Subgroups — C₂×C₂₃×#3460 #19210305

Order 5888.

7994 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3460	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₂₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#542	C₂	1	4	yes	maximal, complemented
4	C₂×C₂₃×#540	C₂	1	4	yes	maximal, complemented
5	C₂×C₂₃×#538	C₂	1	4	yes	maximal, complemented
6	C₂×C₂₃×#537	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#535	C₂	1	2	yes	maximal, complemented
8	C₂×C₂₃×#532	C₂	1	4	yes	maximal, complemented
9	C₂×C₂₃×#529	C₂	1	4	yes	maximal, complemented
10	C₂×C₂₃×#525	C₂	1	4	yes	maximal, complemented
11	C₂×C₄×#41×C₂₃	C₂	1	2	yes	maximal, complemented
12	C₂²×C₄×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₂₃	C₂²	1	2	yes	—
14	C₂²×#41×C₂₃	C₂²	1	4	yes	complemented
15	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₂₃	C₂²	1	2	yes	—
17	C₂₃×#544	C₂²	1	16	yes	complemented
18	C₂₃×#542	C₂²	1	64	yes	complemented
19	C₂₃×#540	C₂²	1	64	yes	complemented
20	C₂₃×#538	C₂²	1	64	yes	complemented
21	C₂₃×#537	C₂²	1	16	yes	complemented
22	C₂₃×#535	C₂²	1	32	yes	complemented
23	C₂₃×#532	C₂²	1	64	yes	complemented
24	C₂×C₂₃×C₄⋊Q₈	C₂²	1	4	yes	complemented
25	C₂×C₂₃×#127	C₂²	1	4	yes	—
26	C₂₃×#529	C₂²	1	64	yes	complemented
27	C₂×C₂₃×#126	C₂²	1	8	yes	complemented
28	C₂×C₂₃×#125	C₂²	1	4	yes	complemented
29	C₂×C₂₃×#124	C₂²	1	4	yes	—
30	C₂×C₂₃×#124	C₂²	1	8	yes	complemented
31	C₂₃×#525	C₂²	1	64	yes	complemented
32	C₂×C₂₃×#123	C₂²	1	8	yes	complemented
33	C₂×C₂₃×#123	C₂²	1	8	yes	complemented
34	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	—
35	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
36	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
37	C₂×C₂₃×#121	C₂²	1	4	yes	—
38	C₂×C₂₃×#121	C₂²	1	4	yes	—
39	C₂×C₂₃×#121	C₂²	1	4	yes	—
40	C₂×C₂₃×#121	C₂²	1	4	yes	complemented
41	C₂×C₂₃×#121	C₂²	1	4	yes	complemented
42	C₂×C₂₃×#121	C₂²	1	8	yes	complemented
43	C₂×C₂₃×#120	C₂²	1	8	yes	—
44	C₄×#41×C₂₃	C₂²	1	32	yes	complemented
45	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
46	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
47	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	—
48	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	—
49	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	—
50	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	—
51	C₂×C₄×D₄×C₂₃	C₂²	1	16	yes	complemented
52	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
53	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
54	C₂×C₄×D₄×C₂₃	C₂²	1	8	yes	complemented
55	C₂×C₂₃×#117	C₂²	1	2	yes	—
56	C₂×C₂₃×#117	C₂²	1	4	yes	complemented
57	C₂×C₂₃×#117	C₂²	1	4	yes	complemented
58	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
59	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
60	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
61	C₂²×C₄²×C₂₃	C₂²	1	4	yes	complemented
62	C₂⁵×C₂₃	C₂³	1	2	yes	—
63	C₂×#41×C₂₃	—	2	16	no	—
64	C₂×#41×C₂₃	—	4	16	no	—
65	C₂×#41×C₂₃	C₂³	1	16	yes	—
66	C₂×#41×C₂₃	C₂³	1	32	yes	complemented
67	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
68	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
69	C₂²×D₄×C₂₃	—	2	8	no	—
70	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
71	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
72	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
73	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
74	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
