Subgroups — C₂₃×#34204 #19181830

Order 5888.

3614 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×#121	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₂₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2363	C₂	1	4	yes	maximal, complemented
5	C₂₃×#2361	C₂	1	4	yes	maximal, complemented
6	C₂₃×#2342	C₂	1	4	yes	maximal, complemented
7	D₄×C₂²⋊C₄×C₂₃	C₂	1	4	yes	maximal, complemented
8	C₂₃×#2324	C₂	1	4	yes	maximal, complemented
9	C₂₃×#2316	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2309	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₂₃×#121	C₂	1	4	yes	maximal, complemented
12	C₂₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2274	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₂₃	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
17	C₂×C₂₃×#121	C₄	1	16	yes	complemented
18	C₂×C₂₃×#121	C₂²	1	2	yes	—
19	C₂×C₂₃×#121	C₂²	1	2	yes	—
20	C₂×C₂₃×#121	C₂²	1	2	yes	—
21	C₂×C₂₃×#121	C₂²	1	2	yes	—
22	C₂₃×#518	—	2	8	no	—
23	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	complemented
24	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	complemented
25	C₂×C₄×D₄×C₂₃	C₂²	1	8	yes	complemented
26	C₂×C₂₃×#117	—	2	8	no	—
27	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#117	C₂²	1	2	yes	—
29	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×#117	C₂²	1	2	yes	complemented
33	C₂×C₂₃×#117	C₂²	1	2	yes	complemented
34	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
36	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
37	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
38	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
39	C₂²×C₄²×C₂₃	C₂²	1	2	yes	complemented
40	C₂₃×#390	C₂²	1	4	yes	complemented
41	C₂₃×#390	C₂²	1	4	yes	complemented
42	C₂₃×#390	C₂²	1	8	yes	complemented
43	C₂₃×#389	C₂²	1	4	yes	complemented
44	C₂₃×#389	C₂²	1	4	yes	complemented
45	C₂₃×#388	C₂²	1	8	yes	complemented
46	C₂₃×#388	C₂²	1	8	yes	complemented
47	C₂₃×#386	C₂²	1	8	yes	complemented
48	C₂₃×#386	C₂²	1	8	yes	complemented
49	C₂₃×#385	C₂²	1	8	yes	complemented
50	C₂₃×#381	C₂²	1	2	yes	—
51	C₂₃×#380	C₂²	1	4	yes	—
52	C₂₃×#380	C₂²	1	2	yes	complemented
53	C₂₃×#380	C₂²	1	2	yes	complemented
54	C₂₃×#379	C₂²	1	2	yes	—
55	C₂₃×#379	C₂²	1	4	yes	—
56	C₄×C₄⋊C₄×C₂₃	C₂²	1	4	yes	complemented
57	C₄×C₄⋊C₄×C₂₃	C₂²	1	4	yes	complemented
58	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
59	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
60	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
61	C₄×C₂²⋊C₄×C₂₃	C₂²	1	8	yes	complemented
62	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
63	C₂⁵×C₂₃	C₂³	1	2	yes	—
64	C₂²×D₄×C₂₃	—	2	4	no	—
65	C₂²×D₄×C₂₃	—	2	4	no	—
66	C₂²×D₄×C₂₃	—	4	8	no	—
67	C₂²×D₄×C₂₃	C₂×C₄	1	8	yes	complemented
68	C₂²×D₄×C₂₃	C₂×C₄	1	16	yes	complemented
69	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
70	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
71	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
72	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
73	C₂³×C₄×C₂₃	—	2	4	no	—
74	C₂³×C₄×C₂₃	—	2	4	no	—
75	C₂³×C₄×C₂₃	C₂×C₄	1	8	yes	complemented
76	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
77	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₂₃	C₂³	1	8	yes	—
83	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
84	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
85	C₂₃×#121	C₂×C₄	1	16	yes	complemented
