Subgroups — C₂×C₃×#2920 #10678724

Order 768.

2806 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₄²	C₂	1	1	yes	maximal, characteristic
2	C₃×#2920	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₃×#432	C₂	1	4	yes	maximal, complemented
4	C₂×C₃×#431	C₂	1	4	yes	maximal, complemented
5	C₂×C₃×#423	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#407	C₂	1	2	yes	maximal
7	C₂×C₃×C₄×M₁₆	C₂	1	2	yes	maximal, complemented
8	C₂×#2920	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₂⁴×C₃×C₄	C₄	1	2	yes	—
10	C₂⁴×C₃×C₄	C₂²	1	1	yes	characteristic
11	C₂²×C₃×M₁₆	C₂²	1	4	yes	—
12	C₂²×C₃×C₄²	C₄	1	8	yes	—
13	C₂²×C₃×C₄²	C₄	1	2	yes	—
14	C₂²×C₃×C₄²	C₄	1	2	yes	—
15	C₂²×C₃×C₄²	C₄	1	2	yes	—
16	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₄²	C₂²	1	2	yes	—
18	C₂²×C₃×C₄²	C₂²	1	8	yes	—
19	C₂²×C₃×C₄²	C₂²	1	2	yes	—
20	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
21	C₃×#432	C₂²	1	32	yes	complemented
22	C₃×#431	C₂²	1	32	yes	complemented
23	C₃×#423	C₂²	1	16	yes	complemented
24	C₂×C₃×C₄⋊C₈	C₂²	1	8	yes	complemented
25	C₃×#407	C₂²	1	16	yes	—
26	C₂×C₃×C₂²⋊C₈	C₂²	1	8	yes	—
27	C₃×C₄×M₁₆	C₂²	1	16	yes	complemented
28	C₂×C₃×#97	C₂²	1	4	yes	complemented
29	C₂×C₃×C₄×C₈	C₂²	1	4	yes	complemented
30	C₂³×C₄²	C₂×C₃	1	1	yes	characteristic
31	#2920	C₂×C₃	1	16	yes	direct product factor
32	C₂×#432	C₂×C₃	1	4	yes	complemented
33	C₂×#431	C₂×C₃	1	4	yes	complemented
34	C₂×#423	C₂×C₃	1	2	yes	complemented
35	C₂×#407	C₂×C₃	1	2	yes	—
36	C₂×C₄×M₁₆	C₂×C₃	1	2	yes	complemented
37	C₂⁵×C₃	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₃×C₄	—	2	16	no	—
39	C₂³×C₃×C₄	—	2	8	no	—
40	C₂³×C₃×C₄	C₂×C₄	1	2	yes	—
41	C₂³×C₃×C₄	C₂×C₄	1	2	yes	—
42	C₂³×C₃×C₄	C₂×C₄	1	2	yes	—
43	C₂³×C₃×C₄	C₂×C₄	1	2	yes	—
44	C₂³×C₃×C₄	C₂×C₄	1	2	yes	—
45	C₂³×C₃×C₄	C₂×C₄	1	16	yes	—
46	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₃×C₄	C₂×C₄	1	4	yes	—
48	C₂³×C₃×C₄	C₂×C₄	1	2	yes	—
49	C₂³×C₃×C₄	C₂×C₄	1	2	yes	—
50	C₂³×C₃×C₄	C₂³	1	2	yes	—
51	C₂³×C₃×C₄	C₂³	1	4	yes	—
52	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
53	C₂×C₃×M₁₆	—	2	16	no	—
54	C₂×C₃×M₁₆	C₂³	1	16	yes	—
55	C₂²×C₃×C₈	C₂³	1	8	yes	—
56	C₂×C₃×C₄²	C₂×C₄	1	2	yes	—
57	C₂×C₃×C₄²	C₂×C₄	1	8	yes	—
58	C₂×C₃×C₄²	C₂×C₄	1	16	yes	—
59	C₂×C₃×C₄²	C₂×C₄	1	16	yes	—
60	C₂×C₃×C₄²	C₂×C₄	1	2	yes	—
61	C₂×C₃×C₄²	C₂×C₄	1	2	yes	—
62	C₂×C₃×C₄²	C₂×C₄	1	16	yes	—
63	C₂×C₃×C₄²	C₂×C₄	1	2	yes	—
64	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
65	C₂×C₃×C₄²	C₂×C₄	1	4	yes	—
66	C₂×C₃×C₄²	C₂×C₄	1	2	yes	—
