Subgroups — C₂×C₂₃×#2898 #19207711

Order 5888.

4882 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2898	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₂₃×#417	C₂	1	3	yes	maximal, complemented
6	C₂×C₂₃×#419	C₂	1	3	yes	maximal, complemented
7	C₂×C₂₃×#416	C₂	1	3	yes	maximal, complemented
8	C₂²×C₂₃×#103	C₂	1	3	yes	maximal, complemented
9	C₂×C₂₃×2₋¹⁺⁴	—	2	8	no	—
10	C₂×C₂₃×2₋¹⁺⁴	—	2	4	no	—
11	C₂×C₂₃×2₋¹⁺⁴	C₄	1	16	yes	complemented
12	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	8	yes	—
13	C₂²×#41×C₂₃	—	2	3	no	—
14	C₂²×#41×C₂₃	C₂²	1	3	yes	—
15	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
16	C₂³×Q₈×C₂₃	—	2	1	no	—
17	C₂³×Q₈×C₂₃	C₂²	1	3	yes	—
18	C₂×C₂₃×#131	—	2	8	no	—
19	C₂×C₂₃×#131	C₂²	1	8	yes	complemented
20	C₂²×M₁₆×C₂₃	C₂²	1	3	yes	—
21	C₂³×C₈×C₂₃	C₂²	1	3	yes	—
22	C₂₃×#520	—	2	4	no	—
23	C₂₃×#520	C₂²	1	8	yes	complemented
24	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
25	C₂×C₄×D₄×C₂₃	—	2	3	no	—
26	C₂×C₂₃×#117	C₂²	1	3	yes	—
27	C₂²×C₄⋊C₄×C₂₃	C₂²	1	3	yes	—
28	C₂₃×#419	C₂²	1	24	yes	complemented
29	C₂₃×#417	C₂²	1	24	yes	complemented
30	C₂₃×#416	C₂²	1	24	yes	complemented
31	C₂×C₂₃×#103	C₂²	1	3	yes	—
32	C₂×C₂₃×#103	C₂²	1	6	yes	—
33	C₂×C₂₃×#103	C₂²	1	3	yes	—
34	C₂×C₂₃×#103	C₂²	1	24	yes	complemented
35	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#102	C₂²	1	3	yes	—
37	C₂₃×2₋¹⁺⁴	—	2	64	no	—
38	C₂₃×2₋¹⁺⁴	—	2	32	no	—
39	C₂₃×2₋¹⁺⁴	C₂×C₄	1	64	yes	complemented
40	C₂×#41×C₂₃	—	2	48	no	—
41	C₂×#41×C₂₃	—	2	24	no	—
42	C₂×#41×C₂₃	—	2	12	no	—
43	C₂×#41×C₂₃	—	2	6	no	—
44	C₂×#41×C₂₃	C₂×C₄	1	8	yes	—
45	C₂×#41×C₂₃	C₂×C₄	1	24	yes	complemented
46	C₂×#41×C₂₃	D₄	1	8	yes	—
47	C₂×#41×C₂₃	D₄	1	4	yes	—
48	C₂×#41×C₂₃	C₂³	1	12	yes	—
49	C₂×#41×C₂₃	C₂³	1	4	yes	—
50	C₂²×Q₈×C₂₃	—	2	16	no	—
51	C₂²×Q₈×C₂₃	—	2	8	no	—
52	C₂²×Q₈×C₂₃	—	2	3	no	—
53	C₂²×Q₈×C₂₃	—	2	12	no	—
54	C₂²×Q₈×C₂₃	—	2	6	no	—
55	C₂²×Q₈×C₂₃	C₂×C₄	1	24	yes	complemented
56	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
57	C₂²×Q₈×C₂₃	C₂³	1	3	yes	—
58	C₂²×Q₈×C₂₃	C₂³	1	12	yes	—
59	C₂²×D₄×C₂₃	—	2	3	no	—
60	C₂²×D₄×C₂₃	D₄	1	3	yes	—
61	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₂₃	—	2	3	no	—
63	C₂³×C₄×C₂₃	—	2	3	no	—
64	C₂³×C₄×C₂₃	—	2	3	no	—
65	C₂³×C₄×C₂₃	C₂³	1	3	yes	—
66	C₂₃×#131	—	2	32	no	—
67	C₂×M₁₆×C₂₃	—	2	12	no	—
68	C₂×M₁₆×C₂₃	C₂³	1	12	yes	—
69	C₂²×C₈×C₂₃	—	2	12	no	—
70	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₂₃	C₂³	1	3	yes	—
72	C₂²×C₈×C₂₃	C₂³	1	12	yes	—
73	C₄×Q₈×C₂₃	—	2	8	no	—
74	C₄×D₄×C₂₃	—	2	24	no	—
75	C₂₃×#117	—	2	6	no	—
76	C₂₃×#117	C₂³	1	12	yes	—
77	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
