Subgroups — #15687008

Order 2944.

1242 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093152	C₂	1	1	yes	maximal, characteristic, complemented
2	#13093128	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093120	C₂	1	2	yes	maximal, complemented
4	#13093115	C₂	1	2	yes	maximal, complemented
5	#13093094	C₂	1	4	yes	maximal, complemented
6	#13093062	C₂	1	2	yes	maximal, complemented
7	#13093058	C₂	1	2	yes	maximal, complemented
8	D₄×D₉₂	C₂	1	1	yes	maximal, characteristic, complemented
9	#13092968	C₂	1	1	yes	maximal, characteristic, complemented
10	#13092953	C₂	1	2	yes	maximal, complemented
11	#13092952	C₂	1	2	yes	maximal, complemented
12	#13092930	C₂	1	4	yes	maximal, complemented
13	C₄×#67292	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#67290	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#10625064	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₂₃	C₂	1	2	yes	maximal, complemented
17	C₂₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#67292	C₂²	1	1	yes	characteristic
19	C₂×#67292	C₂²	1	2	yes	complemented
20	C₂×#67290	C₂²	1	1	yes	characteristic
21	C₂×D₄×D₂₃	C₂²	1	2	yes	—
22	C₂²×D₉₂	C₂²	1	2	yes	—
23	C₂²×C₄×D₂₃	C₂²	1	4	yes	complemented
24	C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₂₃×#125	C₂²	1	2	yes	complemented
26	C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
27	C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
28	C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
29	C₄×D₄×C₂₃	C₂²	1	2	yes	—
30	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
32	#10625118	C₂²	1	2	yes	complemented
33	#10625118	C₂²	1	2	yes	complemented
34	#10625117	C₂²	1	4	yes	complemented
35	Q₈×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
36	D₄×Dic₂₃	C₂²	1	1	yes	characteristic
37	#10625101	C₂²	1	2	yes	—
38	#10625101	C₂²	1	4	yes	complemented
39	C₄×C₂²⋊D₂₃	C₂²	1	4	yes	complemented
40	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
41	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	4	yes	complemented
42	C₂×C₄×Dic₂₃	C₂²	1	2	yes	complemented
43	#10625069	C₂²	1	4	yes	complemented
44	#10625069	C₂²	1	4	yes	complemented
45	#10625068	C₂²	1	2	yes	complemented
46	#10625066	C₂²	1	2	yes	—
47	#10625066	C₂²	1	4	yes	complemented
48	#10625066	C₂²	1	2	yes	complemented
49	#10625066	C₂²	1	2	yes	complemented
50	#10625065	C₂²	1	4	yes	complemented
51	#10625065	C₂²	1	4	yes	complemented
52	#10625065	C₂²	1	4	yes	complemented
53	#10625064	C₂²	1	2	yes	—
54	#10625064	C₂²	1	1	yes	characteristic
55	#10625064	C₂²	1	4	yes	complemented
56	#10625064	C₂²	1	2	yes	complemented
57	#10625064	C₂²	1	2	yes	complemented
58	#10625064	C₂²	1	4	yes	complemented
59	#10625064	C₂²	1	2	yes	complemented
60	#10625064	C₂²	1	2	yes	complemented
61	#10625063	C₂²	1	1	yes	characteristic, complemented
62	#10625063	C₂²	1	2	yes	complemented
63	#10625063	C₂²	1	1	yes	characteristic, complemented
64	#10625063	C₂²	1	4	yes	complemented
65	C₄⋊C₄×D₂₃	C₂²	1	2	yes	complemented
