Subgroups — C₂×C₂₃×#1278 #19155507

Order 5888.

782 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#431	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1278	C₂	1	4	yes	maximal, direct product factor
5	C₂²×M₁₆×C₂₃	C₄	1	2	yes	—
6	C₂³×C₈×C₂₃	—	2	1	no	—
7	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
8	C₂₃×#431	—	2	1	no	—
9	C₂₃×#431	—	2	1	no	—
10	C₂₃×#431	C₄	1	2	yes	—
11	C₂₃×#431	C₂²	1	2	yes	—
12	C₂×C₂₃×C₄⋊C₈	C₄	1	2	yes	—
13	C₂×C₂₃×C₂²⋊C₈	—	2	1	no	—
14	C₄×M₁₆×C₂₃	—	2	1	no	—
15	C₄×M₁₆×C₂₃	—	2	1	no	—
16	C₄×M₁₆×C₂₃	C₄	1	2	yes	—
17	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
18	C₂×C₂₃×#97	—	2	1	no	—
19	C₂×C₄×C₈×C₂₃	—	2	1	no	—
20	C₂×C₄×C₈×C₂₃	—	2	1	no	—
21	C₂×C₄×C₈×C₂₃	—	2	1	no	—
22	C₂×C₄×C₈×C₂₃	—	2	1	no	—
23	C₂×C₄×C₈×C₂₃	—	2	1	no	—
24	C₂×C₄×C₈×C₂₃	C₄	1	2	yes	—
25	C₂×C₄×C₈×C₂₃	C₄	1	2	yes	—
26	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
27	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₂₃	Q₈	1	1	yes	characteristic
30	C₂×M₁₆×C₂₃	—	2	2	no	—
31	C₂×M₁₆×C₂₃	—	2	4	no	—
32	C₂×M₁₆×C₂₃	C₈	1	8	yes	complemented
33	C₂×M₁₆×C₂₃	C₂×C₄	1	4	yes	—
34	C₂²×C₈×C₂₃	—	2	8	no	—
35	C₂²×C₈×C₂₃	—	2	2	no	—
36	C₂²×C₈×C₂₃	—	2	2	no	—
37	C₂²×C₈×C₂₃	—	2	2	no	—
38	C₂²×C₈×C₂₃	—	2	2	no	—
39	C₂²×C₈×C₂₃	—	2	2	no	—
40	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₂₃	Q₈	1	1	yes	characteristic
51	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
52	C₂₃×C₄⋊C₈	—	2	2	no	—
53	C₂₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
54	C₂₃×C₂²⋊C₈	—	2	2	no	—
55	C₂₃×C₂²⋊C₈	—	2	2	no	—
56	C₂₃×#97	—	2	2	no	—
57	C₂₃×#97	—	2	2	no	—
58	C₄×C₈×C₂₃	—	2	2	no	—
59	C₄×C₈×C₂₃	—	2	2	no	—
60	C₄×C₈×C₂₃	—	2	2	no	—
61	C₄×C₈×C₂₃	—	2	2	no	—
62	C₄×C₈×C₂₃	—	2	2	no	—
63	C₄×C₈×C₂₃	—	2	2	no	—
64	C₄×C₈×C₂₃	—	2	2	no	—
65	C₄×C₈×C₂₃	C₂×C₄	1	4	yes	—
66	C₂⁴×C₂₃	C₄⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₂₃	—	2	4	no	—
68	C₂²×C₄×C₂₃	—	2	4	no	—
69	C₂²×C₄×C₂₃	C₄²	1	1	yes	characteristic
70	C₂²×C₄×C₂₃	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₂₃	C₂×C₈	1	4	yes	—
85	C₂²×C₄×C₂₃	M₁₆	1	4	yes	—
86	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
89	M₁₆×C₂₃	—	2	8	no	—
90	M₁₆×C₂₃	—	2	4	no	—
91	M₁₆×C₂₃	C₂×C₈	1	8	yes	complemented
92	C₂×C₈×C₂₃	—	2	8	no	—
93	C₂×C₈×C₂₃	—	2	8	no	—
94	C₂×C₈×C₂₃	—	2	8	no	—
95	C₂×C₈×C₂₃	—	2	8	no	—
96	C₂×C₈×C₂₃	—	2	4	no	—
97	C₂×C₈×C₂₃	—	2	4	no	—
98	C₂×C₈×C₂₃	—	2	4	no	—
99	C₂×C₈×C₂₃	—	4	4	no	—
100	C₄²×C₂₃	C₄²	1	1	yes	characteristic
101	C₄²×C₂₃	C₄²	1	1	yes	characteristic
102	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
103	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
104	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
105	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
106	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
107	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
108	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
111	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
112	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
116	C₂×#1278	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂³×C₂₃	—	2	2	no	—
118	C₂³×C₂₃	—	2	2	no	—
119	C₂³×C₂₃	#95	1	1	yes	characteristic
