Subgroups — C₂₃×#33584 #19181210

Order 5888.

722 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#509	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₂₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2211	C₂	1	4	yes	maximal, complemented
6	C₂₃×#2210	C₂	1	4	yes	maximal, complemented
7	C₂₃×#2150	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2141	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2140	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
11	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
12	C₂²×SD₁₆×C₂₃	—	2	1	no	—
13	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
14	C₂×C₂₃×#124	—	2	1	no	—
15	C₄×#41×C₂₃	—	2	1	no	—
16	C₂₃×#510	—	2	4	no	—
17	C₂₃×#509	—	2	4	no	—
18	C₂×C₂₃×Q₃₂	C₂²	1	2	yes	complemented
19	C₂×C₂₃×SD₃₂	C₂²	1	2	yes	—
20	C₂×C₂₃×SD₃₂	C₂²	1	2	yes	complemented
21	C₂×C₂₃×D₁₆	C₂²	1	2	yes	—
22	C₂×C₂₃×M₃₂	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×M₃₂	C₂²	1	1	yes	characteristic
24	C₂₃×#495	—	2	2	no	—
25	C₂₃×#495	C₂²	1	4	yes	—
26	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
27	C₄×SD₁₆×C₂₃	—	2	2	no	—
28	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
29	C₂₃×#427	C₂²	1	1	yes	characteristic
30	C₂₃×#416	—	2	1	no	—
31	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
32	C₂₃×C₄⋊C₁₆	C₂²	1	4	yes	complemented
33	C₂₃×#358	C₂²	1	4	yes	complemented
34	C₂₃×#357	C₂²	1	4	yes	—
35	C₂×#41×C₂₃	—	2	1	no	—
36	C₂²×Q₈×C₂₃	—	2	1	no	—
37	C₂²×D₄×C₂₃	—	2	1	no	—
38	C₂₃×#135	—	2	2	no	—
39	C₂₃×#135	D₄	1	4	yes	—
40	C₂×Q₁₆×C₂₃	—	2	2	no	—
41	C₂×Q₁₆×C₂₃	—	2	1	no	—
42	C₂×Q₁₆×C₂₃	—	2	2	no	—
43	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
44	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
45	C₂×SD₁₆×C₂₃	—	2	1	no	—
46	C₂×SD₁₆×C₂₃	—	2	4	no	—
47	C₂×SD₁₆×C₂₃	—	4	4	no	—
48	C₂×D₈×C₂₃	—	2	2	no	—
49	C₂×D₈×C₂₃	—	2	1	no	—
50	C₂×D₈×C₂₃	—	2	2	no	—
51	C₂×D₈×C₂₃	C₂³	1	2	yes	—
52	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
54	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
55	C₂₃×#124	—	2	4	no	—
56	C₂₃×#124	—	4	1	no	—
57	C₂₃×#124	—	4	1	no	—
58	C₄×Q₈×C₂₃	—	2	2	no	—
59	C₄×D₄×C₂₃	—	2	2	no	—
60	C₄×D₄×C₂₃	—	4	2	no	—
61	C₂₃×#117	—	2	1	no	—
62	C₂₃×#117	—	4	1	no	—
63	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
64	C₂×C₄²×C₂₃	—	4	1	no	—
65	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
66	C₂₃×Q₃₂	—	2	4	no	—
67	C₂₃×SD₃₂	—	2	4	no	—
68	C₂₃×SD₃₂	—	2	4	no	—
69	C₂₃×D₁₆	—	2	4	no	—
70	C₂₃×M₃₂	—	2	2	no	—
