Subgroups — C₄×#15689224 #26214769

Order 12032.

1206 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689224	C₂	1	2	yes	maximal
2	C₄×Q₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic
4	#20243288	C₂	1	2	yes	maximal, complemented
5	C₄×#13093958	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243220	C₂	1	2	yes	maximal, complemented
7	#20243215	C₂	1	2	yes	maximal
8	C₄×#13093948	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#13093945	C₂	1	1	yes	maximal, characteristic
10	C₄×#13093934	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×SD₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
13	C₂×D₄×Dic₄₇	C₂²	1	2	yes	—
14	C₂²×C₄×Dic₄₇	—	2	1	no	—
15	#15689224	C₄	1	16	yes	direct product factor
16	C₂×#13093958	C₂²	1	2	yes	—
17	C₂×#13093948	C₂²	1	2	yes	—
18	C₂×#13093945	C₂²	1	2	yes	—
19	C₂×#13093934	C₂²	1	2	yes	—
20	C₂×#13093934	C₂²	1	2	yes	—
21	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
22	C₄⋊C₄×Dic₄₇	—	2	2	no	—
23	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
24	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
25	C₄×C₄⋊Dic₄₇	—	2	1	no	—
26	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
28	C₂²⋊C₄×Dic₄₇	—	2	2	no	—
29	C₄×C₂²⋊Dic₄₇	—	2	1	no	—
30	C₄²×Dic₄₇	—	2	1	no	—
31	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
32	#15688886	C₂²	1	2	yes	—
33	#15688885	C₂²	1	2	yes	—
34	#15688885	C₂²	1	2	yes	—
35	C₂²×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
38	C₄×SD₁₆×C₄₇	C₄	1	8	yes	complemented
39	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×#103×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
43	C₂³×Dic₄₇	—	2	2	no	—
44	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
45	Q₈×Dic₄₇	—	2	4	no	—
46	Q₈×Dic₄₇	C₂×C₄	1	8	yes	complemented
47	D₄×Dic₄₇	—	2	4	no	—
48	D₄×Dic₄₇	C₂×C₄	1	8	yes	—
49	C₂×C₄⋊Dic₄₇	—	2	2	no	—
50	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
51	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
52	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
53	C₂×C₄×Dic₄₇	—	2	2	no	—
54	C₂×C₄×Dic₄₇	—	2	1	no	—
55	C₂×C₄×Dic₄₇	—	2	1	no	—
56	C₂×C₄×Dic₄₇	—	2	2	no	—
57	C₂×C₄×Dic₄₇	—	2	2	no	—
58	C₂×C₄×Dic₄₇	—	4	4	no	—
59	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
60	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
61	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
62	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
63	#13093958	C₂×C₄	1	8	yes	complemented
64	#13093948	C₂×C₄	1	8	yes	complemented
65	#13093945	C₂×C₄	1	8	yes	—
66	#13093934	—	2	4	no	—
67	#13093934	C₂×C₄	1	8	yes	complemented
68	C₄×C₄₇⋊C₈	—	2	2	no	—
69	C₄₇⋊#95	—	2	1	no	—
70	C₄₇⋊#95	—	2	1	no	—
71	C₄₇⋊#95	—	2	2	no	—
72	C₄₇⋊#95	—	2	2	no	—
73	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₄₇	—	2	1	no	—
76	C₂×SD₁₆×C₄₇	C₂×C₄	1	8	yes	—
77	C₂×SD₁₆×C₄₇	C₂×C₄	1	4	yes	—
78	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₄×Q₈×C₄₇	—	2	2	no	—
81	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
82	C₄×D₄×C₄₇	—	2	2	no	—
83	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
