Subgroups — #26238534

Order 12032.

1066 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689320	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10625335	C₂	1	2	yes	maximal, complemented
3	C₄⋊C₄×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244195	C₂	1	1	yes	maximal, characteristic
5	#20244151	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244074	C₂	1	2	yes	maximal, complemented
7	#20243746	C₂	1	2	yes	maximal, complemented
8	#20243649	C₂	1	2	yes	maximal, complemented
9	C₄⋊C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#13093947	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2366	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625335	C₂²	1	2	yes	—
13	C₂×C₄×Dic₉₄	C₂²	1	2	yes	—
14	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
15	#15689320	C₄	1	8	yes	complemented
16	C₄×#10625335	—	2	8	no	—
17	C₂×#13093955	C₂²	1	2	yes	—
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×#13093947	C₂²	1	1	yes	characteristic
20	C₂×#13093947	C₂²	1	1	yes	characteristic
21	C₂×#13093945	C₂²	1	2	yes	—
22	C₂×#13093945	C₂²	1	2	yes	—
23	C₂×#13093945	C₂²	1	2	yes	—
24	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
26	#15689021	C₂²	1	2	yes	—
27	#15689020	—	2	2	no	—
28	#15688993	C₂²	1	1	yes	characteristic
29	#15688992	—	2	1	no	—
30	C₄⋊C₄×Dic₄₇	—	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×#127×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₄₇	—	2	1	no	—
37	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
38	C₄₇×#390	—	2	1	no	—
39	C₄₇×#390	C₂²	1	2	yes	—
40	C₄₇×#386	—	2	2	no	—
41	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
44	C₂×#10625335	—	2	4	no	—
45	C₂×#10625335	—	2	4	no	—
46	C₂×#10625335	C₂×C₄	1	8	yes	complemented
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
49	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
50	C₄×Dic₉₄	—	2	2	no	—
51	C₄×Dic₉₄	—	2	4	no	—
52	C₄×Dic₉₄	—	4	2	no	—
53	C₄×Dic₉₄	C₂×C₄	1	4	yes	complemented
54	C₂×C₄⋊Dic₄₇	—	2	1	no	—
55	C₂×C₄⋊Dic₄₇	—	2	1	no	—
56	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
57	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
58	C₂×Dic₄₇⋊C₄	—	2	1	no	—
59	C₂×Dic₄₇⋊C₄	—	2	2	no	—
60	C₂×Dic₄₇⋊C₄	—	2	2	no	—
61	C₂×C₄×Dic₄₇	—	2	1	no	—
62	C₂×C₄×Dic₄₇	—	2	2	no	—
63	#13093955	—	2	4	no	—
64	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
65	#13093947	—	2	2	no	—
66	#13093947	D₄	1	4	yes	complemented
67	#13093945	—	2	4	no	—
68	#13093945	—	4	2	no	—
69	#13093945	C₂×C₄	1	8	yes	complemented
70	C₄×C₄₇⋊C₈	—	2	2	no	—
71	C₄×C₄₇⋊C₈	—	2	4	no	—
72	C₄₇⋊#95	—	2	2	no	—
73	C₂²×D₄×C₄₇	—	2	1	no	—
74	C₂²×D₄×C₄₇	—	2	1	no	—
75	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
76	C₂³×C₄×C₄₇	—	2	2	no	—
77	#127×C₄₇	—	2	2	no	—
78	#127×C₄₇	C₂×C₄	1	4	yes	—
79	C₄×D₄×C₄₇	—	2	4	no	—
80	C₄×D₄×C₄₇	—	4	2	no	—
81	C₄×D₄×C₄₇	—	4	4	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×C₂²⋊C₄×C₄₇	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
89	C₂×C₄²×C₄₇	—	2	1	no	—
90	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
