Subgroups — C₂×C₂₃×#3186 #19208354

Order 5888.

3042 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×#121	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3186	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₂₃×#480	C₂	1	4	yes	maximal, complemented
4	C₂×C₂₃×#466	C₂	1	4	yes	maximal, complemented
5	C₂×C₂₃×#447	C₂	1	4	yes	maximal, complemented
6	C₂²×C₂₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×D₄×C₂₃	—	2	2	no	—
8	C₂³×D₄×C₂₃	C₂²	1	2	yes	complemented
9	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
10	C₂²×D₈×C₂₃	C₂²	1	4	yes	complemented
11	C₂³×C₈×C₂₃	C₂²	1	2	yes	complemented
12	C₂×C₂₃×#121	—	2	2	no	—
13	C₂×C₂₃×#121	—	2	8	no	—
14	C₂×C₂₃×#121	—	2	2	no	—
15	C₂×C₂₃×#121	C₂²	1	4	yes	—
16	C₂×C₂₃×#121	C₂²	1	4	yes	complemented
17	C₂×C₂₃×#121	C₂²	1	16	yes	complemented
18	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
19	C₂²×C₂²⋊C₄×C₂₃	—	2	2	no	—
20	C₂₃×#480	C₂²	1	32	yes	complemented
21	C₂₃×#466	C₂²	1	32	yes	complemented
22	C₂₃×#447	C₂²	1	32	yes	complemented
23	C₂×C₂₃×#107	C₂²	1	4	yes	complemented
24	C₂×C₂₃×#102	C₂²	1	8	yes	complemented
25	C₂×C₂₃×C₂²⋊C₈	C₂²	1	4	yes	complemented
26	C₂×C₂₃×C₂²⋊C₈	C₂²	1	8	yes	complemented
27	C₂⁵×C₂₃	—	2	2	no	—
28	C₂⁵×C₂₃	D₄	1	1	yes	characteristic
29	C₂²×D₄×C₂₃	—	2	4	no	—
30	C₂²×D₄×C₂₃	—	2	16	no	—
31	C₂²×D₄×C₂₃	—	2	4	no	—
32	C₂²×D₄×C₂₃	—	2	4	no	—
33	C₂²×D₄×C₂₃	—	2	2	no	—
34	C₂²×D₄×C₂₃	—	4	8	no	—
35	C₂²×D₄×C₂₃	—	4	16	no	—
36	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
37	C₂²×D₄×C₂₃	C₂³	1	8	yes	complemented
38	C₂³×C₄×C₂₃	—	2	2	no	—
39	C₂³×C₄×C₂₃	—	4	4	no	—
40	C₂³×C₄×C₂₃	D₄	1	2	yes	—
41	C₂³×C₄×C₂₃	D₄	1	4	yes	—
42	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
46	C₂×D₈×C₂₃	—	4	8	no	—
47	C₂×D₈×C₂₃	C₂³	1	16	yes	complemented
48	C₂²×C₈×C₂₃	—	4	4	no	—
49	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
50	C₂²×C₈×C₂₃	C₂³	1	8	yes	complemented
51	C₂₃×#121	—	2	8	no	—
52	C₂₃×#121	—	2	16	no	—
53	C₂₃×#121	—	2	8	no	—
54	C₂₃×#121	—	2	16	no	—
55	C₂₃×#121	C₂³	1	16	yes	—
56	C₂₃×#121	C₂³	1	16	yes	complemented
57	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
58	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
59	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
60	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	complemented
61	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₂₃	—	2	16	no	—
63	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
64	C₂₃×#107	C₂³	1	16	yes	complemented
65	C₂₃×#102	C₂³	1	32	yes	complemented
66	C₂₃×C₂²⋊C₈	C₂³	1	16	yes	complemented
67	C₂⁴×C₂₃	—	2	8	no	—
68	C₂⁴×C₂₃	—	2	4	no	—
69	C₂⁴×C₂₃	—	4	2	no	—
70	C₂⁴×C₂₃	—	4	2	no	—
71	C₂⁴×C₂₃	—	4	8	no	—
72	C₂⁴×C₂₃	—	4	8	no	—
73	C₂⁴×C₂₃	—	4	8	no	—
74	C₂⁴×C₂₃	D₈	1	8	yes	complemented
75	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
76	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
77	C₂⁴×C₂₃	C₂×D₄	1	4	yes	—
78	C₂×D₄×C₂₃	—	2	16	no	—
79	C₂×D₄×C₂₃	—	2	16	no	—
80	C₂×D₄×C₂₃	—	2	4	no	—
