Subgroups — C₂×C₂₃×#3334 #19208851

Order 5888.

2374 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#547	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3334	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₂₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#480	C₂	1	4	yes	maximal, complemented
5	C₂×C₂₃×#474	C₂	1	2	yes	maximal, complemented
6	C₂×C₂₃×#466	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×D₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₈×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₂₃×#107	C₂	1	2	yes	maximal, complemented
10	C₂²×#41×C₂₃	—	2	2	no	—
11	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₂₃	C₂²	1	2	yes	—
13	C₂₃×#547	—	2	8	no	—
14	C₂₃×#547	C₂²	1	16	yes	complemented
15	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₂₃×#123	—	2	4	no	—
17	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
18	C₂×C₂₃×#121	C₂²	1	4	yes	—
19	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
22	C₂₃×#500	C₂²	1	8	yes	complemented
23	C₂₃×#480	C₂²	1	32	yes	complemented
24	C₂₃×#474	C₂²	1	16	yes	complemented
25	C₂₃×#466	C₂²	1	16	yes	complemented
26	C₄×D₈×C₂₃	C₂²	1	8	yes	complemented
27	C₈×D₄×C₂₃	C₂²	1	8	yes	complemented
28	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#107	C₂²	1	2	yes	—
30	C₂×C₂₃×#107	C₂²	1	4	yes	—
31	C₂×C₂₃×#107	C₂²	1	2	yes	—
32	C₂×C₂₃×#107	C₂²	1	16	yes	complemented
33	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#102	C₂²	1	2	yes	—
35	C₂×C₂₃×#102	C₂²	1	4	yes	—
36	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
37	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
38	C₂×#41×C₂₃	—	2	16	no	—
39	C₂×#41×C₂₃	—	4	16	no	—
40	C₂²×Q₈×C₂₃	—	2	2	no	—
41	C₂²×D₄×C₂₃	—	2	4	no	—
42	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
43	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
44	C₂³×C₄×C₂₃	—	2	4	no	—
45	C₂³×C₄×C₂₃	—	2	2	no	—
46	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
47	C₂×D₈×C₂₃	—	2	4	no	—
48	C₂×D₈×C₂₃	C₂³	1	4	yes	—
49	C₂²×C₈×C₂₃	—	2	8	no	—
50	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₂₃	C₂³	1	8	yes	—
52	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
54	C₂₃×C₄⋊Q₈	—	2	4	no	—
55	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	—
56	C₂₃×#123	—	2	32	no	—
57	C₂₃×C₂²⋊Q₈	—	2	16	no	—
58	C₂₃×#121	—	2	8	no	—
59	C₂₃×#121	C₂³	1	16	yes	—
60	C₄×D₄×C₂₃	—	2	4	no	—
61	C₄×D₄×C₂₃	D₄	1	4	yes	—
62	C₄×D₄×C₂₃	C₂³	1	8	yes	—
63	C₄×D₄×C₂₃	C₂³	1	4	yes	—
64	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
65	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
66	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
67	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₂₃	C₂³	1	16	yes	—
69	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
71	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
74	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
75	C₂₃×#107	C₂³	1	4	yes	—
76	C₂₃×#107	C₂³	1	8	yes	—
77	C₂₃×#107	C₂³	1	16	yes	—
78	C₂₃×#107	C₂³	1	8	yes	—
