Subgroups — C₂₃×#34228 #19181854

Order 5888.

2726 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#525	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2368	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2364	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2358	C₂	1	4	yes	maximal, complemented
5	C₂₃×#2357	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2353	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2343	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2339	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2333	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2332	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2318	C₂	1	2	yes	maximal, complemented
12	C₄×C₂₃×#123	C₂	1	4	yes	maximal, complemented
13	C₂×C₂₃×#381	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2275	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×#525	C₄	1	16	yes	complemented
19	C₂×C₂₃×#123	C₂²	1	2	yes	—
20	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#120	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
29	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
31	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
32	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
33	C₂₃×#391	C₂²	1	4	yes	complemented
34	C₂₃×#390	C₂²	1	4	yes	—
35	C₂₃×#388	C₂²	1	4	yes	—
36	C₂₃×#388	C₂²	1	4	yes	—
37	C₂₃×#388	C₂²	1	4	yes	complemented
38	C₂₃×#388	C₂²	1	4	yes	complemented
39	C₂₃×#387	C₂²	1	4	yes	complemented
40	C₂₃×#387	C₂²	1	4	yes	complemented
41	C₂₃×#387	C₂²	1	4	yes	complemented
42	C₂₃×#387	C₂²	1	4	yes	complemented
43	C₂₃×#386	C₂²	1	4	yes	—
44	C₂₃×#386	C₂²	1	4	yes	—
45	C₂₃×#386	C₂²	1	4	yes	—
46	C₂₃×#386	C₂²	1	4	yes	complemented
47	C₂₃×#385	C₂²	1	4	yes	—
48	C₂₃×#385	C₂²	1	4	yes	—
49	C₂₃×#383	C₂²	1	2	yes	complemented
50	C₂₃×#382	C₂²	1	2	yes	complemented
51	C₂₃×#381	C₂²	1	2	yes	—
52	C₂₃×#381	C₂²	1	2	yes	—
53	C₂₃×#381	C₂²	1	2	yes	—
54	C₂₃×#381	C₂²	1	1	yes	characteristic
55	C₂₃×#381	C₂²	1	1	yes	characteristic
56	C₂₃×#381	C₂²	1	2	yes	complemented
57	C₂₃×#380	C₂²	1	2	yes	complemented
58	C₄×C₄⋊C₄×C₂₃	C₂²	1	4	yes	complemented
59	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
60	C₄×C₄⋊C₄×C₂₃	C₂²	1	4	yes	complemented
61	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
62	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
63	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
64	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
65	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
66	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
67	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
68	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	complemented
69	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
70	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	complemented
71	C₂₃×#376	C₂²	1	2	yes	complemented
72	C₂×C₂₃×#95	C₂²	1	2	yes	—
73	C₂×C₂₃×#95	C₂²	1	2	yes	—
74	C₂×C₂₃×#95	C₂²	1	2	yes	—
75	C₂×C₂₃×#95	C₂²	1	2	yes	complemented
76	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
77	C₂×#41×C₂₃	—	4	4	no	—
78	C₂×#41×C₂₃	C₂×C₄	1	8	yes	complemented
79	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
81	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
82	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
84	C₂³×C₄×C₂₃	—	4	4	no	—
85	C₂³×C₄×C₂₃	C₂×C₄	1	8	yes	complemented
