Subgroups — D₂₃×#548 #15686859

Order 2944.

1620 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×Q₈×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093079	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093078	C₂	1	1	yes	maximal, characteristic, complemented
5	#13093077	C₂	1	3	yes	maximal, complemented
6	#13093076	C₂	1	3	yes	maximal, complemented
7	#13093075	C₂	1	3	yes	maximal, complemented
8	#13093074	C₂	1	1	yes	maximal, characteristic, complemented
9	#13093073	C₂	1	3	yes	maximal, complemented
10	#124×D₂₃	C₂	1	3	yes	maximal, complemented
11	C₂²⋊Q₈×D₂₃	C₂	1	3	yes	maximal, complemented
12	#121×D₂₃	C₂	1	3	yes	maximal, complemented
13	C₄×Q₈×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×D₄×D₂₃	C₂	1	3	yes	maximal, complemented
15	C₂₃×#548	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
17	C₂²×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
18	#41×D₂₃	—	2	8	no	—
19	C₂×#67292	C₂²	1	1	yes	characteristic, complemented
20	C₂×Q₈×D₂₃	—	2	8	no	—
21	C₂×Q₈×D₂₃	C₂²	1	3	yes	—
22	C₂×Q₈×D₂₃	C₂²	1	1	yes	characteristic
23	C₂×Q₈×D₂₃	C₂²	1	1	yes	characteristic, complemented
24	C₂×Q₈×D₂₃	C₂²	1	3	yes	complemented
25	C₂×#67290	C₂²	1	3	yes	complemented
26	C₂×D₄×D₂₃	C₂²	1	3	yes	—
27	C₂×D₄×D₂₃	C₂²	1	3	yes	—
28	C₂×#67288	C₂²	1	3	yes	complemented
29	C₂²×C₄×D₂₃	C₂²	1	3	yes	—
30	C₂²×C₄×D₂₃	C₂²	1	3	yes	—
31	C₂²×Dic₄₆	C₂²	1	3	yes	complemented
32	C₂₃×#124	C₂²	1	3	yes	complemented
33	C₂₃×C₂²⋊Q₈	C₂²	1	3	yes	complemented
34	C₂₃×#121	C₂²	1	3	yes	complemented
35	C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
36	C₄×D₄×C₂₃	C₂²	1	3	yes	complemented
37	#10625118	C₂²	1	3	yes	complemented
38	#10625117	C₂²	1	3	yes	complemented
39	Q₈×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
40	#10625110	C₂²	1	6	yes	complemented
41	#10625109	C₂²	1	3	yes	complemented
42	#10625107	C₂²	1	3	yes	complemented
43	D₄×Dic₂₃	C₂²	1	3	yes	complemented
44	#10625101	C₂²	1	3	yes	complemented
45	C₄×C₂²⋊D₂₃	C₂²	1	3	yes	complemented
46	C₄×C₂²⋊D₂₃	C₂²	1	3	yes	complemented
47	#10625095	C₂²	1	3	yes	complemented
48	#10625068	C₂²	1	3	yes	complemented
49	#10625067	C₂²	1	6	yes	complemented
50	#10625066	C₂²	1	3	yes	complemented
