Subgroups — #26219285

Order 12032.

934 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20245853	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244010	C₂	1	2	yes	maximal
4	#20243975	C₂	1	2	yes	maximal, complemented
5	#20243745	C₂	1	2	yes	maximal
6	#20243644	C₂	1	2	yes	maximal, complemented
7	C₄×#13093958	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#13093948	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#13093945	C₂	1	1	yes	maximal, characteristic
10	#20243133	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×#13093983	—	2	1	no	—
14	C₂×#13093958	C₂²	1	2	yes	—
15	C₂×#13093948	C₂²	1	2	yes	—
16	C₂×#13093945	C₂²	1	2	yes	—
17	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
18	#15689026	C₂²	1	2	yes	—
19	#15689022	C₂²	1	2	yes	—
20	#15689016	—	2	2	no	—
21	C₄⋊C₄×Dic₄₇	—	2	2	no	—
22	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
23	C₄×C₄⋊Dic₄₇	—	2	1	no	—
24	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
26	C₄×C₂²⋊Dic₄₇	—	2	1	no	—
27	C₄²×Dic₄₇	—	2	1	no	—
28	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
29	#15688886	C₂²	1	2	yes	—
30	#15688885	C₂²	1	2	yes	—
31	#15688885	C₂²	1	2	yes	—
32	#15688877	C₂²	1	2	yes	—
33	#15688877	C₂²	1	2	yes	—
34	C₂²×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
37	C₄×SD₁₆×C₄₇	C₄	1	8	yes	complemented
38	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×#103×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
43	Q₈×Dic₄₇	—	2	4	no	—
44	Q₈×Dic₄₇	—	2	4	no	—
45	#13093983	—	4	4	no	—
46	C₂×C₄⋊Dic₄₇	—	2	2	no	—
47	C₂×C₄⋊Dic₄₇	—	2	2	no	—
48	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
49	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
50	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
51	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
52	C₂×C₄×Dic₄₇	—	2	2	no	—
53	C₂×C₄×Dic₄₇	—	2	1	no	—
54	C₂×C₄×Dic₄₇	—	2	1	no	—
55	C₂×C₄×Dic₄₇	—	2	2	no	—
56	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
57	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
58	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
59	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
60	#13093958	—	2	4	no	—
61	#13093948	—	2	4	no	—
62	#13093945	—	2	4	no	—
63	C₄×C₄₇⋊C₈	—	2	2	no	—
64	C₄₇⋊#95	—	2	1	no	—
65	C₄₇⋊#95	—	2	1	no	—
66	C₄₇⋊#95	—	2	2	no	—
67	C₄₇⋊#95	—	2	2	no	—
68	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₄₇	—	2	1	no	—
71	C₂×SD₁₆×C₄₇	—	2	4	no	—
72	C₂×SD₁₆×C₄₇	C₂×C₄	1	4	yes	—
73	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
75	C₄×Q₈×C₄₇	—	2	2	no	—
76	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	—
77	C₄×D₄×C₄₇	—	2	2	no	—
78	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
79	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
83	C₂×C₄²×C₄₇	—	2	1	no	—
84	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
85	#106×C₄₇	C₂×C₄	1	4	yes	—
86	#103×C₄₇	C₂×C₄	1	4	yes	—
87	#102×C₄₇	C₂×C₄	1	4	yes	—
88	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	—
89	C₂⁴×C₄₇	—	2	1	no	—
90	C₂×Q₈×C₄₇	—	2	1	no	—
91	C₂×Q₈×C₄₇	—	2	2	no	—
92	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
93	C₂×Q₈×C₄₇	#41	1	4	yes	—
94	C₂×D₄×C₄₇	—	2	2	no	—
95	C₂×D₄×C₄₇	—	2	2	no	—
96	C₂×D₄×C₄₇	—	2	1	no	—
