Subgroups — #15686960

Order 2944.

1132 conjugacy classes of subgroups.

The subgroup lattice has 460 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	#13093132	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093124	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093119	C₂	1	2	yes	maximal, complemented
5	#13093102	C₂	1	2	yes	maximal, complemented
6	#13093101	C₂	1	2	yes	maximal, complemented
7	#13093090	C₂	1	4	yes	maximal, complemented
8	#13093055	C₂	1	2	yes	maximal, complemented
9	#13092972	C₂	1	1	yes	maximal, characteristic, complemented
10	#13092953	C₂	1	2	yes	maximal, complemented
11	#13092944	C₂	1	4	yes	maximal, complemented
12	#13092927	C₂	1	2	yes	maximal, complemented
13	#41×Dic₂₃	C₂	1	2	yes	maximal, complemented
14	C₄×#67290	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×D₄×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10625063	C₂	1	2	yes	maximal, complemented
17	C₂₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#41×C₂₃	C₂²	1	2	yes	—
19	C₂×#67290	C₂²	1	1	yes	characteristic
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×#123	C₂²	1	4	yes	complemented
24	C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
25	C₂₃×#121	C₂²	1	2	yes	complemented
26	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
29	#10625118	C₂²	1	2	yes	—
30	#10625117	C₂²	1	2	yes	—
31	Q₈×Dic₂₃	C₂²	1	2	yes	complemented
32	Q₈×Dic₂₃	C₂²	1	2	yes	complemented
33	#10625110	C₂²	1	4	yes	—
34	#10625109	C₂²	1	2	yes	complemented
35	#10625108	C₂²	1	4	yes	—
36	D₄×Dic₂₃	C₂²	1	2	yes	—
37	D₄×Dic₂₃	C₂²	1	1	yes	characteristic
38	D₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
39	D₄×Dic₂₃	C₂²	1	4	yes	complemented
40	D₄×Dic₂₃	C₂²	1	4	yes	complemented
41	#10625101	C₂²	1	2	yes	—
42	#10625100	C₂²	1	4	yes	—
43	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	—
44	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	—
45	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	4	yes	—
46	#10625097	C₂²	1	2	yes	complemented
47	#10625097	C₂²	1	4	yes	complemented
48	C₂×C₄⋊Dic₂₃	C₂²	1	2	yes	complemented
49	#10625095	C₂²	1	2	yes	complemented
50	C₂×C₄×Dic₂₃	C₂²	1	4	yes	complemented
51	C₂×C₄×Dic₂₃	C₂²	1	2	yes	complemented
52	#10625069	C₂²	1	4	yes	complemented
53	#10625069	C₂²	1	4	yes	complemented
54	#10625068	C₂²	1	2	yes	—
55	#10625068	C₂²	1	2	yes	complemented
56	#10625064	C₂²	1	1	yes	characteristic
57	#10625063	C₂²	1	1	yes	characteristic
58	#10625063	C₂²	1	2	yes	—
59	#10625063	C₂²	1	4	yes	—
60	#10625063	C₂²	1	2	yes	complemented
61	#10625063	C₂²	1	2	yes	complemented
62	#10625063	C₂²	1	4	yes	complemented
63	C₄⋊C₄×D₂₃	C₂²	1	1	yes	characteristic
64	#10625061	C₂²	1	2	yes	complemented
65	#10625061	C₂²	1	2	yes	complemented
66	#10625060	C₂²	1	4	yes	complemented
67	#10625058	C₂²	1	1	yes	characteristic, complemented
