Subgroups — C₂₃×#33519 #19181145

Order 5888.

1144 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#510	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#509	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3050	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2189	C₂	1	4	yes	maximal, complemented
6	C₂₃×#2186	C₂	1	4	yes	maximal, complemented
7	C₂₃×#2141	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2140	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2112	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₂₃	—	2	1	no	—
11	C₂×C₂₃×#135	—	2	4	no	—
12	C₂×C₂₃×#135	—	2	4	no	—
13	C₂×C₂₃×#135	—	2	2	no	—
14	C₂×C₂₃×#135	C₂²	1	4	yes	—
15	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
16	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₂₃	—	2	1	no	—
18	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
20	C₂₃×#525	—	2	1	no	—
21	C₂₃×#510	—	2	4	no	—
22	C₂₃×#509	—	2	4	no	—
23	C₂×C₂₃×Q₃₂	C₂²	1	2	yes	complemented
24	C₂×C₂₃×SD₃₂	C₂²	1	2	yes	complemented
25	C₂×C₂₃×SD₃₂	C₂²	1	2	yes	complemented
26	C₂×C₂₃×D₁₆	C₂²	1	2	yes	complemented
27	C₂×C₂₃×M₃₂	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×M₃₂	C₂²	1	1	yes	characteristic
29	C₂₃×#467	C₂²	1	2	yes	complemented
30	C₂₃×#466	C₂²	1	2	yes	complemented
31	C₂₃×#465	—	2	2	no	—
32	C₂₃×#427	C₂²	1	1	yes	characteristic
33	C₂₃×#416	—	2	1	no	—
34	C₂₃×#358	C₂²	1	4	yes	complemented
35	C₂₃×#357	C₂²	1	4	yes	complemented
36	C₂₃×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
37	C₂×#41×C₂₃	—	2	8	no	—
38	C₂×#41×C₂₃	—	2	4	no	—
39	C₂×#41×C₂₃	—	2	1	no	—
40	C₂×#41×C₂₃	—	4	4	no	—
41	C₂×#41×C₂₃	—	4	2	no	—
42	C₂²×Q₈×C₂₃	—	2	1	no	—
43	C₂²×D₄×C₂₃	—	2	1	no	—
44	C₂²×D₄×C₂₃	—	4	1	no	—
45	C₂³×C₄×C₂₃	—	4	1	no	—
46	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
47	C₂₃×#135	—	2	16	no	—
48	C₂₃×#135	—	2	8	no	—
49	C₂₃×#135	—	2	8	no	—
50	C₂₃×#135	—	2	2	no	—
51	C₂₃×#135	—	2	2	no	—
52	C₂×Q₁₆×C₂₃	—	2	1	no	—
53	C₂×Q₁₆×C₂₃	—	2	2	no	—
54	C₂×Q₁₆×C₂₃	D₄	1	4	yes	complemented
55	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
56	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
57	C₂×SD₁₆×C₂₃	—	2	8	no	—
58	C₂×SD₁₆×C₂₃	—	2	4	no	—
59	C₂×SD₁₆×C₂₃	—	2	1	no	—
60	C₂×D₈×C₂₃	—	2	1	no	—
61	C₂×D₈×C₂₃	—	2	2	no	—
62	C₂×D₈×C₂₃	D₄	1	4	yes	complemented
63	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