84	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
85	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
87	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
88	C₂×C₄²×C₄₇	—	2	1	no	—
89	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
90	#106×C₄₇	C₂×C₄	1	4	yes	complemented
91	#103×C₄₇	C₂×C₄	1	4	yes	complemented
92	#102×C₄₇	C₂×C₄	1	4	yes	—
93	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
94	C₂⁴×C₄₇	—	2	1	no	—
95	C₂×Q₈×C₄₇	—	2	1	no	—
96	C₂×Q₈×C₄₇	—	2	2	no	—
97	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
98	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
99	C₂×D₄×C₄₇	—	2	1	no	—
100	C₂×D₄×C₄₇	—	2	2	no	—
101	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
102	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₄₇	—	2	1	no	—
104	C₂²×C₄×C₄₇	—	2	1	no	—
105	C₂²×C₄×C₄₇	—	2	1	no	—
106	C₂²×C₄×C₄₇	—	2	4	no	—
107	C₂²×C₄×C₄₇	—	4	2	no	—
108	C₂²×C₄×C₄₇	—	4	2	no	—
109	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
112	C₂²×Dic₄₇	—	2	2	no	—
113	C₂²×Dic₄₇	—	2	2	no	—
114	C₂²×Dic₄₇	—	2	8	no	—
115	C₂²×Dic₄₇	—	4	4	no	—
116	C₂²×Dic₄₇	—	4	4	no	—
117	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
118	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
119	SD₁₆×C₄₇	C₄²	1	16	yes	complemented
120	C₂×C₈×C₄₇	—	2	2	no	—
121	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
122	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
123	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
124	C₄⋊C₄×C₄₇	—	2	4	no	—
125	C₄⋊C₄×C₄₇	—	2	1	no	—
126	C₄⋊C₄×C₄₇	—	2	1	no	—
127	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
128	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
129	C₂²⋊C₄×C₄₇	—	2	4	no	—
130	C₄²×C₄₇	—	2	4	no	—
131	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
132	C₄²×C₄₇	#41	1	2	yes	—
133	C₂²⋊Dic₄₇	—	2	8	no	—
134	C₄⋊Dic₄₇	—	2	2	no	—
135	C₄⋊Dic₄₇	—	2	2	no	—
136	C₄⋊Dic₄₇	—	2	8	no	—
137	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
138	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
139	C₄×Dic₄₇	—	2	2	no	—
140	C₄×Dic₄₇	—	2	2	no	—
141	C₄×Dic₄₇	—	2	8	no	—
142	C₄×Dic₄₇	—	4	2	no	—
143	C₄×Dic₄₇	—	4	4	no	—
144	C₄×Dic₄₇	—	4	4	no	—
145	C₄×Dic₄₇	—	4	2	no	—
146	C₄×Dic₄₇	—	4	2	no	—
147	C₄×Dic₄₇	C₂²×C₄	1	4	yes	—
148	C₄×Dic₄₇	#41	1	4	yes	—
149	C₂×C₄₇⋊C₈	—	2	2	no	—
150	C₂×C₄₇⋊C₈	—	2	2	no	—
151	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
152	C₂³×C₄₇	—	2	4	no	—
153	C₂³×C₄₇	—	2	2	no	—
154	C₂³×C₄₇	—	4	1	no	—
155	C₂³×C₄₇	—	4	1	no	—
156	C₂³×C₄₇	—	4	2	no	—
157	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
158	Q₈×C₄₇	—	2	4	no	—
159	Q₈×C₄₇	—	2	2	no	—
160	Q₈×C₄₇	C₂×C₄²	1	4	yes	complemented
161	D₄×C₄₇	—	2	4	no	—
162	D₄×C₄₇	—	2	2	no	—
163	D₄×C₄₇	C₂×C₄²	1	4	yes	—
164	C₂×C₄×C₄₇	—	2	4	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	4	1	no	—
170	C₂×C₄×C₄₇	—	4	1	no	—
171	C₂×C₄×C₄₇	—	4	2	no	—
172	C₂×C₄×C₄₇	—	4	8	no	—
173	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
174	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
175	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
176	C₂×C₄×C₄₇	#137	1	2	yes	—
