Subgroups — C₂²×C₂₃×#482 #19208128

Order 5888.

2702 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×#121	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#482	C₂	1	24	yes	maximal, direct product factor
4	C₂²×C₂₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₂₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₂₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₂₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₂₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₂₃	—	2	1	no	—
10	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
14	C₂×C₂₃×#121	—	2	6	no	—
15	C₂×C₂₃×#121	C₂²	1	12	yes	—
16	C₂×C₂₃×#117	—	2	6	no	—
17	C₂×C₂₃×#117	C₂²	1	12	yes	complemented
18	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊C₄×C₂₃	—	2	1	no	—
22	C₂²×C₂²⋊C₄×C₂₃	—	2	1	no	—
23	C₂²×C₄²×C₂₃	—	2	1	no	—
24	C₂₃×#482	C₂²	1	64	yes	direct product factor
25	C₂×C₂₃×#107	C₂²	1	12	yes	complemented
26	C₂×C₂₃×#106	C₂²	1	12	yes	complemented
27	C₂×C₂₃×#102	C₂²	1	12	yes	complemented
28	C₂×C₂₃×#102	C₂²	1	12	yes	complemented
29	C₂×C₂₃×C₂²⋊C₈	C₂²	1	12	yes	complemented
30	C₂⁵×C₂₃	—	2	1	no	—
31	C₂⁵×C₂₃	D₄	1	1	yes	characteristic
32	C₂²×D₄×C₂₃	—	2	12	no	—
33	C₂²×D₄×C₂₃	—	2	3	no	—
34	C₂²×D₄×C₂₃	—	2	4	no	—
35	C₂²×D₄×C₂₃	—	2	4	no	—
36	C₂²×D₄×C₂₃	—	4	8	no	—
37	C₂²×D₄×C₂₃	C₂³	1	6	yes	—
38	C₂³×C₄×C₂₃	—	2	4	no	—
39	C₂³×C₄×C₂₃	—	2	4	no	—
40	C₂³×C₄×C₂₃	—	2	1	no	—
41	C₂³×C₄×C₂₃	—	2	1	no	—
42	C₂³×C₄×C₂₃	—	2	1	no	—
43	C₂³×C₄×C₂₃	D₄	1	6	yes	—
44	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₂₃	C₂³	1	6	yes	—
46	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₂₃	—	2	4	no	—
48	C₂²×C₈×C₂₃	—	2	4	no	—
49	C₂²×C₈×C₂₃	C₂³	1	6	yes	—
50	C₂²×C₈×C₂₃	C₂³	1	6	yes	—
51	C₂₃×#121	—	2	24	no	—
52	C₂₃×#121	C₂³	1	16	yes	—
53	C₂₃×#117	—	2	24	no	—
54	C₂₃×#117	C₂³	1	16	yes	complemented
55	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
56	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
57	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
58	C₂×C₄⋊C₄×C₂₃	C₂³	1	6	yes	—
59	C₂×C₄⋊C₄×C₂₃	C₂³	1	6	yes	—
60	C₂×C₄⋊C₄×C₂₃	C₂³	1	6	yes	—
61	C₂×C₂²⋊C₄×C₂₃	—	2	12	no	—
62	C₂×C₂²⋊C₄×C₂₃	—	2	12	no	—
63	C₂×C₄²×C₂₃	—	2	12	no	—
64	C₂₃×#107	C₂³	1	16	yes	complemented
65	C₂₃×#106	C₂³	1	16	yes	complemented
66	C₂₃×#102	C₂³	1	16	yes	complemented
67	C₂₃×#102	C₂³	1	16	yes	complemented
68	C₂₃×C₂²⋊C₈	C₂³	1	16	yes	complemented
69	C₂⁴×C₂₃	—	2	4	no	—
70	C₂⁴×C₂₃	—	2	4	no	—
71	C₂⁴×C₂₃	—	2	4	no	—
72	C₂⁴×C₂₃	—	2	6	no	—
73	C₂⁴×C₂₃	—	4	4	no	—
74	C₂⁴×C₂₃	—	4	4	no	—
75	C₂⁴×C₂₃	—	4	4	no	—
76	C₂⁴×C₂₃	C₂×D₄	1	6	yes	—
77	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
78	C₂×D₄×C₂₃	—	2	16	no	—
79	C₂×D₄×C₂₃	—	2	6	no	—
80	C₂×D₄×C₂₃	—	2	12	no	—
