Subgroups — C₂₃×#61828 #19209454

Order 5888.

1914 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3497	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3386	C₂	1	8	yes	maximal, complemented
4	C₂₃×#3368	C₂	1	8	yes	maximal, complemented
5	C₂₃×#3234	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3226	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3112	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3103	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2983	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₃×2₋¹⁺⁴	—	2	1	no	—
11	C₂₃×#557	—	2	4	no	—
12	C₂₃×#557	C₂²	1	8	yes	—
13	C₂₃×#550	C₂²	1	4	yes	—
14	D₄×Q₈×C₂₃	C₂²	1	4	yes	—
15	C₂₃×#548	—	2	4	no	—
16	C₂₃×#537	—	2	1	no	—
17	C₂₃×#537	—	2	2	no	—
18	C₂₃×#532	C₂²	1	2	yes	—
19	C₂₃×#532	C₂²	1	4	yes	—
20	C₂×C₂₃×C₄⋊Q₈	—	2	1	no	—
21	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#125	—	2	2	no	—
23	C₂×C₂₃×#125	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
25	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
28	C₂₃×#501	C₂²	1	8	yes	—
29	C₂₃×#500	C₂²	1	4	yes	—
30	C₂₃×#490	C₂²	1	8	yes	—
31	C₂₃×#486	C₂²	1	4	yes	—
32	C₂₃×#481	C₂²	1	4	yes	—
33	C₂₃×#480	C₂²	1	8	yes	—
34	C₂₃×#478	C₂²	1	16	yes	—
35	C₂₃×#477	C₂²	1	8	yes	—
36	C₂₃×#475	C₂²	1	4	yes	—
37	C₂₃×#474	C₂²	1	8	yes	—
38	C₂₃×#460	C₂²	1	4	yes	—
39	C₂₃×#460	C₂²	1	8	yes	—
40	C₂₃×#448	C₂²	1	4	yes	—
41	C₂₃×#446	C₂²	1	8	yes	—
42	C₂₃×#440	C₂²	1	16	yes	—
43	C₄×SD₁₆×C₂₃	C₂²	1	8	yes	—
44	C₂₃×#432	C₂²	1	4	yes	—
45	C₂₃×#431	C₂²	1	2	yes	—
46	C₂₃×2₋¹⁺⁴	—	4	8	no	—
47	C₂×#41×C₂₃	—	2	4	no	—
48	C₂×#41×C₂₃	—	2	4	no	—
49	C₂×#41×C₂₃	—	2	2	no	—
50	C₂²×Q₈×C₂₃	—	2	4	no	—
51	C₂²×Q₈×C₂₃	—	2	1	no	—
52	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
53	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
54	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	—
55	C₂₃×C₄⋊Q₈	—	2	8	no	—
56	C₂₃×C₄⋊Q₈	—	2	2	no	—
57	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
59	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
60	C₂₃×#127	C₂³	1	2	yes	—
61	C₂₃×#127	C₂³	1	4	yes	—
62	C₂₃×#125	—	2	16	no	—
63	C₂₃×#125	—	2	4	no	—
64	C₂₃×#125	C₂³	1	8	yes	—
65	C₂₃×#124	—	2	4	no	—
66	C₂₃×#124	—	2	2	no	—
67	C₂₃×C₂²⋊Q₈	—	2	4	no	—
68	C₂₃×C₂²⋊Q₈	—	2	8	no	—
69	C₂₃×#121	—	2	4	no	—
70	C₂₃×#121	—	2	2	no	—
71	C₂₃×#121	—	2	4	no	—
72	C₂₃×#121	—	2	8	no	—
73	C₂₃×#121	C₂³	1	4	yes	—
74	C₄×Q₈×C₂₃	—	2	8	no	—
75	C₄×Q₈×C₂₃	—	2	4	no	—
76	C₄×Q₈×C₂₃	—	2	2	no	—
77	C₄×Q₈×C₂₃	D₄	1	4	yes	—
78	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
79	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
80	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
81	C₄×D₄×C₂₃	—	2	4	no	—
82	C₄×D₄×C₂₃	—	2	2	no	—
83	C₄×D₄×C₂₃	C₂³	1	4	yes	—
84	C₄×D₄×C₂₃	C₂³	1	8	yes	—
85	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
86	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
87	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
