Subgroups — C₄×C₈×D₄×C₂₃ #19168109

Order 5888.

1422 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₄×C₂₃	C₂	1	2	yes	maximal
2	C₂²×C₄×C₈×C₂₃	C₂	1	2	yes	maximal, complemented
3	C₄²×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic
4	C₈×C₄⋊C₄×C₂₃	C₂	1	2	yes	maximal, complemented
5	C₄×C₂₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×C₂²⋊C₄×C₂₃	C₂	1	4	yes	maximal, complemented
7	C₄×C₂₃×C₂²⋊C₈	C₂	1	2	yes	maximal, complemented
8	C₄²×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₈×C₂₃	C₂²	1	4	yes	—
10	C₂×C₄×D₄×C₂₃	C₄	1	2	yes	—
11	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
13	C₈×D₄×C₂₃	C₄	1	16	yes	direct product factor
14	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₂₃×C₂²⋊C₈	C₂²	1	4	yes	—
16	C₂×C₄×C₈×C₂₃	—	2	8	no	—
17	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₂₃	C₂²	1	4	yes	—
21	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
23	C₄×C₄⋊C₄×C₂₃	C₄	1	2	yes	—
24	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
25	C₄×C₂²⋊C₄×C₂₃	C₄	1	4	yes	—
26	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
27	C₄³×C₂₃	C₂²	1	1	yes	characteristic
28	C₂₃×#336	C₂²	1	4	yes	—
29	C₂₃×#336	C₂²	1	2	yes	—
30	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₂₃	C₂×C₄	1	4	yes	—
32	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
33	C₂²×C₈×C₂₃	—	2	8	no	—
34	C₂²×C₈×C₂₃	—	2	8	no	—
35	C₂²×C₈×C₂₃	C₂×C₄	1	16	yes	complemented
36	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
37	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
38	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
39	C₄×D₄×C₂₃	C₈	1	16	yes	direct product factor
40	C₄×D₄×C₂₃	C₂×C₄	1	8	yes	—
41	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
43	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
44	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	4	yes	—
45	C₂×C₄²×C₂₃	—	2	4	no	—
46	C₂×C₄²×C₂₃	—	2	4	no	—
47	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₂₃	C₂×C₄	1	4	yes	—
49	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
51	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
52	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
54	C₂₃×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
55	C₂₃×C₂²⋊C₈	C₂×C₄	1	16	yes	complemented
56	C₄×C₈×C₂₃	—	2	8	no	—
57	C₄×C₈×C₂₃	—	2	4	no	—
58	C₄×C₈×C₂₃	—	2	4	no	—
59	C₄×C₈×C₂₃	—	2	2	no	—
60	C₄×C₈×C₂₃	C₂×C₄	1	8	yes	complemented
61	C₄×C₈×C₂₃	D₄	1	4	yes	direct product factor
62	C₂₃×#95	C₂×C₄	1	2	yes	—
63	C₂₃×#95	C₂×C₄	1	4	yes	—
64	C₂⁴×C₂₃	C₂²×C₄	1	2	yes	—
65	C₂×D₄×C₂₃	C₄²	1	4	yes	—
66	C₂×D₄×C₂₃	C₂×C₈	1	8	yes	—
67	C₂²×C₄×C₂₃	—	2	8	no	—
68	C₂²×C₄×C₂₃	—	2	8	no	—
69	C₂²×C₄×C₂₃	—	2	2	no	—
70	C₂²×C₄×C₂₃	—	2	2	no	—
71	C₂²×C₄×C₂₃	—	2	4	no	—
72	C₂²×C₄×C₂₃	C₂×C₈	1	16	yes	complemented
