Subgroups — C₂³×C₃×C₄²×C₁₆ #72185331

Order 6144.

155088 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	C₂³×C₃×C₄²×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×C₃×C₄×C₁₆	C₂	1	6	yes	maximal
3	C₂²×C₃×C₄²×C₁₆	C₂	1	56	yes	maximal, direct product factor
4	C₂³×C₄²×C₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂³×C₃×C₄³	C₄	1	1	yes	characteristic
6	C₂⁴×C₃×C₄×C₈	C₄	1	3	yes	—
7	C₂⁴×C₃×C₄×C₈	C₂²	1	3	yes	—
8	C₂²×C₃×C₄²×C₈	C₄	1	28	yes	—
9	C₂²×C₃×C₄²×C₈	C₂²	1	28	yes	—
10	C₂³×C₃×C₄×C₁₆	C₄	1	192	yes	direct product factor
11	C₂³×C₃×C₄×C₁₆	C₂²	1	168	yes	—
12	C₂⁵×C₃×C₁₆	C₂²	1	4	yes	—
13	C₂×C₃×C₄²×C₁₆	C₂²	1	448	yes	direct product factor
14	C₂³×C₄²×C₈	C₂×C₃	1	1	yes	characteristic
15	C₂⁴×C₄×C₁₆	C₂×C₃	1	6	yes	—
16	C₂²×C₄²×C₁₆	C₂×C₃	1	56	yes	direct product factor
17	C₂⁵×C₃×C₈	C₂×C₄	1	3	yes	—
18	C₂⁵×C₃×C₈	C₂³	1	1	yes	characteristic
19	C₂⁴×C₃×C₄²	C₈	1	4	yes	—
20	C₂⁴×C₃×C₄²	C₂×C₄	1	3	yes	—
21	C₂⁴×C₃×C₁₆	C₂×C₄	1	192	yes	—
22	C₂⁴×C₃×C₁₆	C₂³	1	56	yes	—
23	C₂³×C₃×C₄×C₈	C₈	1	96	yes	—
24	C₂³×C₃×C₄×C₈	C₂×C₄	1	42	yes	—
25	C₂³×C₃×C₄×C₈	C₂×C₄	1	84	yes	—
26	C₂³×C₃×C₄×C₈	C₂×C₄	1	96	yes	—
27	C₂³×C₃×C₄×C₈	C₂³	1	42	yes	—
28	C₂²×C₃×C₄³	C₈	1	28	yes	—
29	C₂²×C₃×C₄³	C₂×C₄	1	28	yes	—
30	C₂²×C₃×C₄×C₁₆	C₂×C₄	1	2688	yes	direct product factor
31	C₂²×C₃×C₄×C₁₆	C₂³	1	672	yes	—
32	C₂×C₃×C₄²×C₈	C₂×C₄	1	336	yes	—
33	C₂×C₃×C₄²×C₈	C₂³	1	112	yes	—
34	C₃×C₄²×C₁₆	C₂³	1	512	yes	direct product factor
35	C₂⁵×C₁₆	C₂²×C₃	1	4	yes	—
36	C₂⁴×C₄×C₈	C₃×C₄	1	3	yes	—
37	C₂⁴×C₄×C₈	C₂²×C₃	1	3	yes	—
38	C₂³×C₄³	C₃×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₆	C₃×C₄	1	192	yes	direct product factor
40	C₂³×C₄×C₁₆	C₂²×C₃	1	168	yes	—
41	C₂²×C₄²×C₈	C₃×C₄	1	28	yes	—
42	C₂²×C₄²×C₈	C₂²×C₃	1	28	yes	—
43	C₂×C₄²×C₁₆	C₂²×C₃	1	448	yes	direct product factor
44	C₂⁵×C₃×C₄	C₂×C₈	1	6	yes	—
45	C₂⁵×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
46	C₂⁴×C₃×C₈	C₄²	1	48	yes	—
47	C₂⁴×C₃×C₈	C₂×C₈	1	96	yes	—
48	C₂⁴×C₃×C₈	C₂²×C₄	1	7	yes	—
49	C₂⁴×C₃×C₈	C₂²×C₄	1	42	yes	—
50	C₂⁴×C₃×C₈	C₂²×C₄	1	48	yes	—
