Subgroups — C₂₃×#60734 #19208360

Order 5888.

2394 conjugacy classes of subgroups.

The subgroup lattice has 700 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	2	yes	maximal, complemented
2	C₂₃×#3191	C₂	1	4	yes	maximal, complemented
3	C₂₃×#3190	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3189	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3188	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3187	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3186	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3091	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3050	C₂	1	4	yes	maximal, complemented
10	C₂₃×#3002	C₂	1	4	yes	maximal, complemented
11	C₂²×C₂₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₂₃	C₂²	1	2	yes	complemented
13	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
14	C₂×C₂₃×#135	C₂²	1	4	yes	complemented
15	C₂³×C₈×C₂₃	C₂²	1	2	yes	complemented
16	C₂₃×#525	—	2	2	no	—
17	C₂₃×#525	—	2	2	no	—
18	C₂₃×#525	—	2	2	no	—
19	C₂₃×#525	—	2	2	no	—
20	C₂₃×#525	C₂²	1	4	yes	—
21	C₂₃×#525	C₂²	1	4	yes	—
22	C₂₃×#525	C₂²	1	4	yes	complemented
23	C₂₃×#525	C₂²	1	4	yes	complemented
24	C₂×C₂₃×#123	—	2	2	no	—
25	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₂×C₂₃×#121	C₂²	1	2	yes	—
28	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
29	C₂×C₂₃×#120	—	2	2	no	—
30	C₂×C₄×D₄×C₂₃	—	2	2	no	—
31	C₂×C₄×D₄×C₂₃	—	2	2	no	—
32	C₂×C₂₃×#117	C₂²	1	2	yes	complemented
33	C₂₃×#485	C₂²	1	8	yes	complemented
34	C₂₃×#484	C₂²	1	4	yes	complemented
35	C₂₃×#483	C₂²	1	4	yes	complemented
36	C₂₃×#482	C₂²	1	8	yes	complemented
37	C₂₃×#481	C₂²	1	4	yes	complemented
38	C₂₃×#480	C₂²	1	4	yes	complemented
39	C₂₃×#467	C₂²	1	4	yes	complemented
40	C₂₃×#467	C₂²	1	4	yes	complemented
41	C₂₃×#466	C₂²	1	4	yes	complemented
42	C₂₃×#466	C₂²	1	4	yes	complemented
43	C₂₃×#465	C₂²	1	8	yes	complemented
44	C₂₃×#465	C₂²	1	8	yes	complemented
45	C₂₃×#452	C₂²	1	8	yes	complemented
46	C₂₃×#451	C₂²	1	4	yes	complemented
47	C₂₃×#450	C₂²	1	4	yes	complemented
48	C₂₃×#449	C₂²	1	8	yes	complemented
49	C₂₃×#448	C₂²	1	4	yes	complemented
50	C₂₃×#447	C₂²	1	4	yes	complemented
51	C₂₃×#427	C₂²	1	4	yes	complemented
52	C₂₃×#416	C₂²	1	8	yes	complemented
53	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
54	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
55	C₂×C₂₃×C₂²⋊C₈	C₂²	1	4	yes	complemented
56	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
57	C₂×C₂₃×C₂²⋊C₈	C₂²	1	4	yes	complemented
58	C₂⁵×C₂₃	D₄	1	1	yes	characteristic
59	C₂×#41×C₂₃	—	2	2	no	—
60	C₂×#41×C₂₃	—	2	2	no	—
61	C₂×#41×C₂₃	—	4	8	no	—
62	C₂×#41×C₂₃	C₂³	1	4	yes	—
63	C₂×#41×C₂₃	C₂³	1	4	yes	—
64	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
65	C₂²×D₄×C₂₃	—	2	2	no	—
66	C₂²×D₄×C₂₃	—	2	2	no	—
67	C₂²×D₄×C₂₃	—	2	2	no	—
68	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
69	C₂³×C₄×C₂₃	—	2	2	no	—
70	C₂³×C₄×C₂₃	—	4	4	no	—
71	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
72	C₂³×C₄×C₂₃	D₄	1	2	yes	—
73	C₂³×C₄×C₂₃	D₄	1	2	yes	—
74	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
75	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
76	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
78	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
80	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
81	C₂₃×#135	—	4	8	no	—
