Subgroups — C₂×C₂₃×#2388 #19182161

Order 5888.

6238 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	C₂³×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₂₃	C₂	1	3	yes	maximal, complemented
3	C₂₃×#2388	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#395	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#394	C₂	1	3	yes	maximal, complemented
6	C₂×C₂₃×#393	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#392	C₂	1	3	yes	maximal, complemented
8	C₂×C₄×C₂²⋊C₄×C₂₃	C₂	1	3	yes	maximal, complemented
9	C₂²×#41×C₂₃	—	2	24	no	—
10	C₂²×#41×C₂₃	C₂²	1	8	yes	complemented
11	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₂₃	C₂²	1	3	yes	—
13	C₂³×D₄×C₂₃	C₂²	1	3	yes	—
14	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₂₃	C₂²	1	3	yes	—
16	C₂×C₄×D₄×C₂₃	—	2	24	no	—
17	C₂×C₄×D₄×C₂₃	C₂²	1	24	yes	complemented
18	C₂²×C₄⋊C₄×C₂₃	C₂²	1	3	yes	—
19	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	3	yes	—
20	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	3	yes	—
21	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	6	yes	—
22	C₂²×C₄²×C₂₃	C₂²	1	3	yes	—
23	C₂₃×#395	C₂²	1	8	yes	complemented
24	C₂₃×#394	C₂²	1	24	yes	complemented
25	C₂₃×#393	C₂²	1	8	yes	complemented
26	C₂₃×#392	C₂²	1	24	yes	complemented
27	C₄×C₂²⋊C₄×C₂₃	C₂²	1	24	yes	complemented
28	C₂×C₂₃×#95	C₂²	1	3	yes	—
29	C₂×C₂₃×#95	C₂²	1	3	yes	—
30	C₂⁵×C₂₃	C₂³	1	3	yes	—
31	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
32	C₂×#41×C₂₃	—	2	128	no	—
33	C₂×#41×C₂₃	—	2	96	no	—
34	C₂²×Q₈×C₂₃	—	2	12	no	—
35	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
36	C₂²×D₄×C₂₃	—	2	24	no	—
37	C₂²×D₄×C₂₃	—	2	12	no	—
38	C₂²×D₄×C₂₃	—	2	12	no	—
39	C₂²×D₄×C₂₃	—	2	12	no	—
40	C₂²×D₄×C₂₃	—	2	12	no	—
41	C₂²×D₄×C₂₃	C₂³	1	12	yes	—
42	C₂²×D₄×C₂₃	C₂³	1	12	yes	—
43	C₂³×C₄×C₂₃	—	2	24	no	—
44	C₂³×C₄×C₂₃	—	2	12	no	—
45	C₂³×C₄×C₂₃	D₄	1	24	yes	complemented
46	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
48	C₂³×C₄×C₂₃	C₂³	1	3	yes	—
49	C₂³×C₄×C₂₃	C₂³	1	3	yes	—
50	C₂³×C₄×C₂₃	C₂³	1	12	yes	—
51	C₂³×C₄×C₂₃	C₂³	1	3	yes	—
52	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
53	C₄×D₄×C₂₃	—	2	96	no	—
54	C₂×C₄⋊C₄×C₂₃	—	2	12	no	—
