Subgroups — C₂²×C₂₃×#450 #19207974

Order 5888.

7126 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂³×SD₁₆×C₂₃	C₂	1	2	yes	maximal, complemented
3	C₂²×C₂₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#450	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₂₃×#102	C₂	1	2	yes	maximal, complemented
6	C₂²×C₂₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂⁶×C₂₃	—	2	1	no	—
8	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
9	C₂³×D₄×C₂₃	—	2	16	no	—
10	C₂³×D₄×C₂₃	—	2	6	no	—
11	C₂³×D₄×C₂₃	—	2	1	no	—
12	C₂³×D₄×C₂₃	C₂²	1	12	yes	—
13	C₂³×D₄×C₂₃	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
15	C₂²×SD₁₆×C₂₃	—	2	16	no	—
16	C₂²×SD₁₆×C₂₃	C₂²	1	24	yes	complemented
17	C₂³×C₈×C₂₃	C₂²	1	2	yes	complemented
18	C₂×C₂₃×C₂²⋊Q₈	—	2	6	no	—
19	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	12	yes	complemented
20	C₂²×C₄⋊C₄×C₂₃	—	2	1	no	—
21	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₂²⋊C₄×C₂₃	—	2	1	no	—
23	C₂₃×#450	C₂²	1	64	yes	direct product factor
24	C₂×C₂₃×#102	C₂²	1	24	yes	complemented
25	C₂×C₂₃×C₂²⋊C₈	C₂²	1	12	yes	complemented
26	C₂⁵×C₂₃	—	2	16	no	—
27	C₂⁵×C₂₃	—	2	12	no	—
28	C₂⁵×C₂₃	—	2	2	no	—
29	C₂⁵×C₂₃	—	4	8	no	—
30	C₂⁵×C₂₃	—	4	8	no	—
31	C₂⁵×C₂₃	D₄	1	1	yes	characteristic
32	C₂²×Q₈×C₂₃	—	2	3	no	—
33	C₂²×Q₈×C₂₃	—	2	8	no	—
34	C₂²×Q₈×C₂₃	C₂³	1	6	yes	complemented
35	C₂²×D₄×C₂₃	—	2	16	no	—
36	C₂²×D₄×C₂₃	—	2	96	no	—
37	C₂²×D₄×C₂₃	—	2	96	no	—
38	C₂²×D₄×C₂₃	—	2	12	no	—
39	C₂²×D₄×C₂₃	—	2	24	no	—
40	C₂²×D₄×C₂₃	—	2	6	no	—
41	C₂²×D₄×C₂₃	—	2	8	no	—
42	C₂²×D₄×C₂₃	D₄	1	16	yes	—
43	C₂²×D₄×C₂₃	C₂³	1	16	yes	—
44	C₂²×D₄×C₂₃	C₂³	1	12	yes	—
45	C₂³×C₄×C₂₃	—	2	8	no	—
46	C₂³×C₄×C₂₃	—	2	1	no	—
47	C₂³×C₄×C₂₃	—	2	1	no	—
48	C₂³×C₄×C₂₃	D₄	1	6	yes	—
49	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₂₃	C₂³	1	6	yes	—
51	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
52	C₂×SD₁₆×C₂₃	—	2	96	no	—
53	C₂×SD₁₆×C₂₃	C₂³	1	32	yes	complemented
54	C₂²×C₈×C₂₃	—	2	8	no	—
55	C₂²×C₈×C₂₃	C₂³	1	12	yes	complemented
56	C₂₃×C₂²⋊Q₈	—	2	24	no	—
57	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
58	C₂×C₄⋊C₄×C₂₃	—	2	12	no	—
59	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
60	C₂×C₄⋊C₄×C₂₃	C₂³	1	6	yes	complemented
61	C₂×C₂²⋊C₄×C₂₃	—	2	12	no	—
62	C₂₃×#102	C₂³	1	32	yes	complemented
