Subgroups — D₂₃×#556 #15686939

Order 2944.

1112 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093141	C₂	1	1	yes	maximal, characteristic, complemented
2	#13093140	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093139	C₂	1	2	yes	maximal, complemented
4	#13093138	C₂	1	2	yes	maximal, complemented
5	#13093137	C₂	1	1	yes	maximal, characteristic, complemented
6	#13093136	C₂	1	2	yes	maximal, complemented
7	#13093135	C₂	1	2	yes	maximal, complemented
8	#13093134	C₂	1	4	yes	maximal, complemented
9	C₄⋊Q₈×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#126×D₂₃	C₂	1	4	yes	maximal, complemented
11	#124×D₂₃	C₂	1	2	yes	maximal
12	C₂²⋊Q₈×D₂₃	C₂	1	2	yes	maximal, complemented
13	C₄×Q₈×D₂₃	C₂	1	2	yes	maximal, complemented
14	C₄×Q₈×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×D₄×D₂₃	C₂	1	1	yes	maximal, characteristic
16	#117×D₂₃	C₂	1	2	yes	maximal, complemented
17	C₂₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×Q₈×D₂₃	C₂²	1	1	yes	characteristic
19	C₂×Q₈×D₂₃	C₂²	1	2	yes	—
20	C₂×D₄×D₂₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₂₃	C₂²	1	2	yes	—
22	C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₂₃×#126	C₂²	1	4	yes	complemented
24	C₂₃×#124	C₂²	1	2	yes	—
25	C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
26	C₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
27	C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
28	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
29	C₂₃×#117	C₂²	1	2	yes	complemented
30	#10625118	C₂²	1	2	yes	—
31	#10625117	C₂²	1	2	yes	complemented
32	Q₈×Dic₂₃	C₂²	1	2	yes	complemented
33	Q₈×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
34	#10625115	C₂²	1	2	yes	complemented
35	#10625107	C₂²	1	2	yes	—
36	D₄×Dic₂₃	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	—
38	#10625097	C₂²	1	2	yes	complemented
39	#10625095	C₂²	1	2	yes	complemented
40	#10625069	C₂²	1	4	yes	complemented
41	#10625069	C₂²	1	4	yes	complemented
42	#10625069	C₂²	1	4	yes	complemented
43	#10625068	C₂²	1	2	yes	complemented
44	#10625067	C₂²	1	4	yes	complemented
45	#10625064	C₂²	1	1	yes	characteristic
46	#10625063	C₂²	1	2	yes	complemented
47	#10625063	C₂²	1	2	yes	complemented
48	C₄⋊C₄×D₂₃	C₂²	1	1	yes	characteristic
49	C₄⋊C₄×D₂₃	C₂²	1	2	yes	—
50	C₄⋊C₄×D₂₃	C₂²	1	1	yes	characteristic
51	C₄⋊C₄×D₂₃	C₂²	1	4	yes	—
52	C₄⋊C₄×D₂₃	C₂²	1	2	yes	—
53	C₄⋊C₄×D₂₃	C₂²	1	2	yes	—
54	#10625059	C₂²	1	2	yes	complemented
55	#10625059	C₂²	1	2	yes	complemented
56	#10625058	C₂²	1	2	yes	complemented
57	#10625058	C₂²	1	4	yes	complemented
58	#10625058	C₂²	1	1	yes	characteristic, complemented
59	#10625058	C₂²	1	2	yes	complemented
60	#10625056	C₂²	1	4	yes	—
61	#10625056	C₂²	1	4	yes	—
62	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	—