86	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
87	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
90	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
91	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
96	C₂₃×#123	C₂×C₄	1	16	yes	complemented
97	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
98	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
99	C₂₃×#121	C₂×C₄	1	8	yes	complemented
100	C₂₃×#121	C₂×C₄	1	8	yes	complemented
101	C₂₃×#120	C₂×C₄	1	16	yes	complemented
102	C₄×D₄×C₂₃	—	2	16	no	—
103	C₄×D₄×C₂₃	—	4	8	no	—
104	C₄×D₄×C₂₃	C₂×C₄	1	16	yes	complemented
105	C₄×D₄×C₂₃	C₂×C₄	1	16	yes	complemented
106	C₂₃×#117	C₂×C₄	1	8	yes	complemented
107	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
108	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
115	C₂×C₂²⋊C₄×C₂₃	—	4	4	no	—
116	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
117	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
119	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
130	C₂×C₄²×C₂₃	—	4	4	no	—
131	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
132	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
133	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
134	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
135	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
136	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
137	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
138	C₂₃×#95	C₂³	1	2	yes	—
139	C₂₃×#95	C₂³	1	2	yes	—
140	C₂₃×#95	C₂³	1	2	yes	—
141	C₂₃×#95	C₂³	1	4	yes	—
142	C₂₃×#95	C₂³	1	2	yes	—
143	C₂₃×#95	C₂³	1	2	yes	—
144	C₂₃×#95	C₂³	1	4	yes	—
145	C₂₃×#95	C₂³	1	2	yes	—
146	C₂₃×#95	C₂³	1	4	yes	—
147	C₂₃×#95	C₂³	1	4	yes	—
148	C₂₃×#95	C₂³	1	4	yes	—
149	C₂₃×#95	C₂³	1	4	yes	—
150	C₂₃×#95	C₂³	1	4	yes	—
151	C₂₃×#95	C₂³	1	4	yes	—
152	C₂₃×#95	C₂³	1	4	yes	—
153	C₂⁴×C₂₃	—	2	4	no	—
154	C₂⁴×C₂₃	—	2	4	no	—
155	C₂⁴×C₂₃	—	4	2	no	—
156	C₂⁴×C₂₃	C₂²×C₄	1	4	yes	—
157	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
158	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
159	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
160	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
161	#41×C₂₃	—	4	16	no	—
162	C₂×Q₈×C₂₃	—	4	2	no	—
163	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
164	C₂×D₄×C₂₃	—	2	8	no	—
165	C₂×D₄×C₂₃	—	2	8	no	—
166	C₂×D₄×C₂₃	—	4	2	no	—
167	C₂×D₄×C₂₃	—	4	2	no	—
168	C₂×D₄×C₂₃	—	4	2	no	—
169	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
170	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
171	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
172	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
173	C₂²×C₄×C₂₃	—	2	4	no	—
174	C₂²×C₄×C₂₃	—	2	4	no	—
175	C₂²×C₄×C₂₃	—	2	8	no	—
176	C₂²×C₄×C₂₃	—	2	8	no	—
177	C₂²×C₄×C₂₃	—	2	8	no	—
178	C₂²×C₄×C₂₃	—	2	8	no	—
179	C₂²×C₄×C₂₃	—	4	16	no	—
180	C₂²×C₄×C₂₃	—	4	2	no	—
181	C₂²×C₄×C₂₃	—	4	2	no	—
182	C₂²×C₄×C₂₃	—	4	2	no	—
183	C₂²×C₄×C₂₃	—	4	2	no	—
184	C₂²×C₄×C₂₃	—	4	4	no	—
185	C₂²×C₄×C₂₃	—	4	4	no	—
186	C₂²×C₄×C₂₃	—	4	4	no	—
187	C₂²×C₄×C₂₃	—	4	4	no	—
188	C₂²×C₄×C₂₃	—	4	4	no	—
189	C₂²×C₄×C₂₃	—	4	4	no	—
190	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
191	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
192	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
193	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
