Subgroups — C₂×C₂₃×#1279 #19155515

Order 5888.

974 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1279	C₂	1	4	yes	maximal, direct product factor
5	C₂³×C₈×C₂₃	—	2	1	no	—
6	C₂³×C₈×C₂₃	—	2	1	no	—
7	C₂²×C₄⋊C₄×C₂₃	C₄	1	2	yes	—
8	C₂²×C₄²×C₂₃	—	2	1	no	—
9	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
10	C₂×C₂₃×C₄⋊C₈	—	2	1	no	—
11	C₂×C₂₃×C₄⋊C₈	—	2	2	no	—
12	C₂×C₂₃×C₄⋊C₈	C₄	1	4	yes	complemented
13	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₂₃	—	2	1	no	—
15	C₂×C₄×C₈×C₂₃	—	2	2	no	—
16	C₂×C₄×C₈×C₂₃	C₄	1	4	yes	complemented
17	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
18	C₄×C₄⋊C₄×C₂₃	—	2	1	no	—
19	C₄×C₄⋊C₄×C₂₃	—	2	1	no	—
20	C₄×C₄⋊C₄×C₂₃	C₄	1	2	yes	—
21	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
22	C₂×C₂₃×#95	—	2	1	no	—
23	C₂³×C₄×C₂₃	—	2	2	no	—
24	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
27	C₂²×C₈×C₂₃	—	2	8	no	—
28	C₂²×C₈×C₂₃	—	2	4	no	—
29	C₂²×C₈×C₂₃	—	2	2	no	—
30	C₂²×C₈×C₂₃	—	2	4	no	—
31	C₂²×C₈×C₂₃	—	2	2	no	—
32	C₂²×C₈×C₂₃	—	4	2	no	—
33	C₂²×C₈×C₂₃	—	4	2	no	—
34	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
35	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
36	C₂×C₄⋊C₄×C₂₃	C₈	1	8	yes	complemented
37	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	4	yes	—
38	C₂×C₄²×C₂₃	—	2	2	no	—
39	C₂×C₄²×C₂₃	—	2	2	no	—
40	C₂×C₄²×C₂₃	—	4	2	no	—
41	C₂×C₄²×C₂₃	—	4	2	no	—
42	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
44	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₂₃	D₄	1	2	yes	—
48	C₂×C₄²×C₂₃	Q₈	1	2	yes	—
49	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
50	C₂₃×C₄⋊C₈	—	2	4	no	—
51	C₂₃×C₄⋊C₈	—	2	2	no	—
52	C₂₃×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
53	C₄×C₈×C₂₃	—	2	4	no	—
54	C₄×C₈×C₂₃	—	2	2	no	—
55	C₄×C₈×C₂₃	C₂×C₄	1	4	yes	complemented
56	C₂₃×#95	—	2	2	no	—
57	C₂₃×#95	—	2	2	no	—
58	C₂⁴×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
59	C₂²×C₄×C₂₃	—	2	4	no	—
60	C₂²×C₄×C₂₃	—	2	8	no	—
61	C₂²×C₄×C₂₃	—	2	4	no	—
62	C₂²×C₄×C₂₃	—	4	4	no	—
63	C₂²×C₄×C₂₃	—	4	4	no	—
64	C₂²×C₄×C₂₃	C₄²	1	2	yes	—
65	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
67	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
70	C₂²×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
71	C₂²×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
72	C₂²×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
73	C₂²×C₄×C₂₃	C₂×C₈	1	4	yes	—
74	C₂²×C₄×C₂₃	M₁₆	1	4	yes	—
75	C₂²×C₄×C₂₃	D₈	1	2	yes	—
76	C₂²×C₄×C₂₃	SD₁₆	1	2	yes	—
77	C₂²×C₄×C₂₃	SD₁₆	1	2	yes	—
78	C₂²×C₄×C₂₃	Q₁₆	1	2	yes	—
