Subgroups — #26232156

Order 12032.

1368 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689245	C₂	1	2	yes	maximal, complemented
2	#20251837	C₂	1	2	yes	maximal, complemented
3	#20244282	C₂	1	2	yes	maximal, complemented
4	#20243717	C₂	1	4	yes	maximal, complemented
5	#20243426	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243332	C₂	1	2	yes	maximal, complemented
7	#20243164	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#135×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂×#13094031	C₂²	1	4	yes	complemented
10	#15689245	—	2	8	no	—
11	C₂×#13093960	C₂²	1	2	yes	complemented
12	C₂×#13093951	C₂²	1	4	yes	complemented
13	C₂×#13093951	C₂²	1	4	yes	complemented
14	#15689090	—	2	4	no	—
15	#15689090	C₂²	1	4	yes	complemented
16	#15689087	—	2	2	no	—
17	#15689087	C₂²	1	2	yes	—
18	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
19	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×#13093934	C₂²	1	2	yes	complemented
21	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
22	#15688888	C₂²	1	2	yes	complemented
23	#15688877	C₂²	1	2	yes	complemented
24	C₂²×#41×C₄₇	C₂²	1	2	yes	—
25	C₂×#135×C₄₇	—	2	8	no	—
26	C₂×#135×C₄₇	C₄	1	1	yes	characteristic, complemented
27	C₂×#135×C₄₇	C₄	1	2	yes	complemented
28	C₂×#135×C₄₇	C₄	1	1	yes	characteristic, complemented
29	C₂×#135×C₄₇	C₂²	1	2	yes	—
30	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
32	C₂²×Q₁₆×C₄₇	C₄	1	1	yes	characteristic, complemented
33	C₂²×SD₁₆×C₄₇	C₄	1	2	yes	complemented
34	C₂²×D₈×C₄₇	C₄	1	1	yes	characteristic, complemented
35	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
36	#13094031	—	2	8	no	—
37	#13094031	—	4	4	no	—
38	C₂×#10625329	—	2	4	no	—
39	C₂×#10625329	C₂³	1	4	yes	—
40	C₂²×C₄₇⋊C₈	—	2	4	no	—
41	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
42	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
43	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
44	#13093960	—	2	4	no	—
45	#13093951	—	2	8	no	—
46	#13093951	—	4	4	no	—
47	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
48	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
49	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
50	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
51	C₂²⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
52	C₂²⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
53	#13093934	—	2	4	no	—
54	C₄₇⋊#95	—	2	1	no	—
55	C₂×#41×C₄₇	—	2	2	no	—
56	C₂×#41×C₄₇	—	2	2	no	—
57	C₂×#41×C₄₇	—	2	8	no	—
58	C₂×#41×C₄₇	—	4	4	no	—
59	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
60	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
61	C₂×#41×C₄₇	C₂³	1	2	yes	—
62	C₂×#41×C₄₇	C₂³	1	2	yes	—
63	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
64	C₂²×D₄×C₄₇	—	2	2	no	—
65	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
