Subgroups — C₂×#20252248 #27080415

Order 12032.

2870 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	C₂×#15689601	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689598	C₂	1	1	yes	maximal, characteristic
3	#20252248	C₂	1	16	yes	maximal, direct product factor
4	C₂×#15689224	C₂	1	4	yes	maximal, complemented
5	C₂×SD₁₆×Dic₄₇	C₂	1	4	yes	maximal, complemented
6	C₂×#15689161	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15689132	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15689128	C₂	1	1	yes	maximal, characteristic
9	C₂×#15689078	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×SD₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
11	C₂²×#10625329	C₂²	1	1	yes	characteristic
12	#15689601	—	2	4	no	—
13	#15689601	C₂²	1	8	yes	complemented
14	#15689598	—	2	4	no	—
15	#15689598	C₂²	1	8	yes	—
16	C₂×Q₈×Dic₄₇	—	2	2	no	—
17	C₂×Q₈×Dic₄₇	C₂²	1	4	yes	complemented
18	C₂×D₄×Dic₄₇	—	2	2	no	—
19	C₂×D₄×Dic₄₇	C₂²	1	4	yes	—
20	C₂×#13093983	—	2	2	no	—
21	C₂×#13093983	C₂²	1	1	yes	characteristic
22	C₂×#13093983	C₂²	1	1	yes	characteristic
23	C₂×#13093983	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊Dic₄₇	—	2	2	no	—
25	#15689224	C₂²	1	32	yes	complemented
26	SD₁₆×Dic₄₇	C₂²	1	32	yes	complemented
27	#15689161	C₂²	1	8	yes	complemented
28	C₂×#13093958	C₂²	1	2	yes	complemented
29	C₂×#13093956	C₂²	1	2	yes	complemented
30	#15689132	C₂²	1	8	yes	complemented
31	#15689128	C₂²	1	8	yes	—
32	C₂×#13093948	C₂²	1	4	yes	complemented
33	C₂×#13093945	C₂²	1	4	yes	—
34	#15689078	C₂²	1	8	yes	complemented
35	C₂×#13093934	C₂²	1	2	yes	complemented
36	C₂×C₈×Dic₄₇	C₂²	1	2	yes	complemented
37	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
39	C₂²×SD₁₆×C₄₇	C₄	1	16	yes	complemented
40	C₂²×SD₁₆×C₄₇	C₂²	1	2	yes	—
41	C₂²×SD₁₆×C₄₇	C₂²	1	8	yes	—
42	C₂²×SD₁₆×C₄₇	C₂²	1	2	yes	—
43	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
44	C₂³×Dic₄₇	—	2	4	no	—
45	C₂×#10625329	—	2	4	no	—
46	C₂×#10625329	C₂³	1	4	yes	—
47	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
48	Q₈×Dic₄₇	—	2	16	no	—
49	Q₈×Dic₄₇	—	2	8	no	—
50	Q₈×Dic₄₇	C₂³	1	16	yes	complemented
51	D₄×Dic₄₇	—	2	16	no	—
52	D₄×Dic₄₇	—	2	8	no	—
53	D₄×Dic₄₇	C₂³	1	16	yes	—
54	#13093983	—	2	2	no	—
55	#13093983	—	2	2	no	—
56	#13093983	—	2	16	no	—
57	#13093983	D₄	1	4	yes	—
58	#13093983	C₂³	1	4	yes	—
59	#13093983	C₂³	1	4	yes	—
60	#13093983	C₂³	1	4	yes	—
61	C₂×C₄⋊Dic₄₇	—	2	4	no	—
62	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
63	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
64	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
65	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
66	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
67	C₂×C₂²⋊Dic₄₇	—	2	4	no	—
68	C₂×C₂²⋊Dic₄₇	—	2	16	no	—
69	C₂×C₂²⋊Dic₄₇	D₄	1	2	yes	—
70	C₂×C₄×Dic₄₇	—	2	1	no	—
71	C₂×C₄×Dic₄₇	—	2	1	no	—
72	C₂×C₄×Dic₄₇	—	2	4	no	—
