Subgroups — C₂×#20243832 #26218032

Order 12032.

2514 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13093951	C₂	1	2	yes	maximal, complemented
3	C₂×#15689087	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243832	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688882	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₇×#525	C₂	1	1	yes	maximal, characteristic
7	C₂⁴×Dic₄₇	—	2	1	no	—
8	C₂²×#10625329	C₂²	1	2	yes	—
9	C₂²×C₄×Dic₄₇	—	2	8	no	—
10	C₂²×C₄×Dic₄₇	—	2	1	no	—
11	C₂²×C₄×Dic₄₇	—	2	2	no	—
12	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
13	C₂²×C₄×Dic₄₇	C₂²	1	4	yes	complemented
14	C₂×#13093951	—	2	8	no	—
15	C₂×#13093951	C₂²	1	8	yes	complemented
16	#15689087	—	2	2	no	—
17	#15689087	C₂²	1	4	yes	complemented
18	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
19	#15688882	C₂²	1	8	yes	complemented
20	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
22	C₄₇×#525	—	2	2	no	—
23	C₄₇×#525	—	2	2	no	—
24	C₄₇×#525	C₄	1	4	yes	complemented
25	C₄₇×#525	C₂²	1	4	yes	—
26	C₂×#123×C₄₇	—	2	1	no	—
27	C₂×C₂²⋊Q₈×C₄₇	C₄	1	2	yes	complemented
28	C₂×#121×C₄₇	C₄	1	2	yes	complemented
29	C₂×#120×C₄₇	—	2	1	no	—
30	C₂×C₄×D₄×C₄₇	—	2	2	no	—
31	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
32	C₂³×Dic₄₇	—	2	8	no	—
33	C₂³×Dic₄₇	—	2	16	no	—
34	C₂³×Dic₄₇	—	2	2	no	—
35	C₂³×Dic₄₇	—	2	4	no	—
36	C₂×#10625329	—	2	2	no	—
37	C₂×#10625329	—	2	4	no	—
38	C₂×#10625329	—	2	4	no	—
39	C₂×#10625329	C₂³	1	4	yes	—
40	C₂²×C₄₇⋊C₈	—	2	2	no	—
41	C₂×C₄×Dic₄₇	—	2	8	no	—
42	C₂×C₄×Dic₄₇	—	2	16	no	—
43	C₂×C₄×Dic₄₇	—	2	2	no	—
44	C₂×C₄×Dic₄₇	—	2	4	no	—
45	C₂×C₄×Dic₄₇	—	2	4	no	—
46	C₂×C₄×Dic₄₇	—	2	16	no	—
47	C₂×C₄×Dic₄₇	D₄	1	8	yes	complemented
48	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
49	#13093951	—	2	16	no	—
50	C₂²⋊(C₄₇⋊C₈)	—	2	8	no	—
51	C₂⁵×C₄₇	D₄	1	1	yes	characteristic
52	C₂×#41×C₄₇	—	2	1	no	—
53	C₂×#41×C₄₇	—	2	1	no	—
54	C₂×#41×C₄₇	—	2	4	no	—
55	C₂×#41×C₄₇	—	2	4	no	—
56	C₂×#41×C₄₇	C₂×C₄	1	2	yes	complemented
57	C₂×#41×C₄₇	C₂³	1	2	yes	—
58	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
59	C₂²×D₄×C₄₇	—	2	2	no	—
60	C₂²×D₄×C₄₇	—	2	1	no	—
61	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
62	C₂³×C₄×C₄₇	—	2	4	no	—
63	C₂³×C₄×C₄₇	—	2	4	no	—
64	C₂³×C₄×C₄₇	—	2	1	no	—
65	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
66	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
67	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
68	C₂³×C₄×C₄₇	D₄	1	2	yes	—
69	C₂³×C₄×C₄₇	D₄	1	2	yes	—
70	C₂³×C₄×C₄₇	D₄	1	2	yes	—
71	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
72	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
73	#123×C₄₇	—	2	4	no	—
74	#123×C₄₇	—	2	4	no	—
75	C₂²⋊Q₈×C₄₇	—	2	4	no	—
76	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
77	#121×C₄₇	—	2	4	no	—
78	#121×C₄₇	C₂×C₄	1	8	yes	complemented
79	#120×C₄₇	—	2	4	no	—
80	#120×C₄₇	—	2	4	no	—
81	C₄×D₄×C₄₇	—	2	8	no	—
82	C₄×D₄×C₄₇	—	2	8	no	—
83	#117×C₄₇	—	2	1	no	—
84	#117×C₄₇	—	2	1	no	—
85	#117×C₄₇	C₂×C₄	1	2	yes	complemented
86	#117×C₄₇	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