120	C₂³×C₂₃	#95	1	1	yes	characteristic
121	C₂³×C₂₃	C₄⋊C₈	1	4	yes	—
122	C₂³×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₄×C₂₃	—	2	2	no	—
124	C₂×C₄×C₂₃	—	2	2	no	—
125	C₂×C₄×C₂₃	—	2	2	no	—
126	C₂×C₄×C₂₃	—	2	2	no	—
127	C₂×C₄×C₂₃	—	2	2	no	—
128	C₂×C₄×C₂₃	—	2	2	no	—
129	C₂×C₄×C₂₃	—	2	2	no	—
130	C₂×C₄×C₂₃	—	2	2	no	—
131	C₂×C₄×C₂₃	—	2	2	no	—
132	C₂×C₄×C₂₃	—	2	2	no	—
133	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
134	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
135	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
136	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
137	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
138	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
139	C₂×C₄×C₂₃	C₄×C₈	1	2	yes	—
140	C₂×C₄×C₂₃	C₄×C₈	1	2	yes	—
141	C₂×C₄×C₂₃	#97	1	2	yes	—
142	C₂×C₄×C₂₃	#97	1	2	yes	—
143	C₂×C₄×C₂₃	C₂²⋊C₈	1	4	yes	—
144	C₂×C₄×C₂₃	C₂²⋊C₈	1	4	yes	—
145	C₂×C₄×C₂₃	#104	1	4	yes	—
146	C₂×C₄×C₂₃	C₄⋊C₈	1	4	yes	—
147	C₂×C₄×C₂₃	#108	1	4	yes	—
148	C₂×C₄×C₂₃	C₂×C₄²	1	1	yes	characteristic
149	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₂₃	C₂²×C₈	1	2	yes	—
155	C₂×C₄×C₂₃	C₂×M₁₆	1	2	yes	—
156	C₈×C₂₃	—	2	8	no	—
157	C₈×C₂₃	—	2	8	no	—
158	C₈×C₂₃	—	4	4	no	—
159	C₂×#431	C₂×C₂₃	1	1	yes	characteristic
160	C₂×C₄×M₁₆	C₂×C₂₃	1	1	yes	characteristic
161	C₂²×C₄×C₈	C₂×C₂₃	1	1	yes	characteristic
162	#1278	C₂×C₂₃	1	4	yes	direct product factor
163	C₂²×C₂₃	—	2	1	no	—
164	C₂²×C₂₃	—	2	1	no	—
165	C₂²×C₂₃	—	2	1	no	—
166	C₂²×C₂₃	—	2	1	no	—
167	C₂²×C₂₃	—	2	8	no	—
168	C₂²×C₂₃	#336	1	2	yes	—
169	C₂²×C₂₃	#336	1	2	yes	—
170	C₂²×C₂₃	#339	1	2	yes	—
171	C₂²×C₂₃	#341	1	2	yes	—
172	C₂²×C₂₃	C₂×#95	1	1	yes	characteristic
173	C₂²×C₂₃	C₂×C₄⋊C₈	1	2	yes	—
174	C₄×C₂₃	—	2	1	no	—
175	C₄×C₂₃	—	2	1	no	—
176	C₄×C₂₃	—	2	1	no	—
177	C₄×C₂₃	—	2	1	no	—
178	C₄×C₂₃	#336	1	2	yes	—
179	C₄×C₂₃	#336	1	2	yes	—
180	C₄×C₂₃	#339	1	2	yes	—
181	C₄×C₂₃	#341	1	2	yes	—
182	C₄×C₂₃	C₂×C₄×C₈	1	1	yes	characteristic
183	C₄×C₂₃	C₂×#97	1	1	yes	characteristic
184	C₄×C₂₃	C₂×C₂²⋊C₈	1	2	yes	—
185	C₄×C₂₃	C₂×#104	1	2	yes	—
186	C₄×C₂₃	C₂×#108	1	2	yes	—
187	C₂²×M₁₆	C₄×C₂₃	1	2	yes	—
188	C₂³×C₈	—	2	1	no	—
189	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
190	#431	—	2	1	no	—
191	#431	—	2	1	no	—
192	#431	C₄×C₂₃	1	2	yes	—
193	#431	C₂²×C₂₃	1	2	yes	—
194	C₂×C₄⋊C₈	C₄×C₂₃	1	2	yes	—
195	C₂×C₂²⋊C₈	—	2	1	no	—
196	C₄×M₁₆	—	2	1	no	—
197	C₄×M₁₆	—	2	1	no	—
198	C₄×M₁₆	C₄×C₂₃	1	2	yes	—
199	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
200	C₂×#97	—	2	1	no	—
201	C₂×C₄×C₈	—	2	1	no	—
202	C₂×C₄×C₈	—	2	1	no	—
203	C₂×C₄×C₈	—	2	1	no	—
204	C₂×C₄×C₈	—	2	1	no	—
205	C₂×C₄×C₈	—	2	1	no	—
206	C₂×C₄×C₈	C₄×C₂₃	1	2	yes	—
207	C₂×C₄×C₈	C₄×C₂₃	1	2	yes	—
208	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
209	C₂×C₂₃	—	2	2	no	—
210	C₂×C₂₃	—	2	2	no	—
211	C₂×C₂₃	#1278	1	4	yes	direct product factor
212	C₂×C₂₃	C₂×#336	1	1	yes	characteristic
213	C₂×C₂₃	C₂×#339	1	1	yes	characteristic
214	C₂×C₂₃	C₂×#341	1	1	yes	characteristic
215	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
216	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
217	C₂³×C₄	Q₈×C₂₃	1	1	yes	characteristic
218	C₂×M₁₆	—	2	2	no	—
219	C₂×M₁₆	—	2	4	no	—