64	C₂×D₈×C₂₃	C₂³	1	2	yes	—
65	C₂²×C₈×C₂₃	—	2	2	no	—
66	C₂²×C₈×C₂₃	—	2	2	no	—
67	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
68	C₂²×C₈×C₂₃	D₄	1	2	yes	—
69	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
70	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
71	C₂₃×#123	—	4	1	no	—
72	C₂₃×C₂²⋊Q₈	—	2	2	no	—
73	C₂₃×#121	—	2	2	no	—
74	C₂₃×#120	—	4	1	no	—
75	C₄×D₄×C₂₃	—	4	2	no	—
76	C₂₃×#117	—	2	1	no	—
77	C₂₃×Q₃₂	—	2	4	no	—
78	C₂₃×SD₃₂	—	2	4	no	—
79	C₂₃×SD₃₂	—	2	4	no	—
80	C₂₃×D₁₆	—	2	4	no	—
81	C₂₃×M₃₂	—	2	2	no	—
82	C₂₃×M₃₂	—	2	2	no	—
83	C₂×C₁₆×C₂₃	C₂³	1	2	yes	—
84	C₂×C₁₆×C₂₃	C₂³	1	2	yes	—
85	C₂₃×#107	C₂³	1	2	yes	—
86	C₂₃×#106	—	2	1	no	—
87	C₂₃×#103	—	2	2	no	—
88	C₂₃×#102	—	2	2	no	—
89	C₂⁴×C₂₃	—	4	1	no	—
90	C₂⁴×C₂₃	D₈	1	1	yes	characteristic
91	#41×C₂₃	—	2	16	no	—
92	#41×C₂₃	—	4	8	no	—
93	#41×C₂₃	—	4	16	no	—
94	#41×C₂₃	—	4	2	no	—
95	#41×C₂₃	—	4	2	no	—
96	C₂×Q₈×C₂₃	—	2	4	no	—
97	C₂×Q₈×C₂₃	—	2	2	no	—
98	C₂×Q₈×C₂₃	—	2	1	no	—
99	C₂×Q₈×C₂₃	—	4	1	no	—
100	C₂×Q₈×C₂₃	—	4	2	no	—
101	C₂×D₄×C₂₃	—	2	4	no	—
102	C₂×D₄×C₂₃	—	2	2	no	—
103	C₂×D₄×C₂₃	—	2	1	no	—
104	C₂×D₄×C₂₃	—	4	8	no	—
105	C₂×D₄×C₂₃	—	4	4	no	—
106	C₂×D₄×C₂₃	—	4	2	no	—
107	C₂×D₄×C₂₃	—	4	1	no	—
108	C₂×D₄×C₂₃	—	4	1	no	—
109	C₂×D₄×C₂₃	—	4	2	no	—
110	C₂²×C₄×C₂₃	—	2	2	no	—
111	C₂²×C₄×C₂₃	—	2	2	no	—
112	C₂²×C₄×C₂₃	—	4	8	no	—
113	C₂²×C₄×C₂₃	—	4	1	no	—
114	C₂²×C₄×C₂₃	—	4	4	no	—
115	C₂²×C₄×C₂₃	—	4	1	no	—
116	C₂²×C₄×C₂₃	D₈	1	2	yes	—
117	C₂²×C₄×C₂₃	D₈	1	1	yes	characteristic
118	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
120	Q₁₆×C₂₃	—	2	4	no	—
121	Q₁₆×C₂₃	—	2	2	no	—
122	Q₁₆×C₂₃	—	2	1	no	—
123	Q₁₆×C₂₃	—	2	1	no	—
124	Q₁₆×C₂₃	C₂×D₄	1	4	yes	—
125	SD₁₆×C₂₃	—	2	16	no	—
126	SD₁₆×C₂₃	—	4	2	no	—
127	D₈×C₂₃	—	2	4	no	—
128	D₈×C₂₃	—	2	2	no	—
129	D₈×C₂₃	—	2	1	no	—
130	D₈×C₂₃	—	2	1	no	—
131	D₈×C₂₃	C₂×D₄	1	4	yes	—
132	C₂×C₈×C₂₃	—	2	2	no	—
133	C₂×C₈×C₂₃	—	2	4	no	—
134	C₂×C₈×C₂₃	—	2	2	no	—
135	C₂×C₈×C₂₃	—	2	2	no	—
136	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
141	C₄⋊C₄×C₂₃	—	2	2	no	—
142	C₄⋊C₄×C₂₃	—	4	2	no	—
143	C₂²⋊C₄×C₂₃	—	4	1	no	—
144	C₂²⋊C₄×C₂₃	—	4	2	no	—
145	C₂²⋊C₄×C₂₃	—	4	2	no	—
146	C₄²×C₂₃	—	4	1	no	—
147	C₁₆×C₂₃	—	2	2	no	—
148	C₁₆×C₂₃	—	2	2	no	—
149	#33519	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂³×C₂₃	—	2	2	no	—
151	C₂³×C₂₃	—	4	2	no	—
152	C₂³×C₂₃	—	4	2	no	—
153	C₂³×C₂₃	—	4	4	no	—
154	C₂³×C₂₃	—	4	1	no	—