67	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
68	C₂×C₃×C₄²	C₂×C₄	1	8	yes	—
69	C₂×C₃×C₄²	C₂×C₄	1	4	yes	—
70	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₄²	C₂³	1	4	yes	—
72	C₂×C₃×C₄²	C₂³	1	2	yes	—
73	C₂×C₃×C₄²	C₂³	1	4	yes	—
74	C₂×C₃×C₄²	C₂³	1	8	yes	—
75	C₂×C₃×C₄²	C₂³	1	8	yes	—
76	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
77	C₃×C₄⋊C₈	C₂³	1	32	yes	complemented
78	C₃×C₂²⋊C₈	C₂³	1	32	yes	—
79	C₃×#97	C₂³	1	16	yes	complemented
80	C₃×C₄×C₈	C₂³	1	16	yes	complemented
81	C₂⁴×C₄	C₃×C₄	1	2	yes	—
82	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic
83	C₂²×M₁₆	C₂²×C₃	1	4	yes	—
84	C₂²×C₄²	C₃×C₄	1	8	yes	—
85	C₂²×C₄²	C₃×C₄	1	2	yes	—
86	C₂²×C₄²	C₃×C₄	1	2	yes	—
87	C₂²×C₄²	C₃×C₄	1	2	yes	—
88	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
89	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
90	C₂²×C₄²	C₂²×C₃	1	2	yes	—
91	C₂²×C₄²	C₂²×C₃	1	2	yes	—
92	C₂²×C₄²	C₂²×C₃	1	8	yes	—
93	#432	C₂²×C₃	1	32	yes	complemented
94	#431	C₂²×C₃	1	32	yes	complemented
95	#423	C₂²×C₃	1	16	yes	complemented
96	C₂×C₄⋊C₈	C₂²×C₃	1	8	yes	complemented
97	#407	C₂²×C₃	1	16	yes	—
98	C₂×C₂²⋊C₈	C₂²×C₃	1	8	yes	—
99	C₄×M₁₆	C₂²×C₃	1	16	yes	complemented
100	C₂×#97	C₂²×C₃	1	4	yes	complemented
101	C₂×C₄×C₈	C₂²×C₃	1	4	yes	complemented
102	C₂⁴×C₃	—	2	4	no	—
103	C₂⁴×C₃	—	2	8	no	—
104	C₂⁴×C₃	C₂²×C₄	1	4	yes	—
105	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
106	C₂⁴×C₃	C₂²×C₄	1	2	yes	—
107	C₂²×C₃×C₄	—	2	4	no	—
108	C₂²×C₃×C₄	—	2	8	no	—
109	C₂²×C₃×C₄	—	2	16	no	—
110	C₂²×C₃×C₄	—	2	8	no	—
111	C₂²×C₃×C₄	—	2	8	no	—
112	C₂²×C₃×C₄	—	2	8	no	—
113	C₂²×C₃×C₄	—	2	8	no	—
114	C₂²×C₃×C₄	—	2	8	no	—
115	C₂²×C₃×C₄	—	2	64	no	—
116	C₂²×C₃×C₄	—	2	8	no	—
117	C₂²×C₃×C₄	—	2	16	no	—
118	C₂²×C₃×C₄	M₁₆	1	16	yes	complemented
119	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
120	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
121	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
122	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
123	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
124	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
125	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
126	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
127	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
128	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
129	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
130	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
