Subgroups — C₂₃×#3300 #15670919

Order 2944.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#548	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#488	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#485	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#480	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×Q₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×Q₈×C₂₃	C₂²	1	1	yes	characteristic
18	C₂×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
20	C₂×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
21	C₂²×C₈×C₂₃	C₂²	1	1	yes	characteristic
22	C₂²×C₈×C₂₃	C₂²	1	1	yes	characteristic
23	C₂₃×#126	—	2	1	no	—
24	C₂₃×#125	—	2	1	no	—
25	C₂₃×#125	C₂²	1	1	yes	characteristic
26	C₂₃×#124	—	2	1	no	—
27	C₂₃×#124	C₂²	1	1	yes	characteristic
28	C₂₃×#123	—	2	1	no	—
29	C₂₃×C₂²⋊Q₈	—	2	1	no	—
30	C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂₃×#121	—	2	1	no	—
34	C₂₃×#121	C₂²	1	1	yes	characteristic
35	C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
36	C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
37	C₄×D₄×C₂₃	—	2	1	no	—
38	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
39	C₂₃×#117	—	2	1	no	—
40	C₂₃×#117	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
42	C₂₃×#107	C₂²	1	1	yes	characteristic
43	C₂₃×#107	C₂²	1	1	yes	characteristic
44	C₂₃×#106	C₂²	1	1	yes	characteristic
45	C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₂₃×#103	C₂²	1	1	yes	characteristic
47	C₂₃×#103	C₂²	1	1	yes	characteristic
48	C₂₃×#103	C₂²	1	1	yes	characteristic
49	C₂₃×#103	C₂²	1	1	yes	characteristic
50	C₂₃×#103	C₂²	1	1	yes	characteristic
51	C₂₃×#103	C₂²	1	1	yes	characteristic
52	C₂₃×#103	C₂²	1	1	yes	characteristic
53	C₂₃×#102	C₂²	1	1	yes	characteristic
54	C₂₃×#102	C₂²	1	1	yes	characteristic
55	C₂₃×#102	C₂²	1	1	yes	characteristic
56	C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
57	C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
58	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
59	#41×C₂₃	—	2	2	no	—
60	#41×C₂₃	—	4	1	no	—
61	C₂×Q₈×C₂₃	—	2	1	no	—
62	C₂×Q₈×C₂₃	—	2	2	no	—
63	C₂×Q₈×C₂₃	—	4	1	no	—
64	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
65	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
66	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
67	C₂×D₄×C₂₃	—	2	1	no	—
68	C₂×D₄×C₂₃	—	2	1	no	—
69	C₂×D₄×C₂₃	D₄	1	1	yes	characteristic
70	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₂₃	—	2	1	no	—
72	C₂²×C₄×C₂₃	—	2	1	no	—
73	C₂²×C₄×C₂₃	—	2	1	no	—
74	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
76	Q₁₆×C₂₃	—	2	2	no	—
77	Q₁₆×C₂₃	—	4	1	no	—
78	SD₁₆×C₂₃	—	4	1	no	—
79	C₂×C₈×C₂₃	—	4	1	no	—
80	C₂×C₈×C₂₃	—	4	1	no	—
81	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
82	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
83	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
84	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
85	C₄⋊C₄×C₂₃	—	2	1	no	—
86	C₄⋊C₄×C₂₃	—	2	1	no	—
87	C₄⋊C₄×C₂₃	—	2	1	no	—
88	C₄⋊C₄×C₂₃	—	2	1	no	—
89	C₄⋊C₄×C₂₃	—	2	1	no	—
90	C₄⋊C₄×C₂₃	—	2	1	no	—
91	C₄⋊C₄×C₂₃	—	2	1	no	—
92	C₄⋊C₄×C₂₃	—	2	1	no	—
93	C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
94	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
