Subgroups — C₉×#5579 #13152700

Order 1728.

754 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#946	C₂	1	2	yes	maximal, complemented
3	C₉×#896	C₂	1	4	yes	maximal, complemented
4	D₃×C₉×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₄×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic
6	C₄×C₉×D₁₂	C₂	1	2	yes	maximal
7	C₉×#870	C₂	1	2	yes	maximal, complemented
8	C₉×#869	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5579	C₃	1	1	yes	maximal, characteristic
10	C₉×#554	—	3	1	no	maximal
11	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
12	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
14	C₂×C₄×D₃×C₉	C₂²	1	4	yes	—
15	C₂×C₉×Dic₆	C₂²	1	2	yes	—
16	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
18	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
19	C₃×C₄²×C₉	C₂²	1	2	yes	—
20	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
21	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
22	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
23	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
24	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
25	C₉×Dic₃⋊C₄	C₂²	1	4	yes	—
26	C₉×Dic₃⋊C₄	C₂²	1	4	yes	—
27	C₃²×C₄×Q₈	C₂×C₃	1	1	yes	characteristic
28	C₃×#946	C₂×C₃	1	2	yes	—
29	C₃×#896	C₂×C₃	1	4	yes	—
30	C₃×D₃×C₄⋊C₄	C₂×C₃	1	2	yes	—
31	C₃×C₄×D₁₂	C₂×C₃	1	2	yes	—
32	C₃×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
33	C₃×#870	C₂×C₃	1	2	yes	—
34	C₃×#869	C₂×C₃	1	1	yes	characteristic
35	C₉×C₄⋊Q₈	—	3	1	no	—
36	C₉×#125	—	3	2	no	—
37	C₉×C₂²⋊Q₈	—	3	2	no	—
38	C₉×C₂²⋊Q₈	—	3	4	no	—
39	C₄×Q₈×C₉	—	2	1	no	—
40	C₄×Q₈×C₉	D₃	1	1	yes	characteristic, complemented
41	C₄×D₄×C₉	—	3	2	no	—
42	C₄×D₄×C₉	—	3	1	no	—
43	C₂×C₉×C₄⋊C₄	—	3	2	no	—
44	C₂²×D₃×C₉	C₂³	1	2	yes	—
45	C₃×Q₈×C₉	—	2	2	no	—
46	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
47	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
48	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
49	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
50	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
51	C₂×C₉×Dic₃	C₂³	1	4	yes	—
52	C₂×C₉×Dic₃	C₂³	1	2	yes	—
53	C₉×D₁₂	Q₈	1	4	yes	complemented
54	C₄×D₃×C₉	—	2	4	no	—
55	C₄×D₃×C₉	—	4	4	no	—
56	C₉×Dic₆	—	4	2	no	—
57	C₃×#554	—	3	1	no	—
58	#5579	C₉	1	1	yes	characteristic, direct product factor
59	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
60	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
61	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
62	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
63	C₂×C₃×Dic₆	C₂²×C₃	1	2	yes	—
64	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
65	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
66	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
67	C₃²×C₄²	C₂²×C₃	1	2	yes	—
68	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
69	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
70	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
71	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
72	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
73	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
74	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
75	C₂×Q₈×C₉	—	2	1	no	—
76	C₂×Q₈×C₉	—	3	2	no	—
77	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
78	C₂×D₄×C₉	—	3	1	no	—
79	C₂²×C₄×C₉	—	3	2	no	—
80	C₂²×C₄×C₉	—	3	4	no	—
81	C₉×C₄⋊C₄	—	2	1	no	—
82	C₉×C₄⋊C₄	—	2	2	no	—