51	C₂⁴×C₃×C₈	C₂⁴	1	7	yes	—
52	C₂³×C₃×C₄²	C₁₆	1	128	yes	direct product factor
53	C₂³×C₃×C₄²	C₄²	1	48	yes	—
54	C₂³×C₃×C₄²	C₂×C₈	1	42	yes	—
55	C₂³×C₃×C₄²	C₂×C₈	1	48	yes	—
56	C₂³×C₃×C₄²	C₂×C₈	1	112	yes	—
57	C₂³×C₃×C₄²	C₂²×C₄	1	42	yes	—
58	C₂³×C₃×C₁₆	C₄²	1	1024	yes	direct product factor
59	C₂³×C₃×C₁₆	C₂²×C₄	1	1344	yes	—
60	C₂³×C₃×C₁₆	C₂⁴	1	112	yes	—
61	C₂²×C₃×C₄×C₈	C₄²	1	672	yes	—
62	C₂²×C₃×C₄×C₈	C₂×C₈	1	1344	yes	—
63	C₂²×C₃×C₄×C₈	C₂²×C₄	1	336	yes	—
64	C₂²×C₃×C₄×C₈	C₂²×C₄	1	672	yes	—
65	C₂²×C₃×C₄×C₈	C₂²×C₄	1	252	yes	—
66	C₂²×C₃×C₄×C₈	C₂⁴	1	84	yes	—
67	C₂×C₃×C₄³	C₂×C₈	1	336	yes	—
68	C₂×C₃×C₄³	C₂²×C₄	1	112	yes	—
69	C₂×C₃×C₄×C₁₆	C₂²×C₄	1	5376	yes	direct product factor
70	C₂×C₃×C₄×C₁₆	C₂⁴	1	384	yes	—
71	C₃×C₄²×C₈	C₂²×C₄	1	448	yes	—
72	C₃×C₄²×C₈	C₂⁴	1	64	yes	—
73	C₂⁵×C₈	C₂×C₃×C₄	1	3	yes	—
74	C₂⁵×C₈	C₂³×C₃	1	1	yes	characteristic
75	C₂⁴×C₄²	C₃×C₈	1	4	yes	—
76	C₂⁴×C₄²	C₂×C₃×C₄	1	3	yes	—
77	C₂⁴×C₁₆	C₂×C₃×C₄	1	192	yes	—
78	C₂⁴×C₁₆	C₂³×C₃	1	56	yes	—
79	C₂³×C₄×C₈	C₃×C₈	1	96	yes	—
80	C₂³×C₄×C₈	C₂×C₃×C₄	1	42	yes	—
81	C₂³×C₄×C₈	C₂×C₃×C₄	1	84	yes	—
82	C₂³×C₄×C₈	C₂×C₃×C₄	1	96	yes	—
83	C₂³×C₄×C₈	C₂³×C₃	1	42	yes	—
84	C₂²×C₄³	C₃×C₈	1	28	yes	—
85	C₂²×C₄³	C₂×C₃×C₄	1	28	yes	—
86	C₂²×C₄×C₁₆	C₂×C₃×C₄	1	2688	yes	direct product factor
87	C₂²×C₄×C₁₆	C₂³×C₃	1	672	yes	—
88	C₂×C₄²×C₈	C₂×C₃×C₄	1	336	yes	—
89	C₂×C₄²×C₈	C₂³×C₃	1	112	yes	—
90	C₄²×C₁₆	C₂³×C₃	1	512	yes	direct product factor
91	C₂⁶×C₃	C₂²×C₈	1	1	yes	characteristic
92	C₂⁴×C₃×C₄	C₄×C₈	1	96	yes	—
93	C₂⁴×C₃×C₄	C₂×C₁₆	1	192	yes	—
94	C₂⁴×C₃×C₄	C₂×C₄²	1	24	yes	—
95	C₂⁴×C₃×C₄	C₂²×C₈	1	7	yes	—
96	C₂⁴×C₃×C₄	C₂²×C₈	1	24	yes	—
97	C₂⁴×C₃×C₄	C₂²×C₈	1	84	yes	—
98	C₂⁴×C₃×C₄	C₂³×C₄	1	7	yes	—
99	C₂³×C₃×C₈	C₄×C₈	1	768	yes	—
100	C₂³×C₃×C₈	C₂×C₄²	1	256	yes	—
101	C₂³×C₃×C₈	C₂×C₄²	1	336	yes	—
102	C₂³×C₃×C₈	C₂×C₄²	1	168	yes	—
103	C₂³×C₃×C₈	C₂²×C₈	1	672	yes	—
104	C₂³×C₃×C₈	C₂³×C₄	1	21	yes	—
105	C₂³×C₃×C₈	C₂³×C₄	1	84	yes	—
106	C₂³×C₃×C₈	C₂³×C₄	1	168	yes	—
107	C₂³×C₃×C₈	C₂⁵	1	7	yes	—
108	C₂²×C₃×C₄²	C₄×C₈	1	672	yes	—
