Subgroups — C₃×#10596054 #13179334

Order 1728.

1432 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#64155	C₂	1	1	yes	maximal, characteristic
3	C₃×#64153	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64107	C₂	1	2	yes	maximal
5	C₃×#64106	C₂	1	1	yes	maximal, characteristic
6	C₃×#64099	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#64098	C₂	1	2	yes	maximal, complemented
8	C₃×#64085	C₂	1	2	yes	maximal
9	C₃×#64081	C₂	1	1	yes	maximal, characteristic
10	C₃×#64079	C₂	1	2	yes	maximal, complemented
11	C₃×C₄×#634	C₂	1	1	yes	maximal, characteristic, complemented
12	#10596054	C₃	1	1	yes	maximal, characteristic, direct product factor
13	C₃×#5583	—	3	4	no	maximal
14	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
16	C₂×C₃×#634	C₂²	1	1	yes	characteristic
17	C₃³×C₄⋊C₄	C₂²	1	2	yes	—
18	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₃³×C₄²	C₂²	1	1	yes	characteristic
20	C₃³×C₄²	C₂²	1	2	yes	—
21	C₃×#3752	C₂²	1	1	yes	characteristic
22	C₃×#3752	C₂²	1	1	yes	characteristic
23	C₃×#3752	C₂²	1	2	yes	—
24	C₃×#3752	C₂²	1	2	yes	—
25	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
26	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
27	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
28	C₃×#3750	C₂²	1	2	yes	—
29	C₃×#3750	C₂²	1	1	yes	characteristic
30	C₃×#3750	C₂²	1	2	yes	—
31	C₃×#3750	C₂²	1	2	yes	—
32	C₃×#3750	C₂²	1	1	yes	characteristic
33	C₃×#3750	C₂²	1	2	yes	—
34	C₃×#3750	C₂²	1	2	yes	—
35	C₃×C₄×C₃⋊Dic₃	C₂²	1	2	yes	—
36	C₃×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
37	C₃²×C₄×Q₈	—	2	4	no	—
38	C₃²×C₄×Q₈	D₃	1	4	yes	complemented
39	C₃²×C₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
40	#64155	C₂×C₃	1	1	yes	characteristic
41	#64153	C₂×C₃	1	1	yes	characteristic, complemented
42	#64107	C₂×C₃	1	2	yes	—
43	#64106	C₂×C₃	1	1	yes	characteristic
44	#64099	C₂×C₃	1	1	yes	characteristic, complemented
45	#64098	C₂×C₃	1	2	yes	complemented
46	#64085	C₂×C₃	1	2	yes	—
47	#64081	C₂×C₃	1	1	yes	characteristic
48	#64079	C₂×C₃	1	2	yes	complemented
49	C₄×#634	C₂×C₃	1	1	yes	characteristic, complemented
50	C₃×#946	—	3	4	no	—
51	C₃×#944	—	3	4	no	—
52	C₃×#898	—	3	8	no	—
53	C₃×#897	—	3	4	no	—
54	C₃×#890	—	3	4	no	—
55	C₃×#889	—	3	8	no	—
56	C₃×#876	—	3	8	no	—
57	C₃×#872	—	3	4	no	—
58	C₃×#870	—	3	8	no	—
59	C₃×C₄×Dic₆	—	3	4	no	—
60	C₂²×C₃×C₃⋊D₃	C₂³	1	1	yes	characteristic
61	C₃³×Q₈	—	2	2	no	—
62	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
63	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
64	C₂×C₃³×C₄	C₂³	1	2	yes	—
65	C₂×C₃³×C₄	C₂³	1	2	yes	—
66	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
