Subgroups — C₂×C₂₃×#3338 #19208855

Order 5888.

1942 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#554	C₂	1	2	yes	maximal
2	C₂₃×#3338	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₂₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#484	C₂	1	4	yes	maximal, complemented
5	C₂×C₂₃×#477	C₂	1	2	yes	maximal, complemented
6	C₂×C₂₃×#467	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×Q₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₈×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₂₃×#107	C₂	1	2	yes	maximal, complemented
10	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₂₃	C₂²	1	2	yes	—
12	C₂₃×#554	—	2	8	no	—
13	C₂₃×#554	C₂²	1	16	yes	—
14	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₂₃×#125	—	2	2	no	—
16	C₂×C₂₃×C₂²⋊Q₈	—	2	4	no	—
17	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	—
18	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₂₃	—	2	2	no	—
20	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
22	C₂₃×#500	C₂²	1	8	yes	complemented
23	C₂₃×#484	C₂²	1	32	yes	complemented
24	C₂₃×#477	C₂²	1	16	yes	complemented
25	C₂₃×#467	C₂²	1	16	yes	complemented
26	C₄×Q₁₆×C₂₃	C₂²	1	8	yes	complemented
27	C₈×D₄×C₂₃	C₂²	1	8	yes	—
28	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#107	C₂²	1	2	yes	—
30	C₂×C₂₃×#107	C₂²	1	4	yes	—
31	C₂×C₂₃×#107	C₂²	1	2	yes	—
32	C₂×C₂₃×#107	C₂²	1	16	yes	complemented
33	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#103	C₂²	1	2	yes	—
35	C₂×C₂₃×#103	C₂²	1	4	yes	—
36	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
37	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
38	C₂²×Q₈×C₂₃	—	2	2	no	—
39	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
40	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₂₃	—	2	4	no	—
42	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
43	C₂×Q₁₆×C₂₃	—	2	4	no	—
44	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
45	C₂²×C₈×C₂₃	—	2	8	no	—
46	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₂₃	C₂³	1	8	yes	—
48	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
50	C₂₃×C₄⋊Q₈	—	2	4	no	—
51	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	—
52	C₂₃×#125	—	2	16	no	—
53	C₂₃×C₂²⋊Q₈	—	2	8	no	—
54	C₂₃×C₂²⋊Q₈	—	2	32	no	—
55	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
56	C₄×Q₈×C₂₃	—	2	4	no	—
57	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
58	C₄×D₄×C₂₃	—	2	16	no	—
59	C₄×D₄×C₂₃	D₄	1	4	yes	—
60	C₄×D₄×C₂₃	C₂³	1	4	yes	—
61	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
62	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
63	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
64	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
65	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
66	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₂₃	C₂³	1	16	yes	—
68	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
70	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
71	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
72	C₂×C₄²×C₂₃	—	2	2	no	—
73	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
74	C₂₃×#107	C₂³	1	4	yes	—
75	C₂₃×#107	C₂³	1	8	yes	—
76	C₂₃×#107	C₂³	1	16	yes	—
77	C₂₃×#107	C₂³	1	8	yes	—
78	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
79	C₂₃×#103	C₂³	1	8	yes	—
80	C₂₃×#103	C₂³	1	16	yes	—
81	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	—
82	C₄×C₈×C₂₃	C₂³	1	4	yes	—
83	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
84	C₂×Q₈×C₂₃	—	2	2	no	—
85	C₂×Q₈×C₂₃	—	2	8	no	—
86	C₂×Q₈×C₂₃	—	2	4	no	—
87	C₂×Q₈×C₂₃	—	2	4	no	—
88	C₂×Q₈×C₂₃	—	8	4	no	—
89	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