73	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
75	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
76	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
77	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
78	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
81	C₂×C₈×C₂₃	—	2	4	no	—
82	C₂×C₈×C₂₃	—	2	4	no	—
83	C₂×C₈×C₂₃	—	2	2	no	—
84	C₂×C₈×C₂₃	—	2	2	no	—
85	C₂×C₈×C₂₃	—	2	32	no	—
86	C₂×C₈×C₂₃	C₂²×C₄	1	8	yes	—
87	C₂×C₈×C₂₃	C₂²×C₄	1	4	yes	—
88	C₂×C₈×C₂₃	C₂²×C₄	1	4	yes	—
89	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	—
90	C₂×C₈×C₂₃	#41	1	4	yes	—
91	C₄⋊C₄×C₂₃	C₄²	1	4	yes	—
92	C₄⋊C₄×C₂₃	C₂×C₈	1	8	yes	complemented
93	C₂²⋊C₄×C₂₃	C₄²	1	8	yes	—
94	C₂²⋊C₄×C₂₃	C₂×C₈	1	16	yes	complemented
95	C₄²×C₂₃	—	2	8	no	—
96	C₄²×C₂₃	—	2	4	no	—
97	C₄²×C₂₃	—	2	2	no	—
98	C₄²×C₂₃	—	2	2	no	—
99	C₄²×C₂₃	—	2	2	no	—
100	C₄²×C₂₃	C₂×C₈	1	8	yes	complemented
101	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
102	C₄²×C₂₃	C₂×D₄	1	2	yes	—
103	C₄²×C₂₃	#41	1	2	yes	—
104	C₄×C₈×D₄	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
105	C₂³×C₂₃	—	2	2	no	—
106	C₂³×C₂₃	—	2	2	no	—
107	C₂³×C₂₃	—	2	4	no	—
108	C₂³×C₂₃	C₂×C₄²	1	4	yes	—
109	C₂³×C₂₃	C₂²×C₈	1	8	yes	—
110	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
111	D₄×C₂₃	C₄×C₈	1	16	yes	direct product factor
112	C₂×C₄×C₂₃	—	2	4	no	—
113	C₂×C₄×C₂₃	—	2	2	no	—
114	C₂×C₄×C₂₃	—	2	2	no	—
115	C₂×C₄×C₂₃	—	2	2	no	—
116	C₂×C₄×C₂₃	—	2	2	no	—
117	C₂×C₄×C₂₃	—	2	2	no	—
118	C₂×C₄×C₂₃	—	2	4	no	—
119	C₂×C₄×C₂₃	—	2	8	no	—
120	C₂×C₄×C₂₃	—	2	8	no	—
121	C₂×C₄×C₂₃	—	2	32	no	—
122	C₂×C₄×C₂₃	C₂×C₄²	1	2	yes	—
123	C₂×C₄×C₂₃	C₂×C₄²	1	4	yes	—
124	C₂×C₄×C₂₃	C₂×C₄²	1	2	yes	—
125	C₂×C₄×C₂₃	C₄×D₄	1	4	yes	—
126	C₂×C₄×C₂₃	C₂²×C₈	1	4	yes	—
127	C₂×C₄×C₂₃	C₂²×C₈	1	8	yes	—
128	C₂×C₄×C₂₃	C₂²×C₈	1	4	yes	—
129	C₂×C₄×C₂₃	C₂²×C₈	1	4	yes	—
130	C₂×C₄×C₂₃	#131	1	4	yes	—
131	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
132	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
133	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
134	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
135	C₈×C₂₃	—	2	8	no	—
136	C₈×C₂₃	—	2	4	no	—
137	C₈×C₂₃	C₄×D₄	1	8	yes	direct product factor
138	C₂×C₈×D₄	C₂×C₂₃	1	2	yes	—
139	C₂²×C₄×C₈	C₂×C₂₃	1	2	yes	complemented
140	C₄²×D₄	C₂×C₂₃	1	1	yes	characteristic
141	C₈×C₄⋊C₄	C₂×C₂₃	1	2	yes	complemented
142	C₄×C₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
143	C₈×C₂²⋊C₄	C₂×C₂₃	1	4	yes	complemented
144	C₄×C₂²⋊C₈	C₂×C₂₃	1	2	yes	complemented
145	C₄²×C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
146	C₂²×C₂₃	—	2	4	no	—
147	C₂²×C₂₃	—	2	8	no	—
148	C₂²×C₂₃	—	2	8	no	—
149	C₂²×C₂₃	—	2	4	no	—
150	C₂²×C₂₃	C₂×C₄×C₈	1	8	yes	complemented
151	C₂²×C₂₃	C₂²×C₄²	1	1	yes	characteristic
152	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