177	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
178	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
180	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
181	C₂×Dic₄₇	—	2	2	no	—
182	C₂×Dic₄₇	—	2	2	no	—
183	C₂×Dic₄₇	—	2	2	no	—
184	C₂×Dic₄₇	—	2	2	no	—
185	C₂×Dic₄₇	—	2	4	no	—
186	C₂×Dic₄₇	—	2	4	no	—
187	C₂×Dic₄₇	—	4	16	no	—
188	C₂×Dic₄₇	—	4	2	no	—
189	C₂×Dic₄₇	—	4	2	no	—
190	C₂×Dic₄₇	—	4	2	no	—
191	C₂×Dic₄₇	—	4	2	no	—
192	C₂×Dic₄₇	C₄×D₄	1	4	yes	—
193	C₂×Dic₄₇	C₄×D₄	1	4	yes	—
194	C₈×C₄₇	—	2	2	no	—
195	C₈×C₄₇	C₂×C₄²	1	4	yes	complemented
196	C₄₇⋊C₈	—	2	4	no	—
197	C₄×#440	—	47	1	no	maximal, Sylow
198	C₂²×C₄₇	—	2	4	no	—
199	C₂²×C₄₇	—	4	2	no	—
200	C₂²×C₄₇	—	4	2	no	—
201	C₂²×C₄₇	—	4	4	no	—
202	C₂²×C₄₇	—	4	4	no	—
203	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
204	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
205	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
206	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
207	C₂²×C₄₇	#575	1	2	yes	—
208	C₄×C₄₇	—	2	2	no	—
209	C₄×C₄₇	—	2	4	no	—
210	C₄×C₄₇	—	4	2	no	—
211	C₄×C₄₇	—	4	2	no	—
212	C₄×C₄₇	#440	1	4	yes	complemented
213	C₄×C₄₇	C₂²×C₄²	1	1	yes	characteristic
214	C₄×C₄₇	C₄×#41	1	2	yes	—
215	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
216	Dic₄₇	—	2	4	no	—
217	Dic₄₇	—	2	4	no	—
218	Dic₄₇	—	4	4	no	—
219	Dic₄₇	—	4	4	no	—
220	C₂×#440	—	47	2	no	—
221	C₂×C₄×SD₁₆	D₄₇	1	1	yes	characteristic
222	C₄²×Q₈	—	47	1	no	—
223	C₄²×D₄	—	47	1	no	—
224	#1776	—	47	2	no	—
225	C₄×#107	—	47	1	no	—
226	#1763	—	47	2	no	—
227	#1762	—	47	2	no	—
228	C₄×#103	—	47	1	no	—
229	C₄×#102	—	47	1	no	—
230	C₄×#97	—	47	1	no	—
231	C₂×C₄₇	—	4	4	no	—
232	C₂×C₄₇	C₄²×D₄	1	1	yes	characteristic
233	C₂×C₄₇	C₂×#440	1	1	yes	characteristic
234	C₂×C₄₇	#2943	1	1	yes	characteristic
235	C₂×C₄₇	C₄×AGL(1,ℤ/8)	1	2	yes	—
236	C₂×C₄₇	C₄×#137	1	2	yes	—
237	C₂²×SD₁₆	C₂×D₄₇	1	1	yes	characteristic
238	C₂×C₄×Q₈	—	47	2	no	—
239	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
240	C₂×C₄×D₄	—	47	2	no	—
241	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
242	C₂²×C₄²	—	94	1	no	—
243	#440	—	47	16	no	—
244	C₄×SD₁₆	Dic₄₇	1	8	yes	complemented
245	C₂×#107	—	47	2	no	—
246	C₂×#106	C₂×D₄₇	1	1	yes	characteristic
247	C₂×#103	—	47	2	no	—
248	C₂×#103	C₂×D₄₇	1	1	yes	characteristic
249	C₂×#102	—	47	2	no	—
250	C₂×#102	C₂×D₄₇	1	1	yes	characteristic
251	C₂×#97	—	47	2	no	—
252	C₂×#97	—	47	2	no	—
253	C₂×C₄×C₈	—	47	1	no	—
254	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
255	C₄×C₄⋊C₄	—	47	2	no	—
256	C₄×C₄⋊C₄	—	47	2	no	—
257	C₄×C₄⋊C₄	—	47	1	no	—
258	C₄×C₄⋊C₄	—	47	1	no	—
259	C₄×C₄⋊C₄	—	94	1	no	—
260	C₄×C₄⋊C₄	—	94	2	no	—
261	C₄×C₂²⋊C₄	—	94	2	no	—
262	C₄×C₂²⋊C₄	—	94	1	no	—
263	C₄³	—	47	1	no	—
264	C₄³	—	94	1	no	—
265	#340	—	47	2	no	—
266	#340	—	47	2	no	—
267	#340	—	47	2	no	—
268	C₄₇	C₄×#440	1	1	yes	characteristic, complemented, Sylow
269	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
270	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
271	C₂³×C₄	—	2	1	no	—
272	C₂³×C₄	—	94	2	no	—
273	C₂×SD₁₆	C₄×D₄₇	1	8	yes	—
274	C₂×SD₁₆	C₂×Dic₄₇	1	4	yes	—
