Subgroups — C₂₃×#19214 #19166840

Order 5888.

658 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	C₂₃×#3209	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3208	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×#486	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1702	C₂	1	4	yes	maximal, complemented
6	C₂₃×#1682	C₂	1	4	yes	maximal, complemented
7	C₂₃×#1564	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1549	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1545	C₂	1	1	yes	maximal, characteristic
10	C₂₃×#533	C₂²	1	1	yes	characteristic
11	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
13	C₂₃×#494	—	2	1	no	—
14	C₂₃×#492	—	2	1	no	—
15	C₂₃×#487	—	2	1	no	—
16	C₂₃×#486	—	2	1	no	—
17	C₂₃×#486	—	2	1	no	—
18	C₂₃×#486	—	2	1	no	—
19	C₂₃×#486	C₂²	1	2	yes	—
20	C₂₃×#486	C₂²	1	2	yes	—
21	C₂₃×#462	C₂²	1	4	yes	complemented
22	C₂₃×#460	C₂²	1	4	yes	—
23	C₂₃×#451	—	2	2	no	—
24	C₂₃×#450	—	2	2	no	—
25	C₂₃×#446	—	2	1	no	—
26	C₂₃×#446	C₂²	1	2	yes	complemented
27	C₈×Q₈×C₂₃	—	2	1	no	—
28	C₈×Q₈×C₂₃	C₂²	1	2	yes	complemented
29	C₂₃×#431	C₂²	1	1	yes	characteristic
30	C₂₃×#431	C₂²	1	1	yes	characteristic
31	C₂₃×#424	—	2	1	no	—
32	C₂₃×#423	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#102	—	2	1	no	—
34	C₂×C₂₃×#102	—	2	1	no	—
35	C₂₃×#405	—	2	1	no	—
36	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
37	C₂₃×#335	C₂²	1	2	yes	complemented
38	C₂₃×#334	C₂²	1	2	yes	complemented
39	C₂₃×#332	C₂²	1	4	yes	complemented
40	C₂₃×#331	C₂²	1	4	yes	—
41	C₂²×Q₈×C₂₃	—	2	1	no	—
42	C₂²×D₄×C₂₃	—	2	1	no	—
43	C₂²×D₄×C₂₃	—	2	1	no	—
44	C₂²×D₄×C₂₃	—	2	1	no	—
45	C₂×Q₁₆×C₂₃	—	2	4	no	—
46	C₂×SD₁₆×C₂₃	—	2	4	no	—
47	C₂×M₁₆×C₂₃	—	2	1	no	—
48	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
49	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
54	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
55	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
56	C₂₃×#127	—	2	1	no	—
57	C₂₃×#127	—	2	1	no	—
58	C₂₃×#127	—	2	1	no	—
59	C₂₃×#127	C₂³	1	2	yes	—
60	C₂₃×#125	—	2	1	no	—
61	C₂₃×C₂²⋊Q₈	—	2	1	no	—
62	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
63	C₄×Q₈×C₂₃	—	2	1	no	—
64	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
65	C₂₃×#117	—	2	1	no	—
66	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
68	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
69	C₂₃×C₄⋊C₈	—	2	2	no	—
70	C₂₃×C₄⋊C₈	—	2	2	no	—
71	C₂₃×C₄⋊C₈	—	2	1	no	—
72	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
73	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
74	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
75	C₂₃×#103	—	2	4	no	—
76	C₂₃×#102	—	2	2	no	—
77	C₂₃×#102	—	2	2	no	—
78	C₂₃×#102	—	2	2	no	—
79	C₂₃×#102	—	2	2	no	—
80	C₂₃×#102	—	2	4	no	—
81	C₂₃×C₂²⋊C₈	—	2	1	no	—
82	C₂₃×C₂²⋊C₈	—	2	1	no	—
83	C₂₃×#97	—	2	2	no	—
84	C₄×C₈×C₂₃	—	2	2	no	—
85	C₄×C₈×C₂₃	—	2	1	no	—
86	C₄×C₈×C₂₃	—	2	1	no	—
87	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
88	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
89	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
