Subgroups — C₂₃×#61570 #19209196

Order 5888.

2234 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#546	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3314	C₂	1	8	yes	maximal, complemented
4	C₂₃×#3266	C₂	1	8	yes	maximal, complemented
5	C₂₃×#3215	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3193	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3189	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3110	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3007	C₂	1	2	yes	maximal, complemented
10	C₂×C₂₃×#450	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2973	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
14	C₂×C₂₃×#137	C₂²	1	4	yes	complemented
15	C₂²×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
16	C₂₃×#554	—	2	4	no	—
17	C₂₃×#554	C₂²	1	4	yes	complemented
18	D₄×Q₈×C₂₃	C₂²	1	4	yes	complemented
19	C₂₃×#546	—	2	4	no	—
20	C₂₃×#546	C₂²	1	8	yes	—
21	C₂₃×#544	—	2	1	no	—
22	C₂₃×#543	—	2	1	no	—
23	C₂₃×#543	—	2	1	no	—
24	C₂₃×#533	C₂²	1	2	yes	complemented
25	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#123	—	2	1	no	—
27	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
30	C₂×C₂₃×#121	—	2	1	no	—
31	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×#120	—	2	1	no	—
33	C₂₃×#518	—	2	1	no	—
34	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₂₃	—	2	1	no	—
37	C₂₃×#497	C₂²	1	4	yes	complemented
38	C₂₃×#489	C₂²	1	4	yes	complemented
39	C₂₃×#484	C₂²	1	4	yes	complemented
40	C₂₃×#484	C₂²	1	4	yes	complemented
41	C₂₃×#480	C₂²	1	4	yes	complemented
42	C₂₃×#474	C₂²	1	4	yes	complemented
43	C₂₃×#468	C₂²	1	8	yes	complemented
44	C₂₃×#467	C₂²	1	8	yes	complemented
45	C₂₃×#464	C₂²	1	8	yes	complemented
46	C₂₃×#461	C₂²	1	4	yes	complemented
47	C₂₃×#452	C₂²	1	8	yes	complemented
48	C₂₃×#451	C₂²	1	4	yes	complemented
49	C₂₃×#451	C₂²	1	4	yes	complemented
50	C₂₃×#450	C₂²	1	4	yes	—
51	C₂₃×#450	C₂²	1	4	yes	—
52	C₂₃×#450	C₂²	1	8	yes	complemented
53	C₂₃×#448	C₂²	1	4	yes	complemented
54	C₂₃×#440	C₂²	1	8	yes	complemented
55	C₂₃×#435	C₂²	1	8	yes	complemented
56	C₂₃×#432	C₂²	1	2	yes	complemented
57	C₂₃×#417	C₂²	1	4	yes	complemented
58	C₂×C₂₃×#102	C₂²	1	4	yes	complemented
59	C₂₃×#407	C₂²	1	2	yes	complemented
60	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
61	C₂⁵×C₂₃	—	2	1	no	—
62	C₂×#41×C₂₃	—	2	2	no	—
63	C₂×#41×C₂₃	—	4	4	no	—
64	C₂×#41×C₂₃	C₂³	1	4	yes	—
65	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
66	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
67	C₂²×Q₈×C₂₃	C₂³	1	2	yes	complemented
68	C₂²×D₄×C₂₃	—	2	1	no	—
69	C₂²×D₄×C₂₃	—	2	1	no	—
70	C₂²×D₄×C₂₃	—	2	1	no	—
71	C₂²×D₄×C₂₃	—	2	2	no	—
72	C₂²×D₄×C₂₃	—	4	4	no	—
73	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
74	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
76	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₂₃	—	2	1	no	—
78	C₂³×C₄×C₂₃	—	2	1	no	—
79	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
81	C₂₃×#137	—	4	8	no	—
82	C₂×Q₁₆×C₂₃	C₂³	1	8	yes	complemented
83	C₂×SD₁₆×C₂₃	—	4	8	no	—
84	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	—
85	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	—
86	C₂×M₁₆×C₂₃	C₂³	1	4	yes	complemented
87	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
