Subgroups — D₃×C₉×#103 #13141880

Order 1728.

528 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×Q₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×D₃×C₈×C₉	C₂	1	1	yes	maximal, characteristic
3	D₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₃×C₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#835	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#816	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#810	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×D₃×#103	C₃	1	1	yes	maximal, characteristic
9	C₂×C₉×#103	—	3	1	no	maximal
10	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
11	D₃×Q₈×C₉	—	2	2	no	—
12	D₃×Q₈×C₉	C₄	1	4	yes	complemented
13	C₂×C₄×D₃×C₉	—	2	1	no	—
14	C₂×C₄×D₃×C₉	—	2	1	no	—
15	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
16	C₂×C₉×Dic₆	—	2	1	no	—
17	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
19	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
21	C₉×Dic₃⋊C₄	—	2	1	no	—
22	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
23	D₃×C₈×C₉	—	2	2	no	—
24	C₂×C₃×D₃×Q₈	C₂×C₃	1	1	yes	characteristic
25	C₂×C₃×D₃×C₈	C₂×C₃	1	1	yes	characteristic
26	C₃×D₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
27	C₂²×Q₈×C₉	—	3	1	no	—
28	C₃²×#103	C₂×C₃	1	1	yes	characteristic
29	C₃×#835	C₂×C₃	1	1	yes	characteristic
30	C₃×#816	C₂×C₃	1	1	yes	characteristic
31	C₃×#810	C₂×C₃	1	1	yes	characteristic
32	C₂²×C₈×C₉	—	3	1	no	—
33	C₂×C₉×C₄⋊C₄	—	3	1	no	—
34	C₉×#103	—	2	1	no	—
35	C₉×#103	—	3	1	no	—
36	C₉×#103	—	3	1	no	—
37	C₉×#103	—	3	1	no	—
38	C₉×#103	D₃	1	1	yes	characteristic, direct product factor
39	C₂²×D₃×C₉	D₄	1	1	yes	characteristic
40	C₃×Q₈×C₉	—	2	1	no	—
41	C₃×Q₈×C₉	C₂×C₄	1	2	yes	complemented
42	C₂×C₃×C₄×C₉	—	2	1	no	—
43	C₂×C₃×C₄×C₉	—	2	1	no	—
44	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
45	C₂×C₉×Dic₃	—	2	1	no	—
46	C₂×C₉×Dic₃	—	2	1	no	—
47	C₂×C₉×Dic₃	D₄	1	1	yes	characteristic
48	C₄×D₃×C₉	—	2	4	no	—
49	C₄×D₃×C₉	—	4	2	no	—
50	C₄×D₃×C₉	C₂×C₄	1	2	yes	—
51	C₄×D₃×C₉	D₄	1	2	yes	—
52	C₉×Dic₆	—	2	1	no	—
53	C₉×Dic₆	—	2	4	no	—
54	C₉×Dic₆	C₂×C₄	1	2	yes	complemented
55	C₃×C₈×C₉	—	2	1	no	—
56	C₉×C₃⋊C₈	—	2	1	no	—
57	C₂×C₃×#103	—	3	1	no	—
58	D₃×#103	C₉	1	1	yes	characteristic, direct product factor
59	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
60	C₃×D₃×Q₈	—	2	2	no	—
61	C₃×D₃×Q₈	C₃×C₄	1	4	yes	—
62	C₂×C₃×C₄×D₃	—	2	1	no	—
63	C₂×C₃×C₄×D₃	—	2	1	no	—
64	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
65	C₂×C₃×Dic₆	—	2	1	no	—
66	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
67	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
68	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
69	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
