Subgroups — #15682654

Order 2944.

754 conjugacy classes of subgroups.

The subgroup lattice has 468 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
2	C₂×#10625089	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10625086	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²⋊Q₈×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#13092581	C₂	1	1	yes	maximal, characteristic, complemented
6	#13092579	C₂	1	1	yes	maximal, characteristic, complemented
7	#13092577	C₂	1	1	yes	maximal, characteristic, complemented
8	#13092574	C₂	1	1	yes	maximal, characteristic, complemented
9	#13092571	C₂	1	1	yes	maximal, characteristic, complemented
10	#13092569	C₂	1	1	yes	maximal, characteristic, complemented
11	#13092566	C₂	1	1	yes	maximal, characteristic, complemented
12	#13092417	C₂	1	1	yes	maximal, characteristic, complemented
13	#13092415	C₂	1	1	yes	maximal, characteristic, complemented
14	#13092379	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₂₃	C₂²	1	1	yes	characteristic
17	#41×D₂₃	—	2	4	no	—
18	#41×D₂₃	—	2	4	no	—
19	C₂×#67292	C₂²	1	1	yes	characteristic
20	C₂×Q₈×D₂₃	C₂²	1	1	yes	characteristic
21	C₂×Q₈×D₂₃	C₂²	1	1	yes	characteristic, complemented
22	C₂×#67290	—	2	1	no	—
23	C₂×#67290	C₂²	1	1	yes	characteristic
24	C₂×D₄×D₂₃	—	2	1	no	—
25	C₂×D₄×D₂₃	C₂²	1	1	yes	characteristic
26	C₂×#67288	—	2	1	no	—
27	C₂×#67288	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₂₃	—	2	1	no	—
29	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
30	C₂×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
32	C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	#10625117	C₂²	1	1	yes	characteristic
34	C₂×#67275	C₂²	1	1	yes	characteristic, complemented
35	C₂×#67275	C₂²	1	1	yes	characteristic, complemented
36	C₂×#67274	C₂²	1	1	yes	characteristic, complemented
37	C₂×#67273	C₂²	1	1	yes	characteristic, complemented
38	#10625095	C₂²	1	1	yes	characteristic, complemented
39	#10625089	—	2	4	no	—
40	#10625086	—	2	4	no	—
41	C₂×Dic₉₂	C₂²	1	1	yes	characteristic, complemented
42	C₂×#67263	C₂²	1	1	yes	characteristic, complemented
43	C₂×#67262	C₂²	1	1	yes	characteristic, complemented
44	C₂×#67262	C₂²	1	1	yes	characteristic, complemented
45	#10625068	C₂²	1	1	yes	characteristic
46	#10625067	—	2	1	no	—
47	C₄⋊C₄×D₂₃	—	2	1	no	—
48	C₄⋊C₄×D₂₃	C₂²	1	1	yes	characteristic, complemented
49	C₂²⋊C₄×D₂₃	—	2	1	no	—
50	#10625049	—	2	1	no	—
51	C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	#10625017	C₂²	1	1	yes	characteristic, complemented
55	#10625014	C₂²	1	1	yes	characteristic, complemented