68	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
69	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
71	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
72	C₃×C₄×C₃⋊D₃	—	2	2	no	—
73	C₃×#634	—	2	2	no	—
74	C₃×#541	—	9	1	no	—
75	#5583	—	3	4	no	—
76	C₂×C₃²×Q₈	—	2	4	no	—
77	C₂×C₃²×Q₈	C₂×D₃	1	4	yes	—
78	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
80	C₂×#634	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₃×C₄×D₃	—	3	4	no	—
82	C₂×C₃×Dic₆	—	3	4	no	—
83	C₃²×C₄⋊C₄	—	2	8	no	—
84	C₃²×C₄⋊C₄	—	2	4	no	—
85	C₃²×C₄⋊C₄	C₂×D₃	1	8	yes	—
86	C₃²×C₄⋊C₄	C₂×D₃	1	4	yes	—
87	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
88	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
89	C₃²×C₄²	—	2	4	no	—
90	C₃²×C₄²	—	2	8	no	—
91	C₃²×C₄²	C₂×D₃	1	4	yes	—
92	C₃²×C₄²	C₂×D₃	1	8	yes	—
93	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
94	C₃²×C₄²	C₂²×C₃	1	2	yes	—
95	#3752	C₂²×C₃	1	1	yes	characteristic
96	#3752	C₂²×C₃	1	1	yes	characteristic
97	#3752	C₂²×C₃	1	2	yes	—
98	#3752	C₂²×C₃	1	2	yes	—
99	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic
100	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	—
101	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	—
102	#3750	C₂²×C₃	1	2	yes	—
103	#3750	C₂²×C₃	1	1	yes	characteristic
104	#3750	C₂²×C₃	1	2	yes	—
105	#3750	C₂²×C₃	1	2	yes	—
106	#3750	C₂²×C₃	1	1	yes	characteristic
107	#3750	C₂²×C₃	1	2	yes	—
108	#3750	C₂²×C₃	1	2	yes	—
109	C₄×C₃⋊Dic₃	C₂²×C₃	1	2	yes	—
110	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
111	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
112	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
113	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
114	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
115	C₃×C₄⋊Dic₃	—	3	8	no	—
116	C₃×C₄⋊Dic₃	—	3	8	no	—
117	C₃×C₄⋊Dic₃	—	3	4	no	—
118	C₃×Dic₃⋊C₄	—	3	4	no	—
119	C₃×Dic₃⋊C₄	—	3	8	no	—
120	C₃×Dic₃⋊C₄	—	3	8	no	—
121	C₃×Dic₃⋊C₄	—	3	8	no	—
122	C₃×Dic₃⋊C₄	—	3	8	no	—
123	C₃×Dic₃⋊C₄	—	3	8	no	—
124	C₃×Dic₃⋊C₄	—	3	4	no	—
125	C₃×C₄×Dic₃	—	3	8	no	—
126	C₃×C₄×Dic₃	—	3	4	no	—
127	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
128	C₂×C₃×C₃⋊D₃	—	2	1	no	—
129	C₂×C₃×C₃⋊D₃	—	2	1	no	—
130	C₂×C₃×C₃⋊D₃	—	2	1	no	—
131	C₃³×C₄	—	2	2	no	—
132	C₃³×C₄	—	2	1	no	—
133	C₃³×C₄	—	2	1	no	—
134	C₃³×C₄	—	2	2	no	—
135	C₃³×C₄	#41	1	2	yes	—
136	C₃×C₃⋊Dic₃	—	2	2	no	—
137	C₃×C₃⋊Dic₃	—	2	1	no	—
138	C₃×C₃⋊Dic₃	—	2	2	no	—
139	C₃×C₃⋊Dic₃	—	2	1	no	—
140	C₃×C₃⋊Dic₃	—	2	1	no	—
141	C₃×C₄⋊Q₈	—	9	1	no	—
142	C₃×#126	—	9	2	no	—
143	C₃×#126	—	9	2	no	—
144	C₃×#125	—	9	2	no	—
145	C₃×#125	—	9	1	no	—
146	C₃×#125	—	9	2	no	—
