Subgroups — C₃×#10596049 #13179329

Order 1728.

1612 conjugacy classes of subgroups.

The subgroup lattice has 470 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×#64106	C₂	1	1	yes	maximal, characteristic
5	C₃×#64105	C₂	1	2	yes	maximal
6	C₃×#64098	C₂	1	2	yes	maximal, complemented
7	C₃×#64097	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64081	C₂	1	2	yes	maximal
9	C₃×C₄²×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
10	C₃×C₄×#634	C₂	1	2	yes	maximal, complemented
11	C₃×C₄×#634	C₂	1	1	yes	maximal, characteristic, complemented
12	#10596049	C₃	1	1	yes	maximal, characteristic, direct product factor
13	C₃×#5578	—	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×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
18	C₂×C₃×#634	C₂²	1	2	yes	—
19	C₂×C₃×#634	C₂²	1	1	yes	characteristic
20	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₃³×C₄⋊C₄	C₂²	1	2	yes	—
22	C₃³×C₄²	C₂²	1	1	yes	characteristic
23	C₃³×C₄²	C₂²	1	2	yes	—
24	C₃×#3752	C₂²	1	2	yes	—
25	C₃×#3752	C₂²	1	2	yes	—
26	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
27	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
28	C₃×#3750	C₂²	1	2	yes	—
29	C₃×#3750	C₂²	1	2	yes	—
30	C₃×#3750	C₂²	1	2	yes	—
31	C₃×#3750	C₂²	1	2	yes	—
32	C₃×#3750	C₂²	1	2	yes	—
33	C₃×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
34	C₃×C₄×C₃⋊Dic₃	C₂²	1	2	yes	—
35	C₃×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
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	#64106	C₂×C₃	1	1	yes	characteristic
43	#64105	C₂×C₃	1	2	yes	—
44	#64098	C₂×C₃	1	2	yes	complemented
45	#64097	C₂×C₃	1	1	yes	characteristic, complemented
46	#64081	C₂×C₃	1	2	yes	—
47	C₄²×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic
48	C₄×#634	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×#897	—	3	4	no	—
53	C₃×#896	—	3	8	no	—
54	C₃×#889	—	3	8	no	—
55	C₃×#888	—	3	4	no	—
56	C₃×#872	—	3	8	no	—
57	C₃×C₄²×D₃	—	3	4	no	—
58	C₃×C₄×Dic₆	—	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	2	yes	—
64	C₂×C₃³×C₄	C₂³	1	2	yes	—
65	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
70	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
72	C₃×C₄×C₃⋊D₃	—	2	2	no	—
73	C₃×C₄×C₃⋊D₃	—	2	2	no	—
74	C₃×C₄×C₃⋊D₃	Q₈	1	4	yes	complemented
75	C₃×#634	—	2	2	no	—
76	C₃×#634	—	2	4	no	—
77	C₃×#533	—	9	1	no	—
78	#5578	—	3	4	no	—
79	C₂×C₃²×Q₈	—	2	4	no	—
80	C₂×C₃²×Q₈	C₂×D₃	1	4	yes	—
81	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
85	C₂×#634	C₂²×C₃	1	2	yes	—
86	C₂×#634	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₃×C₄×D₃	—	3	4	no	—
