Subgroups — C₂₃×#3511 #15671130

Order 2944.

1104 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#556	C₂	1	2	yes	maximal, complemented
2	C₂₃×#555	C₂	1	2	yes	maximal, complemented
3	C₂₃×#554	C₂	1	2	yes	maximal, complemented
4	C₂₃×#553	C₂	1	4	yes	maximal, complemented
5	C₂₃×#548	C₂	1	4	yes	maximal, complemented
6	C₂₃×#547	C₂	1	2	yes	maximal, complemented
7	C₂₃×#542	C₂	1	4	yes	maximal, complemented
8	C₂₃×#537	C₂	1	2	yes	maximal, complemented
9	C₂₃×#533	C₂	1	2	yes	maximal, complemented
10	C₂₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#532	C₂	1	2	yes	maximal, complemented
12	C₂×C₂₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#520	C₂	1	2	yes	maximal, complemented
14	C₄×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#41×C₂₃	C₂²	1	1	yes	characteristic
16	C₂×#41×C₂₃	C₂²	1	2	yes	—
17	C₂×#41×C₂₃	C₂²	1	4	yes	—
18	C₂²×Q₈×C₂₃	C₂²	1	2	yes	—
19	C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
20	C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
21	C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
23	C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂₃×#127	C₂²	1	1	yes	characteristic
25	C₂₃×#126	C₂²	1	8	yes	—
26	C₂₃×#125	C₂²	1	4	yes	—
27	C₂₃×#124	C₂²	1	8	yes	—
28	C₂₃×#124	C₂²	1	4	yes	—
29	C₂₃×#124	C₂²	1	2	yes	—
30	C₂₃×#123	C₂²	1	8	yes	—
31	C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	—
32	C₂₃×C₂²⋊Q₈	C₂²	1	8	yes	—
33	C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	—
34	C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	—
35	C₂₃×#121	C₂²	1	4	yes	—
36	C₂₃×#121	C₂²	1	2	yes	—
37	C₂₃×#121	C₂²	1	8	yes	—
38	C₂₃×#121	C₂²	1	2	yes	—
39	C₂₃×#121	C₂²	1	4	yes	—
40	C₂₃×#121	C₂²	1	4	yes	—
41	C₄×Q₈×C₂₃	C₂²	1	4	yes	—
42	C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
43	C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
44	C₄×Q₈×C₂₃	C₂²	1	4	yes	—
45	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
46	C₄×D₄×C₂₃	C₂²	1	2	yes	—
47	C₄×D₄×C₂₃	C₂²	1	2	yes	—
48	C₄×D₄×C₂₃	C₂²	1	8	yes	—
49	C₄×D₄×C₂₃	C₂²	1	2	yes	—
50	C₄×D₄×C₂₃	C₂²	1	4	yes	—
51	C₄×D₄×C₂₃	C₂²	1	2	yes	—
52	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
53	C₄×D₄×C₂₃	C₂²	1	4	yes	—
54	C₂₃×#117	C₂²	1	4	yes	—
55	C₂₃×#117	C₂²	1	4	yes	—
56	C₂₃×#117	C₂²	1	1	yes	characteristic
57	C₂₃×#117	C₂²	1	2	yes	—
58	C₂×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
59	C₂×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
60	C₂×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
61	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
62	C₂×C₄²×C₂₃	C₂²	1	2	yes	—
63	#41×C₂₃	—	2	4	no	—
64	#41×C₂₃	—	2	8	no	—
65	#41×C₂₃	—	4	8	no	—
66	C₂×Q₈×C₂₃	—	4	4	no	—
67	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
68	C₂×Q₈×C₂₃	C₂³	1	2	yes	—
69	C₂×Q₈×C₂₃	C₂³	1	4	yes	—
70	C₂×Q₈×C₂₃	C₂³	1	4	yes	—
71	C₂×D₄×C₂₃	C₂³	1	2	yes	—
72	C₂×D₄×C₂₃	C₂³	1	2	yes	—
73	C₂×D₄×C₂₃	C₂³	1	4	yes	—
74	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
75	C₂×D₄×C₂₃	C₂³	1	2	yes	—
76	C₂×D₄×C₂₃	C₂³	1	2	yes	—
77	C₂×D₄×C₂₃	C₂³	1	8	yes	—
78	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
80	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
81	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
83	C₂²×C₄×C₂₃	C₂³	1	4	yes	—
84	C₂²×C₄×C₂₃	C₂³	1	4	yes	—
85	C₂²×C₄×C₂₃	C₂³	1	8	yes	—
86	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
87	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
88	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
89	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
90	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
91	C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
92	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
