Subgroups — C₂₃×#10860 #19158486

Order 5888.

782 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×#108	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#427	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₂₃×#97	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₃×#339	C₂	1	2	yes	maximal
5	C₂₃×#1729	C₂	1	2	yes	maximal
6	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	—
7	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
9	C₂×C₂₃×#117	C₂²	1	2	yes	—
10	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
11	C₂×C₂₃×#108	—	2	2	no	—
12	C₂×C₂₃×#108	—	2	2	no	—
13	C₂×C₂₃×#108	C₄	1	4	yes	complemented
14	C₂₃×#427	—	2	2	no	—
15	C₂₃×#427	—	2	2	no	—
16	C₂×C₂₃×#107	C₄	1	2	yes	complemented
17	C₂×C₂₃×#106	C₄	1	2	yes	complemented
18	C₂×C₂₃×#97	—	2	2	no	—
19	C₂×C₂₃×#97	—	2	2	no	—
20	C₂×C₂₃×#97	C₄	1	4	yes	complemented
21	C₂₃×#339	—	2	4	no	—
22	C₂₃×#336	—	2	4	no	—
23	C₂³×C₄×C₂₃	—	2	1	no	—
24	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
25	C₂×M₁₆×C₂₃	—	2	2	no	—
26	C₂×M₁₆×C₂₃	—	2	2	no	—
27	C₂×M₁₆×C₂₃	—	2	2	no	—
28	C₂×M₁₆×C₂₃	—	2	2	no	—
29	C₂×M₁₆×C₂₃	—	2	2	no	—
30	C₂×M₁₆×C₂₃	C₂×C₄	1	4	yes	—
31	C₂²×C₈×C₂₃	—	2	1	no	—
32	C₂²×C₈×C₂₃	—	2	1	no	—
33	C₂²×C₈×C₂₃	—	2	1	no	—
34	C₂²×C₈×C₂₃	—	2	1	no	—
35	C₂²×C₈×C₂₃	—	2	2	no	—
36	C₂²×C₈×C₂₃	C₂×C₄	1	2	yes	—
37	C₂²×C₈×C₂₃	C₂×C₄	1	2	yes	—
38	C₂²×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₂₃	C₂×C₄	1	2	yes	—
41	C₂²×C₈×C₂₃	D₄	1	2	yes	—
42	C₂²×C₈×C₂₃	D₄	1	2	yes	—
43	C₂²×C₈×C₂₃	D₄	1	2	yes	—
44	C₂²×C₈×C₂₃	D₄	1	2	yes	—
45	C₂²×C₈×C₂₃	Q₈	1	2	yes	—
46	C₂²×C₈×C₂₃	Q₈	1	2	yes	—
47	C₂₃×#117	—	2	2	no	—
48	C₂₃×#117	—	2	2	no	—
49	C₂₃×#117	—	2	2	no	—
50	C₂₃×#117	—	2	2	no	—
51	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	4	yes	—
52	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
53	C₂×C₄²×C₂₃	—	2	1	no	—
54	C₂×C₄²×C₂₃	—	2	1	no	—
55	C₂×C₄²×C₂₃	—	2	1	no	—
56	C₂×C₄²×C₂₃	—	2	2	no	—
57	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₂₃	D₄	1	2	yes	—
59	C₂×C₄²×C₂₃	Q₈	1	2	yes	—
60	C₂₃×#108	—	2	8	no	—
61	C₂₃×#107	—	2	4	no	—
62	C₂₃×#106	—	2	4	no	—
63	C₂₃×#97	—	2	8	no	—
64	C₂⁴×C₂₃	#41	1	1	yes	characteristic
65	C₂²×C₄×C₂₃	—	2	2	no	—
66	C₂²×C₄×C₂₃	—	2	2	no	—
67	C₂²×C₄×C₂₃	—	2	2	no	—
68	C₂²×C₄×C₂₃	—	2	4	no	—
69	C₂²×C₄×C₂₃	—	4	4	no	—
70	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
79	C₂²×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
80	C₂²×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
81	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
82	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
83	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
84	M₁₆×C₂₃	—	2	4	no	—
