Subgroups — C₂₃×#61844 #19209470

Order 5888.

1756 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3522	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₈²×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3385	C₂	1	6	yes	maximal, complemented
4	Q₈×Q₁₆×C₂₃	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3375	C₂	1	6	yes	maximal, complemented
6	C₂₃×#3362	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3238	C₂	1	3	yes	maximal, complemented
8	C₂₃×#3226	C₂	1	3	yes	maximal, complemented
9	C₂₃×#3112	C₂	1	3	yes	maximal, complemented
10	C₂₃×#3108	C₂	1	3	yes	maximal, complemented
11	C₂₃×#2984	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#559	C₂²	1	3	yes	—
13	Q₈²×C₂₃	—	2	1	no	—
14	Q₈²×C₂₃	—	2	3	no	—
15	Q₈²×C₂₃	C₂²	1	2	yes	—
16	Q₈²×C₂₃	C₂²	1	6	yes	—
17	Q₈²×C₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×#554	C₂²	1	3	yes	—
19	C₂₃×#550	C₂²	1	1	yes	characteristic
20	C₂₃×#548	—	2	1	no	—
21	C₂₃×#547	—	2	3	no	—
22	C₂₃×#542	—	2	3	no	—
23	C₂₃×#532	C₂²	1	3	yes	—
24	C₂×C₂₃×C₄⋊Q₈	—	2	3	no	—
25	C₂×C₂₃×C₄⋊Q₈	C₂²	1	3	yes	—
26	C₂₃×#529	C₂²	1	3	yes	—
27	C₂₃×#520	—	2	1	no	—
28	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
29	C₂×C₄×Q₈×C₂₃	C₂²	1	3	yes	—
30	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
31	C₂₃×#501	C₂²	1	6	yes	—
32	C₂₃×#500	C₂²	1	6	yes	—
33	C₂₃×#489	C₂²	1	6	yes	—
34	C₂₃×#486	C₂²	1	6	yes	—
35	C₂₃×#483	C₂²	1	3	yes	—
36	C₂₃×#480	C₂²	1	3	yes	—
37	C₂₃×#480	C₂²	1	6	yes	—
38	C₂₃×#479	C₂²	1	6	yes	—
39	C₂₃×#477	C₂²	1	6	yes	—
40	C₂₃×#477	C₂²	1	6	yes	—
41	C₂₃×#476	C₂²	1	6	yes	—
42	C₂₃×#474	C₂²	1	12	yes	—
43	C₂₃×#464	C₂²	1	6	yes	—
44	C₂₃×#460	C₂²	1	6	yes	—
45	C₂₃×#451	C₂²	1	1	yes	characteristic
46	C₂₃×#448	C₂²	1	3	yes	—
47	C₂₃×#446	C₂²	1	6	yes	—
48	C₈×Q₈×C₂₃	C₂²	1	2	yes	—
49	C₂₃×#440	C₂²	1	12	yes	—
50	C₄×Q₁₆×C₂₃	C₂²	1	6	yes	—
51	C₄×SD₁₆×C₂₃	C₂²	1	6	yes	—
52	C₂₃×#432	C₂²	1	3	yes	—
53	C₂₃×#431	C₂²	1	3	yes	—
54	C₂×#41×C₂₃	—	2	1	no	—
55	C₂×#41×C₂₃	—	2	3	no	—
56	C₂²×Q₈×C₂₃	—	2	3	no	—
57	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
58	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
59	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
60	C₂×SD₁₆×C₂₃	C₂³	1	6	yes	—
61	C₂₃×C₄⋊Q₈	—	2	3	no	—
62	C₂₃×C₄⋊Q₈	—	2	6	no	—
63	C₂₃×C₄⋊Q₈	—	2	6	no	—
