Subgroups — C₂×C₂₃×#2583 #19182458

Order 5888.

3094 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2583	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#398	C₂	1	2	yes	maximal, complemented
5	C₂×C₂₃×#395	C₂	1	2	yes	maximal, complemented
6	C₂×C₂₃×#389	C₂	1	4	yes	maximal, complemented
7	C₂×C₂₃×#385	C₂	1	2	yes	maximal
8	C₂×C₂₃×#385	C₂	1	2	yes	maximal
9	C₂×C₄×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
14	C₂×C₂₃×C₂²⋊Q₈	—	2	8	no	—
15	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	8	yes	—
16	C₂²×C₄⋊C₄×C₂₃	—	2	8	no	—
17	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
20	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₂₃	C₂²	1	8	yes	—
22	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
23	C₂²×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
24	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
26	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
27	C₂₃×#398	C₂²	1	16	yes	complemented
28	C₂₃×#395	C₂²	1	16	yes	complemented
29	C₂₃×#389	C₂²	1	32	yes	complemented
30	C₂₃×#385	C₂²	1	16	yes	—
31	C₂₃×#385	C₂²	1	16	yes	—
32	C₄×C₂²⋊C₄×C₂₃	C₂²	1	8	yes	—
33	C₂×C₂₃×#95	C₂²	1	2	yes	—
34	C₂×C₂₃×#95	C₂²	1	4	yes	—
35	C₂×C₂₃×#95	C₂²	1	4	yes	—
36	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
37	C₂²×Q₈×C₂₃	—	2	4	no	—
38	C₂²×Q₈×C₂₃	—	4	4	no	—
39	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
40	C₂³×C₄×C₂₃	—	2	4	no	—
41	C₂³×C₄×C₂₃	—	2	8	no	—
42	C₂³×C₄×C₂₃	—	2	4	no	—
43	C₂³×C₄×C₂₃	—	4	4	no	—
44	C₂³×C₄×C₂₃	—	4	4	no	—
45	C₂³×C₄×C₂₃	D₄	1	8	yes	—
46	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
47	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
48	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
53	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
55	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
56	C₂₃×C₂²⋊Q₈	—	2	32	no	—
57	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
58	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
59	C₂×C₄⋊C₄×C₂₃	—	2	32	no	—
60	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
61	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
62	C₂×C₄⋊C₄×C₂₃	—	2	16	no	—
63	C₂×C₄⋊C₄×C₂₃	—	4	8	no	—
64	C₂×C₄⋊C₄×C₂₃	C₂³	1	16	yes	—
65	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
66	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
67	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
68	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
69	C₂×C₄⋊C₄×C₂₃	C₂³	1	16	yes	—
70	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
71	C₂×C₂²⋊C₄×C₂₃	Q₈	1	16	yes	complemented
72	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
73	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
74	C₂×C₄²×C₂₃	—	4	4	no	—
75	C₂×C₄²×C₂₃	C₂³	1	8	yes	—
76	C₂₃×#95	C₂³	1	8	yes	—
77	C₂₃×#95	C₂³	1	16	yes	—
78	C₂₃×#95	C₂³	1	16	yes	—
79	C₂⁴×C₂₃	—	2	4	no	—
80	C₂⁴×C₂₃	—	2	4	no	—
81	C₂⁴×C₂₃	C₂×D₄	1	4	yes	—