90	C₂×D₄×C₂₃	Q₁₆	1	8	yes	complemented
91	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
92	C₂²×C₄×C₂₃	—	2	4	no	—
93	C₂²×C₄×C₂₃	—	2	4	no	—
94	C₂²×C₄×C₂₃	—	2	2	no	—
95	C₂²×C₄×C₂₃	—	2	2	no	—
96	C₂²×C₄×C₂₃	—	2	4	no	—
97	C₂²×C₄×C₂₃	—	2	16	no	—
98	C₂²×C₄×C₂₃	—	8	8	no	—
99	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
104	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
105	Q₁₆×C₂₃	—	2	8	no	—
106	C₂×C₈×C₂₃	—	2	4	no	—
107	C₂×C₈×C₂₃	—	2	2	no	—
108	C₂×C₈×C₂₃	—	2	16	no	—
109	C₂×C₈×C₂₃	#41	1	4	yes	—
110	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
111	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
112	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
113	C₄⋊C₄×C₂₃	—	2	2	no	—
114	C₄⋊C₄×C₂₃	—	2	16	no	—
115	C₄⋊C₄×C₂₃	—	2	4	no	—
116	C₄⋊C₄×C₂₃	—	2	8	no	—
117	C₄⋊C₄×C₂₃	—	2	8	no	—
118	C₄⋊C₄×C₂₃	—	2	16	no	—
119	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
120	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
121	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
122	C₂²⋊C₄×C₂₃	—	2	16	no	—
123	C₂²⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
124	C₄²×C₂₃	—	2	8	no	—
125	C₄²×C₂₃	C₂×D₄	1	2	yes	—
126	C₄²×C₂₃	C₂⁴	1	2	yes	—
127	C₂×#3338	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂³×C₂₃	—	2	4	no	—
129	C₂³×C₂₃	—	2	4	no	—
130	C₂³×C₂₃	C₂×Q₁₆	1	8	yes	—
131	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
132	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
133	Q₈×C₂₃	—	2	4	no	—
134	Q₈×C₂₃	—	2	4	no	—
135	Q₈×C₂₃	—	4	4	no	—
136	Q₈×C₂₃	—	8	8	no	—
137	D₄×C₂₃	C₂×Q₁₆	1	16	yes	complemented
138	C₂×C₄×C₂₃	—	2	4	no	—
139	C₂×C₄×C₂₃	—	2	2	no	—
140	C₂×C₄×C₂₃	—	2	8	no	—
141	C₂×C₄×C₂₃	—	2	4	no	—
142	C₂×C₄×C₂₃	—	2	4	no	—
143	C₂×C₄×C₂₃	—	2	4	no	—
144	C₂×C₄×C₂₃	—	2	4	no	—
145	C₂×C₄×C₂₃	—	2	8	no	—
146	C₂×C₄×C₂₃	—	4	4	no	—
147	C₂×C₄×C₂₃	—	4	4	no	—
148	C₂×C₄×C₂₃	—	4	8	no	—
149	C₂×C₄×C₂₃	—	8	16	no	—
150	C₂×C₄×C₂₃	C₂×Q₁₆	1	4	yes	—
151	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
152	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
153	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
155	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
156	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
157	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
158	C₈×C₂₃	—	2	4	no	—
159	C₈×C₂₃	—	2	2	no	—
160	C₈×C₂₃	C₂×#41	1	4	yes	—
161	C₂×#554	C₂×C₂₃	1	2	yes	—
162	#3338	C₂×C₂₃	1	16	yes	direct product factor
163	C₂×#500	C₂×C₂₃	1	1	yes	characteristic, complemented
164	C₂×#484	C₂×C₂₃	1	4	yes	complemented
165	C₂×#477	C₂×C₂₃	1	2	yes	complemented
166	C₂×#467	C₂×C₂₃	1	2	yes	complemented
167	C₂×C₄×Q₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
168	C₂×C₈×D₄	C₂×C₂₃	1	1	yes	characteristic
169	C₂²×#107	C₂×C₂₃	1	2	yes	complemented
170	C₂²×C₂₃	—	2	16	no	—
171	C₂²×C₂₃	—	2	4	no	—
172	C₂²×C₂₃	—	2	4	no	—
173	C₂²×C₂₃	#547	1	2	yes	—
174	C₂²×C₂₃	C₂²×Q₁₆	1	8	yes	—
175	C₂²×C₂₃	C₂²×Q₁₆	1	2	yes	—
176	C₂²×C₂₃	#576	1	2	yes	—
177	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
178	C₄×C₂₃	—	2	4	no	—
179	C₄×C₂₃	—	2	2	no	—
180	C₄×C₂₃	—	4	4	no	—
181	C₄×C₂₃	—	4	4	no	—
182	C₄×C₂₃	—	4	8	no	—
183	C₄×C₂₃	#547	1	2	yes	—
184	C₄×C₂₃	C₂²×Q₁₆	1	4	yes	—
185	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
186	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
187	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
188	C₂³×C₈	C₂²×C₂₃	1	2	yes	—
189	#554	—	2	8	no	—
190	#554	C₂²×C₂₃	1	16	yes	—
191	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
192	C₂×#125	—	2	2	no	—
193	C₂×C₂²⋊Q₈	—	2	4	no	—
194	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