194	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
195	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
196	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
197	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
198	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
199	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
208	C₄⋊C₄×C₂₃	—	2	8	no	—
209	C₄⋊C₄×C₂₃	—	4	4	no	—
210	C₄⋊C₄×C₂₃	—	4	4	no	—
211	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
212	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
213	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
214	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
215	C₂²⋊C₄×C₂₃	—	2	4	no	—
216	C₂²⋊C₄×C₂₃	—	2	8	no	—
217	C₂²⋊C₄×C₂₃	—	2	8	no	—
218	C₂²⋊C₄×C₂₃	—	2	8	no	—
219	C₂²⋊C₄×C₂₃	—	4	2	no	—
220	C₂²⋊C₄×C₂₃	—	4	2	no	—
221	C₂²⋊C₄×C₂₃	—	4	4	no	—
222	C₂²⋊C₄×C₂₃	—	4	4	no	—
223	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
224	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
225	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
226	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
227	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
228	C₂²⋊C₄×C₂₃	#41	1	8	yes	complemented
229	C₄²×C₂₃	—	2	8	no	—
230	C₄²×C₂₃	—	4	2	no	—
231	C₄²×C₂₃	—	4	4	no	—
232	C₄²×C₂₃	—	4	2	no	—
233	C₄²×C₂₃	—	4	4	no	—
234	C₄²×C₂₃	—	4	4	no	—
235	C₄²×C₂₃	C₂²×C₄	1	8	yes	—
236	#34228	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂³×C₂₃	—	2	2	no	—
238	C₂³×C₂₃	—	2	2	no	—
239	C₂³×C₂₃	—	2	2	no	—
240	C₂³×C₂₃	—	2	2	no	—
241	C₂³×C₂₃	—	2	8	no	—
242	C₂³×C₂₃	—	2	8	no	—
243	C₂³×C₂₃	—	2	2	no	—
244	C₂³×C₂₃	—	2	4	no	—
245	C₂³×C₂₃	—	2	2	no	—
246	C₂³×C₂₃	—	2	4	no	—
247	C₂³×C₂₃	—	2	2	no	—
248	C₂³×C₂₃	—	2	2	no	—
249	C₂³×C₂₃	—	2	2	no	—
250	C₂³×C₂₃	—	4	4	no	—
251	C₂³×C₂₃	—	4	16	no	—
252	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
253	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
254	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
255	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
256	C₂³×C₂₃	C₂×#41	1	4	yes	—
257	C₂³×C₂₃	H(5,𝔽₂)	1	4	yes	—
258	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
259	Q₈×C₂₃	—	4	4	no	—
260	D₄×C₂₃	—	2	16	no	—
261	D₄×C₂₃	—	2	16	no	—
262	D₄×C₂₃	—	4	8	no	—
263	D₄×C₂₃	—	4	4	no	—
264	C₂×C₄×C₂₃	—	2	8	no	—
265	C₂×C₄×C₂₃	—	2	8	no	—
266	C₂×C₄×C₂₃	—	2	4	no	—
267	C₂×C₄×C₂₃	—	2	4	no	—
268	C₂×C₄×C₂₃	—	2	2	no	—
269	C₂×C₄×C₂₃	—	2	2	no	—
270	C₂×C₄×C₂₃	—	2	4	no	—
271	C₂×C₄×C₂₃	—	2	2	no	—
272	C₂×C₄×C₂₃	—	2	2	no	—
273	C₂×C₄×C₂₃	—	2	2	no	—
274	C₂×C₄×C₂₃	—	2	4	no	—
275	C₂×C₄×C₂₃	—	2	2	no	—
276	C₂×C₄×C₂₃	—	2	4	no	—
277	C₂×C₄×C₂₃	—	2	4	no	—
278	C₂×C₄×C₂₃	—	2	4	no	—
279	C₂×C₄×C₂₃	—	2	4	no	—
280	C₂×C₄×C₂₃	—	2	4	no	—
281	C₂×C₄×C₂₃	—	2	4	no	—
282	C₂×C₄×C₂₃	—	2	4	no	—
283	C₂×C₄×C₂₃	—	2	4	no	—
284	C₂×C₄×C₂₃	—	2	4	no	—
285	C₂×C₄×C₂₃	—	4	4	no	—
286	C₂×C₄×C₂₃	—	4	4	no	—
287	C₂×C₄×C₂₃	—	4	4	no	—
288	C₂×C₄×C₂₃	—	4	4	no	—
289	C₂×C₄×C₂₃	—	4	8	no	—
290	C₂×C₄×C₂₃	—	4	16	no	—
291	C₂×C₄×C₂₃	—	8	8	no	—
292	C₂×C₄×C₂₃	—	8	8	no	—
293	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
294	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
295	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
296	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
297	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
298	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
