Subgroups — C₂×C₂₃×#3154 #19208266

Order 5888.

3342 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₂₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×SD₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3154	C₂	1	16	yes	maximal, direct product factor
8	C₂×C₂₃×#497	C₂	1	2	yes	maximal, complemented
9	C₂×C₂₃×#496	C₂	1	2	yes	maximal, complemented
10	C₂×C₂₃×#495	C₂	1	2	yes	maximal, complemented
11	C₂×C₂₃×#492	C₂	1	2	yes	maximal, complemented
12	C₂×C₂₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
14	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
15	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
17	C₂×C₂₃×#137	—	2	8	no	—
18	C₂×C₂₃×#137	C₂²	1	8	yes	complemented
19	C₂×C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
20	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	8	yes	complemented
21	C₂×C₂₃×#135	—	2	8	no	—
22	C₂×C₂₃×#135	C₂²	1	8	yes	complemented
23	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
24	C₂²×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
25	C₂²×SD₁₆×C₂₃	—	2	8	no	—
26	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	—
27	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	—
28	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	—
29	C₂²×SD₁₆×C₂₃	C₂²	1	8	yes	complemented
30	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
31	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
32	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
33	C₂²×D₈×C₂₃	C₂²	1	2	yes	—
34	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
35	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
36	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
37	C₂₃×#536	—	2	4	no	—
38	C₂₃×#536	C₂²	1	8	yes	complemented
39	C₂₃×#535	—	2	4	no	—
40	C₂₃×#535	C₂²	1	8	yes	complemented
41	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
42	C₂×C₂₃×#127	C₂²	1	2	yes	—
43	C₂×C₂₃×#124	C₂²	1	2	yes	—
44	C₂×C₂₃×#124	C₂²	1	2	yes	complemented
45	C₂×C₂₃×#123	—	2	2	no	—
46	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
47	C₂×C₂₃×#121	—	2	2	no	—
48	C₂×C₂₃×#120	—	2	2	no	—
49	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
50	C₂₃×#497	C₂²	1	16	yes	complemented
51	C₂₃×#496	C₂²	1	16	yes	complemented
52	C₂₃×#495	C₂²	1	16	yes	complemented
53	C₂₃×#492	C₂²	1	16	yes	complemented
54	C₂₃×#405	C₂²	1	8	yes	complemented
55	C₂×C₂₃×#97	C₂²	1	2	yes	complemented
56	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	complemented
57	C₂⁵×C₂₃	—	2	1	no	—
58	C₂×#41×C₂₃	—	2	2	no	—
59	C₂×#41×C₂₃	—	2	2	no	—
60	C₂×#41×C₂₃	—	2	4	no	—
61	C₂×#41×C₂₃	—	2	4	no	—
62	C₂×#41×C₂₃	—	2	4	no	—
63	C₂×#41×C₂₃	—	2	4	no	—
64	C₂×#41×C₂₃	C₂³	1	4	yes	—
65	C₂×#41×C₂₃	C₂³	1	4	yes	—
66	C₂²×Q₈×C₂₃	—	2	1	no	—
67	C₂²×Q₈×C₂₃	—	2	2	no	—
68	C₂²×Q₈×C₂₃	—	2	4	no	—
69	C₂²×Q₈×C₂₃	—	2	4	no	—
70	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
71	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
72	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
73	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₂₃	—	2	1	no	—
75	C₂²×D₄×C₂₃	—	2	1	no	—
76	C₂²×D₄×C₂₃	—	2	4	no	—
77	C₂²×D₄×C₂₃	—	2	4	no	—
78	C₂²×D₄×C₂₃	—	2	1	no	—
79	C₂²×D₄×C₂₃	—	2	2	no	—
80	C₂²×D₄×C₂₃	—	2	4	no	—
81	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