51	#10625064	C₂²	1	3	yes	complemented
52	C₄⋊C₄×D₂₃	C₂²	1	3	yes	—
53	C₄⋊C₄×D₂₃	C₂²	1	3	yes	—
54	#10625058	C₂²	1	3	yes	complemented
55	#10625056	C₂²	1	6	yes	complemented
56	#10625056	C₂²	1	6	yes	complemented
57	#10625055	C₂²	1	6	yes	complemented
58	(C₂²⋊D₂₃)⋊C₄	C₂²	1	3	yes	complemented
59	(C₂²⋊D₂₃)⋊C₄	C₂²	1	3	yes	complemented
60	C₂²⋊C₄×D₂₃	C₂²	1	1	yes	characteristic
61	C₂²⋊C₄×D₂₃	C₂²	1	3	yes	—
62	C₂²⋊C₄×D₂₃	C₂²	1	6	yes	—
63	#10625049	C₂²	1	6	yes	complemented
64	#10625046	C₂²	1	3	yes	complemented
65	C₄×D₉₂	C₂²	1	3	yes	complemented
66	C₄²×D₂₃	C₂²	1	3	yes	—
67	C₄×Dic₄₆	C₂²	1	3	yes	complemented
68	C₂³×D₂₃	C₂³	1	3	yes	—
69	C₂³×D₂₃	C₂³	1	1	yes	characteristic
70	#41×C₂₃	—	2	4	no	—
71	C₂×Q₈×C₂₃	—	2	4	no	—
72	C₂×Q₈×C₂₃	C₂³	1	3	yes	—
73	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
74	C₂×D₄×C₂₃	C₂³	1	3	yes	—
75	C₂×D₄×C₂₃	C₂³	1	3	yes	—
76	C₂²×C₄×C₂₃	C₂³	1	3	yes	—
77	C₂²×C₄×C₂₃	C₂³	1	3	yes	—
78	C₂×C₂²⋊D₂₃	C₂³	1	3	yes	—
79	C₂×C₂²⋊D₂₃	C₂³	1	3	yes	—
80	C₂×C₂²⋊D₂₃	C₂³	1	6	yes	—
81	C₂²×Dic₂₃	C₂³	1	3	yes	—
82	C₂²×Dic₂₃	C₂³	1	3	yes	—
83	#67292	—	2	4	no	—
84	Q₈×D₂₃	—	2	4	no	—
85	Q₈×D₂₃	—	2	12	no	—
86	Q₈×D₂₃	—	2	12	no	—
87	Q₈×D₂₃	D₄	1	8	yes	complemented
88	#67290	—	2	12	no	—
89	D₄×D₂₃	—	2	12	no	—
90	D₄×D₂₃	—	2	12	no	—
91	#67288	—	2	12	no	—
92	C₂×D₉₂	C₂³	1	3	yes	—
93	C₂×D₉₂	C₂³	1	3	yes	—
94	C₂×C₄×D₂₃	—	2	12	no	—
95	C₂×C₄×D₂₃	—	2	12	no	—
96	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
97	C₂×C₄×D₂₃	C₂³	1	3	yes	—
98	C₂×C₄×D₂₃	C₂³	1	3	yes	—
99	C₂×C₄×D₂₃	C₂³	1	3	yes	—
100	C₂×C₄×D₂₃	C₂³	1	3	yes	—
101	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
102	C₂×C₄×D₂₃	C₂³	1	3	yes	—
103	C₂×C₄×D₂₃	C₂³	1	3	yes	—
104	C₂×C₄×D₂₃	C₂³	1	3	yes	—
105	C₂×Dic₄₆	—	2	12	no	—
106	C₂×Dic₄₆	C₂³	1	3	yes	—
107	C₂×Dic₄₆	C₂³	1	6	yes	—
108	C₂×Dic₄₆	C₂³	1	3	yes	—
109	C₄⋊C₄×C₂₃	C₂³	1	3	yes	—
110	C₄⋊C₄×C₂₃	C₂³	1	3	yes	—
111	C₂²⋊C₄×C₂₃	C₂³	1	6	yes	—
112	C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
113	C₂²⋊C₄×C₂₃	C₂³	1	3	yes	—
114	C₄²×C₂₃	C₂³	1	3	yes	—
115	C₂²⋊Dic₂₃	C₂³	1	6	yes	—
116	C₂²⋊Dic₂₃	C₂³	1	3	yes	—
117	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic
118	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