299	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
300	C₂×C₄×C₂₃	C₂×#41	1	8	yes	—
301	C₂×#525	C₂×C₂₃	1	1	yes	characteristic
302	#2368	C₂×C₂₃	1	2	yes	complemented
303	#2364	C₂×C₂₃	1	2	yes	complemented
304	#2358	C₂×C₂₃	1	4	yes	complemented
305	#2357	C₂×C₂₃	1	2	yes	complemented
306	#2353	C₂×C₂₃	1	2	yes	complemented
307	#2343	C₂×C₂₃	1	2	yes	complemented
308	#2339	C₂×C₂₃	1	2	yes	complemented
309	#2333	C₂×C₂₃	1	2	yes	complemented
310	#2332	C₂×C₂₃	1	2	yes	complemented
311	#2318	C₂×C₂₃	1	2	yes	complemented
312	C₄×#123	C₂×C₂₃	1	4	yes	complemented
313	C₂×#381	C₂×C₂₃	1	1	yes	characteristic, complemented
314	#2275	C₂×C₂₃	1	2	yes	complemented
315	C₂×C₄×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
316	C₂²×C₂₃	—	2	2	no	—
317	C₂²×C₂₃	—	2	2	no	—
318	C₂²×C₂₃	—	2	2	no	—
319	C₂²×C₂₃	—	2	2	no	—
320	C₂²×C₂₃	—	2	8	no	—
321	C₂²×C₂₃	—	2	8	no	—
322	C₂²×C₂₃	—	2	4	no	—
323	C₂²×C₂₃	—	2	2	no	—
324	C₂²×C₂₃	—	2	2	no	—
325	C₂²×C₂₃	—	2	4	no	—
326	C₂²×C₂₃	—	2	2	no	—
327	C₂²×C₂₃	—	2	4	no	—
328	C₂²×C₂₃	—	4	16	no	—
329	C₂²×C₂₃	—	4	4	no	—
330	C₂²×C₂₃	—	4	4	no	—
331	C₂²×C₂₃	—	4	4	no	—
332	C₂²×C₂₃	C₄×#41	1	4	yes	—
333	C₂²×C₂₃	#518	1	4	yes	—
334	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
335	C₂²×C₂₃	C₂²×#41	1	2	yes	—
336	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
337	C₂²×C₂₃	#585	1	2	yes	—
338	C₄×C₂₃	—	2	4	no	—
339	C₄×C₂₃	—	2	2	no	—
340	C₄×C₂₃	—	2	2	no	—
341	C₄×C₂₃	—	2	2	no	—
342	C₄×C₂₃	—	2	2	no	—
343	C₄×C₂₃	—	2	4	no	—
344	C₄×C₂₃	—	2	4	no	—
345	C₄×C₂₃	—	2	8	no	—
346	C₄×C₂₃	—	4	4	no	—
347	C₄×C₂₃	—	4	4	no	—
348	C₄×C₂₃	—	4	4	no	—
349	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
350	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
351	#525	C₄×C₂₃	1	16	yes	complemented
352	C₂×#123	C₂²×C₂₃	1	2	yes	—
353	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
354	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
355	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
356	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
357	C₂×#120	C₂²×C₂₃	1	2	yes	—
358	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	—
359	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	—
360	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
361	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
362	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
363	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
364	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
365	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
366	#391	C₂²×C₂₃	1	4	yes	complemented
367	#390	C₂²×C₂₃	1	4	yes	—
368	#388	C₂²×C₂₃	1	4	yes	—
369	#388	C₂²×C₂₃	1	4	yes	—
370	#388	C₂²×C₂₃	1	4	yes	complemented
371	#388	C₂²×C₂₃	1	4	yes	complemented
372	#387	C₂²×C₂₃	1	4	yes	complemented
373	#387	C₂²×C₂₃	1	4	yes	complemented
374	#387	C₂²×C₂₃	1	4	yes	complemented
375	#387	C₂²×C₂₃	1	4	yes	complemented
376	#386	C₂²×C₂₃	1	4	yes	—
377	#386	C₂²×C₂₃	1	4	yes	—
378	#386	C₂²×C₂₃	1	4	yes	—
379	#386	C₂²×C₂₃	1	4	yes	complemented
380	#385	C₂²×C₂₃	1	4	yes	—
381	#385	C₂²×C₂₃	1	4	yes	—
382	#383	C₂²×C₂₃	1	2	yes	complemented
383	#382	C₂²×C₂₃	1	2	yes	complemented
384	#381	C₂²×C₂₃	1	2	yes	—
385	#381	C₂²×C₂₃	1	2	yes	—
386	#381	C₂²×C₂₃	1	1	yes	characteristic
387	#381	C₂²×C₂₃	1	1	yes	characteristic
388	#381	C₂²×C₂₃	1	2	yes	—
389	#381	C₂²×C₂₃	1	2	yes	complemented
390	#380	C₂²×C₂₃	1	2	yes	complemented
