Subgroups — C₂₃×#61906 #19209532

Order 5888.

1748 conjugacy classes of subgroups.

The subgroup lattice has 474 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×C₂₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3400	C₂	1	6	yes	maximal, complemented
4	C₂₃×#3392	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3372	C₂	1	6	yes	maximal, complemented
6	C₂₃×#3363	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3218	C₂	1	3	yes	maximal, complemented
8	C₂₃×#3206	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	C₂²	1	1	yes	characteristic
14	C₂₃×#557	—	2	1	no	—
15	C₂₃×#557	—	2	3	no	—
16	C₂₃×#557	C₂²	1	2	yes	—
17	C₂₃×#557	C₂²	1	6	yes	—
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	C₂²	1	3	yes	—
25	C₂₃×#529	C₂²	1	3	yes	—
26	C₂×C₂₃×#125	—	2	3	no	—
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×#497	C₂²	1	6	yes	—
32	C₂₃×#492	C₂²	1	6	yes	—
33	C₂₃×#491	C₂²	1	6	yes	—
34	C₂₃×#487	C₂²	1	6	yes	—
35	C₂₃×#483	C₂²	1	1	yes	characteristic
36	C₂₃×#480	C₂²	1	3	yes	—
37	C₂₃×#479	C₂²	1	6	yes	—
38	C₂₃×#477	C₂²	1	6	yes	—
39	C₂₃×#464	C₂²	1	6	yes	—
40	C₂₃×#462	C₂²	1	6	yes	—
41	C₂₃×#461	C₂²	1	12	yes	—
42	C₂₃×#461	C₂²	1	6	yes	—
43	C₂₃×#460	C₂²	1	6	yes	—
44	C₂₃×#451	C₂²	1	3	yes	—
45	C₂₃×#448	C₂²	1	3	yes	—
46	C₂₃×#448	C₂²	1	6	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	D₄	1	1	yes	characteristic
57	C₂²×Q₈×C₂₃	C₂³	1	3	yes	—
58	C₂×Q₁₆×C₂₃	C₂³	1	6	yes	—
59	C₂×SD₁₆×C₂₃	C₂³	1	6	yes	—
60	C₂×SD₁₆×C₂₃	C₂³	1	12	yes	—
61	C₂₃×C₄⋊Q₈	—	2	3	no	—
62	C₂₃×C₄⋊Q₈	—	2	3	no	—
63	C₂₃×C₄⋊Q₈	—	2	3	no	—
64	C₂₃×C₄⋊Q₈	C₂³	1	6	yes	—
65	C₂₃×C₄⋊Q₈	C₂³	1	6	yes	—
66	C₂₃×C₄⋊Q₈	C₂³	1	3	yes	—
67	C₂₃×#127	C₂³	1	3	yes	—
68	C₂₃×#126	—	2	3	no	—
69	C₂₃×#125	—	2	6	no	—
70	C₂₃×#125	—	2	6	no	—
71	C₂₃×#125	—	2	12	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	—	2	3	no	—
106	C₂×C₄⋊C₄×C₂₃	D₄	1	3	yes	—
107	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₂₃	—	2	3	no	—
109	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
110	C₂₃×#107	C₂³	1	6	yes	—
111	C₂₃×#106	C₂³	1	2	yes	—
112	C₂₃×C₄⋊C₈	C₂³	1	6	yes	—
113	C₂₃×C₄⋊C₈	C₂³	1	6	yes	—
114	C₂₃×#103	C₂³	1	6	yes	—
115	C₂₃×#103	C₂³	1	2	yes	—
116	C₂₃×#103	C₂³	1	6	yes	—
117	C₂₃×#103	C₂³	1	12	yes	—
118	C₂₃×#102	C₂³	1	6	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	3	no	—
127	C₂×Q₈×C₂₃	—	2	3	no	—
128	C₂×Q₈×C₂₃	—	4	6	no	—
129	C₂×Q₈×C₂₃	C₂×D₄	1	3	yes	—
130	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
131	C₂×Q₈×C₂₃	C₂⁴	1	6	yes	—
132	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
133	C₂×D₄×C₂₃	—	2	3	no	—
