Subgroups — C₂×C₂₃×#1717 #19167235

Order 5888.

966 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#493	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1717	C₂	1	8	yes	maximal, direct product factor
8	C₂×C₂₃×#322	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×SD₁₆×C₂₃	—	2	2	no	—
10	C₂²×D₈×C₂₃	—	2	2	no	—
11	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
14	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
15	C₂₃×#493	—	2	2	no	—
16	C₂₃×#493	C₂²	1	4	yes	—
17	C₂₃×#492	—	2	2	no	—
18	C₂₃×#492	C₂²	1	4	yes	complemented
19	C₂₃×#487	—	2	2	no	—
20	C₂₃×#487	C₂²	1	4	yes	complemented
21	C₂₃×#486	—	2	2	no	—
22	C₂₃×#486	—	2	2	no	—
23	C₂₃×#486	—	2	2	no	—
24	C₂₃×#486	C₂²	1	4	yes	complemented
25	C₂₃×#486	C₂²	1	4	yes	complemented
26	C₂₃×#486	C₂²	1	4	yes	complemented
27	C₂×C₂₃×#103	—	2	2	no	—
28	C₂×C₂₃×#102	—	2	2	no	—
29	C₂×C₂₃×#102	—	2	2	no	—
30	C₂×C₂₃×#102	—	2	2	no	—
31	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
34	C₂₃×#322	C₂²	1	4	yes	complemented
35	C₂²×Q₈×C₂₃	—	2	1	no	—
36	C₂²×Q₈×C₂₃	—	2	1	no	—
37	C₂²×D₄×C₂₃	—	2	1	no	—
38	C₂²×D₄×C₂₃	—	2	1	no	—
39	C₂²×D₄×C₂₃	—	2	1	no	—
40	C₂²×D₄×C₂₃	—	2	1	no	—
41	C₂²×D₄×C₂₃	—	2	1	no	—
42	C₂²×D₄×C₂₃	—	2	1	no	—
43	C₂×SD₁₆×C₂₃	—	2	8	no	—
44	C₂×SD₁₆×C₂₃	—	4	8	no	—
45	C₂×D₈×C₂₃	—	2	8	no	—
46	C₂×D₈×C₂₃	—	4	8	no	—
47	C₂²×C₈×C₂₃	D₄	1	2	yes	—
48	C₂²×C₈×C₂₃	D₄	1	2	yes	—
49	C₂²×C₈×C₂₃	D₄	1	2	yes	—
50	C₂₃×C₄⋊Q₈	—	2	1	no	—
51	C₂₃×C₄⋊Q₈	—	2	1	no	—
52	C₂₃×C₄⋊Q₈	—	2	1	no	—
53	C₂₃×C₄⋊Q₈	—	2	1	no	—
54	C₂₃×C₄⋊Q₈	—	2	1	no	—
55	C₂₃×C₄⋊Q₈	—	2	1	no	—
56	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
57	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₂₃×#127	—	2	1	no	—
59	C₂₃×#127	—	2	1	no	—
60	C₂₃×#127	—	2	1	no	—
61	C₂₃×#127	—	2	1	no	—
62	C₂₃×#127	—	2	1	no	—
63	C₂₃×#127	—	2	1	no	—
64	C₂₃×#127	C₂³	1	2	yes	—
65	C₂₃×#127	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
68	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
69	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
70	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
71	C₂₃×#103	—	2	8	no	—
72	C₂₃×#102	—	2	8	no	—
73	C₂₃×#102	—	2	8	no	—
74	C₂₃×#102	—	2	8	no	—
75	C₄×C₈×C₂₃	D₄	1	2	yes	—
76	C₄×C₈×C₂₃	D₄	1	2	yes	—
77	C₄×C₈×C₂₃	D₄	1	2	yes	—
78	C₄×C₈×C₂₃	C₂³	1	2	yes	—
79	C₄×C₈×C₂₃	C₂³	1	2	yes	—
80	C₄×C₈×C₂₃	C₂³	1	2	yes	—
81	C₂⁴×C₂₃	—	4	1	no	—
82	C₂⁴×C₂₃	—	4	1	no	—
83	C₂×Q₈×C₂₃	—	2	2	no	—
84	C₂×Q₈×C₂₃	—	2	2	no	—
