Subgroups — C₃²×D₃×#103 #13162236

Order 1728.

1140 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×C₃²×D₃×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×D₃×C₈	C₂	1	1	yes	maximal, characteristic
3	C₃²×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₃³×#103	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#835	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#816	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×#810	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃²×#103	—	3	1	no	maximal
9	C₃×D₃×#103	C₃	1	4	yes	maximal, direct product factor
10	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
11	C₃²×D₃×Q₈	—	2	2	no	—
12	C₃²×D₃×Q₈	C₄	1	4	yes	complemented
13	C₂×C₃²×C₄×D₃	—	2	1	no	—
14	C₂×C₃²×C₄×D₃	—	2	1	no	—
15	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
16	C₂×C₃²×Dic₆	—	2	1	no	—
17	C₂×C₃²×Dic₆	C₂²	1	1	yes	characteristic
18	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
19	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
21	C₃²×Dic₃⋊C₄	—	2	1	no	—
22	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₃²×D₃×C₈	—	2	2	no	—
24	C₂²×C₃²×Q₈	—	3	1	no	—
25	C₂×C₃×D₃×Q₈	C₂×C₃	1	4	yes	—
26	C₂²×C₃²×C₈	—	3	1	no	—
27	C₂×C₃²×C₄⋊C₄	—	3	1	no	—
28	C₂×C₃×D₃×C₈	C₂×C₃	1	4	yes	—
29	C₃×D₃×C₄⋊C₄	C₂×C₃	1	4	yes	—
30	C₃²×#103	—	2	4	no	—
31	C₃²×#103	—	3	1	no	—
32	C₃²×#103	—	3	1	no	—
33	C₃²×#103	—	3	1	no	—
34	C₃²×#103	D₃	1	1	yes	characteristic, direct product factor
35	C₃²×#103	C₂×C₃	1	4	yes	complemented
36	C₃×#835	C₂×C₃	1	4	yes	complemented
37	C₃×#816	C₂×C₃	1	4	yes	complemented
38	C₃×#810	C₂×C₃	1	4	yes	complemented
39	C₂²×C₃²×D₃	D₄	1	1	yes	characteristic
40	C₃³×Q₈	—	2	1	no	—
41	C₃³×Q₈	C₂×C₄	1	2	yes	complemented
42	C₂×C₃³×C₄	—	2	1	no	—
43	C₂×C₃³×C₄	—	2	1	no	—
44	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
45	C₂×C₃²×Dic₃	—	2	1	no	—
46	C₂×C₃²×Dic₃	—	2	1	no	—
47	C₂×C₃²×Dic₃	D₄	1	1	yes	characteristic
48	C₃²×C₄×D₃	—	2	4	no	—
49	C₃²×C₄×D₃	—	4	2	no	—
50	C₃²×C₄×D₃	C₂×C₄	1	2	yes	—
51	C₃²×C₄×D₃	D₄	1	2	yes	—
52	C₃²×Dic₆	—	2	1	no	—
53	C₃²×Dic₆	—	2	4	no	—
54	C₃²×Dic₆	C₂×C₄	1	2	yes	complemented
55	C₃³×C₈	—	2	1	no	—
56	C₃²×C₃⋊C₈	—	2	1	no	—
57	C₂×C₃×#103	—	3	4	no	—
58	D₃×#103	C₃²	1	1	yes	characteristic, direct product factor
59	C₂×C₃²×Q₈	—	2	4	no	—
60	C₂×C₃²×Q₈	—	3	4	no	—
61	C₂×C₃²×Q₈	—	3	1	no	—
62	C₂×C₃²×Q₈	—	6	1	no	—
63	C₂×C₃²×Q₈	—	6	2	no	—
64	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
65	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	—
66	C₂²×C₃²×C₄	—	3	1	no	—
67	C₂²×C₃²×C₄	—	6	1	no	—
68	C₂²×C₃²×C₄	—	6	1	no	—
69	C₃×D₃×Q₈	—	2	8	no	—
70	C₃×D₃×Q₈	C₃×C₄	1	16	yes	complemented
71	C₂×C₃×C₄×D₃	—	2	4	no	—