82	C₂⁴×C₂₃	C₂×Q₈	1	8	yes	—
83	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
84	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
85	C₂×Q₈×C₂₃	—	2	8	no	—
86	C₂×Q₈×C₂₃	—	4	8	no	—
87	C₂×Q₈×C₂₃	—	4	16	no	—
88	C₂²×C₄×C₂₃	—	2	32	no	—
89	C₂²×C₄×C₂₃	—	2	8	no	—
90	C₂²×C₄×C₂₃	—	2	4	no	—
91	C₂²×C₄×C₂₃	—	2	8	no	—
92	C₂²×C₄×C₂₃	—	2	4	no	—
93	C₂²×C₄×C₂₃	—	2	8	no	—
94	C₂²×C₄×C₂₃	—	2	4	no	—
95	C₂²×C₄×C₂₃	—	2	4	no	—
96	C₂²×C₄×C₂₃	—	2	16	no	—
97	C₂²×C₄×C₂₃	—	2	4	no	—
98	C₂²×C₄×C₂₃	—	2	4	no	—
99	C₂²×C₄×C₂₃	—	2	8	no	—
100	C₂²×C₄×C₂₃	—	2	4	no	—
101	C₂²×C₄×C₂₃	—	2	8	no	—
102	C₂²×C₄×C₂₃	—	2	8	no	—
103	C₂²×C₄×C₂₃	—	2	8	no	—
104	C₂²×C₄×C₂₃	—	4	16	no	—
105	C₂²×C₄×C₂₃	—	4	8	no	—
106	C₂²×C₄×C₂₃	—	4	8	no	—
107	C₂²×C₄×C₂₃	—	4	16	no	—
108	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₂₃	C₂×D₄	1	16	yes	—
111	C₂²×C₄×C₂₃	C₂×Q₈	1	16	yes	—
112	C₂²×C₄×C₂₃	#41	1	8	yes	—
113	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
114	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
115	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
116	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
117	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
118	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
119	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
120	C₄⋊C₄×C₂₃	—	2	16	no	—
121	C₄⋊C₄×C₂₃	—	2	16	no	—
122	C₄⋊C₄×C₂₃	—	2	8	no	—
123	C₄⋊C₄×C₂₃	—	2	16	no	—
124	C₄⋊C₄×C₂₃	—	2	32	no	—
125	C₄⋊C₄×C₂₃	—	4	16	no	—
126	C₂²⋊C₄×C₂₃	—	2	16	no	—
127	C₂²⋊C₄×C₂₃	C₂×Q₈	1	32	yes	complemented
128	C₄²×C₂₃	—	4	8	no	—
129	C₂×#2583	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₂₃	—	2	8	no	—
131	C₂³×C₂₃	—	2	8	no	—
132	C₂³×C₂₃	—	2	32	no	—
133	C₂³×C₂₃	—	2	4	no	—
134	C₂³×C₂₃	—	2	4	no	—
135	C₂³×C₂₃	C₄⋊Q₈	1	16	yes	—
136	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
137	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
138	C₂³×C₂₃	C₂²×Q₈	1	8	yes	—
139	C₂³×C₂₃	C₂²×Q₈	1	4	yes	—
140	C₂³×C₂₃	C₂×#41	1	4	yes	—
141	C₂³×C₂₃	H(5,𝔽₂)	1	4	yes	—
142	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
143	Q₈×C₂₃	—	4	16	no	—
144	C₂×C₄×C₂₃	—	2	32	no	—
145	C₂×C₄×C₂₃	—	2	16	no	—
146	C₂×C₄×C₂₃	—	2	8	no	—
147	C₂×C₄×C₂₃	—	2	8	no	—
148	C₂×C₄×C₂₃	—	2	32	no	—
149	C₂×C₄×C₂₃	—	2	4	no	—
150	C₂×C₄×C₂₃	—	2	8	no	—
151	C₂×C₄×C₂₃	—	2	4	no	—
152	C₂×C₄×C₂₃	—	2	8	no	—
153	C₂×C₄×C₂₃	—	2	4	no	—
154	C₂×C₄×C₂₃	—	2	4	no	—
155	C₂×C₄×C₂₃	—	2	4	no	—
156	C₂×C₄×C₂₃	—	2	4	no	—
157	C₂×C₄×C₂₃	—	2	4	no	—
158	C₂×C₄×C₂₃	—	2	8	no	—
159	C₂×C₄×C₂₃	—	2	8	no	—
160	C₂×C₄×C₂₃	—	2	8	no	—
161	C₂×C₄×C₂₃	—	4	16	no	—
162	C₂×C₄×C₂₃	—	4	16	no	—
163	C₂×C₄×C₂₃	—	4	8	no	—
164	C₂×C₄×C₂₃	—	4	8	no	—
165	C₂×C₄×C₂₃	—	4	8	no	—
166	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
167	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
168	C₂×C₄×C₂₃	C₂²×Q₈	1	16	yes	—
169	C₂×C₄×C₂₃	C₂×#41	1	8	yes	—
170	C₂²×C₂²⋊Q₈	C₂×C₂₃	1	1	yes	characteristic