82	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	complemented
83	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	complemented
84	C₂×D₈×C₂₃	C₂³	1	4	yes	complemented
85	C₂²×C₈×C₂₃	—	4	4	no	—
86	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
87	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
88	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
89	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
90	C₂₃×#123	—	2	4	no	—
91	C₂₃×#123	—	2	4	no	—
92	C₂₃×#123	—	2	4	no	—
93	C₂₃×#123	—	2	4	no	—
94	C₂₃×C₂²⋊Q₈	—	2	2	no	—
95	C₂₃×C₂²⋊Q₈	—	2	2	no	—
96	C₂₃×C₂²⋊Q₈	—	2	2	no	—
97	C₂₃×C₂²⋊Q₈	—	2	2	no	—
98	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
99	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
100	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
101	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
102	C₂₃×#121	—	2	2	no	—
103	C₂₃×#121	—	2	2	no	—
104	C₂₃×#121	—	2	2	no	—
105	C₂₃×#121	—	2	2	no	—
106	C₂₃×#121	C₂³	1	4	yes	—
107	C₂₃×#121	C₂³	1	4	yes	—
108	C₂₃×#121	C₂³	1	4	yes	—
109	C₂₃×#121	C₂³	1	4	yes	—
110	C₂₃×#120	—	2	4	no	—
111	C₂₃×#120	—	2	4	no	—
112	C₂₃×#120	—	2	4	no	—
113	C₂₃×#120	—	2	4	no	—
114	C₄×D₄×C₂₃	—	2	4	no	—
115	C₄×D₄×C₂₃	—	2	4	no	—
116	C₄×D₄×C₂₃	—	2	4	no	—
117	C₄×D₄×C₂₃	—	2	4	no	—
118	C₄×D₄×C₂₃	—	2	4	no	—
119	C₄×D₄×C₂₃	—	2	4	no	—
120	C₄×D₄×C₂₃	—	2	4	no	—
121	C₄×D₄×C₂₃	—	2	4	no	—
122	C₂₃×#117	—	2	2	no	—
123	C₂₃×#117	—	2	2	no	—
124	C₂₃×#117	C₂³	1	4	yes	—
125	C₂₃×#117	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
127	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
128	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
131	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
132	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
133	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
134	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
135	C₂×C₄²×C₂₃	—	2	2	no	—
136	C₂₃×#107	C₂³	1	4	yes	complemented
137	C₂₃×#107	C₂³	1	4	yes	complemented
138	C₂₃×#106	C₂³	1	8	yes	complemented
139	C₂₃×#103	C₂³	1	8	yes	complemented
140	C₂₃×#103	C₂³	1	8	yes	complemented
141	C₂₃×#102	C₂³	1	8	yes	complemented
142	C₂₃×#102	C₂³	1	8	yes	complemented
143	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
144	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
145	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	—
146	C₂⁴×C₂₃	—	2	4	no	—
147	C₂⁴×C₂₃	—	2	2	no	—
148	C₂⁴×C₂₃	—	4	2	no	—
149	C₂⁴×C₂₃	—	4	2	no	—
150	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
151	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
152	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
153	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
154	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
155	#41×C₂₃	—	2	16	no	—
156	#41×C₂₃	—	4	8	no	—
157	#41×C₂₃	—	4	8	no	—
158	#41×C₂₃	—	4	8	no	—
159	C₂×Q₈×C₂₃	—	2	2	no	—
160	C₂×Q₈×C₂₃	—	4	4	no	—
161	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
162	C₂×D₄×C₂₃	—	2	4	no	—
163	C₂×D₄×C₂₃	—	2	4	no	—
164	C₂×D₄×C₂₃	—	2	4	no	—
165	C₂×D₄×C₂₃	—	2	4	no	—
166	C₂×D₄×C₂₃	—	2	4	no	—
167	C₂×D₄×C₂₃	—	2	4	no	—
168	C₂×D₄×C₂₃	—	2	2	no	—
169	C₂×D₄×C₂₃	—	4	4	no	—
170	C₂×D₄×C₂₃	—	4	8	no	—
171	C₂×D₄×C₂₃	—	4	8	no	—
172	C₂×D₄×C₂₃	—	4	8	no	—
173	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₂₃	—	2	4	no	—
