Subgroups — C₂×C₂₃×#2314 #19181673

Order 5888.

2678 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×#117	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2314	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₂₃×#388	C₂	1	4	yes	maximal
4	C₂×C₂₃×#387	C₂	1	4	yes	maximal, complemented
5	C₂×C₂₃×#384	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#382	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#380	C₂	1	2	yes	maximal
8	C₂×C₄×C₄⋊C₄×C₂₃	C₂	1	2	yes	maximal, complemented
9	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
10	C₂×C₂₃×#117	C₄	1	16	yes	complemented
11	C₂×C₂₃×#117	C₂²	1	8	yes	—
12	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₂₃	C₂²	1	4	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×C₄²×C₂₃	C₂²	1	4	yes	—
19	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
21	C₂₃×#388	C₂²	1	32	yes	—
22	C₂₃×#387	C₂²	1	32	yes	complemented
23	C₂₃×#384	C₂²	1	8	yes	complemented
24	C₂₃×#382	C₂²	1	8	yes	complemented
25	C₂₃×#380	C₂²	1	16	yes	—
26	C₄×C₄⋊C₄×C₂₃	C₂²	1	16	yes	complemented
27	C₂×C₂₃×#95	C₂²	1	4	yes	—
28	C₂×C₂₃×#95	C₂²	1	4	yes	—
29	C₂×C₂₃×#95	C₂²	1	4	yes	—
30	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
31	C₂³×C₄×C₂₃	—	2	4	no	—
32	C₂³×C₄×C₂₃	—	2	4	no	—
33	C₂³×C₄×C₂₃	C₂×C₄	1	8	yes	—
34	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
35	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
36	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
37	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
39	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
40	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
41	C₂₃×#117	C₂×C₄	1	64	yes	complemented
42	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
43	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
44	C₂×C₄⋊C₄×C₂₃	—	4	8	no	—
45	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	16	yes	—
46	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
47	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
48	C₂×C₄⋊C₄×C₂₃	C₂³	1	16	yes	—
49	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
50	C₂×C₂²⋊C₄×C₂₃	—	4	8	no	—
51	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	16	yes	—
52	C₂×C₂²⋊C₄×C₂₃	C₂³	1	16	yes	—
53	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
54	C₂×C₄²×C₂₃	—	4	8	no	—
55	C₂×C₄²×C₂₃	C₂×C₄	1	8	yes	—
56	C₂×C₄²×C₂₃	C₂×C₄	1	8	yes	—
57	C₂×C₄²×C₂₃	C₂³	1	16	yes	—
58	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
59	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
60	C₂₃×#95	C₂³	1	16	yes	—
61	C₂₃×#95	C₂³	1	16	yes	—
62	C₂₃×#95	C₂³	1	16	yes	—
63	C₂⁴×C₂₃	—	2	2	no	—
64	C₂⁴×C₂₃	—	2	2	no	—
65	C₂⁴×C₂₃	—	2	4	no	—
66	C₂⁴×C₂₃	—	2	4	no	—
67	C₂⁴×C₂₃	C₂²×C₄	1	4	yes	—
68	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
69	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
70	C₂²×C₄×C₂₃	—	2	2	no	—
71	C₂²×C₄×C₂₃	—	2	2	no	—
72	C₂²×C₄×C₂₃	—	2	4	no	—
73	C₂²×C₄×C₂₃	—	2	4	no	—
74	C₂²×C₄×C₂₃	—	2	4	no	—
75	C₂²×C₄×C₂₃	—	2	4	no	—
76	C₂²×C₄×C₂₃	—	2	32	no	—
77	C₂²×C₄×C₂₃	—	2	8	no	—
78	C₂²×C₄×C₂₃	—	2	8	no	—
79	C₂²×C₄×C₂₃	—	2	8	no	—
80	C₂²×C₄×C₂₃	—	2	8	no	—
81	C₂²×C₄×C₂₃	—	2	8	no	—
82	C₂²×C₄×C₂₃	—	2	8	no	—
83	C₂²×C₄×C₂₃	—	2	8	no	—
84	C₂²×C₄×C₂₃	—	2	8	no	—
85	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
86	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
87	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₂₃	C₂²×C₄	1	16	yes	—
89	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₂₃	#41	1	4	yes	—