68	#10625058	C₂²	1	2	yes	complemented
69	#10625057	C₂²	1	4	yes	complemented
70	#10625056	C₂²	1	4	yes	complemented
71	#10625054	C₂²	1	4	yes	—
72	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	—
73	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	—
74	(C₂²⋊D₂₃)⋊C₄	C₂²	1	4	yes	complemented
75	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	—
76	#10625050	C₂²	1	4	yes	complemented
77	#10625049	C₂²	1	4	yes	complemented
78	#10625048	C₂²	1	2	yes	complemented
79	C₄×D₉₂	C₂²	1	1	yes	characteristic
80	C₄²×D₂₃	C₂²	1	1	yes	characteristic
81	#10625040	C₂²	1	1	yes	characteristic, complemented
82	C₄×Dic₄₆	C₂²	1	1	yes	characteristic, complemented
83	C₂³×D₂₃	C₂³	1	2	yes	—
84	#41×C₂₃	—	2	8	no	—
85	C₂×Q₈×C₂₃	C₂³	1	2	yes	—
86	C₂×D₄×C₂₃	C₂³	1	4	yes	—
87	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
88	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₂₃	C₂³	1	4	yes	—
90	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
91	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
93	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
94	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
95	C₂²×Dic₂₃	C₂³	1	2	yes	—
96	C₂²×Dic₂₃	C₂³	1	2	yes	—
97	C₂²×Dic₂₃	C₂³	1	4	yes	—
98	C₂²×Dic₂₃	C₂³	1	2	yes	—
99	#67290	—	2	4	no	—
100	D₄×D₂₃	—	2	4	no	—
101	C₂×D₉₂	C₂³	1	1	yes	characteristic
102	C₂×C₄×D₂₃	—	2	8	no	—
103	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
104	C₂×C₄×D₂₃	C₂³	1	2	yes	—
105	C₂×C₄×D₂₃	C₂³	1	2	yes	—
106	C₂×C₄×D₂₃	C₂³	1	2	yes	—
107	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
109	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
110	C₂×Dic₄₆	C₂³	1	2	yes	—
111	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
112	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
113	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
114	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
115	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
116	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
117	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
118	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
119	C₄²×C₂₃	C₂³	1	1	yes	characteristic
120	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
121	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
122	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
123	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
124	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
125	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
126	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
127	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
128	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
129	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
130	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
