Subgroups — C₂₃×#60941 #19208567

Order 5888.

2082 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#532	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3246	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3229	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3227	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3208	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3206	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3187	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3167	C₂	1	4	yes	maximal, complemented
10	C₂₃×#3103	C₂	1	4	yes	maximal, complemented
11	C₂₃×#3101	C₂	1	4	yes	maximal, complemented
12	C₂×C₂₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₂₃	—	2	1	no	—
14	C₂₃×#533	—	2	1	no	—
15	C₂₃×#533	—	2	1	no	—
16	C₂₃×#533	—	2	1	no	—
17	C₂₃×#533	—	2	1	no	—
18	C₂₃×#533	C₂²	1	2	yes	—
19	C₂₃×#533	C₂²	1	2	yes	—
20	C₂₃×#533	C₂²	1	2	yes	complemented
21	C₂₃×#533	C₂²	1	2	yes	complemented
22	C₂₃×#532	—	2	1	no	—
23	C₂₃×#532	—	2	1	no	—
24	C₂₃×#532	—	2	1	no	—
25	C₂₃×#532	—	2	1	no	—
26	C₂₃×#532	C₂²	1	2	yes	—
27	C₂₃×#532	C₂²	1	2	yes	—
28	C₂₃×#532	C₂²	1	2	yes	—
29	C₂₃×#532	C₂²	1	2	yes	—
30	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#125	—	2	1	no	—
35	C₂×C₂₃×#124	—	2	1	no	—
36	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
37	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
38	C₂×C₂₃×#121	—	2	1	no	—
39	C₂×C₂₃×#121	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
41	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
42	C₂×C₄×D₄×C₂₃	—	2	1	no	—
43	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
44	C₂×C₂₃×#117	—	2	1	no	—
45	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
46	C₂₃×#498	C₂²	1	4	yes	complemented
47	C₂₃×#492	C₂²	1	4	yes	complemented
48	C₂₃×#487	C₂²	1	4	yes	complemented
49	C₂₃×#486	C₂²	1	4	yes	complemented
50	C₂₃×#483	C₂²	1	8	yes	—
51	C₂₃×#481	C₂²	1	8	yes	complemented
52	C₂₃×#476	C₂²	1	8	yes	complemented
53	C₂₃×#475	C₂²	1	8	yes	complemented
54	C₂₃×#465	C₂²	1	16	yes	complemented
55	C₂₃×#461	C₂²	1	8	yes	complemented
56	C₂₃×#460	C₂²	1	8	yes	complemented
57	C₂₃×#450	C₂²	1	8	yes	—
58	C₂₃×#448	C₂²	1	8	yes	complemented
59	C₄×SD₁₆×C₂₃	C₂²	1	16	yes	complemented
60	C₂₃×#431	C₂²	1	2	yes	—
61	C₂₃×#431	C₂²	1	2	yes	—
62	C₂₃×#431	C₂²	1	2	yes	complemented
63	C₂₃×#431	C₂²	1	2	yes	complemented
64	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	complemented
65	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
66	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	complemented
67	C₂×#41×C₂₃	—	2	2	no	—
68	C₂×#41×C₂₃	—	2	2	no	—
69	C₂×#41×C₂₃	—	2	2	no	—
70	C₂×#41×C₂₃	—	2	2	no	—
71	C₂×#41×C₂₃	—	4	8	no	—
72	C₂²×Q₈×C₂₃	—	2	1	no	—
73	C₂²×Q₈×C₂₃	—	2	1	no	—
74	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
75	C₂²×D₄×C₂₃	—	2	2	no	—
76	C₂²×D₄×C₂₃	—	2	1	no	—
77	C₂²×D₄×C₂₃	—	2	1	no	—
78	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
79	C₂³×C₄×C₂₃	—	2	2	no	—
80	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
81	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
82	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
83	C₂×SD₁₆×C₂₃	C₂³	1	16	yes	—
84	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
85	C₂₃×C₄⋊Q₈	—	2	1	no	—
