Subgroups — C₂×C₂₃×#551 #15671088

Order 2944.

1328 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#551	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₂₃×#126	C₂	1	2	yes	maximal, complemented
3	C₂×C₂₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#123	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#123	C₂	1	2	yes	maximal, complemented
6	C₂×C₂₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
7	C₂×C₂₃×#120	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×D₄×C₂₃	C₂	1	2	yes	maximal, complemented
9	C₂×C₂₃×#117	C₂	1	2	yes	maximal, complemented
10	C₂²×C₂²⋊C₄×C₂₃	C₂	1	2	yes	maximal, complemented
11	C₂⁵×C₂₃	C₂²	1	1	yes	characteristic
12	C₂²×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
13	C₂²×D₄×C₂₃	C₂²	1	2	yes	—
14	C₂²×D₄×C₂₃	C₂²	1	1	yes	characteristic
15	C₂³×C₄×C₂₃	C₂²	1	2	yes	—
16	C₂³×C₄×C₂₃	C₂²	1	2	yes	—
17	C₂³×C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
18	C₂₃×#126	C₂²	1	16	yes	complemented
19	C₂₃×#124	C₂²	1	8	yes	complemented
20	C₂₃×#123	C₂²	1	8	yes	complemented
21	C₂₃×#123	C₂²	1	16	yes	complemented
22	C₂₃×C₂²⋊Q₈	C₂²	1	16	yes	complemented
23	C₂₃×#120	C₂²	1	8	yes	—
24	C₄×D₄×C₂₃	C₂²	1	16	yes	complemented
25	C₂₃×#117	C₂²	1	16	yes	complemented
26	C₂×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
27	C₂×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
28	C₂×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
29	C₂×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
30	C₂×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
31	C₂×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
32	C₂×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
33	C₂×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
35	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₄×C₂₃	C₂²	1	16	yes	complemented
37	C₂×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
38	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₄²×C₂₃	C₂²	1	2	yes	complemented
41	C₂⁴×C₂₃	—	2	8	no	—
42	C₂⁴×C₂₃	—	4	2	no	—
43	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
44	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
45	C₂⁴×C₂₃	C₂³	1	4	yes	—
46	C₂⁴×C₂₃	C₂³	1	2	yes	—
47	C₂×Q₈×C₂₃	—	4	2	no	—
48	C₂×Q₈×C₂₃	C₂³	1	4	yes	complemented
49	C₂×D₄×C₂₃	—	2	8	no	—
50	C₂×D₄×C₂₃	—	4	2	no	—
51	C₂×D₄×C₂₃	C₂³	1	8	yes	—
52	C₂×D₄×C₂₃	C₂³	1	4	yes	—
53	C₂²×C₄×C₂₃	—	2	8	no	—
54	C₂²×C₄×C₂₃	—	4	4	no	—
55	C₂²×C₄×C₂₃	—	4	2	no	—
56	C₂²×C₄×C₂₃	C₂³	1	8	yes	—
57	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
58	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
