Subgroups — #26238158

Order 12032.

886 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689410	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×D₁₈₈	C₂	1	1	yes	maximal, characteristic
3	#20244350	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244146	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244128	C₂	1	2	yes	maximal, complemented
6	#20243973	C₂	1	2	yes	maximal, complemented
7	#20243634	C₂	1	2	yes	maximal
8	#20243257	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243216	C₂	1	2	yes	maximal
10	C₄×#13093944	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#2369	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
13	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₄×D₄₇	—	2	1	no	—
15	#15689410	C₄	1	8	yes	complemented
16	C₂×#13093957	C₂²	1	2	yes	—
17	C₂×#13093955	C₂²	1	2	yes	—
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×#13093944	C₂²	1	1	yes	characteristic
20	C₂×#13093944	C₂²	1	2	yes	—
21	C₂×#13093944	C₂²	1	1	yes	characteristic
22	C₂×#13093935	C₂²	1	2	yes	—
23	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
24	#15689021	C₂²	1	2	yes	—
25	#15688997	—	2	2	no	—
26	#15688993	C₂²	1	1	yes	characteristic
27	#15688980	—	2	1	no	—
28	#15688885	C₂²	1	1	yes	characteristic
29	#15688885	C₂²	1	2	yes	—
30	#15688885	C₂²	1	2	yes	—
31	#15688885	C₂²	1	1	yes	characteristic
32	#15688885	C₂²	1	2	yes	—
33	#15688878	C₂²	1	2	yes	—
34	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
35	C₄₇×#391	—	2	2	no	—
36	C₄₇×#389	—	2	1	no	—
37	C₄₇×#389	C₂²	1	2	yes	—
38	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
39	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
40	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
42	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
43	C₂²×C₄×D₄₇	—	2	1	no	—
44	C₂²×C₄×D₄₇	—	2	2	no	—
45	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	C₄×D₁₈₈	—	2	2	no	—
49	C₄×D₁₈₈	—	2	4	no	—
50	C₄×D₁₈₈	—	4	2	no	—
51	C₄×D₁₈₈	C₂×C₄	1	4	yes	—
52	C₂×C₄⋊Dic₄₇	—	2	1	no	—
53	C₂×C₄⋊Dic₄₇	—	2	1	no	—
54	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
55	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
56	C₂×Dic₄₇⋊C₄	—	2	2	no	—
57	C₄⋊C₄×D₄₇	—	4	4	no	—
58	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
59	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
60	#13093957	—	4	2	no	—
61	#13093955	C₂×C₄	1	8	yes	complemented
62	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
63	#13093944	—	2	2	no	—
64	#13093944	C₂×C₄	1	8	yes	—
65	#13093944	Q₈	1	4	yes	complemented
66	#13093935	—	4	2	no	—
67	C₄×C₄₇⋊C₈	—	2	2	no	—
68	C₄₇⋊#95	—	2	2	no	—
69	C₂²×Q₈×C₄₇	—	2	1	no	—
70	C₄⋊Q₈×C₄₇	—	2	2	no	—
71	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
72	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
73	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
