Subgroups — C₂×C₂₃×#3272 #19208657

Order 5888.

3226 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
2	C₂×C₂₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄²×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3272	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₂₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#468	C₂	1	2	yes	maximal, complemented
7	C₂×C₂₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#449	C₂	1	2	yes	maximal, complemented
10	C₂×C₂₃×#450	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×D₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₂₃	C₂²	1	2	yes	complemented
14	C₂³×D₄×C₂₃	—	2	1	no	—
15	C₂³×D₄×C₂₃	C₂²	1	2	yes	—
16	C₂×C₂₃×AGL(1,ℤ/8)	—	2	16	no	—
17	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	16	yes	complemented
18	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	—
19	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
20	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
21	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
22	C₂²×D₈×C₂₃	C₂²	1	2	yes	complemented
23	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	complemented
24	C₂₃×#547	—	2	4	no	—
25	C₂₃×#547	C₂²	1	8	yes	complemented
26	D₄²×C₂₃	—	2	4	no	—
27	D₄²×C₂₃	C₂²	1	8	yes	complemented
28	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#123	—	2	2	no	—
31	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
32	C₂×C₂₃×#121	—	2	1	no	—
33	C₂×C₂₃×#121	—	2	1	no	—
34	C₂×C₂₃×#121	C₂²	1	2	yes	—
35	C₂×C₂₃×#120	—	2	2	no	—
36	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₄⋊C₄×C₂₃	—	2	1	no	—
40	C₂₃×#492	C₂²	1	8	yes	complemented
41	C₂₃×#468	C₂²	1	16	yes	complemented
42	C₂₃×#461	C₂²	1	8	yes	complemented
43	C₂₃×#459	C₂²	1	8	yes	complemented
44	C₂₃×#450	C₂²	1	16	yes	complemented
45	C₂₃×#449	C₂²	1	16	yes	complemented
46	C₄×D₈×C₂₃	C₂²	1	8	yes	complemented
47	C₂₃×#436	C₂²	1	8	yes	complemented
48	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₂₃×#103	C₂²	1	2	yes	complemented
51	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
52	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₂₃×#102	C₂²	1	2	yes	complemented
54	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
55	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
56	C₂⁵×C₂₃	—	2	2	no	—
57	C₂×#41×C₂₃	—	2	4	no	—
58	C₂×#41×C₂₃	—	2	8	no	—
59	C₂×#41×C₂₃	—	4	4	no	—
60	C₂×#41×C₂₃	C₂³	1	8	yes	complemented
61	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
62	C₂²×D₄×C₂₃	—	2	8	no	—
63	C₂²×D₄×C₂₃	—	2	2	no	—
64	C₂²×D₄×C₂₃	—	2	2	no	—
65	C₂²×D₄×C₂₃	—	2	8	no	—
66	C₂²×D₄×C₂₃	—	2	1	no	—
67	C₂²×D₄×C₂₃	—	2	2	no	—
68	C₂²×D₄×C₂₃	—	2	4	no	—
69	C₂²×D₄×C₂₃	—	2	1	no	—
70	C₂²×D₄×C₂₃	—	4	4	no	—
71	C₂²×D₄×C₂₃	—	4	8	no	—
72	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
73	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
74	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
75	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₂₃	—	2	1	no	—
78	C₂³×C₄×C₂₃	—	2	2	no	—
79	C₂³×C₄×C₂₃	—	2	1	no	—
80	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
81	C₂₃×AGL(1,ℤ/8)	—	2	64	no	—
82	C₂×SD₁₆×C₂₃	—	2	8	no	—
83	C₂×SD₁₆×C₂₃	—	2	8	no	—
84	C₂×SD₁₆×C₂₃	—	4	4	no	—
85	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	—
86	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	complemented
