Subgroups — C₃×#10595995 #13179278

Order 1728.

2284 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#3828	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃³×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64106	C₂	1	2	yes	maximal, complemented
5	C₃×#64104	C₂	1	2	yes	maximal, complemented
6	C₃×#64095	C₂	1	2	yes	maximal, complemented
7	C₃×#64091	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×C₄⋊(C₃⋊D₃)	C₂	1	4	yes	maximal, complemented
9	#10595995	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₃×#5524	—	3	4	no	maximal
11	C₂³×C₃×C₃⋊D₃	C₂²	1	1	yes	characteristic
12	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
13	C₂×C₃×#638	C₂²	1	2	yes	—
14	C₂²×C₃×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
15	C₃×#3828	—	2	4	no	—
16	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	4	yes	—
17	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₃×C₄×C₃⋊D₃	—	2	4	no	—
19	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	2	yes	—
20	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	2	yes	—
21	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	2	yes	complemented
22	C₂×C₃×#634	C₂²	1	1	yes	characteristic, complemented
23	C₃³×C₄⋊C₄	C₂²	1	2	yes	complemented
24	C₃³×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₃³×C₄²	C₂²	1	2	yes	complemented
26	C₃×#3752	C₂²	1	4	yes	—
27	C₃×#3752	C₂²	1	4	yes	complemented
28	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	4	yes	complemented
29	C₂×#3828	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂²×C₄×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂×C₃×#235	—	3	4	no	—
32	C₂²×C₃×C₄×D₃	—	3	4	no	—
33	C₃²×#117	—	2	4	no	—
34	C₃²×#117	D₃	1	4	yes	complemented
35	C₃²×#117	C₂×C₃	1	1	yes	characteristic, complemented
36	#64106	C₂×C₃	1	2	yes	complemented
37	#64104	C₂×C₃	1	2	yes	complemented
38	#64095	C₂×C₃	1	2	yes	complemented
39	#64091	C₂×C₃	1	2	yes	complemented
40	C₄×C₄⋊(C₃⋊D₃)	C₂×C₃	1	4	yes	complemented
41	C₃×#897	—	3	8	no	—
42	C₃×#895	—	3	8	no	—
43	C₃×#886	—	3	8	no	—
44	C₃×#882	—	3	8	no	—
45	C₃×C₄×D₁₂	—	3	16	no	—
46	C₂³×C₃³	C₂³	1	1	yes	characteristic
47	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
48	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
49	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	—
50	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	—
51	C₂×C₃³×C₄	D₄	1	4	yes	complemented
52	C₂×C₃³×C₄	C₂³	1	4	yes	—
53	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
54	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
55	C₃×#638	—	2	4	no	—
56	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
57	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
58	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
59	C₃×C₄⋊(C₃⋊D₃)	—	2	8	no	—
60	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
