Subgroups — C₂×C₂₃×#2967 #19207825

Order 5888.

1970 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#529	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2967	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₂₃×#446	C₂	1	2	yes	maximal, complemented
4	C₂×C₂₃×#436	C₂	1	2	yes	maximal, complemented
5	C₂×C₂₃×#435	C₂	1	2	yes	maximal, complemented
6	C₂×C₂₃×#435	C₂	1	2	yes	maximal, complemented
7	C₂×C₂₃×#433	C₂	1	2	yes	maximal, complemented
8	C₂×C₂₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#405	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	—
12	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	—
13	C₂³×C₈×C₂₃	C₂²	1	2	yes	—
14	C₂₃×#529	C₄	1	8	yes	—
15	C₂₃×#529	C₂²	1	8	yes	—
16	C₂×C₂₃×#126	C₄	1	2	yes	—
17	C₂×C₂₃×#125	C₄	1	1	yes	characteristic
18	C₂×C₂₃×#124	C₄	1	1	yes	characteristic
19	C₂×C₂₃×#123	C₄	1	2	yes	—
20	C₂×C₂₃×C₂²⋊Q₈	C₄	1	1	yes	characteristic
21	C₂×C₂₃×#121	C₄	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
25	C₂×C₂₃×#117	C₂²	1	2	yes	—
26	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
27	C₂₃×#446	C₂²	1	16	yes	complemented
28	C₂₃×#436	C₂²	1	16	yes	complemented
29	C₂₃×#435	C₂²	1	16	yes	complemented
30	C₂₃×#435	C₂²	1	16	yes	complemented
31	C₂₃×#433	C₂²	1	16	yes	complemented
32	C₂₃×#432	C₂²	1	8	yes	complemented
33	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
34	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
35	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
36	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
39	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
40	C₂₃×#405	C₂²	1	16	yes	complemented
41	C₄×M₁₆×C₂₃	C₂²	1	8	yes	complemented
42	C₂×C₂₃×#97	C₂²	1	2	yes	—
43	C₂×C₂₃×#97	C₂²	1	2	yes	—
44	C₂×C₂₃×#97	C₂²	1	2	yes	—
45	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
47	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
48	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
49	C₂²×D₄×C₂₃	C₂×C₄	1	2	yes	—
50	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
55	C₂×M₁₆×C₂₃	—	2	8	no	—
56	C₂×M₁₆×C₂₃	—	2	8	no	—
57	C₂×M₁₆×C₂₃	C₂³	1	8	yes	—
58	C₂×M₁₆×C₂₃	C₂³	1	8	yes	—
59	C₂²×C₈×C₂₃	—	2	8	no	—
60	C₂²×C₈×C₂₃	C₂³	1	8	yes	—
61	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
62	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
63	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
64	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
65	C₂₃×#126	C₂×C₄	1	16	yes	—
66	C₂₃×#125	C₂×C₄	1	8	yes	—
67	C₂₃×#124	C₂×C₄	1	8	yes	—
68	C₂₃×#123	C₂×C₄	1	16	yes	—
69	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
70	C₂₃×#121	C₂×C₄	1	8	yes	—
71	C₄×Q₈×C₂₃	C₂×C₄	1	4	yes	—
72	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
73	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
74	C₄×D₄×C₂₃	C₂×C₄	1	8	yes	—
75	C₄×D₄×C₂₃	C₂³	1	4	yes	—
76	C₄×D₄×C₂₃	C₂³	1	8	yes	—
77	C₂₃×#117	C₂×C₄	1	8	yes	—
78	C₂₃×#117	C₂³	1	8	yes	—
79	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
80	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
81	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
83	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
85	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
86	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
87	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
88	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
89	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
90	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₂₃	C₂×C₄	1	4	yes	—
93	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
94	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
96	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
97	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
98	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
99	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
100	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
101	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
102	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	—