64	C₂₃×C₄⋊Q₈	—	2	12	no	—
65	C₂₃×C₄⋊Q₈	—	2	3	no	—
66	C₂₃×C₄⋊Q₈	—	2	3	no	—
67	C₂₃×C₄⋊Q₈	C₂³	1	3	yes	—
68	C₂₃×C₄⋊Q₈	C₂³	1	6	yes	—
69	C₂₃×C₄⋊Q₈	C₂³	1	6	yes	—
70	C₂₃×#127	C₂³	1	3	yes	—
71	C₂₃×#126	—	2	3	no	—
72	C₂₃×#125	C₂³	1	3	yes	—
73	C₂₃×#124	—	2	3	no	—
74	C₂₃×#124	—	2	3	no	—
75	C₂₃×#124	C₂³	1	3	yes	—
76	C₂₃×#123	—	2	3	no	—
77	C₂₃×#123	—	2	6	no	—
78	C₂₃×C₂²⋊Q₈	—	2	3	no	—
79	C₂₃×C₂²⋊Q₈	—	2	6	no	—
80	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
81	C₂₃×#121	—	2	3	no	—
82	C₂₃×#121	—	2	3	no	—
83	C₂₃×#121	C₂³	1	3	yes	—
84	C₄×Q₈×C₂₃	—	2	1	no	—
85	C₄×Q₈×C₂₃	—	2	6	no	—
86	C₄×Q₈×C₂₃	—	2	2	no	—
87	C₄×Q₈×C₂₃	—	2	3	no	—
88	C₄×Q₈×C₂₃	—	2	3	no	—
89	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
90	C₄×Q₈×C₂₃	D₄	1	3	yes	—
91	C₄×Q₈×C₂₃	C₂³	1	6	yes	—
92	C₄×Q₈×C₂₃	C₂³	1	6	yes	—
93	C₄×Q₈×C₂₃	C₂³	1	3	yes	—
94	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
95	C₄×Q₈×C₂₃	C₂³	1	3	yes	—
96	C₄×D₄×C₂₃	—	2	3	no	—
97	C₄×D₄×C₂₃	—	2	3	no	—
98	C₄×D₄×C₂₃	—	2	3	no	—
99	C₄×D₄×C₂₃	C₂³	1	3	yes	—
100	C₄×D₄×C₂₃	C₂³	1	6	yes	—
101	C₂₃×#117	—	2	3	no	—
102	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
103	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
104	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
105	C₂×C₄⋊C₄×C₂₃	D₄	1	3	yes	—
106	C₂×C₄⋊C₄×C₂₃	C₂³	1	3	yes	—
107	C₂×C₄²×C₂₃	—	2	3	no	—
108	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
109	C₂₃×#107	C₂³	1	6	yes	—
110	C₂₃×#107	C₂³	1	12	yes	—
111	C₂₃×#106	C₂³	1	6	yes	—
112	C₂₃×C₄⋊C₈	C₂³	1	6	yes	—
113	C₂₃×C₄⋊C₈	C₂³	1	6	yes	—
114	C₂₃×#103	C₂³	1	2	yes	—
115	C₂₃×#103	C₂³	1	6	yes	—
116	C₂₃×#103	C₂³	1	6	yes	—
117	C₂₃×#102	C₂³	1	6	yes	—
118	C₂₃×#102	C₂³	1	12	yes	—
119	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
120	C₂₃×C₂²⋊C₈	C₂³	1	3	yes	—
121	C₂₃×#97	C₂³	1	6	yes	—
122	C₄×C₈×C₂₃	C₂³	1	6	yes	—
123	#41×C₂₃	—	4	4	no	—
124	#41×C₂₃	—	8	6	no	—
125	C₂×Q₈×C₂₃	—	2	4	no	—
126	C₂×Q₈×C₂₃	—	2	4	no	—
127	C₂×Q₈×C₂₃	—	2	1	no	—
128	C₂×Q₈×C₂₃	—	2	3	no	—
129	C₂×Q₈×C₂₃	—	2	6	no	—
130	C₂×Q₈×C₂₃	—	2	6	no	—
131	C₂×Q₈×C₂₃	—	8	6	no	—
132	C₂×Q₈×C₂₃	C₂×D₄	1	3	yes	—
133	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
134	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
135	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
