Subgroups — C₂₃×#62636 #19210262

Order 5888.

2078 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×#3584	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#576	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3416	C₂	1	8	yes	maximal, complemented
4	C₂₃×#3415	C₂	1	8	yes	maximal, complemented
5	C₂₃×#3414	C₂	1	6	yes	maximal, complemented
6	C₂×C₂₃×#509	C₂	1	6	yes	maximal, complemented
7	C₂₃×#3407	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#585	—	2	1	no	—
9	C₂×C₂₃×H(5,𝔽₂)	—	2	1	no	—
10	C₂₃×#578	C₂²	1	4	yes	complemented
11	C₂₃×#577	—	2	4	no	—
12	C₂₃×#576	—	2	4	no	—
13	C₂₃×#576	C₂²	1	8	yes	complemented
14	C₂₃×#576	C₂²	1	4	yes	complemented
15	C₂₃×#575	—	2	3	no	—
16	C₂×C₂₃×AGL(1,ℤ/8)	—	2	3	no	—
17	C₂×C₂₃×#135	C₂²	1	3	yes	complemented
18	C₂×C₂₃×#135	C₂²	1	6	yes	complemented
19	C₂²×D₈×C₂₃	C₂²	1	3	yes	complemented
20	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
21	C₂₃×#510	C₂²	1	4	yes	complemented
22	C₂₃×#510	C₂²	1	12	yes	complemented
23	C₂₃×#509	C₂²	1	12	yes	complemented
24	C₂₃×#509	C₂²	1	24	yes	complemented
25	C₂₃×#509	C₂²	1	12	yes	complemented
26	C₂₃×#508	C₂²	1	24	yes	complemented
27	C₂×C₂₃×SD₃₂	C₂²	1	12	yes	complemented
28	C₂×C₂₃×D₁₆	C₂²	1	12	yes	complemented
29	C₂₃×#504	C₂²	1	8	yes	complemented
30	C₂×C₂₃×M₃₂	C₂²	1	6	yes	complemented
31	C₂₃×2₋¹⁺⁴	—	2	4	no	—
32	C₂₃×2₋¹⁺⁴	—	4	1	no	—
33	C₂₃×H(5,𝔽₂)	—	2	8	no	—
34	C₂₃×H(5,𝔽₂)	—	2	4	no	—
35	C₂₃×H(5,𝔽₂)	—	4	4	no	—
36	C₂₃×H(5,𝔽₂)	—	4	3	no	—
37	C₂×#41×C₂₃	—	2	3	no	—
38	C₂×#41×C₂₃	—	2	6	no	—
39	C₂×#41×C₂₃	—	4	4	no	—
40	C₂×#41×C₂₃	—	4	1	no	—
41	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
42	C₂²×D₄×C₂₃	—	2	3	no	—
43	C₂²×D₄×C₂₃	—	4	3	no	—
44	C₂₃×#137	—	2	12	no	—
45	C₂₃×AGL(1,ℤ/8)	—	2	24	no	—
46	C₂₃×AGL(1,ℤ/8)	—	2	12	no	—
47	C₂₃×#135	—	2	6	no	—
48	C₂₃×#135	—	2	6	no	—
49	C₂₃×#135	—	2	6	no	—
50	C₂₃×#135	C₂³	1	4	yes	—
51	C₂₃×#135	C₂³	1	12	yes	—
52	C₂₃×#135	C₂³	1	12	yes	complemented
53	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
54	C₂×Q₁₆×C₂₃	C₂³	1	6	yes	complemented
55	C₂×SD₁₆×C₂₃	—	2	3	no	—
56	C₂×SD₁₆×C₂₃	—	2	6	no	—
