Subgroups — C₂×C₂₃×#2220 #19181229

Order 5888.

734 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×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#466	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#2220	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₂₃×#366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#358	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#357	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
10	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
12	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
13	C₂×C₂₃×#121	—	2	1	no	—
14	C₂×C₂₃×SD₃₂	—	2	4	no	—
15	C₂×C₂₃×SD₃₂	C₂²	1	4	yes	complemented
16	C₂×C₂₃×M₃₂	—	2	4	no	—
17	C₂×C₂₃×M₃₂	C₂²	1	4	yes	complemented
18	C₂²×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
20	C₂₃×#467	—	2	2	no	—
21	C₂₃×#467	C₂²	1	4	yes	complemented
22	C₂₃×#466	—	2	2	no	—
23	C₂₃×#466	C₂²	1	4	yes	—
24	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#103	—	2	1	no	—
27	C₂×C₂₃×#102	—	2	1	no	—
28	C₂₃×#366	C₂²	1	4	yes	complemented
29	C₂₃×#358	C₂²	1	4	yes	complemented
30	C₂₃×#357	C₂²	1	4	yes	complemented
31	C₂²×Q₈×C₂₃	—	2	1	no	—
32	C₂²×D₄×C₂₃	—	2	1	no	—
33	C₂²×D₄×C₂₃	—	4	1	no	—
34	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
35	C₂×Q₁₆×C₂₃	—	2	2	no	—
36	C₂×Q₁₆×C₂₃	—	2	1	no	—
37	C₂×Q₁₆×C₂₃	—	2	2	no	—
38	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
39	C₂×D₈×C₂₃	—	2	2	no	—
40	C₂×D₈×C₂₃	—	2	1	no	—
41	C₂×D₈×C₂₃	—	2	2	no	—
42	C₂×D₈×C₂₃	C₂³	1	2	yes	—
43	C₂²×C₈×C₂₃	—	2	2	no	—
44	C₂²×C₈×C₂₃	—	2	2	no	—
45	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
46	C₂²×C₈×C₂₃	D₄	1	2	yes	—
47	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
49	C₂₃×C₂²⋊Q₈	—	2	4	no	—
50	C₂₃×C₂²⋊Q₈	—	4	2	no	—
51	C₂₃×#121	—	2	4	no	—
52	C₂₃×#121	—	4	2	no	—
53	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
54	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
55	C₂×C₄⋊C₄×C₂₃	—	4	1	no	—
56	C₂×C₂²⋊C₄×C₂₃	—	4	1	no	—
57	C₂×C₂²⋊C₄×C₂₃	—	4	1	no	—
58	C₂₃×SD₃₂	—	2	8	no	—
59	C₂₃×M₃₂	—	2	8	no	—
60	C₂×C₁₆×C₂₃	—	2	2	no	—
61	C₂×C₁₆×C₂₃	D₄	1	4	yes	complemented
62	C₂×C₁₆×C₂₃	C₂³	1	2	yes	—
63	C₂×C₁₆×C₂₃	C₂³	1	2	yes	—
64	C₂₃×#107	—	2	1	no	—
65	C₂₃×#107	—	2	1	no	—
66	C₂₃×#107	C₂³	1	2	yes	—
67	C₂₃×#107	C₂³	1	2	yes	—
68	C₂₃×#103	—	2	4	no	—
69	C₂₃×#102	—	2	4	no	—
70	C₂⁴×C₂₃	—	4	1	no	—
71	C₂⁴×C₂₃	D₈	1	1	yes	characteristic
72	C₂×Q₈×C₂₃	—	2	2	no	—
