Subgroups — C₂₃×#24989 #19172615

Order 5888.

620 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#473	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2950	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2082	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2049	C₂	1	2	yes	maximal
5	C₂₃×#1979	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1953	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1905	C₂	1	2	yes	maximal
8	C₂₃×#1833	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1830	C₂	1	2	yes	maximal, complemented
10	C₂₃×#1814	C₂	1	1	yes	maximal, characteristic
11	C₂₃×#1757	C₂	1	1	yes	maximal, characteristic
12	C₂×C₂₃×#137	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
14	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
15	C₂₃×#519	C₂²	1	2	yes	—
16	C₂₃×#473	—	2	2	no	—
17	C₂₃×#473	—	2	2	no	—
18	C₂₃×#441	—	2	2	no	—
19	C₄×Q₁₆×C₂₃	—	2	2	no	—
20	C₂₃×#430	C₂²	1	2	yes	—
21	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic
23	C₂₃×#427	C₂²	1	1	yes	characteristic
24	C₂₃×#421	C₂²	1	2	yes	—
25	C₂₃×#419	C₂²	1	2	yes	—
26	C₂₃×#419	C₂²	1	2	yes	—
27	C₂₃×#413	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#101	C₂²	1	2	yes	—
29	C₂×C₂₃×#101	C₂²	1	2	yes	—
30	C₂₃×#410	C₂²	1	1	yes	characteristic
31	C₂₃×#405	C₂²	1	1	yes	characteristic
32	C₂₃×#405	C₂²	1	1	yes	characteristic
33	C₂₃×#344	C₂²	1	2	yes	—
34	C₂₃×#344	C₂²	1	1	yes	characteristic
35	C₂₃×#344	C₂²	1	1	yes	characteristic
36	C₂₃×#344	C₂²	1	2	yes	—
37	C₂₃×#344	C₂²	1	2	yes	—
38	C₂₃×H(3,ℤ/4)	C₂²	1	2	yes	—
39	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
40	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
41	C₂₃×#137	—	2	4	no	—
42	C₂₃×#137	—	4	2	no	—
43	C₂×Q₁₆×C₂₃	—	2	2	no	—
44	C₂×Q₁₆×C₂₃	—	2	1	no	—
45	C₂×Q₁₆×C₂₃	—	2	1	no	—
46	C₂×Q₁₆×C₂₃	—	2	1	no	—
47	C₂×Q₁₆×C₂₃	—	2	1	no	—
48	C₂×Q₁₆×C₂₃	D₄	1	2	yes	—
49	C₂×Q₁₆×C₂₃	D₄	1	2	yes	—
50	C₂×SD₁₆×C₂₃	—	2	2	no	—
51	C₂₃×#131	—	2	1	no	—
52	C₂₃×#131	—	2	1	no	—
53	C₂₃×#131	—	2	1	no	—
54	C₂₃×#131	—	2	1	no	—
55	C₂×M₁₆×C₂₃	—	2	1	no	—
56	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
57	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
58	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
59	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
60	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₂₃	—	2	1	no	—
62	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
63	C₄×Q₈×C₂₃	—	2	4	no	—
64	C₄×Q₈×C₂₃	—	4	2	no	—
65	C₂₃×#117	—	2	4	no	—