88	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	complemented
89	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
92	C₂×C₄²×C₄₇	—	2	1	no	—
93	C₂⁴×C₄₇	—	2	8	no	—
94	C₂⁴×C₄₇	—	2	2	no	—
95	C₂⁴×C₄₇	—	2	2	no	—
96	C₂⁴×C₄₇	—	2	1	no	—
97	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
98	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
99	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
100	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
101	#41×C₄₇	—	2	8	no	—
102	#41×C₄₇	—	2	4	no	—
103	#41×C₄₇	—	2	4	no	—
104	#41×C₄₇	—	4	2	no	—
105	#41×C₄₇	—	4	4	no	—
106	#41×C₄₇	—	4	2	no	—
107	C₂×Q₈×C₄₇	—	2	1	no	—
108	C₂×Q₈×C₄₇	—	2	4	no	—
109	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	complemented
110	C₂×D₄×C₄₇	—	2	8	no	—
111	C₂×D₄×C₄₇	—	2	2	no	—
112	C₂×D₄×C₄₇	—	2	2	no	—
113	C₂×D₄×C₄₇	—	2	1	no	—
114	C₂×D₄×C₄₇	—	2	4	no	—
115	C₂×D₄×C₄₇	—	4	8	no	—
116	C₂×D₄×C₄₇	—	4	2	no	—
117	C₂×D₄×C₄₇	—	4	2	no	—
118	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	complemented
119	C₂²×C₄×C₄₇	—	2	2	no	—
120	C₂²×C₄×C₄₇	—	2	2	no	—
121	C₂²×C₄×C₄₇	—	2	8	no	—
122	C₂²×C₄×C₄₇	—	2	8	no	—
123	C₂²×C₄×C₄₇	—	2	4	no	—
124	C₂²×C₄×C₄₇	—	2	8	no	—
125	C₂²×C₄×C₄₇	—	2	8	no	—
126	C₂²×C₄×C₄₇	—	2	4	no	—
127	C₂²×C₄×C₄₇	—	2	4	no	—
128	C₂²×C₄×C₄₇	—	2	4	no	—
129	C₂²×C₄×C₄₇	—	2	2	no	—
130	C₂²×C₄×C₄₇	—	2	1	no	—
131	C₂²×C₄×C₄₇	—	2	2	no	—
132	C₂²×C₄×C₄₇	—	2	2	no	—
133	C₂²×C₄×C₄₇	—	4	4	no	—
134	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
135	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
136	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
137	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
138	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
139	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
147	C₂²×C₄×C₄₇	#41	1	4	yes	—
148	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
149	C₂²×Dic₄₇	—	2	16	no	—
150	C₂²×Dic₄₇	—	2	64	no	—
151	C₂²×Dic₄₇	—	2	16	no	—
152	C₂²×Dic₄₇	—	2	32	no	—
153	C₂²×Dic₄₇	—	2	8	no	—
154	C₂²×Dic₄₇	—	2	4	no	—
155	C₄⋊C₄×C₄₇	—	2	8	no	—
156	C₄⋊C₄×C₄₇	—	2	2	no	—
157	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	complemented
158	C₂²⋊C₄×C₄₇	—	2	2	no	—
159	C₂²⋊C₄×C₄₇	—	2	8	no	—
160	C₂²⋊C₄×C₄₇	—	2	2	no	—
161	C₂²⋊C₄×C₄₇	—	2	8	no	—
162	C₄²×C₄₇	—	2	2	no	—
163	C₄²×C₄₇	—	2	2	no	—
164	C₄×Dic₄₇	—	2	16	no	—
165	C₄×Dic₄₇	—	2	8	no	—
166	C₄×Dic₄₇	—	2	4	no	—
167	C₄×Dic₄₇	C₂×D₄	1	8	yes	complemented
168	#10625329	—	2	4	no	—
169	#10625329	—	2	4	no	—
170	#10625329	—	4	4	no	—
171	C₂×C₄₇⋊C₈	—	2	4	no	—
172	C₂×C₄₇⋊C₈	—	4	4	no	—
173	C₂³×C₄₇	—	2	16	no	—
174	C₂³×C₄₇	—	2	16	no	—
175	C₂³×C₄₇	—	2	2	no	—
176	C₂³×C₄₇	—	2	2	no	—
177	C₂³×C₄₇	—	2	4	no	—
178	C₂³×C₄₇	—	2	4	no	—
179	C₂³×C₄₇	—	2	4	no	—
180	C₂³×C₄₇	—	2	4	no	—
181	C₂³×C₄₇	—	2	8	no	—
182	C₂³×C₄₇	—	2	8	no	—
183	C₂³×C₄₇	—	2	2	no	—
184	C₂³×C₄₇	—	4	2	no	—
185	C₂³×C₄₇	—	4	4	no	—
186	C₂³×C₄₇	#104	1	8	yes	complemented
187	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
189	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂³×C₄₇	#120	1	2	yes	—
