Subgroups — C₂×C₂₃×#2366 #19181765

Order 5888.

5062 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×#127	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×D₄×C₂₃	C₂	1	4	yes	maximal, complemented
3	C₂₃×#2366	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#390	C₂	1	4	yes	maximal, complemented
5	C₂×C₂₃×#386	C₂	1	4	yes	maximal, complemented
6	C₂×C₄×C₄⋊C₄×C₂₃	C₂	1	2	yes	maximal, complemented
7	C₂³×D₄×C₂₃	C₂²	1	4	yes	—
8	C₂³×D₄×C₂₃	C₂²	1	2	yes	—
9	C₂⁴×C₄×C₂₃	C₂²	1	4	yes	—
10	C₂×C₂₃×#127	C₄	1	16	yes	complemented
11	C₂×C₂₃×#127	C₂²	1	8	yes	—
12	C₂×C₄×D₄×C₂₃	—	2	32	no	—
13	C₂×C₄×D₄×C₂₃	C₂²	1	32	yes	complemented
14	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	8	yes	—
17	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
18	C₂²×C₄²×C₂₃	C₂²	1	4	yes	—
19	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
20	C₂₃×#390	C₂²	1	32	yes	complemented
21	C₂₃×#386	C₂²	1	32	yes	complemented
22	C₄×C₄⋊C₄×C₂₃	C₂²	1	16	yes	complemented
23	C₂×C₂₃×#95	C₂²	1	4	yes	—
24	C₂⁵×C₂₃	C₂³	1	4	yes	—
25	C₂²×D₄×C₂₃	—	2	16	no	—
26	C₂²×D₄×C₂₃	—	2	16	no	—
27	C₂²×D₄×C₂₃	—	4	4	no	—
28	C₂²×D₄×C₂₃	—	4	4	no	—
29	C₂²×D₄×C₂₃	C₂×C₄	1	32	yes	complemented
30	C₂²×D₄×C₂₃	C₂×C₄	1	16	yes	complemented
31	C₂²×D₄×C₂₃	C₂³	1	16	yes	—
32	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
33	C₂³×C₄×C₂₃	—	2	32	no	—
34	C₂³×C₄×C₂₃	—	4	8	no	—
35	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
36	C₂³×C₄×C₂₃	C₂³	1	16	yes	—
37	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
39	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
40	C₂₃×#127	C₂×C₄	1	64	yes	complemented
41	C₄×D₄×C₂₃	—	2	128	no	—
42	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
43	C₂×C₄⋊C₄×C₂₃	D₄	1	16	yes	complemented
44	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
45	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
46	C₂×C₂²⋊C₄×C₂₃	—	2	32	no	—
47	C₂×C₂²⋊C₄×C₂₃	—	4	8	no	—
48	C₂×C₂²⋊C₄×C₂₃	C₂³	1	32	yes	—
49	C₂×C₂²⋊C₄×C₂₃	C₂³	1	16	yes	—
50	C₂×C₄²×C₂₃	—	2	16	no	—
51	C₂×C₄²×C₂₃	C₂×C₄	1	8	yes	complemented
52	C₂×C₄²×C₂₃	C₂³	1	16	yes	—
53	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
54	C₂₃×#95	C₂³	1	16	yes	—
55	C₂⁴×C₂₃	—	2	16	no	—
56	C₂⁴×C₂₃	—	2	16	no	—
57	C₂⁴×C₂₃	—	2	8	no	—
58	C₂⁴×C₂₃	—	2	8	no	—
59	C₂⁴×C₂₃	C₂²×C₄	1	16	yes	—
60	C₂⁴×C₂₃	C₂⁴	1	8	yes	—
61	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
62	C₂×D₄×C₂₃	—	2	128	no	—
63	C₂×D₄×C₂₃	—	2	32	no	—
64	C₂×D₄×C₂₃	—	2	32	no	—
65	C₂×D₄×C₂₃	—	4	32	no	—
66	C₂×D₄×C₂₃	—	4	8	no	—
67	C₂×D₄×C₂₃	—	4	8	no	—
68	C₂×D₄×C₂₃	C₂²×C₄	1	64	yes	complemented
69	C₂×D₄×C₂₃	C₂²×C₄	1	32	yes	complemented
