Subgroups — #26238523

Order 12032.

1030 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×#15689325	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10625336	C₂	1	2	yes	maximal
3	C₄⋊C₄×D₁₈₈	C₂	1	1	yes	maximal, characteristic
4	#20244191	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244151	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244067	C₂	1	2	yes	maximal, complemented
7	#20243725	C₂	1	2	yes	maximal
8	#20243656	C₂	1	2	yes	maximal, complemented
9	C₄⋊C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#13093944	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#2365	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625336	C₂²	1	2	yes	—
13	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
14	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₄×D₄₇	—	2	1	no	—
16	#15689325	C₄	1	8	yes	complemented
17	C₄×#10625336	—	2	8	no	—
18	C₂×#13093955	C₂²	1	2	yes	—
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×#13093948	C₂²	1	2	yes	—
21	C₂×#13093948	C₂²	1	2	yes	—
22	C₂×#13093948	C₂²	1	2	yes	—
23	C₂×#13093944	C₂²	1	1	yes	characteristic
24	C₂×#13093944	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
27	#15689021	C₂²	1	2	yes	—
28	#15688997	—	2	2	no	—
29	#15688993	C₂²	1	1	yes	characteristic
30	#15688980	—	2	1	no	—
31	#15688885	C₂²	1	1	yes	characteristic
32	#15688885	C₂²	1	1	yes	characteristic
33	#15688885	C₂²	1	2	yes	—
34	#15688878	C₂²	1	2	yes	—
35	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
37	C₄₇×#391	C₂²	1	2	yes	—
38	C₄₇×#389	—	2	1	no	—
39	C₄₇×#387	—	2	2	no	—
40	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
41	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
44	C₂²×C₄×D₄₇	—	2	1	no	—
45	C₂²×C₄×D₄₇	—	2	2	no	—
46	C₂×#10625336	—	2	4	no	—
47	C₂×#10625336	—	2	4	no	—
48	C₂×#10625336	C₂×C₄	1	8	yes	—
49	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
51	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
52	C₄×D₁₈₈	—	2	2	no	—
53	C₄×D₁₈₈	—	2	4	no	—
54	C₄×D₁₈₈	—	4	2	no	—
55	C₄×D₁₈₈	C₂×C₄	1	4	yes	—
56	C₂×C₄⋊Dic₄₇	—	2	1	no	—
57	C₂×C₄⋊Dic₄₇	—	2	1	no	—
58	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
59	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
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	#13093955	—	2	4	no	—
65	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
66	#13093948	—	2	4	no	—
67	#13093948	—	4	2	no	—
68	#13093948	C₂×C₄	1	8	yes	complemented
69	#13093944	—	2	2	no	—
70	#13093944	D₄	1	4	yes	—
71	C₄×C₄₇⋊C₈	—	2	2	no	—
72	C₄×C₄₇⋊C₈	—	2	4	no	—
73	C₄₇⋊#95	—	2	2	no	—
74	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
75	C₄⋊Q₈×C₄₇	—	2	2	no	—
76	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
77	C₄×Q₈×C₄₇	—	2	4	no	—
78	C₄×Q₈×C₄₇	—	4	2	no	—
79	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
81	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
