Subgroups — C₂²×C₂₃×#447 #19207973

Order 5888.

7470 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₈×C₂₃	C₂	1	2	yes	maximal, complemented
3	C₂²×C₂₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#447	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₂₃×#102	C₂	1	2	yes	maximal, complemented
6	C₂²×C₂₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂⁶×C₂₃	—	2	1	no	—
8	C₂³×D₄×C₂₃	—	2	16	no	—
9	C₂³×D₄×C₂₃	—	2	1	no	—
10	C₂³×D₄×C₂₃	—	2	6	no	—
11	C₂³×D₄×C₂₃	—	2	1	no	—
12	C₂³×D₄×C₂₃	C₂²	1	2	yes	—
13	C₂³×D₄×C₂₃	C₂²	1	12	yes	complemented
14	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
15	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
16	C₂²×D₈×C₂₃	—	2	16	no	—
17	C₂²×D₈×C₂₃	C₂²	1	24	yes	complemented
18	C₂³×C₈×C₂₃	C₂²	1	2	yes	complemented
19	C₂×C₂₃×#121	—	2	6	no	—
20	C₂×C₂₃×#121	C₂²	1	12	yes	complemented
21	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₂²⋊C₄×C₂₃	—	2	1	no	—
23	C₂₃×#447	C₂²	1	64	yes	direct product factor
24	C₂×C₂₃×#102	C₂²	1	24	yes	complemented
25	C₂×C₂₃×C₂²⋊C₈	C₂²	1	12	yes	complemented
26	C₂⁵×C₂₃	—	2	16	no	—
27	C₂⁵×C₂₃	—	2	12	no	—
28	C₂⁵×C₂₃	—	2	2	no	—
29	C₂⁵×C₂₃	—	2	1	no	—
30	C₂⁵×C₂₃	—	4	8	no	—
31	C₂⁵×C₂₃	—	4	8	no	—
32	C₂⁵×C₂₃	D₄	1	1	yes	characteristic
33	C₂²×D₄×C₂₃	—	2	16	no	—
34	C₂²×D₄×C₂₃	—	2	96	no	—
35	C₂²×D₄×C₂₃	—	2	96	no	—
36	C₂²×D₄×C₂₃	—	2	12	no	—
37	C₂²×D₄×C₂₃	—	2	6	no	—
38	C₂²×D₄×C₂₃	—	2	8	no	—
39	C₂²×D₄×C₂₃	—	2	12	no	—
40	C₂²×D₄×C₂₃	—	2	24	no	—
41	C₂²×D₄×C₂₃	—	2	8	no	—
42	C₂²×D₄×C₂₃	—	2	3	no	—
43	C₂²×D₄×C₂₃	—	4	8	no	—
44	C₂²×D₄×C₂₃	D₄	1	16	yes	complemented
45	C₂²×D₄×C₂₃	C₂³	1	12	yes	—
46	C₂²×D₄×C₂₃	C₂³	1	16	yes	complemented
47	C₂²×D₄×C₂₃	C₂³	1	6	yes	complemented
48	C₂³×C₄×C₂₃	—	2	8	no	—
49	C₂³×C₄×C₂₃	—	2	1	no	—
50	C₂³×C₄×C₂₃	D₄	1	6	yes	—
51	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₂₃	C₂³	1	6	yes	—
53	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
54	C₂×D₈×C₂₃	—	2	96	no	—
55	C₂×D₈×C₂₃	C₂³	1	32	yes	complemented
56	C₂²×C₈×C₂₃	—	2	8	no	—
57	C₂²×C₈×C₂₃	C₂³	1	12	yes	complemented
58	C₂₃×#121	—	2	24	no	—
59	C₂₃×#121	C₂³	1	16	yes	complemented
60	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
61	C₂×C₄⋊C₄×C₂₃	C₂³	1	6	yes	complemented
62	C₂×C₂²⋊C₄×C₂₃	—	2	12	no	—
63	C₂₃×#102	C₂³	1	32	yes	complemented
64	C₂₃×C₂²⋊C₈	C₂³	1	16	yes	complemented
65	C₂⁴×C₂₃	—	2	4	no	—
66	C₂⁴×C₂₃	—	2	4	no	—
67	C₂⁴×C₂₃	—	2	96	no	—
68	C₂⁴×C₂₃	—	2	16	no	—
69	C₂⁴×C₂₃	—	2	12	no	—
