Subgroups — C₂×C₂₃×#3170 #19208298

Order 5888.

2006 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#533	C₂	1	2	yes	maximal
2	C₂₃×#3170	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₂₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#487	C₂	1	2	yes	maximal, complemented
6	C₂×C₂₃×#467	C₂	1	4	yes	maximal
7	C₂×C₄×Q₁₆×C₂₃	C₂	1	4	yes	maximal, complemented
8	C₂²×C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
9	C₂²×Q₁₆×C₂₃	C₂²	1	4	yes	—
10	C₂³×C₈×C₂₃	C₂²	1	2	yes	—
11	C₂₃×#533	—	2	8	no	—
12	C₂₃×#533	C₂²	1	16	yes	—
13	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₂₃×#125	—	2	2	no	—
16	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
17	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	—
18	C₂×C₄×Q₈×C₂₃	—	2	2	no	—
19	C₂×C₄×Q₈×C₂₃	C₂²	1	4	yes	—
20	C₂×C₂₃×#117	—	2	2	no	—
21	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
22	C₂₃×#500	C₂²	1	8	yes	complemented
23	C₂₃×#494	C₂²	1	8	yes	complemented
24	C₂₃×#487	C₂²	1	16	yes	complemented
25	C₂₃×#467	C₂²	1	32	yes	—
26	C₄×Q₁₆×C₂₃	C₂²	1	32	yes	complemented
27	C₂×C₂₃×#107	C₂²	1	4	yes	—
28	C₂×C₂₃×#103	C₂²	1	8	yes	—
29	C₂×C₄×C₈×C₂₃	C₂²	1	8	yes	—
30	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
33	C₂²×Q₈×C₂₃	—	2	2	no	—
34	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
35	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
38	C₂×Q₁₆×C₂₃	—	2	16	no	—
39	C₂×Q₁₆×C₂₃	C₂³	1	16	yes	—
40	C₂²×C₈×C₂₃	—	2	8	no	—
41	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
42	C₂²×C₈×C₂₃	C₂³	1	8	yes	—
43	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
44	C₂₃×C₄⋊Q₈	—	2	4	no	—
45	C₂₃×C₄⋊Q₈	—	2	4	no	—
46	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	—
47	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	—
48	C₂₃×#125	—	2	16	no	—
49	C₂₃×C₂²⋊Q₈	—	2	16	no	—
50	C₂₃×C₂²⋊Q₈	—	2	8	no	—
51	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
52	C₄×Q₈×C₂₃	—	2	16	no	—
53	C₄×Q₈×C₂₃	—	2	8	no	—
54	C₄×Q₈×C₂₃	C₂³	1	16	yes	—
55	C₂₃×#117	—	2	16	no	—
56	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
57	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
58	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
59	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
60	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
61	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
62	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
63	C₂×C₄²×C₂₃	—	2	4	no	—
64	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₂₃	D₄	1	4	yes	—
66	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
69	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
70	C₂₃×#107	C₂³	1	16	yes	—
71	C₂₃×#103	C₂³	1	32	yes	—
72	C₄×C₈×C₂₃	C₂³	1	8	yes	—
73	C₄×C₈×C₂₃	C₂³	1	4	yes	—
74	C₄×C₈×C₂₃	C₂³	1	4	yes	—
75	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
76	C₂×Q₈×C₂₃	—	2	4	no	—
77	C₂×Q₈×C₂₃	—	2	8	no	—
78	C₂×Q₈×C₂₃	—	2	16	no	—
79	C₂×Q₈×C₂₃	—	4	8	no	—
80	C₂×Q₈×C₂₃	C₂⁴	1	8	yes	—
81	C₂²×C₄×C₂₃	—	2	4	no	—
82	C₂²×C₄×C₂₃	—	2	4	no	—
83	C₂²×C₄×C₂₃	—	2	4	no	—
84	C₂²×C₄×C₂₃	—	2	4	no	—
85	C₂²×C₄×C₂₃	Q₁₆	1	8	yes	complemented
86	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
90	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
92	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