83	C₉×C₄⋊C₄	—	3	4	no	—
84	C₉×C₄⋊C₄	—	3	2	no	—
85	C₉×C₄⋊C₄	—	3	1	no	—
86	C₉×C₄⋊C₄	—	3	2	no	—
87	C₉×C₄⋊C₄	—	3	4	no	—
88	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
89	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
90	C₉×C₂²⋊C₄	—	3	2	no	—
91	C₉×C₂²⋊C₄	—	3	4	no	—
92	C₄²×C₉	—	2	2	no	—
93	C₄²×C₉	—	2	1	no	—
94	C₄²×C₉	C₂×D₃	1	2	yes	—
95	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
96	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
97	C₂×D₃×C₉	—	2	2	no	—
98	C₂×D₃×C₉	—	2	2	no	—
99	C₂×D₃×C₉	C₂×Q₈	1	4	yes	—
100	C₃×C₄×C₉	—	2	2	no	—
101	C₃×C₄×C₉	—	2	1	no	—
102	C₃×C₄×C₉	—	2	2	no	—
103	C₃×C₄×C₉	C₂×Q₈	1	2	yes	—
104	C₃×C₄×C₉	#41	1	2	yes	—
105	C₉×Dic₃	—	2	2	no	—
106	C₉×Dic₃	—	2	4	no	—
107	C₃×C₄⋊Q₈	—	3	1	no	—
108	C₃×#125	—	3	2	no	—
109	C₃×C₂²⋊Q₈	—	3	2	no	—
110	C₃×C₂²⋊Q₈	—	3	4	no	—
111	C₃×C₄×Q₈	—	2	1	no	—
112	C₃×C₄×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
113	C₃×C₄×Q₈	C₃×D₃	1	1	yes	characteristic
114	C₃×C₄×D₄	—	3	2	no	—
115	C₃×C₄×D₄	—	3	1	no	—
116	C₂×C₃×C₄⋊C₄	—	3	2	no	—
117	#946	C₂×C₉	1	2	yes	complemented
118	#896	C₂×C₉	1	4	yes	complemented
119	D₃×C₄⋊C₄	C₂×C₉	1	2	yes	complemented
120	C₄×D₁₂	C₂×C₉	1	2	yes	—
121	C₄×D₁₂	C₂×C₉	1	1	yes	characteristic
122	#870	C₂×C₉	1	2	yes	complemented
123	#869	C₂×C₉	1	1	yes	characteristic, complemented
124	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
125	C₃²×Q₈	—	2	2	no	—
126	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
127	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
128	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
129	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
130	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
131	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
132	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
133	C₃×D₁₂	C₃×Q₈	1	4	yes	—
134	C₃×C₄×D₃	—	2	4	no	—
135	C₃×C₄×D₃	—	4	4	no	—
136	C₃×Dic₆	—	4	2	no	—
137	C₂³×C₉	—	3	2	no	—
138	Q₈×C₉	—	2	4	no	—
139	Q₈×C₉	—	2	2	no	—
140	Q₈×C₉	—	12	2	no	—
141	D₄×C₉	—	3	4	no	—
142	C₂×C₄×C₉	—	2	1	no	—
143	C₂×C₄×C₉	—	2	2	no	—
144	C₂×C₄×C₉	—	2	1	no	—
145	C₂×C₄×C₉	—	2	1	no	—
146	C₂×C₄×C₉	—	2	2	no	—
147	C₂×C₄×C₉	—	3	2	no	—
148	C₂×C₄×C₉	—	3	4	no	—
149	C₂×C₄×C₉	—	6	4	no	—
150	C₂×C₄×C₉	—	12	4	no	—
151	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
152	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
153	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
154	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
155	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
156	#554	—	3	1	no	Sylow
157	C₂×C₃×C₉	C₂²×Q₈	1	1	yes	characteristic
158	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
159	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
160	D₃×C₉	—	2	4	no	—
161	C₂×C₃×Q₈	—	2	1	no	—
162	C₂×C₃×Q₈	—	3	2	no	—
163	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
164	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
165	C₂×C₃×D₄	—	3	1	no	—
166	C₂²×C₃×C₄	—	3	2	no	—
167	C₂²×C₃×C₄	—	3	4	no	—
168	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
169	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
170	C₂×C₄×D₃	C₂²×C₉	1	4	yes	—
171	C₂×Dic₆	C₂²×C₉	1	2	yes	—
172	C₃×C₄⋊C₄	—	2	1	no	—
173	C₃×C₄⋊C₄	—	2	2	no	—
174	C₃×C₄⋊C₄	—	3	4	no	—
175	C₃×C₄⋊C₄	—	3	4	no	—
176	C₃×C₄⋊C₄	—	3	2	no	—
177	C₃×C₄⋊C₄	—	3	1	no	—
178	C₃×C₄⋊C₄	—	3	2	no	—
179	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
180	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