70	C₂⁴×C₂₃	—	2	16	no	—
71	C₂⁴×C₂₃	—	2	6	no	—
72	C₂⁴×C₂₃	—	4	48	no	—
73	C₂⁴×C₂₃	—	4	128	no	—
74	C₂⁴×C₂₃	—	4	8	no	—
75	C₂⁴×C₂₃	—	4	48	no	—
76	C₂⁴×C₂₃	—	4	8	no	—
77	C₂⁴×C₂₃	—	4	4	no	—
78	C₂⁴×C₂₃	—	4	4	no	—
79	C₂⁴×C₂₃	—	4	4	no	—
80	C₂⁴×C₂₃	D₈	1	8	yes	complemented
81	C₂⁴×C₂₃	C₂×D₄	1	6	yes	—
82	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
83	C₂×D₄×C₂₃	—	2	96	no	—
84	C₂×D₄×C₂₃	—	2	192	no	—
85	C₂×D₄×C₂₃	—	2	64	no	—
86	C₂×D₄×C₂₃	—	2	16	no	—
87	C₂×D₄×C₂₃	—	2	48	no	—
88	C₂×D₄×C₂₃	—	2	12	no	—
89	C₂×D₄×C₂₃	—	2	24	no	—
90	C₂×D₄×C₂₃	—	2	16	no	—
91	C₂×D₄×C₂₃	—	2	24	no	—
92	C₂×D₄×C₂₃	—	2	6	no	—
93	C₂×D₄×C₂₃	—	4	48	no	—
94	C₂×D₄×C₂₃	—	4	12	no	—
95	C₂×D₄×C₂₃	C₂×D₄	1	48	yes	complemented
96	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
97	C₂×D₄×C₂₃	C₂⁴	1	4	yes	complemented
98	C₂²×C₄×C₂₃	—	2	4	no	—
99	C₂²×C₄×C₂₃	—	2	24	no	—
100	C₂²×C₄×C₂₃	—	2	24	no	—
101	C₂²×C₄×C₂₃	—	2	6	no	—
102	C₂²×C₄×C₂₃	—	4	4	no	—
103	C₂²×C₄×C₂₃	C₂×D₄	1	6	yes	—
104	C₂²×C₄×C₂₃	C₂×D₄	1	12	yes	—
105	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
106	C₂²×C₄×C₂₃	C₂×D₄	1	8	yes	—
107	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
108	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
109	D₈×C₂₃	—	2	64	no	—
110	C₂×C₈×C₂₃	—	2	24	no	—
111	C₂×C₈×C₂₃	C₂⁴	1	8	yes	complemented
112	C₄⋊C₄×C₂₃	—	2	6	no	—
113	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	complemented
114	C₂²⋊C₄×C₂₃	—	2	16	no	—
115	C₂²×#447	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂³×C₂₃	—	2	12	no	—
117	C₂³×C₂₃	—	2	12	no	—
118	C₂³×C₂₃	—	2	32	no	—
119	C₂³×C₂₃	—	2	64	no	—
120	C₂³×C₂₃	—	2	48	no	—
121	C₂³×C₂₃	—	2	8	no	—
122	C₂³×C₂₃	—	2	4	no	—
123	C₂³×C₂₃	—	4	384	no	—
124	C₂³×C₂₃	—	4	32	no	—
125	C₂³×C₂₃	—	4	24	no	—
126	C₂³×C₂₃	—	4	32	no	—
127	C₂³×C₂₃	—	4	24	no	—
128	C₂³×C₂₃	—	4	64	no	—
129	C₂³×C₂₃	—	4	12	no	—
130	C₂³×C₂₃	—	4	12	no	—
131	C₂³×C₂₃	—	4	12	no	—
132	C₂³×C₂₃	—	8	16	no	—
133	C₂³×C₂₃	#120	1	4	yes	—
134	C₂³×C₂₃	C₂×D₈	1	4	yes	—
135	C₂³×C₂₃	C₂×D₈	1	24	yes	complemented
136	C₂³×C₂₃	AGL(1,ℤ/8)	1	4	yes	—
137	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
138	C₂³×C₂₃	C₂²×D₄	1	3	yes	—
139	D₄×C₂₃	—	2	64	no	—
140	D₄×C₂₃	—	2	48	no	—
141	D₄×C₂₃	—	2	8	no	—
142	D₄×C₂₃	—	2	8	no	—
143	D₄×C₂₃	—	4	32	no	—
144	D₄×C₂₃	—	4	12	no	—
145	D₄×C₂₃	C₂²×D₄	1	16	yes	complemented
146	C₂×C₄×C₂₃	—	2	12	no	—
147	C₂×C₄×C₂₃	—	2	24	no	—
148	C₂×C₄×C₂₃	—	2	8	no	—
149	C₂×C₄×C₂₃	—	2	4	no	—