91	C₂⁴×C₂₃	—	4	1	no	—
92	C₂×Q₈×C₂₃	—	2	1	no	—
93	C₂×Q₈×C₂₃	—	2	2	no	—
94	C₂×Q₈×C₂₃	—	4	1	no	—
95	C₂×Q₈×C₂₃	—	8	2	no	—
96	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
97	C₂×D₄×C₂₃	—	2	2	no	—
98	C₂×D₄×C₂₃	—	2	2	no	—
99	C₂×D₄×C₂₃	—	2	2	no	—
100	C₂×D₄×C₂₃	—	4	1	no	—
101	C₂×D₄×C₂₃	—	4	1	no	—
102	C₂×D₄×C₂₃	—	4	1	no	—
103	C₂×D₄×C₂₃	—	4	2	no	—
104	C₂×D₄×C₂₃	—	4	2	no	—
105	C₂×D₄×C₂₃	—	8	2	no	—
106	C₂×D₄×C₂₃	—	8	2	no	—
107	C₂²×C₄×C₂₃	—	4	1	no	—
108	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
111	Q₁₆×C₂₃	—	8	4	no	—
112	SD₁₆×C₂₃	—	8	4	no	—
113	M₁₆×C₂₃	—	4	2	no	—
114	C₂×C₈×C₂₃	—	2	2	no	—
115	C₂×C₈×C₂₃	—	2	2	no	—
116	C₂×C₈×C₂₃	—	2	2	no	—
117	C₂×C₈×C₂₃	—	2	2	no	—
118	C₂×C₈×C₂₃	—	2	2	no	—
119	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
123	C₄⋊C₄×C₂₃	—	2	1	no	—
124	C₄⋊C₄×C₂₃	—	2	1	no	—
125	C₄⋊C₄×C₂₃	—	2	1	no	—
126	C₄⋊C₄×C₂₃	—	2	2	no	—
127	C₄⋊C₄×C₂₃	—	2	2	no	—
128	C₄⋊C₄×C₂₃	—	2	2	no	—
129	C₄⋊C₄×C₂₃	—	2	2	no	—
130	C₄⋊C₄×C₂₃	—	4	1	no	—
131	C₄⋊C₄×C₂₃	—	4	1	no	—
132	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
133	C₂²⋊C₄×C₂₃	—	2	2	no	—
134	C₄²×C₂₃	—	2	2	no	—
135	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₂₃	#41	1	1	yes	characteristic
138	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
139	#19214	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂³×C₂₃	—	4	2	no	—
141	C₂³×C₂₃	—	8	2	no	—
142	C₂³×C₂₃	—	8	2	no	—
143	C₂³×C₂₃	—	8	2	no	—
144	C₂³×C₂₃	#121	1	1	yes	characteristic
145	Q₈×C₂₃	—	2	4	no	—
146	Q₈×C₂₃	—	4	2	no	—
147	Q₈×C₂₃	—	4	4	no	—
148	Q₈×C₂₃	—	8	2	no	—
149	D₄×C₂₃	—	4	2	no	—
150	D₄×C₂₃	—	4	2	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	C₂×C₄×C₂₃	—	2	2	no	—
157	C₂×C₄×C₂₃	—	2	2	no	—
158	C₂×C₄×C₂₃	—	2	2	no	—
159	C₂×C₄×C₂₃	—	2	2	no	—
160	C₂×C₄×C₂₃	—	4	2	no	—
161	C₂×C₄×C₂₃	—	8	2	no	—
162	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
163	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
164	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
165	C₂×C₄×C₂₃	#135	1	2	yes	—
166	C₂×C₄×C₂₃	#137	1	2	yes	—
167	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
170	C₈×C₂₃	—	2	1	no	—
171	C₈×C₂₃	—	2	1	no	—
172	C₈×C₂₃	—	2	1	no	—
173	C₈×C₂₃	—	2	1	no	—
174	C₈×C₂₃	—	4	2	no	—
175	C₈×C₂₃	—	4	2	no	—
176	C₈×C₂₃	—	4	2	no	—
177	#3209	C₂×C₂₃	1	1	yes	characteristic, complemented
178	#3208	C₂×C₂₃	1	1	yes	characteristic
179	C₂×#486	C₂×C₂₃	1	1	yes	characteristic
180	#2960	C₂×C₂₃	1	1	yes	characteristic, complemented
181	#1702	C₂×C₂₃	1	4	yes	complemented
182	#1682	C₂×C₂₃	1	4	yes	complemented
183	#1564	C₂×C₂₃	1	1	yes	characteristic, complemented
184	#1549	C₂×C₂₃	1	1	yes	characteristic, complemented
185	#1545	C₂×C₂₃	1	1	yes	characteristic
186	C₂²×C₂₃	—	2	1	no	—
187	C₂²×C₂₃	—	2	1	no	—
188	C₂²×C₂₃	—	8	2	no	—
189	C₂²×C₂₃	—	8	2	no	—
190	C₂²×C₂₃	—	8	2	no	—
191	C₂²×C₂₃	—	16	4	no	—
192	C₂²×C₂₃	#464	1	2	yes	—
193	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
194	C₄×C₂₃	—	2	1	no	—
195	C₄×C₂₃	—	2	1	no	—
196	C₄×C₂₃	—	4	2	no	—
197	C₄×C₂₃	—	4	2	no	—
198	C₄×C₂₃	—	8	2	no	—
199	C₄×C₂₃	#464	1	2	yes	—
200	C₄×C₂₃	#471	1	2	yes	—