131	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
133	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
134	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
135	C₂²×C₃×C₄	#41	1	8	yes	—
136	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
137	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
138	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
139	C₃×M₁₆	—	2	32	no	—
140	C₂×C₃×C₈	—	2	16	no	—
141	C₂×C₃×C₈	C₂⁴	1	16	yes	—
142	C₃×C₄²	C₂²×C₄	1	8	yes	—
143	C₃×C₄²	C₂²×C₄	1	8	yes	—
144	C₃×C₄²	C₂²×C₄	1	8	yes	—
145	C₃×C₄²	C₂²×C₄	1	8	yes	—
146	C₃×C₄²	C₂²×C₄	1	2	yes	—
147	C₃×C₄²	C₂²×C₄	1	4	yes	—
148	C₃×C₄²	C₂²×C₄	1	8	yes	—
149	C₃×C₄²	C₂²×C₄	1	4	yes	—
150	C₃×C₄²	C₂²×C₄	1	4	yes	—
151	C₃×C₄²	C₂²×C₄	1	2	yes	—
152	C₃×C₄²	C₂⁴	1	2	yes	—
153	C₃×C₄²	C₂⁴	1	2	yes	—
154	C₃×C₄²	C₂⁴	1	4	yes	—
155	C₂⁵	C₂×C₃×C₄	1	1	yes	characteristic
156	C₂³×C₄	—	2	16	no	—
157	C₂³×C₄	—	2	8	no	—
158	C₂³×C₄	C₂×C₃×C₄	1	2	yes	—
159	C₂³×C₄	C₂×C₃×C₄	1	2	yes	—
160	C₂³×C₄	C₂×C₃×C₄	1	2	yes	—
161	C₂³×C₄	C₂×C₃×C₄	1	2	yes	—
162	C₂³×C₄	C₂×C₃×C₄	1	2	yes	—
163	C₂³×C₄	C₂×C₃×C₄	1	16	yes	—
164	C₂³×C₄	C₂×C₃×C₄	1	1	yes	characteristic
165	C₂³×C₄	C₂×C₃×C₄	1	4	yes	—
166	C₂³×C₄	C₂×C₃×C₄	1	2	yes	—
167	C₂³×C₄	C₂×C₃×C₄	1	2	yes	—
168	C₂³×C₄	C₂³×C₃	1	2	yes	—
169	C₂³×C₄	C₂³×C₃	1	4	yes	—
170	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
171	C₂×M₁₆	—	2	16	no	—
172	C₂×M₁₆	C₂³×C₃	1	16	yes	—
173	C₂²×C₈	C₂³×C₃	1	8	yes	—
174	C₂×C₄²	C₂×C₃×C₄	1	2	yes	—
175	C₂×C₄²	C₂×C₃×C₄	1	8	yes	—
176	C₂×C₄²	C₂×C₃×C₄	1	16	yes	—
177	C₂×C₄²	C₂×C₃×C₄	1	16	yes	—
178	C₂×C₄²	C₂×C₃×C₄	1	2	yes	—
179	C₂×C₄²	C₂×C₃×C₄	1	2	yes	—
180	C₂×C₄²	C₂×C₃×C₄	1	8	yes	—
181	C₂×C₄²	C₂×C₃×C₄	1	16	yes	—
182	C₂×C₄²	C₂×C₃×C₄	1	2	yes	—
183	C₂×C₄²	C₂×C₃×C₄	1	4	yes	—
184	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
185	C₂×C₄²	C₂×C₃×C₄	1	4	yes	—
186	C₂×C₄²	C₂×C₃×C₄	1	2	yes	—
187	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
188	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
189	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
190	C₂×C₄²	C₂³×C₃	1	4	yes	—
191	C₂×C₄²	C₂³×C₃	1	2	yes	—
192	C₂×C₄²	C₂³×C₃	1	4	yes	—
193	C₂×C₄²	C₂³×C₃	1	8	yes	—
194	C₂×C₄²	C₂³×C₃	1	8	yes	—
195	C₄⋊C₈	C₂³×C₃	1	32	yes	complemented
196	C₂²⋊C₈	C₂³×C₃	1	32	yes	—
197	#97	C₂³×C₃	1	16	yes	complemented
198	C₄×C₈	C₂³×C₃	1	16	yes	complemented
199	C₂³×C₃	—	2	32	no	—
200	C₂³×C₃	—	2	8	no	—
201	C₂³×C₃	—	2	4	no	—
202	C₂³×C₃	—	2	16	no	—
203	C₂³×C₃	—	2	4	no	—
204	C₂³×C₃	—	2	4	no	—
