Subgroups — C₂₃×#61367 #19208993

Order 5888.

1826 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3389	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3388	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3385	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3384	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3381	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3380	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3166	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3080	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3077	C₂	1	2	yes	maximal, complemented
15	Q₈×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₂₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
17	C₄×C₂₃×AGL(1,ℤ/8)	C₂	1	2	yes	maximal
18	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	Q₈²×C₂₃	C₂²	1	1	yes	characteristic, complemented
20	C₂₃×#557	C₂²	1	1	yes	characteristic, complemented
21	C₂₃×#557	C₂²	1	2	yes	complemented
22	C₂₃×#554	—	2	1	no	—
23	C₂₃×#554	—	2	2	no	—
24	C₂₃×#554	—	2	1	no	—
25	C₂₃×#554	—	2	1	no	—
26	C₂₃×#554	—	2	2	no	—
27	C₂₃×#554	C₂²	1	2	yes	—
28	C₂₃×#554	C₂²	1	2	yes	—
29	C₂₃×#554	C₂²	1	4	yes	—
30	C₂₃×#554	C₂²	1	1	yes	characteristic, complemented
31	C₂₃×#554	C₂²	1	2	yes	complemented
32	D₄×Q₈×C₂₃	—	2	1	no	—
33	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
34	C₂₃×#533	—	2	2	no	—
35	C₂₃×#533	—	2	1	no	—
36	C₂₃×#533	C₂²	1	1	yes	characteristic
37	C₂₃×#533	C₂²	1	2	yes	—
38	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#125	C₂²	1	2	yes	—
40	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
41	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
42	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
43	C₄×#41×C₂₃	C₂²	1	2	yes	—
44	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
45	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
47	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
48	C₂²×C₄⋊C₄×C₂₃	—	2	1	no	—
49	C₂₃×#501	C₂²	1	4	yes	complemented
50	C₂₃×#501	C₂²	1	4	yes	complemented
51	C₂₃×#501	C₂²	1	4	yes	complemented
52	C₂₃×#500	C₂²	1	2	yes	complemented
53	C₂₃×#499	C₂²	1	4	yes	complemented
54	C₂₃×#499	C₂²	1	4	yes	complemented
55	C₂₃×#498	C₂²	1	2	yes	complemented
56	C₂₃×#479	C₂²	1	4	yes	complemented
57	C₂₃×#479	C₂²	1	4	yes	complemented
58	C₂₃×#478	C₂²	1	4	yes	—
59	C₂₃×#478	C₂²	1	4	yes	—
60	C₂₃×#478	C₂²	1	4	yes	—
61	C₂₃×#478	C₂²	1	4	yes	complemented
62	C₂₃×#478	C₂²	1	4	yes	complemented
63	C₂₃×#477	C₂²	1	2	yes	complemented
64	C₂₃×#476	C₂²	1	2	yes	—
65	C₂₃×#476	C₂²	1	4	yes	—
66	C₂₃×#476	C₂²	1	2	yes	complemented
67	C₂₃×#475	C₂²	1	2	yes	complemented
68	C₂₃×#474	C₂²	1	2	yes	—
69	C₂₃×#474	C₂²	1	4	yes	—
70	C₂₃×#474	C₂²	1	2	yes	complemented
71	C₂₃×#446	C₂²	1	2	yes	complemented
72	C₂₃×#446	C₂²	1	4	yes	complemented
73	C₈×Q₈×C₂₃	C₂²	1	2	yes	complemented
74	C₂₃×#442	C₂²	1	4	yes	—
75	C₂₃×#442	C₂²	1	2	yes	—
76	C₂₃×#440	C₂²	1	4	yes	—
77	C₂₃×#440	C₂²	1	2	yes	—
78	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
79	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	—
80	C₄×D₈×C₂₃	C₂²	1	2	yes	—
81	C₄×D₈×C₂₃	C₂²	1	4	yes	—
82	C₂₃×#428	C₂²	1	2	yes	—
83	C₂₃×#428	C₂²	1	2	yes	—
84	C₂₃×#428	C₂²	1	1	yes	characteristic
85	C₂₃×#428	C₂²	1	2	yes	—
86	C₂₃×#428	C₂²	1	2	yes	—
87	C₂₃×#423	C₂²	1	1	yes	characteristic
88	C₂₃×#423	C₂²	1	2	yes	—
89	C₂₃×#418	C₂²	1	2	yes	—
90	C₂₃×#418	C₂²	1	1	yes	characteristic
91	C₂₃×#417	C₂²	1	2	yes	—
92	C₂₃×#417	C₂²	1	1	yes	characteristic
93	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
94	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
95	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₂₃	—	2	1	no	—
97	C₂²×Q₈×C₂₃	—	2	1	no	—
98	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
99	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₂₃	—	2	1	no	—
101	C₂³×C₄×C₂₃	—	2	2	no	—