88	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
89	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
90	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
92	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₂₃	—	2	2	no	—
95	C₂×C₄²×C₂₃	—	2	1	no	—
96	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
98	C₂₃×#107	C₂³	1	16	yes	—
99	C₂₃×#106	C₂³	1	8	yes	—
100	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
101	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
102	C₂₃×#103	C₂³	1	8	yes	—
103	C₂₃×#102	C₂³	1	8	yes	—
104	C₂₃×#102	C₂³	1	16	yes	—
105	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
106	C₂₃×#97	C₂³	1	8	yes	—
107	C₄×C₈×C₂₃	C₂³	1	4	yes	—
108	#41×C₂₃	—	4	16	no	—
109	#41×C₂₃	—	4	16	no	—
110	#41×C₂₃	—	4	8	no	—
111	C₂×Q₈×C₂₃	—	2	4	no	—
112	C₂×Q₈×C₂₃	—	2	4	no	—
113	C₂×Q₈×C₂₃	—	2	1	no	—
114	C₂×Q₈×C₂₃	—	2	4	no	—
115	C₂×Q₈×C₂₃	—	2	4	no	—
116	C₂×Q₈×C₂₃	—	2	2	no	—
117	C₂×Q₈×C₂₃	—	4	16	no	—
118	C₂×Q₈×C₂₃	—	4	4	no	—
119	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	—
120	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
121	C₂×D₄×C₂₃	—	2	4	no	—
122	C₂×D₄×C₂₃	—	2	4	no	—
123	C₂×D₄×C₂₃	—	2	2	no	—
124	C₂×D₄×C₂₃	—	2	4	no	—
125	C₂×D₄×C₂₃	—	2	2	no	—
126	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
127	C₂²×C₄×C₂₃	—	2	1	no	—
128	C₂²×C₄×C₂₃	—	2	1	no	—
129	C₂²×C₄×C₂₃	—	2	2	no	—
130	C₂²×C₄×C₂₃	—	2	8	no	—
131	C₂²×C₄×C₂₃	—	2	4	no	—
132	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
137	SD₁₆×C₂₃	—	2	16	no	—
138	C₂×C₈×C₂₃	C₂⁴	1	8	yes	—
139	C₄⋊C₄×C₂₃	—	2	8	no	—
140	C₄⋊C₄×C₂₃	—	2	4	no	—
141	C₄⋊C₄×C₂₃	—	2	8	no	—
142	C₄⋊C₄×C₂₃	—	2	4	no	—
143	C₄⋊C₄×C₂₃	—	2	8	no	—
144	C₄⋊C₄×C₂₃	—	2	1	no	—
145	C₄⋊C₄×C₂₃	—	2	2	no	—
146	C₄⋊C₄×C₂₃	—	2	4	no	—
147	C₄⋊C₄×C₂₃	—	2	2	no	—
148	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
149	C₄⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
150	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
151	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
152	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
153	C₂²⋊C₄×C₂₃	—	2	4	no	—
154	C₂²⋊C₄×C₂₃	—	2	8	no	—
155	C₂²⋊C₄×C₂₃	—	2	4	no	—
156	C₄²×C₂₃	—	2	8	no	—
157	C₄²×C₂₃	—	2	4	no	—
158	C₄²×C₂₃	C₂×D₄	1	4	yes	—
159	C₄²×C₂₃	C₂×D₄	1	2	yes	—
160	C₄²×C₂₃	C₂⁴	1	4	yes	—
161	C₄²×C₂₃	C₂⁴	1	2	yes	—
162	#61828	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂³×C₂₃	—	2	4	no	—
164	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₂₃	—	2	4	no	—
166	Q₈×C₂₃	—	2	8	no	—
167	Q₈×C₂₃	—	2	2	no	—
168	Q₈×C₂₃	—	4	8	no	—
169	Q₈×C₂₃	—	4	8	no	—
170	Q₈×C₂₃	—	4	4	no	—
171	Q₈×C₂₃	2₋¹⁺⁴	1	4	yes	complemented
172	D₄×C₂₃	—	2	8	no	—
173	D₄×C₂₃	—	4	8	no	—
174	D₄×C₂₃	—	4	8	no	—
175	D₄×C₂₃	—	4	4	no	—
176	D₄×C₂₃	—	8	4	no	—
177	D₄×C₂₃	—	8	2	no	—
178	C₂×C₄×C₂₃	—	2	4	no	—
179	C₂×C₄×C₂₃	—	2	4	no	—
180	C₂×C₄×C₂₃	—	2	2	no	—
181	C₂×C₄×C₂₃	—	2	2	no	—
182	C₂×C₄×C₂₃	—	2	2	no	—
