Subgroups — C₂×C₂₃×#3392 #19209014

Order 5888.

2238 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#550	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3392	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#492	C₂	1	3	yes	maximal, complemented
5	C₂×C₂₃×#460	C₂	1	3	yes	maximal, complemented
6	C₂×C₂₃×#461	C₂	1	3	yes	maximal, complemented
7	C₂×C₈×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×SD₁₆×C₂₃	C₂	1	3	yes	maximal, complemented
9	C₂²×#41×C₂₃	—	2	1	no	—
10	C₂²×SD₁₆×C₂₃	C₂²	1	3	yes	—
11	C₂²×SD₁₆×C₂₃	C₂²	1	6	yes	—
12	C₂₃×#557	—	2	4	no	—
13	C₂₃×#557	C₂²	1	8	yes	complemented
14	C₂₃×#550	—	2	4	no	—
15	C₂₃×#550	C₂²	1	8	yes	—
16	C₂×C₂₃×C₄⋊Q₈	C₂²	1	3	yes	—
17	C₂×C₂₃×#127	C₂²	1	3	yes	—
18	C₂×C₂₃×#125	—	2	3	no	—
19	C₂×C₂₃×#121	—	2	3	no	—
20	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
21	C₂×C₄×Q₈×C₂₃	C₂²	1	3	yes	—
22	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₂₃	C₂²	1	3	yes	—
24	C₂₃×#492	C₂²	1	24	yes	complemented
25	C₂₃×#461	C₂²	1	24	yes	complemented
26	C₂₃×#460	C₂²	1	24	yes	complemented
27	C₈×Q₈×C₂₃	C₂²	1	8	yes	complemented
28	C₄×SD₁₆×C₂₃	C₂²	1	24	yes	complemented
29	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×C₄⋊C₈	C₂²	1	3	yes	—
31	C₂×C₂₃×#103	C₂²	1	3	yes	—
32	C₂×C₂₃×#102	C₂²	1	3	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	D₄	1	1	yes	characteristic
37	C₂²×Q₈×C₂₃	C₂³	1	3	yes	—
38	C₂²×D₄×C₂₃	—	2	3	no	—
39	C₂²×D₄×C₂₃	—	2	3	no	—
40	C₂²×D₄×C₂₃	C₂³	1	3	yes	—
41	C₂³×C₄×C₂₃	—	2	3	no	—
42	C₂×SD₁₆×C₂₃	—	2	12	no	—
43	C₂×SD₁₆×C₂₃	—	4	12	no	—
44	C₂×SD₁₆×C₂₃	C₂³	1	12	yes	—
45	C₂×SD₁₆×C₂₃	C₂³	1	24	yes	—
46	C₂²×C₈×C₂₃	C₂³	1	3	yes	—
47	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
48	C₂₃×C₄⋊Q₈	—	2	6	no	—
49	C₂₃×C₄⋊Q₈	C₂³	1	12	yes	—
50	C₂₃×#127	—	2	6	no	—
51	C₂₃×#127	C₂³	1	12	yes	—
52	C₂₃×#125	—	2	24	no	—
53	C₂₃×#121	—	2	24	no	—
54	C₄×Q₈×C₂₃	—	2	8	no	—
55	C₄×Q₈×C₂₃	—	2	6	no	—
56	C₄×Q₈×C₂₃	D₄	1	4	yes	—
57	C₄×Q₈×C₂₃	C₂³	1	12	yes	—
58	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
59	C₄×D₄×C₂₃	—	2	6	no	—
60	C₄×D₄×C₂₃	C₂³	1	12	yes	—
61	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
62	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
63	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
64	C₂×C₄⋊C₄×C₂₃	D₄	1	3	yes	—
65	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₂₃	—	2	3	no	—
68	C₂×C₄²×C₂₃	—	2	3	no	—
69	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
70	C₂₃×#106	C₂³	1	4	yes	—
71	C₂₃×C₄⋊C₈	C₂³	1	12	yes	—
72	C₂₃×#103	C₂³	1	12	yes	—