91	C₂²×C₄×C₂₃	#41	1	4	yes	—
92	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
93	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
94	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
95	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
96	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
97	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
98	C₄⋊C₄×C₂₃	—	2	16	no	—
99	C₄⋊C₄×C₂₃	—	2	16	no	—
100	C₄⋊C₄×C₂₃	—	4	16	no	—
101	C₄⋊C₄×C₂₃	C₂²×C₄	1	32	yes	—
102	C₂²⋊C₄×C₂₃	—	4	16	no	—
103	C₂²⋊C₄×C₂₃	C₂²×C₄	1	32	yes	—
104	C₄²×C₂₃	—	4	16	no	—
105	C₄²×C₂₃	C₂²×C₄	1	16	yes	—
106	C₄²×C₂₃	C₂²×C₄	1	16	yes	—
107	C₂×#2314	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂³×C₂₃	—	2	8	no	—
109	C₂³×C₂₃	—	2	16	no	—
110	C₂³×C₂₃	—	2	2	no	—
111	C₂³×C₂₃	—	2	2	no	—
112	C₂³×C₂₃	—	2	4	no	—
113	C₂³×C₂₃	—	2	4	no	—
114	C₂³×C₂₃	—	4	4	no	—
115	C₂³×C₂₃	—	4	4	no	—
116	C₂³×C₂₃	—	4	8	no	—
117	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
118	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
119	C₂³×C₂₃	C₂×#41	1	2	yes	—
120	C₂³×C₂₃	C₂×#41	1	2	yes	—
121	C₂³×C₂₃	H(5,𝔽₂)	1	4	yes	—
122	C₂³×C₂₃	2₋¹⁺⁴	1	4	yes	—
123	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
124	C₂×C₄×C₂₃	—	2	8	no	—
125	C₂×C₄×C₂₃	—	2	16	no	—
126	C₂×C₄×C₂₃	—	2	16	no	—
127	C₂×C₄×C₂₃	—	2	2	no	—
128	C₂×C₄×C₂₃	—	2	2	no	—
129	C₂×C₄×C₂₃	—	2	4	no	—
130	C₂×C₄×C₂₃	—	2	4	no	—
131	C₂×C₄×C₂₃	—	2	4	no	—
132	C₂×C₄×C₂₃	—	2	4	no	—
133	C₂×C₄×C₂₃	—	2	32	no	—
134	C₂×C₄×C₂₃	—	2	8	no	—
135	C₂×C₄×C₂₃	—	2	8	no	—
136	C₂×C₄×C₂₃	—	2	8	no	—
137	C₂×C₄×C₂₃	—	2	8	no	—
138	C₂×C₄×C₂₃	—	2	8	no	—
139	C₂×C₄×C₂₃	—	2	8	no	—
140	C₂×C₄×C₂₃	—	4	16	no	—
141	C₂×C₄×C₂₃	—	4	16	no	—
142	C₂×C₄×C₂₃	#117	1	16	yes	—
143	C₂×C₄×C₂₃	C₂³×C₄	1	8	yes	—
144	C₂×C₄×C₂₃	C₂³×C₄	1	8	yes	—
145	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
146	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
147	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
148	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
149	C₂²×#117	C₂×C₂₃	1	1	yes	characteristic
150	#2314	C₂×C₂₃	1	16	yes	direct product factor
151	C₂×#388	C₂×C₂₃	1	4	yes	—
152	C₂×#387	C₂×C₂₃	1	4	yes	complemented
153	C₂×#384	C₂×C₂₃	1	1	yes	characteristic, complemented
154	C₂×#382	C₂×C₂₃	1	1	yes	characteristic, complemented
155	C₂×#380	C₂×C₂₃	1	2	yes	—
156	C₂×C₄×C₄⋊C₄	C₂×C₂₃	1	2	yes	complemented
157	C₂²×C₂₃	—	2	4	no	—
158	C₂²×C₂₃	—	2	8	no	—
159	C₂²×C₂₃	—	4	16	no	—
160	C₂²×C₂₃	—	4	2	no	—
161	C₂²×C₂₃	—	4	2	no	—
162	C₂²×C₂₃	—	4	4	no	—
163	C₂²×C₂₃	C₂×#117	1	4	yes	—
164	C₂²×C₂₃	#520	1	8	yes	—
165	C₂²×C₂₃	#540	1	4	yes	—
166	C₂²×C₂₃	#541	1	4	yes	—
167	C₂²×C₂₃	#542	1	8	yes	—
168	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
169	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
170	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
171	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
172	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
173	C₄×C₂₃	—	2	4	no	—
174	C₄×C₂₃	—	2	8	no	—
175	C₄×C₂₃	—	2	8	no	—
176	C₄×C₂₃	—	4	8	no	—
177	C₄×C₂₃	—	4	8	no	—
178	C₄×C₂₃	C₂×#117	1	8	yes	—
179	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
180	C₂×#117	C₄×C₂₃	1	16	yes	complemented
181	C₂×#117	C₂²×C₂₃	1	8	yes	—
182	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
183	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
184	C₂²×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
185	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
186	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
