Subgroups — C₂₃×#61292 #19208918

Order 5888.

1746 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3507	C₂	1	2	yes	maximal
2	C₂₃×#3349	C₂	1	8	yes	maximal, complemented
3	C₂₃×#3344	C₂	1	8	yes	maximal, complemented
4	C₂₃×#3162	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3097	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3078	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3059	C₂	1	2	yes	maximal, complemented
8	C₂×C₂₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2932	C₂	1	1	yes	maximal, characteristic
10	C₂₃×#2912	C₂	1	2	yes	maximal, complemented
11	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
12	C₂×C₂₃×#131	C₂²	1	2	yes	—
13	C₂₃×#559	—	2	2	no	—
14	C₂₃×#557	—	2	2	no	—
15	C₂₃×#556	—	2	4	no	—
16	C₂₃×#556	C₂²	1	4	yes	—
17	C₂₃×#554	C₂²	1	4	yes	—
18	C₂₃×#552	C₂²	1	8	yes	—
19	C₂₃×#539	—	2	4	no	—
20	C₂₃×#536	C₂²	1	4	yes	—
21	C₂₃×#533	C₂²	1	2	yes	—
22	C₂₃×#532	C₂²	1	1	yes	characteristic
23	C₂₃×#529	—	2	4	no	—
24	C₂₃×#520	C₂²	1	4	yes	—
25	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
26	C₂₃×#501	C₂²	1	4	yes	—
27	C₂₃×#501	C₂²	1	4	yes	—
28	C₂₃×#485	C₂²	1	8	yes	—
29	C₂₃×#485	C₂²	1	8	yes	—
30	C₂₃×#484	C₂²	1	8	yes	—
31	C₂₃×#483	C₂²	1	8	yes	—
32	C₂₃×#479	C₂²	1	8	yes	—
33	C₂₃×#477	C₂²	1	4	yes	—
34	C₂₃×#475	C₂²	1	4	yes	—
35	C₂₃×#470	C₂²	1	4	yes	—
36	C₂₃×#470	C₂²	1	4	yes	—
37	C₂₃×#467	C₂²	1	8	yes	—
38	C₂₃×#441	C₂²	1	8	yes	—
39	C₂₃×#435	C₂²	1	8	yes	—
40	C₂₃×#428	C₂²	1	4	yes	—
41	C₂₃×#428	C₂²	1	8	yes	—
42	C₂₃×#427	C₂²	1	2	yes	—
43	C₂₃×#427	C₂²	1	4	yes	—
44	C₂₃×#427	C₂²	1	2	yes	—
45	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
46	C₂×C₂₃×#106	C₂²	1	4	yes	—
47	C₂₃×#423	C₂²	1	1	yes	characteristic
48	C₂₃×#419	C₂²	1	4	yes	—
49	C₂×C₂₃×#103	C₂²	1	2	yes	—
50	C₂₃×#408	C₂²	1	2	yes	—
51	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
52	C₂×#41×C₂₃	C₂³	1	2	yes	—
53	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
54	C₂×Q₁₆×C₂₃	—	2	4	no	—
55	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
56	C₂₃×#131	—	2	8	no	—
57	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
58	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
59	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
60	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
62	C₂₃×C₄⋊Q₈	—	2	4	no	—
63	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
64	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
65	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
66	C₂₃×#127	D₄	1	1	yes	characteristic
67	C₂₃×#126	—	2	8	no	—
68	C₂₃×#126	—	2	8	no	—
69	C₂₃×#125	—	2	8	no	—
70	C₂₃×#125	—	2	4	no	—
71	C₂₃×#125	C₂³	1	4	yes	—
72	C₂₃×#124	—	2	4	no	—
73	C₂₃×#124	—	2	4	no	—
74	C₂₃×#124	D₄	1	2	yes	—
75	C₂₃×#123	—	2	8	no	—
76	C₂₃×#123	—	2	8	no	—
77	C₂₃×C₂²⋊Q₈	—	2	2	no	—
78	C₂₃×C₂²⋊Q₈	—	2	2	no	—
79	C₂₃×C₂²⋊Q₈	—	2	8	no	—
80	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
81	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
82	C₂₃×#121	D₄	1	4	yes	—
83	C₄×Q₈×C₂₃	—	2	4	no	—
84	C₄×Q₈×C₂₃	—	2	4	no	—
85	C₄×Q₈×C₂₃	—	2	2	no	—
86	C₄×Q₈×C₂₃	—	2	2	no	—
87	C₄×Q₈×C₂₃	—	2	2	no	—