74	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₄₇	—	2	1	no	—
80	C₂×C₄²×C₄₇	—	2	2	no	—
81	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
82	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
83	#95×C₄₇	—	2	2	no	—
84	#95×C₄₇	—	2	2	no	—
85	#95×C₄₇	—	2	1	no	—
86	#95×C₄₇	D₄	1	2	yes	—
87	C₂³×D₄₇	—	2	1	no	—
88	C₂×Q₈×C₄₇	—	2	4	no	—
89	C₂×Q₈×C₄₇	—	8	1	no	—
90	C₂×Q₈×C₄₇	—	8	1	no	—
91	C₂²×C₄×C₄₇	—	2	1	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	1	no	—
94	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
99	C₂²×Dic₄₇	—	2	1	no	—
100	C₂²×Dic₄₇	—	2	2	no	—
101	C₂×D₁₈₈	—	2	1	no	—
102	C₂×D₁₈₈	—	2	1	no	—
103	C₂×D₁₈₈	—	2	1	no	—
104	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
105	C₂×D₁₈₈	C₂×Q₈	1	2	yes	—
106	C₂×D₁₈₈	#41	1	2	yes	—
107	C₂×C₄×D₄₇	—	2	4	no	—
108	C₂×C₄×D₄₇	—	4	2	no	—
109	C₂×C₄×D₄₇	—	4	2	no	—
110	C₂×C₄×D₄₇	—	4	4	no	—
111	C₂×C₄×D₄₇	—	4	4	no	—
112	C₂×C₄×D₄₇	—	8	2	no	—
113	C₄⋊C₄×C₄₇	—	2	4	no	—
114	C₄⋊C₄×C₄₇	—	2	2	no	—
115	C₄⋊C₄×C₄₇	—	2	2	no	—
116	C₄⋊C₄×C₄₇	—	2	2	no	—
117	C₄⋊C₄×C₄₇	—	2	1	no	—
118	C₄⋊C₄×C₄₇	—	2	1	no	—
119	C₄⋊C₄×C₄₇	—	2	1	no	—
120	C₄⋊C₄×C₄₇	—	8	2	no	—
121	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
122	C₄⋊C₄×C₄₇	C₂×Q₈	1	2	yes	—
123	C₄²×C₄₇	—	2	2	no	—
124	C₄²×C₄₇	—	2	2	no	—
125	C₄²×C₄₇	—	4	2	no	—
126	C₄²×C₄₇	—	8	2	no	—
127	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
128	C₄²×C₄₇	#41	1	2	yes	—
129	(C₂×D₄₇)⋊C₄	—	2	4	no	—
130	(C₂×D₄₇)⋊C₄	—	4	4	no	—
131	C₄⋊Dic₄₇	—	2	1	no	—
132	C₄⋊Dic₄₇	—	2	2	no	—
133	C₄⋊Dic₄₇	—	2	2	no	—
134	C₄⋊Dic₄₇	—	4	2	no	—
135	C₄⋊Dic₄₇	—	8	1	no	—
136	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
137	Dic₄₇⋊C₄	—	4	4	no	—
138	C₂×C₄₇⋊C₈	—	2	1	no	—
139	C₂×C₄₇⋊C₈	—	2	1	no	—
140	C₂×C₄₇⋊C₈	—	2	2	no	—
141	C₂×C₄₇⋊C₈	—	2	2	no	—
142	C₂×C₄₇⋊C₈	—	2	1	no	—
143	C₂×C₄₇⋊C₈	—	2	1	no	—
144	C₂×C₄₇⋊C₈	—	2	1	no	—
145	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
146	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
147	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
148	C₂²×D₄₇	—	2	2	no	—
149	C₂²×D₄₇	—	2	2	no	—
150	C₂²×D₄₇	—	2	2	no	—
151	C₂²×D₄₇	—	4	1	no	—
152	C₂²×D₄₇	—	4	1	no	—
153	C₂²×D₄₇	—	4	1	no	—
154	C₂²×D₄₇	—	4	1	no	—
155	Q₈×C₄₇	—	8	4	no	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	2	1	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	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	2	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	4	1	no	—
167	C₂×C₄×C₄₇	—	4	2	no	—
168	C₂×C₄×C₄₇	—	4	1	no	—
169	C₂×C₄×C₄₇	—	4	2	no	—
170	C₂×C₄×C₄₇	—	4	1	no	—
171	C₂×C₄×C₄₇	—	4	1	no	—
172	C₂×C₄×C₄₇	—	4	1	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	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
182	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
183	C₂×Dic₄₇	—	2	2	no	—
184	C₂×Dic₄₇	—	4	1	no	—