78	C₂×C₄⋊C₄×C₂₃	—	2	6	no	—
79	C₂×C₄⋊C₄×C₂₃	C₂³	1	3	yes	—
80	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₂₃	C₂³	1	12	yes	—
82	C₂×C₂²⋊C₄×C₂₃	—	2	3	no	—
83	C₂×C₄²×C₂₃	—	2	3	no	—
84	C₂₃×#103	C₂³	1	12	yes	—
85	C₂₃×#103	C₂³	1	24	yes	—
86	C₂₃×#103	C₂³	1	12	yes	—
87	C₂₃×#102	C₂³	1	4	yes	—
88	C₂₃×#102	C₂³	1	12	yes	—
89	C₂⁴×C₂₃	—	2	1	no	—
90	C₂⁴×C₂₃	C₂×D₄	1	3	yes	—
91	#41×C₂₃	—	2	192	no	—
92	#41×C₂₃	—	2	48	no	—
93	#41×C₂₃	—	2	24	no	—
94	#41×C₂₃	C₂²⋊C₄	1	32	yes	—
95	#41×C₂₃	C₂²×C₄	1	16	yes	—
96	#41×C₂₃	C₂²×C₄	1	48	yes	complemented
97	#41×C₂₃	C₂×D₄	1	16	yes	—
98	C₂×Q₈×C₂₃	—	2	64	no	—
99	C₂×Q₈×C₂₃	—	2	24	no	—
100	C₂×Q₈×C₂₃	—	2	48	no	—
101	C₂×Q₈×C₂₃	—	2	6	no	—
102	C₂×Q₈×C₂₃	—	2	12	no	—
103	C₂×Q₈×C₂₃	—	2	3	no	—
104	C₂×Q₈×C₂₃	—	2	24	no	—
105	C₂×Q₈×C₂₃	C₂²⋊C₄	1	8	yes	—
106	C₂×Q₈×C₂₃	C₂²×C₄	1	12	yes	—
107	C₂×Q₈×C₂₃	C₂²×C₄	1	48	yes	complemented
108	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	—
109	C₂×Q₈×C₂₃	C₂⁴	1	6	yes	—
110	C₂×D₄×C₂₃	—	2	24	no	—
111	C₂×D₄×C₂₃	—	2	12	no	—
112	C₂×D₄×C₂₃	—	2	1	no	—
113	C₂×D₄×C₂₃	—	2	2	no	—
114	C₂×D₄×C₂₃	C₂²⋊C₄	1	24	yes	—
115	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
116	C₂×D₄×C₂₃	C₂×D₄	1	12	yes	—
117	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
118	C₂²×C₄×C₂₃	—	2	24	no	—
119	C₂²×C₄×C₂₃	—	2	12	no	—
120	C₂²×C₄×C₂₃	—	2	3	no	—
121	C₂²×C₄×C₂₃	—	2	24	no	—
122	C₂²×C₄×C₂₃	—	2	12	no	—
123	C₂²×C₄×C₂₃	—	2	1	no	—
124	C₂²×C₄×C₂₃	—	2	3	no	—
125	C₂²×C₄×C₂₃	—	2	12	no	—
126	C₂²×C₄×C₂₃	—	8	6	no	—
127	C₂²×C₄×C₂₃	C₂²×C₄	1	12	yes	—
128	C₂²×C₄×C₂₃	C₂×D₄	1	6	yes	—
129	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
130	C₂²×C₄×C₂₃	C₂×D₄	1	12	yes	—
131	C₂²×C₄×C₂₃	C₂⁴	1	6	yes	—
132	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
133	M₁₆×C₂₃	—	2	24	no	—
134	C₂×C₈×C₂₃	—	2	2	no	—
135	C₂×C₈×C₂₃	—	2	6	no	—
136	C₂×C₈×C₂₃	—	2	24	no	—
137	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
138	C₂×C₈×C₂₃	C₂⁴	1	6	yes	—
139	C₄⋊C₄×C₂₃	—	2	3	no	—
140	C₄⋊C₄×C₂₃	—	2	12	no	—
141	C₄⋊C₄×C₂₃	—	2	1	no	—
142	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
143	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
144	C₂²⋊C₄×C₂₃	—	2	12	no	—
145	C₄²×C₂₃	—	2	12	no	—
146	C₂×#2898	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
147	C₂³×C₂₃	—	2	6	no	—
148	C₂³×C₂₃	—	2	6	no	—
149	C₂³×C₂₃	—	2	4	no	—
150	C₂³×C₂₃	—	2	2	no	—
151	C₂³×C₂₃	—	4	2	no	—
152	C₂³×C₂₃	—	4	2	no	—
153	C₂³×C₂₃	C₂×C₂²⋊C₄	1	12	yes	—
154	C₂³×C₂₃	C₂²×D₄	1	6	yes	—
155	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
156	Q₈×C₂₃	—	2	12	no	—
157	Q₈×C₂₃	—	2	48	no	—
158	Q₈×C₂₃	—	2	6	no	—
