Subgroups — C₂₃×#19397 #19167023

Order 5888.

656 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3206	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3037	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#2982	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1680	C₂	1	4	yes	maximal, complemented
6	C₂₃×#1666	C₂	1	4	yes	maximal, complemented
7	C₂₃×#1570	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1549	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1540	C₂	1	1	yes	maximal, characteristic
10	C₂×C₂₃×#137	—	2	1	no	—
11	C₂₃×#532	C₂²	1	1	yes	characteristic
12	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
14	C₂₃×#492	C₂²	1	2	yes	—
15	C₂₃×#487	C₂²	1	2	yes	—
16	C₂₃×#475	—	2	2	no	—
17	C₂₃×#475	C₂²	1	4	yes	—
18	C₂₃×#464	—	2	2	no	—
19	C₂₃×#462	C₂²	1	2	yes	—
20	C₂₃×#461	—	2	2	no	—
21	C₂₃×#460	C₂²	1	2	yes	—
22	C₂₃×#448	—	2	2	no	—
23	C₈×Q₈×C₂₃	—	2	2	no	—
24	C₈×Q₈×C₂₃	C₂²	1	4	yes	—
25	C₂₃×#431	—	2	2	no	—
26	C₂₃×#431	C₂²	1	1	yes	characteristic
27	C₂₃×#431	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#106	—	2	1	no	—
29	C₂₃×#423	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂₃×#417	—	2	1	no	—
32	C₂×C₂₃×#103	—	2	1	no	—
33	C₂₃×#334	C₂²	1	4	yes	—
34	C₂₃×#332	C₂²	1	4	yes	—
35	C₂₃×#332	C₂²	1	2	yes	—
36	C₂₃×#331	C₂²	1	2	yes	—
37	C₂×#41×C₂₃	—	2	1	no	—
38	C₂²×Q₈×C₂₃	—	2	1	no	—
39	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
40	C₂₃×#137	—	4	4	no	—
41	C₂×Q₁₆×C₂₃	—	2	2	no	—
42	C₂×SD₁₆×C₂₃	—	2	2	no	—
43	C₂×SD₁₆×C₂₃	—	2	4	no	—
44	C₂×M₁₆×C₂₃	—	2	1	no	—
45	C₂²×C₈×C₂₃	—	2	1	no	—
46	C₂₃×C₄⋊Q₈	—	2	1	no	—
47	C₂₃×C₄⋊Q₈	—	2	1	no	—
48	C₂₃×C₄⋊Q₈	—	2	1	no	—
49	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
50	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
51	C₂₃×#127	C₂³	1	1	yes	characteristic
52	C₂₃×#124	—	2	1	no	—
53	C₂₃×#121	—	2	1	no	—
54	C₂₃×#121	—	2	1	no	—
55	C₄×Q₈×C₂₃	—	2	1	no	—
56	C₄×Q₈×C₂₃	—	2	1	no	—
57	C₄×Q₈×C₂₃	D₄	1	2	yes	—
58	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
59	C₄×D₄×C₂₃	—	2	1	no	—
60	C₄×D₄×C₂₃	—	2	1	no	—
61	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
63	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₂₃	—	2	1	no	—
66	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
67	C₂₃×#106	—	2	4	no	—
68	C₂₃×C₄⋊C₈	—	2	4	no	—
69	C₂₃×C₄⋊C₈	—	2	1	no	—
70	C₂₃×C₄⋊C₈	—	2	1	no	—
71	C₂₃×C₄⋊C₈	D₄	1	2	yes	—
72	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
73	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
74	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
75	C₂₃×#103	—	2	4	no	—
76	C₂₃×#103	—	2	4	no	—
77	C₂₃×#103	—	2	2	no	—
78	C₂₃×#102	—	2	2	no	—
79	C₂₃×C₂²⋊C₈	—	2	1	no	—
80	C₂₃×C₂²⋊C₈	D₄	1	2	yes	—
81	C₄×C₈×C₂₃	—	2	4	no	—
82	C₄×C₈×C₂₃	—	2	1	no	—
83	C₄×C₈×C₂₃	C₂³	1	2	yes	—
84	#41×C₂₃	—	4	2	no	—
85	#41×C₂₃	—	4	2	no	—
86	C₂×Q₈×C₂₃	—	2	1	no	—
87	C₂×Q₈×C₂₃	—	2	2	no	—
88	C₂×Q₈×C₂₃	—	2	1	no	—
89	C₂×Q₈×C₂₃	—	2	2	no	—
90	C₂×Q₈×C₂₃	—	4	1	no	—