55	C₂×C₄⋊C₄×C₂₃	C₂³	1	12	yes	—
56	C₂×C₂²⋊C₄×C₂₃	—	2	12	no	—
57	C₂×C₂²⋊C₄×C₂₃	—	2	12	no	—
58	C₂×C₂²⋊C₄×C₂₃	—	2	24	no	—
59	C₂×C₂²⋊C₄×C₂₃	C₂³	1	24	yes	—
60	C₂×C₂²⋊C₄×C₂₃	C₂³	1	12	yes	—
61	C₂×C₂²⋊C₄×C₂₃	C₂³	1	12	yes	—
62	C₂×C₄²×C₂₃	—	2	12	no	—
63	C₂×C₄²×C₂₃	C₂³	1	12	yes	—
64	C₂₃×#95	C₂³	1	12	yes	—
65	C₂₃×#95	C₂³	1	12	yes	—
66	C₂⁴×C₂₃	—	2	6	no	—
67	C₂⁴×C₂₃	—	2	12	no	—
68	C₂⁴×C₂₃	—	2	12	no	—
69	C₂⁴×C₂₃	—	2	6	no	—
70	C₂⁴×C₂₃	—	2	6	no	—
71	C₂⁴×C₂₃	—	2	6	no	—
72	C₂⁴×C₂₃	C₂×D₄	1	12	yes	—
73	C₂⁴×C₂₃	#41	1	4	yes	complemented
74	C₂⁴×C₂₃	C₂⁴	1	6	yes	—
75	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
76	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
77	#41×C₂₃	—	2	256	no	—
78	C₂×Q₈×C₂₃	—	2	32	no	—
79	C₂×Q₈×C₂₃	—	2	24	no	—
80	C₂×D₄×C₂₃	—	2	96	no	—
81	C₂×D₄×C₂₃	—	2	96	no	—
82	C₂×D₄×C₂₃	—	2	24	no	—
83	C₂×D₄×C₂₃	—	2	48	no	—
84	C₂×D₄×C₂₃	—	2	24	no	—
85	C₂×D₄×C₂₃	—	2	24	no	—
86	C₂×D₄×C₂₃	—	2	24	no	—
87	C₂²×C₄×C₂₃	—	2	6	no	—
88	C₂²×C₄×C₂₃	—	2	12	no	—
89	C₂²×C₄×C₂₃	—	2	6	no	—
90	C₂²×C₄×C₂₃	—	2	96	no	—
91	C₂²×C₄×C₂₃	—	2	48	no	—
92	C₂²×C₄×C₂₃	—	2	6	no	—
93	C₂²×C₄×C₂₃	—	2	6	no	—
94	C₂²×C₄×C₂₃	—	2	12	no	—
95	C₂²×C₄×C₂₃	—	2	24	no	—
96	C₂²×C₄×C₂₃	—	4	16	no	—
97	C₂²×C₄×C₂₃	C₂×D₄	1	12	yes	—
98	C₂²×C₄×C₂₃	C₂×D₄	1	12	yes	—
99	C₂²×C₄×C₂₃	C₂×D₄	1	48	yes	complemented
100	C₂²×C₄×C₂₃	#41	1	12	yes	complemented
101	C₂²×C₄×C₂₃	C₂⁴	1	6	yes	—
102	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
103	C₂²×C₄×C₂₃	C₂⁴	1	6	yes	—
104	C₂²×C₄×C₂₃	C₂⁴	1	6	yes	—
105	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
106	C₄⋊C₄×C₂₃	—	2	24	no	—
107	C₂²⋊C₄×C₂₃	—	2	24	no	—
108	C₂²⋊C₄×C₂₃	—	2	24	no	—
109	C₂²⋊C₄×C₂₃	—	2	48	no	—
110	C₄²×C₂₃	—	2	24	no	—
111	C₂×#2388	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂³×C₂₃	—	2	24	no	—
113	C₂³×C₂₃	—	2	24	no	—
114	C₂³×C₂₃	—	2	24	no	—
115	C₂³×C₂₃	—	2	24	no	—
116	C₂³×C₂₃	—	2	6	no	—
117	C₂³×C₂₃	—	2	12	no	—
118	C₂³×C₂₃	—	2	12	no	—
119	C₂³×C₂₃	—	2	6	no	—
120	C₂³×C₂₃	—	2	6	no	—
121	C₂³×C₂₃	—	2	6	no	—
122	C₂³×C₂₃	—	4	4	no	—
123	C₂³×C₂₃	—	4	24	no	—
124	C₂³×C₂₃	—	4	12	no	—
125	C₂³×C₂₃	—	4	24	no	—
126	C₂³×C₂₃	C₂²×D₄	1	12	yes	—
127	C₂³×C₂₃	C₂²×D₄	1	6	yes	—
128	C₂³×C₂₃	C₂×#41	1	2	yes	—