88	C₂₃×C₄⋊Q₈	—	2	4	no	—
89	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
90	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
91	C₂₃×#125	—	2	4	no	—
92	C₂₃×#125	—	2	2	no	—
93	C₂₃×#124	—	2	2	no	—
94	C₂₃×#124	C₂³	1	4	yes	—
95	C₂₃×#123	—	2	8	no	—
96	C₂₃×C₂²⋊Q₈	—	2	2	no	—
97	C₂₃×C₂²⋊Q₈	—	2	2	no	—
98	C₂₃×C₂²⋊Q₈	—	2	2	no	—
99	C₂₃×C₂²⋊Q₈	—	2	2	no	—
100	C₂₃×C₂²⋊Q₈	—	2	2	no	—
101	C₂₃×C₂²⋊Q₈	—	2	2	no	—
102	C₂₃×C₂²⋊Q₈	—	2	4	no	—
103	C₂₃×C₂²⋊Q₈	—	2	4	no	—
104	C₂₃×C₂²⋊Q₈	—	2	4	no	—
105	C₂₃×C₂²⋊Q₈	—	2	4	no	—
106	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
107	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
108	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
109	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	complemented
110	C₂₃×#121	—	2	2	no	—
111	C₂₃×#121	—	2	8	no	—
112	C₂₃×#121	C₂³	1	4	yes	—
113	C₂₃×#120	—	2	8	no	—
114	C₄×Q₈×C₂₃	—	2	2	no	—
115	C₄×Q₈×C₂₃	C₂³	1	4	yes	complemented
116	C₄×D₄×C₂₃	—	2	4	no	—
117	C₄×D₄×C₂₃	—	2	4	no	—
118	C₄×D₄×C₂₃	—	2	2	no	—
119	C₄×D₄×C₂₃	D₄	1	4	yes	—
120	C₄×D₄×C₂₃	C₂³	1	4	yes	—
121	C₄×D₄×C₂₃	C₂³	1	4	yes	—
122	C₂₃×#117	—	2	2	no	—
123	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
124	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
125	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
126	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	complemented
130	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
131	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
132	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
133	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
134	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
135	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
136	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
137	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
138	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
139	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
140	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
141	C₂₃×#107	C₂³	1	8	yes	complemented
142	C₂₃×C₄⋊C₈	C₂³	1	4	yes	complemented
143	C₂₃×#103	C₂³	1	8	yes	complemented
144	C₂₃×#103	C₂³	1	8	yes	complemented
145	C₂₃×#102	C₂³	1	8	yes	—
146	C₂₃×#102	C₂³	1	8	yes	—
147	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
148	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
149	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	complemented
150	C₂₃×#97	C₂³	1	4	yes	complemented
151	C₂⁴×C₂₃	—	2	1	no	—
152	C₂⁴×C₂₃	—	2	1	no	—
153	C₂⁴×C₂₃	—	2	4	no	—
154	C₂⁴×C₂₃	—	4	4	no	—
155	C₂⁴×C₂₃	—	4	4	no	—
156	C₂⁴×C₂₃	—	8	2	no	—
157	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
158	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
159	#41×C₂₃	—	2	8	no	—
160	#41×C₂₃	—	4	4	no	—
161	#41×C₂₃	—	4	8	no	—
162	C₂×Q₈×C₂₃	—	2	1	no	—
163	C₂×Q₈×C₂₃	—	2	2	no	—
164	C₂×Q₈×C₂₃	—	2	2	no	—
165	C₂×Q₈×C₂₃	—	2	2	no	—
166	C₂×Q₈×C₂₃	—	4	2	no	—
167	C₂×Q₈×C₂₃	—	4	4	no	—
168	C₂×Q₈×C₂₃	—	4	4	no	—
169	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
170	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
171	C₂×D₄×C₂₃	—	2	4	no	—
172	C₂×D₄×C₂₃	—	2	4	no	—
173	C₂×D₄×C₂₃	—	2	8	no	—
174	C₂×D₄×C₂₃	—	2	4	no	—
