Subgroups — #26266422

Order 12032.

894 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689408	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₈×D₁₈₈	C₂	1	1	yes	maximal, characteristic
3	#20248383	C₂	1	1	yes	maximal, characteristic
4	#20248306	C₂	1	1	yes	maximal, characteristic
5	#20244827	C₂	1	2	yes	maximal, complemented
6	#20244582	C₂	1	2	yes	maximal, complemented
7	#20244349	C₂	1	1	yes	maximal, characteristic, complemented
8	#20244151	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243808	C₂	1	2	yes	maximal, complemented
10	#20243412	C₂	1	2	yes	maximal, complemented
11	C₄×#103×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₄₇	C₂²	1	2	yes	—
13	C₂×#13094024	C₂²	1	1	yes	characteristic
14	C₂×#13094012	—	2	1	no	—
15	C₂×#13094000	C₂²	1	2	yes	—
16	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
17	#15689408	—	2	4	no	—
18	C₈×D₁₈₈	—	2	4	no	—
19	C₂×#13093955	C₂²	1	2	yes	—
20	C₂×#13093955	C₂²	1	2	yes	—
21	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×#13093948	C₂²	1	2	yes	—
23	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
24	#15689050	—	2	2	no	—
25	#15689045	—	2	2	no	—
26	#15689029	—	2	1	no	—
27	#15689025	—	2	1	no	—
28	#15689021	—	2	1	no	—
29	#15688993	C₂²	1	1	yes	characteristic
30	#15688980	C₂²	1	2	yes	—
31	#15688980	C₂²	1	2	yes	—
32	#15688980	C₂²	1	2	yes	—
33	#15688886	C₂²	1	2	yes	—
34	#15688886	C₂²	1	2	yes	—
35	#15688885	C₂²	1	2	yes	—
36	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×#103×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#103×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
41	C₄₇×#340	C₂²	1	1	yes	characteristic
42	C₄₇×#340	C₂²	1	1	yes	characteristic
43	C₂²×Dic₉₄	—	2	1	no	—
44	C₂²×D₁₈₈	D₄	1	1	yes	characteristic
45	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
46	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
47	C₂×C₈×D₄₇	—	2	4	no	—
48	C₂×C₈×D₄₇	—	2	4	no	—
49	C₂×C₈×D₄₇	—	4	2	no	—
50	#13094024	—	2	2	no	—
51	#13094024	—	2	2	no	—
52	#13094012	—	4	4	no	—
53	#13094000	—	2	4	no	—
54	#13094000	—	4	2	no	—
55	C₄×D₁₈₈	—	2	2	no	—
56	C₄×D₁₈₈	—	2	2	no	—
57	C₂×C₄⋊Dic₄₇	—	2	1	no	—
58	C₂×C₄⋊Dic₄₇	—	2	1	no	—
59	C₂×C₄⋊Dic₄₇	—	2	1	no	—
60	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
61	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
62	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