175	C₂²×C₄×C₂₃	—	2	8	no	—
176	C₂²×C₄×C₂₃	—	2	2	no	—
177	C₂²×C₄×C₂₃	—	2	2	no	—
178	C₂²×C₄×C₂₃	—	2	2	no	—
179	C₂²×C₄×C₂₃	—	2	4	no	—
180	C₂²×C₄×C₂₃	—	2	4	no	—
181	C₂²×C₄×C₂₃	—	4	2	no	—
182	C₂²×C₄×C₂₃	—	4	4	no	—
183	C₂²×C₄×C₂₃	—	4	2	no	—
184	C₂²×C₄×C₂₃	—	4	2	no	—
185	C₂²×C₄×C₂₃	—	4	4	no	—
186	C₂²×C₄×C₂₃	—	4	2	no	—
187	C₂²×C₄×C₂₃	—	4	4	no	—
188	C₂²×C₄×C₂₃	—	4	2	no	—
189	C₂²×C₄×C₂₃	—	4	8	no	—
190	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
191	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
193	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
194	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
197	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
198	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
200	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
201	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₂₃	C₂×D₄	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	1	yes	characteristic
208	Q₁₆×C₂₃	—	4	4	no	—
209	SD₁₆×C₂₃	—	4	8	no	—
210	D₈×C₂₃	—	4	4	no	—
211	C₂×C₈×C₂₃	—	2	8	no	—
212	C₂×C₈×C₂₃	—	4	2	no	—
213	C₂×C₈×C₂₃	—	4	4	no	—
214	C₂×C₈×C₂₃	—	4	2	no	—
215	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
216	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
217	C₄⋊C₄×C₂₃	—	2	4	no	—
218	C₄⋊C₄×C₂₃	—	2	4	no	—
219	C₄⋊C₄×C₂₃	—	2	4	no	—
220	C₄⋊C₄×C₂₃	—	2	4	no	—
221	C₄⋊C₄×C₂₃	—	2	2	no	—
222	C₄⋊C₄×C₂₃	—	2	2	no	—
223	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
224	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
225	C₂²⋊C₄×C₂₃	—	2	4	no	—
226	C₂²⋊C₄×C₂₃	—	2	4	no	—
227	C₂²⋊C₄×C₂₃	—	2	4	no	—
228	C₂²⋊C₄×C₂₃	—	2	4	no	—
229	C₂²⋊C₄×C₂₃	—	2	4	no	—
230	C₂²⋊C₄×C₂₃	—	2	4	no	—
231	C₂²⋊C₄×C₂₃	—	2	4	no	—
232	C₂²⋊C₄×C₂₃	—	2	4	no	—
233	C₂²⋊C₄×C₂₃	—	2	4	no	—
234	C₂²⋊C₄×C₂₃	—	2	4	no	—
235	C₄²×C₂₃	—	2	4	no	—
236	C₄²×C₂₃	—	2	4	no	—
237	#60734	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
238	C₂³×C₂₃	—	2	2	no	—
239	C₂³×C₂₃	—	2	2	no	—
240	C₂³×C₂₃	—	2	2	no	—
241	C₂³×C₂₃	—	2	4	no	—
242	C₂³×C₂₃	—	2	4	no	—
243	C₂³×C₂₃	—	2	4	no	—
244	C₂³×C₂₃	—	2	2	no	—
245	C₂³×C₂₃	—	2	4	no	—
246	C₂³×C₂₃	—	2	4	no	—
247	C₂³×C₂₃	—	4	1	no	—
248	C₂³×C₂₃	—	4	2	no	—
249	C₂³×C₂₃	—	4	1	no	—
250	C₂³×C₂₃	—	4	1	no	—
251	C₂³×C₂₃	—	4	2	no	—
252	C₂³×C₂₃	—	4	1	no	—
253	C₂³×C₂₃	—	4	16	no	—
254	C₂³×C₂₃	—	4	4	no	—
255	C₂³×C₂₃	—	4	4	no	—
256	C₂³×C₂₃	—	4	4	no	—
257	C₂³×C₂₃	#135	1	4	yes	complemented
258	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
259	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
260	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
261	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
262	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
263	Q₈×C₂₃	—	2	8	no	—
264	Q₈×C₂₃	—	4	4	no	—
265	D₄×C₂₃	—	2	8	no	—
266	D₄×C₂₃	—	4	4	no	—
267	D₄×C₂₃	—	4	8	no	—
268	D₄×C₂₃	—	4	8	no	—
269	D₄×C₂₃	—	4	8	no	—
270	D₄×C₂₃	—	4	8	no	—
271	D₄×C₂₃	—	4	8	no	—
272	D₄×C₂₃	—	4	8	no	—
273	C₂×C₄×C₂₃	—	2	2	no	—
274	C₂×C₄×C₂₃	—	2	4	no	—
275	C₂×C₄×C₂₃	—	2	4	no	—
276	C₂×C₄×C₂₃	—	2	2	no	—
277	C₂×C₄×C₂₃	—	2	2	no	—
278	C₂×C₄×C₂₃	—	2	4	no	—
279	C₂×C₄×C₂₃	—	2	2	no	—
280	C₂×C₄×C₂₃	—	2	2	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	—	2	4	no	—
286	C₂×C₄×C₂₃	—	4	1	no	—
287	C₂×C₄×C₂₃	—	4	2	no	—
288	C₂×C₄×C₂₃	—	4	2	no	—
289	C₂×C₄×C₂₃	—	4	2	no	—
290	C₂×C₄×C₂₃	—	4	2	no	—
