Subgroups — C₂₃×#22658 #19170284

Order 5888.

982 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×C₈×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#427	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2354	C₂	1	2	yes	maximal
4	C₂₃×#1948	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1854	C₂	1	4	yes	maximal, complemented
6	C₂₃×#1845	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1808	C₂	1	2	yes	maximal, complemented
8	C₄×C₂₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₈×C₂₃	C₂²	1	2	yes	—
10	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
11	C₂×C₂₃×#117	C₂²	1	4	yes	—
12	C₈×D₄×C₂₃	C₄	1	8	yes	complemented
13	C₂₃×#427	—	2	8	no	—
14	C₂×C₂₃×#107	C₂²	1	2	yes	—
15	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
16	C₂×C₂₃×#107	C₂²	1	2	yes	—
17	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×#106	C₂²	1	4	yes	—
19	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
22	C₂₃×#390	—	2	2	no	—
23	C₂₃×#388	—	2	4	no	—
24	C₂₃×#384	C₂²	1	2	yes	—
25	C₂₃×#380	C₂²	1	4	yes	—
26	C₄×C₄⋊C₄×C₂₃	—	2	2	no	—
27	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
28	C₂₃×#340	C₂²	1	4	yes	—
29	C₂₃×#340	C₂²	1	2	yes	—
30	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
32	C₂²×C₈×C₂₃	—	2	4	no	—
33	C₂²×C₈×C₂₃	—	2	4	no	—
34	C₂²×C₈×C₂₃	C₂×C₄	1	8	yes	—
35	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
36	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
38	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
39	C₄×D₄×C₂₃	Q₈	1	4	yes	—
40	C₂₃×#117	—	2	8	no	—
41	C₂₃×#117	—	4	4	no	—
42	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
43	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
44	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
46	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
47	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
48	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
49	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
50	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
51	C₂×C₄²×C₂₃	—	2	2	no	—
52	C₂×C₄²×C₂₃	—	2	4	no	—
53	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
54	C₂₃×#107	—	2	4	no	—
55	C₂₃×#107	—	2	2	no	—
56	C₂₃×#107	—	4	2	no	—
57	C₂₃×#107	D₄	1	4	yes	complemented
58	C₂₃×#106	—	2	8	no	—
59	C₂₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
60	C₂₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
61	C₄×C₈×C₂₃	C₂×C₄	1	4	yes	—
62	C₂₃×#95	—	2	4	no	—
63	C₂₃×#95	—	2	2	no	—
64	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
65	C₂×D₄×C₂₃	—	2	2	no	—
66	C₂×D₄×C₂₃	—	2	2	no	—
67	C₂×D₄×C₂₃	C₄⋊C₄	1	4	yes	—
68	C₂²×C₄×C₂₃	—	2	2	no	—
69	C₂²×C₄×C₂₃	—	2	2	no	—
70	C₂²×C₄×C₂₃	—	2	2	no	—
71	C₂²×C₄×C₂₃	—	2	2	no	—
72	C₂²×C₄×C₂₃	—	2	2	no	—
73	C₂²×C₄×C₂₃	—	2	4	no	—
74	C₂²×C₄×C₂₃	—	2	2	no	—
75	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
76	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
77	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₂₃	C₂×Q₈	1	4	yes	—
80	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
81	C₂×C₈×C₂₃	—	2	2	no	—
82	C₂×C₈×C₂₃	—	2	2	no	—
83	C₂×C₈×C₂₃	—	2	1	no	—
84	C₂×C₈×C₂₃	—	2	1	no	—
85	C₂×C₈×C₂₃	—	2	16	no	—
86	C₂×C₈×C₂₃	C₂²×C₄	1	4	yes	—
87	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
