C₉×#41	semidirect
352. C₃	C₉×#547	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×C₃×C₉×#41	2
C₃×C₉×C₄⋊Q₈	2
C₃×C₉×#123	2
C₃×C₉×C₂²⋊Q₈	2
C₃×C₉×#121	2
C₃×C₄×D₄×C₉	2
C₂×C₃×C₉×C₄⋊C₄	2
C₃²×#547	3
C₉×#547	3

Subgroups — C3×C9×#547 #13154623

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉×#547 #13154623