63	C₂₃×C₂²⋊C₈	C₂³	1	16	yes	complemented
64	C₂⁴×C₂₃	—	2	4	no	—
65	C₂⁴×C₂₃	—	2	4	no	—
66	C₂⁴×C₂₃	—	2	96	no	—
67	C₂⁴×C₂₃	—	2	16	no	—
68	C₂⁴×C₂₃	—	2	16	no	—
69	C₂⁴×C₂₃	—	2	12	no	—
70	C₂⁴×C₂₃	—	4	48	no	—
71	C₂⁴×C₂₃	—	4	128	no	—
72	C₂⁴×C₂₃	—	4	8	no	—
73	C₂⁴×C₂₃	—	4	48	no	—
74	C₂⁴×C₂₃	—	4	8	no	—
75	C₂⁴×C₂₃	SD₁₆	1	8	yes	complemented
76	C₂⁴×C₂₃	C₂×D₄	1	6	yes	—
77	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
78	C₂×Q₈×C₂₃	—	2	6	no	—
79	C₂×Q₈×C₂₃	—	2	24	no	—
80	C₂×Q₈×C₂₃	—	4	12	no	—
81	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	complemented
82	C₂×D₄×C₂₃	—	2	96	no	—
83	C₂×D₄×C₂₃	—	2	192	no	—
84	C₂×D₄×C₂₃	—	2	64	no	—
85	C₂×D₄×C₂₃	—	2	48	no	—
86	C₂×D₄×C₂₃	—	2	16	no	—
87	C₂×D₄×C₂₃	—	2	12	no	—
88	C₂×D₄×C₂₃	—	2	24	no	—
89	C₂×D₄×C₂₃	C₂×D₄	1	48	yes	—
90	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
91	C₂²×C₄×C₂₃	—	2	4	no	—
92	C₂²×C₄×C₂₃	—	2	24	no	—
93	C₂²×C₄×C₂₃	—	2	24	no	—
94	C₂²×C₄×C₂₃	—	2	6	no	—
95	C₂²×C₄×C₂₃	—	2	6	no	—
96	C₂²×C₄×C₂₃	—	4	4	no	—
97	C₂²×C₄×C₂₃	—	4	4	no	—
98	C₂²×C₄×C₂₃	C₂×D₄	1	6	yes	—
99	C₂²×C₄×C₂₃	C₂×D₄	1	12	yes	—
100	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
101	C₂²×C₄×C₂₃	C₂×D₄	1	8	yes	—
102	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
103	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
104	SD₁₆×C₂₃	—	2	64	no	—
105	C₂×C₈×C₂₃	—	2	24	no	—
106	C₂×C₈×C₂₃	C₂⁴	1	8	yes	complemented
107	C₄⋊C₄×C₂₃	—	2	16	no	—
108	C₄⋊C₄×C₂₃	—	2	6	no	—
109	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	complemented
110	C₂²⋊C₄×C₂₃	—	2	16	no	—
111	C₂²×#450	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂³×C₂₃	—	2	12	no	—
113	C₂³×C₂₃	—	2	12	no	—
114	C₂³×C₂₃	—	2	32	no	—
115	C₂³×C₂₃	—	2	64	no	—
116	C₂³×C₂₃	—	2	48	no	—
117	C₂³×C₂₃	—	2	8	no	—
118	C₂³×C₂₃	—	4	384	no	—
119	C₂³×C₂₃	—	4	32	no	—
120	C₂³×C₂₃	—	4	24	no	—
121	C₂³×C₂₃	—	4	32	no	—
122	C₂³×C₂₃	—	4	24	no	—
123	C₂³×C₂₃	—	4	64	no	—
124	C₂³×C₂₃	#120	1	4	yes	—
125	C₂³×C₂₃	C₂×SD₁₆	1	4	yes	—
126	C₂³×C₂₃	C₂×SD₁₆	1	24	yes	complemented
127	C₂³×C₂₃	AGL(1,ℤ/8)	1	4	yes	—
128	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
129	C₂³×C₂₃	C₂²×D₄	1	3	yes	—
130	Q₈×C₂₃	—	2	8	no	—
131	Q₈×C₂₃	—	4	12	no	—
132	D₄×C₂₃	—	2	64	no	—
133	D₄×C₂₃	—	2	48	no	—
134	D₄×C₂₃	—	2	8	no	—
135	D₄×C₂₃	C₂²×D₄	1	16	yes	—
136	C₂×C₄×C₂₃	—	2	12	no	—
