Subgroups — #15686975

Order 2944.

1068 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093147	C₂	1	1	yes	maximal, characteristic, complemented
2	#13093144	C₂	1	2	yes	maximal, complemented
3	#13093142	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093128	C₂	1	1	yes	maximal, characteristic, complemented
5	#13093125	C₂	1	2	yes	maximal, complemented
6	#13093123	C₂	1	2	yes	maximal, complemented
7	#13093121	C₂	1	4	yes	maximal, complemented
8	#13093082	C₂	1	1	yes	maximal, characteristic, complemented
9	#13093080	C₂	1	2	yes	maximal, complemented
10	#13092971	C₂	1	4	yes	maximal, complemented
11	#13092971	C₂	1	2	yes	maximal, complemented
12	#13092970	C₂	1	2	yes	maximal, complemented
13	C₄×#67288	C₂	1	1	yes	maximal, characteristic
14	#13092885	C₂	1	2	yes	maximal
15	C₂×C₄×Dic₄₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×Q₈×D₂₃	C₂	1	2	yes	maximal, complemented
17	C₂₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×Q₈×D₂₃	C₂²	1	2	yes	—
19	C₂×#67288	C₂²	1	1	yes	characteristic
20	C₂²×Dic₄₆	C₂²	1	1	yes	characteristic
21	C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂₃×#125	C₂²	1	2	yes	—
24	C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₄×Q₈×C₂₃	C₂²	1	2	yes	—
27	C₄×Q₈×C₂₃	C₂²	1	2	yes	—
28	C₂₃×#117	C₂²	1	2	yes	—
29	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
30	#10625117	C₂²	1	4	yes	—
31	#10625117	C₂²	1	2	yes	—
32	Q₈×Dic₂₃	C₂²	1	2	yes	—
33	#10625115	C₂²	1	4	yes	—
34	#10625115	C₂²	1	2	yes	—
35	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	—
36	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	—
37	#10625097	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic
39	C₂×Dic₂₃⋊C₄	C₂²	1	2	yes	—
40	C₂×C₄×Dic₂₃	C₂²	1	2	yes	—
41	#10625068	C₂²	1	4	yes	—
42	#10625068	C₂²	1	2	yes	—
43	#10625067	C₂²	1	4	yes	—
44	#10625067	C₂²	1	4	yes	—
45	#10625067	C₂²	1	4	yes	—
46	#10625064	C₂²	1	2	yes	—
47	#10625064	C₂²	1	2	yes	—
48	C₄⋊C₄×D₂₃	C₂²	1	4	yes	—
49	C₄⋊C₄×D₂₃	C₂²	1	2	yes	—
50	#10625061	C₂²	1	2	yes	—
51	#10625061	C₂²	1	2	yes	—
52	#10625060	C₂²	1	4	yes	—
53	#10625060	C₂²	1	4	yes	—
54	#10625060	C₂²	1	4	yes	—
55	#10625059	C₂²	1	2	yes	—
56	#10625059	C₂²	1	2	yes	—
57	#10625059	C₂²	1	2	yes	—
58	#10625059	C₂²	1	4	yes	—
59	#10625058	C₂²	1	4	yes	—
60	#10625058	C₂²	1	2	yes	—
61	#10625058	C₂²	1	2	yes	—
62	#10625058	C₂²	1	2	yes	—
63	(C₂²⋊D₂₃)⋊C₄	C₂²	1	4	yes	—
64	(C₂²⋊D₂₃)⋊C₄	C₂²	1	4	yes	—
65	#10625049	C₂²	1	4	yes	—
