Subgroups — C₂×C₂₃×#2821 #19184312

Order 5888.

2370 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂₃×#126	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2821	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#400	C₂	1	2	yes	maximal, complemented
5	C₂×C₂₃×#399	C₂	1	2	yes	maximal
6	C₂×C₂₃×#398	C₂	1	2	yes	maximal, complemented
7	C₂×C₂₃×#397	C₂	1	2	yes	maximal
8	C₂×C₂₃×#395	C₂	1	2	yes	maximal, complemented
9	C₂×C₂₃×#393	C₂	1	2	yes	maximal
10	C₂×C₂₃×#383	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×Q₈×C₂₃	C₂²	1	2	yes	—
12	C₂×C₂₃×C₄⋊Q₈	—	2	8	no	—
13	C₂×C₂₃×C₄⋊Q₈	C₂²	1	8	yes	complemented
14	C₂×C₂₃×#126	—	2	8	no	—
15	C₂×C₂₃×#126	C₂²	1	8	yes	—
16	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
20	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
22	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
26	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
27	C₂₃×#400	C₂²	1	16	yes	complemented
28	C₂₃×#399	C₂²	1	16	yes	—
29	C₂₃×#398	C₂²	1	16	yes	complemented
30	C₂₃×#397	C₂²	1	16	yes	—
31	C₂₃×#395	C₂²	1	16	yes	complemented
32	C₂₃×#393	C₂²	1	16	yes	—
33	C₂₃×#383	C₂²	1	8	yes	complemented
34	C₂×C₂₃×#95	C₂²	1	2	yes	—
35	C₂×C₂₃×#95	C₂²	1	2	yes	—
36	C₂×C₂₃×#95	C₂²	1	2	yes	—
37	C₂×C₂₃×#95	C₂²	1	4	yes	—
38	C₂×C₂₃×#95	C₂²	1	4	yes	—
39	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
40	C₂²×Q₈×C₂₃	—	2	8	no	—
41	C₂²×Q₈×C₂₃	—	4	8	no	—
42	C₂²×Q₈×C₂₃	C₂³	1	8	yes	—
43	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
44	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
45	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
51	C₂₃×C₄⋊Q₈	—	2	32	no	—
52	C₂₃×#126	—	2	32	no	—
53	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
54	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
55	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
56	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
57	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
58	C₂×C₄⋊C₄×C₂₃	—	4	8	no	—
59	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
60	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
61	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
62	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
63	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
64	C₂×C₄⋊C₄×C₂₃	C₂³	1	16	yes	—
65	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
66	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
67	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
68	C₂×C₂²⋊C₄×C₂₃	—	4	8	no	—
69	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
70	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
71	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
72	C₂×C₂²⋊C₄×C₂₃	C₂³	1	16	yes	—
73	C₂×C₄²×C₂₃	D₄	1	8	yes	—
74	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
75	C₂₃×#95	C₂³	1	8	yes	—
76	C₂₃×#95	C₂³	1	8	yes	—
77	C₂₃×#95	C₂³	1	8	yes	—
78	C₂₃×#95	C₂³	1	16	yes	—
79	C₂₃×#95	C₂³	1	16	yes	—
80	C₂⁴×C₂₃	—	2	2	no	—
81	C₂⁴×C₂₃	—	2	4	no	—
82	C₂⁴×C₂₃	—	2	4	no	—
83	C₂⁴×C₂₃	—	2	4	no	—
84	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
85	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
86	C₂×Q₈×C₂₃	—	2	16	no	—
87	C₂×Q₈×C₂₃	—	4	16	no	—
88	C₂×Q₈×C₂₃	—	4	32	no	—
89	C₂²×C₄×C₂₃	—	2	4	no	—
90	C₂²×C₄×C₂₃	—	2	4	no	—
91	C₂²×C₄×C₂₃	—	2	4	no	—
92	C₂²×C₄×C₂₃	—	2	2	no	—
93	C₂²×C₄×C₂₃	—	2	2	no	—
94	C₂²×C₄×C₂₃	—	2	2	no	—
95	C₂²×C₄×C₂₃	—	2	8	no	—
96	C₂²×C₄×C₂₃	—	2	8	no	—
97	C₂²×C₄×C₂₃	—	2	8	no	—
98	C₂²×C₄×C₂₃	—	2	4	no	—
99	C₂²×C₄×C₂₃	—	2	8	no	—
100	C₂²×C₄×C₂₃	—	2	4	no	—
101	C₂²×C₄×C₂₃	—	2	4	no	—
102	C₂²×C₄×C₂₃	—	2	8	no	—