82	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₄₇	D₄	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	2	no	—
87	C₂×C₄²×C₄₇	—	2	1	no	—
88	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
89	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
90	#95×C₄₇	—	2	2	no	—
91	#95×C₄₇	—	2	1	no	—
92	#95×C₄₇	—	2	2	no	—
93	#95×C₄₇	D₄	1	2	yes	—
94	C₂³×D₄₇	—	2	1	no	—
95	C₂×Q₈×C₄₇	—	2	2	no	—
96	C₂×Q₈×C₄₇	—	2	2	no	—
97	C₂×Q₈×C₄₇	—	2	2	no	—
98	C₂×Q₈×C₄₇	—	2	2	no	—
99	C₂×Q₈×C₄₇	—	2	2	no	—
100	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₄₇	—	2	1	no	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	—	2	1	no	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
109	C₂²×Dic₄₇	—	2	1	no	—
110	C₂²×Dic₄₇	—	2	2	no	—
111	C₂×D₁₈₈	—	2	1	no	—
112	C₂×D₁₈₈	—	2	1	no	—
113	C₂×D₁₈₈	—	2	1	no	—
114	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
115	C₂×D₁₈₈	C₂×D₄	1	2	yes	—
116	C₂×D₁₈₈	#41	1	2	yes	—
117	C₂×C₄×D₄₇	—	2	4	no	—
118	C₂×C₄×D₄₇	—	4	2	no	—
119	C₂×C₄×D₄₇	—	4	2	no	—
120	C₂×C₄×D₄₇	—	4	4	no	—
121	C₂×C₄×D₄₇	—	4	4	no	—
122	C₂×C₄×D₄₇	—	8	2	no	—
123	C₄⋊C₄×C₄₇	—	2	4	no	—
124	C₄⋊C₄×C₄₇	—	2	4	no	—
125	C₄⋊C₄×C₄₇	—	2	2	no	—
126	C₄⋊C₄×C₄₇	—	2	1	no	—
127	C₄⋊C₄×C₄₇	—	2	1	no	—
128	C₄⋊C₄×C₄₇	—	2	1	no	—
129	C₄⋊C₄×C₄₇	—	4	4	no	—
130	C₄⋊C₄×C₄₇	SD₁₆	1	4	yes	complemented
131	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
132	C₄²×C₄₇	—	2	2	no	—
133	C₄²×C₄₇	—	2	2	no	—
134	C₄²×C₄₇	—	4	4	no	—
135	C₄²×C₄₇	—	4	2	no	—
136	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
137	C₄²×C₄₇	#41	1	2	yes	—
138	#10625336	—	2	16	no	—
139	(C₂×D₄₇)⋊C₄	—	2	4	no	—
140	(C₂×D₄₇)⋊C₄	—	4	4	no	—
141	C₄⋊Dic₄₇	—	2	1	no	—
142	C₄⋊Dic₄₇	—	2	2	no	—
143	C₄⋊Dic₄₇	—	2	2	no	—
144	C₄⋊Dic₄₇	—	4	2	no	—
145	C₄⋊Dic₄₇	—	8	1	no	—
146	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
147	Dic₄₇⋊C₄	—	4	4	no	—
148	C₂×C₄₇⋊C₈	—	2	2	no	—
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	—	2	2	no	—
151	C₂×C₄₇⋊C₈	—	2	1	no	—
152	C₂×C₄₇⋊C₈	—	2	1	no	—
153	C₂×C₄₇⋊C₈	—	2	1	no	—
154	C₂×C₄₇⋊C₈	—	2	1	no	—
155	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
156	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
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	—	4	1	no	—
162	C₂²×D₄₇	—	4	1	no	—
163	C₂²×D₄₇	—	4	1	no	—
164	C₂²×D₄₇	—	4	1	no	—
165	Q₈×C₄₇	—	2	4	no	—
166	Q₈×C₄₇	—	2	4	no	—
167	Q₈×C₄₇	—	4	2	no	—
168	Q₈×C₄₇	—	4	2	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	1	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	2	4	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	4	2	no	—
179	C₂×C₄×C₄₇	—	4	2	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	—	4	1	no	—
184	C₂×C₄×C₄₇	—	4	1	no	—
185	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
187	C₂×C₄×C₄₇	C₂×SD₁₆	1	4	yes	—
188	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
189	C₂×C₄×C₄₇	#135	1	2	yes	—
190	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
191	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