79	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
80	C₂₃×#102	C₂³	1	8	yes	—
81	C₂₃×#102	C₂³	1	16	yes	—
82	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	—
83	C₄×C₈×C₂₃	C₂³	1	4	yes	—
84	C₂⁴×C₂₃	—	2	2	no	—
85	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
86	#41×C₂₃	—	4	64	no	—
87	C₂×Q₈×C₂₃	—	2	8	no	—
88	C₂×Q₈×C₂₃	—	4	8	no	—
89	C₂×D₄×C₂₃	—	2	16	no	—
90	C₂×D₄×C₂₃	—	2	2	no	—
91	C₂×D₄×C₂₃	—	2	4	no	—
92	C₂×D₄×C₂₃	—	2	4	no	—
93	C₂×D₄×C₂₃	—	4	16	no	—
94	C₂×D₄×C₂₃	D₈	1	8	yes	complemented
95	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
96	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
97	C₂²×C₄×C₂₃	—	2	4	no	—
98	C₂²×C₄×C₂₃	—	2	4	no	—
99	C₂²×C₄×C₂₃	—	2	16	no	—
100	C₂²×C₄×C₂₃	—	2	2	no	—
101	C₂²×C₄×C₂₃	—	2	4	no	—
102	C₂²×C₄×C₂₃	—	2	8	no	—
103	C₂²×C₄×C₂₃	—	4	16	no	—
104	C₂²×C₄×C₂₃	—	4	8	no	—
105	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
110	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
111	D₈×C₂₃	—	2	8	no	—
112	C₂×C₈×C₂₃	—	2	4	no	—
113	C₂×C₈×C₂₃	—	2	2	no	—
114	C₂×C₈×C₂₃	—	2	16	no	—
115	C₂×C₈×C₂₃	#41	1	4	yes	complemented
116	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
117	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
118	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
119	C₄⋊C₄×C₂₃	—	2	2	no	—
120	C₄⋊C₄×C₂₃	—	2	4	no	—
121	C₄⋊C₄×C₂₃	—	2	16	no	—
122	C₄⋊C₄×C₂₃	—	2	8	no	—
123	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
124	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
125	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
126	C₂²⋊C₄×C₂₃	—	2	8	no	—
127	C₂²⋊C₄×C₂₃	—	2	16	no	—
128	C₂²⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
129	C₄²×C₂₃	C₂×D₄	1	2	yes	—
130	C₄²×C₂₃	C₂⁴	1	2	yes	—
131	C₂×#3334	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂³×C₂₃	—	2	4	no	—
133	C₂³×C₂₃	—	2	4	no	—
134	C₂³×C₂₃	—	2	4	no	—
135	C₂³×C₂₃	—	4	4	no	—
136	C₂³×C₂₃	—	4	4	no	—
137	C₂³×C₂₃	—	4	4	no	—
138	C₂³×C₂₃	C₂×D₈	1	8	yes	—
139	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
140	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
141	Q₈×C₂₃	—	4	16	no	—
142	D₄×C₂₃	—	2	4	no	—
143	D₄×C₂₃	—	2	4	no	—
144	D₄×C₂₃	—	4	32	no	—
145	D₄×C₂₃	—	4	4	no	—
146	D₄×C₂₃	C₂×D₈	1	16	yes	complemented
147	C₂×C₄×C₂₃	—	2	4	no	—
148	C₂×C₄×C₂₃	—	2	2	no	—
149	C₂×C₄×C₂₃	—	2	8	no	—
150	C₂×C₄×C₂₃	—	2	4	no	—
151	C₂×C₄×C₂₃	—	2	4	no	—
152	C₂×C₄×C₂₃	—	2	4	no	—
153	C₂×C₄×C₂₃	—	2	8	no	—
154	C₂×C₄×C₂₃	—	4	4	no	—
155	C₂×C₄×C₂₃	—	4	8	no	—
156	C₂×C₄×C₂₃	—	4	32	no	—
157	C₂×C₄×C₂₃	—	4	16	no	—
158	C₂×C₄×C₂₃	C₂×D₈	1	4	yes	—
159	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
160	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
161	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
163	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
164	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
165	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
166	C₈×C₂₃	—	2	4	no	—
167	C₈×C₂₃	—	2	2	no	—
168	C₈×C₂₃	C₂×#41	1	4	yes	complemented
169	C₂×#547	C₂×C₂₃	1	2	yes	complemented