66	#10625049	C₂²	1	4	yes	—
67	C₄×D₉₂	C₂²	1	1	yes	characteristic
68	C₄×D₉₂	C₂²	1	1	yes	characteristic
69	#10625043	C₂²	1	4	yes	—
70	#10625043	C₂²	1	2	yes	—
71	C₄²×D₂₃	C₂²	1	4	yes	—
72	C₄²×D₂₃	C₂²	1	2	yes	—
73	C₄×Dic₄₆	C₂²	1	2	yes	—
74	C₄×Dic₄₆	C₂²	1	1	yes	characteristic
75	C₄×Dic₄₆	C₂²	1	1	yes	characteristic
76	C₄×Dic₄₆	C₂²	1	4	yes	—
77	C₄×Dic₄₆	C₂²	1	1	yes	characteristic
78	C₄×Dic₄₆	C₂²	1	2	yes	—
79	C₄×Dic₄₆	C₂²	1	1	yes	characteristic
80	C₄×Dic₄₆	C₂²	1	1	yes	characteristic
81	C₄×Dic₄₆	C₂²	1	1	yes	characteristic
82	C₄×Dic₄₆	C₂²	1	4	yes	—
83	C₂×Q₈×C₂₃	C₂³	1	2	yes	—
84	C₂×Q₈×C₂₃	C₂³	1	2	yes	—
85	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
88	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
89	C₂²×Dic₂₃	C₂³	1	2	yes	—
90	C₂²×Dic₂₃	C₂³	1	2	yes	—
91	Q₈×D₂₃	—	2	8	no	—
92	#67288	Q₈	1	8	yes	complemented
93	C₂×D₉₂	C₂³	1	1	yes	characteristic
94	C₂×C₄×D₂₃	C₂³	1	2	yes	—
95	C₂×C₄×D₂₃	C₂³	1	4	yes	—
96	C₂×C₄×D₂₃	C₂³	1	2	yes	—
97	C₂×C₄×D₂₃	C₂³	1	4	yes	—
98	C₂×C₄×D₂₃	C₂³	1	2	yes	—
99	C₂×Dic₄₆	—	2	4	no	—
100	C₂×Dic₄₆	C₂³	1	2	yes	—
101	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
102	C₂×Dic₄₆	C₂³	1	4	yes	—
103	C₂×Dic₄₆	C₂³	1	4	yes	—
104	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
105	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
106	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
107	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
108	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
109	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
110	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
111	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
112	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
113	C₄²×C₂₃	C₂³	1	1	yes	characteristic
114	C₄²×C₂₃	C₂³	1	1	yes	characteristic
115	C₄²×C₂₃	C₂³	1	1	yes	characteristic
116	C₄²×C₂₃	C₂³	1	4	yes	—
117	C₄²×C₂₃	C₂³	1	1	yes	characteristic
118	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
119	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
120	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
121	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
122	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
123	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
124	C₄⋊Dic₂₃	C₂³	1	2	yes	—
125	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
126	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