205	C₂³×C₃	#117	1	4	yes	—
206	C₂³×C₃	C₂×M₁₆	1	8	yes	—
207	C₂³×C₃	C₂³×C₄	1	2	yes	—
208	C₂³×C₃	C₂³×C₄	1	4	yes	—
209	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
210	C₂×C₃×C₄	—	2	8	no	—
211	C₂×C₃×C₄	—	2	4	no	—
212	C₂×C₃×C₄	—	2	16	no	—
213	C₂×C₃×C₄	—	2	4	no	—
214	C₂×C₃×C₄	—	2	4	no	—
215	C₂×C₃×C₄	—	2	8	no	—
216	C₂×C₃×C₄	—	2	16	no	—
217	C₂×C₃×C₄	—	2	16	no	—
218	C₂×C₃×C₄	—	2	16	no	—
219	C₂×C₃×C₄	—	2	16	no	—
220	C₂×C₃×C₄	—	2	16	no	—
221	C₂×C₃×C₄	—	2	8	no	—
222	C₂×C₃×C₄	#117	1	8	yes	—
223	C₂×C₃×C₄	#117	1	4	yes	—
224	C₂×C₃×C₄	C₂×M₁₆	1	8	yes	—
225	C₂×C₃×C₄	C₂×M₁₆	1	8	yes	—
226	C₂×C₃×C₄	C₂×M₁₆	1	32	yes	complemented
227	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
228	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
229	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
230	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
231	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
232	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
233	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
234	C₂×C₃×C₄	C₂×#41	1	4	yes	—
235	C₂×C₃×C₄	C₂×#41	1	8	yes	—
236	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
237	C₃×C₈	—	2	16	no	—
238	C₂⁴	—	2	4	no	—
239	C₂⁴	—	2	8	no	—
240	C₂⁴	C₂²×C₃×C₄	1	4	yes	—
241	C₂⁴	C₂²×C₃×C₄	1	1	yes	characteristic
242	C₂⁴	C₂²×C₃×C₄	1	2	yes	—
243	C₂²×C₄	—	2	4	no	—
244	C₂²×C₄	—	2	8	no	—
245	C₂²×C₄	—	2	16	no	—
246	C₂²×C₄	—	2	8	no	—
247	C₂²×C₄	—	2	8	no	—
248	C₂²×C₄	—	2	8	no	—
249	C₂²×C₄	—	2	8	no	—
250	C₂²×C₄	—	2	8	no	—
251	C₂²×C₄	—	2	64	no	—
252	C₂²×C₄	—	2	8	no	—
253	C₂²×C₄	—	2	16	no	—
254	C₂²×C₄	C₃×M₁₆	1	16	yes	complemented
255	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
256	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
257	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
258	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
259	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
260	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
261	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
262	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
263	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
264	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
265	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
266	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
267	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
268	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
269	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