109	C₂²×C₃×C₄²	C₂×C₁₆	1	1792	yes	direct product factor
110	C₂²×C₃×C₄²	C₂×C₄²	1	336	yes	—
111	C₂²×C₃×C₄²	C₂²×C₈	1	336	yes	—
112	C₂²×C₃×C₄²	C₂²×C₈	1	448	yes	—
113	C₂²×C₃×C₄²	C₂²×C₈	1	252	yes	—
114	C₂²×C₃×C₄²	C₂³×C₄	1	84	yes	—
115	C₂²×C₃×C₁₆	C₂×C₄²	1	3584	yes	direct product factor
116	C₂²×C₃×C₁₆	C₂³×C₄	1	1344	yes	—
117	C₂²×C₃×C₁₆	C₂⁵	1	32	yes	—
118	C₂×C₃×C₄×C₈	C₂×C₄²	1	2016	yes	—
119	C₂×C₃×C₄×C₈	C₂²×C₈	1	2688	yes	—
120	C₂×C₃×C₄×C₈	C₂³×C₄	1	672	yes	—
121	C₂×C₃×C₄×C₈	C₂³×C₄	1	168	yes	—
122	C₂×C₃×C₄×C₈	C₂³×C₄	1	192	yes	—
123	C₂×C₃×C₄×C₈	C₂⁵	1	24	yes	—
124	C₃×C₄³	C₂²×C₈	1	448	yes	—
125	C₃×C₄³	C₂³×C₄	1	64	yes	—
126	C₃×C₄×C₁₆	C₂³×C₄	1	1536	yes	direct product factor
127	C₂⁵×C₄	C₂×C₃×C₈	1	6	yes	—
128	C₂⁵×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
129	C₂⁴×C₈	C₃×C₄²	1	48	yes	—
130	C₂⁴×C₈	C₂×C₃×C₈	1	96	yes	—
131	C₂⁴×C₈	C₂²×C₃×C₄	1	7	yes	—
132	C₂⁴×C₈	C₂²×C₃×C₄	1	42	yes	—
133	C₂⁴×C₈	C₂²×C₃×C₄	1	48	yes	—
134	C₂⁴×C₈	C₂⁴×C₃	1	7	yes	—
135	C₂³×C₄²	C₃×C₁₆	1	128	yes	direct product factor
136	C₂³×C₄²	C₃×C₄²	1	48	yes	—
137	C₂³×C₄²	C₂×C₃×C₈	1	42	yes	—
138	C₂³×C₄²	C₂×C₃×C₈	1	48	yes	—
139	C₂³×C₄²	C₂×C₃×C₈	1	112	yes	—
140	C₂³×C₄²	C₂²×C₃×C₄	1	42	yes	—
141	C₂³×C₁₆	C₃×C₄²	1	1024	yes	direct product factor
142	C₂³×C₁₆	C₂²×C₃×C₄	1	1344	yes	—
143	C₂³×C₁₆	C₂⁴×C₃	1	112	yes	—
144	C₂²×C₄×C₈	C₃×C₄²	1	672	yes	—
145	C₂²×C₄×C₈	C₂×C₃×C₈	1	1344	yes	—
146	C₂²×C₄×C₈	C₂²×C₃×C₄	1	336	yes	—
147	C₂²×C₄×C₈	C₂²×C₃×C₄	1	672	yes	—
148	C₂²×C₄×C₈	C₂²×C₃×C₄	1	252	yes	—
149	C₂²×C₄×C₈	C₂⁴×C₃	1	84	yes	—
150	C₂×C₄³	C₂×C₃×C₈	1	336	yes	—
151	C₂×C₄³	C₂²×C₃×C₄	1	112	yes	—
152	C₂×C₄×C₁₆	C₂²×C₃×C₄	1	5376	yes	direct product factor
153	C₂×C₄×C₁₆	C₂⁴×C₃	1	384	yes	—
154	C₄²×C₈	C₂²×C₃×C₄	1	448	yes	—
155	C₄²×C₈	C₂⁴×C₃	1	64	yes	—
156	C₂⁵×C₃	C₂×C₄×C₈	1	24	yes	—
157	C₂⁵×C₃	C₂²×C₁₆	1	32	yes	—
158	C₂⁵×C₃	C₂³×C₈	1	7	yes	—
159	C₂³×C₃×C₄	C₄×C₁₆	1	1536	yes	direct product factor
160	C₂³×C₃×C₄	C₄³	1	64	yes	—
161	C₂³×C₃×C₄	C₂×C₄×C₈	1	672	yes	—
162	C₂³×C₃×C₄	C₂×C₄×C₈	1	168	yes	—
163	C₂³×C₃×C₄	C₂×C₄×C₈	1	192	yes	—