70	C₂²×C₄×C₂₃	—	2	8	no	—
71	C₂²×C₄×C₂₃	—	2	8	no	—
72	C₂²×C₄×C₂₃	—	2	2	no	—
73	C₂²×C₄×C₂₃	—	2	2	no	—
74	C₂²×C₄×C₂₃	—	2	8	no	—
75	C₂²×C₄×C₂₃	—	2	8	no	—
76	C₂²×C₄×C₂₃	—	2	8	no	—
77	C₂²×C₄×C₂₃	—	2	64	no	—
78	C₂²×C₄×C₂₃	—	4	16	no	—
79	C₂²×C₄×C₂₃	—	4	64	no	—
80	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
81	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
82	C₂²×C₄×C₂₃	C₂×D₄	1	16	yes	—
83	C₂²×C₄×C₂₃	C₂×D₄	1	8	yes	—
84	C₂²×C₄×C₂₃	#41	1	8	yes	—
85	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
86	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
87	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
88	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
89	C₄⋊C₄×C₂₃	—	2	16	no	—
90	C₄⋊C₄×C₂₃	C₂×D₄	1	32	yes	complemented
91	C₂²⋊C₄×C₂₃	—	2	64	no	—
92	C₂²⋊C₄×C₂₃	—	4	16	no	—
93	C₄²×C₂₃	—	2	32	no	—
94	C₄²×C₂₃	C₂²×C₄	1	16	yes	complemented
95	C₂×#2366	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂³×C₂₃	—	2	64	no	—
97	C₂³×C₂₃	—	2	32	no	—
98	C₂³×C₂₃	—	2	16	no	—
99	C₂³×C₂₃	—	2	16	no	—
100	C₂³×C₂₃	—	2	8	no	—
101	C₂³×C₂₃	—	2	8	no	—
102	C₂³×C₂₃	—	4	16	no	—
103	C₂³×C₂₃	—	4	32	no	—
104	C₂³×C₂₃	—	4	16	no	—
105	C₂³×C₂₃	C₂³×C₄	1	16	yes	—
106	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
107	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
108	C₂³×C₂₃	C₂×#41	1	4	yes	—
109	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
110	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
111	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
112	D₄×C₂₃	—	2	128	no	—
113	D₄×C₂₃	—	4	32	no	—
114	C₂×C₄×C₂₃	—	2	8	no	—
115	C₂×C₄×C₂₃	—	2	32	no	—
116	C₂×C₄×C₂₃	—	2	8	no	—
117	C₂×C₄×C₂₃	—	2	8	no	—
118	C₂×C₄×C₂₃	—	2	2	no	—
119	C₂×C₄×C₂₃	—	2	2	no	—
120	C₂×C₄×C₂₃	—	2	8	no	—
121	C₂×C₄×C₂₃	—	2	8	no	—
122	C₂×C₄×C₂₃	—	2	8	no	—
123	C₂×C₄×C₂₃	—	4	64	no	—
124	C₂×C₄×C₂₃	—	4	16	no	—
125	C₂×C₄×C₂₃	C₄×D₄	1	32	yes	complemented
126	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
127	C₂×C₄×C₂₃	C₂³×C₄	1	8	yes	—
128	C₂×C₄×C₂₃	C₂²×D₄	1	16	yes	—
129	C₂×C₄×C₂₃	C₂²×D₄	1	8	yes	—
130	C₂×C₄×C₂₃	C₂×#41	1	8	yes	—
131	C₂²×#127	C₂×C₂₃	1	1	yes	characteristic
132	C₂²×C₄×D₄	C₂×C₂₃	1	4	yes	complemented
133	#2366	C₂×C₂₃	1	16	yes	direct product factor
134	C₂×#390	C₂×C₂₃	1	4	yes	complemented
135	C₂×#386	C₂×C₂₃	1	4	yes	complemented
136	C₂×C₄×C₄⋊C₄	C₂×C₂₃	1	2	yes	complemented
137	C₂²×C₂₃	—	2	32	no	—
138	C₂²×C₂₃	—	2	16	no	—
139	C₂²×C₂₃	—	4	64	no	—
140	C₂²×C₂₃	—	4	8	no	—
141	C₂²×C₂₃	—	4	16	no	—
142	C₂²×C₂₃	—	4	8	no	—
143	C₂²×C₂₃	C₂×C₄×D₄	1	8	yes	—
144	C₂²×C₂₃	#518	1	4	yes	—