102	C₂₃×AGL(1,ℤ/8)	Q₈	1	8	yes	complemented
103	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
104	C₂×D₈×C₂₃	C₂³	1	2	yes	—
105	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
106	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
107	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
108	C₂₃×C₄⋊Q₈	—	2	1	no	—
109	C₂₃×C₄⋊Q₈	—	2	2	no	—
110	C₂₃×C₄⋊Q₈	—	2	1	no	—
111	C₂₃×C₄⋊Q₈	—	2	2	no	—
112	C₂₃×C₄⋊Q₈	—	2	1	no	—
113	C₂₃×C₄⋊Q₈	—	2	1	no	—
114	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₂₃×#125	—	2	2	no	—
121	C₂₃×#125	—	2	2	no	—
122	C₂₃×#125	—	2	2	no	—
123	C₂₃×#125	—	2	2	no	—
124	C₂₃×#125	—	2	2	no	—
125	C₂₃×#125	C₂³	1	4	yes	—
126	C₂₃×#125	C₂³	1	4	yes	—
127	C₂₃×#125	C₂³	1	2	yes	—
128	C₂₃×#125	C₂³	1	2	yes	—
129	C₂₃×#125	C₂³	1	2	yes	—
130	C₂₃×C₂²⋊Q₈	—	2	1	no	—
131	C₂₃×C₂²⋊Q₈	—	2	2	no	—
132	C₂₃×C₂²⋊Q₈	—	2	2	no	—
133	C₂₃×C₂²⋊Q₈	—	2	2	no	—
134	C₂₃×C₂²⋊Q₈	—	2	4	no	—
135	C₂₃×C₂²⋊Q₈	—	2	1	no	—
136	C₂₃×C₂²⋊Q₈	—	2	2	no	—
137	C₂₃×C₂²⋊Q₈	—	2	1	no	—
138	C₂₃×C₂²⋊Q₈	—	2	2	no	—
139	C₂₃×C₂²⋊Q₈	—	2	1	no	—
140	C₂₃×C₂²⋊Q₈	—	2	2	no	—
141	C₂₃×C₂²⋊Q₈	—	2	4	no	—
142	C₂₃×C₂²⋊Q₈	—	2	4	no	—
143	C₂₃×C₂²⋊Q₈	—	2	4	no	—
144	C₂₃×C₂²⋊Q₈	—	2	4	no	—
145	C₂₃×C₂²⋊Q₈	—	2	2	no	—
146	C₂₃×C₂²⋊Q₈	—	2	2	no	—
147	C₂₃×C₂²⋊Q₈	—	2	2	no	—
148	C₄×Q₈×C₂₃	—	2	1	no	—
149	C₄×Q₈×C₂₃	—	2	1	no	—
150	C₄×Q₈×C₂₃	—	2	2	no	—
151	C₄×Q₈×C₂₃	—	2	2	no	—
152	C₄×Q₈×C₂₃	—	2	1	no	—
153	C₄×Q₈×C₂₃	—	2	2	no	—
154	C₄×Q₈×C₂₃	—	2	1	no	—
155	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
156	C₄×Q₈×C₂₃	D₄	1	2	yes	—
157	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
158	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
159	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
160	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
161	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
162	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
164	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
165	C₄×D₄×C₂₃	—	2	1	no	—
166	C₄×D₄×C₂₃	—	2	2	no	—
167	C₄×D₄×C₂₃	—	2	1	no	—
168	C₄×D₄×C₂₃	—	2	2	no	—
169	C₄×D₄×C₂₃	—	2	2	no	—
170	C₄×D₄×C₂₃	—	2	1	no	—
171	C₄×D₄×C₂₃	—	2	2	no	—
172	C₄×D₄×C₂₃	—	2	1	no	—
173	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
174	C₄×D₄×C₂₃	C₂³	1	2	yes	—
175	C₄×D₄×C₂₃	C₂³	1	2	yes	—
176	C₄×D₄×C₂₃	C₂³	1	4	yes	—
177	C₄×D₄×C₂₃	C₂³	1	4	yes	—
178	C₄×D₄×C₂₃	C₂³	1	2	yes	—
179	C₄×D₄×C₂₃	C₂³	1	2	yes	—
180	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
181	C₂₃×#117	—	2	2	no	—
182	C₂₃×#117	—	2	1	no	—
183	C₂₃×#117	C₂³	1	2	yes	—
184	C₂₃×#117	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
186	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
187	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
188	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
189	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
190	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
191	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
192	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
193	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
195	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
198	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
199	C₂×C₄²×C₂₃	—	2	2	no	—
200	C₂×C₄²×C₂₃	—	2	1	no	—
201	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
202	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
203	C₂₃×#107	C₂³	1	2	yes	—
204	C₂₃×#107	C₂³	1	4	yes	—
205	C₂₃×#107	C₂³	1	4	yes	—
206	C₂₃×#107	C₂³	1	4	yes	—
207	C₂₃×#107	C₂³	1	4	yes	—
208	C₂₃×#106	C₂³	1	4	yes	—
209	C₂₃×#106	C₂³	1	2	yes	—
210	C₂₃×#106	C₂³	1	4	yes	—
211	C₂₃×#106	C₂³	1	4	yes	—
212	C₂₃×#106	C₂³	1	4	yes	—
213	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
214	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
215	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
216	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
