Subgroups — C₂₃×#60424 #19208050

Order 5888.

2674 conjugacy classes of subgroups.

The subgroup lattice has 442 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	2	yes	maximal, complemented
2	C₂₃×#3449	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×#519	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3044	C₂	1	8	yes	maximal, complemented
5	C₂₃×#3043	C₂	1	8	yes	maximal, complemented
6	C₂₃×#3037	C₂	1	8	yes	maximal, complemented
7	C₂₃×#2905	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2896	C₂	1	2	yes	maximal, complemented
9	C₂²×#41×C₂₃	C₂²	1	2	yes	—
10	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
11	C₂×C₂₃×#137	—	2	16	no	—
12	C₂×C₂₃×#137	C₂²	1	8	yes	—
13	C₂×C₂₃×#137	C₂²	1	8	yes	complemented
14	C₂²×Q₁₆×C₂₃	C₂²	1	4	yes	complemented
15	C₂²×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
16	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	—
17	C₂₃×#537	—	2	2	no	—
18	C₂₃×#536	C₂²	1	4	yes	—
19	C₂₃×#535	C₂²	1	4	yes	—
20	C₂₃×#534	—	2	2	no	—
21	C₂₃×#532	C₂²	1	4	yes	—
22	C₂₃×#525	—	2	4	no	—
23	C₂₃×#519	—	2	4	no	—
24	C₂₃×#519	C₂²	1	8	yes	complemented
25	C₂×C₄×Q₈×C₂₃	—	2	2	no	—
26	C₂×C₄×Q₈×C₂₃	C₂²	1	4	yes	complemented
27	C₂×C₂₃×#117	—	2	2	no	—
28	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
30	C₂₃×#464	C₂²	1	32	yes	complemented
31	C₂₃×#462	C₂²	1	16	yes	complemented
32	C₂₃×#460	C₂²	1	16	yes	complemented
33	C₂₃×#424	C₂²	1	8	yes	complemented
34	C₂₃×#423	C₂²	1	4	yes	complemented
35	C₂₃×#419	C₂²	1	4	yes	complemented
36	C₂₃×#418	C₂²	1	4	yes	complemented
37	C₂₃×#417	C₂²	1	8	yes	complemented
38	C₂₃×#416	C₂²	1	8	yes	—
39	C₂×#41×C₂₃	—	2	2	no	—
40	C₂×#41×C₂₃	—	2	2	no	—
41	C₂×#41×C₂₃	—	2	8	no	—
42	C₂×#41×C₂₃	—	2	8	no	—
43	C₂×#41×C₂₃	C₂³	1	4	yes	—
44	C₂×#41×C₂₃	C₂³	1	4	yes	—
45	C₂²×Q₈×C₂₃	—	2	1	no	—
46	C₂²×Q₈×C₂₃	—	2	2	no	—
47	C₂²×Q₈×C₂₃	—	2	4	no	—
48	C₂²×Q₈×C₂₃	D₄	1	8	yes	complemented
49	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
50	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
51	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
52	C₂²×D₄×C₂₃	—	2	2	no	—
53	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₂₃	—	2	1	no	—
55	C₂³×C₄×C₂₃	—	2	2	no	—
56	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
57	C₂₃×#137	—	2	32	no	—
58	C₂₃×#137	—	2	32	no	—
59	C₂×Q₁₆×C₂₃	—	2	16	no	—
60	C₂×Q₁₆×C₂₃	C₂³	1	16	yes	—
61	C₂×SD₁₆×C₂₃	—	2	16	no	—
62	C₂×SD₁₆×C₂₃	C₂³	1	16	yes	—
63	C₂×M₁₆×C₂₃	—	2	8	no	—
64	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
65	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
66	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
67	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
68	C₂₃×#127	C₂³	1	4	yes	—
69	C₂₃×#124	C₂³	1	8	yes	—
70	C₂₃×#123	—	2	8	no	—
71	C₂₃×C₂²⋊Q₈	—	2	8	no	—
72	C₂₃×#121	—	2	8	no	—
73	C₂₃×#121	—	2	8	no	—
74	C₂₃×#120	—	2	8	no	—
75	C₄×Q₈×C₂₃	—	2	16	no	—
76	C₄×Q₈×C₂₃	—	2	8	no	—
77	C₄×Q₈×C₂₃	C₂³	1	16	yes	—
78	C₄×D₄×C₂₃	—	2	8	no	—
79	C₂₃×#117	—	2	2	no	—
80	C₂₃×#117	—	2	16	no	—
81	C₂₃×#117	D₄	1	4	yes	—
82	C₂₃×#117	C₂³	1	4	yes	—
83	C₂₃×#117	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
85	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