220	C₂×M₁₆	C₈×C₂₃	1	8	yes	complemented
221	C₂×M₁₆	C₂×C₄×C₂₃	1	4	yes	—
222	C₂²×C₈	—	2	8	no	—
223	C₂²×C₈	—	2	2	no	—
224	C₂²×C₈	—	2	2	no	—
225	C₂²×C₈	—	2	2	no	—
226	C₂²×C₈	—	2	2	no	—
227	C₂²×C₈	—	2	2	no	—
228	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
229	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
230	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
231	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
232	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
233	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
234	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
235	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
236	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
237	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
238	C₂×C₄²	Q₈×C₂₃	1	1	yes	characteristic
239	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
240	C₄⋊C₈	—	2	2	no	—
241	C₄⋊C₈	C₂×C₄×C₂₃	1	4	yes	—
242	C₂²⋊C₈	—	2	2	no	—
243	C₂²⋊C₈	—	2	2	no	—
244	#97	—	2	2	no	—
245	#97	—	2	2	no	—
246	C₄×C₈	—	2	2	no	—
247	C₄×C₈	—	2	2	no	—
248	C₄×C₈	—	2	2	no	—
249	C₄×C₈	—	2	2	no	—
250	C₄×C₈	—	2	2	no	—
251	C₄×C₈	—	2	2	no	—
252	C₄×C₈	—	2	2	no	—
253	C₄×C₈	C₂×C₄×C₂₃	1	4	yes	—
254	C₂₃	C₂×#1278	1	1	yes	characteristic, direct product factor, Sylow
255	C₂⁴	C₄⋊C₄×C₂₃	1	1	yes	characteristic
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	C₄²×C₂₃	1	1	yes	characteristic
259	C₂²×C₄	C₄²×C₂₃	1	1	yes	characteristic
260	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
261	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
262	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
263	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
264	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
265	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
266	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
267	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
268	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
269	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
270	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
271	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
272	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
273	C₂²×C₄	C₂×C₈×C₂₃	1	4	yes	—
274	C₂²×C₄	M₁₆×C₂₃	1	4	yes	—
275	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
277	C₂²×C₄	C₂×Q₈×C₂₃	1	1	yes	characteristic
278	M₁₆	—	2	4	no	—
279	M₁₆	—	2	8	no	—
280	M₁₆	C₂×C₈×C₂₃	1	8	yes	complemented
281	C₂×C₈	—	2	8	no	—
282	C₂×C₈	—	2	8	no	—
283	C₂×C₈	—	2	8	no	—
284	C₂×C₈	—	2	4	no	—
285	C₂×C₈	—	2	4	no	—
286	C₂×C₈	—	2	8	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	4	4	no	—
289	C₄²	C₄²×C₂₃	1	1	yes	characteristic
290	C₄²	C₄²×C₂₃	1	1	yes	characteristic
291	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
292	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
293	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
294	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
295	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
296	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
297	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