86	C₂₃×#121	C₂×C₄	1	16	yes	complemented
87	C₂₃×#121	C₂×C₄	1	16	yes	complemented
88	C₂₃×#121	C₂×C₄	1	16	yes	complemented
89	C₄×D₄×C₂₃	—	2	16	no	—
90	C₄×D₄×C₂₃	—	2	16	no	—
91	C₄×D₄×C₂₃	—	4	16	no	—
92	C₂₃×#117	—	2	4	no	—
93	C₂₃×#117	—	2	4	no	—
94	C₂₃×#117	—	2	4	no	—
95	C₂₃×#117	—	2	8	no	—
96	C₂₃×#117	—	2	8	no	—
97	C₂₃×#117	—	2	8	no	—
98	C₂₃×#117	D₄	1	8	yes	complemented
99	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
100	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	8	yes	complemented
101	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
104	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
106	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
109	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
110	C₂×C₂²⋊C₄×C₂₃	—	2	16	no	—
111	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	16	yes	complemented
112	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
113	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
114	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
116	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
117	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
118	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
119	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
120	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
121	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
124	C₂×C₄²×C₂₃	—	2	8	no	—
125	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
126	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
127	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
128	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
129	C₂×C₄²×C₂₃	C₂³	1	8	yes	—
130	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
131	C₂₃×#95	C₂³	1	8	yes	—
132	C₂₃×#95	C₂³	1	4	yes	—
133	C₂₃×#95	C₂³	1	8	yes	—
134	C₂₃×#95	C₂³	1	4	yes	—
135	C₂⁴×C₂₃	—	2	2	no	—
136	C₂⁴×C₂₃	—	2	2	no	—
137	C₂⁴×C₂₃	—	2	4	no	—
138	C₂⁴×C₂₃	—	2	4	no	—
139	C₂⁴×C₂₃	—	2	4	no	—
140	C₂⁴×C₂₃	—	4	2	no	—
141	C₂⁴×C₂₃	—	4	4	no	—
142	C₂⁴×C₂₃	—	4	4	no	—
143	C₂⁴×C₂₃	C₂²×C₄	1	4	yes	—
144	C₂⁴×C₂₃	C₂²×C₄	1	8	yes	—
145	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
146	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
147	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
148	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
149	C₂×D₄×C₂₃	—	2	16	no	—
150	C₂×D₄×C₂₃	—	2	32	no	—
151	C₂×D₄×C₂₃	—	2	4	no	—
152	C₂×D₄×C₂₃	—	2	4	no	—
153	C₂×D₄×C₂₃	—	2	4	no	—
154	C₂×D₄×C₂₃	—	2	4	no	—
155	C₂×D₄×C₂₃	—	4	8	no	—
156	C₂×D₄×C₂₃	—	4	32	no	—
157	C₂×D₄×C₂₃	C₂²×C₄	1	16	yes	—
158	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
159	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
160	C₂×D₄×C₂₃	C₂²×C₄	1	16	yes	—
161	C₂²×C₄×C₂₃	—	2	2	no	—
162	C₂²×C₄×C₂₃	—	2	2	no	—
163	C₂²×C₄×C₂₃	—	2	32	no	—
164	C₂²×C₄×C₂₃	—	2	2	no	—
165	C₂²×C₄×C₂₃	—	2	2	no	—
166	C₂²×C₄×C₂₃	—	2	2	no	—
167	C₂²×C₄×C₂₃	—	2	2	no	—
168	C₂²×C₄×C₂₃	—	2	2	no	—
169	C₂²×C₄×C₂₃	—	2	2	no	—
170	C₂²×C₄×C₂₃	—	2	2	no	—
171	C₂²×C₄×C₂₃	—	2	2	no	—
172	C₂²×C₄×C₂₃	—	2	8	no	—
173	C₂²×C₄×C₂₃	—	2	8	no	—
174	C₂²×C₄×C₂₃	—	2	16	no	—
175	C₂²×C₄×C₂₃	—	4	4	no	—
176	C₂²×C₄×C₂₃	—	4	4	no	—
177	C₂²×C₄×C₂₃	—	4	8	no	—
178	C₂²×C₄×C₂₃	—	4	8	no	—
179	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
180	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
181	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