150	C₂×C₄×C₂₃	—	4	12	no	—
151	C₂×C₄×C₂₃	#120	1	12	yes	—
152	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
153	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
154	C₂×C₄×C₂₃	C₂²×D₄	1	12	yes	—
155	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
156	C₈×C₂₃	—	2	8	no	—
157	C₂⁴×D₄	C₂×C₂₃	1	1	yes	characteristic, complemented
158	C₂³×D₈	C₂×C₂₃	1	2	yes	complemented
159	C₂²×#121	C₂×C₂₃	1	1	yes	characteristic, complemented
160	C₂×#447	C₂×C₂₃	1	24	yes	direct product factor
161	C₂²×#102	C₂×C₂₃	1	2	yes	complemented
162	C₂²×C₂²⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
163	C₂²×C₂₃	—	2	4	no	—
164	C₂²×C₂₃	—	2	48	no	—
165	C₂²×C₂₃	—	2	4	no	—
166	C₂²×C₂₃	—	2	16	no	—
167	C₂²×C₂₃	—	4	128	no	—
168	C₂²×C₂₃	—	4	96	no	—
169	C₂²×C₂₃	—	4	8	no	—
170	C₂²×C₂₃	—	4	8	no	—
171	C₂²×C₂₃	—	4	4	no	—
172	C₂²×C₂₃	—	4	4	no	—
173	C₂²×C₂₃	—	4	4	no	—
174	C₂²×C₂₃	—	8	24	no	—
175	C₂²×C₂₃	#447	1	16	yes	direct product factor
176	C₂²×C₂₃	C₂×#120	1	6	yes	—
177	C₂²×C₂₃	C₂²×D₈	1	6	yes	—
178	C₂²×C₂₃	C₂²×D₈	1	8	yes	complemented
179	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	6	yes	—
180	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
181	C₄×C₂₃	—	2	4	no	—
182	C₄×C₂₃	—	4	4	no	—
183	C₄×C₂₃	C₂×#120	1	6	yes	—
184	C₄×C₂₃	C₂³×D₄	1	2	yes	—
185	C₂⁶	—	2	1	no	—
186	C₂³×D₄	—	2	16	no	—
187	C₂³×D₄	—	2	1	no	—
188	C₂³×D₄	—	2	1	no	—
189	C₂³×D₄	—	2	6	no	—
190	C₂³×D₄	C₂²×C₂₃	1	2	yes	—
191	C₂³×D₄	C₂²×C₂₃	1	12	yes	complemented
192	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
193	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
194	C₂²×D₈	—	2	16	no	—
195	C₂²×D₈	C₂²×C₂₃	1	24	yes	complemented
196	C₂³×C₈	C₂²×C₂₃	1	2	yes	complemented
197	C₂×#121	—	2	6	no	—
198	C₂×#121	C₂²×C₂₃	1	12	yes	complemented
199	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
200	C₂²×C₂²⋊C₄	—	2	1	no	—
201	#447	C₂²×C₂₃	1	64	yes	direct product factor
202	C₂×#102	C₂²×C₂₃	1	24	yes	complemented
203	C₂×C₂²⋊C₈	C₂²×C₂₃	1	12	yes	complemented
204	C₂×C₂₃	—	2	8	no	—
205	C₂×C₂₃	—	4	16	no	—
206	C₂×C₂₃	—	8	4	no	—
207	C₂×C₂₃	C₂×#447	1	12	yes	direct product factor
208	C₂×C₂₃	C₂²×#120	1	1	yes	characteristic
209	C₂×C₂₃	C₂³×D₈	1	1	yes	characteristic
210	C₂×C₂₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
211	C₂⁵	—	2	16	no	—
212	C₂⁵	—	2	2	no	—
213	C₂⁵	—	2	12	no	—
214	C₂⁵	—	2	1	no	—
215	C₂⁵	—	4	8	no	—
216	C₂⁵	—	4	8	no	—
217	C₂⁵	D₄×C₂₃	1	1	yes	characteristic
218	C₂²×D₄	—	2	16	no	—
