Subgroups — C₂×C₂₃×#2948 #19207788

Order 5888.

3086 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₈×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#518	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2948	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#442	C₂	1	4	yes	maximal, complemented
5	C₂×C₄×D₈×C₂₃	C₂	1	4	yes	maximal, complemented
6	C₂×C₂₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#418	C₂	1	2	yes	maximal, complemented
8	C₂×C₂₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₂₃	C₂²	1	2	yes	—
10	C₂²×D₈×C₂₃	C₄	1	16	yes	complemented
11	C₂²×D₈×C₂₃	C₂²	1	2	yes	—
12	C₂²×D₈×C₂₃	C₂²	1	2	yes	—
13	C₂²×D₈×C₂₃	C₂²	1	8	yes	—
14	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
16	C₂₃×#518	—	2	8	no	—
17	C₂₃×#518	C₂²	1	16	yes	complemented
18	C₂×C₄×D₄×C₂₃	—	2	4	no	—
19	C₂×C₄×D₄×C₂₃	C₂²	1	8	yes	complemented
20	C₂×C₂₃×#117	C₂²	1	2	yes	—
21	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₂₃	—	2	4	no	—
23	C₂₃×#442	C₂²	1	32	yes	complemented
24	C₄×D₈×C₂₃	C₂²	1	32	yes	complemented
25	C₂₃×#427	C₂²	1	8	yes	complemented
26	C₂×C₂₃×#107	C₂²	1	2	yes	complemented
27	C₂×C₂₃×#106	C₂²	1	2	yes	complemented
28	C₂₃×#418	C₂²	1	16	yes	complemented
29	C₂×C₂₃×#102	C₂²	1	8	yes	complemented
30	C₂₃×#405	C₂²	1	8	yes	complemented
31	C₂×C₂₃×#97	C₂²	1	2	yes	complemented
32	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	complemented
33	C₂⁵×C₂₃	—	2	2	no	—
34	C₂²×D₄×C₂₃	—	2	2	no	—
35	C₂²×D₄×C₂₃	—	2	4	no	—
36	C₂²×D₄×C₂₃	—	2	8	no	—
37	C₂²×D₄×C₂₃	C₂×C₄	1	16	yes	complemented
38	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
39	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
40	C₂³×C₄×C₂₃	—	2	8	no	—
41	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
42	C₂×D₈×C₂₃	C₂×C₄	1	16	yes	complemented
43	C₂×D₈×C₂₃	C₂×C₄	1	16	yes	complemented
44	C₂×D₈×C₂₃	C₂×C₄	1	64	yes	complemented
45	C₂×D₈×C₂₃	C₂³	1	8	yes	—
46	C₂×D₈×C₂₃	C₂³	1	8	yes	—
47	C₂×M₁₆×C₂₃	—	2	4	no	—
48	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
49	C₂²×C₈×C₂₃	C₂×C₄	1	8	yes	complemented
50	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
54	C₄×D₄×C₂₃	—	2	32	no	—
55	C₄×D₄×C₂₃	—	2	16	no	—
56	C₄×D₄×C₂₃	C₂³	1	32	yes	complemented
57	C₂₃×#117	—	2	4	no	—
58	C₂₃×#117	D₄	1	4	yes	—
59	C₂₃×#117	C₂³	1	8	yes	—
60	C₂₃×#117	C₂³	1	4	yes	—
61	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
62	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
63	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
65	C₂×C₂²⋊C₄×C₂₃	—	2	32	no	—
66	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
67	C₂×C₄²×C₂₃	—	2	2	no	—
68	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
69	C₂₃×#107	C₂³	1	8	yes	complemented
70	C₂₃×#106	C₂³	1	8	yes	complemented
71	C₂₃×#102	C₂³	1	32	yes	complemented
72	C₂₃×#97	C₂³	1	8	yes	complemented
73	C₄×C₈×C₂₃	C₂³	1	8	yes	complemented
74	C₂⁴×C₂₃	—	2	4	no	—
75	C₂⁴×C₂₃	—	2	16	no	—
76	C₂⁴×C₂₃	—	2	8	no	—
77	C₂⁴×C₂₃	—	8	8	no	—
78	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
79	C₂×D₄×C₂₃	—	2	32	no	—
80	C₂×D₄×C₂₃	—	2	16	no	—
81	C₂×D₄×C₂₃	—	2	8	no	—