72	C₂×C₃×C₄×D₃	—	2	4	no	—
73	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
74	C₂×C₃×Dic₆	—	2	4	no	—
75	C₂×C₃×Dic₆	C₂²×C₃	1	4	yes	—
76	C₂×C₃²×C₈	—	2	4	no	—
77	C₂×C₃²×C₈	—	3	1	no	—
78	C₂×C₃²×C₈	—	6	2	no	—
79	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
80	C₂×C₃²×C₈	C₂²×C₃	1	4	yes	—
81	C₃²×C₄⋊C₄	—	2	4	no	—
82	C₃²×C₄⋊C₄	—	3	1	no	—
83	C₃²×C₄⋊C₄	—	6	1	no	—
84	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
85	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	—
86	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
87	C₃×Dic₃⋊C₄	—	2	4	no	—
88	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	4	yes	—
89	C₃×D₃×C₈	—	2	8	no	—
90	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
91	C₂×C₃²×D₃	C₂²⋊C₄	1	2	yes	—
92	C₂×C₃²×D₃	SD₁₆	1	2	yes	—
93	C₂×C₃²×D₃	Q₁₆	1	2	yes	—
94	C₃³×C₄	—	2	2	no	—
95	C₃³×C₄	—	4	1	no	—
96	C₃³×C₄	C₂²×C₄	1	1	yes	characteristic
97	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
98	C₃²×Dic₃	—	2	2	no	—
99	C₃²×Dic₃	—	4	1	no	—
100	C₃²×Dic₃	C₂²⋊C₄	1	2	yes	—
101	C₂²×C₃×Q₈	—	3	4	no	—
102	C₂×D₃×Q₈	C₂×C₃²	1	1	yes	characteristic
103	C₂²×C₃×C₈	—	3	4	no	—
104	C₂×C₃×C₄⋊C₄	—	3	4	no	—
105	C₂×D₃×C₈	C₂×C₃²	1	1	yes	characteristic
106	D₃×C₄⋊C₄	C₂×C₃²	1	1	yes	characteristic
107	C₃×#103	—	2	4	no	—
108	C₃×#103	—	3	4	no	—
109	C₃×#103	—	3	4	no	—
110	C₃×#103	—	3	4	no	—
111	C₃×#103	C₃×D₃	1	4	yes	direct product factor
112	C₃×#103	C₂×C₃²	1	1	yes	characteristic, complemented
113	#835	C₂×C₃²	1	1	yes	characteristic, complemented
114	#816	C₂×C₃²	1	1	yes	characteristic, complemented
115	#810	C₂×C₃²	1	1	yes	characteristic, complemented
116	C₂³×C₃²	—	3	1	no	—
117	C₂²×C₃×D₃	C₃×D₄	1	4	yes	—
118	C₃²×Q₈	—	2	1	no	—
119	C₃²×Q₈	—	2	8	no	—
120	C₃²×Q₈	—	2	4	no	—
121	C₃²×Q₈	—	3	2	no	—
122	C₃²×Q₈	—	4	4	no	—
123	C₃²×Q₈	—	6	4	no	—
124	C₃²×Q₈	—	6	1	no	—
125	C₃²×Q₈	C₄×D₃	1	2	yes	complemented
126	C₃²×Q₈	C₂×C₃×C₄	1	8	yes	complemented
127	C₂×C₃²×C₄	—	2	1	no	—
128	C₂×C₃²×C₄	—	2	1	no	—
129	C₂×C₃²×C₄	—	2	4	no	—
130	C₂×C₃²×C₄	—	2	4	no	—
131	C₂×C₃²×C₄	—	2	4	no	—
132	C₂×C₃²×C₄	—	3	1	no	—
133	C₂×C₃²×C₄	—	3	2	no	—
134	C₂×C₃²×C₄	—	3	2	no	—
135	C₂×C₃²×C₄	—	4	4	no	—
136	C₂×C₃²×C₄	—	4	4	no	—
137	C₂×C₃²×C₄	—	6	4	no	—
138	C₂×C₃²×C₄	—	6	1	no	—
139	C₂×C₃²×C₄	—	6	1	no	—
140	C₂×C₃²×C₄	—	12	2	no	—
141	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
142	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
143	C₂×C₃×Dic₃	—	2	4	no	—
144	C₂×C₃×Dic₃	—	2	4	no	—
145	C₂×C₃×Dic₃	C₃×D₄	1	4	yes	—
146	C₃×C₄×D₃	—	2	16	no	—
147	C₃×C₄×D₃	—	4	8	no	—
148	C₃×C₄×D₃	C₂×C₃×C₄	1	8	yes	—
149	C₃×C₄×D₃	C₃×D₄	1	8	yes	—
150	C₃×Dic₆	—	2	4	no	—
151	C₃×Dic₆	—	2	16	no	—
152	C₃×Dic₆	C₂×C₃×C₄	1	8	yes	complemented