95	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
96	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
97	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
98	C₂²⋊C₄×C₂₃	—	2	1	no	—
99	C₂²⋊C₄×C₂₃	—	2	1	no	—
100	C₂²⋊C₄×C₂₃	—	2	1	no	—
101	C₂²⋊C₄×C₂₃	—	2	1	no	—
102	C₂²⋊C₄×C₂₃	—	2	1	no	—
103	C₂²⋊C₄×C₂₃	—	2	1	no	—
104	C₂²⋊C₄×C₂₃	—	2	1	no	—
105	C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
106	C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
107	C₄²×C₂₃	—	2	1	no	—
108	C₄²×C₂₃	—	2	1	no	—
109	C₄²×C₂₃	—	2	1	no	—
110	C₄²×C₂₃	C₂³	1	1	yes	characteristic
111	C₂³×C₂₃	—	2	1	no	—
112	C₂³×C₂₃	C₂×D₄	1	1	yes	characteristic
113	C₂³×C₂₃	C₂×D₄	1	1	yes	characteristic
114	Q₈×C₂₃	—	2	1	no	—
115	Q₈×C₂₃	—	2	1	no	—
116	Q₈×C₂₃	—	2	1	no	—
117	Q₈×C₂₃	—	2	1	no	—
118	Q₈×C₂₃	—	2	1	no	—
119	Q₈×C₂₃	—	4	2	no	—
120	Q₈×C₂₃	#41	1	2	yes	—
121	D₄×C₂₃	—	2	2	no	—
122	D₄×C₂₃	—	2	1	no	—
123	D₄×C₂₃	—	2	1	no	—
124	D₄×C₂₃	—	4	2	no	—
125	D₄×C₂₃	—	4	2	no	—
126	C₂×C₄×C₂₃	—	2	1	no	—
127	C₂×C₄×C₂₃	—	2	1	no	—
128	C₂×C₄×C₂₃	—	2	1	no	—
129	C₂×C₄×C₂₃	—	2	1	no	—
130	C₂×C₄×C₂₃	—	2	1	no	—
131	C₂×C₄×C₂₃	—	2	1	no	—
132	C₂×C₄×C₂₃	—	2	1	no	—
133	C₂×C₄×C₂₃	—	2	1	no	—
134	C₂×C₄×C₂₃	—	2	1	no	—
135	C₂×C₄×C₂₃	—	2	1	no	—
136	C₂×C₄×C₂₃	—	2	1	no	—
137	C₂×C₄×C₂₃	—	4	2	no	—
138	C₂×C₄×C₂₃	—	4	2	no	—
139	C₂×C₄×C₂₃	—	4	2	no	—
140	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
141	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
142	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
143	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
144	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
145	C₈×C₂₃	—	2	1	no	—
146	C₈×C₂₃	—	2	1	no	—
147	C₈×C₂₃	—	2	1	no	—
148	C₈×C₂₃	—	2	1	no	—
149	#3300	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂²×C₂₃	—	2	1	no	—
151	C₂²×C₂₃	—	2	1	no	—
152	C₂²×C₂₃	—	2	1	no	—
153	C₂²×C₂₃	—	2	1	no	—
154	C₂²×C₂₃	—	2	1	no	—
155	C₂²×C₂₃	—	4	1	no	—
156	C₂²×C₂₃	—	4	1	no	—
157	C₂²×C₂₃	—	4	1	no	—
158	C₂²×C₂₃	#135	1	2	yes	—
159	C₂²×C₂₃	C₂²×D₄	1	1	yes	characteristic
160	C₄×C₂₃	—	2	1	no	—
161	C₄×C₂₃	—	2	1	no	—
162	C₄×C₂₃	—	2	2	no	—
163	C₄×C₂₃	—	2	1	no	—
164	C₄×C₂₃	—	2	1	no	—
165	C₄×C₂₃	—	4	1	no	—
166	C₄×C₂₃	—	4	1	no	—
167	C₄×C₂₃	—	4	1	no	—
168	C₄×C₂₃	—	4	1	no	—
169	C₄×C₂₃	—	4	1	no	—
170	C₄×C₂₃	—	4	1	no	—
171	C₄×C₂₃	C₂×#41	1	1	yes	characteristic
172	C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
173	#552	C₂×C₂₃	1	1	yes	characteristic, complemented
174	#548	C₂×C₂₃	1	1	yes	characteristic
175	#488	C₂×C₂₃	1	1	yes	characteristic, complemented
176	#485	C₂×C₂₃	1	1	yes	characteristic, complemented
177	#480	C₂×C₂₃	1	1	yes	characteristic, complemented
178	#479	C₂×C₂₃	1	1	yes	characteristic, complemented
179	#467	C₂×C₂₃	1	1	yes	characteristic, complemented
180	#465	C₂×C₂₃	1	1	yes	characteristic, complemented
181	#464	C₂×C₂₃	1	1	yes	characteristic, complemented
182	#452	C₂×C₂₃	1	1	yes	characteristic, complemented
183	#451	C₂×C₂₃	1	1	yes	characteristic, complemented
184	C₄×Q₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
185	C₈×D₄	C₂×C₂₃	1	1	yes	characteristic, complemented
186	#416	C₂×C₂₃	1	1	yes	characteristic, complemented
187	C₂×#103	C₂×C₂₃	1	1	yes	characteristic, complemented
188	C₂×C₂₃	—	2	2	no	—
189	C₂×C₂₃	—	4	1	no	—
190	C₂×C₂₃	—	8	1	no	—