145	C₂²×C₂₃	D₄²	1	4	yes	—
146	C₂²×C₂₃	#550	1	8	yes	—
147	C₂²×C₂₃	#559	1	4	yes	—
148	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
149	C₂²×C₂₃	C₂³×D₄	1	2	yes	—
150	C₂²×C₂₃	C₂²×#41	1	2	yes	—
151	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
152	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
153	C₄×C₂₃	—	2	4	no	—
154	C₄×C₂₃	—	2	16	no	—
155	C₄×C₂₃	—	4	8	no	—
156	C₄×C₂₃	C₂×C₄×D₄	1	16	yes	complemented
157	C₂³×D₄	C₂²×C₂₃	1	4	yes	—
158	C₂³×D₄	C₂²×C₂₃	1	2	yes	—
159	C₂⁴×C₄	C₂²×C₂₃	1	4	yes	—
160	C₂×#127	C₄×C₂₃	1	16	yes	complemented
161	C₂×#127	C₂²×C₂₃	1	8	yes	—
162	C₂×C₄×D₄	—	2	32	no	—
163	C₂×C₄×D₄	C₂²×C₂₃	1	32	yes	complemented
164	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
165	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
166	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	8	yes	—
167	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
168	C₂²×C₄²	C₂²×C₂₃	1	4	yes	—
169	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
170	#390	C₂²×C₂₃	1	32	yes	complemented
171	#386	C₂²×C₂₃	1	32	yes	complemented
172	C₄×C₄⋊C₄	C₂²×C₂₃	1	16	yes	complemented
173	C₂×#95	C₂²×C₂₃	1	4	yes	—
174	C₂×C₂₃	—	4	16	no	—
175	C₂×C₂₃	#2366	1	8	yes	direct product factor
176	C₂×C₂₃	C₂²×C₄×D₄	1	2	yes	—
177	C₂×C₂₃	C₂×#518	1	1	yes	characteristic
178	C₂×C₂₃	C₂×D₄²	1	1	yes	characteristic
179	C₂×C₂₃	C₂×#550	1	2	yes	—
180	C₂×C₂₃	C₂×#559	1	1	yes	characteristic
181	C₂⁵	C₂³×C₂₃	1	4	yes	—
182	C₂²×D₄	—	2	16	no	—
183	C₂²×D₄	—	2	16	no	—
184	C₂²×D₄	—	4	4	no	—
185	C₂²×D₄	—	4	4	no	—
186	C₂²×D₄	C₂×C₄×C₂₃	1	32	yes	complemented
187	C₂²×D₄	C₂×C₄×C₂₃	1	16	yes	complemented
188	C₂²×D₄	C₂³×C₂₃	1	16	yes	—
189	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
190	C₂³×C₄	—	2	32	no	—
191	C₂³×C₄	—	4	8	no	—
192	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
193	C₂³×C₄	C₂³×C₂₃	1	16	yes	—
194	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
195	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
196	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
197	#127	C₂×C₄×C₂₃	1	64	yes	complemented
198	C₄×D₄	—	2	128	no	—
199	C₂×C₄⋊C₄	—	2	8	no	—
200	C₂×C₄⋊C₄	D₄×C₂₃	1	16	yes	complemented
201	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
202	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
203	C₂×C₂²⋊C₄	—	2	32	no	—
204	C₂×C₂²⋊C₄	—	4	8	no	—
205	C₂×C₂²⋊C₄	C₂³×C₂₃	1	32	yes	—
206	C₂×C₂²⋊C₄	C₂³×C₂₃	1	16	yes	—
207	C₂×C₄²	—	2	16	no	—
208	C₂×C₄²	C₂×C₄×C₂₃	1	8	yes	complemented
209	C₂×C₄²	C₂³×C₂₃	1	16	yes	—
210	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
211	#95	C₂³×C₂₃	1	16	yes	—
