Subgroups — C₃²×#5128 #13162555

Order 1728.

1004 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×C₄×#67	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃²×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#830	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#436	—	3	1	no	maximal
9	C₃×#5128	C₃	1	4	yes	maximal, direct product factor
10	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
11	C₂×C₃²×#67	C₄	1	1	yes	characteristic
12	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
13	C₃³×M₁₆	—	2	2	no	—
14	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
16	C₃²×#217	C₄	1	1	yes	characteristic
17	C₃²×(C₂×D₃)⋊C₄	C₄	1	1	yes	characteristic
18	C₃²×Dic₃⋊C₄	C₄	1	1	yes	characteristic
19	C₃²×C₄×Dic₃	C₂²	1	1	yes	characteristic
20	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic
22	C₃²×ΓL(1,𝔽₂₅)	—	2	2	no	—
23	C₂×C₃²×M₁₆	—	2	4	no	—
24	C₂×C₃²×M₁₆	—	3	1	no	—
25	C₂×C₃²×M₁₆	D₃	1	1	yes	characteristic, complemented
26	C₂×C₃²×M₁₆	C₂×C₃	1	4	yes	complemented
27	C₃²×C₄×D₄	—	3	1	no	—
28	C₃×C₄×#67	C₂×C₃	1	4	yes	—
29	C₂×C₃×ΓL(1,𝔽₂₅)	C₂×C₃	1	4	yes	complemented
30	C₃²×C₄⋊C₈	—	3	1	no	—
31	C₃²×C₂²⋊C₈	—	3	1	no	—
32	C₃²×C₂²⋊C₈	—	3	1	no	—
33	C₃²×C₄×C₈	—	3	1	no	—
34	C₃×#830	C₂×C₃	1	4	yes	complemented
35	C₃×(C₂×D₃)⋊C₈	C₂×C₃	1	4	yes	complemented
36	C₃×Dic₃⋊C₈	C₂×C₃	1	4	yes	complemented
37	C₃×C₈×Dic₃	C₂×C₃	1	4	yes	complemented
38	C₂³×C₃³	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃²×D₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₃³×C₄	—	2	1	no	—
41	C₂×C₃³×C₄	—	2	1	no	—
42	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
44	C₃²×#67	—	2	2	no	—
45	C₂×C₃²×Dic₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃²×Dic₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₃²×Dic₃	C₂×C₄	1	1	yes	characteristic
48	C₃²×C₄×D₃	—	2	1	no	—
49	C₃²×C₄×D₃	—	2	1	no	—
50	C₃³×C₈	—	2	1	no	—
51	C₃³×C₈	D₄	1	2	yes	complemented
52	C₃²×C₃⋊C₈	—	2	1	no	—
53	C₃²×C₃⋊C₈	—	2	1	no	—
54	C₃×#436	—	3	4	no	—
55	#5128	C₃²	1	1	yes	characteristic, direct product factor
56	C₂×C₃²×D₄	—	3	1	no	—
57	C₂²×C₃²×C₄	—	2	4	no	—
58	C₂²×C₃²×C₄	—	3	1	no	—
59	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
60	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
61	C₂×C₃×#67	C₃×C₄	1	4	yes	—
62	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