86	C₂₃×C₄⋊Q₈	—	2	1	no	—
87	C₂₃×C₄⋊Q₈	—	2	1	no	—
88	C₂₃×C₄⋊Q₈	—	2	1	no	—
89	C₂₃×C₄⋊Q₈	—	2	1	no	—
90	C₂₃×C₄⋊Q₈	—	2	1	no	—
91	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
92	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
93	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
94	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
95	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
96	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
97	C₂₃×#127	—	2	1	no	—
98	C₂₃×#127	—	2	1	no	—
99	C₂₃×#127	C₂³	1	2	yes	—
100	C₂₃×#127	C₂³	1	2	yes	—
101	C₂₃×#125	—	2	2	no	—
102	C₂₃×#125	—	2	2	no	—
103	C₂₃×#125	—	2	2	no	—
104	C₂₃×#125	—	2	2	no	—
105	C₂₃×#124	—	2	2	no	—
106	C₂₃×#124	—	2	2	no	—
107	C₂₃×#124	—	2	2	no	—
108	C₂₃×#124	—	2	2	no	—
109	C₂₃×C₂²⋊Q₈	—	2	2	no	—
110	C₂₃×C₂²⋊Q₈	—	2	2	no	—
111	C₂₃×C₂²⋊Q₈	—	2	2	no	—
112	C₂₃×C₂²⋊Q₈	—	2	2	no	—
113	C₂₃×C₂²⋊Q₈	—	2	2	no	—
114	C₂₃×C₂²⋊Q₈	—	2	2	no	—
115	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
116	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
117	C₂₃×#121	—	2	2	no	—
118	C₂₃×#121	—	2	2	no	—
119	C₂₃×#121	—	2	2	no	—
120	C₂₃×#121	—	2	2	no	—
121	C₂₃×#121	—	2	2	no	—
122	C₂₃×#121	—	2	2	no	—
123	C₂₃×#121	C₂³	1	4	yes	—
124	C₂₃×#121	C₂³	1	4	yes	—
125	C₄×Q₈×C₂₃	—	2	2	no	—
126	C₄×Q₈×C₂₃	—	2	2	no	—
127	C₄×Q₈×C₂₃	—	2	2	no	—
128	C₄×Q₈×C₂₃	—	2	2	no	—
129	C₄×Q₈×C₂₃	—	2	2	no	—
130	C₄×Q₈×C₂₃	—	2	2	no	—
131	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
132	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
133	C₄×D₄×C₂₃	—	2	2	no	—
134	C₄×D₄×C₂₃	—	2	2	no	—
135	C₄×D₄×C₂₃	—	2	2	no	—
136	C₄×D₄×C₂₃	—	2	2	no	—
137	C₄×D₄×C₂₃	—	2	2	no	—
138	C₄×D₄×C₂₃	—	2	2	no	—
139	C₄×D₄×C₂₃	C₂³	1	4	yes	—
140	C₄×D₄×C₂₃	C₂³	1	4	yes	—
141	C₂₃×#117	—	2	2	no	—
142	C₂₃×#117	—	2	2	no	—
143	C₂₃×#117	—	2	2	no	—
144	C₂₃×#117	—	2	2	no	—
145	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
146	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
147	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
148	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
149	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
150	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
151	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
154	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
155	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
156	C₂×C₄²×C₂₃	—	2	2	no	—
157	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
158	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
159	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
160	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
161	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
162	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
163	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
169	C₂₃×#106	C₂³	1	16	yes	—
170	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
171	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
172	C₂₃×#103	C₂³	1	16	yes	—
173	C₂₃×#102	C₂³	1	16	yes	—
174	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
175	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
176	C₄×C₈×C₂₃	C₂³	1	4	yes	—
177	C₄×C₈×C₂₃	C₂³	1	4	yes	—
178	C₂⁴×C₂₃	—	2	2	no	—