81	C₂×D₄×C₂₃	—	2	8	no	—
82	C₂×D₄×C₂₃	—	2	16	no	—
83	C₂×D₄×C₂₃	—	4	16	no	—
84	C₂×D₄×C₂₃	—	4	8	no	—
85	C₂×D₄×C₂₃	—	4	16	no	—
86	C₂×D₄×C₂₃	—	4	16	no	—
87	C₂×D₄×C₂₃	—	4	16	no	—
88	C₂×D₄×C₂₃	—	4	64	no	—
89	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
90	C₂²×C₄×C₂₃	—	2	4	no	—
91	C₂²×C₄×C₂₃	—	2	8	no	—
92	C₂²×C₄×C₂₃	—	2	8	no	—
93	C₂²×C₄×C₂₃	—	2	4	no	—
94	C₂²×C₄×C₂₃	—	4	8	no	—
95	C₂²×C₄×C₂₃	—	4	8	no	—
96	C₂²×C₄×C₂₃	—	4	4	no	—
97	C₂²×C₄×C₂₃	—	4	2	no	—
98	C₂²×C₄×C₂₃	—	4	8	no	—
99	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₂₃	C₂×D₄	1	8	yes	—
104	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
105	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
106	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
107	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
108	D₈×C₂₃	—	4	16	no	—
109	C₂×C₈×C₂₃	—	2	8	no	—
110	C₂×C₈×C₂₃	—	4	8	no	—
111	C₂×C₈×C₂₃	C₂⁴	1	8	yes	—
112	C₄⋊C₄×C₂₃	—	2	4	no	—
113	C₄⋊C₄×C₂₃	—	2	8	no	—
114	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
115	C₂²⋊C₄×C₂₃	—	2	16	no	—
116	C₂²⋊C₄×C₂₃	—	2	16	no	—
117	C₂×#3186	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂³×C₂₃	—	2	4	no	—
119	C₂³×C₂₃	—	2	2	no	—
120	C₂³×C₂₃	—	2	4	no	—
121	C₂³×C₂₃	—	2	2	no	—
122	C₂³×C₂₃	—	2	8	no	—
123	C₂³×C₂₃	—	4	4	no	—
124	C₂³×C₂₃	—	4	16	no	—
125	C₂³×C₂₃	—	4	4	no	—
126	C₂³×C₂₃	—	4	16	no	—
127	C₂³×C₂₃	—	4	16	no	—
128	C₂³×C₂₃	—	4	8	no	—
129	C₂³×C₂₃	—	4	16	no	—
130	C₂³×C₂₃	—	4	8	no	—
131	C₂³×C₂₃	—	4	8	no	—
132	C₂³×C₂₃	—	8	32	no	—
133	C₂³×C₂₃	C₂×D₈	1	8	yes	—
134	C₂³×C₂₃	C₂×D₈	1	4	yes	—
135	C₂³×C₂₃	C₂×D₈	1	16	yes	complemented
136	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
137	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
138	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
139	D₄×C₂₃	—	2	16	no	—
140	D₄×C₂₃	—	4	16	no	—
141	D₄×C₂₃	—	4	32	no	—
142	D₄×C₂₃	—	4	32	no	—
143	D₄×C₂₃	—	4	8	no	—
144	C₂×C₄×C₂₃	—	2	2	no	—
145	C₂×C₄×C₂₃	—	2	4	no	—
146	C₂×C₄×C₂₃	—	2	4	no	—
147	C₂×C₄×C₂₃	—	2	8	no	—
148	C₂×C₄×C₂₃	—	2	4	no	—
149	C₂×C₄×C₂₃	—	2	8	no	—
150	C₂×C₄×C₂₃	—	2	8	no	—
151	C₂×C₄×C₂₃	—	4	8	no	—
152	C₂×C₄×C₂₃	—	4	4	no	—
153	C₂×C₄×C₂₃	—	4	16	no	—
154	C₂×C₄×C₂₃	—	4	8	no	—
155	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
156	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
157	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
159	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
160	C₈×C₂₃	—	2	8	no	—
161	C₂²×#121	C₂×C₂₃	1	2	yes	complemented
162	#3186	C₂×C₂₃	1	16	yes	direct product factor
163	C₂×#480	C₂×C₂₃	1	4	yes	complemented
164	C₂×#466	C₂×C₂₃	1	4	yes	complemented
165	C₂×#447	C₂×C₂₃	1	4	yes	complemented
166	C₂²×C₂²⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
167	C₂²×C₂₃	—	2	16	no	—
168	C₂²×C₂₃	—	2	8	no	—
169	C₂²×C₂₃	—	2	4	no	—
170	C₂²×C₂₃	—	2	2	no	—
171	C₂²×C₂₃	—	2	4	no	—
172	C₂²×C₂₃	—	2	2	no	—
173	C₂²×C₂₃	—	4	16	no	—
174	C₂²×C₂₃	—	4	8	no	—
175	C₂²×C₂₃	—	4	8	no	—
176	C₂²×C₂₃	—	4	8	no	—
177	C₂²×C₂₃	—	8	32	no	—