61	C₃×C₄×C₃⋊D₃	—	2	4	no	—
62	C₃×C₄×C₃⋊D₃	—	2	4	no	—
63	C₃×C₄×C₃⋊D₃	—	2	4	no	—
64	C₃×#634	—	2	2	no	—
65	C₃×#525	—	9	1	no	—
66	#5524	—	3	4	no	—
67	C₂³×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
68	C₂³×C₃×D₃	—	3	4	no	—
69	C₂²×C₃²×C₄	—	2	4	no	—
70	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
71	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
72	C₂×#638	C₂²×C₃	1	2	yes	—
73	C₂²×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
74	#3828	—	2	4	no	—
75	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	4	yes	—
76	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic, complemented
77	C₂×C₄×C₃⋊D₃	—	2	4	no	—
78	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	2	yes	—
79	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	2	yes	—
80	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	2	yes	complemented
81	C₂×#634	C₂²×C₃	1	1	yes	characteristic, complemented
82	C₂×C₃×#67	—	3	8	no	—
83	C₂²×C₃×Dic₃	—	3	4	no	—
84	C₃×#235	—	6	16	no	—
85	C₂×C₃×D₁₂	—	3	16	no	—
86	C₂×C₃×D₁₂	—	3	4	no	—
87	C₂×C₃×C₄×D₃	—	3	8	no	—
88	C₂×C₃×C₄×D₃	—	3	8	no	—
89	C₂×C₃×C₄×D₃	—	3	8	no	—
90	C₂×C₃×C₄×D₃	—	6	16	no	—
91	C₂×C₃×Dic₆	—	3	4	no	—
92	C₃²×C₄⋊C₄	—	2	8	no	—
93	C₃²×C₄⋊C₄	C₂×D₃	1	8	yes	complemented
94	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
95	C₃²×C₂²⋊C₄	—	2	8	no	—
96	C₃²×C₂²⋊C₄	C₂×D₃	1	8	yes	—
97	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
98	C₃²×C₄²	—	2	8	no	—
99	C₃²×C₄²	C₂×D₃	1	8	yes	complemented
100	C₃²×C₄²	C₂²×C₃	1	2	yes	complemented
101	#3752	C₂²×C₃	1	4	yes	—
102	#3752	C₂²×C₃	1	4	yes	complemented
103	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	4	yes	complemented
104	C₃×(C₂×D₃)⋊C₄	—	3	16	no	—
105	C₃×(C₂×D₃)⋊C₄	—	3	16	no	—
106	C₃×C₄⋊Dic₃	—	3	16	no	—
107	C₂²×C₃³	—	2	2	no	—
108	C₂²×C₃³	C₂×D₄	1	2	yes	—
109	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
110	C₂×C₃×C₃⋊D₃	—	2	8	no	—
111	C₂×C₃×C₃⋊D₃	—	2	2	no	—
112	C₂×C₃×C₃⋊D₃	—	2	2	no	—
113	C₂×C₃×C₃⋊D₃	—	2	2	no	—
114	C₂×C₃×C₃⋊D₃	—	2	4	no	—
115	C₂×C₃×C₃⋊D₃	#41	1	4	yes	complemented
116	C₃³×C₄	—	2	4	no	—
117	C₃³×C₄	C₂×D₄	1	2	yes	—
118	C₃³×C₄	C₂×D₄	1	2	yes	—
119	C₃×C₃⋊Dic₃	—	2	2	no	—
120	C₃×C₃⋊Dic₃	—	2	2	no	—
121	C₂×C₃×#41	—	9	1	no	—
122	C₂³×C₃×C₄	—	9	1	no	—
123	C₂×#235	—	3	4	no	—
124	C₂²×C₄×D₃	—	3	4	no	—
125	C₃×#123	—	9	2	no	—
126	C₃×C₂²⋊Q₈	—	9	2	no	—
127	C₃×#121	—	9	2	no	—
128	C₃×#120	—	9	2	no	—
129	C₃×C₄×D₄	—	9	4	no	—
130	C₃×#117	—	2	4	no	—
131	C₃×#117	C₃×D₃	1	4	yes	complemented
132	C₃×#117	C₃⋊D₃	1	1	yes	characteristic, complemented
133	#897	—	3	8	no	—
134	#895	—	3	8	no	—
135	#886	—	3	8	no	—
136	#882	—	3	8	no	—
137	C₄×D₁₂	—	3	16	no	—
138	C₂³×C₃²	—	2	4	no	—
139	C₂³×C₃²	C₂²×D₃	1	4	yes	—
140	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
141	C₂²×C₃⋊D₃	—	2	2	no	—