119	(C₂×D₂₃)⋊C₄	C₂³	1	3	yes	—
120	(C₂×D₂₃)⋊C₄	C₂³	1	6	yes	—
121	(C₂×D₂₃)⋊C₄	C₂³	1	6	yes	—
122	(C₂×D₂₃)⋊C₄	C₂³	1	3	yes	—
123	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
124	C₄⋊Dic₂₃	C₂³	1	3	yes	—
125	C₄⋊Dic₂₃	C₂³	1	3	yes	—
126	Dic₂₃⋊C₄	C₂³	1	6	yes	—
127	Dic₂₃⋊C₄	C₂³	1	3	yes	—
128	Dic₂₃⋊C₄	C₂³	1	3	yes	—
129	C₄×Dic₂₃	C₂³	1	3	yes	—
130	C₄×Dic₂₃	C₂³	1	3	yes	—
131	C₄×Dic₂₃	C₂³	1	3	yes	—
132	C₂³×C₂₃	C₂⁴	1	3	yes	—
133	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
134	C₂²×D₂₃	—	2	2	no	—
135	C₂²×D₂₃	—	2	2	no	—
136	C₂²×D₂₃	—	2	6	no	—
137	C₂²×D₂₃	—	2	6	no	—
138	C₂²×D₂₃	—	2	6	no	—
139	C₂²×D₂₃	#41	1	4	yes	complemented
140	C₂²×D₂₃	C₂⁴	1	3	yes	—
141	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
142	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
143	Q₈×C₂₃	—	2	6	no	—
144	Q₈×C₂₃	C₂×D₄	1	4	yes	complemented
145	D₄×C₂₃	—	2	6	no	—
146	D₄×C₂₃	—	2	6	no	—
147	C₂×C₄×C₂₃	—	2	6	no	—
148	C₂×C₄×C₂₃	—	2	6	no	—
149	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
150	C₂×C₄×C₂₃	C₂⁴	1	3	yes	—
151	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
152	C₂×C₄×C₂₃	C₂⁴	1	3	yes	—
153	C₂×C₄×C₂₃	C₂⁴	1	3	yes	—
154	C₂²⋊D₂₃	—	2	6	no	—
155	C₂²⋊D₂₃	—	2	6	no	—
156	C₂²⋊D₂₃	—	2	12	no	—
157	C₂×Dic₂₃	—	2	6	no	—
158	C₂×Dic₂₃	—	2	6	no	—
159	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
160	C₂×Dic₂₃	C₂⁴	1	3	yes	—
161	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
162	C₂×Dic₂₃	C₂⁴	1	3	yes	—
163	C₂×Dic₂₃	C₂⁴	1	3	yes	—
164	D₉₂	—	2	6	no	—
165	D₉₂	—	2	6	no	—
166	C₄×D₂₃	—	2	2	no	—
167	C₄×D₂₃	—	2	6	no	—
168	C₄×D₂₃	—	2	6	no	—
169	C₄×D₂₃	—	2	2	no	—
170	C₄×D₂₃	—	2	6	no	—
171	C₄×D₂₃	—	2	6	no	—
172	C₄×D₂₃	—	2	6	no	—
173	C₄×D₂₃	—	2	6	no	—
174	C₄×D₂₃	C₂×D₄	1	12	yes	—
175	Dic₄₆	—	2	6	no	—
176	Dic₄₆	—	2	12	no	—
177	Dic₄₆	C₂×D₄	1	12	yes	complemented
178	C₂×#548	—	23	1	no	maximal, Sylow
179	C₂²×C₂₃	—	2	1	no	—
180	C₂²×C₂₃	—	2	1	no	—
181	C₂²×C₂₃	—	2	3	no	—
182	C₂²×C₂₃	—	2	3	no	—
183	C₂²×C₂₃	—	2	3	no	—
184	C₂²×C₂₃	C₂×#41	1	2	yes	complemented
185	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
186	C₂×D₂₃	—	2	1	no	—
187	C₂×D₂₃	—	2	1	no	—
188	C₂×D₂₃	—	2	8	no	—
189	C₂×D₂₃	—	2	3	no	—
190	C₂×D₂₃	—	2	3	no	—
