Subgroups — C₃²×#5625 #13179006

Order 1728.

1448 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃²×Q₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#944	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#926	C₂	1	1	yes	maximal, characteristic
5	C₃²×#924	C₂	1	1	yes	maximal, characteristic
6	C₃²×#890	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×#890	C₂	1	2	yes	maximal, complemented
8	C₃²×#889	C₂	1	2	yes	maximal, complemented
9	C₃²×#887	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃²×#879	C₂	1	2	yes	maximal
11	C₃²×#879	C₂	1	2	yes	maximal
12	C₃²×#541	—	3	1	no	maximal
13	C₃×#5625	C₃	1	4	yes	maximal, direct product factor
14	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
15	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃²×Dic₆	C₂²	1	1	yes	characteristic
17	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₃³×C₄⋊C₄	C₂²	1	2	yes	—
19	C₃³×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₃²×#217	C₂²	1	2	yes	—
21	C₃²×#217	C₂²	1	1	yes	characteristic
22	C₃²×#217	C₂²	1	1	yes	characteristic
23	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
24	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
25	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
26	C₃²×C₄⋊Dic₃	C₂²	1	2	yes	—
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	2	yes	—
37	C₃²×C₄⋊Q₈	—	3	1	no	—
38	C₃²×#126	—	3	2	no	—
39	C₃²×#126	—	3	2	no	—
40	C₃²×#125	—	3	2	no	—
41	C₃²×#125	—	3	1	no	—
42	C₃²×#125	—	3	2	no	—
43	C₃²×C₂²⋊Q₈	—	2	4	no	—
44	C₃²×C₂²⋊Q₈	—	3	1	no	—
45	C₃²×C₂²⋊Q₈	D₃	1	1	yes	characteristic
46	C₃²×C₂²⋊Q₈	C₂×C₃	1	4	yes	—
47	C₃²×C₄×Q₈	—	3	1	no	—
48	C₃²×C₄×Q₈	—	3	1	no	—
49	C₃²×#117	—	3	1	no	—
50	C₃×Q₈×Dic₃	C₂×C₃	1	4	yes	complemented
51	C₃×#944	C₂×C₃	1	4	yes	complemented
52	C₃×#926	C₂×C₃	1	4	yes	—
53	C₃×#924	C₂×C₃	1	4	yes	—
54	C₃×#890	C₂×C₃	1	8	yes	complemented
55	C₃×#890	C₂×C₃	1	4	yes	complemented
56	C₃×#889	C₂×C₃	1	8	yes	complemented
57	C₃×#887	C₂×C₃	1	4	yes	complemented
58	C₃×#879	C₂×C₃	1	8	yes	—
59	C₃×#879	C₂×C₃	1	8	yes	—
60	C₂³×C₃³	C₂³	1	1	yes	characteristic
61	C₃³×Q₈	—	2	2	no	—
62	C₂×C₃³×C₄	—	2	2	no	—
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×C₃²×Dic₃	C₂³	1	2	yes	—
68	C₂×C₃²×Dic₃	C₂³	1	1	yes	characteristic
69	C₂×C₃²×Dic₃	C₂³	1	1	yes	characteristic
70	C₂×C₃²×Dic₃	C₂³	1	1	yes	characteristic
71	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
72	C₂×C₃²×Dic₃	C₂³	1	1	yes	characteristic
73	C₃²×Dic₆	—	2	2	no	—
74	C₃×#541	—	3	4	no	—
75	#5625	C₃²	1	1	yes	characteristic, direct product factor
76	C₂×C₃²×Q₈	—	2	4	no	—
77	C₂×C₃²×Q₈	—	3	1	no	—
78	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
79	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	—
