Subgroups — C₂×C₂₃×#3381 #19208980

Order 5888.

1842 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#554	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3381	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#499	C₂	1	2	yes	maximal, complemented
5	C₂×C₂₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#479	C₂	1	2	yes	maximal, complemented
7	C₂×C₂₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#478	C₂	1	2	yes	maximal
9	C₂×C₂₃×#474	C₂	1	1	yes	maximal, characteristic
10	C₂×C₈×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×SD₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×SD₁₆×C₂₃	C₂	1	2	yes	maximal
13	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
14	C₂₃×#557	—	2	4	no	—
15	C₂₃×#557	C₂²	1	8	yes	complemented
16	C₂₃×#554	—	2	4	no	—
17	C₂₃×#554	C₂²	1	8	yes	—
18	C₂×C₂₃×C₄⋊Q₈	—	2	1	no	—
19	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#125	—	2	2	no	—
22	C₂×C₂₃×#125	C₂²	1	2	yes	—
23	C₂×C₂₃×#125	C₂²	1	2	yes	—
24	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
25	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
26	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
27	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
32	C₂²×C₄⋊C₄×C₂₃	—	2	1	no	—
33	C₂₃×#499	C₂²	1	16	yes	complemented
34	C₂₃×#498	C₂²	1	8	yes	complemented
35	C₂₃×#479	C₂²	1	16	yes	complemented
36	C₂₃×#478	C₂²	1	16	yes	—
37	C₂₃×#477	C₂²	1	8	yes	complemented
38	C₂₃×#474	C₂²	1	8	yes	—
39	C₈×Q₈×C₂₃	C₂²	1	8	yes	complemented
40	C₄×SD₁₆×C₂₃	C₂²	1	16	yes	—
41	C₄×SD₁₆×C₂₃	C₂²	1	8	yes	—
42	C₂×C₂₃×#107	C₂²	1	2	yes	—
43	C₂×C₂₃×#107	C₂²	1	2	yes	—
44	C₂×C₂₃×#106	C₂²	1	2	yes	—
45	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
46	C₂×C₂₃×#106	C₂²	1	2	yes	—
47	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
49	C₂×C₂₃×#103	C₂²	1	2	yes	—
50	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
51	C₂×C₂₃×#102	C₂²	1	2	yes	—
52	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
54	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
55	C₂²×Q₈×C₂₃	—	2	1	no	—
56	C₂²×Q₈×C₂₃	—	2	1	no	—
57	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
58	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₂₃	—	2	1	no	—
61	C₂³×C₄×C₂₃	—	2	2	no	—
62	C₂×SD₁₆×C₂₃	Q₈	1	8	yes	complemented
63	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
64	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
66	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
67	C₂₃×C₄⋊Q₈	—	2	8	no	—
68	C₂₃×C₄⋊Q₈	—	2	2	no	—
69	C₂₃×C₄⋊Q₈	—	2	2	no	—
70	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
71	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
72	C₂₃×#125	—	2	16	no	—
73	C₂₃×#125	—	2	4	no	—
74	C₂₃×#125	—	2	4	no	—
75	C₂₃×#125	C₂³	1	8	yes	—
76	C₂₃×#125	C₂³	1	8	yes	—
77	C₂₃×C₂²⋊Q₈	—	2	8	no	—
78	C₂₃×C₂²⋊Q₈	—	2	16	no	—
79	C₄×Q₈×C₂₃	—	2	8	no	—
80	C₄×Q₈×C₂₃	—	2	4	no	—
81	C₄×Q₈×C₂₃	—	2	2	no	—
82	C₄×Q₈×C₂₃	D₄	1	4	yes	—
83	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
84	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