129	C₂³×C₂₃	C₂×#41	1	6	yes	—
130	C₂³×C₂₃	C₂×#41	1	4	yes	complemented
131	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
132	Q₈×C₂₃	—	2	32	no	—
133	D₄×C₂₃	—	2	96	no	—
134	D₄×C₂₃	—	2	96	no	—
135	C₂×C₄×C₂₃	—	2	24	no	—
136	C₂×C₄×C₂₃	—	2	24	no	—
137	C₂×C₄×C₂₃	—	2	6	no	—
138	C₂×C₄×C₂₃	—	2	12	no	—
139	C₂×C₄×C₂₃	—	2	6	no	—
140	C₂×C₄×C₂₃	—	2	96	no	—
141	C₂×C₄×C₂₃	—	2	6	no	—
142	C₂×C₄×C₂₃	—	2	6	no	—
143	C₂×C₄×C₂₃	—	2	12	no	—
144	C₂×C₄×C₂₃	—	4	4	no	—
145	C₂×C₄×C₂₃	—	4	12	no	—
146	C₂×C₄×C₂₃	—	4	16	no	—
147	C₂×C₄×C₂₃	#120	1	16	yes	—
148	C₂×C₄×C₂₃	C₂²×D₄	1	12	yes	—
149	C₂×C₄×C₂₃	C₂²×D₄	1	12	yes	—
150	C₂×C₄×C₂₃	C₂×#41	1	12	yes	complemented
151	C₂³×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
152	C₂²×C₄×D₄	C₂×C₂₃	1	3	yes	complemented
153	#2388	C₂×C₂₃	1	16	yes	direct product factor
154	C₂×#395	C₂×C₂₃	1	1	yes	characteristic, complemented
155	C₂×#394	C₂×C₂₃	1	3	yes	complemented
156	C₂×#393	C₂×C₂₃	1	1	yes	characteristic, complemented
157	C₂×#392	C₂×C₂₃	1	3	yes	complemented
158	C₂×C₄×C₂²⋊C₄	C₂×C₂₃	1	3	yes	complemented
159	C₂²×C₂₃	—	2	12	no	—
160	C₂²×C₂₃	—	2	12	no	—
161	C₂²×C₂₃	—	2	12	no	—
162	C₂²×C₂₃	—	2	12	no	—
163	C₂²×C₂₃	—	4	48	no	—
164	C₂²×C₂₃	—	4	16	no	—
165	C₂²×C₂₃	—	4	2	no	—
166	C₂²×C₂₃	—	4	12	no	—
167	C₂²×C₂₃	—	4	6	no	—
168	C₂²×C₂₃	—	4	12	no	—
169	C₂²×C₂₃	C₂×#120	1	4	yes	—
170	C₂²×C₂₃	#525	1	12	yes	—
171	C₂²×C₂₃	#532	1	12	yes	—
172	C₂²×C₂₃	C₂³×D₄	1	3	yes	—
173	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
174	C₂²×C₂₃	C₂²×#41	1	3	yes	—
175	C₄×C₂₃	—	2	12	no	—
176	C₄×C₂₃	—	2	12	no	—
177	C₄×C₂₃	—	4	2	no	—
178	C₄×C₂₃	—	4	6	no	—
179	C₄×C₂₃	C₂×#120	1	8	yes	—
180	C₂²×#41	—	2	24	no	—
181	C₂²×#41	C₂²×C₂₃	1	8	yes	complemented
182	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
183	C₂³×D₄	C₂²×C₂₃	1	3	yes	—
184	C₂³×D₄	C₂²×C₂₃	1	3	yes	—
185	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
186	C₂⁴×C₄	C₂²×C₂₃	1	3	yes	—
187	C₂×C₄×D₄	—	2	24	no	—
188	C₂×C₄×D₄	C₂²×C₂₃	1	24	yes	complemented
189	C₂²×C₄⋊C₄	C₂²×C₂₃	1	3	yes	—
190	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	3	yes	—
191	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	6	yes	—
192	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	3	yes	—