147	C₃×C₂²⋊Q₈	—	9	1	no	—
148	C₃×C₂²⋊Q₈	—	9	1	no	—
149	C₃×C₄×Q₈	—	2	4	no	—
150	C₃×C₄×Q₈	—	9	1	no	—
151	C₃×C₄×Q₈	C₃×D₃	1	4	yes	complemented
152	C₃×C₄×Q₈	C₃⋊D₃	1	1	yes	characteristic, complemented
153	C₃×#117	—	9	1	no	—
154	#946	—	3	4	no	—
155	#944	—	3	4	no	—
156	#898	—	3	8	no	—
157	#897	—	3	4	no	—
158	#890	—	3	4	no	—
159	#889	—	3	8	no	—
160	#876	—	3	8	no	—
161	#872	—	3	4	no	—
162	#870	—	3	8	no	—
163	C₄×Dic₆	—	3	4	no	—
164	C₂²×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
165	C₂²×C₃×D₃	—	3	4	no	—
166	C₃²×Q₈	—	2	16	no	—
167	C₃²×Q₈	—	2	8	no	—
168	C₃²×Q₈	—	2	2	no	—
169	C₂×C₃²×C₄	—	2	4	no	—
170	C₂×C₃²×C₄	—	2	8	no	—
171	C₂×C₃²×C₄	—	2	4	no	—
172	C₂×C₃²×C₄	—	2	4	no	—
173	C₂×C₃²×C₄	—	2	8	no	—
174	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
175	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
176	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
177	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
178	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
179	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
180	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
181	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
182	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
183	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
184	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
185	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
186	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
187	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
188	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
189	C₄×C₃⋊D₃	—	2	2	no	—
190	#634	—	2	2	no	—
191	C₂×C₃×Dic₃	—	3	4	no	—
192	C₂×C₃×Dic₃	—	3	8	no	—
193	C₂×C₃×Dic₃	—	3	4	no	—
194	C₂×C₃×Dic₃	—	3	8	no	—
195	C₂×C₃×Dic₃	—	3	4	no	—
196	C₃×C₄×D₃	—	6	8	no	—
197	C₃×Dic₆	—	6	8	no	—
198	#541	—	9	1	no	Sylow
199	C₂×C₃³	C₂×#41	1	1	yes	characteristic
200	C₂×C₃³	2₋¹⁺⁴	1	1	yes	characteristic
201	C₂×C₃³	2₋¹⁺⁴	1	1	yes	characteristic
202	C₃×C₃⋊D₃	—	4	1	no	—
203	C₂×C₃×Q₈	—	2	4	no	—
204	C₂×C₃×Q₈	—	9	1	no	—
205	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
206	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	1	yes	characteristic
207	C₂²×C₃×C₄	—	9	1	no	—
208	C₂×C₄×D₃	—	3	4	no	—
209	C₂×Dic₆	—	3	4	no	—
210	C₃×C₄⋊C₄	—	2	4	no	—
211	C₃×C₄⋊C₄	—	2	8	no	—
212	C₃×C₄⋊C₄	—	9	1	no	—
213	C₃×C₄⋊C₄	—	9	1	no	—
214	C₃×C₄⋊C₄	—	9	2	no	—
215	C₃×C₄⋊C₄	—	9	2	no	—
216	C₃×C₄⋊C₄	—	9	2	no	—
217	C₃×C₄⋊C₄	—	9	2	no	—
218	C₃×C₄⋊C₄	—	9	2	no	—
219	C₃×C₄⋊C₄	—	9	1	no	—
220	C₃×C₄⋊C₄	—	9	2	no	—
221	C₃×C₄⋊C₄	—	9	2	no	—
222	C₃×C₄⋊C₄	C₂×C₃×D₃	1	8	yes	—
223	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