155	C₂³×C₂₃	—	8	4	no	—
156	C₂³×C₂₃	C₂×D₈	1	2	yes	—
157	C₂³×C₂₃	C₂×D₈	1	1	yes	characteristic
158	Q₈×C₂₃	—	2	4	no	—
159	Q₈×C₂₃	—	4	2	no	—
160	Q₈×C₂₃	—	4	4	no	—
161	Q₈×C₂₃	—	4	1	no	—
162	Q₈×C₂₃	—	4	1	no	—
163	D₄×C₂₃	—	2	4	no	—
164	D₄×C₂₃	—	4	16	no	—
165	D₄×C₂₃	—	4	1	no	—
166	D₄×C₂₃	—	4	2	no	—
167	D₄×C₂₃	—	4	1	no	—
168	D₄×C₂₃	—	4	4	no	—
169	D₄×C₂₃	—	8	4	no	—
170	D₄×C₂₃	—	8	2	no	—
171	C₂×C₄×C₂₃	—	2	2	no	—
172	C₂×C₄×C₂₃	—	2	2	no	—
173	C₂×C₄×C₂₃	—	2	2	no	—
174	C₂×C₄×C₂₃	—	2	4	no	—
175	C₂×C₄×C₂₃	—	4	16	no	—
176	C₂×C₄×C₂₃	—	4	2	no	—
177	C₂×C₄×C₂₃	—	4	4	no	—
178	C₂×C₄×C₂₃	—	4	2	no	—
179	C₂×C₄×C₂₃	—	4	1	no	—
180	C₂×C₄×C₂₃	—	8	2	no	—
181	C₂×C₄×C₂₃	#120	1	2	yes	—
182	C₂×C₄×C₂₃	C₂×D₈	1	2	yes	—
183	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
184	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
185	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
186	C₈×C₂₃	—	2	2	no	—
187	C₈×C₂₃	#120	1	2	yes	—
188	C₈×C₂₃	C₂²×D₄	1	1	yes	characteristic
189	C₈×C₂₃	C₂²×D₄	1	1	yes	characteristic
190	C₂²×#135	C₂×C₂₃	1	1	yes	characteristic, complemented
191	C₂×#510	C₂×C₂₃	1	1	yes	characteristic, complemented
192	C₂×#509	C₂×C₂₃	1	1	yes	characteristic, complemented
193	#3050	C₂×C₂₃	1	1	yes	characteristic, complemented
194	#2189	C₂×C₂₃	1	4	yes	complemented
195	#2186	C₂×C₂₃	1	4	yes	complemented
196	#2141	C₂×C₂₃	1	1	yes	characteristic, complemented
197	#2140	C₂×C₂₃	1	1	yes	characteristic, complemented
198	#2112	C₂×C₂₃	1	1	yes	characteristic, complemented
199	C₂²×C₂₃	—	2	2	no	—
200	C₂²×C₂₃	—	2	2	no	—
201	C₂²×C₂₃	—	2	2	no	—
202	C₂²×C₂₃	—	2	2	no	—
203	C₂²×C₂₃	—	4	4	no	—
204	C₂²×C₂₃	—	4	4	no	—
205	C₂²×C₂₃	—	8	8	no	—
206	C₂²×C₂₃	—	8	4	no	—
207	C₂²×C₂₃	—	8	2	no	—
208	C₂²×C₂₃	—	8	1	no	—
209	C₂²×C₂₃	#447	1	2	yes	—
210	C₂²×C₂₃	C₂²×D₈	1	1	yes	characteristic
211	C₄×C₂₃	—	2	2	no	—
212	C₄×C₂₃	—	4	4	no	—
213	C₄×C₂₃	—	8	2	no	—
214	C₄×C₂₃	—	8	1	no	—
215	C₄×C₂₃	#447	1	2	yes	—
216	C₄×C₂₃	C₂×#120	1	1	yes	characteristic
217	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
218	C₂²×#41	—	2	1	no	—
219	C₂×#135	—	2	4	no	—
220	C₂×#135	—	2	4	no	—
221	C₂×#135	—	2	2	no	—
222	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
223	C₂×#135	C₂²×C₂₃	1	4	yes	—
224	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
225	C₂²×SD₁₆	—	2	1	no	—
226	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
