Subgroups — C₂×#20244160 #26219795

Order 12032.

938 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13093959	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689146	C₂	1	1	yes	maximal, characteristic
3	C₂²×Dic₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×M₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic
5	#20244160	C₂	1	8	yes	maximal, direct product factor
6	C₂×#15688888	C₂	1	1	yes	maximal, characteristic
7	C₂×#15688887	C₂	1	1	yes	maximal, characteristic
8	C₂²×#108×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×#10625329	C₂²	1	1	yes	characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
13	C₂×#13093959	—	2	4	no	—
14	C₂×#13093959	C₂²	1	4	yes	—
15	#15689146	—	2	2	no	—
16	#15689146	C₂²	1	4	yes	—
17	C₂×Dic₄₇⋊C₈	—	2	1	no	—
18	C₂×Dic₄₇⋊C₈	—	2	1	no	—
19	C₂×Dic₄₇⋊C₈	C₄	1	2	yes	—
20	C₂×Dic₄₇⋊C₈	C₄	1	4	yes	—
21	C₂×Dic₄₇⋊C₈	C₄	1	2	yes	—
22	C₂×Dic₄₇⋊C₈	C₂²	1	4	yes	—
23	M₁₆×Dic₄₇	—	2	2	no	—
24	M₁₆×Dic₄₇	C₂²	1	4	yes	—
25	C₂×#13093934	—	2	1	no	—
26	C₂×C₈×Dic₄₇	—	2	1	no	—
27	#15688888	C₂²	1	4	yes	—
28	#15688887	C₂²	1	4	yes	—
29	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
31	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×#108×C₄₇	—	2	4	no	—
33	C₂×#108×C₄₇	C₂²	1	4	yes	—
34	C₂³×Dic₄₇	Q₈	1	1	yes	characteristic
35	C₂³×Dic₄₇	Q₈	1	1	yes	characteristic
36	C₂×#10625329	—	2	1	no	—
37	C₂×#10625329	—	2	2	no	—
38	C₂×#10625329	—	2	1	no	—
39	C₂×#10625329	—	2	2	no	—
40	C₂×#10625329	—	2	2	no	—
41	C₂×#10625329	Q₈	1	4	yes	—
42	C₂×#10625329	C₂³	1	2	yes	—
43	C₂×#10625329	C₂³	1	2	yes	—
44	C₂²×C₄₇⋊C₈	—	2	1	no	—
45	C₂²×C₄₇⋊C₈	—	2	2	no	—
46	C₂²×C₄₇⋊C₈	—	2	2	no	—
47	C₂²×C₄₇⋊C₈	—	2	1	no	—
48	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
49	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
50	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
51	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
53	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
55	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
56	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
57	C₂×C₄×Dic₄₇	Q₈	1	2	yes	—
58	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
59	#13093959	—	2	8	no	—
60	Dic₄₇⋊C₈	—	2	4	no	—
61	Dic₄₇⋊C₈	—	2	4	no	—
62	Dic₄₇⋊C₈	C₂×C₄	1	8	yes	—
63	Dic₄₇⋊C₈	C₂×C₄	1	8	yes	—
64	#13093934	—	2	4	no	—
65	C₈×Dic₄₇	—	2	4	no	—
66	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
67	C₂×M₁₆×C₄₇	—	2	1	no	—
68	C₂×M₁₆×C₄₇	—	2	2	no	—
69	C₂×M₁₆×C₄₇	—	2	1	no	—
70	C₂×M₁₆×C₄₇	—	2	2	no	—
71	C₂×M₁₆×C₄₇	—	2	2	no	—
72	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
73	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
74	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
75	C₂²×C₈×C₄₇	—	2	1	no	—
76	C₂²×C₈×C₄₇	—	2	2	no	—
77	C₂²×C₈×C₄₇	—	2	2	no	—
78	C₂²×C₈×C₄₇	—	2	1	no	—
79	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