224	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
225	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	2	yes	—
226	C₃×C₂²⋊C₄	—	9	1	no	—
227	C₃×C₂²⋊C₄	—	9	1	no	—
228	C₃×C₂²⋊C₄	—	9	2	no	—
229	C₃×C₂²⋊C₄	—	9	2	no	—
230	C₃×C₄²	—	2	4	no	—
231	C₃×C₄²	—	2	8	no	—
232	C₃×C₄²	—	9	1	no	—
233	C₃×C₄²	—	9	2	no	—
234	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
235	C₃×C₄²	C₂×C₃×D₃	1	8	yes	—
236	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
237	C₃×C₄²	C₂×C₃⋊D₃	1	2	yes	—
238	(C₂×D₃)⋊C₄	—	3	4	no	—
239	(C₂×D₃)⋊C₄	—	3	4	no	—
240	(C₂×D₃)⋊C₄	—	3	8	no	—
241	(C₂×D₃)⋊C₄	—	3	8	no	—
242	C₄⋊Dic₃	—	3	4	no	—
243	C₄⋊Dic₃	—	3	8	no	—
244	C₄⋊Dic₃	—	3	8	no	—
245	Dic₃⋊C₄	—	3	8	no	—
246	Dic₃⋊C₄	—	3	4	no	—
247	Dic₃⋊C₄	—	3	8	no	—
248	Dic₃⋊C₄	—	3	8	no	—
249	Dic₃⋊C₄	—	3	4	no	—
250	Dic₃⋊C₄	—	3	8	no	—
251	Dic₃⋊C₄	—	3	8	no	—
252	C₄×Dic₃	—	3	8	no	—
253	C₄×Dic₃	—	3	4	no	—
254	C₂²×C₃²	—	2	4	no	—
255	C₂²×C₃²	C₂³×D₃	1	4	yes	—
256	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
257	C₂×C₃⋊D₃	—	2	1	no	—
258	C₂×C₃⋊D₃	—	2	1	no	—
259	C₂×C₃⋊D₃	—	2	1	no	—
260	C₂×C₃×D₃	—	6	4	no	—
261	C₂×C₃×D₃	—	6	4	no	—
262	C₂×C₃×D₃	—	6	4	no	—
263	C₃²×C₄	—	2	8	no	—
264	C₃²×C₄	—	2	16	no	—
265	C₃²×C₄	—	2	8	no	—
266	C₃²×C₄	—	2	4	no	—
267	C₃²×C₄	—	2	2	no	—
268	C₃²×C₄	—	2	1	no	—
269	C₃²×C₄	—	2	1	no	—
270	C₃²×C₄	—	2	2	no	—
271	C₃²×C₄	—	2	8	no	—
272	C₃²×C₄	—	2	4	no	—
273	C₃²×C₄	—	2	8	no	—
274	C₃²×C₄	—	4	4	no	—
275	C₃²×C₄	—	4	8	no	—
276	C₃²×C₄	#235	1	8	yes	—
277	C₃²×C₄	C₃×#41	1	2	yes	—
278	C₃⋊Dic₃	—	2	2	no	—
279	C₃⋊Dic₃	—	2	1	no	—
280	C₃⋊Dic₃	—	2	2	no	—
281	C₃⋊Dic₃	—	2	1	no	—
282	C₃⋊Dic₃	—	2	1	no	—
283	C₃×Dic₃	—	6	8	no	—
284	C₃×Dic₃	—	6	4	no	—
285	C₃×Dic₃	—	6	8	no	—
286	C₃×Dic₃	—	6	4	no	—
287	C₃×Dic₃	—	6	4	no	—
288	C₄⋊Q₈	—	9	1	no	—
289	#126	—	9	2	no	—
290	#126	—	9	2	no	—
291	#125	—	9	2	no	—
292	#125	—	9	1	no	—
293	#125	—	9	2	no	—
294	C₂²⋊Q₈	—	9	1	no	—
295	C₂²⋊Q₈	—	9	1	no	—
296	C₄×Q₈	—	9	1	no	—
297	C₄×Q₈	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
298	#117	—	9	1	no	—
299	C₃³	#541	1	1	yes	characteristic, complemented, Sylow
300	C₂³×C₃	—	9	1	no	—
301	C₂²×D₃	—	3	4	no	—
302	C₃×Q₈	—	2	16	no	—
303	C₃×Q₈	—	2	8	no	—
304	C₃×Q₈	—	2	2	no	—
305	C₃×Q₈	—	18	2	no	—
306	C₂×C₃×C₄	—	2	4	no	—
307	C₂×C₃×C₄	—	2	8	no	—
308	C₂×C₃×C₄	—	2	4	no	—
309	C₂×C₃×C₄	—	2	4	no	—
310	C₂×C₃×C₄	—	2	8	no	—
311	C₂×C₃×C₄	—	9	1	no	—
312	C₂×C₃×C₄	—	9	2	no	—
313	C₂×C₃×C₄	—	9	1	no	—
314	C₂×C₃×C₄	—	9	2	no	—
315	C₂×C₃×C₄	—	9	1	no	—
316	C₂×C₃×C₄	—	18	2	no	—
317	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
318	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