142	C₂²×C₃⋊D₃	—	2	4	no	—
143	C₂²×C₃⋊D₃	C₂³×C₃	1	2	yes	—
144	C₂²×C₃⋊D₃	C₂³×C₃	1	2	yes	—
145	C₂²×C₃×D₃	—	3	8	no	—
146	C₂²×C₃×D₃	—	3	8	no	—
147	C₂²×C₃×D₃	—	6	16	no	—
148	C₂²×C₃×D₃	—	6	8	no	—
149	C₂×C₃²×C₄	—	2	16	no	—
150	C₂×C₃²×C₄	—	2	4	no	—
151	C₂×C₃²×C₄	—	2	4	no	—
152	C₂×C₃²×C₄	—	2	16	no	—
153	C₂×C₃²×C₄	D₁₂	1	16	yes	complemented
154	C₂×C₃²×C₄	C₃×D₄	1	4	yes	complemented
155	C₂×C₃²×C₄	C₂²×D₃	1	16	yes	—
156	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
157	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
158	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
159	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
160	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
161	#638	—	2	4	no	—
162	C₂×C₃⋊Dic₃	—	2	2	no	—
163	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
164	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
165	C₄⋊(C₃⋊D₃)	—	2	8	no	—
166	C₄⋊(C₃⋊D₃)	—	2	2	no	—
167	C₄×C₃⋊D₃	—	2	4	no	—
168	C₄×C₃⋊D₃	—	2	4	no	—
169	C₄×C₃⋊D₃	—	2	4	no	—
170	#634	—	2	2	no	—
171	C₃×#67	—	6	16	no	—
172	C₂×C₃×Dic₃	—	3	8	no	—
173	C₂×C₃×Dic₃	—	3	8	no	—
174	C₂×C₃×Dic₃	—	6	8	no	—
175	C₃×D₁₂	—	6	32	no	—
176	C₃×D₁₂	—	6	8	no	—
177	C₃×C₄×D₃	—	6	16	no	—
178	C₃×C₄×D₃	—	6	16	no	—
179	C₃×C₄×D₃	—	6	16	no	—
180	C₃×Dic₆	—	6	8	no	—
181	#525	—	9	1	no	Sylow
182	C₂×C₃³	—	2	2	no	—
183	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₃³	C₂×#41	1	2	yes	—
185	C₃×C₃⋊D₃	—	2	4	no	—
186	C₃×C₃⋊D₃	—	4	2	no	—
187	C₂⁴×C₃	—	9	1	no	—
188	C₂³×D₃	—	3	4	no	—
189	C₃×#41	—	18	4	no	—
190	C₂×C₃×Q₈	—	9	1	no	—
191	C₂×C₃×D₄	—	9	2	no	—
192	C₂×C₃×D₄	—	9	4	no	—
193	C₂×C₃×D₄	—	9	1	no	—
194	C₂²×C₃×C₄	—	2	4	no	—
195	C₂²×C₃×C₄	—	9	1	no	—
196	C₂²×C₃×C₄	—	9	2	no	—
197	C₂²×C₃×C₄	—	9	2	no	—
198	C₂²×C₃×C₄	—	9	2	no	—
199	C₂²×C₃×C₄	—	18	4	no	—
200	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
201	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
202	C₂×#67	—	3	8	no	—
203	C₂²×Dic₃	—	3	4	no	—
204	#235	—	6	16	no	—
205	C₂×D₁₂	—	3	16	no	—
206	C₂×D₁₂	—	3	4	no	—
207	C₂×C₄×D₃	—	3	8	no	—
208	C₂×C₄×D₃	—	3	8	no	—
209	C₂×C₄×D₃	—	3	8	no	—
210	C₂×C₄×D₃	—	6	16	no	—
211	C₂×Dic₆	—	3	4	no	—
212	C₃×C₄⋊C₄	—	2	8	no	—
213	C₃×C₄⋊C₄	—	9	4	no	—
214	C₃×C₄⋊C₄	C₂×C₃×D₃	1	8	yes	complemented
215	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	2	yes	complemented
216	C₃×C₂²⋊C₄	—	2	8	no	—
217	C₃×C₂²⋊C₄	—	9	4	no	—
218	C₃×C₂²⋊C₄	—	9	4	no	—
219	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	8	yes	—
220	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	2	yes	—
221	C₃×C₄²	—	2	8	no	—
222	C₃×C₄²	C₂×C₃×D₃	1	8	yes	complemented
223	C₃×C₄²	C₂×C₃⋊D₃	1	2	yes	complemented
224	(C₂×D₃)⋊C₄	—	3	16	no	—
225	(C₂×D₃)⋊C₄	—	3	16	no	—
226	C₄⋊Dic₃	—	3	16	no	—
227	C₂²×C₃²	—	2	2	no	—
228	C₂²×C₃²	—	2	4	no	—
229	C₂²×C₃²	—	2	8	no	—
230	C₂²×C₃²	—	2	8	no	—