179	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
180	#41×C₂₃	—	4	8	no	—
181	#41×C₂₃	—	4	8	no	—
182	#41×C₂₃	—	4	8	no	—
183	#41×C₂₃	—	4	8	no	—
184	C₂×Q₈×C₂₃	—	2	2	no	—
185	C₂×Q₈×C₂₃	—	2	2	no	—
186	C₂×Q₈×C₂₃	—	2	2	no	—
187	C₂×Q₈×C₂₃	—	2	2	no	—
188	C₂×Q₈×C₂₃	—	2	2	no	—
189	C₂×Q₈×C₂₃	—	4	4	no	—
190	C₂×Q₈×C₂₃	—	4	4	no	—
191	C₂×Q₈×C₂₃	—	4	4	no	—
192	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
193	C₂×D₄×C₂₃	—	2	4	no	—
194	C₂×D₄×C₂₃	—	2	4	no	—
195	C₂×D₄×C₂₃	—	2	2	no	—
196	C₂×D₄×C₂₃	—	2	2	no	—
197	C₂×D₄×C₂₃	—	2	2	no	—
198	C₂×D₄×C₂₃	—	2	2	no	—
199	C₂×D₄×C₂₃	—	2	2	no	—
200	C₂×D₄×C₂₃	—	4	4	no	—
201	C₂×D₄×C₂₃	—	4	4	no	—
202	C₂×D₄×C₂₃	—	4	8	no	—
203	C₂×D₄×C₂₃	—	4	4	no	—
204	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
205	C₂²×C₄×C₂₃	—	2	2	no	—
206	C₂²×C₄×C₂₃	—	2	2	no	—
207	C₂²×C₄×C₂₃	—	2	2	no	—
208	C₂²×C₄×C₂₃	—	2	4	no	—
209	C₂²×C₄×C₂₃	—	2	4	no	—
210	C₂²×C₄×C₂₃	—	4	2	no	—
211	C₂²×C₄×C₂₃	—	4	2	no	—
212	C₂²×C₄×C₂₃	—	4	8	no	—
213	C₂²×C₄×C₂₃	SD₁₆	1	8	yes	complemented
214	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
232	SD₁₆×C₂₃	—	4	16	no	—
233	C₂×C₈×C₂₃	—	4	4	no	—
234	C₂×C₈×C₂₃	C₂⁴	1	8	yes	—
235	C₄⋊C₄×C₂₃	—	2	2	no	—
236	C₄⋊C₄×C₂₃	—	2	2	no	—
237	C₄⋊C₄×C₂₃	—	2	2	no	—
238	C₄⋊C₄×C₂₃	—	2	2	no	—
239	C₄⋊C₄×C₂₃	—	2	2	no	—
240	C₄⋊C₄×C₂₃	—	2	2	no	—
241	C₄⋊C₄×C₂₃	—	2	2	no	—
242	C₄⋊C₄×C₂₃	—	2	2	no	—
243	C₄⋊C₄×C₂₃	—	2	4	no	—
244	C₄⋊C₄×C₂₃	—	2	4	no	—
245	C₄⋊C₄×C₂₃	—	2	4	no	—
246	C₄⋊C₄×C₂₃	—	2	4	no	—
247	C₄⋊C₄×C₂₃	—	2	2	no	—
248	C₄⋊C₄×C₂₃	—	2	2	no	—
249	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
250	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
251	C₂²⋊C₄×C₂₃	—	2	4	no	—
252	C₂²⋊C₄×C₂₃	—	2	4	no	—
253	C₂²⋊C₄×C₂₃	—	2	4	no	—
254	C₂²⋊C₄×C₂₃	—	2	4	no	—
255	C₂²⋊C₄×C₂₃	—	2	4	no	—
256	C₂²⋊C₄×C₂₃	—	2	4	no	—
257	C₄²×C₂₃	—	2	4	no	—
258	C₄²×C₂₃	—	2	4	no	—
259	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
260	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
261	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
262	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
263	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
264	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
265	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
266	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
267	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
268	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
269	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
270	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
271	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
272	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
273	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
274	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
275	#60941	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
276	C₂³×C₂₃	—	2	4	no	—
277	C₂³×C₂₃	—	4	1	no	—
278	C₂³×C₂₃	—	4	1	no	—
279	C₂³×C₂₃	—	4	4	no	—
280	C₂³×C₂₃	—	4	4	no	—
281	C₂³×C₂₃	—	4	4	no	—
282	C₂³×C₂₃	C₂×SD₁₆	1	4	yes	—
283	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
284	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
285	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
286	Q₈×C₂₃	—	2	8	no	—
287	Q₈×C₂₃	—	4	4	no	—