103	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	—
104	C₂₃×#97	C₂³	1	8	yes	—
105	C₂₃×#97	C₂³	1	8	yes	—
106	C₂₃×#97	C₂³	1	8	yes	—
107	C₄×C₈×C₂₃	C₂³	1	4	yes	—
108	C₄×C₈×C₂₃	C₂³	1	4	yes	—
109	C₄×C₈×C₂₃	C₂³	1	8	yes	—
110	C₂⁴×C₂₃	C₂²×C₄	1	2	yes	—
111	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×Q₈×C₂₃	—	4	2	no	—
113	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
114	C₂×D₄×C₂₃	—	4	2	no	—
115	C₂×D₄×C₂₃	—	4	4	no	—
116	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
117	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
118	C₂²×C₄×C₂₃	—	2	4	no	—
119	C₂²×C₄×C₂₃	—	2	4	no	—
120	C₂²×C₄×C₂₃	—	2	4	no	—
121	C₂²×C₄×C₂₃	—	4	2	no	—
122	C₂²×C₄×C₂₃	—	4	2	no	—
123	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
130	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
133	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
134	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
135	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
136	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
138	M₁₆×C₂₃	—	2	16	no	—
139	M₁₆×C₂₃	—	2	16	no	—
140	C₂×C₈×C₂₃	—	2	4	no	—
141	C₂×C₈×C₂₃	—	2	4	no	—
142	C₂×C₈×C₂₃	—	2	4	no	—
143	C₂×C₈×C₂₃	—	2	16	no	—
144	C₂×C₈×C₂₃	#41	1	8	yes	—
145	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
146	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
147	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
148	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
149	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
150	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
151	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
152	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
153	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
154	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
155	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
156	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
157	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
158	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
159	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
160	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
161	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
162	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
163	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
164	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
165	C₄²×C₂₃	C₂⁴	1	2	yes	—
166	C₄²×C₂₃	C₂⁴	1	4	yes	—
167	C₄²×C₂₃	C₂⁴	1	2	yes	—
168	C₂×#2967	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂³×C₂₃	—	2	4	no	—
170	C₂³×C₂₃	—	2	2	no	—
171	C₂³×C₂₃	—	2	2	no	—
172	C₂³×C₂₃	—	2	2	no	—
173	C₂³×C₂₃	—	2	4	no	—
174	C₂³×C₂₃	—	2	4	no	—
175	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
176	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
177	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
178	Q₈×C₂₃	—	4	4	no	—
179	D₄×C₂₃	—	4	4	no	—
180	D₄×C₂₃	—	4	8	no	—
181	C₂×C₄×C₂₃	—	2	4	no	—
182	C₂×C₄×C₂₃	—	2	2	no	—
183	C₂×C₄×C₂₃	—	2	2	no	—
184	C₂×C₄×C₂₃	—	2	2	no	—
185	C₂×C₄×C₂₃	—	2	2	no	—
186	C₂×C₄×C₂₃	—	2	2	no	—
187	C₂×C₄×C₂₃	—	2	4	no	—
188	C₂×C₄×C₂₃	—	2	4	no	—
189	C₂×C₄×C₂₃	—	2	8	no	—
190	C₂×C₄×C₂₃	—	2	4	no	—
191	C₂×C₄×C₂₃	—	2	4	no	—
192	C₂×C₄×C₂₃	—	2	4	no	—
193	C₂×C₄×C₂₃	—	2	4	no	—
194	C₂×C₄×C₂₃	—	4	4	no	—
195	C₂×C₄×C₂₃	—	4	4	no	—
196	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
197	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
198	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
199	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
200	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
201	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
202	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
203	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
204	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
206	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
207	C₈×C₂₃	—	2	4	no	—
208	C₈×C₂₃	—	2	4	no	—
209	C₈×C₂₃	—	2	4	no	—