231	C₂²×C₃²	—	4	8	no	—
232	C₂²×C₃²	C₂×D₁₂	1	8	yes	—
233	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
234	C₂²×C₃²	C₂³×D₃	1	4	yes	—
235	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
236	C₂×C₃⋊D₃	—	2	8	no	—
237	C₂×C₃⋊D₃	—	2	2	no	—
238	C₂×C₃⋊D₃	—	2	2	no	—
239	C₂×C₃⋊D₃	—	2	2	no	—
240	C₂×C₃⋊D₃	—	2	4	no	—
241	C₂×C₃⋊D₃	C₃×#41	1	4	yes	complemented
242	C₂×C₃×D₃	—	3	16	no	—
243	C₂×C₃×D₃	—	6	32	no	—
244	C₂×C₃×D₃	—	6	8	no	—
245	C₂×C₃×D₃	—	6	8	no	—
246	C₂×C₃×D₃	—	6	8	no	—
247	C₂×C₃×D₃	—	6	16	no	—
248	C₃²×C₄	—	2	4	no	—
249	C₃²×C₄	—	2	8	no	—
250	C₃²×C₄	—	2	8	no	—
251	C₃²×C₄	—	2	16	no	—
252	C₃²×C₄	—	4	16	no	—
253	C₃²×C₄	C₂×D₁₂	1	8	yes	—
254	C₃²×C₄	C₂×D₁₂	1	8	yes	—
255	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
256	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
257	C₃⋊Dic₃	—	2	2	no	—
258	C₃⋊Dic₃	—	2	2	no	—
259	C₃×Dic₃	—	6	8	no	—
260	C₃×Dic₃	—	6	8	no	—
261	C₂×#41	—	9	1	no	—
262	C₂³×C₄	—	9	1	no	—
263	#123	—	9	2	no	—
264	C₂²⋊Q₈	—	9	2	no	—
265	#121	—	9	2	no	—
266	#120	—	9	2	no	—
267	C₄×D₄	—	9	4	no	—
268	#117	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
269	C₃³	#525	1	1	yes	characteristic, complemented, Sylow
270	C₂³×C₃	—	2	4	no	—
271	C₂³×C₃	—	9	2	no	—
272	C₂³×C₃	—	9	2	no	—
273	C₂³×C₃	—	18	4	no	—
274	C₂³×C₃	—	18	2	no	—
275	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
276	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
277	C₂²×D₃	—	3	8	no	—
278	C₂²×D₃	—	3	8	no	—
279	C₂²×D₃	—	6	16	no	—
280	C₂²×D₃	—	6	8	no	—
281	C₃×Q₈	—	18	2	no	—
282	C₃×D₄	—	18	8	no	—
283	C₃×D₄	—	18	4	no	—
284	C₃×D₄	—	18	2	no	—
285	C₂×C₃×C₄	—	2	16	no	—
286	C₂×C₃×C₄	—	2	4	no	—
287	C₂×C₃×C₄	—	2	4	no	—
288	C₂×C₃×C₄	—	2	16	no	—
289	C₂×C₃×C₄	—	9	2	no	—
290	C₂×C₃×C₄	—	9	2	no	—
291	C₂×C₃×C₄	—	18	2	no	—
292	C₂×C₃×C₄	—	18	4	no	—
293	C₂×C₃×C₄	—	18	4	no	—
294	C₂×C₃×C₄	—	18	4	no	—
295	C₂×C₃×C₄	C₃×D₁₂	1	16	yes	complemented
296	C₂×C₃×C₄	C₄⋊(C₃⋊D₃)	1	4	yes	complemented
297	C₂×C₃×C₄	C₂²×C₃×D₃	1	16	yes	—
298	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
299	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
300	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	4	yes	—
301	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
303	#67	—	6	16	no	—
304	C₂×Dic₃	—	3	8	no	—
305	C₂×Dic₃	—	3	8	no	—
306	C₂×Dic₃	—	6	8	no	—
307	D₁₂	—	6	32	no	—
308	D₁₂	—	6	8	no	—
309	C₄×D₃	—	6	16	no	—
310	C₄×D₃	—	6	16	no	—
311	C₄×D₃	—	6	16	no	—
312	Dic₆	—	6	8	no	—
313	C₂×C₃²	—	2	2	no	—
314	C₂×C₃²	—	2	4	no	—
315	C₂×C₃²	—	2	8	no	—
316	C₂×C₃²	—	2	8	no	—
317	C₂×C₃²	—	4	8	no	—
318	C₂×C₃²	C₂²×D₁₂	1	4	yes	—
319	C₂×C₃²	D₃×#41	1	8	yes	—
320	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
321	C₂×C₃²	C₂×C₃×#41	1	2	yes	—
322	C₃⋊D₃	—	2	4	no	—
323	C₃⋊D₃	—	4	2	no	—
324	C₃×D₃	—	6	16	no	—
325	C₃×D₃	—	12	8	no	—
326	C₂⁴	—	9	1	no	—
