Subgroups — C₂×C₂₃×#2379 #19181969

Order 5888.

2934 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×#124	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2379	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₂₃×#391	C₂	1	2	yes	maximal, complemented
4	C₂×C₂₃×#388	C₂	1	4	yes	maximal, complemented
5	C₂×C₂₃×#386	C₂	1	2	yes	maximal
6	C₂×C₂₃×#385	C₂	1	4	yes	maximal, complemented
7	C₂×C₂₃×#382	C₂	1	2	yes	maximal, complemented
8	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
9	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₂₃	C₂²	1	2	yes	—
11	C₂×C₂₃×#124	C₄	1	16	yes	complemented
12	C₂×C₂₃×#124	C₂²	1	8	yes	—
13	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
17	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
19	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
20	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
21	C₂₃×#391	C₂²	1	16	yes	complemented
22	C₂₃×#388	C₂²	1	32	yes	complemented
23	C₂₃×#386	C₂²	1	16	yes	—
24	C₂₃×#385	C₂²	1	32	yes	complemented
25	C₂₃×#382	C₂²	1	16	yes	complemented
26	C₂×C₂₃×#95	C₂²	1	4	yes	—
27	C₂×C₂₃×#95	C₂²	1	4	yes	—
28	C₂×C₂₃×#95	C₂²	1	4	yes	—
29	C₂⁵×C₂₃	C₂³	1	2	yes	—
30	C₂²×Q₈×C₂₃	—	4	2	no	—
31	C₂²×Q₈×C₂₃	—	4	2	no	—
32	C₂²×Q₈×C₂₃	C₂×C₄	1	8	yes	complemented
33	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
34	C₂²×D₄×C₂₃	—	4	2	no	—
35	C₂²×D₄×C₂₃	—	4	2	no	—
36	C₂²×D₄×C₂₃	C₂×C₄	1	8	yes	—
37	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
38	C₂³×C₄×C₂₃	—	4	8	no	—
39	C₂³×C₄×C₂₃	—	4	4	no	—
40	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
41	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
42	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
44	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₂₃	C₂³	1	8	yes	—
46	C₂₃×#124	C₂×C₄	1	64	yes	complemented
47	C₂×C₄⋊C₄×C₂₃	—	4	4	no	—
48	C₂×C₄⋊C₄×C₂₃	—	4	4	no	—
49	C₂×C₄⋊C₄×C₂₃	—	4	4	no	—
50	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
51	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
52	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
53	C₂×C₂²⋊C₄×C₂₃	—	4	4	no	—
54	C₂×C₂²⋊C₄×C₂₃	—	4	8	no	—
55	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	32	yes	complemented
56	C₂×C₂²⋊C₄×C₂₃	C₂³	1	16	yes	—
57	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
58	C₂×C₂²⋊C₄×C₂₃	C₂³	1	16	yes	—
59	C₂×C₄²×C₂₃	—	4	4	no	—
60	C₂×C₄²×C₂₃	C₂×C₄	1	8	yes	complemented
61	C₂×C₄²×C₂₃	C₂³	1	8	yes	—
62	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
63	C₂₃×#95	C₂³	1	16	yes	—
64	C₂₃×#95	C₂³	1	16	yes	—
65	C₂₃×#95	C₂³	1	16	yes	—
66	C₂⁴×C₂₃	—	2	8	no	—
67	C₂⁴×C₂₃	—	2	4	no	—
68	C₂⁴×C₂₃	—	2	4	no	—
69	C₂⁴×C₂₃	—	2	8	no	—
70	C₂⁴×C₂₃	C₂²×C₄	1	8	yes	—
71	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
