Subgroups — D₈×#41×C₂₃ #19209051

Order 5888.

2406 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#41×C₂₃	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3391	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×D₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3358	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3334	C₂	1	3	yes	maximal, complemented
6	C₂₃×#3294	C₂	1	6	yes	maximal, complemented
7	D₄×D₈×C₂₃	C₂	1	3	yes	maximal, complemented
8	C₂₃×#3169	C₂	1	3	yes	maximal, complemented
9	C₂₃×#3100	C₂	1	6	yes	maximal, complemented
10	C₈×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×D₈×C₂₃	C₂	1	3	yes	maximal, complemented
12	C₂²×#41×C₂₃	—	2	2	no	—
13	C₂²×D₈×C₂₃	C₂²	1	3	yes	—
14	C₂₃×#550	C₂²	1	2	yes	complemented
15	D₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
16	C₂₃×#548	—	2	2	no	—
17	C₂₃×#547	C₂²	1	6	yes	complemented
18	C₂₃×#546	—	2	6	no	—
19	D₄²×C₂₃	C₂²	1	6	yes	complemented
20	C₂₃×#532	C₂²	1	6	yes	complemented
21	C₂₃×#525	—	2	6	no	—
22	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₂₃	C₂²	1	6	yes	complemented
24	C₂₃×#500	C₂²	1	3	yes	complemented
25	C₂₃×#493	C₂²	1	3	yes	complemented
26	C₂₃×#486	C₂²	1	6	yes	complemented
27	C₂₃×#480	C₂²	1	12	yes	complemented
28	C₂₃×#474	C₂²	1	6	yes	complemented
29	C₂₃×#474	C₂²	1	6	yes	complemented
30	C₂₃×#466	C₂²	1	6	yes	complemented
31	C₂₃×#466	C₂²	1	6	yes	complemented
32	C₂₃×#459	C₂²	1	6	yes	complemented
33	C₂₃×#459	C₂²	1	6	yes	complemented
34	C₂₃×#447	C₂²	1	12	yes	complemented
35	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
36	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
37	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
38	C₄×D₈×C₂₃	C₂²	1	3	yes	—
39	C₄×D₈×C₂₃	C₂²	1	3	yes	complemented
40	C₄×D₈×C₂₃	C₂²	1	6	yes	complemented
41	C₄×D₈×C₂₃	C₂²	1	6	yes	complemented
42	C₄×D₈×C₂₃	C₂²	1	3	yes	complemented
43	C₄×D₈×C₂₃	C₂²	1	6	yes	complemented
44	C₈×D₄×C₂₃	C₂²	1	3	yes	complemented
45	C₈×D₄×C₂₃	C₂²	1	3	yes	complemented
46	C₂₃×#431	C₂²	1	3	yes	complemented
47	C₂×C₂₃×#107	C₂²	1	3	yes	complemented
48	C₂×C₂₃×#102	C₂²	1	6	yes	complemented
49	C₂×C₄×C₈×C₂₃	C₂²	1	3	yes	complemented
50	C₂×#41×C₂₃	—	2	2	no	—
51	C₂×#41×C₂₃	—	2	6	no	—
52	C₂×#41×C₂₃	—	2	6	no	—
53	C₂×#41×C₂₃	—	4	16	no	—