178	C₂²×C₂₃	—	8	16	no	—
179	C₂²×C₂₃	#534	1	2	yes	—
180	C₂²×C₂₃	C₂²×D₈	1	8	yes	—
181	C₂²×C₂₃	C₂²×D₈	1	4	yes	—
182	C₂²×C₂₃	C₂²×D₈	1	2	yes	—
183	C₂²×C₂₃	#575	1	2	yes	—
184	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
185	C₄×C₂₃	—	2	2	no	—
186	C₄×C₂₃	—	2	4	no	—
187	C₄×C₂₃	—	4	8	no	—
188	C₄×C₂₃	#534	1	2	yes	—
189	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
190	C₂³×D₄	—	2	2	no	—
191	C₂³×D₄	C₂²×C₂₃	1	2	yes	complemented
192	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
193	C₂²×D₈	C₂²×C₂₃	1	4	yes	complemented
194	C₂³×C₈	C₂²×C₂₃	1	2	yes	complemented
195	C₂×#121	—	2	2	no	—
196	C₂×#121	—	2	8	no	—
197	C₂×#121	—	2	2	no	—
198	C₂×#121	C₂²×C₂₃	1	4	yes	—
199	C₂×#121	C₂²×C₂₃	1	4	yes	complemented
200	C₂×#121	C₂²×C₂₃	1	16	yes	complemented
201	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
202	C₂²×C₂²⋊C₄	—	2	2	no	—
203	#480	C₂²×C₂₃	1	32	yes	complemented
204	#466	C₂²×C₂₃	1	32	yes	complemented
205	#447	C₂²×C₂₃	1	32	yes	complemented
206	C₂×#107	C₂²×C₂₃	1	4	yes	complemented
207	C₂×#102	C₂²×C₂₃	1	8	yes	complemented
208	C₂×C₂²⋊C₈	C₂²×C₂₃	1	4	yes	complemented
209	C₂×C₂²⋊C₈	C₂²×C₂₃	1	8	yes	complemented
210	C₂×C₂₃	—	2	8	no	—
211	C₂×C₂₃	—	2	4	no	—
212	C₂×C₂₃	—	8	8	no	—
213	C₂×C₂₃	#3186	1	4	yes	direct product factor
214	C₂×C₂₃	C₂×#534	1	1	yes	characteristic
215	C₂×C₂₃	C₂³×D₈	1	1	yes	characteristic
216	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
217	C₂⁵	—	2	2	no	—
218	C₂⁵	D₄×C₂₃	1	1	yes	characteristic
219	C₂²×D₄	—	2	4	no	—
220	C₂²×D₄	—	2	4	no	—
221	C₂²×D₄	—	2	16	no	—
222	C₂²×D₄	—	2	2	no	—
223	C₂²×D₄	—	2	4	no	—
224	C₂²×D₄	—	4	8	no	—
225	C₂²×D₄	—	4	16	no	—
226	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
227	C₂²×D₄	C₂³×C₂₃	1	8	yes	complemented
228	C₂³×C₄	—	2	2	no	—
229	C₂³×C₄	—	4	4	no	—
230	C₂³×C₄	D₄×C₂₃	1	2	yes	—
231	C₂³×C₄	D₄×C₂₃	1	4	yes	—
232	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
233	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
234	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
235	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
236	C₂×D₈	—	4	8	no	—
237	C₂×D₈	C₂³×C₂₃	1	16	yes	complemented
238	C₂²×C₈	—	4	4	no	—
239	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
240	C₂²×C₈	C₂³×C₂₃	1	8	yes	complemented
241	#121	—	2	8	no	—
242	#121	—	2	16	no	—
243	#121	—	2	8	no	—
244	#121	—	2	16	no	—
245	#121	C₂³×C₂₃	1	16	yes	—
246	#121	C₂³×C₂₃	1	16	yes	complemented
247	C₂×C₄⋊C₄	—	2	4	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
250	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	complemented
251	C₂×C₂²⋊C₄	—	2	4	no	—
252	C₂×C₂²⋊C₄	—	2	16	no	—
253	C₂×C₂²⋊C₄	—	2	4	no	—
254	#107	C₂³×C₂₃	1	16	yes	complemented
255	#102	C₂³×C₂₃	1	32	yes	complemented
256	C₂²⋊C₈	C₂³×C₂₃	1	16	yes	complemented
257	C₂₃	C₂×#3186	1	1	yes	characteristic, direct product factor, Sylow
258	C₂⁴	—	2	4	no	—
259	C₂⁴	—	2	8	no	—
260	C₂⁴	—	4	2	no	—
261	C₂⁴	—	4	2	no	—
262	C₂⁴	—	4	8	no	—
263	C₂⁴	—	4	8	no	—