191	C₂×D₂₃	—	2	3	no	—
192	C₂×D₂₃	—	4	12	no	—
193	C₂×D₂₃	C₂²×D₄	1	2	yes	—
194	C₂×D₂₃	C₂×#41	1	2	yes	—
195	C₂×D₂₃	C₂×#41	1	2	yes	complemented
196	C₂×D₂₃	2₋¹⁺⁴	1	2	yes	—
197	C₄×C₂₃	—	2	3	no	—
198	C₄×C₂₃	—	2	1	no	—
199	C₄×C₂₃	—	2	3	no	—
200	C₄×C₂₃	—	2	1	no	—
201	C₄×C₂₃	C₂²×D₄	1	6	yes	—
202	Dic₂₃	—	2	3	no	—
203	Dic₂₃	—	2	1	no	—
204	Dic₂₃	—	2	3	no	—
205	Dic₂₃	—	2	1	no	—
206	Dic₂₃	C₂²×D₄	1	6	yes	—
207	C₂²×#41	—	23	1	no	—
208	C₂³×Q₈	—	23	1	no	—
209	#548	—	23	1	no	—
210	#548	—	23	1	no	—
211	#548	—	23	3	no	—
212	#548	—	23	3	no	—
213	#548	—	23	3	no	—
214	#548	—	23	1	no	—
215	#548	—	23	3	no	—
216	#548	D₂₃	1	1	yes	characteristic, direct product factor
217	C₂×#124	—	23	3	no	—
218	C₂×C₂²⋊Q₈	—	23	3	no	—
219	C₂×#121	—	23	3	no	—
220	C₂×C₄×Q₈	—	23	1	no	—
221	C₂×C₄×D₄	—	23	3	no	—
222	C₂×C₂₃	—	2	2	no	—
223	C₂×C₂₃	—	4	3	no	—
224	C₂×C₂₃	C₂³×D₄	1	1	yes	characteristic
225	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
226	C₂×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
227	D₂₃	—	2	2	no	—
228	D₂₃	—	4	3	no	—
229	D₂₃	#548	1	4	yes	direct product factor
230	C₂×#41	—	23	1	no	—
231	C₂×#41	—	23	3	no	—
232	C₂×#41	—	23	3	no	—
233	C₂×#41	—	46	8	no	—
234	C₂×#41	C₂×D₂₃	1	1	yes	characteristic, complemented
235	C₂²×Q₈	—	23	1	no	—
236	C₂²×Q₈	—	23	3	no	—
237	C₂²×Q₈	—	23	3	no	—
238	C₂²×Q₈	—	23	1	no	—
239	C₂²×Q₈	—	23	3	no	—
240	C₂²×Q₈	—	46	8	no	—
241	C₂²×Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
242	C₂²×D₄	—	23	3	no	—
243	C₂²×D₄	—	23	3	no	—
244	C₂³×C₄	—	23	3	no	—
245	C₂³×C₄	—	23	3	no	—
246	#124	—	23	3	no	—
247	#124	—	23	3	no	—
248	#124	—	23	6	no	—
249	#124	—	23	6	no	—
250	#124	—	23	3	no	—
251	#124	C₂×D₂₃	1	3	yes	complemented
252	C₂²⋊Q₈	—	23	3	no	—
253	C₂²⋊Q₈	—	23	3	no	—
254	C₂²⋊Q₈	—	23	6	no	—
255	C₂²⋊Q₈	—	23	3	no	—
256	C₂²⋊Q₈	—	23	6	no	—
257	C₂²⋊Q₈	C₂×D₂₃	1	3	yes	complemented
258	#121	—	23	3	no	—
259	#121	—	23	6	no	—
260	#121	—	23	3	no	—
261	#121	—	23	3	no	—
262	#121	—	23	6	no	—
263	#121	C₂×D₂₃	1	3	yes	complemented
264	C₄×Q₈	—	23	1	no	—
265	C₄×Q₈	—	23	3	no	—
266	C₄×Q₈	—	23	3	no	—
267	C₄×Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
268	C₄×D₄	—	23	3	no	—
269	C₄×D₄	—	23	3	no	—
270	C₄×D₄	—	23	3	no	—