153	C₃²×C₈	—	2	1	no	—
154	C₃²×C₈	—	2	4	no	—
155	C₃²×C₈	—	4	4	no	—
156	C₃²×C₈	—	6	1	no	—
157	C₃×C₃⋊C₈	—	2	4	no	—
158	C₂×#103	—	3	1	no	Sylow
159	C₂×C₃³	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₃³	C₂×SD₁₆	1	1	yes	characteristic
161	C₂×C₃³	C₂×Q₁₆	1	1	yes	characteristic
162	C₃²×D₃	#103	1	4	yes	direct product factor
163	C₂×C₃×Q₈	—	2	4	no	—
164	C₂×C₃×Q₈	—	3	16	no	—
165	C₂×C₃×Q₈	—	3	4	no	—
166	C₂×C₃×Q₈	—	6	4	no	—
167	C₂×C₃×Q₈	—	6	8	no	—
168	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
169	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic
170	C₂²×C₃×C₄	—	3	4	no	—
171	C₂²×C₃×C₄	—	6	4	no	—
172	C₂²×C₃×C₄	—	6	4	no	—
173	D₃×Q₈	—	2	2	no	—
174	D₃×Q₈	C₃²×C₄	1	4	yes	complemented
175	C₂×C₄×D₃	—	2	1	no	—
176	C₂×C₄×D₃	—	2	1	no	—
177	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
178	C₂×Dic₆	—	2	1	no	—
179	C₂×Dic₆	C₂²×C₃²	1	1	yes	characteristic
180	C₂×C₃×C₈	—	2	4	no	—
181	C₂×C₃×C₈	—	3	4	no	—
182	C₂×C₃×C₈	—	6	8	no	—
183	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
184	C₂×C₃×C₈	C₂²×C₃²	1	1	yes	characteristic
185	C₃×C₄⋊C₄	—	2	4	no	—
186	C₃×C₄⋊C₄	—	3	4	no	—
187	C₃×C₄⋊C₄	—	6	4	no	—
188	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
189	C₃×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
190	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic
191	Dic₃⋊C₄	—	2	1	no	—
192	C₂×C₃⋊C₈	C₂²×C₃²	1	1	yes	characteristic
193	D₃×C₈	—	2	2	no	—
194	C₂²×C₃²	—	2	4	no	—
195	C₂²×C₃²	—	3	2	no	—
196	C₂²×C₃²	—	3	2	no	—
197	C₂²×C₃²	—	3	2	no	—
198	C₂²×C₃²	D₃×D₄	1	1	yes	characteristic
199	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
200	C₂×C₃×D₃	C₃×C₂²⋊C₄	1	8	yes	—
201	C₂×C₃×D₃	C₃×SD₁₆	1	8	yes	—
202	C₂×C₃×D₃	C₃×Q₁₆	1	8	yes	—
203	C₃²×C₄	—	2	2	no	—
204	C₃²×C₄	—	2	4	no	—
205	C₃²×C₄	—	2	4	no	—
206	C₃²×C₄	—	2	8	no	—
207	C₃²×C₄	—	3	2	no	—
208	C₃²×C₄	—	4	8	no	—
209	C₃²×C₄	—	4	1	no	—
210	C₃²×C₄	—	4	4	no	—
211	C₃²×C₄	—	6	2	no	—
212	C₃²×C₄	—	8	4	no	—
213	C₃²×C₄	—	12	1	no	—
214	C₃²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
215	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
216	C₃²×C₄	C₂²×C₃×C₄	1	4	yes	—
217	C₃²×C₄	C₂×C₃×D₄	1	4	yes	—
218	C₃×Dic₃	—	2	8	no	—
219	C₃×Dic₃	—	4	4	no	—
220	C₃×Dic₃	C₃×C₂²⋊C₄	1	8	yes	—
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	C₃²×D₃	1	1	yes	characteristic, direct product factor
228	C₃³	C₂×#103	1	1	yes	characteristic, complemented, Sylow
229	C₂³×C₃	—	3	4	no	—
230	C₂²×D₃	C₃²×D₄	1	1	yes	characteristic
231	C₃×Q₈	—	2	4	no	—
232	C₃×Q₈	—	2	1	no	—
233	C₃×Q₈	—	2	8	no	—
234	C₃×Q₈	—	3	8	no	—
235	C₃×Q₈	—	4	4	no	—
236	C₃×Q₈	—	6	16	no	—
237	C₃×Q₈	—	6	4	no	—
238	C₃×Q₈	C₃×C₄×D₃	1	8	yes	complemented