88	C₄×Q₈×C₂₃	—	2	2	no	—
89	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
90	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
91	C₄×D₄×C₂₃	—	2	4	no	—
92	C₄×D₄×C₂₃	—	2	4	no	—
93	C₄×D₄×C₂₃	—	2	8	no	—
94	C₄×D₄×C₂₃	C₂³	1	4	yes	—
95	C₂₃×#117	—	2	8	no	—
96	C₂₃×#117	C₂³	1	8	yes	—
97	C₂₃×#117	C₂³	1	4	yes	—
98	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
99	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
100	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
101	C₂×C₄²×C₂₃	—	2	2	no	—
102	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
103	C₂₃×#107	C₂³	1	4	yes	—
104	C₂₃×#107	C₂³	1	8	yes	—
105	C₂₃×#107	C₂³	1	4	yes	—
106	C₂₃×#106	C₂³	1	4	yes	—
107	C₂₃×#106	C₂³	1	2	yes	—
108	C₂₃×#106	C₂³	1	8	yes	—
109	C₂₃×#106	C₂³	1	2	yes	—
110	C₂₃×#106	C₂³	1	2	yes	—
111	C₂₃×#106	C₂³	1	2	yes	—
112	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
113	C₂₃×#103	C₂³	1	8	yes	—
114	C₂₃×#103	C₂³	1	8	yes	—
115	C₂₃×#103	C₂³	1	8	yes	—
116	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	—
117	C₂₃×#97	C₂³	1	4	yes	—
118	#41×C₂₃	—	2	4	no	—
119	#41×C₂₃	—	2	4	no	—
120	C₂×Q₈×C₂₃	—	2	2	no	—
121	C₂×Q₈×C₂₃	—	2	2	no	—
122	C₂×Q₈×C₂₃	—	2	2	no	—
123	C₂×Q₈×C₂₃	—	2	4	no	—
124	C₂×Q₈×C₂₃	—	2	4	no	—
125	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
126	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
127	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
128	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
129	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₂₃	—	2	2	no	—
131	C₂²×C₄×C₂₃	—	2	2	no	—
132	C₂²×C₄×C₂₃	—	2	8	no	—
133	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
136	Q₁₆×C₂₃	—	2	8	no	—
137	M₁₆×C₂₃	—	2	4	no	—
138	M₁₆×C₂₃	—	2	8	no	—
139	C₂×C₈×C₂₃	—	2	2	no	—
140	C₂×C₈×C₂₃	—	2	8	no	—
141	C₂×C₈×C₂₃	#41	1	4	yes	—
142	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
143	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
144	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
145	C₄⋊C₄×C₂₃	—	2	4	no	—
146	C₄⋊C₄×C₂₃	—	2	4	no	—
147	C₄⋊C₄×C₂₃	—	2	2	no	—
148	C₄⋊C₄×C₂₃	—	2	8	no	—
149	C₄⋊C₄×C₂₃	—	2	4	no	—
150	C₄⋊C₄×C₂₃	—	2	8	no	—
151	C₄⋊C₄×C₂₃	—	2	2	no	—
152	C₄⋊C₄×C₂₃	—	2	4	no	—
153	C₄⋊C₄×C₂₃	—	2	2	no	—
154	C₄⋊C₄×C₂₃	—	2	8	no	—
155	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
156	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
157	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
158	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
159	C₂²⋊C₄×C₂₃	—	2	8	no	—
160	C₂²⋊C₄×C₂₃	—	2	4	no	—
161	C₂²⋊C₄×C₂₃	—	2	8	no	—
162	C₂²⋊C₄×C₂₃	—	2	8	no	—
163	C₂²⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
164	C₄²×C₂₃	—	2	4	no	—
165	C₄²×C₂₃	—	2	4	no	—
166	C₄²×C₂₃	—	2	8	no	—
167	C₄²×C₂₃	—	2	4	no	—
168	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₂₃	C₂⁴	1	2	yes	—
171	#61292	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
173	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
174	Q₈×C₂₃	—	2	4	no	—
175	Q₈×C₂₃	—	2	4	no	—
176	Q₈×C₂₃	—	2	4	no	—
177	Q₈×C₂₃	—	4	4	no	—
178	Q₈×C₂₃	—	4	4	no	—
179	Q₈×C₂₃	—	8	2	no	—