73	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
74	#13093958	C₂³	1	8	yes	complemented
75	#13093956	C₂³	1	8	yes	complemented
76	#13093948	C₂³	1	16	yes	complemented
77	#13093945	C₂³	1	16	yes	—
78	#13093934	C₂³	1	8	yes	complemented
79	C₈×Dic₄₇	C₂³	1	8	yes	complemented
80	C₂⁵×C₄₇	—	2	1	no	—
81	C₂²×Q₈×C₄₇	—	2	1	no	—
82	C₂²×Q₈×C₄₇	—	2	2	no	—
83	C₂²×Q₈×C₄₇	—	2	4	no	—
84	C₂²×Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
85	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
86	C₂²×Q₈×C₄₇	C₂³	1	4	yes	—
87	C₂²×D₄×C₄₇	—	2	1	no	—
88	C₂²×D₄×C₄₇	—	2	2	no	—
89	C₂²×D₄×C₄₇	—	2	4	no	—
90	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	—
91	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
92	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
93	C₂³×C₄×C₄₇	—	2	1	no	—
94	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
95	C₂×SD₁₆×C₄₇	C₂×C₄	1	16	yes	complemented
96	C₂×SD₁₆×C₄₇	C₂×C₄	1	16	yes	complemented
97	C₂×SD₁₆×C₄₇	C₂×C₄	1	64	yes	complemented
98	C₂×SD₁₆×C₄₇	C₂³	1	8	yes	—
99	C₂×SD₁₆×C₄₇	C₂³	1	8	yes	—
100	C₂²×C₈×C₄₇	C₂×C₄	1	8	yes	complemented
101	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
104	C₂⁴×C₄₇	—	2	2	no	—
105	C₂⁴×C₄₇	—	2	8	no	—
106	C₂⁴×C₄₇	—	2	4	no	—
107	C₂⁴×C₄₇	—	8	4	no	—
108	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂×Q₈×C₄₇	—	2	8	no	—
110	C₂×Q₈×C₄₇	—	2	16	no	—
111	C₂×Q₈×C₄₇	—	2	4	no	—
112	C₂×Q₈×C₄₇	—	2	2	no	—
113	C₂×Q₈×C₄₇	—	2	4	no	—
114	C₂×Q₈×C₄₇	—	2	8	no	—
115	C₂×Q₈×C₄₇	C₂²×C₄	1	8	yes	—
116	C₂×Q₈×C₄₇	C₂²×C₄	1	16	yes	complemented
117	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
118	C₂×D₄×C₄₇	—	2	8	no	—
119	C₂×D₄×C₄₇	—	2	16	no	—
120	C₂×D₄×C₄₇	—	2	4	no	—
121	C₂×D₄×C₄₇	—	2	2	no	—
122	C₂×D₄×C₄₇	—	2	4	no	—
123	C₂×D₄×C₄₇	—	2	8	no	—
124	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
125	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	—
126	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
127	C₂²×C₄×C₄₇	—	2	8	no	—
128	C₂²×C₄×C₄₇	—	2	2	no	—
129	C₂²×C₄×C₄₇	—	2	4	no	—
130	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
131	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₄₇	#41	1	4	yes	—
134	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
135	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
136	C₂²×Dic₄₇	—	2	2	no	—
137	C₂²×Dic₄₇	—	2	2	no	—
138	C₂²×Dic₄₇	—	2	16	no	—
139	C₂²×Dic₄₇	—	8	8	no	—
140	C₂²×Dic₄₇	C₂×D₄	1	4	yes	—
141	SD₁₆×C₄₇	C₂²×C₄	1	32	yes	complemented
142	SD₁₆×C₄₇	C₂²×C₄	1	32	yes	complemented
143	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
144	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
145	C₂×C₈×C₄₇	C₂²×C₄	1	16	yes	complemented
146	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
147	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
148	C₂²⋊Dic₄₇	—	2	4	no	—
149	C₂²⋊Dic₄₇	—	2	4	no	—
150	C₂²⋊Dic₄₇	—	2	16	no	—
151	C₂²⋊Dic₄₇	C₂×D₄	1	8	yes	—
152	C₄⋊Dic₄₇	—	2	2	no	—