264	C₂⁴	—	4	8	no	—
265	C₂⁴	D₈×C₂₃	1	8	yes	complemented
266	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
267	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
268	C₂⁴	C₂×D₄×C₂₃	1	4	yes	—
269	C₂×D₄	—	2	16	no	—
270	C₂×D₄	—	2	16	no	—
271	C₂×D₄	—	2	4	no	—
272	C₂×D₄	—	2	8	no	—
273	C₂×D₄	—	2	16	no	—
274	C₂×D₄	—	4	16	no	—
275	C₂×D₄	—	4	8	no	—
276	C₂×D₄	—	4	16	no	—
277	C₂×D₄	—	4	16	no	—
278	C₂×D₄	—	4	16	no	—
279	C₂×D₄	—	4	64	no	—
280	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	8	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	8	no	—
285	C₂²×C₄	—	4	8	no	—
286	C₂²×C₄	—	4	8	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	4	4	no	—
289	C₂²×C₄	—	4	8	no	—
290	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
292	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
293	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
294	C₂²×C₄	C₂×D₄×C₂₃	1	8	yes	—
295	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
296	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
297	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
298	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
299	D₈	—	4	16	no	—
300	C₂×C₈	—	2	8	no	—
301	C₂×C₈	—	4	8	no	—
302	C₂×C₈	C₂⁴×C₂₃	1	8	yes	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	2	8	no	—
305	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
306	C₂²⋊C₄	—	2	16	no	—
307	C₂²⋊C₄	—	2	16	no	—
308	C₂³	—	2	4	no	—
309	C₂³	—	2	2	no	—
310	C₂³	—	2	4	no	—
311	C₂³	—	2	2	no	—
312	C₂³	—	2	8	no	—
313	C₂³	—	4	4	no	—
314	C₂³	—	4	16	no	—
315	C₂³	—	4	4	no	—
316	C₂³	—	4	16	no	—
317	C₂³	—	4	16	no	—
318	C₂³	—	4	16	no	—
319	C₂³	—	4	8	no	—
320	C₂³	—	4	8	no	—
321	C₂³	—	4	8	no	—
322	C₂³	—	8	32	no	—
323	C₂³	C₂×D₈×C₂₃	1	8	yes	—
324	C₂³	C₂×D₈×C₂₃	1	4	yes	—
325	C₂³	C₂×D₈×C₂₃	1	16	yes	complemented
326	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
327	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
328	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
329	D₄	—	2	16	no	—
330	D₄	—	4	16	no	—
331	D₄	—	4	32	no	—
332	D₄	—	4	32	no	—
333	D₄	—	4	8	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	2	8	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	8	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	8	no	—
343	C₂×C₄	—	4	16	no	—
344	C₂×C₄	—	4	8	no	—
345	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
346	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
347	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
348	C₂×C₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
349	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
350	C₈	—	2	8	no	—
351	C₂²	—	2	16	no	—
352	C₂²	—	2	8	no	—
353	C₂²	—	2	4	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	4	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	4	16	no	—
358	C₂²	—	4	8	no	—
359	C₂²	—	4	8	no	—
360	C₂²	—	4	8	no	—
361	C₂²	—	8	32	no	—
362	C₂²	—	8	16	no	—
363	C₂²	C₂₃×#534	1	2	yes	—
364	C₂²	C₂²×D₈×C₂₃	1	8	yes	—
365	C₂²	C₂²×D₈×C₂₃	1	4	yes	—