85	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
86	C₄×D₄×C₂₃	—	2	4	no	—
87	C₄×D₄×C₂₃	—	2	2	no	—
88	C₄×D₄×C₂₃	C₂³	1	4	yes	—
89	C₄×D₄×C₂₃	C₂³	1	8	yes	—
90	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
91	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
92	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
93	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
94	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
95	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
96	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
97	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
98	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
99	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
101	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
107	C₂×C₄²×C₂₃	—	2	2	no	—
108	C₂×C₄²×C₂₃	—	2	1	no	—
109	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
110	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
111	C₂₃×#107	C₂³	1	8	yes	—
112	C₂₃×#107	C₂³	1	8	yes	—
113	C₂₃×#106	C₂³	1	8	yes	—
114	C₂₃×#106	C₂³	1	4	yes	—
115	C₂₃×#106	C₂³	1	8	yes	—
116	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
117	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
118	C₂₃×#103	C₂³	1	8	yes	—
119	C₂₃×#103	C₂³	1	4	yes	—
120	C₂₃×#102	C₂³	1	8	yes	—
121	C₂₃×#102	C₂³	1	4	yes	—
122	C₄×C₈×C₂₃	C₂³	1	4	yes	—
123	C₄×C₈×C₂₃	C₂³	1	8	yes	—
124	C₂⁴×C₂₃	—	2	1	no	—
125	C₂×Q₈×C₂₃	—	2	4	no	—
126	C₂×Q₈×C₂₃	—	2	1	no	—
127	C₂×Q₈×C₂₃	—	2	4	no	—
128	C₂×Q₈×C₂₃	—	2	4	no	—
129	C₂×Q₈×C₂₃	—	2	2	no	—
130	C₂×Q₈×C₂₃	—	4	4	no	—
131	C₂×Q₈×C₂₃	—	8	2	no	—
132	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	—
133	C₂×Q₈×C₂₃	C₂×Q₈	1	4	yes	—
134	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
135	C₂×D₄×C₂₃	—	2	1	no	—
136	C₂×D₄×C₂₃	—	2	2	no	—
137	C₂×D₄×C₂₃	C₂×Q₈	1	4	yes	—
138	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
139	C₂²×C₄×C₂₃	—	2	1	no	—
140	C₂²×C₄×C₂₃	—	2	1	no	—
141	C₂²×C₄×C₂₃	—	2	2	no	—
142	C₂²×C₄×C₂₃	—	2	1	no	—
143	C₂²×C₄×C₂₃	—	2	2	no	—
144	C₂²×C₄×C₂₃	—	2	4	no	—
145	C₂²×C₄×C₂₃	—	2	8	no	—
146	C₂²×C₄×C₂₃	—	4	4	no	—
147	C₂²×C₄×C₂₃	—	8	4	no	—
148	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
153	SD₁₆×C₂₃	C₂×Q₈	1	16	yes	complemented
154	C₂×C₈×C₂₃	—	2	2	no	—
155	C₂×C₈×C₂₃	—	2	4	no	—
156	C₂×C₈×C₂₃	C₂×Q₈	1	4	yes	—
157	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
158	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
159	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
160	C₄⋊C₄×C₂₃	—	2	8	no	—
161	C₄⋊C₄×C₂₃	—	2	4	no	—
162	C₄⋊C₄×C₂₃	—	2	8	no	—
163	C₄⋊C₄×C₂₃	—	2	4	no	—
164	C₄⋊C₄×C₂₃	—	2	8	no	—
165	C₄⋊C₄×C₂₃	—	2	8	no	—
166	C₄⋊C₄×C₂₃	—	2	4	no	—
167	C₄⋊C₄×C₂₃	—	2	8	no	—
168	C₄⋊C₄×C₂₃	—	2	1	no	—
169	C₄⋊C₄×C₂₃	—	2	2	no	—
170	C₄⋊C₄×C₂₃	—	2	1	no	—
171	C₄⋊C₄×C₂₃	—	2	2	no	—
172	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
173	C₄⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
174	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
175	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
