Subgroups — C₂×C₂₃×#3344 #19208862

Order 5888.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 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	1	yes	maximal, characteristic
2	C₂×C₂₃×#552	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3344	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#501	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#484	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#485	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#483	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#483	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#470	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#435	C₂	1	1	yes	maximal, characteristic
15	C₂×C₂₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₂₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
20	C₂₃×#554	—	2	4	no	—
21	C₂₃×#554	C₂²	1	8	yes	—
22	C₂₃×#552	—	2	4	no	—
23	C₂₃×#552	C₂²	1	8	yes	—
24	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#126	—	2	1	no	—
26	C₂×C₂₃×#125	—	2	1	no	—
27	C₂×C₂₃×#125	—	2	1	no	—
28	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#123	—	2	1	no	—
30	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
31	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
32	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₂₃	—	2	1	no	—
39	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#117	—	2	1	no	—
41	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
42	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
43	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
45	C₂₃×#501	C₂²	1	8	yes	complemented
46	C₂₃×#485	C₂²	1	8	yes	complemented
47	C₂₃×#484	C₂²	1	8	yes	complemented
48	C₂₃×#483	C₂²	1	8	yes	complemented
49	C₂₃×#483	C₂²	1	8	yes	complemented
50	C₂₃×#479	C₂²	1	8	yes	complemented
51	C₂₃×#475	C₂²	1	8	yes	complemented
52	C₂₃×#470	C₂²	1	8	yes	complemented
53	C₂₃×#467	C₂²	1	8	yes	complemented
54	C₂₃×#441	C₂²	1	8	yes	complemented
55	C₂₃×#435	C₂²	1	8	yes	—
56	C₂₃×#428	C₂²	1	8	yes	complemented
57	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
58	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
59	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
60	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
61	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
62	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
63	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
64	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
65	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
66	C₂×C₂₃×#106	C₂²	1	8	yes	complemented
67	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
69	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
70	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
71	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
72	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
73	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
74	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
76	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
77	C₂²×Q₈×C₂₃	—	2	1	no	—
78	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
81	C₂³×C₄×C₂₃	—	2	1	no	—
82	C₂³×C₄×C₂₃	—	2	1	no	—
83	C₂³×C₄×C₂₃	—	2	1	no	—
84	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
86	C₂×Q₁₆×C₂₃	—	2	4	no	—
87	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
88	C₂×M₁₆×C₂₃	—	2	4	no	—
89	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
90	C₂²×C₈×C₂₃	—	2	4	no	—
91	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
93	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
96	C₂₃×C₄⋊Q₈	—	2	2	no	—
97	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