159	Q₈×C₂₃	C₂×C₂²⋊C₄	1	16	yes	—
160	Q₈×C₂₃	C₂³×C₄	1	12	yes	—
161	D₄×C₂₃	—	2	48	no	—
162	D₄×C₂₃	—	2	4	no	—
163	D₄×C₂₃	—	2	2	no	—
164	D₄×C₂₃	C₂×C₂²⋊C₄	1	48	yes	—
165	D₄×C₂₃	C₂³×C₄	1	4	yes	—
166	C₂×C₄×C₂₃	—	2	12	no	—
167	C₂×C₄×C₂₃	—	2	48	no	—
168	C₂×C₄×C₂₃	—	2	6	no	—
169	C₂×C₄×C₂₃	—	2	48	no	—
170	C₂×C₄×C₂₃	—	2	2	no	—
171	C₂×C₄×C₂₃	—	2	6	no	—
172	C₂×C₄×C₂₃	—	4	6	no	—
173	C₂×C₄×C₂₃	—	4	2	no	—
174	C₂×C₄×C₂₃	—	8	12	no	—
175	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	12	yes	—
176	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	24	yes	—
177	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
178	C₂×C₄×C₂₃	C₂³×C₄	1	12	yes	—
179	C₂×C₄×C₂₃	C₂²×D₄	1	6	yes	—
180	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
182	C₂×C₄×C₂₃	C₂²×D₄	1	12	yes	—
183	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
184	C₈×C₂₃	—	2	2	no	—
185	C₈×C₂₃	—	2	6	no	—
186	C₂²×2₋¹⁺⁴	C₂×C₂₃	1	1	yes	characteristic
187	C₂²×#131	C₂×C₂₃	1	1	yes	characteristic, complemented
188	C₂×#520	C₂×C₂₃	1	1	yes	characteristic, complemented
189	#2898	C₂×C₂₃	1	16	yes	direct product factor
190	C₂×#417	C₂×C₂₃	1	3	yes	complemented
191	C₂×#419	C₂×C₂₃	1	3	yes	complemented
192	C₂×#416	C₂×C₂₃	1	3	yes	complemented
193	C₂²×#103	C₂×C₂₃	1	3	yes	complemented
194	C₂²×C₂₃	—	2	24	no	—
195	C₂²×C₂₃	—	2	6	no	—
196	C₂²×C₂₃	—	2	6	no	—
197	C₂²×C₂₃	—	2	4	no	—
198	C₂²×C₂₃	—	4	8	no	—
199	C₂²×C₂₃	—	4	2	no	—
200	C₂²×C₂₃	—	4	2	no	—
201	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	12	yes	—
202	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	2	yes	—
203	C₂²×C₂₃	#577	1	2	yes	—
204	C₂²×C₂₃	#578	1	2	yes	—
205	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
206	C₄×C₂₃	—	2	12	no	—
207	C₄×C₂₃	—	4	6	no	—
208	C₄×C₂₃	—	4	2	no	—
209	C₄×C₂₃	C₂²×C₂²⋊C₄	1	12	yes	—
210	C₄×C₂₃	C₂²×C₂²⋊C₄	1	2	yes	—
211	C₄×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
212	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
213	C₂×2₋¹⁺⁴	—	2	8	no	—
214	C₂×2₋¹⁺⁴	—	2	4	no	—
215	C₂×2₋¹⁺⁴	C₄×C₂₃	1	16	yes	complemented
216	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	8	yes	—
217	C₂²×#41	—	2	3	no	—
218	C₂²×#41	C₂²×C₂₃	1	3	yes	—
219	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
220	C₂³×Q₈	—	2	1	no	—
221	C₂³×Q₈	C₂²×C₂₃	1	3	yes	—
222	C₂×#131	—	2	8	no	—
223	C₂×#131	C₂²×C₂₃	1	8	yes	complemented
224	C₂²×M₁₆	C₂²×C₂₃	1	3	yes	—
225	C₂³×C₈	C₂²×C₂₃	1	3	yes	—
226	#520	—	2	4	no	—
227	#520	C₂²×C₂₃	1	8	yes	complemented
228	C₂×C₄×Q₈	—	2	1	no	—
229	C₂×C₄×D₄	—	2	3	no	—
230	C₂×#117	C₂²×C₂₃	1	3	yes	—
231	C₂²×C₄⋊C₄	C₂²×C₂₃	1	3	yes	—
232	#419	C₂²×C₂₃	1	24	yes	complemented
