Subgroups — C₂×C₂₃×#2855 #19184246

Order 5888.

3246 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄²×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2855	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#391	C₂	1	2	yes	maximal, complemented
5	C₂×C₂₃×#389	C₂	1	2	yes	maximal, complemented
6	C₂×C₂₃×#387	C₂	1	4	yes	maximal, complemented
7	C₂×C₂₃×#385	C₂	1	2	yes	maximal
8	C₂×C₂₃×#381	C₂	1	2	yes	maximal
9	C₂×C₂₃×#380	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
14	C₂×C₂₃×C₂²⋊Q₈	—	2	8	no	—
15	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	8	yes	—
16	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
20	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
22	C₂²×C₄²×C₂₃	—	2	8	no	—
23	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
24	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
25	C₂²×C₄²×C₂₃	C₂²	1	8	yes	—
26	C₂₃×#391	C₂²	1	16	yes	complemented
27	C₂₃×#389	C₂²	1	16	yes	complemented
28	C₂₃×#387	C₂²	1	32	yes	complemented
29	C₂₃×#385	C₂²	1	16	yes	—
30	C₂₃×#381	C₂²	1	16	yes	—
31	C₂₃×#380	C₂²	1	8	yes	—
32	C₂×C₂₃×#95	C₂²	1	2	yes	—
33	C₂×C₂₃×#95	C₂²	1	4	yes	—
34	C₂×C₂₃×#95	C₂²	1	4	yes	—
35	C₂×C₂₃×#95	C₂²	1	4	yes	—
36	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
37	C₂²×Q₈×C₂₃	—	2	4	no	—
38	C₂²×Q₈×C₂₃	—	2	8	no	—
39	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
40	C₂³×C₄×C₂₃	—	2	4	no	—
41	C₂³×C₄×C₂₃	—	2	4	no	—
42	C₂³×C₄×C₂₃	—	2	4	no	—
43	C₂³×C₄×C₂₃	—	2	8	no	—
44	C₂³×C₄×C₂₃	—	2	8	no	—
45	C₂³×C₄×C₂₃	D₄	1	8	yes	—
46	C₂³×C₄×C₂₃	Q₈	1	8	yes	complemented
47	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
48	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
50	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
51	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
52	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
55	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
56	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
57	C₂₃×C₂²⋊Q₈	—	2	32	no	—
58	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
59	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
60	C₂×C₄⋊C₄×C₂₃	—	2	16	no	—
61	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
62	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
63	C₂×C₄⋊C₄×C₂₃	C₂³	1	16	yes	—
64	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
65	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
66	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
67	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
68	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
69	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
70	C₂×C₄²×C₂₃	—	2	8	no	—
71	C₂×C₄²×C₂₃	—	2	32	no	—
72	C₂×C₄²×C₂₃	—	2	8	no	—
73	C₂×C₄²×C₂₃	C₂³	1	8	yes	—
74	C₂×C₄²×C₂₃	C₂³	1	8	yes	—
75	C₂₃×#95	C₂³	1	8	yes	—
76	C₂₃×#95	C₂³	1	16	yes	—
77	C₂₃×#95	C₂³	1	16	yes	—
78	C₂₃×#95	C₂³	1	16	yes	—
79	C₂⁴×C₂₃	—	2	4	no	—
80	C₂⁴×C₂₃	—	2	4	no	—
81	C₂⁴×C₂₃	C₂×D₄	1	4	yes	—
82	C₂⁴×C₂₃	C₂×Q₈	1	4	yes	—
83	C₂⁴×C₂₃	#41	1	4	yes	—