66	C₂³×C₄×C₄₇	—	2	2	no	—
67	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
68	#135×C₄₇	—	2	8	no	—
69	#135×C₄₇	—	2	4	no	—
70	#135×C₄₇	—	2	8	no	—
71	#135×C₄₇	—	2	4	no	—
72	#135×C₄₇	—	2	4	no	—
73	#135×C₄₇	D₄	1	8	yes	—
74	C₂×Q₁₆×C₄₇	—	2	4	no	—
75	C₂×Q₁₆×C₄₇	C₂×C₄	1	2	yes	—
76	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
77	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
78	C₂×SD₁₆×C₄₇	—	2	8	no	—
79	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
80	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
81	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
82	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
83	C₂×D₈×C₄₇	—	2	4	no	—
84	C₂×D₈×C₄₇	C₂×C₄	1	2	yes	—
85	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic
86	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic
87	C₂²×C₈×C₄₇	—	2	4	no	—
88	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
89	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
90	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
91	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
92	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
94	C₂⁴×C₄₇	—	2	2	no	—
95	C₂⁴×C₄₇	#41	1	1	yes	characteristic
96	#41×C₄₇	—	2	4	no	—
97	#41×C₄₇	—	2	4	no	—
98	#41×C₄₇	—	2	4	no	—
99	#41×C₄₇	—	2	4	no	—
100	#41×C₄₇	—	2	4	no	—
101	#41×C₄₇	—	4	8	no	—
102	#41×C₄₇	—	4	2	no	—
103	#41×C₄₇	—	4	2	no	—
104	#41×C₄₇	—	4	8	no	—
105	#41×C₄₇	C₂×D₄	1	8	yes	—
106	C₂×Q₈×C₄₇	—	2	2	no	—
107	C₂×Q₈×C₄₇	—	2	4	no	—
108	C₂×Q₈×C₄₇	—	4	2	no	—
109	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
110	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
111	C₂×D₄×C₄₇	—	2	2	no	—
112	C₂×D₄×C₄₇	—	2	4	no	—
113	C₂×D₄×C₄₇	—	2	2	no	—
114	C₂×D₄×C₄₇	—	2	2	no	—
115	C₂×D₄×C₄₇	—	2	2	no	—
116	C₂×D₄×C₄₇	—	2	2	no	—
117	C₂×D₄×C₄₇	—	4	2	no	—
118	C₂×D₄×C₄₇	—	4	8	no	—
119	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
120	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₄₇	—	2	2	no	—
122	C₂²×C₄×C₄₇	—	2	2	no	—
123	C₂²×C₄×C₄₇	—	2	2	no	—
124	C₂²×C₄×C₄₇	—	2	2	no	—
125	C₂²×C₄×C₄₇	—	2	2	no	—
126	C₂²×C₄×C₄₇	—	2	2	no	—
127	C₂²×C₄×C₄₇	—	2	2	no	—
128	C₂²×C₄×C₄₇	—	4	8	no	—
129	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
134	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
135	C₂²×Dic₄₇	—	2	2	no	—
136	Q₁₆×C₄₇	—	2	4	no	—
137	Q₁₆×C₄₇	—	2	2	no	—
138	Q₁₆×C₄₇	C₂²⋊C₄	1	4	yes	complemented
139	SD₁₆×C₄₇	—	2	4	no	—
140	SD₁₆×C₄₇	—	2	4	no	—
141	SD₁₆×C₄₇	—	2	4	no	—
142	SD₁₆×C₄₇	C₂²⋊C₄	1	8	yes	complemented
143	D₈×C₄₇	—	2	4	no	—
144	D₈×C₄₇	—	2	2	no	—
145	D₈×C₄₇	C₂²⋊C₄	1	4	yes	complemented
146	C₂×C₈×C₄₇	—	2	2	no	—
147	C₂×C₈×C₄₇	—	2	2	no	—
148	C₂×C₈×C₄₇	—	2	2	no	—
149	C₂×C₈×C₄₇	—	2	2	no	—
150	C₂×C₈×C₄₇	—	2	2	no	—
151	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
156	C₂²⋊Dic₄₇	—	4	2	no	—
