Subgroups — C₂₃×#2674 #15670293

Order 2944.

562 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#124	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×#123	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#399	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#396	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#395	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#394	C₂	1	1	yes	maximal, characteristic
10	C₂₃×#393	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#388	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#388	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#387	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₈×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×Q₈×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×D₄×C₂₃	C₂²	1	1	yes	characteristic
19	C₂³×C₄×C₂₃	C₂²	1	1	yes	characteristic
20	C₂₃×C₄⋊Q₈	—	2	4	no	—
21	C₂₃×#124	—	2	4	no	—
22	C₂₃×#123	—	2	4	no	—
23	C₂₃×C₂²⋊Q₈	—	2	4	no	—
24	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
45	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
46	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
47	C₂₃×#95	C₂²	1	1	yes	characteristic
48	C₂₃×#95	C₂²	1	1	yes	characteristic
49	C₂₃×#95	C₂²	1	1	yes	characteristic
50	C₂₃×#95	C₂²	1	1	yes	characteristic
51	C₂₃×#95	C₂²	1	1	yes	characteristic
52	C₂₃×#95	C₂²	1	1	yes	characteristic
53	C₂₃×#95	C₂²	1	1	yes	characteristic
54	C₂₃×#95	C₂²	1	1	yes	characteristic
55	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
56	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
57	C₂×Q₈×C₂₃	—	2	2	no	—
58	C₂×Q₈×C₂₃	—	2	2	no	—
59	C₂×Q₈×C₂₃	—	2	2	no	—
60	C₂×Q₈×C₂₃	—	2	2	no	—
61	C₂×Q₈×C₂₃	—	4	1	no	—
62	C₂×Q₈×C₂₃	—	4	1	no	—
63	C₂×D₄×C₂₃	—	2	2	no	—
64	C₂×D₄×C₂₃	—	2	2	no	—
65	C₂×D₄×C₂₃	—	4	1	no	—
66	C₂²×C₄×C₂₃	—	2	2	no	—
67	C₂²×C₄×C₂₃	—	2	2	no	—
68	C₂²×C₄×C₂₃	—	4	1	no	—
69	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
82	C₄⋊C₄×C₂₃	—	2	2	no	—
83	C₄⋊C₄×C₂₃	—	2	2	no	—
84	C₄⋊C₄×C₂₃	—	2	2	no	—
85	C₄⋊C₄×C₂₃	—	2	2	no	—
86	C₄⋊C₄×C₂₃	—	2	2	no	—
87	C₄⋊C₄×C₂₃	—	2	2	no	—
88	C₄⋊C₄×C₂₃	—	2	2	no	—
89	C₄⋊C₄×C₂₃	—	2	2	no	—
90	C₄⋊C₄×C₂₃	—	4	1	no	—
91	C₄⋊C₄×C₂₃	D₄	1	4	yes	—
92	C₂²⋊C₄×C₂₃	—	2	2	no	—
93	C₂²⋊C₄×C₂₃	—	2	2	no	—
94	C₂²⋊C₄×C₂₃	—	2	2	no	—
95	C₂²⋊C₄×C₂₃	—	2	2	no	—
96	C₂²⋊C₄×C₂₃	—	2	2	no	—
97	C₂²⋊C₄×C₂₃	—	2	2	no	—
98	C₂²⋊C₄×C₂₃	—	2	2	no	—
99	C₂²⋊C₄×C₂₃	—	2	2	no	—
100	C₂²⋊C₄×C₂₃	—	2	2	no	—
101	C₂²⋊C₄×C₂₃	—	4	1	no	—
102	C₂²⋊C₄×C₂₃	D₄	1	4	yes	—
103	C₄²×C₂₃	—	2	2	no	—
104	C₄²×C₂₃	—	2	2	no	—
105	C₂³×C₂₃	—	2	1	no	—
106	C₂³×C₂₃	—	2	1	no	—
107	C₂³×C₂₃	—	2	1	no	—
108	C₂³×C₂₃	—	2	1	no	—
109	C₂³×C₂₃	—	2	1	no	—
110	C₂³×C₂₃	—	2	1	no	—
111	C₂³×C₂₃	—	2	1	no	—
112	C₂³×C₂₃	—	2	1	no	—
113	C₂³×C₂₃	—	2	1	no	—
114	C₂³×C₂₃	—	2	1	no	—
115	C₂³×C₂₃	—	2	1	no	—
116	C₂³×C₂₃	—	2	1	no	—
117	C₂³×C₂₃	—	2	1	no	—
118	C₂³×C₂₃	C₂×D₄	1	2	yes	—
119	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
120	Q₈×C₂₃	—	4	4	no	—
121	Q₈×C₂₃	—	4	4	no	—
122	D₄×C₂₃	—	4	4	no	—
123	C₂×C₄×C₂₃	—	2	1	no	—
124	C₂×C₄×C₂₃	—	2	1	no	—
125	C₂×C₄×C₂₃	—	2	1	no	—
126	C₂×C₄×C₂₃	—	2	1	no	—
127	C₂×C₄×C₂₃	—	2	1	no	—