187	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
188	C₂²×C₄²	C₂²×C₂₃	1	4	yes	—
189	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
190	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
191	#388	C₂²×C₂₃	1	32	yes	—
192	#387	C₂²×C₂₃	1	32	yes	complemented
193	#384	C₂²×C₂₃	1	8	yes	complemented
194	#382	C₂²×C₂₃	1	8	yes	complemented
195	#380	C₂²×C₂₃	1	16	yes	—
196	C₄×C₄⋊C₄	C₂²×C₂₃	1	16	yes	complemented
197	C₂×#95	C₂²×C₂₃	1	4	yes	—
198	C₂×#95	C₂²×C₂₃	1	4	yes	—
199	C₂×#95	C₂²×C₂₃	1	4	yes	—
200	C₂×C₂₃	—	4	4	no	—
201	C₂×C₂₃	#2314	1	8	yes	direct product factor
202	C₂×C₂₃	C₂²×#117	1	1	yes	characteristic
203	C₂×C₂₃	C₂×#520	1	2	yes	—
204	C₂×C₂₃	C₂×#540	1	1	yes	characteristic
205	C₂×C₂₃	C₂×#541	1	1	yes	characteristic
206	C₂×C₂₃	C₂×#542	1	2	yes	—
207	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
208	C₂³×C₄	—	2	4	no	—
209	C₂³×C₄	—	2	4	no	—
210	C₂³×C₄	C₂×C₄×C₂₃	1	8	yes	—
211	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
212	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
213	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
214	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
215	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
216	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
217	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
218	#117	C₂×C₄×C₂₃	1	64	yes	complemented
219	C₂×C₄⋊C₄	—	2	8	no	—
220	C₂×C₄⋊C₄	—	2	8	no	—
221	C₂×C₄⋊C₄	—	4	8	no	—
222	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	16	yes	—
223	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
224	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
225	C₂×C₄⋊C₄	C₂³×C₂₃	1	16	yes	—
226	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
227	C₂×C₂²⋊C₄	—	4	8	no	—
228	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	16	yes	—
229	C₂×C₂²⋊C₄	C₂³×C₂₃	1	16	yes	—
230	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
231	C₂×C₄²	—	4	8	no	—
232	C₂×C₄²	C₂×C₄×C₂₃	1	8	yes	—
233	C₂×C₄²	C₂×C₄×C₂₃	1	8	yes	—
234	C₂×C₄²	C₂³×C₂₃	1	16	yes	—
235	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
236	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
237	#95	C₂³×C₂₃	1	16	yes	—
238	#95	C₂³×C₂₃	1	16	yes	—
239	#95	C₂³×C₂₃	1	16	yes	—
240	C₂₃	C₂×#2314	1	1	yes	characteristic, direct product factor, Sylow
241	C₂⁴	—	2	2	no	—
242	C₂⁴	—	2	2	no	—
243	C₂⁴	—	2	4	no	—
244	C₂⁴	—	2	4	no	—
245	C₂⁴	C₂²×C₄×C₂₃	1	4	yes	—
246	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
247	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	32	no	—
255	C₂²×C₄	—	2	8	no	—
256	C₂²×C₄	—	2	8	no	—
257	C₂²×C₄	—	2	8	no	—
258	C₂²×C₄	—	2	8	no	—
259	C₂²×C₄	—	2	8	no	—
260	C₂²×C₄	—	2	8	no	—
261	C₂²×C₄	—	2	8	no	—
262	C₂²×C₄	—	2	8	no	—
263	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
264	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
265	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
266	C₂²×C₄	C₂²×C₄×C₂₃	1	16	yes	—
267	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
268	C₂²×C₄	#41×C₂₃	1	4	yes	—
269	C₂²×C₄	#41×C₂₃	1	4	yes	—
270	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
271	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
272	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
273	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
274	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
275	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
276	C₄⋊C₄	—	2	16	no	—
277	C₄⋊C₄	—	2	16	no	—
278	C₄⋊C₄	—	4	16	no	—