80	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
81	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
82	#108×C₄₇	—	2	8	no	—
83	C₂⁴×C₄₇	C₂×Q₈	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₄₇	#41	1	2	yes	—
92	C₂²×C₄×C₄₇	#41	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
94	C₂²×Dic₄₇	—	2	4	no	—
95	C₂²×Dic₄₇	—	4	2	no	—
96	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
97	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
98	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
99	C₂²×Dic₄₇	C₄⋊C₄	1	2	yes	—
100	C₂²×Dic₄₇	C₄⋊C₄	1	2	yes	—
101	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
102	C₂²×Dic₄₇	C₂×Q₈	1	2	yes	—
103	C₂²×Dic₄₇	C₂×Q₈	1	2	yes	—
104	M₁₆×C₄₇	—	2	4	no	—
105	M₁₆×C₄₇	—	2	2	no	—
106	M₁₆×C₄₇	—	2	2	no	—
107	M₁₆×C₄₇	—	2	2	no	—
108	M₁₆×C₄₇	—	4	2	no	—
109	M₁₆×C₄₇	C₂×D₄	1	4	yes	—
110	C₂×C₈×C₄₇	—	2	4	no	—
111	C₂×C₈×C₄₇	—	2	4	no	—
112	C₂×C₈×C₄₇	—	2	4	no	—
113	C₂×C₈×C₄₇	—	2	2	no	—
114	C₂×C₈×C₄₇	—	2	2	no	—
115	C₂×C₈×C₄₇	—	2	2	no	—
116	C₂×C₈×C₄₇	—	2	2	no	—
117	C₂×C₈×C₄₇	—	4	2	no	—
118	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
119	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
120	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
121	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
122	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
123	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
124	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
125	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
126	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
127	#10625329	—	2	4	no	—
128	#10625329	—	2	2	no	—
129	#10625329	—	2	2	no	—
130	#10625329	—	2	2	no	—
131	#10625329	—	4	2	no	—
132	#10625329	C₂×Q₈	1	4	yes	—
133	C₂×C₄₇⋊C₈	—	2	4	no	—
134	C₂×C₄₇⋊C₈	—	2	4	no	—
135	C₂×C₄₇⋊C₈	—	2	4	no	—
136	C₂×C₄₇⋊C₈	—	2	2	no	—
137	C₂×C₄₇⋊C₈	—	2	2	no	—
138	C₂×C₄₇⋊C₈	—	2	2	no	—
139	C₂×C₄₇⋊C₈	—	2	2	no	—
140	C₂×C₄₇⋊C₈	—	4	2	no	—
141	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
142	C₂³×C₄₇	—	2	2	no	—
143	C₂³×C₄₇	—	2	2	no	—
144	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂³×C₄₇	#125	1	2	yes	—
147	C₂³×C₄₇	C₄⋊Q₈	1	2	yes	—
148	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
152	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
153	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
154	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
155	C₂×C₄×C₄₇	#121	1	2	yes	—
156	C₂×C₄×C₄₇	#121	1	2	yes	—
157	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
158	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
159	C₂×C₄×C₄₇	#125	1	2	yes	—
160	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
161	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
167	C₂×Dic₄₇	—	2	2	no	—
168	C₂×Dic₄₇	—	2	2	no	—
169	C₂×Dic₄₇	—	2	2	no	—
170	C₂×Dic₄₇	—	2	4	no	—
171	C₂×Dic₄₇	—	2	4	no	—
172	C₂×Dic₄₇	—	4	2	no	—