56	C₂²⋊(C₂₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
57	#10625003	C₂²	1	1	yes	characteristic, complemented
58	(C₂×D₂₃)⋊C₈	C₂²	1	1	yes	characteristic
59	(C₂×D₂₃)⋊C₈	C₂²	1	1	yes	characteristic
60	#10624998	C₂²	1	1	yes	characteristic, complemented
61	#10624992	C₂²	1	1	yes	characteristic, complemented
62	#10624991	C₂²	1	1	yes	characteristic, complemented
63	C₂³×D₂₃	—	2	1	no	—
64	C₂³×D₂₃	D₄	1	1	yes	characteristic
65	#41×C₂₃	—	2	2	no	—
66	#41×C₂₃	—	2	2	no	—
67	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
68	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
69	C₂×D₄×C₂₃	—	2	1	no	—
70	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₂₃	—	2	1	no	—
72	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
73	C₂×C₂²⋊D₂₃	—	2	1	no	—
74	C₂×C₂²⋊D₂₃	—	2	1	no	—
75	C₂×C₂²⋊D₂₃	—	2	1	no	—
76	C₂²×Dic₂₃	—	2	1	no	—
77	C₂²×Dic₂₃	D₄	1	1	yes	characteristic
78	#67292	—	2	2	no	—
79	#67292	D₄	1	4	yes	—
80	Q₈×D₂₃	—	2	2	no	—
81	Q₈×D₂₃	—	2	2	no	—
82	Q₈×D₂₃	—	2	2	no	—
83	Q₈×D₂₃	—	2	2	no	—
84	#67290	—	2	8	no	—
85	#67290	—	2	2	no	—
86	#67290	D₄	1	4	yes	—
87	D₄×D₂₃	—	2	8	no	—
88	D₄×D₂₃	—	2	2	no	—
89	D₄×D₂₃	—	2	2	no	—
90	#67288	—	2	8	no	—
91	#67288	—	2	2	no	—
92	#67288	—	2	2	no	—
93	C₂×D₉₂	—	2	1	no	—
94	C₂×D₉₂	C₂³	1	1	yes	characteristic
95	C₂×C₄×D₂₃	—	2	8	no	—
96	C₂×C₄×D₂₃	—	2	1	no	—
97	C₂×C₄×D₂₃	—	2	1	no	—
98	C₂×C₄×D₂₃	—	2	1	no	—
99	C₂×C₄×D₂₃	—	2	2	no	—
100	C₂×C₄×D₂₃	—	2	2	no	—
101	C₂×C₄×D₂₃	—	2	1	no	—
102	C₂×C₄×D₂₃	—	2	1	no	—
103	C₂×C₄×D₂₃	D₄	1	1	yes	characteristic
104	C₂×C₄×D₂₃	D₄	1	1	yes	characteristic
105	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
107	C₂×Dic₄₆	—	2	1	no	—
108	C₂×Dic₄₆	—	2	1	no	—
109	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
110	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
111	Q₁₆×C₂₃	—	2	2	no	—
112	SD₁₆×C₂₃	—	2	2	no	—
113	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
114	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
115	C₄⋊C₄×C₂₃	—	2	1	no	—
116	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
117	C₂²⋊C₄×C₂₃	—	2	1	no	—
118	C₂²⋊Dic₂₃	—	2	1	no	—
119	#67275	—	2	2	no	—
120	#67275	—	2	2	no	—
121	#67274	—	2	2	no	—
122	#67273	—	2	2	no	—
123	(C₂×D₂₃)⋊C₄	—	2	1	no	—
124	(C₂×D₂₃)⋊C₄	—	2	1	no	—
125	C₄⋊Dic₂₃	—	2	1	no	—
126	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
127	Dic₂₃⋊C₄	—	2	1	no	—
128	Dic₂₃⋊C₄	—	2	1	no	—
129	Dic₂₃⋊C₄	—	2	1	no	—
130	C₂×C₂₃⋊C₈	C₂³	1	1	yes	characteristic
131	C₂×C₂₃⋊C₈	C₂³	1	1	yes	characteristic
132	Dic₉₂	—	2	2	no	—
133	#67263	—	2	2	no	—
134	#67262	—	2	2	no	—