95	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
96	Q₁₆×C₂₃	—	2	32	no	—
97	C₂×C₈×C₂₃	—	2	4	no	—
98	C₂×C₈×C₂₃	—	2	16	no	—
99	C₂×C₈×C₂₃	#41	1	8	yes	—
100	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
101	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
102	C₄⋊C₄×C₂₃	—	2	8	no	—
103	C₄⋊C₄×C₂₃	—	2	8	no	—
104	C₄⋊C₄×C₂₃	—	2	8	no	—
105	C₄⋊C₄×C₂₃	—	2	16	no	—
106	C₄⋊C₄×C₂₃	—	2	16	no	—
107	C₄⋊C₄×C₂₃	—	2	4	no	—
108	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
109	C₂²⋊C₄×C₂₃	—	2	16	no	—
110	C₄²×C₂₃	—	2	16	no	—
111	C₄²×C₂₃	C₂×D₄	1	4	yes	—
112	C₄²×C₂₃	C₂×D₄	1	2	yes	—
113	C₄²×C₂₃	C₂×D₄	1	4	yes	—
114	C₄²×C₂₃	C₂×D₄	1	2	yes	—
115	C₄²×C₂₃	C₂⁴	1	2	yes	—
116	C₄²×C₂₃	C₂⁴	1	2	yes	—
117	C₂×#3170	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂³×C₂₃	—	2	2	no	—
119	C₂³×C₂₃	—	2	2	no	—
120	C₂³×C₂₃	C₂×Q₁₆	1	4	yes	—
121	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
122	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
123	Q₈×C₂₃	—	2	16	no	—
124	Q₈×C₂₃	—	4	8	no	—
125	Q₈×C₂₃	—	4	16	no	—
126	C₂×C₄×C₂₃	—	2	2	no	—
127	C₂×C₄×C₂₃	—	2	2	no	—
128	C₂×C₄×C₂₃	—	2	4	no	—
129	C₂×C₄×C₂₃	—	2	8	no	—
130	C₂×C₄×C₂₃	—	2	4	no	—
131	C₂×C₄×C₂₃	—	2	8	no	—
132	C₂×C₄×C₂₃	—	2	8	no	—
133	C₂×C₄×C₂₃	—	4	8	no	—
134	C₂×C₄×C₂₃	—	4	8	no	—
135	C₂×C₄×C₂₃	C₂×Q₁₆	1	4	yes	—
136	C₂×C₄×C₂₃	C₂×Q₁₆	1	4	yes	—
137	C₂×C₄×C₂₃	C₂×Q₁₆	1	16	yes	complemented
138	C₂×C₄×C₂₃	#135	1	4	yes	—
139	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
140	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
141	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
142	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
143	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
144	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
145	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
146	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
147	C₈×C₂₃	—	2	4	no	—
148	C₈×C₂₃	C₂×#41	1	8	yes	—
149	C₂×#533	C₂×C₂₃	1	2	yes	—
150	#3170	C₂×C₂₃	1	16	yes	direct product factor
151	C₂×#500	C₂×C₂₃	1	1	yes	characteristic, complemented
152	C₂×#494	C₂×C₂₃	1	1	yes	characteristic, complemented
153	C₂×#487	C₂×C₂₃	1	2	yes	complemented
154	C₂×#467	C₂×C₂₃	1	4	yes	—
155	C₂×C₄×Q₁₆	C₂×C₂₃	1	4	yes	complemented
156	C₂²×C₄×C₈	C₂×C₂₃	1	1	yes	characteristic
157	C₂²×C₂₃	—	2	8	no	—
158	C₂²×C₂₃	—	2	2	no	—
159	C₂²×C₂₃	—	2	2	no	—
160	C₂²×C₂₃	#532	1	2	yes	—
161	C₂²×C₂₃	C₂²×Q₁₆	1	4	yes	—
162	C₂²×C₂₃	C₂²×Q₁₆	1	2	yes	—
163	C₂²×C₂₃	C₂×#135	1	2	yes	—
164	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
165	C₄×C₂₃	—	2	2	no	—
166	C₄×C₂₃	—	2	2	no	—
167	C₄×C₂₃	—	4	8	no	—
168	C₄×C₂₃	—	4	8	no	—
169	C₄×C₂₃	#532	1	2	yes	—
170	C₄×C₂₃	C₂²×Q₁₆	1	4	yes	—
171	C₄×C₂₃	C₂²×Q₁₆	1	4	yes	—
172	C₄×C₂₃	C₂×#135	1	4	yes	—
173	C₄×C₂₃	C₂²×#41	1	2	yes	—
174	C₂²×Q₁₆	C₂²×C₂₃	1	4	yes	—
175	C₂³×C₈	C₂²×C₂₃	1	2	yes	—
176	#533	—	2	8	no	—
177	#533	C₂²×C₂₃	1	16	yes	—
178	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
179	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
180	C₂×#125	—	2	2	no	—
181	C₂×C₂²⋊Q₈	—	2	2	no	—
182	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
183	C₂×C₄×Q₈	—	2	2	no	—
184	C₂×C₄×Q₈	C₂²×C₂₃	1	4	yes	—
185	C₂×#117	—	2	2	no	—
186	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
187	#500	C₂²×C₂₃	1	8	yes	complemented