227	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
228	#525	—	2	1	no	—
229	#510	—	2	4	no	—
230	#509	—	2	4	no	—
231	C₂×Q₃₂	C₂²×C₂₃	1	2	yes	complemented
232	C₂×SD₃₂	C₂²×C₂₃	1	2	yes	complemented
233	C₂×SD₃₂	C₂²×C₂₃	1	2	yes	complemented
234	C₂×D₁₆	C₂²×C₂₃	1	2	yes	complemented
235	C₂×M₃₂	C₂²×C₂₃	1	1	yes	characteristic
236	C₂×M₃₂	C₂²×C₂₃	1	1	yes	characteristic
237	#467	C₂²×C₂₃	1	2	yes	complemented
238	#466	C₂²×C₂₃	1	2	yes	complemented
239	#465	—	2	2	no	—
240	#427	C₂²×C₂₃	1	1	yes	characteristic
241	#416	—	2	1	no	—
242	#358	C₂²×C₂₃	1	4	yes	complemented
243	#357	C₂²×C₂₃	1	4	yes	complemented
244	C₂²⋊C₁₆	C₂²×C₂₃	1	4	yes	complemented
245	C₂×C₂₃	—	2	2	no	—
246	C₂×C₂₃	—	4	2	no	—
247	C₂×C₂₃	—	8	4	no	—
248	C₂×C₂₃	—	16	1	no	—
249	C₂×C₂₃	C₂×#447	1	1	yes	characteristic
250	C₂×C₂₃	#3414	1	2	yes	—
251	C₂×#41	—	2	8	no	—
252	C₂×#41	—	2	4	no	—
253	C₂×#41	—	2	1	no	—
254	C₂×#41	—	4	4	no	—
255	C₂×#41	—	4	2	no	—
256	C₂²×Q₈	—	2	1	no	—
257	C₂²×D₄	—	2	1	no	—
258	C₂²×D₄	—	4	1	no	—
259	C₂³×C₄	—	4	1	no	—
260	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
261	#135	—	2	16	no	—
262	#135	—	2	8	no	—
263	#135	—	2	8	no	—
264	#135	—	2	2	no	—
265	#135	—	2	2	no	—
266	C₂×Q₁₆	—	2	1	no	—
267	C₂×Q₁₆	—	2	2	no	—
268	C₂×Q₁₆	D₄×C₂₃	1	4	yes	complemented
269	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
270	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
271	C₂×SD₁₆	—	2	8	no	—
272	C₂×SD₁₆	—	2	4	no	—
273	C₂×SD₁₆	—	2	1	no	—
274	C₂×D₈	—	2	1	no	—
275	C₂×D₈	—	2	2	no	—
276	C₂×D₈	D₄×C₂₃	1	4	yes	complemented
277	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
278	C₂×D₈	C₂³×C₂₃	1	2	yes	—
279	C₂²×C₈	—	2	2	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
282	C₂²×C₈	D₄×C₂₃	1	2	yes	—
283	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
284	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
285	#123	—	4	1	no	—
286	C₂²⋊Q₈	—	2	2	no	—
287	#121	—	2	2	no	—
288	#120	—	4	1	no	—
289	C₄×D₄	—	4	2	no	—
290	#117	—	2	1	no	—
291	Q₃₂	—	2	4	no	—
292	SD₃₂	—	2	4	no	—
293	SD₃₂	—	2	4	no	—
294	D₁₆	—	2	4	no	—
295	M₃₂	—	2	2	no	—
296	M₃₂	—	2	2	no	—
297	C₂×C₁₆	C₂³×C₂₃	1	2	yes	—
298	C₂×C₁₆	C₂³×C₂₃	1	2	yes	—
299	#107	C₂³×C₂₃	1	2	yes	—
300	#106	—	2	1	no	—
301	#103	—	2	2	no	—
302	#102	—	2	2	no	—
303	C₂₃	#33519	1	1	yes	characteristic, direct product factor, Sylow
304	C₂⁴	—	4	1	no	—
305	C₂⁴	D₈×C₂₃	1	1	yes	characteristic