291	C₂×C₄×C₂₃	—	4	2	no	—
292	C₂×C₄×C₂₃	—	4	1	no	—
293	C₂×C₄×C₂₃	—	4	8	no	—
294	C₂×C₄×C₂₃	—	4	4	no	—
295	C₂×C₄×C₂₃	—	4	4	no	—
296	C₂×C₄×C₂₃	—	4	4	no	—
297	C₂×C₄×C₂₃	—	4	8	no	—
298	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
299	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
300	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
301	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
302	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
303	C₂×C₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
304	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
305	C₈×C₂₃	—	2	4	no	—
306	C₈×C₂₃	—	2	4	no	—
307	C₂×#525	C₂×C₂₃	1	2	yes	complemented
308	#3191	C₂×C₂₃	1	4	yes	complemented
309	#3190	C₂×C₂₃	1	4	yes	complemented
310	#3189	C₂×C₂₃	1	1	yes	characteristic, complemented
311	#3188	C₂×C₂₃	1	4	yes	complemented
312	#3187	C₂×C₂₃	1	2	yes	complemented
313	#3186	C₂×C₂₃	1	1	yes	characteristic, complemented
314	#3091	C₂×C₂₃	1	4	yes	complemented
315	#3050	C₂×C₂₃	1	4	yes	complemented
316	#3002	C₂×C₂₃	1	4	yes	complemented
317	C₂²×C₂²⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
318	C₂²×C₂₃	—	2	8	no	—
319	C₂²×C₂₃	—	2	2	no	—
320	C₂²×C₂₃	—	2	1	no	—
321	C₂²×C₂₃	—	2	1	no	—
322	C₂²×C₂₃	—	2	1	no	—
323	C₂²×C₂₃	—	2	1	no	—
324	C₂²×C₂₃	—	2	2	no	—
325	C₂²×C₂₃	—	2	1	no	—
326	C₂²×C₂₃	—	2	1	no	—
327	C₂²×C₂₃	—	2	2	no	—
328	C₂²×C₂₃	—	2	2	no	—
329	C₂²×C₂₃	—	2	2	no	—
330	C₂²×C₂₃	—	4	4	no	—
331	C₂²×C₂₃	—	4	8	no	—
332	C₂²×C₂₃	—	4	8	no	—
333	C₂²×C₂₃	—	4	4	no	—
334	C₂²×C₂₃	—	4	4	no	—
335	C₂²×C₂₃	—	4	4	no	—
336	C₂²×C₂₃	—	4	4	no	—
337	C₂²×C₂₃	—	8	8	no	—
338	C₂²×C₂₃	#534	1	2	yes	—
339	C₂²×C₂₃	C₂×#135	1	4	yes	—
340	C₂²×C₂₃	C₂×#135	1	2	yes	—
341	C₂²×C₂₃	#575	1	2	yes	—
342	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
343	C₄×C₂₃	—	2	2	no	—
344	C₄×C₂₃	—	2	1	no	—
345	C₄×C₂₃	—	2	1	no	—
346	C₄×C₂₃	—	2	2	no	—
347	C₄×C₂₃	—	4	4	no	—
348	C₄×C₂₃	—	4	4	no	—
349	C₄×C₂₃	—	4	4	no	—
350	C₄×C₂₃	#534	1	2	yes	—
351	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
352	C₂²×#41	C₂²×C₂₃	1	2	yes	complemented
353	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
354	C₂×#135	C₂²×C₂₃	1	4	yes	complemented
355	C₂³×C₈	C₂²×C₂₃	1	2	yes	complemented
356	#525	—	2	2	no	—
357	#525	—	2	2	no	—
358	#525	—	2	2	no	—
359	#525	—	2	2	no	—
360	#525	C₂²×C₂₃	1	4	yes	—
361	#525	C₂²×C₂₃	1	4	yes	—
362	#525	C₂²×C₂₃	1	4	yes	complemented
363	#525	C₂²×C₂₃	1	4	yes	complemented
364	C₂×#123	—	2	2	no	—
365	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
366	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
367	C₂×#121	C₂²×C₂₃	1	2	yes	—
368	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
369	C₂×#120	—	2	2	no	—
370	C₂×C₄×D₄	—	2	2	no	—
371	C₂×C₄×D₄	—	2	2	no	—
372	C₂×#117	C₂²×C₂₃	1	2	yes	complemented
373	#485	C₂²×C₂₃	1	8	yes	complemented
374	#484	C₂²×C₂₃	1	4	yes	complemented
375	#483	C₂²×C₂₃	1	4	yes	complemented
376	#482	C₂²×C₂₃	1	8	yes	complemented
377	#481	C₂²×C₂₃	1	4	yes	complemented
378	#480	C₂²×C₂₃	1	4	yes	complemented
379	#467	C₂²×C₂₃	1	4	yes	complemented
380	#467	C₂²×C₂₃	1	4	yes	complemented
381	#466	C₂²×C₂₃	1	4	yes	complemented
382	#466	C₂²×C₂₃	1	4	yes	complemented
383	#465	C₂²×C₂₃	1	8	yes	complemented
384	#465	C₂²×C₂₃	1	8	yes	complemented
385	#452	C₂²×C₂₃	1	8	yes	complemented
386	#451	C₂²×C₂₃	1	4	yes	complemented
