Subgroups — C₂×C₂₃×#3117 #19208166

Order 5888.

2150 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#529	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3117	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#484	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#481	C₂	1	1	yes	maximal, characteristic
6	C₂×C₂₃×#479	C₂	1	2	yes	maximal, complemented
7	C₂×C₂₃×#464	C₂	1	2	yes	maximal, complemented
8	C₂×C₂₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#448	C₂	1	1	yes	maximal, characteristic
10	C₂×C₂₃×#441	C₂	1	2	yes	maximal, complemented
11	C₂×C₂₃×#440	C₂	1	2	yes	maximal, complemented
12	C₂×C₂₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
14	C₂²×Q₁₆×C₂₃	C₂²	1	2	yes	—
15	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	—
16	C₂₃×#529	—	2	4	no	—
17	C₂₃×#529	C₂²	1	8	yes	—
18	C₂×C₂₃×#126	—	2	1	no	—
19	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#123	—	2	1	no	—
22	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
25	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
26	C₂×C₄×Q₈×C₂₃	—	2	4	no	—
27	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₂₃	C₂²	1	8	yes	complemented
31	C₂×C₄×D₄×C₂₃	—	2	1	no	—
32	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#117	—	2	1	no	—
34	C₂²×C₄⋊C₄×C₂₃	—	2	1	no	—
35	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₂₃	—	2	1	no	—
37	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
38	C₂₃×#484	C₂²	1	8	yes	complemented
39	C₂₃×#481	C₂²	1	8	yes	—
40	C₂₃×#479	C₂²	1	16	yes	complemented
41	C₂₃×#464	C₂²	1	16	yes	complemented
42	C₂₃×#451	C₂²	1	8	yes	complemented
43	C₂₃×#448	C₂²	1	8	yes	—
44	C₂₃×#441	C₂²	1	16	yes	complemented
45	C₂₃×#440	C₂²	1	16	yes	complemented
46	C₂₃×#432	C₂²	1	8	yes	complemented
47	C₂×C₂₃×#107	C₂²	1	2	yes	—
48	C₂×C₂₃×#106	C₂²	1	2	yes	—
49	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
50	C₂×C₂₃×#103	C₂²	1	2	yes	—
51	C₂×C₂₃×#103	C₂²	1	2	yes	—
52	C₂×C₂₃×#103	C₂²	1	2	yes	—
53	C₂×C₂₃×#102	C₂²	1	2	yes	—
54	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
55	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
56	C₂×C₂₃×#97	C₂²	1	2	yes	—
57	C₂²×Q₈×C₂₃	—	2	8	no	—
58	C₂²×Q₈×C₂₃	—	2	2	no	—
59	C₂²×Q₈×C₂₃	—	2	1	no	—
60	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
61	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
62	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
63	C₂²×D₄×C₂₃	—	2	1	no	—
64	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₂₃	—	2	1	no	—
66	C₂³×C₄×C₂₃	—	2	1	no	—
67	C₂³×C₄×C₂₃	—	2	1	no	—
68	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
69	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
70	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
71	C₂×Q₁₆×C₂₃	—	2	8	no	—
72	C₂×Q₁₆×C₂₃	C₂³	1	8	yes	—
73	C₂×SD₁₆×C₂₃	—	2	8	no	—
74	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	—
75	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
76	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
77	C₂₃×#126	—	2	8	no	—
78	C₂₃×#125	—	2	2	no	—
79	C₂₃×#125	C₂³	1	4	yes	—
80	C₂₃×#124	—	2	2	no	—
81	C₂₃×#124	C₂³	1	4	yes	—
82	C₂₃×#123	—	2	8	no	—
83	C₂₃×C₂²⋊Q₈	—	2	2	no	—
84	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
85	C₂₃×#121	—	2	2	no	—
86	C₂₃×#121	C₂³	1	4	yes	—
87	C₄×Q₈×C₂₃	—	2	4	no	—
88	C₄×Q₈×C₂₃	—	2	4	no	—
89	C₄×Q₈×C₂₃	—	2	8	no	—
90	C₄×Q₈×C₂₃	—	2	8	no	—