83	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
85	C₂³×C₄×C₂₃	—	2	1	no	—
86	C₂³×C₄×C₂₃	—	2	1	no	—
87	C₂³×C₄×C₂₃	—	2	1	no	—
88	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
89	C₂₃×#137	—	2	32	no	—
90	C₂₃×AGL(1,ℤ/8)	—	2	32	no	—
91	C₂₃×#135	—	2	32	no	—
92	C₂×Q₁₆×C₂₃	—	2	4	no	—
93	C₂×Q₁₆×C₂₃	—	2	8	no	—
94	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	complemented
95	C₂×Q₁₆×C₂₃	C₂³	1	8	yes	complemented
96	C₂×SD₁₆×C₂₃	—	2	8	no	—
97	C₂×SD₁₆×C₂₃	—	2	8	no	—
98	C₂×SD₁₆×C₂₃	—	2	8	no	—
99	C₂×SD₁₆×C₂₃	—	2	4	no	—
100	C₂×SD₁₆×C₂₃	—	2	4	no	—
101	C₂×SD₁₆×C₂₃	—	2	8	no	—
102	C₂×SD₁₆×C₂₃	—	2	32	no	—
103	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	—
104	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	—
105	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	—
106	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	complemented
107	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	complemented
108	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	complemented
109	C₂×D₈×C₂₃	—	2	8	no	—
110	C₂×D₈×C₂₃	—	2	4	no	—
111	C₂×D₈×C₂₃	C₂³	1	8	yes	—
112	C₂×D₈×C₂₃	C₂³	1	4	yes	complemented
113	C₂×M₁₆×C₂₃	D₄	1	8	yes	complemented
114	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
115	C₂²×C₈×C₂₃	D₄	1	8	yes	complemented
116	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
119	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
120	C₂₃×C₄⋊Q₈	—	2	4	no	—
121	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
122	C₂₃×#127	—	2	4	no	—
123	C₂₃×#127	C₂³	1	8	yes	—
124	C₂₃×#124	—	2	4	no	—
125	C₂₃×#124	—	2	4	no	—
126	C₂₃×#124	C₂³	1	8	yes	—
127	C₂₃×#124	C₂³	1	8	yes	complemented
128	C₂₃×#123	—	2	16	no	—
129	C₂₃×C₂²⋊Q₈	—	2	16	no	—
130	C₂₃×#121	—	2	16	no	—
131	C₂₃×#120	—	2	16	no	—
132	C₂₃×#117	D₄	1	4	yes	—
133	C₂₃×#117	C₂³	1	4	yes	—
134	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
135	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
136	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
137	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
138	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
139	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
140	C₂₃×#97	C₂³	1	8	yes	complemented
141	C₄×C₈×C₂₃	C₂³	1	8	yes	complemented
142	C₂⁴×C₂₃	—	2	1	no	—
143	C₂⁴×C₂₃	—	2	2	no	—
144	C₂⁴×C₂₃	—	2	1	no	—
145	C₂⁴×C₂₃	—	2	4	no	—
146	C₂⁴×C₂₃	—	4	4	no	—
147	C₂⁴×C₂₃	—	8	4	no	—
148	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
149	#41×C₂₃	—	2	8	no	—
150	#41×C₂₃	—	2	8	no	—
151	#41×C₂₃	—	2	8	no	—
152	#41×C₂₃	—	2	8	no	—
153	#41×C₂₃	—	4	8	no	—
154	#41×C₂₃	—	4	8	no	—
155	C₂×Q₈×C₂₃	—	2	4	no	—
156	C₂×Q₈×C₂₃	—	2	1	no	—
157	C₂×Q₈×C₂₃	—	2	2	no	—
158	C₂×Q₈×C₂₃	—	2	1	no	—
159	C₂×Q₈×C₂₃	—	2	4	no	—
160	C₂×Q₈×C₂₃	—	2	8	no	—
161	C₂×Q₈×C₂₃	—	2	2	no	—
162	C₂×Q₈×C₂₃	—	2	4	no	—
163	C₂×Q₈×C₂₃	—	2	2	no	—
164	C₂×Q₈×C₂₃	—	2	2	no	—
165	C₂×Q₈×C₂₃	—	2	2	no	—
166	C₂×Q₈×C₂₃	—	2	8	no	—
167	C₂×Q₈×C₂₃	—	4	4	no	—
168	C₂×Q₈×C₂₃	—	4	8	no	—
169	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
170	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
171	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
172	C₂×D₄×C₂₃	—	2	4	no	—
173	C₂×D₄×C₂₃	—	2	4	no	—
174	C₂×D₄×C₂₃	—	2	2	no	—