195	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
196	C₂×Dic₄₇	—	2	2	no	—
197	C₂×Dic₄₇	—	4	1	no	—
198	C₂×Dic₄₇	—	4	1	no	—
199	C₂×Dic₄₇	—	4	2	no	—
200	C₂×Dic₄₇	—	4	2	no	—
201	C₂×Dic₄₇	—	4	2	no	—
202	D₁₈₈	—	2	2	no	—
203	D₁₈₈	—	2	2	no	—
204	D₁₈₈	—	2	2	no	—
205	D₁₈₈	C₄×D₄	1	4	yes	—
206	C₄×D₄₇	—	4	8	no	—
207	C₄×D₄₇	—	8	8	no	—
208	C₄₇⋊C₈	—	2	4	no	—
209	C₄₇⋊C₈	—	2	2	no	—
210	C₄₇⋊C₈	—	4	1	no	—
211	#22996	—	47	1	no	maximal, Sylow
212	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
213	C₂²×C₄₇	D₄²	1	1	yes	characteristic
214	C₂²×C₄₇	#548	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	—	4	2	no	—
221	C₂×D₄₇	—	4	2	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	—	2	4	no	—
228	C₄×C₄₇	—	4	4	no	—
229	C₄×C₄₇	—	4	2	no	—
230	C₄×C₄₇	—	4	2	no	—
231	C₄×C₄₇	—	8	1	no	—
232	C₄×C₄₇	C₄×SD₁₆	1	4	yes	complemented
233	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
234	C₄×C₄₇	#520	1	1	yes	characteristic
235	C₄×C₄₇	#547	1	1	yes	characteristic
236	C₄×C₄₇	#553	1	1	yes	characteristic
237	Dic₄₇	—	4	2	no	—
238	Dic₄₇	—	8	2	no	—
239	C₂×#461	—	47	1	no	—
240	C₂×C₄×SD₁₆	—	47	2	no	—
241	#2365	D₄₇	1	1	yes	characteristic, complemented
242	D₄×C₄⋊C₄	—	47	1	no	—
243	#1956	—	47	1	no	—
244	#1948	—	47	1	no	—
245	#1933	—	47	2	no	—
246	#1877	—	47	2	no	—
247	#1865	—	47	2	no	—
248	C₈×C₄⋊C₄	—	47	1	no	—
249	C₄×#102	—	47	1	no	—
250	C₂×C₄₇	#2361	1	1	yes	characteristic
251	C₂×C₄₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
252	C₂×C₄₇	#2947	1	1	yes	characteristic
253	C₂×C₄₇	D₄×SD₁₆	1	1	yes	characteristic
254	C₂×C₄₇	#3283	1	1	yes	characteristic
255	C₂×C₄₇	#3359	1	1	yes	characteristic
256	C₂×C₄₇	#3360	1	1	yes	characteristic
257	D₄₇	—	4	4	no	—
258	C₂²×SD₁₆	—	47	2	no	—
259	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
260	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
261	C₂×C₄×D₄	—	47	1	no	—
262	C₂×C₄×D₄	—	47	2	no	—
263	C₂²×C₄⋊C₄	—	94	1	no	—
264	#461	—	47	8	no	—
265	C₄×SD₁₆	—	94	8	no	—
266	C₂×#106	—	47	2	no	—
267	C₂×C₄⋊C₈	—	47	1	no	—
268	C₂×#103	—	47	2	no	—
269	C₂×#103	—	47	2	no	—
270	C₂×#103	—	47	2	no	—
271	C₂×#102	—	47	1	no	—
272	C₂×#102	—	47	1	no	—
273	C₂×C₄×C₈	—	47	2	no	—
274	C₂×C₄×C₈	—	47	1	no	—
275	#391	C₂×D₄₇	1	2	yes	—
276	#389	—	2	1	no	—
277	#389	—	47	2	no	—
278	#387	—	2	2	no	—
279	#385	—	94	2	no	—
280	#384	—	47	1	no	—
281	#380	—	94	1	no	—
282	C₄×C₄⋊C₄	—	2	1	no	—
283	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
284	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
285	#340	—	47	1	no	—
286	#340	—	47	2	no	—
287	#340	—	47	1	no	—
288	#336	—	47	2	no	—
289	C₄₇	#22996	1	1	yes	characteristic, complemented, Sylow
290	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
291	C₂²×D₄	—	47	1	no	—
292	C₂³×C₄	—	94	1	no	—
293	C₂³×C₄	—	94	2	no	—
294	C₂×SD₁₆	—	47	8	no	—
295	C₂×SD₁₆	—	94	4	no	—
296	C₂×SD₁₆	—	94	4	no	—
297	C₂²×C₈	—	47	2	no	—
298	C₂²×C₈	—	47	1	no	—