66	C₂₃×#117	C₂³	1	1	yes	characteristic
67	C₂₃×#117	C₂³	1	2	yes	—
68	C₂₃×#117	C₂³	1	1	yes	characteristic
69	C₂₃×#108	—	2	1	no	—
70	C₂₃×#108	—	2	1	no	—
71	C₂₃×#108	—	2	1	no	—
72	C₂₃×#108	—	2	1	no	—
73	C₂₃×#108	—	4	2	no	—
74	C₂₃×#107	—	2	1	no	—
75	C₂₃×#106	—	2	1	no	—
76	C₂₃×#104	—	4	2	no	—
77	C₂₃×#103	—	2	4	no	—
78	C₂₃×#103	—	4	2	no	—
79	C₂₃×#101	—	2	4	no	—
80	C₂₃×#101	—	2	1	no	—
81	C₂₃×#101	—	4	2	no	—
82	C₂₃×#100	—	2	1	no	—
83	C₂₃×#99	—	2	2	no	—
84	C₂₃×#97	—	2	1	no	—
85	C₂₃×#97	—	2	1	no	—
86	C₄×C₈×C₂₃	—	2	1	no	—
87	C₄×C₈×C₂₃	—	2	1	no	—
88	#41×C₂₃	—	2	1	no	—
89	#41×C₂₃	—	2	1	no	—
90	#41×C₂₃	—	2	1	no	—
91	#41×C₂₃	—	2	1	no	—
92	C₂×Q₈×C₂₃	—	2	2	no	—
93	C₂×Q₈×C₂₃	—	2	2	no	—
94	C₂×Q₈×C₂₃	—	2	2	no	—
95	C₂×Q₈×C₂₃	—	2	2	no	—
96	C₂×Q₈×C₂₃	—	2	2	no	—
97	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	—
98	C₂×Q₈×C₂₃	#41	1	1	yes	characteristic
99	C₂×D₄×C₂₃	—	2	1	no	—
100	C₂×D₄×C₂₃	#41	1	1	yes	characteristic
101	C₂²×C₄×C₂₃	—	2	2	no	—
102	C₂²×C₄×C₂₃	—	2	1	no	—
103	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
104	Q₁₆×C₂₃	—	2	2	no	—
105	Q₁₆×C₂₃	—	2	2	no	—
106	Q₁₆×C₂₃	—	2	2	no	—
107	Q₁₆×C₂₃	—	2	2	no	—
108	Q₁₆×C₂₃	—	4	4	no	—
109	SD₁₆×C₂₃	—	4	4	no	—
110	M₁₆×C₂₃	—	2	1	no	—
111	M₁₆×C₂₃	—	2	2	no	—
112	M₁₆×C₂₃	—	2	1	no	—
113	M₁₆×C₂₃	—	2	1	no	—
114	M₁₆×C₂₃	—	2	2	no	—
115	M₁₆×C₂₃	—	2	1	no	—
116	M₁₆×C₂₃	—	2	1	no	—
117	M₁₆×C₂₃	—	2	2	no	—
118	M₁₆×C₂₃	—	2	1	no	—
119	M₁₆×C₂₃	—	2	2	no	—
120	M₁₆×C₂₃	—	4	1	no	—
121	M₁₆×C₂₃	—	4	1	no	—
122	C₂×C₈×C₂₃	—	2	1	no	—
123	C₂×C₈×C₂₃	—	2	1	no	—
124	C₂×C₈×C₂₃	—	2	2	no	—
125	C₂×C₈×C₂₃	—	2	1	no	—
126	C₂×C₈×C₂₃	—	2	2	no	—
127	C₂×C₈×C₂₃	—	4	1	no	—
128	C₂×C₈×C₂₃	—	4	1	no	—
129	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₂₃	#41	1	1	yes	characteristic
132	C₂×C₈×C₂₃	#41	1	1	yes	characteristic
133	C₂×C₈×C₂₃	#41	1	1	yes	characteristic
134	C₂×C₈×C₂₃	#41	1	1	yes	characteristic
135	C₄⋊C₄×C₂₃	—	2	1	no	—
136	C₄⋊C₄×C₂₃	—	2	2	no	—
137	C₄⋊C₄×C₂₃	—	2	1	no	—
138	C₄⋊C₄×C₂₃	—	4	4	no	—
139	C₂²⋊C₄×C₂₃	—	2	1	no	—
140	C₂²⋊C₄×C₂₃	—	2	2	no	—
141	C₂²⋊C₄×C₂₃	#41	1	2	yes	—
142	C₄²×C₂₃	—	2	1	no	—
143	C₄²×C₂₃	—	2	1	no	—
144	C₄²×C₂₃	—	2	2	no	—
145	C₄²×C₂₃	—	4	4	no	—
146	#24989	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
147	C₂³×C₂₃	—	2	1	no	—
148	C₂³×C₂₃	C₂×#41	1	1	yes	characteristic
149	Q₈×C₂₃	—	2	4	no	—
150	Q₈×C₂₃	—	2	4	no	—
151	Q₈×C₂₃	—	2	1	no	—
152	Q₈×C₂₃	—	2	1	no	—
153	Q₈×C₂₃	—	4	2	no	—
154	Q₈×C₂₃	—	4	2	no	—
155	D₄×C₂₃	—	2	1	no	—
156	D₄×C₂₃	—	2	1	no	—
157	D₄×C₂₃	—	4	1	no	—
158	D₄×C₂₃	—	4	1	no	—