288	Q₈×C₂₃	—	4	4	no	—
289	Q₈×C₂₃	—	4	4	no	—
290	Q₈×C₂₃	—	4	4	no	—
291	Q₈×C₂₃	—	4	4	no	—
292	D₄×C₂₃	—	2	8	no	—
293	D₄×C₂₃	—	4	4	no	—
294	D₄×C₂₃	—	4	4	no	—
295	D₄×C₂₃	—	4	8	no	—
296	D₄×C₂₃	—	4	8	no	—
297	D₄×C₂₃	—	4	4	no	—
298	D₄×C₂₃	—	4	4	no	—
299	D₄×C₂₃	—	4	4	no	—
300	C₂×C₄×C₂₃	—	2	2	no	—
301	C₂×C₄×C₂₃	—	2	2	no	—
302	C₂×C₄×C₂₃	—	2	2	no	—
303	C₂×C₄×C₂₃	—	2	2	no	—
304	C₂×C₄×C₂₃	—	2	2	no	—
305	C₂×C₄×C₂₃	—	2	2	no	—
306	C₂×C₄×C₂₃	—	2	4	no	—
307	C₂×C₄×C₂₃	—	2	4	no	—
308	C₂×C₄×C₂₃	—	2	4	no	—
309	C₂×C₄×C₂₃	—	4	1	no	—
310	C₂×C₄×C₂₃	—	4	1	no	—
311	C₂×C₄×C₂₃	—	4	1	no	—
312	C₂×C₄×C₂₃	—	4	1	no	—
313	C₂×C₄×C₂₃	—	4	1	no	—
314	C₂×C₄×C₂₃	—	4	1	no	—
315	C₂×C₄×C₂₃	—	4	4	no	—
316	C₂×C₄×C₂₃	—	4	4	no	—
317	C₂×C₄×C₂₃	—	4	4	no	—
318	C₂×C₄×C₂₃	—	4	8	no	—
319	C₂×C₄×C₂₃	—	4	8	no	—
320	C₂×C₄×C₂₃	C₂×SD₁₆	1	4	yes	—
321	C₂×C₄×C₂₃	C₂×SD₁₆	1	4	yes	—
322	C₂×C₄×C₂₃	C₂×SD₁₆	1	4	yes	—
323	C₂×C₄×C₂₃	C₂×SD₁₆	1	4	yes	—
324	C₂×C₄×C₂₃	C₂×SD₁₆	1	4	yes	—
325	C₂×C₄×C₂₃	C₂×SD₁₆	1	4	yes	—
326	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
338	C₈×C₂₃	—	2	8	no	—
339	C₂×#533	C₂×C₂₃	1	1	yes	characteristic, complemented
340	C₂×#532	C₂×C₂₃	1	1	yes	characteristic
341	#3246	C₂×C₂₃	1	4	yes	complemented
342	#3229	C₂×C₂₃	1	2	yes	complemented
343	#3227	C₂×C₂₃	1	2	yes	complemented
344	#3208	C₂×C₂₃	1	2	yes	complemented
345	#3206	C₂×C₂₃	1	2	yes	complemented
346	#3187	C₂×C₂₃	1	4	yes	complemented
347	#3167	C₂×C₂₃	1	4	yes	complemented
348	#3103	C₂×C₂₃	1	4	yes	complemented
349	#3101	C₂×C₂₃	1	4	yes	complemented
350	C₂×#431	C₂×C₂₃	1	1	yes	characteristic, complemented
351	C₂²×C₂₃	—	2	1	no	—
352	C₂²×C₂₃	—	2	1	no	—
353	C₂²×C₂₃	—	2	1	no	—
354	C₂²×C₂₃	—	2	1	no	—
355	C₂²×C₂₃	—	2	1	no	—
356	C₂²×C₂₃	—	2	1	no	—
357	C₂²×C₂₃	—	4	4	no	—
358	C₂²×C₂₃	—	4	4	no	—
359	C₂²×C₂₃	—	4	4	no	—
360	C₂²×C₂₃	—	4	4	no	—
361	C₂²×C₂₃	—	8	8	no	—
362	C₂²×C₂₃	C₂²×SD₁₆	1	2	yes	—
363	C₂²×C₂₃	C₂²×SD₁₆	1	2	yes	—
364	C₂²×C₂₃	C₂²×SD₁₆	1	2	yes	—
365	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
366	C₄×C₂₃	—	2	1	no	—
367	C₄×C₂₃	—	2	1	no	—
368	C₄×C₂₃	—	2	1	no	—
369	C₄×C₂₃	—	2	1	no	—
370	C₄×C₂₃	—	2	1	no	—
371	C₄×C₂₃	—	2	1	no	—
372	C₄×C₂₃	—	4	4	no	—
373	C₄×C₂₃	—	4	4	no	—
374	C₄×C₂₃	—	4	4	no	—
375	C₄×C₂₃	C₂²×SD₁₆	1	2	yes	—
376	C₄×C₂₃	C₂²×SD₁₆	1	2	yes	—
377	C₄×C₂₃	C₂²×SD₁₆	1	2	yes	—
378	C₄×C₂₃	C₂²×SD₁₆	1	2	yes	—
379	C₄×C₂₃	#575	1	2	yes	—
380	C₄×C₂₃	#585	1	2	yes	—
381	C₂²×#41	—	2	1	no	—
382	#533	—	2	1	no	—
383	#533	—	2	1	no	—
384	#533	—	2	1	no	—
385	#533	—	2	1	no	—
386	#533	C₂²×C₂₃	1	2	yes	—
387	#533	C₂²×C₂₃	1	2	yes	—
388	#533	C₂²×C₂₃	1	2	yes	complemented
389	#533	C₂²×C₂₃	1	2	yes	complemented
390	#532	—	2	1	no	—
391	#532	—	2	1	no	—
392	#532	—	2	1	no	—
393	#532	—	2	1	no	—
394	#532	C₂²×C₂₃	1	2	yes	—
395	#532	C₂²×C₂₃	1	2	yes	—
396	#532	C₂²×C₂₃	1	2	yes	—
397	#532	C₂²×C₂₃	1	2	yes	—
398	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
399	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
400	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
401	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
402	C₂×#125	—	2	1	no	—
403	C₂×#124	—	2	1	no	—
404	C₂×C₂²⋊Q₈	—	2	1	no	—
405	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
406	C₂×#121	—	2	1	no	—
407	C₂×#121	C₂²×C₂₃	1	2	yes	—
408	C₂×C₄×Q₈	—	2	1	no	—