217	C₂₃×#103	C₂³	1	4	yes	—
218	C₂₃×#103	C₂³	1	2	yes	—
219	C₂₃×#102	C₂³	1	4	yes	—
220	C₂₃×#102	C₂³	1	2	yes	—
221	C₂₃×#102	C₂³	1	4	yes	—
222	C₂₃×#102	C₂³	1	2	yes	—
223	C₂₃×#102	C₂³	1	2	yes	—
224	C₂₃×#102	C₂³	1	4	yes	—
225	C₂₃×#97	C₂³	1	2	yes	—
226	C₂₃×#97	C₂³	1	4	yes	—
227	C₄×C₈×C₂₃	C₂³	1	2	yes	—
228	C₄×C₈×C₂₃	C₂³	1	4	yes	—
229	C₂⁴×C₂₃	—	2	1	no	—
230	#41×C₂₃	—	2	2	no	—
231	#41×C₂₃	C₂×Q₈	1	4	yes	—
232	C₂×Q₈×C₂₃	—	2	2	no	—
233	C₂×Q₈×C₂₃	—	2	1	no	—
234	C₂×Q₈×C₂₃	—	2	1	no	—
235	C₂×Q₈×C₂₃	—	2	2	no	—
236	C₂×Q₈×C₂₃	—	2	2	no	—
237	C₂×Q₈×C₂₃	—	2	2	no	—
238	C₂×Q₈×C₂₃	—	4	2	no	—
239	C₂×Q₈×C₂₃	—	4	4	no	—
240	C₂×Q₈×C₂₃	—	8	2	no	—
241	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
242	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
243	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
244	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
245	C₂×D₄×C₂₃	—	2	1	no	—
246	C₂×D₄×C₂₃	—	2	1	no	—
247	C₂×D₄×C₂₃	—	2	2	no	—
248	C₂×D₄×C₂₃	C₂×Q₈	1	4	yes	complemented
249	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
250	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₂₃	—	2	1	no	—
252	C₂²×C₄×C₂₃	—	2	1	no	—
253	C₂²×C₄×C₂₃	—	2	2	no	—
254	C₂²×C₄×C₂₃	—	2	2	no	—
255	C₂²×C₄×C₂₃	—	2	1	no	—
256	C₂²×C₄×C₂₃	—	2	2	no	—
257	C₂²×C₄×C₂₃	—	2	2	no	—
258	C₂²×C₄×C₂₃	—	2	1	no	—
259	C₂²×C₄×C₂₃	—	2	2	no	—
260	C₂²×C₄×C₂₃	—	2	4	no	—
261	C₂²×C₄×C₂₃	—	2	4	no	—
262	C₂²×C₄×C₂₃	—	4	4	no	—
263	C₂²×C₄×C₂₃	—	8	4	no	—
264	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
266	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
268	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
269	SD₁₆×C₂₃	C₂×Q₈	1	8	yes	complemented
270	D₈×C₂₃	C₂×Q₈	1	8	yes	complemented
271	M₁₆×C₂₃	—	2	2	no	—
272	M₁₆×C₂₃	—	2	4	no	—
273	M₁₆×C₂₃	C₂×Q₈	1	4	yes	complemented
274	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
275	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
276	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
277	C₄⋊C₄×C₂₃	—	2	4	no	—
278	C₄⋊C₄×C₂₃	—	2	4	no	—
279	C₄⋊C₄×C₂₃	—	2	2	no	—
280	C₄⋊C₄×C₂₃	—	2	2	no	—
281	C₄⋊C₄×C₂₃	—	2	2	no	—
282	C₄⋊C₄×C₂₃	—	2	2	no	—
283	C₄⋊C₄×C₂₃	—	2	2	no	—
284	C₄⋊C₄×C₂₃	—	2	2	no	—
285	C₄⋊C₄×C₂₃	—	2	1	no	—
286	C₄⋊C₄×C₂₃	—	2	4	no	—
287	C₄⋊C₄×C₂₃	—	2	4	no	—
288	C₄⋊C₄×C₂₃	—	2	1	no	—
289	C₄⋊C₄×C₂₃	—	2	2	no	—
290	C₄⋊C₄×C₂₃	—	2	2	no	—
291	C₄⋊C₄×C₂₃	—	2	1	no	—
292	C₄⋊C₄×C₂₃	—	2	1	no	—
293	C₄⋊C₄×C₂₃	—	2	2	no	—
294	C₄⋊C₄×C₂₃	—	2	1	no	—
295	C₄⋊C₄×C₂₃	—	2	2	no	—
296	C₄⋊C₄×C₂₃	—	2	2	no	—
297	C₄⋊C₄×C₂₃	—	2	2	no	—
298	C₄⋊C₄×C₂₃	—	2	2	no	—
299	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
300	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
302	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
303	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
304	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
305	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
306	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
307	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
308	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
309	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
310	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
311	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
312	C₂²⋊C₄×C₂₃	—	2	2	no	—
313	C₂²⋊C₄×C₂₃	—	2	1	no	—
314	C₂²⋊C₄×C₂₃	—	2	2	no	—
315	C₂²⋊C₄×C₂₃	—	2	2	no	—
316	C₂²⋊C₄×C₂₃	—	2	4	no	—
317	C₂²⋊C₄×C₂₃	—	2	4	no	—
318	C₂²⋊C₄×C₂₃	—	2	2	no	—
319	C₂²⋊C₄×C₂₃	—	2	1	no	—
320	C₂²⋊C₄×C₂₃	—	2	1	no	—
321	C₂²⋊C₄×C₂₃	—	2	2	no	—
322	C₄²×C₂₃	—	2	2	no	—
323	C₄²×C₂₃	—	2	1	no	—
324	C₄²×C₂₃	—	2	1	no	—
325	C₄²×C₂₃	—	2	2	no	—
326	C₄²×C₂₃	—	2	2	no	—
327	C₄²×C₂₃	—	2	1	no	—
328	C₄²×C₂₃	C₂×D₄	1	2	yes	—
329	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₂₃	C₂×D₄	1	2	yes	—
331	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₂₃	C₂⁴	1	2	yes	—