81	C₂×D₄×C₂₃	—	2	12	no	—
82	C₂×D₄×C₂₃	—	4	48	no	—
83	C₂×D₄×C₂₃	—	4	12	no	—
84	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
85	C₂²×C₄×C₂₃	—	2	4	no	—
86	C₂²×C₄×C₂₃	—	2	24	no	—
87	C₂²×C₄×C₂₃	—	2	12	no	—
88	C₂²×C₄×C₂₃	—	2	12	no	—
89	C₂²×C₄×C₂₃	—	2	6	no	—
90	C₂²×C₄×C₂₃	—	2	6	no	—
91	C₂²×C₄×C₂₃	—	2	6	no	—
92	C₂²×C₄×C₂₃	—	4	4	no	—
93	C₂²×C₄×C₂₃	—	4	4	no	—
94	C₂²×C₄×C₂₃	—	4	4	no	—
95	C₂²×C₄×C₂₃	C₂×D₄	1	6	yes	—
96	C₂²×C₄×C₂₃	C₂×D₄	1	12	yes	—
97	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
98	C₂²×C₄×C₂₃	#41	1	4	yes	—
99	C₂²×C₄×C₂₃	#41	1	4	yes	—
100	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
101	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
102	C₂×C₈×C₂₃	—	2	12	no	—
103	C₂×C₈×C₂₃	—	2	12	no	—
104	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
105	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
106	C₄⋊C₄×C₂₃	—	2	6	no	—
107	C₄⋊C₄×C₂₃	—	2	6	no	—
108	C₄⋊C₄×C₂₃	—	2	6	no	—
109	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
110	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
111	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
112	C₂²⋊C₄×C₂₃	—	2	16	no	—
113	C₂²⋊C₄×C₂₃	—	2	16	no	—
114	C₄²×C₂₃	—	2	16	no	—
115	C₂²×#482	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	12	no	—
119	C₂³×C₂₃	—	2	4	no	—
120	C₂³×C₂₃	—	4	16	no	—
121	C₂³×C₂₃	—	4	12	no	—
122	C₂³×C₂₃	—	4	12	no	—
123	C₂³×C₂₃	—	4	12	no	—
124	C₂³×C₂₃	—	8	16	no	—
125	C₂³×C₂₃	#123	1	4	yes	—
126	C₂³×C₂₃	#135	1	4	yes	—
127	C₂³×C₂₃	AGL(1,ℤ/8)	1	4	yes	—
128	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
129	C₂³×C₂₃	C₂²×D₄	1	3	yes	—
130	D₄×C₂₃	—	2	4	no	—
131	D₄×C₂₃	—	2	4	no	—
132	D₄×C₂₃	—	4	32	no	—
133	D₄×C₂₃	—	4	12	no	—
134	C₂×C₄×C₂₃	—	2	12	no	—
135	C₂×C₄×C₂₃	—	2	24	no	—
136	C₂×C₄×C₂₃	—	2	4	no	—
137	C₂×C₄×C₂₃	—	2	4	no	—
138	C₂×C₄×C₂₃	—	2	4	no	—
139	C₂×C₄×C₂₃	—	2	4	no	—
140	C₂×C₄×C₂₃	—	2	4	no	—
141	C₂×C₄×C₂₃	—	4	12	no	—
142	C₂×C₄×C₂₃	—	4	12	no	—
143	C₂×C₄×C₂₃	—	4	12	no	—
144	C₂×C₄×C₂₃	#123	1	12	yes	—
145	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
146	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
147	C₂×C₄×C₂₃	C₂×#41	1	6	yes	—
148	C₂×C₄×C₂₃	C₂×#41	1	6	yes	—
149	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
150	C₈×C₂₃	—	2	4	no	—
151	C₈×C₂₃	—	2	4	no	—
152	C₂²×#121	C₂×C₂₃	1	1	yes	characteristic
153	C₂²×#117	C₂×C₂₃	1	1	yes	characteristic, complemented
154	C₂×#482	C₂×C₂₃	1	24	yes	direct product factor
155	C₂²×#107	C₂×C₂₃	1	1	yes	characteristic, complemented
156	C₂²×#106	C₂×C₂₃	1	1	yes	characteristic, complemented
157	C₂²×#102	C₂×C₂₃	1	1	yes	characteristic, complemented
158	C₂²×#102	C₂×C₂₃	1	1	yes	characteristic, complemented
159	C₂²×C₂²⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