91	C₂×Q₈×C₂₃	—	8	2	no	—
92	C₂×Q₈×C₂₃	SD₁₆	1	4	yes	complemented
93	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
94	C₂×D₄×C₂₃	—	2	1	no	—
95	C₂×D₄×C₂₃	—	2	1	no	—
96	C₂×D₄×C₂₃	—	2	1	no	—
97	C₂×D₄×C₂₃	—	4	1	no	—
98	C₂²×C₄×C₂₃	—	2	1	no	—
99	C₂²×C₄×C₂₃	—	2	1	no	—
100	C₂²×C₄×C₂₃	—	4	1	no	—
101	C₂²×C₄×C₂₃	—	4	1	no	—
102	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
105	Q₁₆×C₂₃	—	4	4	no	—
106	SD₁₆×C₂₃	—	4	4	no	—
107	SD₁₆×C₂₃	—	8	4	no	—
108	M₁₆×C₂₃	—	4	2	no	—
109	C₂×C₈×C₂₃	—	2	2	no	—
110	C₂×C₈×C₂₃	—	2	2	no	—
111	C₂×C₈×C₂₃	—	2	2	no	—
112	C₂×C₈×C₂₃	—	4	2	no	—
113	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	—
114	C₄⋊C₄×C₂₃	—	2	2	no	—
115	C₄⋊C₄×C₂₃	—	2	1	no	—
116	C₄⋊C₄×C₂₃	—	2	2	no	—
117	C₄⋊C₄×C₂₃	—	2	1	no	—
118	C₄⋊C₄×C₂₃	—	2	2	no	—
119	C₄⋊C₄×C₂₃	—	2	2	no	—
120	C₄⋊C₄×C₂₃	—	2	1	no	—
121	C₄⋊C₄×C₂₃	—	4	1	no	—
122	C₄⋊C₄×C₂₃	—	4	1	no	—
123	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
124	C₂²⋊C₄×C₂₃	—	4	1	no	—
125	C₂²⋊C₄×C₂₃	—	4	1	no	—
126	C₄²×C₂₃	—	2	2	no	—
127	C₄²×C₂₃	—	2	2	no	—
128	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₂₃	#41	1	1	yes	characteristic
131	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
132	#19397	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂³×C₂₃	—	4	1	no	—
134	C₂³×C₂₃	#121	1	1	yes	characteristic
135	Q₈×C₂₃	—	2	2	no	—
136	Q₈×C₂₃	—	2	4	no	—
137	Q₈×C₂₃	—	4	1	no	—
138	Q₈×C₂₃	—	4	1	no	—
139	Q₈×C₂₃	—	4	4	no	—
140	Q₈×C₂₃	—	8	2	no	—
141	Q₈×C₂₃	C₂×SD₁₆	1	4	yes	—
142	D₄×C₂₃	—	4	1	no	—
143	D₄×C₂₃	—	4	1	no	—
144	D₄×C₂₃	—	4	2	no	—
145	D₄×C₂₃	—	8	1	no	—
146	D₄×C₂₃	—	8	2	no	—
147	C₂×C₄×C₂₃	—	2	2	no	—
148	C₂×C₄×C₂₃	—	2	4	no	—
149	C₂×C₄×C₂₃	—	2	2	no	—
150	C₂×C₄×C₂₃	—	2	2	no	—
151	C₂×C₄×C₂₃	—	4	1	no	—
152	C₂×C₄×C₂₃	—	4	1	no	—
153	C₂×C₄×C₂₃	—	4	2	no	—
154	C₂×C₄×C₂₃	—	8	1	no	—
155	C₂×C₄×C₂₃	—	8	2	no	—
156	C₂×C₄×C₂₃	—	8	2	no	—
157	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
158	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
159	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
160	C₂×C₄×C₂₃	C₂×SD₁₆	1	2	yes	—
161	C₂×C₄×C₂₃	#135	1	2	yes	—
162	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
165	C₈×C₂₃	—	2	4	no	—
166	C₈×C₂₃	—	4	2	no	—
167	C₈×C₂₃	—	4	2	no	—
168	C₈×C₂₃	—	4	2	no	—
169	#3206	C₂×C₂₃	1	1	yes	characteristic
170	C₂×#475	C₂×C₂₃	1	1	yes	characteristic, complemented
171	#3037	C₂×C₂₃	1	1	yes	characteristic
172	#2982	C₂×C₂₃	1	1	yes	characteristic, complemented
173	#1680	C₂×C₂₃	1	4	yes	complemented
174	#1666	C₂×C₂₃	1	4	yes	complemented
175	#1570	C₂×C₂₃	1	1	yes	characteristic, complemented
176	#1549	C₂×C₂₃	1	1	yes	characteristic, complemented
177	#1540	C₂×C₂₃	1	1	yes	characteristic
178	C₂²×C₂₃	—	2	1	no	—
179	C₂²×C₂₃	—	2	1	no	—
180	C₂²×C₂₃	—	8	1	no	—
181	C₂²×C₂₃	—	8	1	no	—
182	C₂²×C₂₃	—	8	1	no	—
183	C₂²×C₂₃	#465	1	2	yes	—
184	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
185	C₄×C₂₃	—	2	1	no	—
186	C₄×C₂₃	—	2	4	no	—
187	C₄×C₂₃	—	2	1	no	—
188	C₄×C₂₃	—	2	1	no	—
