Subgroups — C₂²×C₂₃×#478 #19208101

Order 5888.

2574 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×#478	C₂	1	24	yes	maximal, direct product factor
4	C₂²×C₂₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₂₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₂₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₂₃×#102	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₂₃×#102	C₂	1	1	yes	maximal, characteristic
9	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₂₃	—	2	1	no	—
11	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
13	C₂×C₂₃×#125	—	2	6	no	—
14	C₂×C₂₃×#125	C₂²	1	12	yes	complemented
15	C₂×C₄×D₄×C₂₃	—	2	6	no	—
16	C₂×C₄×D₄×C₂₃	C₂²	1	12	yes	—
17	C₂²×C₄⋊C₄×C₂₃	—	2	1	no	—
18	C₂²×C₄⋊C₄×C₂₃	—	2	1	no	—
19	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₂₃	—	2	1	no	—
23	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
24	C₂₃×#478	C₂²	1	64	yes	direct product factor
25	C₂×C₂₃×#107	C₂²	1	12	yes	complemented
26	C₂×C₂₃×#106	C₂²	1	12	yes	complemented
27	C₂×C₂₃×C₄⋊C₈	C₂²	1	12	yes	complemented
28	C₂×C₂₃×#102	C₂²	1	12	yes	—
29	C₂×C₂₃×#102	C₂²	1	12	yes	—
30	C₂⁵×C₂₃	—	2	1	no	—
31	C₂²×D₄×C₂₃	—	2	3	no	—
32	C₂²×D₄×C₂₃	—	2	4	no	—
33	C₂²×D₄×C₂₃	Q₈	1	8	yes	—
34	C₂²×D₄×C₂₃	C₂³	1	6	yes	—
35	C₂³×C₄×C₂₃	—	2	1	no	—
36	C₂³×C₄×C₂₃	—	2	1	no	—
37	C₂³×C₄×C₂₃	—	2	1	no	—
38	C₂³×C₄×C₂₃	—	2	12	no	—
39	C₂³×C₄×C₂₃	—	4	8	no	—
40	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₂₃	—	2	4	no	—
44	C₂²×C₈×C₂₃	—	2	4	no	—
45	C₂²×C₈×C₂₃	C₂³	1	6	yes	—
46	C₂²×C₈×C₂₃	C₂³	1	6	yes	—
47	C₂₃×#125	—	2	24	no	—
48	C₂₃×#125	C₂³	1	16	yes	complemented
49	C₄×D₄×C₂₃	—	2	24	no	—
50	C₄×D₄×C₂₃	C₂³	1	16	yes	—
51	C₂×C₄⋊C₄×C₂₃	—	2	12	no	—
52	C₂×C₄⋊C₄×C₂₃	—	2	12	no	—
53	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
54	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
55	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
56	C₂×C₄⋊C₄×C₂₃	C₂³	1	6	yes	—
57	C₂×C₄⋊C₄×C₂₃	C₂³	1	6	yes	—
58	C₂×C₄⋊C₄×C₂₃	C₂³	1	6	yes	—
59	C₂×C₂²⋊C₄×C₂₃	—	2	12	no	—
60	C₂×C₄²×C₂₃	D₄	1	6	yes	—
61	C₂×C₄²×C₂₃	C₂³	1	6	yes	—
62	C₂₃×#107	C₂³	1	16	yes	complemented
63	C₂₃×#106	C₂³	1	16	yes	complemented
64	C₂₃×C₄⋊C₈	C₂³	1	16	yes	complemented
65	C₂₃×#102	C₂³	1	16	yes	—
66	C₂₃×#102	C₂³	1	16	yes	—
67	C₂⁴×C₂₃	—	2	8	no	—
68	C₂⁴×C₂₃	—	2	6	no	—
69	C₂⁴×C₂₃	—	4	4	no	—
70	C₂⁴×C₂₃	—	4	4	no	—
71	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
72	C₂×D₄×C₂₃	—	2	24	no	—
73	C₂×D₄×C₂₃	—	2	6	no	—
74	C₂×D₄×C₂₃	—	2	12	no	—
75	C₂×D₄×C₂₃	C₂×Q₈	1	24	yes	—