75	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
76	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
77	C₂³×C₄×C₂₃	—	4	8	no	—
78	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
79	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
81	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
82	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
83	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
84	C₂³×C₄×C₂₃	C₂³	1	16	yes	—
85	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
87	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
88	C₂₃×C₄⋊Q₈	C₂³	1	32	yes	complemented
89	C₂₃×#127	C₂³	1	32	yes	—
90	C₂₃×#126	C₂³	1	64	yes	complemented
91	C₂₃×#125	C₂³	1	32	yes	complemented
92	C₂₃×#124	C₂³	1	32	yes	—
93	C₂₃×#124	C₂³	1	64	yes	complemented
94	C₂₃×#123	C₂³	1	64	yes	complemented
95	C₂₃×#123	C₂³	1	64	yes	complemented
96	C₂₃×C₂²⋊Q₈	C₂³	1	32	yes	—
97	C₂₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
98	C₂₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
99	C₂₃×#121	C₂³	1	32	yes	—
100	C₂₃×#121	C₂³	1	32	yes	—
101	C₂₃×#121	C₂³	1	32	yes	—
102	C₂₃×#121	C₂³	1	32	yes	complemented
103	C₂₃×#121	C₂³	1	32	yes	complemented
104	C₂₃×#121	C₂³	1	64	yes	complemented
105	C₂₃×#120	C₂³	1	64	yes	—
106	C₄×Q₈×C₂₃	C₂³	1	16	yes	complemented
107	C₄×Q₈×C₂₃	C₂³	1	16	yes	complemented
108	C₄×D₄×C₂₃	C₂³	1	32	yes	—
109	C₄×D₄×C₂₃	C₂³	1	32	yes	—
110	C₄×D₄×C₂₃	C₂³	1	32	yes	—
111	C₄×D₄×C₂₃	C₂³	1	32	yes	—
112	C₄×D₄×C₂₃	C₂³	1	16	yes	complemented
113	C₄×D₄×C₂₃	C₂³	1	16	yes	complemented
114	C₄×D₄×C₂₃	C₂³	1	64	yes	complemented
115	C₂₃×#117	C₂³	1	16	yes	—
116	C₂₃×#117	C₂³	1	32	yes	complemented
117	C₂₃×#117	C₂³	1	32	yes	complemented
118	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
120	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
127	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
128	C₂×C₂²⋊C₄×C₂₃	C₂³	1	16	yes	—
129	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
133	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
134	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
135	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
136	C₂×C₄²×C₂₃	C₂³	1	8	yes	—
137	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
138	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
139	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
140	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
141	C₂×C₄²×C₂₃	C₂³	1	32	yes	complemented
142	C₂⁴×C₂₃	—	2	8	no	—
143	C₂⁴×C₂₃	—	4	4	no	—
144	C₂⁴×C₂₃	—	4	4	no	—
145	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
146	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
147	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
148	C₂⁴×C₂₃	C₂⁴	1	8	yes	—
149	#41×C₂₃	—	2	64	no	—
150	#41×C₂₃	—	4	64	no	—
151	C₂×Q₈×C₂₃	—	2	8	no	—
152	C₂×Q₈×C₂₃	—	4	8	no	—
153	C₂×Q₈×C₂₃	C₂⁴	1	8	yes	—
154	C₂×Q₈×C₂₃	C₂⁴	1	16	yes	—
155	C₂×D₄×C₂₃	—	2	16	no	—
156	C₂×D₄×C₂₃	—	2	16	no	—
157	C₂×D₄×C₂₃	—	2	8	no	—
158	C₂×D₄×C₂₃	—	2	32	no	—
159	C₂×D₄×C₂₃	—	4	16	no	—
160	C₂×D₄×C₂₃	—	4	8	no	—
161	C₂×D₄×C₂₃	—	4	16	no	—
162	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
163	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
164	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
165	C₂×D₄×C₂₃	C₂⁴	1	32	yes	—
166	C₂×D₄×C₂₃	C₂⁴	1	32	yes	—
167	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
168	C₂²×C₄×C₂₃	—	2	16	no	—
169	C₂²×C₄×C₂₃	—	2	4	no	—
170	C₂²×C₄×C₂₃	—	2	16	no	—