63	C₃²×M₁₆	—	2	16	no	—
64	C₃²×M₁₆	—	2	2	no	—
65	C₃²×M₁₆	—	2	8	no	—
66	C₃²×M₁₆	—	6	2	no	—
67	C₂×C₃²×C₈	—	2	4	no	—
68	C₂×C₃²×C₈	—	2	4	no	—
69	C₂×C₃²×C₈	—	3	1	no	—
70	C₂×C₃²×C₈	—	3	1	no	—
71	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
72	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
73	C₂×C₃²×C₈	C₂²×C₃	1	4	yes	—
74	C₂×C₃²×C₈	C₂²×C₃	1	4	yes	—
75	C₃²×C₄⋊C₄	—	3	1	no	—
76	C₃²×C₂²⋊C₄	—	3	1	no	—
77	C₃²×C₂²⋊C₄	—	3	1	no	—
78	C₃²×C₄²	—	3	1	no	—
79	C₃×#217	C₃×C₄	1	4	yes	—
80	C₃×(C₂×D₃)⋊C₄	C₃×C₄	1	4	yes	—
81	C₃×Dic₃⋊C₄	C₃×C₄	1	4	yes	—
82	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
83	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	4	yes	—
84	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	4	yes	—
85	C₃×ΓL(1,𝔽₂₅)	—	2	8	no	—
86	C₂²×C₃³	—	2	1	no	—
87	C₂²×C₃³	—	2	1	no	—
88	C₂²×C₃³	—	2	1	no	—
89	C₂²×C₃³	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₃²×D₃	—	2	1	no	—
91	C₂×C₃²×D₃	—	2	1	no	—
92	C₂×C₃²×D₃	—	2	1	no	—
93	C₃³×C₄	—	2	1	no	—
94	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
95	C₃³×C₄	#41	1	1	yes	characteristic
96	C₃²×Dic₃	—	2	1	no	—
97	C₃²×Dic₃	—	2	1	no	—
98	C₃²×Dic₃	M₁₆	1	2	yes	complemented
99	C₂×C₃×M₁₆	—	2	4	no	—
100	C₂×C₃×M₁₆	—	3	4	no	—
101	C₂×C₃×M₁₆	C₃×D₃	1	4	yes	complemented
102	C₂×C₃×M₁₆	C₂×C₃²	1	1	yes	characteristic, complemented
103	C₃×C₄×D₄	—	3	4	no	—
104	C₄×#67	C₂×C₃²	1	1	yes	characteristic
105	C₂×ΓL(1,𝔽₂₅)	C₂×C₃²	1	1	yes	characteristic, complemented
106	C₃×C₄⋊C₈	—	3	4	no	—
107	C₃×C₂²⋊C₈	—	3	4	no	—
108	C₃×C₂²⋊C₈	—	3	4	no	—
109	C₃×C₄×C₈	—	3	4	no	—
110	#830	C₂×C₃²	1	1	yes	characteristic, complemented
111	(C₂×D₃)⋊C₈	C₂×C₃²	1	1	yes	characteristic, complemented
112	Dic₃⋊C₈	C₂×C₃²	1	1	yes	characteristic, complemented
113	C₈×Dic₃	C₂×C₃²	1	1	yes	characteristic, complemented
114	C₂³×C₃²	—	2	4	no	—
115	C₂³×C₃²	—	3	1	no	—
116	C₂³×C₃²	C₄×D₃	1	1	yes	characteristic
117	C₂³×C₃²	C₂×C₃×C₄	1	4	yes	—
118	C₂²×C₃×D₃	C₂×C₃×C₄	1	4	yes	—
119	C₃²×D₄	—	6	2	no	—
120	C₂×C₃²×C₄	—	2	8	no	—
121	C₂×C₃²×C₄	—	2	8	no	—
122	C₂×C₃²×C₄	—	2	1	no	—
123	C₂×C₃²×C₄	—	2	1	no	—
124	C₂×C₃²×C₄	—	2	4	no	—
125	C₂×C₃²×C₄	—	2	4	no	—
126	C₂×C₃²×C₄	—	2	4	no	—
127	C₂×C₃²×C₄	—	2	4	no	—
128	C₂×C₃²×C₄	—	3	1	no	—
129	C₂×C₃²×C₄	—	3	1	no	—
130	C₂×C₃²×C₄	—	3	1	no	—
131	C₂×C₃²×C₄	—	6	1	no	—