212	C₂₃	C₂×#2366	1	1	yes	characteristic, direct product factor, Sylow
213	C₂⁴	—	2	16	no	—
214	C₂⁴	—	2	16	no	—
215	C₂⁴	—	2	8	no	—
216	C₂⁴	—	2	8	no	—
217	C₂⁴	C₂²×C₄×C₂₃	1	16	yes	—
218	C₂⁴	C₂⁴×C₂₃	1	8	yes	—
219	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
220	C₂×D₄	—	2	128	no	—
221	C₂×D₄	—	2	32	no	—
222	C₂×D₄	—	2	32	no	—
223	C₂×D₄	—	4	32	no	—
224	C₂×D₄	—	4	8	no	—
225	C₂×D₄	—	4	8	no	—
226	C₂×D₄	C₂²×C₄×C₂₃	1	64	yes	complemented
227	C₂×D₄	C₂²×C₄×C₂₃	1	32	yes	complemented
228	C₂²×C₄	—	2	8	no	—
229	C₂²×C₄	—	2	8	no	—
230	C₂²×C₄	—	2	2	no	—
231	C₂²×C₄	—	2	2	no	—
232	C₂²×C₄	—	2	8	no	—
233	C₂²×C₄	—	2	8	no	—
234	C₂²×C₄	—	2	8	no	—
235	C₂²×C₄	—	2	64	no	—
236	C₂²×C₄	—	4	16	no	—
237	C₂²×C₄	—	4	64	no	—
238	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
239	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
240	C₂²×C₄	C₂×D₄×C₂₃	1	16	yes	—
241	C₂²×C₄	C₂×D₄×C₂₃	1	8	yes	—
242	C₂²×C₄	#41×C₂₃	1	8	yes	—
243	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
244	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
245	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
246	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
247	C₄⋊C₄	—	2	16	no	—
248	C₄⋊C₄	C₂×D₄×C₂₃	1	32	yes	complemented
249	C₂²⋊C₄	—	2	64	no	—
250	C₂²⋊C₄	—	4	16	no	—
251	C₄²	—	2	32	no	—
252	C₄²	C₂²×C₄×C₂₃	1	16	yes	complemented
253	C₂³	—	2	16	no	—
254	C₂³	—	2	16	no	—
255	C₂³	—	2	8	no	—
256	C₂³	—	2	8	no	—
257	C₂³	—	2	64	no	—
258	C₂³	—	2	32	no	—
259	C₂³	—	4	32	no	—
260	C₂³	—	4	16	no	—
261	C₂³	—	4	16	no	—
262	C₂³	C₂³×C₄×C₂₃	1	16	yes	—
263	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
264	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
265	C₂³	C₂×#41×C₂₃	1	4	yes	—
266	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
267	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
268	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
269	D₄	—	2	128	no	—
270	D₄	—	4	32	no	—
271	C₂×C₄	—	2	8	no	—
272	C₂×C₄	—	2	8	no	—
273	C₂×C₄	—	2	2	no	—
274	C₂×C₄	—	2	2	no	—
275	C₂×C₄	—	2	8	no	—
276	C₂×C₄	—	2	32	no	—
277	C₂×C₄	—	2	8	no	—
278	C₂×C₄	—	2	8	no	—
279	C₂×C₄	—	2	8	no	—
280	C₂×C₄	—	4	64	no	—
281	C₂×C₄	—	4	16	no	—
282	C₂×C₄	C₄×D₄×C₂₃	1	32	yes	complemented
283	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
284	C₂×C₄	C₂³×C₄×C₂₃	1	8	yes	—
285	C₂×C₄	C₂²×D₄×C₂₃	1	16	yes	—
286	C₂×C₄	C₂²×D₄×C₂₃	1	8	yes	—
287	C₂×C₄	C₂×#41×C₂₃	1	8	yes	—
288	C₂²	—	2	32	no	—
289	C₂²	—	2	16	no	—
290	C₂²	—	4	8	no	—
291	C₂²	—	4	16	no	—
292	C₂²	—	4	8	no	—
293	C₂²	—	4	64	no	—
294	C₂²	C₂×C₄×D₄×C₂₃	1	8	yes	—
295	C₂²	C₂₃×#518	1	4	yes	—
296	C₂²	D₄²×C₂₃	1	4	yes	—