157	C₄×Dic₄₇	—	2	2	no	—
158	C₄×Dic₄₇	—	2	2	no	—
159	#10625329	—	2	4	no	—
160	#10625329	—	2	4	no	—
161	#10625329	—	4	8	no	—
162	C₂×C₄₇⋊C₈	—	2	2	no	—
163	C₂×C₄₇⋊C₈	—	2	2	no	—
164	C₂×C₄₇⋊C₈	—	2	4	no	—
165	C₂×C₄₇⋊C₈	—	4	8	no	—
166	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
167	C₂³×C₄₇	—	2	2	no	—
168	C₂³×C₄₇	—	2	2	no	—
169	C₂³×C₄₇	—	2	2	no	—
170	C₂³×C₄₇	—	2	2	no	—
171	C₂³×C₄₇	—	4	1	no	—
172	C₂³×C₄₇	—	4	4	no	—
173	C₂³×C₄₇	—	4	4	no	—
174	C₂³×C₄₇	—	8	2	no	—
175	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
176	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
177	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
178	Q₈×C₄₇	—	2	2	no	—
179	Q₈×C₄₇	—	2	2	no	—
180	Q₈×C₄₇	—	2	2	no	—
181	Q₈×C₄₇	—	4	4	no	—
182	Q₈×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
183	D₄×C₄₇	—	2	8	no	—
184	D₄×C₄₇	—	2	2	no	—
185	D₄×C₄₇	—	2	2	no	—
186	D₄×C₄₇	—	2	2	no	—
187	D₄×C₄₇	—	4	4	no	—
188	D₄×C₄₇	—	4	4	no	—
189	D₄×C₄₇	—	4	4	no	—
190	D₄×C₄₇	—	4	4	no	—
191	D₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
192	C₂×C₄×C₄₇	—	2	2	no	—
193	C₂×C₄×C₄₇	—	2	2	no	—
194	C₂×C₄×C₄₇	—	2	1	no	—
195	C₂×C₄×C₄₇	—	2	1	no	—
196	C₂×C₄×C₄₇	—	2	1	no	—
197	C₂×C₄×C₄₇	—	2	1	no	—
198	C₂×C₄×C₄₇	—	2	8	no	—
199	C₂×C₄×C₄₇	—	2	2	no	—
200	C₂×C₄×C₄₇	—	2	2	no	—
201	C₂×C₄×C₄₇	—	2	2	no	—
202	C₂×C₄×C₄₇	—	4	4	no	—
203	C₂×C₄×C₄₇	—	4	4	no	—
204	C₂×C₄×C₄₇	—	4	4	no	—
205	C₂×C₄×C₄₇	—	4	4	no	—
206	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
207	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
208	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
211	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
212	C₂×Dic₄₇	—	4	2	no	—
213	C₂×Dic₄₇	—	4	2	no	—
214	C₂×Dic₄₇	—	4	2	no	—
215	C₈×C₄₇	—	2	1	no	—
216	C₈×C₄₇	—	2	1	no	—
217	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
218	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
219	C₄₇⋊C₈	—	2	4	no	—
220	C₄₇⋊C₈	—	4	4	no	—
221	#22452	—	47	1	no	maximal, Sylow
222	C₂²×C₄₇	—	2	1	no	—
223	C₂²×C₄₇	—	2	1	no	—
224	C₂²×C₄₇	—	2	1	no	—
225	C₂²×C₄₇	—	2	1	no	—
226	C₂²×C₄₇	—	2	1	no	—
227	C₂²×C₄₇	—	2	4	no	—
228	C₂²×C₄₇	—	2	1	no	—
229	C₂²×C₄₇	—	2	1	no	—
230	C₂²×C₄₇	—	4	4	no	—
231	C₂²×C₄₇	—	4	2	no	—
232	C₂²×C₄₇	—	4	2	no	—
233	C₂²×C₄₇	—	4	2	no	—
234	C₂²×C₄₇	—	4	2	no	—
235	C₂²×C₄₇	—	4	2	no	—
236	C₂²×C₄₇	—	8	8	no	—
237	C₂²×C₄₇	#444	1	2	yes	complemented
238	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
239	C₂²×C₄₇	#546	1	2	yes	—
240	C₄×C₄₇	—	2	1	no	—
241	C₄×C₄₇	—	2	1	no	—
242	C₄×C₄₇	—	2	4	no	—
243	C₄×C₄₇	—	4	2	no	—
244	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
245	C₄×C₄₇	#518	1	1	yes	characteristic
246	C₄×C₄₇	D₄²	1	2	yes	—
247	Dic₄₇	—	8	2	no	—
248	C₂²×#135	D₄₇	1	1	yes	characteristic
249	C₂×#444	—	47	2	no	—
250	#2880	—	47	2	no	—
251	#1975	—	47	2	no	—
252	#1876	—	47	4	no	—