176	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
177	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
178	C₂²⋊C₄×C₂₃	—	2	4	no	—
179	C₂²⋊C₄×C₂₃	—	2	8	no	—
180	C₄²×C₂₃	—	2	8	no	—
181	C₄²×C₂₃	—	2	4	no	—
182	C₄²×C₂₃	C₂×D₄	1	4	yes	—
183	C₄²×C₂₃	C₂×D₄	1	2	yes	—
184	C₄²×C₂₃	C₂⁴	1	4	yes	—
185	C₄²×C₂₃	C₂⁴	1	2	yes	—
186	C₂×#3381	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂³×C₂₃	—	2	4	no	—
188	C₂³×C₂₃	—	2	2	no	—
189	C₂³×C₂₃	—	4	2	no	—
190	C₂³×C₂₃	—	4	2	no	—
191	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
192	Q₈×C₂₃	—	2	4	no	—
193	Q₈×C₂₃	—	2	8	no	—
194	Q₈×C₂₃	—	2	2	no	—
195	Q₈×C₂₃	—	4	8	no	—
196	Q₈×C₂₃	—	8	4	no	—
197	Q₈×C₂₃	C₂²×Q₈	1	4	yes	—
198	D₄×C₂₃	—	2	4	no	—
199	D₄×C₂₃	—	2	2	no	—
200	D₄×C₂₃	C₂²×Q₈	1	4	yes	—
201	C₂×C₄×C₂₃	—	2	4	no	—
202	C₂×C₄×C₂₃	—	2	4	no	—
203	C₂×C₄×C₂₃	—	2	4	no	—
204	C₂×C₄×C₂₃	—	2	2	no	—
205	C₂×C₄×C₂₃	—	2	2	no	—
206	C₂×C₄×C₂₃	—	2	2	no	—
207	C₂×C₄×C₂₃	—	2	4	no	—
208	C₂×C₄×C₂₃	—	2	2	no	—
209	C₂×C₄×C₂₃	—	2	4	no	—
210	C₂×C₄×C₂₃	—	4	2	no	—
211	C₂×C₄×C₂₃	—	4	4	no	—
212	C₂×C₄×C₂₃	—	4	2	no	—
213	C₂×C₄×C₂₃	—	4	4	no	—
214	C₂×C₄×C₂₃	—	4	8	no	—
215	C₂×C₄×C₂₃	—	8	8	no	—
216	C₂×C₄×C₂₃	#135	1	4	yes	—
217	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
218	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
219	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
220	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
222	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
223	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
224	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
225	C₈×C₂₃	—	2	2	no	—
226	C₈×C₂₃	—	2	4	no	—
227	C₈×C₂₃	C₂²×Q₈	1	4	yes	—
228	C₂×#557	C₂×C₂₃	1	1	yes	characteristic, complemented
229	C₂×#554	C₂×C₂₃	1	1	yes	characteristic
230	#3381	C₂×C₂₃	1	16	yes	direct product factor
231	C₂×#499	C₂×C₂₃	1	2	yes	complemented
232	C₂×#498	C₂×C₂₃	1	1	yes	characteristic, complemented
233	C₂×#479	C₂×C₂₃	1	2	yes	complemented
234	C₂×#477	C₂×C₂₃	1	1	yes	characteristic, complemented
235	C₂×#478	C₂×C₂₃	1	2	yes	—
236	C₂×#474	C₂×C₂₃	1	1	yes	characteristic
237	C₂×C₈×Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
238	C₂×C₄×SD₁₆	C₂×C₂₃	1	2	yes	—
239	C₂×C₄×SD₁₆	C₂×C₂₃	1	1	yes	characteristic
240	C₂²×C₂₃	—	2	4	no	—
241	C₂²×C₂₃	—	4	8	no	—
242	C₂²×C₂₃	—	4	2	no	—
243	C₂²×C₂₃	—	4	2	no	—
244	C₂²×C₂₃	D₄×Q₈	1	2	yes	—
245	C₂²×C₂₃	C₂×#135	1	2	yes	—
246	C₂²×C₂₃	#577	1	2	yes	—
247	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
248	C₄×C₂₃	—	2	4	no	—
249	C₄×C₂₃	—	2	4	no	—
250	C₄×C₂₃	—	2	4	no	—
251	C₄×C₂₃	—	2	2	no	—
252	C₄×C₂₃	—	4	2	no	—
253	C₄×C₂₃	—	4	4	no	—
254	C₄×C₂₃	—	4	2	no	—
255	C₄×C₂₃	—	4	4	no	—
256	C₄×C₂₃	D₄×Q₈	1	2	yes	—
257	C₄×C₂₃	C₂×#135	1	4	yes	—
258	C₄×C₂₃	C₂³×Q₈	1	1	yes	characteristic
259	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
260	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
261	#557	—	2	4	no	—
262	#557	C₂²×C₂₃	1	8	yes	complemented
263	#554	—	2	4	no	—
264	#554	C₂²×C₂₃	1	8	yes	—
265	C₂×C₄⋊Q₈	—	2	1	no	—