128	C₂×C₄×C₂₃	—	2	1	no	—
129	C₂×C₄×C₂₃	—	2	1	no	—
130	C₂×C₄×C₂₃	—	2	1	no	—
131	C₂×C₄×C₂₃	—	2	1	no	—
132	C₂×C₄×C₂₃	—	2	1	no	—
133	C₂×C₄×C₂₃	—	2	1	no	—
134	C₂×C₄×C₂₃	—	2	1	no	—
135	C₂×C₄×C₂₃	—	2	1	no	—
136	C₂×C₄×C₂₃	—	2	1	no	—
137	C₂×C₄×C₂₃	—	2	1	no	—
138	C₂×C₄×C₂₃	—	2	1	no	—
139	C₂×C₄×C₂₃	—	2	1	no	—
140	C₂×C₄×C₂₃	—	2	1	no	—
141	C₂×C₄×C₂₃	—	2	1	no	—
142	C₂×C₄×C₂₃	—	2	1	no	—
143	C₂×C₄×C₂₃	—	2	1	no	—
144	C₂×C₄×C₂₃	—	2	1	no	—
145	C₂×C₄×C₂₃	—	2	1	no	—
146	C₂×C₄×C₂₃	—	2	1	no	—
147	C₂×C₄×C₂₃	—	2	1	no	—
148	C₂×C₄×C₂₃	—	2	1	no	—
149	C₂×C₄×C₂₃	—	2	1	no	—
150	C₂×C₄×C₂₃	—	2	1	no	—
151	C₂×C₄×C₂₃	—	2	1	no	—
152	C₂×C₄×C₂₃	—	2	1	no	—
153	C₂×C₄×C₂₃	—	2	1	no	—
154	C₂×C₄×C₂₃	—	2	1	no	—
155	C₂×C₄×C₂₃	—	2	1	no	—
156	C₂×C₄×C₂₃	—	4	4	no	—
157	C₂×C₄×C₂₃	C₂×D₄	1	2	yes	—
158	C₂×C₄×C₂₃	C₂×D₄	1	2	yes	—
159	C₂×C₄×C₂₃	C₂×D₄	1	2	yes	—
160	C₂×C₄×C₂₃	C₂×D₄	1	2	yes	—
161	C₂×C₄×C₂₃	C₂×D₄	1	2	yes	—
162	C₂×C₄×C₂₃	#41	1	2	yes	—
163	#2674	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂²×C₂₃	—	2	2	no	—
165	C₂²×C₂₃	—	2	2	no	—
166	C₂²×C₂₃	—	2	2	no	—
167	C₂²×C₂₃	—	4	1	no	—
168	C₂²×C₂₃	—	4	1	no	—
169	C₂²×C₂₃	—	4	1	no	—
170	C₂²×C₂₃	—	4	1	no	—
171	C₂²×C₂₃	—	4	1	no	—
172	C₂²×C₂₃	—	4	1	no	—
173	C₂²×C₂₃	—	4	1	no	—
174	C₂²×C₂₃	—	4	1	no	—
175	C₂²×C₂₃	—	4	1	no	—
176	C₂²×C₂₃	—	4	1	no	—
177	C₂²×C₂₃	—	4	1	no	—
178	C₂²×C₂₃	C₂²×D₄	1	1	yes	characteristic
179	C₂²×C₂₃	C₂²×D₄	1	1	yes	characteristic
180	C₂²×C₂₃	C₂×#41	1	1	yes	characteristic
181	C₂²×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
182	C₂²×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
183	C₂²×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
184	C₂²×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
185	C₄×C₂₃	—	2	2	no	—
186	C₄×C₂₃	—	2	2	no	—
187	C₄×C₂₃	—	2	2	no	—
188	C₄×C₂₃	—	2	2	no	—
189	C₄×C₂₃	—	2	2	no	—
190	C₄×C₂₃	—	2	2	no	—
191	C₄×C₂₃	—	4	1	no	—
192	C₄×C₂₃	—	4	1	no	—
193	C₄×C₂₃	—	4	1	no	—
194	C₄×C₂₃	—	4	1	no	—
195	C₄×C₂₃	—	4	1	no	—
196	C₄×C₂₃	—	4	1	no	—
197	C₄×C₂₃	—	4	1	no	—
198	C₂×C₄⋊Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
199	C₂×#124	C₂×C₂₃	1	1	yes	characteristic
200	C₂×#123	C₂×C₂₃	1	1	yes	characteristic
201	C₂×C₂²⋊Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
202	#399	C₂×C₂₃	1	1	yes	characteristic, complemented
203	#397	C₂×C₂₃	1	1	yes	characteristic, complemented
204	#396	C₂×C₂₃	1	1	yes	characteristic, complemented
205	#395	C₂×C₂₃	1	1	yes	characteristic, complemented
206	#394	C₂×C₂₃	1	1	yes	characteristic
207	#393	C₂×C₂₃	1	1	yes	characteristic, complemented
208	#389	C₂×C₂₃	1	1	yes	characteristic, complemented
209	#388	C₂×C₂₃	1	1	yes	characteristic, complemented
210	#388	C₂×C₂₃	1	1	yes	characteristic, complemented
211	#387	C₂×C₂₃	1	1	yes	characteristic, complemented
212	#385	C₂×C₂₃	1	1	yes	characteristic, complemented
213	C₂×C₂₃	—	4	2	no	—
214	C₂×C₂₃	—	8	1	no	—
215	C₂×C₂₃	#536	1	1	yes	characteristic
216	C₂×C₂₃	#536	1	1	yes	characteristic
217	C₂×C₂₃	#542	1	1	yes	characteristic
218	C₂×C₂₃	D₄²	1	1	yes	characteristic
219	C₂×C₂₃	#547	1	1	yes	characteristic
220	C₂×C₂₃	#548	1	1	yes	characteristic
221	C₂×C₂₃	#563	1	1	yes	characteristic