171	C₂³×C₄⋊C₄	C₂×C₂₃	1	1	yes	characteristic
172	#2583	C₂×C₂₃	1	16	yes	direct product factor
173	C₂×#398	C₂×C₂₃	1	2	yes	complemented
174	C₂×#395	C₂×C₂₃	1	2	yes	complemented
175	C₂×#389	C₂×C₂₃	1	4	yes	complemented
176	C₂×#385	C₂×C₂₃	1	2	yes	—
177	C₂×#385	C₂×C₂₃	1	2	yes	—
178	C₂×C₄×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic
179	C₂²×C₂₃	—	2	32	no	—
180	C₂²×C₂₃	—	2	4	no	—
181	C₂²×C₂₃	—	2	4	no	—
182	C₂²×C₂₃	—	2	16	no	—
183	C₂²×C₂₃	#525	1	4	yes	—
184	C₂²×C₂₃	C₂×C₄⋊Q₈	1	8	yes	—
185	C₂²×C₂₃	C₂×C₄⋊Q₈	1	4	yes	—
186	C₂²×C₂₃	#534	1	4	yes	—
187	C₂²×C₂₃	#554	1	16	yes	—
188	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
189	C₂²×C₂₃	C₂³×Q₈	1	2	yes	—
190	C₂²×C₂₃	C₂²×#41	1	2	yes	—
191	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
192	C₄×C₂₃	—	2	8	no	—
193	C₄×C₂₃	—	2	4	no	—
194	C₄×C₂₃	—	2	4	no	—
195	C₄×C₂₃	—	2	16	no	—
196	C₄×C₂₃	—	4	4	no	—
197	C₄×C₂₃	—	4	4	no	—
198	C₄×C₂₃	—	4	4	no	—
199	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
200	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
201	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
202	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
203	C₂×C₂²⋊Q₈	—	2	8	no	—
204	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	8	yes	—
205	C₂²×C₄⋊C₄	—	2	8	no	—
206	C₂²×C₄⋊C₄	C₂²×C₂₃	1	8	yes	—
207	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
208	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
209	C₂²×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
210	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
211	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
212	C₂²×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
213	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
214	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
215	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
216	#398	C₂²×C₂₃	1	16	yes	complemented
217	#395	C₂²×C₂₃	1	16	yes	complemented
218	#389	C₂²×C₂₃	1	32	yes	complemented
219	#385	C₂²×C₂₃	1	16	yes	—
220	#385	C₂²×C₂₃	1	16	yes	—
221	C₄×C₂²⋊C₄	C₂²×C₂₃	1	8	yes	—
222	C₂×#95	C₂²×C₂₃	1	2	yes	—
223	C₂×#95	C₂²×C₂₃	1	4	yes	—
224	C₂×#95	C₂²×C₂₃	1	4	yes	—
225	C₂×C₂₃	—	2	8	no	—
226	C₂×C₂₃	#2583	1	8	yes	direct product factor
227	C₂×C₂₃	C₂×#525	1	1	yes	characteristic
228	C₂×C₂₃	C₂²×C₄⋊Q₈	1	1	yes	characteristic
229	C₂×C₂₃	C₂×#534	1	1	yes	characteristic
230	C₂×C₂₃	C₂×#554	1	4	yes	—
231	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
232	C₂²×Q₈	—	2	4	no	—
233	C₂²×Q₈	—	4	4	no	—
234	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
235	C₂³×C₄	—	2	4	no	—
236	C₂³×C₄	—	2	8	no	—
237	C₂³×C₄	—	2	4	no	—
238	C₂³×C₄	—	4	4	no	—
239	C₂³×C₄	—	4	4	no	—
240	C₂³×C₄	D₄×C₂₃	1	8	yes	—
241	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
242	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
243	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
244	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