98	C₂₃×#126	—	2	8	no	—
99	C₂₃×#125	—	2	8	no	—
100	C₂₃×#125	—	2	8	no	—
101	C₂₃×#125	—	2	2	no	—
102	C₂₃×#125	C₂³	1	4	yes	—
103	C₂₃×#123	—	2	8	no	—
104	C₂₃×C₂²⋊Q₈	—	2	2	no	—
105	C₂₃×C₂²⋊Q₈	—	2	2	no	—
106	C₂₃×C₂²⋊Q₈	—	2	2	no	—
107	C₂₃×C₂²⋊Q₈	—	2	2	no	—
108	C₂₃×C₂²⋊Q₈	—	2	8	no	—
109	C₂₃×C₂²⋊Q₈	—	2	8	no	—
110	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
111	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
112	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
113	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
114	C₄×Q₈×C₂₃	—	2	2	no	—
115	C₄×Q₈×C₂₃	—	2	2	no	—
116	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
117	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
118	C₄×D₄×C₂₃	—	2	8	no	—
119	C₄×D₄×C₂₃	D₄	1	4	yes	—
120	C₄×D₄×C₂₃	C₂³	1	4	yes	—
121	C₂₃×#117	—	2	2	no	—
122	C₂₃×#117	—	2	8	no	—
123	C₂₃×#117	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
125	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
126	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
127	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
128	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
129	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
130	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
131	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
132	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
133	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
134	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
135	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
136	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
137	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
138	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
139	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
141	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
142	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
143	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
150	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
151	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
152	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
153	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
154	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
155	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
156	C₂×C₄²×C₂₃	—	2	1	no	—
157	C₂×C₄²×C₂₃	—	2	1	no	—
158	C₂×C₄²×C₂₃	—	2	1	no	—
159	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
160	C₂₃×#107	C₂³	1	4	yes	—
161	C₂₃×#107	C₂³	1	4	yes	—
162	C₂₃×#107	C₂³	1	4	yes	—
163	C₂₃×#106	C₂³	1	4	yes	—
164	C₂₃×#106	C₂³	1	4	yes	—
165	C₂₃×#106	C₂³	1	4	yes	—
166	C₂₃×#106	C₂³	1	4	yes	—
167	C₂₃×#106	C₂³	1	4	yes	—
168	C₂₃×#106	C₂³	1	4	yes	—
169	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
170	C₂₃×#103	C₂³	1	4	yes	—
171	C₂₃×#103	C₂³	1	4	yes	—
172	C₂₃×#103	C₂³	1	4	yes	—
173	C₂₃×#103	C₂³	1	4	yes	—
174	C₂₃×#103	C₂³	1	4	yes	—
175	C₂₃×#103	C₂³	1	4	yes	—
176	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
177	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
178	C₂₃×#97	C₂³	1	4	yes	—
179	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
180	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
181	C₂×Q₈×C₂₃	—	2	1	no	—
182	C₂×Q₈×C₂₃	—	2	1	no	—
183	C₂×Q₈×C₂₃	—	2	4	no	—
184	C₂×Q₈×C₂₃	—	2	2	no	—
185	C₂×Q₈×C₂₃	—	2	2	no	—
186	C₂×Q₈×C₂₃	—	2	2	no	—
187	C₂×Q₈×C₂₃	—	2	2	no	—
188	C₂×Q₈×C₂₃	—	8	2	no	—
189	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
190	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
191	C₂×D₄×C₂₃	—	2	4	no	—
192	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
193	C₂²×C₄×C₂₃	—	2	2	no	—
194	C₂²×C₄×C₂₃	—	2	2	no	—