79	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
82	C₂×C₈×C₂₃	—	2	16	no	—
83	C₂×C₈×C₂₃	—	2	8	no	—
84	C₂×C₈×C₂₃	—	2	4	no	—
85	C₂×C₈×C₂₃	—	2	4	no	—
86	C₂×C₈×C₂₃	—	4	8	no	—
87	C₂×C₈×C₂₃	—	4	2	no	—
88	C₂×C₈×C₂₃	—	4	2	no	—
89	C₄⋊C₄×C₂₃	—	2	8	no	—
90	C₄⋊C₄×C₂₃	—	2	4	no	—
91	C₄⋊C₄×C₂₃	C₂×C₈	1	8	yes	complemented
92	C₄²×C₂₃	—	4	4	no	—
93	C₄²×C₂₃	—	4	2	no	—
94	C₄²×C₂₃	—	4	2	no	—
95	C₄²×C₂₃	C₄²	1	2	yes	—
96	C₄²×C₂₃	C₂²⋊C₄	1	2	yes	—
97	C₄²×C₂₃	C₂²⋊C₄	1	2	yes	—
98	C₄²×C₂₃	C₄⋊C₄	1	2	yes	—
99	C₄²×C₂₃	C₄⋊C₄	1	2	yes	—
100	C₄²×C₂₃	C₄⋊C₄	1	2	yes	—
101	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
102	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
103	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
104	C₄²×C₂₃	C₂×Q₈	1	1	yes	characteristic
105	C₂×#1279	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂³×C₂₃	#95	1	2	yes	—
107	C₂³×C₂₃	C₂²⋊C₈	1	4	yes	—
108	C₂³×C₂₃	#102	1	2	yes	—
109	C₂³×C₂₃	#103	1	2	yes	—
110	C₂³×C₂₃	#104	1	4	yes	—
111	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
112	C₂×C₄×C₂₃	—	2	4	no	—
113	C₂×C₄×C₂₃	—	2	4	no	—
114	C₂×C₄×C₂₃	—	2	2	no	—
115	C₂×C₄×C₂₃	—	2	2	no	—
116	C₂×C₄×C₂₃	—	2	8	no	—
117	C₂×C₄×C₂₃	—	4	16	no	—
118	C₂×C₄×C₂₃	—	4	4	no	—
119	C₂×C₄×C₂₃	—	4	4	no	—
120	C₂×C₄×C₂₃	#95	1	2	yes	—
121	C₂×C₄×C₂₃	#95	1	2	yes	—
122	C₂×C₄×C₂₃	#95	1	2	yes	—
123	C₂×C₄×C₂₃	C₄×C₈	1	4	yes	—
124	C₂×C₄×C₂₃	#97	1	4	yes	—
125	C₂×C₄×C₂₃	C₂²⋊C₈	1	4	yes	—
126	C₂×C₄×C₂₃	#102	1	2	yes	—
127	C₂×C₄×C₂₃	#102	1	4	yes	—
128	C₂×C₄×C₂₃	#103	1	2	yes	—
129	C₂×C₄×C₂₃	#103	1	4	yes	—
130	C₂×C₄×C₂₃	C₄⋊C₈	1	8	yes	—
131	C₂×C₄×C₂₃	#106	1	4	yes	—
132	C₂×C₄×C₂₃	#107	1	4	yes	—
133	C₂×C₄×C₂₃	C₂×C₄²	1	1	yes	characteristic
134	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₂₃	C₂²×C₈	1	2	yes	—
140	C₂×C₄×C₂₃	C₂×M₁₆	1	2	yes	—
141	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
142	C₂×C₄×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
143	C₂×C₄×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
144	C₂×C₄×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
145	C₈×C₂₃	—	2	8	no	—
146	C₈×C₂₃	—	4	4	no	—
147	C₂²×C₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic
148	C₂²×C₄×C₈	C₂×C₂₃	1	1	yes	characteristic
149	C₂×C₄×C₄⋊C₄	C₂×C₂₃	1	1	yes	characteristic
150	#1279	C₂×C₂₃	1	4	yes	direct product factor
151	C₂²×C₂₃	D₄⋊C₈	1	8	yes	—
152	C₂²×C₂₃	Q₈⋊C₈	1	8	yes	—
153	C₂²×C₂₃	#336	1	4	yes	—
154	C₂²×C₂₃	#339	1	4	yes	—
155	C₂²×C₂₃	#340	1	4	yes	—
156	C₂²×C₂₃	C₂×#95	1	1	yes	characteristic
157	C₂²×C₂₃	C₂×C₂²⋊C₈	1	2	yes	—
158	C₂²×C₂₃	C₂×#102	1	1	yes	characteristic