86	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
87	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
89	C₂×C₄²×C₂₃	—	2	4	no	—
90	C₂×C₄²×C₂₃	—	2	1	no	—
91	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
92	C₂₃×C₄⋊C₈	C₂³	1	16	yes	—
93	C₂₃×#103	C₂³	1	16	yes	—
94	C₂₃×#102	C₂³	1	16	yes	—
95	C₂⁴×C₂₃	—	2	2	no	—
96	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
97	#41×C₂₃	—	2	8	no	—
98	#41×C₂₃	—	2	8	no	—
99	#41×C₂₃	—	2	8	no	—
100	#41×C₂₃	—	2	8	no	—
101	#41×C₂₃	—	4	8	no	—
102	#41×C₂₃	—	4	8	no	—
103	C₂×Q₈×C₂₃	—	2	16	no	—
104	C₂×Q₈×C₂₃	—	2	8	no	—
105	C₂×Q₈×C₂₃	—	2	4	no	—
106	C₂×Q₈×C₂₃	—	2	2	no	—
107	C₂×Q₈×C₂₃	—	2	2	no	—
108	C₂×Q₈×C₂₃	—	2	8	no	—
109	C₂×Q₈×C₂₃	—	2	4	no	—
110	C₂×Q₈×C₂₃	—	2	4	no	—
111	C₂×Q₈×C₂₃	—	2	4	no	—
112	C₂×Q₈×C₂₃	C₂×D₄	1	16	yes	—
113	C₂×Q₈×C₂₃	C₂×D₄	1	8	yes	—
114	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
115	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
116	C₂×D₄×C₂₃	—	2	4	no	—
117	C₂×D₄×C₂₃	—	2	4	no	—
118	C₂×D₄×C₂₃	—	2	4	no	—
119	C₂×D₄×C₂₃	—	2	2	no	—
120	C₂×D₄×C₂₃	—	2	8	no	—
121	C₂×D₄×C₂₃	—	2	4	no	—
122	C₂×D₄×C₂₃	—	4	8	no	—
123	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
124	C₂²×C₄×C₂₃	—	2	8	no	—
125	C₂²×C₄×C₂₃	—	2	2	no	—
126	C₂²×C₄×C₂₃	—	2	4	no	—
127	C₂²×C₄×C₂₃	—	2	2	no	—
128	C₂²×C₄×C₂₃	—	2	2	no	—
129	C₂²×C₄×C₂₃	—	2	4	no	—
130	C₂²×C₄×C₂₃	—	2	4	no	—
131	C₂²×C₄×C₂₃	—	4	8	no	—
132	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
133	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
136	C₂²×C₄×C₂₃	#41	1	4	yes	—
137	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
138	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
139	Q₁₆×C₂₃	—	2	32	no	—
140	SD₁₆×C₂₃	—	2	32	no	—
141	M₁₆×C₂₃	—	2	8	no	—
142	M₁₆×C₂₃	—	2	8	no	—
143	C₂×C₈×C₂₃	—	2	8	no	—
144	C₂×C₈×C₂₃	C₂⁴	1	8	yes	—
145	C₄⋊C₄×C₂₃	—	2	16	no	—
146	C₄⋊C₄×C₂₃	—	2	2	no	—
147	C₄⋊C₄×C₂₃	—	2	8	no	—
148	C₄⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
149	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
150	C₂²⋊C₄×C₂₃	—	2	4	no	—
151	C₂²⋊C₄×C₂₃	—	2	16	no	—
152	C₂²⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
153	C₄²×C₂₃	—	2	16	no	—
154	C₄²×C₂₃	—	2	4	no	—
155	C₄²×C₂₃	C₂×D₄	1	4	yes	—
156	C₄²×C₂₃	C₂⁴	1	4	yes	—
157	#60424	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₂³×C₂₃	—	2	4	no	—
159	C₂³×C₂₃	—	4	2	no	—
160	C₂³×C₂₃	—	4	4	no	—
161	C₂³×C₂₃	—	8	4	no	—
162	C₂³×C₂₃	#121	1	4	yes	—
163	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
164	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₂₃	—	2	8	no	—
166	Q₈×C₂₃	—	2	16	no	—
167	Q₈×C₂₃	—	2	4	no	—
168	Q₈×C₂₃	—	2	4	no	—
169	Q₈×C₂₃	—	2	4	no	—
170	Q₈×C₂₃	—	4	4	no	—
171	Q₈×C₂₃	C₂²×D₄	1	8	yes	—
172	D₄×C₂₃	—	2	4	no	—
173	D₄×C₂₃	—	2	4	no	—
174	D₄×C₂₃	—	4	8	no	—
175	D₄×C₂₃	—	4	8	no	—
176	D₄×C₂₃	—	4	4	no	—
177	D₄×C₂₃	—	8	8	no	—
178	C₂×C₄×C₂₃	—	2	16	no	—
179	C₂×C₄×C₂₃	—	2	8	no	—
180	C₂×C₄×C₂₃	—	2	4	no	—
181	C₂×C₄×C₂₃	—	2	4	no	—
182	C₂×C₄×C₂₃	—	2	4	no	—
183	C₂×C₄×C₂₃	—	4	4	no	—
184	C₂×C₄×C₂₃	—	4	4	no	—
185	C₂×C₄×C₂₃	—	4	4	no	—
186	C₂×C₄×C₂₃	—	4	8	no	—
187	C₂×C₄×C₂₃	—	4	8	no	—
188	C₂×C₄×C₂₃	#121	1	8	yes	—
189	C₂×C₄×C₂₃	#121	1	4	yes	—
190	C₂×C₄×C₂₃	C₂²×D₄	1	8	yes	—