88	C₂×C₃×C₄×D₃	—	3	4	no	—
89	C₂×C₃×C₄×D₃	—	3	4	no	—
90	C₂×C₃×Dic₆	—	3	8	no	—
91	C₂×C₃×Dic₆	—	3	4	no	—
92	C₃²×C₄⋊C₄	—	2	4	no	—
93	C₃²×C₄⋊C₄	—	2	8	no	—
94	C₃²×C₄⋊C₄	C₂×D₃	1	4	yes	—
95	C₃²×C₄⋊C₄	C₂×D₃	1	8	yes	—
96	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
97	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
98	C₃²×C₄²	—	2	4	no	—
99	C₃²×C₄²	—	2	8	no	—
100	C₃²×C₄²	C₂×D₃	1	4	yes	—
101	C₃²×C₄²	C₂×D₃	1	8	yes	—
102	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
103	C₃²×C₄²	C₂²×C₃	1	2	yes	—
104	#3752	C₂²×C₃	1	2	yes	—
105	#3752	C₂²×C₃	1	2	yes	—
106	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic
107	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	—
108	#3750	C₂²×C₃	1	2	yes	—
109	#3750	C₂²×C₃	1	2	yes	—
110	#3750	C₂²×C₃	1	2	yes	—
111	#3750	C₂²×C₃	1	2	yes	—
112	#3750	C₂²×C₃	1	2	yes	—
113	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
114	C₄×C₃⋊Dic₃	C₂²×C₃	1	2	yes	—
115	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
116	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
117	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
118	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
119	C₃×C₄⋊Dic₃	—	3	4	no	—
120	C₃×C₄⋊Dic₃	—	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	8	no	—
125	C₃×Dic₃⋊C₄	—	3	8	no	—
126	C₃×C₄×Dic₃	—	3	4	no	—
127	C₃×C₄×Dic₃	—	3	4	no	—
128	C₃×C₄×Dic₃	—	3	4	no	—
129	C₃×C₄×Dic₃	—	3	8	no	—
130	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
131	C₂×C₃×C₃⋊D₃	—	2	1	no	—
132	C₂×C₃×C₃⋊D₃	—	2	1	no	—
133	C₂×C₃×C₃⋊D₃	C₂×Q₈	1	2	yes	—
134	C₃³×C₄	—	2	2	no	—
135	C₃³×C₄	—	2	2	no	—
136	C₃³×C₄	—	2	1	no	—
137	C₃³×C₄	C₂×Q₈	1	2	yes	—
138	C₃³×C₄	#41	1	2	yes	—
139	C₃×C₃⋊Dic₃	—	2	2	no	—
140	C₃×C₃⋊Dic₃	—	2	2	no	—
141	C₃×C₃⋊Dic₃	—	2	1	no	—
142	C₃×C₃⋊Dic₃	C₂×Q₈	1	2	yes	—
143	C₃×C₃⋊Dic₃	#41	1	2	yes	—
144	C₃×C₄⋊Q₈	—	9	1	no	—
145	C₃×C₄⋊Q₈	—	9	1	no	—
146	C₃×#125	—	9	2	no	—
147	C₃×C₂²⋊Q₈	—	9	1	no	—
148	C₃×C₂²⋊Q₈	—	9	2	no	—
149	C₃×C₂²⋊Q₈	—	9	1	no	—
150	C₃×C₄×Q₈	—	2	4	no	—
151	C₃×C₄×Q₈	—	9	2	no	—
152	C₃×C₄×Q₈	—	9	1	no	—
153	C₃×C₄×Q₈	C₃×D₃	1	4	yes	complemented
154	C₃×C₄×Q₈	C₃⋊D₃	1	1	yes	characteristic, complemented
155	C₃×#117	—	9	2	no	—
156	C₂×C₃×C₄²	—	9	1	no	—
157	#946	—	3	4	no	—
158	#944	—	3	4	no	—
159	#897	—	3	4	no	—
160	#896	—	3	8	no	—
161	#889	—	3	8	no	—
162	#888	—	3	4	no	—
163	#872	—	3	8	no	—
164	C₄²×D₃	—	3	4	no	—
165	C₄×Dic₆	—	3	8	no	—
166	C₄×Dic₆	—	3	4	no	—
167	C₂²×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
168	C₂²×C₃×D₃	—	3	4	no	—
169	C₃²×Q₈	—	2	16	no	—
170	C₃²×Q₈	—	2	8	no	—