153	C₂²×C₂₃	C₄×#41	1	1	yes	characteristic
154	C₂²×C₂₃	C₂³×C₈	1	2	yes	—
155	C₂²×C₂₃	C₂×#131	1	2	yes	—
156	C₄×C₂₃	—	2	2	no	—
157	C₄×C₂₃	—	2	8	no	—
158	C₄×C₂₃	—	2	4	no	—
159	C₄×C₂₃	—	2	4	no	—
160	C₄×C₂₃	C₂×C₄×C₈	1	4	yes	complemented
161	C₄×C₂₃	C₈×D₄	1	8	yes	direct product factor
162	C₄×C₂₃	C₂×C₄×D₄	1	2	yes	—
163	C₄×C₂₃	C₄×#41	1	2	yes	—
164	C₂³×C₈	C₂²×C₂₃	1	4	yes	—
165	C₂×C₄×D₄	C₄×C₂₃	1	2	yes	—
166	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
167	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
168	C₈×D₄	C₄×C₂₃	1	16	yes	direct product factor
169	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
170	C₂×C₂²⋊C₈	C₂²×C₂₃	1	4	yes	—
171	C₂×C₄×C₈	—	2	8	no	—
172	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
173	C₂×C₄×C₈	C₂²×C₂₃	1	4	yes	—
174	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
175	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
176	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
177	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
178	C₄×C₄⋊C₄	C₄×C₂₃	1	2	yes	—
179	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
180	C₄×C₂²⋊C₄	C₄×C₂₃	1	4	yes	—
181	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
182	C₄³	C₂²×C₂₃	1	1	yes	characteristic
183	#336	C₂²×C₂₃	1	4	yes	—
184	#336	C₂²×C₂₃	1	2	yes	—
185	C₂×C₂₃	—	2	8	no	—
186	C₂×C₂₃	C₄²×D₄	1	1	yes	characteristic
187	C₂×C₂₃	C₂²×C₄×C₈	1	1	yes	characteristic
188	C₂×C₂₃	C₄×#131	1	1	yes	characteristic
189	C₂×C₂₃	C₂×C₈×D₄	1	2	yes	—
190	C₂×C₂₃	C₈×#41	1	2	yes	—
191	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
192	C₂³×C₄	C₂×C₄×C₂₃	1	4	yes	—
193	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
194	C₂²×C₈	—	2	8	no	—
195	C₂²×C₈	—	2	8	no	—
196	C₂²×C₈	C₂×C₄×C₂₃	1	16	yes	complemented
197	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
198	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
199	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
200	C₄×D₄	C₈×C₂₃	1	16	yes	direct product factor
201	C₄×D₄	C₂×C₄×C₂₃	1	8	yes	—
202	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
203	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
204	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
205	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	4	yes	—
206	C₂×C₄²	—	2	4	no	—
207	C₂×C₄²	—	2	4	no	—
208	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
209	C₂×C₄²	C₂×C₄×C₂₃	1	4	yes	—
210	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
211	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
212	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
213	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
214	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
215	C₄⋊C₈	C₂×C₄×C₂₃	1	8	yes	complemented
216	C₂²⋊C₈	C₂×C₄×C₂₃	1	16	yes	complemented