183	C₂×C₄×C₂₃	—	2	4	no	—
184	C₂×C₄×C₂₃	—	2	4	no	—
185	C₂×C₄×C₂₃	—	4	2	no	—
186	C₂×C₄×C₂₃	—	4	1	no	—
187	C₂×C₄×C₂₃	—	4	16	no	—
188	C₂×C₄×C₂₃	—	4	2	no	—
189	C₂×C₄×C₂₃	—	4	4	no	—
190	C₂×C₄×C₂₃	—	4	8	no	—
191	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	4	yes	—
192	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
193	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
195	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
196	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
198	C₈×C₂₃	—	2	8	no	—
199	#3497	C₂×C₂₃	1	1	yes	characteristic
200	C₂×#557	C₂×C₂₃	1	1	yes	characteristic, complemented
201	#3386	C₂×C₂₃	1	8	yes	complemented
202	#3368	C₂×C₂₃	1	8	yes	complemented
203	#3234	C₂×C₂₃	1	4	yes	complemented
204	#3226	C₂×C₂₃	1	2	yes	complemented
205	#3112	C₂×C₂₃	1	4	yes	complemented
206	#3103	C₂×C₂₃	1	2	yes	complemented
207	#2983	C₂×C₂₃	1	1	yes	characteristic, complemented
208	C₂²×C₂₃	—	2	1	no	—
209	C₂²×C₂₃	—	2	1	no	—
210	C₂²×C₂₃	—	4	4	no	—
211	C₂²×C₂₃	—	4	4	no	—
212	C₂²×C₂₃	—	4	4	no	—
213	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
214	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
215	C₄×C₂₃	—	2	4	no	—
216	C₄×C₂₃	—	2	2	no	—
217	C₄×C₂₃	—	2	4	no	—
218	C₄×C₂₃	—	2	1	no	—
219	C₄×C₂₃	—	2	4	no	—
220	C₄×C₂₃	—	4	2	no	—
221	C₄×C₂₃	—	4	4	no	—
222	C₄×C₂₃	—	4	4	no	—
223	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
224	C₄×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
225	C₂×2₋¹⁺⁴	—	2	1	no	—
226	#557	—	2	4	no	—
227	#557	C₂²×C₂₃	1	8	yes	—
228	#550	C₂²×C₂₃	1	4	yes	—
229	D₄×Q₈	C₂²×C₂₃	1	4	yes	—
230	#548	—	2	4	no	—
231	#537	—	2	1	no	—
232	#537	—	2	2	no	—
233	#532	C₂²×C₂₃	1	2	yes	—
234	#532	C₂²×C₂₃	1	4	yes	—
235	C₂×C₄⋊Q₈	—	2	1	no	—
236	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
237	C₂×#125	—	2	2	no	—
238	C₂×#125	C₂²×C₂₃	1	2	yes	—
239	C₂×C₄×Q₈	—	2	1	no	—
240	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
241	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
242	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
243	#501	C₂²×C₂₃	1	8	yes	—
244	#500	C₂²×C₂₃	1	4	yes	—
245	#490	C₂²×C₂₃	1	8	yes	—
246	#486	C₂²×C₂₃	1	4	yes	—
247	#481	C₂²×C₂₃	1	4	yes	—
248	#480	C₂²×C₂₃	1	8	yes	—
249	#478	C₂²×C₂₃	1	16	yes	—
250	#477	C₂²×C₂₃	1	8	yes	—
251	#475	C₂²×C₂₃	1	4	yes	—
252	#474	C₂²×C₂₃	1	8	yes	—
253	#460	C₂²×C₂₃	1	4	yes	—
254	#460	C₂²×C₂₃	1	8	yes	—
255	#448	C₂²×C₂₃	1	4	yes	—
256	#446	C₂²×C₂₃	1	8	yes	—
257	#440	C₂²×C₂₃	1	16	yes	—
258	C₄×SD₁₆	C₂²×C₂₃	1	8	yes	—
259	#432	C₂²×C₂₃	1	4	yes	—
260	#431	C₂²×C₂₃	1	2	yes	—
261	C₂×C₂₃	—	2	2	no	—
262	C₂×C₂₃	—	8	4	no	—
263	C₂×C₂₃	#3486	1	1	yes	characteristic
264	C₂×C₂₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
265	C₂×C₂₃	#3586	1	1	yes	characteristic
266	2₋¹⁺⁴	—	4	8	no	—
267	C₂×#41	—	2	4	no	—
268	C₂×#41	—	2	4	no	—
269	C₂×#41	—	2	2	no	—
270	C₂²×Q₈	—	2	4	no	—
271	C₂²×Q₈	—	2	1	no	—