366	C₂²	C₂²×D₈×C₂₃	1	2	yes	—
367	C₂²	C₂₃×#575	1	2	yes	—
368	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
369	C₄	—	2	4	no	—
370	C₄	—	2	2	no	—
371	C₄	—	4	8	no	—
372	C₄	C₂₃×#534	1	2	yes	—
373	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
374	C₂	—	2	8	no	—
375	C₂	—	2	4	no	—
376	C₂	—	8	8	no	—
377	C₂	C₂₃×#3186	1	4	yes	direct product factor
378	C₂	C₂×C₂₃×#534	1	1	yes	characteristic
379	C₂	C₂³×D₈×C₂₃	1	1	yes	characteristic
380	C₂	C₂×C₂₃×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂⁴×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂₃×#121	C₂	semidirect
2. C₂₃×#3186	C₂	direct (N × H)
3. C₂×C₂₃×#480	C₂	semidirect
4. C₂×C₂₃×#466	C₂	semidirect
5. C₂×C₂₃×#447	C₂	semidirect
6. C₂²×C₂₃×C₂²⋊C₈	C₂	semidirect
8. C₂³×D₄×C₂₃	C₂²	semidirect
10. C₂²×D₈×C₂₃	C₂²	semidirect
11. C₂³×C₈×C₂₃	C₂²	semidirect
16. C₂×C₂₃×#121	C₂²	semidirect
17. C₂×C₂₃×#121	C₂²	semidirect
18. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
20. C₂₃×#480	C₂²	semidirect
21. C₂₃×#466	C₂²	semidirect
22. C₂₃×#447	C₂²	semidirect
23. C₂×C₂₃×#107	C₂²	semidirect
24. C₂×C₂₃×#102	C₂²	semidirect
25. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
26. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
37. C₂²×D₄×C₂₃	C₂³	semidirect
47. C₂×D₈×C₂₃	C₂³	semidirect
50. C₂²×C₈×C₂₃	C₂³	semidirect
56. C₂₃×#121	C₂³	semidirect
60. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
64. C₂₃×#107	C₂³	semidirect
65. C₂₃×#102	C₂³	semidirect
66. C₂₃×C₂²⋊C₈	C₂³	semidirect
74. C₂⁴×C₂₃	D₈	semidirect
117. C₂×#3186	C₂₃	direct (N × H)
135. C₂³×C₂₃	C₂×D₈	semidirect
161. C₂²×#121	C₂×C₂₃	semidirect
162. #3186	C₂×C₂₃	direct (N × H)
163. C₂×#480	C₂×C₂₃	semidirect
164. C₂×#466	C₂×C₂₃	semidirect
165. C₂×#447	C₂×C₂₃	semidirect
166. C₂²×C₂²⋊C₈	C₂×C₂₃	semidirect
191. C₂³×D₄	C₂²×C₂₃	semidirect
193. C₂²×D₈	C₂²×C₂₃	semidirect
194. C₂³×C₈	C₂²×C₂₃	semidirect
199. C₂×#121	C₂²×C₂₃	semidirect
200. C₂×#121	C₂²×C₂₃	semidirect
201. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
203. #480	C₂²×C₂₃	semidirect
204. #466	C₂²×C₂₃	semidirect
205. #447	C₂²×C₂₃	semidirect
206. C₂×#107	C₂²×C₂₃	semidirect
207. C₂×#102	C₂²×C₂₃	semidirect
208. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
209. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
213. C₂×C₂₃	#3186	direct (N × H)
227. C₂²×D₄	C₂³×C₂₃	semidirect
237. C₂×D₈	C₂³×C₂₃	semidirect
240. C₂²×C₈	C₂³×C₂₃	semidirect
246. #121	C₂³×C₂₃	semidirect
250. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
254. #107	C₂³×C₂₃	semidirect
255. #102	C₂³×C₂₃	semidirect
256. C₂²⋊C₈	C₂³×C₂₃	semidirect
257. C₂₃	C₂×#3186	direct (N × H)
265. C₂⁴	D₈×C₂₃	semidirect
325. C₂³	C₂×D₈×C₂₃	semidirect
377. C₂	C₂₃×#3186	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₂₃×#121	2
C₂₃×#3186	2
C₂×C₂₃×#480	2
C₂×C₂₃×#466	2
C₂×C₂₃×#447	2
C₂²×C₂₃×C₂²⋊C₈	2
C₂×#3186	23

Subgroups — C2×C23×#3186 #19208354

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3186 #19208354