72	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
73	C₂×Q₈×C₂₃	—	4	16	no	—
74	C₂×Q₈×C₂₃	—	4	4	no	—
75	C₂×Q₈×C₂₃	—	4	4	no	—
76	C₂×Q₈×C₂₃	C₂²×C₄	1	16	yes	complemented
77	C₂×D₄×C₂₃	—	4	16	no	—
78	C₂×D₄×C₂₃	—	4	4	no	—
79	C₂×D₄×C₂₃	—	4	4	no	—
80	C₂×D₄×C₂₃	C₂²×C₄	1	16	yes	—
81	C₂²×C₄×C₂₃	—	2	4	no	—
82	C₂²×C₄×C₂₃	—	2	4	no	—
83	C₂²×C₄×C₂₃	—	2	4	no	—
84	C₂²×C₄×C₂₃	—	2	2	no	—
85	C₂²×C₄×C₂₃	—	2	2	no	—
86	C₂²×C₄×C₂₃	—	2	4	no	—
87	C₂²×C₄×C₂₃	—	2	8	no	—
88	C₂²×C₄×C₂₃	—	2	8	no	—
89	C₂²×C₄×C₂₃	—	2	8	no	—
90	C₂²×C₄×C₂₃	—	2	8	no	—
91	C₂²×C₄×C₂₃	—	2	8	no	—
92	C₂²×C₄×C₂₃	—	2	8	no	—
93	C₂²×C₄×C₂₃	—	4	16	no	—
94	C₂²×C₄×C₂₃	—	4	8	no	—
95	C₂²×C₄×C₂₃	—	4	32	no	—
96	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
97	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
99	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
100	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
101	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
102	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
103	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
104	C₄⋊C₄×C₂₃	—	4	8	no	—
105	C₄⋊C₄×C₂₃	—	4	8	no	—
106	C₄⋊C₄×C₂₃	—	4	8	no	—
107	C₂²⋊C₄×C₂₃	—	4	8	no	—
108	C₂²⋊C₄×C₂₃	—	4	16	no	—
109	C₂²⋊C₄×C₂₃	C₂²×C₄	1	64	yes	complemented
110	C₄²×C₂₃	—	4	8	no	—
111	C₄²×C₂₃	C₂²×C₄	1	16	yes	complemented
112	C₂×#2379	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂³×C₂₃	—	2	16	no	—
114	C₂³×C₂₃	—	2	32	no	—
115	C₂³×C₂₃	—	2	8	no	—
116	C₂³×C₂₃	—	2	4	no	—
117	C₂³×C₂₃	—	2	4	no	—
118	C₂³×C₂₃	—	2	8	no	—
119	C₂³×C₂₃	—	4	8	no	—
120	C₂³×C₂₃	—	4	16	no	—
121	C₂³×C₂₃	—	4	8	no	—
122	C₂³×C₂₃	C₂³×C₄	1	8	yes	—
123	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
124	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
125	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
126	C₂³×C₂₃	H(5,𝔽₂)	1	4	yes	—
127	C₂³×C₂₃	2₋¹⁺⁴	1	4	yes	—
128	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
129	Q₈×C₂₃	—	4	16	no	—
130	D₄×C₂₃	—	4	16	no	—
131	C₂×C₄×C₂₃	—	2	8	no	—
132	C₂×C₄×C₂₃	—	2	16	no	—
133	C₂×C₄×C₂₃	—	2	16	no	—
134	C₂×C₄×C₂₃	—	2	4	no	—
135	C₂×C₄×C₂₃	—	2	4	no	—
136	C₂×C₄×C₂₃	—	2	4	no	—
137	C₂×C₄×C₂₃	—	2	2	no	—
138	C₂×C₄×C₂₃	—	2	2	no	—
139	C₂×C₄×C₂₃	—	2	4	no	—
140	C₂×C₄×C₂₃	—	2	8	no	—
141	C₂×C₄×C₂₃	—	2	8	no	—
142	C₂×C₄×C₂₃	—	2	8	no	—
143	C₂×C₄×C₂₃	—	2	8	no	—
144	C₂×C₄×C₂₃	—	2	8	no	—
145	C₂×C₄×C₂₃	—	2	8	no	—
146	C₂×C₄×C₂₃	—	4	32	no	—
147	C₂×C₄×C₂₃	—	4	16	no	—
148	C₂×C₄×C₂₃	—	4	16	no	—
149	C₂×C₄×C₂₃	C₂³×C₄	1	8	yes	—
150	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
151	C₂×C₄×C₂₃	C₂³×C₄	1	8	yes	—
152	C₂²×#124	C₂×C₂₃	1	1	yes	characteristic
153	#2379	C₂×C₂₃	1	16	yes	direct product factor
154	C₂×#391	C₂×C₂₃	1	2	yes	complemented
155	C₂×#388	C₂×C₂₃	1	4	yes	complemented
156	C₂×#386	C₂×C₂₃	1	2	yes	—
