Subgroups — C₂×C₂₃×#3358 #19208921

Order 5888.

2402 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3358	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#486	C₂	1	3	yes	maximal, complemented
5	C₂×C₂₃×#474	C₂	1	3	yes	maximal, complemented
6	C₂×C₂₃×#459	C₂	1	3	yes	maximal, complemented
7	C₂×C₈×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₈×C₂₃	C₂	1	3	yes	maximal, complemented
9	C₂²×#41×C₂₃	—	2	1	no	—
10	C₂³×Q₈×C₂₃	—	2	1	no	—
11	C₂²×D₈×C₂₃	C₂²	1	3	yes	—
12	C₂₃×#550	—	2	4	no	—
13	C₂₃×#550	C₂²	1	8	yes	complemented
14	D₄×Q₈×C₂₃	—	2	4	no	—
15	D₄×Q₈×C₂₃	C₂²	1	8	yes	complemented
16	C₂×C₂₃×C₄⋊Q₈	C₂²	1	3	yes	—
17	C₂×C₂₃×#127	C₂²	1	3	yes	—
18	C₂×C₂₃×C₂²⋊Q₈	—	2	3	no	—
19	C₂×C₂₃×#121	—	2	3	no	—
20	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₂₃	C₂²	1	3	yes	—
22	C₂×C₄×D₄×C₂₃	C₂²	1	3	yes	—
23	C₂₃×#486	C₂²	1	24	yes	complemented
24	C₂₃×#474	C₂²	1	24	yes	complemented
25	C₂₃×#459	C₂²	1	24	yes	complemented
26	C₈×Q₈×C₂₃	C₂²	1	8	yes	complemented
27	C₄×D₈×C₂₃	C₂²	1	24	yes	complemented
28	C₂×C₂₃×#107	C₂²	1	3	yes	—
29	C₂×C₂₃×C₄⋊C₈	C₂²	1	3	yes	—
30	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#102	C₂²	1	3	yes	—
32	C₂×C₂₃×#102	C₂²	1	6	yes	—
33	C₂×C₄×C₈×C₂₃	C₂²	1	3	yes	—
34	C₂×#41×C₂₃	—	2	8	no	—
35	C₂×#41×C₂₃	—	4	8	no	—
36	C₂²×Q₈×C₂₃	—	2	8	no	—
37	C₂²×Q₈×C₂₃	—	2	3	no	—
38	C₂²×Q₈×C₂₃	—	4	8	no	—
39	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
40	C₂²×D₄×C₂₃	—	2	3	no	—
41	C₂²×D₄×C₂₃	—	2	3	no	—
42	C₂²×D₄×C₂₃	C₂³	1	3	yes	—
43	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₂₃	—	2	3	no	—
45	C₂³×C₄×C₂₃	—	2	3	no	—
46	C₂×D₈×C₂₃	—	2	12	no	—
47	C₂×D₈×C₂₃	C₂³	1	12	yes	—
48	C₂²×C₈×C₂₃	C₂³	1	3	yes	—
49	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
50	C₂₃×C₄⋊Q₈	—	2	6	no	—
51	C₂₃×C₄⋊Q₈	C₂³	1	12	yes	—
52	C₂₃×#127	—	2	6	no	—
53	C₂₃×#127	C₂³	1	12	yes	—
54	C₂₃×C₂²⋊Q₈	—	2	24	no	—
55	C₂₃×#121	—	2	24	no	—
56	C₄×Q₈×C₂₃	D₄	1	4	yes	—
57	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
58	C₄×D₄×C₂₃	—	2	6	no	—
59	C₄×D₄×C₂₃	—	2	6	no	—
60	C₄×D₄×C₂₃	C₂³	1	12	yes	—
61	C₄×D₄×C₂₃	C₂³	1	12	yes	—
62	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
63	C₂×C₄⋊C₄×C₂₃	D₄	1	3	yes	—
64	C₂×C₄⋊C₄×C₂₃	C₂³	1	3	yes	—
65	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₂₃	—	2	3	no	—
67	C₂×C₂²⋊C₄×C₂₃	—	2	3	no	—
68	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
69	C₂₃×#107	C₂³	1	12	yes	—
70	C₂₃×C₄⋊C₈	C₂³	1	12	yes	—
71	C₂₃×#102	C₂³	1	4	yes	—
72	C₂₃×#102	C₂³	1	12	yes	—
73	C₂₃×#102	C₂³	1	24	yes	—
74	C₄×C₈×C₂₃	C₂³	1	12	yes	—
75	C₂⁴×C₂₃	—	2	1	no	—
76	C₂⁴×C₂₃	—	2	3	no	—
77	#41×C₂₃	—	4	32	no	—
78	C₂×Q₈×C₂₃	—	2	12	no	—