84	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
85	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
86	C₂×Q₈×C₂₃	—	2	8	no	—
87	C₂×Q₈×C₂₃	—	2	16	no	—
88	C₂×Q₈×C₂₃	—	4	16	no	—
89	C₂²×C₄×C₂₃	—	2	32	no	—
90	C₂²×C₄×C₂₃	—	2	32	no	—
91	C₂²×C₄×C₂₃	—	2	8	no	—
92	C₂²×C₄×C₂₃	—	2	4	no	—
93	C₂²×C₄×C₂₃	—	2	8	no	—
94	C₂²×C₄×C₂₃	—	2	4	no	—
95	C₂²×C₄×C₂₃	—	2	4	no	—
96	C₂²×C₄×C₂₃	—	2	8	no	—
97	C₂²×C₄×C₂₃	—	2	4	no	—
98	C₂²×C₄×C₂₃	—	2	4	no	—
99	C₂²×C₄×C₂₃	—	2	32	no	—
100	C₂²×C₄×C₂₃	—	2	16	no	—
101	C₂²×C₄×C₂₃	—	2	16	no	—
102	C₂²×C₄×C₂₃	—	2	4	no	—
103	C₂²×C₄×C₂₃	—	2	4	no	—
104	C₂²×C₄×C₂₃	—	2	8	no	—
105	C₂²×C₄×C₂₃	—	2	8	no	—
106	C₂²×C₄×C₂₃	—	2	8	no	—
107	C₂²×C₄×C₂₃	—	2	8	no	—
108	C₂²×C₄×C₂₃	—	2	8	no	—
109	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₂₃	C₂×D₄	1	16	yes	—
111	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
112	C₂²×C₄×C₂₃	C₂×Q₈	1	8	yes	—
113	C₂²×C₄×C₂₃	C₂×Q₈	1	16	yes	complemented
114	C₂²×C₄×C₂₃	#41	1	8	yes	—
115	C₂²×C₄×C₂₃	#41	1	8	yes	—
116	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
117	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
118	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
119	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
120	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
121	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
122	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
123	C₄⋊C₄×C₂₃	—	2	8	no	—
124	C₄⋊C₄×C₂₃	—	2	16	no	—
125	C₄⋊C₄×C₂₃	—	2	32	no	—
126	C₄⋊C₄×C₂₃	—	2	16	no	—
127	C₂²⋊C₄×C₂₃	—	2	16	no	—
128	C₂²⋊C₄×C₂₃	—	2	16	no	—
129	C₄²×C₂₃	—	2	16	no	—
130	C₄²×C₂₃	—	2	16	no	—
131	C₂×#2855	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂³×C₂₃	—	2	8	no	—
133	C₂³×C₂₃	—	2	8	no	—
134	C₂³×C₂₃	—	2	16	no	—
135	C₂³×C₂₃	—	2	16	no	—
136	C₂³×C₂₃	—	2	4	no	—
137	C₂³×C₂₃	—	2	4	no	—
138	C₂³×C₂₃	C₂²⋊Q₈	1	16	yes	—
139	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
140	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
141	C₂³×C₂₃	C₂²×Q₈	1	4	yes	—
142	C₂³×C₂₃	C₂²×Q₈	1	2	yes	—
143	C₂³×C₂₃	C₂×#41	1	4	yes	—
144	C₂³×C₂₃	C₂×#41	1	2	yes	—
145	C₂³×C₂₃	C₂×#41	1	4	yes	—
146	C₂³×C₂₃	C₂×#41	1	4	yes	—
147	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
148	Q₈×C₂₃	—	4	16	no	—
149	C₂×C₄×C₂₃	—	2	32	no	—
150	C₂×C₄×C₂₃	—	2	16	no	—
151	C₂×C₄×C₂₃	—	2	32	no	—
152	C₂×C₄×C₂₃	—	2	8	no	—
153	C₂×C₄×C₂₃	—	2	16	no	—
154	C₂×C₄×C₂₃	—	2	4	no	—
155	C₂×C₄×C₂₃	—	2	4	no	—
156	C₂×C₄×C₂₃	—	2	4	no	—
157	C₂×C₄×C₂₃	—	2	4	no	—
158	C₂×C₄×C₂₃	—	2	4	no	—
159	C₂×C₄×C₂₃	—	2	32	no	—
160	C₂×C₄×C₂₃	—	2	4	no	—
161	C₂×C₄×C₂₃	—	2	4	no	—
162	C₂×C₄×C₂₃	—	2	8	no	—
163	C₂×C₄×C₂₃	—	2	8	no	—
164	C₂×C₄×C₂₃	—	2	8	no	—
165	C₂×C₄×C₂₃	—	2	8	no	—
166	C₂×C₄×C₂₃	—	2	8	no	—
167	C₂×C₄×C₂₃	—	4	8	no	—
168	C₂×C₄×C₂₃	—	4	8	no	—
169	C₂×C₄×C₂₃	—	4	16	no	—
170	C₂×C₄×C₂₃	#123	1	16	yes	—
171	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
172	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
173	C₂×C₄×C₂₃	C₂²×Q₈	1	8	yes	—
174	C₂×C₄×C₂₃	C₂×#41	1	8	yes	—
175	C₂×C₄×C₂₃	C₂×#41	1	8	yes	—