245	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
246	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
247	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
248	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
249	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
250	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
251	C₂²⋊Q₈	—	2	32	no	—
252	C₂×C₄⋊C₄	—	2	8	no	—
253	C₂×C₄⋊C₄	—	2	8	no	—
254	C₂×C₄⋊C₄	—	2	32	no	—
255	C₂×C₄⋊C₄	—	2	4	no	—
256	C₂×C₄⋊C₄	—	2	8	no	—
257	C₂×C₄⋊C₄	—	2	16	no	—
258	C₂×C₄⋊C₄	—	4	8	no	—
259	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
260	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
261	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
262	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
263	C₂×C₄⋊C₄	C₂³×C₂₃	1	16	yes	—
264	C₂×C₄⋊C₄	C₂³×C₂₃	1	16	yes	—
265	C₂×C₂²⋊C₄	—	2	8	no	—
266	C₂×C₂²⋊C₄	Q₈×C₂₃	1	16	yes	complemented
267	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
268	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
269	C₂×C₄²	—	4	4	no	—
270	C₂×C₄²	C₂³×C₂₃	1	8	yes	—
271	#95	C₂³×C₂₃	1	8	yes	—
272	#95	C₂³×C₂₃	1	16	yes	—
273	#95	C₂³×C₂₃	1	16	yes	—
274	C₂₃	C₂×#2583	1	1	yes	characteristic, direct product factor, Sylow
275	C₂⁴	—	2	4	no	—
276	C₂⁴	—	2	4	no	—
277	C₂⁴	C₂×D₄×C₂₃	1	4	yes	—
278	C₂⁴	C₂×Q₈×C₂₃	1	8	yes	—
279	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
280	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
281	C₂×Q₈	—	2	8	no	—
282	C₂×Q₈	—	4	8	no	—
283	C₂×Q₈	—	4	16	no	—
284	C₂²×C₄	—	2	32	no	—
285	C₂²×C₄	—	2	8	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	8	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	8	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	16	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	8	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	8	no	—
298	C₂²×C₄	—	2	8	no	—
299	C₂²×C₄	—	2	8	no	—
300	C₂²×C₄	—	4	16	no	—
301	C₂²×C₄	—	4	8	no	—
302	C₂²×C₄	—	4	8	no	—
303	C₂²×C₄	—	4	16	no	—
304	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
305	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
306	C₂²×C₄	C₂×D₄×C₂₃	1	16	yes	—
307	C₂²×C₄	C₂×Q₈×C₂₃	1	16	yes	—
308	C₂²×C₄	#41×C₂₃	1	8	yes	—
309	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
310	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
311	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
312	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
313	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
314	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
315	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
316	C₄⋊C₄	—	2	16	no	—
317	C₄⋊C₄	—	2	16	no	—
318	C₄⋊C₄	—	2	8	no	—
319	C₄⋊C₄	—	2	16	no	—
320	C₄⋊C₄	—	2	32	no	—
321	C₄⋊C₄	—	4	16	no	—
322	C₂²⋊C₄	—	2	16	no	—
323	C₂²⋊C₄	C₂×Q₈×C₂₃	1	32	yes	complemented
324	C₄²	—	4	8	no	—
325	C₂³	—	2	32	no	—