409	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
410	C₂×C₄×D₄	—	2	1	no	—
411	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
412	C₂×#117	—	2	1	no	—
413	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
414	#498	C₂²×C₂₃	1	4	yes	complemented
415	#492	C₂²×C₂₃	1	4	yes	complemented
416	#487	C₂²×C₂₃	1	4	yes	complemented
417	#486	C₂²×C₂₃	1	4	yes	complemented
418	#483	C₂²×C₂₃	1	8	yes	—
419	#481	C₂²×C₂₃	1	8	yes	complemented
420	#476	C₂²×C₂₃	1	8	yes	complemented
421	#475	C₂²×C₂₃	1	8	yes	complemented
422	#465	C₂²×C₂₃	1	16	yes	complemented
423	#461	C₂²×C₂₃	1	8	yes	complemented
424	#460	C₂²×C₂₃	1	8	yes	complemented
425	#450	C₂²×C₂₃	1	8	yes	—
426	#448	C₂²×C₂₃	1	8	yes	complemented
427	C₄×SD₁₆	C₂²×C₂₃	1	16	yes	complemented
428	#431	C₂²×C₂₃	1	2	yes	—
429	#431	C₂²×C₂₃	1	2	yes	—
430	#431	C₂²×C₂₃	1	2	yes	complemented
431	#431	C₂²×C₂₃	1	2	yes	complemented
432	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	complemented
433	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
434	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	complemented
435	C₂×C₂₃	—	2	2	no	—
436	C₂×C₂₃	—	2	2	no	—
437	C₂×C₂₃	—	2	2	no	—
438	C₂×C₂₃	—	8	4	no	—
439	C₂×C₂₃	#3449	1	1	yes	characteristic
440	C₂×C₂₃	C₂³×SD₁₆	1	1	yes	characteristic
441	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
442	C₂×#41	—	2	2	no	—
443	C₂×#41	—	2	2	no	—
444	C₂×#41	—	2	2	no	—
445	C₂×#41	—	2	2	no	—
446	C₂×#41	—	4	8	no	—
447	C₂²×Q₈	—	2	1	no	—
448	C₂²×Q₈	—	2	1	no	—
449	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
450	C₂²×D₄	—	2	2	no	—
451	C₂²×D₄	—	2	1	no	—
452	C₂²×D₄	—	2	1	no	—
453	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
454	C₂³×C₄	—	2	2	no	—
455	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
456	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
457	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
458	C₂×SD₁₆	C₂³×C₂₃	1	16	yes	—
459	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
460	C₄⋊Q₈	—	2	1	no	—
461	C₄⋊Q₈	—	2	1	no	—
462	C₄⋊Q₈	—	2	1	no	—
463	C₄⋊Q₈	—	2	1	no	—
464	C₄⋊Q₈	—	2	1	no	—
465	C₄⋊Q₈	—	2	1	no	—
466	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
467	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
468	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
469	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
470	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
471	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
472	#127	—	2	1	no	—
473	#127	—	2	1	no	—
474	#127	C₂³×C₂₃	1	2	yes	—
475	#127	C₂³×C₂₃	1	2	yes	—
476	#125	—	2	2	no	—
477	#125	—	2	2	no	—
478	#125	—	2	2	no	—
479	#125	—	2	2	no	—
480	#124	—	2	2	no	—
481	#124	—	2	2	no	—
482	#124	—	2	2	no	—
483	#124	—	2	2	no	—
484	C₂²⋊Q₈	—	2	2	no	—
485	C₂²⋊Q₈	—	2	2	no	—
486	C₂²⋊Q₈	—	2	2	no	—
487	C₂²⋊Q₈	—	2	2	no	—
488	C₂²⋊Q₈	—	2	2	no	—
489	C₂²⋊Q₈	—	2	2	no	—
490	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
491	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
492	#121	—	2	2	no	—
493	#121	—	2	2	no	—
494	#121	—	2	2	no	—
495	#121	—	2	2	no	—
496	#121	—	2	2	no	—
497	#121	—	2	2	no	—
498	#121	C₂³×C₂₃	1	4	yes	—
499	#121	C₂³×C₂₃	1	4	yes	—
500	C₄×Q₈	—	2	2	no	—
501	C₄×Q₈	—	2	2	no	—
502	C₄×Q₈	—	2	2	no	—
503	C₄×Q₈	—	2	2	no	—