57	C₂×D₈×C₂₃	—	2	3	no	—
58	C₂×D₈×C₂₃	—	2	6	no	—
59	C₂×D₈×C₂₃	C₂³	1	3	yes	—
60	C₂×D₈×C₂₃	C₂³	1	12	yes	—
61	C₂×D₈×C₂₃	C₂³	1	6	yes	complemented
62	C₂₃×#131	D₄	1	4	yes	—
63	C₂₃×#131	C₂³	1	4	yes	—
64	C₂×M₁₆×C₂₃	D₄	1	3	yes	—
65	C₂²×C₈×C₂₃	C₂³	1	3	yes	—
66	C₂₃×Q₃₂	C₂³	1	8	yes	complemented
67	C₂₃×SD₃₂	C₂³	1	24	yes	complemented
68	C₂₃×SD₃₂	C₂³	1	8	yes	complemented
69	C₂₃×D₁₆	C₂³	1	24	yes	complemented
70	C₂₃×M₃₂	C₂³	1	4	yes	—
71	C₂₃×M₃₂	C₂³	1	12	yes	complemented
72	C₂×C₁₆×C₂₃	C₂³	1	12	yes	complemented
73	C₂⁴×C₂₃	—	4	3	no	—
74	#41×C₂₃	—	2	4	no	—
75	#41×C₂₃	—	2	12	no	—
76	#41×C₂₃	—	2	12	no	—
77	#41×C₂₃	—	4	8	no	—
78	#41×C₂₃	—	4	4	no	—
79	#41×C₂₃	—	4	12	no	—
80	#41×C₂₃	—	4	6	no	—
81	#41×C₂₃	—	4	6	no	—
82	#41×C₂₃	—	4	6	no	—
83	#41×C₂₃	D₈	1	4	yes	—
84	#41×C₂₃	C₂×D₄	1	4	yes	—
85	C₂×Q₈×C₂₃	—	2	1	no	—
86	C₂×Q₈×C₂₃	—	2	6	no	—
87	C₂×Q₈×C₂₃	—	4	4	no	—
88	C₂×Q₈×C₂₃	D₈	1	1	yes	characteristic
89	C₂×D₄×C₂₃	—	2	3	no	—
90	C₂×D₄×C₂₃	—	2	12	no	—
91	C₂×D₄×C₂₃	—	2	6	no	—
92	C₂×D₄×C₂₃	—	4	3	no	—
93	C₂×D₄×C₂₃	—	4	6	no	—
94	C₂×D₄×C₂₃	—	4	24	no	—
95	C₂×D₄×C₂₃	—	4	12	no	—
96	C₂×D₄×C₂₃	—	4	3	no	—
97	C₂×D₄×C₂₃	—	4	6	no	—
98	C₂×D₄×C₂₃	D₈	1	3	yes	—
99	C₂²×C₄×C₂₃	—	4	3	no	—
100	C₂²×C₄×C₂₃	—	4	6	no	—
101	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
102	Q₁₆×C₂₃	—	2	1	no	—
103	Q₁₆×C₂₃	—	2	6	no	—
104	Q₁₆×C₂₃	C₂⁴	1	4	yes	—
105	Q₁₆×C₂₃	C₂⁴	1	2	yes	—
106	SD₁₆×C₂₃	—	2	4	no	—
107	SD₁₆×C₂₃	—	2	12	no	—
108	SD₁₆×C₂₃	—	2	12	no	—
109	D₈×C₂₃	—	2	3	no	—
110	D₈×C₂₃	—	2	12	no	—
111	D₈×C₂₃	—	2	6	no	—
112	D₈×C₂₃	C₂⁴	1	4	yes	—
113	D₈×C₂₃	C₂⁴	1	6	yes	—
114	M₁₆×C₂₃	C₂×D₄	1	12	yes	—
115	C₂×C₈×C₂₃	C₂×D₄	1	3	yes	—
116	C₂×C₈×C₂₃	C₂×D₄	1	6	yes	—
117	C₂×C₈×C₂₃	C₂⁴	1	6	yes	—
118	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
119	C₁₆×C₂₃	C₂⁴	1	8	yes	—
120	#62636	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂³×C₂₃	—	4	3	no	—
122	C₂³×C₂₃	—	4	6	no	—
123	C₂³×C₂₃	—	4	12	no	—
124	C₂³×C₂₃	—	16	6	no	—
125	C₂³×C₂₃	C₂×D₈	1	3	yes	—
126	Q₈×C₂₃	—	2	2	no	—
127	Q₈×C₂₃	—	2	4	no	—
128	Q₈×C₂₃	—	4	6	no	—
129	Q₈×C₂₃	—	4	1	no	—
130	Q₈×C₂₃	C₂×D₈	1	4	yes	—
131	D₄×C₂₃	—	2	6	no	—