135	#67262	—	2	2	no	—
136	C₂³×C₂₃	—	2	1	no	—
137	C₂³×C₂₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×D₂₃	—	2	4	no	—
139	C₂²×D₂₃	—	2	1	no	—
140	C₂²×D₂₃	—	2	2	no	—
141	C₂²×D₂₃	—	2	2	no	—
142	C₂²×D₂₃	—	4	1	no	—
143	C₂²×D₂₃	—	4	2	no	—
144	C₂²×D₂₃	—	4	2	no	—
145	C₂²×D₂₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×D₂₃	C₂×D₄	1	1	yes	characteristic
147	Q₈×C₂₃	—	2	1	no	—
148	Q₈×C₂₃	—	2	1	no	—
149	Q₈×C₂₃	—	2	1	no	—
150	Q₈×C₂₃	C₂×D₄	1	2	yes	—
151	D₄×C₂₃	—	2	4	no	—
152	D₄×C₂₃	—	2	1	no	—
153	D₄×C₂₃	C₂×D₄	1	2	yes	—
154	C₂×C₄×C₂₃	—	2	4	no	—
155	C₂×C₄×C₂₃	—	2	1	no	—
156	C₂×C₄×C₂₃	—	2	1	no	—
157	C₂×C₄×C₂₃	—	2	1	no	—
158	C₂×C₄×C₂₃	—	2	1	no	—
159	C₂×C₄×C₂₃	—	2	1	no	—
160	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
161	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
162	C₂²⋊D₂₃	—	2	4	no	—
163	C₂²⋊D₂₃	—	2	4	no	—
164	C₂²⋊D₂₃	—	2	4	no	—
165	C₂×Dic₂₃	—	2	1	no	—
166	C₂×Dic₂₃	—	2	2	no	—
167	C₂×Dic₂₃	—	2	4	no	—
168	C₂×Dic₂₃	—	2	1	no	—
169	C₂×Dic₂₃	—	2	1	no	—
170	C₂×Dic₂₃	C₂×D₄	1	1	yes	characteristic
171	C₂×Dic₂₃	C₂×D₄	1	1	yes	characteristic
172	D₉₂	—	2	4	no	—
173	D₉₂	—	2	1	no	—
174	D₉₂	C₂×D₄	1	2	yes	—
175	C₄×D₂₃	—	2	4	no	—
176	C₄×D₂₃	—	2	4	no	—
177	C₄×D₂₃	—	2	2	no	—
178	C₄×D₂₃	—	2	1	no	—
179	C₄×D₂₃	—	2	1	no	—
180	C₄×D₂₃	—	2	2	no	—
181	C₄×D₂₃	—	2	4	no	—
182	C₄×D₂₃	—	4	2	no	—
183	C₄×D₂₃	—	4	2	no	—
184	C₄×D₂₃	C₂×D₄	1	2	yes	—
185	C₄×D₂₃	C₂×D₄	1	2	yes	—
186	Dic₄₆	—	2	4	no	—
187	Dic₄₆	—	2	1	no	—
188	Dic₄₆	—	2	1	no	—
189	Dic₄₆	—	2	1	no	—
190	Dic₄₆	—	4	2	no	—
191	Dic₄₆	C₂×D₄	1	2	yes	—
192	C₈×C₂₃	—	2	1	no	—
193	C₈×C₂₃	—	2	1	no	—
194	C₂₃⋊C₈	—	2	1	no	—
195	C₂₃⋊C₈	—	2	1	no	—
196	#3007	—	23	1	no	maximal, Sylow
197	C₂²×C₂₃	—	2	1	no	—
198	C₂²×C₂₃	—	2	2	no	—
199	C₂²×C₂₃	—	2	1	no	—
200	C₂²×C₂₃	—	2	1	no	—
201	C₂²×C₂₃	—	4	1	no	—
202	C₂²×C₂₃	—	4	1	no	—
203	C₂²×C₂₃	C₂²×D₄	1	1	yes	characteristic
204	C₂×D₂₃	—	2	1	no	—
205	C₂×D₂₃	—	2	1	no	—
206	C₂×D₂₃	—	2	1	no	—
207	C₂×D₂₃	—	2	1	no	—
208	C₂×D₂₃	—	2	2	no	—
209	C₂×D₂₃	—	4	4	no	—
210	C₂×D₂₃	—	4	8	no	—
211	C₂×D₂₃	—	4	1	no	—
212	C₂×D₂₃	—	4	1	no	—
213	C₂×D₂₃	#120	1	2	yes	—
214	C₂×D₂₃	#137	1	2	yes	complemented
215	C₄×C₂₃	—	2	2	no	—
216	C₄×C₂₃	—	2	1	no	—
217	C₄×C₂₃	—	4	1	no	—
218	C₄×C₂₃	—	4	1	no	—
219	C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
220	C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
221	Dic₂₃	—	2	1	no	—
222	Dic₂₃	—	2	2	no	—
223	Dic₂₃	—	4	1	no	—
224	Dic₂₃	—	4	1	no	—
225	Dic₂₃	#120	1	2	yes	—
226	C₂²×#41	—	23	1	no	—
227	C₂×#137	—	23	1	no	—
228	C₂×#137	—	23	1	no	—
229	C₂×C₂²⋊Q₈	—	23	1	no	—
