Subgroups — #26238161

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×#15689414	C₂	1	1	yes	maximal, characteristic
2	#20246477	C₂	1	1	yes	maximal, characteristic, complemented
3	#20246288	C₂	1	1	yes	maximal, characteristic
4	#20244348	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244129	C₂	1	2	yes	maximal, complemented
6	#20243972	C₂	1	2	yes	maximal, complemented
7	#20243632	C₂	1	2	yes	maximal
8	#20243258	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243212	C₂	1	2	yes	maximal
10	C₄×#13093944	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1947	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094024	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
14	C₂×#13093986	C₂²	1	2	yes	—
15	C₂×C₄⋊C₄×D₄₇	—	2	1	no	—
16	#15689414	C₄	1	8	yes	complemented
17	C₂×#13093956	C₂²	1	2	yes	—
18	C₂×#13093946	C₂²	1	2	yes	—
19	C₂×#13093944	C₂²	1	1	yes	characteristic
20	C₂×#13093944	C₂²	1	1	yes	characteristic
21	C₂×#13093934	C₂²	1	2	yes	—
22	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
23	#15689027	—	2	2	no	—
24	#15689021	—	2	1	no	—
25	#15689019	C₂²	1	2	yes	—
26	#15689019	C₂²	1	2	yes	—
27	#15688994	—	2	2	no	—
28	#15688980	—	2	1	no	—
29	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
30	C₄×C₄⋊Dic₄₇	—	2	1	no	—
31	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
32	#15688885	C₂²	1	1	yes	characteristic
33	#15688885	C₂²	1	2	yes	—
34	#15688885	C₂²	1	1	yes	characteristic
35	#15688885	C₂²	1	2	yes	—
36	#15688877	C₂²	1	2	yes	—
37	C₂×#107×C₄₇	C₂²	1	2	yes	—
38	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₄₇×#384	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
41	C₄₇×#340	C₂²	1	2	yes	—
42	C₂²×Dic₉₄	—	2	1	no	—
43	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
44	C₂²×C₄×D₄₇	—	2	1	no	—
45	C₂²×C₄×D₄₇	—	2	2	no	—
46	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	#13094024	—	2	2	no	—
49	#13094024	C₂×C₄	1	4	yes	complemented
50	C₄×D₁₈₈	—	2	2	no	—
51	C₄×D₁₈₈	C₂×C₄	1	4	yes	—
52	#13093986	—	2	4	no	—
53	#13093986	—	4	2	no	—
54	C₂×C₄⋊Dic₄₇	—	2	1	no	—
55	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
56	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
57	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
58	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
59	C₂×Dic₄₇⋊C₄	—	2	2	no	—
60	C₂×Dic₄₇⋊C₄	—	2	2	no	—
61	C₄⋊C₄×D₄₇	—	4	4	no	—
62	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
63	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
64	C₂×C₄×Dic₄₇	—	2	2	no	—
65	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
66	#13093956	C₂×C₄	1	8	yes	complemented
67	#13093946	C₂×C₄	1	8	yes	—
68	#13093944	—	2	2	no	—
69	#13093944	Q₈	1	4	yes	complemented
70	#13093934	—	4	2	no	—
71	C₄×C₄₇⋊C₈	—	2	2	no	—
72	C₄₇⋊#95	—	2	2	no	—
73	C₄₇⋊#95	—	2	2	no	—
74	C₄₇⋊#95	—	2	2	no	—
75	C₄₇⋊#95	D₄	1	2	yes	—
76	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
78	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
79	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₄₇	—	2	1	no	—