171	C₂²×C₄×C₂₃	—	2	16	no	—
172	C₂²×C₄×C₂₃	—	4	32	no	—
173	C₂²×C₄×C₂₃	—	4	8	no	—
174	C₂²×C₄×C₂₃	—	4	4	no	—
175	C₂²×C₄×C₂₃	—	4	2	no	—
176	C₂²×C₄×C₂₃	—	4	8	no	—
177	C₂²×C₄×C₂₃	#41	1	8	yes	complemented
178	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
182	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
185	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
186	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
187	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
188	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
189	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
190	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
191	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
192	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
195	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
196	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
197	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
198	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
199	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
200	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
201	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
202	C₄⋊C₄×C₂₃	C₂⁴	1	32	yes	—
203	C₂²⋊C₄×C₂₃	C₂⁴	1	32	yes	—
204	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
205	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
206	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
207	C₂²⋊C₄×C₂₃	C₂⁴	1	32	yes	—
208	C₂²⋊C₄×C₂₃	C₂⁴	1	32	yes	—
209	C₂²⋊C₄×C₂₃	C₂⁴	1	32	yes	—
210	C₄²×C₂₃	C₂⁴	1	8	yes	—
211	C₄²×C₂₃	C₂⁴	1	8	yes	—
212	C₄²×C₂₃	C₂⁴	1	16	yes	—
213	C₄²×C₂₃	C₂⁴	1	16	yes	—
214	C₄²×C₂₃	C₂⁴	1	16	yes	—
215	C₂×#3460	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂³×C₂₃	—	2	2	no	—
217	C₂³×C₂₃	—	2	2	no	—
218	C₂³×C₂₃	—	2	8	no	—
219	C₂³×C₂₃	—	2	16	no	—
220	C₂³×C₂₃	—	2	8	no	—
221	C₂³×C₂₃	—	2	8	no	—
222	C₂³×C₂₃	—	2	8	no	—
223	C₂³×C₂₃	—	2	8	no	—
224	C₂³×C₂₃	—	2	8	no	—
225	C₂³×C₂₃	—	4	8	no	—
226	C₂³×C₂₃	—	4	8	no	—
227	C₂³×C₂₃	—	4	32	no	—
228	C₂³×C₂₃	C₂×#41	1	4	yes	—
229	C₂³×C₂₃	C₂⁵	1	8	yes	—
230	C₂³×C₂₃	C₂⁵	1	8	yes	—
231	C₂³×C₂₃	C₂⁵	1	2	yes	—
232	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
233	Q₈×C₂₃	—	2	16	no	—
234	Q₈×C₂₃	—	4	16	no	—
235	D₄×C₂₃	—	2	32	no	—
236	D₄×C₂₃	—	2	32	no	—
237	D₄×C₂₃	—	2	16	no	—
238	D₄×C₂₃	—	4	32	no	—
239	D₄×C₂₃	—	4	16	no	—
240	D₄×C₂₃	—	4	32	no	—
241	C₂×C₄×C₂₃	—	2	8	no	—
242	C₂×C₄×C₂₃	—	2	2	no	—
243	C₂×C₄×C₂₃	—	2	8	no	—
244	C₂×C₄×C₂₃	—	2	8	no	—
245	C₂×C₄×C₂₃	—	2	4	no	—
246	C₂×C₄×C₂₃	—	2	8	no	—
247	C₂×C₄×C₂₃	—	2	32	no	—
248	C₂×C₄×C₂₃	—	2	8	no	—
249	C₂×C₄×C₂₃	—	2	32	no	—
250	C₂×C₄×C₂₃	—	2	32	no	—
251	C₂×C₄×C₂₃	—	4	16	no	—
252	C₂×C₄×C₂₃	—	4	8	no	—
253	C₂×C₄×C₂₃	—	4	4	no	—
254	C₂×C₄×C₂₃	—	4	16	no	—
255	C₂×C₄×C₂₃	C₂×#41	1	8	yes	—
256	C₂×C₄×C₂₃	C₂×#41	1	16	yes	complemented
257	C₂×C₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
258	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
259	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
260	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
261	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
262	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
263	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
264	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
265	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
266	#3460	C₂×C₂₃	1	32	yes	direct product factor
267	C₂×#544	C₂×C₂₃	1	1	yes	characteristic, complemented