59	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
60	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
62	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
63	C₂²×C₄×C₂₃	C₂³	1	8	yes	—
64	C₂²×C₄×C₂₃	C₂³	1	4	yes	complemented
65	C₄⋊C₄×C₂₃	C₂³	1	8	yes	complemented
66	C₄⋊C₄×C₂₃	C₂³	1	8	yes	complemented
67	C₄⋊C₄×C₂₃	C₂³	1	8	yes	complemented
68	C₄⋊C₄×C₂₃	C₂³	1	8	yes	complemented
69	C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
70	C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
71	C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
72	C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
73	C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
74	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
75	C₂²⋊C₄×C₂₃	C₂³	1	8	yes	complemented
76	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	complemented
77	C₄²×C₂₃	C₂³	1	4	yes	complemented
78	C₄²×C₂₃	C₂³	1	8	yes	complemented
79	C₂³×C₂₃	—	2	4	no	—
80	C₂³×C₂₃	—	2	4	no	—
81	C₂³×C₂₃	—	2	4	no	—
82	C₂³×C₂₃	—	2	16	no	—
83	C₂³×C₂₃	—	2	4	no	—
84	C₂³×C₂₃	—	2	2	no	—
85	C₂³×C₂₃	—	2	2	no	—
86	C₂³×C₂₃	—	4	4	no	—
87	C₂³×C₂₃	—	4	16	no	—
88	C₂³×C₂₃	#41	1	8	yes	—
89	C₂³×C₂₃	C₂⁴	1	2	yes	—
90	C₂³×C₂₃	C₂⁴	1	2	yes	—
91	C₂³×C₂₃	C₂⁴	1	4	yes	—
92	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
93	Q₈×C₂₃	—	4	4	no	—
94	D₄×C₂₃	—	2	16	no	—
95	D₄×C₂₃	—	4	4	no	—
96	C₂×C₄×C₂₃	—	2	16	no	—
97	C₂×C₄×C₂₃	—	2	4	no	—
98	C₂×C₄×C₂₃	—	2	4	no	—
99	C₂×C₄×C₂₃	—	2	4	no	—
100	C₂×C₄×C₂₃	—	2	4	no	—
101	C₂×C₄×C₂₃	—	2	4	no	—
102	C₂×C₄×C₂₃	—	2	2	no	—
103	C₂×C₄×C₂₃	—	4	8	no	—
104	C₂×C₄×C₂₃	—	4	4	no	—
105	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
106	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
107	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
108	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
109	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
110	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
111	C₂×#551	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂²×C₂₃	—	2	16	no	—
113	C₂²×C₂₃	—	2	4	no	—
114	C₂²×C₂₃	—	2	4	no	—
115	C₂²×C₂₃	—	2	4	no	—
116	C₂²×C₂₃	—	2	4	no	—
117	C₂²×C₂₃	—	2	2	no	—
118	C₂²×C₂₃	—	2	2	no	—
119	C₂²×C₂₃	—	4	16	no	—
120	C₂²×C₂₃	—	4	4	no	—
121	C₂²×C₂₃	—	4	4	no	—
122	C₂²×C₂₃	C₂×#41	1	8	yes	—
123	C₂²×C₂₃	C₂×#41	1	4	yes	—
124	C₂²×C₂₃	H(5,𝔽₂)	1	2	yes	—
125	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
126	C₄×C₂₃	—	2	4	no	—
127	C₄×C₂₃	—	2	4	no	—
128	C₄×C₂₃	—	2	4	no	—
129	C₄×C₂₃	—	2	4	no	—
130	C₄×C₂₃	—	2	4	no	—
131	C₄×C₂₃	—	2	2	no	—
132	#551	C₂×C₂₃	1	16	yes	direct product factor