387	#450	C₂²×C₂₃	1	4	yes	complemented
388	#449	C₂²×C₂₃	1	8	yes	complemented
389	#448	C₂²×C₂₃	1	4	yes	complemented
390	#447	C₂²×C₂₃	1	4	yes	complemented
391	#427	C₂²×C₂₃	1	4	yes	complemented
392	#416	C₂²×C₂₃	1	8	yes	complemented
393	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
394	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
395	C₂×C₂²⋊C₈	C₂²×C₂₃	1	4	yes	complemented
396	C₂×C₂²⋊C₈	C₂²×C₂₃	1	4	yes	complemented
397	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
398	C₂×C₂₃	—	2	2	no	—
399	C₂×C₂₃	—	2	2	no	—
400	C₂×C₂₃	—	2	2	no	—
401	C₂×C₂₃	—	2	4	no	—
402	C₂×C₂₃	—	4	2	no	—
403	C₂×C₂₃	—	8	4	no	—
404	C₂×C₂₃	C₂×#534	1	1	yes	characteristic
405	C₂×C₂₃	C₂²×#135	1	1	yes	characteristic
406	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
407	C₂⁵	D₄×C₂₃	1	1	yes	characteristic
408	C₂×#41	—	2	2	no	—
409	C₂×#41	—	2	2	no	—
410	C₂×#41	—	4	8	no	—
411	C₂×#41	C₂³×C₂₃	1	4	yes	—
412	C₂×#41	C₂³×C₂₃	1	4	yes	—
413	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
414	C₂²×D₄	—	2	2	no	—
415	C₂²×D₄	—	2	2	no	—
416	C₂²×D₄	—	2	2	no	—
417	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
418	C₂³×C₄	—	2	2	no	—
419	C₂³×C₄	—	4	4	no	—
420	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
421	C₂³×C₄	D₄×C₂₃	1	2	yes	—
422	C₂³×C₄	D₄×C₂₃	1	2	yes	—
423	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
424	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
425	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
426	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
427	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
428	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
429	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
430	#135	—	4	8	no	—
431	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	complemented
432	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	complemented
433	C₂×D₈	C₂³×C₂₃	1	4	yes	complemented
434	C₂²×C₈	—	4	4	no	—
435	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
436	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
437	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
438	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
439	#123	—	2	4	no	—
440	#123	—	2	4	no	—
441	#123	—	2	4	no	—
442	#123	—	2	4	no	—
443	C₂²⋊Q₈	—	2	2	no	—
444	C₂²⋊Q₈	—	2	2	no	—
445	C₂²⋊Q₈	—	2	2	no	—
446	C₂²⋊Q₈	—	2	2	no	—
447	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
448	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
449	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
450	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
451	#121	—	2	2	no	—
452	#121	—	2	2	no	—
453	#121	—	2	2	no	—
454	#121	—	2	2	no	—
455	#121	C₂³×C₂₃	1	4	yes	—
456	#121	C₂³×C₂₃	1	4	yes	—
457	#121	C₂³×C₂₃	1	4	yes	—
458	#121	C₂³×C₂₃	1	4	yes	—
459	#120	—	2	4	no	—
460	#120	—	2	4	no	—
461	#120	—	2	4	no	—
462	#120	—	2	4	no	—
463	C₄×D₄	—	2	4	no	—
464	C₄×D₄	—	2	4	no	—
465	C₄×D₄	—	2	4	no	—
466	C₄×D₄	—	2	4	no	—
467	C₄×D₄	—	2	4	no	—
468	C₄×D₄	—	2	4	no	—
469	C₄×D₄	—	2	4	no	—
470	C₄×D₄	—	2	4	no	—
471	#117	—	2	2	no	—
472	#117	—	2	2	no	—
473	#117	C₂³×C₂₃	1	4	yes	—
474	#117	C₂³×C₂₃	1	4	yes	—
475	C₂×C₄⋊C₄	—	2	2	no	—
476	C₂×C₄⋊C₄	—	2	2	no	—
477	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
478	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
479	C₂×C₂²⋊C₄	—	2	2	no	—