54	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
55	C₂²×Q₈×C₂₃	—	2	2	no	—
56	C₂²×D₄×C₂₃	—	2	6	no	—
57	C₂²×D₄×C₂₃	C₂³	1	6	yes	—
58	C₂³×C₄×C₂₃	—	2	6	no	—
59	C₂×D₈×C₂₃	—	2	12	no	—
60	C₂×D₈×C₂₃	C₂³	1	6	yes	—
61	C₂×D₈×C₂₃	C₂³	1	3	yes	—
62	C₂×D₈×C₂₃	C₂³	1	6	yes	—
63	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₂₃	C₂³	1	3	yes	—
65	C₂²×C₈×C₂₃	C₂³	1	3	yes	—
66	C₂₃×C₄⋊Q₈	C₂³	1	6	yes	—
67	C₂₃×#127	C₂³	1	6	yes	—
68	C₂₃×#124	—	2	6	no	—
69	C₂₃×#123	—	2	12	no	—
70	C₂₃×C₂²⋊Q₈	—	2	6	no	—
71	C₂₃×C₂²⋊Q₈	—	2	6	no	—
72	C₂₃×#121	—	2	6	no	—
73	C₂₃×#121	—	2	6	no	—
74	C₂₃×#121	—	2	6	no	—
75	C₂₃×#121	C₂³	1	12	yes	—
76	C₂₃×#120	—	2	12	no	—
77	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
78	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
79	C₄×D₄×C₂₃	—	2	6	no	—
80	C₄×D₄×C₂₃	—	2	6	no	—
81	C₄×D₄×C₂₃	—	2	6	no	—
82	C₄×D₄×C₂₃	D₄	1	3	yes	—
83	C₄×D₄×C₂₃	C₂³	1	6	yes	—
84	C₄×D₄×C₂₃	C₂³	1	6	yes	—
85	C₄×D₄×C₂₃	C₂³	1	2	yes	—
86	C₄×D₄×C₂₃	C₂³	1	6	yes	—
87	C₄×D₄×C₂₃	C₂³	1	3	yes	—
88	C₂₃×#117	D₄	1	3	yes	—
89	C₂×C₄⋊C₄×C₂₃	C₂³	1	6	yes	—
90	C₂×C₂²⋊C₄×C₂₃	—	2	6	no	—
91	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
92	C₂₃×#107	C₂³	1	1	yes	characteristic
93	C₂₃×#107	C₂³	1	3	yes	—
94	C₂₃×#107	C₂³	1	6	yes	—
95	C₂₃×#107	C₂³	1	6	yes	—
96	C₂₃×C₄⋊C₈	C₂³	1	3	yes	—
97	C₂₃×C₄⋊C₈	C₂³	1	3	yes	—
98	C₂₃×#102	C₂³	1	2	yes	—
99	C₂₃×#102	C₂³	1	6	yes	—
100	C₂₃×#102	C₂³	1	6	yes	—
101	C₂₃×#102	C₂³	1	6	yes	—
102	C₂₃×#102	C₂³	1	12	yes	—
103	C₂₃×C₂²⋊C₈	C₂³	1	6	yes	—
104	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
105	C₄×C₈×C₂₃	C₂³	1	3	yes	—
106	C₄×C₈×C₂₃	C₂³	1	3	yes	—
107	C₄×C₈×C₂₃	C₂³	1	3	yes	—
108	C₂⁴×C₂₃	—	2	6	no	—
109	#41×C₂₃	—	4	8	no	—
110	#41×C₂₃	—	4	24	no	—
111	#41×C₂₃	—	4	24	no	—
112	#41×C₂₃	D₈	1	8	yes	direct product factor
113	C₂×Q₈×C₂₃	—	2	6	no	—
114	C₂×Q₈×C₂₃	—	4	8	no	—
115	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
116	C₂×D₄×C₂₃	—	2	12	no	—
117	C₂×D₄×C₂₃	—	2	12	no	—
118	C₂×D₄×C₂₃	—	2	6	no	—
119	C₂×D₄×C₂₃	—	2	6	no	—
120	C₂×D₄×C₂₃	—	2	6	no	—
121	C₂×D₄×C₂₃	—	4	6	no	—
122	C₂×D₄×C₂₃	—	4	24	no	—
123	C₂×D₄×C₂₃	C₂×D₄	1	3	yes	—
124	C₂×D₄×C₂₃	C₂⁴	1	6	yes	—
125	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
126	C₂²×C₄×C₂₃	—	2	6	no	—
127	C₂²×C₄×C₂₃	—	2	6	no	—
128	C₂²×C₄×C₂₃	—	2	6	no	—