306	#41	—	2	16	no	—
307	#41	—	4	8	no	—
308	#41	—	4	16	no	—
309	#41	—	4	2	no	—
310	#41	—	4	2	no	—
311	C₂×Q₈	—	2	4	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	4	1	no	—
315	C₂×Q₈	—	4	2	no	—
316	C₂×D₄	—	2	4	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	4	8	no	—
320	C₂×D₄	—	4	4	no	—
321	C₂×D₄	—	4	2	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	—	4	1	no	—
324	C₂×D₄	—	4	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	4	8	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	—	4	4	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	D₈×C₂₃	1	2	yes	—
332	C₂²×C₄	D₈×C₂₃	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
335	Q₁₆	—	2	4	no	—
336	Q₁₆	—	2	2	no	—
337	Q₁₆	—	2	1	no	—
338	Q₁₆	—	2	1	no	—
339	Q₁₆	C₂×D₄×C₂₃	1	4	yes	—
340	SD₁₆	—	2	16	no	—
341	SD₁₆	—	4	2	no	—
342	D₈	—	2	4	no	—
343	D₈	—	2	2	no	—
344	D₈	—	2	1	no	—
345	D₈	—	2	1	no	—
346	D₈	C₂×D₄×C₂₃	1	4	yes	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	4	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
352	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
353	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
354	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
355	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	4	2	no	—
358	C₂²⋊C₄	—	4	1	no	—
359	C₂²⋊C₄	—	4	2	no	—
360	C₂²⋊C₄	—	4	2	no	—
361	C₄²	—	4	1	no	—
362	C₁₆	—	2	2	no	—
363	C₁₆	—	2	2	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	2	no	—
367	C₂³	—	4	4	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	8	4	no	—
370	C₂³	C₂×D₈×C₂₃	1	2	yes	—
371	C₂³	C₂×D₈×C₂₃	1	1	yes	characteristic
372	Q₈	—	2	4	no	—
373	Q₈	—	4	2	no	—
374	Q₈	—	4	4	no	—
375	Q₈	—	4	1	no	—
376	Q₈	—	4	1	no	—
377	D₄	—	2	4	no	—
378	D₄	—	4	16	no	—
379	D₄	—	4	2	no	—
380	D₄	—	4	1	no	—
381	D₄	—	4	4	no	—
382	D₄	—	4	1	no	—
383	D₄	—	8	4	no	—
384	D₄	—	8	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	16	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	4	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	8	2	no	—
395	C₂×C₄	C₂₃×#120	1	2	yes	—
396	C₂×C₄	C₂×D₈×C₂₃	1	2	yes	—
397	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
398	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
399	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
400	C₈	—	2	2	no	—
401	C₈	C₂₃×#120	1	2	yes	—
402	C₈	C₂²×D₄×C₂₃	1	1	yes	characteristic
