Subgroups — C₂²×C₂₃×#416 #19207705

Order 5888.

5326 conjugacy classes of subgroups.

The subgroup lattice has 336 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
2	C₂⁴×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₂₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#416	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₂₃×#103	C₂	1	2	yes	maximal, complemented
6	C₂²×C₂₃×#102	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₂₃	—	2	8	no	—
8	C₂²×#41×C₂₃	—	2	6	no	—
9	C₂²×#41×C₂₃	C₄	1	16	yes	complemented
10	C₂²×#41×C₂₃	C₂²	1	12	yes	—
11	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₂₃	—	2	1	no	—
13	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₂₃	—	2	1	no	—
15	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₂₃	—	2	8	no	—
17	C₂³×C₈×C₂₃	C₂²	1	2	yes	—
18	C₂³×C₈×C₂₃	C₂²	1	12	yes	complemented
19	C₂×C₂₃×#117	—	2	6	no	—
20	C₂×C₂₃×#117	C₂²	1	12	yes	complemented
21	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₂₃	—	2	1	no	—
23	C₂²×C₄²×C₂₃	—	2	1	no	—
24	C₂₃×#416	C₂²	1	64	yes	direct product factor
25	C₂×C₂₃×#103	C₂²	1	24	yes	complemented
26	C₂×C₂₃×#102	C₂²	1	24	yes	complemented
27	C₂⁵×C₂₃	—	2	1	no	—
28	C₂⁵×C₂₃	D₄	1	1	yes	characteristic
29	C₂×#41×C₂₃	—	2	96	no	—
30	C₂×#41×C₂₃	—	2	48	no	—
31	C₂×#41×C₂₃	—	2	24	no	—
32	C₂×#41×C₂₃	C₂×C₄	1	96	yes	complemented
33	C₂×#41×C₂₃	C₂³	1	16	yes	—
34	C₂²×Q₈×C₂₃	—	2	4	no	—
35	C₂²×Q₈×C₂₃	—	2	3	no	—
36	C₂²×Q₈×C₂₃	C₂×C₄	1	8	yes	—
37	C₂²×Q₈×C₂₃	C₂³	1	6	yes	—
38	C₂²×D₄×C₂₃	—	2	16	no	—
39	C₂²×D₄×C₂₃	—	2	12	no	—
40	C₂²×D₄×C₂₃	—	2	3	no	—
41	C₂²×D₄×C₂₃	—	2	4	no	—
42	C₂²×D₄×C₂₃	C₂×C₄	1	8	yes	—
43	C₂²×D₄×C₂₃	C₂³	1	6	yes	—
44	C₂³×C₄×C₂₃	—	2	1	no	—
45	C₂³×C₄×C₂₃	—	2	16	no	—
46	C₂³×C₄×C₂₃	—	2	12	no	—
47	C₂³×C₄×C₂₃	—	2	2	no	—
48	C₂³×C₄×C₂₃	C₂×C₄	1	8	yes	—
49	C₂³×C₄×C₂₃	D₄	1	6	yes	—
50	C₂³×C₄×C₂₃	D₄	1	8	yes	—
51	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₂₃	C₂³	1	6	yes	—
54	C₂²×C₈×C₂₃	—	2	8	no	—
55	C₂²×C₈×C₂₃	—	2	48	no	—
56	C₂²×C₈×C₂₃	C₂³	1	12	yes	—
57	C₂²×C₈×C₂₃	C₂³	1	16	yes	complemented
58	C₂₃×#117	—	2	24	no	—
59	C₂₃×#117	C₂³	1	16	yes	complemented
60	C₂×C₄⋊C₄×C₂₃	—	2	6	no	—
61	C₂×C₄⋊C₄×C₂₃	C₂³	1	12	yes	—
62	C₂×C₂²⋊C₄×C₂₃	—	2	12	no	—
63	C₂×C₄²×C₂₃	—	2	12	no	—
64	C₂₃×#103	C₂³	1	32	yes	complemented
65	C₂₃×#102	C₂³	1	32	yes	complemented
66	C₂⁴×C₂₃	—	2	8	no	—
67	C₂⁴×C₂₃	—	2	8	no	—
68	C₂⁴×C₂₃	—	2	6	no	—
69	C₂⁴×C₂₃	—	4	8	no	—
70	C₂⁴×C₂₃	C₂²⋊C₄	1	8	yes	—
71	C₂⁴×C₂₃	C₂×D₄	1	6	yes	—
72	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
73	#41×C₂₃	—	2	192	no	—
74	#41×C₂₃	—	2	32	no	—
75	#41×C₂₃	C₂²×C₄	1	64	yes	complemented
76	C₂×Q₈×C₂₃	—	2	24	no	—
77	C₂×Q₈×C₂₃	—	2	12	no	—
78	C₂×Q₈×C₂₃	—	2	6	no	—