103	C₂²×C₄×C₂₃	—	2	8	no	—
104	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
105	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
108	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
109	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
110	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
111	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
112	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
113	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
114	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
115	C₄⋊C₄×C₂₃	—	2	8	no	—
116	C₄⋊C₄×C₂₃	—	2	8	no	—
117	C₄⋊C₄×C₂₃	—	2	8	no	—
118	C₄⋊C₄×C₂₃	—	2	16	no	—
119	C₄⋊C₄×C₂₃	—	2	16	no	—
120	C₄⋊C₄×C₂₃	—	4	16	no	—
121	C₂²⋊C₄×C₂₃	—	2	8	no	—
122	C₂²⋊C₄×C₂₃	—	2	8	no	—
123	C₂²⋊C₄×C₂₃	—	2	8	no	—
124	C₂²⋊C₄×C₂₃	—	4	16	no	—
125	C₄²×C₂₃	C₂×D₄	1	16	yes	—
126	C₂×#2821	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂³×C₂₃	—	2	2	no	—
128	C₂³×C₂₃	—	2	4	no	—
129	C₂³×C₂₃	—	2	4	no	—
130	C₂³×C₂₃	—	2	4	no	—
131	C₂³×C₂₃	—	4	4	no	—
132	C₂³×C₂₃	—	4	4	no	—
133	C₂³×C₂₃	—	4	4	no	—
134	C₂³×C₂₃	—	4	16	no	—
135	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
136	C₂³×C₂₃	H(5,𝔽₂)	1	4	yes	—
137	C₂³×C₂₃	2₋¹⁺⁴	1	4	yes	—
138	C₂³×C₂₃	2₋¹⁺⁴	1	4	yes	—
139	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
140	Q₈×C₂₃	—	4	32	no	—
141	C₂×C₄×C₂₃	—	2	8	no	—
142	C₂×C₄×C₂₃	—	2	8	no	—
143	C₂×C₄×C₂₃	—	2	8	no	—
144	C₂×C₄×C₂₃	—	2	4	no	—
145	C₂×C₄×C₂₃	—	2	4	no	—
146	C₂×C₄×C₂₃	—	2	4	no	—
147	C₂×C₄×C₂₃	—	2	2	no	—
148	C₂×C₄×C₂₃	—	2	2	no	—
149	C₂×C₄×C₂₃	—	2	2	no	—
150	C₂×C₄×C₂₃	—	2	8	no	—
151	C₂×C₄×C₂₃	—	2	8	no	—
152	C₂×C₄×C₂₃	—	2	8	no	—
153	C₂×C₄×C₂₃	—	2	4	no	—
154	C₂×C₄×C₂₃	—	2	8	no	—
155	C₂×C₄×C₂₃	—	2	4	no	—
156	C₂×C₄×C₂₃	—	2	4	no	—
157	C₂×C₄×C₂₃	—	2	8	no	—
158	C₂×C₄×C₂₃	—	2	8	no	—
159	C₂×C₄×C₂₃	—	4	4	no	—
160	C₂×C₄×C₂₃	—	4	16	no	—
161	C₂×C₄×C₂₃	—	4	4	no	—
162	C₂×C₄×C₂₃	—	4	4	no	—
163	C₂×C₄×C₂₃	—	4	16	no	—
164	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
165	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
166	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
167	C₂²×C₄⋊Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
168	C₂²×#126	C₂×C₂₃	1	1	yes	characteristic
169	#2821	C₂×C₂₃	1	16	yes	direct product factor
170	C₂×#400	C₂×C₂₃	1	2	yes	complemented
171	C₂×#399	C₂×C₂₃	1	2	yes	—
172	C₂×#398	C₂×C₂₃	1	2	yes	complemented
173	C₂×#397	C₂×C₂₃	1	2	yes	—
174	C₂×#395	C₂×C₂₃	1	2	yes	complemented
175	C₂×#393	C₂×C₂₃	1	2	yes	—
176	C₂×#383	C₂×C₂₃	1	1	yes	characteristic, complemented
177	C₂²×C₂₃	—	4	2	no	—
178	C₂²×C₂₃	—	4	2	no	—
179	C₂²×C₂₃	—	4	2	no	—
180	C₂²×C₂₃	—	4	8	no	—
181	C₂²×C₂₃	—	8	8	no	—
182	C₂²×C₂₃	#535	1	4	yes	—
183	C₂²×C₂₃	#536	1	4	yes	—
184	C₂²×C₂₃	#536	1	4	yes	—
185	C₂²×C₂₃	#563	1	16	yes	—
186	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
187	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
188	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
189	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
190	C₄×C₂₃	—	2	4	no	—
191	C₄×C₂₃	—	2	4	no	—
192	C₄×C₂₃	—	2	4	no	—
193	C₄×C₂₃	—	4	2	no	—
194	C₄×C₂₃	—	4	8	no	—
195	C₄×C₂₃	—	4	2	no	—
196	C₄×C₂₃	—	4	2	no	—
197	C₄×C₂₃	—	4	8	no	—
198	C₂³×Q₈	C₂²×C₂₃	1	2	yes	—
199	C₂×C₄⋊Q₈	—	2	8	no	—
200	C₂×C₄⋊Q₈	C₂²×C₂₃	1	8	yes	complemented
201	C₂×#126	—	2	8	no	—
202	C₂×#126	C₂²×C₂₃	1	8	yes	—
203	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
204	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
205	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
206	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