63	C₂×Dic₄₇⋊C₄	—	2	2	no	—
64	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
65	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
66	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
67	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
68	C₂×(C₂×D₄₇)⋊C₄	D₄	1	2	yes	—
69	#13093955	—	2	4	no	—
70	#13093955	—	4	2	no	—
71	C₄⋊(C₄₇⋊C₈)	D₄	1	4	yes	—
72	#13093948	—	2	4	no	—
73	(C₂×D₄₇)⋊C₈	—	2	4	no	—
74	C₄₇⋊#95	—	2	2	no	—
75	C₄₇⋊#95	—	2	2	no	—
76	C₄₇⋊#95	—	2	2	no	—
77	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
82	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
83	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₄₇	—	2	1	no	—
87	C₂×C₄²×C₄₇	—	2	1	no	—
88	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
89	#103×C₄₇	—	2	2	no	—
90	#103×C₄₇	—	2	2	no	—
91	C₄×C₈×C₄₇	—	2	2	no	—
92	#95×C₄₇	—	2	1	no	—
93	C₂³×D₄₇	C₂×D₄	1	2	yes	—
94	C₂×Q₈×C₄₇	—	2	1	no	—
95	C₂×Q₈×C₄₇	—	2	1	no	—
96	C₂×Q₈×C₄₇	—	2	1	no	—
97	C₂×Q₈×C₄₇	—	2	1	no	—
98	C₂×Q₈×C₄₇	—	2	1	no	—
99	C₂×Q₈×C₄₇	#41	1	2	yes	—
100	C₂²×C₄×C₄₇	—	2	1	no	—
101	C₂²×C₄×C₄₇	—	2	1	no	—
102	C₂²×C₄×C₄₇	—	2	1	no	—
103	C₂²×C₄×C₄₇	—	2	1	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	C₂×D₁₈₈	—	2	2	no	—
111	C₂×D₁₈₈	—	2	2	no	—
112	C₂×D₁₈₈	SD₁₆	1	4	yes	—
113	C₂×C₄×D₄₇	—	2	2	no	—
114	C₂×C₄×D₄₇	—	2	2	no	—
115	C₂×C₄×D₄₇	—	2	2	no	—
116	C₂×C₄×D₄₇	—	2	2	no	—
117	C₂×C₄×D₄₇	—	2	2	no	—
118	C₂×C₄×D₄₇	—	2	2	no	—
119	C₂×Dic₉₄	—	4	2	no	—
120	C₂×Dic₉₄	—	4	2	no	—
121	C₂×Dic₉₄	—	4	2	no	—
122	C₂×C₈×C₄₇	—	2	1	no	—
123	C₂×C₈×C₄₇	—	2	1	no	—
124	C₂×C₈×C₄₇	—	2	1	no	—
125	C₂×C₈×C₄₇	—	2	1	no	—
126	C₂×C₈×C₄₇	—	2	1	no	—
127	C₂×C₈×C₄₇	#41	1	2	yes	—
128	C₄⋊C₄×C₄₇	—	2	1	no	—
129	C₄⋊C₄×C₄₇	—	2	1	no	—
130	C₄⋊C₄×C₄₇	—	2	1	no	—
131	C₄⋊C₄×C₄₇	—	2	1	no	—
132	C₄⋊C₄×C₄₇	—	2	1	no	—
133	C₄⋊C₄×C₄₇	—	2	1	no	—
134	C₄⋊C₄×C₄₇	—	4	2	no	—
135	C₄²×C₄₇	—	4	2	no	—
136	C₄²×C₄₇	—	4	2	no	—
137	C₄²×C₄₇	C₂×D₄	1	2	yes	—
138	C₄²×C₄₇	#41	1	2	yes	—
139	(C₂×D₄₇)⋊C₄	—	2	4	no	—
140	(C₂×D₄₇)⋊C₄	—	4	4	no	—
141	(C₂×D₄₇)⋊C₄	—	4	4	no	—
142	(C₂×D₄₇)⋊C₄	—	4	4	no	—
143	(C₂×D₄₇)⋊C₄	—	8	2	no	—
144	C₄⋊Dic₄₇	—	2	2	no	—
145	C₄⋊Dic₄₇	—	2	2	no	—
146	C₄⋊Dic₄₇	—	2	2	no	—
147	C₄⋊Dic₄₇	—	2	2	no	—
148	C₄⋊Dic₄₇	—	2	2	no	—
149	C₄⋊Dic₄₇	—	4	2	no	—
150	C₄⋊Dic₄₇	—	4	2	no	—
151	C₄⋊Dic₄₇	—	8	1	no	—
152	Dic₄₇⋊C₄	—	4	4	no	—
153	C₂×C₄₇⋊C₈	—	2	2	no	—
154	C₂×C₄₇⋊C₈	—	2	2	no	—