134	C₂×D₄×C₂₃	—	2	3	no	—
135	C₂×D₄×C₂₃	—	2	3	no	—
136	C₂×D₄×C₂₃	C₂⁴	1	3	yes	—
137	C₂²×C₄×C₂₃	—	2	1	no	—
138	C₂²×C₄×C₂₃	—	2	3	no	—
139	C₂²×C₄×C₂₃	—	2	3	no	—
140	C₂²×C₄×C₂₃	—	2	6	no	—
141	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
142	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
143	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
144	Q₁₆×C₂₃	—	4	6	no	—
145	SD₁₆×C₂₃	—	4	6	no	—
146	SD₁₆×C₂₃	—	4	12	no	—
147	C₂×C₈×C₂₃	C₂⁴	1	6	yes	—
148	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
149	C₄⋊C₄×C₂₃	—	2	3	no	—
150	C₄⋊C₄×C₂₃	—	2	3	no	—
151	C₄⋊C₄×C₂₃	—	2	6	no	—
152	C₄⋊C₄×C₂₃	—	2	6	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	1	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	2	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	#61906	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	6	no	—
184	Q₈×C₂₃	—	2	6	no	—
185	Q₈×C₂₃	—	2	6	no	—
186	Q₈×C₂₃	—	2	2	no	—
187	Q₈×C₂₃	—	4	6	no	—
188	Q₈×C₂₃	—	8	3	no	—
189	Q₈×C₂₃	#137	1	4	yes	—
190	D₄×C₂₃	—	2	6	no	—
191	D₄×C₂₃	—	4	6	no	—
192	D₄×C₂₃	—	4	6	no	—
193	D₄×C₂₃	—	8	3	no	—
194	C₂×C₄×C₂₃	—	2	6	no	—
195	C₂×C₄×C₂₃	—	2	6	no	—
196	C₂×C₄×C₂₃	—	2	2	no	—
197	C₂×C₄×C₂₃	—	2	2	no	—
198	C₂×C₄×C₂₃	—	2	1	no	—
199	C₂×C₄×C₂₃	—	2	6	no	—
200	C₂×C₄×C₂₃	—	2	3	no	—
201	C₂×C₄×C₂₃	—	2	1	no	—
202	C₂×C₄×C₂₃	—	4	6	no	—
203	C₂×C₄×C₂₃	—	4	2	no	—
204	C₂×C₄×C₂₃	—	4	6	no	—
205	C₂×C₄×C₂₃	—	8	6	no	—
206	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
207	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
209	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
210	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
211	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
212	C₈×C₂₃	—	2	2	no	—
213	C₈×C₂₃	—	2	6	no	—
214	#3522	C₂×C₂₃	1	1	yes	characteristic
215	C₂×#557	C₂×C₂₃	1	1	yes	characteristic, complemented
216	#3400	C₂×C₂₃	1	6	yes	complemented
217	#3392	C₂×C₂₃	1	2	yes	complemented
218	#3372	C₂×C₂₃	1	6	yes	complemented
219	#3363	C₂×C₂₃	1	2	yes	complemented
220	#3218	C₂×C₂₃	1	3	yes	complemented
221	#3206	C₂×C₂₃	1	3	yes	complemented
222	#3112	C₂×C₂₃	1	3	yes	complemented
223	#3108	C₂×C₂₃	1	3	yes	complemented
224	#2984	C₂×C₂₃	1	1	yes	characteristic, complemented
225	C₂²×C₂₃	—	2	1	no	—
226	C₂²×C₂₃	—	2	1	no	—
227	C₂²×C₂₃	—	4	3	no	—
228	C₂²×C₂₃	—	4	3	no	—
229	C₂²×C₂₃	—	4	3	no	—
230	C₂²×C₂₃	#577	1	2	yes	—
231	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
232	C₄×C₂₃	—	2	1	no	—
233	C₄×C₂₃	—	2	3	no	—
234	C₄×C₂₃	—	2	3	no	—
235	C₄×C₂₃	—	2	3	no	—
236	C₄×C₂₃	—	4	6	no	—
237	C₄×C₂₃	—	4	1	no	—
238	C₄×C₂₃	—	4	1	no	—