80	C₂²×C₃²×C₄	—	2	4	no	—
81	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
82	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
83	C₂×C₃×Dic₆	C₂²×C₃	1	4	yes	—
84	C₃²×C₄⋊C₄	—	2	4	no	—
85	C₃²×C₄⋊C₄	—	2	8	no	—
86	C₃²×C₄⋊C₄	—	3	1	no	—
87	C₃²×C₄⋊C₄	—	3	1	no	—
88	C₃²×C₄⋊C₄	—	3	1	no	—
89	C₃²×C₄⋊C₄	—	3	2	no	—
90	C₃²×C₄⋊C₄	—	3	2	no	—
91	C₃²×C₄⋊C₄	—	3	2	no	—
92	C₃²×C₄⋊C₄	—	3	2	no	—
93	C₃²×C₄⋊C₄	—	3	2	no	—
94	C₃²×C₄⋊C₄	—	3	2	no	—
95	C₃²×C₄⋊C₄	—	3	2	no	—
96	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
97	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
98	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	—
99	C₃²×C₄⋊C₄	C₂²×C₃	1	8	yes	—
100	C₃²×C₂²⋊C₄	—	2	8	no	—
101	C₃²×C₂²⋊C₄	—	3	1	no	—
102	C₃²×C₂²⋊C₄	—	3	1	no	—
103	C₃²×C₂²⋊C₄	—	3	2	no	—
104	C₃²×C₂²⋊C₄	C₂×D₃	1	2	yes	—
105	C₃²×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
106	C₃²×C₄²	—	3	1	no	—
107	C₃²×C₄²	—	3	1	no	—
108	C₃²×C₄²	—	3	2	no	—
109	C₃²×C₄²	—	3	2	no	—
110	C₃×#217	C₂²×C₃	1	8	yes	—
111	C₃×#217	C₂²×C₃	1	4	yes	—
112	C₃×#217	C₂²×C₃	1	4	yes	—
113	C₃×C₄⋊Dic₃	C₂²×C₃	1	8	yes	—
114	C₃×C₄⋊Dic₃	C₂²×C₃	1	8	yes	—
115	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
116	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
117	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
118	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	yes	—
119	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	yes	—
120	C₃×Dic₃⋊C₄	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×C₄×Dic₃	C₂²×C₃	1	8	yes	—
124	C₃×C₄×Dic₃	C₂²×C₃	1	8	yes	—
125	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
126	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
127	C₂²×C₃³	—	2	1	no	—
128	C₂²×C₃³	—	2	1	no	—
129	C₂²×C₃³	—	2	1	no	—
130	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
131	C₃³×C₄	—	2	1	no	—
132	C₃³×C₄	—	2	2	no	—
133	C₃³×C₄	—	2	2	no	—
134	C₃³×C₄	#41	1	2	yes	—
135	C₃²×Dic₃	—	2	2	no	—
136	C₃²×Dic₃	—	2	1	no	—
137	C₃²×Dic₃	—	2	2	no	—
138	C₃²×Dic₃	—	2	1	no	—
139	C₃²×Dic₃	—	2	1	no	—
140	C₃²×Dic₃	—	2	1	no	—
141	C₃×C₄⋊Q₈	—	3	4	no	—
142	C₃×#126	—	3	8	no	—
143	C₃×#126	—	3	8	no	—
144	C₃×#125	—	3	8	no	—
145	C₃×#125	—	3	4	no	—
146	C₃×#125	—	3	8	no	—
147	C₃×C₂²⋊Q₈	—	2	4	no	—
148	C₃×C₂²⋊Q₈	—	3	4	no	—
149	C₃×C₂²⋊Q₈	C₃×D₃	1	4	yes	—
150	C₃×C₂²⋊Q₈	C₂×C₃²	1	1	yes	characteristic
151	C₃×C₄×Q₈	—	3	4	no	—
152	C₃×C₄×Q₈	—	3	4	no	—
153	C₃×#117	—	3	4	no	—
154	Q₈×Dic₃	C₂×C₃²	1	1	yes	characteristic, complemented
155	#944	C₂×C₃²	1	1	yes	characteristic, complemented
156	#926	C₂×C₃²	1	1	yes	characteristic
157	#924	C₂×C₃²	1	1	yes	characteristic
158	#890	C₂×C₃²	1	2	yes	complemented