175	C₂×D₄×C₂₃	—	2	4	no	—
176	C₂×D₄×C₂₃	—	2	1	no	—
177	C₂×D₄×C₂₃	—	2	4	no	—
178	C₂×D₄×C₂₃	—	2	1	no	—
179	C₂×D₄×C₂₃	—	4	4	no	—
180	C₂×D₄×C₂₃	—	4	2	no	—
181	C₂×D₄×C₂₃	—	4	8	no	—
182	C₂×D₄×C₂₃	—	4	4	no	—
183	C₂×D₄×C₂₃	—	4	4	no	—
184	C₂×D₄×C₂₃	—	8	2	no	—
185	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
186	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
187	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₂₃	—	2	1	no	—
189	C₂²×C₄×C₂₃	—	2	1	no	—
190	C₂²×C₄×C₂₃	—	2	2	no	—
191	C₂²×C₄×C₂₃	—	2	2	no	—
192	C₂²×C₄×C₂₃	—	2	2	no	—
193	C₂²×C₄×C₂₃	—	2	2	no	—
194	C₂²×C₄×C₂₃	—	2	4	no	—
195	C₂²×C₄×C₂₃	—	2	4	no	—
196	C₂²×C₄×C₂₃	—	4	2	no	—
197	C₂²×C₄×C₂₃	—	4	2	no	—
198	C₂²×C₄×C₂₃	—	4	4	no	—
199	C₂²×C₄×C₂₃	—	8	2	no	—
200	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
205	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
206	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
209	Q₁₆×C₂₃	—	4	8	no	—
210	SD₁₆×C₂₃	—	2	16	no	—
211	SD₁₆×C₂₃	—	4	8	no	—
212	M₁₆×C₂₃	—	4	4	no	—
213	C₂×C₈×C₂₃	—	4	4	no	—
214	C₂×C₈×C₂₃	C₂⁴	1	8	yes	—
215	C₄⋊C₄×C₂₃	—	2	4	no	—
216	C₄⋊C₄×C₂₃	—	2	4	no	—
217	C₄⋊C₄×C₂₃	—	2	4	no	—
218	C₄⋊C₄×C₂₃	—	2	4	no	—
219	C₄⋊C₄×C₂₃	—	2	1	no	—
220	C₄⋊C₄×C₂₃	—	2	2	no	—
221	C₄⋊C₄×C₂₃	—	2	2	no	—
222	C₄⋊C₄×C₂₃	—	2	2	no	—
223	C₄⋊C₄×C₂₃	—	2	2	no	—
224	C₄⋊C₄×C₂₃	—	2	2	no	—
225	C₄⋊C₄×C₂₃	—	2	4	no	—
226	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
227	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
228	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
229	C₂²⋊C₄×C₂₃	—	2	4	no	—
230	C₂²⋊C₄×C₂₃	—	2	4	no	—
231	C₂²⋊C₄×C₂₃	—	2	4	no	—
232	C₂²⋊C₄×C₂₃	—	2	4	no	—
233	C₂²⋊C₄×C₂₃	—	2	4	no	—
234	C₂²⋊C₄×C₂₃	—	2	4	no	—
235	C₂²⋊C₄×C₂₃	—	2	4	no	—
236	C₂²⋊C₄×C₂₃	—	2	4	no	—
237	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
238	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
239	C₄²×C₂₃	—	2	4	no	—
240	C₄²×C₂₃	C₂×D₄	1	2	yes	—
241	C₄²×C₂₃	C₂⁴	1	2	yes	—
242	#61570	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₂³×C₂₃	—	2	4	no	—
244	C₂³×C₂₃	—	2	2	no	—
245	C₂³×C₂₃	—	2	2	no	—
246	C₂³×C₂₃	—	2	2	no	—
247	C₂³×C₂₃	—	4	1	no	—
248	C₂³×C₂₃	—	4	1	no	—
249	C₂³×C₂₃	—	4	1	no	—
250	C₂³×C₂₃	—	4	1	no	—
251	C₂³×C₂₃	—	4	8	no	—
252	C₂³×C₂₃	—	4	2	no	—
253	C₂³×C₂₃	—	4	2	no	—
254	C₂³×C₂₃	—	4	2	no	—
255	C₂³×C₂₃	—	4	2	no	—
256	C₂³×C₂₃	—	4	8	no	—
257	C₂³×C₂₃	—	4	2	no	—
258	C₂³×C₂₃	—	8	4	no	—
259	C₂³×C₂₃	—	8	16	no	—
260	C₂³×C₂₃	#137	1	4	yes	complemented
261	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
262	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
263	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
264	Q₈×C₂₃	—	2	8	no	—
265	Q₈×C₂₃	—	2	4	no	—
266	Q₈×C₂₃	—	4	2	no	—
267	Q₈×C₂₃	—	8	2	no	—
268	Q₈×C₂₃	—	8	2	no	—
269	Q₈×C₂₃	—	8	2	no	—
270	D₄×C₂₃	—	2	4	no	—
271	D₄×C₂₃	—	2	8	no	—
272	D₄×C₂₃	—	2	2	no	—
273	D₄×C₂₃	—	2	4	no	—
274	D₄×C₂₃	—	4	8	no	—
275	D₄×C₂₃	—	4	2	no	—
276	D₄×C₂₃	—	4	8	no	—
277	D₄×C₂₃	—	8	4	no	—
278	D₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
279	C₂×C₄×C₂₃	—	2	2	no	—
280	C₂×C₄×C₂₃	—	2	4	no	—
281	C₂×C₄×C₂₃	—	2	4	no	—
282	C₂×C₄×C₂₃	—	2	2	no	—
283	C₂×C₄×C₂₃	—	2	4	no	—
284	C₂×C₄×C₂₃	—	2	4	no	—
285	C₂×C₄×C₂₃	—	2	2	no	—
286	C₂×C₄×C₂₃	—	2	2	no	—
287	C₂×C₄×C₂₃	—	4	1	no	—