182	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
183	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
184	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
185	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
186	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
187	C₂²×C₄×C₂₃	#41	1	4	yes	—
188	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
189	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
190	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
191	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
193	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
194	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
197	C₄⋊C₄×C₂₃	—	2	8	no	—
198	C₄⋊C₄×C₂₃	—	2	4	no	—
199	C₄⋊C₄×C₂₃	—	2	4	no	—
200	C₄⋊C₄×C₂₃	—	2	4	no	—
201	C₄⋊C₄×C₂₃	—	4	8	no	—
202	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
203	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
204	C₄⋊C₄×C₂₃	C₂×D₄	1	8	yes	complemented
205	C₂²⋊C₄×C₂₃	—	2	4	no	—
206	C₂²⋊C₄×C₂₃	—	2	4	no	—
207	C₂²⋊C₄×C₂₃	—	2	4	no	—
208	C₂²⋊C₄×C₂₃	—	2	8	no	—
209	C₂²⋊C₄×C₂₃	—	2	8	no	—
210	C₂²⋊C₄×C₂₃	—	2	16	no	—
211	C₂²⋊C₄×C₂₃	—	4	8	no	—
212	C₂²⋊C₄×C₂₃	—	4	4	no	—
213	C₂²⋊C₄×C₂₃	—	4	8	no	—
214	C₂²⋊C₄×C₂₃	C₂²×C₄	1	16	yes	—
215	C₂²⋊C₄×C₂₃	C₂²×C₄	1	16	yes	—
216	C₂²⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
217	C₄²×C₂₃	—	2	8	no	—
218	C₄²×C₂₃	—	2	4	no	—
219	C₄²×C₂₃	—	2	4	no	—
220	C₄²×C₂₃	—	2	4	no	—
221	C₄²×C₂₃	—	4	8	no	—
222	C₄²×C₂₃	C₂×D₄	1	8	yes	complemented
223	#34204	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
224	C₂³×C₂₃	—	2	1	no	—
225	C₂³×C₂₃	—	2	1	no	—
226	C₂³×C₂₃	—	2	2	no	—
227	C₂³×C₂₃	—	2	2	no	—
228	C₂³×C₂₃	—	2	2	no	—
229	C₂³×C₂₃	—	2	8	no	—
230	C₂³×C₂₃	—	2	8	no	—
231	C₂³×C₂₃	—	2	1	no	—
232	C₂³×C₂₃	—	2	4	no	—
233	C₂³×C₂₃	—	2	1	no	—
234	C₂³×C₂₃	—	2	4	no	—
235	C₂³×C₂₃	—	2	8	no	—
236	C₂³×C₂₃	—	2	2	no	—
237	C₂³×C₂₃	—	2	2	no	—
238	C₂³×C₂₃	—	2	8	no	—
239	C₂³×C₂₃	—	2	16	no	—
240	C₂³×C₂₃	—	4	4	no	—
241	C₂³×C₂₃	—	4	8	no	—
242	C₂³×C₂₃	—	4	8	no	—
243	C₂³×C₂₃	—	4	8	no	—
244	C₂³×C₂₃	—	4	8	no	—
245	C₂³×C₂₃	—	8	8	no	—
246	C₂³×C₂₃	—	8	8	no	—
247	C₂³×C₂₃	C₂³×C₄	1	8	yes	—
248	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
249	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
250	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
251	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
252	C₂³×C₂₃	C₂×#41	1	2	yes	—
253	C₂³×C₂₃	H(5,𝔽₂)	1	4	yes	—
254	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
255	D₄×C₂₃	—	2	32	no	—
256	D₄×C₂₃	—	2	16	no	—
257	D₄×C₂₃	—	2	16	no	—
258	D₄×C₂₃	—	4	16	no	—
259	C₂×C₄×C₂₃	—	2	8	no	—
260	C₂×C₄×C₂₃	—	2	1	no	—
261	C₂×C₄×C₂₃	—	2	1	no	—
262	C₂×C₄×C₂₃	—	2	1	no	—
263	C₂×C₄×C₂₃	—	2	1	no	—
264	C₂×C₄×C₂₃	—	2	4	no	—
265	C₂×C₄×C₂₃	—	2	8	no	—
266	C₂×C₄×C₂₃	—	2	4	no	—
267	C₂×C₄×C₂₃	—	2	8	no	—
268	C₂×C₄×C₂₃	—	2	8	no	—
269	C₂×C₄×C₂₃	—	2	8	no	—
270	C₂×C₄×C₂₃	—	2	8	no	—
271	C₂×C₄×C₂₃	—	2	4	no	—
272	C₂×C₄×C₂₃	—	2	4	no	—
273	C₂×C₄×C₂₃	—	2	4	no	—
274	C₂×C₄×C₂₃	—	2	4	no	—
275	C₂×C₄×C₂₃	—	2	4	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	—	4	8	no	—
281	C₂×C₄×C₂₃	—	4	16	no	—
282	C₂×C₄×C₂₃	—	8	16	no	—
283	C₂×C₄×C₂₃	C₄×D₄	1	16	yes	complemented
284	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
285	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
286	C₂×C₄×C₂₃	C₂³×C₄	1	8	yes	—
287	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