153	C₄⋊Dic₄₇	—	2	2	no	—
154	C₄⋊Dic₄₇	—	2	16	no	—
155	C₄⋊Dic₄₇	C₂×D₄	1	8	yes	—
156	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
157	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
158	C₄×Dic₄₇	—	2	4	no	—
159	C₄×Dic₄₇	—	2	4	no	—
160	C₄×Dic₄₇	—	2	16	no	—
161	C₄×Dic₄₇	C₂×D₄	1	4	yes	—
162	C₄×Dic₄₇	C₂⁴	1	4	yes	—
163	#10625329	—	2	8	no	—
164	C₂×C₄₇⋊C₈	—	2	4	no	—
165	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
166	C₂³×C₄₇	—	2	4	no	—
167	C₂³×C₄₇	—	2	8	no	—
168	C₂³×C₄₇	—	2	4	no	—
169	C₂³×C₄₇	—	2	16	no	—
170	C₂³×C₄₇	—	4	8	no	—
171	C₂³×C₄₇	—	8	16	no	—
172	C₂³×C₄₇	—	8	8	no	—
173	C₂³×C₄₇	C₄×D₄	1	4	yes	—
174	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
175	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
176	Q₈×C₄₇	—	2	8	no	—
177	Q₈×C₄₇	—	2	16	no	—
178	Q₈×C₄₇	—	2	4	no	—
179	Q₈×C₄₇	C₂³×C₄	1	8	yes	—
180	D₄×C₄₇	—	2	8	no	—
181	D₄×C₄₇	—	2	16	no	—
182	D₄×C₄₇	—	2	4	no	—
183	D₄×C₄₇	C₂³×C₄	1	8	yes	—
184	C₂×C₄×C₄₇	—	2	8	no	—
185	C₂×C₄×C₄₇	—	2	16	no	—
186	C₂×C₄×C₄₇	—	2	4	no	—
187	C₂×C₄×C₄₇	C₄×D₄	1	8	yes	—
188	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
189	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
190	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
191	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
192	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
194	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
195	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
196	C₂×Dic₄₇	—	2	8	no	—
197	C₂×Dic₄₇	—	2	4	no	—
198	C₂×Dic₄₇	—	2	4	no	—
199	C₂×Dic₄₇	—	4	4	no	—
200	C₂×Dic₄₇	—	4	4	no	—
201	C₂×Dic₄₇	—	8	16	no	—
202	C₂×Dic₄₇	C₂²×D₄	1	8	yes	—
203	C₈×C₄₇	C₂³×C₄	1	4	yes	—
204	C₈×C₄₇	C₂³×C₄	1	4	yes	—
205	C₄₇⋊C₈	—	2	4	no	—
206	C₂×#2949	—	47	1	no	maximal, Sylow
207	C₂²×C₄₇	—	2	8	no	—
208	C₂²×C₄₇	—	2	4	no	—
209	C₂²×C₄₇	—	2	8	no	—
210	C₂²×C₄₇	—	4	16	no	—
211	C₂²×C₄₇	—	4	8	no	—
212	C₂²×C₄₇	—	8	16	no	—
213	C₂²×C₄₇	C₂×C₄×D₄	1	4	yes	—
214	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
215	C₂²×C₄₇	#577	1	4	yes	—
216	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
217	C₄×C₄₇	—	2	8	no	—
218	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
219	C₄×C₄₇	C₂×C₄×D₄	1	4	yes	—
220	C₄×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
221	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
222	Dic₄₇	—	2	8	no	—
223	Dic₄₇	—	4	4	no	—
224	Dic₄₇	—	4	4	no	—
225	C₂³×SD₁₆	D₄₇	1	1	yes	characteristic
226	C₂×#519	—	47	1	no	—
227	C₂×#518	—	47	1	no	—
228	#2949	—	47	16	no	—
229	C₂×#440	—	47	4	no	—
230	C₂×C₄×SD₁₆	—	47	4	no	—
231	C₂×#427	—	47	1	no	—
232	C₂×#419	—	47	1	no	—
233	C₂×#418	—	47	1	no	—
234	C₂×#405	—	47	1	no	—
235	C₂×C₄₇	—	2	4	no	—
236	C₂×C₄₇	—	4	8	no	—
237	C₂×C₄₇	#2949	1	4	yes	complemented
238	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
239	C₂×C₄₇	C₂×#577	1	2	yes	—
240	C₂³×Q₈	C₂×D₄₇	1	1	yes	characteristic