160	C₂²×C₂₃	—	2	4	no	—
161	C₂²×C₂₃	—	2	4	no	—
162	C₂²×C₂₃	—	2	4	no	—
163	C₂²×C₂₃	—	4	24	no	—
164	C₂²×C₂₃	—	4	4	no	—
165	C₂²×C₂₃	—	4	4	no	—
166	C₂²×C₂₃	—	4	4	no	—
167	C₂²×C₂₃	—	8	24	no	—
168	C₂²×C₂₃	#482	1	16	yes	direct product factor
169	C₂²×C₂₃	C₂×#123	1	6	yes	—
170	C₂²×C₂₃	C₂×#135	1	6	yes	—
171	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	6	yes	—
172	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
173	C₄×C₂₃	—	2	4	no	—
174	C₄×C₂₃	—	4	4	no	—
175	C₄×C₂₃	—	4	4	no	—
176	C₄×C₂₃	—	4	4	no	—
177	C₄×C₂₃	C₂×#123	1	6	yes	—
178	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
179	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
180	C₂³×D₄	—	2	1	no	—
181	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
182	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
183	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
184	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
185	C₂×#121	—	2	6	no	—
186	C₂×#121	C₂²×C₂₃	1	12	yes	—
187	C₂×#117	—	2	6	no	—
188	C₂×#117	C₂²×C₂₃	1	12	yes	complemented
189	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
190	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
191	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
192	C₂²×C₂²⋊C₄	—	2	1	no	—
193	C₂²×C₂²⋊C₄	—	2	1	no	—
194	C₂²×C₄²	—	2	1	no	—
195	#482	C₂²×C₂₃	1	64	yes	direct product factor
196	C₂×#107	C₂²×C₂₃	1	12	yes	complemented
197	C₂×#106	C₂²×C₂₃	1	12	yes	complemented
198	C₂×#102	C₂²×C₂₃	1	12	yes	complemented
199	C₂×#102	C₂²×C₂₃	1	12	yes	complemented
200	C₂×C₂²⋊C₈	C₂²×C₂₃	1	12	yes	complemented
201	C₂×C₂₃	—	4	4	no	—
202	C₂×C₂₃	—	8	4	no	—
203	C₂×C₂₃	C₂×#482	1	12	yes	direct product factor
204	C₂×C₂₃	C₂²×#123	1	1	yes	characteristic
205	C₂×C₂₃	C₂²×#135	1	1	yes	characteristic
206	C₂×C₂₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
207	C₂⁵	—	2	1	no	—
208	C₂⁵	D₄×C₂₃	1	1	yes	characteristic
209	C₂²×D₄	—	2	12	no	—
210	C₂²×D₄	—	2	3	no	—
211	C₂²×D₄	—	2	4	no	—
212	C₂²×D₄	—	2	4	no	—
213	C₂²×D₄	—	4	8	no	—
214	C₂²×D₄	C₂³×C₂₃	1	6	yes	—
215	C₂³×C₄	—	2	4	no	—
216	C₂³×C₄	—	2	4	no	—
217	C₂³×C₄	—	2	1	no	—
218	C₂³×C₄	—	2	1	no	—
219	C₂³×C₄	—	2	1	no	—
220	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
221	C₂³×C₄	D₄×C₂₃	1	6	yes	—
222	C₂³×C₄	C₂³×C₂₃	1	6	yes	—
223	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
224	C₂²×C₈	—	2	4	no	—
225	C₂²×C₈	—	2	4	no	—
226	C₂²×C₈	C₂³×C₂₃	1	6	yes	—
227	C₂²×C₈	C₂³×C₂₃	1	6	yes	—
228	#121	—	2	24	no	—
229	#121	C₂³×C₂₃	1	16	yes	—
230	#117	—	2	24	no	—
231	#117	C₂³×C₂₃	1	16	yes	complemented
232	C₂×C₄⋊C₄	—	2	3	no	—
233	C₂×C₄⋊C₄	—	2	3	no	—
234	C₂×C₄⋊C₄	—	2	3	no	—
235	C₂×C₄⋊C₄	C₂³×C₂₃	1	6	yes	—
236	C₂×C₄⋊C₄	C₂³×C₂₃	1	6	yes	—
237	C₂×C₄⋊C₄	C₂³×C₂₃	1	6	yes	—