83	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
84	#107×C₄₇	—	4	2	no	—
85	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	complemented
86	#95×C₄₇	—	2	1	no	—
87	C₂³×D₄₇	—	2	1	no	—
88	C₂²×C₄×C₄₇	—	2	1	no	—
89	C₂²×C₄×C₄₇	—	2	1	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
94	C₂²×Dic₄₇	—	2	2	no	—
95	C₂²×Dic₄₇	—	2	1	no	—
96	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
97	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
98	C₂×D₁₈₈	—	2	1	no	—
99	C₂×D₁₈₈	—	2	1	no	—
100	C₂×D₁₈₈	—	2	1	no	—
101	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
102	C₂×D₁₈₈	C₂×Q₈	1	2	yes	—
103	C₂×D₁₈₈	#41	1	2	yes	—
104	C₂×C₄×D₄₇	—	2	4	no	—
105	C₂×C₄×D₄₇	—	4	2	no	—
106	C₂×C₄×D₄₇	—	4	2	no	—
107	C₂×C₄×D₄₇	—	4	4	no	—
108	C₂×C₄×D₄₇	—	4	4	no	—
109	C₂×C₄×D₄₇	—	8	2	no	—
110	C₂×Dic₉₄	—	2	4	no	—
111	C₂×Dic₉₄	—	8	1	no	—
112	C₂×Dic₉₄	—	8	1	no	—
113	C₂×C₈×C₄₇	—	2	2	no	—
114	C₂×C₈×C₄₇	—	2	2	no	—
115	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
116	C₄⋊C₄×C₄₇	—	2	1	no	—
117	C₄⋊C₄×C₄₇	—	2	1	no	—
118	C₄⋊C₄×C₄₇	—	2	2	no	—
119	C₄⋊C₄×C₄₇	—	2	1	no	—
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	—	4	2	no	—
122	C₄⋊C₄×C₄₇	—	8	1	no	—
123	C₄⋊C₄×C₄₇	C₂×Q₈	1	2	yes	—
124	C₄²×C₄₇	—	4	2	no	—
125	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
126	C₄²×C₄₇	#41	1	2	yes	—
127	(C₂×D₄₇)⋊C₄	—	2	4	no	—
128	(C₂×D₄₇)⋊C₄	—	4	4	no	—
129	C₄⋊Dic₄₇	—	2	4	no	—
130	C₄⋊Dic₄₇	—	2	2	no	—
131	C₄⋊Dic₄₇	—	2	2	no	—
132	C₄⋊Dic₄₇	—	2	1	no	—
133	C₄⋊Dic₄₇	—	2	2	no	—
134	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
135	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
136	Dic₄₇⋊C₄	—	4	4	no	—
137	Dic₄₇⋊C₄	—	8	2	no	—
138	C₄×Dic₄₇	—	2	2	no	—
139	C₄×Dic₄₇	—	2	2	no	—
140	C₄×Dic₄₇	—	8	2	no	—
141	C₂×C₄₇⋊C₈	—	2	1	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	—	2	1	no	—
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	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	4	1	no	—
159	C₂×C₄×C₄₇	—	4	1	no	—
160	C₂×C₄×C₄₇	—	4	2	no	—
161	C₂×C₄×C₄₇	—	4	1	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	2	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	C₂²×Q₈	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
175	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
176	C₂×Dic₄₇	—	2	4	no	—
177	C₂×Dic₄₇	—	2	2	no	—
178	C₂×Dic₄₇	—	2	2	no	—
179	C₂×Dic₄₇	—	2	2	no	—
180	C₂×Dic₄₇	—	2	2	no	—
181	C₂×Dic₄₇	—	2	2	no	—
182	C₂×Dic₄₇	—	2	2	no	—
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	D₁₈₈	—	2	2	no	—
189	D₁₈₈	—	2	2	no	—
190	D₁₈₈	—	2	2	no	—
191	D₁₈₈	C₄×Q₈	1	4	yes	—
192	C₄×D₄₇	—	4	8	no	—
193	C₄×D₄₇	—	8	8	no	—
194	Dic₉₄	—	8	4	no	—
195	C₈×C₄₇	—	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	—	8	2	no	—
216	C₄×C₄₇	—	8	1	no	—
217	C₄×C₄₇	#440	1	4	yes	—
218	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
219	C₄×C₄₇	#520	1	1	yes	characteristic
220	C₄×C₄₇	#552	1	1	yes	characteristic
221	C₄×C₄₇	#554	1	1	yes	characteristic
222	Dic₄₇	—	4	2	no	—
223	Dic₄₇	—	4	2	no	—