91	C₄×Q₈×C₂₃	—	2	2	no	—
92	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
93	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
94	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
95	C₄×D₄×C₂₃	—	2	8	no	—
96	C₄×D₄×C₂₃	—	2	2	no	—
97	C₄×D₄×C₂₃	C₂³	1	4	yes	—
98	C₂₃×#117	—	2	8	no	—
99	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
100	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
101	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
102	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
103	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
104	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
105	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
106	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
107	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
108	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
117	C₂×C₄²×C₂₃	—	2	2	no	—
118	C₂×C₄²×C₂₃	—	2	2	no	—
119	C₂×C₄²×C₂₃	—	2	8	no	—
120	C₂×C₄²×C₂₃	—	2	1	no	—
121	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
122	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
123	C₂×C₄²×C₂₃	D₄	1	4	yes	—
124	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
127	C₂₃×#107	C₂³	1	8	yes	—
128	C₂₃×#106	C₂³	1	8	yes	—
129	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
130	C₂₃×#103	C₂³	1	8	yes	—
131	C₂₃×#103	C₂³	1	8	yes	—
132	C₂₃×#103	C₂³	1	8	yes	—
133	C₂₃×#102	C₂³	1	8	yes	—
134	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
135	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
136	C₂₃×#97	C₂³	1	8	yes	—
137	C₂⁴×C₂₃	—	2	1	no	—
138	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
139	C₂×Q₈×C₂₃	—	2	16	no	—
140	C₂×Q₈×C₂₃	—	2	8	no	—
141	C₂×Q₈×C₂₃	—	2	16	no	—
142	C₂×Q₈×C₂₃	—	2	4	no	—
143	C₂×Q₈×C₂₃	—	2	2	no	—
144	C₂×Q₈×C₂₃	—	2	1	no	—
145	C₂×Q₈×C₂₃	—	2	4	no	—
146	C₂×Q₈×C₂₃	—	2	4	no	—
147	C₂×Q₈×C₂₃	#41	1	8	yes	—
148	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
149	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
150	C₂×D₄×C₂₃	—	2	4	no	—
151	C₂×D₄×C₂₃	—	2	1	no	—
152	C₂×D₄×C₂₃	—	2	4	no	—
153	C₂×D₄×C₂₃	—	4	4	no	—
154	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
155	C₂²×C₄×C₂₃	—	2	8	no	—
156	C₂²×C₄×C₂₃	—	2	4	no	—
157	C₂²×C₄×C₂₃	—	2	4	no	—
158	C₂²×C₄×C₂₃	—	2	2	no	—
159	C₂²×C₄×C₂₃	—	2	4	no	—
160	C₂²×C₄×C₂₃	—	2	4	no	—
161	C₂²×C₄×C₂₃	—	2	2	no	—
162	C₂²×C₄×C₂₃	—	2	1	no	—
163	C₂²×C₄×C₂₃	—	2	1	no	—
164	C₂²×C₄×C₂₃	—	2	1	no	—
165	C₂²×C₄×C₂₃	—	2	4	no	—
166	C₂²×C₄×C₂₃	—	4	2	no	—
167	C₂²×C₄×C₂₃	—	4	4	no	—
168	C₂²×C₄×C₂₃	—	4	4	no	—
169	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
170	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
177	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
179	Q₁₆×C₂₃	—	2	16	no	—
180	SD₁₆×C₂₃	—	2	16	no	—
181	C₂×C₈×C₂₃	—	2	4	no	—
182	C₂×C₈×C₂₃	—	2	4	no	—
183	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
184	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
185	C₄⋊C₄×C₂₃	—	2	8	no	—
186	C₄⋊C₄×C₂₃	—	2	8	no	—
187	C₄⋊C₄×C₂₃	—	2	4	no	—
188	C₄⋊C₄×C₂₃	—	2	2	no	—
189	C₄⋊C₄×C₂₃	—	2	4	no	—
190	C₄⋊C₄×C₂₃	—	2	4	no	—
191	C₄⋊C₄×C₂₃	—	2	4	no	—
192	C₄⋊C₄×C₂₃	—	2	4	no	—
193	C₄⋊C₄×C₂₃	—	2	1	no	—
194	C₄⋊C₄×C₂₃	—	2	1	no	—
195	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
196	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