175	C₂×D₄×C₂₃	—	2	4	no	—
176	C₂×D₄×C₂₃	—	2	2	no	—
177	C₂×D₄×C₂₃	—	2	2	no	—
178	C₂×D₄×C₂₃	—	2	4	no	—
179	C₂×D₄×C₂₃	—	2	8	no	—
180	C₂×D₄×C₂₃	—	2	2	no	—
181	C₂×D₄×C₂₃	—	2	8	no	—
182	C₂×D₄×C₂₃	—	2	4	no	—
183	C₂×D₄×C₂₃	—	2	1	no	—
184	C₂×D₄×C₂₃	—	2	2	no	—
185	C₂×D₄×C₂₃	—	2	1	no	—
186	C₂×D₄×C₂₃	—	2	16	no	—
187	C₂×D₄×C₂₃	—	4	4	no	—
188	C₂×D₄×C₂₃	—	4	4	no	—
189	C₂×D₄×C₂₃	—	4	4	no	—
190	C₂×D₄×C₂₃	—	4	8	no	—
191	C₂×D₄×C₂₃	—	8	8	no	—
192	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
193	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
194	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₂₃	—	2	4	no	—
196	C₂²×C₄×C₂₃	—	2	1	no	—
197	C₂²×C₄×C₂₃	—	2	2	no	—
198	C₂²×C₄×C₂₃	—	2	1	no	—
199	C₂²×C₄×C₂₃	—	2	4	no	—
200	C₂²×C₄×C₂₃	—	2	4	no	—
201	C₂²×C₄×C₂₃	—	4	4	no	—
202	C₂²×C₄×C₂₃	—	4	4	no	—
203	C₂²×C₄×C₂₃	—	4	4	no	—
204	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
205	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
206	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
208	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
209	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
211	Q₁₆×C₂₃	—	2	8	no	—
212	Q₁₆×C₂₃	—	2	16	no	—
213	SD₁₆×C₂₃	—	2	16	no	—
214	SD₁₆×C₂₃	—	2	16	no	—
215	SD₁₆×C₂₃	—	2	16	no	—
216	SD₁₆×C₂₃	—	2	8	no	—
217	SD₁₆×C₂₃	—	2	8	no	—
218	SD₁₆×C₂₃	—	2	16	no	—
219	D₈×C₂₃	—	2	16	no	—
220	D₈×C₂₃	—	2	8	no	—
221	M₁₆×C₂₃	C₂×D₄	1	16	yes	complemented
222	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	—
223	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	—
224	C₂×C₈×C₂₃	C₂×D₄	1	8	yes	—
225	C₂×C₈×C₂₃	C₂×D₄	1	16	yes	complemented
226	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
227	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
228	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
229	C₄⋊C₄×C₂₃	—	2	16	no	—
230	C₄⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
231	C₂²⋊C₄×C₂₃	—	2	16	no	—
232	C₂²⋊C₄×C₂₃	—	2	16	no	—
233	C₂²⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
234	C₄²×C₂₃	C₂×D₄	1	4	yes	—
235	C₄²×C₂₃	C₂⁴	1	4	yes	—
236	C₂×#3154	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂³×C₂₃	—	2	4	no	—
238	C₂³×C₂₃	—	2	2	no	—
239	C₂³×C₂₃	—	2	4	no	—
240	C₂³×C₂₃	—	2	2	no	—
241	C₂³×C₂₃	—	4	2	no	—
242	C₂³×C₂₃	—	4	2	no	—
243	C₂³×C₂₃	—	4	8	no	—
244	C₂³×C₂₃	—	4	4	no	—
245	C₂³×C₂₃	—	4	4	no	—
246	C₂³×C₂₃	—	4	8	no	—
247	C₂³×C₂₃	—	4	4	no	—
248	C₂³×C₂₃	—	8	8	no	—
249	C₂³×C₂₃	—	8	16	no	—
250	C₂³×C₂₃	#127	1	4	yes	—
251	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
252	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
253	Q₈×C₂₃	—	2	4	no	—
254	Q₈×C₂₃	—	2	2	no	—
255	Q₈×C₂₃	—	2	4	no	—
256	Q₈×C₂₃	—	2	2	no	—
257	Q₈×C₂₃	—	2	2	no	—
258	Q₈×C₂₃	—	2	2	no	—
259	Q₈×C₂₃	—	4	8	no	—
260	Q₈×C₂₃	—	4	4	no	—
261	Q₈×C₂₃	—	4	2	no	—
262	Q₈×C₂₃	—	4	2	no	—
263	D₄×C₂₃	—	2	2	no	—
264	D₄×C₂₃	—	2	4	no	—
265	D₄×C₂₃	—	2	2	no	—
266	D₄×C₂₃	—	2	2	no	—
267	D₄×C₂₃	—	2	4	no	—
268	D₄×C₂₃	—	2	2	no	—
269	D₄×C₂₃	—	4	8	no	—
270	D₄×C₂₃	—	4	8	no	—
271	D₄×C₂₃	—	4	8	no	—
272	D₄×C₂₃	—	4	4	no	—
273	D₄×C₂₃	—	4	2	no	—
274	D₄×C₂₃	—	4	2	no	—
275	D₄×C₂₃	—	8	16	no	—
276	C₂×C₄×C₂₃	—	2	8	no	—
277	C₂×C₄×C₂₃	—	2	2	no	—
278	C₂×C₄×C₂₃	—	2	4	no	—
279	C₂×C₄×C₂₃	—	2	2	no	—
280	C₂×C₄×C₂₃	—	4	2	no	—
281	C₂×C₄×C₂₃	—	4	2	no	—