137	C₂×C₄×C₂₃	—	2	24	no	—
138	C₂×C₄×C₂₃	—	2	8	no	—
139	C₂×C₄×C₂₃	—	2	4	no	—
140	C₂×C₄×C₂₃	—	2	4	no	—
141	C₂×C₄×C₂₃	—	4	12	no	—
142	C₂×C₄×C₂₃	—	4	12	no	—
143	C₂×C₄×C₂₃	#120	1	12	yes	—
144	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
145	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
146	C₂×C₄×C₂₃	C₂²×D₄	1	12	yes	—
147	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
148	C₈×C₂₃	—	2	8	no	—
149	C₂⁴×D₄	C₂×C₂₃	1	1	yes	characteristic
150	C₂³×SD₁₆	C₂×C₂₃	1	2	yes	complemented
151	C₂²×C₂²⋊Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
152	C₂×#450	C₂×C₂₃	1	24	yes	direct product factor
153	C₂²×#102	C₂×C₂₃	1	2	yes	complemented
154	C₂²×C₂²⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
155	C₂²×C₂₃	—	2	4	no	—
156	C₂²×C₂₃	—	2	48	no	—
157	C₂²×C₂₃	—	2	4	no	—
158	C₂²×C₂₃	—	2	16	no	—
159	C₂²×C₂₃	—	4	128	no	—
160	C₂²×C₂₃	—	4	96	no	—
161	C₂²×C₂₃	—	4	8	no	—
162	C₂²×C₂₃	—	4	8	no	—
163	C₂²×C₂₃	#450	1	16	yes	direct product factor
164	C₂²×C₂₃	C₂×#120	1	6	yes	—
165	C₂²×C₂₃	C₂²×SD₁₆	1	6	yes	—
166	C₂²×C₂₃	C₂²×SD₁₆	1	8	yes	complemented
167	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	6	yes	—
168	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
169	C₄×C₂₃	—	2	4	no	—
170	C₄×C₂₃	—	4	4	no	—
171	C₄×C₂₃	—	4	4	no	—
172	C₄×C₂₃	C₂×#120	1	6	yes	—
173	C₄×C₂₃	C₂³×D₄	1	2	yes	—
174	C₂⁶	—	2	1	no	—
175	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
176	C₂³×D₄	—	2	16	no	—
177	C₂³×D₄	—	2	1	no	—
178	C₂³×D₄	—	2	6	no	—
179	C₂³×D₄	C₂²×C₂₃	1	12	yes	—
180	C₂³×D₄	C₂²×C₂₃	1	2	yes	—
181	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
182	C₂²×SD₁₆	—	2	16	no	—
183	C₂²×SD₁₆	C₂²×C₂₃	1	24	yes	complemented
184	C₂³×C₈	C₂²×C₂₃	1	2	yes	complemented
185	C₂×C₂²⋊Q₈	—	2	6	no	—
186	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	12	yes	complemented
187	C₂²×C₄⋊C₄	—	2	1	no	—
188	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
189	C₂²×C₂²⋊C₄	—	2	1	no	—
190	#450	C₂²×C₂₃	1	64	yes	direct product factor
191	C₂×#102	C₂²×C₂₃	1	24	yes	complemented
192	C₂×C₂²⋊C₈	C₂²×C₂₃	1	12	yes	complemented
193	C₂×C₂₃	—	2	8	no	—
194	C₂×C₂₃	—	4	16	no	—
195	C₂×C₂₃	C₂×#450	1	12	yes	direct product factor
196	C₂×C₂₃	C₂²×#120	1	1	yes	characteristic
197	C₂×C₂₃	C₂³×SD₁₆	1	1	yes	characteristic
198	C₂×C₂₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