136	C₂×D₄×C₂₃	—	2	3	no	—
137	C₂×D₄×C₂₃	—	2	3	no	—
138	C₂×D₄×C₂₃	—	2	3	no	—
139	C₂×D₄×C₂₃	C₂⁴	1	3	yes	—
140	C₂²×C₄×C₂₃	—	2	1	no	—
141	C₂²×C₄×C₂₃	—	2	3	no	—
142	C₂²×C₄×C₂₃	—	2	3	no	—
143	C₂²×C₄×C₂₃	—	2	6	no	—
144	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
145	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
146	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
147	Q₁₆×C₂₃	—	2	4	no	—
148	SD₁₆×C₂₃	—	2	12	no	—
149	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
150	C₂×C₈×C₂₃	C₂⁴	1	6	yes	—
151	C₄⋊C₄×C₂₃	—	2	3	no	—
152	C₄⋊C₄×C₂₃	—	2	3	no	—
153	C₄⋊C₄×C₂₃	—	2	6	no	—
154	C₄⋊C₄×C₂₃	—	2	6	no	—
155	C₄⋊C₄×C₂₃	—	2	6	no	—
156	C₄⋊C₄×C₂₃	—	2	6	no	—
157	C₄⋊C₄×C₂₃	—	2	3	no	—
158	C₄⋊C₄×C₂₃	—	2	1	no	—
159	C₄⋊C₄×C₂₃	—	2	3	no	—
160	C₄⋊C₄×C₂₃	—	2	3	no	—
161	C₄⋊C₄×C₂₃	C₂×D₄	1	3	yes	—
162	C₄⋊C₄×C₂₃	C₂×D₄	1	3	yes	—
163	C₄⋊C₄×C₂₃	C₂×D₄	1	6	yes	—
164	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
165	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
166	C₄⋊C₄×C₂₃	C₂⁴	1	3	yes	—
167	C₂²⋊C₄×C₂₃	—	2	1	no	—
168	C₂²⋊C₄×C₂₃	—	2	3	no	—
169	C₂²⋊C₄×C₂₃	—	2	3	no	—
170	C₂²⋊C₄×C₂₃	—	2	3	no	—
171	C₂²⋊C₄×C₂₃	—	2	3	no	—
172	C₂²⋊C₄×C₂₃	—	2	6	no	—
173	C₄²×C₂₃	—	2	6	no	—
174	C₄²×C₂₃	—	2	6	no	—
175	C₄²×C₂₃	—	2	3	no	—
176	C₄²×C₂₃	C₂×D₄	1	3	yes	—
177	C₄²×C₂₃	C₂×D₄	1	3	yes	—
178	C₄²×C₂₃	C₂⁴	1	3	yes	—
179	C₄²×C₂₃	C₂⁴	1	3	yes	—
180	#61844	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂³×C₂₃	—	2	3	no	—
182	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
183	Q₈×C₂₃	—	2	4	no	—
184	Q₈×C₂₃	—	2	6	no	—
185	Q₈×C₂₃	—	2	2	no	—
186	Q₈×C₂₃	—	2	2	no	—
187	Q₈×C₂₃	—	8	6	no	—
188	Q₈×C₂₃	—	8	6	no	—
189	Q₈×C₂₃	—	8	3	no	—
190	Q₈×C₂₃	#137	1	4	yes	—
191	Q₈×C₂₃	2₋¹⁺⁴	1	4	yes	—
192	D₄×C₂₃	—	2	6	no	—
193	D₄×C₂₃	—	4	6	no	—
194	D₄×C₂₃	—	4	6	no	—
195	D₄×C₂₃	—	8	3	no	—
196	C₂×C₄×C₂₃	—	2	4	no	—
197	C₂×C₄×C₂₃	—	2	6	no	—
198	C₂×C₄×C₂₃	—	2	2	no	—
199	C₂×C₄×C₂₃	—	2	6	no	—
200	C₂×C₄×C₂₃	—	2	2	no	—
201	C₂×C₄×C₂₃	—	2	1	no	—
202	C₂×C₄×C₂₃	—	2	6	no	—
203	C₂×C₄×C₂₃	—	2	3	no	—
204	C₂×C₄×C₂₃	—	2	1	no	—
205	C₂×C₄×C₂₃	—	4	6	no	—
206	C₂×C₄×C₂₃	—	4	6	no	—
207	C₂×C₄×C₂₃	—	8	6	no	—
208	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
209	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