282	C₂×C₄×C₂₃	—	4	8	no	—
283	C₂×C₄×C₂₃	—	4	4	no	—
284	C₂×C₄×C₂₃	—	4	8	no	—
285	C₂×C₄×C₂₃	—	4	8	no	—
286	C₂×C₄×C₂₃	#127	1	4	yes	—
287	C₂×C₄×C₂₃	#127	1	8	yes	—
288	C₂×C₄×C₂₃	C₂²×D₄	1	8	yes	—
289	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
291	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
292	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
293	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
294	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
295	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
296	C₈×C₂₃	C₂²×D₄	1	4	yes	—
297	C₈×C₂₃	C₂²×D₄	1	4	yes	—
298	C₈×C₂₃	C₂²×D₄	1	8	yes	—
299	C₂²×#137	C₂×C₂₃	1	1	yes	characteristic, complemented
300	C₂²×AGL(1,ℤ/8)	C₂×C₂₃	1	1	yes	characteristic, complemented
301	C₂²×#135	C₂×C₂₃	1	1	yes	characteristic, complemented
302	C₂³×SD₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
303	C₂×#536	C₂×C₂₃	1	1	yes	characteristic, complemented
304	C₂×#535	C₂×C₂₃	1	1	yes	characteristic, complemented
305	#3154	C₂×C₂₃	1	16	yes	direct product factor
306	C₂×#497	C₂×C₂₃	1	2	yes	complemented
307	C₂×#496	C₂×C₂₃	1	2	yes	complemented
308	C₂×#495	C₂×C₂₃	1	2	yes	complemented
309	C₂×#492	C₂×C₂₃	1	2	yes	complemented
310	C₂×#405	C₂×C₂₃	1	1	yes	characteristic, complemented
311	C₂²×C₂₃	—	2	8	no	—
312	C₂²×C₂₃	—	2	4	no	—
313	C₂²×C₂₃	—	4	2	no	—
314	C₂²×C₂₃	—	4	2	no	—
315	C₂²×C₂₃	—	4	4	no	—
316	C₂²×C₂₃	—	4	4	no	—
317	C₂²×C₂₃	—	4	8	no	—
318	C₂²×C₂₃	—	4	4	no	—
319	C₂²×C₂₃	—	8	16	no	—
320	C₂²×C₂₃	—	8	4	no	—
321	C₂²×C₂₃	—	8	4	no	—
322	C₂²×C₂₃	—	8	8	no	—
323	C₂²×C₂₃	C₂×#127	1	4	yes	—
324	C₂²×C₂₃	C₂×#127	1	2	yes	—
325	C₂²×C₂₃	#577	1	4	yes	—
326	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
327	C₄×C₂₃	—	2	8	no	—
328	C₄×C₂₃	—	4	2	no	—
329	C₄×C₂₃	—	4	2	no	—
330	C₄×C₂₃	—	4	4	no	—
331	C₄×C₂₃	C₂×#127	1	4	yes	—
332	C₄×C₂₃	C₂×#127	1	2	yes	—
333	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
334	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
335	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
336	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
337	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
338	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
339	C₂×#137	—	2	8	no	—
340	C₂×#137	C₂²×C₂₃	1	8	yes	complemented
341	C₂×AGL(1,ℤ/8)	—	2	8	no	—
342	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	8	yes	complemented
343	C₂×#135	—	2	8	no	—
344	C₂×#135	C₂²×C₂₃	1	8	yes	complemented
345	C₂²×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
346	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
347	C₂²×SD₁₆	—	2	8	no	—
348	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	—
349	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	—
350	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	—
351	C₂²×SD₁₆	C₂²×C₂₃	1	8	yes	complemented
352	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
353	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
354	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
355	C₂²×D₈	C₂²×C₂₃	1	2	yes	—
356	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
357	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
358	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
359	#536	—	2	4	no	—