185	C₂×Dic₄₇	—	4	1	no	—
186	C₂×Dic₄₇	—	4	2	no	—
187	C₂×Dic₄₇	—	4	2	no	—
188	C₂×Dic₄₇	—	4	2	no	—
189	D₁₈₈	—	2	2	no	—
190	D₁₈₈	—	2	2	no	—
191	D₁₈₈	—	2	2	no	—
192	D₁₈₈	C₄×Q₈	1	4	yes	—
193	C₄×D₄₇	—	4	8	no	—
194	C₄×D₄₇	—	8	8	no	—
195	C₄₇⋊C₈	—	2	4	no	—
196	C₄₇⋊C₈	—	2	2	no	—
197	C₄₇⋊C₈	—	4	1	no	—
198	#22969	—	47	1	no	maximal, Sylow
199	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
200	C₂²×C₄₇	#546	1	1	yes	characteristic
201	C₂²×C₄₇	D₄×Q₈	1	1	yes	characteristic
202	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
203	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
204	C₂²×C₄₇	#576	1	1	yes	characteristic
205	C₂²×C₄₇	#577	1	1	yes	characteristic
206	C₂×D₄₇	—	2	4	no	—
207	C₂×D₄₇	—	4	2	no	—
208	C₂×D₄₇	—	4	2	no	—
209	C₂×D₄₇	—	4	2	no	—
210	C₂×D₄₇	—	4	2	no	—
211	C₂×D₄₇	—	4	2	no	—
212	C₂×D₄₇	—	4	2	no	—
213	C₄×C₄₇	—	2	2	no	—
214	C₄×C₄₇	—	4	2	no	—
215	C₄×C₄₇	—	4	2	no	—
216	C₄×C₄₇	—	4	4	no	—
217	C₄×C₄₇	—	4	2	no	—
218	C₄×C₄₇	—	8	1	no	—
219	C₄×C₄₇	#440	1	4	yes	—
220	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
221	C₄×C₄₇	#520	1	1	yes	characteristic
222	C₄×C₄₇	#552	1	1	yes	characteristic
223	C₄×C₄₇	#554	1	1	yes	characteristic
224	Dic₄₇	—	4	2	no	—
225	Dic₄₇	—	8	2	no	—
226	C₂×#476	—	47	1	no	—
227	#2369	D₄₇	1	1	yes	characteristic, complemented
228	D₄×C₄⋊C₄	—	47	1	no	—
229	#1990	—	47	1	no	—
230	#1947	—	47	1	no	—
231	#1944	—	47	2	no	—
232	#1920	—	47	2	no	—
233	#1862	—	47	2	no	—
234	#1770	—	47	1	no	—
235	#1762	—	47	2	no	—
236	C₄×#102	—	47	1	no	—
237	C₂×C₄₇	#2360	1	1	yes	characteristic
238	C₂×C₄₇	C₂×#440	1	1	yes	characteristic
239	C₂×C₄₇	#2946	1	1	yes	characteristic
240	C₂×C₄₇	#3325	1	1	yes	characteristic
241	C₂×C₄₇	#3331	1	1	yes	characteristic
242	C₂×C₄₇	#3384	1	1	yes	characteristic
243	C₂×C₄₇	#3385	1	1	yes	characteristic
244	D₄₇	—	4	4	no	—
245	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
246	C₂×C₄×D₄	—	47	1	no	—
247	C₂×C₄×D₄	—	47	2	no	—
248	C₂²×C₄⋊C₄	—	94	1	no	—
249	#476	—	47	8	no	—
250	C₂×#107	—	47	2	no	—
251	C₂×#106	—	47	2	no	—
252	C₂×C₄⋊C₈	—	47	1	no	—
253	C₂×#102	—	47	2	no	—
254	C₂×#102	—	47	1	no	—
255	C₂×#102	—	47	1	no	—
256	C₂×#97	—	47	2	no	—
257	C₂×C₄×C₈	—	47	1	no	—
258	#391	—	2	2	no	—
259	#389	—	2	1	no	—
260	#389	—	47	2	no	—
261	#389	C₂×D₄₇	1	2	yes	—
262	#385	—	94	2	no	—
263	#384	—	47	1	no	—
264	#380	—	94	1	no	—
265	C₄×C₄⋊C₄	—	2	1	no	—
266	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
267	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
268	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
269	#340	—	47	2	no	—
270	#340	—	47	1	no	—
271	#340	—	47	2	no	—
272	#340	—	47	1	no	—
273	#340	—	47	2	no	—
274	#336	—	47	2	no	—
275	C₄₇	#22969	1	1	yes	characteristic, complemented, Sylow
276	C₂²×Q₈	—	2	1	no	—
277	C₂²×D₄	—	47	1	no	—
278	C₂³×C₄	—	94	1	no	—
279	C₂³×C₄	—	94	2	no	—
280	C₂²×C₈	—	47	2	no	—