129	C₂²×C₄×C₂₃	—	2	2	no	—
130	C₂²×C₄×C₂₃	—	2	6	no	—
131	C₂²×C₄×C₂₃	—	4	24	no	—
132	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
133	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
134	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
135	D₈×C₂₃	—	2	12	no	—
136	D₈×C₂₃	—	2	6	no	—
137	D₈×C₂₃	—	4	6	no	—
138	D₈×C₂₃	#41	1	4	yes	direct product factor
139	C₂×C₈×C₂₃	—	2	6	no	—
140	C₂×C₈×C₂₃	—	4	3	no	—
141	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
142	C₂×C₈×C₂₃	C₂⁴	1	3	yes	—
143	C₂×C₈×C₂₃	C₂⁴	1	3	yes	—
144	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
145	C₄⋊C₄×C₂₃	—	2	6	no	—
146	C₄⋊C₄×C₂₃	—	2	6	no	—
147	C₄⋊C₄×C₂₃	C₂×D₄	1	3	yes	—
148	C₄⋊C₄×C₂₃	C₂×D₄	1	3	yes	—
149	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
150	C₄⋊C₄×C₂₃	C₂⁴	1	6	yes	—
151	C₂²⋊C₄×C₂₃	—	2	2	no	—
152	C₂²⋊C₄×C₂₃	—	2	6	no	—
153	C₂²⋊C₄×C₂₃	—	2	6	no	—
154	C₂²⋊C₄×C₂₃	—	2	6	no	—
155	C₂²⋊C₄×C₂₃	—	2	12	no	—
156	C₂²⋊C₄×C₂₃	C₂×D₄	1	6	yes	—
157	C₄²×C₂₃	C₂×D₄	1	3	yes	—
158	C₄²×C₂₃	C₂×D₄	1	3	yes	—
159	C₄²×C₂₃	C₂⁴	1	3	yes	—
160	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
161	D₈×#41	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂³×C₂₃	—	2	2	no	—
163	C₂³×C₂₃	—	2	6	no	—
164	C₂³×C₂₃	—	4	12	no	—
165	C₂³×C₂₃	—	4	12	no	—
166	C₂³×C₂₃	—	8	6	no	—
167	C₂³×C₂₃	C₂²×D₄	1	3	yes	—
168	Q₈×C₂₃	—	4	12	no	—
169	Q₈×C₂₃	C₂×D₈	1	4	yes	complemented
170	D₄×C₂₃	—	2	6	no	—
171	D₄×C₂₃	—	2	2	no	—
172	D₄×C₂₃	—	2	6	no	—
173	D₄×C₂₃	—	4	12	no	—
174	D₄×C₂₃	—	4	24	no	—
175	D₄×C₂₃	—	4	12	no	—
176	D₄×C₂₃	—	8	6	no	—
177	D₄×C₂₃	C₂×D₈	1	12	yes	complemented
178	D₄×C₂₃	C₂×#41	1	4	yes	complemented
179	C₂×C₄×C₂₃	—	2	3	no	—
180	C₂×C₄×C₂₃	—	2	3	no	—
181	C₂×C₄×C₂₃	—	2	2	no	—
182	C₂×C₄×C₂₃	—	2	6	no	—
183	C₂×C₄×C₂₃	—	4	3	no	—
184	C₂×C₄×C₂₃	—	4	12	no	—
185	C₂×C₄×C₂₃	—	4	4	no	—
186	C₂×C₄×C₂₃	—	4	12	no	—
187	C₂×C₄×C₂₃	—	4	12	no	—
188	C₂×C₄×C₂₃	—	4	12	no	—
189	C₂×C₄×C₂₃	C₂×D₈	1	12	yes	complemented
190	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
192	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
193	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
194	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
196	C₈×C₂₃	—	2	3	no	—
197	C₈×C₂₃	—	2	1	no	—
198	C₈×C₂₃	—	2	3	no	—