85	C₂×Q₈×C₂₃	—	4	1	no	—
86	C₂×Q₈×C₂₃	—	4	1	no	—
87	C₂×Q₈×C₂₃	—	4	4	no	—
88	C₂×Q₈×C₂₃	—	4	4	no	—
89	C₂×D₄×C₂₃	—	2	2	no	—
90	C₂×D₄×C₂₃	—	2	2	no	—
91	C₂×D₄×C₂₃	—	2	2	no	—
92	C₂×D₄×C₂₃	—	2	2	no	—
93	C₂×D₄×C₂₃	—	2	2	no	—
94	C₂×D₄×C₂₃	—	2	2	no	—
95	C₂×D₄×C₂₃	—	4	1	no	—
96	C₂×D₄×C₂₃	—	4	1	no	—
97	C₂×D₄×C₂₃	—	4	1	no	—
98	C₂×D₄×C₂₃	—	4	1	no	—
99	C₂×D₄×C₂₃	—	4	1	no	—
100	C₂×D₄×C₂₃	—	4	1	no	—
101	C₂×D₄×C₂₃	—	4	4	no	—
102	C₂×D₄×C₂₃	—	4	4	no	—
103	C₂×D₄×C₂₃	—	4	4	no	—
104	C₂×D₄×C₂₃	—	4	4	no	—
105	C₂×D₄×C₂₃	—	4	4	no	—
106	C₂×D₄×C₂₃	—	4	4	no	—
107	C₂²×C₄×C₂₃	—	4	1	no	—
108	C₂²×C₄×C₂₃	—	4	1	no	—
109	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
112	SD₁₆×C₂₃	—	4	16	no	—
113	D₈×C₂₃	—	4	16	no	—
114	C₂×C₈×C₂₃	—	2	4	no	—
115	C₂×C₈×C₂₃	—	2	4	no	—
116	C₂×C₈×C₂₃	—	2	4	no	—
117	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	—
118	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	—
119	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	—
120	C₄⋊C₄×C₂₃	—	2	2	no	—
121	C₄⋊C₄×C₂₃	—	2	2	no	—
122	C₄⋊C₄×C₂₃	—	2	2	no	—
123	C₄⋊C₄×C₂₃	—	2	2	no	—
124	C₄⋊C₄×C₂₃	—	4	1	no	—
125	C₄⋊C₄×C₂₃	—	4	1	no	—
126	C₄⋊C₄×C₂₃	—	4	1	no	—
127	C₄⋊C₄×C₂₃	—	4	1	no	—
128	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
132	C₂×#1717	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂³×C₂₃	—	4	2	no	—
134	C₂³×C₂₃	—	4	2	no	—
135	C₂³×C₂₃	—	8	2	no	—
136	C₂³×C₂₃	—	8	2	no	—
137	C₂³×C₂₃	—	8	2	no	—
138	C₂³×C₂₃	—	8	2	no	—
139	C₂³×C₂₃	—	8	2	no	—
140	C₂³×C₂₃	—	8	2	no	—
141	C₂³×C₂₃	#127	1	1	yes	characteristic
142	Q₈×C₂₃	—	4	4	no	—
143	Q₈×C₂₃	—	4	4	no	—
144	Q₈×C₂₃	—	8	2	no	—
145	Q₈×C₂₃	—	8	2	no	—
146	D₄×C₂₃	—	4	4	no	—
147	D₄×C₂₃	—	4	4	no	—
148	D₄×C₂₃	—	4	4	no	—
149	D₄×C₂₃	—	4	4	no	—
150	D₄×C₂₃	—	4	4	no	—
151	D₄×C₂₃	—	4	4	no	—
152	D₄×C₂₃	—	8	2	no	—
153	D₄×C₂₃	—	8	2	no	—
154	D₄×C₂₃	—	8	2	no	—
155	D₄×C₂₃	—	8	2	no	—
156	D₄×C₂₃	—	8	2	no	—
157	D₄×C₂₃	—	8	2	no	—
158	C₂×C₄×C₂₃	—	4	2	no	—
159	C₂×C₄×C₂₃	—	4	2	no	—
160	C₂×C₄×C₂₃	—	8	2	no	—
161	C₂×C₄×C₂₃	—	8	2	no	—
162	C₂×C₄×C₂₃	#127	1	1	yes	characteristic
163	C₂×C₄×C₂₃	#127	1	1	yes	characteristic
164	C₂×C₄×C₂₃	#127	1	1	yes	characteristic
165	C₂×C₄×C₂₃	#135	1	4	yes	—
166	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	4	yes	—
167	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	4	yes	—
168	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
171	C₈×C₂₃	—	2	4	no	—
172	C₈×C₂₃	—	2	4	no	—
173	C₈×C₂₃	—	2	4	no	—