85	M₁₆×C₂₃	—	2	4	no	—
86	M₁₆×C₂₃	—	4	2	no	—
87	M₁₆×C₂₃	—	4	2	no	—
88	C₂×C₈×C₂₃	—	2	2	no	—
89	C₂×C₈×C₂₃	—	2	2	no	—
90	C₂×C₈×C₂₃	—	2	2	no	—
91	C₂×C₈×C₂₃	—	2	2	no	—
92	C₂×C₈×C₂₃	—	2	2	no	—
93	C₂×C₈×C₂₃	—	2	2	no	—
94	C₂×C₈×C₂₃	—	2	4	no	—
95	C₂×C₈×C₂₃	—	4	2	no	—
96	C₂×C₈×C₂₃	—	4	2	no	—
97	C₂×C₈×C₂₃	C₄²	1	2	yes	—
98	C₂×C₈×C₂₃	C₄²	1	2	yes	—
99	C₂×C₈×C₂₃	C₂²⋊C₄	1	2	yes	—
100	C₂×C₈×C₂₃	C₂²⋊C₄	1	2	yes	—
101	C₂×C₈×C₂₃	C₂²⋊C₄	1	4	yes	—
102	C₂×C₈×C₂₃	C₂²⋊C₄	1	4	yes	—
103	C₂×C₈×C₂₃	C₄⋊C₄	1	4	yes	—
104	C₂×C₈×C₂₃	C₄⋊C₄	1	4	yes	—
105	C₂×C₈×C₂₃	C₄⋊C₄	1	2	yes	—
106	C₂×C₈×C₂₃	C₄⋊C₄	1	2	yes	—
107	C₂×C₈×C₂₃	C₄⋊C₄	1	4	yes	—
108	C₄⋊C₄×C₂₃	—	2	4	no	—
109	C₄⋊C₄×C₂₃	—	2	4	no	—
110	C₂²⋊C₄×C₂₃	—	4	2	no	—
111	C₂²⋊C₄×C₂₃	—	4	2	no	—
112	C₄²×C₂₃	—	2	2	no	—
113	C₄²×C₂₃	—	2	2	no	—
114	C₄²×C₂₃	—	2	2	no	—
115	C₄²×C₂₃	—	4	2	no	—
116	C₄²×C₂₃	—	4	2	no	—
117	C₄²×C₂₃	C₄⋊C₄	1	4	yes	—
118	#10860	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂³×C₂₃	—	2	4	no	—
120	C₂³×C₂₃	#117	1	1	yes	characteristic
121	C₂³×C₂₃	C₄×D₄	1	1	yes	characteristic
122	C₂³×C₂₃	C₄×Q₈	1	1	yes	characteristic
123	C₂³×C₂₃	#121	1	1	yes	characteristic
124	C₂³×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
125	C₂³×C₂₃	#124	1	1	yes	characteristic
126	C₂³×C₂₃	#125	1	1	yes	characteristic
127	C₂×C₄×C₂₃	—	2	4	no	—
128	C₂×C₄×C₂₃	—	4	4	no	—
129	C₂×C₄×C₂₃	—	4	4	no	—
130	C₂×C₄×C₂₃	—	4	4	no	—
131	C₂×C₄×C₂₃	—	4	4	no	—
132	C₂×C₄×C₂₃	—	4	8	no	—
133	C₂×C₄×C₂₃	C₂×C₄²	1	1	yes	characteristic
134	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₂₃	#117	1	1	yes	characteristic
143	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₂₃	C₄×Q₈	1	1	yes	characteristic
147	C₂×C₄×C₂₃	C₄×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₂₃	C₄×Q₈	1	1	yes	characteristic
149	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
150	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
151	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
152	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
153	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
154	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
155	C₂×C₄×C₂₃	#124	1	1	yes	characteristic
156	C₂×C₄×C₂₃	#125	1	1	yes	characteristic
157	C₂×C₄×C₂₃	#127	1	1	yes	characteristic
158	C₂×C₄×C₂₃	C₄⋊Q₈	1	1	yes	characteristic
159	C₂×C₄×C₂₃	C₄⋊Q₈	1	1	yes	characteristic
160	C₂×C₄×C₂₃	C₄⋊Q₈	1	1	yes	characteristic
161	C₈×C₂₃	—	2	4	no	—
162	C₈×C₂₃	—	4	4	no	—
163	C₈×C₂₃	#95	1	4	yes	—
164	C₈×C₂₃	#95	1	4	yes	—
165	C₂²×#108	C₂×C₂₃	1	1	yes	characteristic
166	C₂×#427	C₂×C₂₃	1	1	yes	characteristic
167	C₂²×#97	C₂×C₂₃	1	1	yes	characteristic
168	C₂×#339	C₂×C₂₃	1	2	yes	—
169	#1729	C₂×C₂₃	1	2	yes	—