76	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
77	C₂²×C₄×C₂₃	—	2	4	no	—
78	C₂²×C₄×C₂₃	—	2	4	no	—
79	C₂²×C₄×C₂₃	—	2	6	no	—
80	C₂²×C₄×C₂₃	—	2	6	no	—
81	C₂²×C₄×C₂₃	—	2	6	no	—
82	C₂²×C₄×C₂₃	—	2	16	no	—
83	C₂²×C₄×C₂₃	—	4	48	no	—
84	C₂²×C₄×C₂₃	—	4	4	no	—
85	C₂²×C₄×C₂₃	—	4	4	no	—
86	C₂²×C₄×C₂₃	—	4	4	no	—
87	C₂²×C₄×C₂₃	C₂×D₄	1	6	yes	—
88	C₂²×C₄×C₂₃	C₂×D₄	1	6	yes	—
89	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
90	C₂²×C₄×C₂₃	C₂×Q₈	1	4	yes	—
91	C₂²×C₄×C₂₃	#41	1	4	yes	—
92	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
93	C₂×C₈×C₂₃	—	2	12	no	—
94	C₂×C₈×C₂₃	—	2	12	no	—
95	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
96	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
97	C₄⋊C₄×C₂₃	—	2	16	no	—
98	C₄⋊C₄×C₂₃	—	2	16	no	—
99	C₄⋊C₄×C₂₃	—	2	6	no	—
100	C₄⋊C₄×C₂₃	—	2	6	no	—
101	C₄⋊C₄×C₂₃	—	2	6	no	—
102	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
103	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
104	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
105	C₂²⋊C₄×C₂₃	—	2	16	no	—
106	C₄²×C₂₃	C₂×D₄	1	12	yes	—
107	C₄²×C₂₃	C₂⁴	1	4	yes	—
108	C₂²×#478	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂³×C₂₃	—	2	24	no	—
110	C₂³×C₂₃	—	2	4	no	—
111	C₂³×C₂₃	—	4	12	no	—
112	C₂³×C₂₃	—	4	12	no	—
113	C₂³×C₂₃	—	4	32	no	—
114	C₂³×C₂₃	C₂²⋊Q₈	1	4	yes	—
115	C₂³×C₂₃	#135	1	4	yes	—
116	C₂³×C₂₃	AGL(1,ℤ/8)	1	4	yes	—
117	C₂³×C₂₃	C₂²×D₄	1	3	yes	—
118	D₄×C₂₃	—	2	24	no	—
119	D₄×C₂₃	—	2	4	no	—
120	D₄×C₂₃	C₂²×Q₈	1	8	yes	—
121	C₂×C₄×C₂₃	—	2	12	no	—
122	C₂×C₄×C₂₃	—	2	12	no	—
123	C₂×C₄×C₂₃	—	2	4	no	—
124	C₂×C₄×C₂₃	—	2	4	no	—
125	C₂×C₄×C₂₃	—	2	4	no	—
126	C₂×C₄×C₂₃	—	4	32	no	—
127	C₂×C₄×C₂₃	—	4	12	no	—
128	C₂×C₄×C₂₃	—	4	12	no	—
129	C₂×C₄×C₂₃	—	4	12	no	—
130	C₂×C₄×C₂₃	C₂²⋊Q₈	1	12	yes	—
131	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
132	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
133	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
134	C₂×C₄×C₂₃	C₂²×Q₈	1	6	yes	—
135	C₂×C₄×C₂₃	C₂×#41	1	6	yes	—
136	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
137	C₈×C₂₃	—	2	4	no	—
138	C₈×C₂₃	—	2	4	no	—
139	C₂²×#125	C₂×C₂₃	1	1	yes	characteristic, complemented
140	C₂²×C₄×D₄	C₂×C₂₃	1	1	yes	characteristic
141	C₂×#478	C₂×C₂₃	1	24	yes	direct product factor
142	C₂²×#107	C₂×C₂₃	1	1	yes	characteristic, complemented
143	C₂²×#106	C₂×C₂₃	1	1	yes	characteristic, complemented
144	C₂²×C₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