239	C₄×C₂₃	—	4	2	no	—
240	C₄×C₂₃	—	4	3	no	—
241	C₄×C₂₃	C₂×#137	1	6	yes	—
242	C₄×C₂₃	#585	1	2	yes	—
243	#559	C₂²×C₂₃	1	3	yes	—
244	Q₈²	C₂²×C₂₃	1	1	yes	characteristic
245	#557	—	2	1	no	—
246	#557	—	2	3	no	—
247	#557	C₂²×C₂₃	1	2	yes	—
248	#557	C₂²×C₂₃	1	6	yes	—
249	#554	C₂²×C₂₃	1	3	yes	—
250	#550	C₂²×C₂₃	1	1	yes	characteristic
251	#548	—	2	1	no	—
252	#547	—	2	3	no	—
253	#542	—	2	3	no	—
254	#532	C₂²×C₂₃	1	3	yes	—
255	C₂×C₄⋊Q₈	C₂²×C₂₃	1	3	yes	—
256	#529	C₂²×C₂₃	1	3	yes	—
257	C₂×#125	—	2	3	no	—
258	#520	—	2	1	no	—
259	C₂×C₄×Q₈	—	2	1	no	—
260	C₂×C₄×Q₈	C₂²×C₂₃	1	3	yes	—
261	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
262	#497	C₂²×C₂₃	1	6	yes	—
263	#492	C₂²×C₂₃	1	6	yes	—
264	#491	C₂²×C₂₃	1	6	yes	—
265	#487	C₂²×C₂₃	1	6	yes	—
266	#483	C₂²×C₂₃	1	1	yes	characteristic
267	#480	C₂²×C₂₃	1	3	yes	—
268	#479	C₂²×C₂₃	1	6	yes	—
269	#477	C₂²×C₂₃	1	6	yes	—
270	#464	C₂²×C₂₃	1	6	yes	—
271	#462	C₂²×C₂₃	1	6	yes	—
272	#461	C₂²×C₂₃	1	6	yes	—
273	#461	C₂²×C₂₃	1	12	yes	—
274	#460	C₂²×C₂₃	1	6	yes	—
275	#451	C₂²×C₂₃	1	3	yes	—
276	#448	C₂²×C₂₃	1	3	yes	—
277	#448	C₂²×C₂₃	1	6	yes	—
278	#446	C₂²×C₂₃	1	6	yes	—
279	C₈×Q₈	C₂²×C₂₃	1	2	yes	—
280	#440	C₂²×C₂₃	1	12	yes	—
281	C₄×Q₁₆	C₂²×C₂₃	1	6	yes	—
282	C₄×SD₁₆	C₂²×C₂₃	1	6	yes	—
283	#432	C₂²×C₂₃	1	3	yes	—
284	#431	C₂²×C₂₃	1	3	yes	—
285	C₂×C₂₃	—	2	2	no	—
286	C₂×C₂₃	—	8	3	no	—
287	C₂×C₂₃	#3487	1	1	yes	characteristic
288	C₂×C₂₃	C₂²×#137	1	1	yes	characteristic
289	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
290	C₂×#41	—	2	1	no	—
291	C₂×#41	—	2	3	no	—
292	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
293	C₂²×Q₈	C₂³×C₂₃	1	3	yes	—
294	C₂×Q₁₆	C₂³×C₂₃	1	6	yes	—
295	C₂×SD₁₆	C₂³×C₂₃	1	6	yes	—
296	C₂×SD₁₆	C₂³×C₂₃	1	12	yes	—
297	C₄⋊Q₈	—	2	3	no	—
298	C₄⋊Q₈	—	2	3	no	—
299	C₄⋊Q₈	—	2	3	no	—
300	C₄⋊Q₈	C₂³×C₂₃	1	6	yes	—
301	C₄⋊Q₈	C₂³×C₂₃	1	6	yes	—
302	C₄⋊Q₈	C₂³×C₂₃	1	3	yes	—
303	#127	C₂³×C₂₃	1	3	yes	—
304	#126	—	2	3	no	—
305	#125	—	2	6	no	—
306	#125	—	2	6	no	—
307	#125	—	2	12	no	—
308	#125	C₂³×C₂₃	1	3	yes	—
309	#124	—	2	3	no	—
310	#124	—	2	3	no	—
311	#124	C₂³×C₂₃	1	3	yes	—
312	#123	—	2	3	no	—
313	#123	—	2	6	no	—
314	C₂²⋊Q₈	—	2	3	no	—
315	C₂²⋊Q₈	—	2	6	no	—
316	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
317	#121	—	2	3	no	—
318	#121	—	2	3	no	—
319	#121	C₂³×C₂₃	1	3	yes	—
320	C₄×Q₈	—	2	6	no	—
321	C₄×Q₈	—	2	2	no	—
322	C₄×Q₈	—	2	1	no	—
323	C₄×Q₈	—	2	3	no	—
324	C₄×Q₈	—	2	3	no	—
325	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
326	C₄×Q₈	D₄×C₂₃	1	3	yes	—
327	C₄×Q₈	C₂³×C₂₃	1	6	yes	—
328	C₄×Q₈	C₂³×C₂₃	1	6	yes	—