91	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
92	#95×C₄₇	—	2	1	no	—
93	#95×C₄₇	D₄	1	2	yes	—
94	C₂⁴×C₄₇	—	2	2	no	—
95	C₂×D₄×C₄₇	—	2	4	no	—
96	C₂×D₄×C₄₇	—	2	4	no	—
97	C₂×D₄×C₄₇	—	2	2	no	—
98	C₂×D₄×C₄₇	—	2	2	no	—
99	C₂×D₄×C₄₇	—	2	2	no	—
100	C₂×D₄×C₄₇	—	2	2	no	—
101	C₂×D₄×C₄₇	—	2	2	no	—
102	C₂×D₄×C₄₇	—	4	2	no	—
103	C₂×D₄×C₄₇	—	4	2	no	—
104	C₂×D₄×C₄₇	—	8	1	no	—
105	C₂×D₄×C₄₇	—	8	1	no	—
106	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
107	C₂²×C₄×C₄₇	—	2	1	no	—
108	C₂²×C₄×C₄₇	—	2	1	no	—
109	C₂²×C₄×C₄₇	—	4	4	no	—
110	C₂²×C₄×C₄₇	—	4	4	no	—
111	C₂²×C₄×C₄₇	—	8	2	no	—
112	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
117	C₂²×Dic₄₇	—	2	1	no	—
118	C₂²×Dic₄₇	—	2	1	no	—
119	C₂²×Dic₄₇	—	2	2	no	—
120	C₂×Dic₉₄	—	2	1	no	—
121	C₂×Dic₉₄	—	2	1	no	—
122	C₂×Dic₉₄	—	2	1	no	—
123	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
124	C₂×Dic₉₄	C₂×D₄	1	2	yes	—
125	C₂×Dic₉₄	#41	1	2	yes	—
126	C₄⋊C₄×C₄₇	—	2	2	no	—
127	C₄⋊C₄×C₄₇	—	2	1	no	—
128	C₄⋊C₄×C₄₇	—	2	1	no	—
129	C₄⋊C₄×C₄₇	—	2	1	no	—
130	C₄⋊C₄×C₄₇	SD₁₆	1	4	yes	complemented
131	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
132	C₂²⋊C₄×C₄₇	—	4	4	no	—
133	C₂²⋊C₄×C₄₇	—	4	4	no	—
134	C₂²⋊C₄×C₄₇	—	8	2	no	—
135	C₄²×C₄₇	—	2	2	no	—
136	C₄²×C₄₇	—	2	2	no	—
137	C₄²×C₄₇	—	4	2	no	—
138	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
139	C₄²×C₄₇	#41	1	2	yes	—
140	#10625335	—	2	16	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	—	2	4	no	—
148	Dic₄₇⋊C₄	—	4	4	no	—
149	Dic₄₇⋊C₄	—	8	2	no	—
150	C₄×Dic₄₇	—	2	4	no	—
151	C₄×Dic₄₇	—	4	4	no	—
152	C₂×C₄₇⋊C₈	—	2	2	no	—
153	C₂×C₄₇⋊C₈	—	2	1	no	—
154	C₂×C₄₇⋊C₈	—	2	2	no	—
155	C₂×C₄₇⋊C₈	—	2	1	no	—
156	C₂×C₄₇⋊C₈	—	2	1	no	—
157	C₂×C₄₇⋊C₈	—	2	1	no	—
158	C₂×C₄₇⋊C₈	—	2	1	no	—
159	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
160	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
161	C₂³×C₄₇	—	2	4	no	—
162	C₂³×C₄₇	—	4	2	no	—
163	C₂³×C₄₇	—	4	2	no	—
164	C₂³×C₄₇	—	4	2	no	—
165	C₂³×C₄₇	—	4	2	no	—
166	C₂³×C₄₇	—	4	2	no	—
167	C₂³×C₄₇	—	4	2	no	—
168	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
169	D₄×C₄₇	—	2	4	no	—
170	D₄×C₄₇	—	2	4	no	—
171	D₄×C₄₇	—	4	2	no	—
172	D₄×C₄₇	—	4	2	no	—
173	D₄×C₄₇	—	4	8	no	—
174	D₄×C₄₇	—	8	4	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	1	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	2	1	no	—
179	C₂×C₄×C₄₇	—	2	2	no	—
180	C₂×C₄×C₄₇	—	2	2	no	—
181	C₂×C₄×C₄₇	—	2	2	no	—
182	C₂×C₄×C₄₇	—	2	2	no	—
183	C₂×C₄×C₄₇	—	4	1	no	—
184	C₂×C₄×C₄₇	—	4	1	no	—
185	C₂×C₄×C₄₇	—	4	1	no	—
186	C₂×C₄×C₄₇	—	4	1	no	—
187	C₂×C₄×C₄₇	—	4	1	no	—
188	C₂×C₄×C₄₇	—	8	8	no	—
189	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
190	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
191	C₂×C₄×C₄₇	C₂×SD₁₆	1	4	yes	—
192	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
193	C₂×C₄×C₄₇	#135	1	2	yes	—
194	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
199	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
200	C₂×Dic₄₇	—	2	2	no	—
201	C₂×Dic₄₇	—	2	2	no	—
202	C₂×Dic₄₇	—	2	2	no	—
203	C₂×Dic₄₇	—	2	2	no	—
204	C₂×Dic₄₇	—	4	1	no	—
205	C₂×Dic₄₇	—	4	1	no	—
