Subgroups — C₂×C₂₃×#3389 #19208989

Order 5888.

1898 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#554	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3389	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₂₃×#501	C₂	1	2	yes	maximal, complemented
4	C₂×C₂₃×#499	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#478	C₂	1	2	yes	maximal, complemented
6	C₂×C₂₃×#478	C₂	1	2	yes	maximal, complemented
7	C₂×C₂₃×#474	C₂	1	2	yes	maximal, complemented
8	C₂×C₂₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#442	C₂	1	2	yes	maximal
10	C₂×C₄×D₈×C₂₃	C₂	1	1	yes	maximal, characteristic
11	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
12	C₂₃×#554	—	2	8	no	—
13	C₂₃×#554	C₂²	1	16	yes	complemented
14	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₂₃×#125	C₂²	1	2	yes	—
16	C₂×C₂₃×#125	C₂²	1	2	yes	—
17	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
18	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
19	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
20	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
24	C₂²×C₄⋊C₄×C₂₃	—	2	2	no	—
25	C₂₃×#501	C₂²	1	16	yes	complemented
26	C₂₃×#499	C₂²	1	8	yes	complemented
27	C₂₃×#478	C₂²	1	16	yes	complemented
28	C₂₃×#478	C₂²	1	16	yes	complemented
29	C₂₃×#474	C₂²	1	16	yes	complemented
30	C₂₃×#446	C₂²	1	8	yes	complemented
31	C₂₃×#442	C₂²	1	16	yes	—
32	C₄×D₈×C₂₃	C₂²	1	8	yes	—
33	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#107	C₂²	1	2	yes	—
36	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#106	C₂²	1	2	yes	—
38	C₂×C₂₃×#106	C₂²	1	2	yes	—
39	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
40	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×#102	C₂²	1	2	yes	—
42	C₂×C₂₃×#102	C₂²	1	2	yes	—
43	C₂×C₂₃×#102	C₂²	1	2	yes	—
44	C₂×C₂₃×#97	C₂²	1	2	yes	—
45	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
46	C₂²×Q₈×C₂₃	—	2	2	no	—
47	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
48	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₂₃	—	2	2	no	—
50	C₂³×C₄×C₂₃	—	2	2	no	—
51	C₂³×C₄×C₂₃	—	2	2	no	—
52	C₂×D₈×C₂₃	Q₈	1	8	yes	complemented
53	C₂×D₈×C₂₃	C₂³	1	4	yes	—
54	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
56	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
57	C₂₃×C₄⋊Q₈	—	2	4	no	—
58	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	—
59	C₂₃×#125	—	2	4	no	—
60	C₂₃×#125	—	2	4	no	—
61	C₂₃×#125	C₂³	1	8	yes	—
62	C₂₃×#125	C₂³	1	8	yes	—
63	C₂₃×C₂²⋊Q₈	—	2	16	no	—
64	C₂₃×C₂²⋊Q₈	—	2	16	no	—
65	C₂₃×C₂²⋊Q₈	—	2	16	no	—
66	C₄×Q₈×C₂₃	D₄	1	4	yes	—
67	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
68	C₄×D₄×C₂₃	—	2	4	no	—
69	C₄×D₄×C₂₃	—	2	4	no	—
70	C₄×D₄×C₂₃	—	2	4	no	—
71	C₄×D₄×C₂₃	C₂³	1	8	yes	—
72	C₄×D₄×C₂₃	C₂³	1	8	yes	—
73	C₄×D₄×C₂₃	C₂³	1	8	yes	—
74	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
75	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
76	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
77	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
78	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