132	D₄×C₂₃	—	2	4	no	—
133	D₄×C₂₃	—	4	12	no	—
134	D₄×C₂₃	—	4	4	no	—
135	D₄×C₂₃	—	4	12	no	—
136	D₄×C₂₃	—	4	3	no	—
137	D₄×C₂₃	—	4	12	no	—
138	D₄×C₂₃	—	4	6	no	—
139	D₄×C₂₃	C₂×D₈	1	12	yes	—
140	C₂×C₄×C₂₃	—	4	1	no	—
141	C₂×C₄×C₂₃	—	4	6	no	—
142	C₂×C₄×C₂₃	—	4	4	no	—
143	C₂×C₄×C₂₃	—	4	12	no	—
144	C₂×C₄×C₂₃	—	4	12	no	—
145	C₂×C₄×C₂₃	C₂×D₈	1	3	yes	—
146	C₂×C₄×C₂₃	C₂×D₈	1	6	yes	—
147	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₂₃	C₂²×D₄	1	6	yes	—
149	C₈×C₂₃	C₂²×D₄	1	1	yes	characteristic
150	C₈×C₂₃	C₂²×D₄	1	6	yes	—
151	C₈×C₂₃	C₂⁵	1	1	yes	characteristic
152	#3584	C₂×C₂₃	1	1	yes	characteristic, complemented
153	C₂×#576	C₂×C₂₃	1	1	yes	characteristic, complemented
154	#3416	C₂×C₂₃	1	8	yes	complemented
155	#3415	C₂×C₂₃	1	8	yes	complemented
156	#3414	C₂×C₂₃	1	6	yes	complemented
157	C₂×#509	C₂×C₂₃	1	6	yes	complemented
158	#3407	C₂×C₂₃	1	1	yes	characteristic, complemented
159	C₂²×C₂₃	—	4	3	no	—
160	C₂²×C₂₃	—	4	4	no	—
161	C₂²×C₂₃	—	4	6	no	—
162	C₂²×C₂₃	—	8	6	no	—
163	C₂²×C₂₃	—	16	6	no	—
164	C₂²×C₂₃	—	16	12	no	—
165	C₂²×C₂₃	C₂²×D₈	1	1	yes	characteristic
166	C₂²×C₂₃	C₂²×D₈	1	6	yes	—
167	C₄×C₂₃	—	4	2	no	—
168	C₄×C₂₃	—	4	4	no	—
169	C₄×C₂₃	C₂²×D₈	1	1	yes	characteristic
170	C₄×C₂₃	C₂²×D₈	1	6	yes	—
171	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
172	#585	—	2	1	no	—
173	C₂×H(5,𝔽₂)	—	2	1	no	—
174	#578	C₂²×C₂₃	1	4	yes	complemented
175	#577	—	2	4	no	—
176	#576	—	2	4	no	—
177	#576	C₂²×C₂₃	1	8	yes	complemented
178	#576	C₂²×C₂₃	1	4	yes	complemented
179	#575	—	2	3	no	—
180	C₂×AGL(1,ℤ/8)	—	2	3	no	—
181	C₂×#135	C₂²×C₂₃	1	3	yes	complemented
182	C₂×#135	C₂²×C₂₃	1	6	yes	complemented
183	C₂²×D₈	C₂²×C₂₃	1	3	yes	complemented
184	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
185	#510	C₂²×C₂₃	1	4	yes	complemented
186	#510	C₂²×C₂₃	1	12	yes	complemented
187	#509	C₂²×C₂₃	1	12	yes	complemented
188	#509	C₂²×C₂₃	1	24	yes	complemented
189	#509	C₂²×C₂₃	1	12	yes	complemented
190	#508	C₂²×C₂₃	1	24	yes	complemented
191	C₂×SD₃₂	C₂²×C₂₃	1	12	yes	complemented
192	C₂×D₁₆	C₂²×C₂₃	1	12	yes	complemented
193	#504	C₂²×C₂₃	1	8	yes	complemented