131	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
132	C₄⋊Dic₂₃	C₂³	1	2	yes	—
133	C₄⋊Dic₂₃	C₂³	1	2	yes	—
134	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
135	C₄⋊Dic₂₃	C₂³	1	4	yes	—
136	C₄⋊Dic₂₃	C₂³	1	4	yes	—
137	C₄⋊Dic₂₃	C₂³	1	4	yes	—
138	Dic₂₃⋊C₄	C₂³	1	2	yes	—
139	Dic₂₃⋊C₄	C₂³	1	2	yes	—
140	Dic₂₃⋊C₄	C₂³	1	4	yes	—
141	Dic₂₃⋊C₄	C₂³	1	2	yes	—
142	Dic₂₃⋊C₄	C₂³	1	4	yes	—
143	C₄×Dic₂₃	C₂³	1	2	yes	—
144	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
145	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
146	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
147	C₄×Dic₂₃	C₂³	1	2	yes	—
148	C₄×Dic₂₃	C₂³	1	4	yes	—
149	C₄×Dic₂₃	C₂³	1	2	yes	—
150	C₄×Dic₂₃	C₂³	1	4	yes	—
151	C₄×Dic₂₃	C₂³	1	4	yes	—
152	C₂³×C₂₃	C₂⁴	1	2	yes	—
153	C₂³×C₂₃	C₂⁴	1	2	yes	—
154	C₂²×D₂₃	—	2	4	no	—
155	C₂²×D₂₃	—	2	4	no	—
156	C₂²×D₂₃	—	4	2	no	—
157	C₂²×D₂₃	C₂⁴	1	2	yes	—
158	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
159	Q₈×C₂₃	—	2	4	no	—
160	D₄×C₂₃	—	2	8	no	—
161	D₄×C₂₃	—	2	2	no	—
162	D₄×C₂₃	#41	1	4	yes	complemented
163	C₂×C₄×C₂₃	—	2	8	no	—
164	C₂×C₄×C₂₃	—	2	4	no	—
165	C₂×C₄×C₂₃	—	2	4	no	—
166	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
167	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
168	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
169	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
170	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
172	C₂²⋊D₂₃	—	2	4	no	—
173	C₂²⋊D₂₃	—	2	4	no	—
174	C₂²⋊D₂₃	—	4	4	no	—
175	C₂×Dic₂₃	—	2	4	no	—
176	C₂×Dic₂₃	—	2	4	no	—
177	C₂×Dic₂₃	—	4	4	no	—
178	C₂×Dic₂₃	—	4	2	no	—
179	C₂×Dic₂₃	C₂⁴	1	2	yes	—
180	C₂×Dic₂₃	C₂⁴	1	2	yes	—
181	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
182	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
183	C₂×Dic₂₃	C₂⁴	1	2	yes	—
184	C₂×Dic₂₃	C₂⁴	1	4	yes	—
185	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
186	D₉₂	—	2	2	no	—
187	C₄×D₂₃	—	2	4	no	—
188	C₄×D₂₃	—	2	4	no	—
189	C₄×D₂₃	—	2	2	no	—
190	C₄×D₂₃	—	2	4	no	—
191	C₄×D₂₃	—	4	1	no	—
192	C₄×D₂₃	#41	1	4	yes	complemented
193	Dic₄₆	—	2	2	no	—
194	Dic₄₆	—	4	2	no	—
195	#3475	—	23	1	no	maximal, Sylow
196	C₂²×C₂₃	—	2	2	no	—
197	C₂²×C₂₃	—	2	2	no	—
198	C₂²×C₂₃	—	2	2	no	—
199	C₂²×C₂₃	—	2	2	no	—
200	C₂²×C₂₃	—	2	2	no	—
201	C₂²×C₂₃	C₂×#41	1	4	yes	—
202	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
203	C₂×D₂₃	—	2	1	no	—
204	C₂×D₂₃	—	2	1	no	—
205	C₂×D₂₃	—	2	2	no	—
206	C₂×D₂₃	—	2	2	no	—
207	C₂×D₂₃	—	2	2	no	—
208	C₂×D₂₃	—	4	8	no	—
209	C₂×D₂₃	C₂×#41	1	2	yes	—
210	C₄×C₂₃	—	2	2	no	—
211	C₄×C₂₃	—	2	2	no	—
212	C₄×C₂₃	—	2	4	no	—
213	C₄×C₂₃	—	2	1	no	—
214	C₄×C₂₃	C₂×#41	1	2	yes	—
215	C₄×C₂₃	C₂×#41	1	2	yes	—
216	Dic₂₃	—	2	2	no	—
217	Dic₂₃	—	2	2	no	—
218	Dic₂₃	—	2	1	no	—
219	Dic₂₃	—	2	4	no	—
220	Dic₂₃	—	2	1	no	—
221	Dic₂₃	—	2	2	no	—
222	Dic₂₃	C₂×#41	1	2	yes	—
223	#556	—	23	1	no	—
224	#555	—	23	1	no	—