288	C₂×C₄×C₂₃	—	4	2	no	—
289	C₂×C₄×C₂₃	—	4	1	no	—
290	C₂×C₄×C₂₃	—	4	2	no	—
291	C₂×C₄×C₂₃	—	4	1	no	—
292	C₂×C₄×C₂₃	—	4	8	no	—
293	C₂×C₄×C₂₃	—	4	2	no	—
294	C₂×C₄×C₂₃	—	4	2	no	—
295	C₂×C₄×C₂₃	—	8	4	no	—
296	C₂×C₄×C₂₃	—	8	2	no	—
297	C₂×C₄×C₂₃	—	8	2	no	—
298	C₂×C₄×C₂₃	—	8	2	no	—
299	C₂×C₄×C₂₃	—	8	2	no	—
300	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
301	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
302	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
303	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
304	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
305	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
306	C₈×C₂₃	—	2	8	no	—
307	#3501	C₂×C₂₃	1	1	yes	characteristic, complemented
308	C₂×#546	C₂×C₂₃	1	1	yes	characteristic
309	#3314	C₂×C₂₃	1	8	yes	complemented
310	#3266	C₂×C₂₃	1	8	yes	complemented
311	#3215	C₂×C₂₃	1	2	yes	complemented
312	#3193	C₂×C₂₃	1	2	yes	complemented
313	#3189	C₂×C₂₃	1	2	yes	complemented
314	#3110	C₂×C₂₃	1	2	yes	complemented
315	#3007	C₂×C₂₃	1	2	yes	complemented
316	C₂×#450	C₂×C₂₃	1	2	yes	complemented
317	#2973	C₂×C₂₃	1	1	yes	characteristic, complemented
318	C₂²×C₂₃	—	2	1	no	—
319	C₂²×C₂₃	—	2	2	no	—
320	C₂²×C₂₃	—	2	1	no	—
321	C₂²×C₂₃	—	2	2	no	—
322	C₂²×C₂₃	—	2	2	no	—
323	C₂²×C₂₃	—	2	2	no	—
324	C₂²×C₂₃	—	2	4	no	—
325	C₂²×C₂₃	—	2	2	no	—
326	C₂²×C₂₃	—	4	4	no	—
327	C₂²×C₂₃	—	4	8	no	—
328	C₂²×C₂₃	—	4	2	no	—
329	C₂²×C₂₃	—	4	2	no	—
330	C₂²×C₂₃	—	4	2	no	—
331	C₂²×C₂₃	—	4	2	no	—
332	C₂²×C₂₃	—	4	2	no	—
333	C₂²×C₂₃	—	8	2	no	—
334	C₂²×C₂₃	—	8	16	no	—
335	C₂²×C₂₃	—	8	4	no	—
336	C₂²×C₂₃	C₂×#137	1	2	yes	—
337	C₂²×C₂₃	C₂×#137	1	4	yes	—
338	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
339	C₄×C₂₃	—	2	2	no	—
340	C₄×C₂₃	—	2	2	no	—
341	C₄×C₂₃	—	2	1	no	—
342	C₄×C₂₃	—	2	2	no	—
343	C₄×C₂₃	—	2	2	no	—
344	C₄×C₂₃	—	4	2	no	—
345	C₄×C₂₃	—	4	4	no	—
346	C₄×C₂₃	—	4	2	no	—
347	C₄×C₂₃	—	4	4	no	—
348	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
349	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
350	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
351	C₂×#137	C₂²×C₂₃	1	4	yes	complemented
352	C₂²×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
353	#554	—	2	4	no	—
354	#554	C₂²×C₂₃	1	4	yes	complemented
355	D₄×Q₈	C₂²×C₂₃	1	4	yes	complemented
356	#546	—	2	4	no	—
357	#546	C₂²×C₂₃	1	8	yes	—
358	#544	—	2	1	no	—
359	#543	—	2	1	no	—
360	#543	—	2	1	no	—
361	#533	C₂²×C₂₃	1	2	yes	complemented
362	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
363	C₂×#123	—	2	1	no	—
364	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
365	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
366	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
367	C₂×#121	—	2	1	no	—
368	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
369	C₂×#120	—	2	1	no	—
370	#518	—	2	1	no	—
371	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
372	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
373	C₂²×C₂²⋊C₄	—	2	1	no	—
374	#497	C₂²×C₂₃	1	4	yes	complemented
375	#489	C₂²×C₂₃	1	4	yes	complemented
376	#484	C₂²×C₂₃	1	4	yes	complemented
377	#484	C₂²×C₂₃	1	4	yes	complemented
378	#480	C₂²×C₂₃	1	4	yes	complemented
379	#474	C₂²×C₂₃	1	4	yes	complemented
380	#468	C₂²×C₂₃	1	8	yes	complemented