88	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
89	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
90	C₂×C₈×C₂₃	#41	1	2	yes	—
91	C₄⋊C₄×C₂₃	—	2	2	no	—
92	C₄⋊C₄×C₂₃	—	2	4	no	—
93	C₄⋊C₄×C₂₃	—	2	2	no	—
94	C₄⋊C₄×C₂₃	—	2	4	no	—
95	C₄⋊C₄×C₂₃	—	2	2	no	—
96	C₄⋊C₄×C₂₃	—	4	4	no	—
97	C₄⋊C₄×C₂₃	—	8	2	no	—
98	C₄⋊C₄×C₂₃	C₄⋊C₄	1	4	yes	—
99	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
100	C₂²⋊C₄×C₂₃	—	4	8	no	—
101	C₂²⋊C₄×C₂₃	—	8	4	no	—
102	C₂²⋊C₄×C₂₃	C₄⋊C₄	1	8	yes	—
103	C₄²×C₂₃	—	4	8	no	—
104	C₄²×C₂₃	—	4	4	no	—
105	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
106	C₄²×C₂₃	C₂×Q₈	1	2	yes	—
107	#22658	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂³×C₂₃	—	2	2	no	—
109	C₂³×C₂₃	—	2	2	no	—
110	C₂³×C₂₃	—	2	2	no	—
111	C₂³×C₂₃	—	2	2	no	—
112	C₂³×C₂₃	—	2	2	no	—
113	C₂³×C₂₃	—	2	2	no	—
114	C₂³×C₂₃	C₂×C₄⋊C₄	1	4	yes	—
115	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
116	D₄×C₂₃	—	2	8	no	—
117	C₂×C₄×C₂₃	—	2	2	no	—
118	C₂×C₄×C₂₃	—	2	2	no	—
119	C₂×C₄×C₂₃	—	2	1	no	—
120	C₂×C₄×C₂₃	—	2	1	no	—
121	C₂×C₄×C₂₃	—	2	4	no	—
122	C₂×C₄×C₂₃	—	2	4	no	—
123	C₂×C₄×C₂₃	—	2	4	no	—
124	C₂×C₄×C₂₃	—	2	4	no	—
125	C₂×C₄×C₂₃	—	2	4	no	—
126	C₂×C₄×C₂₃	—	4	2	no	—
127	C₂×C₄×C₂₃	—	4	2	no	—
128	C₂×C₄×C₂₃	—	4	4	no	—
129	C₂×C₄×C₂₃	—	4	2	no	—
130	C₂×C₄×C₂₃	—	4	2	no	—
131	C₂×C₄×C₂₃	—	4	4	no	—
132	C₂×C₄×C₂₃	—	4	2	no	—
133	C₂×C₄×C₂₃	—	4	4	no	—
134	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	2	yes	—
135	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	4	yes	—
136	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	2	yes	—
137	C₂×C₄×C₂₃	#135	1	2	yes	—
138	C₂×C₄×C₂₃	#135	1	2	yes	—
139	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
140	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
141	C₂×C₄×C₂₃	C₂²×Q₈	1	1	yes	characteristic
142	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
143	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
144	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
145	C₈×C₂₃	—	2	4	no	—
146	C₈×C₂₃	—	2	2	no	—
147	C₈×C₂₃	C₄×D₄	1	4	yes	—
148	C₂×C₈×D₄	C₂×C₂₃	1	1	yes	characteristic
149	C₂×#427	C₂×C₂₃	1	2	yes	complemented
150	#2354	C₂×C₂₃	1	2	yes	—
151	#1948	C₂×C₂₃	1	2	yes	complemented
152	#1854	C₂×C₂₃	1	4	yes	complemented
153	#1845	C₂×C₂₃	1	1	yes	characteristic, complemented
154	#1808	C₂×C₂₃	1	2	yes	complemented
155	C₄×#107	C₂×C₂₃	1	1	yes	characteristic, complemented
156	C₂²×C₂₃	—	2	4	no	—
157	C₂²×C₂₃	—	2	4	no	—
158	C₂²×C₂₃	—	2	4	no	—
159	C₂²×C₂₃	—	4	2	no	—
160	C₂²×C₂₃	—	4	2	no	—
161	C₂²×C₂₃	—	4	2	no	—
162	C₂²×C₂₃	—	4	2	no	—
163	C₂²×C₂₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
164	C₂²×C₂₃	D₄²	1	1	yes	characteristic
165	C₂²×C₂₃	#547	1	1	yes	characteristic
166	C₂²×C₂₃	C₂×#135	1	1	yes	characteristic
167	C₂²×C₂₃	C₂×#135	1	1	yes	characteristic
168	C₂²×C₂₃	#576	1	1	yes	characteristic
169	C₂²×C₂₃	#578	1	1	yes	characteristic
170	C₄×C₂₃	—	2	4	no	—
171	C₄×C₂₃	—	2	2	no	—
172	C₄×C₂₃	—	4	4	no	—
173	C₄×C₂₃	—	8	2	no	—
174	C₄×C₂₃	—	8	4	no	—
175	C₄×C₂₃	#427	1	4	yes	complemented
176	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
177	C₄×C₂₃	#520	1	1	yes	characteristic
178	C₄×C₂₃	D₄×Q₈	1	1	yes	characteristic
179	C₄×C₂₃	#554	1	1	yes	characteristic
180	C₂³×C₈	C₂²×C₂₃	1	2	yes	—
181	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