97	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₇	—	2	1	no	—
99	C₂²×C₄×C₄₇	—	2	1	no	—
100	C₂²×C₄×C₄₇	—	2	1	no	—
101	C₂²×C₄×C₄₇	—	2	4	no	—
102	C₂²×C₄×C₄₇	—	4	2	no	—
103	C₂²×C₄×C₄₇	—	4	2	no	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
107	C₂²×Dic₄₇	—	2	2	no	—
108	C₂²×Dic₄₇	—	2	2	no	—
109	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
110	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
111	SD₁₆×C₄₇	—	2	8	no	—
112	C₂×C₈×C₄₇	—	2	2	no	—
113	C₂×C₈×C₄₇	—	2	2	no	—
114	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
115	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
116	C₄⋊C₄×C₄₇	—	2	4	no	—
117	C₄⋊C₄×C₄₇	—	2	1	no	—
118	C₄⋊C₄×C₄₇	—	2	1	no	—
119	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
120	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
121	C₂²⋊C₄×C₄₇	—	2	4	no	—
122	C₄²×C₄₇	—	2	4	no	—
123	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
124	C₄²×C₄₇	#41	1	2	yes	—
125	C₂²⋊Dic₄₇	—	4	4	no	—
126	C₂²⋊Dic₄₇	—	4	4	no	—
127	C₄⋊Dic₄₇	—	2	8	no	—
128	C₄⋊Dic₄₇	—	2	2	no	—
129	C₄⋊Dic₄₇	—	2	2	no	—
130	C₄⋊Dic₄₇	—	2	2	no	—
131	C₄⋊Dic₄₇	—	4	4	no	—
132	C₄⋊Dic₄₇	#41	1	4	yes	—
133	C₄×Dic₄₇	—	2	8	no	—
134	C₄×Dic₄₇	—	2	2	no	—
135	C₄×Dic₄₇	—	2	2	no	—
136	C₄×Dic₄₇	—	2	2	no	—
137	C₄×Dic₄₇	—	2	2	no	—
138	C₄×Dic₄₇	—	2	4	no	—
139	C₄×Dic₄₇	—	4	2	no	—
140	C₄×Dic₄₇	—	4	2	no	—
141	C₄×Dic₄₇	—	4	4	no	—
142	C₂×C₄₇⋊C₈	—	2	2	no	—
143	C₂×C₄₇⋊C₈	—	2	2	no	—
144	C₂×C₄₇⋊C₈	—	2	2	no	—
145	C₂³×C₄₇	—	2	2	no	—
146	C₂³×C₄₇	—	4	2	no	—
147	C₂³×C₄₇	—	4	2	no	—
148	C₂³×C₄₇	—	4	1	no	—
149	C₂³×C₄₇	—	4	1	no	—
150	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₄₇	—	2	2	no	—
152	Q₈×C₄₇	—	2	4	no	—
153	Q₈×C₄₇	#117	1	4	yes	complemented
154	D₄×C₄₇	—	2	2	no	—
155	D₄×C₄₇	—	2	2	no	—
156	D₄×C₄₇	—	4	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	4	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	—	4	1	no	—
164	C₂×C₄×C₄₇	—	4	1	no	—
165	C₂×C₄×C₄₇	—	4	8	no	—
166	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
168	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
169	C₂×C₄×C₄₇	#137	1	2	yes	—
170	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
172	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
174	C₂×Dic₄₇	—	2	2	no	—
175	C₂×Dic₄₇	—	2	2	no	—
176	C₂×Dic₄₇	—	2	2	no	—
177	C₂×Dic₄₇	—	2	4	no	—
178	C₂×Dic₄₇	—	2	2	no	—
179	C₂×Dic₄₇	—	2	2	no	—
180	C₂×Dic₄₇	—	4	2	no	—
181	C₂×Dic₄₇	—	4	2	no	—
182	C₂×Dic₄₇	—	4	2	no	—
183	C₂×Dic₄₇	—	4	2	no	—
184	C₂×Dic₄₇	—	4	2	no	—
185	C₂×Dic₄₇	#135	1	4	yes	—
186	C₈×C₄₇	—	2	2	no	—
187	C₈×C₄₇	—	2	2	no	—
188	C₄₇⋊C₈	—	4	2	no	—
189	#21120	—	47	1	no	maximal, Sylow
190	C₂²×C₄₇	—	4	2	no	—
191	C₂²×C₄₇	—	4	2	no	—
192	C₂²×C₄₇	—	4	2	no	—
193	C₂²×C₄₇	—	8	2	no	—
194	C₂²×C₄₇	—	8	2	no	—
195	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
196	C₂²×C₄₇	#525	1	2	yes	—
197	C₂²×C₄₇	C₂×#135	1	2	yes	—
198	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
199	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
200	C₄×C₄₇	—	2	2	no	—
201	C₄×C₄₇	—	2	4	no	—
202	C₄×C₄₇	—	4	2	no	—
203	C₄×C₄₇	—	4	2	no	—
204	C₄×C₄₇	#440	1	4	yes	—
205	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
206	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
207	C₄×C₄₇	#529	1	2	yes	—
208	Dic₄₇	—	2	4	no	—
209	Dic₄₇	—	4	2	no	—