230	#452	—	23	1	no	—
231	#452	—	23	1	no	—
232	#452	—	23	1	no	—
233	#452	D₂₃	1	1	yes	characteristic, complemented
234	#451	—	23	1	no	—
235	#451	—	23	1	no	—
236	#450	—	23	1	no	—
237	#450	—	23	1	no	—
238	#417	—	23	1	no	—
239	#417	—	23	1	no	—
240	#407	—	23	1	no	—
241	C₂×C₂₃	—	4	1	no	—
242	C₂×C₂₃	—	4	2	no	—
243	C₂×C₂₃	C₂×#120	1	1	yes	characteristic
244	C₂×C₂₃	C₂×#137	1	1	yes	characteristic
245	C₂×C₂₃	#575	1	1	yes	characteristic
246	D₂₃	—	2	2	no	—
247	D₂₃	—	2	2	no	—
248	D₂₃	—	4	2	no	—
249	C₂×#41	—	23	1	no	—
250	C₂×#41	—	23	1	no	—
251	C₂×#41	—	23	1	no	—
252	C₂×#41	—	46	1	no	—
253	C₂×#41	—	46	1	no	—
254	C₂×#41	—	46	4	no	—
255	C₂×#41	—	46	4	no	—
256	C₂×#41	C₂×D₂₃	1	1	yes	characteristic
257	C₂²×Q₈	—	23	1	no	—
258	C₂²×Q₈	—	23	1	no	—
259	C₂²×D₄	—	23	1	no	—
260	C₂²×D₄	—	46	1	no	—
261	C₂³×C₄	—	23	1	no	—
262	C₂³×C₄	—	46	1	no	—
263	#137	—	46	4	no	—
264	#137	—	46	4	no	—
265	C₂×Q₁₆	—	23	1	no	—
266	C₂×Q₁₆	—	23	1	no	—
267	C₂×Q₁₆	—	23	1	no	—
268	C₂×Q₁₆	C₂×D₂₃	1	1	yes	characteristic, complemented
269	C₂×SD₁₆	—	23	1	no	—
270	C₂×SD₁₆	—	23	1	no	—
271	C₂×SD₁₆	—	23	1	no	—
272	C₂×SD₁₆	C₂×D₂₃	1	1	yes	characteristic, complemented
273	C₂×M₁₆	—	23	1	no	—
274	C₂×M₁₆	—	23	1	no	—
275	C₂²⋊Q₈	—	23	1	no	—
276	C₂²⋊Q₈	—	23	1	no	—
277	C₂²⋊Q₈	—	23	1	no	—
278	C₂²⋊Q₈	—	46	1	no	—
279	C₂²⋊Q₈	—	46	1	no	—
280	C₂²⋊Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
281	C₂×C₄⋊C₄	—	23	1	no	—
282	C₂×C₄⋊C₄	—	46	1	no	—
283	C₂×C₂²⋊C₄	—	46	1	no	—
284	#103	—	23	1	no	—
285	#103	—	23	1	no	—
286	#103	—	23	1	no	—
287	#103	C₂×D₂₃	1	1	yes	characteristic, complemented
288	#102	—	23	1	no	—
289	#102	—	23	1	no	—
290	#102	—	23	1	no	—
291	#102	C₂×D₂₃	1	1	yes	characteristic, complemented
292	C₂²⋊C₈	—	23	1	no	—
293	C₂²⋊C₈	—	23	1	no	—
294	C₂²⋊C₈	—	23	1	no	—
295	C₂²⋊C₈	C₂×D₂₃	1	1	yes	characteristic, complemented
296	C₂₃	#3007	1	1	yes	characteristic, complemented, Sylow
297	C₂⁴	—	23	1	no	—
298	C₂⁴	—	46	1	no	—
299	#41	—	2	2	no	—
300	#41	—	2	2	no	—
301	#41	—	23	4	no	—
302	#41	—	23	4	no	—
303	#41	—	46	2	no	—
304	#41	—	46	2	no	—
305	#41	—	46	8	no	—
306	#41	—	46	2	no	—
307	#41	—	46	2	no	—
308	#41	—	46	8	no	—
309	C₂×Q₈	—	23	1	no	—
310	C₂×Q₈	—	23	1	no	—
311	C₂×Q₈	—	46	1	no	—
312	C₂×Q₈	—	46	1	no	—
313	C₂×Q₈	—	46	2	no	—
314	C₂×Q₈	—	46	2	no	—
315	C₂×Q₈	—	46	2	no	—
316	C₂×Q₈	—	46	2	no	—
317	C₂×Q₈	C₂²×D₂₃	1	1	yes	characteristic
318	C₂×Q₈	C₂²×D₂₃	1	1	yes	characteristic
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	23	1	no	—
321	C₂×D₄	—	46	1	no	—
322	C₂×D₄	—	46	1	no	—
323	C₂×D₄	—	46	2	no	—
324	C₂×D₄	—	46	8	no	—
325	C₂×D₄	—	46	1	no	—