170	#3334	C₂×C₂₃	1	16	yes	direct product factor
171	C₂×#500	C₂×C₂₃	1	1	yes	characteristic, complemented
172	C₂×#480	C₂×C₂₃	1	4	yes	complemented
173	C₂×#474	C₂×C₂₃	1	2	yes	complemented
174	C₂×#466	C₂×C₂₃	1	2	yes	complemented
175	C₂×C₄×D₈	C₂×C₂₃	1	1	yes	characteristic, complemented
176	C₂×C₈×D₄	C₂×C₂₃	1	1	yes	characteristic, complemented
177	C₂²×#107	C₂×C₂₃	1	2	yes	complemented
178	C₂²×C₂₃	—	2	16	no	—
179	C₂²×C₂₃	—	2	4	no	—
180	C₂²×C₂₃	—	2	4	no	—
181	C₂²×C₂₃	—	4	4	no	—
182	C₂²×C₂₃	—	4	4	no	—
183	C₂²×C₂₃	—	4	4	no	—
184	C₂²×C₂₃	—	8	8	no	—
185	C₂²×C₂₃	#547	1	2	yes	—
186	C₂²×C₂₃	C₂²×D₈	1	8	yes	—
187	C₂²×C₂₃	C₂²×D₈	1	2	yes	—
188	C₂²×C₂₃	#578	1	2	yes	—
189	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
190	C₄×C₂₃	—	2	4	no	—
191	C₄×C₂₃	—	2	2	no	—
192	C₄×C₂₃	—	4	4	no	—
193	C₄×C₂₃	—	4	8	no	—
194	C₄×C₂₃	#547	1	2	yes	—
195	C₄×C₂₃	C₂²×D₈	1	4	yes	—
196	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
197	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
198	C₂²×#41	—	2	2	no	—
199	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
200	C₂³×C₈	C₂²×C₂₃	1	2	yes	—
201	#547	—	2	8	no	—
202	#547	C₂²×C₂₃	1	16	yes	complemented
203	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
204	C₂×#123	—	2	4	no	—
205	C₂×C₂²⋊Q₈	—	2	2	no	—
206	C₂×#121	C₂²×C₂₃	1	4	yes	—
207	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
208	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
209	C₂²×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
210	#500	C₂²×C₂₃	1	8	yes	complemented
211	#480	C₂²×C₂₃	1	32	yes	complemented
212	#474	C₂²×C₂₃	1	16	yes	complemented
213	#466	C₂²×C₂₃	1	16	yes	complemented
214	C₄×D₈	C₂²×C₂₃	1	8	yes	complemented
215	C₈×D₄	C₂²×C₂₃	1	8	yes	complemented
216	C₂×#107	C₂²×C₂₃	1	2	yes	—
217	C₂×#107	C₂²×C₂₃	1	4	yes	—
218	C₂×#107	C₂²×C₂₃	1	2	yes	—
219	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
220	C₂×#107	C₂²×C₂₃	1	16	yes	complemented
221	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
222	C₂×#102	C₂²×C₂₃	1	2	yes	—
223	C₂×#102	C₂²×C₂₃	1	4	yes	—
224	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
225	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
226	C₂×C₂₃	—	2	8	no	—
227	C₂×C₂₃	—	8	4	no	—
228	C₂×C₂₃	#3334	1	4	yes	direct product factor
229	C₂×C₂₃	C₂×#547	1	1	yes	characteristic
230	C₂×C₂₃	C₂³×D₈	1	1	yes	characteristic
231	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
232	C₂×#41	—	2	16	no	—
233	C₂×#41	—	4	16	no	—
234	C₂²×Q₈	—	2	2	no	—
235	C₂²×D₄	—	2	4	no	—
236	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
237	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
238	C₂³×C₄	—	2	4	no	—
239	C₂³×C₄	—	2	2	no	—
240	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
241	C₂×D₈	—	2	4	no	—
242	C₂×D₈	C₂³×C₂₃	1	4	yes	—
243	C₂²×C₈	—	2	8	no	—
244	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
245	C₂²×C₈	C₂³×C₂₃	1	8	yes	—
246	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
247	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
248	C₄⋊Q₈	—	2	4	no	—