206	C₂×Dic₄₇	—	4	2	no	—
207	C₂×Dic₄₇	—	4	2	no	—
208	C₂×Dic₄₇	—	4	2	no	—
209	Dic₉₄	—	2	2	no	—
210	Dic₉₄	—	2	2	no	—
211	Dic₉₄	—	2	2	no	—
212	Dic₉₄	C₄×D₄	1	4	yes	complemented
213	C₄₇⋊C₈	—	2	4	no	—
214	C₄₇⋊C₈	—	2	2	no	—
215	C₄₇⋊C₈	—	4	1	no	—
216	#22997	—	47	1	no	maximal, Sylow
217	C₂²×C₄₇	—	4	4	no	—
218	C₂²×C₄₇	—	4	4	no	—
219	C₂²×C₄₇	—	4	4	no	—
220	C₂²×C₄₇	—	8	2	no	—
221	C₂²×C₄₇	—	8	2	no	—
222	C₂²×C₄₇	—	8	2	no	—
223	C₂²×C₄₇	—	8	2	no	—
224	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
225	C₂²×C₄₇	D₄²	1	1	yes	characteristic
226	C₂²×C₄₇	#548	1	1	yes	characteristic
227	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
228	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
229	C₂²×C₄₇	#576	1	1	yes	characteristic
230	C₂²×C₄₇	#577	1	1	yes	characteristic
231	C₄×C₄₇	—	2	2	no	—
232	C₄×C₄₇	—	2	4	no	—
233	C₄×C₄₇	—	4	2	no	—
234	C₄×C₄₇	—	4	2	no	—
235	C₄×C₄₇	—	8	1	no	—
236	C₄×C₄₇	C₄×SD₁₆	1	4	yes	complemented
237	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
238	C₄×C₄₇	#520	1	1	yes	characteristic
239	C₄×C₄₇	#547	1	1	yes	characteristic
240	C₄×C₄₇	#553	1	1	yes	characteristic
241	Dic₄₇	—	2	4	no	—
242	Dic₄₇	—	4	2	no	—
243	Dic₄₇	—	8	2	no	—
244	C₂×#460	—	47	1	no	—
245	C₂×C₄×SD₁₆	—	47	2	no	—
246	#2366	D₄₇	1	1	yes	characteristic
247	Q₈×C₄⋊C₄	—	47	1	no	—
248	#1957	—	47	1	no	—
249	#1948	—	47	1	no	—
250	#1934	—	47	2	no	—
251	#1880	—	47	2	no	—
252	#1864	—	47	2	no	—
253	C₈×C₄⋊C₄	—	47	1	no	—
254	C₄×#103	—	47	1	no	—
255	C₂×C₄₇	—	8	4	no	—
256	C₂×C₄₇	#2361	1	1	yes	characteristic
257	C₂×C₄₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
258	C₂×C₄₇	#2946	1	1	yes	characteristic
259	C₂×C₄₇	D₄×SD₁₆	1	1	yes	characteristic
260	C₂×C₄₇	#3287	1	1	yes	characteristic
261	C₂×C₄₇	#3362	1	1	yes	characteristic
262	C₂×C₄₇	#3365	1	1	yes	characteristic
263	C₂²×SD₁₆	—	47	2	no	—
264	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
265	C₂×C₄×Q₈	—	47	1	no	—
266	C₂×C₄×Q₈	—	47	2	no	—
267	C₂×C₄×D₄	—	2	1	no	—
268	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
269	#460	—	47	8	no	—
270	C₄×SD₁₆	—	94	8	no	—
271	C₂×#106	—	47	2	no	—
272	C₂×C₄⋊C₈	—	47	1	no	—
273	C₂×#103	—	47	1	no	—
274	C₂×#103	—	47	1	no	—
275	C₂×#102	—	47	2	no	—
276	C₂×#102	—	47	2	no	—
277	C₂×#102	—	47	2	no	—
278	C₂×C₄×C₈	—	47	2	no	—
279	C₂×C₄×C₈	—	47	1	no	—
280	#390	—	2	1	no	—
281	#390	C₂×D₄₇	1	2	yes	—
282	#389	—	47	2	no	—
283	#389	—	94	2	no	—
284	#386	—	2	2	no	—
285	#384	—	47	1	no	—
286	#384	—	94	1	no	—
287	C₄×C₄⋊C₄	—	94	1	no	—
288	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
289	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
290	#340	—	47	1	no	—
291	#340	—	47	2	no	—
292	#340	—	47	1	no	—
293	#336	—	47	2	no	—
294	C₄₇	#22997	1	1	yes	characteristic, complemented, Sylow
295	C₂²×Q₈	—	47	1	no	—
296	C₂²×D₄	—	2	1	no	—
297	C₂²×D₄	—	2	1	no	—
298	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
299	C₂³×C₄	—	2	2	no	—
300	C₂×SD₁₆	—	47	8	no	—
301	C₂×SD₁₆	—	94	4	no	—
302	C₂×SD₁₆	—	94	4	no	—
303	C₂²×C₈	—	47	2	no	—
304	C₂²×C₈	—	47	1	no	—
305	C₂²×C₈	—	47	1	no	—
306	#127	—	2	2	no	—