199	C₈×C₂₃	C₂×#41	1	2	yes	complemented
200	D₄×#41	C₂×C₂₃	1	2	yes	complemented
201	#3391	C₂×C₂₃	1	1	yes	characteristic, complemented
202	Q₈×D₈	C₂×C₂₃	1	1	yes	characteristic, complemented
203	#3358	C₂×C₂₃	1	2	yes	complemented
204	#3334	C₂×C₂₃	1	3	yes	complemented
205	#3294	C₂×C₂₃	1	6	yes	complemented
206	D₄×D₈	C₂×C₂₃	1	3	yes	complemented
207	#3169	C₂×C₂₃	1	3	yes	complemented
208	#3100	C₂×C₂₃	1	6	yes	complemented
209	C₈×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
210	C₂×C₄×D₈	C₂×C₂₃	1	3	yes	complemented
211	C₂²×C₂₃	—	2	3	no	—
212	C₂²×C₂₃	—	2	3	no	—
213	C₂²×C₂₃	—	2	4	no	—
214	C₂²×C₂₃	—	4	2	no	—
215	C₂²×C₂₃	—	4	2	no	—
216	C₂²×C₂₃	—	4	6	no	—
217	C₂²×C₂₃	—	4	6	no	—
218	C₂²×C₂₃	—	4	6	no	—
219	C₂²×C₂₃	—	8	24	no	—
220	C₂²×C₂₃	C₂²×D₈	1	6	yes	—
221	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
222	C₄×C₂₃	—	2	1	no	—
223	C₄×C₂₃	—	2	3	no	—
224	C₄×C₂₃	—	2	3	no	—
225	C₄×C₂₃	—	4	2	no	—
226	C₄×C₂₃	—	4	6	no	—
227	C₄×C₂₃	C₂²×D₈	1	2	yes	—
228	C₄×C₂₃	C₂²×D₈	1	6	yes	—
229	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
230	C₄×C₂₃	#585	1	1	yes	characteristic
231	C₂²×#41	—	2	2	no	—
232	C₂²×D₈	C₂²×C₂₃	1	3	yes	—
233	#550	C₂²×C₂₃	1	2	yes	complemented
234	D₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
235	#548	—	2	2	no	—
236	#547	C₂²×C₂₃	1	6	yes	complemented
237	#546	—	2	6	no	—
238	D₄²	C₂²×C₂₃	1	6	yes	complemented
239	#532	C₂²×C₂₃	1	6	yes	complemented
240	#525	—	2	6	no	—
241	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
242	C₂×C₄×D₄	C₂²×C₂₃	1	6	yes	complemented
243	#500	C₂²×C₂₃	1	3	yes	complemented
244	#493	C₂²×C₂₃	1	3	yes	complemented
245	#486	C₂²×C₂₃	1	6	yes	complemented
246	#480	C₂²×C₂₃	1	12	yes	complemented
247	#474	C₂²×C₂₃	1	6	yes	complemented
248	#474	C₂²×C₂₃	1	6	yes	complemented
249	#466	C₂²×C₂₃	1	6	yes	complemented
250	#466	C₂²×C₂₃	1	6	yes	complemented
251	#459	C₂²×C₂₃	1	6	yes	complemented
252	#459	C₂²×C₂₃	1	6	yes	complemented
253	#447	C₂²×C₂₃	1	12	yes	complemented
254	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
255	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
256	C₄×D₈	C₂²×C₂₃	1	3	yes	—
257	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
258	C₄×D₈	C₂²×C₂₃	1	3	yes	complemented
259	C₄×D₈	C₂²×C₂₃	1	6	yes	complemented
260	C₄×D₈	C₂²×C₂₃	1	6	yes	complemented