180	D₄×C₂₃	—	2	8	no	—
181	D₄×C₂₃	—	2	4	no	—
182	D₄×C₂₃	—	4	4	no	—
183	C₂×C₄×C₂₃	—	2	4	no	—
184	C₂×C₄×C₂₃	—	2	4	no	—
185	C₂×C₄×C₂₃	—	2	4	no	—
186	C₂×C₄×C₂₃	—	2	4	no	—
187	C₂×C₄×C₂₃	—	2	4	no	—
188	C₂×C₄×C₂₃	—	2	4	no	—
189	C₂×C₄×C₂₃	—	4	2	no	—
190	C₂×C₄×C₂₃	—	4	4	no	—
191	C₂×C₄×C₂₃	—	8	2	no	—
192	C₂×C₄×C₂₃	—	8	8	no	—
193	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
194	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
195	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
196	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
198	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
199	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
200	C₈×C₂₃	—	2	4	no	—
201	C₈×C₂₃	—	2	2	no	—
202	C₈×C₂₃	C₂×#41	1	4	yes	—
203	#3507	C₂×C₂₃	1	2	yes	—
204	#3349	C₂×C₂₃	1	8	yes	complemented
205	#3344	C₂×C₂₃	1	8	yes	complemented
206	#3162	C₂×C₂₃	1	1	yes	characteristic, complemented
207	#3097	C₂×C₂₃	1	4	yes	complemented
208	#3078	C₂×C₂₃	1	2	yes	complemented
209	#3059	C₂×C₂₃	1	2	yes	complemented
210	C₂×#441	C₂×C₂₃	1	1	yes	characteristic, complemented
211	#2932	C₂×C₂₃	1	1	yes	characteristic
212	#2912	C₂×C₂₃	1	2	yes	complemented
213	C₂²×C₂₃	—	2	2	no	—
214	C₂²×C₂₃	—	2	8	no	—
215	C₂²×C₂₃	—	2	4	no	—
216	C₂²×C₂₃	#547	1	2	yes	—
217	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
218	C₄×C₂₃	—	2	2	no	—
219	C₄×C₂₃	—	2	2	no	—
220	C₄×C₂₃	—	2	4	no	—
221	C₄×C₂₃	—	4	4	no	—
222	C₄×C₂₃	—	4	4	no	—
223	C₄×C₂₃	—	4	4	no	—
224	C₄×C₂₃	—	4	4	no	—
225	C₄×C₂₃	#547	1	2	yes	—
226	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
227	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
228	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
229	C₂×#131	C₂²×C₂₃	1	2	yes	—
230	#559	—	2	2	no	—
231	#557	—	2	2	no	—
232	#556	—	2	4	no	—
233	#556	C₂²×C₂₃	1	4	yes	—
234	#554	C₂²×C₂₃	1	4	yes	—
235	#552	C₂²×C₂₃	1	8	yes	—
236	#539	—	2	4	no	—
237	#536	C₂²×C₂₃	1	4	yes	—
238	#533	C₂²×C₂₃	1	2	yes	—
239	#532	C₂²×C₂₃	1	1	yes	characteristic
240	#529	—	2	4	no	—
241	#520	C₂²×C₂₃	1	4	yes	—
242	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
243	#501	C₂²×C₂₃	1	4	yes	—
244	#501	C₂²×C₂₃	1	4	yes	—
245	#485	C₂²×C₂₃	1	8	yes	—
246	#485	C₂²×C₂₃	1	8	yes	—
247	#484	C₂²×C₂₃	1	8	yes	—
248	#483	C₂²×C₂₃	1	8	yes	—
249	#479	C₂²×C₂₃	1	8	yes	—
250	#477	C₂²×C₂₃	1	4	yes	—
251	#475	C₂²×C₂₃	1	4	yes	—
252	#470	C₂²×C₂₃	1	4	yes	—
253	#470	C₂²×C₂₃	1	4	yes	—
254	#467	C₂²×C₂₃	1	8	yes	—
255	#441	C₂²×C₂₃	1	8	yes	—
256	#435	C₂²×C₂₃	1	8	yes	—
257	#428	C₂²×C₂₃	1	4	yes	—
258	#428	C₂²×C₂₃	1	8	yes	—
259	#427	C₂²×C₂₃	1	4	yes	—
260	#427	C₂²×C₂₃	1	2	yes	—
261	#427	C₂²×C₂₃	1	2	yes	—
262	C₂×#106	C₂²×C₂₃	1	4	yes	—
263	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
264	#423	C₂²×C₂₃	1	1	yes	characteristic
265	#419	C₂²×C₂₃	1	4	yes	—
266	C₂×#103	C₂²×C₂₃	1	2	yes	—
267	#408	C₂²×C₂₃	1	2	yes	—
268	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
269	C₂×C₂₃	—	2	2	no	—
270	C₂×C₂₃	—	4	4	no	—
271	C₂×C₂₃	C₂×#547	1	1	yes	characteristic
272	C₂×C₂₃	#3586	1	2	yes	—
273	C₂×#41	C₂³×C₂₃	1	2	yes	—
274	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