191	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
192	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
194	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
195	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
196	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
197	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
198	C₈×C₂₃	—	2	8	no	—
199	C₂²×#137	C₂×C₂₃	1	2	yes	complemented
200	#3449	C₂×C₂₃	1	1	yes	characteristic
201	C₂×#519	C₂×C₂₃	1	1	yes	characteristic, complemented
202	#3044	C₂×C₂₃	1	8	yes	complemented
203	#3043	C₂×C₂₃	1	8	yes	complemented
204	#3037	C₂×C₂₃	1	8	yes	complemented
205	#2905	C₂×C₂₃	1	1	yes	characteristic, complemented
206	#2896	C₂×C₂₃	1	2	yes	complemented
207	C₂²×C₂₃	—	2	2	no	—
208	C₂²×C₂₃	—	2	4	no	—
209	C₂²×C₂₃	—	4	4	no	—
210	C₂²×C₂₃	—	4	8	no	—
211	C₂²×C₂₃	—	4	4	no	—
212	C₂²×C₂₃	—	8	8	no	—
213	C₂²×C₂₃	C₂×#121	1	4	yes	—
214	C₂²×C₂₃	C₂×#121	1	2	yes	—
215	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
216	C₄×C₂₃	—	2	8	no	—
217	C₄×C₂₃	—	2	8	no	—
218	C₄×C₂₃	—	4	4	no	—
219	C₄×C₂₃	—	4	4	no	—
220	C₄×C₂₃	C₂×#121	1	2	yes	—
221	C₄×C₂₃	C₂×#121	1	4	yes	—
222	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
223	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
224	C₂²×#41	C₂²×C₂₃	1	2	yes	—
225	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
226	C₂×#137	—	2	16	no	—
227	C₂×#137	C₂²×C₂₃	1	8	yes	—
228	C₂×#137	C₂²×C₂₃	1	8	yes	complemented
229	C₂²×Q₁₆	C₂²×C₂₃	1	4	yes	complemented
230	C₂²×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
231	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	—
232	#537	—	2	2	no	—
233	#536	C₂²×C₂₃	1	4	yes	—
234	#535	C₂²×C₂₃	1	4	yes	—
235	#534	—	2	2	no	—
236	#532	C₂²×C₂₃	1	4	yes	—
237	#525	—	2	4	no	—
238	#519	—	2	4	no	—
239	#519	C₂²×C₂₃	1	8	yes	complemented
240	C₂×C₄×Q₈	—	2	2	no	—
241	C₂×C₄×Q₈	C₂²×C₂₃	1	4	yes	complemented
242	C₂×#117	—	2	2	no	—
243	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
244	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
245	#464	C₂²×C₂₃	1	32	yes	complemented
246	#462	C₂²×C₂₃	1	16	yes	complemented
247	#460	C₂²×C₂₃	1	16	yes	complemented
248	#424	C₂²×C₂₃	1	8	yes	complemented
249	#423	C₂²×C₂₃	1	4	yes	complemented
250	#419	C₂²×C₂₃	1	4	yes	complemented
251	#418	C₂²×C₂₃	1	4	yes	complemented
252	#417	C₂²×C₂₃	1	8	yes	complemented
253	#416	C₂²×C₂₃	1	8	yes	—
254	C₂×C₂₃	—	2	4	no	—
255	C₂×C₂₃	—	2	2	no	—
256	C₂×C₂₃	—	8	4	no	—
257	C₂×C₂₃	C₂²×#121	1	1	yes	characteristic
258	C₂×C₂₃	#3586	1	2	yes	—
259	C₂×#41	—	2	2	no	—
260	C₂×#41	—	2	2	no	—
261	C₂×#41	—	2	8	no	—
262	C₂×#41	—	2	8	no	—
263	C₂×#41	C₂³×C₂₃	1	4	yes	—
264	C₂×#41	C₂³×C₂₃	1	4	yes	—
265	C₂²×Q₈	—	2	1	no	—
266	C₂²×Q₈	—	2	2	no	—
267	C₂²×Q₈	—	2	4	no	—
268	C₂²×Q₈	D₄×C₂₃	1	8	yes	complemented
269	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
270	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
271	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
272	C₂²×D₄	—	2	2	no	—
273	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
274	C₂³×C₄	—	2	1	no	—
275	C₂³×C₄	—	2	2	no	—
276	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
277	#137	—	2	32	no	—