145	C₂²×#102	C₂×C₂₃	1	1	yes	characteristic
146	C₂²×#102	C₂×C₂₃	1	1	yes	characteristic
147	C₂²×C₂₃	—	2	8	no	—
148	C₂²×C₂₃	—	4	48	no	—
149	C₂²×C₂₃	—	4	4	no	—
150	C₂²×C₂₃	—	4	4	no	—
151	C₂²×C₂₃	#478	1	16	yes	direct product factor
152	C₂²×C₂₃	C₂×C₂²⋊Q₈	1	6	yes	—
153	C₂²×C₂₃	C₂×#135	1	6	yes	—
154	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	6	yes	—
155	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
156	C₄×C₂₃	—	2	4	no	—
157	C₄×C₂₃	—	2	4	no	—
158	C₄×C₂₃	—	4	4	no	—
159	C₄×C₂₃	—	4	4	no	—
160	C₄×C₂₃	—	4	4	no	—
161	C₄×C₂₃	C₂×C₂²⋊Q₈	1	6	yes	—
162	C₄×C₂₃	C₂³×Q₈	1	1	yes	characteristic
163	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
164	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
165	C₂⁴×C₄	—	2	1	no	—
166	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
167	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
168	C₂×#125	—	2	6	no	—
169	C₂×#125	C₂²×C₂₃	1	12	yes	complemented
170	C₂×C₄×D₄	—	2	6	no	—
171	C₂×C₄×D₄	C₂²×C₂₃	1	12	yes	—
172	C₂²×C₄⋊C₄	—	2	1	no	—
173	C₂²×C₄⋊C₄	—	2	1	no	—
174	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
175	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
176	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
177	C₂²×C₂²⋊C₄	—	2	1	no	—
178	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
179	#478	C₂²×C₂₃	1	64	yes	direct product factor
180	C₂×#107	C₂²×C₂₃	1	12	yes	complemented
181	C₂×#106	C₂²×C₂₃	1	12	yes	complemented
182	C₂×C₄⋊C₈	C₂²×C₂₃	1	12	yes	complemented
183	C₂×#102	C₂²×C₂₃	1	12	yes	—
184	C₂×#102	C₂²×C₂₃	1	12	yes	—
185	C₂×C₂₃	—	4	8	no	—
186	C₂×C₂₃	C₂×#478	1	12	yes	direct product factor
187	C₂×C₂₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
188	C₂×C₂₃	C₂²×#135	1	1	yes	characteristic
189	C₂×C₂₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
190	C₂⁵	—	2	1	no	—
191	C₂²×D₄	—	2	3	no	—
192	C₂²×D₄	—	2	4	no	—
193	C₂²×D₄	Q₈×C₂₃	1	8	yes	—
194	C₂²×D₄	C₂³×C₂₃	1	6	yes	—
195	C₂³×C₄	—	2	1	no	—
196	C₂³×C₄	—	2	1	no	—
197	C₂³×C₄	—	2	1	no	—
198	C₂³×C₄	—	2	12	no	—
199	C₂³×C₄	—	4	8	no	—
200	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
201	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
202	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
203	C₂²×C₈	—	2	4	no	—
204	C₂²×C₈	—	2	4	no	—
205	C₂²×C₈	C₂³×C₂₃	1	6	yes	—
206	C₂²×C₈	C₂³×C₂₃	1	6	yes	—
207	#125	—	2	24	no	—
208	#125	C₂³×C₂₃	1	16	yes	complemented
209	C₄×D₄	—	2	24	no	—
210	C₄×D₄	C₂³×C₂₃	1	16	yes	—
211	C₂×C₄⋊C₄	—	2	12	no	—
212	C₂×C₄⋊C₄	—	2	12	no	—
213	C₂×C₄⋊C₄	—	2	3	no	—