79	C₂×C₄⋊C₄×C₂₃	—	2	16	no	—
80	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
81	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
85	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
88	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
90	C₂₃×#107	C₂³	1	4	yes	—
91	C₂₃×#107	C₂³	1	4	yes	—
92	C₂₃×#107	C₂³	1	8	yes	—
93	C₂₃×#107	C₂³	1	4	yes	—
94	C₂₃×#106	C₂³	1	8	yes	—
95	C₂₃×#106	C₂³	1	8	yes	—
96	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
97	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
98	C₂₃×#102	C₂³	1	8	yes	—
99	C₂₃×#102	C₂³	1	8	yes	—
100	C₂₃×#102	C₂³	1	8	yes	—
101	C₂₃×#97	C₂³	1	8	yes	—
102	C₄×C₈×C₂₃	C₂³	1	4	yes	—
103	C₂⁴×C₂₃	—	2	2	no	—
104	C₂×Q₈×C₂₃	—	2	8	no	—
105	C₂×Q₈×C₂₃	—	4	2	no	—
106	C₂×Q₈×C₂₃	—	8	4	no	—
107	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	—
108	C₂×D₄×C₂₃	—	2	2	no	—
109	C₂×D₄×C₂₃	—	2	4	no	—
110	C₂×D₄×C₂₃	C₂×Q₈	1	8	yes	—
111	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
112	C₂²×C₄×C₂₃	—	2	2	no	—
113	C₂²×C₄×C₂₃	—	2	2	no	—
114	C₂²×C₄×C₂₃	—	2	2	no	—
115	C₂²×C₄×C₂₃	—	2	8	no	—
116	C₂²×C₄×C₂₃	—	2	8	no	—
117	C₂²×C₄×C₂₃	—	2	8	no	—
118	C₂²×C₄×C₂₃	—	4	8	no	—
119	C₂²×C₄×C₂₃	—	8	4	no	—
120	C₂²×C₄×C₂₃	—	8	4	no	—
121	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
126	D₈×C₂₃	C₂×Q₈	1	16	yes	complemented
127	C₂×C₈×C₂₃	—	2	2	no	—
128	C₂×C₈×C₂₃	—	2	4	no	—
129	C₂×C₈×C₂₃	C₂×Q₈	1	4	yes	—
130	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
131	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
132	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
133	C₄⋊C₄×C₂₃	—	2	8	no	—
134	C₄⋊C₄×C₂₃	—	2	8	no	—
135	C₄⋊C₄×C₂₃	—	2	8	no	—
136	C₄⋊C₄×C₂₃	—	2	8	no	—
137	C₄⋊C₄×C₂₃	—	2	8	no	—
138	C₄⋊C₄×C₂₃	—	2	2	no	—
139	C₄⋊C₄×C₂₃	—	2	2	no	—
140	C₄⋊C₄×C₂₃	—	2	2	no	—
141	C₄⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
142	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
143	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
144	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
145	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
146	C₂²⋊C₄×C₂₃	—	2	8	no	—
147	C₂²⋊C₄×C₂₃	—	2	8	no	—
148	C₂²⋊C₄×C₂₃	—	2	8	no	—
149	C₄²×C₂₃	C₂×D₄	1	2	yes	—
150	C₄²×C₂₃	C₂×D₄	1	4	yes	—
151	C₄²×C₂₃	C₂⁴	1	2	yes	—
152	C₄²×C₂₃	C₂⁴	1	4	yes	—
153	C₂×#3389	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂³×C₂₃	—	2	8	no	—
155	C₂³×C₂₃	—	2	4	no	—
156	C₂³×C₂₃	—	4	4	no	—
157	C₂³×C₂₃	—	4	4	no	—
158	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
159	Q₈×C₂₃	—	4	4	no	—
160	Q₈×C₂₃	—	8	8	no	—
161	D₄×C₂₃	—	2	8	no	—
162	D₄×C₂₃	—	2	4	no	—
163	D₄×C₂₃	C₂²×Q₈	1	8	yes	—
164	C₂×C₄×C₂₃	—	2	4	no	—
165	C₂×C₄×C₂₃	—	2	2	no	—
166	C₂×C₄×C₂₃	—	2	2	no	—
167	C₂×C₄×C₂₃	—	2	4	no	—
168	C₂×C₄×C₂₃	—	2	4	no	—
169	C₂×C₄×C₂₃	—	2	4	no	—
170	C₂×C₄×C₂₃	—	2	4	no	—
171	C₂×C₄×C₂₃	—	4	16	no	—
172	C₂×C₄×C₂₃	—	4	4	no	—
173	C₂×C₄×C₂₃	—	4	4	no	—
174	C₂×C₄×C₂₃	—	4	4	no	—
175	C₂×C₄×C₂₃	—	8	8	no	—
176	C₂×C₄×C₂₃	—	8	8	no	—
177	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
178	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