249	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	—
250	#123	—	2	32	no	—
251	C₂²⋊Q₈	—	2	16	no	—
252	#121	—	2	8	no	—
253	#121	C₂³×C₂₃	1	16	yes	—
254	C₄×D₄	—	2	4	no	—
255	C₄×D₄	D₄×C₂₃	1	4	yes	—
256	C₄×D₄	C₂³×C₂₃	1	8	yes	—
257	C₄×D₄	C₂³×C₂₃	1	4	yes	—
258	C₂×C₄⋊C₄	—	2	4	no	—
259	C₂×C₄⋊C₄	—	2	8	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
264	C₂×C₄⋊C₄	C₂³×C₂₃	1	16	yes	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	4	no	—
267	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
268	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
269	#107	C₂³×C₂₃	1	4	yes	—
270	#107	C₂³×C₂₃	1	8	yes	—
271	#107	C₂³×C₂₃	1	16	yes	—
272	#107	C₂³×C₂₃	1	8	yes	—
273	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
274	#102	C₂³×C₂₃	1	8	yes	—
275	#102	C₂³×C₂₃	1	16	yes	—
276	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	—
277	C₄×C₈	C₂³×C₂₃	1	4	yes	—
278	C₂₃	C₂×#3334	1	1	yes	characteristic, direct product factor, Sylow
279	C₂⁴	—	2	2	no	—
280	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
281	#41	—	4	64	no	—
282	C₂×Q₈	—	2	8	no	—
283	C₂×Q₈	—	4	8	no	—
284	C₂×D₄	—	2	16	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	4	no	—
287	C₂×D₄	—	2	4	no	—
288	C₂×D₄	—	4	16	no	—
289	C₂×D₄	D₈×C₂₃	1	8	yes	complemented
290	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
291	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	16	no	—
297	C₂²×C₄	—	2	8	no	—
298	C₂²×C₄	—	4	16	no	—
299	C₂²×C₄	—	4	8	no	—
300	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
303	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
304	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
305	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
306	D₈	—	2	8	no	—
307	C₂×C₈	—	2	4	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	16	no	—
310	C₂×C₈	#41×C₂₃	1	4	yes	complemented
311	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
312	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
313	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	16	no	—
317	C₄⋊C₄	—	2	8	no	—
318	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
319	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
320	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
321	C₂²⋊C₄	—	2	8	no	—
322	C₂²⋊C₄	—	2	16	no	—
323	C₂²⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
324	C₄²	C₂×D₄×C₂₃	1	2	yes	—
325	C₄²	C₂⁴×C₂₃	1	2	yes	—
326	C₂³	—	2	4	no	—
327	C₂³	—	2	4	no	—
328	C₂³	—	2	4	no	—
329	C₂³	—	4	4	no	—
330	C₂³	—	4	4	no	—
331	C₂³	—	4	4	no	—
332	C₂³	C₂×D₈×C₂₃	1	8	yes	—
333	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
334	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
335	Q₈	—	4	16	no	—
336	D₄	—	2	4	no	—
337	D₄	—	2	4	no	—
338	D₄	—	4	32	no	—
339	D₄	—	4	4	no	—
340	D₄	C₂×D₈×C₂₃	1	16	yes	complemented
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	8	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	8	no	—
350	C₂×C₄	—	4	32	no	—
351	C₂×C₄	—	4	16	no	—
352	C₂×C₄	C₂×D₈×C₂₃	1	4	yes	—
353	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