171	C₃²×Q₈	—	2	2	no	—
172	C₂×C₃²×C₄	—	2	4	no	—
173	C₂×C₃²×C₄	—	2	8	no	—
174	C₂×C₃²×C₄	—	2	4	no	—
175	C₂×C₃²×C₄	—	2	4	no	—
176	C₂×C₃²×C₄	—	2	8	no	—
177	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
178	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
179	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
180	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
181	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
182	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
183	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
184	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
185	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
186	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
187	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
188	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
189	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
190	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
191	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
192	C₄×C₃⋊D₃	—	2	2	no	—
193	C₄×C₃⋊D₃	—	2	2	no	—
194	C₄×C₃⋊D₃	C₃×Q₈	1	4	yes	complemented
195	#634	—	2	2	no	—
196	#634	—	2	4	no	—
197	C₂×C₃×Dic₃	—	3	4	no	—
198	C₂×C₃×Dic₃	—	3	4	no	—
199	C₂×C₃×Dic₃	—	3	4	no	—
200	C₂×C₃×Dic₃	—	3	8	no	—
201	C₂×C₃×Dic₃	—	3	8	no	—
202	C₃×C₄×D₃	—	3	16	no	—
203	C₃×C₄×D₃	—	6	8	no	—
204	C₃×C₄×D₃	—	6	8	no	—
205	C₃×Dic₆	—	6	16	no	—
206	C₃×Dic₆	—	6	8	no	—
207	#533	—	9	1	no	Sylow
208	C₂×C₃³	C₂²×Q₈	1	1	yes	characteristic
209	C₂×C₃³	C₂×#41	1	1	yes	characteristic
210	C₂×C₃³	C₂×#41	1	1	yes	characteristic
211	C₃×C₃⋊D₃	—	2	2	no	—
212	C₂×C₃×Q₈	—	2	4	no	—
213	C₂×C₃×Q₈	—	9	2	no	—
214	C₂×C₃×Q₈	—	9	1	no	—
215	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
216	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	1	yes	characteristic
217	C₂²×C₃×C₄	—	9	1	no	—
218	C₂²×C₃×C₄	—	9	1	no	—
219	C₂²×C₃×C₄	—	9	1	no	—
220	C₂×C₄×D₃	—	3	4	no	—
221	C₂×C₄×D₃	—	3	4	no	—
222	C₂×C₄×D₃	—	3	4	no	—
223	C₂×Dic₆	—	3	8	no	—
224	C₂×Dic₆	—	3	4	no	—
225	C₃×C₄⋊C₄	—	2	8	no	—
226	C₃×C₄⋊C₄	—	2	4	no	—
227	C₃×C₄⋊C₄	—	9	2	no	—
228	C₃×C₄⋊C₄	—	9	2	no	—
229	C₃×C₄⋊C₄	—	9	2	no	—
230	C₃×C₄⋊C₄	—	9	2	no	—
231	C₃×C₄⋊C₄	—	9	2	no	—
232	C₃×C₄⋊C₄	—	9	2	no	—
233	C₃×C₄⋊C₄	—	9	1	no	—
234	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
235	C₃×C₄⋊C₄	C₂×C₃×D₃	1	8	yes	—
236	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	2	yes	—
237	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
238	C₃×C₂²⋊C₄	—	9	2	no	—
239	C₃×C₂²⋊C₄	—	9	2	no	—
240	C₃×C₄²	—	2	4	no	—
241	C₃×C₄²	—	2	8	no	—
242	C₃×C₄²	—	9	1	no	—