79	C₂×Q₈×C₂₃	—	4	32	no	—
80	C₂×Q₈×C₂₃	—	4	12	no	—
81	C₂×Q₈×C₂₃	D₈	1	8	yes	complemented
82	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	—
83	C₂×D₄×C₂₃	—	2	1	no	—
84	C₂×D₄×C₂₃	—	2	3	no	—
85	C₂×D₄×C₂₃	—	2	12	no	—
86	C₂×D₄×C₂₃	—	2	12	no	—
87	C₂×D₄×C₂₃	—	2	6	no	—
88	C₂×D₄×C₂₃	—	2	2	no	—
89	C₂×D₄×C₂₃	—	2	6	no	—
90	C₂×D₄×C₂₃	—	4	12	no	—
91	C₂×D₄×C₂₃	—	8	6	no	—
92	C₂×D₄×C₂₃	#41	1	4	yes	complemented
93	C₂×D₄×C₂₃	C₂⁴	1	6	yes	—
94	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
95	C₂²×C₄×C₂₃	—	2	1	no	—
96	C₂²×C₄×C₂₃	—	2	3	no	—
97	C₂²×C₄×C₂₃	—	2	12	no	—
98	C₂²×C₄×C₂₃	—	2	12	no	—
99	C₂²×C₄×C₂₃	—	4	12	no	—
100	C₂²×C₄×C₂₃	—	4	12	no	—
101	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
102	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
103	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
104	D₈×C₂₃	—	2	24	no	—
105	C₂×C₈×C₂₃	—	2	6	no	—
106	C₂×C₈×C₂₃	—	2	2	no	—
107	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
108	C₂×C₈×C₂₃	C₂⁴	1	6	yes	—
109	C₄⋊C₄×C₂₃	—	2	12	no	—
110	C₄⋊C₄×C₂₃	—	2	1	no	—
111	C₄⋊C₄×C₂₃	—	2	3	no	—
112	C₄⋊C₄×C₂₃	C₂×D₄	1	12	yes	—
113	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
114	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
115	C₂²⋊C₄×C₂₃	—	2	12	no	—
116	C₂²⋊C₄×C₂₃	—	2	12	no	—
117	C₄²×C₂₃	C₂×D₄	1	6	yes	—
118	C₄²×C₂₃	C₂⁴	1	6	yes	—
119	C₂×#3358	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂³×C₂₃	—	2	4	no	—
121	C₂³×C₂₃	—	2	2	no	—
122	C₂³×C₂₃	—	2	6	no	—
123	C₂³×C₂₃	—	4	2	no	—
124	C₂³×C₂₃	—	4	2	no	—
125	C₂³×C₂₃	—	4	6	no	—
126	C₂³×C₂₃	—	4	6	no	—
127	C₂³×C₂₃	—	4	6	no	—
128	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
129	Q₈×C₂₃	—	4	24	no	—
130	Q₈×C₂₃	C₂×D₈	1	16	yes	complemented
131	D₄×C₂₃	—	2	4	no	—
132	D₄×C₂₃	—	2	6	no	—
133	D₄×C₂₃	—	2	2	no	—
134	D₄×C₂₃	—	2	6	no	—
135	D₄×C₂₃	—	4	6	no	—
136	D₄×C₂₃	—	4	24	no	—
137	D₄×C₂₃	—	8	12	no	—
138	D₄×C₂₃	C₂×#41	1	4	yes	complemented
139	C₂×C₄×C₂₃	—	2	6	no	—
140	C₂×C₄×C₂₃	—	2	2	no	—
141	C₂×C₄×C₂₃	—	2	6	no	—
142	C₂×C₄×C₂₃	—	4	2	no	—
143	C₂×C₄×C₂₃	—	4	6	no	—
144	C₂×C₄×C₂₃	—	4	24	no	—
145	C₂×C₄×C₂₃	—	4	24	no	—
146	C₂×C₄×C₂₃	C₂×D₈	1	12	yes	—
147	C₂×C₄×C₂₃	C₂²×D₄	1	6	yes	—
148	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₂₃	C₂²×D₄	1	6	yes	—
150	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
151	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
152	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
153	C₈×C₂₃	—	2	6	no	—
154	C₈×C₂₃	—	2	2	no	—
155	C₂×#550	C₂×C₂₃	1	1	yes	characteristic, complemented
156	C₂×D₄×Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
157	#3358	C₂×C₂₃	1	16	yes	direct product factor