189	C₄×C₂₃	—	4	2	no	—
190	C₄×C₂₃	—	8	2	no	—
191	C₄×C₂₃	—	8	1	no	—
192	C₄×C₂₃	#465	1	2	yes	—
193	C₄×C₂₃	C₂²×SD₁₆	1	1	yes	characteristic
194	C₄×C₂₃	C₂×#135	1	1	yes	characteristic
195	C₄×C₂₃	#577	1	2	yes	—
196	C₂×#137	—	2	1	no	—
197	#532	C₂²×C₂₃	1	1	yes	characteristic
198	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
199	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
200	#492	C₂²×C₂₃	1	2	yes	—
201	#487	C₂²×C₂₃	1	2	yes	—
202	#475	—	2	2	no	—
203	#475	C₂²×C₂₃	1	4	yes	—
204	#464	—	2	2	no	—
205	#462	C₂²×C₂₃	1	2	yes	—
206	#461	—	2	2	no	—
207	#460	C₂²×C₂₃	1	2	yes	—
208	#448	—	2	2	no	—
209	C₈×Q₈	—	2	2	no	—
210	C₈×Q₈	C₂²×C₂₃	1	4	yes	—
211	#431	—	2	2	no	—
212	#431	C₂²×C₂₃	1	1	yes	characteristic
213	#431	C₂²×C₂₃	1	1	yes	characteristic
214	C₂×#106	—	2	1	no	—
215	#423	C₂²×C₂₃	1	1	yes	characteristic
216	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
217	#417	—	2	1	no	—
218	C₂×#103	—	2	1	no	—
219	#334	C₂²×C₂₃	1	4	yes	—
220	#332	C₂²×C₂₃	1	2	yes	—
221	#332	C₂²×C₂₃	1	4	yes	—
222	#331	C₂²×C₂₃	1	2	yes	—
223	C₂×C₂₃	—	2	2	no	—
224	C₂×C₂₃	—	16	1	no	—
225	C₂×C₂₃	#3043	1	1	yes	characteristic
226	C₂×C₂₃	C₂×#465	1	1	yes	characteristic
227	C₂×C₂₃	#3069	1	1	yes	characteristic
228	C₂×#41	—	2	1	no	—
229	C₂²×Q₈	—	2	1	no	—
230	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
231	#137	—	4	4	no	—
232	C₂×Q₁₆	—	2	2	no	—
233	C₂×SD₁₆	—	2	2	no	—
234	C₂×SD₁₆	—	2	4	no	—
235	C₂×M₁₆	—	2	1	no	—
236	C₂²×C₈	—	2	1	no	—
237	C₄⋊Q₈	—	2	1	no	—
238	C₄⋊Q₈	—	2	1	no	—
239	C₄⋊Q₈	—	2	1	no	—
240	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
241	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
242	#127	C₂³×C₂₃	1	1	yes	characteristic
243	#124	—	2	1	no	—
244	#121	—	2	1	no	—
245	#121	—	2	1	no	—
246	C₄×Q₈	—	2	1	no	—
247	C₄×Q₈	—	2	1	no	—
248	C₄×Q₈	D₄×C₂₃	1	2	yes	—
249	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
250	C₄×D₄	—	2	1	no	—
251	C₄×D₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
256	C₂×C₄²	—	2	1	no	—
257	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
258	#106	—	2	4	no	—
259	C₄⋊C₈	—	2	4	no	—
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	D₄×C₂₃	1	2	yes	—
263	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
264	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
265	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
266	#103	—	2	4	no	—
267	#103	—	2	4	no	—
268	#103	—	2	2	no	—
269	#102	—	2	2	no	—
270	C₂²⋊C₈	—	2	1	no	—
271	C₂²⋊C₈	D₄×C₂₃	1	2	yes	—
272	C₄×C₈	—	2	4	no	—
273	C₄×C₈	—	2	1	no	—
274	C₄×C₈	C₂³×C₂₃	1	2	yes	—
275	C₂₃	#19397	1	1	yes	characteristic, direct product factor, Sylow
276	#41	—	4	2	no	—
277	#41	—	4	2	no	—
278	C₂×Q₈	—	2	1	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	2	1	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	4	1	no	—
283	C₂×Q₈	—	8	2	no	—
284	C₂×Q₈	SD₁₆×C₂₃	1	4	yes	complemented
285	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	—	2	1	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