194	C₂×M₃₂	C₂²×C₂₃	1	6	yes	complemented
195	C₂×C₂₃	—	2	1	no	—
196	C₂×C₂₃	—	2	6	no	—
197	C₂×C₂₃	—	8	6	no	—
198	C₂×C₂₃	—	8	4	no	—
199	C₂×C₂₃	C₂³×D₈	1	1	yes	characteristic
200	2₋¹⁺⁴	—	2	4	no	—
201	2₋¹⁺⁴	—	4	1	no	—
202	H(5,𝔽₂)	—	2	8	no	—
203	H(5,𝔽₂)	—	2	4	no	—
204	H(5,𝔽₂)	—	4	4	no	—
205	H(5,𝔽₂)	—	4	3	no	—
206	C₂×#41	—	2	3	no	—
207	C₂×#41	—	2	6	no	—
208	C₂×#41	—	4	4	no	—
209	C₂×#41	—	4	1	no	—
210	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
211	C₂²×D₄	—	2	3	no	—
212	C₂²×D₄	—	4	3	no	—
213	#137	—	2	12	no	—
214	AGL(1,ℤ/8)	—	2	24	no	—
215	AGL(1,ℤ/8)	—	2	12	no	—
216	#135	—	2	6	no	—
217	#135	—	2	6	no	—
218	#135	—	2	6	no	—
219	#135	C₂³×C₂₃	1	4	yes	—
220	#135	C₂³×C₂₃	1	12	yes	—
221	#135	C₂³×C₂₃	1	12	yes	complemented
222	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
223	C₂×Q₁₆	C₂³×C₂₃	1	6	yes	complemented
224	C₂×SD₁₆	—	2	3	no	—
225	C₂×SD₁₆	—	2	6	no	—
226	C₂×D₈	—	2	3	no	—
227	C₂×D₈	—	2	6	no	—
228	C₂×D₈	C₂³×C₂₃	1	3	yes	—
229	C₂×D₈	C₂³×C₂₃	1	12	yes	—
230	C₂×D₈	C₂³×C₂₃	1	6	yes	complemented
231	#131	D₄×C₂₃	1	4	yes	—
232	#131	C₂³×C₂₃	1	4	yes	—
233	C₂×M₁₆	D₄×C₂₃	1	3	yes	—
234	C₂²×C₈	C₂³×C₂₃	1	3	yes	—
235	Q₃₂	C₂³×C₂₃	1	8	yes	complemented
236	SD₃₂	C₂³×C₂₃	1	24	yes	complemented
237	SD₃₂	C₂³×C₂₃	1	8	yes	complemented
238	D₁₆	C₂³×C₂₃	1	24	yes	complemented
239	M₃₂	C₂³×C₂₃	1	4	yes	—
240	M₃₂	C₂³×C₂₃	1	12	yes	complemented
241	C₂×C₁₆	C₂³×C₂₃	1	12	yes	complemented
242	C₂₃	#62636	1	1	yes	characteristic, direct product factor, Sylow
243	C₂⁴	—	4	3	no	—
244	#41	—	2	4	no	—
245	#41	—	2	12	no	—
246	#41	—	2	12	no	—
247	#41	—	4	8	no	—
248	#41	—	4	4	no	—
249	#41	—	4	12	no	—
250	#41	—	4	6	no	—
251	#41	—	4	6	no	—
252	#41	—	4	6	no	—
253	#41	D₈×C₂₃	1	4	yes	—
254	#41	C₂×D₄×C₂₃	1	4	yes	—
255	C₂×Q₈	—	2	1	no	—
256	C₂×Q₈	—	2	6	no	—
257	C₂×Q₈	—	4	4	no	—
258	C₂×Q₈	D₈×C₂₃	1	1	yes	characteristic
259	C₂×D₄	—	2	3	no	—
260	C₂×D₄	—	2	12	no	—
261	C₂×D₄	—	2	6	no	—
262	C₂×D₄	—	4	3	no	—
263	C₂×D₄	—	4	6	no	—
264	C₂×D₄	—	4	24	no	—
265	C₂×D₄	—	4	12	no	—
266	C₂×D₄	—	4	3	no	—
267	C₂×D₄	—	4	6	no	—
268	C₂×D₄	D₈×C₂₃	1	3	yes	—
269	C₂²×C₄	—	4	3	no	—
270	C₂²×C₄	—	4	6	no	—