158	C₂×#486	C₂×C₂₃	1	3	yes	complemented
159	C₂×#474	C₂×C₂₃	1	3	yes	complemented
160	C₂×#459	C₂×C₂₃	1	3	yes	complemented
161	C₂×C₈×Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
162	C₂×C₄×D₈	C₂×C₂₃	1	3	yes	complemented
163	C₂²×C₂₃	—	2	4	no	—
164	C₂²×C₂₃	—	4	8	no	—
165	C₂²×C₂₃	—	4	2	no	—
166	C₂²×C₂₃	—	4	2	no	—
167	C₂²×C₂₃	—	4	6	no	—
168	C₂²×C₂₃	—	4	6	no	—
169	C₂²×C₂₃	—	4	6	no	—
170	C₂²×C₂₃	—	8	12	no	—
171	C₂²×C₂₃	#548	1	2	yes	—
172	C₂²×C₂₃	C₂²×D₈	1	2	yes	—
173	C₂²×C₂₃	#577	1	2	yes	—
174	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
175	C₄×C₂₃	—	2	6	no	—
176	C₄×C₂₃	—	4	2	no	—
177	C₄×C₂₃	—	4	6	no	—
178	C₄×C₂₃	#548	1	2	yes	—
179	C₄×C₂₃	C₂²×D₈	1	12	yes	—
180	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
181	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
182	C₂²×#41	—	2	1	no	—
183	C₂³×Q₈	—	2	1	no	—
184	C₂²×D₈	C₂²×C₂₃	1	3	yes	—
185	#550	—	2	4	no	—
186	#550	C₂²×C₂₃	1	8	yes	complemented
187	D₄×Q₈	—	2	4	no	—
188	D₄×Q₈	C₂²×C₂₃	1	8	yes	complemented
189	C₂×C₄⋊Q₈	C₂²×C₂₃	1	3	yes	—
190	C₂×#127	C₂²×C₂₃	1	3	yes	—
191	C₂×C₂²⋊Q₈	—	2	3	no	—
192	C₂×#121	—	2	3	no	—
193	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
194	C₂×C₄×D₄	C₂²×C₂₃	1	3	yes	—
195	C₂×C₄×D₄	C₂²×C₂₃	1	3	yes	—
196	#486	C₂²×C₂₃	1	24	yes	complemented
197	#474	C₂²×C₂₃	1	24	yes	complemented
198	#459	C₂²×C₂₃	1	24	yes	complemented
199	C₈×Q₈	C₂²×C₂₃	1	8	yes	complemented
200	C₄×D₈	C₂²×C₂₃	1	24	yes	complemented
201	C₂×#107	C₂²×C₂₃	1	3	yes	—
202	C₂×C₄⋊C₈	C₂²×C₂₃	1	3	yes	—
203	C₂×#102	C₂²×C₂₃	1	3	yes	—
204	C₂×#102	C₂²×C₂₃	1	6	yes	—
205	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
206	C₂×C₄×C₈	C₂²×C₂₃	1	3	yes	—
207	C₂×C₂₃	—	4	4	no	—
208	C₂×C₂₃	—	8	6	no	—
209	C₂×C₂₃	#3358	1	4	yes	direct product factor
210	C₂×C₂₃	C₂×#548	1	1	yes	characteristic
211	C₂×C₂₃	C₂³×D₈	1	1	yes	characteristic
212	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
213	C₂×#41	—	2	8	no	—
214	C₂×#41	—	4	8	no	—
215	C₂²×Q₈	—	2	8	no	—
216	C₂²×Q₈	—	2	3	no	—
217	C₂²×Q₈	—	4	8	no	—
218	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
219	C₂²×D₄	—	2	3	no	—
220	C₂²×D₄	—	2	3	no	—
221	C₂²×D₄	C₂³×C₂₃	1	3	yes	—
222	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
223	C₂³×C₄	—	2	3	no	—
224	C₂³×C₄	—	2	3	no	—
225	C₂×D₈	—	2	12	no	—
226	C₂×D₈	C₂³×C₂₃	1	12	yes	—
227	C₂²×C₈	C₂³×C₂₃	1	3	yes	—
228	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
229	C₄⋊Q₈	—	2	6	no	—
230	C₄⋊Q₈	C₂³×C₂₃	1	12	yes	—
231	#127	—	2	6	no	—
232	#127	C₂³×C₂₃	1	12	yes	—
233	C₂²⋊Q₈	—	2	24	no	—
234	#121	—	2	24	no	—
235	C₄×Q₈	D₄×C₂₃	1	4	yes	—
236	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
237	C₄×D₄	—	2	6	no	—