132	C₂×C₃²×C₄	—	6	1	no	—
133	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
134	C₂×C₃²×C₄	C₂×C₃×C₄	1	4	yes	—
135	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
136	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
137	C₃×#67	—	2	8	no	—
138	C₂×C₃×Dic₃	C₂×C₃×C₄	1	4	yes	—
139	C₂×C₃×Dic₃	C₂×C₃×C₄	1	4	yes	—
140	C₂×C₃×Dic₃	C₂×C₃×C₄	1	4	yes	—
141	C₃×C₄×D₃	—	2	4	no	—
142	C₃×C₄×D₃	—	2	4	no	—
143	C₃²×C₈	—	2	8	no	—
144	C₃²×C₈	—	2	1	no	—
145	C₃²×C₈	—	2	4	no	—
146	C₃²×C₈	—	2	8	no	—
147	C₃²×C₈	—	6	1	no	—
148	C₃²×C₈	—	6	1	no	—
149	C₃²×C₈	#67	1	2	yes	complemented
150	C₃²×C₈	C₃×D₄	1	8	yes	complemented
151	C₃×C₃⋊C₈	—	2	4	no	—
152	C₃×C₃⋊C₈	—	2	4	no	—
153	#436	—	3	1	no	Sylow
154	C₂×C₃³	—	4	1	no	—
155	C₂×C₃³	C₄×D₄	1	1	yes	characteristic
156	C₂×C₃³	C₂×M₁₆	1	1	yes	characteristic
157	C₂×C₃³	#131	1	1	yes	characteristic
158	C₃²×D₃	—	4	1	no	—
159	C₂×C₃×D₄	—	3	4	no	—
160	C₂²×C₃×C₄	—	2	4	no	—
161	C₂²×C₃×C₄	—	3	4	no	—
162	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
163	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
164	C₂×#67	C₃²×C₄	1	1	yes	characteristic
165	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
166	C₃×M₁₆	—	2	16	no	—
167	C₃×M₁₆	—	2	8	no	—
168	C₃×M₁₆	—	2	2	no	—
169	C₃×M₁₆	—	6	8	no	—
170	C₂×C₃×C₈	—	2	4	no	—
171	C₂×C₃×C₈	—	2	4	no	—
172	C₂×C₃×C₈	—	3	4	no	—
173	C₂×C₃×C₈	—	3	4	no	—
174	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
175	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
176	C₂×C₃×C₈	C₂²×C₃²	1	1	yes	characteristic
177	C₂×C₃×C₈	C₂²×C₃²	1	1	yes	characteristic
178	C₃×C₄⋊C₄	—	3	4	no	—
179	C₃×C₂²⋊C₄	—	3	4	no	—
180	C₃×C₂²⋊C₄	—	3	4	no	—
181	C₃×C₄²	—	3	4	no	—
182	#217	C₃²×C₄	1	1	yes	characteristic
183	(C₂×D₃)⋊C₄	C₃²×C₄	1	1	yes	characteristic
184	Dic₃⋊C₄	C₃²×C₄	1	1	yes	characteristic
185	C₄×Dic₃	C₂²×C₃²	1	1	yes	characteristic
186	C₂×C₃⋊C₈	C₂²×C₃²	1	1	yes	characteristic
187	C₂×C₃⋊C₈	C₂²×C₃²	1	1	yes	characteristic
188	ΓL(1,𝔽₂₅)	—	2	2	no	—
189	C₂²×C₃²	—	2	8	no	—
190	C₂²×C₃²	—	2	1	no	—
191	C₂²×C₃²	—	2	1	no	—
192	C₂²×C₃²	—	2	1	no	—
193	C₂²×C₃²	—	2	4	no	—
194	C₂²×C₃²	—	2	4	no	—
195	C₂²×C₃²	—	2	4	no	—
196	C₂²×C₃²	—	2	4	no	—
197	C₂²×C₃²	—	4	4	no	—
198	C₂²×C₃²	—	4	4	no	—
199	C₂²×C₃²	—	6	1	no	—
200	C₂²×C₃²	—	6	1	no	—
201	C₂²×C₃²	—	6	1	no	—