329	C₄×Q₈	C₂³×C₂₃	1	3	yes	—
330	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
331	C₄×Q₈	C₂³×C₂₃	1	3	yes	—
332	C₄×D₄	—	2	3	no	—
333	C₄×D₄	—	2	3	no	—
334	C₄×D₄	—	2	3	no	—
335	C₄×D₄	C₂³×C₂₃	1	3	yes	—
336	C₄×D₄	C₂³×C₂₃	1	6	yes	—
337	#117	—	2	3	no	—
338	C₂×C₄⋊C₄	—	2	3	no	—
339	C₂×C₄⋊C₄	—	2	3	no	—
340	C₂×C₄⋊C₄	—	2	3	no	—
341	C₂×C₄⋊C₄	—	2	3	no	—
342	C₂×C₄⋊C₄	D₄×C₂₃	1	3	yes	—
343	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
344	C₂×C₄²	—	2	3	no	—
345	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
346	#107	C₂³×C₂₃	1	6	yes	—
347	#106	C₂³×C₂₃	1	2	yes	—
348	C₄⋊C₈	C₂³×C₂₃	1	6	yes	—
349	C₄⋊C₈	C₂³×C₂₃	1	6	yes	—
350	#103	C₂³×C₂₃	1	6	yes	—
351	#103	C₂³×C₂₃	1	2	yes	—
352	#103	C₂³×C₂₃	1	6	yes	—
353	#103	C₂³×C₂₃	1	12	yes	—
354	#102	C₂³×C₂₃	1	6	yes	—
355	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
356	C₂²⋊C₈	C₂³×C₂₃	1	3	yes	—
357	#97	C₂³×C₂₃	1	6	yes	—
358	C₄×C₈	C₂³×C₂₃	1	6	yes	—
359	C₂₃	#61906	1	1	yes	characteristic, direct product factor, Sylow
360	#41	—	4	4	no	—
361	#41	—	8	6	no	—
362	C₂×Q₈	—	2	4	no	—
363	C₂×Q₈	—	2	3	no	—
364	C₂×Q₈	—	2	3	no	—
365	C₂×Q₈	—	4	6	no	—
366	C₂×Q₈	C₂×D₄×C₂₃	1	3	yes	—
367	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
368	C₂×Q₈	C₂⁴×C₂₃	1	6	yes	—
369	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
370	C₂×D₄	—	2	3	no	—
371	C₂×D₄	—	2	3	no	—
372	C₂×D₄	—	2	3	no	—
373	C₂×D₄	C₂⁴×C₂₃	1	3	yes	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	3	no	—
376	C₂²×C₄	—	2	3	no	—
377	C₂²×C₄	—	2	6	no	—
378	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
379	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
380	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
381	Q₁₆	—	4	6	no	—
382	SD₁₆	—	4	6	no	—
383	SD₁₆	—	4	12	no	—
384	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
385	C₂×C₈	C₂⁴×C₂₃	1	6	yes	—
386	C₄⋊C₄	—	2	3	no	—
387	C₄⋊C₄	—	2	3	no	—
388	C₄⋊C₄	—	2	6	no	—
389	C₄⋊C₄	—	2	6	no	—
390	C₄⋊C₄	—	2	6	no	—
391	C₄⋊C₄	—	2	6	no	—
392	C₄⋊C₄	—	2	6	no	—
393	C₄⋊C₄	—	2	6	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	3	no	—
397	C₄⋊C₄	—	2	3	no	—
398	C₄⋊C₄	C₂×D₄×C₂₃	1	3	yes	—
399	C₄⋊C₄	C₂×D₄×C₂₃	1	3	yes	—
400	C₄⋊C₄	C₂×D₄×C₂₃	1	6	yes	—
401	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
402	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
403	C₄⋊C₄	C₂⁴×C₂₃	1	3	yes	—
404	C₂²⋊C₄	—	2	1	no	—
405	C₂²⋊C₄	—	2	3	no	—
406	C₂²⋊C₄	—	2	3	no	—
407	C₂²⋊C₄	—	2	3	no	—
408	C₂²⋊C₄	—	2	3	no	—
409	C₂²⋊C₄	—	2	6	no	—
410	C₄²	—	2	6	no	—
411	C₄²	—	2	6	no	—
412	C₄²	—	2	3	no	—
413	C₄²	C₂×D₄×C₂₃	1	3	yes	—
414	C₄²	C₂×D₄×C₂₃	1	3	yes	—