193	C₂²×C₄²	C₂²×C₂₃	1	3	yes	—
194	#395	C₂²×C₂₃	1	8	yes	complemented
195	#394	C₂²×C₂₃	1	24	yes	complemented
196	#393	C₂²×C₂₃	1	8	yes	complemented
197	#392	C₂²×C₂₃	1	24	yes	complemented
198	C₄×C₂²⋊C₄	C₂²×C₂₃	1	24	yes	complemented
199	C₂×#95	C₂²×C₂₃	1	3	yes	—
200	C₂×#95	C₂²×C₂₃	1	3	yes	—
201	C₂×C₂₃	—	4	12	no	—
202	C₂×C₂₃	—	4	4	no	—
203	C₂×C₂₃	#2388	1	8	yes	direct product factor
204	C₂×C₂₃	C₂²×#120	1	1	yes	characteristic
205	C₂×C₂₃	C₂×#525	1	3	yes	—
206	C₂×C₂₃	C₂×#532	1	3	yes	—
207	C₂⁵	C₂³×C₂₃	1	3	yes	—
208	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
209	C₂×#41	—	2	128	no	—
210	C₂×#41	—	2	96	no	—
211	C₂²×Q₈	—	2	12	no	—
212	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
213	C₂²×D₄	—	2	12	no	—
214	C₂²×D₄	—	2	24	no	—
215	C₂²×D₄	—	2	12	no	—
216	C₂²×D₄	—	2	12	no	—
217	C₂²×D₄	—	2	12	no	—
218	C₂²×D₄	C₂³×C₂₃	1	12	yes	—
219	C₂²×D₄	C₂³×C₂₃	1	12	yes	—
220	C₂³×C₄	—	2	24	no	—
221	C₂³×C₄	—	2	12	no	—
222	C₂³×C₄	D₄×C₂₃	1	24	yes	complemented
223	C₂³×C₄	C₂³×C₂₃	1	3	yes	—
224	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
225	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
226	C₂³×C₄	C₂³×C₂₃	1	3	yes	—
227	C₂³×C₄	C₂³×C₂₃	1	12	yes	—
228	C₂³×C₄	C₂³×C₂₃	1	3	yes	—
229	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
230	C₄×D₄	—	2	96	no	—
231	C₂×C₄⋊C₄	—	2	12	no	—
232	C₂×C₄⋊C₄	C₂³×C₂₃	1	12	yes	—
233	C₂×C₂²⋊C₄	—	2	12	no	—
234	C₂×C₂²⋊C₄	—	2	12	no	—
235	C₂×C₂²⋊C₄	—	2	24	no	—
236	C₂×C₂²⋊C₄	C₂³×C₂₃	1	12	yes	—
237	C₂×C₂²⋊C₄	C₂³×C₂₃	1	12	yes	—
238	C₂×C₂²⋊C₄	C₂³×C₂₃	1	24	yes	—
239	C₂×C₄²	—	2	12	no	—
240	C₂×C₄²	C₂³×C₂₃	1	12	yes	—
241	#95	C₂³×C₂₃	1	12	yes	—
242	#95	C₂³×C₂₃	1	12	yes	—
243	C₂₃	C₂×#2388	1	1	yes	characteristic, direct product factor, Sylow
244	C₂⁴	—	2	6	no	—
245	C₂⁴	—	2	12	no	—
246	C₂⁴	—	2	12	no	—
247	C₂⁴	—	2	6	no	—
248	C₂⁴	—	2	6	no	—
249	C₂⁴	—	2	6	no	—
250	C₂⁴	C₂×D₄×C₂₃	1	12	yes	—
251	C₂⁴	#41×C₂₃	1	4	yes	complemented
252	C₂⁴	C₂⁴×C₂₃	1	6	yes	—
253	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
254	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
255	#41	—	2	256	no	—
256	C₂×Q₈	—	2	32	no	—
257	C₂×Q₈	—	2	24	no	—
258	C₂×D₄	—	2	96	no	—