66	#10625061	C₂²	1	2	yes	complemented
67	#10625058	C₂²	1	1	yes	characteristic, complemented
68	#10625057	C₂²	1	4	yes	complemented
69	#10625053	C₂²	1	4	yes	—
70	#10625053	C₂²	1	4	yes	complemented
71	(C₂²⋊D₂₃)⋊C₄	C₂²	1	4	yes	complemented
72	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
73	C₂²⋊C₄×D₂₃	C₂²	1	4	yes	complemented
74	#10625048	C₂²	1	2	yes	complemented
75	#10625046	C₂²	1	2	yes	complemented
76	#10625045	C₂²	1	1	yes	characteristic
77	C₄×D₉₂	C₂²	1	1	yes	characteristic
78	C₄×D₉₂	C₂²	1	2	yes	complemented
79	C₄×D₉₂	C₂²	1	2	yes	complemented
80	C₄²×D₂₃	C₂²	1	2	yes	complemented
81	C₄²×D₂₃	C₂²	1	1	yes	characteristic, complemented
82	C₄×Dic₄₆	C₂²	1	1	yes	characteristic, complemented
83	C₂³×D₂₃	C₂³	1	4	yes	—
84	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
85	C₂×Q₈×C₂₃	C₂³	1	2	yes	—
86	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
88	C₂²×C₄×C₂₃	C₂³	1	4	yes	—
89	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
90	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
91	C₂²×Dic₂₃	C₂³	1	2	yes	—
92	C₂²×Dic₂₃	C₂³	1	2	yes	—
93	#67292	—	2	4	no	—
94	#67292	—	4	4	no	—
95	#67290	—	2	4	no	—
96	D₄×D₂₃	—	2	8	no	—
97	C₂×D₉₂	—	2	8	no	—
98	C₂×D₉₂	C₂³	1	2	yes	—
99	C₂×D₉₂	C₂³	1	2	yes	—
100	C₂×D₉₂	C₂³	1	2	yes	—
101	C₂×D₉₂	C₂³	1	4	yes	—
102	C₂×D₉₂	C₂³	1	2	yes	—
103	C₂×D₉₂	C₂³	1	4	yes	—
104	C₂×D₉₂	C₂³	1	1	yes	characteristic
105	C₂×C₄×D₂₃	—	4	8	no	—
106	C₂×C₄×D₂₃	C₂³	1	2	yes	—
107	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₂₃	C₂³	1	2	yes	—
109	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
110	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
111	C₂×C₄×D₂₃	C₂³	1	2	yes	—
112	C₂×C₄×D₂₃	C₂³	1	4	yes	—
113	C₂×C₄×D₂₃	C₂³	1	4	yes	—
114	C₂×C₄×D₂₃	C₂³	1	4	yes	—
115	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
117	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
118	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
119	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
120	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
121	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
122	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
123	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
124	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
125	C₄²×C₂₃	C₂³	1	1	yes	characteristic
126	C₄²×C₂₃	C₂³	1	2	yes	—
127	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
128	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
129	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
130	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
131	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
132	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
133	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
134	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
135	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
136	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