173	C₂×Dic₄₇	—	4	2	no	—
174	C₂×Dic₄₇	#108	1	4	yes	complemented
175	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
176	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
177	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
178	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
179	C₈×C₄₇	—	2	4	no	—
180	C₈×C₄₇	—	2	4	no	—
181	C₈×C₄₇	—	4	2	no	—
182	C₄₇⋊C₈	—	2	4	no	—
183	C₄₇⋊C₈	—	2	4	no	—
184	C₄₇⋊C₈	—	4	2	no	—
185	C₂×#1950	—	47	1	no	maximal, Sylow
186	C₂²×C₄₇	—	2	1	no	—
187	C₂²×C₄₇	—	2	1	no	—
188	C₂²×C₄₇	—	2	1	no	—
189	C₂²×C₄₇	—	2	1	no	—
190	C₂²×C₄₇	—	2	4	no	—
191	C₂²×C₄₇	—	2	4	no	—
192	C₂²×C₄₇	#389	1	2	yes	—
193	C₂²×C₄₇	#389	1	2	yes	—
194	C₂²×C₄₇	C₂×#108	1	2	yes	—
195	C₂²×C₄₇	#430	1	2	yes	—
196	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
197	C₂²×C₄₇	C₂×#125	1	1	yes	characteristic
198	C₂²×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
199	C₄×C₄₇	#389	1	2	yes	—
200	C₄×C₄₇	#389	1	2	yes	—
201	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
202	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
203	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
204	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
205	Dic₄₇	—	2	2	no	—
206	Dic₄₇	—	2	2	no	—
207	Dic₄₇	—	2	2	no	—
208	Dic₄₇	C₂×#108	1	4	yes	complemented
209	C₂²×#108	—	47	1	no	—
210	C₂²×#108	D₄₇	1	1	yes	characteristic
211	C₂×#423	—	47	1	no	—
212	C₂²×C₄⋊C₈	—	47	1	no	—
213	C₂×C₄×M₁₆	—	47	1	no	—
214	#1950	—	47	8	no	—
215	C₂×#341	—	47	1	no	—
216	C₂×#341	—	47	1	no	—
217	C₂×C₄₇	—	2	1	no	—
218	C₂×C₄₇	—	2	1	no	—
219	C₂×C₄₇	—	2	2	no	—
220	C₂×C₄₇	#1950	1	4	yes	complemented
221	C₂×C₄₇	C₂×#389	1	1	yes	characteristic
222	C₂×C₄₇	C₂²×#108	1	1	yes	characteristic
223	C₂×C₄₇	C₂×#430	1	1	yes	characteristic
224	C₂²×M₁₆	—	47	1	no	—
225	C₂²×M₁₆	—	47	1	no	—
226	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
227	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
228	C₂³×C₈	—	47	1	no	—
229	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
230	C₂²×C₄²	—	47	1	no	—
231	C₂×#108	—	2	4	no	—
232	C₂×#108	—	47	4	no	—
233	C₂×#108	—	94	4	no	—
234	C₂×#108	C₂×D₄₇	1	4	yes	—
235	#423	—	47	4	no	—
236	#423	—	94	2	no	—
237	C₂×C₄⋊C₈	—	47	2	no	—
238	C₂×C₄⋊C₈	—	47	2	no	—
239	C₂×C₄⋊C₈	—	47	4	no	—
240	C₂×C₄⋊C₈	—	47	4	no	—
241	C₂×C₄⋊C₈	—	94	1	no	—
242	C₂×C₄⋊C₈	—	94	1	no	—
243	C₄×M₁₆	—	47	4	no	—
244	C₄×M₁₆	—	94	2	no	—
245	C₂×#97	—	94	1	no	—
246	C₂×C₄×C₈	—	94	1	no	—
247	#341	—	47	4	no	—
248	#341	—	47	4	no	—
249	C₄₇	C₂×#1950	1	1	yes	characteristic, complemented, Sylow
250	C₂³×C₄	—	47	1	no	—
251	C₂³×C₄	—	47	1	no	—
252	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
253	C₂×M₁₆	—	2	1	no	—
254	C₂×M₁₆	—	2	2	no	—
255	C₂×M₁₆	—	2	1	no	—
256	C₂×M₁₆	—	2	2	no	—
257	C₂×M₁₆	—	2	2	no	—
258	C₂×M₁₆	—	47	4	no	—
259	C₂×M₁₆	—	47	2	no	—
260	C₂×M₁₆	—	47	2	no	—
261	C₂×M₁₆	—	94	2	no	—
262	C₂×M₁₆	—	94	1	no	—