176	C₂²×C₂²⋊Q₈	C₂×C₂₃	1	1	yes	characteristic
177	C₂³×C₄²	C₂×C₂₃	1	1	yes	characteristic
178	#2855	C₂×C₂₃	1	16	yes	direct product factor
179	C₂×#391	C₂×C₂₃	1	2	yes	complemented
180	C₂×#389	C₂×C₂₃	1	2	yes	complemented
181	C₂×#387	C₂×C₂₃	1	4	yes	complemented
182	C₂×#385	C₂×C₂₃	1	2	yes	—
183	C₂×#381	C₂×C₂₃	1	2	yes	—
184	C₂×#380	C₂×C₂₃	1	1	yes	characteristic
185	C₂²×C₂₃	—	2	32	no	—
186	C₂²×C₂₃	—	2	4	no	—
187	C₂²×C₂₃	—	2	4	no	—
188	C₂²×C₂₃	—	2	8	no	—
189	C₂²×C₂₃	—	2	8	no	—
190	C₂²×C₂₃	C₂×C₂²⋊Q₈	1	8	yes	—
191	C₂²×C₂₃	C₂×C₂²⋊Q₈	1	4	yes	—
192	C₂²×C₂₃	C₂×#123	1	4	yes	—
193	C₂²×C₂₃	#525	1	4	yes	—
194	C₂²×C₂₃	#529	1	8	yes	—
195	C₂²×C₂₃	#533	1	8	yes	—
196	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
197	C₂²×C₂₃	C₂³×Q₈	1	1	yes	characteristic
198	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
199	C₂²×C₂₃	C₂²×#41	1	2	yes	—
200	C₂²×C₂₃	C₂²×#41	1	2	yes	—
201	C₄×C₂₃	—	2	8	no	—
202	C₄×C₂₃	—	2	4	no	—
203	C₄×C₂₃	—	2	8	no	—
204	C₄×C₂₃	—	4	4	no	—
205	C₄×C₂₃	—	4	4	no	—
206	C₄×C₂₃	—	4	8	no	—
207	C₄×C₂₃	C₂×#123	1	8	yes	—
208	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
209	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
210	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
211	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
212	C₂×C₂²⋊Q₈	—	2	8	no	—
213	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	8	yes	—
214	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
215	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
216	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
217	C₂²×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
218	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
219	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
220	C₂²×C₄²	—	2	8	no	—
221	C₂²×C₄²	C₂²×C₂₃	1	8	yes	—
222	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
223	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
224	#391	C₂²×C₂₃	1	16	yes	complemented
225	#389	C₂²×C₂₃	1	16	yes	complemented
226	#387	C₂²×C₂₃	1	32	yes	complemented
227	#385	C₂²×C₂₃	1	16	yes	—
228	#381	C₂²×C₂₃	1	16	yes	—
229	#380	C₂²×C₂₃	1	8	yes	—
230	C₂×#95	C₂²×C₂₃	1	2	yes	—
231	C₂×#95	C₂²×C₂₃	1	4	yes	—
232	C₂×#95	C₂²×C₂₃	1	4	yes	—
233	C₂×#95	C₂²×C₂₃	1	4	yes	—
234	C₂×C₂₃	—	2	8	no	—
235	C₂×C₂₃	#2855	1	8	yes	direct product factor
236	C₂×C₂₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
237	C₂×C₂₃	C₂²×#123	1	1	yes	characteristic
238	C₂×C₂₃	C₂×#525	1	1	yes	characteristic
239	C₂×C₂₃	C₂×#529	1	2	yes	—
240	C₂×C₂₃	C₂×#533	1	2	yes	—
241	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
242	C₂²×Q₈	—	2	4	no	—
243	C₂²×Q₈	—	2	8	no	—
244	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
245	C₂³×C₄	—	2	4	no	—
246	C₂³×C₄	—	2	4	no	—
247	C₂³×C₄	—	2	4	no	—
248	C₂³×C₄	—	2	8	no	—
249	C₂³×C₄	—	2	8	no	—
250	C₂³×C₄	D₄×C₂₃	1	8	yes	—
251	C₂³×C₄	Q₈×C₂₃	1	8	yes	complemented
252	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
253	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