207	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
208	C₂²×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
209	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
210	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
211	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
212	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
213	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
214	#400	C₂²×C₂₃	1	16	yes	complemented
215	#399	C₂²×C₂₃	1	16	yes	—
216	#398	C₂²×C₂₃	1	16	yes	complemented
217	#397	C₂²×C₂₃	1	16	yes	—
218	#395	C₂²×C₂₃	1	16	yes	complemented
219	#393	C₂²×C₂₃	1	16	yes	—
220	#383	C₂²×C₂₃	1	8	yes	complemented
221	C₂×#95	C₂²×C₂₃	1	2	yes	—
222	C₂×#95	C₂²×C₂₃	1	4	yes	—
223	C₂×#95	C₂²×C₂₃	1	4	yes	—
224	C₂×#95	C₂²×C₂₃	1	2	yes	—
225	C₂×#95	C₂²×C₂₃	1	2	yes	—
226	C₂×C₂₃	—	8	2	no	—
227	C₂×C₂₃	#2821	1	8	yes	direct product factor
228	C₂×C₂₃	C₂×#535	1	1	yes	characteristic
229	C₂×C₂₃	C₂×#536	1	1	yes	characteristic
230	C₂×C₂₃	C₂×#536	1	1	yes	characteristic
231	C₂×C₂₃	C₂×#563	1	4	yes	—
232	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
233	C₂²×Q₈	—	2	8	no	—
234	C₂²×Q₈	—	4	8	no	—
235	C₂²×Q₈	C₂³×C₂₃	1	8	yes	—
236	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
237	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
238	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
239	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
240	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
241	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
242	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
243	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
244	C₄⋊Q₈	—	2	32	no	—
245	#126	—	2	32	no	—
246	C₂×C₄⋊C₄	—	2	4	no	—
247	C₂×C₄⋊C₄	—	2	4	no	—
248	C₂×C₄⋊C₄	—	2	4	no	—
249	C₂×C₄⋊C₄	—	2	8	no	—
250	C₂×C₄⋊C₄	—	2	8	no	—
251	C₂×C₄⋊C₄	—	4	8	no	—
252	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
253	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
254	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
255	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
256	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
257	C₂×C₄⋊C₄	C₂³×C₂₃	1	16	yes	—
258	C₂×C₂²⋊C₄	—	2	4	no	—
259	C₂×C₂²⋊C₄	—	2	4	no	—
260	C₂×C₂²⋊C₄	—	2	4	no	—
261	C₂×C₂²⋊C₄	—	4	8	no	—
262	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
263	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
264	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
265	C₂×C₂²⋊C₄	C₂³×C₂₃	1	16	yes	—
266	C₂×C₄²	D₄×C₂₃	1	8	yes	—
267	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
268	#95	C₂³×C₂₃	1	8	yes	—
269	#95	C₂³×C₂₃	1	8	yes	—
270	#95	C₂³×C₂₃	1	8	yes	—
271	#95	C₂³×C₂₃	1	16	yes	—
272	#95	C₂³×C₂₃	1	16	yes	—
273	C₂₃	C₂×#2821	1	1	yes	characteristic, direct product factor, Sylow
274	C₂⁴	—	2	2	no	—
275	C₂⁴	—	2	4	no	—
276	C₂⁴	—	2	4	no	—
277	C₂⁴	—	2	4	no	—
278	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
279	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
280	C₂×Q₈	—	2	16	no	—
281	C₂×Q₈	—	4	16	no	—
282	C₂×Q₈	—	4	32	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	8	no	—
290	C₂²×C₄	—	2	8	no	—
291	C₂²×C₄	—	2	8	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	8	no	—
294	C₂²×C₄	—	2	8	no	—
295	C₂²×C₄	—	2	8	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
299	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
300	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
301	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
302	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