266	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
267	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
268	C₂×#125	—	2	2	no	—
269	C₂×#125	C₂²×C₂₃	1	2	yes	—
270	C₂×#125	C₂²×C₂₃	1	2	yes	—
271	C₂×C₂²⋊Q₈	—	2	1	no	—
272	C₂×C₂²⋊Q₈	—	2	2	no	—
273	C₂×C₄×Q₈	—	2	1	no	—
274	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
275	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
276	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
277	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
278	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
279	C₂²×C₄⋊C₄	—	2	1	no	—
280	#499	C₂²×C₂₃	1	16	yes	complemented
281	#498	C₂²×C₂₃	1	8	yes	complemented
282	#479	C₂²×C₂₃	1	16	yes	complemented
283	#478	C₂²×C₂₃	1	16	yes	—
284	#477	C₂²×C₂₃	1	8	yes	complemented
285	#474	C₂²×C₂₃	1	8	yes	—
286	C₈×Q₈	C₂²×C₂₃	1	8	yes	complemented
287	C₄×SD₁₆	C₂²×C₂₃	1	8	yes	—
288	C₄×SD₁₆	C₂²×C₂₃	1	16	yes	—
289	C₂×#107	C₂²×C₂₃	1	2	yes	—
290	C₂×#107	C₂²×C₂₃	1	2	yes	—
291	C₂×#106	C₂²×C₂₃	1	2	yes	—
292	C₂×#106	C₂²×C₂₃	1	2	yes	—
293	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
294	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
295	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
296	C₂×#103	C₂²×C₂₃	1	2	yes	—
297	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
298	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
299	C₂×#102	C₂²×C₂₃	1	2	yes	—
300	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
301	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
302	C₂×C₂₃	—	4	4	no	—
303	C₂×C₂₃	#3381	1	4	yes	direct product factor
304	C₂×C₂₃	C₂×D₄×Q₈	1	1	yes	characteristic
305	C₂×C₂₃	C₂²×#135	1	1	yes	characteristic
306	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
307	C₂²×Q₈	—	2	1	no	—
308	C₂²×Q₈	—	2	1	no	—
309	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
310	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
311	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
312	C₂³×C₄	—	2	1	no	—
313	C₂³×C₄	—	2	2	no	—
314	C₂×SD₁₆	Q₈×C₂₃	1	8	yes	complemented
315	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
316	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
317	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
318	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
319	C₄⋊Q₈	—	2	8	no	—
320	C₄⋊Q₈	—	2	2	no	—
321	C₄⋊Q₈	—	2	2	no	—
322	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
323	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
324	#125	—	2	16	no	—
325	#125	—	2	4	no	—
326	#125	—	2	4	no	—
327	#125	C₂³×C₂₃	1	8	yes	—
328	#125	C₂³×C₂₃	1	8	yes	—
329	C₂²⋊Q₈	—	2	8	no	—
330	C₂²⋊Q₈	—	2	16	no	—
331	C₄×Q₈	—	2	8	no	—
332	C₄×Q₈	—	2	4	no	—
333	C₄×Q₈	—	2	2	no	—
334	C₄×Q₈	D₄×C₂₃	1	4	yes	—
335	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
336	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
337	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
338	C₄×D₄	—	2	4	no	—
339	C₄×D₄	—	2	2	no	—
340	C₄×D₄	C₂³×C₂₃	1	4	yes	—
341	C₄×D₄	C₂³×C₂₃	1	8	yes	—