391	C₄×C₄⋊C₄	C₂²×C₂₃	1	4	yes	complemented
392	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
393	C₄×C₄⋊C₄	C₂²×C₂₃	1	4	yes	complemented
394	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
395	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
396	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
397	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
398	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
399	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
400	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
401	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	complemented
402	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
403	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	complemented
404	#376	C₂²×C₂₃	1	2	yes	complemented
405	C₂×#95	C₂²×C₂₃	1	2	yes	—
406	C₂×#95	C₂²×C₂₃	1	2	yes	—
407	C₂×#95	C₂²×C₂₃	1	2	yes	—
408	C₂×#95	C₂²×C₂₃	1	2	yes	complemented
409	C₂×C₂₃	—	2	4	no	—
410	C₂×C₂₃	—	2	4	no	—
411	C₂×C₂₃	—	4	4	no	—
412	C₂×C₂₃	—	4	2	no	—
413	C₂×C₂₃	C₂×C₄×#41	1	1	yes	characteristic
414	C₂×C₂₃	C₂×#518	1	1	yes	characteristic
415	C₂×C₂₃	#3428	1	1	yes	characteristic
416	C₂×C₂₃	#3513	1	4	yes	—
417	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
418	C₂×#41	—	4	4	no	—
419	C₂×#41	C₂×C₄×C₂₃	1	8	yes	complemented
420	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
421	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
422	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
423	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
424	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
425	C₂³×C₄	—	4	4	no	—
426	C₂³×C₄	C₂×C₄×C₂₃	1	8	yes	complemented
427	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
428	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
429	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
430	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
431	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
432	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
433	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
434	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
435	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
436	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
437	#123	C₂×C₄×C₂₃	1	16	yes	complemented
438	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
439	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
440	#121	C₂×C₄×C₂₃	1	8	yes	complemented
441	#121	C₂×C₄×C₂₃	1	8	yes	complemented
442	#120	C₂×C₄×C₂₃	1	16	yes	complemented
443	C₄×D₄	—	2	16	no	—
444	C₄×D₄	—	4	8	no	—
445	C₄×D₄	C₂×C₄×C₂₃	1	16	yes	complemented
446	C₄×D₄	C₂×C₄×C₂₃	1	16	yes	complemented
447	#117	C₂×C₄×C₂₃	1	8	yes	complemented
448	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
449	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
450	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
451	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
453	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
454	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
455	C₂×C₂²⋊C₄	—	2	8	no	—
456	C₂×C₂²⋊C₄	—	4	4	no	—
457	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
471	C₂×C₄²	—	4	4	no	—
472	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
473	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
474	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