87	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	complemented
88	C₂×D₈×C₂₃	—	2	8	no	—
89	C₂×D₈×C₂₃	D₄	1	8	yes	complemented
90	C₂×D₈×C₂₃	C₂³	1	4	yes	—
91	C₂×D₈×C₂₃	C₂³	1	8	yes	complemented
92	C₂×M₁₆×C₂₃	—	2	8	no	—
93	C₂×M₁₆×C₂₃	C₂³	1	8	yes	complemented
94	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
95	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
97	C₂₃×C₄⋊Q₈	—	2	2	no	—
98	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
99	C₂₃×#127	—	2	2	no	—
100	C₂₃×#127	C₂³	1	4	yes	—
101	C₂₃×#123	—	2	16	no	—
102	C₂₃×C₂²⋊Q₈	—	2	4	no	—
103	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
104	C₂₃×#121	—	2	8	no	—
105	C₂₃×#121	—	2	4	no	—
106	C₂₃×#121	—	2	8	no	—
107	C₂₃×#121	C₂³	1	8	yes	—
108	C₂₃×#120	—	2	16	no	—
109	C₄×D₄×C₂₃	—	2	2	no	—
110	C₄×D₄×C₂₃	—	2	2	no	—
111	C₄×D₄×C₂₃	D₄	1	4	yes	—
112	C₄×D₄×C₂₃	C₂³	1	4	yes	—
113	C₄×D₄×C₂₃	C₂³	1	4	yes	—
114	C₄×D₄×C₂₃	C₂³	1	4	yes	complemented
115	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
116	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
117	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
118	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
119	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
123	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
126	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
127	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
128	C₂₃×#107	C₂³	1	4	yes	complemented
129	C₂₃×C₄⋊C₈	C₂³	1	4	yes	complemented
130	C₂₃×#103	C₂³	1	8	yes	complemented
131	C₂₃×#102	C₂³	1	4	yes	—
132	C₂₃×#102	C₂³	1	4	yes	complemented
133	C₂₃×#102	C₂³	1	8	yes	complemented
134	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	complemented
135	C₄×C₈×C₂₃	C₂³	1	4	yes	complemented
136	C₂⁴×C₂₃	—	2	1	no	—
137	C₂⁴×C₂₃	—	2	1	no	—
138	C₂⁴×C₂₃	—	2	2	no	—
139	C₂⁴×C₂₃	—	2	8	no	—
140	C₂⁴×C₂₃	—	4	8	no	—
141	C₂⁴×C₂₃	—	4	8	no	—
142	C₂⁴×C₂₃	—	8	4	no	—
143	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
144	#41×C₂₃	—	2	16	no	—
145	#41×C₂₃	—	4	8	no	—
146	#41×C₂₃	—	4	16	no	—
147	C₂×Q₈×C₂₃	—	2	2	no	—
148	C₂×Q₈×C₂₃	—	2	4	no	—
149	C₂×Q₈×C₂₃	—	2	4	no	—
150	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
151	C₂×D₄×C₂₃	—	2	16	no	—
152	C₂×D₄×C₂₃	—	2	8	no	—
153	C₂×D₄×C₂₃	—	2	8	no	—
154	C₂×D₄×C₂₃	—	2	4	no	—
155	C₂×D₄×C₂₃	—	2	1	no	—
156	C₂×D₄×C₂₃	—	2	1	no	—
157	C₂×D₄×C₂₃	—	2	4	no	—
158	C₂×D₄×C₂₃	—	2	8	no	—
159	C₂×D₄×C₂₃	—	2	2	no	—
160	C₂×D₄×C₂₃	—	2	4	no	—
161	C₂×D₄×C₂₃	—	2	4	no	—
162	C₂×D₄×C₂₃	—	2	2	no	—
163	C₂×D₄×C₂₃	—	2	2	no	—
164	C₂×D₄×C₂₃	—	2	4	no	—
165	C₂×D₄×C₂₃	—	4	8	no	—
166	C₂×D₄×C₂₃	—	4	16	no	—
167	C₂×D₄×C₂₃	—	4	8	no	—
168	C₂×D₄×C₂₃	—	4	32	no	—
169	C₂×D₄×C₂₃	—	4	8	no	—
170	C₂×D₄×C₂₃	—	4	8	no	—
171	C₂×D₄×C₂₃	—	4	4	no	—
172	C₂×D₄×C₂₃	—	8	2	no	—
173	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
174	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
175	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	complemented
176	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
177	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
178	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₂₃	—	2	4	no	—
180	C₂²×C₄×C₂₃	—	2	4	no	—
181	C₂²×C₄×C₂₃	—	2	1	no	—
182	C₂²×C₄×C₂₃	—	2	1	no	—
183	C₂²×C₄×C₂₃	—	2	2	no	—
184	C₂²×C₄×C₂₃	—	2	4	no	—
185	C₂²×C₄×C₂₃	—	2	8	no	—
186	C₂²×C₄×C₂₃	—	2	4	no	—
187	C₂²×C₄×C₂₃	—	4	8	no	—