342	C₂×C₄⋊C₄	—	2	2	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	2	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄⋊C₄	—	2	8	no	—
351	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
352	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
353	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
355	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
357	C₂×C₂²⋊C₄	—	2	1	no	—
358	C₂×C₂²⋊C₄	—	2	2	no	—
359	C₂×C₄²	—	2	2	no	—
360	C₂×C₄²	—	2	1	no	—
361	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
362	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
363	#107	C₂³×C₂₃	1	8	yes	—
364	#107	C₂³×C₂₃	1	8	yes	—
365	#106	C₂³×C₂₃	1	8	yes	—
366	#106	C₂³×C₂₃	1	4	yes	—
367	#106	C₂³×C₂₃	1	8	yes	—
368	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
369	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
370	#103	C₂³×C₂₃	1	8	yes	—
371	#103	C₂³×C₂₃	1	4	yes	—
372	#102	C₂³×C₂₃	1	8	yes	—
373	#102	C₂³×C₂₃	1	4	yes	—
374	C₄×C₈	C₂³×C₂₃	1	4	yes	—
375	C₄×C₈	C₂³×C₂₃	1	8	yes	—
376	C₂₃	C₂×#3381	1	1	yes	characteristic, direct product factor, Sylow
377	C₂⁴	—	2	1	no	—
378	C₂×Q₈	—	2	4	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	2	4	no	—
381	C₂×Q₈	—	2	4	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	4	4	no	—
384	C₂×Q₈	—	8	2	no	—
385	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	—
386	C₂×Q₈	C₂×Q₈×C₂₃	1	4	yes	—
387	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	C₂×Q₈×C₂₃	1	4	yes	—
391	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	8	no	—
399	C₂²×C₄	—	4	4	no	—
400	C₂²×C₄	—	8	4	no	—
401	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
402	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
403	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
405	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
406	SD₁₆	C₂×Q₈×C₂₃	1	16	yes	complemented
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	4	no	—
409	C₂×C₈	C₂×Q₈×C₂₃	1	4	yes	—
410	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
411	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
412	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
413	C₄⋊C₄	—	2	8	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	8	no	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	—	2	8	no	—
418	C₄⋊C₄	—	2	8	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	8	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
426	C₄⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
427	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
428	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
429	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
430	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
431	C₂²⋊C₄	—	2	4	no	—
432	C₂²⋊C₄	—	2	8	no	—
433	C₄²	—	2	8	no	—
434	C₄²	—	2	4	no	—
435	C₄²	C₂×D₄×C₂₃	1	4	yes	—
436	C₄²	C₂×D₄×C₂₃	1	2	yes	—
437	C₄²	C₂⁴×C₂₃	1	4	yes	—
438	C₄²	C₂⁴×C₂₃	1	2	yes	—
439	C₂³	—	2	4	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	4	2	no	—
442	C₂³	—	4	2	no	—
443	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
444	Q₈	—	2	4	no	—
445	Q₈	—	2	8	no	—