170	C₂²×C₂₃	—	2	2	no	—
171	C₂²×C₂₃	—	2	2	no	—
172	C₂²×C₂₃	—	2	2	no	—
173	C₂²×C₂₃	—	2	2	no	—
174	C₂²×C₂₃	—	2	2	no	—
175	C₂²×C₂₃	—	2	2	no	—
176	C₂²×C₂₃	C₄×C₄⋊C₄	1	1	yes	characteristic
177	C₂²×C₂₃	#380	1	1	yes	characteristic
178	C₂²×C₂₃	#382	1	1	yes	characteristic
179	C₂²×C₂₃	#389	1	1	yes	characteristic
180	C₂²×C₂₃	#389	1	1	yes	characteristic
181	C₂²×C₂₃	#390	1	1	yes	characteristic
182	C₂²×C₂₃	#391	1	1	yes	characteristic
183	C₂²×C₂₃	#444	1	4	yes	—
184	C₄×C₂₃	—	4	4	no	—
185	C₄×C₂₃	—	8	4	no	—
186	C₄×C₂₃	C₂×#95	1	1	yes	characteristic
187	C₄×C₂₃	C₄×C₄⋊C₄	1	1	yes	characteristic
188	C₄×C₂₃	#380	1	1	yes	characteristic
189	C₄×C₂₃	#384	1	1	yes	characteristic
190	C₄×C₂₃	#389	1	1	yes	characteristic
191	C₄×C₂₃	#389	1	1	yes	characteristic
192	C₄×C₂₃	#390	1	1	yes	characteristic
193	C₄×C₂₃	#391	1	1	yes	characteristic
194	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	—
195	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
196	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
197	C₂×#117	C₂²×C₂₃	1	2	yes	—
198	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
199	C₂×#108	—	2	2	no	—
200	C₂×#108	—	2	2	no	—
201	C₂×#108	C₄×C₂₃	1	4	yes	complemented
202	#427	—	2	2	no	—
203	#427	—	2	2	no	—
204	C₂×#107	C₄×C₂₃	1	2	yes	complemented
205	C₂×#106	C₄×C₂₃	1	2	yes	complemented
206	C₂×#97	—	2	2	no	—
207	C₂×#97	—	2	2	no	—
208	C₂×#97	C₄×C₂₃	1	4	yes	complemented
209	#339	—	2	4	no	—
210	#336	—	2	4	no	—
211	C₂×C₂₃	—	2	1	no	—
212	C₂×C₂₃	—	2	1	no	—
213	C₂×C₂₃	—	2	1	no	—
214	C₂×C₂₃	—	2	1	no	—
215	C₂×C₂₃	C₄⋊#95	1	1	yes	characteristic
216	C₂×C₂₃	#1773	1	2	yes	—
217	C₂×C₂₃	#1946	1	2	yes	—
218	C₂×C₂₃	#1975	1	2	yes	—
219	C₂³×C₄	—	2	1	no	—
220	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
221	C₂×M₁₆	—	2	2	no	—
222	C₂×M₁₆	—	2	2	no	—
223	C₂×M₁₆	—	2	2	no	—
224	C₂×M₁₆	—	2	2	no	—
225	C₂×M₁₆	—	2	2	no	—
226	C₂×M₁₆	C₂×C₄×C₂₃	1	4	yes	—
227	C₂²×C₈	—	2	1	no	—
228	C₂²×C₈	—	2	1	no	—
229	C₂²×C₈	—	2	1	no	—
230	C₂²×C₈	—	2	1	no	—
231	C₂²×C₈	—	2	2	no	—
232	C₂²×C₈	C₂×C₄×C₂₃	1	2	yes	—
233	C₂²×C₈	C₂×C₄×C₂₃	1	2	yes	—
234	C₂²×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
235	C₂²×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
236	C₂²×C₈	C₂×C₄×C₂₃	1	2	yes	—
237	C₂²×C₈	D₄×C₂₃	1	2	yes	—
238	C₂²×C₈	D₄×C₂₃	1	2	yes	—
239	C₂²×C₈	D₄×C₂₃	1	2	yes	—
240	C₂²×C₈	D₄×C₂₃	1	2	yes	—
241	C₂²×C₈	Q₈×C₂₃	1	2	yes	—
242	C₂²×C₈	Q₈×C₂₃	1	2	yes	—
243	#117	—	2	2	no	—
244	#117	—	2	2	no	—
245	#117	—	2	2	no	—
246	#117	—	2	2	no	—
247	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	4	yes	—
248	C₂×C₂²⋊C₄	—	2	2	no	—
249	C₂×C₄²	—	2	1	no	—
250	C₂×C₄²	—	2	1	no	—