504	C₄×Q₈	—	2	2	no	—
505	C₄×Q₈	—	2	2	no	—
506	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
507	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
508	C₄×D₄	—	2	2	no	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	—	2	2	no	—
514	C₄×D₄	C₂³×C₂₃	1	4	yes	—
515	C₄×D₄	C₂³×C₂₃	1	4	yes	—
516	#117	—	2	2	no	—
517	#117	—	2	2	no	—
518	#117	—	2	2	no	—
519	#117	—	2	2	no	—
520	C₂×C₄⋊C₄	—	2	1	no	—
521	C₂×C₄⋊C₄	—	2	1	no	—
522	C₂×C₄⋊C₄	—	2	1	no	—
523	C₂×C₄⋊C₄	—	2	1	no	—
524	C₂×C₄⋊C₄	—	2	2	no	—
525	C₂×C₄⋊C₄	—	2	2	no	—
526	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
528	C₂×C₂²⋊C₄	—	2	2	no	—
529	C₂×C₂²⋊C₄	—	2	2	no	—
530	C₂×C₂²⋊C₄	—	2	2	no	—
531	C₂×C₄²	—	2	2	no	—
532	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
533	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
534	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
535	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
536	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
537	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
538	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
539	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
540	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
541	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
542	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
543	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
544	#106	C₂³×C₂₃	1	16	yes	—
545	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
546	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
547	#103	C₂³×C₂₃	1	16	yes	—
548	#102	C₂³×C₂₃	1	16	yes	—
549	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
550	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
551	C₄×C₈	C₂³×C₂₃	1	4	yes	—
552	C₄×C₈	C₂³×C₂₃	1	4	yes	—
553	C₂₃	#60941	1	1	yes	characteristic, direct product factor, Sylow
554	C₂⁴	—	2	2	no	—
555	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
556	#41	—	4	8	no	—
557	#41	—	4	8	no	—
558	#41	—	4	8	no	—
559	#41	—	4	8	no	—
560	C₂×Q₈	—	2	2	no	—
561	C₂×Q₈	—	2	2	no	—
562	C₂×Q₈	—	2	2	no	—
563	C₂×Q₈	—	2	2	no	—
564	C₂×Q₈	—	2	2	no	—
565	C₂×Q₈	—	4	4	no	—
566	C₂×Q₈	—	4	4	no	—
567	C₂×Q₈	—	4	4	no	—
568	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
569	C₂×D₄	—	2	4	no	—
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	—	4	4	no	—
577	C₂×D₄	—	4	4	no	—
578	C₂×D₄	—	4	8	no	—
579	C₂×D₄	—	4	4	no	—
580	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	4	2	no	—
587	C₂²×C₄	—	4	2	no	—
588	C₂²×C₄	—	4	8	no	—
589	C₂²×C₄	SD₁₆×C₂₃	1	8	yes	complemented
590	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
591	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
592	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
593	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
594	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
597	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
598	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
601	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
602	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
603	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
604	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
605	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