263	C₂×M₁₆	—	94	1	no	—
264	C₂×M₁₆	—	94	2	no	—
265	C₂×M₁₆	—	94	2	no	—
266	C₂×M₁₆	C₂²⋊D₄₇	1	4	yes	—
267	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
268	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
269	C₂²×C₈	—	2	2	no	—
270	C₂²×C₈	—	2	1	no	—
271	C₂²×C₈	—	2	2	no	—
272	C₂²×C₈	—	2	1	no	—
273	C₂²×C₈	—	47	2	no	—
274	C₂²×C₈	—	47	2	no	—
275	C₂²×C₈	—	47	2	no	—
276	C₂²×C₈	—	94	2	no	—
277	C₂²×C₈	—	94	1	no	—
278	C₂²×C₈	—	94	2	no	—
279	C₂²×C₈	—	94	1	no	—
280	C₂²×C₈	C₄×D₄₇	1	2	yes	—
281	C₂²×C₈	C₄×D₄₇	1	2	yes	—
282	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
283	C₂×C₄²	—	47	1	no	—
284	C₂×C₄²	—	47	1	no	—
285	C₂×C₄²	—	47	2	no	—
286	C₂×C₄²	—	47	2	no	—
287	C₂×C₄²	—	47	1	no	—
288	C₂×C₄²	—	47	1	no	—
289	C₂×C₄²	—	47	2	no	—
290	C₂×C₄²	—	47	2	no	—
291	#108	—	2	8	no	—
292	#108	—	94	8	no	—
293	C₄⋊C₈	—	47	8	no	—
294	C₄⋊C₈	—	47	8	no	—
295	C₄⋊C₈	—	94	4	no	—
296	C₄⋊C₈	—	94	4	no	—
297	#97	—	94	4	no	—
298	C₄×C₈	—	94	4	no	—
299	C₂⁴	Q₈×D₄₇	1	1	yes	characteristic
300	C₂²×C₄	—	47	1	no	—
301	C₂²×C₄	—	47	2	no	—
302	C₂²×C₄	—	47	1	no	—
303	C₂²×C₄	—	47	1	no	—
304	C₂²×C₄	—	47	1	no	—
305	C₂²×C₄	—	47	2	no	—
306	C₂²×C₄	—	47	2	no	—
307	C₂²×C₄	—	47	2	no	—
308	C₂²×C₄	—	94	4	no	—
309	C₂²×C₄	—	188	2	no	—
310	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
312	C₂²×C₄	#10625350	1	2	yes	—
313	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
314	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
315	C₂²×C₄	#10625352	1	2	yes	—
316	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
317	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
318	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
319	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
320	M₁₆	—	2	4	no	—
321	M₁₆	—	2	2	no	—
322	M₁₆	—	2	2	no	—
323	M₁₆	—	2	2	no	—
324	M₁₆	—	4	2	no	—
325	M₁₆	—	47	4	no	—
326	M₁₆	—	94	4	no	—
327	M₁₆	—	94	2	no	—
328	M₁₆	—	94	2	no	—
329	M₁₆	—	94	2	no	—
330	M₁₆	—	188	2	no	—
331	M₁₆	C₂×C₂²⋊D₄₇	1	4	yes	—
332	C₂×C₈	—	2	4	no	—
333	C₂×C₈	—	2	4	no	—
334	C₂×C₈	—	2	4	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	4	2	no	—
340	C₂×C₈	—	47	4	no	—
341	C₂×C₈	—	94	4	no	—
342	C₂×C₈	—	94	4	no	—
343	C₂×C₈	—	94	4	no	—
344	C₂×C₈	—	94	2	no	—
345	C₂×C₈	—	94	2	no	—
346	C₂×C₈	—	94	2	no	—
347	C₂×C₈	—	94	2	no	—
348	C₂×C₈	—	188	2	no	—
349	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
350	C₄²	—	47	2	no	—
351	C₄²	—	47	2	no	—
352	C₄²	—	47	2	no	—
353	C₄²	—	47	2	no	—
354	C₄²	—	47	2	no	—
355	C₄²	—	47	2	no	—
356	C₄²	—	47	2	no	—
357	C₄²	—	47	2	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	2	no	—
360	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
361	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
362	C₂³	#13094014	1	2	yes	—
363	C₂³	#13094022	1	2	yes	—
364	C₂³	C₂×Q₈×D₄₇	1	1	yes	characteristic
365	C₂×C₄	—	47	2	no	—
366	C₂×C₄	—	47	4	no	—
367	C₂×C₄	—	47	2	no	—
368	C₂×C₄	—	47	2	no	—