275	C₂×Q₁₆	—	2	4	no	—
276	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
277	#131	—	2	8	no	—
278	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
279	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
280	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
281	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
282	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
283	C₄⋊Q₈	—	2	4	no	—
284	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
285	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
286	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
287	#127	D₄×C₂₃	1	1	yes	characteristic
288	#126	—	2	8	no	—
289	#126	—	2	8	no	—
290	#125	—	2	4	no	—
291	#125	—	2	8	no	—
292	#125	C₂³×C₂₃	1	4	yes	—
293	#124	—	2	4	no	—
294	#124	—	2	4	no	—
295	#124	D₄×C₂₃	1	2	yes	—
296	#123	—	2	8	no	—
297	#123	—	2	8	no	—
298	C₂²⋊Q₈	—	2	2	no	—
299	C₂²⋊Q₈	—	2	2	no	—
300	C₂²⋊Q₈	—	2	8	no	—
301	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
302	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
303	#121	D₄×C₂₃	1	4	yes	—
304	C₄×Q₈	—	2	4	no	—
305	C₄×Q₈	—	2	4	no	—
306	C₄×Q₈	—	2	2	no	—
307	C₄×Q₈	—	2	2	no	—
308	C₄×Q₈	—	2	2	no	—
309	C₄×Q₈	—	2	2	no	—
310	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
311	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
312	C₄×D₄	—	2	8	no	—
313	C₄×D₄	—	2	4	no	—
314	C₄×D₄	—	2	4	no	—
315	C₄×D₄	C₂³×C₂₃	1	4	yes	—
316	#117	—	2	8	no	—
317	#117	C₂³×C₂₃	1	4	yes	—
318	#117	C₂³×C₂₃	1	8	yes	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
321	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
322	C₂×C₄²	—	2	2	no	—
323	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
324	#107	C₂³×C₂₃	1	4	yes	—
325	#107	C₂³×C₂₃	1	8	yes	—
326	#107	C₂³×C₂₃	1	4	yes	—
327	#106	C₂³×C₂₃	1	4	yes	—
328	#106	C₂³×C₂₃	1	2	yes	—
329	#106	C₂³×C₂₃	1	8	yes	—
330	#106	C₂³×C₂₃	1	2	yes	—
331	#106	C₂³×C₂₃	1	2	yes	—
332	#106	C₂³×C₂₃	1	2	yes	—
333	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
334	#103	C₂³×C₂₃	1	8	yes	—
335	#103	C₂³×C₂₃	1	8	yes	—
336	#103	C₂³×C₂₃	1	8	yes	—
337	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	—
338	#97	C₂³×C₂₃	1	4	yes	—
339	C₂₃	#61292	1	1	yes	characteristic, direct product factor, Sylow
340	#41	—	2	4	no	—
341	#41	—	2	4	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	4	no	—
346	C₂×Q₈	—	2	4	no	—
347	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
348	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
349	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
350	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
351	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	8	no	—
355	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
356	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
357	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
358	Q₁₆	—	2	8	no	—
359	M₁₆	—	2	4	no	—
360	M₁₆	—	2	8	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	8	no	—
363	C₂×C₈	#41×C₂₃	1	4	yes	—
364	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
365	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