191	C₂×C₂₃	#546	1	1	yes	characteristic
192	C₂×C₂₃	C₂×#135	1	1	yes	characteristic
193	C₂×C₂₃	#578	1	1	yes	characteristic
194	C₂×#41	C₂²×C₂₃	1	1	yes	characteristic
195	C₂²×Q₈	C₂²×C₂₃	1	1	yes	characteristic
196	C₂×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
197	C₂×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
198	C₂×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
199	C₂²×C₈	C₂²×C₂₃	1	1	yes	characteristic
200	C₂²×C₈	C₂²×C₂₃	1	1	yes	characteristic
201	#126	—	2	1	no	—
202	#125	—	2	1	no	—
203	#125	C₂²×C₂₃	1	1	yes	characteristic
204	#124	—	2	1	no	—
205	#124	C₂²×C₂₃	1	1	yes	characteristic
206	#123	—	2	1	no	—
207	C₂²⋊Q₈	—	2	1	no	—
208	C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
209	C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
210	C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
211	#121	—	2	1	no	—
212	#121	C₂²×C₂₃	1	1	yes	characteristic
213	C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
214	C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
215	C₄×D₄	—	2	1	no	—
216	C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
217	#117	—	2	1	no	—
218	#117	C₂²×C₂₃	1	1	yes	characteristic
219	C₂×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
220	#107	C₂²×C₂₃	1	1	yes	characteristic
221	#107	C₂²×C₂₃	1	1	yes	characteristic
222	#106	C₂²×C₂₃	1	1	yes	characteristic
223	C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
224	#103	C₂²×C₂₃	1	1	yes	characteristic
225	#103	C₂²×C₂₃	1	1	yes	characteristic
226	#103	C₂²×C₂₃	1	1	yes	characteristic
227	#103	C₂²×C₂₃	1	1	yes	characteristic
228	#103	C₂²×C₂₃	1	1	yes	characteristic
229	#103	C₂²×C₂₃	1	1	yes	characteristic
230	#103	C₂²×C₂₃	1	1	yes	characteristic
231	#102	C₂²×C₂₃	1	1	yes	characteristic
232	#102	C₂²×C₂₃	1	1	yes	characteristic
233	#102	C₂²×C₂₃	1	1	yes	characteristic
234	C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
235	C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
236	C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
237	C₂₃	#3300	1	1	yes	characteristic, direct product factor, Sylow
238	#41	—	2	2	no	—
239	#41	—	4	1	no	—
240	C₂×Q₈	—	2	1	no	—
241	C₂×Q₈	—	2	2	no	—
242	C₂×Q₈	—	4	1	no	—
243	C₂×Q₈	C₂³×C₂₃	1	1	yes	characteristic
244	C₂×Q₈	C₂³×C₂₃	1	1	yes	characteristic
245	C₂×Q₈	C₂³×C₂₃	1	1	yes	characteristic
246	C₂×D₄	—	2	1	no	—
247	C₂×D₄	—	2	1	no	—
248	C₂×D₄	D₄×C₂₃	1	1	yes	characteristic
249	C₂×D₄	C₂³×C₂₃	1	1	yes	characteristic
250	C₂²×C₄	—	2	1	no	—
251	C₂²×C₄	—	2	1	no	—
252	C₂²×C₄	—	2	1	no	—
253	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
254	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
255	Q₁₆	—	2	2	no	—
256	Q₁₆	—	4	1	no	—
257	SD₁₆	—	4	1	no	—
258	C₂×C₈	—	4	1	no	—
259	C₂×C₈	—	4	1	no	—
260	C₂×C₈	C₂³×C₂₃	1	1	yes	characteristic
261	C₂×C₈	C₂³×C₂₃	1	1	yes	characteristic
262	C₂×C₈	C₂³×C₂₃	1	1	yes	characteristic
263	C₂×C₈	C₂³×C₂₃	1	1	yes	characteristic
264	C₄⋊C₄	—	2	1	no	—
265	C₄⋊C₄	—	2	1	no	—
266	C₄⋊C₄	—	2	1	no	—
267	C₄⋊C₄	—	2	1	no	—
268	C₄⋊C₄	—	2	1	no	—
269	C₄⋊C₄	—	2	1	no	—
270	C₄⋊C₄	—	2	1	no	—
271	C₄⋊C₄	—	2	1	no	—
272	C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
273	C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
274	C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