73	C₂×Q₈×C₂₃	—	4	1	no	—
74	C₂×Q₈×C₂₃	—	4	2	no	—
75	C₂×Q₈×C₂₃	—	4	2	no	—
76	C₂×D₄×C₂₃	—	2	2	no	—
77	C₂×D₄×C₂₃	—	4	4	no	—
78	C₂×D₄×C₂₃	—	4	2	no	—
79	C₂×D₄×C₂₃	—	4	1	no	—
80	C₂×D₄×C₂₃	—	4	2	no	—
81	C₂×D₄×C₂₃	—	8	4	no	—
82	C₂²×C₄×C₂₃	—	2	2	no	—
83	C₂²×C₄×C₂₃	—	2	2	no	—
84	C₂²×C₄×C₂₃	—	4	1	no	—
85	C₂²×C₄×C₂₃	—	4	1	no	—
86	C₂²×C₄×C₂₃	—	4	1	no	—
87	C₂²×C₄×C₂₃	D₈	1	2	yes	—
88	C₂²×C₄×C₂₃	D₈	1	1	yes	characteristic
89	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
91	Q₁₆×C₂₃	—	2	2	no	—
92	Q₁₆×C₂₃	—	2	2	no	—
93	Q₁₆×C₂₃	—	4	2	no	—
94	D₈×C₂₃	—	2	2	no	—
95	D₈×C₂₃	—	2	2	no	—
96	D₈×C₂₃	—	4	2	no	—
97	C₂×C₈×C₂₃	—	2	2	no	—
98	C₂×C₈×C₂₃	—	2	4	no	—
99	C₂×C₈×C₂₃	—	2	2	no	—
100	C₂×C₈×C₂₃	—	2	2	no	—
101	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
102	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
103	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
104	C₂×C₈×C₂₃	#41	1	2	yes	—
105	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
106	C₄⋊C₄×C₂₃	—	2	2	no	—
107	C₄⋊C₄×C₂₃	—	2	2	no	—
108	C₄⋊C₄×C₂₃	—	4	1	no	—
109	C₄⋊C₄×C₂₃	—	4	1	no	—
110	C₄⋊C₄×C₂₃	—	4	4	no	—
111	C₂²⋊C₄×C₂₃	—	4	4	no	—
112	C₂²⋊C₄×C₂₃	—	4	4	no	—
113	C₁₆×C₂₃	—	2	2	no	—
114	C₁₆×C₂₃	C₂×D₄	1	4	yes	complemented
115	C₂×#2220	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂³×C₂₃	—	2	2	no	—
117	C₂³×C₂₃	—	2	2	no	—
118	C₂³×C₂₃	—	2	2	no	—
119	C₂³×C₂₃	—	4	2	no	—
120	C₂³×C₂₃	—	8	2	no	—
121	C₂³×C₂₃	—	8	2	no	—
122	C₂³×C₂₃	—	8	2	no	—
123	C₂³×C₂₃	C₂×D₈	1	2	yes	—
124	C₂³×C₂₃	C₂×D₈	1	1	yes	characteristic
125	Q₈×C₂₃	—	4	2	no	—
126	Q₈×C₂₃	—	4	2	no	—
127	Q₈×C₂₃	—	8	2	no	—
128	D₄×C₂₃	—	4	2	no	—
129	D₄×C₂₃	—	4	2	no	—
130	D₄×C₂₃	—	8	8	no	—
131	D₄×C₂₃	—	8	2	no	—
132	C₂×C₄×C₂₃	—	2	2	no	—
133	C₂×C₄×C₂₃	—	2	2	no	—
134	C₂×C₄×C₂₃	—	2	2	no	—
135	C₂×C₄×C₂₃	—	2	4	no	—
136	C₂×C₄×C₂₃	—	4	2	no	—
137	C₂×C₄×C₂₃	—	4	2	no	—
138	C₂×C₄×C₂₃	—	4	2	no	—
139	C₂×C₄×C₂₃	—	8	2	no	—
140	C₂×C₄×C₂₃	—	8	2	no	—
141	C₂×C₄×C₂₃	—	8	2	no	—
142	C₂×C₄×C₂₃	#121	1	2	yes	—
143	C₂×C₄×C₂₃	C₂×D₈	1	2	yes	—
144	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
145	C₂×C₄×C₂₃	#135	1	2	yes	—
146	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
147	C₈×C₂₃	—	2	2	no	—
148	C₈×C₂₃	#121	1	2	yes	—
149	C₈×C₂₃	C₂²×D₄	1	1	yes	characteristic
150	C₈×C₂₃	C₂×#41	1	1	yes	characteristic
151	C₂²×SD₃₂	C₂×C₂₃	1	1	yes	characteristic, complemented
152	C₂²×M₃₂	C₂×C₂₃	1	1	yes	characteristic, complemented
153	C₂×#467	C₂×C₂₃	1	1	yes	characteristic, complemented