606	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
608	SD₁₆	—	4	16	no	—
609	C₂×C₈	—	4	4	no	—
610	C₂×C₈	C₂⁴×C₂₃	1	8	yes	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	2	no	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
626	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₄²	—	2	4	no	—
634	C₄²	—	2	4	no	—
635	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
636	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
637	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
638	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
639	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
640	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
641	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
642	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
643	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
644	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
645	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
646	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
647	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
648	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
649	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
650	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
651	C₂³	—	2	4	no	—
652	C₂³	—	4	1	no	—
653	C₂³	—	4	1	no	—
654	C₂³	—	4	4	no	—
655	C₂³	—	4	4	no	—
656	C₂³	—	4	4	no	—
657	C₂³	C₂×SD₁₆×C₂₃	1	4	yes	—
658	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
659	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
660	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
661	Q₈	—	2	8	no	—
662	Q₈	—	4	4	no	—
663	Q₈	—	4	4	no	—
664	Q₈	—	4	4	no	—
665	Q₈	—	4	4	no	—
666	Q₈	—	4	4	no	—
667	D₄	—	2	8	no	—
668	D₄	—	4	4	no	—
669	D₄	—	4	4	no	—
670	D₄	—	4	8	no	—
671	D₄	—	4	8	no	—
672	D₄	—	4	4	no	—
673	D₄	—	4	4	no	—
674	D₄	—	4	4	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	2	4	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	4	no	—
691	C₂×C₄	—	4	4	no	—
692	C₂×C₄	—	4	4	no	—
693	C₂×C₄	—	4	8	no	—
694	C₂×C₄	—	4	8	no	—
695	C₂×C₄	C₂×SD₁₆×C₂₃	1	4	yes	—
696	C₂×C₄	C₂×SD₁₆×C₂₃	1	4	yes	—
697	C₂×C₄	C₂×SD₁₆×C₂₃	1	4	yes	—
698	C₂×C₄	C₂×SD₁₆×C₂₃	1	4	yes	—
699	C₂×C₄	C₂×SD₁₆×C₂₃	1	4	yes	—
700	C₂×C₄	C₂×SD₁₆×C₂₃	1	4	yes	—
701	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
702	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
703	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
704	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
705	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
706	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
709	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
710	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
711	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
712	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
713	C₈	—	2	8	no	—
714	C₂²	—	2	1	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	2	1	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	4	4	no	—
721	C₂²	—	4	4	no	—
722	C₂²	—	4	4	no	—
723	C₂²	—	4	4	no	—
724	C₂²	—	8	8	no	—
725	C₂²	C₂²×SD₁₆×C₂₃	1	2	yes	—
726	C₂²	C₂²×SD₁₆×C₂₃	1	2	yes	—
727	C₂²	C₂²×SD₁₆×C₂₃	1	2	yes	—