164	C₂³×C₃×C₄	C₂²×C₁₆	1	1344	yes	—
165	C₂³×C₃×C₄	C₂²×C₄²	1	84	yes	—
166	C₂³×C₃×C₄	C₂³×C₈	1	21	yes	—
167	C₂³×C₃×C₄	C₂³×C₈	1	84	yes	—
168	C₂³×C₃×C₄	C₂³×C₈	1	168	yes	—
169	C₂³×C₃×C₄	C₂⁴×C₄	1	7	yes	—
170	C₂²×C₃×C₈	C₄³	1	448	yes	—
171	C₂²×C₃×C₈	C₂×C₄×C₈	1	2688	yes	—
172	C₂²×C₃×C₈	C₂²×C₄²	1	336	yes	—
173	C₂²×C₃×C₈	C₂²×C₄²	1	448	yes	—
174	C₂²×C₃×C₈	C₂²×C₄²	1	252	yes	—
175	C₂²×C₃×C₈	C₂³×C₈	1	672	yes	—
176	C₂²×C₃×C₈	C₂⁴×C₄	1	7	yes	—
177	C₂²×C₃×C₈	C₂⁴×C₄	1	24	yes	—
178	C₂²×C₃×C₈	C₂⁴×C₄	1	84	yes	—
179	C₂²×C₃×C₈	C₂⁶	1	1	yes	characteristic
180	C₂×C₃×C₄²	C₂×C₄×C₈	1	2016	yes	—
181	C₂×C₃×C₄²	C₂²×C₁₆	1	3584	yes	direct product factor
182	C₂×C₃×C₄²	C₂²×C₄²	1	336	yes	—
183	C₂×C₃×C₄²	C₂³×C₈	1	256	yes	—
184	C₂×C₃×C₄²	C₂³×C₈	1	336	yes	—
185	C₂×C₃×C₄²	C₂³×C₈	1	168	yes	—
186	C₂×C₃×C₄²	C₂⁴×C₄	1	24	yes	—
187	C₂×C₃×C₁₆	C₂²×C₄²	1	1792	yes	direct product factor
188	C₂×C₃×C₁₆	C₂⁴×C₄	1	192	yes	—
189	C₃×C₄×C₈	C₂²×C₄²	1	672	yes	—
190	C₃×C₄×C₈	C₂³×C₈	1	768	yes	—
191	C₃×C₄×C₈	C₂⁴×C₄	1	96	yes	—
192	C₂⁶	C₂²×C₃×C₈	1	1	yes	characteristic
193	C₂⁴×C₄	C₃×C₄×C₈	1	96	yes	—
194	C₂⁴×C₄	C₂×C₃×C₁₆	1	192	yes	—
195	C₂⁴×C₄	C₂×C₃×C₄²	1	24	yes	—
196	C₂⁴×C₄	C₂²×C₃×C₈	1	7	yes	—
197	C₂⁴×C₄	C₂²×C₃×C₈	1	24	yes	—
198	C₂⁴×C₄	C₂²×C₃×C₈	1	84	yes	—
199	C₂⁴×C₄	C₂³×C₃×C₄	1	7	yes	—
200	C₂³×C₈	C₃×C₄×C₈	1	768	yes	—
201	C₂³×C₈	C₂×C₃×C₄²	1	256	yes	—
202	C₂³×C₈	C₂×C₃×C₄²	1	336	yes	—
203	C₂³×C₈	C₂×C₃×C₄²	1	168	yes	—
204	C₂³×C₈	C₂²×C₃×C₈	1	672	yes	—
205	C₂³×C₈	C₂³×C₃×C₄	1	21	yes	—
206	C₂³×C₈	C₂³×C₃×C₄	1	84	yes	—
207	C₂³×C₈	C₂³×C₃×C₄	1	168	yes	—
208	C₂³×C₈	C₂⁵×C₃	1	7	yes	—
209	C₂²×C₄²	C₃×C₄×C₈	1	672	yes	—
210	C₂²×C₄²	C₂×C₃×C₁₆	1	1792	yes	direct product factor
211	C₂²×C₄²	C₂×C₃×C₄²	1	336	yes	—
212	C₂²×C₄²	C₂²×C₃×C₈	1	336	yes	—
213	C₂²×C₄²	C₂²×C₃×C₈	1	448	yes	—
214	C₂²×C₄²	C₂²×C₃×C₈	1	252	yes	—
215	C₂²×C₄²	C₂³×C₃×C₄	1	84	yes	—
216	C₂²×C₁₆	C₂×C₃×C₄²	1	3584	yes	direct product factor
217	C₂²×C₁₆	C₂³×C₃×C₄	1	1344	yes	—
218	C₂²×C₁₆	C₂⁵×C₃	1	32	yes	—
219	C₂×C₄×C₈	C₂×C₃×C₄²	1	2016	yes	—