403	C₈	C₂²×D₄×C₂₃	1	1	yes	characteristic
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	4	4	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	8	8	no	—
411	C₂²	—	8	4	no	—
412	C₂²	—	8	1	no	—
413	C₂²	—	8	2	no	—
414	C₂²	C₂₃×#447	1	2	yes	—
415	C₂²	C₂²×D₈×C₂₃	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	4	4	no	—
418	C₄	—	8	1	no	—
419	C₄	—	8	2	no	—
420	C₄	C₂₃×#447	1	2	yes	—
421	C₄	C₂×C₂₃×#120	1	1	yes	characteristic
422	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
423	C₂	—	2	2	no	—
424	C₂	—	4	2	no	—
425	C₂	—	8	4	no	—
426	C₂	—	16	1	no	—
427	C₂	C₂×C₂₃×#447	1	1	yes	characteristic
428	C₂	C₂₃×#3414	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₂₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂³×C₄×C₂₃ ◁ C₂³×C₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂₃×#135	C₂	semidirect
2. C₂×C₂₃×#510	C₂	semidirect
3. C₂×C₂₃×#509	C₂	semidirect
4. C₂₃×#3050	C₂	semidirect
5. C₂₃×#2189	C₂	semidirect
6. C₂₃×#2186	C₂	semidirect
7. C₂₃×#2141	C₂	semidirect
8. C₂₃×#2140	C₂	semidirect
9. C₂₃×#2112	C₂	semidirect
23. C₂×C₂₃×Q₃₂	C₂²	semidirect
24. C₂×C₂₃×SD₃₂	C₂²	semidirect
25. C₂×C₂₃×SD₃₂	C₂²	semidirect
26. C₂×C₂₃×D₁₆	C₂²	semidirect
29. C₂₃×#467	C₂²	semidirect
30. C₂₃×#466	C₂²	semidirect
34. C₂₃×#358	C₂²	semidirect
35. C₂₃×#357	C₂²	semidirect
36. C₂₃×C₂²⋊C₁₆	C₂²	semidirect
54. C₂×Q₁₆×C₂₃	D₄	semidirect
62. C₂×D₈×C₂₃	D₄	semidirect
149. #33519	C₂₃	direct (N × H)
190. C₂²×#135	C₂×C₂₃	semidirect
191. C₂×#510	C₂×C₂₃	semidirect
192. C₂×#509	C₂×C₂₃	semidirect
193. #3050	C₂×C₂₃	semidirect
194. #2189	C₂×C₂₃	semidirect
195. #2186	C₂×C₂₃	semidirect
196. #2141	C₂×C₂₃	semidirect
197. #2140	C₂×C₂₃	semidirect
198. #2112	C₂×C₂₃	semidirect
231. C₂×Q₃₂	C₂²×C₂₃	semidirect
232. C₂×SD₃₂	C₂²×C₂₃	semidirect
233. C₂×SD₃₂	C₂²×C₂₃	semidirect
234. C₂×D₁₆	C₂²×C₂₃	semidirect
237. #467	C₂²×C₂₃	semidirect
238. #466	C₂²×C₂₃	semidirect
242. #358	C₂²×C₂₃	semidirect
243. #357	C₂²×C₂₃	semidirect
244. C₂²⋊C₁₆	C₂²×C₂₃	semidirect
268. C₂×Q₁₆	D₄×C₂₃	semidirect
276. C₂×D₈	D₄×C₂₃	semidirect
303. C₂₃	#33519	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×#135	2
C₂×C₂₃×#510	2
C₂×C₂₃×#509	2
C₂₃×#3050	2
C₂₃×#2189	2
C₂₃×#2186	2
C₂₃×#2141	2
C₂₃×#2140	2
C₂₃×#2112	2
#33519	23

Subgroups — C23×#33519 #19181145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#33519 #19181145