480	C₂×C₂²⋊C₄	—	2	2	no	—
481	C₂×C₂²⋊C₄	—	2	2	no	—
482	C₂×C₂²⋊C₄	—	2	2	no	—
483	C₂×C₂²⋊C₄	—	2	2	no	—
484	C₂×C₄²	—	2	2	no	—
485	#107	C₂³×C₂₃	1	4	yes	complemented
486	#107	C₂³×C₂₃	1	4	yes	complemented
487	#106	C₂³×C₂₃	1	8	yes	complemented
488	#103	C₂³×C₂₃	1	8	yes	complemented
489	#103	C₂³×C₂₃	1	8	yes	complemented
490	#102	C₂³×C₂₃	1	8	yes	complemented
491	#102	C₂³×C₂₃	1	8	yes	complemented
492	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
493	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
494	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	—
495	C₂₃	#60734	1	1	yes	characteristic, direct product factor, Sylow
496	C₂⁴	—	2	4	no	—
497	C₂⁴	—	2	2	no	—
498	C₂⁴	—	4	2	no	—
499	C₂⁴	—	4	2	no	—
500	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
501	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
502	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
503	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
504	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
505	#41	—	2	16	no	—
506	#41	—	4	8	no	—
507	#41	—	4	8	no	—
508	#41	—	4	8	no	—
509	C₂×Q₈	—	2	2	no	—
510	C₂×Q₈	—	4	4	no	—
511	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
512	C₂×D₄	—	2	4	no	—
513	C₂×D₄	—	2	4	no	—
514	C₂×D₄	—	2	4	no	—
515	C₂×D₄	—	2	4	no	—
516	C₂×D₄	—	2	4	no	—
517	C₂×D₄	—	2	4	no	—
518	C₂×D₄	—	2	2	no	—
519	C₂×D₄	—	4	4	no	—
520	C₂×D₄	—	4	8	no	—
521	C₂×D₄	—	4	8	no	—
522	C₂×D₄	—	4	8	no	—
523	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
524	C₂²×C₄	—	2	4	no	—
525	C₂²×C₄	—	2	8	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	4	no	—
530	C₂²×C₄	—	2	4	no	—
531	C₂²×C₄	—	4	2	no	—
532	C₂²×C₄	—	4	4	no	—
533	C₂²×C₄	—	4	2	no	—
534	C₂²×C₄	—	4	2	no	—
535	C₂²×C₄	—	4	4	no	—
536	C₂²×C₄	—	4	2	no	—
537	C₂²×C₄	—	4	2	no	—
538	C₂²×C₄	—	4	4	no	—
539	C₂²×C₄	—	4	8	no	—
540	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
541	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
542	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
543	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
544	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
545	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
546	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
547	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
548	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
549	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
550	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
551	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
552	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
553	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
554	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
555	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
556	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
557	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
558	Q₁₆	—	4	4	no	—
559	SD₁₆	—	4	8	no	—
560	D₈	—	4	4	no	—
561	C₂×C₈	—	2	8	no	—
562	C₂×C₈	—	4	2	no	—
563	C₂×C₈	—	4	4	no	—
564	C₂×C₈	—	4	2	no	—
565	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
566	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	2	2	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
574	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
575	C₂²⋊C₄	—	2	4	no	—