159	#890	C₂×C₃²	1	1	yes	characteristic, complemented
160	#889	C₂×C₃²	1	2	yes	complemented
161	#887	C₂×C₃²	1	1	yes	characteristic, complemented
162	#879	C₂×C₃²	1	2	yes	—
163	#879	C₂×C₃²	1	2	yes	—
164	C₂³×C₃²	—	2	4	no	—
165	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
166	C₂³×C₃²	C₂³×C₃	1	4	yes	—
167	C₃²×Q₈	—	2	2	no	—
168	C₃²×Q₈	—	2	8	no	—
169	C₃²×Q₈	—	4	8	no	—
170	C₃²×Q₈	—	6	2	no	—
171	C₂×C₃²×C₄	—	2	2	no	—
172	C₂×C₃²×C₄	—	2	4	no	—
173	C₂×C₃²×C₄	—	2	8	no	—
174	C₂×C₃²×C₄	—	2	8	no	—
175	C₂×C₃²×C₄	—	2	4	no	—
176	C₂×C₃²×C₄	—	2	8	no	—
177	C₂×C₃²×C₄	—	3	1	no	—
178	C₂×C₃²×C₄	—	3	1	no	—
179	C₂×C₃²×C₄	—	3	1	no	—
180	C₂×C₃²×C₄	—	3	2	no	—
181	C₂×C₃²×C₄	—	3	1	no	—
182	C₂×C₃²×C₄	—	3	2	no	—
183	C₂×C₃²×C₄	—	4	8	no	—
184	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
185	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
186	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
187	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
188	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
189	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
190	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
191	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
192	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
193	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
194	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
195	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
196	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
197	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
198	C₃×Dic₆	—	2	8	no	—
199	#541	—	3	1	no	Sylow
200	C₂×C₃³	—	4	1	no	—
201	C₂×C₃³	C₂×#41	1	1	yes	characteristic
202	C₂×C₃³	2₋¹⁺⁴	1	1	yes	characteristic
203	C₂×C₃³	2₋¹⁺⁴	1	1	yes	characteristic
204	C₂×C₃×Q₈	—	2	4	no	—
205	C₂×C₃×Q₈	—	3	4	no	—
206	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
207	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic
208	C₂²×C₃×C₄	—	2	4	no	—
209	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
210	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
211	C₂×Dic₆	C₂²×C₃²	1	1	yes	characteristic
212	C₃×C₄⋊C₄	—	2	4	no	—
213	C₃×C₄⋊C₄	—	2	8	no	—
214	C₃×C₄⋊C₄	—	3	8	no	—
215	C₃×C₄⋊C₄	—	3	8	no	—
216	C₃×C₄⋊C₄	—	3	8	no	—
217	C₃×C₄⋊C₄	—	3	8	no	—
218	C₃×C₄⋊C₄	—	3	8	no	—
219	C₃×C₄⋊C₄	—	3	4	no	—
220	C₃×C₄⋊C₄	—	3	4	no	—
221	C₃×C₄⋊C₄	—	3	4	no	—
222	C₃×C₄⋊C₄	—	3	8	no	—
223	C₃×C₄⋊C₄	—	3	8	no	—
224	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
225	C₃×C₄⋊C₄	C₂×C₃×D₃	1	8	yes	—
226	C₃×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
227	C₃×C₄⋊C₄	C₂²×C₃²	1	2	yes	—
228	C₃×C₂²⋊C₄	—	2	8	no	—
229	C₃×C₂²⋊C₄	—	3	4	no	—
230	C₃×C₂²⋊C₄	—	3	4	no	—
231	C₃×C₂²⋊C₄	—	3	8	no	—