199	C₂⁵	—	2	16	no	—
200	C₂⁵	—	2	12	no	—
201	C₂⁵	—	2	2	no	—
202	C₂⁵	—	4	8	no	—
203	C₂⁵	—	4	8	no	—
204	C₂⁵	D₄×C₂₃	1	1	yes	characteristic
205	C₂²×Q₈	—	2	3	no	—
206	C₂²×Q₈	—	2	8	no	—
207	C₂²×Q₈	C₂³×C₂₃	1	6	yes	complemented
208	C₂²×D₄	—	2	16	no	—
209	C₂²×D₄	—	2	96	no	—
210	C₂²×D₄	—	2	96	no	—
211	C₂²×D₄	—	2	12	no	—
212	C₂²×D₄	—	2	24	no	—
213	C₂²×D₄	—	2	6	no	—
214	C₂²×D₄	—	2	8	no	—
215	C₂²×D₄	D₄×C₂₃	1	16	yes	—
216	C₂²×D₄	C₂³×C₂₃	1	16	yes	—
217	C₂²×D₄	C₂³×C₂₃	1	12	yes	—
218	C₂³×C₄	—	2	8	no	—
219	C₂³×C₄	—	2	1	no	—
220	C₂³×C₄	—	2	1	no	—
221	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
222	C₂³×C₄	D₄×C₂₃	1	6	yes	—
223	C₂³×C₄	C₂³×C₂₃	1	6	yes	—
224	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
225	C₂×SD₁₆	—	2	96	no	—
226	C₂×SD₁₆	C₂³×C₂₃	1	32	yes	complemented
227	C₂²×C₈	—	2	8	no	—
228	C₂²×C₈	C₂³×C₂₃	1	12	yes	complemented
229	C₂²⋊Q₈	—	2	24	no	—
230	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	complemented
231	C₂×C₄⋊C₄	—	2	12	no	—
232	C₂×C₄⋊C₄	—	2	3	no	—
233	C₂×C₄⋊C₄	C₂³×C₂₃	1	6	yes	complemented
234	C₂×C₂²⋊C₄	—	2	12	no	—
235	#102	C₂³×C₂₃	1	32	yes	complemented
236	C₂²⋊C₈	C₂³×C₂₃	1	16	yes	complemented
237	C₂₃	C₂²×#450	1	1	yes	characteristic, direct product factor, Sylow
238	C₂⁴	—	2	4	no	—
239	C₂⁴	—	2	4	no	—
240	C₂⁴	—	2	96	no	—
241	C₂⁴	—	2	16	no	—
242	C₂⁴	—	2	16	no	—
243	C₂⁴	—	2	12	no	—
244	C₂⁴	—	4	48	no	—
245	C₂⁴	—	4	128	no	—
246	C₂⁴	—	4	8	no	—
247	C₂⁴	—	4	48	no	—
248	C₂⁴	—	4	8	no	—
249	C₂⁴	SD₁₆×C₂₃	1	8	yes	complemented
250	C₂⁴	C₂×D₄×C₂₃	1	6	yes	—
251	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
252	C₂×Q₈	—	2	6	no	—
253	C₂×Q₈	—	2	24	no	—
254	C₂×Q₈	—	4	12	no	—
255	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	complemented
256	C₂×D₄	—	2	96	no	—
257	C₂×D₄	—	2	192	no	—
258	C₂×D₄	—	2	64	no	—
259	C₂×D₄	—	2	48	no	—
260	C₂×D₄	—	2	16	no	—
261	C₂×D₄	—	2	24	no	—
262	C₂×D₄	—	2	12	no	—
263	C₂×D₄	C₂×D₄×C₂₃	1	48	yes	—
264	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	24	no	—
267	C₂²×C₄	—	2	24	no	—
268	C₂²×C₄	—	2	6	no	—
269	C₂²×C₄	—	2	6	no	—
270	C₂²×C₄	—	4	4	no	—
271	C₂²×C₄	—	4	4	no	—
272	C₂²×C₄	C₂×D₄×C₂₃	1	6	yes	—
273	C₂²×C₄	C₂×D₄×C₂₃	1	12	yes	—
274	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
275	C₂²×C₄	C₂×D₄×C₂₃	1	8	yes	—