137	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
138	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
139	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
140	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
141	C₄⋊Dic₂₃	C₂³	1	2	yes	—
142	C₄⋊Dic₂₃	C₂³	1	4	yes	—
143	Dic₂₃⋊C₄	C₂³	1	2	yes	—
144	Dic₂₃⋊C₄	C₂³	1	2	yes	—
145	Dic₂₃⋊C₄	C₂³	1	4	yes	—
146	C₄×Dic₂₃	C₂³	1	2	yes	—
147	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
148	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
149	C₄×Dic₂₃	C₂³	1	2	yes	—
150	C₄×Dic₂₃	C₂³	1	2	yes	—
151	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
152	C₄×Dic₂₃	C₂³	1	2	yes	—
153	C₄×Dic₂₃	C₂³	1	2	yes	—
154	C₂³×C₂₃	C₂⁴	1	2	yes	—
155	C₂²×D₂₃	—	2	8	no	—
156	C₂²×D₂₃	—	2	8	no	—
157	C₂²×D₂₃	—	4	4	no	—
158	C₂²×D₂₃	C₂⁴	1	4	yes	—
159	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
160	C₂²×D₂₃	C₂⁴	1	2	yes	—
161	Q₈×C₂₃	—	2	2	no	—
162	Q₈×C₂₃	—	4	2	no	—
163	D₄×C₂₃	#41	1	4	yes	complemented
164	C₂×C₄×C₂₃	—	2	4	no	—
165	C₂×C₄×C₂₃	—	4	4	no	—
166	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
167	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
168	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
169	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
170	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
171	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
173	C₂²⋊D₂₃	—	2	8	no	—
174	C₂²⋊D₂₃	—	2	4	no	—
175	C₂×Dic₂₃	—	2	4	no	—
176	C₂×Dic₂₃	—	2	4	no	—
177	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
178	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
179	C₂×Dic₂₃	C₂⁴	1	2	yes	—
180	C₂×Dic₂₃	C₂⁴	1	2	yes	—
181	C₂×Dic₂₃	C₂⁴	1	2	yes	—
182	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
183	D₉₂	—	2	8	no	—
184	D₉₂	—	2	4	no	—
185	D₉₂	—	2	4	no	—
186	D₉₂	—	2	4	no	—
187	D₉₂	—	4	4	no	—
188	D₉₂	—	4	2	no	—
189	D₉₂	#41	1	4	yes	complemented
190	C₄×D₂₃	—	2	4	no	—
191	C₄×D₂₃	—	2	4	no	—
192	C₄×D₂₃	—	2	2	no	—
193	C₄×D₂₃	—	2	2	no	—
194	C₄×D₂₃	—	2	4	no	—
195	C₄×D₂₃	—	2	8	no	—
196	C₄×D₂₃	—	2	2	no	—
197	C₄×D₂₃	—	4	4	no	—
198	C₄×D₂₃	—	4	4	no	—
199	Dic₄₆	—	2	2	no	—
200	#3481	—	23	1	no	maximal, Sylow
201	C₂²×C₂₃	—	2	2	no	—
202	C₂²×C₂₃	—	2	2	no	—
203	C₂²×C₂₃	C₂×#41	1	4	yes	—
204	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
205	C₂×D₂₃	—	2	2	no	—
206	C₂×D₂₃	—	2	2	no	—
207	C₂×D₂₃	—	2	1	no	—
208	C₂×D₂₃	—	2	1	no	—
209	C₂×D₂₃	—	2	4	no	—
210	C₂×D₂₃	—	2	4	no	—
211	C₂×D₂₃	—	2	4	no	—
212	C₂×D₂₃	—	2	1	no	—
213	C₂×D₂₃	—	4	16	no	—
214	C₂×D₂₃	C₂×#41	1	4	yes	—
215	C₄×C₂₃	—	2	2	no	—
216	C₄×C₂₃	—	2	2	no	—
217	C₄×C₂₃	—	2	2	no	—
218	C₄×C₂₃	—	2	4	no	—
219	C₄×C₂₃	—	2	1	no	—
220	C₄×C₂₃	C₂×#41	1	2	yes	—
221	C₄×C₂₃	C₂×#41	1	2	yes	—
222	Dic₂₃	—	2	2	no	—
223	Dic₂₃	—	2	1	no	—
224	Dic₂₃	—	2	1	no	—
225	Dic₂₃	—	2	2	no	—
226	Dic₂₃	—	2	2	no	—
227	Dic₂₃	H(5,𝔽₂)	1	2	yes	—
228	#559	—	23	1	no	—
229	#554	—	23	1	no	—
230	#554	D₂₃	1	1	yes	characteristic, complemented
231	#553	—	23	2	no	—
232	#553	—	23	2	no	—