217	C₄×C₈	—	2	8	no	—
218	C₄×C₈	—	2	4	no	—
219	C₄×C₈	—	2	4	no	—
220	C₄×C₈	—	2	2	no	—
221	C₄×C₈	C₂×C₄×C₂₃	1	8	yes	complemented
222	C₄×C₈	D₄×C₂₃	1	4	yes	direct product factor
223	#95	C₂×C₄×C₂₃	1	2	yes	—
224	#95	C₂×C₄×C₂₃	1	4	yes	—
225	C₂₃	C₄×C₈×D₄	1	1	yes	characteristic, direct product factor, Sylow
226	C₂⁴	C₂²×C₄×C₂₃	1	2	yes	—
227	C₂×D₄	C₄²×C₂₃	1	4	yes	—
228	C₂×D₄	C₂×C₈×C₂₃	1	8	yes	—
229	C₂²×C₄	—	2	8	no	—
230	C₂²×C₄	—	2	8	no	—
231	C₂²×C₄	—	2	2	no	—
232	C₂²×C₄	—	2	2	no	—
233	C₂²×C₄	—	2	4	no	—
234	C₂²×C₄	C₂×C₈×C₂₃	1	16	yes	complemented
235	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
236	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
237	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
238	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
239	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
240	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
241	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
242	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
243	C₂×C₈	—	2	4	no	—
244	C₂×C₈	—	2	2	no	—
245	C₂×C₈	—	2	2	no	—
246	C₂×C₈	—	2	4	no	—
247	C₂×C₈	—	2	32	no	—
248	C₂×C₈	C₂²×C₄×C₂₃	1	4	yes	—
249	C₂×C₈	C₂²×C₄×C₂₃	1	8	yes	—
250	C₂×C₈	C₂²×C₄×C₂₃	1	4	yes	—
251	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	—
252	C₂×C₈	#41×C₂₃	1	4	yes	—
253	C₄⋊C₄	C₄²×C₂₃	1	4	yes	—
254	C₄⋊C₄	C₂×C₈×C₂₃	1	8	yes	complemented
255	C₂²⋊C₄	C₄²×C₂₃	1	8	yes	—
256	C₂²⋊C₄	C₂×C₈×C₂₃	1	16	yes	complemented
257	C₄²	—	2	8	no	—
258	C₄²	—	2	4	no	—
259	C₄²	—	2	2	no	—
260	C₄²	—	2	2	no	—
261	C₄²	—	2	2	no	—
262	C₄²	C₂×C₈×C₂₃	1	8	yes	complemented
263	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
264	C₄²	C₂×D₄×C₂₃	1	2	yes	—
265	C₄²	#41×C₂₃	1	2	yes	—
266	C₂³	—	2	4	no	—
267	C₂³	—	2	2	no	—
268	C₂³	—	2	2	no	—
269	C₂³	C₂×C₄²×C₂₃	1	4	yes	—
270	C₂³	C₂²×C₈×C₂₃	1	8	yes	—
271	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
272	D₄	C₄×C₈×C₂₃	1	16	yes	direct product factor
273	C₂×C₄	—	2	2	no	—
274	C₂×C₄	—	2	2	no	—
275	C₂×C₄	—	2	4	no	—
276	C₂×C₄	—	2	4	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	2	2	no	—
280	C₂×C₄	—	2	32	no	—
281	C₂×C₄	—	2	8	no	—
282	C₂×C₄	—	2	8	no	—
283	C₂×C₄	C₂×C₄²×C₂₃	1	2	yes	—
284	C₂×C₄	C₂×C₄²×C₂₃	1	4	yes	—
285	C₂×C₄	C₂×C₄²×C₂₃	1	2	yes	—
286	C₂×C₄	C₄×D₄×C₂₃	1	4	yes	—
287	C₂×C₄	C₂²×C₈×C₂₃	1	4	yes	—
288	C₂×C₄	C₂²×C₈×C₂₃	1	8	yes	—
289	C₂×C₄	C₂²×C₈×C₂₃	1	4	yes	—
290	C₂×C₄	C₂²×C₈×C₂₃	1	4	yes	—
291	C₂×C₄	C₂₃×#131	1	4	yes	—
292	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
293	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
294	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
295	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
296	C₈	—	2	8	no	—
297	C₈	—	2	4	no	—
298	C₈	C₄×D₄×C₂₃	1	8	yes	direct product factor