195	C₂²×C₄×C₂₃	—	2	2	no	—
196	C₂²×C₄×C₂₃	—	2	2	no	—
197	C₂²×C₄×C₂₃	—	2	4	no	—
198	C₂²×C₄×C₂₃	—	2	1	no	—
199	C₂²×C₄×C₂₃	—	2	1	no	—
200	C₂²×C₄×C₂₃	—	2	1	no	—
201	C₂²×C₄×C₂₃	—	2	1	no	—
202	C₂²×C₄×C₂₃	—	2	1	no	—
203	C₂²×C₄×C₂₃	—	2	1	no	—
204	C₂²×C₄×C₂₃	—	2	1	no	—
205	C₂²×C₄×C₂₃	—	2	1	no	—
206	C₂²×C₄×C₂₃	—	2	4	no	—
207	C₂²×C₄×C₂₃	—	2	4	no	—
208	C₂²×C₄×C₂₃	—	4	4	no	—
209	C₂²×C₄×C₂₃	—	8	2	no	—
210	C₂²×C₄×C₂₃	—	8	2	no	—
211	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
212	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
213	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
220	Q₁₆×C₂₃	—	2	8	no	—
221	M₁₆×C₂₃	—	2	8	no	—
222	C₂×C₈×C₂₃	—	2	2	no	—
223	C₂×C₈×C₂₃	—	2	2	no	—
224	C₂×C₈×C₂₃	—	2	2	no	—
225	C₂×C₈×C₂₃	—	2	8	no	—
226	C₂×C₈×C₂₃	#41	1	4	yes	—
227	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
228	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
229	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
230	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
231	C₄⋊C₄×C₂₃	—	2	1	no	—
232	C₄⋊C₄×C₂₃	—	2	1	no	—
233	C₄⋊C₄×C₂₃	—	2	4	no	—
234	C₄⋊C₄×C₂₃	—	2	4	no	—
235	C₄⋊C₄×C₂₃	—	2	1	no	—
236	C₄⋊C₄×C₂₃	—	2	1	no	—
237	C₄⋊C₄×C₂₃	—	2	1	no	—
238	C₄⋊C₄×C₂₃	—	2	4	no	—
239	C₄⋊C₄×C₂₃	—	2	4	no	—
240	C₄⋊C₄×C₂₃	—	2	4	no	—
241	C₄⋊C₄×C₂₃	—	2	4	no	—
242	C₄⋊C₄×C₂₃	—	2	4	no	—
243	C₄⋊C₄×C₂₃	—	2	4	no	—
244	C₄⋊C₄×C₂₃	—	2	4	no	—
245	C₄⋊C₄×C₂₃	—	2	4	no	—
246	C₄⋊C₄×C₂₃	—	2	4	no	—
247	C₄⋊C₄×C₂₃	—	2	4	no	—
248	C₄⋊C₄×C₂₃	—	2	1	no	—
249	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
250	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
251	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
252	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
253	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
254	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
255	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
256	C₂²⋊C₄×C₂₃	—	2	4	no	—
257	C₂²⋊C₄×C₂₃	—	2	4	no	—
258	C₂²⋊C₄×C₂₃	—	2	4	no	—
259	C₂²⋊C₄×C₂₃	—	2	4	no	—
260	C₂²⋊C₄×C₂₃	—	2	4	no	—
261	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
262	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
263	C₄²×C₂₃	—	2	4	no	—
264	C₄²×C₂₃	—	2	4	no	—
265	C₄²×C₂₃	—	2	4	no	—
266	C₄²×C₂₃	C₂×D₄	1	2	yes	—
267	C₄²×C₂₃	C₂⁴	1	2	yes	—
268	C₂×#3344	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
269	C₂³×C₂₃	—	2	2	no	—
270	C₂³×C₂₃	—	2	2	no	—
271	C₂³×C₂₃	—	2	2	no	—
272	C₂³×C₂₃	—	2	2	no	—
273	C₂³×C₂₃	—	2	2	no	—
274	C₂³×C₂₃	#137	1	4	yes	—
275	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
276	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
277	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
278	Q₈×C₂₃	—	2	2	no	—
279	Q₈×C₂₃	—	2	2	no	—
280	Q₈×C₂₃	—	2	2	no	—
281	Q₈×C₂₃	—	2	2	no	—
282	Q₈×C₂₃	—	4	2	no	—
283	Q₈×C₂₃	—	4	2	no	—
284	Q₈×C₂₃	—	8	4	no	—
285	D₄×C₂₃	—	2	8	no	—
286	C₂×C₄×C₂₃	—	2	2	no	—
287	C₂×C₄×C₂₃	—	2	2	no	—
288	C₂×C₄×C₂₃	—	2	2	no	—
289	C₂×C₄×C₂₃	—	2	2	no	—
290	C₂×C₄×C₂₃	—	2	4	no	—
291	C₂×C₄×C₂₃	—	2	4	no	—
292	C₂×C₄×C₂₃	—	2	2	no	—
293	C₂×C₄×C₂₃	—	2	2	no	—
294	C₂×C₄×C₂₃	—	2	2	no	—
295	C₂×C₄×C₂₃	—	2	2	no	—
296	C₂×C₄×C₂₃	—	2	2	no	—
297	C₂×C₄×C₂₃	—	2	2	no	—
298	C₂×C₄×C₂₃	—	2	2	no	—
299	C₂×C₄×C₂₃	—	2	2	no	—
300	C₂×C₄×C₂₃	—	2	2	no	—
301	C₂×C₄×C₂₃	—	2	2	no	—
302	C₂×C₄×C₂₃	—	2	2	no	—
303	C₂×C₄×C₂₃	—	2	2	no	—
304	C₂×C₄×C₂₃	—	4	2	no	—
305	C₂×C₄×C₂₃	—	4	2	no	—
306	C₂×C₄×C₂₃	—	4	8	no	—
307	C₂×C₄×C₂₃	—	4	2	no	—
308	C₂×C₄×C₂₃	—	4	2	no	—
309	C₂×C₄×C₂₃	—	4	2	no	—
310	C₂×C₄×C₂₃	—	4	2	no	—
311	C₂×C₄×C₂₃	—	4	2	no	—
312	C₂×C₄×C₂₃	—	4	2	no	—
313	C₂×C₄×C₂₃	—	8	4	no	—
314	C₂×C₄×C₂₃	—	8	4	no	—
315	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