259	C₂×D₄	—	2	96	no	—
260	C₂×D₄	—	2	24	no	—
261	C₂×D₄	—	2	48	no	—
262	C₂×D₄	—	2	24	no	—
263	C₂×D₄	—	2	24	no	—
264	C₂×D₄	—	2	24	no	—
265	C₂²×C₄	—	2	6	no	—
266	C₂²×C₄	—	2	12	no	—
267	C₂²×C₄	—	2	6	no	—
268	C₂²×C₄	—	2	96	no	—
269	C₂²×C₄	—	2	48	no	—
270	C₂²×C₄	—	2	6	no	—
271	C₂²×C₄	—	2	6	no	—
272	C₂²×C₄	—	2	12	no	—
273	C₂²×C₄	—	2	24	no	—
274	C₂²×C₄	—	4	16	no	—
275	C₂²×C₄	C₂×D₄×C₂₃	1	12	yes	—
276	C₂²×C₄	C₂×D₄×C₂₃	1	12	yes	—
277	C₂²×C₄	C₂×D₄×C₂₃	1	48	yes	complemented
278	C₂²×C₄	#41×C₂₃	1	12	yes	complemented
279	C₂²×C₄	C₂⁴×C₂₃	1	6	yes	—
280	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
281	C₂²×C₄	C₂⁴×C₂₃	1	6	yes	—
282	C₂²×C₄	C₂⁴×C₂₃	1	6	yes	—
283	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
284	C₄⋊C₄	—	2	24	no	—
285	C₂²⋊C₄	—	2	24	no	—
286	C₂²⋊C₄	—	2	24	no	—
287	C₂²⋊C₄	—	2	48	no	—
288	C₄²	—	2	24	no	—
289	C₂³	—	2	6	no	—
290	C₂³	—	2	12	no	—
291	C₂³	—	2	12	no	—
292	C₂³	—	2	6	no	—
293	C₂³	—	2	6	no	—
294	C₂³	—	2	6	no	—
295	C₂³	—	2	24	no	—
296	C₂³	—	2	24	no	—
297	C₂³	—	2	24	no	—
298	C₂³	—	2	24	no	—
299	C₂³	—	4	4	no	—
300	C₂³	—	4	24	no	—
301	C₂³	—	4	12	no	—
302	C₂³	—	4	24	no	—
303	C₂³	C₂²×D₄×C₂₃	1	12	yes	—
304	C₂³	C₂²×D₄×C₂₃	1	6	yes	—
305	C₂³	C₂×#41×C₂₃	1	2	yes	—
306	C₂³	C₂×#41×C₂₃	1	6	yes	—
307	C₂³	C₂×#41×C₂₃	1	4	yes	complemented
308	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
309	Q₈	—	2	32	no	—
310	D₄	—	2	96	no	—
311	D₄	—	2	96	no	—
312	C₂×C₄	—	2	6	no	—
313	C₂×C₄	—	2	12	no	—
314	C₂×C₄	—	2	6	no	—
315	C₂×C₄	—	2	24	no	—
316	C₂×C₄	—	2	24	no	—
317	C₂×C₄	—	2	96	no	—
318	C₂×C₄	—	2	6	no	—
319	C₂×C₄	—	2	6	no	—
320	C₂×C₄	—	2	12	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	4	12	no	—
323	C₂×C₄	—	4	16	no	—
324	C₂×C₄	C₂₃×#120	1	16	yes	—
325	C₂×C₄	C₂²×D₄×C₂₃	1	12	yes	—
326	C₂×C₄	C₂²×D₄×C₂₃	1	12	yes	—
327	C₂×C₄	C₂×#41×C₂₃	1	12	yes	complemented
328	C₂²	—	2	12	no	—
329	C₂²	—	2	12	no	—
330	C₂²	—	2	12	no	—
331	C₂²	—	2	12	no	—
332	C₂²	—	4	2	no	—
333	C₂²	—	4	12	no	—
334	C₂²	—	4	6	no	—
335	C₂²	—	4	12	no	—
336	C₂²	—	4	48	no	—
337	C₂²	—	4	16	no	—
338	C₂²	C₂×C₂₃×#120	1	4	yes	—
339	C₂²	C₂₃×#525	1	12	yes	—
340	C₂²	C₂₃×#532	1	12	yes	—
341	C₂²	C₂³×D₄×C₂₃	1	3	yes	—
342	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