220	C₂×C₄×C₈	C₂²×C₃×C₈	1	2688	yes	—
221	C₂×C₄×C₈	C₂³×C₃×C₄	1	672	yes	—
222	C₂×C₄×C₈	C₂³×C₃×C₄	1	168	yes	—
223	C₂×C₄×C₈	C₂³×C₃×C₄	1	192	yes	—
224	C₂×C₄×C₈	C₂⁵×C₃	1	24	yes	—
225	C₄³	C₂²×C₃×C₈	1	448	yes	—
226	C₄³	C₂³×C₃×C₄	1	64	yes	—
227	C₄×C₁₆	C₂³×C₃×C₄	1	1536	yes	direct product factor
228	C₂⁴×C₃	C₄²×C₈	1	64	yes	—
229	C₂⁴×C₃	C₂×C₄×C₁₆	1	384	yes	—
230	C₂⁴×C₃	C₂²×C₄×C₈	1	84	yes	—
231	C₂⁴×C₃	C₂³×C₁₆	1	112	yes	—
232	C₂⁴×C₃	C₂⁴×C₈	1	7	yes	—
233	C₂²×C₃×C₄	C₄²×C₈	1	448	yes	—
234	C₂²×C₃×C₄	C₂×C₄×C₁₆	1	5376	yes	direct product factor
235	C₂²×C₃×C₄	C₂×C₄³	1	112	yes	—
236	C₂²×C₃×C₄	C₂²×C₄×C₈	1	336	yes	—
237	C₂²×C₃×C₄	C₂²×C₄×C₈	1	672	yes	—
238	C₂²×C₃×C₄	C₂²×C₄×C₈	1	252	yes	—
239	C₂²×C₃×C₄	C₂³×C₁₆	1	1344	yes	—
240	C₂²×C₃×C₄	C₂³×C₄²	1	42	yes	—
241	C₂²×C₃×C₄	C₂⁴×C₈	1	7	yes	—
242	C₂²×C₃×C₄	C₂⁴×C₈	1	42	yes	—
243	C₂²×C₃×C₄	C₂⁴×C₈	1	48	yes	—
244	C₂²×C₃×C₄	C₂⁵×C₄	1	1	yes	characteristic
245	C₂×C₃×C₈	C₂×C₄³	1	336	yes	—
246	C₂×C₃×C₈	C₂²×C₄×C₈	1	1344	yes	—
247	C₂×C₃×C₈	C₂³×C₄²	1	42	yes	—
248	C₂×C₃×C₈	C₂³×C₄²	1	48	yes	—
249	C₂×C₃×C₈	C₂³×C₄²	1	112	yes	—
250	C₂×C₃×C₈	C₂⁴×C₈	1	96	yes	—
251	C₂×C₃×C₈	C₂⁵×C₄	1	6	yes	—
252	C₃×C₄²	C₂²×C₄×C₈	1	672	yes	—
253	C₃×C₄²	C₂³×C₁₆	1	1024	yes	direct product factor
254	C₃×C₄²	C₂³×C₄²	1	48	yes	—
255	C₃×C₄²	C₂⁴×C₈	1	48	yes	—
256	C₃×C₁₆	C₂³×C₄²	1	128	yes	direct product factor
257	C₂⁵	C₂×C₃×C₄×C₈	1	24	yes	—
258	C₂⁵	C₂²×C₃×C₁₆	1	32	yes	—
259	C₂⁵	C₂³×C₃×C₈	1	7	yes	—
260	C₂³×C₄	C₃×C₄×C₁₆	1	1536	yes	direct product factor
261	C₂³×C₄	C₃×C₄³	1	64	yes	—
262	C₂³×C₄	C₂×C₃×C₄×C₈	1	672	yes	—
263	C₂³×C₄	C₂×C₃×C₄×C₈	1	168	yes	—
264	C₂³×C₄	C₂×C₃×C₄×C₈	1	192	yes	—
265	C₂³×C₄	C₂²×C₃×C₁₆	1	1344	yes	—
266	C₂³×C₄	C₂²×C₃×C₄²	1	84	yes	—
267	C₂³×C₄	C₂³×C₃×C₈	1	21	yes	—
268	C₂³×C₄	C₂³×C₃×C₈	1	84	yes	—
269	C₂³×C₄	C₂³×C₃×C₈	1	168	yes	—
270	C₂³×C₄	C₂⁴×C₃×C₄	1	7	yes	—
271	C₂²×C₈	C₃×C₄³	1	448	yes	—
272	C₂²×C₈	C₂×C₃×C₄×C₈	1	2688	yes	—
273	C₂²×C₈	C₂²×C₃×C₄²	1	336	yes	—
274	C₂²×C₈	C₂²×C₃×C₄²	1	448	yes	—
275	C₂²×C₈	C₂²×C₃×C₄²	1	252	yes	—
276	C₂²×C₈	C₂³×C₃×C₈	1	672	yes	—