179	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
180	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
181	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
183	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
184	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
185	C₈×C₂₃	—	2	4	no	—
186	C₈×C₂₃	—	2	2	no	—
187	C₈×C₂₃	C₂²×Q₈	1	4	yes	—
188	C₂×#554	C₂×C₂₃	1	2	yes	complemented
189	#3389	C₂×C₂₃	1	16	yes	direct product factor
190	C₂×#501	C₂×C₂₃	1	2	yes	complemented
191	C₂×#499	C₂×C₂₃	1	1	yes	characteristic, complemented
192	C₂×#478	C₂×C₂₃	1	2	yes	complemented
193	C₂×#478	C₂×C₂₃	1	2	yes	complemented
194	C₂×#474	C₂×C₂₃	1	2	yes	complemented
195	C₂×#446	C₂×C₂₃	1	1	yes	characteristic, complemented
196	C₂×#442	C₂×C₂₃	1	2	yes	—
197	C₂×C₄×D₈	C₂×C₂₃	1	1	yes	characteristic
198	C₂²×C₂₃	—	2	8	no	—
199	C₂²×C₂₃	—	4	16	no	—
200	C₂²×C₂₃	—	4	4	no	—
201	C₂²×C₂₃	—	4	4	no	—
202	C₂²×C₂₃	D₄×Q₈	1	2	yes	—
203	C₂²×C₂₃	#575	1	2	yes	—
204	C₂²×C₂₃	#576	1	2	yes	—
205	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
206	C₄×C₂₃	—	2	4	no	—
207	C₄×C₂₃	—	2	2	no	—
208	C₄×C₂₃	—	2	2	no	—
209	C₄×C₂₃	—	2	4	no	—
210	C₄×C₂₃	—	4	4	no	—
211	C₄×C₂₃	—	4	4	no	—
212	C₄×C₂₃	—	4	4	no	—
213	C₄×C₂₃	D₄×Q₈	1	2	yes	—
214	C₄×C₂₃	C₂³×Q₈	1	1	yes	characteristic
215	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
216	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
217	#554	—	2	8	no	—
218	#554	C₂²×C₂₃	1	16	yes	complemented
219	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
220	C₂×#125	C₂²×C₂₃	1	2	yes	—
221	C₂×#125	C₂²×C₂₃	1	2	yes	—
222	C₂×C₂²⋊Q₈	—	2	2	no	—
223	C₂×C₂²⋊Q₈	—	2	2	no	—
224	C₂×C₂²⋊Q₈	—	2	2	no	—
225	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
226	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
227	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
228	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
229	C₂²×C₄⋊C₄	—	2	2	no	—
230	#501	C₂²×C₂₃	1	16	yes	complemented
231	#499	C₂²×C₂₃	1	8	yes	complemented
232	#478	C₂²×C₂₃	1	16	yes	complemented
233	#478	C₂²×C₂₃	1	16	yes	complemented
234	#474	C₂²×C₂₃	1	16	yes	complemented
235	#446	C₂²×C₂₃	1	8	yes	complemented
236	#442	C₂²×C₂₃	1	16	yes	—
237	C₄×D₈	C₂²×C₂₃	1	8	yes	—
238	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
239	C₂×#107	C₂²×C₂₃	1	2	yes	—
240	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
241	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
242	C₂×#106	C₂²×C₂₃	1	2	yes	—
243	C₂×#106	C₂²×C₂₃	1	2	yes	—
244	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
245	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
246	C₂×#102	C₂²×C₂₃	1	2	yes	—
247	C₂×#102	C₂²×C₂₃	1	2	yes	—
248	C₂×#102	C₂²×C₂₃	1	2	yes	—
249	C₂×#97	C₂²×C₂₃	1	2	yes	—
250	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
251	C₂×C₂₃	—	4	8	no	—
252	C₂×C₂₃	#3389	1	4	yes	direct product factor
253	C₂×C₂₃	C₂×D₄×Q₈	1	1	yes	characteristic
254	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
255	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