271	C₄×D₄	—	23	3	no	—
272	C₄×D₄	—	23	3	no	—
273	C₄×D₄	—	23	3	no	—
274	C₄×D₄	—	23	3	no	—
275	C₄×D₄	C₂×D₂₃	1	3	yes	complemented
276	C₂×C₄⋊C₄	—	23	3	no	—
277	C₂×C₄⋊C₄	—	23	3	no	—
278	C₂×C₂²⋊C₄	—	23	1	no	—
279	C₂×C₂²⋊C₄	—	23	3	no	—
280	C₂×C₂²⋊C₄	—	23	6	no	—
281	C₂×C₄²	—	23	3	no	—
282	C₂₃	C₂×#548	1	1	yes	characteristic, complemented, Sylow
283	C₂⁴	—	23	1	no	—
284	C₂⁴	—	23	3	no	—
285	#41	—	2	4	no	—
286	#41	—	46	12	no	—
287	#41	—	46	12	no	—
288	#41	—	46	4	no	—
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	—	23	8	no	—
291	C₂×Q₈	—	23	3	no	—
292	C₂×Q₈	—	23	6	no	—
293	C₂×Q₈	—	23	3	no	—
294	C₂×Q₈	—	46	12	no	—
295	C₂×Q₈	—	46	12	no	—
296	C₂×Q₈	—	46	12	no	—
297	C₂×Q₈	—	46	4	no	—
298	C₂×Q₈	C₂²×D₂₃	1	3	yes	—
299	C₂×Q₈	C₂²×D₂₃	1	1	yes	characteristic
300	C₂×D₄	—	23	3	no	—
301	C₂×D₄	—	23	3	no	—
302	C₂×D₄	—	23	6	no	—
303	C₂×D₄	—	23	3	no	—
304	C₂×D₄	—	23	3	no	—
305	C₂×D₄	—	46	12	no	—
306	C₂×D₄	—	46	12	no	—
307	C₂×D₄	C₂²×D₂₃	1	3	yes	—
308	C₂×D₄	C₂²×D₂₃	1	3	yes	—
309	C₂²×C₄	—	23	3	no	—
310	C₂²×C₄	—	23	3	no	—
311	C₂²×C₄	—	23	3	no	—
312	C₂²×C₄	—	23	1	no	—
313	C₂²×C₄	—	23	3	no	—
314	C₂²×C₄	—	23	3	no	—
315	C₂²×C₄	—	23	1	no	—
316	C₂²×C₄	—	23	3	no	—
317	C₂²×C₄	—	23	3	no	—
318	C₂²×C₄	—	23	3	no	—
319	C₂²×C₄	—	23	3	no	—
320	C₂²×C₄	—	46	12	no	—
321	C₂²×C₄	—	46	12	no	—
322	C₂²×C₄	C₂²×D₂₃	1	3	yes	—
323	C₂²×C₄	C₂²×D₂₃	1	3	yes	—
324	C₄⋊C₄	—	23	3	no	—
325	C₄⋊C₄	—	23	3	no	—
326	C₄⋊C₄	—	23	3	no	—
327	C₄⋊C₄	—	23	6	no	—
328	C₄⋊C₄	—	23	3	no	—
329	C₄⋊C₄	C₂²×D₂₃	1	3	yes	—
330	C₄⋊C₄	C₂²×D₂₃	1	3	yes	—
331	C₂²⋊C₄	—	23	1	no	—
332	C₂²⋊C₄	—	23	3	no	—
333	C₂²⋊C₄	—	23	6	no	—
334	C₂²⋊C₄	—	23	1	no	—
335	C₂²⋊C₄	—	23	1	no	—
336	C₂²⋊C₄	—	23	3	no	—
337	C₂²⋊C₄	—	23	3	no	—
338	C₂²⋊C₄	—	23	6	no	—
339	C₂²⋊C₄	—	23	6	no	—
340	C₂²⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
341	C₂²⋊C₄	C₂²×D₂₃	1	3	yes	—
342	C₂²⋊C₄	C₂²×D₂₃	1	6	yes	—
343	C₄²	—	23	3	no	—
344	C₄²	—	23	3	no	—
345	C₄²	—	23	3	no	—
346	C₄²	C₂²×D₂₃	1	3	yes	—
347	C₂³	—	23	1	no	—
348	C₂³	—	23	4	no	—
349	C₂³	—	23	1	no	—
350	C₂³	—	23	3	no	—
351	C₂³	—	46	2	no	—
352	C₂³	—	46	2	no	—
353	C₂³	—	46	6	no	—
354	C₂³	—	46	6	no	—
355	C₂³	—	46	6	no	—
356	C₂³	C₂³×D₂₃	1	3	yes	—
357	C₂³	C₂³×D₂₃	1	1	yes	characteristic