82	C₂×D₄×C₂₃	—	2	4	no	—
83	C₂×D₄×C₂₃	—	2	8	no	—
84	C₂×D₄×C₂₃	—	2	16	no	—
85	C₂×D₄×C₂₃	C₂²×C₄	1	16	yes	—
86	C₂×D₄×C₂₃	C₂²×C₄	1	32	yes	complemented
87	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
88	C₂²×C₄×C₂₃	—	2	4	no	—
89	C₂²×C₄×C₂₃	—	2	32	no	—
90	C₂²×C₄×C₂₃	—	8	16	no	—
91	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
92	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
93	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₂₃	#41	1	4	yes	—
96	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
97	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
98	D₈×C₂₃	C₂²×C₄	1	32	yes	complemented
99	D₈×C₂₃	C₂²×C₄	1	32	yes	complemented
100	M₁₆×C₂₃	—	2	8	no	—
101	C₂×C₈×C₂₃	—	2	4	no	—
102	C₂×C₈×C₂₃	C₂²×C₄	1	4	yes	—
103	C₂×C₈×C₂₃	C₂²×C₄	1	4	yes	—
104	C₂×C₈×C₂₃	C₂²×C₄	1	16	yes	complemented
105	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
106	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
107	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
108	C₄⋊C₄×C₂₃	—	2	4	no	—
109	C₄⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
110	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
111	C₂²⋊C₄×C₂₃	—	2	8	no	—
112	C₂²⋊C₄×C₂₃	—	2	32	no	—
113	C₂²⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
114	C₄²×C₂₃	—	2	8	no	—
115	C₄²×C₂₃	C₂×D₄	1	4	yes	—
116	C₄²×C₂₃	C₂⁴	1	4	yes	—
117	C₂×#2948	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂³×C₂₃	—	2	4	no	—
119	C₂³×C₂₃	—	2	16	no	—
120	C₂³×C₂₃	—	2	8	no	—
121	C₂³×C₂₃	—	2	32	no	—
122	C₂³×C₂₃	—	4	16	no	—
123	C₂³×C₂₃	—	8	32	no	—
124	C₂³×C₂₃	—	8	16	no	—
125	C₂³×C₂₃	C₄×D₄	1	4	yes	—
126	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
127	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
128	D₄×C₂₃	—	2	16	no	—
129	D₄×C₂₃	—	2	32	no	—
130	D₄×C₂₃	—	2	8	no	—
131	D₄×C₂₃	C₂³×C₄	1	16	yes	—
132	C₂×C₄×C₂₃	—	2	8	no	—
133	C₂×C₄×C₂₃	—	2	8	no	—
134	C₂×C₄×C₂₃	—	4	8	no	—
135	C₂×C₄×C₂₃	—	8	32	no	—
136	C₂×C₄×C₂₃	C₄×D₄	1	8	yes	—
137	C₂×C₄×C₂₃	C₄×D₄	1	4	yes	—
138	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
139	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
140	C₂×C₄×C₂₃	C₂²×D₄	1	8	yes	—
141	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
142	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
143	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
144	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
145	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
146	C₈×C₂₃	—	2	4	no	—
147	C₈×C₂₃	C₂³×C₄	1	4	yes	—
148	C₈×C₂₃	C₂³×C₄	1	4	yes	—
149	C₂³×D₈	C₂×C₂₃	1	1	yes	characteristic
150	C₂×#518	C₂×C₂₃	1	2	yes	complemented
151	#2948	C₂×C₂₃	1	16	yes	direct product factor
152	C₂×#442	C₂×C₂₃	1	4	yes	complemented
153	C₂×C₄×D₈	C₂×C₂₃	1	4	yes	complemented
154	C₂×#427	C₂×C₂₃	1	1	yes	characteristic, complemented
155	C₂×#418	C₂×C₂₃	1	2	yes	complemented
156	C₂×#405	C₂×C₂₃	1	1	yes	characteristic, complemented
157	C₂²×C₂₃	—	2	8	no	—
158	C₂²×C₂₃	—	2	4	no	—
159	C₂²×C₂₃	—	2	16	no	—
160	C₂²×C₂₃	—	4	32	no	—
161	C₂²×C₂₃	—	4	16	no	—
162	C₂²×C₂₃	—	8	32	no	—
163	C₂²×C₂₃	C₂×C₄×D₄	1	4	yes	—