298	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
299	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
300	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
301	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
302	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
303	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
304	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
305	C₂³	—	2	2	no	—
306	C₂³	—	2	2	no	—
307	C₂³	C₂₃×#95	1	1	yes	characteristic
308	C₂³	C₂₃×#95	1	1	yes	characteristic
309	C₂³	C₂₃×C₄⋊C₈	1	4	yes	—
310	C₂³	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
322	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
323	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
324	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
325	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
326	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
327	C₂×C₄	C₄×C₈×C₂₃	1	2	yes	—
328	C₂×C₄	C₄×C₈×C₂₃	1	2	yes	—
329	C₂×C₄	C₂₃×#97	1	2	yes	—
330	C₂×C₄	C₂₃×#97	1	2	yes	—
331	C₂×C₄	C₂₃×C₂²⋊C₈	1	4	yes	—
332	C₂×C₄	C₂₃×C₂²⋊C₈	1	4	yes	—
333	C₂×C₄	C₂₃×#104	1	4	yes	—
334	C₂×C₄	C₂₃×C₄⋊C₈	1	4	yes	—
335	C₂×C₄	C₂₃×#108	1	4	yes	—
336	C₂×C₄	C₂×C₄²×C₂₃	1	1	yes	characteristic
337	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
338	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
339	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
340	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
341	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
342	C₂×C₄	C₂²×C₈×C₂₃	1	2	yes	—
343	C₂×C₄	C₂×M₁₆×C₂₃	1	2	yes	—
344	C₈	—	2	8	no	—
345	C₈	—	2	8	no	—
346	C₈	—	4	4	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	8	no	—
352	C₂²	C₂₃×#336	1	2	yes	—
353	C₂²	C₂₃×#336	1	2	yes	—
354	C₂²	C₂₃×#339	1	2	yes	—
355	C₂²	C₂₃×#341	1	2	yes	—
356	C₂²	C₂×C₂₃×#95	1	1	yes	characteristic
357	C₂²	C₂×C₂₃×C₄⋊C₈	1	2	yes	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	C₂₃×#336	1	2	yes	—
363	C₄	C₂₃×#336	1	2	yes	—
364	C₄	C₂₃×#339	1	2	yes	—
365	C₄	C₂₃×#341	1	2	yes	—
366	C₄	C₂×C₄×C₈×C₂₃	1	1	yes	characteristic
367	C₄	C₂×C₂₃×#97	1	1	yes	characteristic
368	C₄	C₂×C₂₃×C₂²⋊C₈	1	2	yes	—
369	C₄	C₂×C₂₃×#104	1	2	yes	—
370	C₄	C₂×C₂₃×#108	1	2	yes	—
371	C₂	—	2	2	no	—
372	C₂	—	2	2	no	—
373	C₂	C₂₃×#1278	1	4	yes	direct product factor
374	C₂	C₂×C₂₃×#336	1	1	yes	characteristic
375	C₂	C₂×C₂₃×#339	1	1	yes	characteristic
376	C₂	C₂×C₂₃×#341	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²×C₂₃	D₄
commutator	C₄	C₂×C₄×C₈×C₂₃
Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
socle	C₂³×C₂₃	#95
prime radical	C₂⁴×C₂₃	C₄⋊C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂₃×#1278	C₂	direct (N × H)
32. C₂×M₁₆×C₂₃	C₈	semidirect
91. M₁₆×C₂₃	C₂×C₈	semidirect
116. C₂×#1278	C₂₃	direct (N × H)
162. #1278	C₂×C₂₃	direct (N × H)
211. C₂×C₂₃	#1278	direct (N × H)
220. C₂×M₁₆	C₈×C₂₃	semidirect
254. C₂₃	C₂×#1278	direct (N × H)
280. M₁₆	C₂×C₈×C₂₃	semidirect
373. C₂	C₂₃×#1278	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#431	2
C₂×C₄×M₁₆×C₂₃	2
C₂²×C₄×C₈×C₂₃	2
C₂₃×#1278	2
C₂×#1278	23

Subgroups — C2×C23×#1278 #19155507

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#1278 #19155507