415	C₄²	C₂⁴×C₂₃	1	3	yes	—
416	C₄²	C₂⁴×C₂₃	1	3	yes	—
417	C₂³	—	2	3	no	—
418	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
419	Q₈	—	2	6	no	—
420	Q₈	—	2	6	no	—
421	Q₈	—	2	6	no	—
422	Q₈	—	2	2	no	—
423	Q₈	—	4	6	no	—
424	Q₈	—	8	3	no	—
425	Q₈	C₂₃×#137	1	4	yes	—
426	D₄	—	2	6	no	—
427	D₄	—	4	6	no	—
428	D₄	—	4	6	no	—
429	D₄	—	8	3	no	—
430	C₂×C₄	—	2	6	no	—
431	C₂×C₄	—	2	6	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	6	no	—
436	C₂×C₄	—	2	3	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	4	6	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	6	no	—
441	C₂×C₄	—	8	6	no	—
442	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
443	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
444	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
445	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
446	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
447	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
448	C₈	—	2	2	no	—
449	C₈	—	2	6	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	4	3	no	—
453	C₂²	—	4	3	no	—
454	C₂²	—	4	3	no	—
455	C₂²	C₂₃×#577	1	2	yes	—
456	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
457	C₄	—	2	1	no	—
458	C₄	—	2	3	no	—
459	C₄	—	2	3	no	—
460	C₄	—	2	3	no	—
461	C₄	—	4	6	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	1	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	3	no	—
466	C₄	C₂×C₂₃×#137	1	6	yes	—
467	C₄	C₂₃×#585	1	2	yes	—
468	C₂	—	2	2	no	—
469	C₂	—	8	3	no	—
470	C₂	C₂₃×#3487	1	1	yes	characteristic
471	C₂	C₂²×C₂₃×#137	1	1	yes	characteristic
472	C₂	C₂×C₂₃×#577	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×C₂₃×#557	C₂	semidirect
3. C₂₃×#3400	C₂	semidirect
4. C₂₃×#3392	C₂	semidirect
5. C₂₃×#3372	C₂	semidirect
6. C₂₃×#3363	C₂	semidirect
7. C₂₃×#3218	C₂	semidirect
8. C₂₃×#3206	C₂	semidirect
9. C₂₃×#3112	C₂	semidirect
10. C₂₃×#3108	C₂	semidirect
11. C₂₃×#2984	C₂	semidirect
180. #61906	C₂₃	direct (N × H)
215. C₂×#557	C₂×C₂₃	semidirect
216. #3400	C₂×C₂₃	semidirect
217. #3392	C₂×C₂₃	semidirect
218. #3372	C₂×C₂₃	semidirect
219. #3363	C₂×C₂₃	semidirect
220. #3218	C₂×C₂₃	semidirect
221. #3206	C₂×C₂₃	semidirect
222. #3112	C₂×C₂₃	semidirect
223. #3108	C₂×C₂₃	semidirect
224. #2984	C₂×C₂₃	semidirect
359. C₂₃	#61906	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×C₂₃×#557	2
C₂₃×#3400	2
C₂₃×#3392	2
C₂₃×#3372	2
C₂₃×#3363	2
C₂₃×#3218	2
C₂₃×#3206	2
C₂₃×#3112	2
C₂₃×#3108	2
C₂₃×#2984	2
#61906	23

Subgroups — C23×#61906 #19209532

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61906 #19209532