93	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
94	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
95	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
96	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
97	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
98	C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
99	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
100	C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
101	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
102	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
103	C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
104	C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
105	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
106	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
107	C₄²×C₂₃	C₂³	1	1	yes	characteristic
108	C₄²×C₂₃	C₂³	1	2	yes	—
109	C₄²×C₂₃	C₂³	1	1	yes	characteristic
110	C₄²×C₂₃	C₂³	1	2	yes	—
111	C₄²×C₂₃	C₂³	1	1	yes	characteristic
112	C₄²×C₂₃	C₂³	1	1	yes	characteristic
113	C₄²×C₂₃	C₂³	1	2	yes	—
114	C₄²×C₂₃	C₂³	1	8	yes	—
115	C₂³×C₂₃	C₂⁴	1	2	yes	—
116	C₂³×C₂₃	C₂⁴	1	4	yes	—
117	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
118	Q₈×C₂₃	—	2	2	no	—
119	Q₈×C₂₃	—	2	4	no	—
120	Q₈×C₂₃	—	2	8	no	—
121	Q₈×C₂₃	—	4	4	no	—
122	D₄×C₂₃	—	2	4	no	—
123	D₄×C₂₃	—	2	8	no	—
124	D₄×C₂₃	—	2	2	no	—
125	D₄×C₂₃	—	2	4	no	—
126	D₄×C₂₃	—	2	4	no	—
127	D₄×C₂₃	—	2	4	no	—
128	D₄×C₂₃	—	4	8	no	—
129	C₂×C₄×C₂₃	—	2	8	no	—
130	C₂×C₄×C₂₃	—	2	4	no	—
131	C₂×C₄×C₂₃	—	2	2	no	—
132	C₂×C₄×C₂₃	—	2	4	no	—
133	C₂×C₄×C₂₃	—	2	2	no	—
134	C₂×C₄×C₂₃	—	2	4	no	—
135	C₂×C₄×C₂₃	—	4	4	no	—
136	C₂×C₄×C₂₃	—	4	8	no	—
137	C₂×C₄×C₂₃	#41	1	4	yes	complemented
138	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
139	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
140	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
141	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
142	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
143	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
144	C₂×C₄×C₂₃	C₂⁴	1	8	yes	—
145	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
146	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
147	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
148	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
149	#3511	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂²×C₂₃	—	2	1	no	—
151	C₂²×C₂₃	—	2	1	no	—
152	C₂²×C₂₃	—	2	2	no	—
153	C₂²×C₂₃	—	2	4	no	—
154	C₂²×C₂₃	—	2	2	no	—
155	C₂²×C₂₃	—	2	4	no	—
156	C₂²×C₂₃	—	2	2	no	—
157	C₂²×C₂₃	—	2	4	no	—
158	C₂²×C₂₃	C₂×#41	1	2	yes	—
159	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
160	C₄×C₂₃	—	2	4	no	—
161	C₄×C₂₃	—	2	2	no	—
162	C₄×C₂₃	—	2	2	no	—
163	C₄×C₂₃	—	2	1	no	—
164	C₄×C₂₃	—	2	8	no	—
165	C₄×C₂₃	—	2	2	no	—
166	C₄×C₂₃	—	2	1	no	—
167	C₄×C₂₃	C₂×#41	1	2	yes	—
168	C₄×C₂₃	C₂×#41	1	2	yes	—
169	C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
170	C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
171	#556	C₂×C₂₃	1	2	yes	complemented
172	#555	C₂×C₂₃	1	2	yes	complemented
173	#554	C₂×C₂₃	1	2	yes	complemented
174	#553	C₂×C₂₃	1	4	yes	complemented
175	#548	C₂×C₂₃	1	4	yes	complemented
176	#547	C₂×C₂₃	1	2	yes	complemented
177	#542	C₂×C₂₃	1	4	yes	complemented
178	#537	C₂×C₂₃	1	2	yes	complemented
179	#533	C₂×C₂₃	1	2	yes	complemented
180	#532	C₂×C₂₃	1	1	yes	characteristic, complemented
181	#532	C₂×C₂₃	1	2	yes	complemented
182	C₂×C₄⋊Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
183	#520	C₂×C₂₃	1	2	yes	complemented
184	C₄×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
185	C₂×C₂₃	—	2	2	no	—
186	C₂×C₂₃	—	4	2	no	—
187	C₂×C₂₃	—	4	4	no	—