288	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
289	C₂×C₄×C₂₃	C₂²×D₄	1	8	yes	—
290	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
291	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
292	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
293	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
294	C₂²×#121	C₂×C₂₃	1	1	yes	characteristic
295	C₂×#518	C₂×C₂₃	1	1	yes	characteristic, complemented
296	C₂²×#117	C₂×C₂₃	1	1	yes	characteristic, complemented
297	#2363	C₂×C₂₃	1	4	yes	complemented
298	#2361	C₂×C₂₃	1	4	yes	complemented
299	#2342	C₂×C₂₃	1	4	yes	complemented
300	D₄×C₂²⋊C₄	C₂×C₂₃	1	4	yes	complemented
301	#2324	C₂×C₂₃	1	4	yes	complemented
302	#2316	C₂×C₂₃	1	1	yes	characteristic, complemented
303	#2309	C₂×C₂₃	1	1	yes	characteristic, complemented
304	C₄×#121	C₂×C₂₃	1	4	yes	complemented
305	#2280	C₂×C₂₃	1	1	yes	characteristic, complemented
306	#2274	C₂×C₂₃	1	1	yes	characteristic, complemented
307	C₂²×C₂₃	—	2	2	no	—
308	C₂²×C₂₃	—	2	2	no	—
309	C₂²×C₂₃	—	2	2	no	—
310	C₂²×C₂₃	—	2	2	no	—
311	C₂²×C₂₃	—	2	4	no	—
312	C₂²×C₂₃	—	2	4	no	—
313	C₂²×C₂₃	—	2	4	no	—
314	C₂²×C₂₃	—	2	4	no	—
315	C₂²×C₂₃	—	2	2	no	—
316	C₂²×C₂₃	—	2	8	no	—
317	C₂²×C₂₃	—	2	8	no	—
318	C₂²×C₂₃	—	2	2	no	—
319	C₂²×C₂₃	—	2	2	no	—
320	C₂²×C₂₃	—	2	8	no	—
321	C₂²×C₂₃	—	4	16	no	—
322	C₂²×C₂₃	—	4	8	no	—
323	C₂²×C₂₃	—	4	2	no	—
324	C₂²×C₂₃	—	4	2	no	—
325	C₂²×C₂₃	—	4	8	no	—
326	C₂²×C₂₃	—	8	16	no	—
327	C₂²×C₂₃	C₂×C₄×D₄	1	4	yes	—
328	C₂²×C₂₃	#518	1	4	yes	complemented
329	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
330	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
331	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
332	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
333	C₂²×C₂₃	#585	1	2	yes	—
334	C₄×C₂₃	—	2	2	no	—
335	C₄×C₂₃	—	2	2	no	—
336	C₄×C₂₃	—	2	8	no	—
337	C₄×C₂₃	—	2	8	no	—
338	C₄×C₂₃	—	4	4	no	—
339	C₄×C₂₃	—	4	4	no	—
340	C₄×C₂₃	—	4	4	no	—
341	C₄×C₂₃	C₂×C₄×D₄	1	4	yes	—
342	C₄×C₂₃	C₂×C₄×D₄	1	4	yes	—
343	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
344	C₂³×D₄	C₂²×C₂₃	1	2	yes	—
345	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
346	C₂×#121	C₄×C₂₃	1	16	yes	complemented
347	C₂×#121	C₂²×C₂₃	1	2	yes	—
348	C₂×#121	C₂²×C₂₃	1	2	yes	—
349	C₂×#121	C₂²×C₂₃	1	2	yes	—
350	C₂×#121	C₂²×C₂₃	1	2	yes	—
351	#518	—	2	8	no	—
352	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	complemented
353	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	complemented
354	C₂×C₄×D₄	C₂²×C₂₃	1	8	yes	complemented
355	C₂×#117	—	2	8	no	—
356	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
357	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
358	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
359	C₂×#117	C₂²×C₂₃	1	2	yes	—
360	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
361	C₂×#117	C₂²×C₂₃	1	2	yes	complemented
362	C₂×#117	C₂²×C₂₃	1	2	yes	complemented
363	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
364	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
365	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
366	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
367	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
368	C₂²×C₄²	C₂²×C₂₃	1	2	yes	complemented
369	#390	C₂²×C₂₃	1	4	yes	complemented
370	#390	C₂²×C₂₃	1	4	yes	complemented
371	#390	C₂²×C₂₃	1	8	yes	complemented
372	#389	C₂²×C₂₃	1	4	yes	complemented
373	#389	C₂²×C₂₃	1	4	yes	complemented