63	C₂²⋊C₄×D₂₃	C₂²	1	4	yes	—
64	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	—
65	C₂²⋊C₄×D₂₃	C₂²	1	4	yes	—
66	#10625050	C₂²	1	4	yes	complemented
67	#10625050	C₂²	1	4	yes	complemented
68	#10625050	C₂²	1	4	yes	complemented
69	#10625049	C₂²	1	4	yes	complemented
70	#10625048	C₂²	1	4	yes	complemented
71	#10625047	C₂²	1	4	yes	complemented
72	#10625046	C₂²	1	2	yes	—
73	C₄×D₉₂	C₂²	1	1	yes	characteristic
74	#10625043	C₂²	1	4	yes	complemented
75	C₄²×D₂₃	C₂²	1	4	yes	—
76	C₄²×D₂₃	C₂²	1	1	yes	characteristic
77	C₄²×D₂₃	C₂²	1	2	yes	—
78	#10625040	C₂²	1	1	yes	characteristic, complemented
79	C₄×Dic₄₆	C₂²	1	4	yes	complemented
80	C₄×Dic₄₆	C₂²	1	2	yes	complemented
81	C₄×Dic₄₆	C₂²	1	2	yes	complemented
82	C₄×Dic₄₆	C₂²	1	1	yes	characteristic, complemented
83	C₂³×D₂₃	C₂³	1	2	yes	—
84	C₂×Q₈×C₂₃	C₂³	1	2	yes	—
85	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
88	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
89	C₂²×Dic₂₃	C₂³	1	2	yes	—
90	Q₈×D₂₃	—	2	4	no	—
91	Q₈×D₂₃	—	2	8	no	—
92	D₄×D₂₃	—	2	4	no	—
93	C₂×D₉₂	C₂³	1	1	yes	characteristic
94	C₂×C₄×D₂₃	—	2	8	no	—
95	C₂×C₄×D₂₃	C₂³	1	2	yes	—
96	C₂×C₄×D₂₃	C₂³	1	2	yes	—
97	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
98	C₂×C₄×D₂₃	C₂³	1	4	yes	—
99	C₂×C₄×D₂₃	C₂³	1	2	yes	—
100	C₂×C₄×D₂₃	C₂³	1	2	yes	—
101	C₂×C₄×D₂₃	C₂³	1	2	yes	—
102	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
103	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
104	C₂×Dic₄₆	C₂³	1	2	yes	—
105	C₂×Dic₄₆	C₂³	1	2	yes	—
106	C₂×Dic₄₆	C₂³	1	4	yes	—
107	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
108	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
109	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
110	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
111	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
112	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
113	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
114	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
115	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
116	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
117	C₄²×C₂₃	C₂³	1	2	yes	—
118	C₄²×C₂₃	C₂³	1	1	yes	characteristic
119	C₄²×C₂₃	C₂³	1	4	yes	—
120	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
121	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
122	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
123	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
124	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
125	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
126	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
127	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
128	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
129	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