188	C₂²×C₄×C₂₃	—	4	4	no	—
189	C₂²×C₄×C₂₃	—	4	4	no	—
190	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
191	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
193	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
196	SD₁₆×C₂₃	—	2	16	no	—
197	SD₁₆×C₂₃	—	2	16	no	—
198	SD₁₆×C₂₃	—	4	8	no	—
199	D₈×C₂₃	—	2	16	no	—
200	D₈×C₂₃	C₂×D₄	1	16	yes	complemented
201	M₁₆×C₂₃	—	2	16	no	—
202	C₂×C₈×C₂₃	—	2	4	no	—
203	C₂×C₈×C₂₃	—	2	2	no	—
204	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	complemented
205	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
206	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
207	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
208	C₄⋊C₄×C₂₃	—	2	4	no	—
209	C₄⋊C₄×C₂₃	—	2	8	no	—
210	C₄⋊C₄×C₂₃	—	2	4	no	—
211	C₄⋊C₄×C₂₃	—	2	1	no	—
212	C₄⋊C₄×C₂₃	—	2	1	no	—
213	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
214	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
215	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
216	C₂²⋊C₄×C₂₃	—	2	8	no	—
217	C₂²⋊C₄×C₂₃	—	2	4	no	—
218	C₂²⋊C₄×C₂₃	—	2	4	no	—
219	C₂²⋊C₄×C₂₃	—	2	8	no	—
220	C₂²⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
221	C₄²×C₂₃	C₂×D₄	1	2	yes	—
222	C₄²×C₂₃	C₂⁴	1	2	yes	—
223	C₂×#3272	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
224	C₂³×C₂₃	—	2	4	no	—
225	C₂³×C₂₃	—	2	4	no	—
226	C₂³×C₂₃	—	2	4	no	—
227	C₂³×C₂₃	—	2	4	no	—
228	C₂³×C₂₃	—	2	4	no	—
229	C₂³×C₂₃	—	2	2	no	—
230	C₂³×C₂₃	—	2	2	no	—
231	C₂³×C₂₃	—	2	4	no	—
232	C₂³×C₂₃	—	4	16	no	—
233	C₂³×C₂₃	—	4	16	no	—
234	C₂³×C₂₃	—	4	2	no	—
235	C₂³×C₂₃	—	4	2	no	—
236	C₂³×C₂₃	—	4	2	no	—
237	C₂³×C₂₃	—	4	2	no	—
238	C₂³×C₂₃	—	4	4	no	—
239	C₂³×C₂₃	—	4	4	no	—
240	C₂³×C₂₃	—	4	4	no	—
241	C₂³×C₂₃	—	8	8	no	—
242	C₂³×C₂₃	—	8	32	no	—
243	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
244	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
245	Q₈×C₂₃	—	2	4	no	—
246	Q₈×C₂₃	—	2	4	no	—
247	Q₈×C₂₃	—	4	4	no	—
248	D₄×C₂₃	—	2	4	no	—
249	D₄×C₂₃	—	2	4	no	—
250	D₄×C₂₃	—	2	8	no	—
251	D₄×C₂₃	—	2	4	no	—
252	D₄×C₂₃	—	2	2	no	—
253	D₄×C₂₃	—	2	2	no	—
254	D₄×C₂₃	—	2	4	no	—
255	D₄×C₂₃	—	4	16	no	—
256	D₄×C₂₃	—	4	16	no	—
257	D₄×C₂₃	—	4	16	no	—
258	D₄×C₂₃	—	4	4	no	—
259	D₄×C₂₃	—	4	8	no	—
260	D₄×C₂₃	—	8	4	no	—
261	D₄×C₂₃	C₂²×D₄	1	4	yes	—
262	D₄×C₂₃	C₂²×D₄	1	4	yes	complemented
263	C₂×C₄×C₂₃	—	2	4	no	—
264	C₂×C₄×C₂₃	—	2	2	no	—
265	C₂×C₄×C₂₃	—	2	8	no	—
266	C₂×C₄×C₂₃	—	2	4	no	—
267	C₂×C₄×C₂₃	—	2	4	no	—
268	C₂×C₄×C₂₃	—	2	2	no	—
269	C₂×C₄×C₂₃	—	2	2	no	—
270	C₂×C₄×C₂₃	—	2	4	no	—
271	C₂×C₄×C₂₃	—	4	16	no	—
272	C₂×C₄×C₂₃	—	4	4	no	—
273	C₂×C₄×C₂₃	—	4	2	no	—
274	C₂×C₄×C₂₃	—	4	2	no	—
275	C₂×C₄×C₂₃	—	4	8	no	—
276	C₂×C₄×C₂₃	—	4	8	no	—
277	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	4	yes	complemented
278	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
279	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
280	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
282	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
283	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
284	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
285	C₈×C₂₃	—	2	4	no	—
286	C₈×C₂₃	—	2	2	no	—
287	C₈×C₂₃	C₂²×D₄	1	4	yes	complemented
288	C₂²×AGL(1,ℤ/8)	C₂×C₂₃	1	2	yes	complemented
289	C₂×#547	C₂×C₂₃	1	1	yes	characteristic, complemented
290	C₂×D₄²	C₂×C₂₃	1	1	yes	characteristic, complemented