374	#388	C₂²×C₂₃	1	8	yes	complemented
375	#388	C₂²×C₂₃	1	8	yes	complemented
376	#386	C₂²×C₂₃	1	8	yes	complemented
377	#386	C₂²×C₂₃	1	8	yes	complemented
378	#385	C₂²×C₂₃	1	8	yes	complemented
379	#381	C₂²×C₂₃	1	2	yes	—
380	#380	C₂²×C₂₃	1	4	yes	—
381	#380	C₂²×C₂₃	1	2	yes	complemented
382	#380	C₂²×C₂₃	1	2	yes	complemented
383	#379	C₂²×C₂₃	1	4	yes	—
384	#379	C₂²×C₂₃	1	2	yes	—
385	C₄×C₄⋊C₄	C₂²×C₂₃	1	4	yes	complemented
386	C₄×C₄⋊C₄	C₂²×C₂₃	1	4	yes	complemented
387	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
388	C₄×C₂²⋊C₄	C₂²×C₂₃	1	8	yes	complemented
389	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
390	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
391	C₂×C₂₃	—	2	4	no	—
392	C₂×C₂₃	—	2	4	no	—
393	C₂×C₂₃	—	4	2	no	—
394	C₂×C₂₃	—	4	8	no	—
395	C₂×C₂₃	C₂²×C₄×D₄	1	1	yes	characteristic
396	C₂×C₂₃	C₂×#518	1	1	yes	characteristic
397	C₂×C₂₃	#3428	1	1	yes	characteristic
398	C₂×C₂₃	#3488	1	2	yes	—
399	C₂×C₂₃	#3494	1	2	yes	—
400	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
401	C₂⁵	C₂³×C₂₃	1	2	yes	—
402	C₂²×D₄	—	2	4	no	—
403	C₂²×D₄	—	2	4	no	—
404	C₂²×D₄	—	4	8	no	—
405	C₂²×D₄	C₂×C₄×C₂₃	1	8	yes	complemented
406	C₂²×D₄	C₂×C₄×C₂₃	1	16	yes	complemented
407	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
408	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
409	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
410	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
411	C₂³×C₄	—	2	4	no	—
412	C₂³×C₄	—	2	4	no	—
413	C₂³×C₄	C₂×C₄×C₂₃	1	8	yes	complemented
414	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
415	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
416	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
417	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
418	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
419	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
420	C₂³×C₄	C₂³×C₂₃	1	8	yes	—
421	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
422	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
423	#121	C₂×C₄×C₂₃	1	16	yes	complemented
424	#121	C₂×C₄×C₂₃	1	16	yes	complemented
425	#121	C₂×C₄×C₂₃	1	16	yes	complemented
426	#121	C₂×C₄×C₂₃	1	16	yes	complemented
427	C₄×D₄	—	2	16	no	—
428	C₄×D₄	—	2	16	no	—
429	C₄×D₄	—	4	16	no	—
430	#117	—	2	4	no	—
431	#117	—	2	4	no	—
432	#117	—	2	4	no	—
433	#117	—	2	8	no	—
434	#117	—	2	8	no	—
435	#117	—	2	8	no	—
436	#117	D₄×C₂₃	1	8	yes	complemented
437	C₂×C₄⋊C₄	—	2	8	no	—
438	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	8	yes	complemented
439	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
440	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
441	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
442	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
443	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
444	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
445	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
446	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
447	C₂×C₂²⋊C₄	—	2	8	no	—
448	C₂×C₂²⋊C₄	—	2	16	no	—
449	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	16	yes	complemented
450	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	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×C₄²	—	2	8	no	—
463	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
464	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