211	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
212	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
213	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
214	C₈×C₂₃	—	2	6	no	—
215	C₈×C₂₃	—	2	2	no	—
216	#3522	C₂×C₂₃	1	1	yes	characteristic
217	C₂×Q₈²	C₂×C₂₃	1	1	yes	characteristic, complemented
218	#3385	C₂×C₂₃	1	6	yes	complemented
219	Q₈×Q₁₆	C₂×C₂₃	1	2	yes	complemented
220	#3375	C₂×C₂₃	1	6	yes	complemented
221	#3362	C₂×C₂₃	1	2	yes	complemented
222	#3238	C₂×C₂₃	1	3	yes	complemented
223	#3226	C₂×C₂₃	1	3	yes	complemented
224	#3112	C₂×C₂₃	1	3	yes	complemented
225	#3108	C₂×C₂₃	1	3	yes	complemented
226	#2984	C₂×C₂₃	1	1	yes	characteristic, complemented
227	C₂²×C₂₃	—	2	1	no	—
228	C₂²×C₂₃	—	2	1	no	—
229	C₂²×C₂₃	—	4	3	no	—
230	C₂²×C₂₃	—	4	3	no	—
231	C₂²×C₂₃	—	4	3	no	—
232	C₂²×C₂₃	#576	1	2	yes	—
233	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
234	C₄×C₂₃	—	2	4	no	—
235	C₄×C₂₃	—	2	1	no	—
236	C₄×C₂₃	—	2	3	no	—
237	C₄×C₂₃	—	2	3	no	—
238	C₄×C₂₃	—	2	3	no	—
239	C₄×C₂₃	—	4	1	no	—
240	C₄×C₂₃	—	4	1	no	—
241	C₄×C₂₃	—	4	6	no	—
242	C₄×C₂₃	—	4	3	no	—
243	C₄×C₂₃	C₂×#137	1	6	yes	—
244	C₄×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
245	#559	C₂²×C₂₃	1	3	yes	—
246	Q₈²	—	2	1	no	—
247	Q₈²	—	2	3	no	—
248	Q₈²	C₂²×C₂₃	1	2	yes	—
249	Q₈²	C₂²×C₂₃	1	6	yes	—
250	Q₈²	C₂²×C₂₃	1	1	yes	characteristic
251	#554	C₂²×C₂₃	1	3	yes	—
252	#550	C₂²×C₂₃	1	1	yes	characteristic
253	#548	—	2	1	no	—
254	#547	—	2	3	no	—
255	#542	—	2	3	no	—
256	#532	C₂²×C₂₃	1	3	yes	—
257	C₂×C₄⋊Q₈	—	2	3	no	—
258	C₂×C₄⋊Q₈	C₂²×C₂₃	1	3	yes	—
259	#529	C₂²×C₂₃	1	3	yes	—
260	#520	—	2	1	no	—
261	C₂×C₄×Q₈	—	2	1	no	—
262	C₂×C₄×Q₈	C₂²×C₂₃	1	3	yes	—
263	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
264	#501	C₂²×C₂₃	1	6	yes	—
265	#500	C₂²×C₂₃	1	6	yes	—
266	#489	C₂²×C₂₃	1	6	yes	—
267	#486	C₂²×C₂₃	1	6	yes	—
268	#483	C₂²×C₂₃	1	3	yes	—
269	#480	C₂²×C₂₃	1	3	yes	—
270	#480	C₂²×C₂₃	1	6	yes	—
271	#479	C₂²×C₂₃	1	6	yes	—
272	#477	C₂²×C₂₃	1	6	yes	—
273	#477	C₂²×C₂₃	1	6	yes	—
274	#476	C₂²×C₂₃	1	6	yes	—
275	#474	C₂²×C₂₃	1	12	yes	—
276	#464	C₂²×C₂₃	1	6	yes	—
277	#460	C₂²×C₂₃	1	6	yes	—
278	#451	C₂²×C₂₃	1	1	yes	characteristic
279	#448	C₂²×C₂₃	1	3	yes	—
280	#446	C₂²×C₂₃	1	6	yes	—
281	C₈×Q₈	C₂²×C₂₃	1	2	yes	—
282	#440	C₂²×C₂₃	1	12	yes	—