233	#417	C₂²×C₂₃	1	24	yes	complemented
234	#416	C₂²×C₂₃	1	24	yes	complemented
235	C₂×#103	C₂²×C₂₃	1	3	yes	—
236	C₂×#103	C₂²×C₂₃	1	6	yes	—
237	C₂×#103	C₂²×C₂₃	1	3	yes	—
238	C₂×#103	C₂²×C₂₃	1	24	yes	complemented
239	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
240	C₂×#102	C₂²×C₂₃	1	3	yes	—
241	C₂×C₂₃	—	2	12	no	—
242	C₂×C₂₃	—	4	4	no	—
243	C₂×C₂₃	#2898	1	4	yes	direct product factor
244	C₂×C₂₃	C₂³×C₂²⋊C₄	1	1	yes	characteristic
245	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
246	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
247	2₋¹⁺⁴	—	2	64	no	—
248	2₋¹⁺⁴	—	2	32	no	—
249	2₋¹⁺⁴	C₂×C₄×C₂₃	1	64	yes	complemented
250	C₂×#41	—	2	48	no	—
251	C₂×#41	—	2	24	no	—
252	C₂×#41	—	2	12	no	—
253	C₂×#41	—	2	6	no	—
254	C₂×#41	C₂×C₄×C₂₃	1	8	yes	—
255	C₂×#41	C₂×C₄×C₂₃	1	24	yes	complemented
256	C₂×#41	D₄×C₂₃	1	8	yes	—
257	C₂×#41	D₄×C₂₃	1	4	yes	—
258	C₂×#41	C₂³×C₂₃	1	12	yes	—
259	C₂×#41	C₂³×C₂₃	1	4	yes	—
260	C₂²×Q₈	—	2	16	no	—
261	C₂²×Q₈	—	2	8	no	—
262	C₂²×Q₈	—	2	3	no	—
263	C₂²×Q₈	—	2	12	no	—
264	C₂²×Q₈	—	2	6	no	—
265	C₂²×Q₈	C₂×C₄×C₂₃	1	24	yes	complemented
266	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
267	C₂²×Q₈	C₂³×C₂₃	1	3	yes	—
268	C₂²×Q₈	C₂³×C₂₃	1	12	yes	—
269	C₂²×D₄	—	2	3	no	—
270	C₂²×D₄	D₄×C₂₃	1	3	yes	—
271	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
272	C₂³×C₄	—	2	3	no	—
273	C₂³×C₄	—	2	3	no	—
274	C₂³×C₄	—	2	3	no	—
275	C₂³×C₄	C₂³×C₂₃	1	3	yes	—
276	#131	—	2	32	no	—
277	C₂×M₁₆	—	2	12	no	—
278	C₂×M₁₆	C₂³×C₂₃	1	12	yes	—
279	C₂²×C₈	—	2	12	no	—
280	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₂₃	1	3	yes	—
282	C₂²×C₈	C₂³×C₂₃	1	12	yes	—
283	C₄×Q₈	—	2	8	no	—
284	C₄×D₄	—	2	24	no	—
285	#117	—	2	6	no	—
286	#117	C₂³×C₂₃	1	12	yes	—
287	C₂×C₄⋊C₄	—	2	3	no	—
288	C₂×C₄⋊C₄	—	2	6	no	—
289	C₂×C₄⋊C₄	C₂³×C₂₃	1	3	yes	—
290	C₂×C₄⋊C₄	C₂³×C₂₃	1	12	yes	—
291	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
292	C₂×C₂²⋊C₄	—	2	3	no	—
293	C₂×C₄²	—	2	3	no	—
294	#103	C₂³×C₂₃	1	12	yes	—
295	#103	C₂³×C₂₃	1	24	yes	—
296	#103	C₂³×C₂₃	1	12	yes	—
297	#102	C₂³×C₂₃	1	4	yes	—
298	#102	C₂³×C₂₃	1	12	yes	—
299	C₂₃	C₂×#2898	1	1	yes	characteristic, direct product factor, Sylow
300	C₂⁴	—	2	1	no	—
301	C₂⁴	C₂×D₄×C₂₃	1	3	yes	—
302	#41	—	2	192	no	—
303	#41	—	2	48	no	—
304	#41	—	2	24	no	—
305	#41	C₂²⋊C₄×C₂₃	1	32	yes	—
306	#41	C₂²×C₄×C₂₃	1	16	yes	—
307	#41	C₂²×C₄×C₂₃	1	48	yes	complemented
308	#41	C₂×D₄×C₂₃	1	16	yes	—
309	C₂×Q₈	—	2	64	no	—
310	C₂×Q₈	—	2	24	no	—
311	C₂×Q₈	—	2	48	no	—
312	C₂×Q₈	—	2	12	no	—
313	C₂×Q₈	—	2	3	no	—
314	C₂×Q₈	—	2	6	no	—
315	C₂×Q₈	—	2	24	no	—
316	C₂×Q₈	C₂²⋊C₄×C₂₃	1	8	yes	—