261	C₄×D₈	C₂²×C₂₃	1	6	yes	complemented
262	C₄×D₈	C₂²×C₂₃	1	3	yes	complemented
263	C₈×D₄	C₂²×C₂₃	1	3	yes	complemented
264	C₈×D₄	C₂²×C₂₃	1	3	yes	complemented
265	#431	C₂²×C₂₃	1	3	yes	complemented
266	C₂×#107	C₂²×C₂₃	1	3	yes	complemented
267	C₂×#102	C₂²×C₂₃	1	6	yes	complemented
268	C₂×C₄×C₈	C₂²×C₂₃	1	3	yes	complemented
269	C₂×C₂₃	—	2	6	no	—
270	C₂×C₂₃	—	4	4	no	—
271	C₂×C₂₃	—	8	6	no	—
272	C₂×C₂₃	D₄×#41	1	1	yes	characteristic
273	C₂×C₂₃	C₂³×D₈	1	1	yes	characteristic
274	C₂×C₂₃	#3584	1	1	yes	characteristic
275	C₂×#41	—	2	2	no	—
276	C₂×#41	—	2	6	no	—
277	C₂×#41	—	2	6	no	—
278	C₂×#41	—	4	16	no	—
279	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
280	C₂²×Q₈	—	2	2	no	—
281	C₂²×D₄	—	2	6	no	—
282	C₂²×D₄	C₂³×C₂₃	1	6	yes	—
283	C₂³×C₄	—	2	6	no	—
284	C₂×D₈	—	2	12	no	—
285	C₂×D₈	C₂³×C₂₃	1	6	yes	—
286	C₂×D₈	C₂³×C₂₃	1	3	yes	—
287	C₂×D₈	C₂³×C₂₃	1	6	yes	—
288	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₂₃	1	3	yes	—
290	C₂²×C₈	C₂³×C₂₃	1	3	yes	—
291	C₄⋊Q₈	C₂³×C₂₃	1	6	yes	—
292	#127	C₂³×C₂₃	1	6	yes	—
293	#124	—	2	6	no	—
294	#123	—	2	12	no	—
295	C₂²⋊Q₈	—	2	6	no	—
296	C₂²⋊Q₈	—	2	6	no	—
297	#121	—	2	6	no	—
298	#121	—	2	6	no	—
299	#121	—	2	6	no	—
300	#121	C₂³×C₂₃	1	12	yes	—
301	#120	—	2	12	no	—
302	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
303	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
304	C₄×D₄	—	2	6	no	—
305	C₄×D₄	—	2	6	no	—
306	C₄×D₄	—	2	6	no	—
307	C₄×D₄	D₄×C₂₃	1	3	yes	—
308	C₄×D₄	C₂³×C₂₃	1	2	yes	—
309	C₄×D₄	C₂³×C₂₃	1	6	yes	—
310	C₄×D₄	C₂³×C₂₃	1	6	yes	—
311	C₄×D₄	C₂³×C₂₃	1	6	yes	—
312	C₄×D₄	C₂³×C₂₃	1	3	yes	—
313	#117	D₄×C₂₃	1	3	yes	—
314	C₂×C₄⋊C₄	C₂³×C₂₃	1	6	yes	—
315	C₂×C₂²⋊C₄	—	2	6	no	—
316	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
317	#107	C₂³×C₂₃	1	1	yes	characteristic
318	#107	C₂³×C₂₃	1	3	yes	—
319	#107	C₂³×C₂₃	1	6	yes	—
320	#107	C₂³×C₂₃	1	6	yes	—
321	C₄⋊C₈	C₂³×C₂₃	1	3	yes	—
322	C₄⋊C₈	C₂³×C₂₃	1	3	yes	—
323	#102	C₂³×C₂₃	1	2	yes	—
324	#102	C₂³×C₂₃	1	6	yes	—
325	#102	C₂³×C₂₃	1	6	yes	—
326	#102	C₂³×C₂₃	1	6	yes	—
327	#102	C₂³×C₂₃	1	12	yes	—
328	C₂²⋊C₈	C₂³×C₂₃	1	6	yes	—
329	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
330	C₄×C₈	C₂³×C₂₃	1	3	yes	—
331	C₄×C₈	C₂³×C₂₃	1	3	yes	—
332	C₄×C₈	C₂³×C₂₃	1	3	yes	—