154	C₂×#466	C₂×C₂₃	1	1	yes	characteristic
155	#2220	C₂×C₂₃	1	8	yes	direct product factor
156	C₂×#366	C₂×C₂₃	1	1	yes	characteristic, complemented
157	C₂×#358	C₂×C₂₃	1	1	yes	characteristic, complemented
158	C₂×#357	C₂×C₂₃	1	1	yes	characteristic, complemented
159	C₂²×C₂₃	—	2	2	no	—
160	C₂²×C₂₃	—	2	2	no	—
161	C₂²×C₂₃	—	2	2	no	—
162	C₂²×C₂₃	—	4	4	no	—
163	C₂²×C₂₃	—	8	2	no	—
164	C₂²×C₂₃	—	8	2	no	—
165	C₂²×C₂₃	—	8	2	no	—
166	C₂²×C₂₃	—	16	4	no	—
167	C₂²×C₂₃	#466	1	2	yes	—
168	C₂²×C₂₃	#509	1	2	yes	—
169	C₂²×C₂₃	#510	1	2	yes	—
170	C₂²×C₂₃	C₂²×D₈	1	1	yes	characteristic
171	C₄×C₂₃	—	2	2	no	—
172	C₄×C₂₃	—	8	2	no	—
173	C₄×C₂₃	—	8	2	no	—
174	C₄×C₂₃	—	8	2	no	—
175	C₄×C₂₃	#466	1	2	yes	—
176	C₄×C₂₃	C₂×#121	1	1	yes	characteristic
177	C₄×C₂₃	C₂×#135	1	1	yes	characteristic
178	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
179	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
180	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
181	C₂×C₂²⋊Q₈	—	2	1	no	—
182	C₂×#121	—	2	1	no	—
183	C₂×SD₃₂	—	2	4	no	—
184	C₂×SD₃₂	C₂²×C₂₃	1	4	yes	complemented
185	C₂×M₃₂	—	2	4	no	—
186	C₂×M₃₂	C₂²×C₂₃	1	4	yes	complemented
187	C₂²×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
188	C₂²×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
189	#467	—	2	2	no	—
190	#467	C₂²×C₂₃	1	4	yes	complemented
191	#466	—	2	2	no	—
192	#466	C₂²×C₂₃	1	4	yes	—
193	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
194	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
195	C₂×#103	—	2	1	no	—
196	C₂×#102	—	2	1	no	—
197	#366	C₂²×C₂₃	1	4	yes	complemented
198	#358	C₂²×C₂₃	1	4	yes	complemented
199	#357	C₂²×C₂₃	1	4	yes	complemented
200	C₂×C₂₃	—	4	2	no	—
201	C₂×C₂₃	—	16	2	no	—
202	C₂×C₂₃	#2220	1	4	yes	direct product factor
203	C₂×C₂₃	C₂×#466	1	1	yes	characteristic
204	C₂×C₂₃	C₂×#509	1	1	yes	characteristic
205	C₂×C₂₃	C₂×#510	1	1	yes	characteristic
206	C₂²×Q₈	—	2	1	no	—
207	C₂²×D₄	—	2	1	no	—
208	C₂²×D₄	—	4	1	no	—
209	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
210	C₂×Q₁₆	—	2	2	no	—
211	C₂×Q₁₆	—	2	1	no	—
212	C₂×Q₁₆	—	2	2	no	—
213	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
214	C₂×D₈	—	2	2	no	—
215	C₂×D₈	—	2	1	no	—
216	C₂×D₈	—	2	2	no	—
217	C₂×D₈	C₂³×C₂₃	1	2	yes	—
218	C₂²×C₈	—	2	2	no	—
219	C₂²×C₈	—	2	2	no	—
220	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
221	C₂²×C₈	D₄×C₂₃	1	2	yes	—