238	C₄×D₄	—	2	6	no	—
239	C₄×D₄	C₂³×C₂₃	1	12	yes	—
240	C₄×D₄	C₂³×C₂₃	1	12	yes	—
241	C₂×C₄⋊C₄	—	2	3	no	—
242	C₂×C₄⋊C₄	D₄×C₂₃	1	3	yes	—
243	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂³×C₂₃	1	3	yes	—
245	C₂×C₂²⋊C₄	—	2	3	no	—
246	C₂×C₂²⋊C₄	—	2	3	no	—
247	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
248	#107	C₂³×C₂₃	1	12	yes	—
249	C₄⋊C₈	C₂³×C₂₃	1	12	yes	—
250	#102	C₂³×C₂₃	1	4	yes	—
251	#102	C₂³×C₂₃	1	12	yes	—
252	#102	C₂³×C₂₃	1	24	yes	—
253	C₄×C₈	C₂³×C₂₃	1	12	yes	—
254	C₂₃	C₂×#3358	1	1	yes	characteristic, direct product factor, Sylow
255	C₂⁴	—	2	1	no	—
256	C₂⁴	—	2	3	no	—
257	#41	—	4	32	no	—
258	C₂×Q₈	—	2	12	no	—
259	C₂×Q₈	—	4	32	no	—
260	C₂×Q₈	—	4	12	no	—
261	C₂×Q₈	D₈×C₂₃	1	8	yes	complemented
262	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	—
263	C₂×D₄	—	2	1	no	—
264	C₂×D₄	—	2	3	no	—
265	C₂×D₄	—	2	12	no	—
266	C₂×D₄	—	2	12	no	—
267	C₂×D₄	—	2	6	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	2	6	no	—
270	C₂×D₄	—	4	12	no	—
271	C₂×D₄	—	8	6	no	—
272	C₂×D₄	#41×C₂₃	1	4	yes	complemented
273	C₂×D₄	C₂⁴×C₂₃	1	6	yes	—
274	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	3	no	—
277	C₂²×C₄	—	2	12	no	—
278	C₂²×C₄	—	2	12	no	—
279	C₂²×C₄	—	4	12	no	—
280	C₂²×C₄	—	4	12	no	—
281	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
282	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
283	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
284	D₈	—	2	24	no	—
285	C₂×C₈	—	2	6	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
288	C₂×C₈	C₂⁴×C₂₃	1	6	yes	—
289	C₄⋊C₄	—	2	12	no	—
290	C₄⋊C₄	—	2	1	no	—
291	C₄⋊C₄	—	2	3	no	—
292	C₄⋊C₄	C₂×D₄×C₂₃	1	12	yes	—
293	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
294	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
295	C₂²⋊C₄	—	2	12	no	—
296	C₂²⋊C₄	—	2	12	no	—
297	C₄²	C₂×D₄×C₂₃	1	6	yes	—
298	C₄²	C₂⁴×C₂₃	1	6	yes	—
299	C₂³	—	2	4	no	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	6	no	—
302	C₂³	—	4	2	no	—
303	C₂³	—	4	2	no	—
304	C₂³	—	4	6	no	—
305	C₂³	—	4	6	no	—
306	C₂³	—	4	6	no	—
307	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
308	Q₈	—	4	24	no	—
309	Q₈	C₂×D₈×C₂₃	1	16	yes	complemented
310	D₄	—	2	4	no	—
311	D₄	—	2	6	no	—
312	D₄	—	2	2	no	—
313	D₄	—	2	6	no	—
314	D₄	—	4	6	no	—
315	D₄	—	4	24	no	—
316	D₄	—	8	12	no	—
317	D₄	C₂×#41×C₂₃	1	4	yes	complemented
318	C₂×C₄	—	2	6	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	6	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	6	no	—
323	C₂×C₄	—	4	24	no	—
324	C₂×C₄	—	4	24	no	—
325	C₂×C₄	C₂×D₈×C₂₃	1	12	yes	—
326	C₂×C₄	C₂²×D₄×C₂₃	1	6	yes	—
327	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