224	Dic₄₇	—	4	4	no	—
225	Dic₄₇	—	4	2	no	—
226	C₂×#476	—	47	1	no	—
227	#2369	—	47	1	no	—
228	D₄×C₄⋊C₄	—	47	1	no	—
229	#1990	—	47	1	no	—
230	#1947	D₄₇	1	1	yes	characteristic, complemented
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	—	47	1	no	—
246	C₂×C₄×D₄	—	47	2	no	—
247	C₂×C₄×D₄	—	47	1	no	—
248	C₂²×C₄⋊C₄	—	94	1	no	—
249	#476	—	47	8	no	—
250	C₂×#107	C₂×D₄₇	1	2	yes	—
251	C₂×#106	—	47	2	no	—
252	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
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	—	94	2	no	—
259	#389	—	47	2	no	—
260	#389	—	47	2	no	—
261	#389	—	94	1	no	—
262	#385	—	94	2	no	—
263	#384	C₂×D₄₇	1	1	yes	characteristic
264	#380	—	94	1	no	—
265	C₄×C₄⋊C₄	—	47	1	no	—
266	C₄×C₄⋊C₄	—	47	2	no	—
267	C₄×C₄⋊C₄	—	94	1	no	—
268	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
269	#340	—	47	2	no	—
270	#340	—	47	1	no	—
271	#340	—	47	1	no	—
272	#340	—	47	2	no	—
273	#340	C₂×D₄₇	1	2	yes	—
274	#336	—	47	2	no	—
275	C₄₇	#22969	1	1	yes	characteristic, complemented, Sylow
276	C₂²×Q₈	—	94	1	no	—
277	C₂²×D₄	—	47	1	no	—
278	C₂³×C₄	—	94	2	no	—
279	C₂³×C₄	—	94	1	no	—
280	C₂²×C₈	—	47	1	no	—
281	C₂²×C₈	—	47	1	no	—
282	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
283	C₄⋊Q₈	—	47	4	no	—
284	C₄⋊Q₈	—	94	2	no	—
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	1	no	—
291	C₂×C₄⋊C₄	—	47	1	no	—
292	C₂×C₄⋊C₄	—	47	2	no	—
293	C₂×C₄⋊C₄	—	47	1	no	—
294	C₂×C₄⋊C₄	—	47	1	no	—
295	C₂×C₄⋊C₄	—	94	1	no	—
296	C₂×C₄⋊C₄	—	94	2	no	—
297	C₂×C₄⋊C₄	—	94	2	no	—
298	C₂×C₄⋊C₄	—	188	4	no	—
299	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
300	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
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	—	47	2	no	—
306	C₂×C₄²	—	94	2	no	—
307	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
308	#107	—	4	2	no	—
309	#106	—	47	8	no	—
310	C₄⋊C₈	C₄×D₄₇	1	4	yes	complemented
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	1	no	—
317	#95	—	47	2	no	—
318	#95	—	94	2	no	—
319	#95	—	94	2	no	—
320	#95	—	94	2	no	—
321	C₂⁴	—	94	1	no	—
322	C₂×Q₈	—	94	4	no	—
323	C₂×Q₈	—	376	1	no	—
324	C₂×Q₈	—	376	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	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	47	2	no	—
335	C₂²×C₄	—	47	2	no	—
336	C₂²×C₄	—	94	2	no	—
337	C₂²×C₄	—	94	1	no	—
338	C₂²×C₄	—	94	4	no	—
339	C₂²×C₄	—	376	2	no	—
340	C₂²×C₄	—	188	4	no	—
341	C₂²×C₄	—	188	4	no	—
342	C₂²×C₄	—	188	2	no	—
343	C₂²×C₄	—	188	2	no	—
344	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
345	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
346	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	47	2	no	—
350	C₂×C₈	—	94	1	no	—
351	C₂×C₈	—	94	1	no	—
352	C₂×C₈	—	94	1	no	—
353	C₂×C₈	—	94	1	no	—
354	C₂×C₈	—	94	1	no	—
355	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	4	2	no	—
362	C₄⋊C₄	—	8	1	no	—
363	C₄⋊C₄	—	47	4	no	—
364	C₄⋊C₄	—	47	2	no	—
365	C₄⋊C₄	—	94	4	no	—
366	C₄⋊C₄	—	94	2	no	—
367	C₄⋊C₄	—	94	2	no	—
368	C₄⋊C₄	—	94	1	no	—
369	C₄⋊C₄	—	94	2	no	—
370	C₄⋊C₄	—	376	2	no	—
