Subgroups — C₃²×#5578 #13178955

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

	subgroup	G/H
center	C₂×C₃²×C₄	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₃²
Frattini	C₂²	C₂³×C₃²×D₃
Fitting	C₃³×C₄×Q₈	C₂
socle	C₂²×C₃³	C₂⁴
prime radical	C₂²×C₃²×D₃	C₂³
hypercenter	C₃²×C₄×Q₈	D₃
hypocenter	C₃	C₃²×#533
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃²×C₄ ◁ C₃²×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. C₃²×#944	C₂	semidirect
6. C₃²×#889	C₂	semidirect
7. C₃²×#888	C₂	semidirect
10. C₃²×C₄×Dic₆	C₂	semidirect
11. C₃²×C₄×Dic₆	C₂	semidirect
13. C₃×#5578	C₃	direct (N × H)
46. C₃²×C₄×Q₈	D₃	semidirect
47. C₃²×C₄×Q₈	C₂×C₃	semidirect
51. C₃×#944	C₂×C₃	semidirect
54. C₃×#889	C₂×C₃	semidirect
55. C₃×#888	C₂×C₃	semidirect
58. C₃×C₄×Dic₆	C₂×C₃	semidirect
59. C₃×C₄×Dic₆	C₂×C₃	semidirect
74. C₃²×C₄×D₃	Q₈	semidirect
78. #5578	C₃²	direct (N × H)
153. C₃×C₄×Q₈	C₃×D₃	semidirect
154. C₃×C₄×Q₈	C₂×C₃²	semidirect
158. #944	C₂×C₃²	semidirect
161. #889	C₂×C₃²	semidirect
162. #888	C₂×C₃²	semidirect
165. C₄×Dic₆	C₂×C₃²	semidirect
166. C₄×Dic₆	C₂×C₃²	semidirect
204. C₃×C₄×D₃	C₃×Q₈	semidirect
305. C₄×Q₈	C₃²×D₃	semidirect
308. C₃³	#533	semidirect
346. C₄×D₃	C₃²×Q₈	semidirect
418. C₃²	#5578	direct (N × H)
419. C₃²	C₃×#533	semidirect
463. C₃	C₃×#5578	direct (N × H)
464. C₃	C₃²×#533	semidirect

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
C₃²×#946	2
C₃²×#944	2
C₃²×#897	2
C₃²×#896	2
C₃²×#889	2
C₃²×#888	2
C₃²×#872	2
C₃²×C₄²×D₃	2
C₃²×C₄×Dic₆	2
C₃²×#533	3
C₃×#5578	3

Subgroups — C32×#5578 #13178955

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5578 #13178955