159	C₂²×C₂₃	C₂×#103	1	1	yes	characteristic
160	C₂²×C₂₃	C₂×#104	1	2	yes	—
161	C₄×C₂₃	—	2	1	no	—
162	C₄×C₂₃	—	2	2	no	—
163	C₄×C₂₃	—	2	1	no	—
164	C₄×C₂₃	—	4	8	no	—
165	C₄×C₂₃	#336	1	4	yes	—
166	C₄×C₂₃	#340	1	4	yes	—
167	C₄×C₂₃	C₂×C₄×C₈	1	1	yes	characteristic
168	C₄×C₂₃	C₂×#97	1	1	yes	characteristic
169	C₄×C₂₃	C₂×#102	1	1	yes	characteristic
170	C₄×C₂₃	C₂×#103	1	1	yes	characteristic
171	C₄×C₂₃	C₂×C₄⋊C₈	1	2	yes	—
172	C₄×C₂₃	C₂×#106	1	1	yes	characteristic
173	C₄×C₂₃	C₂×#107	1	1	yes	characteristic
174	C₂³×C₈	—	2	1	no	—
175	C₂³×C₈	—	2	1	no	—
176	C₂²×C₄⋊C₄	C₄×C₂₃	1	2	yes	—
177	C₂²×C₄²	—	2	1	no	—
178	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
179	C₂×C₄⋊C₈	—	2	1	no	—
180	C₂×C₄⋊C₈	—	2	2	no	—
181	C₂×C₄⋊C₈	C₄×C₂₃	1	4	yes	complemented
182	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
183	C₂×C₄×C₈	—	2	1	no	—
184	C₂×C₄×C₈	—	2	2	no	—
185	C₂×C₄×C₈	C₄×C₂₃	1	4	yes	complemented
186	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
187	C₄×C₄⋊C₄	—	2	1	no	—
188	C₄×C₄⋊C₄	—	2	1	no	—
189	C₄×C₄⋊C₄	C₄×C₂₃	1	2	yes	—
190	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
191	C₂×#95	—	2	1	no	—
192	C₂×C₂₃	#1279	1	8	yes	direct product factor
193	C₂×C₂₃	C₂×D₄⋊C₈	1	2	yes	—
194	C₂×C₂₃	C₂×Q₈⋊C₈	1	2	yes	—
195	C₂×C₂₃	C₂×#336	1	1	yes	characteristic
196	C₂×C₂₃	C₂×#339	1	1	yes	characteristic
197	C₂×C₂₃	C₂×#340	1	1	yes	characteristic
198	C₂³×C₄	—	2	2	no	—
199	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
200	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
201	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
202	C₂²×C₈	—	2	8	no	—
203	C₂²×C₈	—	2	4	no	—
204	C₂²×C₈	—	2	2	no	—
205	C₂²×C₈	—	2	4	no	—
206	C₂²×C₈	—	2	2	no	—
207	C₂²×C₈	—	4	2	no	—
208	C₂²×C₈	—	4	2	no	—
209	C₂×C₄⋊C₄	—	2	2	no	—
210	C₂×C₄⋊C₄	—	2	4	no	—
211	C₂×C₄⋊C₄	C₈×C₂₃	1	8	yes	complemented
212	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	4	yes	—
213	C₂×C₄²	—	2	2	no	—
214	C₂×C₄²	—	2	2	no	—
215	C₂×C₄²	—	4	2	no	—
216	C₂×C₄²	—	4	2	no	—
217	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
218	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
219	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
220	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
221	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
222	C₂×C₄²	D₄×C₂₃	1	2	yes	—
223	C₂×C₄²	Q₈×C₂₃	1	2	yes	—
224	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
225	C₄⋊C₈	—	2	4	no	—
226	C₄⋊C₈	—	2	2	no	—
227	C₄⋊C₈	C₂×C₄×C₂₃	1	4	yes	complemented
228	C₄×C₈	—	2	4	no	—
229	C₄×C₈	—	2	2	no	—