268	C₂×#542	C₂×C₂₃	1	4	yes	complemented
269	C₂×#540	C₂×C₂₃	1	4	yes	complemented
270	C₂×#538	C₂×C₂₃	1	4	yes	complemented
271	C₂×#537	C₂×C₂₃	1	1	yes	characteristic, complemented
272	C₂×#535	C₂×C₂₃	1	2	yes	complemented
273	C₂×#532	C₂×C₂₃	1	4	yes	complemented
274	C₂×#529	C₂×C₂₃	1	4	yes	complemented
275	C₂×#525	C₂×C₂₃	1	4	yes	complemented
276	C₂×C₄×#41	C₂×C₂₃	1	2	yes	complemented
277	C₂²×C₄×D₄	C₂×C₂₃	1	1	yes	characteristic, complemented
278	C₂²×C₂₃	—	2	2	no	—
279	C₂²×C₂₃	—	2	2	no	—
280	C₂²×C₂₃	—	2	8	no	—
281	C₂²×C₂₃	—	2	8	no	—
282	C₂²×C₂₃	—	2	8	no	—
283	C₂²×C₂₃	—	2	8	no	—
284	C₂²×C₂₃	—	2	8	no	—
285	C₂²×C₂₃	—	2	8	no	—
286	C₂²×C₂₃	—	2	8	no	—
287	C₂²×C₂₃	—	4	32	no	—
288	C₂²×C₂₃	—	4	16	no	—
289	C₂²×C₂₃	—	4	16	no	—
290	C₂²×C₂₃	C₂²×#41	1	4	yes	—
291	C₂²×C₂₃	C₂²×#41	1	2	yes	—
292	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
293	C₂²×C₂₃	#585	1	2	yes	—
294	C₂²×C₂₃	C₂⁶	1	1	yes	characteristic
295	C₄×C₂₃	—	2	8	no	—
296	C₄×C₂₃	—	2	2	no	—
297	C₄×C₂₃	—	2	8	no	—
298	C₄×C₂₃	—	2	8	no	—
299	C₄×C₂₃	—	2	4	no	—
300	C₄×C₂₃	—	2	8	no	—
301	C₄×C₂₃	C₂²×#41	1	8	yes	—
302	C₄×C₂₃	C₂×H(5,𝔽₂)	1	4	yes	—
303	C₂²×#41	C₂²×C₂₃	1	2	yes	—
304	C₂²×#41	C₂²×C₂₃	1	4	yes	complemented
305	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
306	C₂⁴×C₄	C₂²×C₂₃	1	2	yes	—
307	#544	C₂²×C₂₃	1	16	yes	complemented
308	#542	C₂²×C₂₃	1	64	yes	complemented
309	#540	C₂²×C₂₃	1	64	yes	complemented
310	#538	C₂²×C₂₃	1	64	yes	complemented
311	#537	C₂²×C₂₃	1	16	yes	complemented
312	#535	C₂²×C₂₃	1	32	yes	complemented
313	#532	C₂²×C₂₃	1	64	yes	complemented
314	C₂×C₄⋊Q₈	C₂²×C₂₃	1	4	yes	complemented
315	C₂×#127	C₂²×C₂₃	1	4	yes	—
316	#529	C₂²×C₂₃	1	64	yes	complemented
317	C₂×#126	C₂²×C₂₃	1	8	yes	complemented
318	C₂×#125	C₂²×C₂₃	1	4	yes	complemented
319	C₂×#124	C₂²×C₂₃	1	4	yes	—
320	C₂×#124	C₂²×C₂₃	1	8	yes	complemented
321	#525	C₂²×C₂₃	1	64	yes	complemented
322	C₂×#123	C₂²×C₂₃	1	8	yes	complemented
323	C₂×#123	C₂²×C₂₃	1	8	yes	complemented
324	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
325	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	complemented
326	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	complemented
327	C₂×#121	C₂²×C₂₃	1	4	yes	—
328	C₂×#121	C₂²×C₂₃	1	4	yes	—
329	C₂×#121	C₂²×C₂₃	1	4	yes	—
330	C₂×#121	C₂²×C₂₃	1	4	yes	complemented
331	C₂×#121	C₂²×C₂₃	1	4	yes	complemented
332	C₂×#121	C₂²×C₂₃	1	8	yes	complemented
333	C₂×#120	C₂²×C₂₃	1	8	yes	—
334	C₄×#41	C₂²×C₂₃	1	32	yes	complemented
335	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
336	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
337	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	—
338	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	—
339	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	—
340	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	—
341	C₂×C₄×D₄	C₂²×C₂₃	1	16	yes	complemented
342	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
343	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
344	C₂×C₄×D₄	C₂²×C₂₃	1	8	yes	complemented
345	C₂×#117	C₂²×C₂₃	1	2	yes	—
346	C₂×#117	C₂²×C₂₃	1	4	yes	complemented
347	C₂×#117	C₂²×C₂₃	1	4	yes	complemented
348	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
349	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
350	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
351	C₂²×C₄²	C₂²×C₂₃	1	4	yes	complemented
352	C₂×C₂₃	—	2	4	no	—
353	C₂×C₂₃	—	4	8	no	—
354	C₂×C₂₃	—	4	8	no	—
355	C₂×C₂₃	#3460	1	4	yes	direct product factor