369	C₂×C₄	—	47	2	no	—
370	C₂×C₄	—	94	4	no	—
371	C₂×C₄	—	94	4	no	—
372	C₂×C₄	—	94	2	no	—
373	C₂×C₄	—	94	2	no	—
374	C₂×C₄	—	94	2	no	—
375	C₂×C₄	—	188	2	no	—
376	C₂×C₄	—	188	2	no	—
377	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
378	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
379	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
380	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
381	C₂×C₄	#13093989	1	2	yes	—
382	C₂×C₄	#13093989	1	2	yes	—
383	C₂×C₄	#13093996	1	2	yes	—
384	C₂×C₄	#13093996	1	2	yes	—
385	C₂×C₄	#13094002	1	2	yes	—
386	C₂×C₄	#13094002	1	2	yes	—
387	C₂×C₄	#13094014	1	2	yes	—
388	C₂×C₄	#13094022	1	2	yes	—
389	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
390	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
391	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
392	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
393	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
394	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
395	C₈	—	2	4	no	—
396	C₈	—	2	4	no	—
397	C₈	—	4	2	no	—
398	C₈	—	94	4	no	—
399	C₈	—	94	4	no	—
400	C₈	—	188	2	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	4	no	—
406	C₂²	—	2	4	no	—
407	C₂²	#15689018	1	2	yes	—
408	C₂²	#15689018	1	2	yes	—
409	C₂²	#108×D₄₇	1	2	yes	—
410	C₂²	#15689170	1	2	yes	—
411	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
412	C₂²	C₂×#13094014	1	1	yes	characteristic
413	C₂²	C₂×#13094022	1	1	yes	characteristic
414	C₄	—	47	4	no	—
415	C₄	—	94	2	no	—
416	C₄	—	94	2	no	—
417	C₄	—	94	2	no	—
418	C₄	#15689018	1	2	yes	—
419	C₄	#15689018	1	2	yes	—
420	C₄	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
421	C₄	C₂×#13093989	1	1	yes	characteristic
422	C₄	C₂×#13093996	1	1	yes	characteristic
423	C₄	C₂×#13094002	1	1	yes	characteristic
424	C₂	—	2	2	no	—
425	C₂	—	2	1	no	—
426	C₂	—	2	1	no	—
427	C₂	#20244160	1	4	yes	direct product factor
428	C₂	C₂×#15689018	1	1	yes	characteristic
429	C₂	C₂×#108×D₄₇	1	1	yes	characteristic
430	C₂	C₂×#15689170	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂²×#108×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₄⋊C₄
prime radical	C₂⁴×C₄₇	C₂×Q₈
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂²×#108	D₄₇
hypocenter	C₄₇	C₂×#1950
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂²×#108

Complements

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

N	H ≅ G/N	type
5. #20244160	C₂	direct (N × H)
174. C₂×Dic₄₇	#108	semidirect
208. Dic₄₇	C₂×#108	semidirect
220. C₂×C₄₇	#1950	semidirect
249. C₄₇	C₂×#1950	semidirect
427. C₂	#20244160	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13093959	2
C₂×#15689146	2
C₂²×Dic₄₇⋊C₈	2
C₂×M₁₆×Dic₄₇	2
#20244160	2
C₂×#15688888	2
C₂×#15688887	2
C₂²×#108×C₄₇	2
C₂×#1950	47

Subgroups — C2×#20244160 #26219795

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20244160 #26219795