291	#3272	C₂×C₂₃	1	16	yes	direct product factor
292	C₂×#492	C₂×C₂₃	1	1	yes	characteristic, complemented
293	C₂×#468	C₂×C₂₃	1	2	yes	complemented
294	C₂×#461	C₂×C₂₃	1	1	yes	characteristic, complemented
295	C₂×#459	C₂×C₂₃	1	1	yes	characteristic, complemented
296	C₂×#449	C₂×C₂₃	1	2	yes	complemented
297	C₂×#450	C₂×C₂₃	1	2	yes	complemented
298	C₂×C₄×D₈	C₂×C₂₃	1	1	yes	characteristic, complemented
299	C₂×#436	C₂×C₂₃	1	1	yes	characteristic, complemented
300	C₂²×C₂₃	—	2	4	no	—
301	C₂²×C₂₃	—	2	4	no	—
302	C₂²×C₂₃	—	2	4	no	—
303	C₂²×C₂₃	—	2	4	no	—
304	C₂²×C₂₃	—	2	4	no	—
305	C₂²×C₂₃	—	4	8	no	—
306	C₂²×C₂₃	—	4	8	no	—
307	C₂²×C₂₃	—	4	8	no	—
308	C₂²×C₂₃	—	4	2	no	—
309	C₂²×C₂₃	—	4	2	no	—
310	C₂²×C₂₃	—	4	2	no	—
311	C₂²×C₂₃	—	4	2	no	—
312	C₂²×C₂₃	—	4	4	no	—
313	C₂²×C₂₃	—	4	4	no	—
314	C₂²×C₂₃	—	4	4	no	—
315	C₂²×C₂₃	—	8	32	no	—
316	C₂²×C₂₃	—	8	8	no	—
317	C₂²×C₂₃	D₄²	1	2	yes	—
318	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
319	C₂²×C₂₃	#577	1	2	yes	—
320	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
321	C₄×C₂₃	—	2	4	no	—
322	C₄×C₂₃	—	2	2	no	—
323	C₄×C₂₃	—	4	4	no	—
324	C₄×C₂₃	—	4	2	no	—
325	C₄×C₂₃	—	4	2	no	—
326	C₄×C₂₃	D₄²	1	2	yes	—
327	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	4	yes	complemented
328	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
329	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
330	C₂²×#41	C₂²×C₂₃	1	2	yes	complemented
331	C₂³×D₄	—	2	1	no	—
332	C₂³×D₄	C₂²×C₂₃	1	2	yes	—
333	C₂×AGL(1,ℤ/8)	—	2	16	no	—
334	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	16	yes	complemented
335	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	—
336	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
337	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
338	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
339	C₂²×D₈	C₂²×C₂₃	1	2	yes	complemented
340	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	complemented
341	#547	—	2	4	no	—
342	#547	C₂²×C₂₃	1	8	yes	complemented
343	D₄²	—	2	4	no	—
344	D₄²	C₂²×C₂₃	1	8	yes	complemented
345	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
346	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
347	C₂×#123	—	2	2	no	—
348	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
349	C₂×#121	—	2	1	no	—
350	C₂×#121	—	2	1	no	—
351	C₂×#121	C₂²×C₂₃	1	2	yes	—
352	C₂×#120	—	2	2	no	—
353	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
354	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
355	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
356	C₂²×C₄⋊C₄	—	2	1	no	—
357	#492	C₂²×C₂₃	1	8	yes	complemented
358	#468	C₂²×C₂₃	1	16	yes	complemented
359	#461	C₂²×C₂₃	1	8	yes	complemented
360	#459	C₂²×C₂₃	1	8	yes	complemented
361	#450	C₂²×C₂₃	1	16	yes	complemented
362	#449	C₂²×C₂₃	1	16	yes	complemented
363	C₄×D₈	C₂²×C₂₃	1	8	yes	complemented
364	#436	C₂²×C₂₃	1	8	yes	complemented
365	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic, complemented
366	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
367	C₂×#103	C₂²×C₂₃	1	2	yes	complemented
368	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
369	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
370	C₂×#102	C₂²×C₂₃	1	2	yes	complemented
371	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
372	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