155	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
156	C₈×D₄₇	—	4	8	no	—
157	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
158	C₂²×D₄₇	—	2	2	no	—
159	C₂²×D₄₇	—	2	2	no	—
160	C₂²×D₄₇	—	2	2	no	—
161	C₂²×D₄₇	—	2	2	no	—
162	C₂²×D₄₇	—	2	2	no	—
163	C₂²×D₄₇	—	2	2	no	—
164	C₂²×D₄₇	C₂×SD₁₆	1	4	yes	—
165	Q₈×C₄₇	—	2	2	no	—
166	Q₈×C₄₇	—	2	2	no	—
167	Q₈×C₄₇	—	4	1	no	—
168	Q₈×C₄₇	—	4	1	no	—
169	C₂×C₄×C₄₇	—	2	1	no	—
170	C₂×C₄×C₄₇	—	2	1	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	4	1	no	—
173	C₂×C₄×C₄₇	—	4	1	no	—
174	C₂×C₄×C₄₇	—	4	1	no	—
175	C₂×C₄×C₄₇	—	4	1	no	—
176	C₂×C₄×C₄₇	—	4	1	no	—
177	C₂×C₄×C₄₇	—	4	1	no	—
178	C₂×C₄×C₄₇	—	4	1	no	—
179	C₂×C₄×C₄₇	—	4	1	no	—
180	C₂×C₄×C₄₇	—	4	1	no	—
181	C₂×C₄×C₄₇	—	4	1	no	—
182	C₂×C₄×C₄₇	—	4	1	no	—
183	C₂×C₄×C₄₇	#121	1	2	yes	—
184	C₂×C₄×C₄₇	#121	1	2	yes	—
185	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
186	C₂×C₄×C₄₇	#135	1	2	yes	—
187	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
192	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
193	C₂×Dic₄₇	—	2	2	no	—
194	C₂×Dic₄₇	—	2	2	no	—
195	C₂×Dic₄₇	—	2	2	no	—
196	C₂×Dic₄₇	—	4	2	no	—
197	C₂×Dic₄₇	—	4	2	no	—
198	C₂×Dic₄₇	—	4	2	no	—
199	C₂×Dic₄₇	—	4	2	no	—
200	C₂×Dic₄₇	—	4	2	no	—
201	C₂×Dic₄₇	—	4	2	no	—
202	D₁₈₈	—	2	8	no	—
203	C₄×D₄₇	—	4	2	no	—
204	C₄×D₄₇	—	4	2	no	—
205	C₄×D₄₇	—	4	2	no	—
206	C₄×D₄₇	—	4	2	no	—
207	Dic₉₄	—	8	4	no	—
208	C₈×C₄₇	—	2	2	no	—
209	C₈×C₄₇	—	4	1	no	—
210	C₄₇⋊C₈	—	2	4	no	—
211	#25341	—	47	1	no	maximal, Sylow
212	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
213	C₂²×C₄₇	#546	1	1	yes	characteristic
214	C₂²×C₄₇	#547	1	1	yes	characteristic
215	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
216	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
217	C₂²×C₄₇	#577	1	1	yes	characteristic
218	C₂²×C₄₇	#578	1	1	yes	characteristic
219	C₂×D₄₇	—	2	4	no	—
220	C₂×D₄₇	—	2	4	no	—
221	C₂×D₄₇	—	2	4	no	—
222	C₂×D₄₇	—	4	2	no	—
223	C₂×D₄₇	—	4	2	no	—
224	C₂×D₄₇	—	4	2	no	—
225	C₂×D₄₇	—	4	2	no	—
226	C₄×C₄₇	—	2	2	no	—
227	C₄×C₄₇	—	4	2	no	—
228	C₄×C₄₇	—	8	1	no	—
229	C₄×C₄₇	—	8	1	no	—
230	C₄×C₄₇	—	8	1	no	—
231	C₄×C₄₇	#465	1	4	yes	—
232	C₄×C₄₇	#529	1	1	yes	characteristic
233	C₄×C₄₇	#542	1	1	yes	characteristic
234	C₄×C₄₇	#546	1	1	yes	characteristic
235	C₄×C₄₇	#548	1	1	yes	characteristic
236	Dic₄₇	—	4	2	no	—
237	Dic₄₇	—	8	2	no	—
238	Dic₄₇	—	8	2	no	—
239	C₂×#475	—	47	1	no	—