358	Q₈	—	2	6	no	—
359	Q₈	—	23	12	no	—
360	Q₈	—	46	12	no	—
361	Q₈	—	46	6	no	—
362	Q₈	D₄×D₂₃	1	4	yes	complemented
363	D₄	—	2	6	no	—
364	D₄	—	2	6	no	—
365	D₄	—	46	6	no	—
366	D₄	—	46	12	no	—
367	D₄	—	46	6	no	—
368	D₄	—	46	6	no	—
369	D₄	—	46	6	no	—
370	C₂×C₄	—	2	6	no	—
371	C₂×C₄	—	2	6	no	—
372	C₂×C₄	—	23	3	no	—
373	C₂×C₄	—	23	12	no	—
374	C₂×C₄	—	23	1	no	—
375	C₂×C₄	—	23	3	no	—
376	C₂×C₄	—	23	3	no	—
377	C₂×C₄	—	23	1	no	—
378	C₂×C₄	—	46	6	no	—
379	C₂×C₄	—	46	6	no	—
380	C₂×C₄	—	46	2	no	—
381	C₂×C₄	—	46	6	no	—
382	C₂×C₄	—	46	6	no	—
383	C₂×C₄	—	46	2	no	—
384	C₂×C₄	—	46	6	no	—
385	C₂×C₄	—	46	6	no	—
386	C₂×C₄	—	46	6	no	—
387	C₂×C₄	—	46	6	no	—
388	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
389	C₂×C₄	C₂³×D₂₃	1	3	yes	—
390	C₂×C₄	C₂³×D₂₃	1	3	yes	—
391	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₂₃	1	3	yes	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	3	no	—
396	C₂²	—	2	3	no	—
397	C₂²	—	2	3	no	—
398	C₂²	—	23	2	no	—
399	C₂²	—	23	2	no	—
400	C₂²	—	23	2	no	—
401	C₂²	—	23	2	no	—
402	C₂²	—	46	8	no	—
403	C₂²	—	46	1	no	—
404	C₂²	—	46	1	no	—
405	C₂²	—	46	3	no	—
406	C₂²	—	46	3	no	—
407	C₂²	—	46	3	no	—
408	C₂²	—	92	12	no	—
409	C₂²	#41×D₂₃	1	2	yes	complemented
410	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	3	no	—
413	C₄	—	2	3	no	—
414	C₄	—	2	1	no	—
415	C₄	—	23	6	no	—
416	C₄	—	46	1	no	—
417	C₄	—	46	3	no	—
418	C₄	—	46	3	no	—
419	C₄	—	46	1	no	—
420	C₄	C₂×D₄×D₂₃	1	6	yes	—
421	C₂	—	2	2	no	—
422	C₂	—	4	3	no	—
423	C₂	—	23	4	no	—
424	C₂	—	46	2	no	—
425	C₂	—	92	3	no	—
426	C₂	C₂²×D₄×D₂₃	1	1	yes	characteristic
427	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
428	C₂	2₋¹⁺⁴×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁵
Fitting	C₂₃×#548	C₂
hypercenter	#548	D₂₃
hypocenter	C₂₃	C₂×#548
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ #548

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₂₃	C₂	semidirect
2. C₂²×Q₈×D₂₃	C₂	semidirect
3. #13093079	C₂	semidirect
4. #13093078	C₂	semidirect
5. #13093077	C₂	semidirect
6. #13093076	C₂	semidirect
7. #13093075	C₂	semidirect
8. #13093074	C₂	semidirect
9. #13093073	C₂	semidirect
10. #124×D₂₃	C₂	semidirect