381	#467	C₂²×C₂₃	1	8	yes	complemented
382	#464	C₂²×C₂₃	1	8	yes	complemented
383	#461	C₂²×C₂₃	1	4	yes	complemented
384	#452	C₂²×C₂₃	1	8	yes	complemented
385	#451	C₂²×C₂₃	1	4	yes	complemented
386	#451	C₂²×C₂₃	1	4	yes	complemented
387	#450	C₂²×C₂₃	1	4	yes	—
388	#450	C₂²×C₂₃	1	4	yes	—
389	#450	C₂²×C₂₃	1	8	yes	complemented
390	#448	C₂²×C₂₃	1	4	yes	complemented
391	#440	C₂²×C₂₃	1	8	yes	complemented
392	#435	C₂²×C₂₃	1	8	yes	complemented
393	#432	C₂²×C₂₃	1	2	yes	complemented
394	#417	C₂²×C₂₃	1	4	yes	complemented
395	C₂×#102	C₂²×C₂₃	1	4	yes	complemented
396	#407	C₂²×C₂₃	1	2	yes	complemented
397	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
398	C₂×C₂₃	—	2	2	no	—
399	C₂×C₂₃	—	2	4	no	—
400	C₂×C₂₃	—	4	2	no	—
401	C₂×C₂₃	—	4	4	no	—
402	C₂×C₂₃	—	8	2	no	—
403	C₂×C₂₃	#3484	1	1	yes	characteristic
404	C₂×C₂₃	C₂²×#137	1	1	yes	characteristic
405	C₂×C₂₃	#3585	1	1	yes	characteristic
406	C₂⁵	—	2	1	no	—
407	C₂×#41	—	2	2	no	—
408	C₂×#41	—	4	4	no	—
409	C₂×#41	C₂³×C₂₃	1	4	yes	—
410	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
411	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
412	C₂²×Q₈	C₂³×C₂₃	1	2	yes	complemented
413	C₂²×D₄	—	2	1	no	—
414	C₂²×D₄	—	2	1	no	—
415	C₂²×D₄	—	2	1	no	—
416	C₂²×D₄	—	2	2	no	—
417	C₂²×D₄	—	4	4	no	—
418	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
419	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
420	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
421	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
422	C₂³×C₄	—	2	1	no	—
423	C₂³×C₄	—	2	1	no	—
424	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
425	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
426	#137	—	4	8	no	—
427	C₂×Q₁₆	C₂³×C₂₃	1	8	yes	complemented
428	C₂×SD₁₆	—	4	8	no	—
429	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	—
430	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	—
431	C₂×M₁₆	C₂³×C₂₃	1	4	yes	complemented
432	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
433	C₄⋊Q₈	—	2	4	no	—
434	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	complemented
435	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	complemented
436	#125	—	2	4	no	—
437	#125	—	2	2	no	—
438	#124	—	2	2	no	—
439	#124	C₂³×C₂₃	1	4	yes	—
440	#123	—	2	8	no	—
441	C₂²⋊Q₈	—	2	2	no	—
442	C₂²⋊Q₈	—	2	2	no	—
443	C₂²⋊Q₈	—	2	2	no	—
444	C₂²⋊Q₈	—	2	2	no	—
445	C₂²⋊Q₈	—	2	2	no	—
446	C₂²⋊Q₈	—	2	2	no	—
447	C₂²⋊Q₈	—	2	4	no	—
448	C₂²⋊Q₈	—	2	4	no	—
449	C₂²⋊Q₈	—	2	4	no	—
450	C₂²⋊Q₈	—	2	4	no	—
451	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
452	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
453	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
454	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	complemented
455	#121	—	2	2	no	—
456	#121	—	2	8	no	—
457	#121	C₂³×C₂₃	1	4	yes	—
458	#120	—	2	8	no	—
459	C₄×Q₈	—	2	2	no	—
460	C₄×Q₈	C₂³×C₂₃	1	4	yes	complemented
461	C₄×D₄	—	2	4	no	—
462	C₄×D₄	—	2	4	no	—
463	C₄×D₄	—	2	2	no	—
464	C₄×D₄	D₄×C₂₃	1	4	yes	—
465	C₄×D₄	C₂³×C₂₃	1	4	yes	—
466	C₄×D₄	C₂³×C₂₃	1	4	yes	—
467	#117	—	2	2	no	—
468	C₂×C₄⋊C₄	—	2	1	no	—
469	C₂×C₄⋊C₄	—	2	2	no	—
470	C₂×C₄⋊C₄	—	2	2	no	—
471	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