278	#137	—	2	32	no	—
279	C₂×Q₁₆	—	2	16	no	—
280	C₂×Q₁₆	C₂³×C₂₃	1	16	yes	—
281	C₂×SD₁₆	—	2	16	no	—
282	C₂×SD₁₆	C₂³×C₂₃	1	16	yes	—
283	C₂×M₁₆	—	2	8	no	—
284	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
285	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
286	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
287	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
288	#127	C₂³×C₂₃	1	4	yes	—
289	#124	C₂³×C₂₃	1	8	yes	—
290	#123	—	2	8	no	—
291	C₂²⋊Q₈	—	2	8	no	—
292	#121	—	2	8	no	—
293	#121	—	2	8	no	—
294	#120	—	2	8	no	—
295	C₄×Q₈	—	2	16	no	—
296	C₄×Q₈	—	2	8	no	—
297	C₄×Q₈	C₂³×C₂₃	1	16	yes	—
298	C₄×D₄	—	2	8	no	—
299	#117	—	2	2	no	—
300	#117	—	2	16	no	—
301	#117	D₄×C₂₃	1	4	yes	—
302	#117	C₂³×C₂₃	1	4	yes	—
303	#117	C₂³×C₂₃	1	4	yes	—
304	C₂×C₄⋊C₄	—	2	4	no	—
305	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
306	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
307	C₂×C₂²⋊C₄	—	2	1	no	—
308	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
309	C₂×C₄²	—	2	4	no	—
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
312	C₄⋊C₈	C₂³×C₂₃	1	16	yes	—
313	#103	C₂³×C₂₃	1	16	yes	—
314	#102	C₂³×C₂₃	1	16	yes	—
315	C₂₃	#60424	1	1	yes	characteristic, direct product factor, Sylow
316	C₂⁴	—	2	2	no	—
317	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
318	#41	—	2	8	no	—
319	#41	—	2	8	no	—
320	#41	—	2	8	no	—
321	#41	—	2	8	no	—
322	#41	—	4	8	no	—
323	#41	—	4	8	no	—
324	C₂×Q₈	—	2	16	no	—
325	C₂×Q₈	—	2	8	no	—
326	C₂×Q₈	—	2	4	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	8	no	—
330	C₂×Q₈	—	2	4	no	—
331	C₂×Q₈	—	2	4	no	—
332	C₂×Q₈	—	2	4	no	—
333	C₂×Q₈	C₂×D₄×C₂₃	1	16	yes	—
334	C₂×Q₈	C₂×D₄×C₂₃	1	8	yes	—
335	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
336	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	2	4	no	—
339	C₂×D₄	—	2	4	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	8	no	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	4	8	no	—
344	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
345	C₂²×C₄	—	2	8	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	4	8	no	—
353	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
354	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
357	C₂²×C₄	#41×C₂₃	1	4	yes	—
358	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
359	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
360	Q₁₆	—	2	32	no	—
361	SD₁₆	—	2	32	no	—
362	M₁₆	—	2	8	no	—
363	M₁₆	—	2	8	no	—
364	C₂×C₈	—	2	8	no	—
365	C₂×C₈	C₂⁴×C₂₃	1	8	yes	—
366	C₄⋊C₄	—	2	16	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	8	no	—
369	C₄⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
370	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₂²⋊C₄	—	2	16	no	—
373	C₂²⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
374	C₄²	—	2	16	no	—
375	C₄²	—	2	4	no	—
376	C₄²	C₂×D₄×C₂₃	1	4	yes	—
377	C₄²	C₂⁴×C₂₃	1	4	yes	—
378	C₂³	—	2	4	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	4	no	—
381	C₂³	—	8	4	no	—
382	C₂³	C₂₃×#121	1	4	yes	—
383	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
384	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
385	Q₈	—	2	4	no	—
386	Q₈	—	2	8	no	—
387	Q₈	—	2	16	no	—