256	C₂²×Q₈	—	2	2	no	—
257	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
258	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
259	C₂³×C₄	—	2	2	no	—
260	C₂³×C₄	—	2	2	no	—
261	C₂³×C₄	—	2	2	no	—
262	C₂×D₈	Q₈×C₂₃	1	8	yes	complemented
263	C₂×D₈	C₂³×C₂₃	1	4	yes	—
264	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
266	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
267	C₄⋊Q₈	—	2	4	no	—
268	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	—
269	#125	—	2	4	no	—
270	#125	—	2	4	no	—
271	#125	C₂³×C₂₃	1	8	yes	—
272	#125	C₂³×C₂₃	1	8	yes	—
273	C₂²⋊Q₈	—	2	16	no	—
274	C₂²⋊Q₈	—	2	16	no	—
275	C₂²⋊Q₈	—	2	16	no	—
276	C₄×Q₈	D₄×C₂₃	1	4	yes	—
277	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
278	C₄×D₄	—	2	4	no	—
279	C₄×D₄	—	2	4	no	—
280	C₄×D₄	—	2	4	no	—
281	C₄×D₄	C₂³×C₂₃	1	8	yes	—
282	C₄×D₄	C₂³×C₂₃	1	8	yes	—
283	C₄×D₄	C₂³×C₂₃	1	8	yes	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	16	no	—
290	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
291	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
299	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
300	#107	C₂³×C₂₃	1	4	yes	—
301	#107	C₂³×C₂₃	1	4	yes	—
302	#107	C₂³×C₂₃	1	8	yes	—
303	#107	C₂³×C₂₃	1	4	yes	—
304	#106	C₂³×C₂₃	1	8	yes	—
305	#106	C₂³×C₂₃	1	8	yes	—
306	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
307	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
308	#102	C₂³×C₂₃	1	8	yes	—
309	#102	C₂³×C₂₃	1	8	yes	—
310	#102	C₂³×C₂₃	1	8	yes	—
311	#97	C₂³×C₂₃	1	8	yes	—
312	C₄×C₈	C₂³×C₂₃	1	4	yes	—
313	C₂₃	C₂×#3389	1	1	yes	characteristic, direct product factor, Sylow
314	C₂⁴	—	2	2	no	—
315	C₂×Q₈	—	2	8	no	—
316	C₂×Q₈	—	4	2	no	—
317	C₂×Q₈	—	8	4	no	—
318	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	4	no	—
321	C₂×D₄	C₂×Q₈×C₂₃	1	8	yes	—
322	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	8	no	—
327	C₂²×C₄	—	2	8	no	—
328	C₂²×C₄	—	2	8	no	—
329	C₂²×C₄	—	4	8	no	—
330	C₂²×C₄	—	8	4	no	—
331	C₂²×C₄	—	8	4	no	—
332	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
336	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
337	D₈	C₂×Q₈×C₂₃	1	16	yes	complemented
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	4	no	—
340	C₂×C₈	C₂×Q₈×C₂₃	1	4	yes	—
341	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
342	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
343	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
344	C₄⋊C₄	—	2	8	no	—
345	C₄⋊C₄	—	2	8	no	—
346	C₄⋊C₄	—	2	8	no	—
347	C₄⋊C₄	—	2	8	no	—
348	C₄⋊C₄	—	2	8	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
353	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
354	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
355	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
356	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
357	C₂²⋊C₄	—	2	8	no	—
358	C₂²⋊C₄	—	2	8	no	—
359	C₂²⋊C₄	—	2	8	no	—
360	C₄²	C₂×D₄×C₂₃	1	2	yes	—
361	C₄²	C₂×D₄×C₂₃	1	4	yes	—
362	C₄²	C₂⁴×C₂₃	1	2	yes	—
363	C₄²	C₂⁴×C₂₃	1	4	yes	—
364	C₂³	—	2	8	no	—
365	C₂³	—	2	4	no	—
366	C₂³	—	4	4	no	—
367	C₂³	—	4	4	no	—