576	C₂²⋊C₄	—	2	4	no	—
577	C₂²⋊C₄	—	2	4	no	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	—	2	4	no	—
580	C₂²⋊C₄	—	2	4	no	—
581	C₂²⋊C₄	—	2	4	no	—
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₄²	—	2	4	no	—
586	C₄²	—	2	4	no	—
587	C₂³	—	2	2	no	—
588	C₂³	—	2	2	no	—
589	C₂³	—	2	2	no	—
590	C₂³	—	2	4	no	—
591	C₂³	—	2	4	no	—
592	C₂³	—	2	2	no	—
593	C₂³	—	2	4	no	—
594	C₂³	—	2	4	no	—
595	C₂³	—	2	4	no	—
596	C₂³	—	4	1	no	—
597	C₂³	—	4	2	no	—
598	C₂³	—	4	1	no	—
599	C₂³	—	4	1	no	—
600	C₂³	—	4	2	no	—
601	C₂³	—	4	1	no	—
602	C₂³	—	4	16	no	—
603	C₂³	—	4	4	no	—
604	C₂³	—	4	4	no	—
605	C₂³	—	4	4	no	—
606	C₂³	C₂₃×#135	1	4	yes	complemented
607	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
608	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
609	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
610	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
611	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
612	Q₈	—	2	8	no	—
613	Q₈	—	4	4	no	—
614	D₄	—	2	8	no	—
615	D₄	—	4	4	no	—
616	D₄	—	4	8	no	—
617	D₄	—	4	8	no	—
618	D₄	—	4	8	no	—
619	D₄	—	4	8	no	—
620	D₄	—	4	8	no	—
621	D₄	—	4	8	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	4	no	—
627	C₂×C₄	—	2	4	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	2	no	—
637	C₂×C₄	—	4	2	no	—
638	C₂×C₄	—	4	2	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	2	no	—
641	C₂×C₄	—	4	2	no	—
642	C₂×C₄	—	4	8	no	—
643	C₂×C₄	—	4	4	no	—
644	C₂×C₄	—	4	4	no	—
645	C₂×C₄	—	4	4	no	—
646	C₂×C₄	—	4	8	no	—
647	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
648	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
649	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
650	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
651	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
652	C₂×C₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
653	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
654	C₈	—	2	4	no	—
655	C₈	—	2	4	no	—
656	C₂²	—	2	8	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	2	2	no	—
667	C₂²	—	2	2	no	—
668	C₂²	—	4	4	no	—
669	C₂²	—	4	8	no	—
670	C₂²	—	4	8	no	—
671	C₂²	—	4	4	no	—
672	C₂²	—	4	4	no	—
673	C₂²	—	4	4	no	—
674	C₂²	—	4	4	no	—
675	C₂²	—	8	8	no	—
676	C₂²	C₂₃×#534	1	2	yes	—
677	C₂²	C₂×C₂₃×#135	1	4	yes	—
678	C₂²	C₂×C₂₃×#135	1	2	yes	—
679	C₂²	C₂₃×#575	1	2	yes	—
680	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
681	C₄	—	2	2	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	4	4	no	—
686	C₄	—	4	4	no	—
687	C₄	—	4	4	no	—
688	C₄	C₂₃×#534	1	2	yes	—
689	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
690	C₂	—	2	2	no	—
691	C₂	—	2	2	no	—
692	C₂	—	2	2	no	—
693	C₂	—	2	4	no	—
694	C₂	—	4	2	no	—
695	C₂	—	8	4	no	—
696	C₂	C₂×C₂₃×#534	1	1	yes	characteristic
697	C₂	C₂²×C₂₃×#135	1	1	yes	characteristic
698	C₂	C₂×C₂₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂⁴×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#525	C₂	semidirect
2. C₂₃×#3191	C₂	semidirect
3. C₂₃×#3190	C₂	semidirect
4. C₂₃×#3189	C₂	semidirect
5. C₂₃×#3188	C₂	semidirect
6. C₂₃×#3187	C₂	semidirect
7. C₂₃×#3186	C₂	semidirect
8. C₂₃×#3091	C₂	semidirect
9. C₂₃×#3050	C₂	semidirect
10. C₂₃×#3002	C₂	semidirect
11. C₂²×C₂₃×C₂²⋊C₈	C₂	semidirect
12. C₂²×#41×C₂₃	C₂²	semidirect
14. C₂×C₂₃×#135	C₂²	semidirect
15. C₂³×C₈×C₂₃	C₂²	semidirect