333	C₂₃	D₈×#41	1	1	yes	characteristic, direct product factor, Sylow
334	C₂⁴	—	2	6	no	—
335	#41	—	4	8	no	—
336	#41	—	4	24	no	—
337	#41	—	4	24	no	—
338	#41	D₈×C₂₃	1	8	yes	direct product factor
339	C₂×Q₈	—	2	6	no	—
340	C₂×Q₈	—	4	8	no	—
341	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
342	C₂×D₄	—	2	12	no	—
343	C₂×D₄	—	2	12	no	—
344	C₂×D₄	—	2	6	no	—
345	C₂×D₄	—	2	6	no	—
346	C₂×D₄	—	2	6	no	—
347	C₂×D₄	—	4	6	no	—
348	C₂×D₄	—	4	24	no	—
349	C₂×D₄	C₂×D₄×C₂₃	1	3	yes	—
350	C₂×D₄	C₂⁴×C₂₃	1	6	yes	—
351	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
352	C₂²×C₄	—	2	6	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	6	no	—
355	C₂²×C₄	—	2	6	no	—
356	C₂²×C₄	—	2	6	no	—
357	C₂²×C₄	—	4	24	no	—
358	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
359	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
360	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
361	D₈	—	2	12	no	—
362	D₈	—	2	6	no	—
363	D₈	—	4	6	no	—
364	D₈	#41×C₂₃	1	4	yes	direct product factor
365	C₂×C₈	—	2	6	no	—
366	C₂×C₈	—	4	3	no	—
367	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
368	C₂×C₈	C₂⁴×C₂₃	1	3	yes	—
369	C₂×C₈	C₂⁴×C₂₃	1	3	yes	—
370	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
371	C₄⋊C₄	—	2	6	no	—
372	C₄⋊C₄	—	2	6	no	—
373	C₄⋊C₄	C₂×D₄×C₂₃	1	3	yes	—
374	C₄⋊C₄	C₂×D₄×C₂₃	1	3	yes	—
375	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
376	C₄⋊C₄	C₂⁴×C₂₃	1	6	yes	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	6	no	—
379	C₂²⋊C₄	—	2	6	no	—
380	C₂²⋊C₄	—	2	6	no	—
381	C₂²⋊C₄	—	2	12	no	—
382	C₂²⋊C₄	C₂×D₄×C₂₃	1	6	yes	—
383	C₄²	C₂×D₄×C₂₃	1	3	yes	—
384	C₄²	C₂×D₄×C₂₃	1	3	yes	—
385	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
386	C₄²	C₂⁴×C₂₃	1	3	yes	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	6	no	—
389	C₂³	—	4	12	no	—
390	C₂³	—	4	12	no	—
391	C₂³	—	8	6	no	—
392	C₂³	C₂²×D₄×C₂₃	1	3	yes	—
393	Q₈	—	4	12	no	—
394	Q₈	C₂×D₈×C₂₃	1	4	yes	complemented
395	D₄	—	2	6	no	—
396	D₄	—	2	2	no	—
397	D₄	—	2	6	no	—
398	D₄	—	4	12	no	—
399	D₄	—	4	24	no	—
400	D₄	—	4	12	no	—
401	D₄	—	8	6	no	—
402	D₄	C₂×D₈×C₂₃	1	12	yes	complemented
403	D₄	C₂×#41×C₂₃	1	4	yes	complemented
404	C₂×C₄	—	2	3	no	—
405	C₂×C₄	—	2	3	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	6	no	—
408	C₂×C₄	—	4	3	no	—