197	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
198	C₂²⋊C₄×C₂₃	—	2	4	no	—
199	C₂²⋊C₄×C₂₃	—	2	4	no	—
200	C₂²⋊C₄×C₂₃	—	2	4	no	—
201	C₂²⋊C₄×C₂₃	—	2	4	no	—
202	C₂²⋊C₄×C₂₃	—	2	4	no	—
203	C₄²×C₂₃	—	2	8	no	—
204	C₄²×C₂₃	—	2	8	no	—
205	C₄²×C₂₃	—	2	4	no	—
206	C₄²×C₂₃	C₂×D₄	1	4	yes	—
207	C₄²×C₂₃	C₂×D₄	1	2	yes	—
208	C₄²×C₂₃	C₂×D₄	1	2	yes	—
209	C₄²×C₂₃	C₂×D₄	1	4	yes	—
210	C₄²×C₂₃	C₂⁴	1	2	yes	—
211	C₄²×C₂₃	C₂⁴	1	2	yes	—
212	C₂×#3117	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂³×C₂₃	—	2	2	no	—
214	C₂³×C₂₃	—	2	2	no	—
215	C₂³×C₂₃	—	2	2	no	—
216	C₂³×C₂₃	—	4	2	no	—
217	C₂³×C₂₃	—	4	2	no	—
218	C₂³×C₂₃	—	4	2	no	—
219	C₂³×C₂₃	#137	1	4	yes	—
220	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
221	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
222	Q₈×C₂₃	—	2	16	no	—
223	Q₈×C₂₃	—	2	8	no	—
224	Q₈×C₂₃	—	2	4	no	—
225	Q₈×C₂₃	—	2	4	no	—
226	Q₈×C₂₃	—	4	2	no	—
227	Q₈×C₂₃	C₂×#41	1	8	yes	—
228	D₄×C₂₃	—	2	4	no	—
229	D₄×C₂₃	—	4	8	no	—
230	D₄×C₂₃	—	4	2	no	—
231	C₂×C₄×C₂₃	—	2	16	no	—
232	C₂×C₄×C₂₃	—	2	8	no	—
233	C₂×C₄×C₂₃	—	2	2	no	—
234	C₂×C₄×C₂₃	—	2	8	no	—
235	C₂×C₄×C₂₃	—	2	2	no	—
236	C₂×C₄×C₂₃	—	2	2	no	—
237	C₂×C₄×C₂₃	—	2	2	no	—
238	C₂×C₄×C₂₃	—	2	2	no	—
239	C₂×C₄×C₂₃	—	2	4	no	—
240	C₂×C₄×C₂₃	—	2	4	no	—
241	C₂×C₄×C₂₃	—	2	4	no	—
242	C₂×C₄×C₂₃	—	2	4	no	—
243	C₂×C₄×C₂₃	—	2	2	no	—
244	C₂×C₄×C₂₃	—	2	2	no	—
245	C₂×C₄×C₂₃	—	2	2	no	—
246	C₂×C₄×C₂₃	—	4	4	no	—
247	C₂×C₄×C₂₃	—	4	8	no	—
248	C₂×C₄×C₂₃	—	4	8	no	—
249	C₂×C₄×C₂₃	—	4	2	no	—
250	C₂×C₄×C₂₃	—	4	2	no	—
251	C₂×C₄×C₂₃	—	4	4	no	—
252	C₂×C₄×C₂₃	—	4	2	no	—
253	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
254	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
255	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
256	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
257	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
258	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
260	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
261	C₈×C₂₃	—	2	4	no	—
262	C₈×C₂₃	—	2	4	no	—
263	C₂×#529	C₂×C₂₃	1	1	yes	characteristic
264	C₂²×C₄×Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
265	#3117	C₂×C₂₃	1	16	yes	direct product factor
266	C₂×#484	C₂×C₂₃	1	1	yes	characteristic, complemented
267	C₂×#481	C₂×C₂₃	1	1	yes	characteristic
268	C₂×#479	C₂×C₂₃	1	2	yes	complemented
269	C₂×#464	C₂×C₂₃	1	2	yes	complemented
270	C₂×#451	C₂×C₂₃	1	1	yes	characteristic, complemented
271	C₂×#448	C₂×C₂₃	1	1	yes	characteristic
272	C₂×#441	C₂×C₂₃	1	2	yes	complemented
273	C₂×#440	C₂×C₂₃	1	2	yes	complemented
274	C₂×#432	C₂×C₂₃	1	1	yes	characteristic, complemented
275	C₂²×C₂₃	—	2	8	no	—
276	C₂²×C₂₃	—	2	2	no	—
277	C₂²×C₂₃	—	2	2	no	—
278	C₂²×C₂₃	—	4	2	no	—
279	C₂²×C₂₃	—	4	2	no	—
280	C₂²×C₂₃	—	4	2	no	—
281	C₂²×C₂₃	—	8	4	no	—
282	C₂²×C₂₃	#525	1	2	yes	—
283	C₂²×C₂₃	C₂×#137	1	4	yes	—
284	C₂²×C₂₃	C₂×#137	1	2	yes	—
285	C₂²×C₂₃	#575	1	2	yes	—
286	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
287	C₄×C₂₃	—	2	8	no	—
288	C₄×C₂₃	—	2	2	no	—
289	C₄×C₂₃	—	2	2	no	—
290	C₄×C₂₃	—	2	2	no	—
291	C₄×C₂₃	—	2	2	no	—
292	C₄×C₂₃	—	2	2	no	—
293	C₄×C₂₃	—	4	2	no	—
294	C₄×C₂₃	—	4	2	no	—
295	C₄×C₂₃	—	4	4	no	—
296	C₄×C₂₃	—	4	2	no	—
297	C₄×C₂₃	#525	1	2	yes	—
298	C₄×C₂₃	C₂²×#41	1	2	yes	—
299	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
300	C₂²×Q₁₆	C₂²×C₂₃	1	2	yes	—
301	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	—