222	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
223	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
224	C₂²⋊Q₈	—	2	4	no	—
225	C₂²⋊Q₈	—	4	2	no	—
226	#121	—	2	4	no	—
227	#121	—	4	2	no	—
228	C₂×C₄⋊C₄	—	2	1	no	—
229	C₂×C₄⋊C₄	—	2	1	no	—
230	C₂×C₄⋊C₄	—	4	1	no	—
231	C₂×C₂²⋊C₄	—	4	1	no	—
232	C₂×C₂²⋊C₄	—	4	1	no	—
233	SD₃₂	—	2	8	no	—
234	M₃₂	—	2	8	no	—
235	C₂×C₁₆	—	2	2	no	—
236	C₂×C₁₆	D₄×C₂₃	1	4	yes	complemented
237	C₂×C₁₆	C₂³×C₂₃	1	2	yes	—
238	C₂×C₁₆	C₂³×C₂₃	1	2	yes	—
239	#107	—	2	1	no	—
240	#107	—	2	1	no	—
241	#107	C₂³×C₂₃	1	2	yes	—
242	#107	C₂³×C₂₃	1	2	yes	—
243	#103	—	2	4	no	—
244	#102	—	2	4	no	—
245	C₂₃	C₂×#2220	1	1	yes	characteristic, direct product factor, Sylow
246	C₂⁴	—	4	1	no	—
247	C₂⁴	D₈×C₂₃	1	1	yes	characteristic
248	C₂×Q₈	—	2	2	no	—
249	C₂×Q₈	—	4	1	no	—
250	C₂×Q₈	—	4	2	no	—
251	C₂×Q₈	—	4	2	no	—
252	C₂×D₄	—	2	2	no	—
253	C₂×D₄	—	4	4	no	—
254	C₂×D₄	—	4	2	no	—
255	C₂×D₄	—	4	1	no	—
256	C₂×D₄	—	4	2	no	—
257	C₂×D₄	—	8	4	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	4	1	no	—
261	C₂²×C₄	—	4	1	no	—
262	C₂²×C₄	—	4	1	no	—
263	C₂²×C₄	D₈×C₂₃	1	1	yes	characteristic
264	C₂²×C₄	D₈×C₂₃	1	2	yes	—
265	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
266	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
267	Q₁₆	—	2	2	no	—
268	Q₁₆	—	2	2	no	—
269	Q₁₆	—	4	2	no	—
270	D₈	—	2	2	no	—
271	D₈	—	2	2	no	—
272	D₈	—	4	2	no	—
273	C₂×C₈	—	2	2	no	—
274	C₂×C₈	—	2	4	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
278	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
279	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
280	C₂×C₈	#41×C₂₃	1	2	yes	—
281	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
282	C₄⋊C₄	—	2	2	no	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	4	1	no	—
285	C₄⋊C₄	—	4	1	no	—
286	C₄⋊C₄	—	4	4	no	—
287	C₂²⋊C₄	—	4	4	no	—
288	C₂²⋊C₄	—	4	4	no	—
289	C₁₆	—	2	2	no	—
290	C₁₆	C₂×D₄×C₂₃	1	4	yes	complemented
291	C₂³	—	2	2	no	—
292	C₂³	—	2	2	no	—
293	C₂³	—	2	2	no	—
294	C₂³	—	4	2	no	—
295	C₂³	—	8	2	no	—
296	C₂³	—	8	2	no	—
297	C₂³	—	8	2	no	—
298	C₂³	C₂×D₈×C₂₃	1	2	yes	—
299	C₂³	C₂×D₈×C₂₃	1	1	yes	characteristic
300	Q₈	—	4	2	no	—
301	Q₈	—	4	2	no	—
302	Q₈	—	8	2	no	—
303	D₄	—	4	2	no	—
304	D₄	—	4	2	no	—
305	D₄	—	8	8	no	—
306	D₄	—	8	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	8	2	no	—
315	C₂×C₄	—	8	2	no	—
316	C₂×C₄	—	8	2	no	—
317	C₂×C₄	C₂₃×#121	1	2	yes	—
318	C₂×C₄	C₂×D₈×C₂₃	1	2	yes	—