388	Q₈	—	2	4	no	—
389	Q₈	—	2	4	no	—
390	Q₈	—	4	4	no	—
391	Q₈	C₂²×D₄×C₂₃	1	8	yes	—
392	D₄	—	2	4	no	—
393	D₄	—	2	4	no	—
394	D₄	—	4	8	no	—
395	D₄	—	4	8	no	—
396	D₄	—	4	4	no	—
397	D₄	—	8	8	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	16	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	8	no	—
407	C₂×C₄	—	4	8	no	—
408	C₂×C₄	C₂₃×#121	1	8	yes	—
409	C₂×C₄	C₂₃×#121	1	4	yes	—
410	C₂×C₄	C₂²×D₄×C₂₃	1	8	yes	—
411	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
412	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
413	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
414	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
415	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
416	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
417	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
418	C₈	—	2	8	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	4	no	—
421	C₂²	—	4	4	no	—
422	C₂²	—	4	4	no	—
423	C₂²	—	4	8	no	—
424	C₂²	—	8	8	no	—
425	C₂²	C₂×C₂₃×#121	1	4	yes	—
426	C₂²	C₂×C₂₃×#121	1	2	yes	—
427	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
428	C₄	—	2	8	no	—
429	C₄	—	2	8	no	—
430	C₄	—	4	4	no	—
431	C₄	—	4	4	no	—
432	C₄	C₂×C₂₃×#121	1	2	yes	—
433	C₄	C₂×C₂₃×#121	1	4	yes	—
434	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
435	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
436	C₂	—	2	4	no	—
437	C₂	—	2	2	no	—
438	C₂	—	8	4	no	—
439	C₂	C₂²×C₂₃×#121	1	1	yes	characteristic
440	C₂	C₂₃×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×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
3. C₂×C₂₃×#519	C₂	semidirect
4. C₂₃×#3044	C₂	semidirect
5. C₂₃×#3043	C₂	semidirect
6. C₂₃×#3037	C₂	semidirect
7. C₂₃×#2905	C₂	semidirect
8. C₂₃×#2896	C₂	semidirect
13. C₂×C₂₃×#137	C₂²	semidirect
14. C₂²×Q₁₆×C₂₃	C₂²	semidirect
15. C₂²×SD₁₆×C₂₃	C₂²	semidirect
24. C₂₃×#519	C₂²	semidirect
26. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
30. C₂₃×#464	C₂²	semidirect
31. C₂₃×#462	C₂²	semidirect
32. C₂₃×#460	C₂²	semidirect
33. C₂₃×#424	C₂²	semidirect
34. C₂₃×#423	C₂²	semidirect
35. C₂₃×#419	C₂²	semidirect
36. C₂₃×#418	C₂²	semidirect
37. C₂₃×#417	C₂²	semidirect
48. C₂²×Q₈×C₂₃	D₄	semidirect
157. #60424	C₂₃	direct (N × H)
199. C₂²×#137	C₂×C₂₃	semidirect
201. C₂×#519	C₂×C₂₃	semidirect
202. #3044	C₂×C₂₃	semidirect
203. #3043	C₂×C₂₃	semidirect
204. #3037	C₂×C₂₃	semidirect
205. #2905	C₂×C₂₃	semidirect
206. #2896	C₂×C₂₃	semidirect
228. C₂×#137	C₂²×C₂₃	semidirect
229. C₂²×Q₁₆	C₂²×C₂₃	semidirect
230. C₂²×SD₁₆	C₂²×C₂₃	semidirect
239. #519	C₂²×C₂₃	semidirect
241. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
245. #464	C₂²×C₂₃	semidirect
246. #462	C₂²×C₂₃	semidirect
247. #460	C₂²×C₂₃	semidirect
248. #424	C₂²×C₂₃	semidirect
249. #423	C₂²×C₂₃	semidirect
250. #419	C₂²×C₂₃	semidirect
251. #418	C₂²×C₂₃	semidirect
252. #417	C₂²×C₂₃	semidirect
268. C₂²×Q₈	D₄×C₂₃	semidirect
315. C₂₃	#60424	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
C₂₃×#3449	2
C₂×C₂₃×#519	2
C₂₃×#3044	2
C₂₃×#3043	2
C₂₃×#3037	2
C₂₃×#2905	2
C₂₃×#2896	2
#60424	23

Subgroups — C23×#60424 #19208050

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60424 #19208050