276	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
277	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
278	SD₁₆	—	2	64	no	—
279	C₂×C₈	—	2	24	no	—
280	C₂×C₈	C₂⁴×C₂₃	1	8	yes	complemented
281	C₄⋊C₄	—	2	16	no	—
282	C₄⋊C₄	—	2	6	no	—
283	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	complemented
284	C₂²⋊C₄	—	2	16	no	—
285	C₂³	—	2	12	no	—
286	C₂³	—	2	32	no	—
287	C₂³	—	2	12	no	—
288	C₂³	—	2	64	no	—
289	C₂³	—	2	8	no	—
290	C₂³	—	2	48	no	—
291	C₂³	—	4	384	no	—
292	C₂³	—	4	32	no	—
293	C₂³	—	4	24	no	—
294	C₂³	—	4	32	no	—
295	C₂³	—	4	24	no	—
296	C₂³	—	4	64	no	—
297	C₂³	C₂₃×#120	1	4	yes	—
298	C₂³	C₂×SD₁₆×C₂₃	1	4	yes	—
299	C₂³	C₂×SD₁₆×C₂₃	1	24	yes	complemented
300	C₂³	C₂₃×AGL(1,ℤ/8)	1	4	yes	—
301	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
302	C₂³	C₂²×D₄×C₂₃	1	3	yes	—
303	Q₈	—	2	8	no	—
304	Q₈	—	4	12	no	—
305	D₄	—	2	64	no	—
306	D₄	—	2	8	no	—
307	D₄	—	2	48	no	—
308	D₄	C₂²×D₄×C₂₃	1	16	yes	—
309	C₂×C₄	—	2	12	no	—
310	C₂×C₄	—	2	8	no	—
311	C₂×C₄	—	2	24	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	4	12	no	—
315	C₂×C₄	—	4	12	no	—
316	C₂×C₄	C₂₃×#120	1	12	yes	—
317	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
318	C₂×C₄	C₂²×D₄×C₂₃	1	12	yes	—
319	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
320	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
321	C₈	—	2	8	no	—
322	C₂²	—	2	4	no	—
323	C₂²	—	2	48	no	—
324	C₂²	—	2	4	no	—
325	C₂²	—	2	16	no	—
326	C₂²	—	4	128	no	—
327	C₂²	—	4	96	no	—
328	C₂²	—	4	8	no	—
329	C₂²	—	4	8	no	—
330	C₂²	C₂₃×#450	1	16	yes	direct product factor
331	C₂²	C₂×C₂₃×#120	1	6	yes	—
332	C₂²	C₂²×SD₁₆×C₂₃	1	6	yes	—
333	C₂²	C₂²×SD₁₆×C₂₃	1	8	yes	complemented
334	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	6	yes	—
335	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
336	C₄	—	2	4	no	—
337	C₄	—	4	4	no	—
338	C₄	—	4	4	no	—
339	C₄	C₂×C₂₃×#120	1	6	yes	—
340	C₄	C₂³×D₄×C₂₃	1	2	yes	—
341	C₂	—	2	8	no	—
342	C₂	—	4	16	no	—
343	C₂	C₂×C₂₃×#450	1	12	yes	direct product factor
344	C₂	C₂²×C₂₃×#120	1	1	yes	characteristic
345	C₂	C₂³×SD₁₆×C₂₃	1	1	yes	characteristic
346	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	C₂⁴×D₄×C₂₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₃ ◁ C₂⁴×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×SD₁₆×C₂₃	C₂	semidirect