70	C₃×Dic₃⋊C₄	—	2	1	no	—
71	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
72	C₃×D₃×C₈	—	2	2	no	—
73	C₂×Q₈×C₉	—	2	1	no	—
74	C₂×Q₈×C₉	—	3	4	no	—
75	C₂×Q₈×C₉	—	3	1	no	—
76	C₂×Q₈×C₉	—	6	1	no	—
77	C₂×Q₈×C₉	—	6	2	no	—
78	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
79	C₂²×C₄×C₉	—	3	1	no	—
80	C₂²×C₄×C₉	—	6	1	no	—
81	C₂²×C₄×C₉	—	6	1	no	—
82	C₂×C₈×C₉	—	2	1	no	—
83	C₂×C₈×C₉	—	3	1	no	—
84	C₂×C₈×C₉	—	6	2	no	—
85	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic
86	C₉×C₄⋊C₄	—	2	1	no	—
87	C₉×C₄⋊C₄	—	3	1	no	—
88	C₉×C₄⋊C₄	—	6	1	no	—
89	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
90	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
91	C₂×D₃×C₉	C₂²⋊C₄	1	2	yes	—
92	C₂×D₃×C₉	SD₁₆	1	2	yes	—
93	C₂×D₃×C₉	Q₁₆	1	2	yes	—
94	C₃×C₄×C₉	—	2	2	no	—
95	C₃×C₄×C₉	—	4	1	no	—
96	C₃×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
97	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
98	C₉×Dic₃	—	2	2	no	—
99	C₉×Dic₃	—	4	1	no	—
100	C₉×Dic₃	C₂²⋊C₄	1	2	yes	—
101	C₂²×C₃×Q₈	—	3	1	no	—
102	C₂×D₃×Q₈	C₂×C₉	1	1	yes	characteristic
103	C₂²×C₃×C₈	—	3	1	no	—
104	C₂×C₃×C₄⋊C₄	—	3	1	no	—
105	C₂×D₃×C₈	C₂×C₉	1	1	yes	characteristic
106	D₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic
107	C₃×#103	—	2	1	no	—
108	C₃×#103	—	3	1	no	—
109	C₃×#103	—	3	1	no	—
110	C₃×#103	—	3	1	no	—
111	C₃×#103	C₂×C₉	1	1	yes	characteristic, complemented
112	C₃×#103	C₃×D₃	1	1	yes	characteristic
113	#835	C₂×C₉	1	1	yes	characteristic, complemented
114	#816	C₂×C₉	1	1	yes	characteristic, complemented
115	#810	C₂×C₉	1	1	yes	characteristic, complemented
116	C₂²×C₃×D₃	C₃×D₄	1	1	yes	characteristic
117	C₃²×Q₈	—	2	1	no	—
118	C₃²×Q₈	C₂×C₃×C₄	1	2	yes	—
119	C₂×C₃²×C₄	—	2	1	no	—
120	C₂×C₃²×C₄	—	2	1	no	—
121	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
122	C₂×C₃×Dic₃	—	2	1	no	—
123	C₂×C₃×Dic₃	—	2	1	no	—
124	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
125	C₃×C₄×D₃	—	2	4	no	—
126	C₃×C₄×D₃	—	4	2	no	—
127	C₃×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
128	C₃×C₄×D₃	C₃×D₄	1	2	yes	—
129	C₃×Dic₆	—	2	1	no	—
130	C₃×Dic₆	—	2	4	no	—
131	C₃×Dic₆	C₂×C₃×C₄	1	2	yes	—
132	C₂³×C₉	—	3	1	no	—
133	C₃²×C₈	—	2	1	no	—
134	C₃×C₃⋊C₈	—	2	1	no	—
135	Q₈×C₉	—	2	1	no	—
136	Q₈×C₉	—	2	2	no	—
137	Q₈×C₉	—	3	2	no	—
138	Q₈×C₉	—	4	1	no	—
139	Q₈×C₉	—	6	4	no	—
140	Q₈×C₉	—	6	1	no	—
141	Q₈×C₉	C₄×D₃	1	2	yes	complemented
142	C₂×C₄×C₉	—	2	1	no	—
143	C₂×C₄×C₉	—	2	1	no	—
144	C₂×C₄×C₉	—	2	1	no	—
145	C₂×C₄×C₉	—	3	1	no	—
146	C₂×C₄×C₉	—	3	2	no	—
147	C₂×C₄×C₉	—	3	2	no	—
148	C₂×C₄×C₉	—	4	1	no	—
149	C₂×C₄×C₉	—	4	1	no	—
150	C₂×C₄×C₉	—	6	4	no	—
151	C₂×C₄×C₉	—	6	1	no	—
152	C₂×C₄×C₉	—	6	1	no	—
153	C₂×C₄×C₉	—	12	2	no	—
154	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