191	C₂³×C₄₇	#123	1	2	yes	—
192	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
193	Q₈×C₄₇	—	2	4	no	—
194	Q₈×C₄₇	—	4	2	no	—
195	D₄×C₄₇	—	2	4	no	—
196	D₄×C₄₇	—	4	2	no	—
197	D₄×C₄₇	—	4	2	no	—
198	D₄×C₄₇	—	4	4	no	—
199	D₄×C₄₇	—	4	16	no	—
200	D₄×C₄₇	—	4	2	no	—
201	C₂×C₄×C₄₇	—	2	2	no	—
202	C₂×C₄×C₄₇	—	2	2	no	—
203	C₂×C₄×C₄₇	—	2	4	no	—
204	C₂×C₄×C₄₇	—	2	4	no	—
205	C₂×C₄×C₄₇	—	2	8	no	—
206	C₂×C₄×C₄₇	—	2	8	no	—
207	C₂×C₄×C₄₇	—	2	8	no	—
208	C₂×C₄×C₄₇	—	2	8	no	—
209	C₂×C₄×C₄₇	—	2	4	no	—
210	C₂×C₄×C₄₇	—	2	2	no	—
211	C₂×C₄×C₄₇	—	4	2	no	—
212	C₂×C₄×C₄₇	—	4	4	no	—
213	C₂×C₄×C₄₇	—	4	4	no	—
214	C₂×C₄×C₄₇	—	4	4	no	—
215	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
216	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
219	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
220	C₂×C₄×C₄₇	#120	1	2	yes	—
221	C₂×C₄×C₄₇	#121	1	4	yes	—
222	C₂×C₄×C₄₇	#121	1	4	yes	—
223	C₂×C₄×C₄₇	#123	1	2	yes	—
224	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
225	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
226	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
228	C₂×Dic₄₇	—	2	64	no	—
229	C₂×Dic₄₇	—	2	16	no	—
230	C₂×Dic₄₇	—	2	32	no	—
231	C₂×Dic₄₇	—	2	8	no	—
232	C₄₇⋊C₈	—	4	4	no	—
233	C₂×#1896	—	47	1	no	maximal, Sylow
234	C₂²×C₄₇	—	2	8	no	—
235	C₂²×C₄₇	—	2	8	no	—
236	C₂²×C₄₇	—	2	16	no	—
237	C₂²×C₄₇	—	2	2	no	—
238	C₂²×C₄₇	—	2	2	no	—
239	C₂²×C₄₇	—	2	4	no	—
240	C₂²×C₄₇	—	2	4	no	—
241	C₂²×C₄₇	—	2	16	no	—
242	C₂²×C₄₇	—	2	4	no	—
243	C₂²×C₄₇	—	2	4	no	—
244	C₂²×C₄₇	—	4	4	no	—
245	C₂²×C₄₇	—	4	2	no	—
246	C₂²×C₄₇	—	8	4	no	—
247	C₂²×C₄₇	#386	1	2	yes	—
248	C₂²×C₄₇	#386	1	2	yes	—
249	C₂²×C₄₇	C₂×#104	1	4	yes	—
250	C₂²×C₄₇	C₂×#104	1	8	yes	complemented
251	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
252	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
253	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
254	C₄×C₄₇	—	2	4	no	—
255	C₄×C₄₇	—	4	4	no	—
256	C₄×C₄₇	—	4	2	no	—
257	C₄×C₄₇	#386	1	2	yes	—
258	C₄×C₄₇	#386	1	2	yes	—
259	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
260	C₄×C₄₇	C₂×#121	1	2	yes	—
261	Dic₄₇	—	2	16	no	—
262	C₂×#525	D₄₇	1	1	yes	characteristic
263	C₂³×C₄²	—	47	1	no	—
264	C₂²×#104	—	47	2	no	—
265	C₂×#407	—	47	1	no	—
266	#1896	—	47	8	no	—
267	C₂×#339	—	47	2	no	—
268	C₂×C₄₇	—	2	1	no	—
269	C₂×C₄₇	—	2	1	no	—
270	C₂×C₄₇	—	2	2	no	—
271	C₂×C₄₇	—	2	8	no	—
272	C₂×C₄₇	—	8	2	no	—
273	C₂×C₄₇	#1896	1	4	yes	complemented
274	C₂×C₄₇	C₂×#386	1	1	yes	characteristic
275	C₂×C₄₇	C₂²×#104	1	2	yes	—
276	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
277	C₂⁴×C₄	—	94	1	no	—
278	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
279	C₂²×M₁₆	—	47	2	no	—
280	#525	—	2	2	no	—
281	#525	—	2	2	no	—
282	#525	Dic₄₇	1	4	yes	complemented
283	#525	C₂×D₄₇	1	4	yes	—
284	C₂×#123	—	2	1	no	—
285	C₂×C₂²⋊Q₈	Dic₄₇	1	2	yes	complemented
286	C₂×#121	Dic₄₇	1	2	yes	complemented
287	C₂×#120	—	2	1	no	—
288	C₂×C₄×D₄	—	2	2	no	—
289	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
290	C₂²×C₄²	—	47	2	no	—
291	C₂²×C₄²	—	47	4	no	—
292	C₂²×C₄²	—	94	8	no	—