3. C₂²×C₂₃×C₂²⋊Q₈	C₂	semidirect
4. C₂×C₂₃×#450	C₂	direct (N × H)
5. C₂²×C₂₃×#102	C₂	semidirect
6. C₂²×C₂₃×C₂²⋊C₈	C₂	semidirect
8. C₂³×Q₈×C₂₃	C₂²	semidirect
16. C₂²×SD₁₆×C₂₃	C₂²	semidirect
17. C₂³×C₈×C₂₃	C₂²	semidirect
19. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
21. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
23. C₂₃×#450	C₂²	direct (N × H)
24. C₂×C₂₃×#102	C₂²	semidirect
25. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
34. C₂²×Q₈×C₂₃	C₂³	semidirect
53. C₂×SD₁₆×C₂₃	C₂³	semidirect
55. C₂²×C₈×C₂₃	C₂³	semidirect
57. C₂₃×C₂²⋊Q₈	C₂³	semidirect
60. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
62. C₂₃×#102	C₂³	semidirect
63. C₂₃×C₂²⋊C₈	C₂³	semidirect
75. C₂⁴×C₂₃	SD₁₆	semidirect
81. C₂×Q₈×C₂₃	C₂⁴	semidirect
106. C₂×C₈×C₂₃	C₂⁴	semidirect
109. C₄⋊C₄×C₂₃	C₂⁴	semidirect
111. C₂²×#450	C₂₃	direct (N × H)
126. C₂³×C₂₃	C₂×SD₁₆	semidirect
150. C₂³×SD₁₆	C₂×C₂₃	semidirect
151. C₂²×C₂²⋊Q₈	C₂×C₂₃	semidirect
152. C₂×#450	C₂×C₂₃	direct (N × H)
153. C₂²×#102	C₂×C₂₃	semidirect
154. C₂²×C₂²⋊C₈	C₂×C₂₃	semidirect
163. C₂²×C₂₃	#450	direct (N × H)
166. C₂²×C₂₃	C₂²×SD₁₆	semidirect
175. C₂³×Q₈	C₂²×C₂₃	semidirect
183. C₂²×SD₁₆	C₂²×C₂₃	semidirect
184. C₂³×C₈	C₂²×C₂₃	semidirect
186. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
188. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
190. #450	C₂²×C₂₃	direct (N × H)
191. C₂×#102	C₂²×C₂₃	semidirect
192. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
195. C₂×C₂₃	C₂×#450	direct (N × H)
207. C₂²×Q₈	C₂³×C₂₃	semidirect
226. C₂×SD₁₆	C₂³×C₂₃	semidirect
228. C₂²×C₈	C₂³×C₂₃	semidirect
230. C₂²⋊Q₈	C₂³×C₂₃	semidirect
233. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
235. #102	C₂³×C₂₃	semidirect
236. C₂²⋊C₈	C₂³×C₂₃	semidirect
237. C₂₃	C₂²×#450	direct (N × H)
249. C₂⁴	SD₁₆×C₂₃	semidirect
255. C₂×Q₈	C₂⁴×C₂₃	semidirect
280. C₂×C₈	C₂⁴×C₂₃	semidirect
283. C₄⋊C₄	C₂⁴×C₂₃	semidirect
299. C₂³	C₂×SD₁₆×C₂₃	semidirect
330. C₂²	C₂₃×#450	direct (N × H)
333. C₂²	C₂²×SD₁₆×C₂₃	semidirect
343. C₂	C₂×C₂₃×#450	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂⁴×D₄×C₂₃	2
C₂³×SD₁₆×C₂₃	2
C₂²×C₂₃×C₂²⋊Q₈	2
C₂×C₂₃×#450	2
C₂²×C₂₃×#102	2
C₂²×C₂₃×C₂²⋊C₈	2
C₂²×#450	23

Subgroups — C22×C23×#450 #19207974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₂₃×#450 #19207974