360	#536	C₂²×C₂₃	1	8	yes	complemented
361	#535	—	2	4	no	—
362	#535	C₂²×C₂₃	1	8	yes	complemented
363	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
364	C₂×#127	C₂²×C₂₃	1	2	yes	—
365	C₂×#124	C₂²×C₂₃	1	2	yes	—
366	C₂×#124	C₂²×C₂₃	1	2	yes	complemented
367	C₂×#123	—	2	2	no	—
368	C₂×C₂²⋊Q₈	—	2	2	no	—
369	C₂×#121	—	2	2	no	—
370	C₂×#120	—	2	2	no	—
371	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
372	#497	C₂²×C₂₃	1	16	yes	complemented
373	#496	C₂²×C₂₃	1	16	yes	complemented
374	#495	C₂²×C₂₃	1	16	yes	complemented
375	#492	C₂²×C₂₃	1	16	yes	complemented
376	#405	C₂²×C₂₃	1	8	yes	complemented
377	C₂×#97	C₂²×C₂₃	1	2	yes	complemented
378	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	complemented
379	C₂×C₂₃	—	2	4	no	—
380	C₂×C₂₃	—	8	2	no	—
381	C₂×C₂₃	—	8	2	no	—
382	C₂×C₂₃	—	8	4	no	—
383	C₂×C₂₃	#3154	1	4	yes	direct product factor
384	C₂×C₂₃	C₂²×#127	1	1	yes	characteristic
385	C₂×C₂₃	C₂×#577	1	2	yes	—
386	C₂⁵	—	2	1	no	—
387	C₂×#41	—	2	2	no	—
388	C₂×#41	—	2	2	no	—
389	C₂×#41	—	2	4	no	—
390	C₂×#41	—	2	4	no	—
391	C₂×#41	—	2	4	no	—
392	C₂×#41	—	2	4	no	—
393	C₂×#41	C₂³×C₂₃	1	4	yes	—
394	C₂×#41	C₂³×C₂₃	1	4	yes	—
395	C₂²×Q₈	—	2	1	no	—
396	C₂²×Q₈	—	2	2	no	—
397	C₂²×Q₈	—	2	4	no	—
398	C₂²×Q₈	—	2	4	no	—
399	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
400	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
401	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
402	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
403	C₂²×D₄	—	2	1	no	—
404	C₂²×D₄	—	2	1	no	—
405	C₂²×D₄	—	2	4	no	—
406	C₂²×D₄	—	2	4	no	—
407	C₂²×D₄	—	2	1	no	—
408	C₂²×D₄	—	2	2	no	—
409	C₂²×D₄	—	2	4	no	—
410	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
411	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
412	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
413	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
414	C₂³×C₄	—	2	1	no	—
415	C₂³×C₄	—	2	1	no	—
416	C₂³×C₄	—	2	1	no	—
417	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
418	#137	—	2	32	no	—
419	AGL(1,ℤ/8)	—	2	32	no	—
420	#135	—	2	32	no	—
421	C₂×Q₁₆	—	2	4	no	—
422	C₂×Q₁₆	—	2	8	no	—
423	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	complemented
424	C₂×Q₁₆	C₂³×C₂₃	1	8	yes	complemented
425	C₂×SD₁₆	—	2	8	no	—
426	C₂×SD₁₆	—	2	8	no	—
427	C₂×SD₁₆	—	2	8	no	—
428	C₂×SD₁₆	—	2	4	no	—
429	C₂×SD₁₆	—	2	4	no	—
430	C₂×SD₁₆	—	2	8	no	—
431	C₂×SD₁₆	—	2	32	no	—
432	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	—
433	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	—
434	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	—
435	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	complemented
436	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	complemented
437	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	complemented
438	C₂×D₈	—	2	8	no	—
439	C₂×D₈	—	2	4	no	—
440	C₂×D₈	C₂³×C₂₃	1	8	yes	—
441	C₂×D₈	C₂³×C₂₃	1	4	yes	complemented
442	C₂×M₁₆	D₄×C₂₃	1	8	yes	complemented
443	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
444	C₂²×C₈	D₄×C₂₃	1	8	yes	complemented
445	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
446	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
447	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