356	C₂×C₂₃	C₂³×#41	1	1	yes	characteristic
357	C₂×C₂₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
358	C₂×C₂₃	C₂×#585	1	1	yes	characteristic
359	C₂⁵	C₂³×C₂₃	1	2	yes	—
360	C₂×#41	—	2	16	no	—
361	C₂×#41	—	4	16	no	—
362	C₂×#41	C₂³×C₂₃	1	16	yes	—
363	C₂×#41	C₂³×C₂₃	1	32	yes	complemented
364	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
365	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
366	C₂²×D₄	—	2	8	no	—
367	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
368	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
369	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
370	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
371	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
372	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
373	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
374	C₂³×C₄	—	4	8	no	—
375	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
376	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
377	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
378	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
379	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
380	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
381	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
382	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
383	C₂³×C₄	C₂³×C₂₃	1	16	yes	—
384	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
385	C₄⋊Q₈	C₂³×C₂₃	1	32	yes	complemented
386	#127	C₂³×C₂₃	1	32	yes	—
387	#126	C₂³×C₂₃	1	64	yes	complemented
388	#125	C₂³×C₂₃	1	32	yes	complemented
389	#124	C₂³×C₂₃	1	32	yes	—
390	#124	C₂³×C₂₃	1	64	yes	complemented
391	#123	C₂³×C₂₃	1	64	yes	complemented
392	#123	C₂³×C₂₃	1	64	yes	complemented
393	C₂²⋊Q₈	C₂³×C₂₃	1	32	yes	—
394	C₂²⋊Q₈	C₂³×C₂₃	1	32	yes	complemented
395	C₂²⋊Q₈	C₂³×C₂₃	1	32	yes	complemented
396	#121	C₂³×C₂₃	1	32	yes	—
397	#121	C₂³×C₂₃	1	32	yes	—
398	#121	C₂³×C₂₃	1	32	yes	—
399	#121	C₂³×C₂₃	1	32	yes	complemented
400	#121	C₂³×C₂₃	1	32	yes	complemented
401	#121	C₂³×C₂₃	1	64	yes	complemented
402	#120	C₂³×C₂₃	1	64	yes	—
403	C₄×Q₈	C₂³×C₂₃	1	16	yes	complemented
404	C₄×Q₈	C₂³×C₂₃	1	16	yes	complemented
405	C₄×D₄	C₂³×C₂₃	1	32	yes	—
406	C₄×D₄	C₂³×C₂₃	1	32	yes	—
407	C₄×D₄	C₂³×C₂₃	1	32	yes	—
408	C₄×D₄	C₂³×C₂₃	1	32	yes	—
409	C₄×D₄	C₂³×C₂₃	1	16	yes	complemented
410	C₄×D₄	C₂³×C₂₃	1	16	yes	complemented
411	C₄×D₄	C₂³×C₂₃	1	64	yes	complemented
412	#117	C₂³×C₂₃	1	16	yes	—
413	#117	C₂³×C₂₃	1	32	yes	complemented
414	#117	C₂³×C₂₃	1	32	yes	complemented
415	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
416	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
417	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
418	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
419	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
420	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
421	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
422	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
423	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₂₃	1	16	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
432	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
433	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
434	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
435	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
436	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
437	C₂×C₄²	C₂³×C₂₃	1	8	yes	—