283	C₄×Q₁₆	C₂²×C₂₃	1	6	yes	—
284	C₄×SD₁₆	C₂²×C₂₃	1	6	yes	—
285	#432	C₂²×C₂₃	1	3	yes	—
286	#431	C₂²×C₂₃	1	3	yes	—
287	C₂×C₂₃	—	2	2	no	—
288	C₂×C₂₃	—	8	3	no	—
289	C₂×C₂₃	#3486	1	1	yes	characteristic
290	C₂×C₂₃	C₂²×#137	1	1	yes	characteristic
291	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
292	C₂×#41	—	2	1	no	—
293	C₂×#41	—	2	3	no	—
294	C₂²×Q₈	—	2	3	no	—
295	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
296	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
297	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
298	C₂×SD₁₆	C₂³×C₂₃	1	6	yes	—
299	C₄⋊Q₈	—	2	6	no	—
300	C₄⋊Q₈	—	2	6	no	—
301	C₄⋊Q₈	—	2	12	no	—
302	C₄⋊Q₈	—	2	3	no	—
303	C₄⋊Q₈	—	2	3	no	—
304	C₄⋊Q₈	—	2	3	no	—
305	C₄⋊Q₈	C₂³×C₂₃	1	6	yes	—
306	C₄⋊Q₈	C₂³×C₂₃	1	6	yes	—
307	C₄⋊Q₈	C₂³×C₂₃	1	3	yes	—
308	#127	C₂³×C₂₃	1	3	yes	—
309	#126	—	2	3	no	—
310	#125	C₂³×C₂₃	1	3	yes	—
311	#124	—	2	3	no	—
312	#124	—	2	3	no	—
313	#124	C₂³×C₂₃	1	3	yes	—
314	#123	—	2	3	no	—
315	#123	—	2	6	no	—
316	C₂²⋊Q₈	—	2	3	no	—
317	C₂²⋊Q₈	—	2	6	no	—
318	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
319	#121	—	2	3	no	—
320	#121	—	2	3	no	—
321	#121	C₂³×C₂₃	1	3	yes	—
322	C₄×Q₈	—	2	6	no	—
323	C₄×Q₈	—	2	2	no	—
324	C₄×Q₈	—	2	1	no	—
325	C₄×Q₈	—	2	3	no	—
326	C₄×Q₈	—	2	3	no	—
327	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
328	C₄×Q₈	D₄×C₂₃	1	3	yes	—
329	C₄×Q₈	C₂³×C₂₃	1	6	yes	—
330	C₄×Q₈	C₂³×C₂₃	1	6	yes	—
331	C₄×Q₈	C₂³×C₂₃	1	3	yes	—
332	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
333	C₄×Q₈	C₂³×C₂₃	1	3	yes	—
334	C₄×D₄	—	2	3	no	—
335	C₄×D₄	—	2	3	no	—
336	C₄×D₄	—	2	3	no	—
337	C₄×D₄	C₂³×C₂₃	1	3	yes	—
338	C₄×D₄	C₂³×C₂₃	1	6	yes	—
339	#117	—	2	3	no	—
340	C₂×C₄⋊C₄	—	2	3	no	—
341	C₂×C₄⋊C₄	—	2	3	no	—
342	C₂×C₄⋊C₄	—	2	3	no	—
343	C₂×C₄⋊C₄	D₄×C₂₃	1	3	yes	—
344	C₂×C₄⋊C₄	C₂³×C₂₃	1	3	yes	—
345	C₂×C₄²	—	2	3	no	—
346	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
347	#107	C₂³×C₂₃	1	6	yes	—
348	#107	C₂³×C₂₃	1	12	yes	—
349	#106	C₂³×C₂₃	1	6	yes	—
350	C₄⋊C₈	C₂³×C₂₃	1	6	yes	—
351	C₄⋊C₈	C₂³×C₂₃	1	6	yes	—
352	#103	C₂³×C₂₃	1	2	yes	—
353	#103	C₂³×C₂₃	1	6	yes	—
354	#103	C₂³×C₂₃	1	6	yes	—
355	#102	C₂³×C₂₃	1	6	yes	—
356	#102	C₂³×C₂₃	1	12	yes	—
357	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
358	C₂²⋊C₈	C₂³×C₂₃	1	3	yes	—