728	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
729	C₄	—	2	1	no	—
730	C₄	—	2	1	no	—
731	C₄	—	2	1	no	—
732	C₄	—	2	1	no	—
733	C₄	—	2	1	no	—
734	C₄	—	2	1	no	—
735	C₄	—	4	4	no	—
736	C₄	—	4	4	no	—
737	C₄	—	4	4	no	—
738	C₄	C₂²×SD₁₆×C₂₃	1	2	yes	—
739	C₄	C₂²×SD₁₆×C₂₃	1	2	yes	—
740	C₄	C₂²×SD₁₆×C₂₃	1	2	yes	—
741	C₄	C₂²×SD₁₆×C₂₃	1	2	yes	—
742	C₄	C₂₃×#575	1	2	yes	—
743	C₄	C₂₃×#585	1	2	yes	—
744	C₂	—	2	2	no	—
745	C₂	—	2	2	no	—
746	C₂	—	2	2	no	—
747	C₂	—	8	4	no	—
748	C₂	C₂₃×#3449	1	1	yes	characteristic
749	C₂	C₂³×SD₁₆×C₂₃	1	1	yes	characteristic
750	C₂	C₂×C₂₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂³×D₄
prime radical	C₂×C₂₃×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#533	C₂	semidirect
3. C₂₃×#3246	C₂	semidirect
4. C₂₃×#3229	C₂	semidirect
5. C₂₃×#3227	C₂	semidirect
6. C₂₃×#3208	C₂	semidirect
7. C₂₃×#3206	C₂	semidirect
8. C₂₃×#3187	C₂	semidirect
9. C₂₃×#3167	C₂	semidirect
10. C₂₃×#3103	C₂	semidirect
11. C₂₃×#3101	C₂	semidirect
12. C₂×C₂₃×#431	C₂	semidirect
20. C₂₃×#533	C₂²	semidirect
21. C₂₃×#533	C₂²	semidirect
31. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
32. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
41. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
46. C₂₃×#498	C₂²	semidirect
47. C₂₃×#492	C₂²	semidirect
48. C₂₃×#487	C₂²	semidirect
49. C₂₃×#486	C₂²	semidirect
51. C₂₃×#481	C₂²	semidirect
52. C₂₃×#476	C₂²	semidirect
53. C₂₃×#475	C₂²	semidirect
54. C₂₃×#465	C₂²	semidirect
55. C₂₃×#461	C₂²	semidirect
56. C₂₃×#460	C₂²	semidirect
58. C₂₃×#448	C₂²	semidirect
59. C₄×SD₁₆×C₂₃	C₂²	semidirect
62. C₂₃×#431	C₂²	semidirect
63. C₂₃×#431	C₂²	semidirect
64. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
66. C₂×C₄×C₈×C₂₃	C₂²	semidirect
213. C₂²×C₄×C₂₃	SD₁₆	semidirect
275. #60941	C₂₃	direct (N × H)
339. C₂×#533	C₂×C₂₃	semidirect
341. #3246	C₂×C₂₃	semidirect
342. #3229	C₂×C₂₃	semidirect
343. #3227	C₂×C₂₃	semidirect
344. #3208	C₂×C₂₃	semidirect
345. #3206	C₂×C₂₃	semidirect
346. #3187	C₂×C₂₃	semidirect
347. #3167	C₂×C₂₃	semidirect
348. #3103	C₂×C₂₃	semidirect
349. #3101	C₂×C₂₃	semidirect
350. C₂×#431	C₂×C₂₃	semidirect
388. #533	C₂²×C₂₃	semidirect
389. #533	C₂²×C₂₃	semidirect
399. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
400. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
409. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
414. #498	C₂²×C₂₃	semidirect
415. #492	C₂²×C₂₃	semidirect
416. #487	C₂²×C₂₃	semidirect
417. #486	C₂²×C₂₃	semidirect
419. #481	C₂²×C₂₃	semidirect
420. #476	C₂²×C₂₃	semidirect
421. #475	C₂²×C₂₃	semidirect
422. #465	C₂²×C₂₃	semidirect
423. #461	C₂²×C₂₃	semidirect
424. #460	C₂²×C₂₃	semidirect
426. #448	C₂²×C₂₃	semidirect
427. C₄×SD₁₆	C₂²×C₂₃	semidirect
430. #431	C₂²×C₂₃	semidirect
431. #431	C₂²×C₂₃	semidirect
432. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
434. C₂×C₄×C₈	C₂²×C₂₃	semidirect
553. C₂₃	#60941	direct (N × H)
589. C₂²×C₄	SD₁₆×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#533	2
C₂×C₂₃×#532	2
C₂₃×#3246	2
C₂₃×#3229	2
C₂₃×#3227	2
C₂₃×#3208	2
C₂₃×#3206	2
C₂₃×#3187	2
C₂₃×#3167	2
C₂₃×#3103	2
C₂₃×#3101	2
C₂×C₂₃×#431	2
#60941	23

Subgroups — C23×#60941 #19208567

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60941 #19208567