174	C₂×#493	C₂×C₂₃	1	1	yes	characteristic
175	C₂×#492	C₂×C₂₃	1	1	yes	characteristic, complemented
176	C₂×#487	C₂×C₂₃	1	1	yes	characteristic, complemented
177	C₂×#486	C₂×C₂₃	1	1	yes	characteristic, complemented
178	C₂×#486	C₂×C₂₃	1	1	yes	characteristic, complemented
179	C₂×#486	C₂×C₂₃	1	1	yes	characteristic, complemented
180	#1717	C₂×C₂₃	1	8	yes	direct product factor
181	C₂×#322	C₂×C₂₃	1	1	yes	characteristic, complemented
182	C₂²×C₂₃	—	8	2	no	—
183	C₂²×C₂₃	—	8	2	no	—
184	C₂²×C₂₃	—	8	2	no	—
185	C₂²×C₂₃	—	8	2	no	—
186	C₂²×C₂₃	—	8	2	no	—
187	C₂²×C₂₃	—	8	2	no	—
188	C₂²×C₂₃	—	16	4	no	—
189	C₂²×C₂₃	—	16	4	no	—
190	C₂²×C₂₃	#495	1	2	yes	—
191	C₂²×C₂₃	#496	1	2	yes	—
192	C₂²×C₂₃	#496	1	2	yes	—
193	C₂²×C₂₃	C₂×#127	1	1	yes	characteristic
194	C₄×C₂₃	—	8	2	no	—
195	C₄×C₂₃	—	8	2	no	—
196	C₄×C₂₃	#495	1	2	yes	—
197	C₄×C₂₃	#496	1	2	yes	—
198	C₄×C₂₃	#496	1	2	yes	—
199	C₄×C₂₃	C₂×#135	1	2	yes	—
200	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
201	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
202	C₂²×SD₁₆	—	2	2	no	—
203	C₂²×D₈	—	2	2	no	—
204	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
205	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
206	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
207	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
208	#493	—	2	2	no	—
209	#493	C₂²×C₂₃	1	4	yes	—
210	#492	—	2	2	no	—
211	#492	C₂²×C₂₃	1	4	yes	complemented
212	#487	—	2	2	no	—
213	#487	C₂²×C₂₃	1	4	yes	complemented
214	#486	—	2	2	no	—
215	#486	—	2	2	no	—
216	#486	—	2	2	no	—
217	#486	C₂²×C₂₃	1	4	yes	complemented
218	#486	C₂²×C₂₃	1	4	yes	complemented
219	#486	C₂²×C₂₃	1	4	yes	complemented
220	C₂×#103	—	2	2	no	—
221	C₂×#102	—	2	2	no	—
222	C₂×#102	—	2	2	no	—
223	C₂×#102	—	2	2	no	—
224	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
225	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
226	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
227	#322	C₂²×C₂₃	1	4	yes	complemented
228	C₂×C₂₃	—	16	2	no	—
229	C₂×C₂₃	—	16	2	no	—
230	C₂×C₂₃	#1717	1	4	yes	direct product factor
231	C₂×C₂₃	C₂×#495	1	1	yes	characteristic
232	C₂×C₂₃	C₂×#496	1	1	yes	characteristic
233	C₂×C₂₃	C₂×#496	1	1	yes	characteristic
234	C₂²×Q₈	—	2	1	no	—
235	C₂²×Q₈	—	2	1	no	—
236	C₂²×D₄	—	2	1	no	—
237	C₂²×D₄	—	2	1	no	—
238	C₂²×D₄	—	2	1	no	—
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂²×D₄	—	2	1	no	—
242	C₂×SD₁₆	—	2	8	no	—
243	C₂×SD₁₆	—	4	8	no	—