319	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
320	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
321	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
322	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
323	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
324	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
325	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
326	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
327	C₂×Dic₃	—	3	4	no	—
328	C₂×Dic₃	—	3	8	no	—
329	C₂×Dic₃	—	3	4	no	—
330	C₂×Dic₃	—	3	8	no	—
331	C₂×Dic₃	—	3	4	no	—
332	C₄×D₃	—	6	8	no	—
333	Dic₆	—	6	8	no	—
334	C₂×C₃²	—	2	4	no	—
335	C₂×C₃²	—	2	4	no	—
336	C₂×C₃²	—	2	4	no	—
337	C₂×C₃²	C₂×#235	1	4	yes	—
338	C₂×C₃²	#1007	1	4	yes	—
339	C₂×C₃²	#1010	1	4	yes	—
340	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
341	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
342	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
343	C₃⋊D₃	—	4	1	no	—
344	C₃×D₃	—	12	4	no	—
345	C₂×Q₈	—	9	1	no	—
346	C₂×Q₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
347	C₂²×C₄	—	9	1	no	—
348	C₄⋊C₄	—	9	1	no	—
349	C₄⋊C₄	—	9	1	no	—
350	C₄⋊C₄	—	9	1	no	—
351	C₄⋊C₄	—	9	2	no	—
352	C₄⋊C₄	—	9	2	no	—
353	C₄⋊C₄	—	9	2	no	—
354	C₄⋊C₄	—	9	2	no	—
355	C₄⋊C₄	—	9	2	no	—
356	C₄⋊C₄	—	9	2	no	—
357	C₄⋊C₄	—	9	2	no	—
358	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
359	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
360	C₂²⋊C₄	—	9	1	no	—
361	C₂²⋊C₄	—	9	1	no	—
362	C₂²⋊C₄	—	9	2	no	—
363	C₂²⋊C₄	—	9	2	no	—
364	C₄²	—	9	1	no	—
365	C₄²	—	9	2	no	—
366	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
367	C₄²	C₂×C₃×C₃⋊D₃	1	2	yes	—
368	C₂²×C₃	—	2	4	no	—
369	C₂²×C₃	—	18	1	no	—
370	C₂²×C₃	—	18	1	no	—
371	C₂²×C₃	—	18	1	no	—
372	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
373	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
374	C₂×D₃	—	6	4	no	—
375	C₂×D₃	—	6	4	no	—
376	C₂×D₃	—	6	4	no	—
377	C₃×C₄	—	2	16	no	—
378	C₃×C₄	—	2	8	no	—
379	C₃×C₄	—	2	8	no	—
380	C₃×C₄	—	2	4	no	—
381	C₃×C₄	—	2	4	no	—
382	C₃×C₄	—	2	8	no	—
383	C₃×C₄	—	2	2	no	—
384	C₃×C₄	—	2	1	no	—
385	C₃×C₄	—	2	1	no	—
386	C₃×C₄	—	2	2	no	—
387	C₃×C₄	—	2	8	no	—
388	C₃×C₄	—	4	4	no	—
389	C₃×C₄	—	4	8	no	—
390	C₃×C₄	—	18	1	no	—
391	C₃×C₄	—	18	2	no	—
392	C₃×C₄	—	18	1	no	—
393	C₃×C₄	—	18	2	no	—
394	C₃×C₄	—	18	1	no	—
395	C₃×C₄	C₃×#235	1	8	yes	—
396	C₃×C₄	#3828	1	2	yes	—
397	Dic₃	—	6	8	no	—
398	Dic₃	—	6	4	no	—
399	Dic₃	—	6	8	no	—
400	Dic₃	—	6	4	no	—
401	Dic₃	—	6	4	no	—
402	C₃²	—	2	4	no	—
403	C₃²	#5583	1	4	yes	complemented
404	C₃²	C₃×#541	1	1	yes	characteristic, complemented
405	C₂³	—	9	1	no	—