275	C₂²×C₈	—	47	2	no	—
276	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
277	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
278	C₄×Q₈	—	2	2	no	—
279	C₄×Q₈	—	47	8	no	—
280	C₄×Q₈	—	94	4	no	—
281	C₄×Q₈	C₂×Dic₄₇	1	4	yes	complemented
282	C₄×D₄	—	2	2	no	—
283	C₄×D₄	—	47	8	no	—
284	C₄×D₄	—	94	4	no	—
285	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	47	2	no	—
288	C₂×C₄⋊C₄	—	47	2	no	—
289	C₂×C₄⋊C₄	—	94	2	no	—
290	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	94	2	no	—
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	—	47	2	no	—
296	C₂×C₄²	—	47	1	no	—
297	C₂×C₄²	—	47	1	no	—
298	C₂×C₄²	—	47	2	no	—
299	C₂×C₄²	—	94	2	no	—
300	C₂×C₄²	—	94	2	no	—
301	C₂×C₄²	—	94	2	no	—
302	C₂×C₄²	—	94	1	no	—
303	C₂×C₄²	—	94	1	no	—
304	C₂×C₄²	—	188	4	no	—
305	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
306	#107	—	47	8	no	—
307	#106	C₂×Dic₄₇	1	4	yes	complemented
308	#103	—	47	8	no	—
309	#103	C₂×Dic₄₇	1	4	yes	complemented
310	#102	—	47	8	no	—
311	#102	C₂×Dic₄₇	1	4	yes	—
312	#97	—	47	8	no	—
313	#97	—	94	4	no	—
314	C₄×C₈	—	94	2	no	—
315	C₄×C₈	C₂×Dic₄₇	1	4	yes	complemented
316	#95	—	94	2	no	—
317	#95	—	94	2	no	—
318	#95	—	94	1	no	—
319	#95	—	94	1	no	—
320	C₂⁴	—	2	1	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	C₂×C₄×D₄₇	1	4	yes	—
324	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	C₂×C₄×D₄₇	1	4	yes	—
328	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	—	47	2	no	—
336	C₂²×C₄	—	47	2	no	—
337	C₂²×C₄	—	94	8	no	—
338	C₂²×C₄	—	94	2	no	—
339	C₂²×C₄	—	94	2	no	—
340	C₂²×C₄	—	188	4	no	—
341	C₂²×C₄	—	188	4	no	—
342	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
343	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
344	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
345	SD₁₆	C₄×Dic₄₇	1	16	yes	complemented
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	47	4	no	—
348	C₂×C₈	—	94	2	no	—
349	C₂×C₈	—	94	2	no	—
350	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
351	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
352	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
353	C₄⋊C₄	—	2	4	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	47	4	no	—
357	C₄⋊C₄	—	47	4	no	—
358	C₄⋊C₄	—	94	8	no	—
359	C₄⋊C₄	—	94	2	no	—
360	C₄⋊C₄	—	94	2	no	—
361	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
362	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
363	C₂²⋊C₄	—	2	4	no	—
364	C₂²⋊C₄	—	94	8	no	—
365	C₄²	—	2	4	no	—
366	C₄²	—	47	4	no	—
367	C₄²	—	47	4	no	—
368	C₄²	—	94	8	no	—
369	C₄²	—	94	2	no	—
370	C₄²	—	94	2	no	—
371	C₄²	—	188	2	no	—
372	C₄²	—	188	4	no	—
373	C₄²	—	188	4	no	—
374	C₄²	—	188	2	no	—
375	C₄²	—	188	2	no	—
376	C₄²	#10625352	1	2	yes	—
377	C₄²	C₂²×Dic₄₇	1	2	yes	—
378	C₂³	—	2	4	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	2	no	—
383	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
384	Q₈	—	2	4	no	—
385	Q₈	—	2	2	no	—
386	Q₈	C₂×C₄×Dic₄₇	1	4	yes	complemented
387	D₄	—	2	4	no	—
388	D₄	—	2	2	no	—
389	D₄	C₂×C₄×Dic₄₇	1	4	yes	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	8	no	—
399	C₂×C₄	—	47	4	no	—