195	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
196	C₂×C₄×D₄	—	2	2	no	—
197	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
198	C₂²×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
199	#500	C₂²×C₂₃	1	8	yes	complemented
200	#484	C₂²×C₂₃	1	32	yes	complemented
201	#477	C₂²×C₂₃	1	16	yes	complemented
202	#467	C₂²×C₂₃	1	16	yes	complemented
203	C₄×Q₁₆	C₂²×C₂₃	1	8	yes	complemented
204	C₈×D₄	C₂²×C₂₃	1	8	yes	—
205	C₂×#107	C₂²×C₂₃	1	4	yes	—
206	C₂×#107	C₂²×C₂₃	1	2	yes	—
207	C₂×#107	C₂²×C₂₃	1	2	yes	—
208	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
209	C₂×#107	C₂²×C₂₃	1	16	yes	complemented
210	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
211	C₂×#103	C₂²×C₂₃	1	4	yes	—
212	C₂×#103	C₂²×C₂₃	1	2	yes	—
213	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
214	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
215	C₂×C₂₃	—	2	8	no	—
216	C₂×C₂₃	#3338	1	4	yes	direct product factor
217	C₂×C₂₃	C₂×#547	1	1	yes	characteristic
218	C₂×C₂₃	C₂³×Q₁₆	1	1	yes	characteristic
219	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
220	C₂²×Q₈	—	2	2	no	—
221	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
222	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
223	C₂³×C₄	—	2	4	no	—
224	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
225	C₂×Q₁₆	—	2	4	no	—
226	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
227	C₂²×C₈	—	2	8	no	—
228	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
229	C₂²×C₈	C₂³×C₂₃	1	8	yes	—
230	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
231	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
232	C₄⋊Q₈	—	2	4	no	—
233	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	—
234	#125	—	2	16	no	—
235	C₂²⋊Q₈	—	2	8	no	—
236	C₂²⋊Q₈	—	2	32	no	—
237	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
238	C₄×Q₈	—	2	4	no	—
239	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
240	C₄×D₄	—	2	16	no	—
241	C₄×D₄	D₄×C₂₃	1	4	yes	—
242	C₄×D₄	C₂³×C₂₃	1	4	yes	—
243	C₂×C₄⋊C₄	—	2	4	no	—
244	C₂×C₄⋊C₄	—	2	8	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	4	no	—
248	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
250	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
251	C₂×C₄⋊C₄	C₂³×C₂₃	1	16	yes	—
252	C₂×C₂²⋊C₄	—	2	4	no	—
253	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
254	C₂×C₄²	—	2	2	no	—
255	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
256	#107	C₂³×C₂₃	1	4	yes	—
257	#107	C₂³×C₂₃	1	8	yes	—
258	#107	C₂³×C₂₃	1	16	yes	—
259	#107	C₂³×C₂₃	1	8	yes	—
260	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
261	#103	C₂³×C₂₃	1	8	yes	—
262	#103	C₂³×C₂₃	1	16	yes	—
263	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	—
264	C₄×C₈	C₂³×C₂₃	1	4	yes	—
265	C₂₃	C₂×#3338	1	1	yes	characteristic, direct product factor, Sylow
266	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
267	C₂×Q₈	—	2	2	no	—
268	C₂×Q₈	—	2	8	no	—
269	C₂×Q₈	—	2	4	no	—
270	C₂×Q₈	—	2	4	no	—
271	C₂×Q₈	—	8	4	no	—
272	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
273	C₂×D₄	Q₁₆×C₂₃	1	8	yes	complemented
274	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	16	no	—
281	C₂²×C₄	—	8	8	no	—
282	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
284	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
285	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
286	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
287	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
288	Q₁₆	—	2	8	no	—
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	16	no	—
292	C₂×C₈	#41×C₂₃	1	4	yes	—
293	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