71	C₂₃×M₃₂	—	2	2	no	—
72	C₂×C₁₆×C₂₃	C₂³	1	2	yes	—
73	C₂×C₁₆×C₂₃	C₂³	1	2	yes	—
74	C₂₃×#107	C₂³	1	2	yes	—
75	C₂₃×#106	—	2	1	no	—
76	C₂₃×#103	—	2	2	no	—
77	C₂₃×#102	—	2	2	no	—
78	C₄×C₈×C₂₃	D₄	1	2	yes	—
79	C₄×C₈×C₂₃	C₂³	1	2	yes	—
80	C₂⁴×C₂₃	—	4	1	no	—
81	#41×C₂₃	—	2	4	no	—
82	#41×C₂₃	—	4	2	no	—
83	C₂×Q₈×C₂₃	—	2	1	no	—
84	C₂×Q₈×C₂₃	—	2	2	no	—
85	C₂×Q₈×C₂₃	—	4	1	no	—
86	C₂×Q₈×C₂₃	—	4	2	no	—
87	C₂×Q₈×C₂₃	—	4	2	no	—
88	C₂×D₄×C₂₃	—	2	1	no	—
89	C₂×D₄×C₂₃	—	2	2	no	—
90	C₂×D₄×C₂₃	—	4	1	no	—
91	C₂×D₄×C₂₃	—	4	2	no	—
92	C₂×D₄×C₂₃	—	4	1	no	—
93	C₂×D₄×C₂₃	—	4	2	no	—
94	C₂²×C₄×C₂₃	—	4	1	no	—
95	C₂²×C₄×C₂₃	—	4	1	no	—
96	C₂²×C₄×C₂₃	—	4	2	no	—
97	C₂²×C₄×C₂₃	D₈	1	2	yes	—
98	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
99	Q₁₆×C₂₃	—	2	2	no	—
100	Q₁₆×C₂₃	—	2	1	no	—
101	Q₁₆×C₂₃	—	2	2	no	—
102	Q₁₆×C₂₃	—	4	2	no	—
103	Q₁₆×C₂₃	C₂×D₄	1	2	yes	—
104	SD₁₆×C₂₃	—	2	4	no	—
105	SD₁₆×C₂₃	—	4	8	no	—
106	D₈×C₂₃	—	2	2	no	—
107	D₈×C₂₃	—	2	1	no	—
108	D₈×C₂₃	—	2	2	no	—
109	D₈×C₂₃	—	4	2	no	—
110	D₈×C₂₃	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₂₃	—	2	2	no	—
112	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
113	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₂₃	#41	1	2	yes	—
116	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
117	C₄⋊C₄×C₂₃	—	2	2	no	—
118	C₄⋊C₄×C₂₃	—	4	2	no	—
119	C₂²⋊C₄×C₂₃	—	4	1	no	—
120	C₂²⋊C₄×C₂₃	—	4	4	no	—
121	C₂²⋊C₄×C₂₃	—	4	4	no	—
122	C₂²⋊C₄×C₂₃	—	4	2	no	—
123	C₄²×C₂₃	—	4	1	no	—
124	C₄²×C₂₃	—	4	2	no	—
125	C₄²×C₂₃	D₈	1	1	yes	characteristic
126	C₄²×C₂₃	D₈	1	1	yes	characteristic
127	C₄²×C₂₃	C₂×D₄	1	2	yes	—
128	C₁₆×C₂₃	—	2	2	no	—
129	C₁₆×C₂₃	—	2	2	no	—
130	#33584	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂³×C₂₃	—	4	1	no	—
132	C₂³×C₂₃	—	4	2	no	—
133	C₂³×C₂₃	—	8	4	no	—
134	C₂³×C₂₃	—	8	2	no	—
135	C₂³×C₂₃	C₂×D₈	1	1	yes	characteristic
136	Q₈×C₂₃	—	2	2	no	—
137	Q₈×C₂₃	—	4	1	no	—
138	Q₈×C₂₃	—	4	2	no	—
139	Q₈×C₂₃	—	4	2	no	—
140	Q₈×C₂₃	—	8	2	no	—
141	D₄×C₂₃	—	2	2	no	—
142	D₄×C₂₃	—	4	4	no	—
143	D₄×C₂₃	—	4	2	no	—
144	D₄×C₂₃	—	4	1	no	—
145	D₄×C₂₃	—	4	2	no	—
146	D₄×C₂₃	—	8	2	no	—
147	C₂×C₄×C₂₃	—	4	2	no	—
148	C₂×C₄×C₂₃	—	4	1	no	—
149	C₂×C₄×C₂₃	—	4	4	no	—
150	C₂×C₄×C₂₃	—	4	2	no	—
151	C₂×C₄×C₂₃	—	4	2	no	—
152	C₂×C₄×C₂₃	—	8	4	no	—
153	C₂×C₄×C₂₃	—	8	2	no	—
154	C₂×C₄×C₂₃	#121	1	2	yes	—
155	C₂×C₄×C₂₃	C₂×D₈	1	2	yes	—
156	C₂×C₄×C₂₃	C₂×D₈	1	2	yes	—
157	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
158	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