244	C₂×D₈	—	2	8	no	—
245	C₂×D₈	—	4	8	no	—
246	C₂²×C₈	D₄×C₂₃	1	2	yes	—
247	C₂²×C₈	D₄×C₂₃	1	2	yes	—
248	C₂²×C₈	D₄×C₂₃	1	2	yes	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	—	2	1	no	—
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	—	2	1	no	—
255	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
256	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
257	#127	—	2	1	no	—
258	#127	—	2	1	no	—
259	#127	—	2	1	no	—
260	#127	—	2	1	no	—
261	#127	—	2	1	no	—
262	#127	—	2	1	no	—
263	#127	C₂³×C₂₃	1	2	yes	—
264	#127	C₂³×C₂₃	1	2	yes	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
270	#103	—	2	8	no	—
271	#102	—	2	8	no	—
272	#102	—	2	8	no	—
273	#102	—	2	8	no	—
274	C₄×C₈	D₄×C₂₃	1	2	yes	—
275	C₄×C₈	D₄×C₂₃	1	2	yes	—
276	C₄×C₈	D₄×C₂₃	1	2	yes	—
277	C₄×C₈	C₂³×C₂₃	1	2	yes	—
278	C₄×C₈	C₂³×C₂₃	1	2	yes	—
279	C₄×C₈	C₂³×C₂₃	1	2	yes	—
280	C₂₃	C₂×#1717	1	1	yes	characteristic, direct product factor, Sylow
281	C₂⁴	—	4	1	no	—
282	C₂⁴	—	4	1	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	4	1	no	—
286	C₂×Q₈	—	4	1	no	—
287	C₂×Q₈	—	4	4	no	—
288	C₂×Q₈	—	4	4	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	—	4	4	no	—
302	C₂×D₄	—	4	4	no	—
303	C₂×D₄	—	4	4	no	—
304	C₂×D₄	—	4	4	no	—
305	C₂×D₄	—	4	4	no	—
306	C₂×D₄	—	4	4	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	—	4	1	no	—
309	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
312	SD₁₆	—	4	16	no	—
313	D₈	—	4	16	no	—
314	C₂×C₈	—	2	4	no	—
315	C₂×C₈	—	2	4	no	—
316	C₂×C₈	—	2	4	no	—
317	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	—
318	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	—
319	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
329	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
330	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
331	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	8	2	no	—
335	C₂³	—	8	2	no	—
336	C₂³	—	8	2	no	—
337	C₂³	—	8	2	no	—
338	C₂³	—	8	2	no	—
339	C₂³	—	8	2	no	—
340	C₂³	C₂₃×#127	1	1	yes	characteristic
341	Q₈	—	4	4	no	—
342	Q₈	—	4	4	no	—
343	Q₈	—	8	2	no	—
344	Q₈	—	8	2	no	—
345	D₄	—	4	4	no	—
346	D₄	—	4	4	no	—
347	D₄	—	4	4	no	—
348	D₄	—	4	4	no	—
349	D₄	—	4	4	no	—
350	D₄	—	4	4	no	—
351	D₄	—	8	2	no	—
352	D₄	—	8	2	no	—
353	D₄	—	8	2	no	—
354	D₄	—	8	2	no	—
355	D₄	—	8	2	no	—
356	D₄	—	8	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	8	2	no	—
360	C₂×C₄	—	8	2	no	—
361	C₂×C₄	C₂₃×#127	1	1	yes	characteristic