164	C₂²×C₂₃	C₂×C₄×D₄	1	2	yes	—
165	C₂²×C₂₃	#576	1	4	yes	—
166	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
167	C₄×C₂₃	—	2	8	no	—
168	C₄×C₂₃	—	4	8	no	—
169	C₄×C₂₃	C₂×C₄×D₄	1	2	yes	—
170	C₄×C₂₃	C₂×C₄×D₄	1	4	yes	—
171	C₄×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
172	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
173	C₂³×D₄	C₂²×C₂₃	1	2	yes	—
174	C₂²×D₈	C₄×C₂₃	1	16	yes	complemented
175	C₂²×D₈	C₂²×C₂₃	1	2	yes	—
176	C₂²×D₈	C₂²×C₂₃	1	2	yes	—
177	C₂²×D₈	C₂²×C₂₃	1	8	yes	—
178	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
179	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
180	#518	—	2	8	no	—
181	#518	C₂²×C₂₃	1	16	yes	complemented
182	C₂×C₄×D₄	—	2	4	no	—
183	C₂×C₄×D₄	C₂²×C₂₃	1	8	yes	complemented
184	C₂×#117	C₂²×C₂₃	1	2	yes	—
185	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
186	C₂²×C₂²⋊C₄	—	2	4	no	—
187	#442	C₂²×C₂₃	1	32	yes	complemented
188	C₄×D₈	C₂²×C₂₃	1	32	yes	complemented
189	#427	C₂²×C₂₃	1	8	yes	complemented
190	C₂×#107	C₂²×C₂₃	1	2	yes	complemented
191	C₂×#106	C₂²×C₂₃	1	2	yes	complemented
192	#418	C₂²×C₂₃	1	16	yes	complemented
193	C₂×#102	C₂²×C₂₃	1	8	yes	complemented
194	#405	C₂²×C₂₃	1	8	yes	complemented
195	C₂×#97	C₂²×C₂₃	1	2	yes	complemented
196	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	complemented
197	C₂×C₂₃	—	2	4	no	—
198	C₂×C₂₃	—	4	16	no	—
199	C₂×C₂₃	#2948	1	4	yes	direct product factor
200	C₂×C₂₃	C₂²×C₄×D₄	1	1	yes	characteristic
201	C₂×C₂₃	C₂×#576	1	2	yes	—
202	C₂⁵	—	2	2	no	—
203	C₂²×D₄	—	2	2	no	—
204	C₂²×D₄	—	2	4	no	—
205	C₂²×D₄	—	2	8	no	—
206	C₂²×D₄	C₂×C₄×C₂₃	1	16	yes	complemented
207	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
208	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
209	C₂³×C₄	—	2	8	no	—
210	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
211	C₂×D₈	C₂×C₄×C₂₃	1	16	yes	complemented
212	C₂×D₈	C₂×C₄×C₂₃	1	16	yes	complemented
213	C₂×D₈	C₂×C₄×C₂₃	1	64	yes	complemented
214	C₂×D₈	C₂³×C₂₃	1	8	yes	—
215	C₂×D₈	C₂³×C₂₃	1	8	yes	—
216	C₂×M₁₆	—	2	4	no	—
217	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
218	C₂²×C₈	C₂×C₄×C₂₃	1	8	yes	complemented
219	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
220	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
221	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
222	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
223	C₄×D₄	—	2	32	no	—
224	C₄×D₄	—	2	16	no	—
225	C₄×D₄	C₂³×C₂₃	1	32	yes	complemented
226	#117	—	2	4	no	—
227	#117	D₄×C₂₃	1	4	yes	—
228	#117	C₂³×C₂₃	1	8	yes	—
229	#117	C₂³×C₂₃	1	4	yes	—
230	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
231	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
232	C₂×C₂²⋊C₄	—	2	2	no	—
233	C₂×C₂²⋊C₄	—	2	8	no	—
234	C₂×C₂²⋊C₄	—	2	32	no	—
235	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
236	C₂×C₄²	—	2	2	no	—
237	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
238	#107	C₂³×C₂₃	1	8	yes	complemented
239	#106	C₂³×C₂₃	1	8	yes	complemented
240	#102	C₂³×C₂₃	1	32	yes	complemented
241	#97	C₂³×C₂₃	1	8	yes	complemented
242	C₄×C₈	C₂³×C₂₃	1	8	yes	complemented