133	C₂×#126	C₂×C₂₃	1	2	yes	complemented
134	C₂×#124	C₂×C₂₃	1	1	yes	characteristic, complemented
135	C₂×#123	C₂×C₂₃	1	1	yes	characteristic, complemented
136	C₂×#123	C₂×C₂₃	1	2	yes	complemented
137	C₂×C₂²⋊Q₈	C₂×C₂₃	1	2	yes	complemented
138	C₂×#120	C₂×C₂₃	1	1	yes	characteristic
139	C₂×C₄×D₄	C₂×C₂₃	1	2	yes	complemented
140	C₂×#117	C₂×C₂₃	1	2	yes	complemented
141	C₂²×C₂²⋊C₄	C₂×C₂₃	1	2	yes	complemented
142	C₂×C₂₃	—	2	8	no	—
143	C₂×C₂₃	—	4	2	no	—
144	C₂×C₂₃	—	4	2	no	—
145	C₂×C₂₃	#551	1	4	yes	direct product factor
146	C₂×C₂₃	C₂²×#41	1	2	yes	—
147	C₂×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
148	C₂⁵	C₂²×C₂₃	1	1	yes	characteristic
149	C₂²×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
150	C₂²×D₄	C₂²×C₂₃	1	2	yes	—
151	C₂²×D₄	C₂²×C₂₃	1	1	yes	characteristic
152	C₂³×C₄	C₂²×C₂₃	1	2	yes	—
153	C₂³×C₄	C₂²×C₂₃	1	2	yes	—
154	C₂³×C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
155	#126	C₂²×C₂₃	1	16	yes	complemented
156	#124	C₂²×C₂₃	1	8	yes	complemented
157	#123	C₂²×C₂₃	1	8	yes	complemented
158	#123	C₂²×C₂₃	1	16	yes	complemented
159	C₂²⋊Q₈	C₂²×C₂₃	1	16	yes	complemented
160	#120	C₂²×C₂₃	1	8	yes	—
161	C₄×D₄	C₂²×C₂₃	1	16	yes	complemented
162	#117	C₂²×C₂₃	1	16	yes	complemented
163	C₂×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
164	C₂×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
165	C₂×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
166	C₂×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
167	C₂×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
168	C₂×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
169	C₂×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
170	C₂×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
171	C₂×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
172	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
173	C₂×C₂²⋊C₄	C₂²×C₂₃	1	16	yes	complemented
174	C₂×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
175	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
176	C₂×C₄²	C₂²×C₂₃	1	1	yes	characteristic, complemented
177	C₂×C₄²	C₂²×C₂₃	1	2	yes	complemented
178	C₂₃	C₂×#551	1	1	yes	characteristic, direct product factor, Sylow
179	C₂⁴	—	2	8	no	—
180	C₂⁴	—	4	2	no	—
181	C₂⁴	C₂³×C₂₃	1	1	yes	characteristic
182	C₂⁴	C₂³×C₂₃	1	1	yes	characteristic
183	C₂⁴	C₂³×C₂₃	1	4	yes	—
184	C₂⁴	C₂³×C₂₃	1	2	yes	—
185	C₂×Q₈	—	4	2	no	—
186	C₂×Q₈	C₂³×C₂₃	1	4	yes	complemented
187	C₂×D₄	—	2	8	no	—
188	C₂×D₄	—	4	2	no	—
189	C₂×D₄	C₂³×C₂₃	1	8	yes	—
190	C₂×D₄	C₂³×C₂₃	1	4	yes	—
191	C₂²×C₄	—	2	8	no	—
192	C₂²×C₄	—	4	4	no	—