233	#551	—	23	4	no	—
234	#546	—	23	2	no	—
235	#546	—	23	2	no	—
236	D₄²	—	23	1	no	—
237	#532	—	23	1	no	—
238	#529	—	23	2	no	—
239	#529	—	23	2	no	—
240	#525	—	23	4	no	—
241	C₄×#41	—	23	1	no	—
242	C₄×#41	—	23	1	no	—
243	C₂×C₄×D₄	—	23	2	no	—
244	C₂×C₄×D₄	—	23	2	no	—
245	C₂×C₂₃	—	2	4	no	—
246	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
247	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
248	C₂×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
249	D₂₃	—	2	4	no	—
250	D₂₃	—	4	1	no	—
251	D₂₃	—	4	4	no	—
252	C₂×#41	—	23	1	no	—
253	C₂×#41	—	23	2	no	—
254	C₂×#41	—	23	1	no	—
255	C₂²×D₄	—	23	2	no	—
256	C₂²×D₄	—	23	2	no	—
257	C₂³×C₄	—	23	4	no	—
258	C₄⋊Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
259	#127	—	23	1	no	—
260	#126	—	23	4	no	—
261	#126	—	23	4	no	—
262	#125	—	23	2	no	—
263	#125	C₂×D₂₃	1	2	yes	complemented
264	#124	—	23	2	no	—
265	#124	—	23	2	no	—
266	#124	—	23	2	no	—
267	#123	—	23	4	no	—
268	#123	—	23	4	no	—
269	#123	—	23	4	no	—
270	#123	—	23	4	no	—
271	C₂²⋊Q₈	—	23	4	no	—
272	C₂²⋊Q₈	—	23	2	no	—
273	C₂²⋊Q₈	C₂×D₂₃	1	4	yes	complemented
274	C₂²⋊Q₈	C₂×D₂₃	1	2	yes	complemented
275	#121	—	23	4	no	—
276	#121	—	23	2	no	—
277	#121	—	23	4	no	—
278	#121	—	23	2	no	—
279	#121	—	23	2	no	—
280	#121	—	23	2	no	—
281	#120	—	23	4	no	—
282	#120	—	23	4	no	—
283	C₄×Q₈	—	23	1	no	—
284	C₄×Q₈	—	23	1	no	—
285	C₄×Q₈	—	23	1	no	—
286	C₄×Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
287	C₄×D₄	—	23	1	no	—
288	C₄×D₄	—	23	4	no	—
289	C₄×D₄	—	23	2	no	—
290	C₄×D₄	—	23	1	no	—
291	C₄×D₄	—	23	4	no	—
292	C₄×D₄	—	23	2	no	—
293	C₄×D₄	—	23	2	no	—
294	C₄×D₄	—	23	2	no	—
295	C₄×D₄	—	23	4	no	—
296	C₄×D₄	—	23	2	no	—
297	C₄×D₄	—	23	2	no	—
298	C₄×D₄	—	23	4	no	—
299	C₄×D₄	—	23	2	no	—
300	C₄×D₄	—	23	2	no	—
301	C₄×D₄	—	23	1	no	—
302	C₄×D₄	—	23	2	no	—
303	C₄×D₄	C₂×D₂₃	1	2	yes	—
304	C₄×D₄	C₂×D₂₃	1	1	yes	characteristic
305	#117	—	23	2	no	—
306	#117	—	23	1	no	—
307	#117	—	23	1	no	—
308	#117	—	23	4	no	—
309	#117	—	23	2	no	—
310	C₂×C₄⋊C₄	—	23	2	no	—
311	C₂×C₄⋊C₄	C₂×D₂₃	1	2	yes	complemented
312	C₂×C₂²⋊C₄	—	23	4	no	—
313	C₂×C₂²⋊C₄	—	23	4	no	—
314	C₂×C₄²	—	23	2	no	—
315	C₂×C₄²	—	23	2	no	—
316	C₂×C₄²	—	23	1	no	—
317	C₂₃	#3481	1	1	yes	characteristic, complemented, Sylow
318	C₂⁴	—	23	4	no	—
319	#41	—	46	4	no	—
320	#41	—	46	4	no	—
321	#41	—	92	4	no	—
322	C₂×Q₈	—	23	1	no	—
323	C₂×Q₈	C₂²×D₂₃	1	1	yes	characteristic
324	C₂×Q₈	C₂²×D₂₃	1	2	yes	—
325	C₂×D₄	—	23	2	no	—
326	C₂×D₄	—	23	4	no	—
327	C₂×D₄	—	23	1	no	—
328	C₂×D₄	—	23	2	no	—
329	C₂×D₄	—	23	4	no	—
330	C₂×D₄	—	23	2	no	—
331	C₂×D₄	—	23	2	no	—
332	C₂×D₄	—	23	2	no	—
333	C₂×D₄	—	23	4	no	—
334	C₂×D₄	—	46	8	no	—
335	C₂×D₄	—	46	8	no	—
336	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
337	C₂²×C₄	—	23	2	no	—
338	C₂²×C₄	—	23	2	no	—
339	C₂²×C₄	—	23	2	no	—
340	C₂²×C₄	—	23	2	no	—
341	C₂²×C₄	—	23	1	no	—
342	C₂²×C₄	—	23	1	no	—
343	C₂²×C₄	—	23	2	no	—
344	C₂²×C₄	—	23	1	no	—
345	C₂²×C₄	—	23	4	no	—
346	C₂²×C₄	—	23	4	no	—
347	C₂²×C₄	—	23	4	no	—