272	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
273	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
274	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	—
275	C₄⋊Q₈	—	2	8	no	—
276	C₄⋊Q₈	—	2	2	no	—
277	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
278	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
279	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
280	#127	C₂³×C₂₃	1	2	yes	—
281	#127	C₂³×C₂₃	1	4	yes	—
282	#125	—	2	16	no	—
283	#125	—	2	4	no	—
284	#125	C₂³×C₂₃	1	8	yes	—
285	#124	—	2	4	no	—
286	#124	—	2	2	no	—
287	C₂²⋊Q₈	—	2	4	no	—
288	C₂²⋊Q₈	—	2	8	no	—
289	#121	—	2	4	no	—
290	#121	—	2	2	no	—
291	#121	—	2	4	no	—
292	#121	—	2	8	no	—
293	#121	C₂³×C₂₃	1	4	yes	—
294	C₄×Q₈	—	2	8	no	—
295	C₄×Q₈	—	2	4	no	—
296	C₄×Q₈	—	2	2	no	—
297	C₄×Q₈	D₄×C₂₃	1	4	yes	—
298	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
299	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
300	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
301	C₄×D₄	—	2	4	no	—
302	C₄×D₄	—	2	2	no	—
303	C₄×D₄	C₂³×C₂₃	1	4	yes	—
304	C₄×D₄	C₂³×C₂₃	1	8	yes	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
311	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
312	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
314	C₂×C₄²	—	2	2	no	—
315	C₂×C₄²	—	2	1	no	—
316	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
317	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
318	#107	C₂³×C₂₃	1	16	yes	—
319	#106	C₂³×C₂₃	1	8	yes	—
320	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
321	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
322	#103	C₂³×C₂₃	1	8	yes	—
323	#102	C₂³×C₂₃	1	8	yes	—
324	#102	C₂³×C₂₃	1	16	yes	—
325	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
326	#97	C₂³×C₂₃	1	8	yes	—
327	C₄×C₈	C₂³×C₂₃	1	4	yes	—
328	C₂₃	#61828	1	1	yes	characteristic, direct product factor, Sylow
329	#41	—	4	16	no	—
330	#41	—	4	16	no	—
331	#41	—	4	8	no	—
332	C₂×Q₈	—	2	4	no	—
333	C₂×Q₈	—	2	4	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	4	no	—
336	C₂×Q₈	—	2	4	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	4	16	no	—
339	C₂×Q₈	—	4	4	no	—
340	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	—
341	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	4	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	8	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
354	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
355	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
357	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
358	SD₁₆	—	2	16	no	—
359	C₂×C₈	C₂⁴×C₂₃	1	8	yes	—
360	C₄⋊C₄	—	2	8	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	8	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	8	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
370	C₄⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
371	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