193	C₂²×C₄	—	4	2	no	—
194	C₂²×C₄	C₂³×C₂₃	1	2	yes	—
195	C₂²×C₄	C₂³×C₂₃	1	2	yes	—
196	C₂²×C₄	C₂³×C₂₃	1	2	yes	—
197	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
198	C₂²×C₄	C₂³×C₂₃	1	2	yes	—
199	C₂²×C₄	C₂³×C₂₃	1	2	yes	—
200	C₂²×C₄	C₂³×C₂₃	1	8	yes	—
201	C₂²×C₄	C₂³×C₂₃	1	8	yes	—
202	C₂²×C₄	C₂³×C₂₃	1	4	yes	complemented
203	C₄⋊C₄	C₂³×C₂₃	1	8	yes	complemented
204	C₄⋊C₄	C₂³×C₂₃	1	8	yes	complemented
205	C₄⋊C₄	C₂³×C₂₃	1	8	yes	complemented
206	C₄⋊C₄	C₂³×C₂₃	1	8	yes	complemented
207	C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
208	C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
209	C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
210	C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
211	C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
212	C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
213	C₂²⋊C₄	C₂³×C₂₃	1	8	yes	complemented
214	C₂²⋊C₄	C₂³×C₂₃	1	4	yes	complemented
215	C₄²	C₂³×C₂₃	1	4	yes	complemented
216	C₄²	C₂³×C₂₃	1	8	yes	complemented
217	C₂³	—	2	4	no	—
218	C₂³	—	2	4	no	—
219	C₂³	—	2	4	no	—
220	C₂³	—	2	16	no	—
221	C₂³	—	2	4	no	—
222	C₂³	—	2	2	no	—
223	C₂³	—	2	2	no	—
224	C₂³	—	4	4	no	—
225	C₂³	—	4	16	no	—
226	C₂³	#41×C₂₃	1	8	yes	—
227	C₂³	C₂⁴×C₂₃	1	2	yes	—
228	C₂³	C₂⁴×C₂₃	1	2	yes	—
229	C₂³	C₂⁴×C₂₃	1	4	yes	—
230	C₂³	C₂⁴×C₂₃	1	1	yes	characteristic
231	Q₈	—	4	4	no	—
232	D₄	—	2	16	no	—
233	D₄	—	4	4	no	—
234	C₂×C₄	—	2	16	no	—
235	C₂×C₄	—	2	4	no	—
236	C₂×C₄	—	2	4	no	—
237	C₂×C₄	—	2	4	no	—
238	C₂×C₄	—	2	4	no	—
239	C₂×C₄	—	2	4	no	—
240	C₂×C₄	—	2	2	no	—
241	C₂×C₄	—	4	8	no	—
242	C₂×C₄	—	4	4	no	—
243	C₂×C₄	C₂⁴×C₂₃	1	4	yes	—
244	C₂×C₄	C₂⁴×C₂₃	1	4	yes	—
245	C₂×C₄	C₂⁴×C₂₃	1	4	yes	—
246	C₂×C₄	C₂⁴×C₂₃	1	2	yes	—
247	C₂×C₄	C₂⁴×C₂₃	1	4	yes	—
248	C₂×C₄	C₂⁴×C₂₃	1	4	yes	—
249	C₂²	—	2	16	no	—
250	C₂²	—	2	4	no	—
251	C₂²	—	2	4	no	—
252	C₂²	—	2	4	no	—
253	C₂²	—	2	4	no	—
254	C₂²	—	2	2	no	—
255	C₂²	—	2	2	no	—
256	C₂²	—	4	16	no	—
257	C₂²	—	4	4	no	—
258	C₂²	—	4	4	no	—
259	C₂²	C₂×#41×C₂₃	1	8	yes	—
260	C₂²	C₂×#41×C₂₃	1	4	yes	—
261	C₂²	C₂₃×H(5,𝔽₂)	1	2	yes	—
262	C₂²	C₂⁵×C₂₃	1	1	yes	characteristic
263	C₄	—	2	4	no	—
264	C₄	—	2	4	no	—
265	C₄	—	2	4	no	—
266	C₄	—	2	4	no	—
267	C₄	—	2	4	no	—
268	C₄	—	2	2	no	—
269	C₂	—	2	8	no	—
270	C₂	—	4	2	no	—
271	C₂	—	4	2	no	—
272	C₂	C₂₃×#551	1	4	yes	direct product factor
273	C₂	C₂²×#41×C₂₃	1	2	yes	—
274	C₂	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#120	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#551	C₂	direct (N × H)
2. C₂×C₂₃×#126	C₂	semidirect
3. C₂×C₂₃×#124	C₂	semidirect
4. C₂×C₂₃×#123	C₂	semidirect
5. C₂×C₂₃×#123	C₂	semidirect