243	C₃×C₄²	—	9	1	no	—
244	C₃×C₄²	—	9	1	no	—
245	C₃×C₄²	—	9	2	no	—
246	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
247	C₃×C₄²	C₂×C₃×D₃	1	8	yes	—
248	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
249	C₃×C₄²	C₂×C₃⋊D₃	1	2	yes	—
250	(C₂×D₃)⋊C₄	—	3	8	no	—
251	(C₂×D₃)⋊C₄	—	3	8	no	—
252	C₄⋊Dic₃	—	3	4	no	—
253	C₄⋊Dic₃	—	3	8	no	—
254	Dic₃⋊C₄	—	3	8	no	—
255	Dic₃⋊C₄	—	3	8	no	—
256	Dic₃⋊C₄	—	3	8	no	—
257	Dic₃⋊C₄	—	3	8	no	—
258	Dic₃⋊C₄	—	3	8	no	—
259	C₄×Dic₃	—	3	4	no	—
260	C₄×Dic₃	—	3	8	no	—
261	C₄×Dic₃	—	3	4	no	—
262	C₄×Dic₃	—	3	4	no	—
263	C₂²×C₃²	—	2	4	no	—
264	C₂²×C₃²	C₂³×D₃	1	4	yes	—
265	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
266	C₂×C₃⋊D₃	—	2	1	no	—
267	C₂×C₃⋊D₃	—	2	1	no	—
268	C₂×C₃⋊D₃	C₂×C₃×Q₈	1	2	yes	—
269	C₂×C₃×D₃	—	3	8	no	—
270	C₂×C₃×D₃	—	6	4	no	—
271	C₂×C₃×D₃	—	6	4	no	—
272	C₃²×C₄	—	2	16	no	—
273	C₃²×C₄	—	2	8	no	—
274	C₃²×C₄	—	2	2	no	—
275	C₃²×C₄	—	2	1	no	—
276	C₃²×C₄	—	2	2	no	—
277	C₃²×C₄	—	2	8	no	—
278	C₃²×C₄	—	2	8	no	—
279	C₃²×C₄	—	2	8	no	—
280	C₃²×C₄	—	2	4	no	—
281	C₃²×C₄	—	4	8	no	—
282	C₃²×C₄	—	4	4	no	—
283	C₃²×C₄	#235	1	8	yes	—
284	C₃²×C₄	D₃×Q₈	1	8	yes	—
285	C₃²×C₄	C₂×C₃×Q₈	1	2	yes	—
286	C₃²×C₄	C₃×#41	1	2	yes	—
287	C₃⋊Dic₃	—	2	2	no	—
288	C₃⋊Dic₃	—	2	2	no	—
289	C₃⋊Dic₃	—	2	1	no	—
290	C₃⋊Dic₃	C₂×C₃×Q₈	1	2	yes	—
291	C₃⋊Dic₃	C₃×#41	1	2	yes	—
292	C₃×Dic₃	—	3	8	no	—
293	C₃×Dic₃	—	3	8	no	—
294	C₃×Dic₃	—	6	8	no	—
295	C₃×Dic₃	—	6	4	no	—
296	C₃×Dic₃	—	6	8	no	—
297	C₄⋊Q₈	—	9	1	no	—
298	C₄⋊Q₈	—	9	1	no	—
299	#125	—	9	2	no	—
300	C₂²⋊Q₈	—	9	1	no	—
301	C₂²⋊Q₈	—	9	2	no	—
302	C₂²⋊Q₈	—	9	1	no	—
303	C₄×Q₈	—	9	2	no	—
304	C₄×Q₈	—	9	1	no	—
305	C₄×Q₈	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
306	#117	—	9	2	no	—
307	C₂×C₄²	—	9	1	no	—
308	C₃³	#533	1	1	yes	characteristic, complemented, Sylow
309	C₂³×C₃	—	9	1	no	—
310	C₂²×D₃	—	3	4	no	—
311	C₃×Q₈	—	2	16	no	—
312	C₃×Q₈	—	2	8	no	—
313	C₃×Q₈	—	2	2	no	—
314	C₃×Q₈	—	18	4	no	—
315	C₃×Q₈	—	18	2	no	—
316	C₂×C₃×C₄	—	2	4	no	—
317	C₂×C₃×C₄	—	2	8	no	—
318	C₂×C₃×C₄	—	2	4	no	—
319	C₂×C₃×C₄	—	2	4	no	—
320	C₂×C₃×C₄	—	2	8	no	—
321	C₂×C₃×C₄	—	9	1	no	—
322	C₂×C₃×C₄	—	9	1	no	—
323	C₂×C₃×C₄	—	9	4	no	—
324	C₂×C₃×C₄	—	9	1	no	—
325	C₂×C₃×C₄	—	9	2	no	—
326	C₂×C₃×C₄	—	9	2	no	—
327	C₂×C₃×C₄	—	18	2	no	—
328	C₂×C₃×C₄	—	18	2	no	—
329	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
330	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
331	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
332	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
333	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