293	C₂²×C₄²	—	94	1	no	—
294	C₂²×C₄²	—	94	2	no	—
295	C₂×#104	—	47	8	no	—
296	C₂×#104	—	94	8	no	—
297	#407	—	47	4	no	—
298	#407	—	94	2	no	—
299	C₂×C₂²⋊C₈	—	94	2	no	—
300	#339	—	47	8	no	—
301	C₄₇	C₂×#1896	1	1	yes	characteristic, complemented, Sylow
302	C₂⁵	C₂²⋊D₄₇	1	1	yes	characteristic
303	C₂×#41	—	2	1	no	—
304	C₂×#41	—	2	1	no	—
305	C₂×#41	—	2	4	no	—
306	C₂×#41	—	2	4	no	—
307	C₂×#41	C₂×Dic₄₇	1	2	yes	complemented
308	C₂×#41	C₂²×D₄₇	1	2	yes	—
309	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic, complemented
310	C₂²×D₄	—	2	2	no	—
311	C₂²×D₄	—	2	1	no	—
312	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic, complemented
313	C₂³×C₄	—	2	4	no	—
314	C₂³×C₄	—	2	4	no	—
315	C₂³×C₄	—	2	1	no	—
316	C₂³×C₄	—	94	16	no	—
317	C₂³×C₄	—	94	8	no	—
318	C₂³×C₄	—	94	4	no	—
319	C₂³×C₄	—	94	2	no	—
320	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
321	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
322	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
323	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
324	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
325	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
326	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
327	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
328	C₂×M₁₆	—	47	4	no	—
329	C₂×M₁₆	—	94	2	no	—
330	C₂×M₁₆	—	94	4	no	—
331	C₂×M₁₆	—	94	4	no	—
332	C₂²×C₈	—	94	2	no	—
333	#123	—	2	4	no	—
334	#123	—	2	4	no	—
335	C₂²⋊Q₈	—	2	4	no	—
336	C₂²⋊Q₈	C₂×Dic₄₇	1	8	yes	complemented
337	#121	—	2	4	no	—
338	#121	C₂×Dic₄₇	1	8	yes	complemented
339	#120	—	2	4	no	—
340	#120	—	2	4	no	—
341	C₄×D₄	—	2	8	no	—
342	C₄×D₄	—	2	8	no	—
343	#117	—	2	1	no	—
344	#117	—	2	1	no	—
345	#117	C₂×Dic₄₇	1	2	yes	complemented
346	#117	C₂²×D₄₇	1	2	yes	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	complemented
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	C₂×C₂²⋊C₄	—	2	1	no	—
351	C₂×C₂²⋊C₄	—	2	2	no	—
352	C₂×C₄²	—	2	1	no	—
353	C₂×C₄²	—	47	8	no	—
354	C₂×C₄²	—	47	4	no	—
355	C₂×C₄²	—	94	16	no	—
356	C₂×C₄²	—	94	8	no	—
357	C₂×C₄²	—	94	16	no	—
358	C₂×C₄²	—	94	4	no	—
359	C₂×C₄²	—	94	4	no	—
360	C₂×C₄²	—	94	2	no	—
361	#104	—	94	16	no	—
362	C₂²⋊C₈	—	94	8	no	—
363	C₂⁴	—	2	8	no	—
364	C₂⁴	—	2	2	no	—
365	C₂⁴	—	2	2	no	—
366	C₂⁴	—	2	1	no	—
367	C₂⁴	C₂²⋊Dic₄₇	1	2	yes	—
368	C₂⁴	C₂²⋊Dic₄₇	1	2	yes	—
369	C₂⁴	C₂×C₂²⋊D₄₇	1	2	yes	—
370	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
371	#41	—	2	8	no	—
372	#41	—	2	4	no	—
373	#41	—	2	4	no	—
374	#41	—	4	2	no	—
375	#41	—	4	4	no	—
376	#41	—	4	2	no	—
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	2	4	no	—
379	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	complemented
380	C₂×D₄	—	2	8	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	1	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	4	8	no	—
386	C₂×D₄	—	4	2	no	—
387	C₂×D₄	—	4	2	no	—
388	C₂×D₄	C₂²×Dic₄₇	1	2	yes	complemented
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	8	no	—
392	C₂²×C₄	—	2	8	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	8	no	—