307	#127	C₄×D₄₇	1	4	yes	—
308	C₄×Q₈	—	47	4	no	—
309	C₄×Q₈	—	94	4	no	—
310	C₄×Q₈	—	94	2	no	—
311	C₄×Q₈	—	188	2	no	—
312	C₄×D₄	—	2	4	no	—
313	C₄×D₄	—	4	2	no	—
314	C₄×D₄	—	4	4	no	—
315	C₂×C₄⋊C₄	—	47	1	no	—
316	C₂×C₄⋊C₄	—	47	2	no	—
317	C₂×C₄⋊C₄	—	94	1	no	—
318	C₂×C₄⋊C₄	—	94	2	no	—
319	C₂×C₄⋊C₄	—	94	1	no	—
320	C₂×C₄⋊C₄	—	94	2	no	—
321	C₂×C₄⋊C₄	—	94	1	no	—
322	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₂²⋊C₄	—	2	2	no	—
328	C₂×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₄²	—	2	1	no	—
330	C₂×C₄²	—	94	1	no	—
331	C₂×C₄²	—	94	2	no	—
332	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
333	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
334	#106	—	94	4	no	—
335	C₄⋊C₈	—	47	4	no	—
336	#103	—	47	4	no	—
337	#103	—	94	2	no	—
338	#102	—	47	8	no	—
339	#102	—	94	4	no	—
340	#102	—	188	2	no	—
341	C₄×C₈	—	94	4	no	—
342	C₄×C₈	—	94	2	no	—
343	#95	—	2	1	no	—
344	#95	—	94	2	no	—
345	#95	C₂²⋊D₄₇	1	2	yes	—
346	C₂⁴	—	2	2	no	—
347	C₂×Q₈	—	47	2	no	—
348	C₂×Q₈	—	47	2	no	—
349	C₂×Q₈	—	47	2	no	—
350	C₂×Q₈	—	94	1	no	—
351	C₂×Q₈	—	94	1	no	—
352	C₂×Q₈	—	94	1	no	—
353	C₂×D₄	—	2	4	no	—
354	C₂×D₄	—	2	4	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	4	2	no	—
361	C₂×D₄	—	4	2	no	—
362	C₂×D₄	—	8	1	no	—
363	C₂×D₄	—	8	1	no	—
364	C₂×D₄	C₂×C₄×D₄₇	1	4	yes	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	4	4	no	—
368	C₂²×C₄	—	4	4	no	—
369	C₂²×C₄	—	8	2	no	—
370	C₂²×C₄	—	94	1	no	—
371	C₂²×C₄	—	94	1	no	—
372	C₂²×C₄	—	94	2	no	—
373	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
374	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
375	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
376	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
377	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
378	SD₁₆	—	94	16	no	—
379	C₂×C₈	—	47	4	no	—
380	C₂×C₈	—	47	2	no	—
381	C₂×C₈	—	94	2	no	—
382	C₂×C₈	—	94	2	no	—
383	C₂×C₈	—	94	1	no	—
384	C₂×C₈	—	94	1	no	—
385	C₂×C₈	—	94	1	no	—
386	C₂×C₈	—	94	1	no	—
387	C₂×C₈	—	94	1	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	47	2	no	—
393	C₄⋊C₄	—	94	4	no	—
394	C₄⋊C₄	—	94	1	no	—
395	C₄⋊C₄	—	94	2	no	—
396	C₄⋊C₄	—	94	2	no	—
397	C₄⋊C₄	—	376	2	no	—
398	C₄⋊C₄	—	376	1	no	—
399	C₄⋊C₄	—	188	4	no	—
400	C₄⋊C₄	—	188	2	no	—
401	C₄⋊C₄	#10625335	1	4	yes	complemented
402	C₄⋊C₄	D₄×D₄₇	1	2	yes	—
403	C₂²⋊C₄	—	4	4	no	—
404	C₂²⋊C₄	—	4	4	no	—
405	C₂²⋊C₄	—	8	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	2	2	no	—
408	C₄²	—	4	2	no	—
409	C₄²	—	94	4	no	—
410	C₄²	—	188	4	no	—
411	C₄²	C₂×C₄×D₄₇	1	2	yes	—
412	C₄²	#10625350	1	2	yes	—
413	C₂³	—	2	4	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	4	2	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	2	no	—
420	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
421	Q₈	—	47	4	no	—
422	Q₈	—	94	2	no	—
423	Q₈	—	94	2	no	—
424	Q₈	—	94	2	no	—
425	D₄	—	2	4	no	—
426	D₄	—	2	4	no	—
427	D₄	—	4	2	no	—
428	D₄	—	4	2	no	—
429	D₄	—	4	8	no	—
430	D₄	—	8	4	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	8	8	no	—
445	C₂×C₄	—	94	2	no	—
446	C₂×C₄	—	94	2	no	—
447	C₂×C₄	—	94	2	no	—