438	C₂×C₄²	C₂³×C₂₃	1	32	yes	complemented
439	C₂₃	C₂×#3460	1	1	yes	characteristic, direct product factor, Sylow
440	C₂⁴	—	2	8	no	—
441	C₂⁴	—	4	4	no	—
442	C₂⁴	—	4	4	no	—
443	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
444	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
445	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
446	C₂⁴	C₂⁴×C₂₃	1	8	yes	—
447	#41	—	2	64	no	—
448	#41	—	4	64	no	—
449	C₂×Q₈	—	2	8	no	—
450	C₂×Q₈	—	4	8	no	—
451	C₂×Q₈	C₂⁴×C₂₃	1	8	yes	—
452	C₂×Q₈	C₂⁴×C₂₃	1	16	yes	—
453	C₂×D₄	—	2	16	no	—
454	C₂×D₄	—	2	16	no	—
455	C₂×D₄	—	2	8	no	—
456	C₂×D₄	—	2	32	no	—
457	C₂×D₄	—	4	8	no	—
458	C₂×D₄	—	4	16	no	—
459	C₂×D₄	—	4	16	no	—
460	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
461	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
462	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
463	C₂×D₄	C₂⁴×C₂₃	1	32	yes	—
464	C₂×D₄	C₂⁴×C₂₃	1	32	yes	—
465	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
466	C₂²×C₄	—	2	16	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	16	no	—
469	C₂²×C₄	—	2	16	no	—
470	C₂²×C₄	—	4	32	no	—
471	C₂²×C₄	—	4	8	no	—
472	C₂²×C₄	—	4	4	no	—
473	C₂²×C₄	—	4	2	no	—
474	C₂²×C₄	—	4	8	no	—
475	C₂²×C₄	#41×C₂₃	1	8	yes	complemented
476	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
477	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
478	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
479	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
480	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
481	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
482	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
483	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
484	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
485	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
486	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
487	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
488	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
489	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
490	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
491	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
492	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
493	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
494	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
495	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
496	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
497	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
498	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
499	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
500	C₄⋊C₄	C₂⁴×C₂₃	1	32	yes	—
501	C₂²⋊C₄	C₂⁴×C₂₃	1	32	yes	—
502	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
503	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
504	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
505	C₂²⋊C₄	C₂⁴×C₂₃	1	32	yes	—
506	C₂²⋊C₄	C₂⁴×C₂₃	1	32	yes	—
507	C₂²⋊C₄	C₂⁴×C₂₃	1	32	yes	—
508	C₄²	C₂⁴×C₂₃	1	8	yes	—
509	C₄²	C₂⁴×C₂₃	1	8	yes	—
510	C₄²	C₂⁴×C₂₃	1	16	yes	—
511	C₄²	C₂⁴×C₂₃	1	16	yes	—
512	C₄²	C₂⁴×C₂₃	1	16	yes	—
513	C₂³	—	2	2	no	—
514	C₂³	—	2	2	no	—
515	C₂³	—	2	8	no	—
516	C₂³	—	2	16	no	—
517	C₂³	—	2	8	no	—
518	C₂³	—	2	8	no	—
519	C₂³	—	2	8	no	—
520	C₂³	—	2	8	no	—
521	C₂³	—	2	8	no	—
522	C₂³	—	4	8	no	—
523	C₂³	—	4	8	no	—
524	C₂³	—	4	32	no	—
525	C₂³	C₂×#41×C₂₃	1	4	yes	—
526	C₂³	C₂⁵×C₂₃	1	8	yes	—
527	C₂³	C₂⁵×C₂₃	1	8	yes	—