238	C₂×C₂²⋊C₄	—	2	12	no	—
239	C₂×C₂²⋊C₄	—	2	12	no	—
240	C₂×C₄²	—	2	12	no	—
241	#107	C₂³×C₂₃	1	16	yes	complemented
242	#106	C₂³×C₂₃	1	16	yes	complemented
243	#102	C₂³×C₂₃	1	16	yes	complemented
244	#102	C₂³×C₂₃	1	16	yes	complemented
245	C₂²⋊C₈	C₂³×C₂₃	1	16	yes	complemented
246	C₂₃	C₂²×#482	1	1	yes	characteristic, direct product factor, Sylow
247	C₂⁴	—	2	4	no	—
248	C₂⁴	—	2	4	no	—
249	C₂⁴	—	2	4	no	—
250	C₂⁴	—	2	6	no	—
251	C₂⁴	—	4	4	no	—
252	C₂⁴	—	4	4	no	—
253	C₂⁴	—	4	4	no	—
254	C₂⁴	C₂×D₄×C₂₃	1	6	yes	—
255	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
256	C₂×D₄	—	2	16	no	—
257	C₂×D₄	—	2	6	no	—
258	C₂×D₄	—	2	12	no	—
259	C₂×D₄	—	2	12	no	—
260	C₂×D₄	—	4	48	no	—
261	C₂×D₄	—	4	12	no	—
262	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	24	no	—
265	C₂²×C₄	—	2	12	no	—
266	C₂²×C₄	—	2	12	no	—
267	C₂²×C₄	—	2	6	no	—
268	C₂²×C₄	—	2	6	no	—
269	C₂²×C₄	—	2	6	no	—
270	C₂²×C₄	—	4	4	no	—
271	C₂²×C₄	—	4	4	no	—
272	C₂²×C₄	—	4	4	no	—
273	C₂²×C₄	C₂×D₄×C₂₃	1	6	yes	—
274	C₂²×C₄	C₂×D₄×C₂₃	1	12	yes	—
275	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
276	C₂²×C₄	#41×C₂₃	1	4	yes	—
277	C₂²×C₄	#41×C₂₃	1	4	yes	—
278	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
279	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
280	C₂×C₈	—	2	12	no	—
281	C₂×C₈	—	2	12	no	—
282	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
283	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
284	C₄⋊C₄	—	2	6	no	—
285	C₄⋊C₄	—	2	6	no	—
286	C₄⋊C₄	—	2	6	no	—
287	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
288	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
289	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
290	C₂²⋊C₄	—	2	16	no	—
291	C₂²⋊C₄	—	2	16	no	—
292	C₄²	—	2	16	no	—
293	C₂³	—	2	12	no	—
294	C₂³	—	2	12	no	—
295	C₂³	—	2	12	no	—
296	C₂³	—	2	4	no	—
297	C₂³	—	4	16	no	—
298	C₂³	—	4	12	no	—
299	C₂³	—	4	12	no	—
300	C₂³	—	4	12	no	—
301	C₂³	—	8	16	no	—
302	C₂³	C₂₃×#123	1	4	yes	—
303	C₂³	C₂₃×#135	1	4	yes	—
304	C₂³	C₂₃×AGL(1,ℤ/8)	1	4	yes	—
305	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
306	C₂³	C₂²×D₄×C₂₃	1	3	yes	—
307	D₄	—	2	4	no	—
308	D₄	—	2	4	no	—
309	D₄	—	4	32	no	—
310	D₄	—	4	12	no	—
311	C₂×C₄	—	2	12	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	24	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	4	12	no	—
319	C₂×C₄	—	4	12	no	—
320	C₂×C₄	—	4	12	no	—
321	C₂×C₄	C₂₃×#123	1	12	yes	—
322	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
323	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
324	C₂×C₄	C₂×#41×C₂₃	1	6	yes	—
325	C₂×C₄	C₂×#41×C₂₃	1	6	yes	—
326	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
327	C₈	—	2	4	no	—
328	C₈	—	2	4	no	—
329	C₂²	—	2	4	no	—