230	C₄×C₈	C₂×C₄×C₂₃	1	4	yes	complemented
231	#95	—	2	2	no	—
232	#95	—	2	2	no	—
233	C₂₃	C₂×#1279	1	1	yes	characteristic, direct product factor, Sylow
234	C₂⁴	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
235	C₂²×C₄	—	2	4	no	—
236	C₂²×C₄	—	2	4	no	—
237	C₂²×C₄	—	2	8	no	—
238	C₂²×C₄	—	4	4	no	—
239	C₂²×C₄	—	4	4	no	—
240	C₂²×C₄	C₄²×C₂₃	1	2	yes	—
241	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
242	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
243	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
244	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
245	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
246	C₂²×C₄	C₄⋊C₄×C₂₃	1	2	yes	—
247	C₂²×C₄	C₄⋊C₄×C₂₃	1	2	yes	—
248	C₂²×C₄	C₄⋊C₄×C₂₃	1	2	yes	—
249	C₂²×C₄	C₂×C₈×C₂₃	1	4	yes	—
250	C₂²×C₄	M₁₆×C₂₃	1	4	yes	—
251	C₂²×C₄	D₈×C₂₃	1	2	yes	—
252	C₂²×C₄	SD₁₆×C₂₃	1	2	yes	—
253	C₂²×C₄	SD₁₆×C₂₃	1	2	yes	—
254	C₂²×C₄	Q₁₆×C₂₃	1	2	yes	—
255	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
256	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
257	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
258	C₂×C₈	—	2	16	no	—
259	C₂×C₈	—	2	8	no	—
260	C₂×C₈	—	2	4	no	—
261	C₂×C₈	—	2	4	no	—
262	C₂×C₈	—	4	8	no	—
263	C₂×C₈	—	4	2	no	—
264	C₂×C₈	—	4	2	no	—
265	C₄⋊C₄	—	2	4	no	—
266	C₄⋊C₄	—	2	8	no	—
267	C₄⋊C₄	C₂×C₈×C₂₃	1	8	yes	complemented
268	C₄²	—	4	4	no	—
269	C₄²	—	4	2	no	—
270	C₄²	—	4	2	no	—
271	C₄²	C₄²×C₂₃	1	2	yes	—
272	C₄²	C₂²⋊C₄×C₂₃	1	2	yes	—
273	C₄²	C₂²⋊C₄×C₂₃	1	2	yes	—
274	C₄²	C₄⋊C₄×C₂₃	1	2	yes	—
275	C₄²	C₄⋊C₄×C₂₃	1	2	yes	—
276	C₄²	C₄⋊C₄×C₂₃	1	2	yes	—
277	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
278	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
279	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
280	C₄²	C₂×Q₈×C₂₃	1	1	yes	characteristic
281	C₂³	C₂₃×#95	1	2	yes	—
282	C₂³	C₂₃×C₂²⋊C₈	1	4	yes	—
283	C₂³	C₂₃×#102	1	2	yes	—
284	C₂³	C₂₃×#103	1	2	yes	—
285	C₂³	C₂₃×#104	1	4	yes	—
286	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	8	no	—
292	C₂×C₄	—	4	16	no	—
293	C₂×C₄	—	4	4	no	—
294	C₂×C₄	—	4	4	no	—
295	C₂×C₄	C₂₃×#95	1	2	yes	—
296	C₂×C₄	C₂₃×#95	1	2	yes	—
297	C₂×C₄	C₂₃×#95	1	2	yes	—
298	C₂×C₄	C₄×C₈×C₂₃	1	4	yes	—
299	C₂×C₄	C₂₃×#97	1	4	yes	—
300	C₂×C₄	C₂₃×C₂²⋊C₈	1	4	yes	—
301	C₂×C₄	C₂₃×#102	1	2	yes	—
302	C₂×C₄	C₂₃×#102	1	4	yes	—
303	C₂×C₄	C₂₃×#103	1	2	yes	—
304	C₂×C₄	C₂₃×#103	1	4	yes	—
305	C₂×C₄	C₂₃×C₄⋊C₈	1	8	yes	—
306	C₂×C₄	C₂₃×#106	1	4	yes	—
307	C₂×C₄	C₂₃×#107	1	4	yes	—
308	C₂×C₄	C₂×C₄²×C₂₃	1	1	yes	characteristic
309	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