275	C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
276	C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
277	C₂²⋊C₄	—	2	1	no	—
278	C₂²⋊C₄	—	2	1	no	—
279	C₂²⋊C₄	—	2	1	no	—
280	C₂²⋊C₄	—	2	1	no	—
281	C₂²⋊C₄	—	2	1	no	—
282	C₂²⋊C₄	—	2	1	no	—
283	C₂²⋊C₄	—	2	1	no	—
284	C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
285	C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
286	C₄²	—	2	1	no	—
287	C₄²	—	2	1	no	—
288	C₄²	—	2	1	no	—
289	C₄²	C₂³×C₂₃	1	1	yes	characteristic
290	C₂³	—	2	1	no	—
291	C₂³	C₂×D₄×C₂₃	1	1	yes	characteristic
292	C₂³	C₂×D₄×C₂₃	1	1	yes	characteristic
293	Q₈	—	2	1	no	—
294	Q₈	—	2	1	no	—
295	Q₈	—	2	1	no	—
296	Q₈	—	2	1	no	—
297	Q₈	—	2	1	no	—
298	Q₈	—	4	2	no	—
299	Q₈	#41×C₂₃	1	2	yes	—
300	D₄	—	2	2	no	—
301	D₄	—	2	1	no	—
302	D₄	—	2	1	no	—
303	D₄	—	4	2	no	—
304	D₄	—	4	2	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
320	C₂×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
321	C₂×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
322	C₂×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
323	C₂×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
324	C₈	—	2	1	no	—
325	C₈	—	2	1	no	—
326	C₈	—	2	1	no	—
327	C₈	—	2	1	no	—
328	C₂²	—	2	1	no	—
329	C₂²	—	2	1	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	2	1	no	—
332	C₂²	—	2	1	no	—
333	C₂²	—	4	1	no	—
334	C₂²	—	4	1	no	—
335	C₂²	—	4	1	no	—
336	C₂²	C₂₃×#135	1	2	yes	—
337	C₂²	C₂²×D₄×C₂₃	1	1	yes	characteristic
338	C₄	—	2	1	no	—
339	C₄	—	2	1	no	—
340	C₄	—	2	1	no	—
341	C₄	—	2	1	no	—
342	C₄	—	2	2	no	—
343	C₄	—	4	1	no	—
344	C₄	—	4	1	no	—
345	C₄	—	4	1	no	—
346	C₄	—	4	1	no	—
347	C₄	—	4	1	no	—
348	C₄	—	4	1	no	—
349	C₄	C₂×#41×C₂₃	1	1	yes	characteristic
350	C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
351	C₂	—	2	2	no	—
352	C₂	—	4	1	no	—
353	C₂	—	8	1	no	—
354	C₂	C₂₃×#546	1	1	yes	characteristic
355	C₂	C₂×C₂₃×#135	1	1	yes	characteristic
356	C₂	C₂₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
prime radical	C₂₃×#548	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄×D₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#552	C₂	semidirect
3. C₂₃×#488	C₂	semidirect
4. C₂₃×#485	C₂	semidirect
5. C₂₃×#480	C₂	semidirect
6. C₂₃×#479	C₂	semidirect
7. C₂₃×#467	C₂	semidirect
8. C₂₃×#465	C₂	semidirect
9. C₂₃×#464	C₂	semidirect
10. C₂₃×#452	C₂	semidirect
11. C₂₃×#451	C₂	semidirect
12. C₄×Q₁₆×C₂₃	C₂	semidirect
13. C₈×D₄×C₂₃	C₂	semidirect
14. C₂₃×#416	C₂	semidirect
15. C₂×C₂₃×#103	C₂	semidirect
149. #3300	C₂₃	direct (N × H)
173. #552	C₂×C₂₃	semidirect
175. #488	C₂×C₂₃	semidirect
176. #485	C₂×C₂₃	semidirect
177. #480	C₂×C₂₃	semidirect
178. #479	C₂×C₂₃	semidirect
179. #467	C₂×C₂₃	semidirect
180. #465	C₂×C₂₃	semidirect
181. #464	C₂×C₂₃	semidirect
182. #452	C₂×C₂₃	semidirect
183. #451	C₂×C₂₃	semidirect
184. C₄×Q₁₆	C₂×C₂₃	semidirect
185. C₈×D₄	C₂×C₂₃	semidirect
186. #416	C₂×C₂₃	semidirect
187. C₂×#103	C₂×C₂₃	semidirect
237. C₂₃	#3300	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×#552	2
C₂₃×#548	2
C₂₃×#488	2
C₂₃×#485	2
C₂₃×#480	2
C₂₃×#479	2
C₂₃×#467	2
C₂₃×#465	2
C₂₃×#464	2
C₂₃×#452	2
C₂₃×#451	2
C₄×Q₁₆×C₂₃	2
C₈×D₄×C₂₃	2
C₂₃×#416	2
C₂×C₂₃×#103	2
#3300	23

Subgroups — C23×#3300 #15670919

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#3300 #15670919