79	C₂×Q₈×C₂₃	C₂²×C₄	1	24	yes	—
80	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
81	C₂×D₄×C₂₃	—	2	96	no	—
82	C₂×D₄×C₂₃	—	2	16	no	—
83	C₂×D₄×C₂₃	—	2	24	no	—
84	C₂×D₄×C₂₃	—	2	6	no	—
85	C₂×D₄×C₂₃	—	2	12	no	—
86	C₂×D₄×C₂₃	C₂²×C₄	1	24	yes	—
87	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
88	C₂²×C₄×C₂₃	—	2	8	no	—
89	C₂²×C₄×C₂₃	—	2	6	no	—
90	C₂²×C₄×C₂₃	—	2	96	no	—
91	C₂²×C₄×C₂₃	—	2	16	no	—
92	C₂²×C₄×C₂₃	—	2	12	no	—
93	C₂²×C₄×C₂₃	—	4	8	no	—
94	C₂²×C₄×C₂₃	C₂²⋊C₄	1	8	yes	—
95	C₂²×C₄×C₂₃	C₂²⋊C₄	1	48	yes	—
96	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₂₃	C₂²×C₄	1	24	yes	—
98	C₂²×C₄×C₂₃	C₂×D₄	1	6	yes	—
99	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
100	C₂²×C₄×C₂₃	C₂×D₄	1	12	yes	—
101	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
102	C₂²×C₄×C₂₃	C₂×D₄	1	24	yes	—
103	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
104	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
105	C₂×C₈×C₂₃	—	2	24	no	—
106	C₂×C₈×C₂₃	—	2	32	no	—
107	C₂×C₈×C₂₃	C₂⁴	1	8	yes	—
108	C₄⋊C₄×C₂₃	—	2	12	no	—
109	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
110	C₂²⋊C₄×C₂₃	—	2	16	no	—
111	C₄²×C₂₃	—	2	16	no	—
112	C₂²×#416	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂³×C₂₃	—	2	24	no	—
114	C₂³×C₂₃	—	2	32	no	—
115	C₂³×C₂₃	—	2	24	no	—
116	C₂³×C₂₃	—	2	4	no	—
117	C₂³×C₂₃	—	4	24	no	—
118	C₂³×C₂₃	—	4	32	no	—
119	C₂³×C₂₃	C₂×C₂²⋊C₄	1	24	yes	—
120	C₂³×C₂₃	C₂×C₂²⋊C₄	1	4	yes	—
121	C₂³×C₂₃	#135	1	8	yes	—
122	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
123	C₂³×C₂₃	C₂²×D₄	1	3	yes	—
124	Q₈×C₂₃	—	2	24	no	—
125	Q₈×C₂₃	—	2	4	no	—
126	Q₈×C₂₃	C₂³×C₄	1	8	yes	—
127	D₄×C₂₃	—	2	64	no	—
128	D₄×C₂₃	—	2	24	no	—
129	D₄×C₂₃	—	2	4	no	—
130	D₄×C₂₃	C₂³×C₄	1	8	yes	—
131	C₂×C₄×C₂₃	—	2	24	no	—
132	C₂×C₄×C₂₃	—	2	4	no	—
133	C₂×C₄×C₂₃	—	2	64	no	—
134	C₂×C₄×C₂₃	—	2	8	no	—
135	C₂×C₄×C₂₃	—	4	24	no	—
136	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	24	yes	—
137	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	12	yes	—
138	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	48	yes	—
139	C₂×C₄×C₂₃	C₂³×C₄	1	6	yes	—
140	C₂×C₄×C₂₃	C₂³×C₄	1	8	yes	—
141	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
142	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
143	C₂×C₄×C₂₃	C₂²×D₄	1	6	yes	—
144	C₂×C₄×C₂₃	C₂²×D₄	1	8	yes	—
145	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
146	C₈×C₂₃	—	2	8	no	—
147	C₂³×#41	C₂×C₂₃	1	1	yes	characteristic
148	C₂⁴×C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
149	C₂²×#117	C₂×C₂₃	1	1	yes	characteristic, complemented
150	C₂×#416	C₂×C₂₃	1	24	yes	direct product factor
151	C₂²×#103	C₂×C₂₃	1	2	yes	complemented