299	C₂²	—	2	8	no	—
300	C₂²	—	2	8	no	—
301	C₂²	—	2	4	no	—
302	C₂²	—	2	4	no	—
303	C₂²	C₂×C₄×C₈×C₂₃	1	8	yes	complemented
304	C₂²	C₂²×C₄²×C₂₃	1	1	yes	characteristic
305	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
306	C₂²	C₄×#41×C₂₃	1	1	yes	characteristic
307	C₂²	C₂³×C₈×C₂₃	1	2	yes	—
308	C₂²	C₂×C₂₃×#131	1	2	yes	—
309	C₄	—	2	8	no	—
310	C₄	—	2	4	no	—
311	C₄	—	2	4	no	—
312	C₄	—	2	2	no	—
313	C₄	C₂×C₄×C₈×C₂₃	1	4	yes	complemented
314	C₄	C₈×D₄×C₂₃	1	8	yes	direct product factor
315	C₄	C₂×C₄×D₄×C₂₃	1	2	yes	—
316	C₄	C₄×#41×C₂₃	1	2	yes	—
317	C₂	—	2	8	no	—
318	C₂	C₄²×D₄×C₂₃	1	1	yes	characteristic
319	C₂	C₂²×C₄×C₈×C₂₃	1	1	yes	characteristic
320	C₂	C₄×C₂₃×#131	1	1	yes	characteristic
321	C₂	C₂×C₈×D₄×C₂₃	1	2	yes	—
322	C₂	C₈×#41×C₂₃	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₈×C₂₃	C₂²
commutator	C₂	C₂²×C₄×C₈×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
socle	C₂³×C₂₃	C₂³×C₄
prime radical	C₂²×D₄×C₂₃	C₂×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×C₈×C₂₃	C₂	semidirect
4. C₈×C₄⋊C₄×C₂₃	C₂	semidirect
5. C₄×C₂₃×C₄⋊C₈	C₂	semidirect
6. C₈×C₂²⋊C₄×C₂₃	C₂	semidirect
7. C₄×C₂₃×C₂²⋊C₈	C₂	semidirect
8. C₄²×C₈×C₂₃	C₂	semidirect
13. C₈×D₄×C₂₃	C₄	direct (N × H)
35. C₂²×C₈×C₂₃	C₂×C₄	semidirect
39. C₄×D₄×C₂₃	C₈	direct (N × H)
54. C₂₃×C₄⋊C₈	C₂×C₄	semidirect
55. C₂₃×C₂²⋊C₈	C₂×C₄	semidirect
60. C₄×C₈×C₂₃	C₂×C₄	semidirect
61. C₄×C₈×C₂₃	D₄	direct (N × H)
72. C₂²×C₄×C₂₃	C₂×C₈	semidirect
92. C₄⋊C₄×C₂₃	C₂×C₈	semidirect
94. C₂²⋊C₄×C₂₃	C₂×C₈	semidirect
100. C₄²×C₂₃	C₂×C₈	semidirect
104. C₄×C₈×D₄	C₂₃	direct (N × H)
111. D₄×C₂₃	C₄×C₈	direct (N × H)
137. C₈×C₂₃	C₄×D₄	direct (N × H)
139. C₂²×C₄×C₈	C₂×C₂₃	semidirect
141. C₈×C₄⋊C₄	C₂×C₂₃	semidirect
142. C₄×C₄⋊C₈	C₂×C₂₃	semidirect
143. C₈×C₂²⋊C₄	C₂×C₂₃	semidirect
144. C₄×C₂²⋊C₈	C₂×C₂₃	semidirect
145. C₄²×C₈	C₂×C₂₃	semidirect
150. C₂²×C₂₃	C₂×C₄×C₈	semidirect
160. C₄×C₂₃	C₂×C₄×C₈	semidirect
161. C₄×C₂₃	C₈×D₄	direct (N × H)
168. C₈×D₄	C₄×C₂₃	direct (N × H)
196. C₂²×C₈	C₂×C₄×C₂₃	semidirect
200. C₄×D₄	C₈×C₂₃	direct (N × H)
215. C₄⋊C₈	C₂×C₄×C₂₃	semidirect
216. C₂²⋊C₈	C₂×C₄×C₂₃	semidirect
221. C₄×C₈	C₂×C₄×C₂₃	semidirect
222. C₄×C₈	D₄×C₂₃	direct (N × H)
225. C₂₃	C₄×C₈×D₄	direct (N × H)
234. C₂²×C₄	C₂×C₈×C₂₃	semidirect
254. C₄⋊C₄	C₂×C₈×C₂₃	semidirect
256. C₂²⋊C₄	C₂×C₈×C₂₃	semidirect
262. C₄²	C₂×C₈×C₂₃	semidirect
272. D₄	C₄×C₈×C₂₃	direct (N × H)
298. C₈	C₄×D₄×C₂₃	direct (N × H)
303. C₂²	C₂×C₄×C₈×C₂₃	semidirect
313. C₄	C₂×C₄×C₈×C₂₃	semidirect
314. C₄	C₈×D₄×C₂₃	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×C₈×D₄×C₂₃	2
C₂²×C₄×C₈×C₂₃	2
C₄²×D₄×C₂₃	2
C₈×C₄⋊C₄×C₂₃	2
C₄×C₂₃×C₄⋊C₈	2
C₈×C₂²⋊C₄×C₂₃	2
C₄×C₂₃×C₂²⋊C₈	2
C₄²×C₈×C₂₃	2
C₄×C₈×D₄	23

Subgroups — C4×C8×D4×C23 #19168109

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₈×D₄×C₂₃ #19168109