188	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
189	C₂×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
190	C₂×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
191	C₂×#41	C₂²×C₂₃	1	1	yes	characteristic
192	C₂×#41	C₂²×C₂₃	1	2	yes	—
193	C₂×#41	C₂²×C₂₃	1	4	yes	—
194	C₂²×Q₈	C₂²×C₂₃	1	2	yes	—
195	C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
196	C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
197	C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
198	C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
199	C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
200	#127	C₂²×C₂₃	1	1	yes	characteristic
201	#126	C₂²×C₂₃	1	8	yes	—
202	#125	C₂²×C₂₃	1	4	yes	—
203	#124	C₂²×C₂₃	1	2	yes	—
204	#124	C₂²×C₂₃	1	4	yes	—
205	#124	C₂²×C₂₃	1	8	yes	—
206	#123	C₂²×C₂₃	1	8	yes	—
207	C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
208	C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
209	C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
210	C₂²⋊Q₈	C₂²×C₂₃	1	8	yes	—
211	#121	C₂²×C₂₃	1	4	yes	—
212	#121	C₂²×C₂₃	1	2	yes	—
213	#121	C₂²×C₂₃	1	2	yes	—
214	#121	C₂²×C₂₃	1	4	yes	—
215	#121	C₂²×C₂₃	1	4	yes	—
216	#121	C₂²×C₂₃	1	8	yes	—
217	C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
218	C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
219	C₄×Q₈	C₂²×C₂₃	1	4	yes	—
220	C₄×Q₈	C₂²×C₂₃	1	4	yes	—
221	C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
222	C₄×D₄	C₂²×C₂₃	1	2	yes	—
223	C₄×D₄	C₂²×C₂₃	1	2	yes	—
224	C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
225	C₄×D₄	C₂²×C₂₃	1	4	yes	—
226	C₄×D₄	C₂²×C₂₃	1	8	yes	—
227	C₄×D₄	C₂²×C₂₃	1	2	yes	—
228	C₄×D₄	C₂²×C₂₃	1	4	yes	—
229	C₄×D₄	C₂²×C₂₃	1	2	yes	—
230	#117	C₂²×C₂₃	1	1	yes	characteristic
231	#117	C₂²×C₂₃	1	2	yes	—
232	#117	C₂²×C₂₃	1	4	yes	—
233	#117	C₂²×C₂₃	1	4	yes	—
234	C₂×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
235	C₂×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
236	C₂×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
237	C₂×C₄²	C₂²×C₂₃	1	1	yes	characteristic
238	C₂×C₄²	C₂²×C₂₃	1	2	yes	—
239	C₂₃	#3511	1	1	yes	characteristic, direct product factor, Sylow
240	#41	—	2	4	no	—
241	#41	—	2	8	no	—
242	#41	—	4	8	no	—
243	C₂×Q₈	—	4	4	no	—
244	C₂×Q₈	C₂³×C₂₃	1	1	yes	characteristic
245	C₂×Q₈	C₂³×C₂₃	1	2	yes	—
246	C₂×Q₈	C₂³×C₂₃	1	4	yes	—
247	C₂×Q₈	C₂³×C₂₃	1	4	yes	—
248	C₂×D₄	C₂³×C₂₃	1	2	yes	—
249	C₂×D₄	C₂³×C₂₃	1	2	yes	—
250	C₂×D₄	C₂³×C₂₃	1	4	yes	—
251	C₂×D₄	C₂³×C₂₃	1	1	yes	characteristic
252	C₂×D₄	C₂³×C₂₃	1	2	yes	—
253	C₂×D₄	C₂³×C₂₃	1	2	yes	—
254	C₂×D₄	C₂³×C₂₃	1	8	yes	—
255	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
256	C₂²×C₄	C₂³×C₂₃	1	2	yes	—
257	C₂²×C₄	C₂³×C₂₃	1	2	yes	—
258	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
259	C₂²×C₄	C₂³×C₂₃	1	2	yes	—
260	C₂²×C₄	C₂³×C₂₃	1	4	yes	—
261	C₂²×C₄	C₂³×C₂₃	1	4	yes	—
262	C₂²×C₄	C₂³×C₂₃	1	8	yes	—
263	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
264	C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
265	C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
266	C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
267	C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
268	C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
269	C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
270	C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
271	C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
272	C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
273	C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
274	C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
275	C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