472	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
474	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	complemented
475	C₂×C₂²⋊C₄	—	2	1	no	—
476	C₂×C₂²⋊C₄	—	2	2	no	—
477	C₂×C₂²⋊C₄	—	2	2	no	—
478	C₂×C₂²⋊C₄	—	2	1	no	—
479	C₂×C₂²⋊C₄	—	2	1	no	—
480	C₂×C₂²⋊C₄	—	2	1	no	—
481	C₂×C₂²⋊C₄	—	2	1	no	—
482	C₂×C₂²⋊C₄	—	2	8	no	—
483	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
484	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
485	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
486	#107	C₂³×C₂₃	1	8	yes	complemented
487	C₄⋊C₈	C₂³×C₂₃	1	4	yes	complemented
488	#103	C₂³×C₂₃	1	8	yes	complemented
489	#103	C₂³×C₂₃	1	8	yes	complemented
490	#102	C₂³×C₂₃	1	8	yes	—
491	#102	C₂³×C₂₃	1	8	yes	—
492	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
493	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
494	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	complemented
495	#97	C₂³×C₂₃	1	4	yes	complemented
496	C₂₃	#61570	1	1	yes	characteristic, direct product factor, Sylow
497	C₂⁴	—	2	1	no	—
498	C₂⁴	—	2	1	no	—
499	C₂⁴	—	2	4	no	—
500	C₂⁴	—	4	4	no	—
501	C₂⁴	—	4	4	no	—
502	C₂⁴	—	8	2	no	—
503	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
504	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
505	#41	—	2	8	no	—
506	#41	—	4	4	no	—
507	#41	—	4	8	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	2	no	—
510	C₂×Q₈	—	2	2	no	—
511	C₂×Q₈	—	2	2	no	—
512	C₂×Q₈	—	4	2	no	—
513	C₂×Q₈	—	4	4	no	—
514	C₂×Q₈	—	4	4	no	—
515	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
516	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
517	C₂×D₄	—	2	4	no	—
518	C₂×D₄	—	2	4	no	—
519	C₂×D₄	—	2	8	no	—
520	C₂×D₄	—	2	4	no	—
521	C₂×D₄	—	2	4	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	4	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	—	4	4	no	—
526	C₂×D₄	—	4	2	no	—
527	C₂×D₄	—	4	8	no	—
528	C₂×D₄	—	4	4	no	—
529	C₂×D₄	—	4	4	no	—
530	C₂×D₄	—	8	2	no	—
531	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
532	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
533	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	2	2	no	—
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	—	2	4	no	—
541	C₂²×C₄	—	2	4	no	—
542	C₂²×C₄	—	4	2	no	—
543	C₂²×C₄	—	4	2	no	—
544	C₂²×C₄	—	4	4	no	—
545	C₂²×C₄	—	8	2	no	—
546	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
547	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
548	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
549	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
550	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
551	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
554	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
555	Q₁₆	—	4	8	no	—
556	SD₁₆	—	2	16	no	—
557	SD₁₆	—	4	8	no	—
558	M₁₆	—	4	4	no	—
559	C₂×C₈	—	4	4	no	—
560	C₂×C₈	C₂⁴×C₂₃	1	8	yes	—
561	C₄⋊C₄	—	2	4	no	—
562	C₄⋊C₄	—	2	4	no	—
563	C₄⋊C₄	—	2	4	no	—
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	4	no	—
572	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
573	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
574	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
575	C₂²⋊C₄	—	2	4	no	—
576	C₂²⋊C₄	—	2	4	no	—
577	C₂²⋊C₄	—	2	4	no	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	—	2	4	no	—