155	C₈×C₉	—	2	1	no	—
156	C₈×C₉	—	4	1	no	—
157	C₈×C₉	—	6	1	no	—
158	C₂×#103	—	3	1	no	Sylow
159	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₃×C₉	C₂×SD₁₆	1	1	yes	characteristic
161	C₂×C₃×C₉	C₂×Q₁₆	1	1	yes	characteristic
162	D₃×C₉	#103	1	4	yes	direct product factor
163	C₂×C₃×Q₈	—	2	1	no	—
164	C₂×C₃×Q₈	—	3	4	no	—
165	C₂×C₃×Q₈	—	3	1	no	—
166	C₂×C₃×Q₈	—	6	1	no	—
167	C₂×C₃×Q₈	—	6	2	no	—
168	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
169	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
170	C₂²×C₃×C₄	—	3	1	no	—
171	C₂²×C₃×C₄	—	6	1	no	—
172	C₂²×C₃×C₄	—	6	1	no	—
173	D₃×Q₈	—	2	2	no	—
174	D₃×Q₈	C₄×C₉	1	4	yes	complemented
175	C₂×C₄×D₃	—	2	1	no	—
176	C₂×C₄×D₃	—	2	1	no	—
177	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
178	C₂×Dic₆	—	2	1	no	—
179	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
180	C₂×C₃×C₈	—	2	1	no	—
181	C₂×C₃×C₈	—	3	1	no	—
182	C₂×C₃×C₈	—	6	2	no	—
183	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic
184	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
185	C₃×C₄⋊C₄	—	2	1	no	—
186	C₃×C₄⋊C₄	—	3	1	no	—
187	C₃×C₄⋊C₄	—	6	1	no	—
188	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
189	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
190	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
191	Dic₃⋊C₄	—	2	1	no	—
192	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
193	D₃×C₈	—	2	2	no	—
194	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
195	C₂×C₃×D₃	C₃×C₂²⋊C₄	1	2	yes	—
196	C₂×C₃×D₃	C₃×SD₁₆	1	2	yes	—
197	C₂×C₃×D₃	C₃×Q₁₆	1	2	yes	—
198	C₃²×C₄	—	2	2	no	—
199	C₃²×C₄	—	4	1	no	—
200	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
201	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
202	C₃×Dic₃	—	2	2	no	—
203	C₃×Dic₃	—	4	1	no	—
204	C₃×Dic₃	C₃×C₂²⋊C₄	1	2	yes	—
205	C₂²×C₉	—	2	1	no	—
206	C₂²×C₉	—	3	2	no	—
207	C₂²×C₉	—	3	2	no	—
208	C₂²×C₉	—	3	2	no	—
209	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
210	C₄×C₉	—	2	2	no	—
211	C₄×C₉	—	2	1	no	—
212	C₄×C₉	—	2	1	no	—
213	C₄×C₉	—	3	2	no	—
214	C₄×C₉	—	4	2	no	—
215	C₄×C₉	—	4	1	no	—
216	C₄×C₉	—	6	2	no	—
217	C₄×C₉	—	8	1	no	—
218	C₄×C₉	—	12	1	no	—
219	C₄×C₉	C₂×C₄×D₃	1	1	yes	characteristic
220	C₄×C₉	D₃×D₄	1	1	yes	characteristic
221	C₂²×Q₈	—	3	1	no	—
222	C₂²×C₈	—	3	1	no	—
223	C₂×C₄⋊C₄	—	3	1	no	—
224	#103	—	3	1	no	—
225	#103	—	3	1	no	—
226	#103	—	3	1	no	—
227	#103	D₃×C₉	1	1	yes	characteristic, direct product factor
228	C₃×C₉	C₂×#103	1	1	yes	characteristic, complemented, Sylow
229	C₂³×C₃	—	3	1	no	—
230	C₂²×D₃	D₄×C₉	1	1	yes	characteristic
231	C₃×Q₈	—	2	1	no	—
232	C₃×Q₈	—	2	1	no	—
233	C₃×Q₈	—	2	2	no	—
234	C₃×Q₈	—	3	2	no	—
235	C₃×Q₈	—	4	1	no	—
236	C₃×Q₈	—	6	4	no	—
237	C₃×Q₈	—	6	1	no	—