334	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
335	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
336	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
337	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
338	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
339	C₂×Dic₃	—	3	4	no	—
340	C₂×Dic₃	—	3	4	no	—
341	C₂×Dic₃	—	3	4	no	—
342	C₂×Dic₃	—	3	8	no	—
343	C₂×Dic₃	—	3	8	no	—
344	C₄×D₃	—	3	16	no	—
345	C₄×D₃	—	6	8	no	—
346	C₄×D₃	—	6	8	no	—
347	Dic₆	—	6	16	no	—
348	Dic₆	—	6	8	no	—
349	C₂×C₃²	—	2	4	no	—
350	C₂×C₃²	—	2	4	no	—
351	C₂×C₃²	—	2	4	no	—
352	C₂×C₃²	C₂×#235	1	4	yes	—
353	C₂×C₃²	C₂×D₃×Q₈	1	4	yes	—
354	C₂×C₃²	D₃×#41	1	4	yes	—
355	C₂×C₃²	C₂²×C₃×Q₈	1	1	yes	characteristic
356	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
357	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
358	C₃⋊D₃	—	2	2	no	—
359	C₃×D₃	—	6	8	no	—
360	C₂×Q₈	—	9	2	no	—
361	C₂×Q₈	—	9	1	no	—
362	C₂×Q₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
363	C₂²×C₄	—	9	1	no	—
364	C₂²×C₄	—	9	1	no	—
365	C₂²×C₄	—	9	1	no	—
366	C₄⋊C₄	—	9	2	no	—
367	C₄⋊C₄	—	9	2	no	—
368	C₄⋊C₄	—	9	2	no	—
369	C₄⋊C₄	—	9	2	no	—
370	C₄⋊C₄	—	9	2	no	—
371	C₄⋊C₄	—	9	2	no	—
372	C₄⋊C₄	—	9	1	no	—
373	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
374	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
375	C₂²⋊C₄	—	9	2	no	—
376	C₂²⋊C₄	—	9	2	no	—
377	C₄²	—	9	1	no	—
378	C₄²	—	9	1	no	—
379	C₄²	—	9	1	no	—
380	C₄²	—	9	2	no	—
381	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
382	C₄²	C₂×C₃×C₃⋊D₃	1	2	yes	—
383	C₂²×C₃	—	2	4	no	—
384	C₂²×C₃	—	9	2	no	—
385	C₂²×C₃	—	18	1	no	—
386	C₂²×C₃	—	18	1	no	—
387	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
388	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
389	C₂×D₃	—	3	8	no	—
390	C₂×D₃	—	6	4	no	—
391	C₂×D₃	—	6	4	no	—
392	C₃×C₄	—	2	16	no	—
393	C₃×C₄	—	2	8	no	—
394	C₃×C₄	—	2	8	no	—
395	C₃×C₄	—	2	4	no	—
396	C₃×C₄	—	2	2	no	—
397	C₃×C₄	—	2	1	no	—
398	C₃×C₄	—	2	2	no	—
399	C₃×C₄	—	2	8	no	—
400	C₃×C₄	—	2	8	no	—
401	C₃×C₄	—	4	4	no	—
402	C₃×C₄	—	4	8	no	—
403	C₃×C₄	—	9	2	no	—
404	C₃×C₄	—	9	2	no	—
405	C₃×C₄	—	18	1	no	—
406	C₃×C₄	—	18	2	no	—
407	C₃×C₄	—	18	2	no	—
408	C₃×C₄	C₃×#235	1	8	yes	—
409	C₃×C₄	C₃×D₃×Q₈	1	8	yes	—
410	C₃×C₄	#3828	1	2	yes	—
411	C₃×C₄	Q₈×C₃⋊D₃	1	2	yes	—
412	Dic₃	—	3	8	no	—
413	Dic₃	—	3	8	no	—
414	Dic₃	—	6	8	no	—
415	Dic₃	—	6	4	no	—
416	Dic₃	—	6	8	no	—
417	C₃²	—	2	4	no	—
418	C₃²	#5578	1	4	yes	complemented
419	C₃²	C₃×#533	1	1	yes	characteristic, complemented
420	C₂³	—	9	1	no	—
421	Q₈	—	2	2	no	—
422	Q₈	—	18	4	no	—