130	C₄⋊Dic₂₃	C₂³	1	4	yes	—
131	C₄⋊Dic₂₃	C₂³	1	2	yes	—
132	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
133	C₄⋊Dic₂₃	C₂³	1	2	yes	—
134	C₄⋊Dic₂₃	C₂³	1	2	yes	—
135	Dic₂₃⋊C₄	C₂³	1	2	yes	—
136	Dic₂₃⋊C₄	C₂³	1	2	yes	—
137	Dic₂₃⋊C₄	C₂³	1	2	yes	—
138	Dic₂₃⋊C₄	C₂³	1	4	yes	—
139	Dic₂₃⋊C₄	C₂³	1	4	yes	—
140	Dic₂₃⋊C₄	C₂³	1	2	yes	—
141	Dic₂₃⋊C₄	C₂³	1	4	yes	—
142	Dic₂₃⋊C₄	C₂³	1	4	yes	—
143	C₄×Dic₂₃	C₂³	1	4	yes	—
144	C₄×Dic₂₃	C₂³	1	2	yes	—
145	C₄×Dic₂₃	C₂³	1	2	yes	—
146	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
147	C₄×Dic₂₃	C₂³	1	4	yes	—
148	C₄×Dic₂₃	C₂³	1	4	yes	—
149	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
150	C₄×Dic₂₃	C₂³	1	2	yes	—
151	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
152	C₂³×C₂₃	C₂⁴	1	2	yes	—
153	C₂²×D₂₃	—	2	4	no	—
154	C₂²×D₂₃	—	2	4	no	—
155	C₂²×D₂₃	—	2	4	no	—
156	C₂²×D₂₃	C₂⁴	1	2	yes	—
157	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
158	Q₈×C₂₃	—	2	4	no	—
159	Q₈×C₂₃	—	2	2	no	—
160	D₄×C₂₃	—	2	2	no	—
161	C₂×C₄×C₂₃	—	2	4	no	—
162	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
163	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
164	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
166	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
167	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
168	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
169	C₂²⋊D₂₃	—	2	4	no	—
170	C₂×Dic₂₃	—	2	4	no	—
171	C₂×Dic₂₃	C₂⁴	1	2	yes	—
172	C₂×Dic₂₃	C₂⁴	1	2	yes	—
173	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
174	C₂×Dic₂₃	C₂⁴	1	4	yes	—
175	C₂×Dic₂₃	C₂⁴	1	2	yes	—
176	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
177	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
178	D₉₂	—	2	2	no	—
179	C₄×D₂₃	—	2	4	no	—
180	C₄×D₂₃	—	2	4	no	—
181	C₄×D₂₃	—	2	8	no	—
182	C₄×D₂₃	—	2	4	no	—
183	C₄×D₂₃	—	2	2	no	—
184	C₄×D₂₃	—	2	4	no	—
185	C₄×D₂₃	—	2	4	no	—
186	C₄×D₂₃	#41	1	4	yes	—
187	C₄×D₂₃	#41	1	4	yes	—
188	Dic₄₆	—	2	4	no	—
189	Dic₄₆	—	2	2	no	—
190	Dic₄₆	—	2	8	no	—
191	Dic₄₆	—	2	4	no	—
192	C₂×#556	—	23	1	no	maximal, Sylow
193	C₂²×C₂₃	—	2	2	no	—
194	C₂²×C₂₃	—	2	2	no	—
195	C₂²×C₂₃	—	2	2	no	—
196	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
197	C₂×D₂₃	—	2	2	no	—
198	C₂×D₂₃	—	2	2	no	—
199	C₂×D₂₃	—	2	2	no	—
200	C₂×D₂₃	—	4	8	no	—
201	C₂×D₂₃	C₂×#41	1	2	yes	—
202	C₂×D₂₃	C₂×#41	1	2	yes	—
203	C₂×D₂₃	2₋¹⁺⁴	1	2	yes	—
204	C₄×C₂₃	—	2	4	no	—
205	C₄×C₂₃	—	2	2	no	—
206	C₄×C₂₃	—	2	2	no	—
207	C₄×C₂₃	—	2	2	no	—
208	C₄×C₂₃	—	2	1	no	—
209	C₄×C₂₃	C₂×#41	1	2	yes	—
210	C₄×C₂₃	C₂×#41	1	2	yes	—
211	Dic₂₃	—	2	4	no	—
212	Dic₂₃	—	2	2	no	—
213	Dic₂₃	—	2	2	no	—
214	Dic₂₃	—	2	2	no	—
215	Dic₂₃	—	2	1	no	—
216	Dic₂₃	C₂×#41	1	2	yes	—
217	Dic₂₃	C₂×#41	1	2	yes	—
218	#556	—	23	1	no	—
219	#556	—	23	4	no	—