225	#554	—	23	1	no	—
226	#553	—	23	2	no	—
227	#552	—	23	2	no	—
228	#552	—	23	2	no	—
229	#551	—	23	4	no	—
230	#547	D₂₃	1	1	yes	characteristic, complemented
231	#546	—	23	2	no	—
232	#533	—	23	1	no	—
233	#529	—	23	4	no	—
234	#529	—	23	2	no	—
235	#525	—	23	2	no	—
236	C₄×#41	—	23	2	no	—
237	C₄×#41	—	23	1	no	—
238	C₂×C₄×D₄	—	23	1	no	—
239	C₂×#117	—	23	2	no	—
240	C₂×C₂₃	—	2	4	no	—
241	C₂×C₂₃	—	4	2	no	—
242	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
243	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
244	C₂×C₂₃	#585	1	1	yes	characteristic
245	D₂₃	—	2	2	no	—
246	D₂₃	—	4	2	no	—
247	C₂×#41	—	23	1	no	—
248	C₂×#41	C₂×D₂₃	1	2	yes	—
249	C₂²×D₄	—	23	1	no	—
250	C₂³×C₄	—	23	2	no	—
251	C₄⋊Q₈	—	23	1	no	—
252	C₄⋊Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
253	#126	—	23	4	no	—
254	#126	—	23	4	no	—
255	#126	—	23	4	no	—
256	#125	—	23	4	no	—
257	#125	—	23	2	no	—
258	#125	—	23	2	no	—
259	#124	—	23	2	no	—
260	#124	—	23	4	no	—
261	#123	—	23	4	no	—
262	#123	—	23	4	no	—
263	#123	—	23	4	no	—
264	#123	C₂×D₂₃	1	4	yes	complemented
265	C₂²⋊Q₈	—	23	2	no	—
266	C₂²⋊Q₈	—	23	2	no	—
267	C₂²⋊Q₈	—	23	2	no	—
268	C₂²⋊Q₈	—	23	2	no	—
269	C₂²⋊Q₈	—	23	4	no	—
270	C₂²⋊Q₈	C₂×D₂₃	1	2	yes	complemented
271	#121	—	23	2	no	—
272	#121	—	23	4	no	—
273	#121	—	23	2	no	—
274	#121	C₂×D₂₃	1	2	yes	complemented
275	#120	—	23	4	no	—
276	C₄×Q₈	—	23	2	no	—
277	C₄×Q₈	—	23	2	no	—
278	C₄×Q₈	—	23	1	no	—
279	C₄×Q₈	—	23	2	no	—
280	C₄×Q₈	—	23	1	no	—
281	C₄×D₄	—	23	1	no	—
282	C₄×D₄	—	23	4	no	—
283	C₄×D₄	—	23	2	no	—
284	C₄×D₄	—	23	4	no	—
285	C₄×D₄	—	23	1	no	—
286	C₄×D₄	—	23	2	no	—
287	C₄×D₄	—	23	2	no	—
288	C₄×D₄	—	23	1	no	—
289	C₄×D₄	—	23	2	no	—
290	C₄×D₄	—	23	2	no	—
291	C₄×D₄	—	23	4	no	—
292	C₄×D₄	—	23	1	no	—
293	C₄×D₄	C₂×D₂₃	1	1	yes	characteristic
294	C₄×D₄	C₂×D₂₃	1	1	yes	characteristic, complemented
295	#117	—	23	4	no	—
296	#117	—	23	2	no	—
297	#117	—	23	1	no	—
298	#117	—	23	2	no	—
299	#117	—	23	4	no	—
300	#117	—	23	4	no	—
301	#117	—	23	2	no	—
302	#117	—	23	2	no	—
303	#117	—	23	2	no	—
304	C₂×C₄⋊C₄	—	23	2	no	—
305	C₂×C₄⋊C₄	—	23	1	no	—
306	C₂×C₄⋊C₄	C₂×D₂₃	1	2	yes	complemented
307	C₂×C₂²⋊C₄	—	23	4	no	—
308	C₂×C₂²⋊C₄	—	23	2	no	—
309	C₂×C₄²	—	23	4	no	—
310	C₂×C₄²	—	23	2	no	—
311	C₂×C₄²	—	23	1	no	—
312	C₂₃	#3475	1	1	yes	characteristic, complemented, Sylow
313	C₂⁴	—	23	2	no	—
314	#41	—	2	8	no	—
315	#41	—	46	4	no	—
316	C₂×Q₈	—	23	1	no	—
317	C₂×Q₈	—	23	2	no	—
318	C₂×Q₈	C₂²×D₂₃	1	2	yes	—
319	C₂×D₄	—	23	2	no	—
320	C₂×D₄	—	23	2	no	—
321	C₂×D₄	—	23	4	no	—
322	C₂×D₄	—	23	1	no	—
323	C₂×D₄	—	46	4	no	—
324	C₂×D₄	C₂²×D₂₃	1	4	yes	—
325	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
326	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
327	C₂²×C₄	—	23	1	no	—
328	C₂²×C₄	—	23	2	no	—
329	C₂²×C₄	—	23	2	no	—
330	C₂²×C₄	—	23	4	no	—
331	C₂²×C₄	—	23	2	no	—
332	C₂²×C₄	—	23	1	no	—