277	C₂²×C₈	C₂⁴×C₃×C₄	1	7	yes	—
278	C₂²×C₈	C₂⁴×C₃×C₄	1	24	yes	—
279	C₂²×C₈	C₂⁴×C₃×C₄	1	84	yes	—
280	C₂²×C₈	C₂⁶×C₃	1	1	yes	characteristic
281	C₂×C₄²	C₂×C₃×C₄×C₈	1	2016	yes	—
282	C₂×C₄²	C₂²×C₃×C₁₆	1	3584	yes	direct product factor
283	C₂×C₄²	C₂²×C₃×C₄²	1	336	yes	—
284	C₂×C₄²	C₂³×C₃×C₈	1	256	yes	—
285	C₂×C₄²	C₂³×C₃×C₈	1	336	yes	—
286	C₂×C₄²	C₂³×C₃×C₈	1	168	yes	—
287	C₂×C₄²	C₂⁴×C₃×C₄	1	24	yes	—
288	C₂×C₁₆	C₂²×C₃×C₄²	1	1792	yes	direct product factor
289	C₂×C₁₆	C₂⁴×C₃×C₄	1	192	yes	—
290	C₄×C₈	C₂²×C₃×C₄²	1	672	yes	—
291	C₄×C₈	C₂³×C₃×C₈	1	768	yes	—
292	C₄×C₈	C₂⁴×C₃×C₄	1	96	yes	—
293	C₂³×C₃	C₄²×C₁₆	1	512	yes	direct product factor
294	C₂³×C₃	C₂×C₄²×C₈	1	112	yes	—
295	C₂³×C₃	C₂²×C₄×C₁₆	1	672	yes	—
296	C₂³×C₃	C₂³×C₄×C₈	1	42	yes	—
297	C₂³×C₃	C₂⁴×C₁₆	1	56	yes	—
298	C₂³×C₃	C₂⁵×C₈	1	1	yes	characteristic
299	C₂×C₃×C₄	C₂×C₄²×C₈	1	336	yes	—
300	C₂×C₃×C₄	C₂²×C₄×C₁₆	1	2688	yes	direct product factor
301	C₂×C₃×C₄	C₂²×C₄³	1	28	yes	—
302	C₂×C₃×C₄	C₂³×C₄×C₈	1	42	yes	—
303	C₂×C₃×C₄	C₂³×C₄×C₈	1	84	yes	—
304	C₂×C₃×C₄	C₂³×C₄×C₈	1	96	yes	—
305	C₂×C₃×C₄	C₂⁴×C₁₆	1	192	yes	—
306	C₂×C₃×C₄	C₂⁴×C₄²	1	3	yes	—
307	C₂×C₃×C₄	C₂⁵×C₈	1	3	yes	—
308	C₃×C₈	C₂²×C₄³	1	28	yes	—
309	C₃×C₈	C₂³×C₄×C₈	1	96	yes	—
310	C₃×C₈	C₂⁴×C₄²	1	4	yes	—
311	C₂⁴	C₃×C₄²×C₈	1	64	yes	—
312	C₂⁴	C₂×C₃×C₄×C₁₆	1	384	yes	—
313	C₂⁴	C₂²×C₃×C₄×C₈	1	84	yes	—
314	C₂⁴	C₂³×C₃×C₁₆	1	112	yes	—
315	C₂⁴	C₂⁴×C₃×C₈	1	7	yes	—
316	C₂²×C₄	C₃×C₄²×C₈	1	448	yes	—
317	C₂²×C₄	C₂×C₃×C₄×C₁₆	1	5376	yes	direct product factor
318	C₂²×C₄	C₂×C₃×C₄³	1	112	yes	—
319	C₂²×C₄	C₂²×C₃×C₄×C₈	1	336	yes	—
320	C₂²×C₄	C₂²×C₃×C₄×C₈	1	672	yes	—
321	C₂²×C₄	C₂²×C₃×C₄×C₈	1	252	yes	—
322	C₂²×C₄	C₂³×C₃×C₁₆	1	1344	yes	—
323	C₂²×C₄	C₂³×C₃×C₄²	1	42	yes	—
324	C₂²×C₄	C₂⁴×C₃×C₈	1	7	yes	—
325	C₂²×C₄	C₂⁴×C₃×C₈	1	42	yes	—
326	C₂²×C₄	C₂⁴×C₃×C₈	1	48	yes	—
327	C₂²×C₄	C₂⁵×C₃×C₄	1	1	yes	characteristic
328	C₂×C₈	C₂×C₃×C₄³	1	336	yes	—
329	C₂×C₈	C₂²×C₃×C₄×C₈	1	1344	yes	—
330	C₂×C₈	C₂³×C₃×C₄²	1	42	yes	—
331	C₂×C₈	C₂³×C₃×C₄²	1	48	yes	—
332	C₂×C₈	C₂³×C₃×C₄²	1	112	yes	—