157	C₂×#385	C₂×C₂₃	1	4	yes	complemented
158	C₂×#382	C₂×C₂₃	1	2	yes	complemented
159	C₂²×C₂₃	—	2	8	no	—
160	C₂²×C₂₃	—	2	16	no	—
161	C₂²×C₂₃	—	4	32	no	—
162	C₂²×C₂₃	—	4	4	no	—
163	C₂²×C₂₃	—	4	8	no	—
164	C₂²×C₂₃	—	4	4	no	—
165	C₂²×C₂₃	#518	1	4	yes	—
166	C₂²×C₂₃	#520	1	8	yes	—
167	C₂²×C₂₃	H(3,𝔽₄)	1	4	yes	—
168	C₂²×C₂₃	#562	1	8	yes	—
169	C₂²×C₂₃	#563	1	4	yes	—
170	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
171	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
172	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
173	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
174	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
175	C₄×C₂₃	—	2	4	no	—
176	C₄×C₂₃	—	2	8	no	—
177	C₄×C₂₃	—	2	8	no	—
178	C₄×C₂₃	—	4	8	no	—
179	C₄×C₂₃	—	4	8	no	—
180	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
181	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
182	C₂⁴×C₄	C₂²×C₂₃	1	2	yes	—
183	C₂×#124	C₄×C₂₃	1	16	yes	complemented
184	C₂×#124	C₂²×C₂₃	1	8	yes	—
185	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
186	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
187	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
188	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
189	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
190	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
191	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
192	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
193	#391	C₂²×C₂₃	1	16	yes	complemented
194	#388	C₂²×C₂₃	1	32	yes	complemented
195	#386	C₂²×C₂₃	1	16	yes	—
196	#385	C₂²×C₂₃	1	32	yes	complemented
197	#382	C₂²×C₂₃	1	16	yes	complemented
198	C₂×#95	C₂²×C₂₃	1	4	yes	—
199	C₂×#95	C₂²×C₂₃	1	4	yes	—
200	C₂×#95	C₂²×C₂₃	1	4	yes	—
201	C₂×C₂₃	—	4	8	no	—
202	C₂×C₂₃	#2379	1	8	yes	direct product factor
203	C₂×C₂₃	C₂×#518	1	1	yes	characteristic
204	C₂×C₂₃	C₂×#520	1	2	yes	—
205	C₂×C₂₃	C₂×H(3,𝔽₄)	1	1	yes	characteristic
206	C₂×C₂₃	C₂×#562	1	2	yes	—
207	C₂×C₂₃	C₂×#563	1	1	yes	characteristic
208	C₂⁵	C₂³×C₂₃	1	2	yes	—
209	C₂²×Q₈	—	4	2	no	—
210	C₂²×Q₈	—	4	2	no	—
211	C₂²×Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
212	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
213	C₂²×D₄	—	4	2	no	—
214	C₂²×D₄	—	4	2	no	—
215	C₂²×D₄	C₂×C₄×C₂₃	1	8	yes	—
216	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
217	C₂³×C₄	—	4	8	no	—
218	C₂³×C₄	—	4	4	no	—
219	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
220	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
221	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
222	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
223	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
224	C₂³×C₄	C₂³×C₂₃	1	8	yes	—
225	#124	C₂×C₄×C₂₃	1	64	yes	complemented
226	C₂×C₄⋊C₄	—	4	4	no	—