201	C₄×C₂₃	C₂×#135	1	1	yes	characteristic
202	C₄×C₂₃	C₂×#137	1	1	yes	characteristic
203	C₄×C₂₃	#576	1	2	yes	—
204	#533	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	#494	—	2	1	no	—
208	#492	—	2	1	no	—
209	#487	—	2	1	no	—
210	#486	—	2	1	no	—
211	#486	—	2	1	no	—
212	#486	—	2	1	no	—
213	#486	C₂²×C₂₃	1	2	yes	—
214	#486	C₂²×C₂₃	1	2	yes	—
215	#462	C₂²×C₂₃	1	4	yes	complemented
216	#460	C₂²×C₂₃	1	4	yes	—
217	#451	—	2	2	no	—
218	#450	—	2	2	no	—
219	#446	—	2	1	no	—
220	#446	C₂²×C₂₃	1	2	yes	complemented
221	C₈×Q₈	—	2	1	no	—
222	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
223	#431	C₂²×C₂₃	1	1	yes	characteristic
224	#431	C₂²×C₂₃	1	1	yes	characteristic
225	#424	—	2	1	no	—
226	#423	C₂²×C₂₃	1	1	yes	characteristic
227	C₂×#102	—	2	1	no	—
228	C₂×#102	—	2	1	no	—
229	#405	—	2	1	no	—
230	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
231	#335	C₂²×C₂₃	1	2	yes	complemented
232	#334	C₂²×C₂₃	1	2	yes	complemented
233	#332	C₂²×C₂₃	1	4	yes	complemented
234	#331	C₂²×C₂₃	1	4	yes	—
235	C₂×C₂₃	—	2	2	no	—
236	C₂×C₂₃	—	16	2	no	—
237	C₂×C₂₃	C₂×#464	1	1	yes	characteristic
238	C₂×C₂₃	#3058	1	1	yes	characteristic
239	C₂×C₂₃	C₂×#471	1	1	yes	characteristic
240	C₂²×Q₈	—	2	1	no	—
241	C₂²×D₄	—	2	1	no	—
242	C₂²×D₄	—	2	1	no	—
243	C₂²×D₄	—	2	1	no	—
244	C₂×Q₁₆	—	2	4	no	—
245	C₂×SD₁₆	—	2	4	no	—
246	C₂×M₁₆	—	2	1	no	—
247	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
248	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	—	2	1	no	—
252	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
253	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
254	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
255	#127	—	2	1	no	—
256	#127	—	2	1	no	—
257	#127	—	2	1	no	—
258	#127	C₂³×C₂₃	1	2	yes	—
259	#125	—	2	1	no	—
260	C₂²⋊Q₈	—	2	1	no	—
261	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
262	C₄×Q₈	—	2	1	no	—
263	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
264	#117	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
268	C₄⋊C₈	—	2	2	no	—
269	C₄⋊C₈	—	2	2	no	—
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
272	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
273	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
274	#103	—	2	4	no	—
275	#102	—	2	2	no	—
276	#102	—	2	2	no	—
277	#102	—	2	2	no	—
278	#102	—	2	2	no	—
279	#102	—	2	4	no	—
280	C₂²⋊C₈	—	2	1	no	—
281	C₂²⋊C₈	—	2	1	no	—
282	#97	—	2	2	no	—
283	C₄×C₈	—	2	2	no	—
284	C₄×C₈	—	2	1	no	—
285	C₄×C₈	—	2	1	no	—
286	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
287	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
288	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
289	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
290	C₂₃	#19214	1	1	yes	characteristic, direct product factor, Sylow
291	C₂⁴	—	4	1	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	4	1	no	—
295	C₂×Q₈	—	8	2	no	—
296	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	—	4	1	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	8	2	no	—
306	C₂×D₄	—	8	2	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