188	#494	C₂²×C₂₃	1	8	yes	complemented
189	#487	C₂²×C₂₃	1	16	yes	complemented
190	#467	C₂²×C₂₃	1	32	yes	—
191	C₄×Q₁₆	C₂²×C₂₃	1	32	yes	complemented
192	C₂×#107	C₂²×C₂₃	1	4	yes	—
193	C₂×#103	C₂²×C₂₃	1	8	yes	—
194	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
195	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
196	C₂×C₄×C₈	C₂²×C₂₃	1	8	yes	—
197	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
198	C₂×C₂₃	—	2	4	no	—
199	C₂×C₂₃	#3170	1	4	yes	direct product factor
200	C₂×C₂₃	C₂×#532	1	1	yes	characteristic
201	C₂×C₂₃	C₂³×Q₁₆	1	1	yes	characteristic
202	C₂×C₂₃	C₂²×#135	1	1	yes	characteristic
203	C₂²×Q₈	—	2	2	no	—
204	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
205	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
206	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
207	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
208	C₂×Q₁₆	—	2	16	no	—
209	C₂×Q₁₆	C₂³×C₂₃	1	16	yes	—
210	C₂²×C₈	—	2	8	no	—
211	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
212	C₂²×C₈	C₂³×C₂₃	1	8	yes	—
213	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
214	C₄⋊Q₈	—	2	4	no	—
215	C₄⋊Q₈	—	2	4	no	—
216	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	—
217	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	—
218	#125	—	2	16	no	—
219	C₂²⋊Q₈	—	2	16	no	—
220	C₂²⋊Q₈	—	2	8	no	—
221	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
222	C₄×Q₈	—	2	16	no	—
223	C₄×Q₈	—	2	8	no	—
224	C₄×Q₈	C₂³×C₂₃	1	16	yes	—
225	#117	—	2	16	no	—
226	C₂×C₄⋊C₄	—	2	2	no	—
227	C₂×C₄⋊C₄	—	2	2	no	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	2	4	no	—
230	C₂×C₄⋊C₄	—	2	4	no	—
231	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
232	C₂×C₂²⋊C₄	—	2	4	no	—
233	C₂×C₄²	—	2	4	no	—
234	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
235	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
236	C₂×C₄²	D₄×C₂₃	1	4	yes	—
237	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
238	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
239	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
240	#107	C₂³×C₂₃	1	16	yes	—
241	#103	C₂³×C₂₃	1	32	yes	—
242	C₄×C₈	C₂³×C₂₃	1	8	yes	—
243	C₄×C₈	C₂³×C₂₃	1	4	yes	—
244	C₄×C₈	C₂³×C₂₃	1	4	yes	—
245	C₂₃	C₂×#3170	1	1	yes	characteristic, direct product factor, Sylow
246	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
247	C₂×Q₈	—	2	4	no	—
248	C₂×Q₈	—	2	8	no	—
249	C₂×Q₈	—	2	16	no	—
250	C₂×Q₈	—	4	8	no	—
251	C₂×Q₈	C₂⁴×C₂₃	1	8	yes	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	Q₁₆×C₂₃	1	8	yes	complemented
257	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
258	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
259	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
260	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
261	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
262	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
263	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
264	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
265	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
266	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
267	Q₁₆	—	2	32	no	—
268	C₂×C₈	—	2	4	no	—
269	C₂×C₈	—	2	16	no	—
270	C₂×C₈	#41×C₂₃	1	8	yes	—
271	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