409	C₂×C₄	—	4	12	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	4	12	no	—
412	C₂×C₄	—	4	12	no	—
413	C₂×C₄	—	4	12	no	—
414	C₂×C₄	C₂×D₈×C₂₃	1	12	yes	complemented
415	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
417	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
418	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
419	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
420	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
421	C₈	—	2	3	no	—
422	C₈	—	2	1	no	—
423	C₈	—	2	3	no	—
424	C₈	C₂×#41×C₂₃	1	2	yes	complemented
425	C₂²	—	2	3	no	—
426	C₂²	—	2	3	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	6	no	—
431	C₂²	—	4	6	no	—
432	C₂²	—	4	6	no	—
433	C₂²	—	8	24	no	—
434	C₂²	C₂²×D₈×C₂₃	1	6	yes	—
435	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
436	C₄	—	2	3	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	3	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	6	no	—
441	C₄	C₂²×D₈×C₂₃	1	2	yes	—
442	C₄	C₂²×D₈×C₂₃	1	6	yes	—
443	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
444	C₄	C₂₃×#585	1	1	yes	characteristic
445	C₂	—	2	6	no	—
446	C₂	—	4	4	no	—
447	C₂	—	8	6	no	—
448	C₂	D₄×#41×C₂₃	1	1	yes	characteristic
449	C₂	C₂³×D₈×C₂₃	1	1	yes	characteristic
450	C₂	C₂₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. D₄×#41×C₂₃	C₂	semidirect
2. C₂₃×#3391	C₂	semidirect
3. Q₈×D₈×C₂₃	C₂	semidirect
4. C₂₃×#3358	C₂	semidirect
5. C₂₃×#3334	C₂	semidirect
6. C₂₃×#3294	C₂	semidirect
7. D₄×D₈×C₂₃	C₂	semidirect
8. C₂₃×#3169	C₂	semidirect
9. C₂₃×#3100	C₂	semidirect
10. C₈×#41×C₂₃	C₂	semidirect
11. C₂×C₄×D₈×C₂₃	C₂	semidirect
14. C₂₃×#550	C₂²	semidirect
15. D₄×Q₈×C₂₃	C₂²	semidirect
17. C₂₃×#547	C₂²	semidirect
19. D₄²×C₂₃	C₂²	semidirect
20. C₂₃×#532	C₂²	semidirect
23. C₂×C₄×D₄×C₂₃	C₂²	semidirect
24. C₂₃×#500	C₂²	semidirect
25. C₂₃×#493	C₂²	semidirect
26. C₂₃×#486	C₂²	semidirect
27. C₂₃×#480	C₂²	semidirect
28. C₂₃×#474	C₂²	semidirect
29. C₂₃×#474	C₂²	semidirect
30. C₂₃×#466	C₂²	semidirect
31. C₂₃×#466	C₂²	semidirect
32. C₂₃×#459	C₂²	semidirect
33. C₂₃×#459	C₂²	semidirect
34. C₂₃×#447	C₂²	semidirect
35. C₈×Q₈×C₂₃	C₂²	semidirect
36. C₈×Q₈×C₂₃	C₂²	semidirect
39. C₄×D₈×C₂₃	C₂²	semidirect
40. C₄×D₈×C₂₃	C₂²	semidirect
41. C₄×D₈×C₂₃	C₂²	semidirect
42. C₄×D₈×C₂₃	C₂²	semidirect