219	C₂²×D₄	—	2	96	no	—
220	C₂²×D₄	—	2	96	no	—
221	C₂²×D₄	—	2	12	no	—
222	C₂²×D₄	—	2	6	no	—
223	C₂²×D₄	—	2	8	no	—
224	C₂²×D₄	—	2	12	no	—
225	C₂²×D₄	—	2	24	no	—
226	C₂²×D₄	—	2	8	no	—
227	C₂²×D₄	—	2	3	no	—
228	C₂²×D₄	—	4	8	no	—
229	C₂²×D₄	D₄×C₂₃	1	16	yes	complemented
230	C₂²×D₄	C₂³×C₂₃	1	12	yes	—
231	C₂²×D₄	C₂³×C₂₃	1	16	yes	complemented
232	C₂²×D₄	C₂³×C₂₃	1	6	yes	complemented
233	C₂³×C₄	—	2	8	no	—
234	C₂³×C₄	—	2	1	no	—
235	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
236	C₂³×C₄	D₄×C₂₃	1	6	yes	—
237	C₂³×C₄	C₂³×C₂₃	1	6	yes	—
238	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
239	C₂×D₈	—	2	96	no	—
240	C₂×D₈	C₂³×C₂₃	1	32	yes	complemented
241	C₂²×C₈	—	2	8	no	—
242	C₂²×C₈	C₂³×C₂₃	1	12	yes	complemented
243	#121	—	2	24	no	—
244	#121	C₂³×C₂₃	1	16	yes	complemented
245	C₂×C₄⋊C₄	—	2	3	no	—
246	C₂×C₄⋊C₄	C₂³×C₂₃	1	6	yes	complemented
247	C₂×C₂²⋊C₄	—	2	12	no	—
248	#102	C₂³×C₂₃	1	32	yes	complemented
249	C₂²⋊C₈	C₂³×C₂₃	1	16	yes	complemented
250	C₂₃	C₂²×#447	1	1	yes	characteristic, direct product factor, Sylow
251	C₂⁴	—	2	4	no	—
252	C₂⁴	—	2	4	no	—
253	C₂⁴	—	2	96	no	—
254	C₂⁴	—	2	16	no	—
255	C₂⁴	—	2	12	no	—
256	C₂⁴	—	2	16	no	—
257	C₂⁴	—	2	6	no	—
258	C₂⁴	—	4	48	no	—
259	C₂⁴	—	4	128	no	—
260	C₂⁴	—	4	8	no	—
261	C₂⁴	—	4	48	no	—
262	C₂⁴	—	4	8	no	—
263	C₂⁴	—	4	4	no	—
264	C₂⁴	—	4	4	no	—
265	C₂⁴	—	4	4	no	—
266	C₂⁴	D₈×C₂₃	1	8	yes	complemented
267	C₂⁴	C₂×D₄×C₂₃	1	6	yes	—
268	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
269	C₂×D₄	—	2	96	no	—
270	C₂×D₄	—	2	192	no	—
271	C₂×D₄	—	2	64	no	—
272	C₂×D₄	—	2	16	no	—
273	C₂×D₄	—	2	48	no	—
274	C₂×D₄	—	2	24	no	—
275	C₂×D₄	—	2	12	no	—
276	C₂×D₄	—	2	16	no	—
277	C₂×D₄	—	2	24	no	—
278	C₂×D₄	—	2	6	no	—
279	C₂×D₄	—	4	48	no	—
280	C₂×D₄	—	4	12	no	—
281	C₂×D₄	C₂×D₄×C₂₃	1	48	yes	complemented
282	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
283	C₂×D₄	C₂⁴×C₂₃	1	4	yes	complemented
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	24	no	—
286	C₂²×C₄	—	2	24	no	—
287	C₂²×C₄	—	2	6	no	—
288	C₂²×C₄	—	4	4	no	—
289	C₂²×C₄	C₂×D₄×C₂₃	1	6	yes	—
290	C₂²×C₄	C₂×D₄×C₂₃	1	12	yes	—
291	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
292	C₂²×C₄	C₂×D₄×C₂₃	1	8	yes	—
293	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
294	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
295	D₈	—	2	64	no	—
296	C₂×C₈	—	2	24	no	—
297	C₂×C₈	C₂⁴×C₂₃	1	8	yes	complemented
298	C₄⋊C₄	—	2	6	no	—