580	C₂²⋊C₄	—	2	4	no	—
581	C₂²⋊C₄	—	2	4	no	—
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
584	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
585	C₄²	—	2	4	no	—
586	C₄²	C₂×D₄×C₂₃	1	2	yes	—
587	C₄²	C₂⁴×C₂₃	1	2	yes	—
588	C₂³	—	2	4	no	—
589	C₂³	—	2	2	no	—
590	C₂³	—	2	2	no	—
591	C₂³	—	2	2	no	—
592	C₂³	—	4	1	no	—
593	C₂³	—	4	1	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	1	no	—
596	C₂³	—	4	8	no	—
597	C₂³	—	4	2	no	—
598	C₂³	—	4	2	no	—
599	C₂³	—	4	2	no	—
600	C₂³	—	4	2	no	—
601	C₂³	—	4	8	no	—
602	C₂³	—	4	2	no	—
603	C₂³	—	8	4	no	—
604	C₂³	—	8	16	no	—
605	C₂³	C₂₃×#137	1	4	yes	complemented
606	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
607	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
608	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
609	Q₈	—	2	8	no	—
610	Q₈	—	2	4	no	—
611	Q₈	—	4	2	no	—
612	Q₈	—	8	2	no	—
613	Q₈	—	8	2	no	—
614	Q₈	—	8	2	no	—
615	D₄	—	2	4	no	—
616	D₄	—	2	8	no	—
617	D₄	—	2	2	no	—
618	D₄	—	2	4	no	—
619	D₄	—	4	8	no	—
620	D₄	—	4	2	no	—
621	D₄	—	4	8	no	—
622	D₄	—	8	4	no	—
623	D₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	2	4	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	2	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	2	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	8	no	—
638	C₂×C₄	—	4	2	no	—
639	C₂×C₄	—	4	2	no	—
640	C₂×C₄	—	8	4	no	—
641	C₂×C₄	—	8	2	no	—
642	C₂×C₄	—	8	2	no	—
643	C₂×C₄	—	8	2	no	—
644	C₂×C₄	—	8	2	no	—
645	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
646	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
647	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
648	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
649	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
650	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
651	C₈	—	2	8	no	—
652	C₂²	—	2	1	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	4	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	4	4	no	—
661	C₂²	—	4	8	no	—
662	C₂²	—	4	2	no	—
663	C₂²	—	4	2	no	—
664	C₂²	—	4	2	no	—
665	C₂²	—	4	2	no	—
666	C₂²	—	4	2	no	—
667	C₂²	—	8	2	no	—
668	C₂²	—	8	16	no	—
669	C₂²	—	8	4	no	—
670	C₂²	C₂×C₂₃×#137	1	2	yes	—
671	C₂²	C₂×C₂₃×#137	1	4	yes	—
672	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
673	C₄	—	2	2	no	—
674	C₄	—	2	1	no	—
675	C₄	—	2	2	no	—
676	C₄	—	2	2	no	—
677	C₄	—	2	2	no	—
678	C₄	—	4	2	no	—
679	C₄	—	4	4	no	—
680	C₄	—	4	2	no	—
681	C₄	—	4	4	no	—
682	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
683	C₂	—	2	2	no	—
684	C₂	—	2	4	no	—
685	C₂	—	4	2	no	—
686	C₂	—	4	4	no	—
687	C₂	—	8	2	no	—
688	C₂	C₂₃×#3484	1	1	yes	characteristic
689	C₂	C₂²×C₂₃×#137	1	1	yes	characteristic
690	C₂	C₂₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#546	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄×D₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3501	C₂	semidirect
3. C₂₃×#3314	C₂	semidirect
4. C₂₃×#3266	C₂	semidirect
5. C₂₃×#3215	C₂	semidirect
6. C₂₃×#3193	C₂	semidirect
7. C₂₃×#3189	C₂	semidirect
8. C₂₃×#3110	C₂	semidirect
9. C₂₃×#3007	C₂	semidirect
10. C₂×C₂₃×#450	C₂	semidirect
11. C₂₃×#2973	C₂	semidirect
14. C₂×C₂₃×#137	C₂²	semidirect
15. C₂²×SD₁₆×C₂₃	C₂²	semidirect