251	C₂×C₄²	—	2	1	no	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
254	C₂×C₄²	D₄×C₂₃	1	2	yes	—
255	C₂×C₄²	Q₈×C₂₃	1	2	yes	—
256	#108	—	2	8	no	—
257	#107	—	2	4	no	—
258	#106	—	2	4	no	—
259	#97	—	2	8	no	—
260	C₂₃	#10860	1	1	yes	characteristic, direct product factor, Sylow
261	C₂⁴	#41×C₂₃	1	1	yes	characteristic
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	4	4	no	—
267	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
268	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
269	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
271	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
275	C₂²×C₄	C₂×Q₈×C₂₃	1	1	yes	characteristic
276	C₂²×C₄	C₂×Q₈×C₂₃	1	1	yes	characteristic
277	C₂²×C₄	C₂×Q₈×C₂₃	1	1	yes	characteristic
278	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
279	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
280	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
281	M₁₆	—	2	4	no	—
282	M₁₆	—	2	4	no	—
283	M₁₆	—	4	2	no	—
284	M₁₆	—	4	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	4	no	—
292	C₂×C₈	—	4	2	no	—
293	C₂×C₈	—	4	2	no	—
294	C₂×C₈	C₄²×C₂₃	1	2	yes	—
295	C₂×C₈	C₄²×C₂₃	1	2	yes	—
296	C₂×C₈	C₂²⋊C₄×C₂₃	1	4	yes	—
297	C₂×C₈	C₂²⋊C₄×C₂₃	1	2	yes	—
298	C₂×C₈	C₂²⋊C₄×C₂₃	1	2	yes	—
299	C₂×C₈	C₂²⋊C₄×C₂₃	1	4	yes	—
300	C₂×C₈	C₄⋊C₄×C₂₃	1	4	yes	—
301	C₂×C₈	C₄⋊C₄×C₂₃	1	4	yes	—
302	C₂×C₈	C₄⋊C₄×C₂₃	1	2	yes	—
303	C₂×C₈	C₄⋊C₄×C₂₃	1	2	yes	—
304	C₂×C₈	C₄⋊C₄×C₂₃	1	4	yes	—
305	C₄⋊C₄	—	2	4	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₂²⋊C₄	—	4	2	no	—
308	C₂²⋊C₄	—	4	2	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	4	2	no	—
313	C₄²	—	4	2	no	—
314	C₄²	C₄⋊C₄×C₂₃	1	4	yes	—
315	C₂³	—	2	4	no	—
316	C₂³	C₂₃×#117	1	1	yes	characteristic
317	C₂³	C₄×D₄×C₂₃	1	1	yes	characteristic
318	C₂³	C₄×Q₈×C₂₃	1	1	yes	characteristic
319	C₂³	C₂₃×#121	1	1	yes	characteristic
320	C₂³	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
321	C₂³	C₂₃×#124	1	1	yes	characteristic
322	C₂³	C₂₃×#125	1	1	yes	characteristic
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	8	no	—
329	C₂×C₄	C₂×C₄²×C₂₃	1	1	yes	characteristic
330	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
331	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
332	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
333	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
334	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
335	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
336	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
337	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
338	C₂×C₄	C₂₃×#117	1	1	yes	characteristic
339	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