238	C₃×Q₈	C₂×C₄×C₉	1	2	yes	complemented
239	C₃×Q₈	C₃×C₄×D₃	1	2	yes	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	—	2	1	no	—
242	C₂×C₃×C₄	—	2	1	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	—	3	2	no	—
247	C₂×C₃×C₄	—	3	2	no	—
248	C₂×C₃×C₄	—	4	1	no	—
249	C₂×C₃×C₄	—	4	1	no	—
250	C₂×C₃×C₄	—	6	4	no	—
251	C₂×C₃×C₄	—	6	1	no	—
252	C₂×C₃×C₄	—	6	1	no	—
253	C₂×C₃×C₄	—	12	2	no	—
254	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
256	C₂×Dic₃	—	2	1	no	—
257	C₂×Dic₃	—	2	1	no	—
258	C₂×Dic₃	D₄×C₉	1	1	yes	characteristic
259	C₄×D₃	—	2	4	no	—
260	C₄×D₃	—	4	2	no	—
261	C₄×D₃	C₂×C₄×C₉	1	2	yes	—
262	C₄×D₃	D₄×C₉	1	2	yes	—
263	Dic₆	—	2	1	no	—
264	Dic₆	—	2	4	no	—
265	Dic₆	C₂×C₄×C₉	1	2	yes	complemented
266	C₃×C₈	—	2	1	no	—
267	C₃×C₈	—	2	1	no	—
268	C₃×C₈	—	4	1	no	—
269	C₃×C₈	—	6	1	no	—
270	C₃⋊C₈	—	2	1	no	—
271	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₃²	C₂×C₃×SD₁₆	1	1	yes	characteristic
273	C₂×C₃²	C₂×C₃×Q₁₆	1	1	yes	characteristic
274	C₃×D₃	C₃×#103	1	4	yes	—
275	C₂×C₉	—	2	1	no	—
276	C₂×C₉	—	2	1	no	—
277	C₂×C₉	—	2	1	no	—
278	C₂×C₉	—	3	4	no	—
279	C₂×C₉	D₃×C₂²⋊C₄	1	1	yes	characteristic
280	C₂×C₉	D₃×SD₁₆	1	1	yes	characteristic
281	C₂×C₉	D₃×Q₁₆	1	1	yes	characteristic
282	C₂×Q₈	—	3	4	no	—
283	C₂×Q₈	—	3	1	no	—
284	C₂×Q₈	—	6	1	no	—
285	C₂×Q₈	—	6	2	no	—
286	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
287	C₂²×C₄	—	3	1	no	—
288	C₂²×C₄	—	6	1	no	—
289	C₂²×C₄	—	6	1	no	—
290	C₂×C₈	—	3	1	no	—
291	C₂×C₈	—	6	2	no	—
292	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic
293	C₄⋊C₄	—	3	1	no	—
294	C₄⋊C₄	—	6	1	no	—
295	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
296	C₂²×C₃	—	2	1	no	—
297	C₂²×C₃	—	3	2	no	—
298	C₂²×C₃	—	3	2	no	—
299	C₂²×C₃	—	3	2	no	—
300	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
301	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
302	C₂×D₃	C₉×C₂²⋊C₄	1	2	yes	—
303	C₂×D₃	C₉×SD₁₆	1	2	yes	—
304	C₂×D₃	C₉×Q₁₆	1	2	yes	—
305	C₃×C₄	—	2	2	no	—
306	C₃×C₄	—	2	2	no	—
307	C₃×C₄	—	2	1	no	—
308	C₃×C₄	—	2	1	no	—
309	C₃×C₄	—	3	2	no	—
310	C₃×C₄	—	4	2	no	—
311	C₃×C₄	—	4	1	no	—
312	C₃×C₄	—	4	1	no	—
313	C₃×C₄	—	6	2	no	—
314	C₃×C₄	—	8	1	no	—
315	C₃×C₄	—	12	1	no	—
316	C₃×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
317	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
318	C₃×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
319	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
320	Dic₃	—	2	2	no	—
321	Dic₃	—	4	1	no	—
322	Dic₃	C₉×C₂²⋊C₄	1	2	yes	—
323	C₃²	C₂×C₃×#103	1	1	yes	characteristic
324	C₉	—	2	1	no	—
325	C₉	D₃×#103	1	1	yes	characteristic, direct product factor
326	C₂³	—	3	1	no	—
327	Q₈	—	2	1	no	—
328	Q₈	—	3	2	no	—
329	Q₈	—	6	4	no	—
330	Q₈	—	6	1	no	—