222	C₂²×Q₈	C₂²×C₂₃	1	1	yes	characteristic
223	C₂²×Q₈	C₂²×C₂₃	1	1	yes	characteristic
224	C₂²×D₄	C₂²×C₂₃	1	1	yes	characteristic
225	C₂³×C₄	C₂²×C₂₃	1	1	yes	characteristic
226	C₄⋊Q₈	—	2	4	no	—
227	#124	—	2	4	no	—
228	#123	—	2	4	no	—
229	C₂²⋊Q₈	—	2	4	no	—
230	C₂×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
231	C₂×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
232	C₂×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
236	C₂×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
239	C₂×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
240	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
241	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
242	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
243	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
244	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
245	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
246	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
247	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
248	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
250	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
251	C₂×C₄²	C₂²×C₂₃	1	1	yes	characteristic
252	C₂×C₄²	C₂²×C₂₃	1	1	yes	characteristic
253	#95	C₂²×C₂₃	1	1	yes	characteristic
254	#95	C₂²×C₂₃	1	1	yes	characteristic
255	#95	C₂²×C₂₃	1	1	yes	characteristic
256	#95	C₂²×C₂₃	1	1	yes	characteristic
257	#95	C₂²×C₂₃	1	1	yes	characteristic
258	#95	C₂²×C₂₃	1	1	yes	characteristic
259	#95	C₂²×C₂₃	1	1	yes	characteristic
260	#95	C₂²×C₂₃	1	1	yes	characteristic
261	C₂₃	#2674	1	1	yes	characteristic, direct product factor, Sylow
262	C₂⁴	C₂³×C₂₃	1	1	yes	characteristic
263	C₂⁴	C₂³×C₂₃	1	1	yes	characteristic
264	C₂×Q₈	—	2	2	no	—
265	C₂×Q₈	—	2	2	no	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	2	2	no	—
268	C₂×Q₈	—	4	1	no	—
269	C₂×Q₈	—	4	1	no	—
270	C₂×D₄	—	2	2	no	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	4	1	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	4	1	no	—
276	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
277	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
278	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
279	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
280	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
281	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
282	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
283	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
284	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
285	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
286	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
287	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
288	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	4	1	no	—
298	C₄⋊C₄	D₄×C₂₃	1	4	yes	—
299	C₂²⋊C₄	—	2	2	no	—
300	C₂²⋊C₄	—	2	2	no	—
301	C₂²⋊C₄	—	2	2	no	—
302	C₂²⋊C₄	—	2	2	no	—
303	C₂²⋊C₄	—	2	2	no	—
304	C₂²⋊C₄	—	2	2	no	—
305	C₂²⋊C₄	—	2	2	no	—
306	C₂²⋊C₄	—	2	2	no	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₂²⋊C₄	—	4	1	no	—