127	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
128	C₄⋊Dic₂₃	C₂³	1	4	yes	—
129	C₄⋊Dic₂₃	C₂³	1	4	yes	—
130	Dic₂₃⋊C₄	C₂³	1	2	yes	—
131	Dic₂₃⋊C₄	C₂³	1	2	yes	—
132	Dic₂₃⋊C₄	C₂³	1	2	yes	—
133	Dic₂₃⋊C₄	C₂³	1	2	yes	—
134	Dic₂₃⋊C₄	C₂³	1	2	yes	—
135	Dic₂₃⋊C₄	C₂³	1	2	yes	—
136	Dic₂₃⋊C₄	C₂³	1	4	yes	—
137	Dic₂₃⋊C₄	C₂³	1	4	yes	—
138	Dic₂₃⋊C₄	C₂³	1	4	yes	—
139	Dic₂₃⋊C₄	C₂³	1	4	yes	—
140	Dic₂₃⋊C₄	C₂³	1	4	yes	—
141	Dic₂₃⋊C₄	C₂³	1	4	yes	—
142	C₄×Dic₂₃	C₂³	1	2	yes	—
143	C₄×Dic₂₃	C₂³	1	2	yes	—
144	C₄×Dic₂₃	C₂³	1	2	yes	—
145	C₄×Dic₂₃	C₂³	1	2	yes	—
146	C₄×Dic₂₃	C₂³	1	2	yes	—
147	C₄×Dic₂₃	C₂³	1	2	yes	—
148	C₄×Dic₂₃	C₂³	1	2	yes	—
149	C₄×Dic₂₃	C₂³	1	4	yes	—
150	C₄×Dic₂₃	C₂³	1	4	yes	—
151	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
152	C₂²×D₂₃	C₂⁴	1	2	yes	—
153	Q₈×C₂₃	—	2	4	no	—
154	Q₈×C₂₃	—	4	2	no	—
155	C₂×C₄×C₂₃	—	2	2	no	—
156	C₂×C₄×C₂₃	—	4	1	no	—
157	C₂×C₄×C₂₃	C₂×Q₈	1	4	yes	complemented
158	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
159	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
160	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
161	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
162	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
163	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
164	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
166	C₂²⋊D₂₃	C₂×Q₈	1	8	yes	complemented
167	C₂×Dic₂₃	—	2	4	no	—
168	C₂×Dic₂₃	—	4	2	no	—
169	C₂×Dic₂₃	C₂⁴	1	2	yes	—
170	C₂×Dic₂₃	C₂⁴	1	2	yes	—
171	C₂×Dic₂₃	C₂⁴	1	2	yes	—
172	C₂×Dic₂₃	C₂⁴	1	2	yes	—
173	C₂×Dic₂₃	C₂⁴	1	2	yes	—
174	C₂×Dic₂₃	C₂⁴	1	2	yes	—
175	C₂×Dic₂₃	C₂⁴	1	2	yes	—
176	D₉₂	C₂×Q₈	1	4	yes	complemented
177	C₄×D₂₃	—	2	4	no	—
178	C₄×D₂₃	—	2	8	no	—
179	C₄×D₂₃	—	4	2	no	—
180	C₄×D₂₃	—	4	4	no	—
181	C₄×D₂₃	C₂×Q₈	1	8	yes	complemented
182	Dic₄₆	—	2	2	no	—
183	Dic₄₆	—	2	4	no	—
184	Dic₄₆	—	2	8	no	—
185	Dic₄₆	—	4	4	no	—
186	Dic₄₆	C₂×Q₈	1	4	yes	complemented
187	Dic₄₆	#41	1	4	yes	complemented
188	Q₈×#41	—	23	1	no	maximal, Sylow
189	C₂²×C₂₃	—	2	1	no	—
190	C₂²×C₂₃	—	2	1	no	—
191	C₂²×C₂₃	C₂²×Q₈	1	2	yes	—
192	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
193	C₂×D₂₃	—	2	2	no	—
194	C₂×D₂₃	—	2	2	no	—
195	C₂×D₂₃	C₂²×Q₈	1	4	yes	—
196	C₄×C₂₃	—	2	1	no	—
197	C₄×C₂₃	—	2	4	no	—
198	C₄×C₂₃	—	2	4	no	—
199	C₄×C₂₃	—	2	1	no	—
200	C₄×C₂₃	—	2	1	no	—
201	C₄×C₂₃	C₂²×Q₈	1	2	yes	—
202	C₄×C₂₃	C₂²×Q₈	1	2	yes	—
203	C₄×C₂₃	C₂×#41	1	2	yes	—
204	Dic₂₃	—	2	2	no	—
205	Dic₂₃	—	2	2	no	—