220	#556	—	23	2	no	—
221	#556	—	23	2	no	—
222	#556	—	23	2	no	—
223	#556	—	23	1	no	—
224	#556	—	23	1	no	—
225	#556	—	23	2	no	—
226	#556	D₂₃	1	1	yes	characteristic, direct product factor
227	C₂×C₄⋊Q₈	—	23	1	no	—
228	C₂×#126	—	23	4	no	—
229	C₂×#124	—	23	2	no	—
230	C₂×C₂²⋊Q₈	—	23	2	no	—
231	C₂×C₄×Q₈	—	23	2	no	—
232	C₂×C₄×Q₈	—	23	1	no	—
233	C₂×C₄×D₄	—	23	1	no	—
234	C₂×#117	—	23	2	no	—
235	C₂×C₂₃	—	4	2	no	—
236	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
237	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
238	C₂×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
239	D₂₃	—	4	2	no	—
240	D₂₃	#556	1	4	yes	direct product factor
241	C₂²×Q₈	—	23	1	no	—
242	C₂²×Q₈	—	23	2	no	—
243	C₂²×D₄	—	23	1	no	—
244	C₂³×C₄	—	23	2	no	—
245	C₄⋊Q₈	—	23	2	no	—
246	C₄⋊Q₈	—	23	2	no	—
247	C₄⋊Q₈	—	23	2	no	—
248	C₄⋊Q₈	—	23	1	no	—
249	C₄⋊Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
250	#126	—	23	4	no	—
251	#126	—	23	4	no	—
252	#126	—	23	4	no	—
253	#126	—	23	4	no	—
254	#126	—	23	4	no	—
255	#126	—	23	4	no	—
256	#126	—	23	4	no	—
257	#126	C₂×D₂₃	1	4	yes	complemented
258	#124	—	23	2	no	—
259	#124	—	23	2	no	—
260	#124	—	23	4	no	—
261	#124	—	23	4	no	—
262	#124	—	23	2	no	—
263	#124	C₂×D₂₃	1	2	yes	—
264	C₂²⋊Q₈	—	23	2	no	—
265	C₂²⋊Q₈	—	23	2	no	—
266	C₂²⋊Q₈	—	23	4	no	—
267	C₂²⋊Q₈	—	23	2	no	—
268	C₂²⋊Q₈	—	23	4	no	—
269	C₂²⋊Q₈	C₂×D₂₃	1	2	yes	complemented
270	C₄×Q₈	—	23	2	no	—
271	C₄×Q₈	—	23	1	no	—
272	C₄×Q₈	—	23	4	no	—
273	C₄×Q₈	—	23	2	no	—
274	C₄×Q₈	—	23	2	no	—
275	C₄×Q₈	—	23	1	no	—
276	C₄×Q₈	—	23	2	no	—
277	C₄×Q₈	—	23	4	no	—
278	C₄×Q₈	—	23	2	no	—
279	C₄×Q₈	—	23	1	no	—
280	C₄×Q₈	C₂×D₂₃	1	2	yes	complemented
281	C₄×Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
282	C₄×D₄	—	23	1	no	—
283	C₄×D₄	—	23	2	no	—
284	C₄×D₄	—	23	1	no	—
285	C₄×D₄	—	23	2	no	—
286	C₄×D₄	—	23	1	no	—
287	C₄×D₄	C₂×D₂₃	1	1	yes	characteristic
288	#117	—	23	2	no	—
289	#117	—	23	2	no	—
290	#117	—	23	2	no	—
291	#117	—	23	4	no	—
292	#117	—	23	4	no	—
293	#117	C₂×D₂₃	1	2	yes	complemented
294	C₂×C₄⋊C₄	—	23	1	no	—
295	C₂×C₄⋊C₄	—	23	2	no	—
296	C₂×C₄⋊C₄	—	23	1	no	—
297	C₂×C₄⋊C₄	—	23	4	no	—
298	C₂×C₄⋊C₄	—	23	2	no	—
299	C₂×C₄⋊C₄	—	23	2	no	—
300	C₂×C₂²⋊C₄	—	23	4	no	—
301	C₂×C₂²⋊C₄	—	23	2	no	—
302	C₂×C₂²⋊C₄	—	23	4	no	—
303	C₂×C₄²	—	23	4	no	—
304	C₂×C₄²	—	23	1	no	—
305	C₂×C₄²	—	23	2	no	—
306	C₂₃	C₂×#556	1	1	yes	characteristic, complemented, Sylow
307	C₂⁴	—	23	2	no	—
308	C₂×Q₈	—	23	2	no	—
309	C₂×Q₈	—	23	1	no	—
310	C₂×Q₈	—	23	4	no	—
311	C₂×Q₈	—	23	2	no	—
312	C₂×Q₈	—	46	4	no	—
313	C₂×Q₈	—	46	8	no	—
314	C₂×Q₈	C₂²×D₂₃	1	1	yes	characteristic
315	C₂×Q₈	C₂²×D₂₃	1	2	yes	—
316	C₂×D₄	—	23	2	no	—
317	C₂×D₄	—	23	1	no	—
318	C₂×D₄	—	46	4	no	—
319	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
320	C₂²×C₄	—	23	1	no	—
321	C₂²×C₄	—	23	1	no	—