316	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
317	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
321	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
322	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
323	C₈×C₂₃	—	2	2	no	—
324	C₈×C₂₃	—	2	2	no	—
325	C₈×C₂₃	—	2	2	no	—
326	C₈×C₂₃	C₂×#41	1	4	yes	—
327	C₂×#554	C₂×C₂₃	1	1	yes	characteristic
328	C₂×#552	C₂×C₂₃	1	1	yes	characteristic
329	#3344	C₂×C₂₃	1	16	yes	direct product factor
330	C₂×#501	C₂×C₂₃	1	1	yes	characteristic, complemented
331	C₂×#484	C₂×C₂₃	1	1	yes	characteristic, complemented
332	C₂×#485	C₂×C₂₃	1	1	yes	characteristic, complemented
333	C₂×#483	C₂×C₂₃	1	1	yes	characteristic, complemented
334	C₂×#483	C₂×C₂₃	1	1	yes	characteristic, complemented
335	C₂×#479	C₂×C₂₃	1	1	yes	characteristic, complemented
336	C₂×#475	C₂×C₂₃	1	1	yes	characteristic, complemented
337	C₂×#470	C₂×C₂₃	1	1	yes	characteristic, complemented
338	C₂×#467	C₂×C₂₃	1	1	yes	characteristic, complemented
339	C₂×#441	C₂×C₂₃	1	1	yes	characteristic, complemented
340	C₂×#435	C₂×C₂₃	1	1	yes	characteristic
341	C₂×#428	C₂×C₂₃	1	1	yes	characteristic, complemented
342	C₂²×#106	C₂×C₂₃	1	1	yes	characteristic, complemented
343	C₂²×C₂₃	—	2	8	no	—
344	C₂²×C₂₃	—	2	2	no	—
345	C₂²×C₂₃	—	2	2	no	—
346	C₂²×C₂₃	—	2	2	no	—
347	C₂²×C₂₃	—	2	2	no	—
348	C₂²×C₂₃	—	2	2	no	—
349	C₂²×C₂₃	—	4	4	no	—
350	C₂²×C₂₃	#547	1	2	yes	—
351	C₂²×C₂₃	C₂×#137	1	4	yes	—
352	C₂²×C₂₃	C₂×#137	1	2	yes	—
353	C₂²×C₂₃	#577	1	2	yes	—
354	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
355	C₄×C₂₃	—	2	2	no	—
356	C₄×C₂₃	—	2	2	no	—
357	C₄×C₂₃	—	2	2	no	—
358	C₄×C₂₃	—	2	2	no	—
359	C₄×C₂₃	—	4	2	no	—
360	C₄×C₂₃	—	4	2	no	—
361	C₄×C₂₃	—	4	2	no	—
362	C₄×C₂₃	—	4	2	no	—
363	C₄×C₂₃	—	4	2	no	—
364	C₄×C₂₃	—	4	2	no	—
365	C₄×C₂₃	—	4	2	no	—
366	C₄×C₂₃	—	4	2	no	—
367	C₄×C₂₃	#547	1	2	yes	—
368	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
369	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
370	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
371	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
372	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
373	#554	—	2	4	no	—
374	#554	C₂²×C₂₃	1	8	yes	—
375	#552	—	2	4	no	—
376	#552	C₂²×C₂₃	1	8	yes	—
377	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
378	C₂×#126	—	2	1	no	—
379	C₂×#125	—	2	1	no	—
380	C₂×#125	—	2	1	no	—
381	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
382	C₂×#123	—	2	1	no	—
383	C₂×C₂²⋊Q₈	—	2	1	no	—
384	C₂×C₂²⋊Q₈	—	2	1	no	—
385	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
386	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
387	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
388	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
389	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
390	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
391	C₂×C₄×D₄	—	2	1	no	—
392	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
393	C₂×#117	—	2	1	no	—
394	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
395	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
396	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
397	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
398	#501	C₂²×C₂₃	1	8	yes	complemented
399	#485	C₂²×C₂₃	1	8	yes	complemented
400	#484	C₂²×C₂₃	1	8	yes	complemented
401	#483	C₂²×C₂₃	1	8	yes	complemented
402	#483	C₂²×C₂₃	1	8	yes	complemented
403	#479	C₂²×C₂₃	1	8	yes	complemented
404	#475	C₂²×C₂₃	1	8	yes	complemented
405	#470	C₂²×C₂₃	1	8	yes	complemented
406	#467	C₂²×C₂₃	1	8	yes	complemented
407	#441	C₂²×C₂₃	1	8	yes	complemented
408	#435	C₂²×C₂₃	1	8	yes	—
409	#428	C₂²×C₂₃	1	8	yes	complemented