299	C₂²×C₈	—	47	1	no	—
300	C₄⋊Q₈	—	2	2	no	—
301	C₄⋊Q₈	C₄×D₄₇	1	4	yes	complemented
302	C₄×Q₈	—	2	4	no	—
303	C₄×Q₈	—	4	2	no	—
304	C₄×D₄	—	47	4	no	—
305	C₄×D₄	—	94	4	no	—
306	C₄×D₄	—	94	2	no	—
307	C₄×D₄	—	188	2	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	47	1	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	—	188	4	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×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
321	C₂×C₂²⋊C₄	—	94	1	no	—
322	C₂×C₂²⋊C₄	—	94	2	no	—
323	C₂×C₄²	—	2	2	no	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
326	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
327	#106	—	94	4	no	—
328	C₄⋊C₈	—	47	4	no	—
329	#103	—	47	8	no	—
330	#103	—	94	4	no	—
331	#103	—	188	2	no	—
332	#102	—	47	4	no	—
333	#102	—	94	2	no	—
334	C₄×C₈	—	94	4	no	—
335	C₄×C₈	—	94	2	no	—
336	#95	—	2	2	no	—
337	#95	—	2	1	no	—
338	#95	—	2	2	no	—
339	#95	—	94	2	no	—
340	#95	C₂²⋊D₄₇	1	2	yes	—
341	C₂⁴	—	94	1	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	C₂×C₄×D₄₇	1	4	yes	—
348	C₂×D₄	—	47	2	no	—
349	C₂×D₄	—	47	2	no	—
350	C₂×D₄	—	47	2	no	—
351	C₂×D₄	—	94	1	no	—
352	C₂×D₄	—	94	1	no	—
353	C₂×D₄	—	94	1	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	94	1	no	—
358	C₂²×C₄	—	94	4	no	—
359	C₂²×C₄	—	94	2	no	—
360	C₂²×C₄	—	376	2	no	—
361	C₂²×C₄	—	188	4	no	—
362	C₂²×C₄	—	188	4	no	—
363	C₂²×C₄	—	188	2	no	—
364	C₂²×C₄	—	188	2	no	—
365	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
366	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
367	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
368	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
369	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
370	SD₁₆	—	94	16	no	—
371	C₂×C₈	—	47	4	no	—
372	C₂×C₈	—	47	2	no	—
373	C₂×C₈	—	94	2	no	—
374	C₂×C₈	—	94	2	no	—
375	C₂×C₈	—	94	1	no	—
376	C₂×C₈	—	94	1	no	—
377	C₂×C₈	—	94	1	no	—
378	C₂×C₈	—	94	1	no	—
379	C₂×C₈	—	94	1	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	4	4	no	—
387	C₄⋊C₄	—	47	2	no	—
388	C₄⋊C₄	—	94	1	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	#10625336	1	4	yes	complemented
395	C₄⋊C₄	D₄×D₄₇	1	2	yes	—
396	C₂²⋊C₄	—	94	4	no	—
397	C₂²⋊C₄	—	188	4	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	4	4	no	—
401	C₄²	—	4	2	no	—
402	C₄²	C₂×C₄×D₄₇	1	2	yes	—
403	C₄²	#10625350	1	2	yes	—
404	C₂³	—	94	2	no	—
405	C₂³	—	94	2	no	—
406	C₂³	—	94	2	no	—
407	C₂³	—	188	1	no	—
408	C₂³	—	188	1	no	—
409	C₂³	—	188	1	no	—
410	C₂³	—	188	1	no	—
411	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
412	Q₈	—	2	4	no	—
413	Q₈	—	2	4	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	4	2	no	—
416	D₄	—	47	4	no	—
417	D₄	—	94	2	no	—
418	D₄	—	94	2	no	—
419	D₄	—	94	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	94	2	no	—
437	C₂×C₄	—	376	8	no	—
438	C₂×C₄	—	188	2	no	—
439	C₂×C₄	—	188	2	no	—
440	C₂×C₄	—	188	2	no	—
441	C₂×C₄	—	188	1	no	—
442	C₂×C₄	—	188	1	no	—