395	C₂²×C₄	—	2	8	no	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	4	4	no	—
404	C₂²×C₄	—	94	16	no	—
405	C₂²×C₄	—	94	64	no	—
406	C₂²×C₄	—	94	16	no	—
407	C₂²×C₄	—	94	32	no	—
408	C₂²×C₄	—	94	8	no	—
409	C₂²×C₄	—	94	4	no	—
410	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
411	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
412	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
413	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
414	C₂²×C₄	D₄×D₄₇	1	4	yes	—
415	C₂²×C₄	#10625352	1	4	yes	—
416	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
417	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
418	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
419	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
420	C₂²×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
421	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
422	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
423	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
424	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
425	M₁₆	—	94	4	no	—
426	M₁₆	—	94	4	no	—
427	M₁₆	—	188	4	no	—
428	C₂×C₈	—	94	4	no	—
429	C₂×C₈	—	188	4	no	—
430	C₄⋊C₄	—	2	8	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	complemented
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	8	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	8	no	—
437	C₄²	—	2	2	no	—
438	C₄²	—	2	2	no	—
439	C₄²	—	47	8	no	—
440	C₄²	—	94	16	no	—
441	C₄²	—	94	8	no	—
442	C₄²	—	94	4	no	—
443	C₂³	—	2	16	no	—
444	C₂³	—	2	16	no	—
445	C₂³	—	2	4	no	—
446	C₂³	—	2	4	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	4	no	—
450	C₂³	—	2	4	no	—
451	C₂³	—	2	8	no	—
452	C₂³	—	2	8	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	4	4	no	—
456	C₂³	#13093951	1	8	yes	complemented
457	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
458	C₂³	C₂×C₂²⋊Dic₄₇	1	4	yes	—
459	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
460	C₂³	#13093992	1	2	yes	—
461	C₂³	#13094005	1	2	yes	—
462	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
463	Q₈	—	2	4	no	—
464	Q₈	—	4	2	no	—
465	D₄	—	2	4	no	—
466	D₄	—	4	4	no	—
467	D₄	—	4	2	no	—
468	D₄	—	4	2	no	—
469	D₄	—	4	16	no	—
470	D₄	—	4	2	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	8	no	—
476	C₂×C₄	—	2	8	no	—
477	C₂×C₄	—	2	8	no	—
478	C₂×C₄	—	2	8	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	4	no	—
483	C₂×C₄	—	4	4	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	94	64	no	—
486	C₂×C₄	—	94	16	no	—
487	C₂×C₄	—	94	32	no	—
488	C₂×C₄	—	94	8	no	—
489	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
490	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
491	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
492	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
493	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
494	C₂×C₄	#13093992	1	2	yes	—
495	C₂×C₄	#13093996	1	4	yes	—
496	C₂×C₄	#13093996	1	4	yes	—
497	C₂×C₄	#13094005	1	2	yes	—
498	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
499	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