159	C₂×C₄×C₂₃	—	2	1	no	—
160	C₂×C₄×C₂₃	—	2	2	no	—
161	C₂×C₄×C₂₃	—	2	4	no	—
162	C₂×C₄×C₂₃	—	4	2	no	—
163	C₂×C₄×C₂₃	—	4	2	no	—
164	C₂×C₄×C₂₃	—	4	1	no	—
165	C₂×C₄×C₂₃	—	4	1	no	—
166	C₂×C₄×C₂₃	—	4	2	no	—
167	C₂×C₄×C₂₃	—	4	1	no	—
168	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
174	C₈×C₂₃	—	4	1	no	—
175	C₈×C₂₃	—	4	2	no	—
176	C₈×C₂₃	—	4	1	no	—
177	C₈×C₂₃	—	4	2	no	—
178	C₈×C₂₃	—	4	1	no	—
179	C₈×C₂₃	#123	1	1	yes	characteristic
180	C₈×C₂₃	#123	1	1	yes	characteristic
181	C₈×C₂₃	#123	1	1	yes	characteristic
182	C₈×C₂₃	#123	1	1	yes	characteristic
183	C₂×#473	C₂×C₂₃	1	1	yes	characteristic
184	#2950	C₂×C₂₃	1	1	yes	characteristic, complemented
185	#2082	C₂×C₂₃	1	2	yes	complemented
186	#2049	C₂×C₂₃	1	2	yes	—
187	#1979	C₂×C₂₃	1	1	yes	characteristic, complemented
188	#1953	C₂×C₂₃	1	1	yes	characteristic, complemented
189	#1905	C₂×C₂₃	1	2	yes	—
190	#1833	C₂×C₂₃	1	1	yes	characteristic, complemented
191	#1830	C₂×C₂₃	1	2	yes	complemented
192	#1814	C₂×C₂₃	1	1	yes	characteristic
193	#1757	C₂×C₂₃	1	1	yes	characteristic
194	C₂²×C₂₃	—	4	1	no	—
195	C₂²×C₂₃	—	4	1	no	—
196	C₂²×C₂₃	—	8	1	no	—
197	C₂²×C₂₃	#529	1	1	yes	characteristic
198	C₂²×C₂₃	#546	1	1	yes	characteristic
199	C₂²×C₂₃	#555	1	1	yes	characteristic
200	C₄×C₂₃	—	4	2	no	—
201	C₄×C₂₃	—	4	1	no	—
202	C₄×C₂₃	—	4	4	no	—
203	C₄×C₂₃	—	8	2	no	—
204	C₄×C₂₃	—	8	1	no	—
205	C₄×C₂₃	C₂×#123	1	1	yes	characteristic
206	C₄×C₂₃	#540	1	1	yes	characteristic
207	C₄×C₂₃	#546	1	1	yes	characteristic
208	C₄×C₂₃	#553	1	1	yes	characteristic
209	C₂×#137	C₂²×C₂₃	1	2	yes	—
210	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
211	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
212	#519	C₂²×C₂₃	1	2	yes	—
213	#473	—	2	2	no	—
214	#473	—	2	2	no	—
215	#441	—	2	2	no	—
216	C₄×Q₁₆	—	2	2	no	—
217	#430	C₂²×C₂₃	1	2	yes	—
218	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic
219	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic
220	#427	C₂²×C₂₃	1	1	yes	characteristic
221	#421	C₂²×C₂₃	1	2	yes	—
222	#419	C₂²×C₂₃	1	2	yes	—
223	#419	C₂²×C₂₃	1	2	yes	—
224	#413	C₂²×C₂₃	1	1	yes	characteristic
225	C₂×#101	C₂²×C₂₃	1	2	yes	—
226	C₂×#101	C₂²×C₂₃	1	2	yes	—
227	#410	C₂²×C₂₃	1	1	yes	characteristic
228	#405	C₂²×C₂₃	1	1	yes	characteristic
229	#405	C₂²×C₂₃	1	1	yes	characteristic
230	#344	C₂²×C₂₃	1	2	yes	—
231	#344	C₂²×C₂₃	1	2	yes	—
232	#344	C₂²×C₂₃	1	1	yes	characteristic
233	#344	C₂²×C₂₃	1	1	yes	characteristic
234	#344	C₂²×C₂₃	1	2	yes	—
235	H(3,ℤ/4)	C₂²×C₂₃	1	2	yes	—
236	C₂×C₂₃	—	2	1	no	—
237	C₂×C₂₃	—	2	1	no	—