210	Dic₄₇	—	4	4	no	—
211	Dic₄₇	—	8	2	no	—
212	C₂×C₄×SD₁₆	D₄₇	1	1	yes	characteristic
213	#2293	—	47	1	no	—
214	C₄²×Q₈	—	47	1	no	—
215	#1925	—	47	2	no	—
216	#1920	—	47	2	no	—
217	#1880	—	47	2	no	—
218	#1863	—	47	2	no	—
219	C₄×#107	—	47	1	no	—
220	C₄×#103	—	47	1	no	—
221	C₄×#102	—	47	1	no	—
222	#1744	—	47	1	no	—
223	C₂×C₄₇	—	8	2	no	—
224	C₂×C₄₇	#2290	1	1	yes	characteristic
225	C₂×C₄₇	C₄×#135	1	1	yes	characteristic
226	C₂×C₄₇	C₂×#440	1	1	yes	characteristic
227	C₂×C₄₇	#3106	1	2	yes	—
228	C₂×C₄₇	#3108	1	2	yes	—
229	C₂²×SD₁₆	C₂×D₄₇	1	1	yes	characteristic
230	C₂×C₄×Q₈	—	47	2	no	—
231	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
232	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
233	C₂×#117	—	94	1	no	—
234	C₄×SD₁₆	Dic₄₇	1	8	yes	complemented
235	C₂×#107	—	47	2	no	—
236	C₂×#106	C₂×D₄₇	1	1	yes	characteristic
237	C₂×#103	—	47	2	no	—
238	C₂×#103	C₂×D₄₇	1	1	yes	characteristic
239	C₂×#102	—	47	2	no	—
240	C₂×#102	C₂×D₄₇	1	1	yes	characteristic
241	C₂×C₄×C₈	—	47	1	no	—
242	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
243	#390	—	47	2	no	—
244	#389	—	47	2	no	—
245	#388	—	94	2	no	—
246	C₄×C₄⋊C₄	—	47	2	no	—
247	C₄×C₄⋊C₄	—	47	1	no	—
248	C₄×C₄⋊C₄	—	47	1	no	—
249	C₄×C₄⋊C₄	—	94	1	no	—
250	C₄×C₄⋊C₄	—	94	2	no	—
251	C₄×C₂²⋊C₄	—	94	1	no	—
252	C₄³	—	47	1	no	—
253	C₄³	—	94	1	no	—
254	#340	—	47	2	no	—
255	#340	—	47	2	no	—
256	#340	—	47	2	no	—
257	#336	—	47	2	no	—
258	#336	—	47	2	no	—
259	C₄₇	#21120	1	1	yes	characteristic, complemented, Sylow
260	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
261	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
262	C₂³×C₄	—	2	1	no	—
263	C₂×SD₁₆	—	2	4	no	—
264	C₂×SD₁₆	C₂×Dic₄₇	1	4	yes	—
265	C₂²×C₈	—	47	2	no	—
266	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
267	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
268	C₄×Q₈	—	2	2	no	—
269	C₄×Q₈	—	94	4	no	—
270	C₄×Q₈	—	94	4	no	—
271	C₄×Q₈	C₂×Dic₄₇	1	4	yes	—
272	C₄×D₄	—	2	2	no	—
273	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
274	#117	—	188	4	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	47	2	no	—
277	C₂×C₄⋊C₄	—	47	2	no	—
278	C₂×C₄⋊C₄	—	94	2	no	—
279	C₂×C₄⋊C₄	—	94	2	no	—
280	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₂²⋊C₄	—	94	2	no	—
284	C₂×C₂²⋊C₄	—	94	2	no	—
285	C₂×C₄²	—	2	1	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	—	94	2	no	—
291	C₂×C₄²	—	94	2	no	—
292	C₂×C₄²	—	94	1	no	—
293	C₂×C₄²	—	94	1	no	—
294	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
295	#107	—	94	4	no	—
296	#106	C₂×Dic₄₇	1	4	yes	—
297	#103	—	94	4	no	—
298	#103	C₂×Dic₄₇	1	4	yes	—
299	#102	—	94	4	no	—
300	#102	C₂×Dic₄₇	1	4	yes	—
301	C₄×C₈	—	94	2	no	—
302	C₄×C₈	C₂×Dic₄₇	1	4	yes	—
303	#95	—	94	2	no	—
304	#95	—	94	2	no	—
305	#95	—	94	1	no	—
306	#95	—	94	1	no	—
307	C₂⁴	—	2	1	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×Q₈	#10625350	1	4	yes	—
311	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	47	2	no	—
323	C₂²×C₄	—	47	2	no	—
324	C₂²×C₄	—	94	2	no	—
325	C₂²×C₄	—	94	2	no	—
326	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
327	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
328	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
329	SD₁₆	—	2	8	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	94	2	no	—