317	C₂×Q₈	C₂²×C₄×C₂₃	1	12	yes	—
318	C₂×Q₈	C₂²×C₄×C₂₃	1	48	yes	complemented
319	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	—
320	C₂×Q₈	C₂⁴×C₂₃	1	6	yes	—
321	C₂×D₄	—	2	24	no	—
322	C₂×D₄	—	2	12	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	C₂²⋊C₄×C₂₃	1	24	yes	—
326	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
327	C₂×D₄	C₂×D₄×C₂₃	1	12	yes	—
328	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
329	C₂²×C₄	—	2	24	no	—
330	C₂²×C₄	—	2	3	no	—
331	C₂²×C₄	—	2	12	no	—
332	C₂²×C₄	—	2	24	no	—
333	C₂²×C₄	—	2	12	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	3	no	—
336	C₂²×C₄	—	2	12	no	—
337	C₂²×C₄	—	8	6	no	—
338	C₂²×C₄	C₂²×C₄×C₂₃	1	12	yes	—
339	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
340	C₂²×C₄	C₂×D₄×C₂₃	1	6	yes	—
341	C₂²×C₄	C₂×D₄×C₂₃	1	12	yes	—
342	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
343	C₂²×C₄	C₂⁴×C₂₃	1	6	yes	—
344	M₁₆	—	2	24	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	6	no	—
347	C₂×C₈	—	2	24	no	—
348	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
349	C₂×C₈	C₂⁴×C₂₃	1	6	yes	—
350	C₄⋊C₄	—	2	3	no	—
351	C₄⋊C₄	—	2	12	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
354	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
355	C₂²⋊C₄	—	2	12	no	—
356	C₄²	—	2	12	no	—
357	C₂³	—	2	6	no	—
358	C₂³	—	2	6	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	2	no	—
363	C₂³	C₂×C₂²⋊C₄×C₂₃	1	12	yes	—
364	C₂³	C₂²×D₄×C₂₃	1	6	yes	—
365	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
366	Q₈	—	2	6	no	—
367	Q₈	—	2	12	no	—
368	Q₈	—	2	48	no	—
369	Q₈	C₂×C₂²⋊C₄×C₂₃	1	16	yes	—
370	Q₈	C₂³×C₄×C₂₃	1	12	yes	—
371	D₄	—	2	48	no	—
372	D₄	—	2	2	no	—
373	D₄	—	2	4	no	—
374	D₄	C₂×C₂²⋊C₄×C₂₃	1	48	yes	—
375	D₄	C₂³×C₄×C₂₃	1	4	yes	—
376	C₂×C₄	—	2	6	no	—
377	C₂×C₄	—	2	12	no	—
378	C₂×C₄	—	2	48	no	—
379	C₂×C₄	—	2	48	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	6	no	—
382	C₂×C₄	—	4	6	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	8	12	no	—
385	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	12	yes	—
386	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	24	yes	—
387	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
388	C₂×C₄	C₂³×C₄×C₂₃	1	12	yes	—
389	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
390	C₂×C₄	C₂²×D₄×C₂₃	1	12	yes	—
391	C₂×C₄	C₂²×D₄×C₂₃	1	6	yes	—
392	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
393	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
394	C₈	—	2	2	no	—
395	C₈	—	2	6	no	—
396	C₂²	—	2	6	no	—
397	C₂²	—	2	6	no	—
398	C₂²	—	2	24	no	—
399	C₂²	—	2	4	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	8	no	—