406	Q₈	—	2	2	no	—
407	Q₈	—	18	2	no	—
408	C₂×C₄	—	9	1	no	—
409	C₂×C₄	—	9	2	no	—
410	C₂×C₄	—	9	1	no	—
411	C₂×C₄	—	9	2	no	—
412	C₂×C₄	—	9	1	no	—
413	C₂×C₄	—	18	2	no	—
414	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
415	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
416	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
417	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
418	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
419	C₂×C₃	—	2	4	no	—
420	C₂×C₃	—	2	4	no	—
421	C₂×C₃	—	2	4	no	—
422	C₂×C₃	—	36	1	no	—
423	C₂×C₃	C₂×C₃×#235	1	4	yes	—
424	C₂×C₃	C₃×#1007	1	4	yes	—
425	C₂×C₃	C₃×#1010	1	4	yes	—
426	C₂×C₃	C₂×#3828	1	1	yes	characteristic
427	C₂×C₃	#64364	1	1	yes	characteristic
428	C₂×C₃	#64367	1	1	yes	characteristic
429	D₃	—	12	4	no	—
430	C₂²	—	18	1	no	—
431	C₂²	—	18	1	no	—
432	C₂²	—	18	1	no	—
433	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
434	C₄	—	2	2	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	2	no	—
438	C₄	—	18	1	no	—
439	C₄	—	18	2	no	—
440	C₄	—	18	1	no	—
441	C₄	—	18	2	no	—
442	C₄	—	18	1	no	—
443	C₄	C₃×#3828	1	2	yes	—
444	C₃	—	2	4	no	—
445	C₃	C₃×#5583	1	4	yes	complemented
446	C₃	#10596054	1	1	yes	characteristic, direct product factor
447	C₂	—	36	1	no	—
448	C₂	C₂×C₃×#3828	1	1	yes	characteristic
449	C₂	C₃×#64364	1	1	yes	characteristic
450	C₂	C₃×#64367	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×C₃⋊D₃
commutator, cosocle	C₂²×C₃²	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×C₃⋊D₃
Fitting	C₃³×C₄×Q₈	C₂
socle	C₂²×C₃³	C₂⁴
prime radical	C₂²×C₃×C₃⋊D₃	C₂³
hypercenter	C₃×C₄×Q₈	C₃⋊D₃
hypocenter	C₃²	C₃×#541
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₃³×C₄×Q₈	C₂	semidirect
3. C₃×#64153	C₂	semidirect
6. C₃×#64099	C₂	semidirect
7. C₃×#64098	C₂	semidirect
10. C₃×#64079	C₂	semidirect
11. C₃×C₄×#634	C₂	semidirect
12. #10596054	C₃	direct (N × H)
38. C₃²×C₄×Q₈	D₃	semidirect
39. C₃²×C₄×Q₈	C₂×C₃	semidirect
41. #64153	C₂×C₃	semidirect
44. #64099	C₂×C₃	semidirect
45. #64098	C₂×C₃	semidirect
48. #64079	C₂×C₃	semidirect
49. C₄×#634	C₂×C₃	semidirect
151. C₃×C₄×Q₈	C₃×D₃	semidirect
152. C₃×C₄×Q₈	C₃⋊D₃	semidirect
297. C₄×Q₈	C₃×C₃⋊D₃	semidirect
299. C₃³	#541	semidirect
403. C₃²	#5583	semidirect
404. C₃²	C₃×#541	semidirect
445. C₃	C₃×#5583	semidirect
446. C₃	#10596054	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×C₄×Q₈	2
C₃×#64155	2
C₃×#64153	2
C₃×#64107	2
C₃×#64106	2
C₃×#64099	2
C₃×#64098	2
C₃×#64085	2
C₃×#64081	2
C₃×#64079	2
C₃×C₄×#634	2
#10596054	3
C₃×#5583	3

Subgroups — C3×#10596054 #13179334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596054 #13179334