340	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
341	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
342	C₂×C₄	C₄×Q₈×C₂₃	1	1	yes	characteristic
343	C₂×C₄	C₄×Q₈×C₂₃	1	1	yes	characteristic
344	C₂×C₄	C₄×Q₈×C₂₃	1	1	yes	characteristic
345	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
346	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
347	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
348	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
349	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
350	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
351	C₂×C₄	C₂₃×#124	1	1	yes	characteristic
352	C₂×C₄	C₂₃×#125	1	1	yes	characteristic
353	C₂×C₄	C₂₃×#127	1	1	yes	characteristic
354	C₂×C₄	C₂₃×C₄⋊Q₈	1	1	yes	characteristic
355	C₂×C₄	C₂₃×C₄⋊Q₈	1	1	yes	characteristic
356	C₂×C₄	C₂₃×C₄⋊Q₈	1	1	yes	characteristic
357	C₈	—	2	4	no	—
358	C₈	—	4	4	no	—
359	C₈	C₂₃×#95	1	4	yes	—
360	C₈	C₂₃×#95	1	4	yes	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	C₄×C₄⋊C₄×C₂₃	1	1	yes	characteristic
368	C₂²	C₂₃×#380	1	1	yes	characteristic
369	C₂²	C₂₃×#382	1	1	yes	characteristic
370	C₂²	C₂₃×#389	1	1	yes	characteristic
371	C₂²	C₂₃×#389	1	1	yes	characteristic
372	C₂²	C₂₃×#390	1	1	yes	characteristic
373	C₂²	C₂₃×#391	1	1	yes	characteristic
374	C₂²	C₂₃×#444	1	4	yes	—
375	C₄	—	4	4	no	—
376	C₄	—	8	4	no	—
377	C₄	C₂×C₂₃×#95	1	1	yes	characteristic
378	C₄	C₄×C₄⋊C₄×C₂₃	1	1	yes	characteristic
379	C₄	C₂₃×#380	1	1	yes	characteristic
380	C₄	C₂₃×#384	1	1	yes	characteristic
381	C₄	C₂₃×#389	1	1	yes	characteristic
382	C₄	C₂₃×#389	1	1	yes	characteristic
383	C₄	C₂₃×#390	1	1	yes	characteristic
384	C₄	C₂₃×#391	1	1	yes	characteristic
385	C₂	—	2	1	no	—
386	C₂	—	2	1	no	—
387	C₂	—	2	1	no	—
388	C₂	—	2	1	no	—
389	C₂	C₂₃×C₄⋊#95	1	1	yes	characteristic
390	C₂	C₂₃×#1773	1	2	yes	—
391	C₂	C₂₃×#1946	1	2	yes	—
392	C₂	C₂₃×#1975	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₂₃
Frattini, cosocle	C₂³×C₄	C₂³×C₂₃
socle	C₂³×C₂₃	C₄×D₄
prime radical	C₂⁴×C₂₃	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ C₂³×C₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
13. C₂×C₂₃×#108	C₄	semidirect
16. C₂×C₂₃×#107	C₄	semidirect
17. C₂×C₂₃×#106	C₄	semidirect
20. C₂×C₂₃×#97	C₄	semidirect
118. #10860	C₂₃	direct (N × H)
201. C₂×#108	C₄×C₂₃	semidirect
204. C₂×#107	C₄×C₂₃	semidirect
205. C₂×#106	C₄×C₂₃	semidirect
208. C₂×#97	C₄×C₂₃	semidirect
260. C₂₃	#10860	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×#108	2
C₂×C₂₃×#427	2
C₂²×C₂₃×#97	2
C₂×C₂₃×#339	2
C₂₃×#1729	2
#10860	23

Subgroups — C23×#10860 #19158486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#10860 #19158486