227	C₂×C₄⋊C₄	—	4	4	no	—
228	C₂×C₄⋊C₄	—	4	4	no	—
229	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
230	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
231	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
232	C₂×C₂²⋊C₄	—	4	4	no	—
233	C₂×C₂²⋊C₄	—	4	8	no	—
234	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	32	yes	complemented
235	C₂×C₂²⋊C₄	C₂³×C₂₃	1	16	yes	—
236	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
237	C₂×C₂²⋊C₄	C₂³×C₂₃	1	16	yes	—
238	C₂×C₄²	—	4	4	no	—
239	C₂×C₄²	C₂×C₄×C₂₃	1	8	yes	complemented
240	C₂×C₄²	C₂³×C₂₃	1	8	yes	—
241	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
242	#95	C₂³×C₂₃	1	16	yes	—
243	#95	C₂³×C₂₃	1	16	yes	—
244	#95	C₂³×C₂₃	1	16	yes	—
245	C₂₃	C₂×#2379	1	1	yes	characteristic, direct product factor, Sylow
246	C₂⁴	—	2	8	no	—
247	C₂⁴	—	2	4	no	—
248	C₂⁴	—	2	4	no	—
249	C₂⁴	—	2	8	no	—
250	C₂⁴	C₂²×C₄×C₂₃	1	8	yes	—
251	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
252	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
253	C₂×Q₈	—	4	16	no	—
254	C₂×Q₈	—	4	4	no	—
255	C₂×Q₈	—	4	4	no	—
256	C₂×Q₈	C₂²×C₄×C₂₃	1	16	yes	complemented
257	C₂×D₄	—	4	16	no	—
258	C₂×D₄	—	4	4	no	—
259	C₂×D₄	—	4	4	no	—
260	C₂×D₄	C₂²×C₄×C₂₃	1	16	yes	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	8	no	—
268	C₂²×C₄	—	2	8	no	—
269	C₂²×C₄	—	2	8	no	—
270	C₂²×C₄	—	2	8	no	—
271	C₂²×C₄	—	2	8	no	—
272	C₂²×C₄	—	2	8	no	—
273	C₂²×C₄	—	4	16	no	—
274	C₂²×C₄	—	4	8	no	—
275	C₂²×C₄	—	4	32	no	—
276	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
277	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
278	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
279	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
280	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
281	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
282	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
283	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
284	C₄⋊C₄	—	4	8	no	—
285	C₄⋊C₄	—	4	8	no	—
286	C₄⋊C₄	—	4	8	no	—
287	C₂²⋊C₄	—	4	8	no	—
288	C₂²⋊C₄	—	4	16	no	—
289	C₂²⋊C₄	C₂²×C₄×C₂₃	1	64	yes	complemented
290	C₄²	—	4	8	no	—
291	C₄²	C₂²×C₄×C₂₃	1	16	yes	complemented
292	C₂³	—	2	8	no	—
293	C₂³	—	2	4	no	—
294	C₂³	—	2	4	no	—
295	C₂³	—	2	8	no	—
296	C₂³	—	2	16	no	—
297	C₂³	—	2	32	no	—
298	C₂³	—	4	8	no	—
299	C₂³	—	4	16	no	—
300	C₂³	—	4	8	no	—
301	C₂³	C₂³×C₄×C₂₃	1	8	yes	—
302	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
303	C₂³	C₂₃×H(5,𝔽₂)	1	4	yes	—
304	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
305	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
306	C₂³	C₂₃×2₋¹⁺⁴	1	4	yes	—
307	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
308	Q₈	—	4	16	no	—
309	D₄	—	4	16	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	2	16	no	—