241	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
242	C₂²×SD₁₆	Dic₄₇	1	16	yes	complemented
243	C₂²×SD₁₆	C₂×D₄₇	1	2	yes	—
244	C₂²×SD₁₆	C₂×D₄₇	1	2	yes	—
245	C₂²×SD₁₆	C₂×D₄₇	1	8	yes	—
246	C₂²×M₁₆	—	47	1	no	—
247	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
248	#519	—	47	8	no	—
249	#519	—	94	4	no	—
250	#518	—	47	8	no	—
251	#518	—	94	4	no	—
252	C₂×C₄×Q₈	—	47	4	no	—
253	C₂×C₄×Q₈	—	94	2	no	—
254	C₂×C₄×D₄	—	47	4	no	—
255	C₂×C₄×D₄	—	94	2	no	—
256	C₂×#117	—	47	1	no	—
257	C₂×#117	—	47	1	no	—
258	C₂×#117	—	47	1	no	—
259	C₂×#117	—	94	2	no	—
260	C₂²×C₂²⋊C₄	—	94	2	no	—
261	#440	—	47	32	no	—
262	C₄×SD₁₆	—	47	32	no	—
263	#427	—	47	8	no	—
264	C₂×#107	—	47	2	no	—
265	C₂×#106	—	47	2	no	—
266	#419	—	47	8	no	—
267	#418	—	47	8	no	—
268	C₂×#103	—	47	4	no	—
269	C₂×#102	—	47	4	no	—
270	#405	—	47	8	no	—
271	C₂×#97	—	47	2	no	—
272	C₂×C₄×C₈	—	47	2	no	—
273	C₄₇	C₂×#2949	1	1	yes	characteristic, complemented, Sylow
274	C₂⁵	—	2	1	no	—
275	C₂²×Q₈	—	2	1	no	—
276	C₂²×Q₈	—	2	2	no	—
277	C₂²×Q₈	—	2	4	no	—
278	C₂²×Q₈	C₂×Dic₄₇	1	8	yes	complemented
279	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
280	C₂²×Q₈	C₂²×D₄₇	1	4	yes	—
281	C₂²×D₄	—	2	1	no	—
282	C₂²×D₄	—	2	2	no	—
283	C₂²×D₄	—	2	4	no	—
284	C₂²×D₄	C₂×Dic₄₇	1	8	yes	—
285	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
286	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
287	C₂³×C₄	—	2	1	no	—
288	C₂³×C₄	—	94	4	no	—
289	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
290	C₂×SD₁₆	C₂×Dic₄₇	1	16	yes	complemented
291	C₂×SD₁₆	C₂×Dic₄₇	1	16	yes	complemented
292	C₂×SD₁₆	C₂×Dic₄₇	1	64	yes	complemented
293	C₂×SD₁₆	C₂²×D₄₇	1	8	yes	—
294	C₂×SD₁₆	C₂²×D₄₇	1	8	yes	—
295	C₂×M₁₆	—	47	4	no	—
296	C₂×M₁₆	—	94	4	no	—
297	C₂²×C₈	—	47	2	no	—
298	C₂²×C₈	C₂×Dic₄₇	1	8	yes	complemented
299	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
300	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
301	C₂²×C₈	C₂²×D₄₇	1	4	yes	—
302	C₄×Q₈	—	47	16	no	—
303	C₄×Q₈	—	94	8	no	—
304	C₄×Q₈	—	94	16	no	—
305	C₄×D₄	—	47	16	no	—
306	C₄×D₄	—	94	8	no	—
307	C₄×D₄	—	94	16	no	—
308	#117	—	47	4	no	—
309	#117	—	47	4	no	—
310	#117	—	47	4	no	—
311	#117	—	47	4	no	—
312	#117	—	94	16	no	—
313	#117	—	94	2	no	—
314	#117	—	94	2	no	—
315	C₂×C₄⋊C₄	—	47	2	no	—
316	C₂×C₄⋊C₄	—	47	2	no	—
317	C₂×C₄⋊C₄	—	47	2	no	—
318	C₂×C₄⋊C₄	—	94	4	no	—
319	C₂×C₂²⋊C₄	—	47	2	no	—
320	C₂×C₂²⋊C₄	—	94	16	no	—
321	C₂×C₂²⋊C₄	—	94	4	no	—
322	C₂×C₂²⋊C₄	—	94	1	no	—
323	C₂×C₂²⋊C₄	—	94	1	no	—
324	C₂×C₄²	—	47	2	no	—
325	C₂×C₄²	—	94	4	no	—
326	C₂×C₄²	—	94	1	no	—
327	C₂×C₄²	—	94	1	no	—
328	#107	—	47	8	no	—
329	#106	—	47	8	no	—
330	#103	—	47	16	no	—
331	#102	—	47	16	no	—
332	#97	—	47	8	no	—
333	C₄×C₈	—	47	8	no	—
334	C₂⁴	—	2	2	no	—
335	C₂⁴	—	2	8	no	—
336	C₂⁴	—	2	4	no	—
337	C₂⁴	—	8	4	no	—
338	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
339	C₂×Q₈	—	2	8	no	—