475	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
476	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
477	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
478	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
479	#95	C₂³×C₂₃	1	2	yes	—
480	#95	C₂³×C₂₃	1	2	yes	—
481	#95	C₂³×C₂₃	1	2	yes	—
482	#95	C₂³×C₂₃	1	4	yes	—
483	#95	C₂³×C₂₃	1	2	yes	—
484	#95	C₂³×C₂₃	1	2	yes	—
485	#95	C₂³×C₂₃	1	4	yes	—
486	#95	C₂³×C₂₃	1	2	yes	—
487	#95	C₂³×C₂₃	1	4	yes	—
488	#95	C₂³×C₂₃	1	4	yes	—
489	#95	C₂³×C₂₃	1	4	yes	—
490	#95	C₂³×C₂₃	1	4	yes	—
491	#95	C₂³×C₂₃	1	4	yes	—
492	#95	C₂³×C₂₃	1	4	yes	—
493	#95	C₂³×C₂₃	1	4	yes	—
494	C₂₃	#34228	1	1	yes	characteristic, direct product factor, Sylow
495	C₂⁴	—	2	4	no	—
496	C₂⁴	—	2	4	no	—
497	C₂⁴	—	4	2	no	—
498	C₂⁴	C₂²×C₄×C₂₃	1	4	yes	—
499	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
500	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
501	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
502	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
503	#41	—	4	16	no	—
504	C₂×Q₈	—	4	2	no	—
505	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
506	C₂×D₄	—	2	8	no	—
507	C₂×D₄	—	2	8	no	—
508	C₂×D₄	—	4	2	no	—
509	C₂×D₄	—	4	2	no	—
510	C₂×D₄	—	4	2	no	—
511	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
512	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
513	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
514	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
515	C₂²×C₄	—	2	4	no	—
516	C₂²×C₄	—	2	4	no	—
517	C₂²×C₄	—	2	8	no	—
518	C₂²×C₄	—	2	8	no	—
519	C₂²×C₄	—	2	8	no	—
520	C₂²×C₄	—	2	8	no	—
521	C₂²×C₄	—	4	16	no	—
522	C₂²×C₄	—	4	2	no	—
523	C₂²×C₄	—	4	2	no	—
524	C₂²×C₄	—	4	2	no	—
525	C₂²×C₄	—	4	2	no	—
526	C₂²×C₄	—	4	4	no	—
527	C₂²×C₄	—	4	4	no	—
528	C₂²×C₄	—	4	4	no	—
529	C₂²×C₄	—	4	4	no	—
530	C₂²×C₄	—	4	4	no	—
531	C₂²×C₄	—	4	4	no	—
532	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
533	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
534	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
535	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
536	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
537	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
538	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
539	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
540	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
541	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
542	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
543	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
544	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
545	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
546	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
547	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
548	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
550	C₄⋊C₄	—	2	8	no	—
551	C₄⋊C₄	—	4	4	no	—
552	C₄⋊C₄	—	4	4	no	—
553	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
554	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
555	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
556	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
557	C₂²⋊C₄	—	2	4	no	—
558	C₂²⋊C₄	—	2	8	no	—
559	C₂²⋊C₄	—	2	8	no	—
560	C₂²⋊C₄	—	2	8	no	—
561	C₂²⋊C₄	—	4	2	no	—
562	C₂²⋊C₄	—	4	2	no	—
563	C₂²⋊C₄	—	4	4	no	—
564	C₂²⋊C₄	—	4	4	no	—