326	C₂×D₄	—	46	1	no	—
327	C₂×D₄	—	46	2	no	—
328	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	23	1	no	—
331	C₂²×C₄	—	23	1	no	—
332	C₂²×C₄	—	23	1	no	—
333	C₂²×C₄	—	23	1	no	—
334	C₂²×C₄	—	23	1	no	—
335	C₂²×C₄	—	46	2	no	—
336	C₂²×C₄	—	46	2	no	—
337	C₂²×C₄	—	46	1	no	—
338	C₂²×C₄	—	46	1	no	—
339	C₂²×C₄	—	46	8	no	—
340	C₂²×C₄	—	46	1	no	—
341	C₂²×C₄	—	46	1	no	—
342	C₂²×C₄	—	46	1	no	—
343	C₂²×C₄	—	46	1	no	—
344	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
345	Q₁₆	—	2	2	no	—
346	Q₁₆	—	46	2	no	—
347	Q₁₆	—	46	2	no	—
348	Q₁₆	—	46	2	no	—
349	SD₁₆	—	2	2	no	—
350	SD₁₆	—	46	2	no	—
351	SD₁₆	—	46	2	no	—
352	SD₁₆	—	46	2	no	—
353	M₁₆	—	46	2	no	—
354	M₁₆	—	46	2	no	—
355	C₂×C₈	—	23	1	no	—
356	C₂×C₈	—	23	1	no	—
357	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
358	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	23	1	no	—
361	C₄⋊C₄	—	46	1	no	—
362	C₄⋊C₄	—	46	1	no	—
363	C₄⋊C₄	—	46	1	no	—
364	C₄⋊C₄	—	46	1	no	—
365	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	46	1	no	—
368	C₂²⋊C₄	—	46	1	no	—
369	C₂²⋊C₄	—	46	1	no	—
370	C₂³	—	2	1	no	—
371	C₂³	—	23	1	no	—
372	C₂³	—	23	1	no	—
373	C₂³	—	46	2	no	—
374	C₂³	—	46	2	no	—
375	C₂³	—	46	4	no	—
376	C₂³	—	46	1	no	—
377	C₂³	—	92	1	no	—
378	C₂³	—	92	2	no	—
379	C₂³	—	92	2	no	—
380	C₂³	D₄×D₂₃	1	1	yes	characteristic
381	Q₈	—	2	1	no	—
382	Q₈	—	2	1	no	—
383	Q₈	—	2	1	no	—
384	Q₈	—	23	2	no	—
385	Q₈	—	46	4	no	—
386	Q₈	—	46	1	no	—
387	Q₈	—	46	1	no	—
388	Q₈	—	46	1	no	—
389	Q₈	—	92	2	no	—
390	Q₈	D₄×D₂₃	1	2	yes	—
391	D₄	—	2	4	no	—
392	D₄	—	2	1	no	—
393	D₄	—	23	2	no	—
394	D₄	—	46	4	no	—
395	D₄	—	46	4	no	—
396	D₄	—	46	4	no	—
397	D₄	—	46	4	no	—
398	D₄	—	46	1	no	—
399	D₄	D₄×D₂₃	1	2	yes	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	23	1	no	—
407	C₂×C₄	—	23	2	no	—
408	C₂×C₄	—	23	2	no	—
409	C₂×C₄	—	23	1	no	—
410	C₂×C₄	—	46	2	no	—
411	C₂×C₄	—	46	4	no	—
412	C₂×C₄	—	46	2	no	—
413	C₂×C₄	—	46	4	no	—
414	C₂×C₄	—	46	4	no	—
415	C₂×C₄	—	46	2	no	—
416	C₂×C₄	—	46	4	no	—
417	C₂×C₄	—	46	1	no	—
418	C₂×C₄	—	46	1	no	—
419	C₂×C₄	—	46	1	no	—
420	C₂×C₄	—	46	1	no	—
421	C₂×C₄	—	46	1	no	—
422	C₂×C₄	—	92	2	no	—
423	C₂×C₄	—	92	2	no	—
424	C₂×C₄	D₄×D₂₃	1	1	yes	characteristic
425	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
426	C₈	—	2	1	no	—
427	C₈	—	2	1	no	—
428	C₈	—	46	1	no	—
429	C₈	—	46	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	23	2	no	—
437	C₂²	—	23	2	no	—
438	C₂²	—	46	1	no	—
439	C₂²	—	46	1	no	—
440	C₂²	—	46	1	no	—
441	C₂²	—	46	1	no	—
442	C₂²	—	46	2	no	—
443	C₂²	—	92	4	no	—
444	C₂²	—	92	8	no	—
445	C₂²	—	92	1	no	—