403	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	12	yes	—
404	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	2	yes	—
405	C₂²	C₂₃×#577	1	2	yes	—
406	C₂²	C₂₃×#578	1	2	yes	—
407	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
408	C₄	—	2	12	no	—
409	C₄	—	4	6	no	—
410	C₄	—	4	2	no	—
411	C₄	C₂²×C₂²⋊C₄×C₂₃	1	12	yes	—
412	C₄	C₂²×C₂²⋊C₄×C₂₃	1	2	yes	—
413	C₄	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
414	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
415	C₂	—	2	12	no	—
416	C₂	—	4	4	no	—
417	C₂	C₂₃×#2898	1	4	yes	direct product factor
418	C₂	C₂³×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
419	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
420	C₂	C₂×C₂₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator	C₄	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂²×C₂₃×2₋¹⁺⁴	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂²×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₂₃×#131	C₂	semidirect
3. C₂×C₂₃×#520	C₂	semidirect
4. C₂₃×#2898	C₂	direct (N × H)
5. C₂×C₂₃×#417	C₂	semidirect
6. C₂×C₂₃×#419	C₂	semidirect
7. C₂×C₂₃×#416	C₂	semidirect
8. C₂²×C₂₃×#103	C₂	semidirect
11. C₂×C₂₃×2₋¹⁺⁴	C₄	semidirect
19. C₂×C₂₃×#131	C₂²	semidirect
23. C₂₃×#520	C₂²	semidirect
28. C₂₃×#419	C₂²	semidirect
29. C₂₃×#417	C₂²	semidirect
30. C₂₃×#416	C₂²	semidirect
34. C₂×C₂₃×#103	C₂²	semidirect
39. C₂₃×2₋¹⁺⁴	C₂×C₄	semidirect
45. C₂×#41×C₂₃	C₂×C₄	semidirect
55. C₂²×Q₈×C₂₃	C₂×C₄	semidirect
96. #41×C₂₃	C₂²×C₄	semidirect
107. C₂×Q₈×C₂₃	C₂²×C₄	semidirect
146. C₂×#2898	C₂₃	direct (N × H)
187. C₂²×#131	C₂×C₂₃	semidirect
188. C₂×#520	C₂×C₂₃	semidirect
189. #2898	C₂×C₂₃	direct (N × H)
190. C₂×#417	C₂×C₂₃	semidirect
191. C₂×#419	C₂×C₂₃	semidirect
192. C₂×#416	C₂×C₂₃	semidirect
193. C₂²×#103	C₂×C₂₃	semidirect
215. C₂×2₋¹⁺⁴	C₄×C₂₃	semidirect
223. C₂×#131	C₂²×C₂₃	semidirect
227. #520	C₂²×C₂₃	semidirect
232. #419	C₂²×C₂₃	semidirect
233. #417	C₂²×C₂₃	semidirect
234. #416	C₂²×C₂₃	semidirect
238. C₂×#103	C₂²×C₂₃	semidirect
243. C₂×C₂₃	#2898	direct (N × H)
249. 2₋¹⁺⁴	C₂×C₄×C₂₃	semidirect
255. C₂×#41	C₂×C₄×C₂₃	semidirect
265. C₂²×Q₈	C₂×C₄×C₂₃	semidirect
299. C₂₃	C₂×#2898	direct (N × H)
307. #41	C₂²×C₄×C₂₃	semidirect
318. C₂×Q₈	C₂²×C₄×C₂₃	semidirect
417. C₂	C₂₃×#2898	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×C₂₃×2₋¹⁺⁴	2
C₂²×C₂₃×#131	2
C₂×C₂₃×#520	2
C₂₃×#2898	2
C₂×C₂₃×#417	2
C₂×C₂₃×#419	2
C₂×C₂₃×#416	2
C₂²×C₂₃×#103	2
C₂×#2898	23

Subgroups — C2×C23×#2898 #19207711

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#2898 #19207711