310	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
311	Q₁₆	—	8	4	no	—
312	SD₁₆	—	8	4	no	—
313	M₁₆	—	4	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
320	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
321	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
322	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
333	C₂²⋊C₄	—	2	2	no	—
334	C₄²	—	2	2	no	—
335	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
336	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
337	C₄²	#41×C₂₃	1	1	yes	characteristic
338	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
339	C₂³	—	4	2	no	—
340	C₂³	—	8	2	no	—
341	C₂³	—	8	2	no	—
342	C₂³	—	8	2	no	—
343	C₂³	C₂₃×#121	1	1	yes	characteristic
344	Q₈	—	2	4	no	—
345	Q₈	—	4	2	no	—
346	Q₈	—	4	4	no	—
347	Q₈	—	8	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	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	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	8	2	no	—
361	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
362	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
363	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
364	C₂×C₄	C₂₃×#135	1	2	yes	—
365	C₂×C₄	C₂₃×#137	1	2	yes	—
366	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
367	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
368	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
369	C₈	—	2	1	no	—
370	C₈	—	2	1	no	—
371	C₈	—	2	1	no	—
372	C₈	—	2	1	no	—
373	C₈	—	4	2	no	—
374	C₈	—	4	2	no	—
375	C₈	—	4	2	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	—	16	4	no	—
382	C₂²	C₂₃×#464	1	2	yes	—
383	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	4	2	no	—
387	C₄	—	4	2	no	—
388	C₄	—	8	2	no	—
389	C₄	C₂₃×#464	1	2	yes	—
390	C₄	C₂₃×#471	1	2	yes	—
391	C₄	C₂×C₂₃×#135	1	1	yes	characteristic
392	C₄	C₂×C₂₃×#137	1	1	yes	characteristic
393	C₄	C₂₃×#576	1	2	yes	—
394	C₂	—	2	2	no	—
395	C₂	—	16	2	no	—
396	C₂	C₂×C₂₃×#464	1	1	yes	characteristic
397	C₂	C₂₃×#3058	1	1	yes	characteristic
398	C₂	C₂×C₂₃×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3209	C₂	semidirect
4. C₂₃×#2960	C₂	semidirect
5. C₂₃×#1702	C₂	semidirect
6. C₂₃×#1682	C₂	semidirect
7. C₂₃×#1564	C₂	semidirect
8. C₂₃×#1549	C₂	semidirect
21. C₂₃×#462	C₂²	semidirect
26. C₂₃×#446	C₂²	semidirect
28. C₈×Q₈×C₂₃	C₂²	semidirect
37. C₂₃×#335	C₂²	semidirect
38. C₂₃×#334	C₂²	semidirect
39. C₂₃×#332	C₂²	semidirect
139. #19214	C₂₃	direct (N × H)
177. #3209	C₂×C₂₃	semidirect
180. #2960	C₂×C₂₃	semidirect
181. #1702	C₂×C₂₃	semidirect
182. #1682	C₂×C₂₃	semidirect
183. #1564	C₂×C₂₃	semidirect
184. #1549	C₂×C₂₃	semidirect
215. #462	C₂²×C₂₃	semidirect
220. #446	C₂²×C₂₃	semidirect
222. C₈×Q₈	C₂²×C₂₃	semidirect
231. #335	C₂²×C₂₃	semidirect
232. #334	C₂²×C₂₃	semidirect
233. #332	C₂²×C₂₃	semidirect
290. C₂₃	#19214	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3209	2
C₂₃×#3208	2
C₂×C₂₃×#486	2
C₂₃×#2960	2
C₂₃×#1702	2
C₂₃×#1682	2
C₂₃×#1564	2
C₂₃×#1549	2
C₂₃×#1545	2
#19214	23

Subgroups — C23×#19214 #19166840

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#19214 #19166840