272	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
273	C₄⋊C₄	—	2	8	no	—
274	C₄⋊C₄	—	2	8	no	—
275	C₄⋊C₄	—	2	8	no	—
276	C₄⋊C₄	—	2	16	no	—
277	C₄⋊C₄	—	2	16	no	—
278	C₄⋊C₄	—	2	4	no	—
279	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
280	C₂²⋊C₄	—	2	16	no	—
281	C₄²	—	2	16	no	—
282	C₄²	C₂×D₄×C₂₃	1	4	yes	—
283	C₄²	C₂×D₄×C₂₃	1	2	yes	—
284	C₄²	C₂×D₄×C₂₃	1	4	yes	—
285	C₄²	C₂×D₄×C₂₃	1	2	yes	—
286	C₄²	C₂⁴×C₂₃	1	2	yes	—
287	C₄²	C₂⁴×C₂₃	1	2	yes	—
288	C₂³	—	2	2	no	—
289	C₂³	—	2	2	no	—
290	C₂³	C₂×Q₁₆×C₂₃	1	4	yes	—
291	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
292	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
293	Q₈	—	2	16	no	—
294	Q₈	—	4	16	no	—
295	Q₈	—	4	8	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	8	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	4	8	no	—
304	C₂×C₄	—	4	8	no	—
305	C₂×C₄	C₂×Q₁₆×C₂₃	1	4	yes	—
306	C₂×C₄	C₂×Q₁₆×C₂₃	1	4	yes	—
307	C₂×C₄	C₂×Q₁₆×C₂₃	1	16	yes	complemented
308	C₂×C₄	C₂₃×#135	1	4	yes	—
309	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
310	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
311	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
312	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
313	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
314	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
315	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
316	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
317	C₈	—	2	4	no	—
318	C₈	C₂×#41×C₂₃	1	8	yes	—
319	C₂²	—	2	8	no	—
320	C₂²	—	2	2	no	—
321	C₂²	—	2	2	no	—
322	C₂²	C₂₃×#532	1	2	yes	—
323	C₂²	C₂²×Q₁₆×C₂₃	1	4	yes	—
324	C₂²	C₂²×Q₁₆×C₂₃	1	2	yes	—
325	C₂²	C₂×C₂₃×#135	1	2	yes	—
326	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
327	C₄	—	2	2	no	—
328	C₄	—	2	2	no	—
329	C₄	—	4	8	no	—
330	C₄	—	4	8	no	—
331	C₄	C₂₃×#532	1	2	yes	—
332	C₄	C₂²×Q₁₆×C₂₃	1	4	yes	—
333	C₄	C₂²×Q₁₆×C₂₃	1	4	yes	—
334	C₄	C₂×C₂₃×#135	1	4	yes	—
335	C₄	C₂²×#41×C₂₃	1	2	yes	—
336	C₂	—	2	4	no	—
337	C₂	C₂₃×#3170	1	4	yes	direct product factor
338	C₂	C₂×C₂₃×#532	1	1	yes	characteristic
339	C₂	C₂³×Q₁₆×C₂₃	1	1	yes	characteristic
340	C₂	C₂²×C₂₃×#135	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂₃×#3170	C₂	direct (N × H)
3. C₂×C₂₃×#500	C₂	semidirect
4. C₂×C₂₃×#494	C₂	semidirect
5. C₂×C₂₃×#487	C₂	semidirect
7. C₂×C₄×Q₁₆×C₂₃	C₂	semidirect
22. C₂₃×#500	C₂²	semidirect
23. C₂₃×#494	C₂²	semidirect
24. C₂₃×#487	C₂²	semidirect
26. C₄×Q₁₆×C₂₃	C₂²	semidirect
85. C₂²×C₄×C₂₃	Q₁₆	semidirect
117. C₂×#3170	C₂₃	direct (N × H)
137. C₂×C₄×C₂₃	C₂×Q₁₆	semidirect
150. #3170	C₂×C₂₃	direct (N × H)
151. C₂×#500	C₂×C₂₃	semidirect
152. C₂×#494	C₂×C₂₃	semidirect
153. C₂×#487	C₂×C₂₃	semidirect
155. C₂×C₄×Q₁₆	C₂×C₂₃	semidirect
187. #500	C₂²×C₂₃	semidirect
188. #494	C₂²×C₂₃	semidirect
189. #487	C₂²×C₂₃	semidirect
191. C₄×Q₁₆	C₂²×C₂₃	semidirect
199. C₂×C₂₃	#3170	direct (N × H)
245. C₂₃	C₂×#3170	direct (N × H)
256. C₂²×C₄	Q₁₆×C₂₃	semidirect
307. C₂×C₄	C₂×Q₁₆×C₂₃	semidirect
337. C₂	C₂₃×#3170	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#533	2
C₂₃×#3170	2
C₂×C₂₃×#500	2
C₂×C₂₃×#494	2
C₂×C₂₃×#487	2
C₂×C₂₃×#467	2
C₂×C₄×Q₁₆×C₂₃	2
C₂²×C₄×C₈×C₂₃	2
C₂×#3170	23

Subgroups — C2×C23×#3170 #19208298

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3170 #19208298