333	C₂²×C₄	—	23	2	no	—
334	C₂²×C₄	—	23	2	no	—
335	C₂²×C₄	—	23	2	no	—
336	C₂²×C₄	—	23	1	no	—
337	C₂²×C₄	—	46	8	no	—
338	C₂²×C₄	C₂²×D₂₃	1	4	yes	—
339	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
340	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
341	C₄⋊C₄	—	23	1	no	—
342	C₄⋊C₄	—	23	1	no	—
343	C₄⋊C₄	—	23	2	no	—
344	C₄⋊C₄	—	23	4	no	—
345	C₄⋊C₄	—	23	2	no	—
346	C₄⋊C₄	—	23	2	no	—
347	C₄⋊C₄	—	23	2	no	—
348	C₄⋊C₄	—	23	4	no	—
349	C₄⋊C₄	—	23	4	no	—
350	C₄⋊C₄	—	23	2	no	—
351	C₄⋊C₄	—	23	4	no	—
352	C₄⋊C₄	—	23	4	no	—
353	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
354	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
355	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
356	C₄⋊C₄	C₂²×D₂₃	1	4	yes	—
357	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
358	C₂²⋊C₄	—	23	2	no	—
359	C₂²⋊C₄	—	23	4	no	—
360	C₂²⋊C₄	—	23	2	no	—
361	C₂²⋊C₄	—	23	4	no	—
362	C₂²⋊C₄	—	23	2	no	—
363	C₂²⋊C₄	—	23	4	no	—
364	C₂²⋊C₄	—	23	4	no	—
365	C₂²⋊C₄	—	23	4	no	—
366	C₂²⋊C₄	—	23	2	no	—
367	C₂²⋊C₄	—	23	2	no	—
368	C₂²⋊C₄	—	23	4	no	—
369	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
370	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
371	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	—
372	C₄²	—	23	2	no	—
373	C₄²	—	23	1	no	—
374	C₄²	—	23	4	no	—
375	C₄²	—	23	4	no	—
376	C₄²	—	23	1	no	—
377	C₄²	—	23	4	no	—
378	C₄²	—	23	2	no	—
379	C₄²	—	23	1	no	—
380	C₄²	—	23	2	no	—
381	C₄²	C₂²×D₂₃	1	1	yes	characteristic
382	C₂³	—	23	1	no	—
383	C₂³	—	23	2	no	—
384	C₂³	—	46	4	no	—
385	C₂³	—	46	4	no	—
386	C₂³	—	92	2	no	—
387	C₂³	C₂³×D₂₃	1	2	yes	—
388	C₂³	C₂³×D₂₃	1	2	yes	—
389	Q₈	—	2	4	no	—
390	Q₈	—	46	2	no	—
391	Q₈	—	92	2	no	—
392	D₄	—	2	8	no	—
393	D₄	—	2	2	no	—
394	D₄	—	46	4	no	—
395	D₄	—	46	4	no	—
396	D₄	—	46	2	no	—
397	D₄	—	92	4	no	—
398	D₄	#67290	1	4	yes	complemented
399	C₂×C₄	—	2	8	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	23	1	no	—
403	C₂×C₄	—	23	4	no	—
404	C₂×C₄	—	23	2	no	—
405	C₂×C₄	—	23	2	no	—
406	C₂×C₄	—	23	1	no	—
407	C₂×C₄	—	23	2	no	—
408	C₂×C₄	—	23	4	no	—
409	C₂×C₄	—	23	1	no	—
410	C₂×C₄	—	46	4	no	—
411	C₂×C₄	—	46	4	no	—
412	C₂×C₄	—	46	4	no	—
413	C₂×C₄	—	46	4	no	—
414	C₂×C₄	—	46	2	no	—
415	C₂×C₄	—	46	4	no	—
416	C₂×C₄	—	92	1	no	—
417	C₂×C₄	—	92	2	no	—
418	C₂×C₄	—	92	4	no	—
419	C₂×C₄	C₂³×D₂₃	1	2	yes	—
420	C₂×C₄	C₂³×D₂₃	1	4	yes	—
421	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
422	C₂×C₄	C₂³×D₂₃	1	2	yes	—
423	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
424	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	23	2	no	—
431	C₂²	—	46	1	no	—
432	C₂²	—	46	1	no	—
433	C₂²	—	46	2	no	—
434	C₂²	—	46	2	no	—
435	C₂²	—	46	2	no	—
436	C₂²	—	92	8	no	—
437	C₂²	C₂×#67290	1	4	yes	—
438	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	4	no	—
442	C₄	—	2	1	no	—
443	C₄	—	23	2	no	—
444	C₄	—	46	2	no	—
445	C₄	—	46	2	no	—