500	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
501	C₂×C₄	C₂×#10625352	1	2	yes	—
502	C₈	—	188	4	no	—
503	C₂²	—	2	8	no	—
504	C₂²	—	2	16	no	—
505	C₂²	—	2	8	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	2	4	no	—
509	C₂²	—	2	4	no	—
510	C₂²	—	2	4	no	—
511	C₂²	—	2	16	no	—
512	C₂²	—	2	4	no	—
513	C₂²	—	4	4	no	—
514	C₂²	—	4	2	no	—
515	C₂²	—	8	4	no	—
516	C₂²	#15689003	1	2	yes	—
517	C₂²	#15689003	1	2	yes	—
518	C₂²	C₂×#13093951	1	4	yes	—
519	C₂²	C₂×#13093951	1	8	yes	complemented
520	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
521	C₂²	C₂×#13093992	1	1	yes	characteristic
522	C₂²	C₂×#13094005	1	1	yes	characteristic
523	C₄	—	2	4	no	—
524	C₄	—	4	4	no	—
525	C₄	—	4	2	no	—
526	C₄	—	94	16	no	—
527	C₄	#15689003	1	2	yes	—
528	C₄	#15689003	1	2	yes	—
529	C₄	C₂×D₄×Dic₄₇	1	2	yes	—
530	C₄	C₂×#13093996	1	2	yes	—
531	C₂	—	2	1	no	—
532	C₂	—	2	2	no	—
533	C₂	—	2	1	no	—
534	C₂	—	2	8	no	—
535	C₂	—	8	2	no	—
536	C₂	#20243832	1	4	yes	direct product factor
537	C₂	C₂×#15689003	1	1	yes	characteristic
538	C₂	C₂²×#13093951	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₂×C₄₇×#525	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#525	D₄₇
hypocenter	C₄₇	C₂×#1896
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂⁴×C₄ ◁ C₂×#525

Complements

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

N	H ≅ G/N	type
1. C₂³×C₄×Dic₄₇	C₂	semidirect
2. C₂²×#13093951	C₂	semidirect
3. C₂×#15689087	C₂	semidirect
4. #20243832	C₂	direct (N × H)
5. C₂×#15688882	C₂	semidirect
13. C₂²×C₄×Dic₄₇	C₂²	semidirect
15. C₂×#13093951	C₂²	semidirect
17. #15689087	C₂²	semidirect
19. #15688882	C₂²	semidirect
24. C₄₇×#525	C₄	semidirect
27. C₂×C₂²⋊Q₈×C₄₇	C₄	semidirect
28. C₂×#121×C₄₇	C₄	semidirect
47. C₂×C₄×Dic₄₇	D₄	semidirect
56. C₂×#41×C₄₇	C₂×C₄	semidirect
58. C₂²×Q₈×C₄₇	C₂×C₄	semidirect
61. C₂²×D₄×C₄₇	C₂×C₄	semidirect
76. C₂²⋊Q₈×C₄₇	C₂×C₄	semidirect
78. #121×C₄₇	C₂×C₄	semidirect
85. #117×C₄₇	C₂×C₄	semidirect
88. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
109. C₂×Q₈×C₄₇	C₂²×C₄	semidirect
118. C₂×D₄×C₄₇	C₂²×C₄	semidirect
157. C₄⋊C₄×C₄₇	C₂²×C₄	semidirect
167. C₄×Dic₄₇	C₂×D₄	semidirect
186. C₂³×C₄₇	#104	semidirect
250. C₂²×C₄₇	C₂×#104	semidirect
273. C₂×C₄₇	#1896	semidirect
282. #525	Dic₄₇	semidirect
285. C₂×C₂²⋊Q₈	Dic₄₇	semidirect
286. C₂×#121	Dic₄₇	semidirect
301. C₄₇	C₂×#1896	semidirect
307. C₂×#41	C₂×Dic₄₇	semidirect
309. C₂²×Q₈	C₂×Dic₄₇	semidirect
312. C₂²×D₄	C₂×Dic₄₇	semidirect
336. C₂²⋊Q₈	C₂×Dic₄₇	semidirect
338. #121	C₂×Dic₄₇	semidirect
345. #117	C₂×Dic₄₇	semidirect
348. C₂×C₄⋊C₄	C₂×Dic₄₇	semidirect
379. C₂×Q₈	C₂²×Dic₄₇	semidirect
388. C₂×D₄	C₂²×Dic₄₇	semidirect
432. C₄⋊C₄	C₂²×Dic₄₇	semidirect
456. C₂³	#13093951	semidirect
519. C₂²	C₂×#13093951	semidirect
536. C₂	#20243832	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄×Dic₄₇	2
C₂²×#13093951	2
C₂×#15689087	2
#20243832	2
C₂×#15688882	2
C₂×C₄₇×#525	2
C₂×#1896	47

Subgroups — C2×#20243832 #26218032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243832 #26218032