276	C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
277	C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
278	C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
279	C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
280	C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
281	C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
282	C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
283	C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
284	C₄²	C₂³×C₂₃	1	1	yes	characteristic
285	C₄²	C₂³×C₂₃	1	2	yes	—
286	C₄²	C₂³×C₂₃	1	1	yes	characteristic
287	C₄²	C₂³×C₂₃	1	2	yes	—
288	C₄²	C₂³×C₂₃	1	1	yes	characteristic
289	C₄²	C₂³×C₂₃	1	1	yes	characteristic
290	C₄²	C₂³×C₂₃	1	2	yes	—
291	C₄²	C₂³×C₂₃	1	8	yes	—
292	C₂³	C₂⁴×C₂₃	1	2	yes	—
293	C₂³	C₂⁴×C₂₃	1	4	yes	—
294	C₂³	C₂⁴×C₂₃	1	1	yes	characteristic
295	Q₈	—	2	2	no	—
296	Q₈	—	2	4	no	—
297	Q₈	—	2	8	no	—
298	Q₈	—	4	4	no	—
299	D₄	—	2	4	no	—
300	D₄	—	2	8	no	—
301	D₄	—	2	2	no	—
302	D₄	—	2	4	no	—
303	D₄	—	2	4	no	—
304	D₄	—	2	4	no	—
305	D₄	—	4	8	no	—
306	C₂×C₄	—	2	8	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	4	4	no	—
313	C₂×C₄	—	4	8	no	—
314	C₂×C₄	#41×C₂₃	1	4	yes	complemented
315	C₂×C₄	C₂⁴×C₂₃	1	2	yes	—
316	C₂×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
317	C₂×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
318	C₂×C₄	C₂⁴×C₂₃	1	2	yes	—
319	C₂×C₄	C₂⁴×C₂₃	1	4	yes	—
320	C₂×C₄	C₂⁴×C₂₃	1	2	yes	—
321	C₂×C₄	C₂⁴×C₂₃	1	8	yes	—
322	C₂×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
323	C₂×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
324	C₂×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
325	C₂×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
326	C₂²	—	2	1	no	—
327	C₂²	—	2	1	no	—
328	C₂²	—	2	2	no	—
329	C₂²	—	2	4	no	—
330	C₂²	—	2	2	no	—
331	C₂²	—	2	4	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	4	no	—
334	C₂²	C₂×#41×C₂₃	1	2	yes	—
335	C₂²	C₂⁵×C₂₃	1	1	yes	characteristic
336	C₄	—	2	4	no	—
337	C₄	—	2	2	no	—
338	C₄	—	2	2	no	—
339	C₄	—	2	1	no	—
340	C₄	—	2	8	no	—
341	C₄	—	2	2	no	—
342	C₄	—	2	1	no	—
343	C₄	C₂×#41×C₂₃	1	2	yes	—
344	C₄	C₂×#41×C₂₃	1	2	yes	—
345	C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
346	C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
347	C₂	—	2	2	no	—
348	C₂	—	4	2	no	—
349	C₂	—	4	4	no	—
350	C₂	C₂²×#41×C₂₃	1	1	yes	characteristic
351	C₂	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
352	C₂	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂₃×#556	C₂	semidirect
2. C₂₃×#555	C₂	semidirect
3. C₂₃×#554	C₂	semidirect
4. C₂₃×#553	C₂	semidirect
5. C₂₃×#548	C₂	semidirect
6. C₂₃×#547	C₂	semidirect
7. C₂₃×#542	C₂	semidirect
8. C₂₃×#537	C₂	semidirect
9. C₂₃×#533	C₂	semidirect
10. C₂₃×#532	C₂	semidirect
11. C₂₃×#532	C₂	semidirect
12. C₂×C₂₃×C₄⋊Q₈	C₂	semidirect
13. C₂₃×#520	C₂	semidirect
14. C₄×#41×C₂₃	C₂	semidirect
137. C₂×C₄×C₂₃	#41	semidirect
149. #3511	C₂₃	direct (N × H)
171. #556	C₂×C₂₃	semidirect
172. #555	C₂×C₂₃	semidirect
173. #554	C₂×C₂₃	semidirect
174. #553	C₂×C₂₃	semidirect
175. #548	C₂×C₂₃	semidirect
176. #547	C₂×C₂₃	semidirect
177. #542	C₂×C₂₃	semidirect
178. #537	C₂×C₂₃	semidirect
179. #533	C₂×C₂₃	semidirect
180. #532	C₂×C₂₃	semidirect
181. #532	C₂×C₂₃	semidirect
182. C₂×C₄⋊Q₈	C₂×C₂₃	semidirect
183. #520	C₂×C₂₃	semidirect
184. C₄×#41	C₂×C₂₃	semidirect
239. C₂₃	#3511	direct (N × H)
314. C₂×C₄	#41×C₂₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#556	2
C₂₃×#555	2
C₂₃×#554	2
C₂₃×#553	2
C₂₃×#548	2
C₂₃×#547	2
C₂₃×#542	2
C₂₃×#537	2
C₂₃×#533	2
C₂₃×#532	2
C₂×C₂₃×C₄⋊Q₈	2
C₂₃×#520	2
C₄×#41×C₂₃	2
#3511	23

Subgroups — C23×#3511 #15671130

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#3511 #15671130