448	C₂×C₄	—	94	2	no	—
449	C₂×C₄	—	188	2	no	—
450	C₂×C₄	—	188	2	no	—
451	C₂×C₄	—	188	2	no	—
452	C₂×C₄	—	188	1	no	—
453	C₂×C₄	—	188	1	no	—
454	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
455	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
456	C₂×C₄	C₂×#10625335	1	4	yes	—
457	C₂×C₄	C₂×#10625335	1	2	yes	—
458	C₂×C₄	#13094044	1	2	yes	—
459	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
460	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
461	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
462	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
463	C₂×C₄	#13094069	1	1	yes	characteristic
464	C₂×C₄	#13094071	1	1	yes	characteristic
465	C₈	—	94	2	no	—
466	C₈	—	94	4	no	—
467	C₈	—	188	1	no	—
468	C₂²	—	4	4	no	—
469	C₂²	—	4	4	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	8	2	no	—
472	C₂²	—	8	2	no	—
473	C₂²	—	8	2	no	—
474	C₂²	—	8	2	no	—
475	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
476	C₂²	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
477	C₂²	#15689780	1	1	yes	characteristic
478	C₂²	C₂²×#10625335	1	1	yes	characteristic
479	C₂²	C₂×#13094044	1	1	yes	characteristic
480	C₂²	#15689926	1	1	yes	characteristic
481	C₂²	#15689934	1	1	yes	characteristic
482	C₄	—	2	2	no	—
483	C₄	—	2	4	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	8	1	no	—
487	C₄	—	94	4	no	—
488	C₄	—	376	2	no	—
489	C₄	—	188	2	no	—
490	C₄	C₄×#10625335	1	4	yes	complemented
491	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
492	C₄	#15689602	1	1	yes	characteristic
493	C₄	#15689778	1	1	yes	characteristic
494	C₄	#15689823	1	1	yes	characteristic
495	C₂	—	8	4	no	—
496	C₂	#20246400	1	1	yes	characteristic
497	C₂	C₂×C₄×#10625335	1	1	yes	characteristic
498	C₂	#20252220	1	1	yes	characteristic
499	C₂	D₄×#10625335	1	1	yes	characteristic
500	C₂	#20255144	1	1	yes	characteristic
501	C₂	#20256055	1	1	yes	characteristic
502	C₂	#20256080	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×#2366	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂×#127×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2366	D₄₇
hypocenter	C₄₇	#22997
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄ ◁ #2366

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#10625335	C₂	semidirect
3. C₄⋊C₄×Dic₉₄	C₂	semidirect
5. #20244151	C₂	semidirect
6. #20244074	C₂	semidirect
7. #20243746	C₂	semidirect
8. #20243649	C₂	semidirect
9. C₄⋊C₄×C₄₇⋊C₈	C₂	semidirect
10. C₄×#13093947	C₂	semidirect
15. #15689320	C₄	semidirect
46. C₂×#10625335	C₂×C₄	semidirect
53. C₄×Dic₉₄	C₂×C₄	semidirect
64. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
66. #13093947	D₄	semidirect
69. #13093945	C₂×C₄	semidirect
130. C₄⋊C₄×C₄₇	SD₁₆	semidirect
212. Dic₉₄	C₄×D₄	semidirect
236. C₄×C₄₇	C₄×SD₁₆	semidirect
294. C₄₇	#22997	semidirect
401. C₄⋊C₄	#10625335	semidirect
490. C₄	C₄×#10625335	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689320	2
C₂×C₄×#10625335	2
C₄⋊C₄×Dic₉₄	2
#20244195	2
#20244151	2
#20244074	2
#20243746	2
#20243649	2
C₄⋊C₄×C₄₇⋊C₈	2
C₄×#13093947	2
C₄₇×#2366	2
#22997	47