299	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	complemented
300	C₂²⋊C₄	—	2	16	no	—
301	C₂³	—	2	12	no	—
302	C₂³	—	2	32	no	—
303	C₂³	—	2	12	no	—
304	C₂³	—	2	64	no	—
305	C₂³	—	2	8	no	—
306	C₂³	—	2	48	no	—
307	C₂³	—	2	4	no	—
308	C₂³	—	4	384	no	—
309	C₂³	—	4	32	no	—
310	C₂³	—	4	24	no	—
311	C₂³	—	4	32	no	—
312	C₂³	—	4	24	no	—
313	C₂³	—	4	64	no	—
314	C₂³	—	4	12	no	—
315	C₂³	—	4	12	no	—
316	C₂³	—	4	12	no	—
317	C₂³	—	8	16	no	—
318	C₂³	C₂₃×#120	1	4	yes	—
319	C₂³	C₂×D₈×C₂₃	1	4	yes	—
320	C₂³	C₂×D₈×C₂₃	1	24	yes	complemented
321	C₂³	C₂₃×AGL(1,ℤ/8)	1	4	yes	—
322	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
323	C₂³	C₂²×D₄×C₂₃	1	3	yes	—
324	D₄	—	2	64	no	—
325	D₄	—	2	8	no	—
326	D₄	—	2	8	no	—
327	D₄	—	2	48	no	—
328	D₄	—	4	32	no	—
329	D₄	—	4	12	no	—
330	D₄	C₂²×D₄×C₂₃	1	16	yes	complemented
331	C₂×C₄	—	2	12	no	—
332	C₂×C₄	—	2	8	no	—
333	C₂×C₄	—	2	24	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	4	12	no	—
336	C₂×C₄	C₂₃×#120	1	12	yes	—
337	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
338	C₂×C₄	C₂²×D₄×C₂₃	1	12	yes	—
339	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
340	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
341	C₈	—	2	8	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	48	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	2	16	no	—
346	C₂²	—	4	128	no	—
347	C₂²	—	4	96	no	—
348	C₂²	—	4	8	no	—
349	C₂²	—	4	8	no	—
350	C₂²	—	4	4	no	—
351	C₂²	—	4	4	no	—
352	C₂²	—	4	4	no	—
353	C₂²	—	8	24	no	—
354	C₂²	C₂₃×#447	1	16	yes	direct product factor
355	C₂²	C₂×C₂₃×#120	1	6	yes	—
356	C₂²	C₂²×D₈×C₂₃	1	6	yes	—
357	C₂²	C₂²×D₈×C₂₃	1	8	yes	complemented
358	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	6	yes	—
359	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
360	C₄	—	2	4	no	—
361	C₄	—	4	4	no	—
362	C₄	C₂×C₂₃×#120	1	6	yes	—
363	C₄	C₂³×D₄×C₂₃	1	2	yes	—
364	C₂	—	2	8	no	—
365	C₂	—	4	16	no	—
366	C₂	—	8	4	no	—
367	C₂	C₂×C₂₃×#447	1	12	yes	direct product factor
368	C₂	C₂²×C₂₃×#120	1	1	yes	characteristic
369	C₂	C₂³×D₈×C₂₃	1	1	yes	characteristic
370	C₂	C₂²×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₂₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₃ ◁ C₂⁴×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁴×D₄×C₂₃	C₂	semidirect
2. C₂³×D₈×C₂₃	C₂	semidirect
3. C₂²×C₂₃×#121	C₂	semidirect
4. C₂×C₂₃×#447	C₂	direct (N × H)
5. C₂²×C₂₃×#102	C₂	semidirect
6. C₂²×C₂₃×C₂²⋊C₈	C₂	semidirect