322	C₂²×C₄	—	23	2	no	—
323	C₂²×C₄	—	23	2	no	—
324	C₂²×C₄	—	23	2	no	—
325	C₂²×C₄	—	23	1	no	—
326	C₂²×C₄	—	23	4	no	—
327	C₂²×C₄	—	23	2	no	—
328	C₂²×C₄	—	23	2	no	—
329	C₂²×C₄	—	23	2	no	—
330	C₂²×C₄	—	46	8	no	—
331	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
332	C₄⋊C₄	—	23	2	no	—
333	C₄⋊C₄	—	23	1	no	—
334	C₄⋊C₄	—	23	4	no	—
335	C₄⋊C₄	—	23	2	no	—
336	C₄⋊C₄	—	23	2	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	—	23	2	no	—
342	C₄⋊C₄	—	23	2	no	—
343	C₄⋊C₄	—	23	2	no	—
344	C₄⋊C₄	—	23	4	no	—
345	C₄⋊C₄	—	23	2	no	—
346	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
347	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
348	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
349	C₄⋊C₄	C₂²×D₂₃	1	4	yes	—
350	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
351	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
352	C₂²⋊C₄	—	23	4	no	—
353	C₂²⋊C₄	—	23	2	no	—
354	C₂²⋊C₄	—	23	4	no	—
355	C₂²⋊C₄	—	23	4	no	—
356	C₂²⋊C₄	—	23	4	no	—
357	C₂²⋊C₄	—	23	2	no	—
358	C₂²⋊C₄	—	23	2	no	—
359	C₂²⋊C₄	—	23	4	no	—
360	C₂²⋊C₄	—	23	4	no	—
361	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	—
362	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
363	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	—
364	C₄²	—	23	4	no	—
365	C₄²	—	23	4	no	—
366	C₄²	—	23	4	no	—
367	C₄²	—	23	1	no	—
368	C₄²	—	23	1	no	—
369	C₄²	—	23	1	no	—
370	C₄²	—	23	2	no	—
371	C₄²	—	23	2	no	—
372	C₄²	—	23	2	no	—
373	C₄²	C₂²×D₂₃	1	4	yes	—
374	C₄²	C₂²×D₂₃	1	1	yes	characteristic
375	C₄²	C₂²×D₂₃	1	2	yes	—
376	C₂³	—	23	1	no	—
377	C₂³	—	23	2	no	—
378	C₂³	—	46	4	no	—
379	C₂³	—	46	4	no	—
380	C₂³	—	46	4	no	—
381	C₂³	C₂³×D₂₃	1	2	yes	—
382	Q₈	—	2	2	no	—
383	Q₈	—	2	4	no	—
384	Q₈	—	46	4	no	—
385	Q₈	—	46	8	no	—
386	Q₈	—	46	2	no	—
387	Q₈	—	46	4	no	—
388	D₄	—	2	2	no	—
389	D₄	—	46	4	no	—
390	D₄	—	46	2	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	23	1	no	—
393	C₂×C₄	—	23	1	no	—
394	C₂×C₄	—	23	4	no	—
395	C₂×C₄	—	23	4	no	—
396	C₂×C₄	—	23	2	no	—
397	C₂×C₄	—	23	2	no	—
398	C₂×C₄	—	23	1	no	—
399	C₂×C₄	—	23	4	no	—
400	C₂×C₄	—	23	2	no	—
401	C₂×C₄	—	46	4	no	—
402	C₂×C₄	—	46	4	no	—
403	C₂×C₄	—	46	4	no	—
404	C₂×C₄	—	46	8	no	—
405	C₂×C₄	—	46	4	no	—
406	C₂×C₄	—	46	2	no	—
407	C₂×C₄	—	46	4	no	—
408	C₂×C₄	—	46	4	no	—
409	C₂×C₄	C₂³×D₂₃	1	2	yes	—
410	C₂×C₄	C₂³×D₂₃	1	2	yes	—
411	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
412	C₂×C₄	C₂³×D₂₃	1	4	yes	—
413	C₂×C₄	C₂³×D₂₃	1	2	yes	—
414	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
415	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	23	2	no	—
420	C₂²	—	23	2	no	—
421	C₂²	—	23	2	no	—
422	C₂²	—	46	2	no	—
423	C₂²	—	46	2	no	—
424	C₂²	—	46	2	no	—
425	C₂²	—	92	8	no	—
426	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	2	4	no	—