528	C₂³	C₂⁵×C₂₃	1	2	yes	—
529	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
530	Q₈	—	2	16	no	—
531	Q₈	—	4	16	no	—
532	D₄	—	2	32	no	—
533	D₄	—	2	32	no	—
534	D₄	—	2	16	no	—
535	D₄	—	4	16	no	—
536	D₄	—	4	32	no	—
537	D₄	—	4	32	no	—
538	C₂×C₄	—	2	8	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	8	no	—
541	C₂×C₄	—	2	8	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	8	no	—
544	C₂×C₄	—	2	32	no	—
545	C₂×C₄	—	2	8	no	—
546	C₂×C₄	—	2	32	no	—
547	C₂×C₄	—	2	32	no	—
548	C₂×C₄	—	4	16	no	—
549	C₂×C₄	—	4	8	no	—
550	C₂×C₄	—	4	4	no	—
551	C₂×C₄	—	4	16	no	—
552	C₂×C₄	C₂×#41×C₂₃	1	8	yes	—
553	C₂×C₄	C₂×#41×C₂₃	1	16	yes	complemented
554	C₂×C₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
555	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
556	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
557	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
558	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
559	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
560	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
561	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
562	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
563	C₂²	—	2	8	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	2	8	no	—
567	C₂²	—	2	8	no	—
568	C₂²	—	2	8	no	—
569	C₂²	—	2	8	no	—
570	C₂²	—	2	8	no	—
571	C₂²	—	2	8	no	—
572	C₂²	—	4	32	no	—
573	C₂²	—	4	16	no	—
574	C₂²	—	4	16	no	—
575	C₂²	C₂²×#41×C₂₃	1	4	yes	—
576	C₂²	C₂²×#41×C₂₃	1	2	yes	—
577	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
578	C₂²	C₂₃×#585	1	2	yes	—
579	C₂²	C₂⁶×C₂₃	1	1	yes	characteristic
580	C₄	—	2	8	no	—
581	C₄	—	2	2	no	—
582	C₄	—	2	8	no	—
583	C₄	—	2	8	no	—
584	C₄	—	2	4	no	—
585	C₄	—	2	8	no	—
586	C₄	C₂²×#41×C₂₃	1	8	yes	—
587	C₄	C₂×C₂₃×H(5,𝔽₂)	1	4	yes	—
588	C₂	—	2	4	no	—
589	C₂	—	4	8	no	—
590	C₂	—	4	8	no	—
591	C₂	C₂₃×#3460	1	4	yes	direct product factor
592	C₂	C₂³×#41×C₂₃	1	1	yes	characteristic
593	C₂	C₂²×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
594	C₂	C₂×C₂₃×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₂₃
socle	C₂³×C₂₃	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3460	C₂	direct (N × H)
2. C₂×C₂₃×#544	C₂	semidirect
3. C₂×C₂₃×#542	C₂	semidirect
4. C₂×C₂₃×#540	C₂	semidirect
5. C₂×C₂₃×#538	C₂	semidirect
6. C₂×C₂₃×#537	C₂	semidirect
7. C₂×C₂₃×#535	C₂	semidirect
8. C₂×C₂₃×#532	C₂	semidirect
9. C₂×C₂₃×#529	C₂	semidirect
10. C₂×C₂₃×#525	C₂	semidirect
11. C₂×C₄×#41×C₂₃	C₂	semidirect
12. C₂²×C₄×D₄×C₂₃	C₂	semidirect
14. C₂²×#41×C₂₃	C₂²	semidirect
17. C₂₃×#544	C₂²	semidirect
18. C₂₃×#542	C₂²	semidirect
19. C₂₃×#540	C₂²	semidirect
20. C₂₃×#538	C₂²	semidirect
21. C₂₃×#537	C₂²	semidirect
22. C₂₃×#535	C₂²	semidirect
23. C₂₃×#532	C₂²	semidirect
24. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
26. C₂₃×#529	C₂²	semidirect
27. C₂×C₂₃×#126	C₂²	semidirect
28. C₂×C₂₃×#125	C₂²	semidirect
30. C₂×C₂₃×#124	C₂²	semidirect
31. C₂₃×#525	C₂²	semidirect
32. C₂×C₂₃×#123	C₂²	semidirect
33. C₂×C₂₃×#123	C₂²	semidirect
35. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
36. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
40. C₂×C₂₃×#121	C₂²	semidirect
41. C₂×C₂₃×#121	C₂²	semidirect
42. C₂×C₂₃×#121	C₂²	semidirect
44. C₄×#41×C₂₃	C₂²	semidirect
45. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
46. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
51. C₂×C₄×D₄×C₂₃	C₂²	semidirect
52. C₂×C₄×D₄×C₂₃	C₂²	semidirect
53. C₂×C₄×D₄×C₂₃	C₂²	semidirect