238	C₂×C₂₃	—	2	1	no	—
239	C₂×C₂₃	—	8	1	no	—
240	C₂×C₂₃	#2420	1	1	yes	characteristic
241	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
242	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
243	#137	—	2	4	no	—
244	#137	—	4	2	no	—
245	C₂×Q₁₆	—	2	2	no	—
246	C₂×Q₁₆	—	2	1	no	—
247	C₂×Q₁₆	—	2	1	no	—
248	C₂×Q₁₆	—	2	1	no	—
249	C₂×Q₁₆	—	2	1	no	—
250	C₂×Q₁₆	D₄×C₂₃	1	2	yes	—
251	C₂×Q₁₆	D₄×C₂₃	1	2	yes	—
252	C₂×SD₁₆	—	2	2	no	—
253	#131	—	2	1	no	—
254	#131	—	2	1	no	—
255	#131	—	2	1	no	—
256	#131	—	2	1	no	—
257	C₂×M₁₆	—	2	1	no	—
258	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
259	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
260	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
261	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
262	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
265	C₄×Q₈	—	2	4	no	—
266	C₄×Q₈	—	4	2	no	—
267	#117	—	2	4	no	—
268	#117	C₂³×C₂₃	1	2	yes	—
269	#117	C₂³×C₂₃	1	1	yes	characteristic
270	#117	C₂³×C₂₃	1	1	yes	characteristic
271	#108	—	2	1	no	—
272	#108	—	2	1	no	—
273	#108	—	2	1	no	—
274	#108	—	2	1	no	—
275	#108	—	4	2	no	—
276	#107	—	2	1	no	—
277	#106	—	2	1	no	—
278	#104	—	4	2	no	—
279	#103	—	2	4	no	—
280	#103	—	4	2	no	—
281	#101	—	2	4	no	—
282	#101	—	2	1	no	—
283	#101	—	4	2	no	—
284	#100	—	2	1	no	—
285	#99	—	2	2	no	—
286	#97	—	2	1	no	—
287	#97	—	2	1	no	—
288	C₄×C₈	—	2	1	no	—
289	C₄×C₈	—	2	1	no	—
290	C₂₃	#24989	1	1	yes	characteristic, direct product factor, Sylow
291	#41	—	2	1	no	—
292	#41	—	2	1	no	—
293	#41	—	2	1	no	—
294	#41	—	2	1	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	—
301	C₂×Q₈	#41×C₂₃	1	1	yes	characteristic
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	#41×C₂₃	1	1	yes	characteristic
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
307	Q₁₆	—	2	2	no	—
308	Q₁₆	—	2	2	no	—
309	Q₁₆	—	2	2	no	—
310	Q₁₆	—	2	2	no	—
311	Q₁₆	—	4	4	no	—
312	SD₁₆	—	4	4	no	—
313	M₁₆	—	2	1	no	—
314	M₁₆	—	2	2	no	—
315	M₁₆	—	2	1	no	—
316	M₁₆	—	2	1	no	—
317	M₁₆	—	2	2	no	—
318	M₁₆	—	2	1	no	—
319	M₁₆	—	2	1	no	—
320	M₁₆	—	2	2	no	—
321	M₁₆	—	2	1	no	—
322	M₁₆	—	2	2	no	—
323	M₁₆	—	4	1	no	—
324	M₁₆	—	4	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	4	1	no	—
332	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
333	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
334	C₂×C₈	#41×C₂₃	1	1	yes	characteristic
335	C₂×C₈	#41×C₂₃	1	1	yes	characteristic
336	C₂×C₈	#41×C₂₃	1	1	yes	characteristic
337	C₂×C₈	#41×C₂₃	1	1	yes	characteristic