271	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
272	Q₁₆	—	2	1	no	—
273	Q₁₆	—	2	6	no	—
274	Q₁₆	C₂⁴×C₂₃	1	4	yes	—
275	Q₁₆	C₂⁴×C₂₃	1	2	yes	—
276	SD₁₆	—	2	4	no	—
277	SD₁₆	—	2	12	no	—
278	SD₁₆	—	2	12	no	—
279	D₈	—	2	3	no	—
280	D₈	—	2	12	no	—
281	D₈	—	2	6	no	—
282	D₈	C₂⁴×C₂₃	1	4	yes	—
283	D₈	C₂⁴×C₂₃	1	6	yes	—
284	M₁₆	C₂×D₄×C₂₃	1	12	yes	—
285	C₂×C₈	C₂×D₄×C₂₃	1	3	yes	—
286	C₂×C₈	C₂×D₄×C₂₃	1	6	yes	—
287	C₂×C₈	C₂⁴×C₂₃	1	6	yes	—
288	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
289	C₁₆	C₂⁴×C₂₃	1	8	yes	—
290	C₂³	—	4	3	no	—
291	C₂³	—	4	6	no	—
292	C₂³	—	4	12	no	—
293	C₂³	—	16	6	no	—
294	C₂³	C₂×D₈×C₂₃	1	3	yes	—
295	Q₈	—	2	2	no	—
296	Q₈	—	2	4	no	—
297	Q₈	—	4	6	no	—
298	Q₈	—	4	1	no	—
299	Q₈	C₂×D₈×C₂₃	1	4	yes	—
300	D₄	—	2	6	no	—
301	D₄	—	2	4	no	—
302	D₄	—	4	12	no	—
303	D₄	—	4	4	no	—
304	D₄	—	4	12	no	—
305	D₄	—	4	3	no	—
306	D₄	—	4	12	no	—
307	D₄	—	4	6	no	—
308	D₄	C₂×D₈×C₂₃	1	12	yes	—
309	C₂×C₄	—	4	1	no	—
310	C₂×C₄	—	4	6	no	—
311	C₂×C₄	—	4	4	no	—
312	C₂×C₄	—	4	12	no	—
313	C₂×C₄	—	4	12	no	—
314	C₂×C₄	C₂×D₈×C₂₃	1	3	yes	—
315	C₂×C₄	C₂×D₈×C₂₃	1	6	yes	—
316	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
317	C₂×C₄	C₂²×D₄×C₂₃	1	6	yes	—
318	C₈	C₂²×D₄×C₂₃	1	1	yes	characteristic
319	C₈	C₂²×D₄×C₂₃	1	6	yes	—
320	C₈	C₂⁵×C₂₃	1	1	yes	characteristic
321	C₂²	—	4	3	no	—
322	C₂²	—	4	4	no	—
323	C₂²	—	4	6	no	—
324	C₂²	—	8	6	no	—
325	C₂²	—	16	12	no	—
326	C₂²	—	16	6	no	—
327	C₂²	C₂²×D₈×C₂₃	1	1	yes	characteristic
328	C₂²	C₂²×D₈×C₂₃	1	6	yes	—
329	C₄	—	4	2	no	—
330	C₄	—	4	4	no	—
331	C₄	C₂²×D₈×C₂₃	1	1	yes	characteristic
332	C₄	C₂²×D₈×C₂₃	1	6	yes	—
333	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
334	C₂	—	2	1	no	—
335	C₂	—	2	6	no	—
336	C₂	—	8	6	no	—
337	C₂	—	8	4	no	—
338	C₂	C₂³×D₈×C₂₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₂₃	C₂³×D₈
commutator, Frattini, cosocle	C₈	C₂⁵×C₂₃
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂×#41×C₂₃ ◁ C₂×C₂₃×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3584	C₂	semidirect
2. C₂×C₂₃×#576	C₂	semidirect
3. C₂₃×#3416	C₂	semidirect
4. C₂₃×#3415	C₂	semidirect