254	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
255	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
256	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
257	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
258	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
259	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
260	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
261	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
262	C₂²⋊Q₈	—	2	32	no	—
263	C₂×C₄⋊C₄	—	2	4	no	—
264	C₂×C₄⋊C₄	—	2	8	no	—
265	C₂×C₄⋊C₄	—	2	16	no	—
266	C₂×C₄⋊C₄	—	2	8	no	—
267	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
268	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
269	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
270	C₂×C₄⋊C₄	C₂³×C₂₃	1	16	yes	—
271	C₂×C₂²⋊C₄	—	2	8	no	—
272	C₂×C₂²⋊C₄	—	2	8	no	—
273	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
274	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
275	C₂×C₄²	—	2	8	no	—
276	C₂×C₄²	—	2	32	no	—
277	C₂×C₄²	—	2	8	no	—
278	C₂×C₄²	C₂³×C₂₃	1	8	yes	—
279	C₂×C₄²	C₂³×C₂₃	1	8	yes	—
280	#95	C₂³×C₂₃	1	8	yes	—
281	#95	C₂³×C₂₃	1	16	yes	—
282	#95	C₂³×C₂₃	1	16	yes	—
283	#95	C₂³×C₂₃	1	16	yes	—
284	C₂₃	C₂×#2855	1	1	yes	characteristic, direct product factor, Sylow
285	C₂⁴	—	2	4	no	—
286	C₂⁴	—	2	4	no	—
287	C₂⁴	C₂×D₄×C₂₃	1	4	yes	—
288	C₂⁴	C₂×Q₈×C₂₃	1	4	yes	—
289	C₂⁴	#41×C₂₃	1	4	yes	—
290	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
291	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
292	C₂×Q₈	—	2	8	no	—
293	C₂×Q₈	—	2	16	no	—
294	C₂×Q₈	—	4	16	no	—
295	C₂²×C₄	—	2	32	no	—
296	C₂²×C₄	—	2	32	no	—
297	C₂²×C₄	—	2	8	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	8	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	8	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	32	no	—
306	C₂²×C₄	—	2	16	no	—
307	C₂²×C₄	—	2	16	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	8	no	—
311	C₂²×C₄	—	2	8	no	—
312	C₂²×C₄	—	2	8	no	—
313	C₂²×C₄	—	2	8	no	—
314	C₂²×C₄	—	2	8	no	—
315	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
316	C₂²×C₄	C₂×D₄×C₂₃	1	16	yes	—
317	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
318	C₂²×C₄	C₂×Q₈×C₂₃	1	8	yes	—
319	C₂²×C₄	C₂×Q₈×C₂₃	1	16	yes	complemented
320	C₂²×C₄	#41×C₂₃	1	8	yes	—
321	C₂²×C₄	#41×C₂₃	1	8	yes	—
322	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
323	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
324	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
325	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
326	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
327	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
328	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
329	C₄⋊C₄	—	2	8	no	—
330	C₄⋊C₄	—	2	16	no	—
331	C₄⋊C₄	—	2	32	no	—
332	C₄⋊C₄	—	2	16	no	—
333	C₂²⋊C₄	—	2	16	no	—
334	C₂²⋊C₄	—	2	16	no	—
335	C₄²	—	2	16	no	—
336	C₄²	—	2	16	no	—
337	C₂³	—	2	4	no	—
338	C₂³	—	2	4	no	—
339	C₂³	—	2	8	no	—
340	C₂³	—	2	8	no	—
341	C₂³	—	2	16	no	—
342	C₂³	—	2	16	no	—