181	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
182	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
183	C₃×C₂²⋊C₄	—	3	2	no	—
184	C₃×C₂²⋊C₄	—	3	4	no	—
185	C₃×C₄²	—	2	2	no	—
186	C₃×C₄²	—	2	1	no	—
187	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
188	C₃×C₄²	C₂²×C₉	1	2	yes	—
189	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
190	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
191	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
192	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	—
193	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
194	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
195	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
196	Dic₃⋊C₄	C₂²×C₉	1	4	yes	—
197	Dic₃⋊C₄	C₂²×C₉	1	4	yes	—
198	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
199	C₂×C₃×D₃	—	2	2	no	—
200	C₂×C₃×D₃	—	2	2	no	—
201	C₂×C₃×D₃	C₂×C₃×Q₈	1	4	yes	—
202	C₃²×C₄	—	2	2	no	—
203	C₃²×C₄	—	2	1	no	—
204	C₃²×C₄	—	2	2	no	—
205	C₃²×C₄	C₂×C₃×Q₈	1	2	yes	—
206	C₃²×C₄	C₃×#41	1	2	yes	—
207	C₃×Dic₃	—	2	2	no	—
208	C₃×Dic₃	—	2	4	no	—
209	C₂²×C₉	—	2	1	no	—
210	C₂²×C₉	—	3	4	no	—
211	C₂²×C₉	—	6	2	no	—
212	C₂²×C₉	—	6	2	no	—
213	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
214	C₄×C₉	—	2	4	no	—
215	C₄×C₉	—	2	2	no	—
216	C₄×C₉	—	2	2	no	—
217	C₄×C₉	—	2	1	no	—
218	C₄×C₉	—	2	2	no	—
219	C₄×C₉	—	2	2	no	—
220	C₄×C₉	—	4	2	no	—
221	C₄×C₉	—	4	1	no	—
222	C₄×C₉	—	6	2	no	—
223	C₄×C₉	—	6	4	no	—
224	C₄×C₉	#235	1	2	yes	—
225	C₄×C₉	D₃×Q₈	1	2	yes	—
226	C₄⋊Q₈	—	3	1	no	—
227	#125	—	3	2	no	—
228	C₂²⋊Q₈	—	3	2	no	—
229	C₂²⋊Q₈	—	3	4	no	—
230	C₄×Q₈	D₃×C₉	1	1	yes	characteristic, complemented
231	C₄×D₄	—	3	2	no	—
232	C₄×D₄	—	3	1	no	—
233	C₂×C₄⋊C₄	—	3	2	no	—
234	C₃×C₉	#554	1	1	yes	characteristic, complemented, Sylow
235	C₂³×C₃	—	3	2	no	—
236	C₂²×D₃	C₂³×C₉	1	2	yes	—
237	C₃×Q₈	—	2	4	no	—
238	C₃×Q₈	—	2	2	no	—
239	C₃×Q₈	—	2	2	no	—
240	C₃×Q₈	—	12	2	no	—
241	C₃×D₄	—	3	4	no	—
242	C₂×C₃×C₄	—	2	1	no	—
243	C₂×C₃×C₄	—	2	2	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	2	2	no	—
247	C₂×C₃×C₄	—	3	2	no	—
248	C₂×C₃×C₄	—	3	4	no	—
249	C₂×C₃×C₄	—	6	4	no	—
250	C₂×C₃×C₄	—	12	4	no	—
251	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
252	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
253	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
257	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
259	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
261	C₂×Dic₃	C₂³×C₉	1	2	yes	—
262	C₂×Dic₃	C₂³×C₉	1	4	yes	—
263	D₁₂	Q₈×C₉	1	4	yes	complemented
264	C₄×D₃	—	2	4	no	—
265	C₄×D₃	—	4	4	no	—
266	Dic₆	—	4	2	no	—
267	C₂×C₃²	C₂²×C₃×Q₈	1	1	yes	characteristic
268	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
269	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
270	C₃×D₃	—	2	4	no	—
271	C₂×C₉	—	2	1	no	—
272	C₂×C₉	—	2	1	no	—
273	C₂×C₉	—	2	1	no	—
274	C₂×C₉	—	6	4	no	—
275	C₂×C₉	C₂×#235	1	1	yes	characteristic
276	C₂×C₉	C₂×D₃×Q₈	1	1	yes	characteristic
277	C₂×C₉	#1009	1	1	yes	characteristic
278	C₂×Q₈	—	3	2	no	—
279	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
280	C₂×D₄	—	3	1	no	—
281	C₂²×C₄	—	3	2	no	—
282	C₂²×C₄	—	3	4	no	—
283	C₄⋊C₄	—	3	4	no	—
284	C₄⋊C₄	—	3	2	no	—
285	C₄⋊C₄	—	3	1	no	—
286	C₄⋊C₄	—	3	2	no	—
287	C₄⋊C₄	—	3	4	no	—
288	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
289	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
290	C₂²⋊C₄	—	3	2	no	—