331	Q₈	C₄×D₃×C₉	1	2	yes	complemented
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	3	1	no	—
335	C₂×C₄	—	3	2	no	—
336	C₂×C₄	—	3	2	no	—
337	C₂×C₄	—	6	4	no	—
338	C₂×C₄	—	6	1	no	—
339	C₂×C₄	—	6	1	no	—
340	C₂×C₄	—	12	2	no	—
341	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
342	C₈	—	2	1	no	—
343	C₈	—	6	1	no	—
344	C₂×C₃	—	2	1	no	—
345	C₂×C₃	—	2	1	no	—
346	C₂×C₃	—	2	1	no	—
347	C₂×C₃	—	3	4	no	—
348	C₂×C₃	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
349	C₂×C₃	C₂×C₉×SD₁₆	1	1	yes	characteristic
350	C₂×C₃	C₂×C₉×Q₁₆	1	1	yes	characteristic
351	C₂×C₃	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
352	C₂×C₃	C₃×D₃×SD₁₆	1	1	yes	characteristic
353	C₂×C₃	C₃×D₃×Q₁₆	1	1	yes	characteristic
354	D₃	C₉×#103	1	4	yes	direct product factor
355	C₂²	—	3	2	no	—
356	C₂²	—	3	2	no	—
357	C₂²	—	3	2	no	—
358	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
359	C₄	—	2	2	no	—
360	C₄	—	3	2	no	—
361	C₄	—	4	1	no	—
362	C₄	—	6	2	no	—
363	C₄	—	12	1	no	—
364	C₄	C₂×C₄×D₃×C₉	1	1	yes	characteristic
365	C₄	D₃×D₄×C₉	1	1	yes	characteristic
366	C₃	—	2	1	no	—
367	C₃	C₂×C₉×#103	1	1	yes	characteristic, complemented
368	C₃	C₃×D₃×#103	1	1	yes	characteristic
369	C₂	—	3	4	no	—
370	C₂	D₃×C₉×C₂²⋊C₄	1	1	yes	characteristic
371	C₂	D₃×C₉×SD₁₆	1	1	yes	characteristic
372	C₂	D₃×C₉×Q₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	D₃×D₄
commutator	C₃×C₄	C₂²×C₄×C₉
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₃×C₉×#103	C₂
socle	C₂²×C₃²	C₂×C₃×D₄
prime radical	C₂²×C₃×D₃	C₃×D₄
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₉×#103	D₃
hypocenter	C₃	C₂×C₉×#103
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₄×C₉ ◁ C₉×#103

Complements

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

N	H ≅ G/N	type
4. C₃×C₉×#103	C₂	semidirect
5. C₉×#835	C₂	semidirect
6. C₉×#816	C₂	semidirect
7. C₉×#810	C₂	semidirect
12. D₃×Q₈×C₉	C₄	semidirect
38. C₉×#103	D₃	direct (N × H)
41. C₃×Q₈×C₉	C₂×C₄	semidirect
54. C₉×Dic₆	C₂×C₄	semidirect
58. D₃×#103	C₉	direct (N × H)
111. C₃×#103	C₂×C₉	semidirect
113. #835	C₂×C₉	semidirect
114. #816	C₂×C₉	semidirect
115. #810	C₂×C₉	semidirect
141. Q₈×C₉	C₄×D₃	semidirect
162. D₃×C₉	#103	direct (N × H)
174. D₃×Q₈	C₄×C₉	semidirect
227. #103	D₃×C₉	direct (N × H)
228. C₃×C₉	C₂×#103	semidirect
238. C₃×Q₈	C₂×C₄×C₉	semidirect
265. Dic₆	C₂×C₄×C₉	semidirect
325. C₉	D₃×#103	direct (N × H)
331. Q₈	C₄×D₃×C₉	semidirect
354. D₃	C₉×#103	direct (N × H)
367. C₃	C₂×C₉×#103	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×Q₈×C₉	2
C₂×D₃×C₈×C₉	2
D₃×C₉×C₄⋊C₄	2
C₃×C₉×#103	2
C₉×#835	2
C₉×#816	2
C₉×#810	2
C₃×D₃×#103	3
C₂×C₉×#103	3

Subgroups — D3×C9×#103 #13141880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₉×#103 #13141880