279	C₄⋊C₄	C₂²×C₄×C₂₃	1	32	yes	—
280	C₂²⋊C₄	—	4	16	no	—
281	C₂²⋊C₄	C₂²×C₄×C₂₃	1	32	yes	—
282	C₄²	—	4	16	no	—
283	C₄²	C₂²×C₄×C₂₃	1	16	yes	—
284	C₄²	C₂²×C₄×C₂₃	1	16	yes	—
285	C₂³	—	2	2	no	—
286	C₂³	—	2	2	no	—
287	C₂³	—	2	4	no	—
288	C₂³	—	2	4	no	—
289	C₂³	—	2	8	no	—
290	C₂³	—	2	16	no	—
291	C₂³	—	4	4	no	—
292	C₂³	—	4	4	no	—
293	C₂³	—	4	8	no	—
294	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
295	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
296	C₂³	C₂×#41×C₂₃	1	2	yes	—
297	C₂³	C₂×#41×C₂₃	1	2	yes	—
298	C₂³	C₂₃×H(5,𝔽₂)	1	4	yes	—
299	C₂³	C₂₃×2₋¹⁺⁴	1	4	yes	—
300	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	8	no	—
308	C₂×C₄	—	2	16	no	—
309	C₂×C₄	—	2	16	no	—
310	C₂×C₄	—	2	32	no	—
311	C₂×C₄	—	2	8	no	—
312	C₂×C₄	—	2	8	no	—
313	C₂×C₄	—	2	8	no	—
314	C₂×C₄	—	2	8	no	—
315	C₂×C₄	—	2	8	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	4	16	no	—
318	C₂×C₄	—	4	16	no	—
319	C₂×C₄	C₂₃×#117	1	16	yes	—
320	C₂×C₄	C₂³×C₄×C₂₃	1	8	yes	—
321	C₂×C₄	C₂³×C₄×C₂₃	1	8	yes	—
322	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
323	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
324	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
325	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
326	C₂²	—	2	4	no	—
327	C₂²	—	2	8	no	—
328	C₂²	—	4	2	no	—
329	C₂²	—	4	2	no	—
330	C₂²	—	4	4	no	—
331	C₂²	—	4	16	no	—
332	C₂²	C₂×C₂₃×#117	1	4	yes	—
333	C₂²	C₂₃×#520	1	8	yes	—
334	C₂²	C₂₃×#540	1	4	yes	—
335	C₂²	C₂₃×#541	1	4	yes	—
336	C₂²	C₂₃×#542	1	8	yes	—
337	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
338	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
339	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
340	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
341	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
342	C₄	—	2	4	no	—
343	C₄	—	2	8	no	—
344	C₄	—	2	8	no	—
345	C₄	—	4	8	no	—
346	C₄	—	4	8	no	—
347	C₄	C₂×C₂₃×#117	1	8	yes	—
348	C₂	—	4	4	no	—
349	C₂	C₂₃×#2314	1	8	yes	direct product factor
350	C₂	C₂²×C₂₃×#117	1	1	yes	characteristic
351	C₂	C₂×C₂₃×#520	1	2	yes	—
352	C₂	C₂×C₂₃×#540	1	1	yes	characteristic
353	C₂	C₂×C₂₃×#541	1	1	yes	characteristic
354	C₂	C₂×C₂₃×#542	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₂₃	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂⁵×C₂₃	C₂³
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×#2314	C₂	direct (N × H)
4. C₂×C₂₃×#387	C₂	semidirect
5. C₂×C₂₃×#384	C₂	semidirect
6. C₂×C₂₃×#382	C₂	semidirect
8. C₂×C₄×C₄⋊C₄×C₂₃	C₂	semidirect
10. C₂×C₂₃×#117	C₄	semidirect
22. C₂₃×#387	C₂²	semidirect
23. C₂₃×#384	C₂²	semidirect
24. C₂₃×#382	C₂²	semidirect
26. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
41. C₂₃×#117	C₂×C₄	semidirect
107. C₂×#2314	C₂₃	direct (N × H)
150. #2314	C₂×C₂₃	direct (N × H)
152. C₂×#387	C₂×C₂₃	semidirect
153. C₂×#384	C₂×C₂₃	semidirect
154. C₂×#382	C₂×C₂₃	semidirect
156. C₂×C₄×C₄⋊C₄	C₂×C₂₃	semidirect
180. C₂×#117	C₄×C₂₃	semidirect
192. #387	C₂²×C₂₃	semidirect
193. #384	C₂²×C₂₃	semidirect
194. #382	C₂²×C₂₃	semidirect
196. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
201. C₂×C₂₃	#2314	direct (N × H)
218. #117	C₂×C₄×C₂₃	semidirect
240. C₂₃	C₂×#2314	direct (N × H)
349. C₂	C₂₃×#2314	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×#117	2
C₂₃×#2314	2
C₂×C₂₃×#388	2
C₂×C₂₃×#387	2
C₂×C₂₃×#384	2
C₂×C₂₃×#382	2
C₂×C₂₃×#380	2
C₂×C₄×C₄⋊C₄×C₂₃	2
C₂×#2314	23

Subgroups — C2×C23×#2314 #19181673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#2314 #19181673