73	C₂₃×#102	C₂³	1	12	yes	—
74	C₄×C₈×C₂₃	C₂³	1	12	yes	—
75	C₂⁴×C₂₃	—	2	3	no	—
76	#41×C₂₃	—	4	32	no	—
77	C₂×Q₈×C₂₃	—	2	3	no	—
78	C₂×Q₈×C₂₃	—	2	6	no	—
79	C₂×Q₈×C₂₃	—	2	6	no	—
80	C₂×Q₈×C₂₃	SD₁₆	1	8	yes	complemented
81	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	—
82	C₂×Q₈×C₂₃	C₂⁴	1	6	yes	—
83	C₂×D₄×C₂₃	—	2	3	no	—
84	C₂×D₄×C₂₃	—	2	12	no	—
85	C₂×D₄×C₂₃	—	2	12	no	—
86	C₂×D₄×C₂₃	—	2	6	no	—
87	C₂×D₄×C₂₃	—	2	6	no	—
88	C₂×D₄×C₂₃	—	4	12	no	—
89	C₂×D₄×C₂₃	—	8	6	no	—
90	C₂×D₄×C₂₃	C₂⁴	1	6	yes	—
91	C₂²×C₄×C₂₃	—	2	1	no	—
92	C₂²×C₄×C₂₃	—	2	3	no	—
93	C₂²×C₄×C₂₃	—	2	1	no	—
94	C₂²×C₄×C₂₃	—	2	12	no	—
95	C₂²×C₄×C₂₃	—	4	12	no	—
96	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
97	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
98	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
99	SD₁₆×C₂₃	—	2	24	no	—
100	SD₁₆×C₂₃	—	4	24	no	—
101	C₂×C₈×C₂₃	—	2	6	no	—
102	C₂×C₈×C₂₃	#41	1	4	yes	complemented
103	C₂×C₈×C₂₃	C₂⁴	1	6	yes	—
104	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
105	C₄⋊C₄×C₂₃	—	2	12	no	—
106	C₄⋊C₄×C₂₃	—	2	12	no	—
107	C₄⋊C₄×C₂₃	—	2	12	no	—
108	C₄⋊C₄×C₂₃	—	2	1	no	—
109	C₄⋊C₄×C₂₃	—	2	1	no	—
110	C₄⋊C₄×C₂₃	C₂×D₄	1	12	yes	—
111	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
112	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
113	C₂²⋊C₄×C₂₃	—	2	12	no	—
114	C₄²×C₂₃	—	2	12	no	—
115	C₄²×C₂₃	C₂×D₄	1	6	yes	—
116	C₄²×C₂₃	C₂⁴	1	6	yes	—
117	C₂×#3392	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂³×C₂₃	—	2	6	no	—
119	C₂³×C₂₃	—	4	6	no	—
120	C₂³×C₂₃	—	4	6	no	—
121	C₂³×C₂₃	—	4	6	no	—
122	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
123	Q₈×C₂₃	—	2	6	no	—
124	Q₈×C₂₃	—	2	6	no	—
125	Q₈×C₂₃	—	4	6	no	—
126	Q₈×C₂₃	C₂×SD₁₆	1	16	yes	complemented
127	D₄×C₂₃	—	2	6	no	—
128	D₄×C₂₃	—	2	6	no	—
129	D₄×C₂₃	—	4	6	no	—
130	D₄×C₂₃	—	4	24	no	—
131	D₄×C₂₃	—	8	12	no	—
132	C₂×C₄×C₂₃	—	2	6	no	—
133	C₂×C₄×C₂₃	—	2	2	no	—
134	C₂×C₄×C₂₃	—	2	6	no	—
135	C₂×C₄×C₂₃	—	2	2	no	—
136	C₂×C₄×C₂₃	—	4	6	no	—
137	C₂×C₄×C₂₃	—	4	2	no	—
138	C₂×C₄×C₂₃	—	4	2	no	—
139	C₂×C₄×C₂₃	—	4	24	no	—
140	C₂×C₄×C₂₃	C₂×SD₁₆	1	12	yes	—
141	C₂×C₄×C₂₃	C₂²×D₄	1	6	yes	—
142	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
143	C₂×C₄×C₂₃	C₂²×D₄	1	6	yes	—
144	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
145	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
146	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
147	C₈×C₂₃	—	2	6	no	—
148	C₈×C₂₃	C₂×#41	1	4	yes	complemented
149	C₂×#557	C₂×C₂₃	1	1	yes	characteristic, complemented
150	C₂×#550	C₂×C₂₃	1	1	yes	characteristic