366	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	8	no	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	8	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	8	no	—
377	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
378	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
379	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
380	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
381	C₂²⋊C₄	—	2	8	no	—
382	C₂²⋊C₄	—	2	4	no	—
383	C₂²⋊C₄	—	2	8	no	—
384	C₂²⋊C₄	—	2	8	no	—
385	C₂²⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
386	C₄²	—	2	4	no	—
387	C₄²	—	2	4	no	—
388	C₄²	—	2	8	no	—
389	C₄²	—	2	4	no	—
390	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
391	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
392	C₄²	C₂⁴×C₂₃	1	2	yes	—
393	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
394	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
395	Q₈	—	2	4	no	—
396	Q₈	—	2	4	no	—
397	Q₈	—	2	4	no	—
398	Q₈	—	4	4	no	—
399	Q₈	—	4	4	no	—
400	Q₈	—	8	2	no	—
401	D₄	—	2	8	no	—
402	D₄	—	2	4	no	—
403	D₄	—	4	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	8	2	no	—
413	C₂×C₄	—	8	8	no	—
414	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
415	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
416	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
417	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
418	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
419	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
420	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
421	C₈	—	2	4	no	—
422	C₈	—	2	2	no	—
423	C₈	C₂×#41×C₂₃	1	4	yes	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	2	8	no	—
427	C₂²	C₂₃×#547	1	2	yes	—
428	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
429	C₄	—	2	4	no	—
430	C₄	—	2	2	no	—
431	C₄	—	2	2	no	—
432	C₄	—	4	4	no	—
433	C₄	—	4	4	no	—
434	C₄	—	4	4	no	—
435	C₄	—	4	4	no	—
436	C₄	C₂₃×#547	1	2	yes	—
437	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
438	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
439	C₂	—	2	2	no	—
440	C₂	—	4	4	no	—
441	C₂	C₂×C₂₃×#547	1	1	yes	characteristic
442	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×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#3349	C₂	semidirect
3. C₂₃×#3344	C₂	semidirect
4. C₂₃×#3162	C₂	semidirect
5. C₂₃×#3097	C₂	semidirect
6. C₂₃×#3078	C₂	semidirect
7. C₂₃×#3059	C₂	semidirect
8. C₂×C₂₃×#441	C₂	semidirect
10. C₂₃×#2912	C₂	semidirect
171. #61292	C₂₃	direct (N × H)
204. #3349	C₂×C₂₃	semidirect
205. #3344	C₂×C₂₃	semidirect
206. #3162	C₂×C₂₃	semidirect
207. #3097	C₂×C₂₃	semidirect
208. #3078	C₂×C₂₃	semidirect
209. #3059	C₂×C₂₃	semidirect
210. C₂×#441	C₂×C₂₃	semidirect
212. #2912	C₂×C₂₃	semidirect
339. C₂₃	#61292	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×#3507	2
C₂₃×#3349	2
C₂₃×#3344	2
C₂₃×#3162	2
C₂₃×#3097	2
C₂₃×#3078	2
C₂₃×#3059	2
C₂×C₂₃×#441	2
C₂₃×#2932	2
C₂₃×#2912	2
#61292	23

Subgroups — C23×#61292 #19208918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61292 #19208918