202	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
203	C₂²×C₃²	C₂²×C₃×C₄	1	4	yes	—
204	C₂×C₃×D₃	—	2	4	no	—
205	C₂×C₃×D₃	—	2	4	no	—
206	C₂×C₃×D₃	—	2	4	no	—
207	C₃²×C₄	—	2	8	no	—
208	C₃²×C₄	—	2	1	no	—
209	C₃²×C₄	—	2	4	no	—
210	C₃²×C₄	—	2	4	no	—
211	C₃²×C₄	—	2	4	no	—
212	C₃²×C₄	—	3	2	no	—
213	C₃²×C₄	—	6	1	no	—
214	C₃²×C₄	—	6	1	no	—
215	C₃²×C₄	#235	1	1	yes	characteristic
216	C₃²×C₄	C₂×#67	1	1	yes	characteristic
217	C₃²×C₄	C₂×C₃×D₄	1	4	yes	—
218	C₃²×C₄	C₃×#41	1	4	yes	—
219	C₃×Dic₃	—	2	4	no	—
220	C₃×Dic₃	—	2	4	no	—
221	C₃×Dic₃	C₃×M₁₆	1	8	yes	complemented
222	C₂×M₁₆	—	3	1	no	—
223	C₂×M₁₆	C₃²×D₃	1	1	yes	characteristic, complemented
224	C₄×D₄	—	3	1	no	—
225	C₄⋊C₈	—	3	1	no	—
226	C₂²⋊C₈	—	3	1	no	—
227	C₂²⋊C₈	—	3	1	no	—
228	C₄×C₈	—	3	1	no	—
229	C₃³	#436	1	1	yes	characteristic, complemented, Sylow
230	C₂³×C₃	—	2	4	no	—
231	C₂³×C₃	—	3	4	no	—
232	C₂³×C₃	C₃×C₄×D₃	1	4	yes	—
233	C₂³×C₃	C₂×C₃²×C₄	1	1	yes	characteristic
234	C₂²×D₃	C₂×C₃²×C₄	1	1	yes	characteristic
235	C₃×D₄	—	6	8	no	—
236	C₂×C₃×C₄	—	2	8	no	—
237	C₂×C₃×C₄	—	2	8	no	—
238	C₂×C₃×C₄	—	2	4	no	—
239	C₂×C₃×C₄	—	2	4	no	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	—	2	1	no	—
242	C₂×C₃×C₄	—	2	4	no	—
243	C₂×C₃×C₄	—	2	4	no	—
244	C₂×C₃×C₄	—	3	4	no	—
245	C₂×C₃×C₄	—	3	4	no	—
246	C₂×C₃×C₄	—	3	4	no	—
247	C₂×C₃×C₄	—	6	4	no	—
248	C₂×C₃×C₄	—	6	4	no	—
249	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
250	C₂×C₃×C₄	C₂×C₃²×C₄	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
252	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
253	#67	—	2	2	no	—
254	C₂×Dic₃	C₂×C₃²×C₄	1	1	yes	characteristic
255	C₂×Dic₃	C₂×C₃²×C₄	1	1	yes	characteristic
256	C₂×Dic₃	C₂×C₃²×C₄	1	1	yes	characteristic
257	C₄×D₃	—	2	1	no	—
258	C₄×D₃	—	2	1	no	—
259	C₃×C₈	—	2	8	no	—
260	C₃×C₈	—	2	4	no	—
261	C₃×C₈	—	2	1	no	—
262	C₃×C₈	—	2	8	no	—
263	C₃×C₈	—	6	4	no	—
264	C₃×C₈	—	6	4	no	—
265	C₃×C₈	C₃×#67	1	8	yes	complemented
266	C₃×C₈	C₃²×D₄	1	2	yes	complemented
267	C₃⋊C₈	—	2	1	no	—
268	C₃⋊C₈	—	2	1	no	—
269	C₂×C₃²	—	2	4	no	—
270	C₂×C₃²	—	2	4	no	—
271	C₂×C₃²	—	2	4	no	—
272	C₂×C₃²	—	4	8	no	—
273	C₂×C₃²	—	4	1	no	—
274	C₂×C₃²	—	4	4	no	—
275	C₂×C₃²	—	12	1	no	—
276	C₂×C₃²	D₃×M₁₆	1	1	yes	characteristic
277	C₂×C₃²	#907	1	1	yes	characteristic
278	C₂×C₃²	C₄×#67	1	1	yes	characteristic
279	C₂×C₃²	C₃×C₄×D₄	1	4	yes	—