410	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
411	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
412	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
413	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
414	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
415	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
416	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
417	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
418	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
419	C₂×#106	C₂²×C₂₃	1	8	yes	complemented
420	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
421	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
422	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
423	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
424	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
425	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
426	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
427	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
428	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
429	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
430	C₂×C₂₃	—	2	4	no	—
431	C₂×C₂₃	—	4	2	no	—
432	C₂×C₂₃	#3344	1	4	yes	direct product factor
433	C₂×C₂₃	C₂×#547	1	1	yes	characteristic
434	C₂×C₂₃	C₂²×#137	1	1	yes	characteristic
435	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
436	C₂²×Q₈	—	2	1	no	—
437	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
438	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
439	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
440	C₂³×C₄	—	2	1	no	—
441	C₂³×C₄	—	2	1	no	—
442	C₂³×C₄	—	2	1	no	—
443	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
444	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
445	C₂×Q₁₆	—	2	4	no	—
446	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
447	C₂×M₁₆	—	2	4	no	—
448	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
449	C₂²×C₈	—	2	4	no	—
450	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
451	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
452	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
453	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
454	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
455	C₄⋊Q₈	—	2	2	no	—
456	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
457	#126	—	2	8	no	—
458	#125	—	2	8	no	—
459	#125	—	2	8	no	—
460	#125	—	2	2	no	—
461	#125	C₂³×C₂₃	1	4	yes	—
462	#123	—	2	8	no	—
463	C₂²⋊Q₈	—	2	2	no	—
464	C₂²⋊Q₈	—	2	2	no	—
465	C₂²⋊Q₈	—	2	2	no	—
466	C₂²⋊Q₈	—	2	2	no	—
467	C₂²⋊Q₈	—	2	8	no	—
468	C₂²⋊Q₈	—	2	8	no	—
469	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
470	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
471	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
472	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
473	C₄×Q₈	—	2	2	no	—
474	C₄×Q₈	—	2	2	no	—
475	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
476	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
477	C₄×D₄	—	2	8	no	—
478	C₄×D₄	D₄×C₂₃	1	4	yes	—
479	C₄×D₄	C₂³×C₂₃	1	4	yes	—
480	#117	—	2	2	no	—
481	#117	—	2	8	no	—
482	#117	C₂³×C₂₃	1	4	yes	—
483	C₂×C₄⋊C₄	—	2	1	no	—
484	C₂×C₄⋊C₄	—	2	1	no	—
485	C₂×C₄⋊C₄	—	2	1	no	—
486	C₂×C₄⋊C₄	—	2	2	no	—
487	C₂×C₄⋊C₄	—	2	2	no	—
488	C₂×C₄⋊C₄	—	2	2	no	—
489	C₂×C₄⋊C₄	—	2	1	no	—
490	C₂×C₄⋊C₄	—	2	1	no	—
491	C₂×C₄⋊C₄	—	2	1	no	—
492	C₂×C₄⋊C₄	—	2	1	no	—
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	—	2	1	no	—
495	C₂×C₄⋊C₄	—	2	1	no	—
496	C₂×C₄⋊C₄	—	2	1	no	—
497	C₂×C₄⋊C₄	—	2	1	no	—
498	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
505	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