270	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
271	C₂²×C₄	C₃×#41	1	8	yes	—
272	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
273	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
274	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
275	M₁₆	—	2	32	no	—
276	C₂×C₈	—	2	16	no	—
277	C₂×C₈	C₂⁴×C₃	1	16	yes	—
278	C₄²	C₂²×C₃×C₄	1	8	yes	—
279	C₄²	C₂²×C₃×C₄	1	8	yes	—
280	C₄²	C₂²×C₃×C₄	1	8	yes	—
281	C₄²	C₂²×C₃×C₄	1	8	yes	—
282	C₄²	C₂²×C₃×C₄	1	2	yes	—
283	C₄²	C₂²×C₃×C₄	1	4	yes	—
284	C₄²	C₂²×C₃×C₄	1	8	yes	—
285	C₄²	C₂²×C₃×C₄	1	4	yes	—
286	C₄²	C₂²×C₃×C₄	1	2	yes	—
287	C₄²	C₂²×C₃×C₄	1	4	yes	—
288	C₄²	C₂⁴×C₃	1	2	yes	—
289	C₄²	C₂⁴×C₃	1	2	yes	—
290	C₄²	C₂⁴×C₃	1	4	yes	—
291	C₂²×C₃	—	2	32	no	—
292	C₂²×C₃	—	2	4	no	—
293	C₂²×C₃	—	2	8	no	—
294	C₂²×C₃	—	2	16	no	—
295	C₂²×C₃	—	2	4	no	—
296	C₂²×C₃	—	2	4	no	—
297	C₂²×C₃	C₂×#117	1	4	yes	—
298	C₂²×C₃	C₂×#117	1	2	yes	—
299	C₂²×C₃	C₂²×M₁₆	1	8	yes	—
300	C₂²×C₃	C₂²×M₁₆	1	4	yes	—
301	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
302	C₃×C₄	—	2	4	no	—
303	C₃×C₄	—	2	4	no	—
304	C₃×C₄	—	2	4	no	—
305	C₃×C₄	C₂×#117	1	2	yes	—
306	C₃×C₄	C₂×#117	1	4	yes	—
307	C₃×C₄	C₂²×M₁₆	1	8	yes	—
308	C₃×C₄	C₂²×M₁₆	1	8	yes	—
309	C₃×C₄	C₂²×#41	1	2	yes	—
310	C₂³	—	2	32	no	—
311	C₂³	—	2	16	no	—
312	C₂³	—	2	4	no	—
313	C₂³	—	2	4	no	—
314	C₂³	—	2	8	no	—
315	C₂³	—	2	4	no	—
316	C₂³	C₃×#117	1	4	yes	—
317	C₂³	C₂×C₃×M₁₆	1	8	yes	—
318	C₂³	C₂³×C₃×C₄	1	4	yes	—
319	C₂³	C₂³×C₃×C₄	1	2	yes	—
320	C₂³	C₂³×C₃×C₄	1	1	yes	characteristic
321	C₂×C₄	—	2	16	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	8	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	16	no	—
327	C₂×C₄	—	2	16	no	—
328	C₂×C₄	—	2	16	no	—
329	C₂×C₄	—	2	16	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	2	16	no	—
333	C₂×C₄	C₃×#117	1	8	yes	—
334	C₂×C₄	C₃×#117	1	4	yes	—
335	C₂×C₄	C₂×C₃×M₁₆	1	8	yes	—
336	C₂×C₄	C₂×C₃×M₁₆	1	8	yes	—
337	C₂×C₄	C₂×C₃×M₁₆	1	32	yes	complemented
338	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
339	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
340	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
341	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
342	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
343	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
344	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
345	C₂×C₄	C₂×C₃×#41	1	4	yes	—
346	C₂×C₄	C₂×C₃×#41	1	8	yes	—
347	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