333	C₂×C₈	C₂⁴×C₃×C₈	1	96	yes	—
334	C₂×C₈	C₂⁵×C₃×C₄	1	6	yes	—
335	C₄²	C₂²×C₃×C₄×C₈	1	672	yes	—
336	C₄²	C₂³×C₃×C₁₆	1	1024	yes	direct product factor
337	C₄²	C₂³×C₃×C₄²	1	48	yes	—
338	C₄²	C₂⁴×C₃×C₈	1	48	yes	—
339	C₁₆	C₂³×C₃×C₄²	1	128	yes	direct product factor
340	C₂²×C₃	C₂×C₄²×C₁₆	1	448	yes	direct product factor
341	C₂²×C₃	C₂²×C₄²×C₈	1	28	yes	—
342	C₂²×C₃	C₂³×C₄×C₁₆	1	168	yes	—
343	C₂²×C₃	C₂⁴×C₄×C₈	1	3	yes	—
344	C₂²×C₃	C₂⁵×C₁₆	1	4	yes	—
345	C₃×C₄	C₂²×C₄²×C₈	1	28	yes	—
346	C₃×C₄	C₂³×C₄×C₁₆	1	192	yes	direct product factor
347	C₃×C₄	C₂³×C₄³	1	1	yes	characteristic
348	C₃×C₄	C₂⁴×C₄×C₈	1	3	yes	—
349	C₂³	C₃×C₄²×C₁₆	1	512	yes	direct product factor
350	C₂³	C₂×C₃×C₄²×C₈	1	112	yes	—
351	C₂³	C₂²×C₃×C₄×C₁₆	1	672	yes	—
352	C₂³	C₂³×C₃×C₄×C₈	1	42	yes	—
353	C₂³	C₂⁴×C₃×C₁₆	1	56	yes	—
354	C₂³	C₂⁵×C₃×C₈	1	1	yes	characteristic
355	C₂×C₄	C₂×C₃×C₄²×C₈	1	336	yes	—
356	C₂×C₄	C₂²×C₃×C₄×C₁₆	1	2688	yes	direct product factor
357	C₂×C₄	C₂²×C₃×C₄³	1	28	yes	—
358	C₂×C₄	C₂³×C₃×C₄×C₈	1	42	yes	—
359	C₂×C₄	C₂³×C₃×C₄×C₈	1	84	yes	—
360	C₂×C₄	C₂³×C₃×C₄×C₈	1	96	yes	—
361	C₂×C₄	C₂⁴×C₃×C₁₆	1	192	yes	—
362	C₂×C₄	C₂⁴×C₃×C₄²	1	3	yes	—
363	C₂×C₄	C₂⁵×C₃×C₈	1	3	yes	—
364	C₈	C₂²×C₃×C₄³	1	28	yes	—
365	C₈	C₂³×C₃×C₄×C₈	1	96	yes	—
366	C₈	C₂⁴×C₃×C₄²	1	4	yes	—
367	C₂×C₃	C₂²×C₄²×C₁₆	1	56	yes	direct product factor
368	C₂×C₃	C₂⁴×C₄×C₁₆	1	6	yes	—
369	C₂×C₃	C₂³×C₄²×C₈	1	1	yes	characteristic
370	C₂²	C₂×C₃×C₄²×C₁₆	1	448	yes	direct product factor
371	C₂²	C₂⁵×C₃×C₁₆	1	4	yes	—
372	C₂²	C₂³×C₃×C₄×C₁₆	1	168	yes	—
373	C₂²	C₂²×C₃×C₄²×C₈	1	28	yes	—
374	C₂²	C₂⁴×C₃×C₄×C₈	1	3	yes	—
375	C₄	C₂³×C₃×C₄×C₁₆	1	192	yes	direct product factor
376	C₄	C₂²×C₃×C₄²×C₈	1	28	yes	—
377	C₄	C₂⁴×C₃×C₄×C₈	1	3	yes	—
378	C₄	C₂³×C₃×C₄³	1	1	yes	characteristic
379	C₃	C₂³×C₄²×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
380	C₂	C₂²×C₃×C₄²×C₁₆	1	56	yes	direct product factor
381	C₂	C₂⁴×C₃×C₄×C₁₆	1	6	yes	—
382	C₂	C₂³×C₃×C₄²×C₈	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₈	C₂⁶×C₃