232	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	8	yes	—
233	C₃×C₂²⋊C₄	C₂²×C₃²	1	2	yes	—
234	C₃×C₄²	—	3	4	no	—
235	C₃×C₄²	—	3	4	no	—
236	C₃×C₄²	—	3	8	no	—
237	C₃×C₄²	—	3	8	no	—
238	#217	C₂²×C₃²	1	2	yes	—
239	#217	C₂²×C₃²	1	1	yes	characteristic
240	#217	C₂²×C₃²	1	1	yes	characteristic
241	C₄⋊Dic₃	C₂²×C₃²	1	2	yes	—
242	C₄⋊Dic₃	C₂²×C₃²	1	2	yes	—
243	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic
244	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic
245	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic
246	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	—
247	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	—
248	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	—
249	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	—
250	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	—
251	C₄×Dic₃	C₂²×C₃²	1	2	yes	—
252	C₄×Dic₃	C₂²×C₃²	1	2	yes	—
253	C₄×Dic₃	C₂²×C₃²	1	1	yes	characteristic
254	C₄×Dic₃	C₂²×C₃²	1	1	yes	characteristic
255	C₂²×C₃²	—	2	8	no	—
256	C₂²×C₃²	—	2	1	no	—
257	C₂²×C₃²	—	2	1	no	—
258	C₂²×C₃²	—	2	1	no	—
259	C₂²×C₃²	—	2	4	no	—
260	C₂²×C₃²	—	2	4	no	—
261	C₂²×C₃²	—	2	4	no	—
262	C₂²×C₃²	—	2	4	no	—
263	C₂²×C₃²	—	4	4	no	—
264	C₂²×C₃²	—	4	4	no	—
265	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
266	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
267	C₃²×C₄	—	2	1	no	—
268	C₃²×C₄	—	2	2	no	—
269	C₃²×C₄	—	2	2	no	—
270	C₃²×C₄	—	2	8	no	—
271	C₃²×C₄	—	2	4	no	—
272	C₃²×C₄	—	2	8	no	—
273	C₃²×C₄	—	2	8	no	—
274	C₃²×C₄	—	4	8	no	—
275	C₃²×C₄	—	4	4	no	—
276	C₃²×C₄	—	4	8	no	—
277	C₃²×C₄	—	6	2	no	—
278	C₃²×C₄	—	6	1	no	—
279	C₃²×C₄	—	6	1	no	—
280	C₃²×C₄	—	6	2	no	—
281	C₃²×C₄	—	6	1	no	—
282	C₃²×C₄	—	6	1	no	—
283	C₃²×C₄	#237	1	2	yes	—
284	C₃²×C₄	C₃×#41	1	8	yes	—
285	C₃×Dic₃	—	2	8	no	—
286	C₃×Dic₃	—	2	4	no	—
287	C₃×Dic₃	—	2	8	no	—
288	C₃×Dic₃	—	2	4	no	—
289	C₃×Dic₃	—	2	4	no	—
290	C₃×Dic₃	—	2	4	no	—
291	C₄⋊Q₈	—	3	1	no	—
292	#126	—	3	2	no	—
293	#126	—	3	2	no	—
294	#125	—	3	2	no	—
295	#125	—	3	1	no	—
296	#125	—	3	2	no	—
297	C₂²⋊Q₈	—	3	1	no	—
298	C₂²⋊Q₈	C₃²×D₃	1	1	yes	characteristic
299	C₄×Q₈	—	3	1	no	—
300	C₄×Q₈	—	3	1	no	—
301	#117	—	3	1	no	—
302	C₃³	#541	1	1	yes	characteristic, complemented, Sylow
303	C₂³×C₃	—	2	4	no	—
304	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
305	C₂³×C₃	C₂³×C₃²	1	1	yes	characteristic
306	C₃×Q₈	—	2	8	no	—
307	C₃×Q₈	—	2	2	no	—
308	C₃×Q₈	—	4	8	no	—
309	C₃×Q₈	—	6	8	no	—
310	C₂×C₃×C₄	—	2	8	no	—
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	—	2	4	no	—
313	C₂×C₃×C₄	—	2	8	no	—
314	C₂×C₃×C₄	—	2	8	no	—
315	C₂×C₃×C₄	—	2	4	no	—
316	C₂×C₃×C₄	—	3	4	no	—
317	C₂×C₃×C₄	—	3	4	no	—