328	C₂×C₄	C₂²×D₄×C₂₃	1	6	yes	—
329	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
330	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
331	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
332	C₈	—	2	6	no	—
333	C₈	—	2	2	no	—
334	C₂²	—	2	4	no	—
335	C₂²	—	4	2	no	—
336	C₂²	—	4	2	no	—
337	C₂²	—	4	8	no	—
338	C₂²	—	4	6	no	—
339	C₂²	—	4	6	no	—
340	C₂²	—	4	6	no	—
341	C₂²	—	8	12	no	—
342	C₂²	C₂₃×#548	1	2	yes	—
343	C₂²	C₂²×D₈×C₂₃	1	2	yes	—
344	C₂²	C₂₃×#577	1	2	yes	—
345	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
346	C₄	—	2	6	no	—
347	C₄	—	4	2	no	—
348	C₄	—	4	6	no	—
349	C₄	C₂₃×#548	1	2	yes	—
350	C₄	C₂²×D₈×C₂₃	1	12	yes	—
351	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
352	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
353	C₂	—	4	4	no	—
354	C₂	—	8	6	no	—
355	C₂	C₂₃×#3358	1	4	yes	direct product factor
356	C₂	C₂×C₂₃×#548	1	1	yes	characteristic
357	C₂	C₂³×D₈×C₂₃	1	1	yes	characteristic
358	C₂	C₂×C₂₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄×Q₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#550	C₂	semidirect
2. C₂×D₄×Q₈×C₂₃	C₂	semidirect
3. C₂₃×#3358	C₂	direct (N × H)
4. C₂×C₂₃×#486	C₂	semidirect
5. C₂×C₂₃×#474	C₂	semidirect
6. C₂×C₂₃×#459	C₂	semidirect
7. C₂×C₈×Q₈×C₂₃	C₂	semidirect
8. C₂×C₄×D₈×C₂₃	C₂	semidirect
13. C₂₃×#550	C₂²	semidirect
15. D₄×Q₈×C₂₃	C₂²	semidirect
23. C₂₃×#486	C₂²	semidirect
24. C₂₃×#474	C₂²	semidirect
25. C₂₃×#459	C₂²	semidirect
26. C₈×Q₈×C₂₃	C₂²	semidirect
27. C₄×D₈×C₂₃	C₂²	semidirect
81. C₂×Q₈×C₂₃	D₈	semidirect
92. C₂×D₄×C₂₃	#41	semidirect
119. C₂×#3358	C₂₃	direct (N × H)
130. Q₈×C₂₃	C₂×D₈	semidirect
138. D₄×C₂₃	C₂×#41	semidirect
155. C₂×#550	C₂×C₂₃	semidirect
156. C₂×D₄×Q₈	C₂×C₂₃	semidirect
157. #3358	C₂×C₂₃	direct (N × H)
158. C₂×#486	C₂×C₂₃	semidirect
159. C₂×#474	C₂×C₂₃	semidirect
160. C₂×#459	C₂×C₂₃	semidirect
161. C₂×C₈×Q₈	C₂×C₂₃	semidirect
162. C₂×C₄×D₈	C₂×C₂₃	semidirect
186. #550	C₂²×C₂₃	semidirect
188. D₄×Q₈	C₂²×C₂₃	semidirect
196. #486	C₂²×C₂₃	semidirect
197. #474	C₂²×C₂₃	semidirect
198. #459	C₂²×C₂₃	semidirect
199. C₈×Q₈	C₂²×C₂₃	semidirect
200. C₄×D₈	C₂²×C₂₃	semidirect
209. C₂×C₂₃	#3358	direct (N × H)
254. C₂₃	C₂×#3358	direct (N × H)
261. C₂×Q₈	D₈×C₂₃	semidirect
272. C₂×D₄	#41×C₂₃	semidirect
309. Q₈	C₂×D₈×C₂₃	semidirect
317. D₄	C₂×#41×C₂₃	semidirect
355. C₂	C₂₃×#3358	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×#550	2
C₂×D₄×Q₈×C₂₃	2
C₂₃×#3358	2
C₂×C₂₃×#486	2
C₂×C₂₃×#474	2
C₂×C₂₃×#459	2
C₂×C₈×Q₈×C₂₃	2
C₂×C₄×D₈×C₂₃	2
C₂×#3358	23

Subgroups — C2×C23×#3358 #19208921

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3358 #19208921