333	C₄²×C₂₃	C₂⁴	1	2	yes	—
334	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
335	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
336	#61367	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
337	C₂³×C₂₃	—	2	4	no	—
338	C₂³×C₂₃	—	2	1	no	—
339	C₂³×C₂₃	—	2	2	no	—
340	C₂³×C₂₃	—	4	2	no	—
341	C₂³×C₂₃	—	4	2	no	—
342	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
343	Q₈×C₂₃	—	2	2	no	—
344	Q₈×C₂₃	—	2	2	no	—
345	Q₈×C₂₃	—	2	1	no	—
346	Q₈×C₂₃	—	4	2	no	—
347	Q₈×C₂₃	—	4	4	no	—
348	Q₈×C₂₃	—	4	2	no	—
349	Q₈×C₂₃	—	8	2	no	—
350	Q₈×C₂₃	—	8	1	no	—
351	Q₈×C₂₃	—	8	2	no	—
352	Q₈×C₂₃	—	8	2	no	—
353	Q₈×C₂₃	C₂²×Q₈	1	2	yes	—
354	D₄×C₂₃	—	2	4	no	—
355	D₄×C₂₃	—	2	4	no	—
356	D₄×C₂₃	—	2	2	no	—
357	D₄×C₂₃	—	2	1	no	—
358	D₄×C₂₃	C₂²×Q₈	1	2	yes	—
359	D₄×C₂₃	C₂²×Q₈	1	4	yes	—
360	C₂×C₄×C₂₃	—	2	1	no	—
361	C₂×C₄×C₂₃	—	2	4	no	—
362	C₂×C₄×C₂₃	—	2	2	no	—
363	C₂×C₄×C₂₃	—	2	2	no	—
364	C₂×C₄×C₂₃	—	2	1	no	—
365	C₂×C₄×C₂₃	—	2	2	no	—
366	C₂×C₄×C₂₃	—	2	1	no	—
367	C₂×C₄×C₂₃	—	2	2	no	—
368	C₂×C₄×C₂₃	—	2	4	no	—
369	C₂×C₄×C₂₃	—	4	2	no	—
370	C₂×C₄×C₂₃	—	4	2	no	—
371	C₂×C₄×C₂₃	—	4	1	no	—
372	C₂×C₄×C₂₃	—	4	4	no	—
373	C₂×C₄×C₂₃	—	4	4	no	—
374	C₂×C₄×C₂₃	—	4	2	no	—
375	C₂×C₄×C₂₃	—	4	4	no	—
376	C₂×C₄×C₂₃	—	4	4	no	—
377	C₂×C₄×C₂₃	—	4	2	no	—
378	C₂×C₄×C₂₃	—	8	2	no	—
379	C₂×C₄×C₂₃	—	8	1	no	—
380	C₂×C₄×C₂₃	—	8	4	no	—
381	C₂×C₄×C₂₃	—	8	4	no	—
382	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
383	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
385	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
386	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
389	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
392	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
393	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
394	C₈×C₂₃	—	2	4	no	—
395	C₈×C₂₃	—	2	2	no	—
396	C₈×C₂₃	C₂²×Q₈	1	4	yes	—
397	Q₈×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
398	C₂×#554	C₂×C₂₃	1	1	yes	characteristic, complemented
399	#3389	C₂×C₂₃	1	4	yes	complemented
400	#3388	C₂×C₂₃	1	4	yes	complemented
401	#3385	C₂×C₂₃	1	2	yes	complemented
402	#3384	C₂×C₂₃	1	2	yes	complemented
403	#3381	C₂×C₂₃	1	2	yes	complemented
404	#3380	C₂×C₂₃	1	2	yes	complemented
405	#3166	C₂×C₂₃	1	2	yes	complemented
406	#3165	C₂×C₂₃	1	1	yes	characteristic, complemented
407	#3080	C₂×C₂₃	1	2	yes	complemented
408	#3079	C₂×C₂₃	1	1	yes	characteristic, complemented
409	#3077	C₂×C₂₃	1	1	yes	characteristic, complemented
410	#3077	C₂×C₂₃	1	2	yes	complemented
411	Q₈×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
412	C₄×AGL(1,ℤ/8)	C₂×C₂₃	1	1	yes	characteristic
413	C₄×AGL(1,ℤ/8)	C₂×C₂₃	1	2	yes	—
414	C₂²×C₂₃	—	2	1	no	—
415	C₂²×C₂₃	—	2	1	no	—
416	C₂²×C₂₃	—	2	2	no	—
417	C₂²×C₂₃	—	2	4	no	—
418	C₂²×C₂₃	—	4	8	no	—
419	C₂²×C₂₃	—	4	2	no	—
420	C₂²×C₂₃	—	4	1	no	—
421	C₂²×C₂₃	—	4	1	no	—
422	C₂²×C₂₃	—	4	2	no	—
423	C₂²×C₂₃	D₄×Q₈	1	2	yes	—
424	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
425	C₄×C₂₃	—	2	2	no	—
426	C₄×C₂₃	—	2	2	no	—
427	C₄×C₂₃	—	2	1	no	—
428	C₄×C₂₃	—	2	1	no	—
429	C₄×C₂₃	—	2	2	no	—
430	C₄×C₂₃	—	2	1	no	—
431	C₄×C₂₃	—	2	2	no	—
432	C₄×C₂₃	—	2	2	no	—
433	C₄×C₂₃	—	4	4	no	—
434	C₄×C₂₃	—	4	2	no	—
435	C₄×C₂₃	—	4	1	no	—
436	C₄×C₂₃	—	4	2	no	—
437	C₄×C₂₃	—	4	2	no	—
438	C₄×C₂₃	—	4	1	no	—
439	C₄×C₂₃	D₄×Q₈	1	2	yes	—
440	C₄×C₂₃	#575	1	2	yes	—
441	C₄×C₂₃	C₂³×Q₈	1	1	yes	characteristic
442	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
443	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
444	Q₈²	C₂²×C₂₃	1	1	yes	characteristic, complemented
445	#557	C₂²×C₂₃	1	1	yes	characteristic, complemented
446	#557	C₂²×C₂₃	1	2	yes	complemented
447	#554	—	2	1	no	—
448	#554	—	2	2	no	—
449	#554	—	2	1	no	—
450	#554	—	2	1	no	—
451	#554	—	2	2	no	—
452	#554	C₂²×C₂₃	1	2	yes	—
453	#554	C₂²×C₂₃	1	2	yes	—
454	#554	C₂²×C₂₃	1	4	yes	—