373	C₂×C₂₃	—	4	4	no	—
374	C₂×C₂₃	—	4	4	no	—
375	C₂×C₂₃	—	4	4	no	—
376	C₂×C₂₃	—	8	4	no	—
377	C₂×C₂₃	#3272	1	4	yes	direct product factor
378	C₂×C₂₃	C₂×D₄²	1	1	yes	characteristic
379	C₂×C₂₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
380	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
381	C₂⁵	—	2	2	no	—
382	C₂×#41	—	2	4	no	—
383	C₂×#41	—	2	8	no	—
384	C₂×#41	—	4	4	no	—
385	C₂×#41	C₂³×C₂₃	1	8	yes	complemented
386	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
387	C₂²×D₄	—	2	8	no	—
388	C₂²×D₄	—	2	2	no	—
389	C₂²×D₄	—	2	2	no	—
390	C₂²×D₄	—	2	8	no	—
391	C₂²×D₄	—	2	2	no	—
392	C₂²×D₄	—	2	1	no	—
393	C₂²×D₄	—	2	4	no	—
394	C₂²×D₄	—	2	1	no	—
395	C₂²×D₄	—	4	4	no	—
396	C₂²×D₄	—	4	8	no	—
397	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
398	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
399	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
400	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
401	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
402	C₂³×C₄	—	2	1	no	—
403	C₂³×C₄	—	2	2	no	—
404	C₂³×C₄	—	2	1	no	—
405	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
406	AGL(1,ℤ/8)	—	2	64	no	—
407	C₂×SD₁₆	—	2	8	no	—
408	C₂×SD₁₆	—	2	8	no	—
409	C₂×SD₁₆	—	4	4	no	—
410	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	—
411	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	complemented
412	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	complemented
413	C₂×D₈	—	2	8	no	—
414	C₂×D₈	D₄×C₂₃	1	8	yes	complemented
415	C₂×D₈	C₂³×C₂₃	1	4	yes	—
416	C₂×D₈	C₂³×C₂₃	1	8	yes	complemented
417	C₂×M₁₆	—	2	8	no	—
418	C₂×M₁₆	C₂³×C₂₃	1	8	yes	complemented
419	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
420	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
421	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
422	C₄⋊Q₈	—	2	2	no	—
423	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	complemented
424	#127	—	2	2	no	—
425	#127	C₂³×C₂₃	1	4	yes	—
426	#123	—	2	16	no	—
427	C₂²⋊Q₈	—	2	4	no	—
428	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	complemented
429	#121	—	2	8	no	—
430	#121	—	2	4	no	—
431	#121	—	2	8	no	—
432	#121	C₂³×C₂₃	1	8	yes	—
433	#120	—	2	16	no	—
434	C₄×D₄	—	2	2	no	—
435	C₄×D₄	—	2	2	no	—
436	C₄×D₄	D₄×C₂₃	1	4	yes	—
437	C₄×D₄	C₂³×C₂₃	1	4	yes	—
438	C₄×D₄	C₂³×C₂₃	1	4	yes	—
439	C₄×D₄	C₂³×C₂₃	1	4	yes	complemented
440	C₂×C₄⋊C₄	—	2	1	no	—
441	C₂×C₄⋊C₄	—	2	2	no	—
442	C₂×C₄⋊C₄	—	2	1	no	—
443	C₂×C₄⋊C₄	—	2	8	no	—
444	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
445	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
447	C₂×C₂²⋊C₄	—	2	2	no	—
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₂²⋊C₄	—	2	2	no	—
451	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
452	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
453	#107	C₂³×C₂₃	1	4	yes	complemented
454	C₄⋊C₈	C₂³×C₂₃	1	4	yes	complemented
455	#103	C₂³×C₂₃	1	8	yes	complemented
456	#102	C₂³×C₂₃	1	4	yes	—
457	#102	C₂³×C₂₃	1	4	yes	complemented
458	#102	C₂³×C₂₃	1	8	yes	complemented
459	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	complemented
460	C₄×C₈	C₂³×C₂₃	1	4	yes	complemented
461	C₂₃	C₂×#3272	1	1	yes	characteristic, direct product factor, Sylow
462	C₂⁴	—	2	1	no	—
463	C₂⁴	—	2	1	no	—
464	C₂⁴	—	2	2	no	—
465	C₂⁴	—	2	8	no	—
466	C₂⁴	—	4	8	no	—