446	C₄	—	46	1	no	—
447	C₄	—	46	1	no	—
448	C₄	—	46	2	no	—
449	C₄	—	46	4	no	—
450	C₄	C₂×#67290	1	2	yes	—
451	C₄	#41×D₂₃	1	2	yes	—
452	C₂	—	2	4	no	—
453	C₂	—	4	2	no	—
454	C₂	—	46	2	no	—
455	C₂	—	92	2	no	—
456	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
457	C₂	C₂²×#67290	1	1	yes	characteristic
458	C₂	#13093254	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁵
Fitting	C₂₃×#547	C₂
hypercenter	#547	D₂₃
hypocenter	C₂₃	#3475
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ #547

Complements

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

N	H ≅ G/N	type
1. #13093141	C₂	semidirect
2. #13093132	C₂	semidirect
3. #13093124	C₂	semidirect
4. #13093119	C₂	semidirect
5. #13093102	C₂	semidirect
6. #13093101	C₂	semidirect
7. #13093090	C₂	semidirect
8. #13093055	C₂	semidirect
9. #13092972	C₂	semidirect
10. #13092953	C₂	semidirect
11. #13092944	C₂	semidirect
12. #13092927	C₂	semidirect
13. #41×Dic₂₃	C₂	semidirect
14. C₄×#67290	C₂	semidirect
15. C₄×D₄×D₂₃	C₂	semidirect
16. C₂×#10625063	C₂	semidirect
17. C₂₃×#547	C₂	semidirect
22. C₂₃×C₄⋊Q₈	C₂²	semidirect
23. C₂₃×#123	C₂²	semidirect
24. C₂₃×C₂²⋊Q₈	C₂²	semidirect
25. C₂₃×#121	C₂²	semidirect
27. C₄×D₄×C₂₃	C₂²	semidirect
28. C₂×C₄⋊C₄×C₂₃	C₂²	semidirect
31. Q₈×Dic₂₃	C₂²	semidirect
32. Q₈×Dic₂₃	C₂²	semidirect
34. #10625109	C₂²	semidirect
38. D₄×Dic₂₃	C₂²	semidirect
39. D₄×Dic₂₃	C₂²	semidirect
40. D₄×Dic₂₃	C₂²	semidirect
46. #10625097	C₂²	semidirect
47. #10625097	C₂²	semidirect
48. C₂×C₄⋊Dic₂₃	C₂²	semidirect
49. #10625095	C₂²	semidirect
50. C₂×C₄×Dic₂₃	C₂²	semidirect
51. C₂×C₄×Dic₂₃	C₂²	semidirect
52. #10625069	C₂²	semidirect
53. #10625069	C₂²	semidirect
55. #10625068	C₂²	semidirect
60. #10625063	C₂²	semidirect
61. #10625063	C₂²	semidirect
62. #10625063	C₂²	semidirect
64. #10625061	C₂²	semidirect
65. #10625061	C₂²	semidirect
66. #10625060	C₂²	semidirect
67. #10625058	C₂²	semidirect
68. #10625058	C₂²	semidirect
69. #10625057	C₂²	semidirect
70. #10625056	C₂²	semidirect
74. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
76. #10625050	C₂²	semidirect
77. #10625049	C₂²	semidirect
78. #10625048	C₂²	semidirect
81. #10625040	C₂²	semidirect
82. C₄×Dic₄₆	C₂²	semidirect
162. D₄×C₂₃	#41	semidirect
192. C₄×D₂₃	#41	semidirect
230. #547	D₂₃	semidirect
252. C₄⋊Q₈	C₂×D₂₃	semidirect
264. #123	C₂×D₂₃	semidirect
270. C₂²⋊Q₈	C₂×D₂₃	semidirect
274. #121	C₂×D₂₃	semidirect
294. C₄×D₄	C₂×D₂₃	semidirect
306. C₂×C₄⋊C₄	C₂×D₂₃	semidirect
312. C₂₃	#3475	semidirect
398. D₄	#67290	semidirect

Maximal subgroups

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

subgroup	index
#13093141	2
#13093132	2
#13093124	2
#13093119	2
#13093102	2
#13093101	2
#13093090	2
#13093055	2
#13092972	2
#13092953	2
#13092944	2
#13092927	2
#41×Dic₂₃	2
C₄×#67290	2
C₄×D₄×D₂₃	2
C₂×#10625063	2
C₂₃×#547	2
#3475	23