565	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
566	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
567	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
568	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
569	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
570	C₂²⋊C₄	#41×C₂₃	1	8	yes	complemented
571	C₄²	—	2	8	no	—
572	C₄²	—	4	2	no	—
573	C₄²	—	4	4	no	—
574	C₄²	—	4	2	no	—
575	C₄²	—	4	4	no	—
576	C₄²	—	4	4	no	—
577	C₄²	C₂²×C₄×C₂₃	1	8	yes	—
578	C₂³	—	2	2	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	2	2	no	—
581	C₂³	—	2	2	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	4	no	—
584	C₂³	—	2	2	no	—
585	C₂³	—	2	4	no	—
586	C₂³	—	2	2	no	—
587	C₂³	—	2	2	no	—
588	C₂³	—	2	2	no	—
589	C₂³	—	2	8	no	—
590	C₂³	—	2	8	no	—
591	C₂³	—	4	4	no	—
592	C₂³	—	4	16	no	—
593	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
594	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
595	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
596	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
597	C₂³	C₂×#41×C₂₃	1	4	yes	—
598	C₂³	C₂₃×H(5,𝔽₂)	1	4	yes	—
599	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
600	Q₈	—	4	4	no	—
601	D₄	—	2	16	no	—
602	D₄	—	2	16	no	—
603	D₄	—	4	4	no	—
604	D₄	—	4	8	no	—
605	C₂×C₄	—	2	4	no	—
606	C₂×C₄	—	2	4	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	8	no	—
616	C₂×C₄	—	2	8	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	4	4	no	—
627	C₂×C₄	—	4	4	no	—
628	C₂×C₄	—	4	4	no	—
629	C₂×C₄	—	4	4	no	—
630	C₂×C₄	—	4	8	no	—
631	C₂×C₄	—	4	16	no	—
632	C₂×C₄	—	8	8	no	—
633	C₂×C₄	—	8	8	no	—
634	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
635	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
636	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
637	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
638	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
639	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
640	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
641	C₂×C₄	C₂×#41×C₂₃	1	8	yes	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	8	no	—
647	C₂²	—	2	8	no	—
648	C₂²	—	2	4	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	4	no	—
652	C₂²	—	2	2	no	—
653	C₂²	—	2	4	no	—
654	C₂²	—	4	16	no	—
655	C₂²	—	4	4	no	—
656	C₂²	—	4	4	no	—
657	C₂²	—	4	4	no	—
658	C₂²	C₄×#41×C₂₃	1	4	yes	—
659	C₂²	C₂₃×#518	1	4	yes	—
660	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
661	C₂²	C₂²×#41×C₂₃	1	2	yes	—
662	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
663	C₂²	C₂₃×#585	1	2	yes	—
664	C₄	—	2	4	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	2	no	—
669	C₄	—	2	4	no	—
670	C₄	—	2	4	no	—
671	C₄	—	2	8	no	—
672	C₄	—	4	4	no	—
673	C₄	—	4	4	no	—
674	C₄	—	4	4	no	—
675	C₂	—	2	4	no	—
676	C₂	—	2	4	no	—
677	C₂	—	4	2	no	—
678	C₂	—	4	4	no	—
679	C₂	C₂×C₄×#41×C₂₃	1	1	yes	characteristic
680	C₂	C₂×C₂₃×#518	1	1	yes	characteristic
681	C₂	C₂₃×#3428	1	1	yes	characteristic
682	C₂	C₂₃×#3513	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#525	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2368	C₂	semidirect
3. C₂₃×#2364	C₂	semidirect
4. C₂₃×#2358	C₂	semidirect
5. C₂₃×#2357	C₂	semidirect
6. C₂₃×#2353	C₂	semidirect
7. C₂₃×#2343	C₂	semidirect
8. C₂₃×#2339	C₂	semidirect
9. C₂₃×#2333	C₂	semidirect
10. C₂₃×#2332	C₂	semidirect
11. C₂₃×#2318	C₂	semidirect
12. C₄×C₂₃×#123	C₂	semidirect
13. C₂×C₂₃×#381	C₂	semidirect