330	C₂²	—	2	4	no	—
331	C₂²	—	2	4	no	—
332	C₂²	—	4	24	no	—
333	C₂²	—	4	4	no	—
334	C₂²	—	4	4	no	—
335	C₂²	—	4	4	no	—
336	C₂²	—	8	24	no	—
337	C₂²	C₂₃×#482	1	16	yes	direct product factor
338	C₂²	C₂×C₂₃×#123	1	6	yes	—
339	C₂²	C₂×C₂₃×#135	1	6	yes	—
340	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	6	yes	—
341	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
342	C₄	—	2	4	no	—
343	C₄	—	4	4	no	—
344	C₄	—	4	4	no	—
345	C₄	—	4	4	no	—
346	C₄	C₂×C₂₃×#123	1	6	yes	—
347	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
348	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
349	C₂	—	4	4	no	—
350	C₂	—	8	4	no	—
351	C₂	C₂×C₂₃×#482	1	12	yes	direct product factor
352	C₂	C₂²×C₂₃×#123	1	1	yes	characteristic
353	C₂	C₂²×C₂₃×#135	1	1	yes	characteristic
354	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
prime radical	C₂²×C₂₃×#121	C₂
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
2. C₂²×C₂₃×#117	C₂	semidirect
3. C₂×C₂₃×#482	C₂	direct (N × H)
4. C₂²×C₂₃×#107	C₂	semidirect
5. C₂²×C₂₃×#106	C₂	semidirect
6. C₂²×C₂₃×#102	C₂	semidirect
7. C₂²×C₂₃×#102	C₂	semidirect
8. C₂²×C₂₃×C₂²⋊C₈	C₂	semidirect
17. C₂×C₂₃×#117	C₂²	semidirect
24. C₂₃×#482	C₂²	direct (N × H)
25. C₂×C₂₃×#107	C₂²	semidirect
26. C₂×C₂₃×#106	C₂²	semidirect
27. C₂×C₂₃×#102	C₂²	semidirect
28. C₂×C₂₃×#102	C₂²	semidirect
29. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
54. C₂₃×#117	C₂³	semidirect
64. C₂₃×#107	C₂³	semidirect
65. C₂₃×#106	C₂³	semidirect
66. C₂₃×#102	C₂³	semidirect
67. C₂₃×#102	C₂³	semidirect
68. C₂₃×C₂²⋊C₈	C₂³	semidirect
115. C₂²×#482	C₂₃	direct (N × H)
153. C₂²×#117	C₂×C₂₃	semidirect
154. C₂×#482	C₂×C₂₃	direct (N × H)
155. C₂²×#107	C₂×C₂₃	semidirect
156. C₂²×#106	C₂×C₂₃	semidirect
157. C₂²×#102	C₂×C₂₃	semidirect
158. C₂²×#102	C₂×C₂₃	semidirect
159. C₂²×C₂²⋊C₈	C₂×C₂₃	semidirect
168. C₂²×C₂₃	#482	direct (N × H)
188. C₂×#117	C₂²×C₂₃	semidirect
195. #482	C₂²×C₂₃	direct (N × H)
196. C₂×#107	C₂²×C₂₃	semidirect
197. C₂×#106	C₂²×C₂₃	semidirect
198. C₂×#102	C₂²×C₂₃	semidirect
199. C₂×#102	C₂²×C₂₃	semidirect
200. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
203. C₂×C₂₃	C₂×#482	direct (N × H)
231. #117	C₂³×C₂₃	semidirect
241. #107	C₂³×C₂₃	semidirect
242. #106	C₂³×C₂₃	semidirect
243. #102	C₂³×C₂₃	semidirect
244. #102	C₂³×C₂₃	semidirect
245. C₂²⋊C₈	C₂³×C₂₃	semidirect
246. C₂₃	C₂²×#482	direct (N × H)
337. C₂²	C₂₃×#482	direct (N × H)
351. C₂	C₂×C₂₃×#482	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×#121	2
C₂²×C₂₃×#117	2
C₂×C₂₃×#482	2
C₂²×C₂₃×#107	2
C₂²×C₂₃×#106	2
C₂²×C₂₃×#102	2
C₂²×C₂₃×C₂²⋊C₈	2
C₂²×#482	23

Subgroups — C22×C23×#482 #19208128

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₂₃×#482 #19208128