210	C₈×C₂₃	C₂×#41	1	8	yes	—
211	C₂×#529	C₂×C₂₃	1	1	yes	characteristic
212	#2967	C₂×C₂₃	1	16	yes	direct product factor
213	C₂×#446	C₂×C₂₃	1	2	yes	complemented
214	C₂×#436	C₂×C₂₃	1	2	yes	complemented
215	C₂×#435	C₂×C₂₃	1	2	yes	complemented
216	C₂×#435	C₂×C₂₃	1	2	yes	complemented
217	C₂×#433	C₂×C₂₃	1	2	yes	complemented
218	C₂×#432	C₂×C₂₃	1	1	yes	characteristic, complemented
219	C₂×#405	C₂×C₂₃	1	2	yes	complemented
220	C₂×C₄×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
221	C₂²×C₂₃	—	2	4	no	—
222	C₂²×C₂₃	—	2	2	no	—
223	C₂²×C₂₃	—	2	2	no	—
224	C₂²×C₂₃	—	2	2	no	—
225	C₂²×C₂₃	—	2	4	no	—
226	C₂²×C₂₃	—	2	4	no	—
227	C₂²×C₂₃	—	4	4	no	—
228	C₂²×C₂₃	—	4	8	no	—
229	C₂²×C₂₃	C₄×#41	1	2	yes	—
230	C₂²×C₂₃	#568	1	2	yes	—
231	C₂²×C₂₃	#568	1	2	yes	—
232	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
233	C₄×C₂₃	—	2	4	no	—
234	C₄×C₂₃	—	2	2	no	—
235	C₄×C₂₃	—	2	2	no	—
236	C₄×C₂₃	—	2	2	no	—
237	C₄×C₂₃	—	2	2	no	—
238	C₄×C₂₃	—	2	2	no	—
239	C₄×C₂₃	—	2	4	no	—
240	C₄×C₂₃	—	2	4	no	—
241	C₄×C₂₃	C₄×#41	1	2	yes	—
242	C₄×C₂₃	C₂²×#41	1	2	yes	—
243	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	—
244	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	—
245	C₂³×C₈	C₂²×C₂₃	1	2	yes	—
246	#529	C₄×C₂₃	1	8	yes	—
247	#529	C₂²×C₂₃	1	8	yes	—
248	C₂×#126	C₄×C₂₃	1	2	yes	—
249	C₂×#125	C₄×C₂₃	1	1	yes	characteristic
250	C₂×#124	C₄×C₂₃	1	1	yes	characteristic
251	C₂×#123	C₄×C₂₃	1	2	yes	—
252	C₂×C₂²⋊Q₈	C₄×C₂₃	1	1	yes	characteristic
253	C₂×#121	C₄×C₂₃	1	1	yes	characteristic
254	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
255	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
256	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
257	C₂×#117	C₂²×C₂₃	1	2	yes	—
258	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
259	#446	C₂²×C₂₃	1	16	yes	complemented
260	#436	C₂²×C₂₃	1	16	yes	complemented
261	#435	C₂²×C₂₃	1	16	yes	complemented
262	#435	C₂²×C₂₃	1	16	yes	complemented
263	#433	C₂²×C₂₃	1	16	yes	complemented
264	#432	C₂²×C₂₃	1	8	yes	complemented
265	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
266	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
267	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
268	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
269	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
270	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
271	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
272	#405	C₂²×C₂₃	1	16	yes	complemented
273	C₄×M₁₆	C₂²×C₂₃	1	8	yes	complemented
274	C₂×#97	C₂²×C₂₃	1	2	yes	—
275	C₂×#97	C₂²×C₂₃	1	2	yes	—
276	C₂×#97	C₂²×C₂₃	1	2	yes	—
277	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
278	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
279	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
280	C₂×C₂₃	—	4	2	no	—
281	C₂×C₂₃	—	4	4	no	—
282	C₂×C₂₃	#2967	1	4	yes	direct product factor
283	C₂×C₂₃	C₂×C₄×#41	1	1	yes	characteristic
284	C₂×C₂₃	C₂×#568	1	1	yes	characteristic
285	C₂×C₂₃	C₂×#568	1	1	yes	characteristic
286	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
287	C₂²×D₄	C₂×C₄×C₂₃	1	2	yes	—
288	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
289	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
290	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
291	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
292	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
293	C₂×M₁₆	—	2	8	no	—
294	C₂×M₁₆	—	2	8	no	—
295	C₂×M₁₆	C₂³×C₂₃	1	8	yes	—
296	C₂×M₁₆	C₂³×C₂₃	1	8	yes	—
297	C₂²×C₈	—	2	8	no	—
298	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
299	C₂²×C₈	C₂³×C₂₃	1	8	yes	—
300	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
301	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
302	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
303	#126	C₂×C₄×C₂₃	1	16	yes	—
304	#125	C₂×C₄×C₂₃	1	8	yes	—
305	#124	C₂×C₄×C₂₃	1	8	yes	—
306	#123	C₂×C₄×C₂₃	1	16	yes	—
307	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	—
308	#121	C₂×C₄×C₂₃	1	8	yes	—
309	C₄×Q₈	C₂×C₄×C₂₃	1	4	yes	—