214	C₂×C₄⋊C₄	—	2	3	no	—
215	C₂×C₄⋊C₄	—	2	3	no	—
216	C₂×C₄⋊C₄	C₂³×C₂₃	1	6	yes	—
217	C₂×C₄⋊C₄	C₂³×C₂₃	1	6	yes	—
218	C₂×C₄⋊C₄	C₂³×C₂₃	1	6	yes	—
219	C₂×C₂²⋊C₄	—	2	12	no	—
220	C₂×C₄²	D₄×C₂₃	1	6	yes	—
221	C₂×C₄²	C₂³×C₂₃	1	6	yes	—
222	#107	C₂³×C₂₃	1	16	yes	complemented
223	#106	C₂³×C₂₃	1	16	yes	complemented
224	C₄⋊C₈	C₂³×C₂₃	1	16	yes	complemented
225	#102	C₂³×C₂₃	1	16	yes	—
226	#102	C₂³×C₂₃	1	16	yes	—
227	C₂₃	C₂²×#478	1	1	yes	characteristic, direct product factor, Sylow
228	C₂⁴	—	2	8	no	—
229	C₂⁴	—	2	6	no	—
230	C₂⁴	—	4	4	no	—
231	C₂⁴	—	4	4	no	—
232	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
233	C₂×D₄	—	2	24	no	—
234	C₂×D₄	—	2	6	no	—
235	C₂×D₄	—	2	12	no	—
236	C₂×D₄	C₂×Q₈×C₂₃	1	24	yes	—
237	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
238	C₂²×C₄	—	2	4	no	—
239	C₂²×C₄	—	2	4	no	—
240	C₂²×C₄	—	2	6	no	—
241	C₂²×C₄	—	2	6	no	—
242	C₂²×C₄	—	2	6	no	—
243	C₂²×C₄	—	2	16	no	—
244	C₂²×C₄	—	4	48	no	—
245	C₂²×C₄	—	4	4	no	—
246	C₂²×C₄	—	4	4	no	—
247	C₂²×C₄	—	4	4	no	—
248	C₂²×C₄	C₂×D₄×C₂₃	1	6	yes	—
249	C₂²×C₄	C₂×D₄×C₂₃	1	6	yes	—
250	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
251	C₂²×C₄	C₂×Q₈×C₂₃	1	4	yes	—
252	C₂²×C₄	#41×C₂₃	1	4	yes	—
253	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
254	C₂×C₈	—	2	12	no	—
255	C₂×C₈	—	2	12	no	—
256	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
257	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
258	C₄⋊C₄	—	2	16	no	—
259	C₄⋊C₄	—	2	16	no	—
260	C₄⋊C₄	—	2	6	no	—
261	C₄⋊C₄	—	2	6	no	—
262	C₄⋊C₄	—	2	6	no	—
263	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
264	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
265	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
266	C₂²⋊C₄	—	2	16	no	—
267	C₄²	C₂×D₄×C₂₃	1	12	yes	—
268	C₄²	C₂⁴×C₂₃	1	4	yes	—
269	C₂³	—	2	4	no	—
270	C₂³	—	2	24	no	—
271	C₂³	—	4	12	no	—
272	C₂³	—	4	12	no	—
273	C₂³	—	4	32	no	—
274	C₂³	C₂₃×C₂²⋊Q₈	1	4	yes	—
275	C₂³	C₂₃×#135	1	4	yes	—
276	C₂³	C₂₃×AGL(1,ℤ/8)	1	4	yes	—
277	C₂³	C₂²×D₄×C₂₃	1	3	yes	—
278	D₄	—	2	4	no	—
279	D₄	—	2	24	no	—
280	D₄	C₂²×Q₈×C₂₃	1	8	yes	—
281	C₂×C₄	—	2	12	no	—
282	C₂×C₄	—	2	12	no	—
283	C₂×C₄	—	2	4	no	—
284	C₂×C₄	—	2	4	no	—
285	C₂×C₄	—	2	4	no	—
286	C₂×C₄	—	4	32	no	—
287	C₂×C₄	—	4	12	no	—
288	C₂×C₄	—	4	12	no	—
289	C₂×C₄	—	4	12	no	—
290	C₂×C₄	C₂₃×C₂²⋊Q₈	1	12	yes	—
291	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
292	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
293	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