43. C₄×D₈×C₂₃	C₂²	semidirect
44. C₈×D₄×C₂₃	C₂²	semidirect
45. C₈×D₄×C₂₃	C₂²	semidirect
46. C₂₃×#431	C₂²	semidirect
47. C₂×C₂₃×#107	C₂²	semidirect
48. C₂×C₂₃×#102	C₂²	semidirect
49. C₂×C₄×C₈×C₂₃	C₂²	semidirect
112. #41×C₂₃	D₈	direct (N × H)
138. D₈×C₂₃	#41	direct (N × H)
161. D₈×#41	C₂₃	direct (N × H)
169. Q₈×C₂₃	C₂×D₈	semidirect
177. D₄×C₂₃	C₂×D₈	semidirect
178. D₄×C₂₃	C₂×#41	semidirect
189. C₂×C₄×C₂₃	C₂×D₈	semidirect
199. C₈×C₂₃	C₂×#41	semidirect
200. D₄×#41	C₂×C₂₃	semidirect
201. #3391	C₂×C₂₃	semidirect
202. Q₈×D₈	C₂×C₂₃	semidirect
203. #3358	C₂×C₂₃	semidirect
204. #3334	C₂×C₂₃	semidirect
205. #3294	C₂×C₂₃	semidirect
206. D₄×D₈	C₂×C₂₃	semidirect
207. #3169	C₂×C₂₃	semidirect
208. #3100	C₂×C₂₃	semidirect
209. C₈×#41	C₂×C₂₃	semidirect
210. C₂×C₄×D₈	C₂×C₂₃	semidirect
233. #550	C₂²×C₂₃	semidirect
234. D₄×Q₈	C₂²×C₂₃	semidirect
236. #547	C₂²×C₂₃	semidirect
238. D₄²	C₂²×C₂₃	semidirect
239. #532	C₂²×C₂₃	semidirect
242. C₂×C₄×D₄	C₂²×C₂₃	semidirect
243. #500	C₂²×C₂₃	semidirect
244. #493	C₂²×C₂₃	semidirect
245. #486	C₂²×C₂₃	semidirect
246. #480	C₂²×C₂₃	semidirect
247. #474	C₂²×C₂₃	semidirect
248. #474	C₂²×C₂₃	semidirect
249. #466	C₂²×C₂₃	semidirect
250. #466	C₂²×C₂₃	semidirect
251. #459	C₂²×C₂₃	semidirect
252. #459	C₂²×C₂₃	semidirect
253. #447	C₂²×C₂₃	semidirect
254. C₈×Q₈	C₂²×C₂₃	semidirect
255. C₈×Q₈	C₂²×C₂₃	semidirect
258. C₄×D₈	C₂²×C₂₃	semidirect
259. C₄×D₈	C₂²×C₂₃	semidirect
260. C₄×D₈	C₂²×C₂₃	semidirect
261. C₄×D₈	C₂²×C₂₃	semidirect
262. C₄×D₈	C₂²×C₂₃	semidirect
263. C₈×D₄	C₂²×C₂₃	semidirect
264. C₈×D₄	C₂²×C₂₃	semidirect
265. #431	C₂²×C₂₃	semidirect
266. C₂×#107	C₂²×C₂₃	semidirect
267. C₂×#102	C₂²×C₂₃	semidirect
268. C₂×C₄×C₈	C₂²×C₂₃	semidirect
333. C₂₃	D₈×#41	direct (N × H)
338. #41	D₈×C₂₃	direct (N × H)
364. D₈	#41×C₂₃	direct (N × H)
394. Q₈	C₂×D₈×C₂₃	semidirect
402. D₄	C₂×D₈×C₂₃	semidirect
403. D₄	C₂×#41×C₂₃	semidirect
414. C₂×C₄	C₂×D₈×C₂₃	semidirect
424. C₈	C₂×#41×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
D₄×#41×C₂₃	2
C₂₃×#3391	2
Q₈×D₈×C₂₃	2
C₂₃×#3358	2
C₂₃×#3334	2
C₂₃×#3294	2
D₄×D₈×C₂₃	2
C₂₃×#3169	2
C₂₃×#3100	2
C₈×#41×C₂₃	2
C₂×C₄×D₈×C₂₃	2
D₈×#41	23

Subgroups — D8×#41×C23 #19209051

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₈×#41×C₂₃ #19209051