152	C₂²×#102	C₂×C₂₃	1	2	yes	complemented
153	C₂²×C₂₃	—	2	48	no	—
154	C₂²×C₂₃	—	2	8	no	—
155	C₂²×C₂₃	—	2	8	no	—
156	C₂²×C₂₃	—	4	48	no	—
157	C₂²×C₂₃	—	4	8	no	—
158	C₂²×C₂₃	#416	1	16	yes	direct product factor
159	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	8	yes	—
160	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	6	yes	—
161	C₂²×C₂₃	C₂×#135	1	12	yes	—
162	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
163	C₄×C₂₃	—	2	8	no	—
164	C₄×C₂₃	—	4	8	no	—
165	C₄×C₂₃	C₂²×C₂²⋊C₄	1	8	yes	—
166	C₄×C₂₃	C₂²×C₂²⋊C₄	1	6	yes	—
167	C₄×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
168	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
169	C₂²×#41	—	2	8	no	—
170	C₂²×#41	—	2	6	no	—
171	C₂²×#41	C₄×C₂₃	1	16	yes	complemented
172	C₂²×#41	C₂²×C₂₃	1	12	yes	—
173	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
174	C₂³×D₄	—	2	1	no	—
175	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
176	C₂⁴×C₄	—	2	1	no	—
177	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
178	C₂³×C₈	—	2	8	no	—
179	C₂³×C₈	C₂²×C₂₃	1	2	yes	—
180	C₂³×C₈	C₂²×C₂₃	1	12	yes	complemented
181	C₂×#117	—	2	6	no	—
182	C₂×#117	C₂²×C₂₃	1	12	yes	complemented
183	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
184	C₂²×C₂²⋊C₄	—	2	1	no	—
185	C₂²×C₄²	—	2	1	no	—
186	#416	C₂²×C₂₃	1	64	yes	direct product factor
187	C₂×#103	C₂²×C₂₃	1	24	yes	complemented
188	C₂×#102	C₂²×C₂₃	1	24	yes	complemented
189	C₂×C₂₃	—	2	8	no	—
190	C₂×C₂₃	—	4	8	no	—
191	C₂×C₂₃	C₂×#416	1	12	yes	direct product factor
192	C₂×C₂₃	C₂³×C₂²⋊C₄	1	1	yes	characteristic
193	C₂×C₂₃	C₂²×#135	1	2	yes	—
194	C₂⁵	—	2	1	no	—
195	C₂⁵	D₄×C₂₃	1	1	yes	characteristic
196	C₂×#41	—	2	96	no	—
197	C₂×#41	—	2	48	no	—
198	C₂×#41	—	2	24	no	—
199	C₂×#41	C₂×C₄×C₂₃	1	96	yes	complemented
200	C₂×#41	C₂³×C₂₃	1	16	yes	—
201	C₂²×Q₈	—	2	4	no	—
202	C₂²×Q₈	—	2	3	no	—
203	C₂²×Q₈	C₂×C₄×C₂₃	1	8	yes	—
204	C₂²×Q₈	C₂³×C₂₃	1	6	yes	—
205	C₂²×D₄	—	2	16	no	—
206	C₂²×D₄	—	2	12	no	—
207	C₂²×D₄	—	2	3	no	—
208	C₂²×D₄	—	2	4	no	—
209	C₂²×D₄	C₂×C₄×C₂₃	1	8	yes	—
210	C₂²×D₄	C₂³×C₂₃	1	6	yes	—
211	C₂³×C₄	—	2	1	no	—
212	C₂³×C₄	—	2	16	no	—
213	C₂³×C₄	—	2	12	no	—
214	C₂³×C₄	—	2	2	no	—
215	C₂³×C₄	C₂×C₄×C₂₃	1	8	yes	—
216	C₂³×C₄	D₄×C₂₃	1	6	yes	—
217	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
218	C₂³×C₄	D₄×C₂₃	1	8	yes	—
219	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
220	C₂³×C₄	C₂³×C₂₃	1	6	yes	—
221	C₂²×C₈	—	2	8	no	—
222	C₂²×C₈	—	2	48	no	—
223	C₂²×C₈	C₂³×C₂₃	1	12	yes	—
224	C₂²×C₈	C₂³×C₂₃	1	16	yes	complemented
225	#117	—	2	24	no	—
226	#117	C₂³×C₂₃	1	16	yes	complemented
227	C₂×C₄⋊C₄	—	2	6	no	—
228	C₂×C₄⋊C₄	C₂³×C₂₃	1	12	yes	—
229	C₂×C₂²⋊C₄	—	2	12	no	—
230	C₂×C₄²	—	2	12	no	—