443	C₂×C₄	—	188	8	no	—
444	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
445	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
446	C₂×C₄	C₂×#10625336	1	4	yes	—
447	C₂×C₄	C₂×#10625336	1	2	yes	—
448	C₂×C₄	#13094044	1	2	yes	—
449	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
450	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
451	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
452	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
453	C₂×C₄	#13094069	1	1	yes	characteristic
454	C₂×C₄	#13094071	1	1	yes	characteristic
455	C₈	—	94	2	no	—
456	C₈	—	94	4	no	—
457	C₈	—	188	1	no	—
458	C₂²	—	94	4	no	—
459	C₂²	—	188	2	no	—
460	C₂²	—	188	2	no	—
461	C₂²	—	188	2	no	—
462	C₂²	—	188	2	no	—
463	C₂²	—	188	2	no	—
464	C₂²	—	188	2	no	—
465	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
466	C₂²	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
467	C₂²	#15689780	1	1	yes	characteristic
468	C₂²	C₂²×#10625336	1	1	yes	characteristic
469	C₂²	C₂×#13094044	1	1	yes	characteristic
470	C₂²	#15689931	1	1	yes	characteristic
471	C₂²	#15689938	1	1	yes	characteristic
472	C₄	—	2	2	no	—
473	C₄	—	2	4	no	—
474	C₄	—	4	4	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	8	1	no	—
478	C₄	—	376	2	no	—
479	C₄	—	188	2	no	—
480	C₄	C₄×#10625336	1	4	yes	complemented
481	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
482	C₄	#15689602	1	1	yes	characteristic
483	C₄	#15689778	1	1	yes	characteristic
484	C₄	#15689823	1	1	yes	characteristic
485	C₂	—	188	4	no	—
486	C₂	#20246400	1	1	yes	characteristic
487	C₂	C₂×C₄×#10625336	1	1	yes	characteristic
488	C₂	#20252231	1	1	yes	characteristic
489	C₂	D₄×#10625336	1	1	yes	characteristic
490	C₂	#20255106	1	1	yes	characteristic
491	C₂	#20256026	1	1	yes	characteristic
492	C₂	#20256033	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×#2365	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₁₈₈	C₂³
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2365	D₄₇
hypocenter	C₄₇	#22996
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄ ◁ #2365

Complements

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

N	H ≅ G/N	type
4. #20244191	C₂	semidirect
5. #20244151	C₂	semidirect
6. #20244067	C₂	semidirect
8. #20243656	C₂	semidirect
9. C₄⋊C₄×C₄₇⋊C₈	C₂	semidirect
11. C₄₇×#2365	C₂	semidirect
16. #15689325	C₄	semidirect
65. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
68. #13093948	C₂×C₄	semidirect
76. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
130. C₄⋊C₄×C₄₇	SD₁₆	semidirect
232. C₄×C₄₇	C₄×SD₁₆	semidirect
241. #2365	D₄₇	semidirect
289. C₄₇	#22996	semidirect
301. C₄⋊Q₈	C₄×D₄₇	semidirect
394. C₄⋊C₄	#10625336	semidirect
480. C₄	C₄×#10625336	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689325	2
C₂×C₄×#10625336	2
C₄⋊C₄×D₁₈₈	2
#20244191	2
#20244151	2
#20244067	2
#20243725	2
#20243656	2
C₄⋊C₄×C₄₇⋊C₈	2
C₄×#13093944	2
C₄₇×#2365	2
#22996	47