182	C₂×#117	C₂²×C₂₃	1	4	yes	—
183	C₈×D₄	C₄×C₂₃	1	8	yes	complemented
184	#427	—	2	8	no	—
185	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
186	C₂×#107	C₂²×C₂₃	1	2	yes	—
187	C₂×#107	C₂²×C₂₃	1	2	yes	—
188	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
189	C₂×#106	C₂²×C₂₃	1	4	yes	—
190	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
191	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
192	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
193	#390	—	2	2	no	—
194	#388	—	2	4	no	—
195	#384	C₂²×C₂₃	1	2	yes	—
196	#380	C₂²×C₂₃	1	4	yes	—
197	C₄×C₄⋊C₄	—	2	2	no	—
198	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
199	#340	C₂²×C₂₃	1	4	yes	—
200	#340	C₂²×C₂₃	1	2	yes	—
201	C₂×C₂₃	—	4	4	no	—
202	C₂×C₂₃	D₄×C₄⋊C₄	1	1	yes	characteristic
203	C₂×C₂₃	C₂×#427	1	1	yes	characteristic
204	C₂×C₂₃	#2913	1	1	yes	characteristic
205	C₂×C₂₃	#3283	1	1	yes	characteristic
206	C₂×C₂₃	#3287	1	1	yes	characteristic
207	C₂×C₂₃	#3341	1	1	yes	characteristic
208	C₂×C₂₃	#3342	1	1	yes	characteristic
209	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
210	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
211	C₂²×C₈	—	2	4	no	—
212	C₂²×C₈	—	2	4	no	—
213	C₂²×C₈	C₂×C₄×C₂₃	1	8	yes	—
214	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
215	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
216	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
217	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
218	C₄×D₄	Q₈×C₂₃	1	4	yes	—
219	#117	—	2	8	no	—
220	#117	—	4	4	no	—
221	C₂×C₄⋊C₄	—	2	2	no	—
222	C₂×C₄⋊C₄	—	2	2	no	—
223	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
224	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
225	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
226	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
227	C₂×C₂²⋊C₄	—	2	4	no	—
228	C₂×C₂²⋊C₄	—	2	4	no	—
229	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
230	C₂×C₄²	—	2	4	no	—
231	C₂×C₄²	—	2	2	no	—
232	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
233	#107	—	2	4	no	—
234	#107	—	2	2	no	—
235	#107	—	4	2	no	—
236	#107	D₄×C₂₃	1	4	yes	complemented
237	#106	—	2	8	no	—
238	C₄⋊C₈	C₂×C₄×C₂₃	1	4	yes	—
239	C₂²⋊C₈	C₂×C₄×C₂₃	1	8	yes	—
240	C₄×C₈	C₂×C₄×C₂₃	1	4	yes	—
241	#95	—	2	4	no	—
242	#95	—	2	2	no	—
243	C₂₃	#22658	1	1	yes	characteristic, direct product factor, Sylow
244	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
245	C₂×D₄	—	2	2	no	—
246	C₂×D₄	—	2	2	no	—
247	C₂×D₄	C₄⋊C₄×C₂₃	1	4	yes	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
256	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
257	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
258	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
259	C₂²×C₄	C₂×Q₈×C₂₃	1	4	yes	—
260	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	1	no	—
264	C₂×C₈	—	2	1	no	—
265	C₂×C₈	—	2	16	no	—
266	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
267	C₂×C₈	C₂²×C₄×C₂₃	1	4	yes	—
268	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
269	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
270	C₂×C₈	#41×C₂₃	1	2	yes	—
271	C₄⋊C₄	—	2	2	no	—
272	C₄⋊C₄	—	2	4	no	—
273	C₄⋊C₄	—	2	2	no	—
274	C₄⋊C₄	—	2	4	no	—
275	C₄⋊C₄	—	2	2	no	—
276	C₄⋊C₄	—	4	4	no	—
277	C₄⋊C₄	—	8	2	no	—
278	C₄⋊C₄	C₄⋊C₄×C₂₃	1	4	yes	—