297	C₂²	C₂₃×#550	1	8	yes	—
298	C₂²	C₂₃×#559	1	4	yes	—
299	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
300	C₂²	C₂³×D₄×C₂₃	1	2	yes	—
301	C₂²	C₂²×#41×C₂₃	1	2	yes	—
302	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
303	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
304	C₄	—	2	4	no	—
305	C₄	—	2	16	no	—
306	C₄	—	4	8	no	—
307	C₄	C₂×C₄×D₄×C₂₃	1	16	yes	complemented
308	C₂	—	4	16	no	—
309	C₂	C₂₃×#2366	1	8	yes	direct product factor
310	C₂	C₂²×C₄×D₄×C₂₃	1	2	yes	—
311	C₂	C₂×C₂₃×#518	1	1	yes	characteristic
312	C₂	C₂×D₄²×C₂₃	1	1	yes	characteristic
313	C₂	C₂×C₂₃×#550	1	2	yes	—
314	C₂	C₂×C₂₃×#559	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₂₃	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂²×C₂₃×#127	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×D₄×C₂₃	C₂	semidirect
3. C₂₃×#2366	C₂	direct (N × H)
4. C₂×C₂₃×#390	C₂	semidirect
5. C₂×C₂₃×#386	C₂	semidirect
6. C₂×C₄×C₄⋊C₄×C₂₃	C₂	semidirect
10. C₂×C₂₃×#127	C₄	semidirect
13. C₂×C₄×D₄×C₂₃	C₂²	semidirect
20. C₂₃×#390	C₂²	semidirect
21. C₂₃×#386	C₂²	semidirect
22. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
29. C₂²×D₄×C₂₃	C₂×C₄	semidirect
30. C₂²×D₄×C₂₃	C₂×C₄	semidirect
40. C₂₃×#127	C₂×C₄	semidirect
43. C₂×C₄⋊C₄×C₂₃	D₄	semidirect
51. C₂×C₄²×C₂₃	C₂×C₄	semidirect
68. C₂×D₄×C₂₃	C₂²×C₄	semidirect
69. C₂×D₄×C₂₃	C₂²×C₄	semidirect
90. C₄⋊C₄×C₂₃	C₂×D₄	semidirect
94. C₄²×C₂₃	C₂²×C₄	semidirect
95. C₂×#2366	C₂₃	direct (N × H)
125. C₂×C₄×C₂₃	C₄×D₄	semidirect
132. C₂²×C₄×D₄	C₂×C₂₃	semidirect
133. #2366	C₂×C₂₃	direct (N × H)
134. C₂×#390	C₂×C₂₃	semidirect
135. C₂×#386	C₂×C₂₃	semidirect
136. C₂×C₄×C₄⋊C₄	C₂×C₂₃	semidirect
156. C₄×C₂₃	C₂×C₄×D₄	semidirect
160. C₂×#127	C₄×C₂₃	semidirect
163. C₂×C₄×D₄	C₂²×C₂₃	semidirect
170. #390	C₂²×C₂₃	semidirect
171. #386	C₂²×C₂₃	semidirect
172. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
175. C₂×C₂₃	#2366	direct (N × H)
186. C₂²×D₄	C₂×C₄×C₂₃	semidirect
187. C₂²×D₄	C₂×C₄×C₂₃	semidirect
197. #127	C₂×C₄×C₂₃	semidirect
200. C₂×C₄⋊C₄	D₄×C₂₃	semidirect
208. C₂×C₄²	C₂×C₄×C₂₃	semidirect
212. C₂₃	C₂×#2366	direct (N × H)
226. C₂×D₄	C₂²×C₄×C₂₃	semidirect
227. C₂×D₄	C₂²×C₄×C₂₃	semidirect
248. C₄⋊C₄	C₂×D₄×C₂₃	semidirect
252. C₄²	C₂²×C₄×C₂₃	semidirect
282. C₂×C₄	C₄×D₄×C₂₃	semidirect
307. C₄	C₂×C₄×D₄×C₂₃	semidirect
309. C₂	C₂₃×#2366	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×#127	2
C₂²×C₄×D₄×C₂₃	2
C₂₃×#2366	2
C₂×C₂₃×#390	2
C₂×C₂₃×#386	2
C₂×C₄×C₄⋊C₄×C₂₃	2
C₂×#2366	23

Subgroups — C2×C23×#2366 #19181765

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#2366 #19181765