423	Q₈	—	18	2	no	—
424	C₂×C₄	—	9	1	no	—
425	C₂×C₄	—	9	1	no	—
426	C₂×C₄	—	9	4	no	—
427	C₂×C₄	—	9	1	no	—
428	C₂×C₄	—	9	2	no	—
429	C₂×C₄	—	9	2	no	—
430	C₂×C₄	—	18	2	no	—
431	C₂×C₄	—	18	2	no	—
432	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
433	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
434	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
435	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
436	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
437	C₂×C₃	—	2	4	no	—
438	C₂×C₃	—	2	4	no	—
439	C₂×C₃	—	2	4	no	—
440	C₂×C₃	—	18	2	no	—
441	C₂×C₃	C₂×C₃×#235	1	4	yes	—
442	C₂×C₃	C₂×C₃×D₃×Q₈	1	4	yes	—
443	C₂×C₃	C₃×D₃×#41	1	4	yes	—
444	C₂×C₃	C₂×#3828	1	1	yes	characteristic
445	C₂×C₃	C₂×Q₈×C₃⋊D₃	1	1	yes	characteristic
446	C₂×C₃	#41×C₃⋊D₃	1	1	yes	characteristic
447	D₃	—	6	8	no	—
448	C₂²	—	9	2	no	—
449	C₂²	—	18	1	no	—
450	C₂²	—	18	1	no	—
451	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
452	C₄	—	2	2	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	2	no	—
455	C₄	—	9	2	no	—
456	C₄	—	9	2	no	—
457	C₄	—	18	1	no	—
458	C₄	—	18	2	no	—
459	C₄	—	18	2	no	—
460	C₄	C₃×#3828	1	2	yes	—
461	C₄	C₃×Q₈×C₃⋊D₃	1	2	yes	—
462	C₃	—	2	4	no	—
463	C₃	C₃×#5578	1	4	yes	complemented
464	C₃	#10596049	1	1	yes	characteristic, direct product factor
465	C₂	—	18	2	no	—
466	C₂	C₂×C₃×#3828	1	1	yes	characteristic
467	C₂	C₂×C₃×Q₈×C₃⋊D₃	1	1	yes	characteristic
468	C₂	C₃×#41×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×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×#533
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃×C₄ ◁ 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×#64098	C₂	semidirect
7. C₃×#64097	C₂	semidirect
10. C₃×C₄×#634	C₂	semidirect
11. C₃×C₄×#634	C₂	semidirect
12. #10596049	C₃	direct (N × H)
38. C₃²×C₄×Q₈	D₃	semidirect
39. C₃²×C₄×Q₈	C₂×C₃	semidirect
41. #64153	C₂×C₃	semidirect
44. #64098	C₂×C₃	semidirect
45. #64097	C₂×C₃	semidirect
48. C₄×#634	C₂×C₃	semidirect
49. C₄×#634	C₂×C₃	semidirect
74. C₃×C₄×C₃⋊D₃	Q₈	semidirect
153. C₃×C₄×Q₈	C₃×D₃	semidirect
154. C₃×C₄×Q₈	C₃⋊D₃	semidirect
194. C₄×C₃⋊D₃	C₃×Q₈	semidirect
305. C₄×Q₈	C₃×C₃⋊D₃	semidirect
308. C₃³	#533	semidirect
418. C₃²	#5578	semidirect
419. C₃²	C₃×#533	semidirect
463. C₃	C₃×#5578	semidirect
464. C₃	#10596049	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×#64106	2
C₃×#64105	2
C₃×#64098	2
C₃×#64097	2
C₃×#64081	2
C₃×C₄²×C₃⋊D₃	2
C₃×C₄×#634	2
#10596049	3
C₃×#5578	3

Subgroups — C3×#10596049 #13179329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596049 #13179329