14. C₂₃×#2275	C₂	semidirect
15. C₂×C₄×C₂²⋊C₄×C₂₃	C₂	semidirect
18. C₂₃×#525	C₄	semidirect
33. C₂₃×#391	C₂²	semidirect
37. C₂₃×#388	C₂²	semidirect
38. C₂₃×#388	C₂²	semidirect
39. C₂₃×#387	C₂²	semidirect
40. C₂₃×#387	C₂²	semidirect
41. C₂₃×#387	C₂²	semidirect
42. C₂₃×#387	C₂²	semidirect
46. C₂₃×#386	C₂²	semidirect
49. C₂₃×#383	C₂²	semidirect
50. C₂₃×#382	C₂²	semidirect
56. C₂₃×#381	C₂²	semidirect
57. C₂₃×#380	C₂²	semidirect
58. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
59. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
60. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
68. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
69. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
70. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
71. C₂₃×#376	C₂²	semidirect
75. C₂×C₂₃×#95	C₂²	semidirect
78. C₂×#41×C₂₃	C₂×C₄	semidirect
85. C₂³×C₄×C₂₃	C₂×C₄	semidirect
96. C₂₃×#123	C₂×C₄	semidirect
97. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
98. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
99. C₂₃×#121	C₂×C₄	semidirect
100. C₂₃×#121	C₂×C₄	semidirect
101. C₂₃×#120	C₂×C₄	semidirect
104. C₄×D₄×C₂₃	C₂×C₄	semidirect
105. C₄×D₄×C₂₃	C₂×C₄	semidirect
106. C₂₃×#117	C₂×C₄	semidirect
228. C₂²⋊C₄×C₂₃	#41	semidirect
236. #34228	C₂₃	direct (N × H)
302. #2368	C₂×C₂₃	semidirect
303. #2364	C₂×C₂₃	semidirect
304. #2358	C₂×C₂₃	semidirect
305. #2357	C₂×C₂₃	semidirect
306. #2353	C₂×C₂₃	semidirect
307. #2343	C₂×C₂₃	semidirect
308. #2339	C₂×C₂₃	semidirect
309. #2333	C₂×C₂₃	semidirect
310. #2332	C₂×C₂₃	semidirect
311. #2318	C₂×C₂₃	semidirect
312. C₄×#123	C₂×C₂₃	semidirect
313. C₂×#381	C₂×C₂₃	semidirect
314. #2275	C₂×C₂₃	semidirect
315. C₂×C₄×C₂²⋊C₄	C₂×C₂₃	semidirect
351. #525	C₄×C₂₃	semidirect
366. #391	C₂²×C₂₃	semidirect
370. #388	C₂²×C₂₃	semidirect
371. #388	C₂²×C₂₃	semidirect
372. #387	C₂²×C₂₃	semidirect
373. #387	C₂²×C₂₃	semidirect
374. #387	C₂²×C₂₃	semidirect
375. #387	C₂²×C₂₃	semidirect
379. #386	C₂²×C₂₃	semidirect
382. #383	C₂²×C₂₃	semidirect
383. #382	C₂²×C₂₃	semidirect
389. #381	C₂²×C₂₃	semidirect
390. #380	C₂²×C₂₃	semidirect
391. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
392. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
393. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
401. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
402. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
403. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
404. #376	C₂²×C₂₃	semidirect
408. C₂×#95	C₂²×C₂₃	semidirect
419. C₂×#41	C₂×C₄×C₂₃	semidirect
426. C₂³×C₄	C₂×C₄×C₂₃	semidirect
437. #123	C₂×C₄×C₂₃	semidirect
438. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
439. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
440. #121	C₂×C₄×C₂₃	semidirect
441. #121	C₂×C₄×C₂₃	semidirect
442. #120	C₂×C₄×C₂₃	semidirect
445. C₄×D₄	C₂×C₄×C₂₃	semidirect
446. C₄×D₄	C₂×C₄×C₂₃	semidirect
447. #117	C₂×C₄×C₂₃	semidirect
494. C₂₃	#34228	direct (N × H)
570. C₂²⋊C₄	#41×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#525	2
C₂₃×#2368	2
C₂₃×#2364	2
C₂₃×#2358	2
C₂₃×#2357	2
C₂₃×#2353	2
C₂₃×#2343	2
C₂₃×#2339	2
C₂₃×#2333	2
C₂₃×#2332	2
C₂₃×#2318	2
C₄×C₂₃×#123	2
C₂×C₂₃×#381	2
C₂₃×#2275	2
C₂×C₄×C₂²⋊C₄×C₂₃	2
#34228	23

Subgroups — C23×#34228 #19181854

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#34228 #19181854