359	#97	C₂³×C₂₃	1	6	yes	—
360	C₄×C₈	C₂³×C₂₃	1	6	yes	—
361	C₂₃	#61844	1	1	yes	characteristic, direct product factor, Sylow
362	#41	—	4	4	no	—
363	#41	—	8	6	no	—
364	C₂×Q₈	—	2	4	no	—
365	C₂×Q₈	—	2	4	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	—	2	3	no	—
368	C₂×Q₈	—	2	6	no	—
369	C₂×Q₈	—	2	6	no	—
370	C₂×Q₈	—	8	6	no	—
371	C₂×Q₈	C₂×D₄×C₂₃	1	3	yes	—
372	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
373	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
374	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
375	C₂×D₄	—	2	3	no	—
376	C₂×D₄	—	2	3	no	—
377	C₂×D₄	—	2	3	no	—
378	C₂×D₄	C₂⁴×C₂₃	1	3	yes	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	3	no	—
381	C₂²×C₄	—	2	3	no	—
382	C₂²×C₄	—	2	6	no	—
383	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
384	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
385	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
386	Q₁₆	—	2	4	no	—
387	SD₁₆	—	2	12	no	—
388	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
389	C₂×C₈	C₂⁴×C₂₃	1	6	yes	—
390	C₄⋊C₄	—	2	3	no	—
391	C₄⋊C₄	—	2	3	no	—
392	C₄⋊C₄	—	2	6	no	—
393	C₄⋊C₄	—	2	6	no	—
394	C₄⋊C₄	—	2	6	no	—
395	C₄⋊C₄	—	2	6	no	—
396	C₄⋊C₄	—	2	3	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	3	no	—
399	C₄⋊C₄	—	2	3	no	—
400	C₄⋊C₄	C₂×D₄×C₂₃	1	3	yes	—
401	C₄⋊C₄	C₂×D₄×C₂₃	1	3	yes	—
402	C₄⋊C₄	C₂×D₄×C₂₃	1	6	yes	—
403	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
404	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
405	C₄⋊C₄	C₂⁴×C₂₃	1	3	yes	—
406	C₂²⋊C₄	—	2	1	no	—
407	C₂²⋊C₄	—	2	3	no	—
408	C₂²⋊C₄	—	2	3	no	—
409	C₂²⋊C₄	—	2	3	no	—
410	C₂²⋊C₄	—	2	3	no	—
411	C₂²⋊C₄	—	2	6	no	—
412	C₄²	—	2	6	no	—
413	C₄²	—	2	6	no	—
414	C₄²	—	2	3	no	—
415	C₄²	C₂×D₄×C₂₃	1	3	yes	—
416	C₄²	C₂×D₄×C₂₃	1	3	yes	—
417	C₄²	C₂⁴×C₂₃	1	3	yes	—
418	C₄²	C₂⁴×C₂₃	1	3	yes	—
419	C₂³	—	2	3	no	—
420	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
421	Q₈	—	2	4	no	—
422	Q₈	—	2	6	no	—
423	Q₈	—	2	2	no	—
424	Q₈	—	2	2	no	—
425	Q₈	—	8	6	no	—
426	Q₈	—	8	6	no	—
427	Q₈	—	8	3	no	—
428	Q₈	C₂₃×#137	1	4	yes	—
429	Q₈	C₂₃×2₋¹⁺⁴	1	4	yes	—
430	D₄	—	2	6	no	—
431	D₄	—	4	6	no	—
432	D₄	—	4	6	no	—
433	D₄	—	8	3	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	6	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	6	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	6	no	—