296	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
297	Q₁₆	—	4	4	no	—
298	SD₁₆	—	4	4	no	—
299	SD₁₆	—	8	4	no	—
300	M₁₆	—	4	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	4	2	no	—
305	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	1	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
316	C₂²⋊C₄	—	4	1	no	—
317	C₂²⋊C₄	—	4	1	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
321	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
322	C₄²	#41×C₂₃	1	1	yes	characteristic
323	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
324	C₂³	—	4	1	no	—
325	C₂³	C₂₃×#121	1	1	yes	characteristic
326	Q₈	—	2	2	no	—
327	Q₈	—	2	4	no	—
328	Q₈	—	4	1	no	—
329	Q₈	—	4	1	no	—
330	Q₈	—	4	4	no	—
331	Q₈	—	8	2	no	—
332	Q₈	C₂×SD₁₆×C₂₃	1	4	yes	—
333	D₄	—	4	1	no	—
334	D₄	—	4	1	no	—
335	D₄	—	4	2	no	—
336	D₄	—	8	1	no	—
337	D₄	—	8	2	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	8	1	no	—
346	C₂×C₄	—	8	2	no	—
347	C₂×C₄	—	8	2	no	—
348	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
349	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
350	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
351	C₂×C₄	C₂×SD₁₆×C₂₃	1	2	yes	—
352	C₂×C₄	C₂₃×#135	1	2	yes	—
353	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
354	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
355	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
356	C₈	—	2	4	no	—
357	C₈	—	4	2	no	—
358	C₈	—	4	2	no	—
359	C₈	—	4	2	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	8	1	no	—
363	C₂²	—	8	1	no	—
364	C₂²	—	8	1	no	—
365	C₂²	C₂₃×#465	1	2	yes	—
366	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
367	C₄	—	2	1	no	—
368	C₄	—	2	4	no	—
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	4	2	no	—
372	C₄	—	8	2	no	—
373	C₄	—	8	1	no	—
374	C₄	C₂₃×#465	1	2	yes	—
375	C₄	C₂²×SD₁₆×C₂₃	1	1	yes	characteristic
376	C₄	C₂×C₂₃×#135	1	1	yes	characteristic
377	C₄	C₂₃×#577	1	2	yes	—
378	C₂	—	2	2	no	—
379	C₂	—	16	1	no	—
380	C₂	C₂₃×#3043	1	1	yes	characteristic
381	C₂	C₂×C₂₃×#465	1	1	yes	characteristic
382	C₂	C₂₃×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₃
prime radical	C₂₃×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#475	C₂	semidirect
4. C₂₃×#2982	C₂	semidirect
5. C₂₃×#1680	C₂	semidirect
6. C₂₃×#1666	C₂	semidirect
7. C₂₃×#1570	C₂	semidirect
8. C₂₃×#1549	C₂	semidirect
92. C₂×Q₈×C₂₃	SD₁₆	semidirect
132. #19397	C₂₃	direct (N × H)
170. C₂×#475	C₂×C₂₃	semidirect
172. #2982	C₂×C₂₃	semidirect
173. #1680	C₂×C₂₃	semidirect
174. #1666	C₂×C₂₃	semidirect
175. #1570	C₂×C₂₃	semidirect
176. #1549	C₂×C₂₃	semidirect
275. C₂₃	#19397	direct (N × H)
284. C₂×Q₈	SD₁₆×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3206	2
C₂×C₂₃×#475	2
C₂₃×#3037	2
C₂₃×#2982	2
C₂₃×#1680	2
C₂₃×#1666	2
C₂₃×#1570	2
C₂₃×#1549	2
C₂₃×#1540	2
#19397	23

Subgroups — C23×#19397 #19167023

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#19397 #19167023