294	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
295	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	16	no	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	—	2	8	no	—
300	C₄⋊C₄	—	2	8	no	—
301	C₄⋊C₄	—	2	16	no	—
302	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
303	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
304	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
305	C₂²⋊C₄	—	2	16	no	—
306	C₂²⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
307	C₄²	—	2	8	no	—
308	C₄²	C₂×D₄×C₂₃	1	2	yes	—
309	C₄²	C₂⁴×C₂₃	1	2	yes	—
310	C₂³	—	2	4	no	—
311	C₂³	—	2	4	no	—
312	C₂³	C₂×Q₁₆×C₂₃	1	8	yes	—
313	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
314	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
315	Q₈	—	2	4	no	—
316	Q₈	—	2	4	no	—
317	Q₈	—	4	4	no	—
318	Q₈	—	8	8	no	—
319	D₄	C₂×Q₁₆×C₂₃	1	16	yes	complemented
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	8	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	8	no	—
331	C₂×C₄	—	8	16	no	—
332	C₂×C₄	C₂×Q₁₆×C₂₃	1	4	yes	—
333	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
334	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
335	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
336	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
337	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
338	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
339	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
340	C₈	—	2	4	no	—
341	C₈	—	2	2	no	—
342	C₈	C₂×#41×C₂₃	1	4	yes	—
343	C₂²	—	2	4	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	2	16	no	—
346	C₂²	C₂₃×#547	1	2	yes	—
347	C₂²	C₂²×Q₁₆×C₂₃	1	8	yes	—
348	C₂²	C₂²×Q₁₆×C₂₃	1	2	yes	—
349	C₂²	C₂₃×#576	1	2	yes	—
350	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
351	C₄	—	2	4	no	—
352	C₄	—	2	2	no	—
353	C₄	—	4	4	no	—
354	C₄	—	4	4	no	—
355	C₄	—	4	8	no	—
356	C₄	C₂₃×#547	1	2	yes	—
357	C₄	C₂²×Q₁₆×C₂₃	1	4	yes	—
358	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
359	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
360	C₂	—	2	8	no	—
361	C₂	C₂₃×#3338	1	4	yes	direct product factor
362	C₂	C₂×C₂₃×#547	1	1	yes	characteristic
363	C₂	C₂³×Q₁₆×C₂₃	1	1	yes	characteristic
364	C₂	C₂×C₂₃×#576	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂₃×#3338	C₂	direct (N × H)
3. C₂×C₂₃×#500	C₂	semidirect
4. C₂×C₂₃×#484	C₂	semidirect
5. C₂×C₂₃×#477	C₂	semidirect
6. C₂×C₂₃×#467	C₂	semidirect
7. C₂×C₄×Q₁₆×C₂₃	C₂	semidirect
9. C₂²×C₂₃×#107	C₂	semidirect
22. C₂₃×#500	C₂²	semidirect
23. C₂₃×#484	C₂²	semidirect
24. C₂₃×#477	C₂²	semidirect
25. C₂₃×#467	C₂²	semidirect
26. C₄×Q₁₆×C₂₃	C₂²	semidirect
32. C₂×C₂₃×#107	C₂²	semidirect
90. C₂×D₄×C₂₃	Q₁₆	semidirect
127. C₂×#3338	C₂₃	direct (N × H)
137. D₄×C₂₃	C₂×Q₁₆	semidirect
162. #3338	C₂×C₂₃	direct (N × H)
163. C₂×#500	C₂×C₂₃	semidirect
164. C₂×#484	C₂×C₂₃	semidirect
165. C₂×#477	C₂×C₂₃	semidirect
166. C₂×#467	C₂×C₂₃	semidirect
167. C₂×C₄×Q₁₆	C₂×C₂₃	semidirect
169. C₂²×#107	C₂×C₂₃	semidirect
199. #500	C₂²×C₂₃	semidirect
200. #484	C₂²×C₂₃	semidirect
201. #477	C₂²×C₂₃	semidirect
202. #467	C₂²×C₂₃	semidirect
203. C₄×Q₁₆	C₂²×C₂₃	semidirect
209. C₂×#107	C₂²×C₂₃	semidirect
216. C₂×C₂₃	#3338	direct (N × H)
265. C₂₃	C₂×#3338	direct (N × H)
273. C₂×D₄	Q₁₆×C₂₃	semidirect
319. D₄	C₂×Q₁₆×C₂₃	semidirect
361. C₂	C₂₃×#3338	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×#554	2
C₂₃×#3338	2
C₂×C₂₃×#500	2
C₂×C₂₃×#484	2
C₂×C₂₃×#477	2
C₂×C₂₃×#467	2
C₂×C₄×Q₁₆×C₂₃	2
C₂×C₈×D₄×C₂₃	2
C₂²×C₂₃×#107	2
C₂×#3338	23

Subgroups — C2×C23×#3338 #19208855

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3338 #19208855