467	C₂⁴	—	4	8	no	—
468	C₂⁴	—	8	4	no	—
469	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
470	#41	—	2	16	no	—
471	#41	—	4	8	no	—
472	#41	—	4	16	no	—
473	C₂×Q₈	—	2	2	no	—
474	C₂×Q₈	—	2	4	no	—
475	C₂×Q₈	—	2	4	no	—
476	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
477	C₂×D₄	—	2	16	no	—
478	C₂×D₄	—	2	8	no	—
479	C₂×D₄	—	2	8	no	—
480	C₂×D₄	—	2	4	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	4	no	—
484	C₂×D₄	—	2	8	no	—
485	C₂×D₄	—	2	2	no	—
486	C₂×D₄	—	2	4	no	—
487	C₂×D₄	—	2	4	no	—
488	C₂×D₄	—	2	2	no	—
489	C₂×D₄	—	2	2	no	—
490	C₂×D₄	—	2	4	no	—
491	C₂×D₄	—	4	8	no	—
492	C₂×D₄	—	4	16	no	—
493	C₂×D₄	—	4	8	no	—
494	C₂×D₄	—	4	32	no	—
495	C₂×D₄	—	4	8	no	—
496	C₂×D₄	—	4	8	no	—
497	C₂×D₄	—	4	4	no	—
498	C₂×D₄	—	8	2	no	—
499	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
500	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
501	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	complemented
502	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
503	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
504	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
505	C₂²×C₄	—	2	4	no	—
506	C₂²×C₄	—	2	4	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	2	no	—
510	C₂²×C₄	—	2	4	no	—
511	C₂²×C₄	—	2	8	no	—
512	C₂²×C₄	—	2	4	no	—
513	C₂²×C₄	—	4	8	no	—
514	C₂²×C₄	—	4	4	no	—
515	C₂²×C₄	—	4	4	no	—
516	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
517	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
518	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
519	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
520	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
521	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
522	SD₁₆	—	2	16	no	—
523	SD₁₆	—	2	16	no	—
524	SD₁₆	—	4	8	no	—
525	D₈	—	2	16	no	—
526	D₈	C₂×D₄×C₂₃	1	16	yes	complemented
527	M₁₆	—	2	16	no	—
528	C₂×C₈	—	2	4	no	—
529	C₂×C₈	—	2	2	no	—
530	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	complemented
531	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
532	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
533	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
534	C₄⋊C₄	—	2	4	no	—
535	C₄⋊C₄	—	2	8	no	—
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
540	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
541	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
542	C₂²⋊C₄	—	2	8	no	—
543	C₂²⋊C₄	—	2	4	no	—
544	C₂²⋊C₄	—	2	4	no	—
545	C₂²⋊C₄	—	2	8	no	—
546	C₂²⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
547	C₄²	C₂×D₄×C₂₃	1	2	yes	—
548	C₄²	C₂⁴×C₂₃	1	2	yes	—
549	C₂³	—	2	4	no	—
550	C₂³	—	2	4	no	—
551	C₂³	—	2	2	no	—
552	C₂³	—	2	2	no	—
553	C₂³	—	2	4	no	—
554	C₂³	—	2	4	no	—
555	C₂³	—	2	4	no	—
556	C₂³	—	2	4	no	—
557	C₂³	—	4	16	no	—
558	C₂³	—	4	16	no	—
559	C₂³	—	4	2	no	—
560	C₂³	—	4	2	no	—
561	C₂³	—	4	2	no	—
562	C₂³	—	4	2	no	—
563	C₂³	—	4	4	no	—
564	C₂³	—	4	4	no	—
565	C₂³	—	4	4	no	—
566	C₂³	—	8	8	no	—
567	C₂³	—	8	32	no	—
568	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
569	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
570	Q₈	—	2	4	no	—
571	Q₈	—	2	4	no	—
572	Q₈	—	4	4	no	—
573	D₄	—	2	8	no	—
574	D₄	—	2	4	no	—
575	D₄	—	2	2	no	—
576	D₄	—	2	2	no	—
577	D₄	—	2	4	no	—
578	D₄	—	2	4	no	—
579	D₄	—	2	4	no	—
580	D₄	—	4	16	no	—
581	D₄	—	4	16	no	—
582	D₄	—	4	16	no	—
583	D₄	—	4	8	no	—