206	Dic₂₃	—	2	2	no	—
207	Dic₂₃	—	2	2	no	—
208	Dic₂₃	—	2	2	no	—
209	Dic₂₃	C₂²×Q₈	1	4	yes	—
210	Dic₂₃	C₂×#41	1	4	yes	—
211	Q₈²	—	23	1	no	—
212	#557	—	23	1	no	—
213	#557	—	23	2	no	—
214	#554	—	23	1	no	—
215	#554	—	23	2	no	—
216	#554	—	23	4	no	—
217	#554	—	23	2	no	—
218	D₄×Q₈	—	23	1	no	—
219	D₄×Q₈	—	23	2	no	—
220	#533	—	23	4	no	—
221	#533	—	23	2	no	—
222	#533	—	23	2	no	—
223	#533	D₂₃	1	1	yes	characteristic, complemented
224	C₄×#41	—	23	2	no	—
225	C₄×#41	—	23	1	no	—
226	C₂×C₄×Q₈	—	23	2	no	—
227	C₂×C₄×Q₈	—	23	1	no	—
228	C₂×C₂₃	—	2	2	no	—
229	C₂×C₂₃	C₂³×Q₈	1	1	yes	characteristic
230	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
231	C₂×C₂₃	#585	1	1	yes	characteristic
232	D₂₃	—	2	4	no	—
233	C₂×#41	—	23	1	no	—
234	C₂²×Q₈	—	23	2	no	—
235	C₂²×Q₈	—	23	1	no	—
236	C₄⋊Q₈	—	23	2	no	—
237	C₄⋊Q₈	—	23	4	no	—
238	C₄⋊Q₈	—	23	4	no	—
239	C₄⋊Q₈	—	23	2	no	—
240	C₄⋊Q₈	—	23	2	no	—
241	C₄⋊Q₈	—	23	2	no	—
242	C₄⋊Q₈	C₂×D₂₃	1	1	yes	characteristic
243	C₄⋊Q₈	C₂×D₂₃	1	1	yes	characteristic
244	#125	—	23	4	no	—
245	#125	—	23	4	no	—
246	#125	—	23	4	no	—
247	#125	—	23	2	no	—
248	#125	—	23	2	no	—
249	#125	C₂×D₂₃	1	2	yes	—
250	C₂²⋊Q₈	—	23	2	no	—
251	C₂²⋊Q₈	—	23	4	no	—
252	C₂²⋊Q₈	—	23	4	no	—
253	C₂²⋊Q₈	—	23	4	no	—
254	C₂²⋊Q₈	—	23	2	no	—
255	C₂²⋊Q₈	—	23	4	no	—
256	C₂²⋊Q₈	—	23	4	no	—
257	C₂²⋊Q₈	—	23	4	no	—
258	C₂²⋊Q₈	—	23	4	no	—
259	C₂²⋊Q₈	C₂×D₂₃	1	2	yes	—
260	C₂²⋊Q₈	C₂×D₂₃	1	2	yes	—
261	C₄×Q₈	—	23	2	no	—
262	C₄×Q₈	—	23	2	no	—
263	C₄×Q₈	—	23	4	no	—
264	C₄×Q₈	—	23	2	no	—
265	C₄×Q₈	—	23	2	no	—
266	C₄×Q₈	—	23	1	no	—
267	C₄×Q₈	—	23	4	no	—
268	C₄×Q₈	—	23	2	no	—
269	C₄×Q₈	—	23	1	no	—
270	C₄×Q₈	—	23	1	no	—
271	C₄×Q₈	—	23	1	no	—
272	C₄×Q₈	—	23	2	no	—
273	C₄×Q₈	—	23	1	no	—
274	C₄×Q₈	—	23	1	no	—
275	C₄×Q₈	—	23	4	no	—
276	C₄×Q₈	C₂×D₂₃	1	2	yes	—
277	C₄×Q₈	C₂×D₂₃	1	2	yes	—
278	C₄×D₄	—	23	2	no	—
279	C₄×D₄	—	23	2	no	—
280	C₄×D₄	—	23	2	no	—
281	C₄×D₄	—	23	2	no	—
282	C₄×D₄	—	23	4	no	—
283	C₄×D₄	—	23	4	no	—
284	C₄×D₄	—	23	1	no	—
285	C₄×D₄	—	23	1	no	—
286	#117	—	23	1	no	—
287	#117	—	23	4	no	—
288	#117	—	23	2	no	—
289	#117	C₂×D₂₃	1	2	yes	—
290	C₂×C₄⋊C₄	—	23	2	no	—
291	C₂×C₄⋊C₄	—	23	1	no	—
292	C₂×C₄⋊C₄	—	23	4	no	—
293	C₂×C₄⋊C₄	—	23	2	no	—
294	C₂×C₄²	—	23	2	no	—
295	C₂×C₄²	—	23	4	no	—
296	C₂×C₄²	—	23	2	no	—
297	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
298	C₂₃	Q₈×#41	1	1	yes	characteristic, complemented, Sylow
299	#41	—	23	8	no	—
300	C₂×Q₈	—	23	1	no	—
301	C₂×Q₈	—	23	1	no	—