231	#103	C₂³×C₂₃	1	32	yes	complemented
232	#102	C₂³×C₂₃	1	32	yes	complemented
233	C₂₃	C₂²×#416	1	1	yes	characteristic, direct product factor, Sylow
234	C₂⁴	—	2	8	no	—
235	C₂⁴	—	2	8	no	—
236	C₂⁴	—	2	6	no	—
237	C₂⁴	—	4	8	no	—
238	C₂⁴	C₂²⋊C₄×C₂₃	1	8	yes	—
239	C₂⁴	C₂×D₄×C₂₃	1	6	yes	—
240	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
241	#41	—	2	192	no	—
242	#41	—	2	32	no	—
243	#41	C₂²×C₄×C₂₃	1	64	yes	complemented
244	C₂×Q₈	—	2	24	no	—
245	C₂×Q₈	—	2	6	no	—
246	C₂×Q₈	—	2	12	no	—
247	C₂×Q₈	C₂²×C₄×C₂₃	1	24	yes	—
248	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
249	C₂×D₄	—	2	96	no	—
250	C₂×D₄	—	2	16	no	—
251	C₂×D₄	—	2	24	no	—
252	C₂×D₄	—	2	12	no	—
253	C₂×D₄	—	2	6	no	—
254	C₂×D₄	C₂²×C₄×C₂₃	1	24	yes	—
255	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
256	C₂²×C₄	—	2	8	no	—
257	C₂²×C₄	—	2	6	no	—
258	C₂²×C₄	—	2	96	no	—
259	C₂²×C₄	—	2	16	no	—
260	C₂²×C₄	—	2	12	no	—
261	C₂²×C₄	—	4	8	no	—
262	C₂²×C₄	C₂²⋊C₄×C₂₃	1	8	yes	—
263	C₂²×C₄	C₂²⋊C₄×C₂₃	1	48	yes	—
264	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
265	C₂²×C₄	C₂²×C₄×C₂₃	1	24	yes	—
266	C₂²×C₄	C₂×D₄×C₂₃	1	6	yes	—
267	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
268	C₂²×C₄	C₂×D₄×C₂₃	1	12	yes	—
269	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
270	C₂²×C₄	C₂×D₄×C₂₃	1	24	yes	—
271	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
272	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
273	C₂×C₈	—	2	24	no	—
274	C₂×C₈	—	2	32	no	—
275	C₂×C₈	C₂⁴×C₂₃	1	8	yes	—
276	C₄⋊C₄	—	2	12	no	—
277	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
278	C₂²⋊C₄	—	2	16	no	—
279	C₄²	—	2	16	no	—
280	C₂³	—	2	24	no	—
281	C₂³	—	2	32	no	—
282	C₂³	—	2	4	no	—
283	C₂³	—	2	24	no	—
284	C₂³	—	4	24	no	—
285	C₂³	—	4	32	no	—
286	C₂³	C₂×C₂²⋊C₄×C₂₃	1	24	yes	—
287	C₂³	C₂×C₂²⋊C₄×C₂₃	1	4	yes	—
288	C₂³	C₂₃×#135	1	8	yes	—
289	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
290	C₂³	C₂²×D₄×C₂₃	1	3	yes	—
291	Q₈	—	2	4	no	—
292	Q₈	—	2	24	no	—
293	Q₈	C₂³×C₄×C₂₃	1	8	yes	—
294	D₄	—	2	64	no	—
295	D₄	—	2	4	no	—
296	D₄	—	2	24	no	—
297	D₄	C₂³×C₄×C₂₃	1	8	yes	—
298	C₂×C₄	—	2	4	no	—
299	C₂×C₄	—	2	24	no	—
300	C₂×C₄	—	2	64	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	4	24	no	—
303	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	24	yes	—
304	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	12	yes	—
305	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	48	yes	—
306	C₂×C₄	C₂³×C₄×C₂₃	1	6	yes	—
307	C₂×C₄	C₂³×C₄×C₂₃	1	8	yes	—
308	C₂×C₄	C₂²×D₄×C₂₃	1	6	yes	—
309	C₂×C₄	C₂²×D₄×C₂₃	1	8	yes	—
310	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
311	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