310	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
311	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
312	C₄×D₄	C₂×C₄×C₂₃	1	8	yes	—
313	C₄×D₄	C₂³×C₂₃	1	4	yes	—
314	C₄×D₄	C₂³×C₂₃	1	8	yes	—
315	#117	C₂×C₄×C₂₃	1	8	yes	—
316	#117	C₂³×C₂₃	1	8	yes	—
317	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
318	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
319	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
320	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
321	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
323	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
324	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
325	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
326	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
327	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
328	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
329	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
330	C₂×C₄²	C₂×C₄×C₂₃	1	4	yes	—
331	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
332	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
333	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
334	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
335	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
336	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
337	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
338	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
339	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
340	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	—
341	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	—
342	#97	C₂³×C₂₃	1	8	yes	—
343	#97	C₂³×C₂₃	1	8	yes	—
344	#97	C₂³×C₂₃	1	8	yes	—
345	C₄×C₈	C₂³×C₂₃	1	4	yes	—
346	C₄×C₈	C₂³×C₂₃	1	4	yes	—
347	C₄×C₈	C₂³×C₂₃	1	8	yes	—
348	C₂₃	C₂×#2967	1	1	yes	characteristic, direct product factor, Sylow
349	C₂⁴	C₂²×C₄×C₂₃	1	2	yes	—
350	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
351	C₂×Q₈	—	4	2	no	—
352	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
353	C₂×D₄	—	4	2	no	—
354	C₂×D₄	—	4	4	no	—
355	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
356	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	4	2	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
363	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
364	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
365	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
366	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
367	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
368	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
369	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
370	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
371	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
372	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
373	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
374	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
375	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
376	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
377	M₁₆	—	2	16	no	—
378	M₁₆	—	2	16	no	—
379	C₂×C₈	—	2	4	no	—
380	C₂×C₈	—	2	4	no	—
381	C₂×C₈	—	2	4	no	—
382	C₂×C₈	—	2	16	no	—
383	C₂×C₈	#41×C₂₃	1	8	yes	—
384	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
385	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
386	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
387	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
388	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
389	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
390	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
391	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
392	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
393	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
394	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
395	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
396	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