318	C₂×C₃×C₄	—	3	4	no	—
319	C₂×C₃×C₄	—	3	8	no	—
320	C₂×C₃×C₄	—	3	4	no	—
321	C₂×C₃×C₄	—	3	8	no	—
322	C₂×C₃×C₄	—	4	8	no	—
323	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
324	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
325	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
326	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
327	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
328	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
329	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
330	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
331	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
332	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
333	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
334	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
335	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
336	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
337	Dic₆	—	2	2	no	—
338	C₂×C₃²	—	2	4	no	—
339	C₂×C₃²	—	2	4	no	—
340	C₂×C₃²	—	2	4	no	—
341	C₂×C₃²	—	4	8	no	—
342	C₂×C₃²	—	4	4	no	—
343	C₂×C₃²	—	4	1	no	—
344	C₂×C₃²	C₂×#237	1	1	yes	characteristic
345	C₂×C₃²	#1007	1	1	yes	characteristic
346	C₂×C₃²	#1010	1	1	yes	characteristic
347	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
348	C₂×C₃²	C₃×2₋¹⁺⁴	1	4	yes	—
349	C₂×C₃²	C₃×2₋¹⁺⁴	1	4	yes	—
350	C₂×Q₈	—	3	1	no	—
351	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
353	C₄⋊C₄	—	3	1	no	—
354	C₄⋊C₄	—	3	1	no	—
355	C₄⋊C₄	—	3	1	no	—
356	C₄⋊C₄	—	3	2	no	—
357	C₄⋊C₄	—	3	2	no	—
358	C₄⋊C₄	—	3	2	no	—
359	C₄⋊C₄	—	3	2	no	—
360	C₄⋊C₄	—	3	2	no	—
361	C₄⋊C₄	—	3	2	no	—
362	C₄⋊C₄	—	3	2	no	—
363	C₄⋊C₄	C₂×C₃²×D₃	1	1	yes	characteristic
364	C₄⋊C₄	C₂×C₃²×D₃	1	2	yes	—
365	C₂²⋊C₄	—	3	1	no	—
366	C₂²⋊C₄	—	3	1	no	—
367	C₂²⋊C₄	—	3	2	no	—
368	C₂²⋊C₄	C₂×C₃²×D₃	1	2	yes	—
369	C₄²	—	3	1	no	—
370	C₄²	—	3	1	no	—
371	C₄²	—	3	2	no	—
372	C₄²	—	3	2	no	—
373	C₂²×C₃	—	2	8	no	—
374	C₂²×C₃	—	2	4	no	—
375	C₂²×C₃	—	2	4	no	—
376	C₂²×C₃	—	2	4	no	—
377	C₂²×C₃	—	2	1	no	—
378	C₂²×C₃	—	2	1	no	—
379	C₂²×C₃	—	2	1	no	—
380	C₂²×C₃	—	2	4	no	—
381	C₂²×C₃	—	4	4	no	—
382	C₂²×C₃	—	4	4	no	—
383	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
384	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
385	C₃×C₄	—	2	4	no	—
386	C₃×C₄	—	2	8	no	—
387	C₃×C₄	—	2	8	no	—
388	C₃×C₄	—	2	1	no	—
389	C₃×C₄	—	2	2	no	—
390	C₃×C₄	—	2	2	no	—
391	C₃×C₄	—	2	8	no	—
392	C₃×C₄	—	4	4	no	—
393	C₃×C₄	—	4	8	no	—
394	C₃×C₄	—	4	8	no	—
395	C₃×C₄	—	6	8	no	—
396	C₃×C₄	—	6	4	no	—
397	C₃×C₄	—	6	4	no	—
398	C₃×C₄	—	6	8	no	—
399	C₃×C₄	—	6	4	no	—
400	C₃×C₄	—	6	4	no	—
401	C₃×C₄	C₃×#237	1	8	yes	—
402	C₃×C₄	C₃²×#41	1	2	yes	—
403	Dic₃	—	2	2	no	—