455	#554	C₂²×C₂₃	1	1	yes	characteristic, complemented
456	#554	C₂²×C₂₃	1	2	yes	complemented
457	D₄×Q₈	—	2	1	no	—
458	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
459	#533	—	2	2	no	—
460	#533	—	2	1	no	—
461	#533	C₂²×C₂₃	1	1	yes	characteristic
462	#533	C₂²×C₂₃	1	2	yes	—
463	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
464	C₂×#125	C₂²×C₂₃	1	2	yes	—
465	C₂×C₂²⋊Q₈	—	2	1	no	—
466	C₂×C₂²⋊Q₈	—	2	2	no	—
467	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
468	C₄×#41	C₂²×C₂₃	1	2	yes	—
469	C₂×C₄×Q₈	—	2	1	no	—
470	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
471	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
472	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
473	C₂²×C₄⋊C₄	—	2	1	no	—
474	#501	C₂²×C₂₃	1	4	yes	complemented
475	#501	C₂²×C₂₃	1	4	yes	complemented
476	#501	C₂²×C₂₃	1	4	yes	complemented
477	#500	C₂²×C₂₃	1	2	yes	complemented
478	#499	C₂²×C₂₃	1	4	yes	complemented
479	#499	C₂²×C₂₃	1	4	yes	complemented
480	#498	C₂²×C₂₃	1	2	yes	complemented
481	#479	C₂²×C₂₃	1	4	yes	complemented
482	#479	C₂²×C₂₃	1	4	yes	complemented
483	#478	C₂²×C₂₃	1	4	yes	—
484	#478	C₂²×C₂₃	1	4	yes	—
485	#478	C₂²×C₂₃	1	4	yes	—
486	#478	C₂²×C₂₃	1	4	yes	complemented
487	#478	C₂²×C₂₃	1	4	yes	complemented
488	#477	C₂²×C₂₃	1	2	yes	complemented
489	#476	C₂²×C₂₃	1	2	yes	—
490	#476	C₂²×C₂₃	1	4	yes	—
491	#476	C₂²×C₂₃	1	2	yes	complemented
492	#475	C₂²×C₂₃	1	2	yes	complemented
493	#474	C₂²×C₂₃	1	2	yes	—
494	#474	C₂²×C₂₃	1	4	yes	—
495	#474	C₂²×C₂₃	1	2	yes	complemented
496	#446	C₂²×C₂₃	1	2	yes	complemented
497	#446	C₂²×C₂₃	1	4	yes	complemented
498	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
499	#442	C₂²×C₂₃	1	4	yes	—
500	#442	C₂²×C₂₃	1	2	yes	—
501	#440	C₂²×C₂₃	1	4	yes	—
502	#440	C₂²×C₂₃	1	2	yes	—
503	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
504	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	—
505	C₄×D₈	C₂²×C₂₃	1	2	yes	—
506	C₄×D₈	C₂²×C₂₃	1	4	yes	—
507	#428	C₂²×C₂₃	1	2	yes	—
508	#428	C₂²×C₂₃	1	2	yes	—
509	#428	C₂²×C₂₃	1	2	yes	—
510	#428	C₂²×C₂₃	1	2	yes	—
511	#428	C₂²×C₂₃	1	1	yes	characteristic
512	#423	C₂²×C₂₃	1	1	yes	characteristic
513	#423	C₂²×C₂₃	1	2	yes	—
514	#418	C₂²×C₂₃	1	2	yes	—
515	#418	C₂²×C₂₃	1	1	yes	characteristic
516	#417	C₂²×C₂₃	1	2	yes	—
517	#417	C₂²×C₂₃	1	1	yes	characteristic
518	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
519	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
520	C₂×C₂₃	—	2	2	no	—
521	C₂×C₂₃	—	4	2	no	—
522	C₂×C₂₃	—	4	4	no	—
523	C₂×C₂₃	C₂×D₄×Q₈	1	1	yes	characteristic
524	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
525	C₂×C₂₃	#3585	1	1	yes	characteristic
526	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
527	C₂²×Q₈	—	2	1	no	—
528	C₂²×Q₈	—	2	1	no	—
529	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
530	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
531	C₂³×C₄	—	2	1	no	—
532	C₂³×C₄	—	2	2	no	—
533	AGL(1,ℤ/8)	Q₈×C₂₃	1	8	yes	complemented
534	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
535	C₂×D₈	C₂³×C₂₃	1	2	yes	—
536	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
537	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
538	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
539	C₄⋊Q₈	—	2	1	no	—
540	C₄⋊Q₈	—	2	2	no	—
541	C₄⋊Q₈	—	2	1	no	—
542	C₄⋊Q₈	—	2	2	no	—
543	C₄⋊Q₈	—	2	1	no	—
544	C₄⋊Q₈	—	2	1	no	—
545	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
546	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
547	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
548	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
549	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
550	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
551	#125	—	2	2	no	—
552	#125	—	2	2	no	—
553	#125	—	2	2	no	—
554	#125	—	2	2	no	—
555	#125	—	2	2	no	—
556	#125	C₂³×C₂₃	1	4	yes	—