326	C₂³	—	2	4	no	—
327	C₂³	—	2	4	no	—
328	C₂³	—	2	8	no	—
329	C₂³	—	2	8	no	—
330	C₂³	C₂₃×C₄⋊Q₈	1	16	yes	—
331	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
332	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
333	C₂³	C₂²×Q₈×C₂₃	1	8	yes	—
334	C₂³	C₂²×Q₈×C₂₃	1	4	yes	—
335	C₂³	C₂×#41×C₂₃	1	4	yes	—
336	C₂³	C₂₃×H(5,𝔽₂)	1	4	yes	—
337	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
338	Q₈	—	4	16	no	—
339	C₂×C₄	—	2	32	no	—
340	C₂×C₄	—	2	32	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	8	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	8	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	16	no	—
348	C₂×C₄	—	2	8	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	8	no	—
354	C₂×C₄	—	2	8	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	4	16	no	—
357	C₂×C₄	—	4	16	no	—
358	C₂×C₄	—	4	8	no	—
359	C₂×C₄	—	4	8	no	—
360	C₂×C₄	—	4	8	no	—
361	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
362	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
363	C₂×C₄	C₂²×Q₈×C₂₃	1	16	yes	—
364	C₂×C₄	C₂×#41×C₂₃	1	8	yes	—
365	C₂²	—	2	4	no	—
366	C₂²	—	2	4	no	—
367	C₂²	—	2	16	no	—
368	C₂²	—	2	32	no	—
369	C₂²	C₂₃×#525	1	4	yes	—
370	C₂²	C₂×C₂₃×C₄⋊Q₈	1	8	yes	—
371	C₂²	C₂×C₂₃×C₄⋊Q₈	1	4	yes	—
372	C₂²	C₂₃×#534	1	4	yes	—
373	C₂²	C₂₃×#554	1	16	yes	—
374	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
375	C₂²	C₂³×Q₈×C₂₃	1	2	yes	—
376	C₂²	C₂²×#41×C₂₃	1	2	yes	—
377	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
378	C₄	—	2	8	no	—
379	C₄	—	2	4	no	—
380	C₄	—	2	4	no	—
381	C₄	—	2	16	no	—
382	C₄	—	4	4	no	—
383	C₄	—	4	4	no	—
384	C₄	—	4	4	no	—
385	C₂	—	2	8	no	—
386	C₂	C₂₃×#2583	1	8	yes	direct product factor
387	C₂	C₂×C₂₃×#525	1	1	yes	characteristic
388	C₂	C₂²×C₂₃×C₄⋊Q₈	1	1	yes	characteristic
389	C₂	C₂×C₂₃×#534	1	1	yes	characteristic
390	C₂	C₂×C₂₃×#554	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂⁵×C₂₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂₃×#2583	C₂	direct (N × H)
4. C₂×C₂₃×#398	C₂	semidirect
5. C₂×C₂₃×#395	C₂	semidirect
6. C₂×C₂₃×#389	C₂	semidirect
27. C₂₃×#398	C₂²	semidirect
28. C₂₃×#395	C₂²	semidirect
29. C₂₃×#389	C₂²	semidirect
71. C₂×C₂²⋊C₄×C₂₃	Q₈	semidirect
127. C₂²⋊C₄×C₂₃	C₂×Q₈	semidirect
129. C₂×#2583	C₂₃	direct (N × H)
172. #2583	C₂×C₂₃	direct (N × H)
173. C₂×#398	C₂×C₂₃	semidirect
174. C₂×#395	C₂×C₂₃	semidirect
175. C₂×#389	C₂×C₂₃	semidirect
216. #398	C₂²×C₂₃	semidirect
217. #395	C₂²×C₂₃	semidirect
218. #389	C₂²×C₂₃	semidirect
226. C₂×C₂₃	#2583	direct (N × H)
266. C₂×C₂²⋊C₄	Q₈×C₂₃	semidirect
274. C₂₃	C₂×#2583	direct (N × H)
323. C₂²⋊C₄	C₂×Q₈×C₂₃	semidirect
386. C₂	C₂₃×#2583	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₂₃×C₂²⋊Q₈	2
C₂³×C₄⋊C₄×C₂₃	2
C₂₃×#2583	2
C₂×C₂₃×#398	2
C₂×C₂₃×#395	2
C₂×C₂₃×#389	2
C₂×C₂₃×#385	2
C₂×C₄×C₂²⋊C₄×C₂₃	2
C₂×#2583	23

Subgroups — C2×C23×#2583 #19182458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#2583 #19182458