312	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
313	C₈	—	2	8	no	—
314	C₂²	—	2	8	no	—
315	C₂²	—	2	48	no	—
316	C₂²	—	2	8	no	—
317	C₂²	—	4	8	no	—
318	C₂²	—	4	48	no	—
319	C₂²	C₂₃×#416	1	16	yes	direct product factor
320	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	8	yes	—
321	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	6	yes	—
322	C₂²	C₂×C₂₃×#135	1	12	yes	—
323	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
324	C₄	—	2	8	no	—
325	C₄	—	4	8	no	—
326	C₄	C₂²×C₂²⋊C₄×C₂₃	1	8	yes	—
327	C₄	C₂²×C₂²⋊C₄×C₂₃	1	6	yes	—
328	C₄	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
329	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
330	C₂	—	2	8	no	—
331	C₂	—	4	8	no	—
332	C₂	C₂×C₂₃×#416	1	12	yes	direct product factor
333	C₂	C₂³×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
334	C₂	C₂²×C₂₃×#135	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₂₃	D₄
commutator	C₄	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂⁴×C₂₃	C₂×D₄
prime radical	C₂³×#41×C₂₃	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₂₃ ◁ C₂⁴×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂⁴×C₈×C₂₃	C₂	semidirect
3. C₂²×C₂₃×#117	C₂	semidirect
4. C₂×C₂₃×#416	C₂	direct (N × H)
5. C₂²×C₂₃×#103	C₂	semidirect
6. C₂²×C₂₃×#102	C₂	semidirect
9. C₂²×#41×C₂₃	C₄	semidirect
18. C₂³×C₈×C₂₃	C₂²	semidirect
20. C₂×C₂₃×#117	C₂²	semidirect
24. C₂₃×#416	C₂²	direct (N × H)
25. C₂×C₂₃×#103	C₂²	semidirect
26. C₂×C₂₃×#102	C₂²	semidirect
32. C₂×#41×C₂₃	C₂×C₄	semidirect
57. C₂²×C₈×C₂₃	C₂³	semidirect
59. C₂₃×#117	C₂³	semidirect
64. C₂₃×#103	C₂³	semidirect
65. C₂₃×#102	C₂³	semidirect
75. #41×C₂₃	C₂²×C₄	semidirect
112. C₂²×#416	C₂₃	direct (N × H)
148. C₂⁴×C₈	C₂×C₂₃	semidirect
149. C₂²×#117	C₂×C₂₃	semidirect
150. C₂×#416	C₂×C₂₃	direct (N × H)
151. C₂²×#103	C₂×C₂₃	semidirect
152. C₂²×#102	C₂×C₂₃	semidirect
158. C₂²×C₂₃	#416	direct (N × H)
171. C₂²×#41	C₄×C₂₃	semidirect
180. C₂³×C₈	C₂²×C₂₃	semidirect
182. C₂×#117	C₂²×C₂₃	semidirect
186. #416	C₂²×C₂₃	direct (N × H)
187. C₂×#103	C₂²×C₂₃	semidirect
188. C₂×#102	C₂²×C₂₃	semidirect
191. C₂×C₂₃	C₂×#416	direct (N × H)
199. C₂×#41	C₂×C₄×C₂₃	semidirect
224. C₂²×C₈	C₂³×C₂₃	semidirect
226. #117	C₂³×C₂₃	semidirect
231. #103	C₂³×C₂₃	semidirect
232. #102	C₂³×C₂₃	semidirect
233. C₂₃	C₂²×#416	direct (N × H)
243. #41	C₂²×C₄×C₂₃	semidirect
319. C₂²	C₂₃×#416	direct (N × H)
332. C₂	C₂×C₂₃×#416	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
C₂⁴×C₈×C₂₃	2
C₂²×C₂₃×#117	2
C₂×C₂₃×#416	2
C₂²×C₂₃×#103	2
C₂²×C₂₃×#102	2
C₂²×#416	23

Subgroups — C22×C23×#416 #19207705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₂₃×#416 #19207705