448	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
449	C₄⋊Q₈	—	2	4	no	—
450	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	complemented
451	#127	—	2	4	no	—
452	#127	C₂³×C₂₃	1	8	yes	—
453	#124	—	2	4	no	—
454	#124	—	2	4	no	—
455	#124	C₂³×C₂₃	1	8	yes	—
456	#124	C₂³×C₂₃	1	8	yes	complemented
457	#123	—	2	16	no	—
458	C₂²⋊Q₈	—	2	16	no	—
459	#121	—	2	16	no	—
460	#120	—	2	16	no	—
461	#117	D₄×C₂₃	1	4	yes	—
462	#117	C₂³×C₂₃	1	4	yes	—
463	C₂×C₄⋊C₄	—	2	4	no	—
464	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
465	C₂×C₂²⋊C₄	—	2	4	no	—
466	C₂×C₂²⋊C₄	—	2	4	no	—
467	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
468	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
469	#97	C₂³×C₂₃	1	8	yes	complemented
470	C₄×C₈	C₂³×C₂₃	1	8	yes	complemented
471	C₂₃	C₂×#3154	1	1	yes	characteristic, direct product factor, Sylow
472	C₂⁴	—	2	1	no	—
473	C₂⁴	—	2	2	no	—
474	C₂⁴	—	2	1	no	—
475	C₂⁴	—	2	4	no	—
476	C₂⁴	—	4	4	no	—
477	C₂⁴	—	8	4	no	—
478	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
479	#41	—	2	8	no	—
480	#41	—	2	8	no	—
481	#41	—	2	8	no	—
482	#41	—	2	8	no	—
483	#41	—	4	8	no	—
484	#41	—	4	8	no	—
485	C₂×Q₈	—	2	4	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	2	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	2	4	no	—
490	C₂×Q₈	—	2	8	no	—
491	C₂×Q₈	—	2	2	no	—
492	C₂×Q₈	—	2	4	no	—
493	C₂×Q₈	—	2	2	no	—
494	C₂×Q₈	—	2	2	no	—
495	C₂×Q₈	—	2	2	no	—
496	C₂×Q₈	—	2	8	no	—
497	C₂×Q₈	—	4	4	no	—
498	C₂×Q₈	—	4	8	no	—
499	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
500	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
501	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
502	C₂×D₄	—	2	4	no	—
503	C₂×D₄	—	2	4	no	—
504	C₂×D₄	—	2	2	no	—
505	C₂×D₄	—	2	4	no	—
506	C₂×D₄	—	2	2	no	—
507	C₂×D₄	—	2	2	no	—
508	C₂×D₄	—	2	4	no	—
509	C₂×D₄	—	2	8	no	—
510	C₂×D₄	—	2	2	no	—
511	C₂×D₄	—	2	8	no	—
512	C₂×D₄	—	2	4	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	2	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	2	16	no	—
517	C₂×D₄	—	4	4	no	—
518	C₂×D₄	—	4	4	no	—
519	C₂×D₄	—	4	4	no	—
520	C₂×D₄	—	4	8	no	—
521	C₂×D₄	—	8	8	no	—
522	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
523	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
524	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	4	no	—
529	C₂²×C₄	—	2	4	no	—
530	C₂²×C₄	—	2	4	no	—
531	C₂²×C₄	—	4	4	no	—
532	C₂²×C₄	—	4	4	no	—
533	C₂²×C₄	—	4	4	no	—
534	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
535	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
536	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
537	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
538	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
539	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
540	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
541	Q₁₆	—	2	8	no	—
542	Q₁₆	—	2	16	no	—
543	SD₁₆	—	2	16	no	—
544	SD₁₆	—	2	16	no	—
545	SD₁₆	—	2	16	no	—
546	SD₁₆	—	2	8	no	—
547	SD₁₆	—	2	8	no	—
548	SD₁₆	—	2	16	no	—
549	D₈	—	2	16	no	—
550	D₈	—	2	8	no	—
551	M₁₆	C₂×D₄×C₂₃	1	16	yes	complemented
552	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	—
553	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	—
554	C₂×C₈	C₂×D₄×C₂₃	1	8	yes	—