243	C₂₃	C₂×#2948	1	1	yes	characteristic, direct product factor, Sylow
244	C₂⁴	—	2	4	no	—
245	C₂⁴	—	2	16	no	—
246	C₂⁴	—	2	8	no	—
247	C₂⁴	—	8	8	no	—
248	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
249	C₂×D₄	—	2	32	no	—
250	C₂×D₄	—	2	16	no	—
251	C₂×D₄	—	2	8	no	—
252	C₂×D₄	—	2	4	no	—
253	C₂×D₄	—	2	8	no	—
254	C₂×D₄	—	2	16	no	—
255	C₂×D₄	C₂²×C₄×C₂₃	1	16	yes	—
256	C₂×D₄	C₂²×C₄×C₂₃	1	32	yes	complemented
257	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	32	no	—
260	C₂²×C₄	—	8	16	no	—
261	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
262	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
263	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
264	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
265	C₂²×C₄	#41×C₂₃	1	4	yes	—
266	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
267	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
268	D₈	C₂²×C₄×C₂₃	1	32	yes	complemented
269	D₈	C₂²×C₄×C₂₃	1	32	yes	complemented
270	M₁₆	—	2	8	no	—
271	C₂×C₈	—	2	4	no	—
272	C₂×C₈	C₂²×C₄×C₂₃	1	4	yes	—
273	C₂×C₈	C₂²×C₄×C₂₃	1	4	yes	—
274	C₂×C₈	C₂²×C₄×C₂₃	1	16	yes	complemented
275	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
276	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
277	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
278	C₄⋊C₄	—	2	4	no	—
279	C₄⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
280	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
281	C₂²⋊C₄	—	2	8	no	—
282	C₂²⋊C₄	—	2	32	no	—
283	C₂²⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
284	C₄²	—	2	8	no	—
285	C₄²	C₂×D₄×C₂₃	1	4	yes	—
286	C₄²	C₂⁴×C₂₃	1	4	yes	—
287	C₂³	—	2	4	no	—
288	C₂³	—	2	8	no	—
289	C₂³	—	2	16	no	—
290	C₂³	—	2	32	no	—
291	C₂³	—	4	16	no	—
292	C₂³	—	8	32	no	—
293	C₂³	—	8	16	no	—
294	C₂³	C₄×D₄×C₂₃	1	4	yes	—
295	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
296	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
297	D₄	—	2	8	no	—
298	D₄	—	2	16	no	—
299	D₄	—	2	32	no	—
300	D₄	C₂³×C₄×C₂₃	1	16	yes	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	4	8	no	—
304	C₂×C₄	—	8	32	no	—
305	C₂×C₄	C₄×D₄×C₂₃	1	8	yes	—
306	C₂×C₄	C₄×D₄×C₂₃	1	4	yes	—
307	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
308	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
309	C₂×C₄	C₂²×D₄×C₂₃	1	8	yes	—
310	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
311	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
312	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
313	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
314	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
315	C₈	—	2	4	no	—
316	C₈	C₂³×C₄×C₂₃	1	4	yes	—
317	C₈	C₂³×C₄×C₂₃	1	4	yes	—
318	C₂²	—	2	8	no	—
319	C₂²	—	2	4	no	—
320	C₂²	—	2	16	no	—
321	C₂²	—	4	32	no	—
322	C₂²	—	4	16	no	—
323	C₂²	—	8	32	no	—
324	C₂²	C₂×C₄×D₄×C₂₃	1	4	yes	—
325	C₂²	C₂×C₄×D₄×C₂₃	1	2	yes	—
326	C₂²	C₂₃×#576	1	4	yes	—
327	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
328	C₄	—	2	8	no	—
329	C₄	—	4	8	no	—
330	C₄	C₂×C₄×D₄×C₂₃	1	2	yes	—
331	C₄	C₂×C₄×D₄×C₂₃	1	4	yes	—