291	C₂²⋊C₄	—	3	4	no	—
292	C₄²	C₂×D₃×C₉	1	2	yes	—
293	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
294	C₂²×C₃	—	2	1	no	—
295	C₂²×C₃	—	3	4	no	—
296	C₂²×C₃	—	6	2	no	—
297	C₂²×C₃	—	6	2	no	—
298	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
299	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
300	C₂×D₃	—	2	2	no	—
301	C₂×D₃	—	2	2	no	—
302	C₂×D₃	C₂×Q₈×C₉	1	4	yes	—
303	C₃×C₄	—	2	4	no	—
304	C₃×C₄	—	2	2	no	—
305	C₃×C₄	—	2	2	no	—
306	C₃×C₄	—	2	1	no	—
307	C₃×C₄	—	2	2	no	—
308	C₃×C₄	—	2	1	no	—
309	C₃×C₄	—	2	2	no	—
310	C₃×C₄	—	2	2	no	—
311	C₃×C₄	—	2	2	no	—
312	C₃×C₄	—	4	2	no	—
313	C₃×C₄	—	4	1	no	—
314	C₃×C₄	—	6	2	no	—
315	C₃×C₄	—	6	4	no	—
316	C₃×C₄	C₂×Q₈×C₉	1	2	yes	—
317	C₃×C₄	C₉×#41	1	2	yes	—
318	C₃×C₄	C₃×#235	1	2	yes	—
319	C₃×C₄	C₃×D₃×Q₈	1	2	yes	—
320	Dic₃	—	2	2	no	—
321	Dic₃	—	2	4	no	—
322	C₃²	C₃×#554	1	1	yes	characteristic
323	C₉	—	2	1	no	—
324	C₉	#5579	1	1	yes	characteristic, direct product factor
325	C₂³	—	3	2	no	—
326	Q₈	—	2	2	no	—
327	Q₈	—	12	2	no	—
328	D₄	—	3	4	no	—
329	C₂×C₄	—	3	2	no	—
330	C₂×C₄	—	3	4	no	—
331	C₂×C₄	—	6	4	no	—
332	C₂×C₄	—	12	4	no	—
333	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
334	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
335	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
336	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
337	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
338	C₂×C₃	—	2	1	no	—
339	C₂×C₃	—	2	1	no	—
340	C₂×C₃	—	2	1	no	—
341	C₂×C₃	—	6	4	no	—
342	C₂×C₃	C₂²×Q₈×C₉	1	1	yes	characteristic
343	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
344	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
345	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
346	C₂×C₃	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
347	C₂×C₃	C₃×#1009	1	1	yes	characteristic
348	D₃	—	2	4	no	—
349	C₂²	—	3	4	no	—
350	C₂²	—	6	2	no	—
351	C₂²	—	6	2	no	—
352	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
353	C₄	—	2	2	no	—
354	C₄	—	2	2	no	—
355	C₄	—	2	1	no	—
356	C₄	—	6	2	no	—
357	C₄	—	6	4	no	—
358	C₄	C₉×#235	1	2	yes	—
359	C₄	D₃×Q₈×C₉	1	2	yes	—
360	C₃	—	2	1	no	—
361	C₃	C₉×#554	1	1	yes	characteristic, complemented
362	C₃	C₃×#5579	1	1	yes	characteristic
363	C₂	—	6	4	no	—
364	C₂	C₂×C₉×#235	1	1	yes	characteristic
365	C₂	C₂×D₃×Q₈×C₉	1	1	yes	characteristic
366	C₂	C₉×#1009	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₄×Q₈×C₉	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₂×C₃×D₁₂	C₂²×C₃
hypercenter	C₄×Q₈×C₉	D₃
hypocenter	C₃	C₉×#554
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₄×Q₈×C₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₄×Q₈×C₉	C₂	semidirect
2. C₉×#946	C₂	semidirect
3. C₉×#896	C₂	semidirect
4. D₃×C₉×C₄⋊C₄	C₂	semidirect
7. C₉×#870	C₂	semidirect
8. C₉×#869	C₂	semidirect
40. C₄×Q₈×C₉	D₃	semidirect
53. C₉×D₁₂	Q₈	semidirect
58. #5579	C₉	direct (N × H)
112. C₃×C₄×Q₈	C₂×C₉	semidirect
117. #946	C₂×C₉	semidirect
118. #896	C₂×C₉	semidirect
119. D₃×C₄⋊C₄	C₂×C₉	semidirect
122. #870	C₂×C₉	semidirect
123. #869	C₂×C₉	semidirect
230. C₄×Q₈	D₃×C₉	semidirect
234. C₃×C₉	#554	semidirect
263. D₁₂	Q₈×C₉	semidirect
324. C₉	#5579	direct (N × H)
361. C₃	C₉×#554	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×Q₈×C₉	2
C₉×#946	2
C₉×#896	2
D₃×C₉×C₄⋊C₄	2
C₄×C₉×D₁₂	2
C₉×#870	2
C₉×#869	2
C₃×#5579	3
C₉×#554	3

Subgroups — C9×#5579 #13152700

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5579 #13152700