253	#1810	—	47	1	no	—
254	#1789	—	47	2	no	—
255	#1752	—	47	1	no	—
256	C₂×C₄₇	—	2	2	no	—
257	C₂×C₄₇	—	2	2	no	—
258	C₂×C₄₇	—	4	1	no	—
259	C₂×C₄₇	—	4	4	no	—
260	C₂×C₄₇	—	8	2	no	—
261	C₂×C₄₇	D₄×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×C₄₇	C₂×#444	1	1	yes	characteristic
263	C₂×C₄₇	#2957	1	1	yes	characteristic
264	C₂²×#41	C₂×D₄₇	1	2	yes	—
265	C₂×#135	—	2	8	no	—
266	C₂×#135	Dic₄₇	1	1	yes	characteristic, complemented
267	C₂×#135	Dic₄₇	1	2	yes	complemented
268	C₂×#135	Dic₄₇	1	1	yes	characteristic, complemented
269	C₂×#135	C₂×D₄₇	1	2	yes	—
270	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
271	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
272	C₂²×Q₁₆	Dic₄₇	1	1	yes	characteristic, complemented
273	C₂²×SD₁₆	Dic₄₇	1	2	yes	complemented
274	C₂²×D₈	Dic₄₇	1	1	yes	characteristic, complemented
275	C₂×#131	—	47	4	no	—
276	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
277	#444	—	94	8	no	—
278	C₂×#108	—	47	2	no	—
279	C₂×#104	—	47	4	no	—
280	C₂×#104	—	47	4	no	—
281	#408	—	47	4	no	—
282	#408	—	94	4	no	—
283	#407	—	47	2	no	—
284	#407	—	94	2	no	—
285	C₂×C₂²⋊C₈	—	47	1	no	—
286	C₂×C₂²⋊C₈	—	94	2	no	—
287	C₂×#97	—	47	2	no	—
288	C₄×C₂²⋊C₄	—	47	1	no	—
289	#341	—	47	2	no	—
290	#336	—	47	2	no	—
291	C₄₇	#22452	1	1	yes	characteristic, complemented, Sylow
292	C₂×#41	—	2	2	no	—
293	C₂×#41	—	2	2	no	—
294	C₂×#41	—	2	8	no	—
295	C₂×#41	—	4	4	no	—
296	C₂×#41	C₂×Dic₄₇	1	2	yes	—
297	C₂×#41	C₂×Dic₄₇	1	2	yes	—
298	C₂×#41	C₂²×D₄₇	1	2	yes	—
299	C₂×#41	C₂²×D₄₇	1	2	yes	—
300	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
301	C₂²×D₄	—	2	2	no	—
302	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
303	C₂³×C₄	—	2	2	no	—
304	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
305	#135	—	2	8	no	—
306	#135	—	2	4	no	—
307	#135	—	2	8	no	—
308	#135	—	2	4	no	—
309	#135	—	2	4	no	—
310	#135	C₂²⋊D₄₇	1	8	yes	—
311	C₂×Q₁₆	—	2	4	no	—
312	C₂×Q₁₆	C₂×Dic₄₇	1	2	yes	—
313	C₂×Q₁₆	C₂×Dic₄₇	1	1	yes	characteristic
314	C₂×Q₁₆	C₂×Dic₄₇	1	1	yes	characteristic
315	C₂×SD₁₆	—	2	8	no	—
316	C₂×SD₁₆	C₂×Dic₄₇	1	2	yes	—
317	C₂×SD₁₆	C₂×Dic₄₇	1	2	yes	—
318	C₂×SD₁₆	C₂×Dic₄₇	1	2	yes	—
319	C₂×SD₁₆	C₂×Dic₄₇	1	2	yes	—
320	C₂×D₈	—	2	4	no	—
321	C₂×D₈	C₂×Dic₄₇	1	2	yes	—
322	C₂×D₈	C₂×Dic₄₇	1	1	yes	characteristic
323	C₂×D₈	C₂×Dic₄₇	1	1	yes	characteristic
324	#131	—	94	8	no	—
325	#131	—	188	4	no	—
326	C₂×M₁₆	—	47	4	no	—
327	C₂×M₁₆	—	94	4	no	—
328	C₂²×C₈	—	2	4	no	—
329	C₂²×C₈	—	47	2	no	—
330	C₂²×C₈	—	94	4	no	—
331	C₂²×C₈	C₂×Dic₄₇	1	1	yes	characteristic
332	C₂²×C₈	C₂×Dic₄₇	1	1	yes	characteristic
333	C₂²×C₈	C₂×Dic₄₇	1	1	yes	characteristic
334	C₂²×C₈	C₂×Dic₄₇	1	1	yes	characteristic
335	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
336	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
337	C₂×C₂²⋊C₄	—	94	1	no	—
338	C₂×C₄²	—	47	2	no	—
339	#108	—	94	4	no	—