555	C₂×C₈	C₂×D₄×C₂₃	1	16	yes	complemented
556	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
557	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
558	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
559	C₄⋊C₄	—	2	16	no	—
560	C₄⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
561	C₂²⋊C₄	—	2	16	no	—
562	C₂²⋊C₄	—	2	16	no	—
563	C₂²⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
564	C₄²	C₂×D₄×C₂₃	1	4	yes	—
565	C₄²	C₂⁴×C₂₃	1	4	yes	—
566	C₂³	—	2	4	no	—
567	C₂³	—	2	2	no	—
568	C₂³	—	2	4	no	—
569	C₂³	—	2	2	no	—
570	C₂³	—	4	4	no	—
571	C₂³	—	4	8	no	—
572	C₂³	—	4	4	no	—
573	C₂³	—	4	2	no	—
574	C₂³	—	4	2	no	—
575	C₂³	—	4	8	no	—
576	C₂³	—	4	4	no	—
577	C₂³	—	8	8	no	—
578	C₂³	—	8	16	no	—
579	C₂³	C₂₃×#127	1	4	yes	—
580	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
581	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
582	Q₈	—	2	4	no	—
583	Q₈	—	2	2	no	—
584	Q₈	—	2	4	no	—
585	Q₈	—	2	2	no	—
586	Q₈	—	2	2	no	—
587	Q₈	—	2	2	no	—
588	Q₈	—	4	8	no	—
589	Q₈	—	4	4	no	—
590	Q₈	—	4	2	no	—
591	Q₈	—	4	2	no	—
592	D₄	—	2	2	no	—
593	D₄	—	2	4	no	—
594	D₄	—	2	2	no	—
595	D₄	—	2	2	no	—
596	D₄	—	2	4	no	—
597	D₄	—	2	2	no	—
598	D₄	—	4	8	no	—
599	D₄	—	4	8	no	—
600	D₄	—	4	8	no	—
601	D₄	—	4	4	no	—
602	D₄	—	4	2	no	—
603	D₄	—	4	2	no	—
604	D₄	—	8	16	no	—
605	C₂×C₄	—	2	8	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	8	no	—
612	C₂×C₄	—	4	4	no	—
613	C₂×C₄	—	4	8	no	—
614	C₂×C₄	—	4	8	no	—
615	C₂×C₄	C₂₃×#127	1	4	yes	—
616	C₂×C₄	C₂₃×#127	1	8	yes	—
617	C₂×C₄	C₂²×D₄×C₂₃	1	8	yes	—
618	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
619	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
620	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
621	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
622	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
623	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
624	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
625	C₈	C₂²×D₄×C₂₃	1	4	yes	—
626	C₈	C₂²×D₄×C₂₃	1	4	yes	—
627	C₈	C₂²×D₄×C₂₃	1	8	yes	—
628	C₂²	—	2	4	no	—
629	C₂²	—	2	8	no	—
630	C₂²	—	4	2	no	—
631	C₂²	—	4	2	no	—
632	C₂²	—	4	4	no	—
633	C₂²	—	4	4	no	—
634	C₂²	—	4	8	no	—
635	C₂²	—	4	4	no	—
636	C₂²	—	8	16	no	—
637	C₂²	—	8	8	no	—
638	C₂²	—	8	4	no	—
639	C₂²	—	8	4	no	—
640	C₂²	C₂×C₂₃×#127	1	4	yes	—
641	C₂²	C₂×C₂₃×#127	1	2	yes	—
642	C₂²	C₂₃×#577	1	4	yes	—
643	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
644	C₄	—	2	8	no	—
645	C₄	—	4	2	no	—
646	C₄	—	4	2	no	—
647	C₄	—	4	4	no	—
648	C₄	C₂×C₂₃×#127	1	4	yes	—
649	C₄	C₂×C₂₃×#127	1	2	yes	—
650	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
651	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
652	C₂	—	2	4	no	—
653	C₂	—	8	4	no	—
654	C₂	—	8	2	no	—
655	C₂	—	8	2	no	—
656	C₂	C₂₃×#3154	1	4	yes	direct product factor
657	C₂	C₂²×C₂₃×#127	1	1	yes	characteristic
658	C₂	C₂×C₂₃×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₂₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂₃×#137	C₂	semidirect
2. C₂²×C₂₃×AGL(1,ℤ/8)	C₂	semidirect
3. C₂²×C₂₃×#135	C₂	semidirect
4. C₂³×SD₁₆×C₂₃	C₂	semidirect
5. C₂×C₂₃×#536	C₂	semidirect
6. C₂×C₂₃×#535	C₂	semidirect
7. C₂₃×#3154	C₂	direct (N × H)
8. C₂×C₂₃×#497	C₂	semidirect
9. C₂×C₂₃×#496	C₂	semidirect