54. C₂×C₄×D₄×C₂₃	C₂²	semidirect
56. C₂×C₂₃×#117	C₂²	semidirect
57. C₂×C₂₃×#117	C₂²	semidirect
61. C₂²×C₄²×C₂₃	C₂²	semidirect
66. C₂×#41×C₂₃	C₂³	semidirect
88. C₂₃×C₄⋊Q₈	C₂³	semidirect
90. C₂₃×#126	C₂³	semidirect
91. C₂₃×#125	C₂³	semidirect
93. C₂₃×#124	C₂³	semidirect
94. C₂₃×#123	C₂³	semidirect
95. C₂₃×#123	C₂³	semidirect
97. C₂₃×C₂²⋊Q₈	C₂³	semidirect
98. C₂₃×C₂²⋊Q₈	C₂³	semidirect
102. C₂₃×#121	C₂³	semidirect
103. C₂₃×#121	C₂³	semidirect
104. C₂₃×#121	C₂³	semidirect
106. C₄×Q₈×C₂₃	C₂³	semidirect
107. C₄×Q₈×C₂₃	C₂³	semidirect
112. C₄×D₄×C₂₃	C₂³	semidirect
113. C₄×D₄×C₂₃	C₂³	semidirect
114. C₄×D₄×C₂₃	C₂³	semidirect
116. C₂₃×#117	C₂³	semidirect
117. C₂₃×#117	C₂³	semidirect
141. C₂×C₄²×C₂₃	C₂³	semidirect
177. C₂²×C₄×C₂₃	#41	semidirect
215. C₂×#3460	C₂₃	direct (N × H)
256. C₂×C₄×C₂₃	C₂×#41	semidirect
266. #3460	C₂×C₂₃	direct (N × H)
267. C₂×#544	C₂×C₂₃	semidirect
268. C₂×#542	C₂×C₂₃	semidirect
269. C₂×#540	C₂×C₂₃	semidirect
270. C₂×#538	C₂×C₂₃	semidirect
271. C₂×#537	C₂×C₂₃	semidirect
272. C₂×#535	C₂×C₂₃	semidirect
273. C₂×#532	C₂×C₂₃	semidirect
274. C₂×#529	C₂×C₂₃	semidirect
275. C₂×#525	C₂×C₂₃	semidirect
276. C₂×C₄×#41	C₂×C₂₃	semidirect
277. C₂²×C₄×D₄	C₂×C₂₃	semidirect
304. C₂²×#41	C₂²×C₂₃	semidirect
307. #544	C₂²×C₂₃	semidirect
308. #542	C₂²×C₂₃	semidirect
309. #540	C₂²×C₂₃	semidirect
310. #538	C₂²×C₂₃	semidirect
311. #537	C₂²×C₂₃	semidirect
312. #535	C₂²×C₂₃	semidirect
313. #532	C₂²×C₂₃	semidirect
314. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
316. #529	C₂²×C₂₃	semidirect
317. C₂×#126	C₂²×C₂₃	semidirect
318. C₂×#125	C₂²×C₂₃	semidirect
320. C₂×#124	C₂²×C₂₃	semidirect
321. #525	C₂²×C₂₃	semidirect
322. C₂×#123	C₂²×C₂₃	semidirect
323. C₂×#123	C₂²×C₂₃	semidirect
325. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
326. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
330. C₂×#121	C₂²×C₂₃	semidirect
331. C₂×#121	C₂²×C₂₃	semidirect
332. C₂×#121	C₂²×C₂₃	semidirect
334. C₄×#41	C₂²×C₂₃	semidirect
335. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
336. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
341. C₂×C₄×D₄	C₂²×C₂₃	semidirect
342. C₂×C₄×D₄	C₂²×C₂₃	semidirect
343. C₂×C₄×D₄	C₂²×C₂₃	semidirect
344. C₂×C₄×D₄	C₂²×C₂₃	semidirect
346. C₂×#117	C₂²×C₂₃	semidirect
347. C₂×#117	C₂²×C₂₃	semidirect
351. C₂²×C₄²	C₂²×C₂₃	semidirect
355. C₂×C₂₃	#3460	direct (N × H)
363. C₂×#41	C₂³×C₂₃	semidirect
385. C₄⋊Q₈	C₂³×C₂₃	semidirect
387. #126	C₂³×C₂₃	semidirect
388. #125	C₂³×C₂₃	semidirect
390. #124	C₂³×C₂₃	semidirect
391. #123	C₂³×C₂₃	semidirect
392. #123	C₂³×C₂₃	semidirect
394. C₂²⋊Q₈	C₂³×C₂₃	semidirect
395. C₂²⋊Q₈	C₂³×C₂₃	semidirect
399. #121	C₂³×C₂₃	semidirect
400. #121	C₂³×C₂₃	semidirect
401. #121	C₂³×C₂₃	semidirect
403. C₄×Q₈	C₂³×C₂₃	semidirect
404. C₄×Q₈	C₂³×C₂₃	semidirect
409. C₄×D₄	C₂³×C₂₃	semidirect
410. C₄×D₄	C₂³×C₂₃	semidirect
411. C₄×D₄	C₂³×C₂₃	semidirect
413. #117	C₂³×C₂₃	semidirect
414. #117	C₂³×C₂₃	semidirect
438. C₂×C₄²	C₂³×C₂₃	semidirect
439. C₂₃	C₂×#3460	direct (N × H)
475. C₂²×C₄	#41×C₂₃	semidirect
553. C₂×C₄	C₂×#41×C₂₃	semidirect
591. C₂	C₂₃×#3460	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3460	2
C₂×C₂₃×#544	2
C₂×C₂₃×#542	2
C₂×C₂₃×#540	2
C₂×C₂₃×#538	2
C₂×C₂₃×#537	2
C₂×C₂₃×#535	2
C₂×C₂₃×#532	2
C₂×C₂₃×#529	2
C₂×C₂₃×#525	2
C₂×C₄×#41×C₂₃	2
C₂²×C₄×D₄×C₂₃	2
C₂×#3460	23

Subgroups — C2×C23×#3460 #19210305

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3460 #19210305