302	#529	—	2	4	no	—
303	#529	C₂²×C₂₃	1	8	yes	—
304	C₂×#126	—	2	1	no	—
305	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
306	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
307	C₂×#123	—	2	1	no	—
308	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
309	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
310	C₂×C₄×Q₈	—	2	1	no	—
311	C₂×C₄×Q₈	—	2	1	no	—
312	C₂×C₄×Q₈	—	2	4	no	—
313	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
314	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
315	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
316	C₂×C₄×Q₈	C₂²×C₂₃	1	8	yes	complemented
317	C₂×C₄×D₄	—	2	1	no	—
318	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
319	C₂×#117	—	2	1	no	—
320	C₂²×C₄⋊C₄	—	2	1	no	—
321	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
322	C₂²×C₄²	—	2	1	no	—
323	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
324	#484	C₂²×C₂₃	1	8	yes	complemented
325	#481	C₂²×C₂₃	1	8	yes	—
326	#479	C₂²×C₂₃	1	16	yes	complemented
327	#464	C₂²×C₂₃	1	16	yes	complemented
328	#451	C₂²×C₂₃	1	8	yes	complemented
329	#448	C₂²×C₂₃	1	8	yes	—
330	#441	C₂²×C₂₃	1	16	yes	complemented
331	#440	C₂²×C₂₃	1	16	yes	complemented
332	#432	C₂²×C₂₃	1	8	yes	complemented
333	C₂×#107	C₂²×C₂₃	1	2	yes	—
334	C₂×#106	C₂²×C₂₃	1	2	yes	—
335	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
336	C₂×#103	C₂²×C₂₃	1	2	yes	—
337	C₂×#103	C₂²×C₂₃	1	2	yes	—
338	C₂×#103	C₂²×C₂₃	1	2	yes	—
339	C₂×#102	C₂²×C₂₃	1	2	yes	—
340	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
341	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
342	C₂×#97	C₂²×C₂₃	1	2	yes	—
343	C₂×C₂₃	—	2	4	no	—
344	C₂×C₂₃	—	8	2	no	—
345	C₂×C₂₃	#3117	1	4	yes	direct product factor
346	C₂×C₂₃	C₂×#525	1	1	yes	characteristic
347	C₂×C₂₃	C₂²×#137	1	1	yes	characteristic
348	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
349	C₂²×Q₈	—	2	8	no	—
350	C₂²×Q₈	—	2	1	no	—
351	C₂²×Q₈	—	2	2	no	—
352	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
353	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
354	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
355	C₂²×D₄	—	2	1	no	—
356	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
357	C₂³×C₄	—	2	1	no	—
358	C₂³×C₄	—	2	1	no	—
359	C₂³×C₄	—	2	1	no	—
360	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
361	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
362	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
363	C₂×Q₁₆	—	2	8	no	—
364	C₂×Q₁₆	C₂³×C₂₃	1	8	yes	—
365	C₂×SD₁₆	—	2	8	no	—
366	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	—
367	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
368	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
369	#126	—	2	8	no	—
370	#125	—	2	2	no	—
371	#125	C₂³×C₂₃	1	4	yes	—
372	#124	—	2	2	no	—
373	#124	C₂³×C₂₃	1	4	yes	—
374	#123	—	2	8	no	—
375	C₂²⋊Q₈	—	2	2	no	—
376	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
377	#121	—	2	2	no	—
378	#121	C₂³×C₂₃	1	4	yes	—
379	C₄×Q₈	—	2	4	no	—
380	C₄×Q₈	—	2	4	no	—
381	C₄×Q₈	—	2	8	no	—
382	C₄×Q₈	—	2	8	no	—
383	C₄×Q₈	—	2	2	no	—
384	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
385	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
386	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
387	C₄×D₄	—	2	8	no	—
388	C₄×D₄	—	2	2	no	—
389	C₄×D₄	C₂³×C₂₃	1	4	yes	—
390	#117	—	2	8	no	—