372	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
373	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	2	8	no	—
376	C₂²⋊C₄	—	2	4	no	—
377	C₄²	—	2	8	no	—
378	C₄²	—	2	4	no	—
379	C₄²	C₂×D₄×C₂₃	1	4	yes	—
380	C₄²	C₂×D₄×C₂₃	1	2	yes	—
381	C₄²	C₂⁴×C₂₃	1	2	yes	—
382	C₄²	C₂⁴×C₂₃	1	4	yes	—
383	C₂³	—	2	4	no	—
384	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
385	Q₈	—	2	4	no	—
386	Q₈	—	2	8	no	—
387	Q₈	—	2	2	no	—
388	Q₈	—	4	8	no	—
389	Q₈	—	4	4	no	—
390	Q₈	—	4	8	no	—
391	Q₈	C₂₃×2₋¹⁺⁴	1	4	yes	complemented
392	D₄	—	2	8	no	—
393	D₄	—	4	8	no	—
394	D₄	—	4	8	no	—
395	D₄	—	4	4	no	—
396	D₄	—	8	4	no	—
397	D₄	—	8	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	16	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	4	8	no	—
411	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	4	yes	—
412	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
413	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
414	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
415	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
416	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
417	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
418	C₈	—	2	8	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	4	4	no	—
422	C₂²	—	4	4	no	—
423	C₂²	—	4	4	no	—
424	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
425	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
426	C₄	—	2	4	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	4	no	—
429	C₄	—	2	4	no	—
430	C₄	—	2	2	no	—
431	C₄	—	4	4	no	—
432	C₄	—	4	4	no	—
433	C₄	—	4	2	no	—
434	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	4	yes	—
435	C₄	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
436	C₂	—	2	2	no	—
437	C₂	—	8	4	no	—
438	C₂	C₂₃×#3486	1	1	yes	characteristic
439	C₂	C₂²×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
440	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3497	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄×Q₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#557	C₂	semidirect
3. C₂₃×#3386	C₂	semidirect
4. C₂₃×#3368	C₂	semidirect
5. C₂₃×#3234	C₂	semidirect
6. C₂₃×#3226	C₂	semidirect
7. C₂₃×#3112	C₂	semidirect
8. C₂₃×#3103	C₂	semidirect
9. C₂₃×#2983	C₂	semidirect
162. #61828	C₂₃	direct (N × H)
171. Q₈×C₂₃	2₋¹⁺⁴	semidirect
200. C₂×#557	C₂×C₂₃	semidirect
201. #3386	C₂×C₂₃	semidirect
202. #3368	C₂×C₂₃	semidirect
203. #3234	C₂×C₂₃	semidirect
204. #3226	C₂×C₂₃	semidirect
205. #3112	C₂×C₂₃	semidirect
206. #3103	C₂×C₂₃	semidirect
207. #2983	C₂×C₂₃	semidirect
328. C₂₃	#61828	direct (N × H)
391. Q₈	C₂₃×2₋¹⁺⁴	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3497	2
C₂×C₂₃×#557	2
C₂₃×#3386	2
C₂₃×#3368	2
C₂₃×#3234	2
C₂₃×#3226	2
C₂₃×#3112	2
C₂₃×#3103	2
C₂₃×#2983	2
#61828	23

Subgroups — C23×#61828 #19209454

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61828 #19209454