348	C₂²×C₄	—	92	8	no	—
349	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
350	C₂²×C₄	C₂²×D₂₃	1	4	yes	—
351	C₄⋊C₄	—	23	1	no	—
352	C₄⋊C₄	—	23	4	no	—
353	C₄⋊C₄	—	23	1	no	—
354	C₄⋊C₄	—	23	2	no	—
355	C₄⋊C₄	—	23	2	no	—
356	C₄⋊C₄	—	23	2	no	—
357	C₄⋊C₄	—	23	4	no	—
358	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
359	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
360	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
361	C₄⋊C₄	C₂²×D₂₃	1	4	yes	—
362	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
363	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
364	C₄⋊C₄	C₂²×D₂₃	1	4	yes	—
365	C₂²⋊C₄	—	23	2	no	—
366	C₂²⋊C₄	—	23	2	no	—
367	C₂²⋊C₄	—	23	4	no	—
368	C₂²⋊C₄	—	23	4	no	—
369	C₂²⋊C₄	—	23	4	no	—
370	C₂²⋊C₄	—	23	4	no	—
371	C₂²⋊C₄	—	23	4	no	—
372	C₂²⋊C₄	—	23	2	no	—
373	C₂²⋊C₄	—	23	2	no	—
374	C₂²⋊C₄	—	23	2	no	—
375	C₂²⋊C₄	—	23	4	no	—
376	C₂²⋊C₄	—	23	4	no	—
377	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	—
378	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
379	C₄²	—	23	1	no	—
380	C₄²	—	23	1	no	—
381	C₄²	—	23	1	no	—
382	C₄²	—	23	2	no	—
383	C₄²	—	23	2	no	—
384	C₄²	—	23	2	no	—
385	C₄²	—	23	2	no	—
386	C₄²	—	23	2	no	—
387	C₄²	C₂²×D₂₃	1	2	yes	—
388	C₄²	C₂²×D₂₃	1	1	yes	characteristic
389	C₂³	—	23	2	no	—
390	C₂³	—	23	4	no	—
391	C₂³	—	23	1	no	—
392	C₂³	—	46	8	no	—
393	C₂³	—	46	8	no	—
394	C₂³	—	92	4	no	—
395	C₂³	C₂³×D₂₃	1	2	yes	—
396	Q₈	—	2	2	no	—
397	Q₈	—	4	2	no	—
398	Q₈	—	46	2	no	—
399	D₄	—	23	4	no	—
400	D₄	—	46	8	no	—
401	D₄	—	46	4	no	—
402	D₄	—	46	8	no	—
403	D₄	—	46	4	no	—
404	D₄	—	46	4	no	—
405	D₄	—	46	4	no	—
406	D₄	—	92	4	no	—
407	D₄	—	92	2	no	—
408	D₄	#67292	1	4	yes	complemented
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	23	1	no	—
412	C₂×C₄	—	23	1	no	—
413	C₂×C₄	—	23	1	no	—
414	C₂×C₄	—	23	2	no	—
415	C₂×C₄	—	23	2	no	—
416	C₂×C₄	—	23	2	no	—
417	C₂×C₄	—	46	4	no	—
418	C₂×C₄	—	46	8	no	—
419	C₂×C₄	—	46	2	no	—
420	C₂×C₄	—	46	4	no	—
421	C₂×C₄	—	46	4	no	—
422	C₂×C₄	—	46	4	no	—
423	C₂×C₄	—	46	4	no	—
424	C₂×C₄	—	46	2	no	—
425	C₂×C₄	—	46	2	no	—
426	C₂×C₄	—	92	4	no	—
427	C₂×C₄	—	92	4	no	—
428	C₂×C₄	C₂³×D₂₃	1	2	yes	—
429	C₂×C₄	C₂³×D₂₃	1	2	yes	—
430	C₂×C₄	C₂³×D₂₃	1	2	yes	—
431	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
432	C₂×C₄	C₂³×D₂₃	1	4	yes	—
433	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
434	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	23	4	no	—
438	C₂²	—	46	2	no	—
439	C₂²	—	46	2	no	—
440	C₂²	—	46	1	no	—
441	C₂²	—	46	4	no	—
442	C₂²	—	46	1	no	—
443	C₂²	—	46	4	no	—
444	C₂²	—	46	4	no	—
445	C₂²	—	46	1	no	—
446	C₂²	—	92	16	no	—
447	C₂²	C₂×#67292	1	4	yes	—
448	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	2	4	no	—
453	C₄	—	2	1	no	—
454	C₄	—	23	2	no	—
455	C₄	—	46	1	no	—
456	C₄	—	46	1	no	—
457	C₄	—	46	2	no	—
458	C₄	—	46	2	no	—
459	C₄	—	46	2	no	—
460	C₄	C₂×#67292	1	2	yes	—
461	C₄	#41×D₂₃	1	2	yes	—
462	C₂	—	2	4	no	—
463	C₂	—	46	4	no	—
464	C₂	—	92	4	no	—
465	C₂	—	92	1	no	—