506	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
507	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	—	2	1	no	—
513	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
514	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
515	C₂×C₄²	—	2	1	no	—
516	C₂×C₄²	—	2	1	no	—
517	C₂×C₄²	—	2	1	no	—
518	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
519	#107	C₂³×C₂₃	1	4	yes	—
520	#107	C₂³×C₂₃	1	4	yes	—
521	#107	C₂³×C₂₃	1	4	yes	—
522	#106	C₂³×C₂₃	1	4	yes	—
523	#106	C₂³×C₂₃	1	4	yes	—
524	#106	C₂³×C₂₃	1	4	yes	—
525	#106	C₂³×C₂₃	1	4	yes	—
526	#106	C₂³×C₂₃	1	4	yes	—
527	#106	C₂³×C₂₃	1	4	yes	—
528	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
529	#103	C₂³×C₂₃	1	4	yes	—
530	#103	C₂³×C₂₃	1	4	yes	—
531	#103	C₂³×C₂₃	1	4	yes	—
532	#103	C₂³×C₂₃	1	4	yes	—
533	#103	C₂³×C₂₃	1	4	yes	—
534	#103	C₂³×C₂₃	1	4	yes	—
535	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
536	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
537	#97	C₂³×C₂₃	1	4	yes	—
538	C₂₃	C₂×#3344	1	1	yes	characteristic, direct product factor, Sylow
539	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
540	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
541	C₂×Q₈	—	2	1	no	—
542	C₂×Q₈	—	2	1	no	—
543	C₂×Q₈	—	2	4	no	—
544	C₂×Q₈	—	2	2	no	—
545	C₂×Q₈	—	2	2	no	—
546	C₂×Q₈	—	2	2	no	—
547	C₂×Q₈	—	2	2	no	—
548	C₂×Q₈	—	8	2	no	—
549	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
550	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
551	C₂×D₄	—	2	4	no	—
552	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	2	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	4	no	—
566	C₂²×C₄	—	2	4	no	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	—	4	4	no	—
569	C₂²×C₄	—	8	2	no	—
570	C₂²×C₄	—	8	2	no	—
571	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
572	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
573	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
574	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
575	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
576	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
580	Q₁₆	—	2	8	no	—
581	M₁₆	—	2	8	no	—
582	C₂×C₈	—	2	2	no	—
583	C₂×C₈	—	2	2	no	—
584	C₂×C₈	—	2	2	no	—
585	C₂×C₈	—	2	8	no	—
586	C₂×C₈	#41×C₂₃	1	4	yes	—
587	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
588	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
589	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
590	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	4	no	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
610	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
611	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
612	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
613	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
614	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
615	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
622	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
623	C₄²	—	2	4	no	—
624	C₄²	—	2	4	no	—
625	C₄²	—	2	4	no	—
626	C₄²	C₂×D₄×C₂₃	1	2	yes	—
627	C₄²	C₂⁴×C₂₃	1	2	yes	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	2	no	—
633	C₂³	C₂₃×#137	1	4	yes	—
634	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
635	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
636	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
637	Q₈	—	2	2	no	—
638	Q₈	—	2	2	no	—
639	Q₈	—	2	2	no	—
640	Q₈	—	2	2	no	—
641	Q₈	—	4	2	no	—
642	Q₈	—	4	2	no	—
643	Q₈	—	8	4	no	—
644	D₄	—	2	8	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	2	4	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	4	2	no	—
664	C₂×C₄	—	4	2	no	—
665	C₂×C₄	—	4	8	no	—