151	#3392	C₂×C₂₃	1	16	yes	direct product factor
152	C₂×#492	C₂×C₂₃	1	3	yes	complemented
153	C₂×#460	C₂×C₂₃	1	3	yes	complemented
154	C₂×#461	C₂×C₂₃	1	3	yes	complemented
155	C₂×C₈×Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
156	C₂×C₄×SD₁₆	C₂×C₂₃	1	3	yes	complemented
157	C₂²×C₂₃	—	4	6	no	—
158	C₂²×C₂₃	—	4	6	no	—
159	C₂²×C₂₃	—	4	6	no	—
160	C₂²×C₂₃	—	8	12	no	—
161	C₂²×C₂₃	#550	1	2	yes	—
162	C₂²×C₂₃	C₂²×SD₁₆	1	2	yes	—
163	C₂²×C₂₃	#577	1	2	yes	—
164	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
165	C₄×C₂₃	—	2	6	no	—
166	C₄×C₂₃	—	4	6	no	—
167	C₄×C₂₃	—	4	2	no	—
168	C₄×C₂₃	—	4	2	no	—
169	C₄×C₂₃	#550	1	2	yes	—
170	C₄×C₂₃	C₂²×SD₁₆	1	12	yes	—
171	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
172	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
173	C₂²×#41	—	2	1	no	—
174	C₂²×SD₁₆	C₂²×C₂₃	1	3	yes	—
175	C₂²×SD₁₆	C₂²×C₂₃	1	6	yes	—
176	#557	—	2	4	no	—
177	#557	C₂²×C₂₃	1	8	yes	complemented
178	#550	—	2	4	no	—
179	#550	C₂²×C₂₃	1	8	yes	—
180	C₂×C₄⋊Q₈	C₂²×C₂₃	1	3	yes	—
181	C₂×#127	C₂²×C₂₃	1	3	yes	—
182	C₂×#125	—	2	3	no	—
183	C₂×#121	—	2	3	no	—
184	C₂×C₄×Q₈	—	2	1	no	—
185	C₂×C₄×Q₈	C₂²×C₂₃	1	3	yes	—
186	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
187	C₂×C₄×D₄	C₂²×C₂₃	1	3	yes	—
188	#492	C₂²×C₂₃	1	24	yes	complemented
189	#461	C₂²×C₂₃	1	24	yes	complemented
190	#460	C₂²×C₂₃	1	24	yes	complemented
191	C₈×Q₈	C₂²×C₂₃	1	8	yes	complemented
192	C₄×SD₁₆	C₂²×C₂₃	1	24	yes	complemented
193	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
194	C₂×C₄⋊C₈	C₂²×C₂₃	1	3	yes	—
195	C₂×#103	C₂²×C₂₃	1	3	yes	—
196	C₂×#102	C₂²×C₂₃	1	3	yes	—
197	C₂×C₄×C₈	C₂²×C₂₃	1	3	yes	—
198	C₂×C₂₃	—	8	6	no	—
199	C₂×C₂₃	#3392	1	4	yes	direct product factor
200	C₂×C₂₃	C₂×#550	1	1	yes	characteristic
201	C₂×C₂₃	C₂³×SD₁₆	1	1	yes	characteristic
202	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
203	C₂×#41	—	2	8	no	—
204	C₂×#41	—	4	8	no	—
205	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
206	C₂²×Q₈	C₂³×C₂₃	1	3	yes	—
207	C₂²×D₄	—	2	3	no	—
208	C₂²×D₄	—	2	3	no	—
209	C₂²×D₄	C₂³×C₂₃	1	3	yes	—
210	C₂³×C₄	—	2	3	no	—
211	C₂×SD₁₆	—	2	12	no	—
212	C₂×SD₁₆	—	4	12	no	—
213	C₂×SD₁₆	C₂³×C₂₃	1	12	yes	—
214	C₂×SD₁₆	C₂³×C₂₃	1	24	yes	—
215	C₂²×C₈	C₂³×C₂₃	1	3	yes	—
216	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
217	C₄⋊Q₈	—	2	6	no	—
218	C₄⋊Q₈	C₂³×C₂₃	1	12	yes	—
219	#127	—	2	6	no	—
220	#127	C₂³×C₂₃	1	12	yes	—
221	#125	—	2	24	no	—
222	#121	—	2	24	no	—
223	C₄×Q₈	—	2	8	no	—
224	C₄×Q₈	—	2	6	no	—
225	C₄×Q₈	D₄×C₂₃	1	4	yes	—
226	C₄×Q₈	C₂³×C₂₃	1	12	yes	—