466	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
467	C₂	C₂²×#67292	1	1	yes	characteristic
468	C₂	H(5,𝔽₂)×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁵
Fitting	C₂₃×#554	C₂
hypercenter	#554	D₂₃
hypocenter	C₂₃	#3481
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #13093152	C₂	semidirect
2. #13093128	C₂	semidirect
3. #13093120	C₂	semidirect
4. #13093115	C₂	semidirect
5. #13093094	C₂	semidirect
6. #13093062	C₂	semidirect
7. #13093058	C₂	semidirect
8. D₄×D₉₂	C₂	semidirect
9. #13092968	C₂	semidirect
10. #13092953	C₂	semidirect
11. #13092952	C₂	semidirect
12. #13092930	C₂	semidirect
13. C₄×#67292	C₂	semidirect
14. C₄×#67290	C₂	semidirect
15. C₂×#10625064	C₂	semidirect
16. C₄×D₄×D₂₃	C₂	semidirect
17. C₂₃×#554	C₂	semidirect
19. C₂×#67292	C₂²	semidirect
23. C₂²×C₄×D₂₃	C₂²	semidirect
24. C₂₃×C₄⋊Q₈	C₂²	semidirect
25. C₂₃×#125	C₂²	semidirect
26. C₂₃×C₂²⋊Q₈	C₂²	semidirect
27. C₂₃×C₂²⋊Q₈	C₂²	semidirect
28. C₄×Q₈×C₂₃	C₂²	semidirect
31. C₂×C₄⋊C₄×C₂₃	C₂²	semidirect
32. #10625118	C₂²	semidirect
33. #10625118	C₂²	semidirect
34. #10625117	C₂²	semidirect
35. Q₈×Dic₂₃	C₂²	semidirect
38. #10625101	C₂²	semidirect
39. C₄×C₂²⋊D₂₃	C₂²	semidirect
40. C₄×C₂²⋊D₂₃	C₂²	semidirect
41. C₂×(C₂×D₂₃)⋊C₄	C₂²	semidirect
42. C₂×C₄×Dic₂₃	C₂²	semidirect
43. #10625069	C₂²	semidirect
44. #10625069	C₂²	semidirect
45. #10625068	C₂²	semidirect
47. #10625066	C₂²	semidirect
48. #10625066	C₂²	semidirect
49. #10625066	C₂²	semidirect
50. #10625065	C₂²	semidirect
51. #10625065	C₂²	semidirect
52. #10625065	C₂²	semidirect
55. #10625064	C₂²	semidirect
56. #10625064	C₂²	semidirect
57. #10625064	C₂²	semidirect
58. #10625064	C₂²	semidirect
59. #10625064	C₂²	semidirect
60. #10625064	C₂²	semidirect
61. #10625063	C₂²	semidirect
62. #10625063	C₂²	semidirect
63. #10625063	C₂²	semidirect
64. #10625063	C₂²	semidirect
65. C₄⋊C₄×D₂₃	C₂²	semidirect
66. #10625061	C₂²	semidirect
67. #10625058	C₂²	semidirect
68. #10625057	C₂²	semidirect
70. #10625053	C₂²	semidirect
71. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
72. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
73. C₂²⋊C₄×D₂₃	C₂²	semidirect
74. #10625048	C₂²	semidirect
75. #10625046	C₂²	semidirect
78. C₄×D₉₂	C₂²	semidirect
79. C₄×D₉₂	C₂²	semidirect
80. C₄²×D₂₃	C₂²	semidirect
81. C₄²×D₂₃	C₂²	semidirect
82. C₄×Dic₄₆	C₂²	semidirect
163. D₄×C₂₃	#41	semidirect
189. D₉₂	#41	semidirect
230. #554	D₂₃	semidirect
258. C₄⋊Q₈	C₂×D₂₃	semidirect
263. #125	C₂×D₂₃	semidirect
273. C₂²⋊Q₈	C₂×D₂₃	semidirect
274. C₂²⋊Q₈	C₂×D₂₃	semidirect
286. C₄×Q₈	C₂×D₂₃	semidirect
311. C₂×C₄⋊C₄	C₂×D₂₃	semidirect
317. C₂₃	#3481	semidirect
408. D₄	#67292	semidirect

Maximal subgroups

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

subgroup	index
#13093152	2
#13093128	2
#13093120	2
#13093115	2
#13093094	2
#13093062	2
#13093058	2
D₄×D₉₂	2
#13092968	2
#13092953	2
#13092952	2
#13092930	2
C₄×#67292	2
C₄×#67290	2
C₂×#10625064	2
C₄×D₄×D₂₃	2
C₂₃×#554	2
#3481	23