11. C₂²⋊Q₈×D₂₃	C₂	semidirect
12. #121×D₂₃	C₂	semidirect
13. C₄×Q₈×D₂₃	C₂	semidirect
14. C₄×D₄×D₂₃	C₂	semidirect
15. C₂₃×#548	C₂	semidirect
16. C₂×#41×C₂₃	C₂²	semidirect
17. C₂²×Q₈×C₂₃	C₂²	semidirect
19. C₂×#67292	C₂²	semidirect
23. C₂×Q₈×D₂₃	C₂²	semidirect
24. C₂×Q₈×D₂₃	C₂²	semidirect
25. C₂×#67290	C₂²	semidirect
28. C₂×#67288	C₂²	semidirect
31. C₂²×Dic₄₆	C₂²	semidirect
32. C₂₃×#124	C₂²	semidirect
33. C₂₃×C₂²⋊Q₈	C₂²	semidirect
34. C₂₃×#121	C₂²	semidirect
35. C₄×Q₈×C₂₃	C₂²	semidirect
36. C₄×D₄×C₂₃	C₂²	semidirect
37. #10625118	C₂²	semidirect
38. #10625117	C₂²	semidirect
39. Q₈×Dic₂₃	C₂²	semidirect
40. #10625110	C₂²	semidirect
41. #10625109	C₂²	semidirect
42. #10625107	C₂²	semidirect
43. D₄×Dic₂₃	C₂²	semidirect
44. #10625101	C₂²	semidirect
45. C₄×C₂²⋊D₂₃	C₂²	semidirect
46. C₄×C₂²⋊D₂₃	C₂²	semidirect
47. #10625095	C₂²	semidirect
48. #10625068	C₂²	semidirect
49. #10625067	C₂²	semidirect
50. #10625066	C₂²	semidirect
51. #10625064	C₂²	semidirect
54. #10625058	C₂²	semidirect
55. #10625056	C₂²	semidirect
56. #10625056	C₂²	semidirect
57. #10625055	C₂²	semidirect
58. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
59. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
63. #10625049	C₂²	semidirect
64. #10625046	C₂²	semidirect
65. C₄×D₉₂	C₂²	semidirect
67. C₄×Dic₄₆	C₂²	semidirect
87. Q₈×D₂₃	D₄	semidirect
139. C₂²×D₂₃	#41	semidirect
144. Q₈×C₂₃	C₂×D₄	semidirect
177. Dic₄₆	C₂×D₄	semidirect
184. C₂²×C₂₃	C₂×#41	semidirect
195. C₂×D₂₃	C₂×#41	semidirect
216. #548	D₂₃	direct (N × H)
229. D₂₃	#548	direct (N × H)
234. C₂×#41	C₂×D₂₃	semidirect
241. C₂²×Q₈	C₂×D₂₃	semidirect
251. #124	C₂×D₂₃	semidirect
257. C₂²⋊Q₈	C₂×D₂₃	semidirect
263. #121	C₂×D₂₃	semidirect
267. C₄×Q₈	C₂×D₂₃	semidirect
275. C₄×D₄	C₂×D₂₃	semidirect
282. C₂₃	C₂×#548	semidirect
362. Q₈	D₄×D₂₃	semidirect
409. C₂²	#41×D₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×D₂₃	2
C₂²×Q₈×D₂₃	2
#13093079	2
#13093078	2
#13093077	2
#13093076	2
#13093075	2
#13093074	2
#13093073	2
#124×D₂₃	2
C₂²⋊Q₈×D₂₃	2
#121×D₂₃	2
C₄×Q₈×D₂₃	2
C₄×D₄×D₂₃	2
C₂₃×#548	2
C₂×#548	23

Subgroups — D23×#548 #15686859

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₃×#548 #15686859