446	C₂²	—	92	1	no	—
447	C₂²	C₂×D₄×D₂₃	1	1	yes	characteristic
448	C₄	—	2	1	no	—
449	C₄	—	2	2	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	1	no	—
452	C₄	—	23	2	no	—
453	C₄	—	46	1	no	—
454	C₄	—	46	2	no	—
455	C₄	—	92	1	no	—
456	C₄	—	92	1	no	—
457	C₄	C₂×D₄×D₂₃	1	1	yes	characteristic
458	C₄	C₂×D₄×D₂₃	1	1	yes	characteristic
459	C₂	—	4	1	no	—
460	C₂	—	4	2	no	—
461	C₂	—	46	2	no	—
462	C₂	—	46	2	no	—
463	C₂	—	92	2	no	—
464	C₂	#120×D₂₃	1	1	yes	characteristic
465	C₂	#137×D₂₃	1	1	yes	characteristic
466	C₂	#13093214	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₂₃
commutator, cosocle	C₂×C₄×C₂₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₂₃
Fitting	C₂₃×#452	C₂
socle	C₂²×C₂₃	C₂²×D₄
prime radical	C₂×#41×D₂₃	C₂
hypercenter	#452	D₂₃
hypocenter	C₂₃	#3007
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #452

Complements

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

N	H ≅ G/N	type
2. C₂×#10625089	C₂	semidirect
3. C₂×#10625086	C₂	semidirect
4. C₂²⋊Q₈×D₂₃	C₂	semidirect
5. #13092581	C₂	semidirect
6. #13092579	C₂	semidirect
7. #13092577	C₂	semidirect
8. #13092574	C₂	semidirect
9. #13092571	C₂	semidirect
10. #13092569	C₂	semidirect
11. #13092566	C₂	semidirect
12. #13092417	C₂	semidirect
13. #13092415	C₂	semidirect
14. #13092379	C₂	semidirect
15. C₂₃×#452	C₂	semidirect
21. C₂×Q₈×D₂₃	C₂²	semidirect
30. C₂×Q₁₆×C₂₃	C₂²	semidirect
31. C₂×SD₁₆×C₂₃	C₂²	semidirect
32. C₂₃×C₂²⋊Q₈	C₂²	semidirect
34. C₂×#67275	C₂²	semidirect
35. C₂×#67275	C₂²	semidirect
36. C₂×#67274	C₂²	semidirect
37. C₂×#67273	C₂²	semidirect
38. #10625095	C₂²	semidirect
41. C₂×Dic₉₂	C₂²	semidirect
42. C₂×#67263	C₂²	semidirect
43. C₂×#67262	C₂²	semidirect
44. C₂×#67262	C₂²	semidirect
48. C₄⋊C₄×D₂₃	C₂²	semidirect
51. C₂₃×#103	C₂²	semidirect
52. C₂₃×#102	C₂²	semidirect
53. C₂₃×C₂²⋊C₈	C₂²	semidirect
54. #10625017	C₂²	semidirect
55. #10625014	C₂²	semidirect
56. C₂²⋊(C₂₃⋊C₈)	C₂²	semidirect
57. #10625003	C₂²	semidirect
60. #10624998	C₂²	semidirect
61. #10624992	C₂²	semidirect
62. #10624991	C₂²	semidirect
214. C₂×D₂₃	#137	semidirect
233. #452	D₂₃	semidirect
268. C₂×Q₁₆	C₂×D₂₃	semidirect
272. C₂×SD₁₆	C₂×D₂₃	semidirect
280. C₂²⋊Q₈	C₂×D₂₃	semidirect
287. #103	C₂×D₂₃	semidirect
291. #102	C₂×D₂₃	semidirect
295. C₂²⋊C₈	C₂×D₂₃	semidirect
296. C₂₃	#3007	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
C₂×#10625089	2
C₂×#10625086	2
C₂²⋊Q₈×D₂₃	2
#13092581	2
#13092579	2
#13092577	2
#13092574	2
#13092571	2
#13092569	2
#13092566	2
#13092417	2
#13092415	2
#13092379	2
C₂₃×#452	2
#3007	23