400	C₂×C₄	—	47	4	no	—
401	C₂×C₄	—	94	2	no	—
402	C₂×C₄	—	94	2	no	—
403	C₂×C₄	—	94	2	no	—
404	C₂×C₄	—	94	2	no	—
405	C₂×C₄	—	94	4	no	—
406	C₂×C₄	—	94	4	no	—
407	C₂×C₄	—	188	16	no	—
408	C₂×C₄	—	188	2	no	—
409	C₂×C₄	—	188	2	no	—
410	C₂×C₄	—	188	2	no	—
411	C₂×C₄	—	188	2	no	—
412	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
413	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
414	C₂×C₄	#13094051	1	2	yes	—
415	C₂×C₄	#13094053	1	2	yes	—
416	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
417	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
418	C₂×C₄	#41×D₄₇	1	2	yes	—
419	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
420	C₈	—	2	2	no	—
421	C₈	—	94	4	no	—
422	C₈	C₂×C₄×Dic₄₇	1	4	yes	complemented
423	C₂²	—	2	4	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	4	4	no	—
428	C₂²	C₄×D₄×D₄₇	1	2	yes	—
429	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
430	C₂²	C₂×#13094051	1	1	yes	characteristic
431	C₂²	C₂×#13094053	1	1	yes	characteristic
432	C₂²	#15689920	1	2	yes	—
433	C₄	—	2	2	no	—
434	C₄	—	2	4	no	—
435	C₄	—	4	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	94	4	no	—
438	C₄	—	94	4	no	—
439	C₄	—	188	4	no	—
440	C₄	—	188	4	no	—
441	C₄	#15689224	1	4	yes	direct product factor
442	C₄	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
443	C₄	C₄×#10625352	1	2	yes	—
444	C₄	#41×Dic₄₇	1	1	yes	characteristic
445	C₂	—	4	4	no	—
446	C₂	C₄×D₄×Dic₄₇	1	1	yes	characteristic
447	C₂	C₂×#15689224	1	1	yes	characteristic
448	C₂	#20252189	1	1	yes	characteristic
449	C₂	C₄×#13094051	1	2	yes	—
450	C₂	C₄×#13094053	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄×SD₁₆×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₄×C₄₇	C₂³
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₄×SD₁₆	D₄₇
hypocenter	C₄₇	C₄×#440
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
2. C₄×Q₈×Dic₄₇	C₂	semidirect
4. #20243288	C₂	semidirect
5. C₄×#13093958	C₂	semidirect
6. #20243220	C₂	semidirect
8. C₄×#13093948	C₂	semidirect
10. C₄×#13093934	C₂	semidirect
15. #15689224	C₄	direct (N × H)
38. C₄×SD₁₆×C₄₇	C₄	semidirect
46. Q₈×Dic₄₇	C₂×C₄	semidirect
63. #13093958	C₂×C₄	semidirect
64. #13093948	C₂×C₄	semidirect
67. #13093934	C₂×C₄	semidirect
81. C₄×Q₈×C₄₇	C₂×C₄	semidirect
90. #106×C₄₇	C₂×C₄	semidirect
91. #103×C₄₇	C₂×C₄	semidirect
93. C₄×C₈×C₄₇	C₂×C₄	semidirect
119. SD₁₆×C₄₇	C₄²	semidirect
160. Q₈×C₄₇	C₂×C₄²	semidirect
195. C₈×C₄₇	C₂×C₄²	semidirect
212. C₄×C₄₇	#440	semidirect
244. C₄×SD₁₆	Dic₄₇	semidirect
268. C₄₇	C₄×#440	semidirect
281. C₄×Q₈	C₂×Dic₄₇	semidirect
307. #106	C₂×Dic₄₇	semidirect
309. #103	C₂×Dic₄₇	semidirect
315. C₄×C₈	C₂×Dic₄₇	semidirect
345. SD₁₆	C₄×Dic₄₇	semidirect
386. Q₈	C₂×C₄×Dic₄₇	semidirect
422. C₈	C₂×C₄×Dic₄₇	semidirect
441. C₄	#15689224	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×#15689224	2
C₄×Q₈×Dic₄₇	2
C₄×D₄×Dic₄₇	2
#20243288	2
C₄×#13093958	2
#20243220	2
#20243215	2
C₄×#13093948	2
C₄×#13093945	2
C₄×#13093934	2
C₂×C₄×SD₁₆×C₄₇	2
C₄×#440	47

Subgroups — C4×#15689224 #26214769

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#15689224 #26214769