391	C₂×C₄⋊C₄	—	2	2	no	—
392	C₂×C₄⋊C₄	—	2	2	no	—
393	C₂×C₄⋊C₄	—	2	8	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	2	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
401	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
402	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₂²⋊C₄	—	2	1	no	—
407	C₂×C₂²⋊C₄	—	2	1	no	—
408	C₂×C₂²⋊C₄	—	2	1	no	—
409	C₂×C₄²	—	2	1	no	—
410	C₂×C₄²	—	2	2	no	—
411	C₂×C₄²	—	2	2	no	—
412	C₂×C₄²	—	2	8	no	—
413	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
414	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
415	C₂×C₄²	D₄×C₂₃	1	4	yes	—
416	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
417	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
418	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
419	#107	C₂³×C₂₃	1	8	yes	—
420	#106	C₂³×C₂₃	1	8	yes	—
421	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
422	#103	C₂³×C₂₃	1	8	yes	—
423	#103	C₂³×C₂₃	1	8	yes	—
424	#103	C₂³×C₂₃	1	8	yes	—
425	#102	C₂³×C₂₃	1	8	yes	—
426	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
427	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
428	#97	C₂³×C₂₃	1	8	yes	—
429	C₂₃	C₂×#3117	1	1	yes	characteristic, direct product factor, Sylow
430	C₂⁴	—	2	1	no	—
431	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
432	C₂×Q₈	—	2	16	no	—
433	C₂×Q₈	—	2	8	no	—
434	C₂×Q₈	—	2	16	no	—
435	C₂×Q₈	—	2	4	no	—
436	C₂×Q₈	—	2	2	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	4	no	—
439	C₂×Q₈	—	2	4	no	—
440	C₂×Q₈	#41×C₂₃	1	8	yes	—
441	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
442	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
443	C₂×D₄	—	2	4	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	4	no	—
446	C₂×D₄	—	4	4	no	—
447	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
448	C₂²×C₄	—	2	8	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	4	2	no	—
460	C₂²×C₄	—	4	4	no	—
461	C₂²×C₄	—	4	4	no	—
462	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
463	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
465	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
468	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
470	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
471	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
472	Q₁₆	—	2	16	no	—
473	SD₁₆	—	2	16	no	—
474	C₂×C₈	—	2	4	no	—
475	C₂×C₈	—	2	4	no	—
476	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
477	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
478	C₄⋊C₄	—	2	8	no	—
479	C₄⋊C₄	—	2	8	no	—
480	C₄⋊C₄	—	2	4	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	4	no	—
483	C₄⋊C₄	—	2	4	no	—
484	C₄⋊C₄	—	2	4	no	—
485	C₄⋊C₄	—	2	4	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
489	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
490	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	2	4	no	—
493	C₂²⋊C₄	—	2	4	no	—
494	C₂²⋊C₄	—	2	4	no	—
495	C₂²⋊C₄	—	2	4	no	—
496	C₄²	—	2	8	no	—
497	C₄²	—	2	8	no	—
498	C₄²	—	2	4	no	—
499	C₄²	C₂×D₄×C₂₃	1	4	yes	—
500	C₄²	C₂×D₄×C₂₃	1	2	yes	—
501	C₄²	C₂×D₄×C₂₃	1	2	yes	—
502	C₄²	C₂×D₄×C₂₃	1	4	yes	—
503	C₄²	C₂⁴×C₂₃	1	2	yes	—
504	C₄²	C₂⁴×C₂₃	1	2	yes	—
505	C₂³	—	2	2	no	—
506	C₂³	—	2	2	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	4	2	no	—
509	C₂³	—	4	2	no	—
510	C₂³	—	4	2	no	—
511	C₂³	C₂₃×#137	1	4	yes	—
512	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