343	C₂²	C₂²×#41×C₂₃	1	3	yes	—
344	C₄	—	2	12	no	—
345	C₄	—	2	12	no	—
346	C₄	—	4	2	no	—
347	C₄	—	4	6	no	—
348	C₄	C₂×C₂₃×#120	1	8	yes	—
349	C₂	—	4	12	no	—
350	C₂	—	4	4	no	—
351	C₂	C₂₃×#2388	1	8	yes	direct product factor
352	C₂	C₂²×C₂₃×#120	1	1	yes	characteristic
353	C₂	C₂×C₂₃×#525	1	3	yes	—
354	C₂	C₂×C₂₃×#532	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂³×#41×C₂₃	C₂	semidirect
2. C₂²×C₄×D₄×C₂₃	C₂	semidirect
3. C₂₃×#2388	C₂	direct (N × H)
4. C₂×C₂₃×#395	C₂	semidirect
5. C₂×C₂₃×#394	C₂	semidirect
6. C₂×C₂₃×#393	C₂	semidirect
7. C₂×C₂₃×#392	C₂	semidirect
8. C₂×C₄×C₂²⋊C₄×C₂₃	C₂	semidirect
10. C₂²×#41×C₂₃	C₂²	semidirect
17. C₂×C₄×D₄×C₂₃	C₂²	semidirect
23. C₂₃×#395	C₂²	semidirect
24. C₂₃×#394	C₂²	semidirect
25. C₂₃×#393	C₂²	semidirect
26. C₂₃×#392	C₂²	semidirect
27. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
45. C₂³×C₄×C₂₃	D₄	semidirect
73. C₂⁴×C₂₃	#41	semidirect
99. C₂²×C₄×C₂₃	C₂×D₄	semidirect
100. C₂²×C₄×C₂₃	#41	semidirect
111. C₂×#2388	C₂₃	direct (N × H)
130. C₂³×C₂₃	C₂×#41	semidirect
150. C₂×C₄×C₂₃	C₂×#41	semidirect
151. C₂³×#41	C₂×C₂₃	semidirect
152. C₂²×C₄×D₄	C₂×C₂₃	semidirect
153. #2388	C₂×C₂₃	direct (N × H)
154. C₂×#395	C₂×C₂₃	semidirect
155. C₂×#394	C₂×C₂₃	semidirect
156. C₂×#393	C₂×C₂₃	semidirect
157. C₂×#392	C₂×C₂₃	semidirect
158. C₂×C₄×C₂²⋊C₄	C₂×C₂₃	semidirect
181. C₂²×#41	C₂²×C₂₃	semidirect
188. C₂×C₄×D₄	C₂²×C₂₃	semidirect
194. #395	C₂²×C₂₃	semidirect
195. #394	C₂²×C₂₃	semidirect
196. #393	C₂²×C₂₃	semidirect
197. #392	C₂²×C₂₃	semidirect
198. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
203. C₂×C₂₃	#2388	direct (N × H)
222. C₂³×C₄	D₄×C₂₃	semidirect
243. C₂₃	C₂×#2388	direct (N × H)
251. C₂⁴	#41×C₂₃	semidirect
277. C₂²×C₄	C₂×D₄×C₂₃	semidirect
278. C₂²×C₄	#41×C₂₃	semidirect
307. C₂³	C₂×#41×C₂₃	semidirect
327. C₂×C₄	C₂×#41×C₂₃	semidirect
351. C₂	C₂₃×#2388	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×#41×C₂₃	2
C₂²×C₄×D₄×C₂₃	2
C₂₃×#2388	2
C₂×C₂₃×#395	2
C₂×C₂₃×#394	2
C₂×C₂₃×#393	2
C₂×C₂₃×#392	2
C₂×C₄×C₂²⋊C₄×C₂₃	2
C₂×#2388	23

Subgroups — C2×C23×#2388 #19182161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#2388 #19182161