13. C₂³×D₄×C₂₃	C₂²	semidirect
14. C₂³×D₄×C₂₃	C₂²	semidirect
17. C₂²×D₈×C₂₃	C₂²	semidirect
18. C₂³×C₈×C₂₃	C₂²	semidirect
20. C₂×C₂₃×#121	C₂²	semidirect
21. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
23. C₂₃×#447	C₂²	direct (N × H)
24. C₂×C₂₃×#102	C₂²	semidirect
25. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
44. C₂²×D₄×C₂₃	D₄	semidirect
46. C₂²×D₄×C₂₃	C₂³	semidirect
47. C₂²×D₄×C₂₃	C₂³	semidirect
55. C₂×D₈×C₂₃	C₂³	semidirect
57. C₂²×C₈×C₂₃	C₂³	semidirect
59. C₂₃×#121	C₂³	semidirect
61. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
63. C₂₃×#102	C₂³	semidirect
64. C₂₃×C₂²⋊C₈	C₂³	semidirect
80. C₂⁴×C₂₃	D₈	semidirect
95. C₂×D₄×C₂₃	C₂×D₄	semidirect
97. C₂×D₄×C₂₃	C₂⁴	semidirect
111. C₂×C₈×C₂₃	C₂⁴	semidirect
113. C₄⋊C₄×C₂₃	C₂⁴	semidirect
115. C₂²×#447	C₂₃	direct (N × H)
135. C₂³×C₂₃	C₂×D₈	semidirect
145. D₄×C₂₃	C₂²×D₄	semidirect
157. C₂⁴×D₄	C₂×C₂₃	semidirect
158. C₂³×D₈	C₂×C₂₃	semidirect
159. C₂²×#121	C₂×C₂₃	semidirect
160. C₂×#447	C₂×C₂₃	direct (N × H)
161. C₂²×#102	C₂×C₂₃	semidirect
162. C₂²×C₂²⋊C₈	C₂×C₂₃	semidirect
175. C₂²×C₂₃	#447	direct (N × H)
178. C₂²×C₂₃	C₂²×D₈	semidirect
191. C₂³×D₄	C₂²×C₂₃	semidirect
192. C₂³×D₄	C₂²×C₂₃	semidirect
195. C₂²×D₈	C₂²×C₂₃	semidirect
196. C₂³×C₈	C₂²×C₂₃	semidirect
198. C₂×#121	C₂²×C₂₃	semidirect
199. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
201. #447	C₂²×C₂₃	direct (N × H)
202. C₂×#102	C₂²×C₂₃	semidirect
203. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
207. C₂×C₂₃	C₂×#447	direct (N × H)
229. C₂²×D₄	D₄×C₂₃	semidirect
231. C₂²×D₄	C₂³×C₂₃	semidirect
232. C₂²×D₄	C₂³×C₂₃	semidirect
240. C₂×D₈	C₂³×C₂₃	semidirect
242. C₂²×C₈	C₂³×C₂₃	semidirect
244. #121	C₂³×C₂₃	semidirect
246. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
248. #102	C₂³×C₂₃	semidirect
249. C₂²⋊C₈	C₂³×C₂₃	semidirect
250. C₂₃	C₂²×#447	direct (N × H)
266. C₂⁴	D₈×C₂₃	semidirect
281. C₂×D₄	C₂×D₄×C₂₃	semidirect
283. C₂×D₄	C₂⁴×C₂₃	semidirect
297. C₂×C₈	C₂⁴×C₂₃	semidirect
299. C₄⋊C₄	C₂⁴×C₂₃	semidirect
320. C₂³	C₂×D₈×C₂₃	semidirect
330. D₄	C₂²×D₄×C₂₃	semidirect
354. C₂²	C₂₃×#447	direct (N × H)
357. C₂²	C₂²×D₈×C₂₃	semidirect
367. C₂	C₂×C₂₃×#447	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₄×C₂₃	2
C₂³×D₈×C₂₃	2
C₂²×C₂₃×#121	2
C₂×C₂₃×#447	2
C₂²×C₂₃×#102	2
C₂²×C₂₃×C₂²⋊C₈	2
C₂²×#447	23

Subgroups — C22×C23×#447 #19207973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₂₃×#447 #19207973