159	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
160	C₈×C₂₃	—	2	2	no	—
161	C₈×C₂₃	#121	1	2	yes	—
162	C₈×C₂₃	C₂²×D₄	1	1	yes	characteristic
163	C₈×C₂₃	C₂×#41	1	1	yes	characteristic
164	C₂×#510	C₂×C₂₃	1	1	yes	characteristic, complemented
165	C₂×#509	C₂×C₂₃	1	1	yes	characteristic
166	C₂×#495	C₂×C₂₃	1	1	yes	characteristic, complemented
167	C₄×#135	C₂×C₂₃	1	1	yes	characteristic, complemented
168	#2211	C₂×C₂₃	1	4	yes	complemented
169	#2210	C₂×C₂₃	1	4	yes	complemented
170	#2150	C₂×C₂₃	1	1	yes	characteristic, complemented
171	#2141	C₂×C₂₃	1	1	yes	characteristic, complemented
172	#2140	C₂×C₂₃	1	1	yes	characteristic, complemented
173	C₂²×C₂₃	—	2	2	no	—
174	C₂²×C₂₃	—	4	2	no	—
175	C₂²×C₂₃	—	8	2	no	—
176	C₂²×C₂₃	—	8	4	no	—
177	C₂²×C₂₃	—	8	2	no	—
178	C₂²×C₂₃	—	16	4	no	—
179	C₂²×C₂₃	#459	1	2	yes	—
180	C₂²×C₂₃	C₂²×D₈	1	1	yes	characteristic
181	C₄×C₂₃	—	2	2	no	—
182	C₄×C₂₃	—	2	2	no	—
183	C₄×C₂₃	—	4	2	no	—
184	C₄×C₂₃	—	8	2	no	—
185	C₄×C₂₃	—	8	2	no	—
186	C₄×C₂₃	#459	1	2	yes	—
187	C₄×C₂₃	C₂×#121	1	1	yes	characteristic
188	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
189	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
190	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
191	C₂²×SD₁₆	—	2	1	no	—
192	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
193	C₂×#124	—	2	1	no	—
194	C₄×#41	—	2	1	no	—
195	#510	—	2	4	no	—
196	#509	—	2	4	no	—
197	C₂×Q₃₂	C₂²×C₂₃	1	2	yes	complemented
198	C₂×SD₃₂	C₂²×C₂₃	1	2	yes	—
199	C₂×SD₃₂	C₂²×C₂₃	1	2	yes	complemented
200	C₂×D₁₆	C₂²×C₂₃	1	2	yes	—
201	C₂×M₃₂	C₂²×C₂₃	1	1	yes	characteristic
202	C₂×M₃₂	C₂²×C₂₃	1	1	yes	characteristic
203	#495	—	2	2	no	—
204	#495	C₂²×C₂₃	1	4	yes	—
205	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
206	C₄×SD₁₆	—	2	2	no	—
207	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
208	#427	C₂²×C₂₃	1	1	yes	characteristic
209	#416	—	2	1	no	—
210	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
211	C₄⋊C₁₆	C₂²×C₂₃	1	4	yes	complemented
212	#358	C₂²×C₂₃	1	4	yes	complemented
213	#357	C₂²×C₂₃	1	4	yes	—
214	C₂×C₂₃	—	2	2	no	—
215	C₂×C₂₃	—	8	2	no	—
216	C₂×C₂₃	—	16	2	no	—
217	C₂×C₂₃	C₂×#459	1	1	yes	characteristic
218	C₂×C₂₃	#3414	1	2	yes	—
219	C₂×#41	—	2	1	no	—
220	C₂²×Q₈	—	2	1	no	—
221	C₂²×D₄	—	2	1	no	—
222	#135	—	2	2	no	—
223	#135	D₄×C₂₃	1	4	yes	—
224	C₂×Q₁₆	—	2	2	no	—
225	C₂×Q₁₆	—	2	1	no	—
226	C₂×Q₁₆	—	2	2	no	—
227	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
228	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