371	C₄⋊C₄	—	188	4	no	—
372	C₄⋊C₄	Q₈×D₄₇	1	2	yes	—
373	C₂²⋊C₄	—	94	4	no	—
374	C₂²⋊C₄	—	188	4	no	—
375	C₄²	—	4	2	no	—
376	C₄²	—	94	2	no	—
377	C₄²	—	94	2	no	—
378	C₄²	—	376	2	no	—
379	C₄²	C₂×C₄×D₄₇	1	2	yes	—
380	C₄²	#10625354	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	C₂×D₄×D₄₇	1	1	yes	characteristic
389	Q₈	—	376	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	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	94	2	no	—
406	C₂×C₄	—	94	2	no	—
407	C₂×C₄	—	94	2	no	—
408	C₂×C₄	—	94	4	no	—
409	C₂×C₄	—	94	2	no	—
410	C₂×C₄	—	94	2	no	—
411	C₂×C₄	—	94	2	no	—
412	C₂×C₄	—	94	2	no	—
413	C₂×C₄	—	376	8	no	—
414	C₂×C₄	—	188	1	no	—
415	C₂×C₄	—	188	1	no	—
416	C₂×C₄	—	188	2	no	—
417	C₂×C₄	—	188	2	no	—
418	C₂×C₄	—	188	8	no	—
419	C₂×C₄	#13093986	1	2	yes	—
420	C₂×C₄	#13093986	1	2	yes	—
421	C₂×C₄	#13094048	1	2	yes	—
422	C₂×C₄	#13094056	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×#10625354	1	1	yes	characteristic
427	C₂×C₄	#13094069	1	1	yes	characteristic
428	C₂×C₄	#13094071	1	1	yes	characteristic
429	C₈	—	2	4	no	—
430	C₈	—	94	2	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×#13093986	1	1	yes	characteristic
440	C₂²	#15689770	1	1	yes	characteristic
441	C₂²	#15689786	1	1	yes	characteristic
442	C₂²	C₂×#13094048	1	1	yes	characteristic
443	C₂²	C₂×#13094056	1	1	yes	characteristic
444	C₂²	#15689927	1	1	yes	characteristic
445	C₂²	#15689932	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	8	2	no	—
449	C₄	—	8	1	no	—
450	C₄	—	188	2	no	—
451	C₄	—	188	4	no	—
452	C₄	—	188	2	no	—
453	C₄	—	188	2	no	—
454	C₄	#15689222	1	4	yes	—
455	C₄	C₄×Q₈×D₄₇	1	1	yes	characteristic
456	C₄	#15689602	1	1	yes	characteristic
457	C₄	#15689811	1	1	yes	characteristic
458	C₄	#15689834	1	1	yes	characteristic
459	C₂	—	188	4	no	—
460	C₂	#20246392	1	1	yes	characteristic
461	C₂	C₂×#15689222	1	1	yes	characteristic
462	C₂	#20252218	1	1	yes	characteristic
463	C₂	#20255633	1	1	yes	characteristic
464	C₂	#20255707	1	1	yes	characteristic
465	C₂	#20256291	1	1	yes	characteristic
466	C₂	#20256297	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1947	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₁₈₈	C₂³
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1947	D₄₇
hypocenter	C₄₇	#22969
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1947

Complements

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

N	H ≅ G/N	type
2. #20246477	C₂	semidirect
4. #20244348	C₂	semidirect
5. #20244129	C₂	semidirect
6. #20243972	C₂	semidirect
8. #20243258	C₂	semidirect
11. C₄₇×#1947	C₂	semidirect
16. #15689414	C₄	semidirect
49. #13094024	C₂×C₄	semidirect
66. #13093956	C₂×C₄	semidirect
69. #13093944	Q₈	semidirect
85. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
230. #1947	D₄₇	semidirect
275. C₄₇	#22969	semidirect
310. C₄⋊C₈	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×#15689414	2
#20246477	2
#20246288	2
#20244348	2
#20244129	2
#20243972	2
#20243632	2
#20243258	2
#20243212	2
C₄×#13093944	2
C₄₇×#1947	2
#22969	47