348	C₈	—	2	16	no	—
349	C₂×C₃	—	2	4	no	—
350	C₂×C₃	—	2	8	no	—
351	C₂×C₃	#2920	1	4	yes	direct product factor
352	C₂×C₃	C₂²×#117	1	1	yes	characteristic
353	C₂×C₃	C₂³×M₁₆	1	2	yes	—
354	C₂²	—	2	32	no	—
355	C₂²	—	2	4	no	—
356	C₂²	—	2	8	no	—
357	C₂²	—	2	16	no	—
358	C₂²	—	2	4	no	—
359	C₂²	—	2	4	no	—
360	C₂²	C₂×C₃×#117	1	4	yes	—
361	C₂²	C₂×C₃×#117	1	2	yes	—
362	C₂²	C₂²×C₃×M₁₆	1	8	yes	—
363	C₂²	C₂²×C₃×M₁₆	1	4	yes	—
364	C₂²	C₂⁴×C₃×C₄	1	1	yes	characteristic
365	C₄	—	2	4	no	—
366	C₄	—	2	4	no	—
367	C₄	—	2	4	no	—
368	C₄	C₂×C₃×#117	1	2	yes	—
369	C₄	C₂×C₃×#117	1	4	yes	—
370	C₄	C₂²×C₃×M₁₆	1	8	yes	—
371	C₄	C₂²×C₃×M₁₆	1	8	yes	—
372	C₄	C₂²×C₃×#41	1	2	yes	—
373	C₃	C₂×#2920	1	1	yes	characteristic, direct product factor, Sylow
374	C₂	—	2	8	no	—
375	C₂	—	2	4	no	—
376	C₂	C₃×#2920	1	4	yes	direct product factor
377	C₂	C₂²×C₃×#117	1	1	yes	characteristic
378	C₂	C₂³×C₃×M₁₆	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄²	C₂³
commutator	C₂²	C₂⁴×C₃×C₄
Frattini, cosocle	C₂×C₄	C₂⁵×C₃
socle	C₂³×C₃	C₂³×C₄
prime radical	C₂⁵×C₃	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#2920	C₂	direct (N × H)
3. C₂×C₃×#432	C₂	semidirect
4. C₂×C₃×#431	C₂	semidirect
5. C₂×C₃×#423	C₂	semidirect
7. C₂×C₃×C₄×M₁₆	C₂	semidirect
8. C₂×#2920	C₃	direct (N × H)
21. C₃×#432	C₂²	semidirect
22. C₃×#431	C₂²	semidirect
23. C₃×#423	C₂²	semidirect
24. C₂×C₃×C₄⋊C₈	C₂²	semidirect
27. C₃×C₄×M₁₆	C₂²	semidirect
28. C₂×C₃×#97	C₂²	semidirect
29. C₂×C₃×C₄×C₈	C₂²	semidirect
31. #2920	C₂×C₃	direct (N × H)
32. C₂×#432	C₂×C₃	semidirect
33. C₂×#431	C₂×C₃	semidirect
34. C₂×#423	C₂×C₃	semidirect
36. C₂×C₄×M₁₆	C₂×C₃	semidirect
77. C₃×C₄⋊C₈	C₂³	semidirect
79. C₃×#97	C₂³	semidirect
80. C₃×C₄×C₈	C₂³	semidirect
93. #432	C₂²×C₃	semidirect
94. #431	C₂²×C₃	semidirect
95. #423	C₂²×C₃	semidirect
96. C₂×C₄⋊C₈	C₂²×C₃	semidirect
99. C₄×M₁₆	C₂²×C₃	semidirect
100. C₂×#97	C₂²×C₃	semidirect
101. C₂×C₄×C₈	C₂²×C₃	semidirect
118. C₂²×C₃×C₄	M₁₆	semidirect
195. C₄⋊C₈	C₂³×C₃	semidirect
197. #97	C₂³×C₃	semidirect
198. C₄×C₈	C₂³×C₃	semidirect
226. C₂×C₃×C₄	C₂×M₁₆	semidirect
254. C₂²×C₄	C₃×M₁₆	semidirect
337. C₂×C₄	C₂×C₃×M₁₆	semidirect
351. C₂×C₃	#2920	direct (N × H)
373. C₃	C₂×#2920	direct (N × H)
376. C₂	C₃×#2920	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	2
C₃×#2920	2
C₂×C₃×#432	2
C₂×C₃×#431	2
C₂×C₃×#423	2
C₂×C₃×#407	2
C₂×C₃×C₄×M₁₆	2
C₂×#2920	3

Subgroups — C2×C3×#2920 #10678724

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#2920 #10678724