404	Dic₃	—	2	1	no	—
405	Dic₃	—	2	2	no	—
406	Dic₃	—	2	1	no	—
407	Dic₃	—	2	1	no	—
408	Dic₃	—	2	1	no	—
409	C₃²	—	2	4	no	—
410	C₃²	#5625	1	1	yes	characteristic, direct product factor
411	C₃²	C₃×#541	1	4	yes	complemented
412	C₂³	C₂²×C₃²×D₃	1	1	yes	characteristic
413	Q₈	—	2	2	no	—
414	Q₈	—	6	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	3	1	no	—
417	C₂×C₄	—	3	1	no	—
418	C₂×C₄	—	3	1	no	—
419	C₂×C₄	—	3	2	no	—
420	C₂×C₄	—	3	1	no	—
421	C₂×C₄	—	3	2	no	—
422	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
423	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
424	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
425	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
426	C₂×C₃	—	2	4	no	—
427	C₂×C₃	—	2	4	no	—
428	C₂×C₃	—	2	4	no	—
429	C₂×C₃	—	4	8	no	—
430	C₂×C₃	—	4	4	no	—
431	C₂×C₃	—	4	1	no	—
432	C₂×C₃	C₂×C₃×#237	1	4	yes	—
433	C₂×C₃	C₃×#1007	1	4	yes	—
434	C₂×C₃	C₃×#1010	1	4	yes	—
435	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
436	C₂×C₃	C₃²×2₋¹⁺⁴	1	1	yes	characteristic
437	C₂×C₃	C₃²×2₋¹⁺⁴	1	1	yes	characteristic
438	C₂²	—	2	1	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
442	C₄	—	2	1	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	6	2	no	—
446	C₄	—	6	1	no	—
447	C₄	—	6	1	no	—
448	C₄	—	6	2	no	—
449	C₄	—	6	1	no	—
450	C₄	—	6	1	no	—
451	C₄	C₃²×#237	1	2	yes	—
452	C₃	—	2	4	no	—
453	C₃	C₃×#5625	1	4	yes	direct product factor
454	C₃	C₃²×#541	1	1	yes	characteristic, complemented
455	C₂	—	4	1	no	—
456	C₂	C₂×C₃²×#237	1	1	yes	characteristic
457	C₂	C₃²×#1007	1	1	yes	characteristic
458	C₂	C₃²×#1010	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₃²×Q₈×Dic₃	C₂	semidirect
3. C₃²×#944	C₂	semidirect
6. C₃²×#890	C₂	semidirect
7. C₃²×#890	C₂	semidirect
8. C₃²×#889	C₂	semidirect
9. C₃²×#887	C₂	semidirect
13. C₃×#5625	C₃	direct (N × H)
50. C₃×Q₈×Dic₃	C₂×C₃	semidirect
51. C₃×#944	C₂×C₃	semidirect
54. C₃×#890	C₂×C₃	semidirect
55. C₃×#890	C₂×C₃	semidirect
56. C₃×#889	C₂×C₃	semidirect
57. C₃×#887	C₂×C₃	semidirect
75. #5625	C₃²	direct (N × H)
154. Q₈×Dic₃	C₂×C₃²	semidirect
155. #944	C₂×C₃²	semidirect
158. #890	C₂×C₃²	semidirect
159. #890	C₂×C₃²	semidirect
160. #889	C₂×C₃²	semidirect
161. #887	C₂×C₃²	semidirect
302. C₃³	#541	semidirect
410. C₃²	#5625	direct (N × H)
411. C₃²	C₃×#541	semidirect
453. C₃	C₃×#5625	direct (N × H)
454. C₃	C₃²×#541	semidirect

Maximal subgroups

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

subgroup	index
C₃³×C₂²⋊Q₈	2
C₃²×Q₈×Dic₃	2
C₃²×#944	2
C₃²×#926	2
C₃²×#924	2
C₃²×#890	2
C₃²×#889	2
C₃²×#887	2
C₃²×#879	2
C₃²×#541	3
C₃×#5625	3

Subgroups — C32×#5625 #13179006

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5625 #13179006