557	#125	C₂³×C₂₃	1	4	yes	—
558	#125	C₂³×C₂₃	1	2	yes	—
559	#125	C₂³×C₂₃	1	2	yes	—
560	#125	C₂³×C₂₃	1	2	yes	—
561	C₂²⋊Q₈	—	2	2	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	—	2	4	no	—
564	C₂²⋊Q₈	—	2	1	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	—	2	1	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	1	no	—
569	C₂²⋊Q₈	—	2	2	no	—
570	C₂²⋊Q₈	—	2	4	no	—
571	C₂²⋊Q₈	—	2	4	no	—
572	C₂²⋊Q₈	—	2	4	no	—
573	C₂²⋊Q₈	—	2	4	no	—
574	C₂²⋊Q₈	—	2	1	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	—	2	2	no	—
579	C₄×Q₈	—	2	1	no	—
580	C₄×Q₈	—	2	1	no	—
581	C₄×Q₈	—	2	2	no	—
582	C₄×Q₈	—	2	2	no	—
583	C₄×Q₈	—	2	1	no	—
584	C₄×Q₈	—	2	2	no	—
585	C₄×Q₈	—	2	1	no	—
586	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
587	C₄×Q₈	D₄×C₂₃	1	2	yes	—
588	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
589	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
590	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
591	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
592	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
593	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
594	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
595	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	—	2	1	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	—	2	2	no	—
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	C₂³×C₂₃	1	2	yes	—
605	C₄×D₄	C₂³×C₂₃	1	4	yes	—
606	C₄×D₄	C₂³×C₂₃	1	4	yes	—
607	C₄×D₄	C₂³×C₂₃	1	2	yes	—
608	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
609	C₄×D₄	C₂³×C₂₃	1	2	yes	—
610	C₄×D₄	C₂³×C₂₃	1	2	yes	—
611	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
612	#117	—	2	2	no	—
613	#117	—	2	1	no	—
614	#117	C₂³×C₂₃	1	1	yes	characteristic
615	#117	C₂³×C₂₃	1	2	yes	—
616	C₂×C₄⋊C₄	—	2	2	no	—
617	C₂×C₄⋊C₄	—	2	1	no	—
618	C₂×C₄⋊C₄	—	2	2	no	—
619	C₂×C₄⋊C₄	—	2	2	no	—
620	C₂×C₄⋊C₄	—	2	4	no	—
621	C₂×C₄⋊C₄	—	2	2	no	—
622	C₂×C₄⋊C₄	—	2	1	no	—
623	C₂×C₄⋊C₄	—	2	2	no	—
624	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
625	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
628	C₂×C₂²⋊C₄	—	2	1	no	—
629	C₂×C₂²⋊C₄	—	2	2	no	—
630	C₂×C₄²	—	2	2	no	—
631	C₂×C₄²	—	2	1	no	—
632	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
633	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
634	#107	C₂³×C₂₃	1	2	yes	—
635	#107	C₂³×C₂₃	1	4	yes	—
636	#107	C₂³×C₂₃	1	4	yes	—
637	#107	C₂³×C₂₃	1	4	yes	—
638	#107	C₂³×C₂₃	1	4	yes	—
639	#106	C₂³×C₂₃	1	4	yes	—
640	#106	C₂³×C₂₃	1	2	yes	—
641	#106	C₂³×C₂₃	1	4	yes	—
642	#106	C₂³×C₂₃	1	4	yes	—
643	#106	C₂³×C₂₃	1	4	yes	—
644	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
645	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
646	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
647	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
648	#103	C₂³×C₂₃	1	4	yes	—
649	#103	C₂³×C₂₃	1	2	yes	—
650	#102	C₂³×C₂₃	1	4	yes	—
651	#102	C₂³×C₂₃	1	2	yes	—
652	#102	C₂³×C₂₃	1	4	yes	—
653	#102	C₂³×C₂₃	1	2	yes	—
654	#102	C₂³×C₂₃	1	2	yes	—
655	#102	C₂³×C₂₃	1	4	yes	—
656	#97	C₂³×C₂₃	1	2	yes	—
657	#97	C₂³×C₂₃	1	4	yes	—
658	C₄×C₈	C₂³×C₂₃	1	2	yes	—
659	C₄×C₈	C₂³×C₂₃	1	4	yes	—
660	C₂₃	#61367	1	1	yes	characteristic, direct product factor, Sylow
661	C₂⁴	—	2	1	no	—
662	#41	—	2	2	no	—
663	#41	C₂×Q₈×C₂₃	1	4	yes	—
664	C₂×Q₈	—	2	2	no	—
665	C₂×Q₈	—	2	1	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	2	2	no	—
668	C₂×Q₈	—	2	2	no	—
669	C₂×Q₈	—	2	2	no	—
670	C₂×Q₈	—	4	2	no	—
671	C₂×Q₈	—	4	4	no	—
672	C₂×Q₈	—	8	2	no	—
673	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
674	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
675	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
676	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	C₂×Q₈×C₂₃	1	4	yes	complemented
681	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