294	C₂×C₄	C₂²×Q₈×C₂₃	1	6	yes	—
295	C₂×C₄	C₂×#41×C₂₃	1	6	yes	—
296	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
297	C₈	—	2	4	no	—
298	C₈	—	2	4	no	—
299	C₂²	—	2	8	no	—
300	C₂²	—	4	4	no	—
301	C₂²	—	4	4	no	—
302	C₂²	—	4	48	no	—
303	C₂²	C₂₃×#478	1	16	yes	direct product factor
304	C₂²	C₂×C₂₃×C₂²⋊Q₈	1	6	yes	—
305	C₂²	C₂×C₂₃×#135	1	6	yes	—
306	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	6	yes	—
307	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
308	C₄	—	2	4	no	—
309	C₄	—	2	4	no	—
310	C₄	—	4	4	no	—
311	C₄	—	4	4	no	—
312	C₄	—	4	4	no	—
313	C₄	C₂×C₂₃×C₂²⋊Q₈	1	6	yes	—
314	C₄	C₂³×Q₈×C₂₃	1	1	yes	characteristic
315	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
316	C₂	—	4	8	no	—
317	C₂	C₂×C₂₃×#478	1	12	yes	direct product factor
318	C₂	C₂²×C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
319	C₂	C₂²×C₂₃×#135	1	1	yes	characteristic
320	C₂	C₂²×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₂₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂³×D₄×C₂₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂₃×#125	C₂	semidirect
3. C₂×C₂₃×#478	C₂	direct (N × H)
4. C₂²×C₂₃×#107	C₂	semidirect
5. C₂²×C₂₃×#106	C₂	semidirect
6. C₂²×C₂₃×C₄⋊C₈	C₂	semidirect
14. C₂×C₂₃×#125	C₂²	semidirect
24. C₂₃×#478	C₂²	direct (N × H)
25. C₂×C₂₃×#107	C₂²	semidirect
26. C₂×C₂₃×#106	C₂²	semidirect
27. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
48. C₂₃×#125	C₂³	semidirect
62. C₂₃×#107	C₂³	semidirect
63. C₂₃×#106	C₂³	semidirect
64. C₂₃×C₄⋊C₈	C₂³	semidirect
108. C₂²×#478	C₂₃	direct (N × H)
139. C₂²×#125	C₂×C₂₃	semidirect
141. C₂×#478	C₂×C₂₃	direct (N × H)
142. C₂²×#107	C₂×C₂₃	semidirect
143. C₂²×#106	C₂×C₂₃	semidirect
144. C₂²×C₄⋊C₈	C₂×C₂₃	semidirect
151. C₂²×C₂₃	#478	direct (N × H)
169. C₂×#125	C₂²×C₂₃	semidirect
179. #478	C₂²×C₂₃	direct (N × H)
180. C₂×#107	C₂²×C₂₃	semidirect
181. C₂×#106	C₂²×C₂₃	semidirect
182. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
186. C₂×C₂₃	C₂×#478	direct (N × H)
208. #125	C₂³×C₂₃	semidirect
222. #107	C₂³×C₂₃	semidirect
223. #106	C₂³×C₂₃	semidirect
224. C₄⋊C₈	C₂³×C₂₃	semidirect
227. C₂₃	C₂²×#478	direct (N × H)
303. C₂²	C₂₃×#478	direct (N × H)
317. C₂	C₂×C₂₃×#478	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×#125	2
C₂²×C₄×D₄×C₂₃	2
C₂×C₂₃×#478	2
C₂²×C₂₃×#107	2
C₂²×C₂₃×#106	2
C₂²×C₂₃×C₄⋊C₈	2
C₂²×C₂₃×#102	2
C₂²×#478	23

Subgroups — C22×C23×#478 #19208101

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₂₃×#478 #19208101