240	C₂×C₈×D₄	—	47	1	no	—
241	#2547	—	47	1	no	—
242	#2538	—	47	1	no	—
243	#2077	—	47	2	no	—
244	#2035	—	47	2	no	—
245	#1990	—	47	1	no	—
246	#1948	—	47	1	no	—
247	#1892	—	47	2	no	—
248	#1807	—	47	2	no	—
249	C₄×#103	D₄₇	1	1	yes	characteristic, complemented
250	C₂×C₄₇	#2427	1	1	yes	characteristic
251	C₂×C₄₇	C₂×#465	1	1	yes	characteristic
252	C₂×C₄₇	#3063	1	1	yes	characteristic
253	C₂×C₄₇	#3298	1	1	yes	characteristic
254	C₂×C₄₇	#3304	1	1	yes	characteristic
255	C₂×C₄₇	#3335	1	1	yes	characteristic
256	C₂×C₄₇	#3342	1	1	yes	characteristic
257	D₄₇	—	4	4	no	—
258	C₂³×C₈	—	47	2	no	—
259	C₂×C₄⋊Q₈	—	47	1	no	—
260	C₂×#124	—	94	1	no	—
261	C₂×C₂²⋊Q₈	—	47	2	no	—
262	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
263	C₂×C₄×D₄	—	47	1	no	—
264	#475	—	94	4	no	—
265	C₈×D₄	—	94	4	no	—
266	C₂×#106	—	47	2	no	—
267	C₂×#106	—	47	2	no	—
268	C₂×C₄⋊C₈	—	47	1	no	—
269	C₂×#103	—	47	2	no	—
270	C₂×#103	C₂×D₄₇	1	1	yes	characteristic
271	C₂×#103	C₂×D₄₇	1	1	yes	characteristic
272	C₂×C₂²⋊C₈	—	47	2	no	—
273	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
274	#397	—	94	2	no	—
275	#396	—	94	2	no	—
276	#391	—	94	1	no	—
277	#390	—	94	1	no	—
278	#389	—	94	1	no	—
279	#384	—	47	1	no	—
280	#380	—	47	2	no	—
281	#380	—	47	2	no	—
282	#380	—	47	2	no	—
283	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
284	#340	—	47	2	no	—
285	#340	—	47	2	no	—
286	#340	—	47	2	no	—
287	#340	C₂×D₄₇	1	1	yes	characteristic
288	#340	C₂×D₄₇	1	1	yes	characteristic
289	C₄₇	#25341	1	1	yes	characteristic, complemented, Sylow
290	C₂²×Q₈	—	94	1	no	—
291	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
292	C₂²×D₄	—	47	1	no	—
293	C₂³×C₄	—	47	2	no	—
294	C₂²×C₈	—	47	2	no	—
295	C₂²×C₈	—	94	4	no	—
296	C₂²×C₈	—	94	4	no	—
297	C₂²×C₈	—	188	2	no	—
298	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
299	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
300	C₄⋊Q₈	—	94	2	no	—
301	C₄⋊Q₈	—	94	2	no	—
302	#124	—	188	4	no	—
303	C₂²⋊Q₈	—	94	4	no	—
304	C₂²⋊Q₈	—	188	2	no	—
305	C₄×Q₈	—	2	2	no	—
306	C₄×Q₈	—	2	2	no	—
307	C₄×D₄	—	94	2	no	—
308	C₄×D₄	—	94	2	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	47	1	no	—
311	C₂×C₄⋊C₄	—	47	2	no	—
312	C₂×C₄⋊C₄	—	47	2	no	—
313	C₂×C₄⋊C₄	—	94	1	no	—
314	C₂×C₄⋊C₄	—	94	2	no	—
315	C₂×C₄⋊C₄	—	94	1	no	—
316	C₂×C₄⋊C₄	—	94	1	no	—
317	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
320	C₂×C₂²⋊C₄	—	47	2	no	—