362	C₂×C₄	C₂₃×#127	1	1	yes	characteristic
363	C₂×C₄	C₂₃×#127	1	1	yes	characteristic
364	C₂×C₄	C₂₃×#135	1	4	yes	—
365	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	4	yes	—
366	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	4	yes	—
367	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
368	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
369	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
370	C₈	—	2	4	no	—
371	C₈	—	2	4	no	—
372	C₈	—	2	4	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	16	4	no	—
380	C₂²	—	16	4	no	—
381	C₂²	C₂₃×#495	1	2	yes	—
382	C₂²	C₂₃×#496	1	2	yes	—
383	C₂²	C₂₃×#496	1	2	yes	—
384	C₂²	C₂×C₂₃×#127	1	1	yes	characteristic
385	C₄	—	8	2	no	—
386	C₄	—	8	2	no	—
387	C₄	C₂₃×#495	1	2	yes	—
388	C₄	C₂₃×#496	1	2	yes	—
389	C₄	C₂₃×#496	1	2	yes	—
390	C₄	C₂×C₂₃×#135	1	2	yes	—
391	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
392	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
393	C₂	—	16	2	no	—
394	C₂	—	16	2	no	—
395	C₂	C₂₃×#1717	1	4	yes	direct product factor
396	C₂	C₂×C₂₃×#495	1	1	yes	characteristic
397	C₂	C₂×C₂₃×#496	1	1	yes	characteristic
398	C₂	C₂×C₂₃×#496	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#493	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#492	C₂	semidirect
3. C₂×C₂₃×#487	C₂	semidirect
4. C₂×C₂₃×#486	C₂	semidirect
5. C₂×C₂₃×#486	C₂	semidirect
6. C₂×C₂₃×#486	C₂	semidirect
7. C₂₃×#1717	C₂	direct (N × H)
8. C₂×C₂₃×#322	C₂	semidirect
18. C₂₃×#492	C₂²	semidirect
20. C₂₃×#487	C₂²	semidirect
24. C₂₃×#486	C₂²	semidirect
25. C₂₃×#486	C₂²	semidirect
26. C₂₃×#486	C₂²	semidirect
34. C₂₃×#322	C₂²	semidirect
132. C₂×#1717	C₂₃	direct (N × H)
175. C₂×#492	C₂×C₂₃	semidirect
176. C₂×#487	C₂×C₂₃	semidirect
177. C₂×#486	C₂×C₂₃	semidirect
178. C₂×#486	C₂×C₂₃	semidirect
179. C₂×#486	C₂×C₂₃	semidirect
180. #1717	C₂×C₂₃	direct (N × H)
181. C₂×#322	C₂×C₂₃	semidirect
211. #492	C₂²×C₂₃	semidirect
213. #487	C₂²×C₂₃	semidirect
217. #486	C₂²×C₂₃	semidirect
218. #486	C₂²×C₂₃	semidirect
219. #486	C₂²×C₂₃	semidirect
227. #322	C₂²×C₂₃	semidirect
230. C₂×C₂₃	#1717	direct (N × H)
280. C₂₃	C₂×#1717	direct (N × H)
395. C₂	C₂₃×#1717	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×#493	2
C₂×C₂₃×#492	2
C₂×C₂₃×#487	2
C₂×C₂₃×#486	2
C₂₃×#1717	2
C₂×C₂₃×#322	2
C₂×#1717	23

Subgroups — C2×C23×#1717 #19167235

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#1717 #19167235