318	C₂×C₄	—	2	16	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	2	8	no	—
321	C₂×C₄	—	2	8	no	—
322	C₂×C₄	—	2	8	no	—
323	C₂×C₄	—	2	8	no	—
324	C₂×C₄	—	2	8	no	—
325	C₂×C₄	—	4	32	no	—
326	C₂×C₄	—	4	16	no	—
327	C₂×C₄	—	4	16	no	—
328	C₂×C₄	C₂³×C₄×C₂₃	1	8	yes	—
329	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
330	C₂×C₄	C₂³×C₄×C₂₃	1	8	yes	—
331	C₂²	—	2	8	no	—
332	C₂²	—	2	16	no	—
333	C₂²	—	4	4	no	—
334	C₂²	—	4	8	no	—
335	C₂²	—	4	4	no	—
336	C₂²	—	4	32	no	—
337	C₂²	C₂₃×#518	1	4	yes	—
338	C₂²	C₂₃×#520	1	8	yes	—
339	C₂²	C₂₃×H(3,𝔽₄)	1	4	yes	—
340	C₂²	C₂₃×#562	1	8	yes	—
341	C₂²	C₂₃×#563	1	4	yes	—
342	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
343	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
344	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
345	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
346	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
347	C₄	—	2	4	no	—
348	C₄	—	2	8	no	—
349	C₄	—	2	8	no	—
350	C₄	—	4	8	no	—
351	C₄	—	4	8	no	—
352	C₂	—	4	8	no	—
353	C₂	C₂₃×#2379	1	8	yes	direct product factor
354	C₂	C₂×C₂₃×#518	1	1	yes	characteristic
355	C₂	C₂×C₂₃×#520	1	2	yes	—
356	C₂	C₂×C₂₃×H(3,𝔽₄)	1	1	yes	characteristic
357	C₂	C₂×C₂₃×#562	1	2	yes	—
358	C₂	C₂×C₂₃×#563	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2379	C₂	direct (N × H)
3. C₂×C₂₃×#391	C₂	semidirect
4. C₂×C₂₃×#388	C₂	semidirect
6. C₂×C₂₃×#385	C₂	semidirect
7. C₂×C₂₃×#382	C₂	semidirect
11. C₂×C₂₃×#124	C₄	semidirect
21. C₂₃×#391	C₂²	semidirect
22. C₂₃×#388	C₂²	semidirect
24. C₂₃×#385	C₂²	semidirect
25. C₂₃×#382	C₂²	semidirect
32. C₂²×Q₈×C₂₃	C₂×C₄	semidirect
46. C₂₃×#124	C₂×C₄	semidirect
55. C₂×C₂²⋊C₄×C₂₃	C₂×C₄	semidirect
60. C₂×C₄²×C₂₃	C₂×C₄	semidirect
76. C₂×Q₈×C₂₃	C₂²×C₄	semidirect
109. C₂²⋊C₄×C₂₃	C₂²×C₄	semidirect
111. C₄²×C₂₃	C₂²×C₄	semidirect
112. C₂×#2379	C₂₃	direct (N × H)
153. #2379	C₂×C₂₃	direct (N × H)
154. C₂×#391	C₂×C₂₃	semidirect
155. C₂×#388	C₂×C₂₃	semidirect
157. C₂×#385	C₂×C₂₃	semidirect
158. C₂×#382	C₂×C₂₃	semidirect
183. C₂×#124	C₄×C₂₃	semidirect
193. #391	C₂²×C₂₃	semidirect
194. #388	C₂²×C₂₃	semidirect
196. #385	C₂²×C₂₃	semidirect
197. #382	C₂²×C₂₃	semidirect
202. C₂×C₂₃	#2379	direct (N × H)
211. C₂²×Q₈	C₂×C₄×C₂₃	semidirect
225. #124	C₂×C₄×C₂₃	semidirect
234. C₂×C₂²⋊C₄	C₂×C₄×C₂₃	semidirect
239. C₂×C₄²	C₂×C₄×C₂₃	semidirect
245. C₂₃	C₂×#2379	direct (N × H)
256. C₂×Q₈	C₂²×C₄×C₂₃	semidirect
289. C₂²⋊C₄	C₂²×C₄×C₂₃	semidirect
291. C₄²	C₂²×C₄×C₂₃	semidirect
353. C₂	C₂₃×#2379	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×#124	2
C₂₃×#2379	2
C₂×C₂₃×#391	2
C₂×C₂₃×#388	2
C₂×C₂₃×#386	2
C₂×C₂₃×#385	2
C₂×C₂₃×#382	2
C₂×#2379	23

Subgroups — C2×C23×#2379 #19181969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#2379 #19181969