227	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
228	C₄×D₄	—	2	6	no	—
229	C₄×D₄	C₂³×C₂₃	1	12	yes	—
230	C₂×C₄⋊C₄	—	2	3	no	—
231	C₂×C₄⋊C₄	—	2	3	no	—
232	C₂×C₄⋊C₄	—	2	3	no	—
233	C₂×C₄⋊C₄	D₄×C₂₃	1	3	yes	—
234	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
236	C₂×C₂²⋊C₄	—	2	3	no	—
237	C₂×C₄²	—	2	3	no	—
238	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
239	#106	C₂³×C₂₃	1	4	yes	—
240	C₄⋊C₈	C₂³×C₂₃	1	12	yes	—
241	#103	C₂³×C₂₃	1	12	yes	—
242	#102	C₂³×C₂₃	1	12	yes	—
243	C₄×C₈	C₂³×C₂₃	1	12	yes	—
244	C₂₃	C₂×#3392	1	1	yes	characteristic, direct product factor, Sylow
245	C₂⁴	—	2	3	no	—
246	#41	—	4	32	no	—
247	C₂×Q₈	—	2	3	no	—
248	C₂×Q₈	—	2	6	no	—
249	C₂×Q₈	—	2	6	no	—
250	C₂×Q₈	SD₁₆×C₂₃	1	8	yes	complemented
251	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	—
252	C₂×Q₈	C₂⁴×C₂₃	1	6	yes	—
253	C₂×D₄	—	2	3	no	—
254	C₂×D₄	—	2	12	no	—
255	C₂×D₄	—	2	12	no	—
256	C₂×D₄	—	2	6	no	—
257	C₂×D₄	—	2	6	no	—
258	C₂×D₄	—	4	12	no	—
259	C₂×D₄	—	8	6	no	—
260	C₂×D₄	C₂⁴×C₂₃	1	6	yes	—
261	C₂²×C₄	—	2	1	no	—
262	C₂²×C₄	—	2	3	no	—
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	2	12	no	—
265	C₂²×C₄	—	4	12	no	—
266	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
267	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
268	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
269	SD₁₆	—	2	24	no	—
270	SD₁₆	—	4	24	no	—
271	C₂×C₈	—	2	6	no	—
272	C₂×C₈	#41×C₂₃	1	4	yes	complemented
273	C₂×C₈	C₂⁴×C₂₃	1	6	yes	—
274	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
275	C₄⋊C₄	—	2	12	no	—
276	C₄⋊C₄	—	2	12	no	—
277	C₄⋊C₄	—	2	12	no	—
278	C₄⋊C₄	—	2	1	no	—
279	C₄⋊C₄	—	2	1	no	—
280	C₄⋊C₄	C₂×D₄×C₂₃	1	12	yes	—
281	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
282	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
283	C₂²⋊C₄	—	2	12	no	—
284	C₄²	—	2	12	no	—
285	C₄²	C₂×D₄×C₂₃	1	6	yes	—
286	C₄²	C₂⁴×C₂₃	1	6	yes	—
287	C₂³	—	2	6	no	—
288	C₂³	—	4	6	no	—
289	C₂³	—	4	6	no	—
290	C₂³	—	4	6	no	—
291	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
292	Q₈	—	2	6	no	—
293	Q₈	—	2	6	no	—
294	Q₈	—	4	6	no	—
295	Q₈	C₂×SD₁₆×C₂₃	1	16	yes	complemented
296	D₄	—	2	6	no	—
297	D₄	—	2	6	no	—
298	D₄	—	4	6	no	—
299	D₄	—	4	24	no	—
300	D₄	—	8	12	no	—
301	C₂×C₄	—	2	6	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	6	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	4	6	no	—
306	C₂×C₄	—	4	2	no	—
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	—	4	24	no	—
309	C₂×C₄	C₂×SD₁₆×C₂₃	1	12	yes	—
310	C₂×C₄	C₂²×D₄×C₂₃	1	6	yes	—