465	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
466	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
467	C₂×C₄²	C₂³×C₂₃	1	8	yes	—
468	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
469	#95	C₂³×C₂₃	1	8	yes	—
470	#95	C₂³×C₂₃	1	4	yes	—
471	#95	C₂³×C₂₃	1	8	yes	—
472	#95	C₂³×C₂₃	1	4	yes	—
473	C₂₃	#34204	1	1	yes	characteristic, direct product factor, Sylow
474	C₂⁴	—	2	2	no	—
475	C₂⁴	—	2	2	no	—
476	C₂⁴	—	2	4	no	—
477	C₂⁴	—	2	4	no	—
478	C₂⁴	—	2	4	no	—
479	C₂⁴	—	4	2	no	—
480	C₂⁴	—	4	4	no	—
481	C₂⁴	—	4	4	no	—
482	C₂⁴	C₂²×C₄×C₂₃	1	4	yes	—
483	C₂⁴	C₂²×C₄×C₂₃	1	8	yes	—
484	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
485	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
486	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
487	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
488	C₂×D₄	—	2	16	no	—
489	C₂×D₄	—	2	32	no	—
490	C₂×D₄	—	2	4	no	—
491	C₂×D₄	—	2	4	no	—
492	C₂×D₄	—	2	4	no	—
493	C₂×D₄	—	2	4	no	—
494	C₂×D₄	—	4	8	no	—
495	C₂×D₄	—	4	32	no	—
496	C₂×D₄	C₂²×C₄×C₂₃	1	16	yes	—
497	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
498	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
499	C₂×D₄	C₂²×C₄×C₂₃	1	16	yes	—
500	C₂²×C₄	—	2	2	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	32	no	—
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	2	2	no	—
507	C₂²×C₄	—	2	2	no	—
508	C₂²×C₄	—	2	2	no	—
509	C₂²×C₄	—	2	2	no	—
510	C₂²×C₄	—	2	2	no	—
511	C₂²×C₄	—	2	8	no	—
512	C₂²×C₄	—	2	8	no	—
513	C₂²×C₄	—	2	16	no	—
514	C₂²×C₄	—	4	4	no	—
515	C₂²×C₄	—	4	4	no	—
516	C₂²×C₄	—	4	8	no	—
517	C₂²×C₄	—	4	8	no	—
518	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
519	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
520	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
521	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
522	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
523	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
524	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
525	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
526	C₂²×C₄	#41×C₂₃	1	4	yes	—
527	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
528	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
529	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
530	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
531	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
532	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
534	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
535	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
536	C₄⋊C₄	—	2	8	no	—
537	C₄⋊C₄	—	2	4	no	—
538	C₄⋊C₄	—	2	4	no	—
539	C₄⋊C₄	—	2	4	no	—
540	C₄⋊C₄	—	4	8	no	—
541	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
542	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
543	C₄⋊C₄	C₂×D₄×C₂₃	1	8	yes	complemented
544	C₂²⋊C₄	—	2	4	no	—
545	C₂²⋊C₄	—	2	4	no	—
546	C₂²⋊C₄	—	2	4	no	—
547	C₂²⋊C₄	—	2	8	no	—
548	C₂²⋊C₄	—	2	8	no	—
549	C₂²⋊C₄	—	2	16	no	—
550	C₂²⋊C₄	—	4	8	no	—
551	C₂²⋊C₄	—	4	8	no	—
552	C₂²⋊C₄	—	4	4	no	—
553	C₂²⋊C₄	C₂²×C₄×C₂₃	1	16	yes	—
554	C₂²⋊C₄	C₂²×C₄×C₂₃	1	16	yes	—
555	C₂²⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
556	C₄²	—	2	8	no	—
557	C₄²	—	2	4	no	—
558	C₄²	—	2	4	no	—
559	C₄²	—	2	4	no	—
560	C₄²	—	4	8	no	—
561	C₄²	C₂×D₄×C₂₃	1	8	yes	complemented
562	C₂³	—	2	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	2	no	—
565	C₂³	—	2	2	no	—
566	C₂³	—	2	2	no	—