340	#104	—	94	8	no	—
341	#104	—	188	4	no	—
342	C₂²⋊C₈	—	47	2	no	—
343	C₂²⋊C₈	—	47	2	no	—
344	C₂²⋊C₈	—	94	4	no	—
345	C₂²⋊C₈	—	94	4	no	—
346	C₂²⋊C₈	—	94	2	no	—
347	C₂²⋊C₈	—	94	2	no	—
348	#97	—	94	4	no	—
349	#95	—	94	1	no	—
350	C₂⁴	—	2	2	no	—
351	C₂⁴	#10625352	1	1	yes	characteristic
352	#41	—	2	4	no	—
353	#41	—	2	4	no	—
354	#41	—	2	4	no	—
355	#41	—	2	4	no	—
356	#41	—	2	4	no	—
357	#41	—	4	8	no	—
358	#41	—	4	2	no	—
359	#41	—	4	2	no	—
360	#41	—	4	8	no	—
361	#41	C₂×C₂²⋊D₄₇	1	8	yes	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	4	no	—
364	C₂×Q₈	—	4	2	no	—
365	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
366	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	4	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	4	2	no	—
374	C₂×D₄	—	4	8	no	—
375	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
376	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	4	8	no	—
385	C₂²×C₄	—	94	2	no	—
386	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
387	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
388	C₂²×C₄	#10625352	1	1	yes	characteristic
389	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
390	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
391	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
392	Q₁₆	—	2	4	no	—
393	Q₁₆	—	2	2	no	—
394	Q₁₆	C₂²⋊Dic₄₇	1	4	yes	complemented
395	SD₁₆	—	2	4	no	—
396	SD₁₆	—	2	4	no	—
397	SD₁₆	—	2	4	no	—
398	SD₁₆	C₂²⋊Dic₄₇	1	8	yes	complemented
399	D₈	—	2	4	no	—
400	D₈	—	2	2	no	—
401	D₈	C₂²⋊Dic₄₇	1	4	yes	complemented
402	M₁₆	—	94	4	no	—
403	M₁₆	—	94	4	no	—
404	M₁₆	—	188	8	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	47	4	no	—
411	C₂×C₈	—	94	2	no	—
412	C₂×C₈	—	94	2	no	—
413	C₂×C₈	—	94	4	no	—
414	C₂×C₈	—	188	8	no	—
415	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
416	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
417	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
418	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
419	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
420	C₂²⋊C₄	—	188	2	no	—
421	C₄²	—	94	2	no	—
422	C₄²	—	94	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	2	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	4	4	no	—
429	C₂³	—	4	4	no	—
430	C₂³	—	8	2	no	—
431	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
432	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
433	C₂³	C₂×#10625352	1	1	yes	characteristic
434	Q₈	—	2	2	no	—
435	Q₈	—	2	2	no	—
436	Q₈	—	2	2	no	—
437	Q₈	—	4	4	no	—
438	Q₈	C₂×C₂²⋊Dic₄₇	1	4	yes	—
439	D₄	—	2	8	no	—
440	D₄	—	2	2	no	—
441	D₄	—	2	2	no	—
442	D₄	—	2	2	no	—
443	D₄	—	4	4	no	—
444	D₄	—	4	4	no	—
445	D₄	—	4	4	no	—
446	D₄	—	4	4	no	—
447	D₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	8	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	4	4	no	—