321	C₂×C₂²⋊C₄	—	94	2	no	—
322	C₂×C₂²⋊C₄	—	94	2	no	—
323	C₂×C₂²⋊C₄	—	94	2	no	—
324	C₂×C₂²⋊C₄	—	94	2	no	—
325	C₂×C₄²	—	2	1	no	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
328	#106	—	94	4	no	—
329	#106	—	188	2	no	—
330	C₄⋊C₈	—	47	4	no	—
331	#103	—	2	2	no	—
332	#103	—	2	2	no	—
333	#103	—	94	4	no	—
334	C₂²⋊C₈	—	94	4	no	—
335	C₄×C₈	—	2	2	no	—
336	#95	—	2	1	no	—
337	#95	—	94	2	no	—
338	#95	—	94	2	no	—
339	#95	—	94	2	no	—
340	C₂⁴	—	47	2	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	188	2	no	—
347	C₂×Q₈	—	188	2	no	—
348	C₂×Q₈	—	188	2	no	—
349	C₂×Q₈	#10625350	1	2	yes	—
350	C₂×D₄	—	47	4	no	—
351	C₂×D₄	—	94	2	no	—
352	C₂×D₄	—	94	2	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	47	2	no	—
358	C₂²×C₄	—	94	2	no	—
359	C₂²×C₄	—	94	2	no	—
360	C₂²×C₄	—	94	2	no	—
361	C₂²×C₄	—	94	2	no	—
362	C₂²×C₄	—	94	2	no	—
363	C₂²×C₄	—	94	2	no	—
364	C₂²×C₄	—	94	2	no	—
365	C₂²×C₄	—	94	2	no	—
366	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
367	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
368	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	47	4	no	—
375	C₂×C₈	—	94	2	no	—
376	C₂×C₈	—	94	2	no	—
377	C₂×C₈	—	188	8	no	—
378	C₂×C₈	#10625350	1	2	yes	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₄⋊C₄	—	94	2	no	—
387	C₄⋊C₄	—	94	2	no	—
388	C₄⋊C₄	—	94	2	no	—
389	C₄⋊C₄	—	94	2	no	—
390	C₄⋊C₄	—	94	2	no	—
391	C₄⋊C₄	—	376	1	no	—
392	C₄⋊C₄	—	188	4	no	—
393	C₄⋊C₄	—	188	2	no	—
394	C₄⋊C₄	—	188	2	no	—
395	C₂²⋊C₄	—	94	4	no	—
396	C₂²⋊C₄	—	376	2	no	—
397	C₂²⋊C₄	—	188	4	no	—
398	C₂²⋊C₄	—	188	4	no	—
399	C₂²⋊C₄	—	188	4	no	—
400	C₄²	—	4	2	no	—
401	C₄²	—	4	2	no	—
402	C₄²	#10625350	1	2	yes	—
403	C₄²	D₄×D₄₇	1	2	yes	—
404	C₂³	—	47	4	no	—
405	C₂³	—	94	2	no	—
406	C₂³	—	94	2	no	—
407	C₂³	—	94	2	no	—
408	C₂³	—	94	2	no	—
409	C₂³	—	94	2	no	—
410	C₂³	—	94	2	no	—
411	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
412	Q₈	—	2	2	no	—
413	Q₈	—	2	2	no	—
414	Q₈	—	4	1	no	—
415	Q₈	—	4	1	no	—
416	Q₈	—	376	4	no	—
417	D₄	—	94	8	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	94	2	no	—
433	C₂×C₄	—	94	2	no	—
434	C₂×C₄	—	94	2	no	—
435	C₂×C₄	—	188	2	no	—
436	C₂×C₄	—	188	2	no	—
437	C₂×C₄	—	188	2	no	—
438	C₂×C₄	—	188	2	no	—
439	C₂×C₄	—	188	2	no	—
440	C₂×C₄	—	188	2	no	—
441	C₂×C₄	—	188	2	no	—
442	C₂×C₄	—	188	2	no	—
443	C₂×C₄	—	188	2	no	—
444	C₂×C₄	—	188	2	no	—
445	C₂×C₄	#13093997	1	2	yes	—