6. C₂×C₂₃×C₂²⋊Q₈	C₂	semidirect
8. C₂×C₄×D₄×C₂₃	C₂	semidirect
9. C₂×C₂₃×#117	C₂	semidirect
10. C₂²×C₂²⋊C₄×C₂₃	C₂	semidirect
12. C₂²×Q₈×C₂₃	C₂²	semidirect
17. C₂³×C₄×C₂₃	C₂²	semidirect
18. C₂₃×#126	C₂²	semidirect
19. C₂₃×#124	C₂²	semidirect
20. C₂₃×#123	C₂²	semidirect
21. C₂₃×#123	C₂²	semidirect
22. C₂₃×C₂²⋊Q₈	C₂²	semidirect
24. C₄×D₄×C₂₃	C₂²	semidirect
25. C₂₃×#117	C₂²	semidirect
26. C₂×C₄⋊C₄×C₂₃	C₂²	semidirect
27. C₂×C₄⋊C₄×C₂₃	C₂²	semidirect
28. C₂×C₄⋊C₄×C₂₃	C₂²	semidirect
29. C₂×C₄⋊C₄×C₂₃	C₂²	semidirect
36. C₂×C₂²⋊C₄×C₂₃	C₂²	semidirect
37. C₂×C₂²⋊C₄×C₂₃	C₂²	semidirect
38. C₂×C₂²⋊C₄×C₂₃	C₂²	semidirect
39. C₂×C₄²×C₂₃	C₂²	semidirect
40. C₂×C₄²×C₂₃	C₂²	semidirect
48. C₂×Q₈×C₂₃	C₂³	semidirect
64. C₂²×C₄×C₂₃	C₂³	semidirect
65. C₄⋊C₄×C₂₃	C₂³	semidirect
66. C₄⋊C₄×C₂₃	C₂³	semidirect
67. C₄⋊C₄×C₂₃	C₂³	semidirect
68. C₄⋊C₄×C₂₃	C₂³	semidirect
75. C₂²⋊C₄×C₂₃	C₂³	semidirect
76. C₂²⋊C₄×C₂₃	C₂³	semidirect
77. C₄²×C₂₃	C₂³	semidirect
78. C₄²×C₂₃	C₂³	semidirect
111. C₂×#551	C₂₃	direct (N × H)
132. #551	C₂×C₂₃	direct (N × H)
133. C₂×#126	C₂×C₂₃	semidirect
134. C₂×#124	C₂×C₂₃	semidirect
135. C₂×#123	C₂×C₂₃	semidirect
136. C₂×#123	C₂×C₂₃	semidirect
137. C₂×C₂²⋊Q₈	C₂×C₂₃	semidirect
139. C₂×C₄×D₄	C₂×C₂₃	semidirect
140. C₂×#117	C₂×C₂₃	semidirect
141. C₂²×C₂²⋊C₄	C₂×C₂₃	semidirect
145. C₂×C₂₃	#551	direct (N × H)
149. C₂²×Q₈	C₂²×C₂₃	semidirect
154. C₂³×C₄	C₂²×C₂₃	semidirect
155. #126	C₂²×C₂₃	semidirect
156. #124	C₂²×C₂₃	semidirect
157. #123	C₂²×C₂₃	semidirect
158. #123	C₂²×C₂₃	semidirect
159. C₂²⋊Q₈	C₂²×C₂₃	semidirect
161. C₄×D₄	C₂²×C₂₃	semidirect
162. #117	C₂²×C₂₃	semidirect
163. C₂×C₄⋊C₄	C₂²×C₂₃	semidirect
164. C₂×C₄⋊C₄	C₂²×C₂₃	semidirect
165. C₂×C₄⋊C₄	C₂²×C₂₃	semidirect
166. C₂×C₄⋊C₄	C₂²×C₂₃	semidirect
173. C₂×C₂²⋊C₄	C₂²×C₂₃	semidirect
174. C₂×C₂²⋊C₄	C₂²×C₂₃	semidirect
175. C₂×C₂²⋊C₄	C₂²×C₂₃	semidirect
176. C₂×C₄²	C₂²×C₂₃	semidirect
177. C₂×C₄²	C₂²×C₂₃	semidirect
178. C₂₃	C₂×#551	direct (N × H)
186. C₂×Q₈	C₂³×C₂₃	semidirect
202. C₂²×C₄	C₂³×C₂₃	semidirect
203. C₄⋊C₄	C₂³×C₂₃	semidirect
204. C₄⋊C₄	C₂³×C₂₃	semidirect
205. C₄⋊C₄	C₂³×C₂₃	semidirect
206. C₄⋊C₄	C₂³×C₂₃	semidirect
213. C₂²⋊C₄	C₂³×C₂₃	semidirect
214. C₂²⋊C₄	C₂³×C₂₃	semidirect
215. C₄²	C₂³×C₂₃	semidirect
216. C₄²	C₂³×C₂₃	semidirect
272. C₂	C₂₃×#551	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×#551	2
C₂×C₂₃×#126	2
C₂×C₂₃×#124	2
C₂×C₂₃×#123	2
C₂×C₂₃×C₂²⋊Q₈	2
C₂×C₂₃×#120	2
C₂×C₄×D₄×C₂₃	2
C₂×C₂₃×#117	2
C₂²×C₂²⋊C₄×C₂₃	2
C₂×#551	23

Subgroups — C2×C23×#551 #15671088

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#551 #15671088