22. C₂₃×#525	C₂²	semidirect
23. C₂₃×#525	C₂²	semidirect
26. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
28. C₂×C₂₃×#121	C₂²	semidirect
32. C₂×C₂₃×#117	C₂²	semidirect
33. C₂₃×#485	C₂²	semidirect
34. C₂₃×#484	C₂²	semidirect
35. C₂₃×#483	C₂²	semidirect
36. C₂₃×#482	C₂²	semidirect
37. C₂₃×#481	C₂²	semidirect
38. C₂₃×#480	C₂²	semidirect
39. C₂₃×#467	C₂²	semidirect
40. C₂₃×#467	C₂²	semidirect
41. C₂₃×#466	C₂²	semidirect
42. C₂₃×#466	C₂²	semidirect
43. C₂₃×#465	C₂²	semidirect
44. C₂₃×#465	C₂²	semidirect
45. C₂₃×#452	C₂²	semidirect
46. C₂₃×#451	C₂²	semidirect
47. C₂₃×#450	C₂²	semidirect
48. C₂₃×#449	C₂²	semidirect
49. C₂₃×#448	C₂²	semidirect
50. C₂₃×#447	C₂²	semidirect
51. C₂₃×#427	C₂²	semidirect
52. C₂₃×#416	C₂²	semidirect
55. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
56. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
57. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
82. C₂×Q₁₆×C₂₃	C₂³	semidirect
83. C₂×SD₁₆×C₂₃	C₂³	semidirect
84. C₂×D₈×C₂₃	C₂³	semidirect
136. C₂₃×#107	C₂³	semidirect
137. C₂₃×#107	C₂³	semidirect
138. C₂₃×#106	C₂³	semidirect
139. C₂₃×#103	C₂³	semidirect
140. C₂₃×#103	C₂³	semidirect
141. C₂₃×#102	C₂³	semidirect
142. C₂₃×#102	C₂³	semidirect
237. #60734	C₂₃	direct (N × H)
257. C₂³×C₂₃	#135	semidirect
307. C₂×#525	C₂×C₂₃	semidirect
308. #3191	C₂×C₂₃	semidirect
309. #3190	C₂×C₂₃	semidirect
310. #3189	C₂×C₂₃	semidirect
311. #3188	C₂×C₂₃	semidirect
312. #3187	C₂×C₂₃	semidirect
313. #3186	C₂×C₂₃	semidirect
314. #3091	C₂×C₂₃	semidirect
315. #3050	C₂×C₂₃	semidirect
316. #3002	C₂×C₂₃	semidirect
317. C₂²×C₂²⋊C₈	C₂×C₂₃	semidirect
352. C₂²×#41	C₂²×C₂₃	semidirect
354. C₂×#135	C₂²×C₂₃	semidirect
355. C₂³×C₈	C₂²×C₂₃	semidirect
362. #525	C₂²×C₂₃	semidirect
363. #525	C₂²×C₂₃	semidirect
366. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
368. C₂×#121	C₂²×C₂₃	semidirect
372. C₂×#117	C₂²×C₂₃	semidirect
373. #485	C₂²×C₂₃	semidirect
374. #484	C₂²×C₂₃	semidirect
375. #483	C₂²×C₂₃	semidirect
376. #482	C₂²×C₂₃	semidirect
377. #481	C₂²×C₂₃	semidirect
378. #480	C₂²×C₂₃	semidirect
379. #467	C₂²×C₂₃	semidirect
380. #467	C₂²×C₂₃	semidirect
381. #466	C₂²×C₂₃	semidirect
382. #466	C₂²×C₂₃	semidirect
383. #465	C₂²×C₂₃	semidirect
384. #465	C₂²×C₂₃	semidirect
385. #452	C₂²×C₂₃	semidirect
386. #451	C₂²×C₂₃	semidirect
387. #450	C₂²×C₂₃	semidirect
388. #449	C₂²×C₂₃	semidirect
389. #448	C₂²×C₂₃	semidirect
390. #447	C₂²×C₂₃	semidirect
391. #427	C₂²×C₂₃	semidirect
392. #416	C₂²×C₂₃	semidirect
395. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
396. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
397. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
431. C₂×Q₁₆	C₂³×C₂₃	semidirect
432. C₂×SD₁₆	C₂³×C₂₃	semidirect
433. C₂×D₈	C₂³×C₂₃	semidirect
485. #107	C₂³×C₂₃	semidirect
486. #107	C₂³×C₂₃	semidirect
487. #106	C₂³×C₂₃	semidirect
488. #103	C₂³×C₂₃	semidirect
489. #103	C₂³×C₂₃	semidirect
490. #102	C₂³×C₂₃	semidirect
491. #102	C₂³×C₂₃	semidirect
495. C₂₃	#60734	direct (N × H)
606. C₂³	C₂₃×#135	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×#3191	2
C₂₃×#3190	2
C₂₃×#3189	2
C₂₃×#3188	2
C₂₃×#3187	2
C₂₃×#3186	2
C₂₃×#3091	2
C₂₃×#3050	2
C₂₃×#3002	2
C₂²×C₂₃×C₂²⋊C₈	2
#60734	23

Subgroups — C23×#60734 #19208360

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60734 #19208360