311	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
312	C₂×C₄	C₂²×D₄×C₂₃	1	6	yes	—
313	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
314	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
315	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
316	C₈	—	2	6	no	—
317	C₈	C₂×#41×C₂₃	1	4	yes	complemented
318	C₂²	—	4	6	no	—
319	C₂²	—	4	6	no	—
320	C₂²	—	4	6	no	—
321	C₂²	—	8	12	no	—
322	C₂²	C₂₃×#550	1	2	yes	—
323	C₂²	C₂²×SD₁₆×C₂₃	1	2	yes	—
324	C₂²	C₂₃×#577	1	2	yes	—
325	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
326	C₄	—	2	6	no	—
327	C₄	—	4	6	no	—
328	C₄	—	4	2	no	—
329	C₄	—	4	2	no	—
330	C₄	C₂₃×#550	1	2	yes	—
331	C₄	C₂²×SD₁₆×C₂₃	1	12	yes	—
332	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
333	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
334	C₂	—	8	6	no	—
335	C₂	C₂₃×#3392	1	4	yes	direct product factor
336	C₂	C₂×C₂₃×#550	1	1	yes	characteristic
337	C₂	C₂³×SD₁₆×C₂₃	1	1	yes	characteristic
338	C₂	C₂×C₂₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#550	C₂
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×#557	C₂	semidirect
3. C₂₃×#3392	C₂	direct (N × H)
4. C₂×C₂₃×#492	C₂	semidirect
5. C₂×C₂₃×#460	C₂	semidirect
6. C₂×C₂₃×#461	C₂	semidirect
7. C₂×C₈×Q₈×C₂₃	C₂	semidirect
8. C₂×C₄×SD₁₆×C₂₃	C₂	semidirect
13. C₂₃×#557	C₂²	semidirect
24. C₂₃×#492	C₂²	semidirect
25. C₂₃×#461	C₂²	semidirect
26. C₂₃×#460	C₂²	semidirect
27. C₈×Q₈×C₂₃	C₂²	semidirect
28. C₄×SD₁₆×C₂₃	C₂²	semidirect
80. C₂×Q₈×C₂₃	SD₁₆	semidirect
102. C₂×C₈×C₂₃	#41	semidirect
117. C₂×#3392	C₂₃	direct (N × H)
126. Q₈×C₂₃	C₂×SD₁₆	semidirect
148. C₈×C₂₃	C₂×#41	semidirect
149. C₂×#557	C₂×C₂₃	semidirect
151. #3392	C₂×C₂₃	direct (N × H)
152. C₂×#492	C₂×C₂₃	semidirect
153. C₂×#460	C₂×C₂₃	semidirect
154. C₂×#461	C₂×C₂₃	semidirect
155. C₂×C₈×Q₈	C₂×C₂₃	semidirect
156. C₂×C₄×SD₁₆	C₂×C₂₃	semidirect
177. #557	C₂²×C₂₃	semidirect
188. #492	C₂²×C₂₃	semidirect
189. #461	C₂²×C₂₃	semidirect
190. #460	C₂²×C₂₃	semidirect
191. C₈×Q₈	C₂²×C₂₃	semidirect
192. C₄×SD₁₆	C₂²×C₂₃	semidirect
199. C₂×C₂₃	#3392	direct (N × H)
244. C₂₃	C₂×#3392	direct (N × H)
250. C₂×Q₈	SD₁₆×C₂₃	semidirect
272. C₂×C₈	#41×C₂₃	semidirect
295. Q₈	C₂×SD₁₆×C₂₃	semidirect
317. C₈	C₂×#41×C₂₃	semidirect
335. C₂	C₂₃×#3392	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×#557	2
C₂×C₂₃×#550	2
C₂₃×#3392	2
C₂×C₂₃×#492	2
C₂×C₂₃×#460	2
C₂×C₂₃×#461	2
C₂×C₈×Q₈×C₂₃	2
C₂×C₄×SD₁₆×C₂₃	2
C₂×#3392	23

Subgroups — C2×C23×#3392 #19209014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3392 #19209014