446	C₂×C₄	#13093997	1	2	yes	—
447	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
448	C₂×C₄	#13094047	1	2	yes	—
449	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
450	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
451	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
452	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
453	C₂×C₄	#13094070	1	1	yes	characteristic
454	C₂×C₄	#13094071	1	1	yes	characteristic
455	C₈	—	2	2	no	—
456	C₈	—	4	1	no	—
457	C₈	—	94	4	no	—
458	C₂²	—	94	4	no	—
459	C₂²	—	94	4	no	—
460	C₂²	—	94	4	no	—
461	C₂²	—	188	2	no	—
462	C₂²	—	188	2	no	—
463	C₂²	—	188	2	no	—
464	C₂²	—	188	2	no	—
465	C₂²	C₂×#13093997	1	1	yes	characteristic
466	C₂²	#15689769	1	1	yes	characteristic
467	C₂²	#15689778	1	1	yes	characteristic
468	C₂²	C₂×SD₁₆×D₄₇	1	1	yes	characteristic
469	C₂²	C₂×#13094047	1	1	yes	characteristic
470	C₂²	#15689930	1	1	yes	characteristic
471	C₂²	#15689937	1	1	yes	characteristic
472	C₄	—	2	2	no	—
473	C₄	—	4	2	no	—
474	C₄	—	8	1	no	—
475	C₄	—	8	1	no	—
476	C₄	—	8	1	no	—
477	C₄	—	376	2	no	—
478	C₄	—	376	2	no	—
479	C₄	—	188	2	no	—
480	C₄	#15689355	1	4	yes	—
481	C₄	#15689657	1	1	yes	characteristic
482	C₄	#15689744	1	1	yes	characteristic
483	C₄	#15689769	1	1	yes	characteristic
484	C₄	#15689782	1	1	yes	characteristic
485	C₂	—	188	4	no	—
486	C₂	#20246965	1	1	yes	characteristic
487	C₂	C₂×#15689355	1	1	yes	characteristic
488	C₂	#20253082	1	1	yes	characteristic
489	C₂	#20255255	1	1	yes	characteristic
490	C₂	#20255329	1	1	yes	characteristic
491	C₂	#20255747	1	1	yes	characteristic
492	C₂	#20255820	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄×#103×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₁₈₈	D₄
hypercenter	C₄×#103	D₄₇
hypocenter	C₄₇	#25341
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₄×#103

Complements

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

N	H ≅ G/N	type
1. C₂×#15689408	C₂	semidirect
5. #20244827	C₂	semidirect
6. #20244582	C₂	semidirect
7. #20244349	C₂	semidirect
8. #20244151	C₂	semidirect
9. #20243808	C₂	semidirect
10. #20243412	C₂	semidirect
11. C₄×#103×C₄₇	C₂	semidirect
249. C₄×#103	D₄₇	semidirect
289. C₄₇	#25341	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689408	2
C₂×C₈×D₁₈₈	2
#20248383	2
#20248306	2
#20244827	2
#20244582	2
#20244349	2
#20244151	2
#20243808	2
#20243412	2
C₄×#103×C₄₇	2
#25341	47