17. C₂₃×#554	C₂²	semidirect
18. D₄×Q₈×C₂₃	C₂²	semidirect
24. C₂₃×#533	C₂²	semidirect
29. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
37. C₂₃×#497	C₂²	semidirect
38. C₂₃×#489	C₂²	semidirect
39. C₂₃×#484	C₂²	semidirect
40. C₂₃×#484	C₂²	semidirect
41. C₂₃×#480	C₂²	semidirect
42. C₂₃×#474	C₂²	semidirect
43. C₂₃×#468	C₂²	semidirect
44. C₂₃×#467	C₂²	semidirect
45. C₂₃×#464	C₂²	semidirect
46. C₂₃×#461	C₂²	semidirect
47. C₂₃×#452	C₂²	semidirect
48. C₂₃×#451	C₂²	semidirect
49. C₂₃×#451	C₂²	semidirect
52. C₂₃×#450	C₂²	semidirect
53. C₂₃×#448	C₂²	semidirect
54. C₂₃×#440	C₂²	semidirect
55. C₂₃×#435	C₂²	semidirect
56. C₂₃×#432	C₂²	semidirect
57. C₂₃×#417	C₂²	semidirect
58. C₂×C₂₃×#102	C₂²	semidirect
59. C₂₃×#407	C₂²	semidirect
67. C₂²×Q₈×C₂₃	C₂³	semidirect
82. C₂×Q₁₆×C₂₃	C₂³	semidirect
86. C₂×M₁₆×C₂₃	C₂³	semidirect
89. C₂₃×C₄⋊Q₈	C₂³	semidirect
90. C₂₃×C₄⋊Q₈	C₂³	semidirect
109. C₂₃×C₂²⋊Q₈	C₂³	semidirect
115. C₄×Q₈×C₂₃	C₂³	semidirect
129. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
141. C₂₃×#107	C₂³	semidirect
142. C₂₃×C₄⋊C₈	C₂³	semidirect
143. C₂₃×#103	C₂³	semidirect
144. C₂₃×#103	C₂³	semidirect
149. C₂₃×C₂²⋊C₈	C₂³	semidirect
150. C₂₃×#97	C₂³	semidirect
242. #61570	C₂₃	direct (N × H)
260. C₂³×C₂₃	#137	semidirect
307. #3501	C₂×C₂₃	semidirect
309. #3314	C₂×C₂₃	semidirect
310. #3266	C₂×C₂₃	semidirect
311. #3215	C₂×C₂₃	semidirect
312. #3193	C₂×C₂₃	semidirect
313. #3189	C₂×C₂₃	semidirect
314. #3110	C₂×C₂₃	semidirect
315. #3007	C₂×C₂₃	semidirect
316. C₂×#450	C₂×C₂₃	semidirect
317. #2973	C₂×C₂₃	semidirect
351. C₂×#137	C₂²×C₂₃	semidirect
352. C₂²×SD₁₆	C₂²×C₂₃	semidirect
354. #554	C₂²×C₂₃	semidirect
355. D₄×Q₈	C₂²×C₂₃	semidirect
361. #533	C₂²×C₂₃	semidirect
366. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
374. #497	C₂²×C₂₃	semidirect
375. #489	C₂²×C₂₃	semidirect
376. #484	C₂²×C₂₃	semidirect
377. #484	C₂²×C₂₃	semidirect
378. #480	C₂²×C₂₃	semidirect
379. #474	C₂²×C₂₃	semidirect
380. #468	C₂²×C₂₃	semidirect
381. #467	C₂²×C₂₃	semidirect
382. #464	C₂²×C₂₃	semidirect
383. #461	C₂²×C₂₃	semidirect
384. #452	C₂²×C₂₃	semidirect
385. #451	C₂²×C₂₃	semidirect
386. #451	C₂²×C₂₃	semidirect
389. #450	C₂²×C₂₃	semidirect
390. #448	C₂²×C₂₃	semidirect
391. #440	C₂²×C₂₃	semidirect
392. #435	C₂²×C₂₃	semidirect
393. #432	C₂²×C₂₃	semidirect
394. #417	C₂²×C₂₃	semidirect
395. C₂×#102	C₂²×C₂₃	semidirect
396. #407	C₂²×C₂₃	semidirect
412. C₂²×Q₈	C₂³×C₂₃	semidirect
427. C₂×Q₁₆	C₂³×C₂₃	semidirect
431. C₂×M₁₆	C₂³×C₂₃	semidirect
434. C₄⋊Q₈	C₂³×C₂₃	semidirect
435. C₄⋊Q₈	C₂³×C₂₃	semidirect
454. C₂²⋊Q₈	C₂³×C₂₃	semidirect
460. C₄×Q₈	C₂³×C₂₃	semidirect
474. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
486. #107	C₂³×C₂₃	semidirect
487. C₄⋊C₈	C₂³×C₂₃	semidirect
488. #103	C₂³×C₂₃	semidirect
489. #103	C₂³×C₂₃	semidirect
494. C₂²⋊C₈	C₂³×C₂₃	semidirect
495. #97	C₂³×C₂₃	semidirect
496. C₂₃	#61570	direct (N × H)
605. C₂³	C₂₃×#137	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3501	2
C₂×C₂₃×#546	2
C₂₃×#3314	2
C₂₃×#3266	2
C₂₃×#3215	2
C₂₃×#3193	2
C₂₃×#3189	2
C₂₃×#3110	2
C₂₃×#3007	2
C₂×C₂₃×#450	2
C₂₃×#2973	2
#61570	23

Subgroups — C23×#61570 #19209196

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61570 #19209196