584	D₄	—	4	4	no	—
585	D₄	—	8	4	no	—
586	D₄	C₂²×D₄×C₂₃	1	4	yes	—
587	D₄	C₂²×D₄×C₂₃	1	4	yes	complemented
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	8	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	4	no	—
596	C₂×C₄	—	4	16	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	4	no	—
600	C₂×C₄	—	4	8	no	—
601	C₂×C₄	—	4	8	no	—
602	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	4	yes	complemented
603	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
604	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
605	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
606	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
607	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
608	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
609	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
610	C₈	—	2	4	no	—
611	C₈	—	2	2	no	—
612	C₈	C₂²×D₄×C₂₃	1	4	yes	complemented
613	C₂²	—	2	4	no	—
614	C₂²	—	2	4	no	—
615	C₂²	—	2	4	no	—
616	C₂²	—	2	4	no	—
617	C₂²	—	2	4	no	—
618	C₂²	—	4	8	no	—
619	C₂²	—	4	8	no	—
620	C₂²	—	4	8	no	—
621	C₂²	—	4	2	no	—
622	C₂²	—	4	2	no	—
623	C₂²	—	4	2	no	—
624	C₂²	—	4	2	no	—
625	C₂²	—	4	4	no	—
626	C₂²	—	4	4	no	—
627	C₂²	—	4	4	no	—
628	C₂²	—	8	32	no	—
629	C₂²	—	8	8	no	—
630	C₂²	D₄²×C₂₃	1	2	yes	—
631	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
632	C₂²	C₂₃×#577	1	2	yes	—
633	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
634	C₄	—	2	4	no	—
635	C₄	—	2	2	no	—
636	C₄	—	4	4	no	—
637	C₄	—	4	2	no	—
638	C₄	—	4	2	no	—
639	C₄	D₄²×C₂₃	1	2	yes	—
640	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	4	yes	complemented
641	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
642	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
643	C₂	—	4	4	no	—
644	C₂	—	4	4	no	—
645	C₂	—	4	4	no	—
646	C₂	—	8	4	no	—
647	C₂	C₂₃×#3272	1	4	yes	direct product factor
648	C₂	C₂×D₄²×C₂₃	1	1	yes	characteristic
649	C₂	C₂²×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
650	C₂	C₂×C₂₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄×D₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂₃×AGL(1,ℤ/8)	C₂	semidirect
2. C₂×C₂₃×#547	C₂	semidirect
3. C₂×D₄²×C₂₃	C₂	semidirect
4. C₂₃×#3272	C₂	direct (N × H)
5. C₂×C₂₃×#492	C₂	semidirect
6. C₂×C₂₃×#468	C₂	semidirect
7. C₂×C₂₃×#461	C₂	semidirect
8. C₂×C₂₃×#459	C₂	semidirect
9. C₂×C₂₃×#449	C₂	semidirect
10. C₂×C₂₃×#450	C₂	semidirect
11. C₂×C₄×D₈×C₂₃	C₂	semidirect
12. C₂×C₂₃×#436	C₂	semidirect
13. C₂²×#41×C₂₃	C₂²	semidirect
17. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
19. C₂²×SD₁₆×C₂₃	C₂²	semidirect
20. C₂²×SD₁₆×C₂₃	C₂²	semidirect
22. C₂²×D₈×C₂₃	C₂²	semidirect
23. C₂²×M₁₆×C₂₃	C₂²	semidirect
25. C₂₃×#547	C₂²	semidirect
27. D₄²×C₂₃	C₂²	semidirect
28. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
31. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
38. C₂×C₄×D₄×C₂₃	C₂²	semidirect
40. C₂₃×#492	C₂²	semidirect
41. C₂₃×#468	C₂²	semidirect
42. C₂₃×#461	C₂²	semidirect
43. C₂₃×#459	C₂²	semidirect
44. C₂₃×#450	C₂²	semidirect
45. C₂₃×#449	C₂²	semidirect
46. C₄×D₈×C₂₃	C₂²	semidirect
47. C₂₃×#436	C₂²	semidirect
48. C₂×C₂₃×#107	C₂²	semidirect
49. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
50. C₂×C₂₃×#103	C₂²	semidirect
52. C₂×C₂₃×#102	C₂²	semidirect
53. C₂×C₂₃×#102	C₂²	semidirect
54. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
55. C₂×C₄×C₈×C₂₃	C₂²	semidirect
60. C₂×#41×C₂₃	C₂³	semidirect
86. C₂×SD₁₆×C₂₃	C₂³	semidirect
87. C₂×SD₁₆×C₂₃	C₂³	semidirect
89. C₂×D₈×C₂₃	D₄	semidirect
91. C₂×D₈×C₂₃	C₂³	semidirect
93. C₂×M₁₆×C₂₃	C₂³	semidirect
98. C₂₃×C₄⋊Q₈	C₂³	semidirect
103. C₂₃×C₂²⋊Q₈	C₂³	semidirect
114. C₄×D₄×C₂₃	C₂³	semidirect
128. C₂₃×#107	C₂³	semidirect
129. C₂₃×C₄⋊C₈	C₂³	semidirect
130. C₂₃×#103	C₂³	semidirect
132. C₂₃×#102	C₂³	semidirect
133. C₂₃×#102	C₂³	semidirect
134. C₂₃×C₂²⋊C₈	C₂³	semidirect
135. C₄×C₈×C₂₃	C₂³	semidirect
175. C₂×D₄×C₂₃	C₂×D₄	semidirect
200. D₈×C₂₃	C₂×D₄	semidirect
204. C₂×C₈×C₂₃	C₂×D₄	semidirect
223. C₂×#3272	C₂₃	direct (N × H)
262. D₄×C₂₃	C₂²×D₄	semidirect
277. C₂×C₄×C₂₃	AGL(1,ℤ/8)	semidirect
287. C₈×C₂₃	C₂²×D₄	semidirect
288. C₂²×AGL(1,ℤ/8)	C₂×C₂₃	semidirect
289. C₂×#547	C₂×C₂₃	semidirect
290. C₂×D₄²	C₂×C₂₃	semidirect
291. #3272	C₂×C₂₃	direct (N × H)
292. C₂×#492	C₂×C₂₃	semidirect
293. C₂×#468	C₂×C₂₃	semidirect
294. C₂×#461	C₂×C₂₃	semidirect
295. C₂×#459	C₂×C₂₃	semidirect
296. C₂×#449	C₂×C₂₃	semidirect
297. C₂×#450	C₂×C₂₃	semidirect
298. C₂×C₄×D₈	C₂×C₂₃	semidirect
299. C₂×#436	C₂×C₂₃	semidirect
327. C₄×C₂₃	C₂×AGL(1,ℤ/8)	semidirect
330. C₂²×#41	C₂²×C₂₃	semidirect
334. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
336. C₂²×SD₁₆	C₂²×C₂₃	semidirect
337. C₂²×SD₁₆	C₂²×C₂₃	semidirect
339. C₂²×D₈	C₂²×C₂₃	semidirect
340. C₂²×M₁₆	C₂²×C₂₃	semidirect
342. #547	C₂²×C₂₃	semidirect
344. D₄²	C₂²×C₂₃	semidirect
345. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
348. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
355. C₂×C₄×D₄	C₂²×C₂₃	semidirect
357. #492	C₂²×C₂₃	semidirect
358. #468	C₂²×C₂₃	semidirect
359. #461	C₂²×C₂₃	semidirect
360. #459	C₂²×C₂₃	semidirect
361. #450	C₂²×C₂₃	semidirect
362. #449	C₂²×C₂₃	semidirect
363. C₄×D₈	C₂²×C₂₃	semidirect
364. #436	C₂²×C₂₃	semidirect
365. C₂×#107	C₂²×C₂₃	semidirect
366. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
367. C₂×#103	C₂²×C₂₃	semidirect
369. C₂×#102	C₂²×C₂₃	semidirect
370. C₂×#102	C₂²×C₂₃	semidirect
371. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
372. C₂×C₄×C₈	C₂²×C₂₃	semidirect
377. C₂×C₂₃	#3272	direct (N × H)
385. C₂×#41	C₂³×C₂₃	semidirect
411. C₂×SD₁₆	C₂³×C₂₃	semidirect
412. C₂×SD₁₆	C₂³×C₂₃	semidirect
414. C₂×D₈	D₄×C₂₃	semidirect
416. C₂×D₈	C₂³×C₂₃	semidirect
418. C₂×M₁₆	C₂³×C₂₃	semidirect
423. C₄⋊Q₈	C₂³×C₂₃	semidirect
428. C₂²⋊Q₈	C₂³×C₂₃	semidirect
439. C₄×D₄	C₂³×C₂₃	semidirect
453. #107	C₂³×C₂₃	semidirect
454. C₄⋊C₈	C₂³×C₂₃	semidirect
455. #103	C₂³×C₂₃	semidirect
457. #102	C₂³×C₂₃	semidirect
458. #102	C₂³×C₂₃	semidirect
459. C₂²⋊C₈	C₂³×C₂₃	semidirect
460. C₄×C₈	C₂³×C₂₃	semidirect
461. C₂₃	C₂×#3272	direct (N × H)
501. C₂×D₄	C₂×D₄×C₂₃	semidirect
526. D₈	C₂×D₄×C₂₃	semidirect
530. C₂×C₈	C₂×D₄×C₂₃	semidirect
587. D₄	C₂²×D₄×C₂₃	semidirect
602. C₂×C₄	C₂₃×AGL(1,ℤ/8)	semidirect
612. C₈	C₂²×D₄×C₂₃	semidirect
640. C₄	C₂×C₂₃×AGL(1,ℤ/8)	semidirect
647. C₂	C₂₃×#3272	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₂₃×AGL(1,ℤ/8)	2
C₂×C₂₃×#547	2
C₂×D₄²×C₂₃	2
C₂₃×#3272	2
C₂×C₂₃×#492	2
C₂×C₂₃×#468	2
C₂×C₂₃×#461	2
C₂×C₂₃×#459	2
C₂×C₂₃×#449	2
C₂×C₂₃×#450	2
C₂×C₄×D₈×C₂₃	2
C₂×C₂₃×#436	2
C₂×#3272	23

Subgroups — C2×C23×#3272 #19208657

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3272 #19208657