229	C₂×SD₁₆	—	2	1	no	—
230	C₂×SD₁₆	—	2	4	no	—
231	C₂×SD₁₆	—	4	4	no	—
232	C₂×D₈	—	2	2	no	—
233	C₂×D₈	—	2	1	no	—
234	C₂×D₈	—	2	2	no	—
235	C₂×D₈	C₂³×C₂₃	1	2	yes	—
236	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
237	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
238	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
239	#124	—	2	4	no	—
240	#124	—	4	1	no	—
241	#124	—	4	1	no	—
242	C₄×Q₈	—	2	2	no	—
243	C₄×D₄	—	2	2	no	—
244	C₄×D₄	—	4	2	no	—
245	#117	—	2	1	no	—
246	#117	—	4	1	no	—
247	C₂×C₂²⋊C₄	—	4	2	no	—
248	C₂×C₄²	—	4	1	no	—
249	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
250	Q₃₂	—	2	4	no	—
251	SD₃₂	—	2	4	no	—
252	SD₃₂	—	2	4	no	—
253	D₁₆	—	2	4	no	—
254	M₃₂	—	2	2	no	—
255	M₃₂	—	2	2	no	—
256	C₂×C₁₆	C₂³×C₂₃	1	2	yes	—
257	C₂×C₁₆	C₂³×C₂₃	1	2	yes	—
258	#107	C₂³×C₂₃	1	2	yes	—
259	#106	—	2	1	no	—
260	#103	—	2	2	no	—
261	#102	—	2	2	no	—
262	C₄×C₈	D₄×C₂₃	1	2	yes	—
263	C₄×C₈	C₂³×C₂₃	1	2	yes	—
264	C₂₃	#33584	1	1	yes	characteristic, direct product factor, Sylow
265	C₂⁴	—	4	1	no	—
266	#41	—	2	4	no	—
267	#41	—	4	2	no	—
268	C₂×Q₈	—	2	1	no	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	—	4	1	no	—
271	C₂×Q₈	—	4	2	no	—
272	C₂×Q₈	—	4	2	no	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	—	4	1	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	—	4	1	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	—	4	1	no	—
281	C₂²×C₄	—	4	2	no	—
282	C₂²×C₄	D₈×C₂₃	1	2	yes	—
283	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
284	Q₁₆	—	2	2	no	—
285	Q₁₆	—	2	1	no	—
286	Q₁₆	—	2	2	no	—
287	Q₁₆	—	4	2	no	—
288	Q₁₆	C₂×D₄×C₂₃	1	2	yes	—
289	SD₁₆	—	2	4	no	—
290	SD₁₆	—	4	8	no	—
291	D₈	—	2	2	no	—
292	D₈	—	2	1	no	—
293	D₈	—	2	2	no	—
294	D₈	—	4	2	no	—
295	D₈	C₂×D₄×C₂₃	1	2	yes	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
298	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
299	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
300	C₂×C₈	#41×C₂₃	1	2	yes	—
301	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	4	2	no	—
304	C₂²⋊C₄	—	4	1	no	—
305	C₂²⋊C₄	—	4	4	no	—
306	C₂²⋊C₄	—	4	4	no	—
307	C₂²⋊C₄	—	4	2	no	—
308	C₄²	—	4	1	no	—
309	C₄²	—	4	2	no	—
310	C₄²	D₈×C₂₃	1	1	yes	characteristic
311	C₄²	D₈×C₂₃	1	1	yes	characteristic
312	C₄²	C₂×D₄×C₂₃	1	2	yes	—
313	C₁₆	—	2	2	no	—
314	C₁₆	—	2	2	no	—
315	C₂³	—	4	1	no	—
316	C₂³	—	4	2	no	—
317	C₂³	—	8	4	no	—
318	C₂³	—	8	2	no	—
319	C₂³	C₂×D₈×C₂₃	1	1	yes	characteristic
320	Q₈	—	2	2	no	—
321	Q₈	—	4	1	no	—
322	Q₈	—	4	2	no	—
323	Q₈	—	4	2	no	—