327	#41	—	18	4	no	—
328	C₂×Q₈	—	9	1	no	—
329	C₂×D₄	—	9	2	no	—
330	C₂×D₄	—	9	4	no	—
331	C₂×D₄	—	9	1	no	—
332	C₂²×C₄	—	9	1	no	—
333	C₂²×C₄	—	9	2	no	—
334	C₂²×C₄	—	9	2	no	—
335	C₂²×C₄	—	9	2	no	—
336	C₂²×C₄	—	18	4	no	—
337	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
338	C₄⋊C₄	—	9	4	no	—
339	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
340	C₂²⋊C₄	—	9	4	no	—
341	C₂²⋊C₄	—	9	4	no	—
342	C₂²⋊C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
343	C₄²	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
344	C₂²×C₃	—	2	8	no	—
345	C₂²×C₃	—	2	2	no	—
346	C₂²×C₃	—	2	4	no	—
347	C₂²×C₃	—	2	8	no	—
348	C₂²×C₃	—	4	8	no	—
349	C₂²×C₃	—	9	4	no	—
350	C₂²×C₃	—	18	8	no	—
351	C₂²×C₃	—	18	2	no	—
352	C₂²×C₃	—	18	2	no	—
353	C₂²×C₃	—	18	2	no	—
354	C₂²×C₃	—	18	4	no	—
355	C₂²×C₃	C₂×C₃×D₁₂	1	8	yes	—
356	C₂²×C₃	C₂×C₄⋊(C₃⋊D₃)	1	2	yes	—
357	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
358	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
359	C₂×D₃	—	3	16	no	—
360	C₂×D₃	—	6	32	no	—
361	C₂×D₃	—	6	8	no	—
362	C₂×D₃	—	6	8	no	—
363	C₂×D₃	—	6	8	no	—
364	C₂×D₃	—	6	16	no	—
365	C₃×C₄	—	2	16	no	—
366	C₃×C₄	—	2	4	no	—
367	C₃×C₄	—	2	8	no	—
368	C₃×C₄	—	2	8	no	—
369	C₃×C₄	—	4	16	no	—
370	C₃×C₄	—	18	2	no	—
371	C₃×C₄	—	18	2	no	—
372	C₃×C₄	C₂×C₃×D₁₂	1	8	yes	—
373	C₃×C₄	C₂×C₃×D₁₂	1	8	yes	—
374	C₃×C₄	C₂×C₄⋊(C₃⋊D₃)	1	2	yes	—
375	C₃×C₄	C₂×C₄⋊(C₃⋊D₃)	1	2	yes	—
376	Dic₃	—	6	8	no	—
377	Dic₃	—	6	8	no	—
378	C₃²	—	2	4	no	—
379	C₃²	#5524	1	4	yes	complemented
380	C₃²	C₃×#525	1	1	yes	characteristic, complemented
381	C₂³	—	9	2	no	—
382	C₂³	—	9	2	no	—
383	C₂³	—	18	4	no	—
384	C₂³	—	18	2	no	—
385	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
386	Q₈	—	18	2	no	—
387	D₄	—	18	8	no	—
388	D₄	—	18	4	no	—
389	D₄	—	18	2	no	—
390	C₂×C₄	—	9	2	no	—
391	C₂×C₄	—	9	2	no	—
392	C₂×C₄	—	18	2	no	—
393	C₂×C₄	—	18	4	no	—
394	C₂×C₄	—	18	4	no	—
395	C₂×C₄	—	18	4	no	—
396	C₂×C₄	C₃×C₄⋊(C₃⋊D₃)	1	4	yes	complemented
397	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	4	yes	—
398	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
399	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
400	C₂×C₃	—	2	8	no	—
401	C₂×C₃	—	2	2	no	—
402	C₂×C₃	—	2	4	no	—
403	C₂×C₃	—	2	8	no	—
404	C₂×C₃	—	4	8	no	—
405	C₂×C₃	—	18	4	no	—
406	C₂×C₃	—	36	2	no	—
407	C₂×C₃	C₂²×C₃×D₁₂	1	4	yes	—
408	C₂×C₃	C₃×D₃×#41	1	8	yes	—
409	C₂×C₃	C₂²×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
410	C₂×C₃	#41×C₃⋊D₃	1	2	yes	—
411	D₃	—	6	16	no	—
412	D₃	—	12	8	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	9	4	no	—
415	C₂²	—	18	8	no	—
416	C₂²	—	18	2	no	—
417	C₂²	—	18	2	no	—
418	C₂²	—	18	2	no	—
419	C₂²	—	18	4	no	—
420	C₂²	C₂×C₃×C₄⋊(C₃⋊D₃)	1	2	yes	—
421	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
422	C₄	—	2	4	no	—
423	C₄	—	18	2	no	—
424	C₄	—	18	2	no	—