302	C₂×Q₈	—	23	4	no	—
303	C₂×Q₈	—	23	2	no	—
304	C₂×Q₈	—	23	1	no	—
305	C₂×Q₈	—	23	4	no	—
306	C₂×Q₈	—	46	4	no	—
307	C₂×Q₈	—	46	8	no	—
308	C₂×Q₈	C₂²×D₂₃	1	2	yes	—
309	C₂×Q₈	C₂²×D₂₃	1	2	yes	—
310	C₂×D₄	—	23	2	no	—
311	C₂×D₄	—	23	1	no	—
312	C₂²×C₄	—	23	2	no	—
313	C₂²×C₄	—	23	2	no	—
314	C₂²×C₄	—	23	2	no	—
315	C₂²×C₄	—	23	4	no	—
316	C₂²×C₄	—	23	2	no	—
317	C₂²×C₄	—	23	4	no	—
318	C₂²×C₄	—	23	2	no	—
319	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
320	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
321	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
322	C₄⋊C₄	—	23	2	no	—
323	C₄⋊C₄	—	23	1	no	—
324	C₄⋊C₄	—	23	4	no	—
325	C₄⋊C₄	—	23	2	no	—
326	C₄⋊C₄	—	23	2	no	—
327	C₄⋊C₄	—	23	4	no	—
328	C₄⋊C₄	—	23	2	no	—
329	C₄⋊C₄	—	23	4	no	—
330	C₄⋊C₄	—	23	2	no	—
331	C₄⋊C₄	—	23	1	no	—
332	C₄⋊C₄	—	23	4	no	—
333	C₄⋊C₄	—	23	4	no	—
334	C₄⋊C₄	—	23	2	no	—
335	C₄⋊C₄	—	23	2	no	—
336	C₄⋊C₄	—	23	1	no	—
337	C₄⋊C₄	—	23	1	no	—
338	C₄⋊C₄	—	23	4	no	—
339	C₄⋊C₄	—	23	4	no	—
340	C₄⋊C₄	—	23	4	no	—
341	C₄⋊C₄	C₂²×D₂₃	1	4	yes	—
342	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
343	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
344	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
345	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
346	C₄⋊C₄	C₂²×D₂₃	1	4	yes	—
347	C₂²⋊C₄	—	23	2	no	—
348	C₂²⋊C₄	—	23	4	no	—
349	C₂²⋊C₄	—	23	4	no	—
350	C₂²⋊C₄	—	23	2	no	—
351	C₂²⋊C₄	—	23	2	no	—
352	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	—
353	C₄²	—	23	4	no	—
354	C₄²	—	23	2	no	—
355	C₄²	—	23	2	no	—
356	C₄²	—	23	4	no	—
357	C₄²	—	23	2	no	—
358	C₄²	—	23	2	no	—
359	C₄²	—	23	2	no	—
360	C₄²	—	23	2	no	—
361	C₄²	—	23	2	no	—
362	C₄²	C₂²×D₂₃	1	1	yes	characteristic
363	C₄²	C₂²×D₂₃	1	1	yes	characteristic
364	C₄²	C₂²×D₂₃	1	1	yes	characteristic
365	C₄²	C₂²×D₂₃	1	4	yes	—
366	C₄²	C₂²×D₂₃	1	1	yes	characteristic
367	C₂³	—	23	2	no	—
368	C₂³	C₂³×D₂₃	1	1	yes	characteristic
369	Q₈	—	2	4	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	23	4	no	—
372	Q₈	—	23	4	no	—
373	Q₈	—	46	4	no	—
374	Q₈	—	46	8	no	—
375	Q₈	—	46	2	no	—
376	Q₈	—	92	4	no	—
377	D₄	—	23	8	no	—
378	D₄	—	23	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	23	2	no	—
382	C₂×C₄	—	23	2	no	—
383	C₂×C₄	—	23	8	no	—
384	C₂×C₄	—	23	2	no	—
385	C₂×C₄	—	23	2	no	—
386	C₂×C₄	—	23	2	no	—
387	C₂×C₄	—	23	2	no	—
388	C₂×C₄	—	23	2	no	—
389	C₂×C₄	—	46	8	no	—
390	C₂×C₄	—	46	4	no	—
391	C₂×C₄	—	46	4	no	—