239	C₃×Q₈	C₂×C₃²×C₄	1	2	yes	complemented
240	C₂×C₃×C₄	—	2	4	no	—
241	C₂×C₃×C₄	—	2	1	no	—
242	C₂×C₃×C₄	—	2	4	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	2	4	no	—
245	C₂×C₃×C₄	—	3	4	no	—
246	C₂×C₃×C₄	—	3	8	no	—
247	C₂×C₃×C₄	—	3	8	no	—
248	C₂×C₃×C₄	—	4	4	no	—
249	C₂×C₃×C₄	—	4	4	no	—
250	C₂×C₃×C₄	—	6	16	no	—
251	C₂×C₃×C₄	—	6	4	no	—
252	C₂×C₃×C₄	—	6	4	no	—
253	C₂×C₃×C₄	—	12	8	no	—
254	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
255	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
256	C₂×Dic₃	—	2	1	no	—
257	C₂×Dic₃	—	2	1	no	—
258	C₂×Dic₃	C₃²×D₄	1	1	yes	characteristic
259	C₄×D₃	—	2	4	no	—
260	C₄×D₃	—	4	2	no	—
261	C₄×D₃	C₂×C₃²×C₄	1	2	yes	—
262	C₄×D₃	C₃²×D₄	1	2	yes	—
263	Dic₆	—	2	1	no	—
264	Dic₆	—	2	4	no	—
265	Dic₆	C₂×C₃²×C₄	1	2	yes	complemented
266	C₃×C₈	—	2	4	no	—
267	C₃×C₈	—	2	1	no	—
268	C₃×C₈	—	4	4	no	—
269	C₃×C₈	—	6	4	no	—
270	C₃⋊C₈	—	2	1	no	—
271	C₂×C₃²	—	2	4	no	—
272	C₂×C₃²	—	2	4	no	—
273	C₂×C₃²	—	2	4	no	—
274	C₂×C₃²	—	3	4	no	—
275	C₂×C₃²	D₃×C₂²⋊C₄	1	1	yes	characteristic
276	C₂×C₃²	D₃×SD₁₆	1	1	yes	characteristic
277	C₂×C₃²	D₃×Q₁₆	1	1	yes	characteristic
278	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	4	yes	—
279	C₂×C₃²	C₂×C₃×SD₁₆	1	4	yes	—
280	C₂×C₃²	C₂×C₃×Q₁₆	1	4	yes	—
281	C₃×D₃	C₃×#103	1	16	yes	direct product factor
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×C₃²×D₃	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×C₃²×D₃	1	1	yes	characteristic
293	C₄⋊C₄	—	3	1	no	—
294	C₄⋊C₄	—	6	1	no	—
295	C₄⋊C₄	C₂×C₃²×D₃	1	1	yes	characteristic
296	C₂²×C₃	—	2	4	no	—
297	C₂²×C₃	—	3	8	no	—
298	C₂²×C₃	—	3	8	no	—
299	C₂²×C₃	—	3	8	no	—
300	C₂²×C₃	C₃×D₃×D₄	1	4	yes	—
301	C₂²×C₃	C₂×C₃²×D₄	1	1	yes	characteristic
302	C₂×D₃	C₃²×C₂²⋊C₄	1	2	yes	—
303	C₂×D₃	C₃²×SD₁₆	1	2	yes	—
304	C₂×D₃	C₃²×Q₁₆	1	2	yes	—
305	C₃×C₄	—	2	8	no	—
306	C₃×C₄	—	2	2	no	—
307	C₃×C₄	—	2	4	no	—
308	C₃×C₄	—	2	4	no	—
309	C₃×C₄	—	3	8	no	—
310	C₃×C₄	—	4	8	no	—
311	C₃×C₄	—	4	4	no	—
312	C₃×C₄	—	4	1	no	—
313	C₃×C₄	—	6	8	no	—
314	C₃×C₄	—	8	4	no	—
315	C₃×C₄	—	12	4	no	—
316	C₃×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
317	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
318	C₃×C₄	C₂²×C₃²×C₄	1	1	yes	characteristic
319	C₃×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
320	Dic₃	—	2	2	no	—
321	Dic₃	—	4	1	no	—
322	Dic₃	C₃²×C₂²⋊C₄	1	2	yes	—
323	C₃²	—	2	4	no	—
324	C₃²	D₃×#103	1	1	yes	characteristic, direct product factor
325	C₃²	C₂×C₃×#103	1	4	yes	complemented
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	C₃²×C₄×D₃	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×C₃²×D₃	1	1	yes	characteristic
342	C₈	—	2	1	no	—
343	C₈	—	6	1	no	—