279	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
280	C₂²⋊C₄	—	4	8	no	—
281	C₂²⋊C₄	—	8	4	no	—
282	C₂²⋊C₄	C₄⋊C₄×C₂₃	1	8	yes	—
283	C₄²	—	4	8	no	—
284	C₄²	—	4	4	no	—
285	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
286	C₄²	C₂×Q₈×C₂₃	1	2	yes	—
287	C₂³	—	2	2	no	—
288	C₂³	—	2	2	no	—
289	C₂³	—	2	2	no	—
290	C₂³	—	2	2	no	—
291	C₂³	—	2	2	no	—
292	C₂³	—	2	2	no	—
293	C₂³	C₂×C₄⋊C₄×C₂₃	1	4	yes	—
294	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
295	D₄	—	2	8	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	4	2	no	—
306	C₂×C₄	—	4	2	no	—
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	4	4	no	—
310	C₂×C₄	—	4	2	no	—
311	C₂×C₄	—	4	4	no	—
312	C₂×C₄	—	4	4	no	—
313	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	2	yes	—
314	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	4	yes	—
315	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	2	yes	—
316	C₂×C₄	C₂₃×#135	1	2	yes	—
317	C₂×C₄	C₂₃×#135	1	2	yes	—
318	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
319	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
320	C₂×C₄	C₂²×Q₈×C₂₃	1	1	yes	characteristic
321	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
322	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
323	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
324	C₈	—	2	4	no	—
325	C₈	—	2	2	no	—
326	C₈	C₄×D₄×C₂₃	1	4	yes	—
327	C₂²	—	2	4	no	—
328	C₂²	—	2	4	no	—
329	C₂²	—	2	4	no	—
330	C₂²	—	4	2	no	—
331	C₂²	—	4	2	no	—
332	C₂²	—	4	2	no	—
333	C₂²	—	4	2	no	—
334	C₂²	C₂²×C₄⋊C₄×C₂₃	1	1	yes	characteristic
335	C₂²	D₄²×C₂₃	1	1	yes	characteristic
336	C₂²	C₂₃×#547	1	1	yes	characteristic
337	C₂²	C₂×C₂₃×#135	1	1	yes	characteristic
338	C₂²	C₂×C₂₃×#135	1	1	yes	characteristic
339	C₂²	C₂₃×#576	1	1	yes	characteristic
340	C₂²	C₂₃×#578	1	1	yes	characteristic
341	C₄	—	2	2	no	—
342	C₄	—	2	4	no	—
343	C₄	—	4	4	no	—
344	C₄	—	8	4	no	—
345	C₄	—	8	2	no	—
346	C₄	C₂₃×#427	1	4	yes	complemented
347	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
348	C₄	C₂₃×#520	1	1	yes	characteristic
349	C₄	D₄×Q₈×C₂₃	1	1	yes	characteristic
350	C₄	C₂₃×#554	1	1	yes	characteristic
351	C₂	—	4	4	no	—
352	C₂	D₄×C₄⋊C₄×C₂₃	1	1	yes	characteristic
353	C₂	C₂×C₂₃×#427	1	1	yes	characteristic
354	C₂	C₂₃×#2913	1	1	yes	characteristic
355	C₂	C₂₃×#3283	1	1	yes	characteristic
356	C₂	C₂₃×#3287	1	1	yes	characteristic
357	C₂	C₂₃×#3341	1	1	yes	characteristic
358	C₂	C₂₃×#3342	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#427	C₂	semidirect
4. C₂₃×#1948	C₂	semidirect
5. C₂₃×#1854	C₂	semidirect
6. C₂₃×#1845	C₂	semidirect
7. C₂₃×#1808	C₂	semidirect
8. C₄×C₂₃×#107	C₂	semidirect
12. C₈×D₄×C₂₃	C₄	semidirect
57. C₂₃×#107	D₄	semidirect
107. #22658	C₂₃	direct (N × H)
149. C₂×#427	C₂×C₂₃	semidirect
151. #1948	C₂×C₂₃	semidirect
152. #1854	C₂×C₂₃	semidirect
153. #1845	C₂×C₂₃	semidirect
154. #1808	C₂×C₂₃	semidirect
155. C₄×#107	C₂×C₂₃	semidirect
175. C₄×C₂₃	#427	semidirect
183. C₈×D₄	C₄×C₂₃	semidirect
236. #107	D₄×C₂₃	semidirect
243. C₂₃	#22658	direct (N × H)
346. C₄	C₂₃×#427	semidirect

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
C₂×C₂₃×#427	2
C₂₃×#2354	2
C₂₃×#1948	2
C₂₃×#1854	2
C₂₃×#1845	2
C₂₃×#1808	2
C₄×C₂₃×#107	2
#22658	23

Subgroups — C23×#22658 #19170284

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#22658 #19170284