425	C₄	C₂×C₃×C₄⋊(C₃⋊D₃)	1	2	yes	—
426	C₄	C₂×C₃×C₄⋊(C₃⋊D₃)	1	2	yes	—
427	C₃	—	2	4	no	—
428	C₃	C₃×#5524	1	4	yes	complemented
429	C₃	#10595995	1	1	yes	characteristic, direct product factor
430	C₂	—	2	2	no	—
431	C₂	—	18	4	no	—
432	C₂	—	36	2	no	—
433	C₂	C₂²×C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
434	C₂	C₃×#41×C₃⋊D₃	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×C₃⋊D₃
commutator, cosocle	C₂²×C₃²	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×C₃⋊D₃
Fitting	C₃³×#117	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₃×#117	C₃⋊D₃
hypocenter	C₃²	C₃×#525
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#117

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#3828	C₂	semidirect
2. C₂²×C₃×C₄×C₃⋊D₃	C₂	semidirect
3. C₃³×#117	C₂	semidirect
4. C₃×#64106	C₂	semidirect
5. C₃×#64104	C₂	semidirect
6. C₃×#64095	C₂	semidirect
7. C₃×#64091	C₂	semidirect
8. C₃×C₄×C₄⋊(C₃⋊D₃)	C₂	semidirect
9. #10595995	C₃	direct (N × H)
17. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
21. C₂×C₃×C₄×C₃⋊D₃	C₂²	semidirect
22. C₂×C₃×#634	C₂²	semidirect
23. C₃³×C₄⋊C₄	C₂²	semidirect
25. C₃³×C₄²	C₂²	semidirect
27. C₃×#3752	C₂²	semidirect
28. C₃×C₄⋊(C₃⋊Dic₃)	C₂²	semidirect
29. C₂×#3828	C₂×C₃	semidirect
30. C₂²×C₄×C₃⋊D₃	C₂×C₃	semidirect
34. C₃²×#117	D₃	semidirect
35. C₃²×#117	C₂×C₃	semidirect
36. #64106	C₂×C₃	semidirect
37. #64104	C₂×C₃	semidirect
38. #64095	C₂×C₃	semidirect
39. #64091	C₂×C₃	semidirect
40. C₄×C₄⋊(C₃⋊D₃)	C₂×C₃	semidirect
51. C₂×C₃³×C₄	D₄	semidirect
76. C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	semidirect
80. C₂×C₄×C₃⋊D₃	C₂²×C₃	semidirect
81. C₂×#634	C₂²×C₃	semidirect
93. C₃²×C₄⋊C₄	C₂×D₃	semidirect
94. C₃²×C₄⋊C₄	C₂²×C₃	semidirect
99. C₃²×C₄²	C₂×D₃	semidirect
100. C₃²×C₄²	C₂²×C₃	semidirect
102. #3752	C₂²×C₃	semidirect
103. C₄⋊(C₃⋊Dic₃)	C₂²×C₃	semidirect
115. C₂×C₃×C₃⋊D₃	#41	semidirect
131. C₃×#117	C₃×D₃	semidirect
132. C₃×#117	C₃⋊D₃	semidirect
153. C₂×C₃²×C₄	D₁₂	semidirect
154. C₂×C₃²×C₄	C₃×D₄	semidirect
214. C₃×C₄⋊C₄	C₂×C₃×D₃	semidirect
215. C₃×C₄⋊C₄	C₂×C₃⋊D₃	semidirect
222. C₃×C₄²	C₂×C₃×D₃	semidirect
223. C₃×C₄²	C₂×C₃⋊D₃	semidirect
241. C₂×C₃⋊D₃	C₃×#41	semidirect
268. #117	C₃×C₃⋊D₃	semidirect
269. C₃³	#525	semidirect
295. C₂×C₃×C₄	C₃×D₁₂	semidirect
296. C₂×C₃×C₄	C₄⋊(C₃⋊D₃)	semidirect
339. C₄⋊C₄	C₂×C₃×C₃⋊D₃	semidirect
343. C₄²	C₂×C₃×C₃⋊D₃	semidirect
379. C₃²	#5524	semidirect
380. C₃²	C₃×#525	semidirect
396. C₂×C₄	C₃×C₄⋊(C₃⋊D₃)	semidirect
428. C₃	C₃×#5524	semidirect
429. C₃	#10595995	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×#3828	2
C₂²×C₃×C₄×C₃⋊D₃	2
C₃³×#117	2
C₃×#64106	2
C₃×#64104	2
C₃×#64095	2
C₃×#64091	2
C₃×C₄×C₄⋊(C₃⋊D₃)	2
#10595995	3
C₃×#5524	3

Subgroups — C3×#10595995 #13179278

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10595995 #13179278