430	C₄	—	2	2	no	—
431	C₄	—	2	1	no	—
432	C₄	—	23	2	no	—
433	C₄	—	23	2	no	—
434	C₄	—	46	2	no	—
435	C₄	—	46	2	no	—
436	C₄	—	46	4	no	—
437	C₄	—	46	2	no	—
438	C₄	—	46	1	no	—
439	C₄	#41×D₂₃	1	2	yes	—
440	C₄	#41×D₂₃	1	2	yes	—
441	C₂	—	4	2	no	—
442	C₂	—	23	4	no	—
443	C₂	—	92	2	no	—
444	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
445	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
446	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×#556	C₂
prime radical	C₂×D₄×D₂₃	C₂²
hypercenter	#556	D₂₃
hypocenter	C₂₃	C₂×#556
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. #13093141	C₂	semidirect
2. #13093140	C₂	semidirect
3. #13093139	C₂	semidirect
4. #13093138	C₂	semidirect
5. #13093137	C₂	semidirect
6. #13093136	C₂	semidirect
7. #13093135	C₂	semidirect
8. #13093134	C₂	semidirect
9. C₄⋊Q₈×D₂₃	C₂	semidirect
10. #126×D₂₃	C₂	semidirect
12. C₂²⋊Q₈×D₂₃	C₂	semidirect
13. C₄×Q₈×D₂₃	C₂	semidirect
14. C₄×Q₈×D₂₃	C₂	semidirect
16. #117×D₂₃	C₂	semidirect
17. C₂₃×#556	C₂	semidirect
22. C₂₃×C₄⋊Q₈	C₂²	semidirect
23. C₂₃×#126	C₂²	semidirect
25. C₂₃×C₂²⋊Q₈	C₂²	semidirect
26. C₄×Q₈×C₂₃	C₂²	semidirect
27. C₄×Q₈×C₂₃	C₂²	semidirect
29. C₂₃×#117	C₂²	semidirect
31. #10625117	C₂²	semidirect
32. Q₈×Dic₂₃	C₂²	semidirect
33. Q₈×Dic₂₃	C₂²	semidirect
34. #10625115	C₂²	semidirect
38. #10625097	C₂²	semidirect
39. #10625095	C₂²	semidirect
40. #10625069	C₂²	semidirect
41. #10625069	C₂²	semidirect
42. #10625069	C₂²	semidirect
43. #10625068	C₂²	semidirect
44. #10625067	C₂²	semidirect
46. #10625063	C₂²	semidirect
47. #10625063	C₂²	semidirect
54. #10625059	C₂²	semidirect
55. #10625059	C₂²	semidirect
56. #10625058	C₂²	semidirect
57. #10625058	C₂²	semidirect
58. #10625058	C₂²	semidirect
59. #10625058	C₂²	semidirect
66. #10625050	C₂²	semidirect
67. #10625050	C₂²	semidirect
68. #10625050	C₂²	semidirect
69. #10625049	C₂²	semidirect
70. #10625048	C₂²	semidirect
71. #10625047	C₂²	semidirect
74. #10625043	C₂²	semidirect
78. #10625040	C₂²	semidirect
79. C₄×Dic₄₆	C₂²	semidirect
80. C₄×Dic₄₆	C₂²	semidirect
81. C₄×Dic₄₆	C₂²	semidirect
82. C₄×Dic₄₆	C₂²	semidirect
226. #556	D₂₃	direct (N × H)
240. D₂₃	#556	direct (N × H)
249. C₄⋊Q₈	C₂×D₂₃	semidirect
257. #126	C₂×D₂₃	semidirect
269. C₂²⋊Q₈	C₂×D₂₃	semidirect
280. C₄×Q₈	C₂×D₂₃	semidirect
281. C₄×Q₈	C₂×D₂₃	semidirect
293. #117	C₂×D₂₃	semidirect
306. C₂₃	C₂×#556	semidirect

Maximal subgroups

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

subgroup	index
#13093141	2
#13093140	2
#13093139	2
#13093138	2
#13093137	2
#13093136	2
#13093135	2
#13093134	2
C₄⋊Q₈×D₂₃	2
#126×D₂₃	2
#124×D₂₃	2
C₂²⋊Q₈×D₂₃	2
C₄×Q₈×D₂₃	2
C₄×D₄×D₂₃	2
#117×D₂₃	2
C₂₃×#556	2
C₂×#556	23

Subgroups — D23×#556 #15686939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₃×#556 #15686939