392	C₂×C₄	—	92	2	no	—
393	C₂×C₄	—	92	4	no	—
394	C₂×C₄	—	92	2	no	—
395	C₂×C₄	Q₈×D₂₃	1	4	yes	complemented
396	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
397	C₂×C₄	C₂³×D₂₃	1	4	yes	—
398	C₂×C₄	C₂³×D₂₃	1	4	yes	—
399	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
400	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
401	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
402	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
403	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	23	4	no	—
407	C₂²	—	46	2	no	—
408	C₂²	—	46	2	no	—
409	C₂²	C₂×Q₈×D₂₃	1	2	yes	—
410	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	4	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	4	no	—
416	C₄	—	23	4	no	—
417	C₄	—	23	4	no	—
418	C₄	—	46	2	no	—
419	C₄	—	46	2	no	—
420	C₄	—	46	2	no	—
421	C₄	—	46	2	no	—
422	C₄	—	46	2	no	—
423	C₄	C₂×Q₈×D₂₃	1	2	yes	—
424	C₄	C₂×Q₈×D₂₃	1	2	yes	—
425	C₄	#41×D₂₃	1	2	yes	—
426	C₂	—	2	2	no	—
427	C₂	—	46	4	no	—
428	C₂	C₂²×Q₈×D₂₃	1	1	yes	characteristic
429	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
430	C₂	#13093253	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁵
Frattini	C₂²	C₂⁴×D₂₃
Fitting	C₂₃×#533	C₂
prime radical	C₂×#67288	C₂²
hypercenter	#533	D₂₃
hypocenter	C₂₃	Q₈×#41
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ #533

Complements

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

N	H ≅ G/N	type
1. #13093147	C₂	semidirect
2. #13093144	C₂	semidirect
3. #13093142	C₂	semidirect
4. #13093128	C₂	semidirect
5. #13093125	C₂	semidirect
6. #13093123	C₂	semidirect
7. #13093121	C₂	semidirect
8. #13093082	C₂	semidirect
9. #13093080	C₂	semidirect
10. #13092971	C₂	semidirect
11. #13092971	C₂	semidirect
12. #13092970	C₂	semidirect
15. C₂×C₄×Dic₄₆	C₂	semidirect
16. C₄×Q₈×D₂₃	C₂	semidirect
17. C₂₃×#533	C₂	semidirect
92. #67288	Q₈	semidirect
157. C₂×C₄×C₂₃	C₂×Q₈	semidirect
166. C₂²⋊D₂₃	C₂×Q₈	semidirect
176. D₉₂	C₂×Q₈	semidirect
181. C₄×D₂₃	C₂×Q₈	semidirect
186. Dic₄₆	C₂×Q₈	semidirect
187. Dic₄₆	#41	semidirect
223. #533	D₂₃	semidirect
298. C₂₃	Q₈×#41	semidirect
395. C₂×C₄	Q₈×D₂₃	semidirect

Maximal subgroups

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

subgroup	index
#13093147	2
#13093144	2
#13093142	2
#13093128	2
#13093125	2
#13093123	2
#13093121	2
#13093082	2
#13093080	2
#13092971	2
#13092970	2
C₄×#67288	2
#13092885	2
C₂×C₄×Dic₄₆	2
C₄×Q₈×D₂₃	2
C₂₃×#533	2
Q₈×#41	23