354	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
355	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
356	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
357	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
358	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
359	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
360	C₈	—	2	4	no	—
361	C₈	—	2	2	no	—
362	C₈	C₂×#41×C₂₃	1	4	yes	complemented
363	C₂²	—	2	4	no	—
364	C₂²	—	2	4	no	—
365	C₂²	—	2	16	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	4	4	no	—
369	C₂²	—	8	8	no	—
370	C₂²	C₂₃×#547	1	2	yes	—
371	C₂²	C₂²×D₈×C₂₃	1	8	yes	—
372	C₂²	C₂²×D₈×C₂₃	1	2	yes	—
373	C₂²	C₂₃×#578	1	2	yes	—
374	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
375	C₄	—	2	4	no	—
376	C₄	—	2	2	no	—
377	C₄	—	4	4	no	—
378	C₄	—	4	8	no	—
379	C₄	C₂₃×#547	1	2	yes	—
380	C₄	C₂²×D₈×C₂₃	1	4	yes	—
381	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
382	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
383	C₂	—	2	8	no	—
384	C₂	—	8	4	no	—
385	C₂	C₂₃×#3334	1	4	yes	direct product factor
386	C₂	C₂×C₂₃×#547	1	1	yes	characteristic
387	C₂	C₂³×D₈×C₂₃	1	1	yes	characteristic
388	C₂	C₂×C₂₃×#578	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 ◁ C₂×C₄×D₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#547	C₂	semidirect
2. C₂₃×#3334	C₂	direct (N × H)
3. C₂×C₂₃×#500	C₂	semidirect
4. C₂×C₂₃×#480	C₂	semidirect
5. C₂×C₂₃×#474	C₂	semidirect
6. C₂×C₂₃×#466	C₂	semidirect
7. C₂×C₄×D₈×C₂₃	C₂	semidirect
8. C₂×C₈×D₄×C₂₃	C₂	semidirect
9. C₂²×C₂₃×#107	C₂	semidirect
14. C₂₃×#547	C₂²	semidirect
22. C₂₃×#500	C₂²	semidirect
23. C₂₃×#480	C₂²	semidirect
24. C₂₃×#474	C₂²	semidirect
25. C₂₃×#466	C₂²	semidirect
26. C₄×D₈×C₂₃	C₂²	semidirect
27. C₈×D₄×C₂₃	C₂²	semidirect
32. C₂×C₂₃×#107	C₂²	semidirect
94. C₂×D₄×C₂₃	D₈	semidirect
115. C₂×C₈×C₂₃	#41	semidirect
131. C₂×#3334	C₂₃	direct (N × H)
146. D₄×C₂₃	C₂×D₈	semidirect
168. C₈×C₂₃	C₂×#41	semidirect
169. C₂×#547	C₂×C₂₃	semidirect
170. #3334	C₂×C₂₃	direct (N × H)
171. C₂×#500	C₂×C₂₃	semidirect
172. C₂×#480	C₂×C₂₃	semidirect
173. C₂×#474	C₂×C₂₃	semidirect
174. C₂×#466	C₂×C₂₃	semidirect
175. C₂×C₄×D₈	C₂×C₂₃	semidirect
176. C₂×C₈×D₄	C₂×C₂₃	semidirect
177. C₂²×#107	C₂×C₂₃	semidirect
202. #547	C₂²×C₂₃	semidirect
210. #500	C₂²×C₂₃	semidirect
211. #480	C₂²×C₂₃	semidirect
212. #474	C₂²×C₂₃	semidirect
213. #466	C₂²×C₂₃	semidirect
214. C₄×D₈	C₂²×C₂₃	semidirect
215. C₈×D₄	C₂²×C₂₃	semidirect
220. C₂×#107	C₂²×C₂₃	semidirect
228. C₂×C₂₃	#3334	direct (N × H)
278. C₂₃	C₂×#3334	direct (N × H)
289. C₂×D₄	D₈×C₂₃	semidirect
310. C₂×C₈	#41×C₂₃	semidirect
340. D₄	C₂×D₈×C₂₃	semidirect
362. C₈	C₂×#41×C₂₃	semidirect
385. C₂	C₂₃×#3334	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#547	2
C₂₃×#3334	2
C₂×C₂₃×#500	2
C₂×C₂₃×#480	2
C₂×C₂₃×#474	2
C₂×C₂₃×#466	2
C₂×C₄×D₈×C₂₃	2
C₂×C₈×D₄×C₂₃	2
C₂²×C₂₃×#107	2
C₂×#3334	23

Subgroups — C2×C23×#3334 #19208851

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3334 #19208851