socle, prime radical	C₂⁶×C₃	C₂²×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂²×C₃×C₄²×C₁₆	C₂	direct (N × H)
4. C₂³×C₄²×C₁₆	C₃	direct (N × H)
10. C₂³×C₃×C₄×C₁₆	C₄	direct (N × H)
13. C₂×C₃×C₄²×C₁₆	C₂²	direct (N × H)
16. C₂²×C₄²×C₁₆	C₂×C₃	direct (N × H)
30. C₂²×C₃×C₄×C₁₆	C₂×C₄	direct (N × H)
34. C₃×C₄²×C₁₆	C₂³	direct (N × H)
39. C₂³×C₄×C₁₆	C₃×C₄	direct (N × H)
43. C₂×C₄²×C₁₆	C₂²×C₃	direct (N × H)
52. C₂³×C₃×C₄²	C₁₆	direct (N × H)
58. C₂³×C₃×C₁₆	C₄²	direct (N × H)
69. C₂×C₃×C₄×C₁₆	C₂²×C₄	direct (N × H)
86. C₂²×C₄×C₁₆	C₂×C₃×C₄	direct (N × H)
90. C₄²×C₁₆	C₂³×C₃	direct (N × H)
109. C₂²×C₃×C₄²	C₂×C₁₆	direct (N × H)
115. C₂²×C₃×C₁₆	C₂×C₄²	direct (N × H)
126. C₃×C₄×C₁₆	C₂³×C₄	direct (N × H)
135. C₂³×C₄²	C₃×C₁₆	direct (N × H)
141. C₂³×C₁₆	C₃×C₄²	direct (N × H)
152. C₂×C₄×C₁₆	C₂²×C₃×C₄	direct (N × H)
159. C₂³×C₃×C₄	C₄×C₁₆	direct (N × H)
181. C₂×C₃×C₄²	C₂²×C₁₆	direct (N × H)
187. C₂×C₃×C₁₆	C₂²×C₄²	direct (N × H)
210. C₂²×C₄²	C₂×C₃×C₁₆	direct (N × H)
216. C₂²×C₁₆	C₂×C₃×C₄²	direct (N × H)
227. C₄×C₁₆	C₂³×C₃×C₄	direct (N × H)
234. C₂²×C₃×C₄	C₂×C₄×C₁₆	direct (N × H)
253. C₃×C₄²	C₂³×C₁₆	direct (N × H)
256. C₃×C₁₆	C₂³×C₄²	direct (N × H)
260. C₂³×C₄	C₃×C₄×C₁₆	direct (N × H)
282. C₂×C₄²	C₂²×C₃×C₁₆	direct (N × H)
288. C₂×C₁₆	C₂²×C₃×C₄²	direct (N × H)
293. C₂³×C₃	C₄²×C₁₆	direct (N × H)
300. C₂×C₃×C₄	C₂²×C₄×C₁₆	direct (N × H)
317. C₂²×C₄	C₂×C₃×C₄×C₁₆	direct (N × H)
336. C₄²	C₂³×C₃×C₁₆	direct (N × H)
339. C₁₆	C₂³×C₃×C₄²	direct (N × H)
340. C₂²×C₃	C₂×C₄²×C₁₆	direct (N × H)
346. C₃×C₄	C₂³×C₄×C₁₆	direct (N × H)
349. C₂³	C₃×C₄²×C₁₆	direct (N × H)
356. C₂×C₄	C₂²×C₃×C₄×C₁₆	direct (N × H)
367. C₂×C₃	C₂²×C₄²×C₁₆	direct (N × H)
370. C₂²	C₂×C₃×C₄²×C₁₆	direct (N × H)
375. C₄	C₂³×C₃×C₄×C₁₆	direct (N × H)
379. C₃	C₂³×C₄²×C₁₆	direct (N × H)
380. C₂	C₂²×C₃×C₄²×C₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₄²×C₈	2
C₂⁴×C₃×C₄×C₁₆	2
C₂²×C₃×C₄²×C₁₆	2
C₂³×C₄²×C₁₆	3

Subgroups — C23×C3×C42×C16 #72185331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₃×C₄²×C₁₆ #72185331