368	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
369	Q₈	—	4	4	no	—
370	Q₈	—	8	8	no	—
371	D₄	—	2	8	no	—
372	D₄	—	2	4	no	—
373	D₄	C₂²×Q₈×C₂₃	1	8	yes	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	4	16	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	—	8	8	no	—
386	C₂×C₄	—	8	8	no	—
387	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
388	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
389	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
390	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
391	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
392	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
393	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
394	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	2	4	no	—
397	C₈	C₂²×Q₈×C₂₃	1	4	yes	—
398	C₂²	—	2	8	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	4	16	no	—
402	C₂²	D₄×Q₈×C₂₃	1	2	yes	—
403	C₂²	C₂₃×#575	1	2	yes	—
404	C₂²	C₂₃×#576	1	2	yes	—
405	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
406	C₄	—	2	4	no	—
407	C₄	—	2	2	no	—
408	C₄	—	2	2	no	—
409	C₄	—	2	4	no	—
410	C₄	—	4	4	no	—
411	C₄	—	4	4	no	—
412	C₄	—	4	4	no	—
413	C₄	D₄×Q₈×C₂₃	1	2	yes	—
414	C₄	C₂³×Q₈×C₂₃	1	1	yes	characteristic
415	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
416	C₂	—	4	8	no	—
417	C₂	C₂₃×#3389	1	4	yes	direct product factor
418	C₂	C₂×D₄×Q₈×C₂₃	1	1	yes	characteristic
419	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
420	C₂	C₂×C₂₃×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂²×D₈×C₂₃	C₂²
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×#554	C₂	semidirect
2. C₂₃×#3389	C₂	direct (N × H)
3. C₂×C₂₃×#501	C₂	semidirect
4. C₂×C₂₃×#499	C₂	semidirect
5. C₂×C₂₃×#478	C₂	semidirect
6. C₂×C₂₃×#478	C₂	semidirect
7. C₂×C₂₃×#474	C₂	semidirect
8. C₂×C₂₃×#446	C₂	semidirect
13. C₂₃×#554	C₂²	semidirect
25. C₂₃×#501	C₂²	semidirect
26. C₂₃×#499	C₂²	semidirect
27. C₂₃×#478	C₂²	semidirect
28. C₂₃×#478	C₂²	semidirect
29. C₂₃×#474	C₂²	semidirect
30. C₂₃×#446	C₂²	semidirect
52. C₂×D₈×C₂₃	Q₈	semidirect
126. D₈×C₂₃	C₂×Q₈	semidirect
153. C₂×#3389	C₂₃	direct (N × H)
188. C₂×#554	C₂×C₂₃	semidirect
189. #3389	C₂×C₂₃	direct (N × H)
190. C₂×#501	C₂×C₂₃	semidirect
191. C₂×#499	C₂×C₂₃	semidirect
192. C₂×#478	C₂×C₂₃	semidirect
193. C₂×#478	C₂×C₂₃	semidirect
194. C₂×#474	C₂×C₂₃	semidirect
195. C₂×#446	C₂×C₂₃	semidirect
218. #554	C₂²×C₂₃	semidirect
230. #501	C₂²×C₂₃	semidirect
231. #499	C₂²×C₂₃	semidirect
232. #478	C₂²×C₂₃	semidirect
233. #478	C₂²×C₂₃	semidirect
234. #474	C₂²×C₂₃	semidirect
235. #446	C₂²×C₂₃	semidirect
252. C₂×C₂₃	#3389	direct (N × H)
262. C₂×D₈	Q₈×C₂₃	semidirect
313. C₂₃	C₂×#3389	direct (N × H)
337. D₈	C₂×Q₈×C₂₃	semidirect
417. C₂	C₂₃×#3389	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×#554	2
C₂₃×#3389	2
C₂×C₂₃×#501	2
C₂×C₂₃×#499	2
C₂×C₂₃×#478	2
C₂×C₂₃×#474	2
C₂×C₂₃×#446	2
C₂×C₂₃×#442	2
C₂×C₄×D₈×C₂₃	2
C₂×#3389	23

Subgroups — C2×C23×#3389 #19208989

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3389 #19208989