281	C₂²×C₈	—	47	1	no	—
282	C₂²×C₈	—	47	1	no	—
283	C₄⋊Q₈	—	2	2	no	—
284	C₄⋊Q₈	C₄×D₄₇	1	4	yes	complemented
285	C₄×D₄	—	47	4	no	—
286	C₄×D₄	—	94	4	no	—
287	C₄×D₄	—	94	2	no	—
288	C₄×D₄	—	188	2	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	47	1	no	—
292	C₂×C₄⋊C₄	—	47	2	no	—
293	C₂×C₄⋊C₄	—	94	1	no	—
294	C₂×C₄⋊C₄	—	94	2	no	—
295	C₂×C₄⋊C₄	—	94	1	no	—
296	C₂×C₄⋊C₄	—	188	4	no	—
297	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
301	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
302	C₂×C₂²⋊C₄	—	94	1	no	—
303	C₂×C₂²⋊C₄	—	94	2	no	—
304	C₂×C₄²	—	2	1	no	—
305	C₂×C₄²	—	2	2	no	—
306	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
307	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
308	#107	—	188	2	no	—
309	#106	—	47	8	no	—
310	C₄⋊C₈	—	47	4	no	—
311	#102	—	47	8	no	—
312	#102	—	47	4	no	—
313	#102	—	94	2	no	—
314	#97	—	188	2	no	—
315	C₄×C₈	—	94	2	no	—
316	#95	—	2	2	no	—
317	#95	—	2	2	no	—
318	#95	—	2	1	no	—
319	#95	—	94	2	no	—
320	#95	C₂²⋊D₄₇	1	2	yes	—
321	C₂⁴	—	94	1	no	—
322	C₂×Q₈	—	2	4	no	—
323	C₂×Q₈	—	8	1	no	—
324	C₂×Q₈	—	8	1	no	—
325	C₂×D₄	—	47	2	no	—
326	C₂×D₄	—	47	2	no	—
327	C₂×D₄	—	47	2	no	—
328	C₂×D₄	—	94	1	no	—
329	C₂×D₄	—	94	1	no	—
330	C₂×D₄	—	94	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	94	1	no	—
335	C₂²×C₄	—	94	4	no	—
336	C₂²×C₄	—	94	2	no	—
337	C₂²×C₄	—	376	2	no	—
338	C₂²×C₄	—	188	4	no	—
339	C₂²×C₄	—	188	4	no	—
340	C₂²×C₄	—	188	2	no	—
341	C₂²×C₄	—	188	2	no	—
342	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
343	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
344	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
345	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
346	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
347	C₂×C₈	—	47	4	no	—
348	C₂×C₈	—	47	2	no	—
349	C₂×C₈	—	94	1	no	—
350	C₂×C₈	—	94	1	no	—
351	C₂×C₈	—	94	2	no	—
352	C₂×C₈	—	94	2	no	—
353	C₂×C₈	—	94	1	no	—
354	C₂×C₈	—	94	1	no	—
355	C₂×C₈	—	94	1	no	—
356	C₄⋊C₄	—	2	4	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	8	2	no	—
364	C₄⋊C₄	—	47	2	no	—
365	C₄⋊C₄	—	94	1	no	—
366	C₄⋊C₄	—	94	2	no	—
367	C₄⋊C₄	—	94	2	no	—
368	C₄⋊C₄	—	376	1	no	—
369	C₄⋊C₄	—	188	4	no	—
370	C₄⋊C₄	—	188	2	no	—
371	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
372	C₄⋊C₄	Q₈×D₄₇	1	2	yes	—
373	C₂²⋊C₄	—	94	4	no	—
374	C₂²⋊C₄	—	188	4	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	4	2	no	—
378	C₄²	—	8	2	no	—
379	C₄²	C₂×C₄×D₄₇	1	2	yes	—
380	C₄²	#10625350	1	2	yes	—
381	C₂³	—	94	2	no	—
382	C₂³	—	94	2	no	—
383	C₂³	—	94	2	no	—
384	C₂³	—	188	1	no	—
385	C₂³	—	188	1	no	—
386	C₂³	—	188	1	no	—
387	C₂³	—	188	1	no	—
388	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
389	Q₈	—	8	4	no	—
390	D₄	—	47	4	no	—
391	D₄	—	94	2	no	—
392	D₄	—	94	2	no	—
393	D₄	—	94	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	94	2	no	—