567	C₂³	—	2	1	no	—
568	C₂³	—	2	4	no	—
569	C₂³	—	2	1	no	—
570	C₂³	—	2	4	no	—
571	C₂³	—	2	8	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	8	no	—
575	C₂³	—	2	8	no	—
576	C₂³	—	2	8	no	—
577	C₂³	—	2	16	no	—
578	C₂³	—	4	4	no	—
579	C₂³	—	4	8	no	—
580	C₂³	—	4	8	no	—
581	C₂³	—	4	8	no	—
582	C₂³	—	4	8	no	—
583	C₂³	—	8	8	no	—
584	C₂³	—	8	8	no	—
585	C₂³	C₂³×C₄×C₂₃	1	8	yes	—
586	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
587	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
588	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
589	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
590	C₂³	C₂×#41×C₂₃	1	2	yes	—
591	C₂³	C₂₃×H(5,𝔽₂)	1	4	yes	—
592	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
593	D₄	—	2	32	no	—
594	D₄	—	2	16	no	—
595	D₄	—	2	16	no	—
596	D₄	—	4	16	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	4	no	—
602	C₂×C₄	—	2	8	no	—
603	C₂×C₄	—	2	4	no	—
604	C₂×C₄	—	2	8	no	—
605	C₂×C₄	—	2	8	no	—
606	C₂×C₄	—	2	8	no	—
607	C₂×C₄	—	2	8	no	—
608	C₂×C₄	—	2	8	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	4	8	no	—
619	C₂×C₄	—	4	16	no	—
620	C₂×C₄	—	8	16	no	—
621	C₂×C₄	C₄×D₄×C₂₃	1	16	yes	complemented
622	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
623	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
624	C₂×C₄	C₂³×C₄×C₂₃	1	8	yes	—
625	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
626	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
627	C₂×C₄	C₂²×D₄×C₂₃	1	8	yes	—
628	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
629	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
630	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
631	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	4	no	—
637	C₂²	—	2	4	no	—
638	C₂²	—	2	4	no	—
639	C₂²	—	2	4	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	8	no	—
642	C₂²	—	2	8	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	8	no	—
646	C₂²	—	4	16	no	—
647	C₂²	—	4	8	no	—
648	C₂²	—	4	2	no	—
649	C₂²	—	4	2	no	—
650	C₂²	—	4	8	no	—
651	C₂²	—	8	16	no	—
652	C₂²	C₂×C₄×D₄×C₂₃	1	4	yes	—
653	C₂²	C₂₃×#518	1	4	yes	complemented
654	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
655	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
656	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
657	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
658	C₂²	C₂₃×#585	1	2	yes	—
659	C₄	—	2	2	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	8	no	—
662	C₄	—	2	8	no	—
663	C₄	—	4	4	no	—
664	C₄	—	4	4	no	—
665	C₄	—	4	4	no	—
666	C₄	C₂×C₄×D₄×C₂₃	1	4	yes	—
667	C₄	C₂×C₄×D₄×C₂₃	1	4	yes	—
668	C₂	—	2	4	no	—
669	C₂	—	2	4	no	—
670	C₂	—	4	2	no	—
671	C₂	—	4	8	no	—
672	C₂	C₂²×C₄×D₄×C₂₃	1	1	yes	characteristic
673	C₂	C₂×C₂₃×#518	1	1	yes	characteristic
674	C₂	C₂₃×#3428	1	1	yes	characteristic
675	C₂	C₂₃×#3488	1	2	yes	—
676	C₂	C₂₃×#3494	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂²×C₂₃×#121	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. C₂×C₂₃×#518	C₂	semidirect
3. C₂²×C₂₃×#117	C₂	semidirect
4. C₂₃×#2363	C₂	semidirect
5. C₂₃×#2361	C₂	semidirect
6. C₂₃×#2342	C₂	semidirect
7. D₄×C₂²⋊C₄×C₂₃	C₂	semidirect
8. C₂₃×#2324	C₂	semidirect
9. C₂₃×#2316	C₂	semidirect
10. C₂₃×#2309	C₂	semidirect
11. C₄×C₂₃×#121	C₂	semidirect
12. C₂₃×#2280	C₂	semidirect
13. C₂₃×#2274	C₂	semidirect
17. C₂×C₂₃×#121	C₄	semidirect
23. C₂×C₄×D₄×C₂₃	C₂²	semidirect
24. C₂×C₄×D₄×C₂₃	C₂²	semidirect
25. C₂×C₄×D₄×C₂₃	C₂²	semidirect