666	C₂×C₄	—	4	2	no	—
667	C₂×C₄	—	4	2	no	—
668	C₂×C₄	—	4	2	no	—
669	C₂×C₄	—	4	2	no	—
670	C₂×C₄	—	4	2	no	—
671	C₂×C₄	—	4	2	no	—
672	C₂×C₄	—	8	4	no	—
673	C₂×C₄	—	8	4	no	—
674	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
675	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
676	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
677	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
678	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
679	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
680	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
681	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
682	C₈	—	2	2	no	—
683	C₈	—	2	2	no	—
684	C₈	—	2	2	no	—
685	C₈	C₂×#41×C₂₃	1	4	yes	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	2	8	no	—
689	C₂²	—	2	2	no	—
690	C₂²	—	2	2	no	—
691	C₂²	—	2	2	no	—
692	C₂²	—	4	4	no	—
693	C₂²	C₂₃×#547	1	2	yes	—
694	C₂²	C₂×C₂₃×#137	1	4	yes	—
695	C₂²	C₂×C₂₃×#137	1	2	yes	—
696	C₂²	C₂₃×#577	1	2	yes	—
697	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
698	C₄	—	2	2	no	—
699	C₄	—	2	2	no	—
700	C₄	—	2	2	no	—
701	C₄	—	2	2	no	—
702	C₄	—	4	2	no	—
703	C₄	—	4	2	no	—
704	C₄	—	4	2	no	—
705	C₄	—	4	2	no	—
706	C₄	—	4	2	no	—
707	C₄	—	4	2	no	—
708	C₄	—	4	2	no	—
709	C₄	—	4	2	no	—
710	C₄	C₂₃×#547	1	2	yes	—
711	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
712	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
713	C₂	—	2	4	no	—
714	C₂	—	4	2	no	—
715	C₂	C₂₃×#3344	1	4	yes	direct product factor
716	C₂	C₂×C₂₃×#547	1	1	yes	characteristic
717	C₂	C₂²×C₂₃×#137	1	1	yes	characteristic
718	C₂	C₂×C₂₃×#577	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
3. C₂₃×#3344	C₂	direct (N × H)
4. C₂×C₂₃×#501	C₂	semidirect
5. C₂×C₂₃×#484	C₂	semidirect
6. C₂×C₂₃×#485	C₂	semidirect
7. C₂×C₂₃×#483	C₂	semidirect
8. C₂×C₂₃×#483	C₂	semidirect
9. C₂×C₂₃×#479	C₂	semidirect
10. C₂×C₂₃×#475	C₂	semidirect
11. C₂×C₂₃×#470	C₂	semidirect
12. C₂×C₂₃×#467	C₂	semidirect
13. C₂×C₂₃×#441	C₂	semidirect
15. C₂×C₂₃×#428	C₂	semidirect
16. C₂²×C₂₃×#106	C₂	semidirect
45. C₂₃×#501	C₂²	semidirect
46. C₂₃×#485	C₂²	semidirect
47. C₂₃×#484	C₂²	semidirect
48. C₂₃×#483	C₂²	semidirect
49. C₂₃×#483	C₂²	semidirect
50. C₂₃×#479	C₂²	semidirect
51. C₂₃×#475	C₂²	semidirect
52. C₂₃×#470	C₂²	semidirect
53. C₂₃×#467	C₂²	semidirect
54. C₂₃×#441	C₂²	semidirect
56. C₂₃×#428	C₂²	semidirect
66. C₂×C₂₃×#106	C₂²	semidirect
268. C₂×#3344	C₂₃	direct (N × H)
329. #3344	C₂×C₂₃	direct (N × H)
330. C₂×#501	C₂×C₂₃	semidirect
331. C₂×#484	C₂×C₂₃	semidirect
332. C₂×#485	C₂×C₂₃	semidirect
333. C₂×#483	C₂×C₂₃	semidirect
334. C₂×#483	C₂×C₂₃	semidirect
335. C₂×#479	C₂×C₂₃	semidirect
336. C₂×#475	C₂×C₂₃	semidirect
337. C₂×#470	C₂×C₂₃	semidirect
338. C₂×#467	C₂×C₂₃	semidirect
339. C₂×#441	C₂×C₂₃	semidirect
341. C₂×#428	C₂×C₂₃	semidirect
342. C₂²×#106	C₂×C₂₃	semidirect
398. #501	C₂²×C₂₃	semidirect
399. #485	C₂²×C₂₃	semidirect
400. #484	C₂²×C₂₃	semidirect
401. #483	C₂²×C₂₃	semidirect
402. #483	C₂²×C₂₃	semidirect
403. #479	C₂²×C₂₃	semidirect
404. #475	C₂²×C₂₃	semidirect
405. #470	C₂²×C₂₃	semidirect
406. #467	C₂²×C₂₃	semidirect
407. #441	C₂²×C₂₃	semidirect
409. #428	C₂²×C₂₃	semidirect
419. C₂×#106	C₂²×C₂₃	semidirect
432. C₂×C₂₃	#3344	direct (N × H)
538. C₂₃	C₂×#3344	direct (N × H)
715. C₂	C₂₃×#3344	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
C₂×C₂₃×#552	2
C₂₃×#3344	2
C₂×C₂₃×#501	2
C₂×C₂₃×#484	2
C₂×C₂₃×#485	2
C₂×C₂₃×#483	2
C₂×C₂₃×#479	2
C₂×C₂₃×#475	2
C₂×C₂₃×#470	2
C₂×C₂₃×#467	2
C₂×C₂₃×#441	2
C₂×C₂₃×#435	2
C₂×C₂₃×#428	2
C₂²×C₂₃×#106	2
C₂×#3344	23

Subgroups — C2×C23×#3344 #19208862

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3344 #19208862