459	C₂×C₄	—	4	4	no	—
460	C₂×C₄	—	4	4	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	188	2	no	—
463	C₂×C₄	—	188	2	no	—
464	C₂×C₄	—	188	2	no	—
465	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
466	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
467	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
468	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
469	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
470	C₂×C₄	#13094069	1	2	yes	—
471	C₈	—	2	1	no	—
472	C₈	—	2	1	no	—
473	C₈	—	94	4	no	—
474	C₈	—	188	4	no	—
475	C₈	C₂×C₂²⋊Dic₄₇	1	2	yes	—
476	C₈	C₂×C₂²⋊Dic₄₇	1	2	yes	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	4	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	4	2	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	8	8	no	—
492	C₂²	#15689245	1	2	yes	complemented
493	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
494	C₂²	#15689767	1	2	yes	—
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	2	4	no	—
498	C₄	—	4	2	no	—
499	C₄	—	376	2	no	—
500	C₄	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
501	C₄	#15689598	1	1	yes	characteristic
502	C₄	D₄×C₂²⋊D₄₇	1	2	yes	—
503	C₂	—	2	2	no	—
504	C₂	—	2	2	no	—
505	C₂	—	4	1	no	—
506	C₂	—	4	4	no	—
507	C₂	—	8	2	no	—
508	C₂	D₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
509	C₂	C₂×#15689245	1	1	yes	characteristic
510	C₂	#20252305	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₂²×#135×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂²×#135	D₄₇
hypocenter	C₄₇	#22452
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#15689245	C₂	semidirect
2. #20251837	C₂	semidirect
3. #20244282	C₂	semidirect
4. #20243717	C₂	semidirect
5. #20243426	C₂	semidirect
6. #20243332	C₂	semidirect
7. #20243164	C₂	semidirect
9. C₂×#13094031	C₂²	semidirect
11. C₂×#13093960	C₂²	semidirect
12. C₂×#13093951	C₂²	semidirect
13. C₂×#13093951	C₂²	semidirect
15. #15689090	C₂²	semidirect
20. C₂×#13093934	C₂²	semidirect
22. #15688888	C₂²	semidirect
23. #15688877	C₂²	semidirect
26. C₂×#135×C₄₇	C₄	semidirect
27. C₂×#135×C₄₇	C₄	semidirect
28. C₂×#135×C₄₇	C₄	semidirect
32. C₂²×Q₁₆×C₄₇	C₄	semidirect
33. C₂²×SD₁₆×C₄₇	C₄	semidirect
34. C₂²×D₈×C₄₇	C₄	semidirect
138. Q₁₆×C₄₇	C₂²⋊C₄	semidirect
142. SD₁₆×C₄₇	C₂²⋊C₄	semidirect
145. D₈×C₄₇	C₂²⋊C₄	semidirect
237. C₂²×C₄₇	#444	semidirect
266. C₂×#135	Dic₄₇	semidirect
267. C₂×#135	Dic₄₇	semidirect
268. C₂×#135	Dic₄₇	semidirect
272. C₂²×Q₁₆	Dic₄₇	semidirect
273. C₂²×SD₁₆	Dic₄₇	semidirect
274. C₂²×D₈	Dic₄₇	semidirect
291. C₄₇	#22452	semidirect
394. Q₁₆	C₂²⋊Dic₄₇	semidirect
398. SD₁₆	C₂²⋊Dic₄₇	semidirect
401. D₈	C₂²⋊Dic₄₇	semidirect
492. C₂²	#15689245	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689245	2
#20251837	2
#20244282	2
#20243717	2
#20243426	2
#20243332	2
#20243164	2
C₂²×#135×C₄₇	2
#22452	47