340	C₂×Q₈	—	2	16	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	4	no	—
343	C₂×Q₈	—	2	4	no	—
344	C₂×Q₈	—	2	8	no	—
345	C₂×Q₈	C₂²×Dic₄₇	1	8	yes	—
346	C₂×Q₈	C₂²×Dic₄₇	1	16	yes	complemented
347	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
348	C₂×D₄	—	2	8	no	—
349	C₂×D₄	—	2	16	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	4	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	8	no	—
354	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
355	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
356	C₂×D₄	C₂³×D₄₇	1	4	yes	—
357	C₂²×C₄	—	2	8	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	47	4	no	—
361	C₂²×C₄	—	94	16	no	—
362	C₂²×C₄	—	94	2	no	—
363	C₂²×C₄	—	94	2	no	—
364	C₂²×C₄	—	376	8	no	—
365	C₂²×C₄	D₄×D₄₇	1	2	yes	—
366	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
367	C₂²×C₄	#10625352	1	4	yes	—
368	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
369	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
370	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
371	SD₁₆	C₂²×Dic₄₇	1	32	yes	complemented
372	SD₁₆	C₂²×Dic₄₇	1	32	yes	complemented
373	M₁₆	—	94	8	no	—
374	C₂×C₈	—	47	4	no	—
375	C₂×C₈	—	94	4	no	—
376	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
377	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
378	C₂×C₈	C₂²×Dic₄₇	1	16	yes	complemented
379	C₂×C₈	C₂³×D₄₇	1	2	yes	—
380	C₂×C₈	C₂³×D₄₇	1	2	yes	—
381	C₄⋊C₄	—	47	8	no	—
382	C₄⋊C₄	—	47	4	no	—
383	C₄⋊C₄	—	47	4	no	—
384	C₄⋊C₄	—	94	16	no	—
385	C₄⋊C₄	—	94	2	no	—
386	C₄⋊C₄	—	94	2	no	—
387	C₂²⋊C₄	—	47	8	no	—
388	C₂²⋊C₄	—	94	16	no	—
389	C₂²⋊C₄	—	94	4	no	—
390	C₂²⋊C₄	—	94	4	no	—
391	C₄²	—	47	4	no	—
392	C₄²	—	47	4	no	—
393	C₄²	—	94	16	no	—
394	C₄²	—	94	4	no	—
395	C₄²	—	94	4	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	2	8	no	—
398	C₂³	—	2	4	no	—
399	C₂³	—	2	16	no	—
400	C₂³	—	4	8	no	—
401	C₂³	—	8	16	no	—
402	C₂³	—	8	8	no	—
403	C₂³	D₄×Dic₄₇	1	4	yes	—
404	C₂³	C₂×D₄×D₄₇	1	2	yes	—
405	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
406	Q₈	—	2	8	no	—
407	Q₈	—	2	16	no	—
408	Q₈	—	2	4	no	—
409	Q₈	C₂³×Dic₄₇	1	8	yes	—
410	D₄	—	2	8	no	—
411	D₄	—	2	16	no	—
412	D₄	—	2	4	no	—
413	D₄	C₂³×Dic₄₇	1	8	yes	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	16	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	47	8	no	—
418	C₂×C₄	—	94	8	no	—
419	C₂×C₄	—	94	4	no	—
420	C₂×C₄	—	94	4	no	—
421	C₂×C₄	—	376	16	no	—
422	C₂×C₄	—	188	4	no	—
423	C₂×C₄	—	188	4	no	—
424	C₂×C₄	D₄×Dic₄₇	1	8	yes	—
425	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
426	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
427	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
428	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
429	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
430	C₂×C₄	C₂×#10625352	1	2	yes	—
431	C₂×C₄	C₂×#10625352	1	4	yes	—
432	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
433	C₈	—	94	4	no	—