682	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	1	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	2	4	no	—
694	C₂²×C₄	—	4	4	no	—
695	C₂²×C₄	—	8	4	no	—
696	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
697	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
698	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
699	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
700	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
701	SD₁₆	C₂×Q₈×C₂₃	1	8	yes	complemented
702	D₈	C₂×Q₈×C₂₃	1	8	yes	complemented
703	M₁₆	—	2	2	no	—
704	M₁₆	—	2	4	no	—
705	M₁₆	C₂×Q₈×C₂₃	1	4	yes	complemented
706	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
707	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
708	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
732	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
733	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
734	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
735	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
736	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
737	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
738	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
739	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
740	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
741	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
742	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
743	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	—	2	1	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₄²	—	2	2	no	—
755	C₄²	—	2	1	no	—
756	C₄²	—	2	1	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	2	2	no	—
759	C₄²	—	2	1	no	—
760	C₄²	C₂×D₄×C₂₃	1	2	yes	—
761	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
762	C₄²	C₂×D₄×C₂₃	1	2	yes	—
763	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
764	C₄²	C₂⁴×C₂₃	1	2	yes	—
765	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
766	C₄²	C₂⁴×C₂₃	1	2	yes	—
767	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
768	C₂³	—	2	4	no	—
769	C₂³	—	2	1	no	—
770	C₂³	—	2	2	no	—
771	C₂³	—	4	2	no	—
772	C₂³	—	4	2	no	—
773	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
774	Q₈	—	2	2	no	—
775	Q₈	—	2	2	no	—
776	Q₈	—	2	1	no	—
777	Q₈	—	4	2	no	—
778	Q₈	—	4	4	no	—
779	Q₈	—	4	2	no	—
780	Q₈	—	8	2	no	—
781	Q₈	—	8	2	no	—
782	Q₈	—	8	2	no	—
783	Q₈	—	8	1	no	—
784	Q₈	C₂²×Q₈×C₂₃	1	2	yes	—
785	D₄	—	2	4	no	—
786	D₄	—	2	4	no	—
787	D₄	—	2	2	no	—
788	D₄	—	2	1	no	—
789	D₄	C₂²×Q₈×C₂₃	1	2	yes	—
790	D₄	C₂²×Q₈×C₂₃	1	4	yes	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	4	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	4	no	—
800	C₂×C₄	—	4	2	no	—
801	C₂×C₄	—	4	2	no	—
802	C₂×C₄	—	4	1	no	—
803	C₂×C₄	—	4	4	no	—
804	C₂×C₄	—	4	4	no	—
805	C₂×C₄	—	4	2	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	4	4	no	—
808	C₂×C₄	—	4	2	no	—
809	C₂×C₄	—	8	4	no	—
810	C₂×C₄	—	8	4	no	—
811	C₂×C₄	—	8	2	no	—
812	C₂×C₄	—	8	1	no	—
813	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
814	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
816	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
817	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
819	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
820	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
821	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
822	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
823	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
824	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
825	C₈	—	2	2	no	—
826	C₈	—	2	4	no	—
827	C₈	C₂²×Q₈×C₂₃	1	4	yes	—
828	C₂²	—	2	1	no	—
829	C₂²	—	2	1	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	4	no	—
832	C₂²	—	4	8	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	1	no	—
837	C₂²	D₄×Q₈×C₂₃	1	2	yes	—