319	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
320	C₂×C₄	C₂₃×#135	1	2	yes	—
321	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
322	C₈	—	2	2	no	—
323	C₈	C₂₃×#121	1	2	yes	—
324	C₈	C₂²×D₄×C₂₃	1	1	yes	characteristic
325	C₈	C₂×#41×C₂₃	1	1	yes	characteristic
326	C₂²	—	2	2	no	—
327	C₂²	—	2	2	no	—
328	C₂²	—	2	2	no	—
329	C₂²	—	4	4	no	—
330	C₂²	—	8	2	no	—
331	C₂²	—	8	2	no	—
332	C₂²	—	8	2	no	—
333	C₂²	—	16	4	no	—
334	C₂²	C₂₃×#466	1	2	yes	—
335	C₂²	C₂₃×#509	1	2	yes	—
336	C₂²	C₂₃×#510	1	2	yes	—
337	C₂²	C₂²×D₈×C₂₃	1	1	yes	characteristic
338	C₄	—	2	2	no	—
339	C₄	—	8	2	no	—
340	C₄	—	8	2	no	—
341	C₄	—	8	2	no	—
342	C₄	C₂₃×#466	1	2	yes	—
343	C₄	C₂×C₂₃×#121	1	1	yes	characteristic
344	C₄	C₂×C₂₃×#135	1	1	yes	characteristic
345	C₂	—	4	2	no	—
346	C₂	—	16	2	no	—
347	C₂	C₂₃×#2220	1	4	yes	direct product factor
348	C₂	C₂×C₂₃×#466	1	1	yes	characteristic
349	C₂	C₂×C₂₃×#509	1	1	yes	characteristic
350	C₂	C₂×C₂₃×#510	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#466	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂³×C₄×C₂₃ ◁ C₂³×C₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂₃×SD₃₂	C₂	semidirect
2. C₂²×C₂₃×M₃₂	C₂	semidirect
3. C₂×C₂₃×#467	C₂	semidirect
5. C₂₃×#2220	C₂	direct (N × H)
6. C₂×C₂₃×#366	C₂	semidirect
7. C₂×C₂₃×#358	C₂	semidirect
8. C₂×C₂₃×#357	C₂	semidirect
15. C₂×C₂₃×SD₃₂	C₂²	semidirect
17. C₂×C₂₃×M₃₂	C₂²	semidirect
21. C₂₃×#467	C₂²	semidirect
28. C₂₃×#366	C₂²	semidirect
29. C₂₃×#358	C₂²	semidirect
30. C₂₃×#357	C₂²	semidirect
61. C₂×C₁₆×C₂₃	D₄	semidirect
114. C₁₆×C₂₃	C₂×D₄	semidirect
115. C₂×#2220	C₂₃	direct (N × H)
151. C₂²×SD₃₂	C₂×C₂₃	semidirect
152. C₂²×M₃₂	C₂×C₂₃	semidirect
153. C₂×#467	C₂×C₂₃	semidirect
155. #2220	C₂×C₂₃	direct (N × H)
156. C₂×#366	C₂×C₂₃	semidirect
157. C₂×#358	C₂×C₂₃	semidirect
158. C₂×#357	C₂×C₂₃	semidirect
184. C₂×SD₃₂	C₂²×C₂₃	semidirect
186. C₂×M₃₂	C₂²×C₂₃	semidirect
190. #467	C₂²×C₂₃	semidirect
197. #366	C₂²×C₂₃	semidirect
198. #358	C₂²×C₂₃	semidirect
199. #357	C₂²×C₂₃	semidirect
202. C₂×C₂₃	#2220	direct (N × H)
236. C₂×C₁₆	D₄×C₂₃	semidirect
245. C₂₃	C₂×#2220	direct (N × H)
290. C₁₆	C₂×D₄×C₂₃	semidirect
347. C₂	C₂₃×#2220	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×SD₃₂	2
C₂²×C₂₃×M₃₂	2
C₂×C₂₃×#467	2
C₂×C₂₃×#466	2
C₂₃×#2220	2
C₂×C₂₃×#366	2
C₂×C₂₃×#358	2
C₂×C₂₃×#357	2
C₂×#2220	23

Subgroups — C2×C23×#2220 #19181229

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#2220 #19181229