397	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
398	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
399	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
400	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
401	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
402	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
403	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
404	C₄²	C₂⁴×C₂₃	1	2	yes	—
405	C₄²	C₂⁴×C₂₃	1	4	yes	—
406	C₄²	C₂⁴×C₂₃	1	2	yes	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	4	no	—
410	C₂³	—	2	4	no	—
411	C₂³	—	2	4	no	—
412	C₂³	—	2	2	no	—
413	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
414	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
415	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
416	Q₈	—	4	4	no	—
417	D₄	—	4	4	no	—
418	D₄	—	4	8	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	8	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	4	4	no	—
433	C₂×C₄	—	4	4	no	—
434	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
435	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
436	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
437	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
438	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
439	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
440	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
441	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
442	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
443	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
444	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
445	C₈	—	2	4	no	—
446	C₈	—	2	4	no	—
447	C₈	—	2	4	no	—
448	C₈	C₂×#41×C₂₃	1	8	yes	—
449	C₂²	—	2	4	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	4	no	—
454	C₂²	—	2	4	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	8	no	—
457	C₂²	C₄×#41×C₂₃	1	2	yes	—
458	C₂²	C₂₃×#568	1	2	yes	—
459	C₂²	C₂₃×#568	1	2	yes	—
460	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
461	C₄	—	2	4	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	2	no	—
465	C₄	—	2	2	no	—
466	C₄	—	2	2	no	—
467	C₄	—	2	4	no	—
468	C₄	—	2	4	no	—
469	C₄	C₄×#41×C₂₃	1	2	yes	—
470	C₄	C₂²×#41×C₂₃	1	2	yes	—
471	C₂	—	4	2	no	—
472	C₂	—	4	4	no	—
473	C₂	C₂₃×#2967	1	4	yes	direct product factor
474	C₂	C₂×C₄×#41×C₂₃	1	1	yes	characteristic
475	C₂	C₂×C₂₃×#568	1	1	yes	characteristic
476	C₂	C₂×C₂₃×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂³×C₂₃	C₂³×C₄
prime radical	C₂×C₂₃×#121	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2967	C₂	direct (N × H)
3. C₂×C₂₃×#446	C₂	semidirect
4. C₂×C₂₃×#436	C₂	semidirect
5. C₂×C₂₃×#435	C₂	semidirect
6. C₂×C₂₃×#435	C₂	semidirect
7. C₂×C₂₃×#433	C₂	semidirect
8. C₂×C₂₃×#432	C₂	semidirect
9. C₂×C₂₃×#405	C₂	semidirect
10. C₂×C₄×M₁₆×C₂₃	C₂	semidirect
27. C₂₃×#446	C₂²	semidirect
28. C₂₃×#436	C₂²	semidirect
29. C₂₃×#435	C₂²	semidirect
30. C₂₃×#435	C₂²	semidirect
31. C₂₃×#433	C₂²	semidirect
32. C₂₃×#432	C₂²	semidirect
40. C₂₃×#405	C₂²	semidirect
41. C₄×M₁₆×C₂₃	C₂²	semidirect
168. C₂×#2967	C₂₃	direct (N × H)
212. #2967	C₂×C₂₃	direct (N × H)
213. C₂×#446	C₂×C₂₃	semidirect
214. C₂×#436	C₂×C₂₃	semidirect
215. C₂×#435	C₂×C₂₃	semidirect
216. C₂×#435	C₂×C₂₃	semidirect
217. C₂×#433	C₂×C₂₃	semidirect
218. C₂×#432	C₂×C₂₃	semidirect
219. C₂×#405	C₂×C₂₃	semidirect
220. C₂×C₄×M₁₆	C₂×C₂₃	semidirect
259. #446	C₂²×C₂₃	semidirect
260. #436	C₂²×C₂₃	semidirect
261. #435	C₂²×C₂₃	semidirect
262. #435	C₂²×C₂₃	semidirect
263. #433	C₂²×C₂₃	semidirect
264. #432	C₂²×C₂₃	semidirect
272. #405	C₂²×C₂₃	semidirect
273. C₄×M₁₆	C₂²×C₂₃	semidirect
282. C₂×C₂₃	#2967	direct (N × H)
348. C₂₃	C₂×#2967	direct (N × H)
473. C₂	C₂₃×#2967	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#529	2
C₂₃×#2967	2
C₂×C₂₃×#446	2
C₂×C₂₃×#436	2
C₂×C₂₃×#435	2
C₂×C₂₃×#433	2
C₂×C₂₃×#432	2
C₂×C₂₃×#405	2
C₂×C₄×M₁₆×C₂₃	2
C₂×#2967	23

Subgroups — C2×C23×#2967 #19207825

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#2967 #19207825