446	Q₈	—	2	2	no	—
447	Q₈	—	4	8	no	—
448	Q₈	—	8	4	no	—
449	Q₈	C₂²×Q₈×C₂₃	1	4	yes	—
450	D₄	—	2	4	no	—
451	D₄	—	2	2	no	—
452	D₄	C₂²×Q₈×C₂₃	1	4	yes	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	8	no	—
467	C₂×C₄	—	8	8	no	—
468	C₂×C₄	C₂₃×#135	1	4	yes	—
469	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
470	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
471	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
472	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
473	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
474	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
475	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
476	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
477	C₈	—	2	2	no	—
478	C₈	—	2	4	no	—
479	C₈	C₂²×Q₈×C₂₃	1	4	yes	—
480	C₂²	—	2	4	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	8	no	—
484	C₂²	D₄×Q₈×C₂₃	1	2	yes	—
485	C₂²	C₂×C₂₃×#135	1	2	yes	—
486	C₂²	C₂₃×#577	1	2	yes	—
487	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
488	C₄	—	2	4	no	—
489	C₄	—	2	4	no	—
490	C₄	—	2	4	no	—
491	C₄	—	2	2	no	—
492	C₄	—	4	2	no	—
493	C₄	—	4	4	no	—
494	C₄	—	4	4	no	—
495	C₄	—	4	2	no	—
496	C₄	D₄×Q₈×C₂₃	1	2	yes	—
497	C₄	C₂×C₂₃×#135	1	4	yes	—
498	C₄	C₂³×Q₈×C₂₃	1	1	yes	characteristic
499	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
500	C₂	—	4	4	no	—
501	C₂	C₂₃×#3381	1	4	yes	direct product factor
502	C₂	C₂×D₄×Q₈×C₂₃	1	1	yes	characteristic
503	C₂	C₂²×C₂₃×#135	1	1	yes	characteristic
504	C₂	C₂×C₂₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂²×D₄×C₂₃	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄×Q₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#557	C₂	semidirect
3. C₂₃×#3381	C₂	direct (N × H)
4. C₂×C₂₃×#499	C₂	semidirect
5. C₂×C₂₃×#498	C₂	semidirect
6. C₂×C₂₃×#479	C₂	semidirect
7. C₂×C₂₃×#477	C₂	semidirect
10. C₂×C₈×Q₈×C₂₃	C₂	semidirect
15. C₂₃×#557	C₂²	semidirect
33. C₂₃×#499	C₂²	semidirect
34. C₂₃×#498	C₂²	semidirect
35. C₂₃×#479	C₂²	semidirect
37. C₂₃×#477	C₂²	semidirect
39. C₈×Q₈×C₂₃	C₂²	semidirect
62. C₂×SD₁₆×C₂₃	Q₈	semidirect
153. SD₁₆×C₂₃	C₂×Q₈	semidirect
186. C₂×#3381	C₂₃	direct (N × H)
228. C₂×#557	C₂×C₂₃	semidirect
230. #3381	C₂×C₂₃	direct (N × H)
231. C₂×#499	C₂×C₂₃	semidirect
232. C₂×#498	C₂×C₂₃	semidirect
233. C₂×#479	C₂×C₂₃	semidirect
234. C₂×#477	C₂×C₂₃	semidirect
237. C₂×C₈×Q₈	C₂×C₂₃	semidirect
262. #557	C₂²×C₂₃	semidirect
280. #499	C₂²×C₂₃	semidirect
281. #498	C₂²×C₂₃	semidirect
282. #479	C₂²×C₂₃	semidirect
284. #477	C₂²×C₂₃	semidirect
286. C₈×Q₈	C₂²×C₂₃	semidirect
303. C₂×C₂₃	#3381	direct (N × H)
314. C₂×SD₁₆	Q₈×C₂₃	semidirect
376. C₂₃	C₂×#3381	direct (N × H)
406. SD₁₆	C₂×Q₈×C₂₃	semidirect
501. C₂	C₂₃×#3381	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#557	2
C₂×C₂₃×#554	2
C₂₃×#3381	2
C₂×C₂₃×#499	2
C₂×C₂₃×#498	2
C₂×C₂₃×#479	2
C₂×C₂₃×#477	2
C₂×C₂₃×#478	2
C₂×C₂₃×#474	2
C₂×C₈×Q₈×C₂₃	2
C₂×C₄×SD₁₆×C₂₃	2
C₂×#3381	23

Subgroups — C2×C23×#3381 #19208980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3381 #19208980