441	C₂×C₄	—	2	3	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	4	6	no	—
444	C₂×C₄	—	4	6	no	—
445	C₂×C₄	—	8	6	no	—
446	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
447	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
448	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
449	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
450	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
451	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
452	C₈	—	2	6	no	—
453	C₈	—	2	2	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	4	3	no	—
457	C₂²	—	4	3	no	—
458	C₂²	—	4	3	no	—
459	C₂²	C₂₃×#576	1	2	yes	—
460	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
461	C₄	—	2	4	no	—
462	C₄	—	2	1	no	—
463	C₄	—	2	3	no	—
464	C₄	—	2	3	no	—
465	C₄	—	2	3	no	—
466	C₄	—	4	1	no	—
467	C₄	—	4	1	no	—
468	C₄	—	4	6	no	—
469	C₄	—	4	3	no	—
470	C₄	C₂×C₂₃×#137	1	6	yes	—
471	C₄	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
472	C₂	—	2	2	no	—
473	C₂	—	8	3	no	—
474	C₂	C₂₃×#3486	1	1	yes	characteristic
475	C₂	C₂²×C₂₃×#137	1	1	yes	characteristic
476	C₂	C₂×C₂₃×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3522	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄×Q₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×Q₈²×C₂₃	C₂	semidirect
3. C₂₃×#3385	C₂	semidirect
4. Q₈×Q₁₆×C₂₃	C₂	semidirect
5. C₂₃×#3375	C₂	semidirect
6. C₂₃×#3362	C₂	semidirect
7. C₂₃×#3238	C₂	semidirect
8. C₂₃×#3226	C₂	semidirect
9. C₂₃×#3112	C₂	semidirect
10. C₂₃×#3108	C₂	semidirect
11. C₂₃×#2984	C₂	semidirect
180. #61844	C₂₃	direct (N × H)
217. C₂×Q₈²	C₂×C₂₃	semidirect
218. #3385	C₂×C₂₃	semidirect
219. Q₈×Q₁₆	C₂×C₂₃	semidirect
220. #3375	C₂×C₂₃	semidirect
221. #3362	C₂×C₂₃	semidirect
222. #3238	C₂×C₂₃	semidirect
223. #3226	C₂×C₂₃	semidirect
224. #3112	C₂×C₂₃	semidirect
225. #3108	C₂×C₂₃	semidirect
226. #2984	C₂×C₂₃	semidirect
361. C₂₃	#61844	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3522	2
C₂×Q₈²×C₂₃	2
C₂₃×#3385	2
Q₈×Q₁₆×C₂₃	2
C₂₃×#3375	2
C₂₃×#3362	2
C₂₃×#3238	2
C₂₃×#3226	2
C₂₃×#3112	2
C₂₃×#3108	2
C₂₃×#2984	2
#61844	23

Subgroups — C23×#61844 #19209470

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61844 #19209470