303	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
304	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
305	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
306	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
307	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
308	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
309	C₄⋊C₄	—	2	8	no	—
310	C₄⋊C₄	—	2	8	no	—
311	C₄⋊C₄	—	2	8	no	—
312	C₄⋊C₄	—	2	16	no	—
313	C₄⋊C₄	—	2	16	no	—
314	C₄⋊C₄	—	4	16	no	—
315	C₂²⋊C₄	—	2	8	no	—
316	C₂²⋊C₄	—	2	8	no	—
317	C₂²⋊C₄	—	2	8	no	—
318	C₂²⋊C₄	—	4	16	no	—
319	C₄²	C₂×D₄×C₂₃	1	16	yes	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	4	no	—
322	C₂³	—	2	4	no	—
323	C₂³	—	2	4	no	—
324	C₂³	—	4	16	no	—
325	C₂³	—	4	4	no	—
326	C₂³	—	4	4	no	—
327	C₂³	—	4	4	no	—
328	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
329	C₂³	C₂₃×H(5,𝔽₂)	1	4	yes	—
330	C₂³	C₂₃×2₋¹⁺⁴	1	4	yes	—
331	C₂³	C₂₃×2₋¹⁺⁴	1	4	yes	—
332	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
333	Q₈	—	4	32	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	2	8	no	—
339	C₂×C₄	—	2	8	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	—	2	8	no	—
345	C₂×C₄	—	2	8	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	8	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	8	no	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	4	16	no	—
353	C₂×C₄	—	4	16	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
358	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
359	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
360	C₂²	—	4	2	no	—
361	C₂²	—	4	2	no	—
362	C₂²	—	4	2	no	—
363	C₂²	—	4	8	no	—
364	C₂²	—	8	8	no	—
365	C₂²	C₂₃×#535	1	4	yes	—
366	C₂²	C₂₃×#536	1	4	yes	—
367	C₂²	C₂₃×#536	1	4	yes	—
368	C₂²	C₂₃×#563	1	16	yes	—
369	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
370	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
371	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
372	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
373	C₄	—	2	4	no	—
374	C₄	—	2	4	no	—
375	C₄	—	2	4	no	—
376	C₄	—	4	8	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	2	no	—
379	C₄	—	4	2	no	—
380	C₄	—	4	8	no	—
381	C₂	—	8	2	no	—
382	C₂	C₂₃×#2821	1	8	yes	direct product factor
383	C₂	C₂×C₂₃×#535	1	1	yes	characteristic
384	C₂	C₂×C₂₃×#536	1	1	yes	characteristic
385	C₂	C₂×C₂₃×#536	1	1	yes	characteristic
386	C₂	C₂×C₂₃×#563	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂₃×C₄⋊Q₈	C₂	semidirect
3. C₂₃×#2821	C₂	direct (N × H)
4. C₂×C₂₃×#400	C₂	semidirect
6. C₂×C₂₃×#398	C₂	semidirect
8. C₂×C₂₃×#395	C₂	semidirect
10. C₂×C₂₃×#383	C₂	semidirect
13. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
27. C₂₃×#400	C₂²	semidirect
29. C₂₃×#398	C₂²	semidirect
31. C₂₃×#395	C₂²	semidirect
33. C₂₃×#383	C₂²	semidirect
126. C₂×#2821	C₂₃	direct (N × H)
167. C₂²×C₄⋊Q₈	C₂×C₂₃	semidirect
169. #2821	C₂×C₂₃	direct (N × H)
170. C₂×#400	C₂×C₂₃	semidirect
172. C₂×#398	C₂×C₂₃	semidirect
174. C₂×#395	C₂×C₂₃	semidirect
176. C₂×#383	C₂×C₂₃	semidirect
200. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
214. #400	C₂²×C₂₃	semidirect
216. #398	C₂²×C₂₃	semidirect
218. #395	C₂²×C₂₃	semidirect
220. #383	C₂²×C₂₃	semidirect
227. C₂×C₂₃	#2821	direct (N × H)
273. C₂₃	C₂×#2821	direct (N × H)
382. C₂	C₂₃×#2821	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×C₄⋊Q₈	2
C₂²×C₂₃×#126	2
C₂₃×#2821	2
C₂×C₂₃×#400	2
C₂×C₂₃×#399	2
C₂×C₂₃×#398	2
C₂×C₂₃×#397	2
C₂×C₂₃×#395	2
C₂×C₂₃×#393	2
C₂×C₂₃×#383	2
C₂×#2821	23

Subgroups — C2×C23×#2821 #19184312

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#2821 #19184312