332	C₄	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
333	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
334	C₂	—	2	4	no	—
335	C₂	—	4	16	no	—
336	C₂	C₂₃×#2948	1	4	yes	direct product factor
337	C₂	C₂²×C₄×D₄×C₂₃	1	1	yes	characteristic
338	C₂	C₂×C₂₃×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator	C₄	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂³×D₈×C₂₃	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₂₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#518	C₂	semidirect
3. C₂₃×#2948	C₂	direct (N × H)
4. C₂×C₂₃×#442	C₂	semidirect
5. C₂×C₄×D₈×C₂₃	C₂	semidirect
6. C₂×C₂₃×#427	C₂	semidirect
7. C₂×C₂₃×#418	C₂	semidirect
8. C₂×C₂₃×#405	C₂	semidirect
10. C₂²×D₈×C₂₃	C₄	semidirect
17. C₂₃×#518	C₂²	semidirect
19. C₂×C₄×D₄×C₂₃	C₂²	semidirect
23. C₂₃×#442	C₂²	semidirect
24. C₄×D₈×C₂₃	C₂²	semidirect
25. C₂₃×#427	C₂²	semidirect
26. C₂×C₂₃×#107	C₂²	semidirect
27. C₂×C₂₃×#106	C₂²	semidirect
28. C₂₃×#418	C₂²	semidirect
29. C₂×C₂₃×#102	C₂²	semidirect
30. C₂₃×#405	C₂²	semidirect
31. C₂×C₂₃×#97	C₂²	semidirect
32. C₂×C₄×C₈×C₂₃	C₂²	semidirect
37. C₂²×D₄×C₂₃	C₂×C₄	semidirect
42. C₂×D₈×C₂₃	C₂×C₄	semidirect
43. C₂×D₈×C₂₃	C₂×C₄	semidirect
44. C₂×D₈×C₂₃	C₂×C₄	semidirect
49. C₂²×C₈×C₂₃	C₂×C₄	semidirect
56. C₄×D₄×C₂₃	C₂³	semidirect
69. C₂₃×#107	C₂³	semidirect
70. C₂₃×#106	C₂³	semidirect
71. C₂₃×#102	C₂³	semidirect
72. C₂₃×#97	C₂³	semidirect
73. C₄×C₈×C₂₃	C₂³	semidirect
86. C₂×D₄×C₂₃	C₂²×C₄	semidirect
98. D₈×C₂₃	C₂²×C₄	semidirect
99. D₈×C₂₃	C₂²×C₄	semidirect
104. C₂×C₈×C₂₃	C₂²×C₄	semidirect
117. C₂×#2948	C₂₃	direct (N × H)
150. C₂×#518	C₂×C₂₃	semidirect
151. #2948	C₂×C₂₃	direct (N × H)
152. C₂×#442	C₂×C₂₃	semidirect
153. C₂×C₄×D₈	C₂×C₂₃	semidirect
154. C₂×#427	C₂×C₂₃	semidirect
155. C₂×#418	C₂×C₂₃	semidirect
156. C₂×#405	C₂×C₂₃	semidirect
174. C₂²×D₈	C₄×C₂₃	semidirect
181. #518	C₂²×C₂₃	semidirect
183. C₂×C₄×D₄	C₂²×C₂₃	semidirect
187. #442	C₂²×C₂₃	semidirect
188. C₄×D₈	C₂²×C₂₃	semidirect
189. #427	C₂²×C₂₃	semidirect
190. C₂×#107	C₂²×C₂₃	semidirect
191. C₂×#106	C₂²×C₂₃	semidirect
192. #418	C₂²×C₂₃	semidirect
193. C₂×#102	C₂²×C₂₃	semidirect
194. #405	C₂²×C₂₃	semidirect
195. C₂×#97	C₂²×C₂₃	semidirect
196. C₂×C₄×C₈	C₂²×C₂₃	semidirect
199. C₂×C₂₃	#2948	direct (N × H)
206. C₂²×D₄	C₂×C₄×C₂₃	semidirect
211. C₂×D₈	C₂×C₄×C₂₃	semidirect
212. C₂×D₈	C₂×C₄×C₂₃	semidirect
213. C₂×D₈	C₂×C₄×C₂₃	semidirect
218. C₂²×C₈	C₂×C₄×C₂₃	semidirect
225. C₄×D₄	C₂³×C₂₃	semidirect
238. #107	C₂³×C₂₃	semidirect
239. #106	C₂³×C₂₃	semidirect
240. #102	C₂³×C₂₃	semidirect
241. #97	C₂³×C₂₃	semidirect
242. C₄×C₈	C₂³×C₂₃	semidirect
243. C₂₃	C₂×#2948	direct (N × H)
256. C₂×D₄	C₂²×C₄×C₂₃	semidirect
268. D₈	C₂²×C₄×C₂₃	semidirect
269. D₈	C₂²×C₄×C₂₃	semidirect
274. C₂×C₈	C₂²×C₄×C₂₃	semidirect
336. C₂	C₂₃×#2948	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₈×C₂₃	2
C₂×C₂₃×#518	2
C₂₃×#2948	2
C₂×C₂₃×#442	2
C₂×C₄×D₈×C₂₃	2
C₂×C₂₃×#427	2
C₂×C₂₃×#418	2
C₂×C₂₃×#405	2
C₂×#2948	23

Subgroups — C2×C23×#2948 #19207788

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#2948 #19207788