838	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
839	C₄	—	2	2	no	—
840	C₄	—	2	1	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	2	no	—
845	C₄	—	2	1	no	—
846	C₄	—	2	1	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	1	no	—
850	C₄	—	4	4	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	1	no	—
853	C₄	D₄×Q₈×C₂₃	1	2	yes	—
854	C₄	C₂₃×#575	1	2	yes	—
855	C₄	C₂³×Q₈×C₂₃	1	1	yes	characteristic
856	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
857	C₂	—	2	2	no	—
858	C₂	—	4	4	no	—
859	C₂	—	4	2	no	—
860	C₂	C₂×D₄×Q₈×C₂₃	1	1	yes	characteristic
861	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
862	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×AGL(1,ℤ/8)	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄×Q₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. Q₈×#41×C₂₃	C₂	semidirect
2. C₂×C₂₃×#554	C₂	semidirect
3. C₂₃×#3389	C₂	semidirect
4. C₂₃×#3388	C₂	semidirect
5. C₂₃×#3385	C₂	semidirect
6. C₂₃×#3384	C₂	semidirect
7. C₂₃×#3381	C₂	semidirect
8. C₂₃×#3380	C₂	semidirect
9. C₂₃×#3166	C₂	semidirect
10. C₂₃×#3165	C₂	semidirect
11. C₂₃×#3080	C₂	semidirect
12. C₂₃×#3079	C₂	semidirect
13. C₂₃×#3077	C₂	semidirect
14. C₂₃×#3077	C₂	semidirect
15. Q₈×M₁₆×C₂₃	C₂	semidirect
19. Q₈²×C₂₃	C₂²	semidirect
20. C₂₃×#557	C₂²	semidirect
21. C₂₃×#557	C₂²	semidirect
30. C₂₃×#554	C₂²	semidirect
31. C₂₃×#554	C₂²	semidirect
33. D₄×Q₈×C₂₃	C₂²	semidirect
49. C₂₃×#501	C₂²	semidirect
50. C₂₃×#501	C₂²	semidirect
51. C₂₃×#501	C₂²	semidirect
52. C₂₃×#500	C₂²	semidirect
53. C₂₃×#499	C₂²	semidirect
54. C₂₃×#499	C₂²	semidirect
55. C₂₃×#498	C₂²	semidirect
56. C₂₃×#479	C₂²	semidirect
57. C₂₃×#479	C₂²	semidirect
61. C₂₃×#478	C₂²	semidirect
62. C₂₃×#478	C₂²	semidirect
63. C₂₃×#477	C₂²	semidirect
66. C₂₃×#476	C₂²	semidirect
67. C₂₃×#475	C₂²	semidirect
70. C₂₃×#474	C₂²	semidirect
71. C₂₃×#446	C₂²	semidirect
72. C₂₃×#446	C₂²	semidirect
73. C₈×Q₈×C₂₃	C₂²	semidirect
102. C₂₃×AGL(1,ℤ/8)	Q₈	semidirect
248. C₂×D₄×C₂₃	C₂×Q₈	semidirect
269. SD₁₆×C₂₃	C₂×Q₈	semidirect
270. D₈×C₂₃	C₂×Q₈	semidirect
273. M₁₆×C₂₃	C₂×Q₈	semidirect
336. #61367	C₂₃	direct (N × H)
397. Q₈×#41	C₂×C₂₃	semidirect
398. C₂×#554	C₂×C₂₃	semidirect
399. #3389	C₂×C₂₃	semidirect
400. #3388	C₂×C₂₃	semidirect
401. #3385	C₂×C₂₃	semidirect
402. #3384	C₂×C₂₃	semidirect
403. #3381	C₂×C₂₃	semidirect
404. #3380	C₂×C₂₃	semidirect
405. #3166	C₂×C₂₃	semidirect
406. #3165	C₂×C₂₃	semidirect
407. #3080	C₂×C₂₃	semidirect
408. #3079	C₂×C₂₃	semidirect
409. #3077	C₂×C₂₃	semidirect
410. #3077	C₂×C₂₃	semidirect
411. Q₈×M₁₆	C₂×C₂₃	semidirect
444. Q₈²	C₂²×C₂₃	semidirect
445. #557	C₂²×C₂₃	semidirect
446. #557	C₂²×C₂₃	semidirect
455. #554	C₂²×C₂₃	semidirect
456. #554	C₂²×C₂₃	semidirect
458. D₄×Q₈	C₂²×C₂₃	semidirect
474. #501	C₂²×C₂₃	semidirect
475. #501	C₂²×C₂₃	semidirect
476. #501	C₂²×C₂₃	semidirect
477. #500	C₂²×C₂₃	semidirect
478. #499	C₂²×C₂₃	semidirect
479. #499	C₂²×C₂₃	semidirect
480. #498	C₂²×C₂₃	semidirect
481. #479	C₂²×C₂₃	semidirect
482. #479	C₂²×C₂₃	semidirect
486. #478	C₂²×C₂₃	semidirect
487. #478	C₂²×C₂₃	semidirect
488. #477	C₂²×C₂₃	semidirect
491. #476	C₂²×C₂₃	semidirect
492. #475	C₂²×C₂₃	semidirect
495. #474	C₂²×C₂₃	semidirect
496. #446	C₂²×C₂₃	semidirect
497. #446	C₂²×C₂₃	semidirect
498. C₈×Q₈	C₂²×C₂₃	semidirect
533. AGL(1,ℤ/8)	Q₈×C₂₃	semidirect
660. C₂₃	#61367	direct (N × H)
680. C₂×D₄	C₂×Q₈×C₂₃	semidirect
701. SD₁₆	C₂×Q₈×C₂₃	semidirect
702. D₈	C₂×Q₈×C₂₃	semidirect
705. M₁₆	C₂×Q₈×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#41×C₂₃	2
C₂×C₂₃×#554	2
C₂₃×#3389	2
C₂₃×#3388	2
C₂₃×#3385	2
C₂₃×#3384	2
C₂₃×#3381	2
C₂₃×#3380	2
C₂₃×#3166	2
C₂₃×#3165	2
C₂₃×#3080	2
C₂₃×#3079	2
C₂₃×#3077	2
Q₈×M₁₆×C₂₃	2
C₄×C₂₃×AGL(1,ℤ/8)	2
#61367	23

Subgroups — C23×#61367 #19208993

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61367 #19208993