434	C₈	C₂³×Dic₄₇	1	4	yes	—
435	C₈	C₂³×Dic₄₇	1	4	yes	—
436	C₂²	—	2	8	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	2	8	no	—
439	C₂²	—	4	16	no	—
440	C₂²	—	4	8	no	—
441	C₂²	—	8	16	no	—
442	C₂²	C₂×D₄×Dic₄₇	1	4	yes	—
443	C₂²	C₂×D₄×Dic₄₇	1	2	yes	—
444	C₂²	#15689929	1	4	yes	—
445	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
446	C₄	—	2	8	no	—
447	C₄	—	94	8	no	—
448	C₄	—	188	4	no	—
449	C₄	—	188	4	no	—
450	C₄	C₂×D₄×Dic₄₇	1	2	yes	—
451	C₄	C₂×D₄×Dic₄₇	1	4	yes	—
452	C₄	C₂⁴×Dic₄₇	1	1	yes	characteristic
453	C₄	C₂²×#10625352	1	1	yes	characteristic
454	C₂	—	2	4	no	—
455	C₂	—	4	8	no	—
456	C₂	#20252248	1	4	yes	direct product factor
457	C₂	C₂²×D₄×Dic₄₇	1	1	yes	characteristic
458	C₂	C₂×#15689929	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂³×SD₁₆×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂³×D₄×C₄₇	C₂²
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂³×SD₁₆	D₄₇
hypocenter	C₄₇	C₂×#2949
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×SD₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#15689601	C₂	semidirect
3. #20252248	C₂	direct (N × H)
4. C₂×#15689224	C₂	semidirect
5. C₂×SD₁₆×Dic₄₇	C₂	semidirect
6. C₂×#15689161	C₂	semidirect
7. C₂×#15689132	C₂	semidirect
9. C₂×#15689078	C₂	semidirect
13. #15689601	C₂²	semidirect
17. C₂×Q₈×Dic₄₇	C₂²	semidirect
25. #15689224	C₂²	semidirect
26. SD₁₆×Dic₄₇	C₂²	semidirect
27. #15689161	C₂²	semidirect
28. C₂×#13093958	C₂²	semidirect
29. C₂×#13093956	C₂²	semidirect
30. #15689132	C₂²	semidirect
32. C₂×#13093948	C₂²	semidirect
34. #15689078	C₂²	semidirect
35. C₂×#13093934	C₂²	semidirect
36. C₂×C₈×Dic₄₇	C₂²	semidirect
39. C₂²×SD₁₆×C₄₇	C₄	semidirect
50. Q₈×Dic₄₇	C₂³	semidirect
74. #13093958	C₂³	semidirect
75. #13093956	C₂³	semidirect
76. #13093948	C₂³	semidirect
78. #13093934	C₂³	semidirect
79. C₈×Dic₄₇	C₂³	semidirect
84. C₂²×Q₈×C₄₇	C₂×C₄	semidirect
95. C₂×SD₁₆×C₄₇	C₂×C₄	semidirect
96. C₂×SD₁₆×C₄₇	C₂×C₄	semidirect
97. C₂×SD₁₆×C₄₇	C₂×C₄	semidirect
100. C₂²×C₈×C₄₇	C₂×C₄	semidirect
116. C₂×Q₈×C₄₇	C₂²×C₄	semidirect
141. SD₁₆×C₄₇	C₂²×C₄	semidirect
142. SD₁₆×C₄₇	C₂²×C₄	semidirect
145. C₂×C₈×C₄₇	C₂²×C₄	semidirect
237. C₂×C₄₇	#2949	semidirect
242. C₂²×SD₁₆	Dic₄₇	semidirect
273. C₄₇	C₂×#2949	semidirect
278. C₂²×Q₈	C₂×Dic₄₇	semidirect
290. C₂×SD₁₆	C₂×Dic₄₇	semidirect
291. C₂×SD₁₆	C₂×Dic₄₇	semidirect
292. C₂×SD₁₆	C₂×Dic₄₇	semidirect
298. C₂²×C₈	C₂×Dic₄₇	semidirect
346. C₂×Q₈	C₂²×Dic₄₇	semidirect
371. SD₁₆	C₂²×Dic₄₇	semidirect
372. SD₁₆	C₂²×Dic₄₇	semidirect
378. C₂×C₈	C₂²×Dic₄₇	semidirect
456. C₂	#20252248	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#15689601	2
C₂×#15689598	2
#20252248	2
C₂×#15689224	2
C₂×SD₁₆×Dic₄₇	2
C₂×#15689161	2
C₂×#15689132	2
C₂×#15689128	2
C₂×#15689078	2
C₂³×SD₁₆×C₄₇	2
C₂×#2949	47

Subgroups — C2×#20252248 #27080415

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20252248 #27080415