32. C₂×C₂₃×#117	C₂²	semidirect
33. C₂×C₂₃×#117	C₂²	semidirect
35. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
39. C₂²×C₄²×C₂₃	C₂²	semidirect
40. C₂₃×#390	C₂²	semidirect
41. C₂₃×#390	C₂²	semidirect
42. C₂₃×#390	C₂²	semidirect
43. C₂₃×#389	C₂²	semidirect
44. C₂₃×#389	C₂²	semidirect
45. C₂₃×#388	C₂²	semidirect
46. C₂₃×#388	C₂²	semidirect
47. C₂₃×#386	C₂²	semidirect
48. C₂₃×#386	C₂²	semidirect
49. C₂₃×#385	C₂²	semidirect
52. C₂₃×#380	C₂²	semidirect
53. C₂₃×#380	C₂²	semidirect
56. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
57. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
59. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
60. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
61. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
67. C₂²×D₄×C₂₃	C₂×C₄	semidirect
68. C₂²×D₄×C₂₃	C₂×C₄	semidirect
75. C₂³×C₄×C₂₃	C₂×C₄	semidirect
85. C₂₃×#121	C₂×C₄	semidirect
86. C₂₃×#121	C₂×C₄	semidirect
87. C₂₃×#121	C₂×C₄	semidirect
88. C₂₃×#121	C₂×C₄	semidirect
98. C₂₃×#117	D₄	semidirect
100. C₂×C₄⋊C₄×C₂₃	C₂×C₄	semidirect
111. C₂×C₂²⋊C₄×C₂₃	C₂×C₄	semidirect
204. C₄⋊C₄×C₂₃	C₂×D₄	semidirect
222. C₄²×C₂₃	C₂×D₄	semidirect
223. #34204	C₂₃	direct (N × H)
283. C₂×C₄×C₂₃	C₄×D₄	semidirect
295. C₂×#518	C₂×C₂₃	semidirect
296. C₂²×#117	C₂×C₂₃	semidirect
297. #2363	C₂×C₂₃	semidirect
298. #2361	C₂×C₂₃	semidirect
299. #2342	C₂×C₂₃	semidirect
300. D₄×C₂²⋊C₄	C₂×C₂₃	semidirect
301. #2324	C₂×C₂₃	semidirect
302. #2316	C₂×C₂₃	semidirect
303. #2309	C₂×C₂₃	semidirect
304. C₄×#121	C₂×C₂₃	semidirect
305. #2280	C₂×C₂₃	semidirect
306. #2274	C₂×C₂₃	semidirect
328. C₂²×C₂₃	#518	semidirect
346. C₂×#121	C₄×C₂₃	semidirect
352. C₂×C₄×D₄	C₂²×C₂₃	semidirect
353. C₂×C₄×D₄	C₂²×C₂₃	semidirect
354. C₂×C₄×D₄	C₂²×C₂₃	semidirect
361. C₂×#117	C₂²×C₂₃	semidirect
362. C₂×#117	C₂²×C₂₃	semidirect
364. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
368. C₂²×C₄²	C₂²×C₂₃	semidirect
369. #390	C₂²×C₂₃	semidirect
370. #390	C₂²×C₂₃	semidirect
371. #390	C₂²×C₂₃	semidirect
372. #389	C₂²×C₂₃	semidirect
373. #389	C₂²×C₂₃	semidirect
374. #388	C₂²×C₂₃	semidirect
375. #388	C₂²×C₂₃	semidirect
376. #386	C₂²×C₂₃	semidirect
377. #386	C₂²×C₂₃	semidirect
378. #385	C₂²×C₂₃	semidirect
381. #380	C₂²×C₂₃	semidirect
382. #380	C₂²×C₂₃	semidirect
385. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
386. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
388. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
389. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
390. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
405. C₂²×D₄	C₂×C₄×C₂₃	semidirect
406. C₂²×D₄	C₂×C₄×C₂₃	semidirect
413. C₂³×C₄	C₂×C₄×C₂₃	semidirect
423. #121	C₂×C₄×C₂₃	semidirect
424. #121	C₂×C₄×C₂₃	semidirect
425. #121	C₂×C₄×C₂₃	semidirect
426. #121	C₂×C₄×C₂₃	semidirect
436. #117	D₄×C₂₃	semidirect
438. C₂×C₄⋊C₄	C₂×C₄×C₂₃	semidirect
449. C₂×C₂²⋊C₄	C₂×C₄×C₂₃	semidirect
473. C₂₃	#34204	direct (N × H)
543. C₄⋊C₄	C₂×D₄×C₂₃	semidirect
561. C₄²	C₂×D₄×C₂₃	semidirect
621. C₂×C₄	C₄×D₄×C₂₃	semidirect
653. C₂²	C₂₃×#518	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₂₃×#121	2
C₂×C₂₃×#518	2
C₂²×C₂₃×#117	2
C₂₃×#2363	2
C₂₃×#2361	2
C₂₃×#2342	2
D₄×C₂²⋊C₄×C₂₃	2
C₂₃×#2324	2
C₂₃×#2316	2
C₂₃×#2309	2
C₄×C₂₃×#121	2
C₂₃×#2280	2
C₂₃×#2274	2
#34204	23

Subgroups — C23×#34204 #19181830

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#34204 #19181830