343	C₂³	C₂₃×C₂²⋊Q₈	1	16	yes	—
344	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
345	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
346	C₂³	C₂²×Q₈×C₂₃	1	4	yes	—
347	C₂³	C₂²×Q₈×C₂₃	1	2	yes	—
348	C₂³	C₂×#41×C₂₃	1	4	yes	—
349	C₂³	C₂×#41×C₂₃	1	2	yes	—
350	C₂³	C₂×#41×C₂₃	1	4	yes	—
351	C₂³	C₂×#41×C₂₃	1	4	yes	—
352	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
353	Q₈	—	4	16	no	—
354	C₂×C₄	—	2	32	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	16	no	—
361	C₂×C₄	—	2	32	no	—
362	C₂×C₄	—	2	8	no	—
363	C₂×C₄	—	2	16	no	—
364	C₂×C₄	—	2	32	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	8	no	—
368	C₂×C₄	—	2	8	no	—
369	C₂×C₄	—	2	8	no	—
370	C₂×C₄	—	2	8	no	—
371	C₂×C₄	—	2	8	no	—
372	C₂×C₄	—	4	8	no	—
373	C₂×C₄	—	4	8	no	—
374	C₂×C₄	—	4	16	no	—
375	C₂×C₄	C₂₃×#123	1	16	yes	—
376	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
377	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
378	C₂×C₄	C₂²×Q₈×C₂₃	1	8	yes	—
379	C₂×C₄	C₂×#41×C₂₃	1	8	yes	—
380	C₂×C₄	C₂×#41×C₂₃	1	8	yes	—
381	C₂²	—	2	4	no	—
382	C₂²	—	2	4	no	—
383	C₂²	—	2	8	no	—
384	C₂²	—	2	8	no	—
385	C₂²	—	2	32	no	—
386	C₂²	C₂×C₂₃×C₂²⋊Q₈	1	8	yes	—
387	C₂²	C₂×C₂₃×C₂²⋊Q₈	1	4	yes	—
388	C₂²	C₂×C₂₃×#123	1	4	yes	—
389	C₂²	C₂₃×#525	1	4	yes	—
390	C₂²	C₂₃×#529	1	8	yes	—
391	C₂²	C₂₃×#533	1	8	yes	—
392	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
393	C₂²	C₂³×Q₈×C₂₃	1	1	yes	characteristic
394	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
395	C₂²	C₂²×#41×C₂₃	1	2	yes	—
396	C₂²	C₂²×#41×C₂₃	1	2	yes	—
397	C₄	—	2	8	no	—
398	C₄	—	2	4	no	—
399	C₄	—	2	8	no	—
400	C₄	—	4	4	no	—
401	C₄	—	4	4	no	—
402	C₄	—	4	8	no	—
403	C₄	C₂×C₂₃×#123	1	8	yes	—
404	C₂	—	2	8	no	—
405	C₂	C₂₃×#2855	1	8	yes	direct product factor
406	C₂	C₂²×C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
407	C₂	C₂²×C₂₃×#123	1	1	yes	characteristic
408	C₂	C₂×C₂₃×#525	1	1	yes	characteristic
409	C₂	C₂×C₂₃×#529	1	2	yes	—
410	C₂	C₂×C₂₃×#533	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂⁵×C₂₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂₃×#2855	C₂	direct (N × H)
4. C₂×C₂₃×#391	C₂	semidirect
5. C₂×C₂₃×#389	C₂	semidirect
6. C₂×C₂₃×#387	C₂	semidirect
26. C₂₃×#391	C₂²	semidirect
27. C₂₃×#389	C₂²	semidirect
28. C₂₃×#387	C₂²	semidirect
46. C₂³×C₄×C₂₃	Q₈	semidirect
113. C₂²×C₄×C₂₃	C₂×Q₈	semidirect
131. C₂×#2855	C₂₃	direct (N × H)
178. #2855	C₂×C₂₃	direct (N × H)
179. C₂×#391	C₂×C₂₃	semidirect
180. C₂×#389	C₂×C₂₃	semidirect
181. C₂×#387	C₂×C₂₃	semidirect
224. #391	C₂²×C₂₃	semidirect
225. #389	C₂²×C₂₃	semidirect
226. #387	C₂²×C₂₃	semidirect
235. C₂×C₂₃	#2855	direct (N × H)
251. C₂³×C₄	Q₈×C₂₃	semidirect
284. C₂₃	C₂×#2855	direct (N × H)
319. C₂²×C₄	C₂×Q₈×C₂₃	semidirect
405. C₂	C₂₃×#2855	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×C₂²⋊Q₈	2
C₂³×C₄²×C₂₃	2
C₂₃×#2855	2
C₂×C₂₃×#391	2
C₂×C₂₃×#389	2
C₂×C₂₃×#387	2
C₂×C₂₃×#385	2
C₂×C₂₃×#381	2
C₂×C₂₃×#380	2
C₂×#2855	23

Subgroups — C2×C23×#2855 #19184246

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#2855 #19184246