10. C₂×C₂₃×#495	C₂	semidirect
11. C₂×C₂₃×#492	C₂	semidirect
12. C₂×C₂₃×#405	C₂	semidirect
18. C₂×C₂₃×#137	C₂²	semidirect
20. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
22. C₂×C₂₃×#135	C₂²	semidirect
23. C₂²×Q₁₆×C₂₃	C₂²	semidirect
24. C₂²×Q₁₆×C₂₃	C₂²	semidirect
29. C₂²×SD₁₆×C₂₃	C₂²	semidirect
30. C₂²×SD₁₆×C₂₃	C₂²	semidirect
31. C₂²×SD₁₆×C₂₃	C₂²	semidirect
32. C₂²×SD₁₆×C₂₃	C₂²	semidirect
34. C₂²×D₈×C₂₃	C₂²	semidirect
38. C₂₃×#536	C₂²	semidirect
40. C₂₃×#535	C₂²	semidirect
41. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
44. C₂×C₂₃×#124	C₂²	semidirect
50. C₂₃×#497	C₂²	semidirect
51. C₂₃×#496	C₂²	semidirect
52. C₂₃×#495	C₂²	semidirect
53. C₂₃×#492	C₂²	semidirect
54. C₂₃×#405	C₂²	semidirect
55. C₂×C₂₃×#97	C₂²	semidirect
56. C₂×C₄×C₈×C₂₃	C₂²	semidirect
94. C₂×Q₁₆×C₂₃	C₂³	semidirect
95. C₂×Q₁₆×C₂₃	C₂³	semidirect
106. C₂×SD₁₆×C₂₃	C₂³	semidirect
107. C₂×SD₁₆×C₂₃	C₂³	semidirect
108. C₂×SD₁₆×C₂₃	C₂³	semidirect
112. C₂×D₈×C₂₃	C₂³	semidirect
113. C₂×M₁₆×C₂₃	D₄	semidirect
115. C₂²×C₈×C₂₃	D₄	semidirect
121. C₂₃×C₄⋊Q₈	C₂³	semidirect
127. C₂₃×#124	C₂³	semidirect
140. C₂₃×#97	C₂³	semidirect
141. C₄×C₈×C₂₃	C₂³	semidirect
221. M₁₆×C₂₃	C₂×D₄	semidirect
225. C₂×C₈×C₂₃	C₂×D₄	semidirect
236. C₂×#3154	C₂₃	direct (N × H)
299. C₂²×#137	C₂×C₂₃	semidirect
300. C₂²×AGL(1,ℤ/8)	C₂×C₂₃	semidirect
301. C₂²×#135	C₂×C₂₃	semidirect
302. C₂³×SD₁₆	C₂×C₂₃	semidirect
303. C₂×#536	C₂×C₂₃	semidirect
304. C₂×#535	C₂×C₂₃	semidirect
305. #3154	C₂×C₂₃	direct (N × H)
306. C₂×#497	C₂×C₂₃	semidirect
307. C₂×#496	C₂×C₂₃	semidirect
308. C₂×#495	C₂×C₂₃	semidirect
309. C₂×#492	C₂×C₂₃	semidirect
310. C₂×#405	C₂×C₂₃	semidirect
340. C₂×#137	C₂²×C₂₃	semidirect
342. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
344. C₂×#135	C₂²×C₂₃	semidirect
345. C₂²×Q₁₆	C₂²×C₂₃	semidirect
346. C₂²×Q₁₆	C₂²×C₂₃	semidirect
351. C₂²×SD₁₆	C₂²×C₂₃	semidirect
352. C₂²×SD₁₆	C₂²×C₂₃	semidirect
353. C₂²×SD₁₆	C₂²×C₂₃	semidirect
354. C₂²×SD₁₆	C₂²×C₂₃	semidirect
356. C₂²×D₈	C₂²×C₂₃	semidirect
360. #536	C₂²×C₂₃	semidirect
362. #535	C₂²×C₂₃	semidirect
363. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
366. C₂×#124	C₂²×C₂₃	semidirect
372. #497	C₂²×C₂₃	semidirect
373. #496	C₂²×C₂₃	semidirect
374. #495	C₂²×C₂₃	semidirect
375. #492	C₂²×C₂₃	semidirect
376. #405	C₂²×C₂₃	semidirect
377. C₂×#97	C₂²×C₂₃	semidirect
378. C₂×C₄×C₈	C₂²×C₂₃	semidirect
383. C₂×C₂₃	#3154	direct (N × H)
423. C₂×Q₁₆	C₂³×C₂₃	semidirect
424. C₂×Q₁₆	C₂³×C₂₃	semidirect
435. C₂×SD₁₆	C₂³×C₂₃	semidirect
436. C₂×SD₁₆	C₂³×C₂₃	semidirect
437. C₂×SD₁₆	C₂³×C₂₃	semidirect
441. C₂×D₈	C₂³×C₂₃	semidirect
442. C₂×M₁₆	D₄×C₂₃	semidirect
444. C₂²×C₈	D₄×C₂₃	semidirect
450. C₄⋊Q₈	C₂³×C₂₃	semidirect
456. #124	C₂³×C₂₃	semidirect
469. #97	C₂³×C₂₃	semidirect
470. C₄×C₈	C₂³×C₂₃	semidirect
471. C₂₃	C₂×#3154	direct (N × H)
551. M₁₆	C₂×D₄×C₂₃	semidirect
555. C₂×C₈	C₂×D₄×C₂₃	semidirect
656. C₂	C₂₃×#3154	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×#137	2
C₂²×C₂₃×AGL(1,ℤ/8)	2
C₂²×C₂₃×#135	2
C₂³×SD₁₆×C₂₃	2
C₂×C₂₃×#536	2
C₂×C₂₃×#535	2
C₂₃×#3154	2
C₂×C₂₃×#497	2
C₂×C₂₃×#496	2
C₂×C₂₃×#495	2
C₂×C₂₃×#492	2
C₂×C₂₃×#405	2
C₂×#3154	23

Subgroups — C2×C23×#3154 #19208266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3154 #19208266