344	C₂×C₃	—	2	4	no	—
345	C₂×C₃	—	2	4	no	—
346	C₂×C₃	—	2	4	no	—
347	C₂×C₃	—	3	16	no	—
348	C₂×C₃	C₃×D₃×C₂²⋊C₄	1	4	yes	—
349	C₂×C₃	C₃×D₃×SD₁₆	1	4	yes	—
350	C₂×C₃	C₃×D₃×Q₁₆	1	4	yes	—
351	C₂×C₃	C₂×C₃²×C₂²⋊C₄	1	1	yes	characteristic
352	C₂×C₃	C₂×C₃²×SD₁₆	1	1	yes	characteristic
353	C₂×C₃	C₂×C₃²×Q₁₆	1	1	yes	characteristic
354	D₃	C₃²×#103	1	4	yes	direct product factor
355	C₂²	—	3	2	no	—
356	C₂²	—	3	2	no	—
357	C₂²	—	3	2	no	—
358	C₂²	C₃²×D₃×D₄	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×C₃²×C₄×D₃	1	1	yes	characteristic
365	C₄	C₃²×D₃×D₄	1	1	yes	characteristic
366	C₃	—	2	4	no	—
367	C₃	C₃×D₃×#103	1	4	yes	direct product factor
368	C₃	C₂×C₃²×#103	1	1	yes	characteristic, complemented
369	C₂	—	3	4	no	—
370	C₂	C₃²×D₃×C₂²⋊C₄	1	1	yes	characteristic
371	C₂	C₃²×D₃×SD₁₆	1	1	yes	characteristic
372	C₂	C₃²×D₃×Q₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃²	D₃×D₄
commutator	C₃×C₄	C₂²×C₃²×C₄
Frattini	C₂×C₄	C₂²×C₃²×D₃
Fitting	C₃³×#103	C₂
socle	C₂²×C₃³	C₂×D₄
prime radical	C₂²×C₃²×D₃	D₄
cosocle	C₂×C₃×C₄	C₂³×C₃²
hypercenter	C₃²×#103	D₃
hypocenter	C₃	C₂×C₃²×#103
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₂×C₃²×C₄ ◁ C₃²×#103

Complements

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

N	H ≅ G/N	type
4. C₃³×#103	C₂	semidirect
5. C₃²×#835	C₂	semidirect
6. C₃²×#816	C₂	semidirect
7. C₃²×#810	C₂	semidirect
9. C₃×D₃×#103	C₃	direct (N × H)
12. C₃²×D₃×Q₈	C₄	semidirect
34. C₃²×#103	D₃	direct (N × H)
35. C₃²×#103	C₂×C₃	semidirect
36. C₃×#835	C₂×C₃	semidirect
37. C₃×#816	C₂×C₃	semidirect
38. C₃×#810	C₂×C₃	semidirect
41. C₃³×Q₈	C₂×C₄	semidirect
54. C₃²×Dic₆	C₂×C₄	semidirect
58. D₃×#103	C₃²	direct (N × H)
70. C₃×D₃×Q₈	C₃×C₄	semidirect
111. C₃×#103	C₃×D₃	direct (N × H)
112. C₃×#103	C₂×C₃²	semidirect
113. #835	C₂×C₃²	semidirect
114. #816	C₂×C₃²	semidirect
115. #810	C₂×C₃²	semidirect
125. C₃²×Q₈	C₄×D₃	semidirect
126. C₃²×Q₈	C₂×C₃×C₄	semidirect
152. C₃×Dic₆	C₂×C₃×C₄	semidirect
162. C₃²×D₃	#103	direct (N × H)
174. D₃×Q₈	C₃²×C₄	semidirect
227. #103	C₃²×D₃	direct (N × H)
228. C₃³	C₂×#103	semidirect
238. C₃×Q₈	C₃×C₄×D₃	semidirect
239. C₃×Q₈	C₂×C₃²×C₄	semidirect
265. Dic₆	C₂×C₃²×C₄	semidirect
281. C₃×D₃	C₃×#103	direct (N × H)
324. C₃²	D₃×#103	direct (N × H)
325. C₃²	C₂×C₃×#103	semidirect
331. Q₈	C₃²×C₄×D₃	semidirect
354. D₃	C₃²×#103	direct (N × H)
367. C₃	C₃×D₃×#103	direct (N × H)
368. C₃	C₂×C₃²×#103	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×D₃×Q₈	2
C₂×C₃²×D₃×C₈	2
C₃²×D₃×C₄⋊C₄	2
C₃³×#103	2
C₃²×#835	2
C₃²×#816	2
C₃²×#810	2
C₂×C₃²×#103	3
C₃×D₃×#103	3

Subgroups — C32×D3×#103 #13162236

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×D₃×#103 #13162236