280	C₂×C₃²	C₂×C₃×M₁₆	1	4	yes	—
281	C₂×C₃²	C₃×#131	1	4	yes	—
282	C₃×D₃	—	4	4	no	—
283	C₂×D₄	—	3	1	no	—
284	C₂²×C₄	—	3	1	no	—
285	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
286	M₁₆	—	2	2	no	—
287	M₁₆	—	6	2	no	—
288	C₂×C₈	—	3	1	no	—
289	C₂×C₈	—	3	1	no	—
290	C₂×C₈	C₂×C₃²×D₃	1	1	yes	characteristic
291	C₂×C₈	C₂×C₃²×D₃	1	1	yes	characteristic
292	C₄⋊C₄	—	3	1	no	—
293	C₂²⋊C₄	—	3	1	no	—
294	C₂²⋊C₄	—	3	1	no	—
295	C₄²	—	3	1	no	—
296	C₂²×C₃	—	2	8	no	—
297	C₂²×C₃	—	2	4	no	—
298	C₂²×C₃	—	2	4	no	—
299	C₂²×C₃	—	2	4	no	—
300	C₂²×C₃	—	2	1	no	—
301	C₂²×C₃	—	2	1	no	—
302	C₂²×C₃	—	2	1	no	—
303	C₂²×C₃	—	2	4	no	—
304	C₂²×C₃	—	4	4	no	—
305	C₂²×C₃	—	4	4	no	—
306	C₂²×C₃	—	6	4	no	—
307	C₂²×C₃	—	6	4	no	—
308	C₂²×C₃	—	6	4	no	—
309	C₂²×C₃	C₂×C₃×C₄×D₃	1	4	yes	—
310	C₂²×C₃	C₂²×C₃²×C₄	1	1	yes	characteristic
311	C₂×D₃	—	2	1	no	—
312	C₂×D₃	—	2	1	no	—
313	C₂×D₃	—	2	1	no	—
314	C₃×C₄	—	2	8	no	—
315	C₃×C₄	—	2	4	no	—
316	C₃×C₄	—	2	1	no	—
317	C₃×C₄	—	2	4	no	—
318	C₃×C₄	—	2	4	no	—
319	C₃×C₄	—	3	8	no	—
320	C₃×C₄	—	6	4	no	—
321	C₃×C₄	—	6	4	no	—
322	C₃×C₄	C₃×#235	1	4	yes	—
323	C₃×C₄	C₂×C₃×#67	1	4	yes	—
324	C₃×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
325	C₃×C₄	C₃²×#41	1	1	yes	characteristic
326	Dic₃	—	2	1	no	—
327	Dic₃	—	2	1	no	—
328	Dic₃	C₃²×M₁₆	1	2	yes	complemented
329	C₃²	—	2	4	no	—
330	C₃²	#5128	1	1	yes	characteristic, direct product factor
331	C₃²	C₃×#436	1	4	yes	complemented
332	C₂³	—	3	1	no	—
333	C₂³	C₃²×C₄×D₃	1	1	yes	characteristic
334	D₄	—	6	2	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	3	1	no	—
338	C₂×C₄	—	3	1	no	—
339	C₂×C₄	—	3	1	no	—
340	C₂×C₄	—	6	1	no	—
341	C₂×C₄	—	6	1	no	—
342	C₂×C₄	C₃²×C₄×D₃	1	1	yes	characteristic
343	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
344	C₈	—	2	1	no	—
345	C₈	—	6	1	no	—
346	C₈	—	6	1	no	—
347	C₈	C₃²×#67	1	2	yes	complemented
348	C₂×C₃	—	2	4	no	—
349	C₂×C₃	—	2	4	no	—
350	C₂×C₃	—	2	4	no	—
351	C₂×C₃	—	4	8	no	—
352	C₂×C₃	—	4	4	no	—
353	C₂×C₃	—	4	1	no	—
354	C₂×C₃	—	12	4	no	—
355	C₂×C₃	C₃×D₃×M₁₆	1	4	yes	—
356	C₂×C₃	C₃×#907	1	4	yes	—
357	C₂×C₃	C₃×C₄×#67	1	4	yes	—
358	C₂×C₃	C₃²×C₄×D₄	1	1	yes	characteristic
359	C₂×C₃	C₂×C₃²×M₁₆	1	1	yes	characteristic
360	C₂×C₃	C₃²×#131	1	1	yes	characteristic
361	D₃	—	4	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	6	1	no	—