412	C₂×C₄	—	376	8	no	—
413	C₂×C₄	—	188	2	no	—
414	C₂×C₄	—	188	2	no	—
415	C₂×C₄	—	188	2	no	—
416	C₂×C₄	—	188	1	no	—
417	C₂×C₄	—	188	1	no	—
418	C₂×C₄	—	188	8	no	—
419	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
420	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
421	C₂×C₄	#13094049	1	2	yes	—
422	C₂×C₄	#13094055	1	2	yes	—
423	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
424	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
425	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
426	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
427	C₂×C₄	#13094070	1	1	yes	characteristic
428	C₂×C₄	#13094072	1	1	yes	characteristic
429	C₈	—	94	2	no	—
430	C₈	—	94	4	no	—
431	C₈	—	188	1	no	—
432	C₂²	—	94	4	no	—
433	C₂²	—	188	2	no	—
434	C₂²	—	188	2	no	—
435	C₂²	—	188	2	no	—
436	C₂²	—	188	2	no	—
437	C₂²	—	188	2	no	—
438	C₂²	—	188	2	no	—
439	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
440	C₂²	#15689761	1	1	yes	characteristic
441	C₂²	Q₈×C₂²⋊D₄₇	1	1	yes	characteristic
442	C₂²	C₂×#13094049	1	1	yes	characteristic
443	C₂²	C₂×#13094055	1	1	yes	characteristic
444	C₂²	#15689926	1	1	yes	characteristic
445	C₂²	#15689934	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	4	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	2	no	—
451	C₄	—	8	1	no	—
452	C₄	—	376	2	no	—
453	C₄	—	188	2	no	—
454	C₄	#15689221	1	4	yes	—
455	C₄	C₄×Q₈×D₄₇	1	1	yes	characteristic
456	C₄	#15689605	1	1	yes	characteristic
457	C₄	#15689814	1	1	yes	characteristic
458	C₄	#15689833	1	1	yes	characteristic
459	C₂	—	188	4	no	—
460	C₂	#20246389	1	1	yes	characteristic
461	C₂	C₂×#15689221	1	1	yes	characteristic
462	C₂	#20252220	1	1	yes	characteristic
463	C₂	#20255624	1	1	yes	characteristic
464	C₂	#20255698	1	1	yes	characteristic
465	C₂	#20256287	1	1	yes	characteristic
466	C₂	#20256294	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2369	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₁₈₈	C₂³
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2369	D₄₇
hypocenter	C₄₇	#22969
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄ ◁ #2369

Complements

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

N	H ≅ G/N	type
3. #20244350	C₂	semidirect
4. #20244146	C₂	semidirect
5. #20244128	C₂	semidirect
6. #20243973	C₂	semidirect
8. #20243257	C₂	semidirect
11. C₄₇×#2369	C₂	semidirect
15. #15689410	C₄	semidirect
61. #13093955	C₂×C₄	semidirect
62. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
65. #13093944	Q₈	semidirect
71. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
227. #2369	D₄₇	semidirect
275. C₄₇	#22969	semidirect
284. C₄⋊Q₈	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689410	2
C₄⋊C₄×D₁₈₈	2
#20244350	2
#20244146	2
#20244128	2
#20243973	2
#20243634	2
#20243257	2
#20243216	2
C₄×#13093944	2
C₄₇×#2369	2
#22969	47