5. C₂₃×#3414	C₂	semidirect
6. C₂×C₂₃×#509	C₂	semidirect
7. C₂₃×#3407	C₂	semidirect
10. C₂₃×#578	C₂²	semidirect
13. C₂₃×#576	C₂²	semidirect
14. C₂₃×#576	C₂²	semidirect
17. C₂×C₂₃×#135	C₂²	semidirect
18. C₂×C₂₃×#135	C₂²	semidirect
19. C₂²×D₈×C₂₃	C₂²	semidirect
21. C₂₃×#510	C₂²	semidirect
22. C₂₃×#510	C₂²	semidirect
23. C₂₃×#509	C₂²	semidirect
24. C₂₃×#509	C₂²	semidirect
25. C₂₃×#509	C₂²	semidirect
26. C₂₃×#508	C₂²	semidirect
27. C₂×C₂₃×SD₃₂	C₂²	semidirect
28. C₂×C₂₃×D₁₆	C₂²	semidirect
29. C₂₃×#504	C₂²	semidirect
30. C₂×C₂₃×M₃₂	C₂²	semidirect
52. C₂₃×#135	C₂³	semidirect
54. C₂×Q₁₆×C₂₃	C₂³	semidirect
61. C₂×D₈×C₂₃	C₂³	semidirect
66. C₂₃×Q₃₂	C₂³	semidirect
67. C₂₃×SD₃₂	C₂³	semidirect
68. C₂₃×SD₃₂	C₂³	semidirect
69. C₂₃×D₁₆	C₂³	semidirect
71. C₂₃×M₃₂	C₂³	semidirect
72. C₂×C₁₆×C₂₃	C₂³	semidirect
120. #62636	C₂₃	direct (N × H)
152. #3584	C₂×C₂₃	semidirect
153. C₂×#576	C₂×C₂₃	semidirect
154. #3416	C₂×C₂₃	semidirect
155. #3415	C₂×C₂₃	semidirect
156. #3414	C₂×C₂₃	semidirect
157. C₂×#509	C₂×C₂₃	semidirect
158. #3407	C₂×C₂₃	semidirect
174. #578	C₂²×C₂₃	semidirect
177. #576	C₂²×C₂₃	semidirect
178. #576	C₂²×C₂₃	semidirect
181. C₂×#135	C₂²×C₂₃	semidirect
182. C₂×#135	C₂²×C₂₃	semidirect
183. C₂²×D₈	C₂²×C₂₃	semidirect
185. #510	C₂²×C₂₃	semidirect
186. #510	C₂²×C₂₃	semidirect
187. #509	C₂²×C₂₃	semidirect
188. #509	C₂²×C₂₃	semidirect
189. #509	C₂²×C₂₃	semidirect
190. #508	C₂²×C₂₃	semidirect
191. C₂×SD₃₂	C₂²×C₂₃	semidirect
192. C₂×D₁₆	C₂²×C₂₃	semidirect
193. #504	C₂²×C₂₃	semidirect
194. C₂×M₃₂	C₂²×C₂₃	semidirect
221. #135	C₂³×C₂₃	semidirect
223. C₂×Q₁₆	C₂³×C₂₃	semidirect
230. C₂×D₈	C₂³×C₂₃	semidirect
235. Q₃₂	C₂³×C₂₃	semidirect
236. SD₃₂	C₂³×C₂₃	semidirect
237. SD₃₂	C₂³×C₂₃	semidirect
238. D₁₆	C₂³×C₂₃	semidirect
240. M₃₂	C₂³×C₂₃	semidirect
241. C₂×C₁₆	C₂³×C₂₃	semidirect
242. C₂₃	#62636	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×#3584	2
C₂×C₂₃×#576	2
C₂₃×#3416	2
C₂₃×#3415	2
C₂₃×#3414	2
C₂×C₂₃×#509	2
C₂₃×#3407	2
#62636	23

Subgroups — C23×#62636 #19210262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#62636 #19210262