333	C₂×C₈	—	94	2	no	—
334	C₂×C₈	—	94	2	no	—
335	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
336	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
337	C₄⋊C₄	—	2	4	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	47	4	no	—
341	C₄⋊C₄	—	94	8	no	—
342	C₄⋊C₄	—	94	2	no	—
343	C₄⋊C₄	—	94	2	no	—
344	C₄⋊C₄	—	94	2	no	—
345	C₄⋊C₄	—	188	4	no	—
346	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
347	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
348	C₂²⋊C₄	—	2	4	no	—
349	C₂²⋊C₄	—	188	4	no	—
350	C₂²⋊C₄	—	188	4	no	—
351	C₄²	—	2	4	no	—
352	C₄²	—	94	4	no	—
353	C₄²	—	94	8	no	—
354	C₄²	—	94	2	no	—
355	C₄²	—	94	2	no	—
356	C₄²	—	94	2	no	—
357	C₄²	—	94	2	no	—
358	C₄²	—	188	4	no	—
359	C₄²	—	188	2	no	—
360	C₄²	—	188	2	no	—
361	C₄²	#10625352	1	2	yes	—
362	C₄²	C₂²×Dic₄₇	1	2	yes	—
363	C₂³	—	2	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	1	no	—
368	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
369	Q₈	—	2	2	no	—
370	Q₈	—	2	4	no	—
371	Q₈	#13093983	1	4	yes	complemented
372	D₄	—	2	2	no	—
373	D₄	—	2	2	no	—
374	D₄	—	4	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	8	no	—
384	C₂×C₄	—	47	4	no	—
385	C₂×C₄	—	94	2	no	—
386	C₂×C₄	—	94	2	no	—
387	C₂×C₄	—	94	4	no	—
388	C₂×C₄	—	94	2	no	—
389	C₂×C₄	—	94	2	no	—
390	C₂×C₄	—	94	2	no	—
391	C₂×C₄	—	188	2	no	—
392	C₂×C₄	—	188	2	no	—
393	C₂×C₄	—	188	2	no	—
394	C₂×C₄	—	188	2	no	—
395	C₂×C₄	—	188	2	no	—
396	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
397	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
398	C₂×C₄	#13094051	1	2	yes	—
399	C₂×C₄	#13094053	1	2	yes	—
400	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
401	C₂×C₄	#41×D₄₇	1	2	yes	—
402	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
403	C₂×C₄	C₂×#10625350	1	2	yes	—
404	C₈	—	2	2	no	—
405	C₈	—	2	2	no	—
406	C₈	—	188	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
413	C₂²	#15689632	1	2	yes	—
414	C₂²	#135×D₄₇	1	2	yes	—
415	C₂²	C₂×#13094051	1	1	yes	characteristic
416	C₂²	C₂×#13094053	1	1	yes	characteristic
417	C₄	—	2	2	no	—
418	C₄	—	2	4	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	94	4	no	—
422	C₄	—	376	2	no	—
423	C₄	—	188	2	no	—
424	C₄	—	188	4	no	—
425	C₄	#15689224	1	4	yes	—
426	C₄	C₂×#13093983	1	1	yes	characteristic
427	C₄	#41×Dic₄₇	1	1	yes	characteristic
428	C₄	#15689653	1	2	yes	—
429	C₂	—	8	2	no	—
430	C₂	#20245833	1	1	yes	characteristic
431	C₂	#135×Dic₄₇	1	1	yes	characteristic
432	C₂	C₂×#15689224	1	1	yes	characteristic
433	C₂	#20253446	1	2	yes	—
434	C₂	#20253466	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
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	#21120
LCS	G ▷ C₂×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. #20243975	C₂	semidirect
6. #20243644	C₂	semidirect
7. C₄×#13093958	C₂	semidirect
8. C₄×#13093948	C₂	semidirect
10. #20243133	C₂	semidirect
37. C₄×SD₁₆×C₄₇	C₄	semidirect
153. Q₈×C₄₇	#117	semidirect
234. C₄×SD₁₆	Dic₄₇	semidirect
259. C₄₇	#21120	semidirect
371. Q₈	#13093983	semidirect

Maximal subgroups

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

subgroup	index
#20245853	2
C₄×Q₈×Dic₄₇	2
#20244010	2
#20243975	2
#20243745	2
#20243644	2
C₄×#13093958	2
C₄×#13093948	2
C₄×#13093945	2
#20243133	2
C₂×C₄×SD₁₆×C₄₇	2
#21120	47