513	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
514	Q₈	—	2	16	no	—
515	Q₈	—	2	4	no	—
516	Q₈	—	2	8	no	—
517	Q₈	—	2	4	no	—
518	Q₈	—	4	2	no	—
519	Q₈	C₂×#41×C₂₃	1	8	yes	—
520	D₄	—	2	4	no	—
521	D₄	—	4	8	no	—
522	D₄	—	4	2	no	—
523	C₂×C₄	—	2	16	no	—
524	C₂×C₄	—	2	8	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	8	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	4	4	no	—
539	C₂×C₄	—	4	8	no	—
540	C₂×C₄	—	4	8	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	4	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
546	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
547	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
548	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
549	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
550	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
551	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
552	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
553	C₈	—	2	4	no	—
554	C₈	—	2	4	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	8	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	8	4	no	—
562	C₂²	C₂₃×#525	1	2	yes	—
563	C₂²	C₂×C₂₃×#137	1	4	yes	—
564	C₂²	C₂×C₂₃×#137	1	2	yes	—
565	C₂²	C₂₃×#575	1	2	yes	—
566	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
567	C₄	—	2	8	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	2	no	—
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	4	2	no	—
574	C₄	—	4	2	no	—
575	C₄	—	4	4	no	—
576	C₄	—	4	2	no	—
577	C₄	C₂₃×#525	1	2	yes	—
578	C₄	C₂²×#41×C₂₃	1	2	yes	—
579	C₂	—	2	4	no	—
580	C₂	—	8	2	no	—
581	C₂	C₂₃×#3117	1	4	yes	direct product factor
582	C₂	C₂×C₂₃×#525	1	1	yes	characteristic
583	C₂	C₂²×C₂₃×#137	1	1	yes	characteristic
584	C₂	C₂×C₂₃×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×Q₈×C₂₃	C₂	semidirect
3. C₂₃×#3117	C₂	direct (N × H)
4. C₂×C₂₃×#484	C₂	semidirect
6. C₂×C₂₃×#479	C₂	semidirect
7. C₂×C₂₃×#464	C₂	semidirect
8. C₂×C₂₃×#451	C₂	semidirect
10. C₂×C₂₃×#441	C₂	semidirect
11. C₂×C₂₃×#440	C₂	semidirect
12. C₂×C₂₃×#432	C₂	semidirect
30. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
38. C₂₃×#484	C₂²	semidirect
40. C₂₃×#479	C₂²	semidirect
41. C₂₃×#464	C₂²	semidirect
42. C₂₃×#451	C₂²	semidirect
44. C₂₃×#441	C₂²	semidirect
45. C₂₃×#440	C₂²	semidirect
46. C₂₃×#432	C₂²	semidirect
212. C₂×#3117	C₂₃	direct (N × H)
264. C₂²×C₄×Q₈	C₂×C₂₃	semidirect
265. #3117	C₂×C₂₃	direct (N × H)
266. C₂×#484	C₂×C₂₃	semidirect
268. C₂×#479	C₂×C₂₃	semidirect
269. C₂×#464	C₂×C₂₃	semidirect
270. C₂×#451	C₂×C₂₃	semidirect
272. C₂×#441	C₂×C₂₃	semidirect
273. C₂×#440	C₂×C₂₃	semidirect
274. C₂×#432	C₂×C₂₃	semidirect
316. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
324. #484	C₂²×C₂₃	semidirect
326. #479	C₂²×C₂₃	semidirect
327. #464	C₂²×C₂₃	semidirect
328. #451	C₂²×C₂₃	semidirect
330. #441	C₂²×C₂₃	semidirect
331. #440	C₂²×C₂₃	semidirect
332. #432	C₂²×C₂₃	semidirect
345. C₂×C₂₃	#3117	direct (N × H)
429. C₂₃	C₂×#3117	direct (N × H)
581. C₂	C₂₃×#3117	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×#529	2
C₂²×C₄×Q₈×C₂₃	2
C₂₃×#3117	2
C₂×C₂₃×#484	2
C₂×C₂₃×#481	2
C₂×C₂₃×#479	2
C₂×C₂₃×#464	2
C₂×C₂₃×#451	2
C₂×C₂₃×#448	2
C₂×C₂₃×#441	2
C₂×C₂₃×#440	2
C₂×C₂₃×#432	2
C₂×#3117	23

Subgroups — C2×C23×#3117 #19208166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3117 #19208166