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	4	4	no	—
342	C₂²⋊C₄	—	2	1	no	—
343	C₂²⋊C₄	—	2	2	no	—
344	C₂²⋊C₄	#41×C₂₃	1	2	yes	—
345	C₄²	—	2	1	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	4	4	no	—
349	C₂³	—	2	1	no	—
350	C₂³	C₂×#41×C₂₃	1	1	yes	characteristic
351	Q₈	—	2	1	no	—
352	Q₈	—	2	4	no	—
353	Q₈	—	2	4	no	—
354	Q₈	—	2	1	no	—
355	Q₈	—	4	2	no	—
356	Q₈	—	4	2	no	—
357	D₄	—	2	1	no	—
358	D₄	—	2	1	no	—
359	D₄	—	4	1	no	—
360	D₄	—	4	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
371	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
372	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
373	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
374	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
375	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
376	C₈	—	4	1	no	—
377	C₈	—	4	1	no	—
378	C₈	—	4	2	no	—
379	C₈	—	4	2	no	—
380	C₈	—	4	1	no	—
381	C₈	C₂₃×#123	1	1	yes	characteristic
382	C₈	C₂₃×#123	1	1	yes	characteristic
383	C₈	C₂₃×#123	1	1	yes	characteristic
384	C₈	C₂₃×#123	1	1	yes	characteristic
385	C₂²	—	4	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	8	1	no	—
388	C₂²	C₂₃×#529	1	1	yes	characteristic
389	C₂²	C₂₃×#546	1	1	yes	characteristic
390	C₂²	C₂₃×#555	1	1	yes	characteristic
391	C₄	—	4	2	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	4	no	—
394	C₄	—	8	2	no	—
395	C₄	—	8	1	no	—
396	C₄	C₂×C₂₃×#123	1	1	yes	characteristic
397	C₄	C₂₃×#540	1	1	yes	characteristic
398	C₄	C₂₃×#546	1	1	yes	characteristic
399	C₄	C₂₃×#553	1	1	yes	characteristic
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	—	2	1	no	—
403	C₂	—	8	1	no	—
404	C₂	C₂₃×#2420	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₂₃	#2420
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂×#41×C₂₃	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2950	C₂	semidirect
3. C₂₃×#2082	C₂	semidirect
5. C₂₃×#1979	C₂	semidirect
6. C₂₃×#1953	C₂	semidirect
8. C₂₃×#1833	C₂	semidirect
9. C₂₃×#1830	C₂	semidirect
146. #24989	C₂₃	direct (N × H)
184. #2950	C₂×C₂₃	semidirect
185. #2082	C₂×C₂₃	semidirect
187. #1979	C₂×C₂₃	semidirect
188. #1953	C₂×C₂₃	semidirect
190. #1833	C₂×C₂₃	semidirect
191. #1830	C₂×C₂₃	semidirect
290. C₂₃	#24989	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×#473	2
C₂₃×#2950	2
C₂₃×#2082	2
C₂₃×#2049	2
C₂₃×#1979	2
C₂₃×#1953	2
C₂₃×#1905	2
C₂₃×#1833	2
C₂₃×#1830	2
C₂₃×#1814	2
C₂₃×#1757	2
#24989	23

Subgroups — C23×#24989 #19172615

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#24989 #19172615