310	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
311	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
312	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
313	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
314	C₂×C₄	C₂²×C₈×C₂₃	1	2	yes	—
315	C₂×C₄	C₂×M₁₆×C₂₃	1	2	yes	—
316	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
317	C₂×C₄	C₂×SD₁₆×C₂₃	1	1	yes	characteristic
318	C₂×C₄	C₂×SD₁₆×C₂₃	1	1	yes	characteristic
319	C₂×C₄	C₂×Q₁₆×C₂₃	1	1	yes	characteristic
320	C₈	—	2	8	no	—
321	C₈	—	4	4	no	—
322	C₂²	C₂₃×D₄⋊C₈	1	8	yes	—
323	C₂²	C₂₃×Q₈⋊C₈	1	8	yes	—
324	C₂²	C₂₃×#336	1	4	yes	—
325	C₂²	C₂₃×#339	1	4	yes	—
326	C₂²	C₂₃×#340	1	4	yes	—
327	C₂²	C₂×C₂₃×#95	1	1	yes	characteristic
328	C₂²	C₂×C₂₃×C₂²⋊C₈	1	2	yes	—
329	C₂²	C₂×C₂₃×#102	1	1	yes	characteristic
330	C₂²	C₂×C₂₃×#103	1	1	yes	characteristic
331	C₂²	C₂×C₂₃×#104	1	2	yes	—
332	C₄	—	2	1	no	—
333	C₄	—	2	1	no	—
334	C₄	—	2	2	no	—
335	C₄	—	4	8	no	—
336	C₄	C₂₃×#336	1	4	yes	—
337	C₄	C₂₃×#340	1	4	yes	—
338	C₄	C₂×C₄×C₈×C₂₃	1	1	yes	characteristic
339	C₄	C₂×C₂₃×#97	1	1	yes	characteristic
340	C₄	C₂×C₂₃×#102	1	1	yes	characteristic
341	C₄	C₂×C₂₃×#103	1	1	yes	characteristic
342	C₄	C₂×C₂₃×C₄⋊C₈	1	2	yes	—
343	C₄	C₂×C₂₃×#106	1	1	yes	characteristic
344	C₄	C₂×C₂₃×#107	1	1	yes	characteristic
345	C₂	C₂₃×#1279	1	8	yes	direct product factor
346	C₂	C₂×C₂₃×D₄⋊C₈	1	2	yes	—
347	C₂	C₂×C₂₃×Q₈⋊C₈	1	2	yes	—
348	C₂	C₂×C₂₃×#336	1	1	yes	characteristic
349	C₂	C₂×C₂₃×#339	1	1	yes	characteristic
350	C₂	C₂×C₂₃×#340	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄×C₂₃	D₄
commutator	C₄	C₂×C₄×C₈×C₂₃
Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
socle, prime radical	C₂⁴×C₂₃	C₂²⋊C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂₃×#1279	C₂	direct (N × H)
12. C₂×C₂₃×C₄⋊C₈	C₄	semidirect
16. C₂×C₄×C₈×C₂₃	C₄	semidirect
36. C₂×C₄⋊C₄×C₂₃	C₈	semidirect
52. C₂₃×C₄⋊C₈	C₂×C₄	semidirect
55. C₄×C₈×C₂₃	C₂×C₄	semidirect
91. C₄⋊C₄×C₂₃	C₂×C₈	semidirect
105. C₂×#1279	C₂₃	direct (N × H)
150. #1279	C₂×C₂₃	direct (N × H)
181. C₂×C₄⋊C₈	C₄×C₂₃	semidirect
185. C₂×C₄×C₈	C₄×C₂₃	semidirect
192. C₂×C₂₃	#1279	direct (N × H)
211. C₂×C₄⋊C₄	C₈×C₂₃	semidirect
227. C₄⋊C₈	C₂×C₄×C₂₃	semidirect
230. C₄×C₈	C₂×C₄×C₂₃	semidirect
233. C₂₃	C₂×#1279	direct (N × H)
267. C₄⋊C₄	C₂×C₈×C₂₃	semidirect
345. C₂	C₂₃×#1279	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×C₄⋊C₈	2
C₂²×C₄×C₈×C₂₃	2
C₂×C₄×C₄⋊C₄×C₂₃	2
C₂₃×#1279	2
C₂×#1279	23

Subgroups — C2×C23×#1279 #19155515

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#1279 #19155515