309	C₂²⋊C₄	D₄×C₂₃	1	4	yes	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₂³	—	2	1	no	—
313	C₂³	—	2	1	no	—
314	C₂³	—	2	1	no	—
315	C₂³	—	2	1	no	—
316	C₂³	—	2	1	no	—
317	C₂³	—	2	1	no	—
318	C₂³	—	2	1	no	—
319	C₂³	—	2	1	no	—
320	C₂³	—	2	1	no	—
321	C₂³	—	2	1	no	—
322	C₂³	—	2	1	no	—
323	C₂³	—	2	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	C₂×D₄×C₂₃	1	2	yes	—
326	C₂³	C₂⁴×C₂₃	1	1	yes	characteristic
327	Q₈	—	4	4	no	—
328	Q₈	—	4	4	no	—
329	D₄	—	4	4	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	C₂×D₄×C₂₃	1	2	yes	—
365	C₂×C₄	C₂×D₄×C₂₃	1	2	yes	—
366	C₂×C₄	C₂×D₄×C₂₃	1	2	yes	—
367	C₂×C₄	C₂×D₄×C₂₃	1	2	yes	—
368	C₂×C₄	C₂×D₄×C₂₃	1	2	yes	—
369	C₂×C₄	#41×C₂₃	1	2	yes	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	2	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	4	1	no	—
374	C₂²	—	4	1	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	1	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	4	1	no	—
380	C₂²	—	4	1	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	1	no	—
384	C₂²	C₂²×D₄×C₂₃	1	1	yes	characteristic
385	C₂²	C₂²×D₄×C₂₃	1	1	yes	characteristic
386	C₂²	C₂×#41×C₂₃	1	1	yes	characteristic
387	C₂²	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
388	C₂²	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
389	C₂²	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
390	C₂²	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
391	C₄	—	2	2	no	—
392	C₄	—	2	2	no	—
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	2	2	no	—
397	C₄	—	4	1	no	—
398	C₄	—	4	1	no	—
399	C₄	—	4	1	no	—
400	C₄	—	4	1	no	—
401	C₄	—	4	1	no	—
402	C₄	—	4	1	no	—
403	C₄	—	4	1	no	—
404	C₂	—	4	2	no	—
405	C₂	—	8	1	no	—
406	C₂	C₂₃×#536	1	1	yes	characteristic
407	C₂	C₂₃×#536	1	1	yes	characteristic
408	C₂	C₂₃×#542	1	1	yes	characteristic
409	C₂	D₄²×C₂₃	1	1	yes	characteristic
410	C₂	C₂₃×#547	1	1	yes	characteristic
411	C₂	C₂₃×#548	1	1	yes	characteristic
412	C₂	C₂₃×#563	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₃
prime radical	C₂²×D₄×C₂₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×C₄⋊Q₈	C₂	semidirect
4. C₂×C₂₃×C₂²⋊Q₈	C₂	semidirect
5. C₂₃×#399	C₂	semidirect
6. C₂₃×#397	C₂	semidirect
7. C₂₃×#396	C₂	semidirect
8. C₂₃×#395	C₂	semidirect
10. C₂₃×#393	C₂	semidirect
11. C₂₃×#389	C₂	semidirect
12. C₂₃×#388	C₂	semidirect
13. C₂₃×#388	C₂	semidirect
14. C₂₃×#387	C₂	semidirect
15. C₂₃×#385	C₂	semidirect
163. #2674	C₂₃	direct (N × H)
198. C₂×C₄⋊Q₈	C₂×C₂₃	semidirect
201. C₂×C₂²⋊Q₈	C₂×C₂₃	semidirect
202. #399	C₂×C₂₃	semidirect
203. #397	C₂×C₂₃	semidirect
204. #396	C₂×C₂₃	semidirect
205. #395	C₂×C₂₃	semidirect
207. #393	C₂×C₂₃	semidirect
208. #389	C₂×C₂₃	semidirect
209. #388	C₂×C₂₃	semidirect
210. #388	C₂×C₂₃	semidirect
211. #387	C₂×C₂₃	semidirect
212. #385	C₂×C₂₃	semidirect
261. C₂₃	#2674	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×C₄⋊Q₈	2
C₂×C₂₃×#124	2
C₂×C₂₃×#123	2
C₂×C₂₃×C₂²⋊Q₈	2
C₂₃×#399	2
C₂₃×#397	2
C₂₃×#396	2
C₂₃×#395	2
C₂₃×#394	2
C₂₃×#393	2
C₂₃×#389	2
C₂₃×#388	2
C₂₃×#387	2
C₂₃×#385	2
#2674	23

Subgroups — C23×#2674 #15670293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#2674 #15670293