324	Q₈	—	8	2	no	—
325	D₄	—	2	2	no	—
326	D₄	—	4	4	no	—
327	D₄	—	4	1	no	—
328	D₄	—	4	2	no	—
329	D₄	—	4	2	no	—
330	D₄	—	8	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	8	4	no	—
337	C₂×C₄	—	8	2	no	—
338	C₂×C₄	C₂₃×#121	1	2	yes	—
339	C₂×C₄	C₂×D₈×C₂₃	1	2	yes	—
340	C₂×C₄	C₂×D₈×C₂₃	1	2	yes	—
341	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
342	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
343	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
344	C₈	—	2	2	no	—
345	C₈	C₂₃×#121	1	2	yes	—
346	C₈	C₂²×D₄×C₂₃	1	1	yes	characteristic
347	C₈	C₂×#41×C₂₃	1	1	yes	characteristic
348	C₂²	—	2	2	no	—
349	C₂²	—	4	2	no	—
350	C₂²	—	8	2	no	—
351	C₂²	—	8	2	no	—
352	C₂²	—	8	4	no	—
353	C₂²	—	16	4	no	—
354	C₂²	C₂₃×#459	1	2	yes	—
355	C₂²	C₂²×D₈×C₂₃	1	1	yes	characteristic
356	C₄	—	2	2	no	—
357	C₄	—	2	2	no	—
358	C₄	—	4	2	no	—
359	C₄	—	8	2	no	—
360	C₄	—	8	2	no	—
361	C₄	C₂₃×#459	1	2	yes	—
362	C₄	C₂×C₂₃×#121	1	1	yes	characteristic
363	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
364	C₂	—	2	2	no	—
365	C₂	—	8	2	no	—
366	C₂	—	16	2	no	—
367	C₂	C₂×C₂₃×#459	1	1	yes	characteristic
368	C₂	C₂₃×#3414	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#509	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ C₂×C₄×C₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#510	C₂	semidirect
3. C₂×C₂₃×#495	C₂	semidirect
4. C₄×C₂₃×#135	C₂	semidirect
5. C₂₃×#2211	C₂	semidirect
6. C₂₃×#2210	C₂	semidirect
7. C₂₃×#2150	C₂	semidirect
8. C₂₃×#2141	C₂	semidirect
9. C₂₃×#2140	C₂	semidirect
18. C₂×C₂₃×Q₃₂	C₂²	semidirect
20. C₂×C₂₃×SD₃₂	C₂²	semidirect
26. C₄×Q₁₆×C₂₃	C₂²	semidirect
28. C₄×D₈×C₂₃	C₂²	semidirect
32. C₂₃×C₄⋊C₁₆	C₂²	semidirect
33. C₂₃×#358	C₂²	semidirect
130. #33584	C₂₃	direct (N × H)
164. C₂×#510	C₂×C₂₃	semidirect
166. C₂×#495	C₂×C₂₃	semidirect
167. C₄×#135	C₂×C₂₃	semidirect
168. #2211	C₂×C₂₃	semidirect
169. #2210	C₂×C₂₃	semidirect
170. #2150	C₂×C₂₃	semidirect
171. #2141	C₂×C₂₃	semidirect
172. #2140	C₂×C₂₃	semidirect
197. C₂×Q₃₂	C₂²×C₂₃	semidirect
199. C₂×SD₃₂	C₂²×C₂₃	semidirect
205. C₄×Q₁₆	C₂²×C₂₃	semidirect
207. C₄×D₈	C₂²×C₂₃	semidirect
211. C₄⋊C₁₆	C₂²×C₂₃	semidirect
212. #358	C₂²×C₂₃	semidirect
264. C₂₃	#33584	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×#510	2
C₂×C₂₃×#509	2
C₂×C₂₃×#495	2
C₄×C₂₃×#135	2
C₂₃×#2211	2
C₂₃×#2210	2
C₂₃×#2150	2
C₂₃×#2141	2
C₂₃×#2140	2
#33584	23

Subgroups — C23×#33584 #19181210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#33584 #19181210