366	C₂²	—	6	1	no	—
367	C₂²	—	6	1	no	—
368	C₂²	C₂×C₃²×C₄×D₃	1	1	yes	characteristic
369	C₄	—	2	1	no	—
370	C₄	—	3	2	no	—
371	C₄	—	6	1	no	—
372	C₄	—	6	1	no	—
373	C₄	C₃²×#235	1	1	yes	characteristic
374	C₄	C₂×C₃²×#67	1	1	yes	characteristic
375	C₃	—	2	4	no	—
376	C₃	C₃×#5128	1	4	yes	direct product factor
377	C₃	C₃²×#436	1	1	yes	characteristic, complemented
378	C₂	—	4	1	no	—
379	C₂	—	12	1	no	—
380	C₂	C₃²×D₃×M₁₆	1	1	yes	characteristic
381	C₂	C₃²×#907	1	1	yes	characteristic
382	C₂	C₃²×C₄×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃²×C₄	C₂²×D₃
commutator	C₂²×C₃	C₂²×C₃²×C₄
Frattini	C₂×C₄	C₂²×C₃²×D₃
Fitting	C₂×C₃³×M₁₆	C₂
socle	C₂²×C₃³	C₂²×C₄
prime radical	C₂×C₃²×#67	C₄
cosocle	C₂×C₃×C₄	C₂³×C₃²
hypercenter	C₂×C₃²×M₁₆	D₃
hypocenter	C₃	C₃²×#436
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃²×C₄ ◁ C₂×C₃²×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×C₃³×M₁₆	C₂	semidirect
3. C₂×C₃²×ΓL(1,𝔽₂₅)	C₂	semidirect
4. C₃²×#830	C₂	semidirect
5. C₃²×(C₂×D₃)⋊C₈	C₂	semidirect
6. C₃²×Dic₃⋊C₈	C₂	semidirect
7. C₃²×C₈×Dic₃	C₂	semidirect
9. C₃×#5128	C₃	direct (N × H)
25. C₂×C₃²×M₁₆	D₃	semidirect
26. C₂×C₃²×M₁₆	C₂×C₃	semidirect
29. C₂×C₃×ΓL(1,𝔽₂₅)	C₂×C₃	semidirect
34. C₃×#830	C₂×C₃	semidirect
35. C₃×(C₂×D₃)⋊C₈	C₂×C₃	semidirect
36. C₃×Dic₃⋊C₈	C₂×C₃	semidirect
37. C₃×C₈×Dic₃	C₂×C₃	semidirect
51. C₃³×C₈	D₄	semidirect
55. #5128	C₃²	direct (N × H)
98. C₃²×Dic₃	M₁₆	semidirect
101. C₂×C₃×M₁₆	C₃×D₃	semidirect
102. C₂×C₃×M₁₆	C₂×C₃²	semidirect
105. C₂×ΓL(1,𝔽₂₅)	C₂×C₃²	semidirect
110. #830	C₂×C₃²	semidirect
111. (C₂×D₃)⋊C₈	C₂×C₃²	semidirect
112. Dic₃⋊C₈	C₂×C₃²	semidirect
113. C₈×Dic₃	C₂×C₃²	semidirect
149. C₃²×C₈	#67	semidirect
150. C₃²×C₈	C₃×D₄	semidirect
221. C₃×Dic₃	C₃×M₁₆	semidirect
223. C₂×M₁₆	C₃²×D₃	semidirect
229. C₃³	#436	semidirect
265. C₃×C₈	C₃×#67	semidirect
266. C₃×C₈	C₃²×D₄	semidirect
328. Dic₃	C₃²×M₁₆	semidirect
330. C₃²	#5128	direct (N × H)
331. C₃²	C₃×#436	semidirect
347. C₈	C₃²×#67	semidirect
376. C₃	C₃×#5128	direct (N × H)
377. C₃	C₃²×#436	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃³×M₁₆	2
C₃²×C₄×#67	2
C₂×C₃²×ΓL(1,𝔽₂₅)	2
C₃²×#830	2
C₃²×(C₂×D₃)⋊C₈	2
C₃²×Dic₃⋊C₈	2
C₃²×C₈×Dic₃	2
C₃²×#436	3
C₃×#5128	3

Subgroups — C32×#5128 #13162555

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5128 #13162555